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And the rate of flow of fluids and their cargoes into, through, and out of the lacunocanalicular sponge is determined by how often and how tightly the sponge is squeezed by breathing in the case of the ribs and by walking, running, and other activities Burger et al. This immense osteocyte internet is the "cell phone" with which they tell each another and lining cells about strains and microcracks and mobilize the appropriate responses.
Unnecessary digging and patching of undamaged bone is prevented by the signals from the cyclic squeezing of the sponges by the owner's breathing and variously moving around. The resulting inhibitory signals in the normal bone sent from the osteocytes and spread though the osteointernet via gap junctions to lining cells on the bone surface and between the lining cells to the adjacent endothelial cells of the osteonal blood vessel or marrow to talk to osteoclast precursors and osteoprogenitors R.
Martin, a , b , ; Klein-Nulent et al. A microcrack or an orthopedic implant screw cuts osteointernet connections and produces a layer of dying cells bordering the crack, which triggers BMU formation by stopping the flow of inhibitory signals from the osteocytes to the lining cells and cuts off the flow of fluid and the oxygen and essential nutrients it contains to surrounding cells Dodd et al. The alarm-sounding osteocytes surrounding the microcrack self-destruct by making the deadly, apoptosis-driving Bax protein and things that attract "vulturing" osteoclasts, but the wave of apoptotic damage is stopped from spreading too far beyond the crack by the more distant cells raising an anti-apoptosis "firewall" by making the anti-apoptosis Bcl-2 protein Verborgt et al.
The storm hits! A microcrack slices through the dense tangle of canalicular communication lines through which the osteocytes received nutrients and oxygen, got rid of their wastes, and sent a stream of strain-generated signals to the retired osteoblasts, more Because of ruptured supply lines, the starving and suffocating osteocytes bordering a microcrack start the self-destructive apoptotic mechanism, which is driven in part by the increasingly expressed Bax protein.
However, to stop the death zone from spreading, more The normal patterns of squeezing and stretching of the bones of an active skeleton, particularly in the hip and distal leg bones by heel striking and in the ribs by breathing, pushes and sucks the fluid in the osteocytes' lacunas and canaliculi back and forth and into and out of the canaliculi's pores in the osteonal walls to produce pulsing shear forces on the cells and their processes Cowin, ; Burr et al. According to Burger et al.
Static strain is a one-shot suck or push with a change in position without the subsequent pumping action needed to drive osteocyte signaling—the fluid in the lacunas and canaliculi must slosh back and forth within a certain frequency range to keep the osteocytes informed of the level of bone function and signaling appropriately to its fellows in the osteointernet Burr et al.
As I said above, cyclic pumping is what keeps food and oxygen coming to the osteocytes and their wastes being carried away. Thus, stopping the pumping strangles the osteocytes. This is why Lanyon and Rubin found that cyclically loading turkey wing ulna induced new bone formation while stopping the pumping by static loading caused holes to appear in the cortex. But there is an interesting aspect of strain cycles that affects osteogenic signaling in long bones.
Srinivasan and Gross , using the mid-diaphysis of the avian wing ulna, reported that flow rates are maximum during the first load cycle in which fluid is squeezed out of the osteocyte lacunae into the canaliculi. When the load is lifted, the fluid flows back into the lacunae.
But if the next loading happens before the lacunae are refilled, there is less fluid to be squeezed into the canaliculi. If this continues, fluid flows and with them osteocyte signaling drop off to produce a steady state equilibrium. This means that if fluid pulsing and signaling are to be maintained at an optimal level, there must be rest periods between the loadings to allow the lacunae to be fully refilled.
Srinivasan et al. In all cases, inserting rest periods between load cycles enhanced the osteogenicity of low-level loading protocols. For example, 5 consecutive days of low-level loading did not affect the tibial periosteal bone formation rate, but putting 10 seconds of rest between every 10 cycles increased the signaling so that the periosteal bone formation rate increased 8-fold Sirinvasan et al. How do osteocytes sense fluid sloshing?
Donahue et al. One thing they, like most other nonproliferating cells, have is a strain-sensing gadget that could produce such oscillations see www. This is the nonmotile primary or solitary cilium which, unlike a motile cilium with 9 peripheral microtubule doublets, each with attached ciliary dynein motors to move them, and 2 central singlet microtubules, consists of 9 peripheral doublets but no central tubules Alieva et al.
It is the cell's eyes, nose, and flowmeter. It grows from the mother centriole of the mother-daughter pair of centrioles embedded in the cell's microtubule-organizing centrosome lying beside, and orienting, the nucleus with the Golgi apparatus. Of course the cilium is at its most glorious complexity in the light-sensing retinal rods and cones.
Osteoblasts, osteocytes, and their chondrocyte cousins also have them Doxsey, ; Matthews and Martin, ; Poole et al. A striking example provided by Dr. Sam Bowser of the antenna-like primary cilium sticking out of a PtK kangaroo rat kidney epithelial cell can be seen in Figure 5.
An osteocyte might also use its cilium to assess the levels of key components in its surroundings and measure fluid sloshing caused by heel strikes and tell other cells in the network about them Whitfield, a. Most cells, osteoblasts, and osteocytes included Ilaria del Pra, Ubaldo Armato and your author, as yet unpublished observations appear to have a strain-sensing device known as the primary or solitary cilium that extends into the extracellular fluid more If the cilium is a flowmeter, then the volume and frequency of the signaling would depend on how much and how often the cilium is bent by the extracellular fluid.
And it is Praetorius and Spring, ! Therefore, the cilium would be a reliable flowmeter for measuring the sloshing of extracellular lacunar fluid caused by the squeezing and stretching of bone during a walking or running cycle for example. It is as if the bending of the cilium by sloshing lacunar fluid acts like a signal lamp that sends flashes of light coursing through the osteocyte fiberoptic network to lining cells on the bone surface and beyond.
How the bending of a femoral for example osteocyte's primary cilium by fluid sloshing back and forth in the cell's lacuna, when the bone's owner is walking, running, or breathing can send signals streaming through the osteointernet.
The bending of the more How could bending a cilium send a signal spreading from an osteocyte in its lacuna in the depths of femoral cortical bone through a lacunocanalicular labyrinth to cells lining the osteonal canal or endosteal surface? The answer may have been found in kidney cells which also monitor fluid flow. However, in both the dog and mouse cells, the result is a cascade of events spreading through the cytoplasm and nucleus and then into the neighboring cells.
Since osteocytes also have these little antennae, the sloshing canalicular fluid in their lacunae in an active skeleton Tami et al. Disrupting the kidney cell's cilium eliminates its ability to sense changes in extracellular fluid flow rate Praetorius and Spring, a. The horrendous consequence of this "deafening" in both humans and mice—is polycystic kidney disease PKD caused by disrupting the kidney tubule cells' gene for PC-1 or PC-2 Calvert, ; Pazour and Witman, ; Yoder et al.
If I am right and the osteocyte's primary cilium is used to measure bone strain, and if the osteoblasts remember they too have them use their cilia for detecting and initiating the reponse to various things such as growth factors and hormones in their extracellular fluid, PKD should be accompanied by severe skeletal deformation. And this is precisely what happens when the mouse's PCencoding Pkd1 gene is disabled Boulter et al.
Lu et al. Signals from the osteocytes' primary cilia would be accompanied especially at higher strains by the tugging on the signal-generating integrins and associated cytoskeleton that attach the cell and its processes to the osteopontin lining the walls of the lacunae and canaliculi like waves cause a ship to pull on its mooring lines matricrine signaling. But in this case, the cells' mooring lines are linked to sophisticated signaling instruments Denhardt et al.
Chan et al. Bakker et al. Martin, ; Noble, ; Noble and Reeve, ; Noda et al. The signals from bending cilia, stretched cell membranes, and tugged cadherins and integrins turn on osteogenic genes such as the gene for the strongly osteogenic PTHrP, which will be a very important part of things to come further on in our story X. Chen, C. Macica et al. The mechanism goes something like this. The basic "take-home" message from this complicated cluster of cell surface deformation-triggered events is really quite simple to remember.
One of these mechanosensitive genes codes for PTHrP which, as we shall see further on, is a towering figure in osteoblast differentiation X. The steady strain-driven maintenance of a supply of PTHrP by osteocytes could, for example, facilitate crack repair by promoting the flow of osteoprogenitors into the mature BMU osteoblast pool.
To make the strain-response story more complicated, stretching does something rather astonishing—it can activate MLO-Y4 osteocytic cells' nongenomic membrane-based estrogen receptors, the signals from which send ERK2 into their nuclei and oppose the initiation of apoptosis by etoposide Aguirre et al.
In other words, strain can activate estrogen receptors without estrogen i. In general terms, it seems as if moderate normal body movements keep signals flowing steadily through the extensive osteocyte network which because of gap junctions is really a giant gated syncytium from bending cilia. But more strenuous body movements add signals from cadherin and integrin tugging. As we shall see in the next section, in addition to reshaping gene promoters the intercellular chattering caused by mechanical strain looks a lot like neural network crosstalking.
Maybe osteocytes could be called "honorary neurons". This triggers the release into the synaptic cleft of packets of a neurotransmitter such as L-glutamate, which activates receptors on a post-synaptic neuron. Taylor, ! If the battering be too severe it can actually break the local connections of the osteointernet as well as trigger apoptotic self destruction Noble, ; Noble and Reeve, ; Skerry, ; Schaffler, The death of the overstrained osteocytes would lift the restraints on lining cells as effectively as a microcrack fig.
Thus are recruited the first, or shall we say pathfinder, BMUs to start fixing the damaged bone. As in a highway repair crew, the first on the job are the diggers—multinuclear osteoclasts armed with a protein shredder protease called cathepsin K to chop up the demineralized matrix proteins and heavily loaded with mitochondria to make the large amounts of ATP fuel needed to feed the pump which sprays HCl hydrochloric acid to dissolve the bone mineral and the garbage disposal pump which picks up matrix debris at the digging apical end of the cell and dumps it out of the other basal end of the cell Blair, ; Noble, ; Noble and Reeve, ; Skerry, ; Troen, ; Whitfield et al.
And one of the first responses of osteocytes to the strain around the microcrack is to make osteopontin to help attract the diggers and to glue them to the damaged patch Nomura and Takano-Yamamoto, But how the osteocytes summon these diggers to the damaged patch is still a mystery, although we shall see further on that it may be the "smell" of the osteocytes' corpses that does it.
Osteocytes can be induced to self destruct and in the process trigger BMU activation either by very low or by very high strain, but they function best when the strain is within a site-appropriate range of frequencies and strengths produced by normal body movements such as heel or paw strikes during walking or running cycles or the incessant tugging on the ribs by the muscles of breathing Noble and Reeve, The pulsing strain pumps blood and extracellular fluid throughout the network of blood vessels and the osteocytes' lacunocanalicular network.
This delivers food and oxygen to the osteocytes and flushes out their waste. On the other hand, if the matrix strain rises above a certain level, as happens at the tip of a microcrack where it can be 15 times above average e. However, osteocytes further away from the crack respond to a less severe interruption of nutrient deliveries and prevent the damage from spreading by erecting an anti-apoptosis "firewall" of the anti-apoptosis Bax protein Verborgt et al.
But let's have a look at what happens to gene expressions when osteocytes' oxygen supply is cut off and they rapidly become hypoxic by the failure of the bone fluid pumping action due to the stopping of loading cycles either by disuse or the severing of canaliculi by a microcrack Dodd et al. All of our cells can respond to an oxygen shortage by turning on or turning up two dozen or more so-called hypoxia-inducible genes, the products of which are meant to maintain at least a minimal supply of ATP fuel and other components for at least a short-term survival.
Huang and Bunn, ; Latchman, ; Marx, ; Wenger, The p can then interact with components of the basal RNA polymerase II gene-transcriber complex for recruiting the polymerase transcriber to these genes's promoters Latchman, Huang and Bunn, ; Schipani et al. But another gene, the gene for the anti-apoptosis Bcl-2 protein, is turned down or off, and the gene for the pro-apoptosis Nip3 protein is turned up.
This means that the struggling osteocyte will be able to hang on only for a while by making more ATP by the glycolytic mechanism, but it is now vulnerable to such things as a reoxygenation, in which the sudden surge of accumulated substrates into the mitochondria and the consequent intermediate "traffic jams" in the chain of oxidative enzymes can cause a lethal spray of ROS reactive oxygen species from the mitochondria.
Of course, the glycolytic mechanism is less efficient at making ATP fuel than the oxygen-driven mitochondrial ATP-making machinery, so the osteocytes need more glucose, and the glycolytic end product pyruvate will be reduced protonated to lactate instead of being processed into acetylCoA and fed into the mitochondrial machinery. The accumulating lactate increases the cellular acidity i. Since the glucose supply is reduced to a trickle or completely cut off, the osteocyte will soon run out of fuel unless the supply lines are reopened, perhaps by the resumption of loading but not if the fuel lines have been severed.
To make matters worse, an apoptosis-triggering leakage of agents such as cytochrome c from the mitochondria can no longer be stopped by the Bcl-2 protein, and the cell finally, with the help of the apoptogenic p53 protein, does the "honorable" thing and kills itself. This is the honorable way to go, because an apoptosing cell does not perforate its membrane and release dangerous enzymes that would kill any viable bystanders in the osteointernet. The death of the osteocytes around the crack cuts off the signals they were sending to the local lining cells in the osteonal central canals to NOT call up BMU digging crews R.
Martin a , b ; Marotti, The specifically RANKL-competent immature osteoblastic marrow stromal cells they will lose this ability as they mature put out on their surfaces RANKL ligands which can bind to osteoclast precursors' RANK receptors, signals from which can stimulate the precursors to differentiate. Another possibility is that inflammatory agents seeping into the blood from the injured bone patch would attract these developing osteoclast precursors to the site, where vascular endothelial cells start grabbing them from the passing blood.
At this point, we must try to see what controls the ability of immature osteoblastic cells in the marrow to make the RANKL mature osteoblasts can't do this needed to drive the development of osteoclast precursors Atkins et al. Thomas et al. The upshot of all of this is the arrival of BMU diggers at the damage site to dig out the microcrack and prepare the site for the making of a new canal by osteoblasts Marotti, As the osteoclasts are tunneling through the wall of a Haversian canal in cortical bone or digging a trench on or in a trabecula fig.
The tunnel being dug in cortical bone has a cutting front or cone, an intermediate resting or pause zone, and a closing or filling tail, along which is a gradient of strains produced by pulse-loading by walking, running, etc. Smit et al. It is important to remember for things to come later that at the cutting front, this activity-loading stops the lacunocanalicular extracellular fluid sloshing, which, of course, to the ever-alert osteocytes means "bone-not-in-use" and accordingly tells the diggers to get rid of it while further along the tunnel the strain rises and generates signals which mean "bone-in-heavy-use" and thus calls for osteoblasts to make more bone to reduce strain Klein-Nulent et al.
More of this later. You may remember that I pointed out at the beginning of this chapter that bone cells unexpectedly share with neurons such things as memory and the ablility to exchange information with each other through extensive networks. Well, this sharing looks as if it runs much deeper than expected. This raises the possibility of there being osteosynapses that are similar to neuronal synapses and T-lymphocye-dendritic Langerhans cell synapses Dustin and Colman, But so far no such synapses have yet been seen, although osteocyte processes have been found terminating "suggestively" on osteoblasts during bone formation Menton et al.
Osteocytes, with their primary cilia flowmeters incidentally neurons also have primarty cilia Whitfield, waving back and forth in the sloshing extracellular fluid, are not glutamate targets. In other words, they can send, but not receive, glutamate signals. Moreover, as Laketic-Ljubojevic et al.
Mature osteoblasts also have GLAST EAAT 1 transporters needed to recharge their glutamate stores, to clear their surroundings of released glutamate to avoid prolonged signaling from their glutamate receptors and prevent cell death caused by excessively prolonged glutamate signaling, and to maintain a high glutamate signal-to-noise ratio as exactly the same transporters in glial cells do in neuronal synaptic clefts Carmignoto, ; Chenu, ; Fields and Stevens-Graham, ; Hinoi et al.
Indeed, this is particulary important for bone cells because of the large amount of glutamic acid circulating in the blood which would otherwise saturate the receptors and "jam" signaling Hinoi et al. To recharge glutamate stores, maybe they and osteocytes do the same thing as glial cells in the brain. They might sweep up glutamate released by neighboring osteocytes or nerves with their GLAST transporters, convert it to glutamine, and send it back to the osteocytes or the Haversian nerves' axon terminals to be reconverted to glutamate and refill the secretory vesicles Chenu, These receptors and the synapse-like connections they rather loudly suggest are not mere osteoblast or preosteoblast ornaments.
All of this evokes the image of a network of nerves, precursor cells, osteoblasts, osteocytes, and maybe lining cells talking to each other in fluent glutamate! While a strain-induced glutamate surge stimulates osteoblast generation, it also stimulates osteoclast generation via the baby osteoclasts' wet nurses—immature bone marrow osteoblastic cells Atkins et al. It stimulates the immature, osteoblastic marrow stromal cells to put RANKL on their surfaces while mature, matrix-making osteoblasts cannot make RANKL apparently because its gene's promoter is locked shut by having its CpG sequences methylated at some point during maturation Atkins et al.
The flow of blood from the arterioles into the sprouting capillaries is increased by the vasodilating NO and the membrane-associated guanylyl cyclase and guanylyl cyclase-dependent protein kinase PKG it stimulates Krainock and Murphy, ; Lincoln et al.
The cells at the leading edge of the vascular loop switch on a set of genes, the products of which make the cells' surfaces selectively sticky—"velcroize" them—to snatch appropriately addressed preosteoclasts from the passing blood Parfitt, , a , b , ; Ruoslathi and Rayotte, ; Springer, A model for osteoclast grabbing has been proposed by Parfitt , a , b , According to this model, all appropriately addressed preosteoclasts, be they summoned to cortical bone or to trabecular bone, are plucked from the blood circulating, respectively, through the Haverserian tunnels or the marrow sinusoids.
When preosteoclasts flying along in the blood hear the osteocytes' distress signals and feel the altered blood vessel walls near the damaged site they, like neutrophils sailing into an infected tissue battle zone see Sompayrac for a wonderful description of this " rolling-sniffing-stop-exit" sequence , start putting selectin-binding selectin ligand proteins out on their surfaces.
After several passes through the region they ultimately become sufficiently and selectively velcroized by putting enough selectin ligand on their surfaces to be grabbed rather loosely by the selectin on the blood vessels' lining i. This slows them down, and they start rolling along the vessel wall "sniffing" for damage signals. When they find them, they put integrin hooks out on their surfaces to grab hold of ICAMs intercellular adhesion moleculse on the endothelial cell surfaces like descending aircrafts' tail hooks grabbing the arresting wires on an aircraft carrier's deck.
This stops them, and they are lured from the blood vessel and into the bone by various chemoattractant chemokines released by the stressed osteocytes and lining cells. The preosteoclasts squeeze "diapedese" between the vascular loop's cells to leave the blood and fuse with others to form large active multinuclear 5 or more nuclei osteoclasts, each of which digs for the next weeks.
The osteoclasts first dig into the wall of the osteon at a right angle and then turn to tunnel parallel to the osteonal columns. As they tunnel along, they are followed by the vascular loop with new preosteoclasts squeezing out of its tip, along with the nutrients and the lots of oxygen needed by the osteoclasts to do their job. Actually, there are only about 10 osteoclasts in a BMU R. Indeed, an osteoclast is a very strange and often a very large beast—a sort of cellular collective in which nuclei actually come and go e.
But what kind of "pheromone" keeps the osteoclasts tunneling through a microcracked patch like "truffle hound" pigs after mushrooms? What are they digging for? What are the "mushrooms"? Remember that osteocytes are driven to self destruct by apoptosis when a microcrack cuts off their supply lines and they are hit by the huge strain spreading from the tip of the crack fig. Moreover, remember that according to Klein-Nulent et al.
This means that the osteocytes need oxygen. Thus, even the osteocytes that were not immediately cut off or hyperstrained by the microcrack are also gasping and may start making inducible NOS-2, which in turn makes dangerously large amounts of NO that could induce neighbors to kill themselves. But of all things, the most important for answering this question is that deep down in their tiny souls, osteoclasts are "professional" macrophages with a vulture's taste for apoptotic carrion.
The answer to what drives osteoclast tunneling might go something like this, starting with a dying osteocyte. The dying osteocye also inactivates the "flippase" that has been keeping phosphatidylserine on the inner leaflet of the cell membrane but now activates a nonspecific, bidirectional phospholipid "scramblase" that loads phosphatidylserine onto patches or scaffolds on the membrane's outer leaflet Grimsley and Ravichandran, Along with this, annexin I is translocated from the cytosol to the outer surface, where it associates with the phosphatidylserine patches to produce an " eat-me!
This is what the relentlessly digging osteoclast, driven by a rising "scent" of LPC, bumps into at the head of the trail. Then its PSRs phosphatidylserine receptors bind to the osteocyte corpse's phosphatidylserine annexin I complexes. The signals from the vulturing osteoclast's PSRs trigger the mechanism with which the osteoclast "eats" the osteocye corpse. Things are different in trabecular cancellous bone and the endocortical surfaces facing the bone marrow fig.
There, the osteoclasts dig trenches instead of tunnels. Something remarkable happens when the lining cells on a trabecula are uncoupled from the underlying osteocytes. A kind of blister—the "bone-remodeling compartment BRC —forms on the trabecular surface Hauge et al.
It appears that the aroused lining cells start making collagenase to remove the matrix cover and lift off the surface to form a kind of tent over the future work site. This blister forms a pseudoblood vessel with a wall of osteoprogenitors and lining cells instead of true CDbearing endothelial cells Hauge et al. The blister vessel plugs into the local marrow blood sinusoids to bring preosteoclasts to the worksite. At first sight, it might be assumed that the trabeculae and endocortical bone would enjoy a direct supply of preosteoclasts from the red marrow nursery.
But while this may be true in children, the marrow in most peripheral bones in adults is nonhemopoietic fatty yellow marrow so preosteoclasts must be shipped in, sometimes from distant places such as the residual islands of hemopoietic marrow in the upper femurs and the red marrow in the bones of the central skeleton including the ilium. Caplan in Davies, , p. As the the vulturing "truffle hound" osteoclasts are tunneling through the cortical bone looking for dying osteocytes and in the process digging out the microcrack and a large patch of bone around it by spraying the protein-shredding cathepsin K and mineral-dissolving HCl onto the bone, they release a pack of factors e.
It is widely assumed in the Bone Community that these liberated factors, particularly the FGF-2, and the IGFs, form an immediately accessible store of osteoblast generators that can be drawn on by a subsequent BMU to locally increase osteoblast generation by stimulating osteoprogenitor proliferation to start new bone growth for repairing a microcrack.
But the osteoclasts leave a trail of chemokine droppings that attract osteoblastic cells. This cytokine is Mim-1 myb-induced myeloid protein 1 Falany et al. Serotonin may also be put into the matrix by osteoblasts and subsequently released by the diggers from a future BMU. Osteoblasts and periosteal fibroblastic osteoblast precursors express serotonin receptors and have the machinery to release and reaccumulate it Bliziotes et al. And Chopra and Anastassiades have reported that one of the matrix components—bone sialoprotein BSP —binds serotonin, receptors for which might be on the osteoblast primary cilium as they are in neurons in certain parts of the brain Brailov et al.
Although what serotonin does in bone is unknown, it may be another of the several factors that stimulate the proliferation of serotonin-receptor-bearing osteoprogenitor cells which in turn generate crack-filling osteoblasts Westbroek et al.
Yamaguchi, ; Zaidi et al. But if it cannot find another place to attach itself by its integrins, in time to generate the matricrine signals neeed to hold off apoptosis, it will self-destruct—a drastic response to unemployment and homelessness known as anoikis or homelessness-induced apoptosis Frisch and Screaton, ; Lorget et al. Yamaguchi et al. Yamaguchi, ; T. Rubin et al. This NO also stimulates the enzyme, guanylyl cyclase, in nearby vascular cells by attaching to the enzyme's heme group Lincoln et al.
The cyclic GMP produced by the cyclase relaxes arterioles, the overall effect of which is to increase the delivery of blood-borne nutrients through the advancing blood capillaries to the filler crews Lincoln et al. This is all very interesting, but where do the osteoblasts come from to make a new Haversian canal surrounded by concentric layers of bone? The band of proliferating mesenchymal cells advancing along the tunnel wall throw off preosteoblasts that dismantle their mitogenic machinery and become osteoblasts which start depositing layers or lamellae of bone around the tunnel walls.
The result of this is the layering of lamellae around the new blood vessels and nerves. The question remains as to whether one generation or band of osteoblasts fills the tunnel except of course the vascular "right-of way" , taking rest breaks between each pair of lamellae or whether several generations of osteoblasts are needed do the job, which would mean that osteoblasts are still being generated by progenitors on the new surfaces.
Probably several osteoblast generations are needed for the refill job Martin et al. As the refilling progresses, the rate of formation drops for at least two reasons. First, as the lamellan build-up approaches the central blood vessel, the shrinking space somehow interferes with osteoblast differentiation, and second, the progressive drop in stresses with the increasing lamellar build-up results in a fading of the strain signals needed for osteoblast differentiation that were at their peak in the microcrack and at the head of the cutting cone R.
At a repair site on the trabecular or endosteal surface, the osteoblasts come from the preosteoblasts from the adjacent marrow and the lining cells that make up the canopy of the repair "blister" mentioned above i. If any of the BMP-2 liberated by the osteoclasts from the matrix has escaped being shredded by the osteoclasts' proteases, it would kick osteoprogenitors along the osteoblast differentiation pathway Chen et al.
They would then be stimulated to start working by the signals from other receptors which include the CaRs in the caveolar pouches in their cell membranes Brown and MacLeod, ; Kifor et al. Another factor that drives the osteoprogenitor proliferation and maturation comes from the cells of the advancing blood vessels. That factor is endothelin-1 which binds to, and activates, the osteoprogenitors' endothelin-A receptors Mohammad et al.
Signaling by glutamate from the dying or hypoxic osteocytes or from invading or adjacent nerves is also needed. However, the osteoblasts also release glutamate using exactly the same vesicular release machinery as neurons Bhangu et al. This incidentally suggests the extremely important possibility that glutamate has been a covert signaler for osteoblasts in standard culture media.
Despite this, the importance of glutamate as an osteogenic osteotransmitter is still uncertain, because although Dobson and Skerry and Taylor et al. But Skerry et al. One of the most serious errors in Gray et al. These antagonists simply could not compete with the high levels of glutamate in a culture medium that are needed to support the growth of osteoblastic cells A.
The upshot of all of this is that osteoblast differentiation and osteocyte functions, such as sensing and memorizing strain pulse frequency, involves glutamate, and to do their job these cells use exactly the same signaling machinery and transmitters as central neurons Skerry and Taylor, ; Spencer et al. In other words, it looks as if we have been looking at "osteoneurons"—what a fantastic change in our view of these cells and the smart bones they make!!
These unexpected neural similarities are not restricted to glutamate receptors and transporters! Of course, you might say that this BDNF is simply used to stimulate the innervation of new bone. However, the osteoblasts' TrkB receptors mean that they too use their BDNF to stimulate themselves and their neighbors for some aspect of bone making.
Before the osteoblasts arrive on the scene to start filling in the trench or tunnel, the lining cells must sweep up the litter left by the untidy osteoclasts on the resorption cavity floor Everts et al. There are collagen "bristles" sticking out of the cavity floor.
The lining cells then move onto the surface to give it a good shave and make a smooth surface upon which they slap a layer of osteopontin to glue the new collagen that will be made by the incoming osteoblasts Everts et al. As we shall see below, the residual phosphate from the dissolved bone mineral in the resorption cavity could be the stimulator of this first burst of osteopontin expression Beck, ; Beck and Knecht, ; Beck et al.
These lining cell janitors are in fact reversibly retired osteoblasts who when stimulated by agents such as PTHs can revert to full osteoblasthood to give a first wave of osteoblasts to "kindle" bone building. As mentioned above, the strained osteocytes in the microcracked site make and release NO gas, but it cannot save those Bax-makers closest to "ground zero" fig. But it increases arteriolar dilation and the movement of osteoclast precursors into the cortical tunnels and trabecular and endocortical trabecular blisters; NO also stimulates the migration of osteoblasts into the site Afzal et al.
While there were as few as 10 osteoclasts doing the digging, there may be hundreds of osteoblasts working in a tunnel or trench R. Despite their numbers, the osteoblasts take about times longer to fill the cortical tunnels and trabecular "blister"-covered trenches than the osteoclasts took to dig them. Therefore, at any moment in the microfracture sites, a mature bone has holes that are being dug or have been recently dug by the microcrack-repairing BMUs—these holes together make up the remodeling space.
When the new patch is finally in place months later and the osteocytes start sending the signals needed to prevent lining cells from unnecessarily summoning osteoclast precursors from the blood vessels running through the cortical Haversian canals or from forming a BMU-activating blister on endosteal or trabecular surfaces, the members of the last osteoblast crew are now out of work—they have become redundant!
Those that have failed to find a free space on which to settle as lining cells or osteocytes to keep their surface-sensing integrins emitting their survival-promoting signals trigger apoptosis and self-destruct like the unemployed osteoclasts before them Frisch and Screaton, ; Stupack and Cheresh, ; Whitfield et al. However, the doomed, self-destructing osteoblasts make one final contribution to bone formation, specifically mineralization, by dumping alkaline phosphatase into the new matrix in vesicles released from their blebbing surfaces Farley and Stilt-Coffing, Some of this alkaline phosphatase will get into the blood to tell the outside World of bone being made and osteoblasts dying.
Most of the self-destructing apoptosing cells in bone are located in microcrack sites being repaired by BMUs. The appropriately named and deadly Diablo neutralizes a group of caspase inhibitors, and cytochrome c forms a complex with APAF-1, which causes caspase-9 to auto-activate and trigger a lethal cascade of so-called "executioner" caspase protein shredders Crompton, ; Finkel, This ability of P i to greatly promote apoptogenesis was first noticed by me nearly 40 years ago, when I was searching for a way to enhance the radiation-induced apoptosis of rat thymic lymphocytes and human peripheral blood lymphocytes for an ultra-sensitive radiation bio-dosimeter e.
Meleti et al. However, as we shall see later on, this could be dangerously counterproductive, because the transporter is also a key player in osteoid mineralization. The apoptogenic action of P i in cultured human osteoblasts from bone fragments and murine MC3T3-E1 preosteoblasts is greatly enhanced by a small, itself harmless, increase 0.
The relation between proliferative activity and PTHR1 and PTHrP expressions at the various stages of osteoblastic differentiation, using the information provided by Aubin and Aubin and Triffitt as the foundation of the scheme. The appearance more Finally, osteoblasts are recruited in load-bearing mature human bones only for remodeling BMUs to repair microcracks.
But the osteoblast recruitment and osteoclast activity are not coupled in growing bone. Clusters of osteoblasts operate independently from osteoclasts in the growing, so-called modeling, bones of rat pups and human children Frost, ; R. And as we shall see below, PTHs can stimulate a massive layering of osteoblasts on trabeculae and bone formation without a prior activation of osteoclasts.
Indeed, growing mutant mice, which cannot generate functional osteoclasts, become osteopetrotic due to unopposed bone building by osteoblasts; and mutant mice that cannot generate functional osteoblasts become the opposite, osteoporotic, due to the unopposed osteoclast activity Karsenty, ; Whitfield et al.
At this point, we should take a quick look at osteoblasts which don't live in bone, but instead appear in and ossify stressed and injured arteries and aortic valves and thus cause heart attacks and death of atherosclerotics and persons with end-stage kidney disease as well as cause the vascular impairment and consequent amputation of diabetics' limbs reviewed by T.
Doherty et al. They come from a subpopulation of redifferentiation-competent vascular smooth muscle cells known as "calcifying vascular smooth muscle cells" or CVCs T. They lay down sheets of bone and deposit bone nodules in the walls of affected vessels—they literally make stiff armored blood vessels T. A very strong support for what follows further on in our discussion of PTH's cyclic AMP cyclic adenosine-3',5'-monophosphate -triggered bone-building action is the ability of a short exposure to cyclic AMP to cause CVCs to stop proliferating and assume a classical cuboidal osteoblast shape and functions Tintutt et al.
With advancing age and decades of microcrack remodeling repair, the density of osteons and their Haversian canals in the compact bone rises with the replacement of primary bone with secondary bone—the bone becomes increasingly "worm-eaten". Since osteons are effectively hollow i.
And of course with this weakening comes a higher frequency of microdamage and remodeling at prime loading sites—a vicious cycle has begun operating fig. With advancing age, remodeling and the remodeling hole-refilling deficit rise, which more Contributing to this weakening with advancing age is the fact that BMUs are not as good at patching as interstate highway repair crews. But to be fair to the BMUs, the highway repair crews have a great advantage over the bone repair crews—when there has been too much patching, they can tear up the whole road and replace it, which cannot be done with an old patched-up skeleton.
First, the availability of osteoblasts for BMUs drops with advancing age as the number of osteoprogenitor cells and possibly stem cells? Osteoblasts working on the walls of the osteon tunnels in endocortical bone and the trabecular trenches in the cancellous trabecular compartment of bone do not completely refill the osteoclasts' excavations, but periosteal osteoblasts tend to overfill the holes Eriksen, ; Eriksen et al.
Therefore, with advancing age the cortical shells become thinner as the endocortical and trabecular parts of the bones waste away R. Fortunately the periosteal overfilling increases the diameters of load-bearing bones such as the femur , which somewhat compensates for the overall thinning and loss by resisting an increase in the bone's vulnerability to bending and breaking Einhorn, But the cortex of the femoral neck becomes thinner without increasing in diameter because there are no periosteal BMUs Einhorn, This combination of a thinning cortical shell with perforated plates and severed struts in the cancellous trabecular compartment without an increase in the neck's diameter makes the aging hip especially vulnerable to bending and breaking by the huge loads, as much as 5 times the total body weight, that are put on it during a normal walking cycle Einhorn, ; R.
The amount of bone removed by the osteoclasts of remodeling BMUs depends on the number of preosteoclasts that can be grabbed from the passing blood as well as the lifespans of the osteoclasts into which they fuse Manolagas, ; Parfitt, a. When the signaling from a repaired patch stops, i. However, depending on the number of osteoclasts in the excavation, less focused digging may go on for some time after the signaling has stopped Parfitt, , a , b.
Indeed once a BMU starts tunneling, it tends to keep going for a while R. Therefore, any antiresorptive or antiremodeling agent that lowers the number of osteoclasts by reducing their recruitment or killing them can reduce or even stop resorption and remodeling. But as is true for so many good things, there is a rub—reducing remodeling reduces microcrack repair.
This would result in a limited amount of bone growth as the unaffected osteoblasts continue filling the existing holes without having to contend with osteoclasts digging more holes faster than they can be filled. But the owner continues to move and crack bone, the accumulated microarchitecural deformation of which has not been reversed, and the continuing microdamage is not as easily repaired i. The amount of new bone put into the osteoclast excavations is a function of the number of mature osteoblasts and how long they can work.
As we shall see, definitely the PTHs, probably leptin, and possibly lipophilic statins, are just such anabolic bone-builders, some of which, like the PTHs, can stimulate bone growth without compromising crack repair. So far, it has seemed that estrogen is the primum inter pares of an ever-growing number of agents that control bone growth and strength in both women and, perhaps surprisingly, men Baylink et al. Now it appears that bones are also the direct and indirect targets of one of the principal operators of the mechanism that was originally discovered managing the white fat energy reserves in mice Ducy et al.
As more additional pieces of the puzzle are found, more perplexities arise and more extra pieces are needed. At first, it was white fat cells in mice and then a lot of other cells, including brain cells and osteoblasts, were found to make a helical cytokine hormone belonging to the IL interleukin -6 family of cytokines, the amino acid, The production of leptin by fat cells is a function of their fat load.
This means that the amount of circulating leptin tells the neurons in the hypothalamic arcuate nucleus of the size of the fat stores—it's a kind of fuel gauge needle. From the mouse model, leptin got the reputation of being a satiety signaler—a "Fat-O-Stat"—that inhibits the secretion of the orexigenic eating-stimulator neuropeptide Y NPY by arcuate neurons Ahima and Flier, ; J.
Friedman, ; Himms-Hagen, ; Pedrazzini et al. If the fat load is at the body's optimal set point, the circulating leptin holds NPY secretion from the arcuate nucleus at the appropriate level. However, if the fat load and with it leptin production drops below a critical limit, NPY secretion, and eating, rise to refill the fat fuel tanks and raise the circulating leptin concentration, which puts the brakes on eating.
But there is a problem with this popular mouse story. In her hard-hitting review, Himms-Hagen has presented a convincing case for leptin not being being a significant satiety hormone in humans. As she has pointed out, the very name leptin, which was of course coined for the mouse model, is wrong for humans—it is not a "Fat-O-Stat" in humans. Leptin's main role in humans is to serve as an energy monitor, the loss of which, when food becomes scarce enough to critically deplete the leptin-generating fat stores, sets off alarm bells that unleash a set of responses that try to maintain energy reserves without reducing activity e.
But leptin doesn't just monitor energy store and couple the level of this store to ovarian cycling. It also stimulates sympathetic activity that may be responsible for the deadly hypertension of obesity, and injecting it into the brain can activate sympathetic nerves in various regions of the body, including the rat hindlimb Rahmouni and Haynes, This driving of sympathetic nerve activity is separable from the arcuate-based metabolic effects, but of course sympathetic activity drives the burning of fat to extract the energy needed to try to replenish the fat stores by hunting for food Rahmouni and Haynes, And most important for our story—it can also affect bone growth by modulating sympathetic nerve activity.
It isn't the arcuate nucleus through which leptin operates on bone from the brain. Karsenty's group have recently found the boney consequences of leptin stimulating the neurons of the ventral medial hypothalamic nuclei VMHN , which projects to the sympathetic nervous system S.
And directly tweaking the VMHN neurons by squirting leptin into the cerebral ventricles of a mouse affects the beast's bones. But I am getting ahead of myself. Of course bones are affected by leptin's stimulation of GnRH gonadotropin-releasing hormone secretion and the estrogen-dependence of the Lep gene originally called the Ob gene for the obese mouse in which it was discovered gene expression Ahima and Flier, ; Brann et al.
Friedman, ; Himms-Hagen, Therefore, when either the Lep Ob gene or the LepRb receptor Sweeny, is disabled, the animal will have reduced sympathetic activity and thus be hypotensive Mark et al. And it will also make too much cortisol and too little estrogen and therefore should be osteopenic. This should be very bad for bones! Since the lack of estrogen increases osteoclast production, they do have more osteoclasts than normal, lean animals but only a normal number of hyperactive osteoblasts that override the diggers by making twice as much bone matrix as the osteoblasts in lean mice Ducy et al.
Moreover, bone loss can be caused by intracerebroventricular leptin injection into normally boned, lean mice—leptin seems to cause the release from the brain of an osteoblast suppressor. But no—cerebrally injected NPY does the same thing as leptin—it causes bone loss Ducy et al. Thus, it seems that in mice, a set-point level of leptin might stimulate the neurons in some hypothalamic nucleus to produce a hypothalamic osteoblast inhibitory factor, a HOBIF, that somehow holds osteoblast activity at some optimal level Ducy et al.
It appeared at one point that the nNOS neural nitric oxide synthase might be part of this brain-based leptin signaling mechanism that dampens osteoblast activity, because knocking out the nNOS gene causes large increases in bone mass van't Hof et al. At any rate, without signals from leptin-activated receptors on hypothalamic neurons, there is no osteoblast restraining HOBIF production, and bone growth climbs along with the food consumption and body weight fig.
But is all of this just much ado about nothing?! The bone growth in a fat mouse could simply be driven by the escalating loading by the massive increase in body weight and the consequent operation of the body's "mechanostat" to make more bone to reduce the strain as we have learned in the last chapters.
But the bone mass starts rising before the weight rises. The Karsenty group S. In mice, and probably humans, leptin operates on bone independently from the appetite and body weight controlling hypothalamic neurons of the arcuate nuclei which, as noted above, can be destroyed without affecting bone mass by stimulating the sympathetic nervous system via the LepRb receptor-bearing cells of the ventromedial hypothalamic nucleus Funahashi et al.
But there is something inconsistent with their earlier paper. According to Ducy et al. On the basis of leptin's indirect, hypothalamically mediated, osteoblast-suppressing action, Karsenty b has called it the osteoblast-suppressing equivalent of the osteoclast-suppressing OPG. But it isn't Gordeladze et al. While the primary adult mouse osteoblasts in the experiments of Ducy et al. Liu et al. Steppan et al. But Hamrick et al. It turns out that Steppan et al. Leptin lack does indeed shorten femurs and reduce BMD, bone mineral content, cortical thickness, trabecular thickness, and trabecular volume in the femur.
And according to Hamrick et al. Hamrick et al. This suggested to Hamrick et al. The loss of long bone appendicular skeleton mass is likely due in part to severely reduced loading because of a significant drop in muscle e. As discussed in detail in Chapter 1, this would stress osteocytes and ultimately trigger their self-destruction and osteoclast scavenging of the cadavers by restricting the transcanalicular provision of nutrients and clearance of waste.
And of course, another contributor would be the lack of leptin's direct anabolic action discovered in mice by Liu et al. Therefore, all that remains of the Karsenty mouse story is the ability of an intracerebroventricular shot of leptin to stimulate the VMHN-neurons and through them the preganglionic sympathetic neurons of the lateral cell columns of the spinal cord and the bones to which they project.
Cornish et al. And Picheret et al. This is supported by Tamasi et al. Moreover, Maor et al. Leptin is also one of the drivers of endochondral bone formation in the mouse. And Dumond et al. Large amounts of the cytokine are made specifically by hypertrophic chondrocytes see Chapter 5v to find out what these cells do near invading capillaries and osteoblasts in the primary spongiosa extending from the growth plate of long bones Kerr, It seems that the chondrocytes use leptin to get the blood vessel cells moving and proliferating and making matrix metalloproteinases-2 and —9 which they use as drills for tunneling through the collagenous matrix to deliver blood-borne osteoprogenitor cells and other essentials to the construction sites Kume et al.
Freshly isolated human osteoblasts e. Horne Tooke would have been pleased with the sagacity of a child of five years old S—— who called laughing an interjection. If too much is expected from them, the disappointment, which must be quickly felt, and will be quickly shown by the preceptor, will discourage the pupil. We must repeat, that the first steps should be frequently retraced: a child should be for some weeks accustomed to distinguish an active verb, and its agent, or nominative case, from every other word in a sentence, before we attempt to advance.
The objects of actions are the next class of words that should be selected. The fanciful, or at least what appears to the moderns fanciful, arrangement of the cases amongst grammarians, may be dispensed with for the present. The idea, that the nominative is a direct, upright case , and that the genitive declines with the smallest obliquity from it; the dative, accusative, and ablative, falling further and further from the perpendicularity of speech, is a species of metaphysics not very edifying to a child.
Into what absurdity men of abilities may be led by the desire of explaining what they do not sufficiently understand, is fully exemplified in other sciences as well as grammar. The discoveries made by the author of Epea Pteroenta, show the difference between a vain attempt to substitute analogy and rhetoric in the place of demonstration and common sense. When a child has been patiently taught in conversation to analyze what he says, he will take great pleasure in the exercise of his new talent; he will soon discover, that the cause of the action does not always come before the verb in a sentence, that sometimes it follows the verb.
A [Pg 17] child of moderate capacity, after he has been familiarized to this general idea of a verb active and passive, and after he has been taught the names of the cases, will probably, without much difficulty, discover that the nominative case to a passive verb becomes the accusative case to a verb active. We need not, however, be in any hurry to teach our pupil the names of the cases; technical grammar may be easily learned, after a general idea of rational grammar has been obtained.
For instance, the verb means only the word , or the principal word in a sentence; a child can easily learn this after he has learnt what is meant by a sentence; but it would be extremely difficult to make him comprehend it before he could distinguish a verb from a noun, and before he had any idea of the structure of a common sentence. From easy, we should proceed to more complicated, sentences. The grammatical construction of the following lines, for example, may not be immediately apparent to a child:.
It is asserted from experience, that this method of instructing children in grammar by conversation, is not only practicable, but perfectly easy, and that the minds of children are adapted to this species of knowledge. During life, we learn with eagerness whatever is congenial with our present pursuits, and the acquisition of language [Pg 18] is one of the most earnest occupations of childhood.
After distinct and ready knowledge of the verb and nominative case has been acquired, the pupil should be taught to distinguish the object of an action, or, in other words, the objective or accusative case. He should be exercised in this, as in the former lessons, repeatedly, until it becomes perfectly familiar; and he should be encouraged to converse about these lessons, and to make his own observations concerning grammar, without fear of the preceptor's peremptory frown, or positive reference to " his rules.
We acknowledge that Wilkins and Tooke have shown masters how to teach grammar a little better than it was formerly taught. Fortunately for the rising generation, all the words under the denomination of adverbs, prepositions, and conjunctions, which were absolute nonsense to us, may be easily explained to them, and the commencement of instruction need no longer lay the foundation of implicit acquiescence in nonsense. We refer to Mr. Horne Tooke's "Epea Pteroenta," forbearing to dilate upon the principles of his work, lest we should appear in the invidious light of authors who rob the works of others to adorn their own.
We cannot help expressing a wish, that Mr. Horne Tooke would have the philanthropic patience to write an elementary work in a simple style , unfolding his grammatical discoveries to the rising generation. When children have thus by gentle degrees, and by short and clear conversations, been initiated in general grammar, and familiarized to its technical terms, the first page of tremendous Lilly will lose much of its horror.
It has been taken for granted, that at the age of which we have been speaking, a child can read English tolerably well, and that he has been used to employ a dictionary. He may now proceed to translate from some easy books a few short sentences: the first word will probably be an adverb or conjunction; either of them may readily be found in the Latin dictionary, and the young scholar will exult in having translated one word of Latin; but the next word, a substantive or verb, perhaps will elude his search.
Now the grammar may be produced, and something of the various terminations of a noun may be explained. If musam be searched for in the dictionary, it cannot be found, but musa catches the eye, and, with the assistance of the grammar, it may be shown, that the meaning of words may be discovered by the united helps of the dictionary and grammar. After some days patient continuation of this exercise, the use of the grammar, and of its uncouth collection of words and syllables, will be apparent to the pupil: he will perceive that the grammar is a sort of appendix to the dictionary.
After the preparation which we have recommended, the singular number of a declension will be learnt in a few minutes by a child of ordinary capacity, and after two or three days repetition, the plural number may be added. The whole of the first declension should be well fixed in the memory before a second is attempted. During this process, a few words at every lesson may be translated from Latin to English, and such nouns as are of the first declension, may be compared with musa , and may be declined according to the same form.
Tedious as this method [Pg 20] may appear, it will in the end be found expeditious. Omitting some of the theoretic or didactic part of the grammar, which should only be read, and which may be explained with care and patience, the whole of the declensions, pronouns, conjugations, the list of prepositions and conjunctions, interjections, some adverbs, the concords, and common rules of syntax, may be comprised with sufficient repetitions in about two or three hundred lessons of ten minutes each; that is to say, ten minutes application of the scholar in the presence of the teacher.
A young boy should never be set to learn a lesson by heart when alone. Forty hours! Is this tedious? If you are afraid of losing time, begin a few months earlier; but begin when you will, forty hours is surely no great waste of time: the whole, or even half of this short time, is not spent in the labour of getting jargon by rote; each day some slight advance is made in the knowledge of words, and in the knowledge of their combinations.
What we insist upon is, that nothing should be done to disgust the pupil : steady perseverance, with uniform gentleness, will induce habit, and nothing should ever interrupt the regular return of the daily lesson. If absence, business, illness, or any other cause, prevent the attendance of the teacher, a substitute must be appointed; the idea of relaxation on Sunday, or a holyday, should never be permitted.
In most public seminaries above one third, in some nearly one half, of the year is permitted to idleness: it is the comparison between severe labour and dissipation, that renders learning hateful. Johnson is made to say by one of his female biographers,  that no child loves the person who teaches him Latin; yet the author of this chapter would not take all the doctor's fame, and all the lady's wit and riches, in exchange for the hourly, unfeigned, unremitting friendship, which he enjoys with a son who had no other master than his father.
So far from being [Pg 21] laborious or troublesome, he has found it an agreeable employment to instruct his children in grammar and the learned languages. In the midst of a variety of other occupations, half an hour every morning for many years, during the time of dressing, has been allotted to the instruction of boys of different ages in languages, and no other time has been spent in this employment.
Were it asserted that these boys made a reasonable progress , the expression would convey no distinct meaning to the reader; we shall, therefore, mention an experiment tried this morning, November 8th, , to ascertain the progress of one of these pupils. Without previous study, he translated twenty lines of the story of Ceyx and Alcyone, from Ovid, consulting the dictionary only twice: he was then desired to translate the passage which he had read into English verse; and in two or three hours he produced the following version.
Much of the time was spent in copying the lines fairly, as this opportunity was taken of exciting his attention to writing and spelling, to associate the habit of application with the pleasure of voluntary exertion. The curious may, if they think it worth their while, see the various readings and corrections of the translation V. Chapter on Conversation, and Anecdotes of Children which were carefully preserved, not as " Curiosities of Literature ," but for the sake of truth, and with a desire to show, that the pupil had the patience to correct.
A genius may hit off a few tolerable lines; but if a child is willing and able to criticise and correct what he writes, he shows that he selects his expressions from choice, and not from chance or imitation; and he gives to a judicious tutor the certain promise of future improvement. S——, the boy who made this translation, was just ten years old; he had made but three previous attempts in versification; his reading in poetry had been some of Gay's fables, parts of the Minstrel, three odes of Gray, the Elegy in a Country Church-yard, the Tears of Old May-day, and parts of the second volume of Dr.
Darwin's Botannic Garden; Dryden's translations of the fable of Ceyx and Alcyone he had never seen; the book had always been locked up. These circumstances are mentioned thus minutely, to afford the inquisitive teacher materials for an accurate estimate of the progress made by our method of instruction.
Perhaps most boys of S——'s age, in our great public seminaries, would, upon a similar trial, be found superior. Competition in the art of translation is not our object; our object is to show, that half an hour a day, steadily appropriated to grammar and Latin, would be sufficient to secure a boy of this age, from any danger of ignorance in classical learning; and that the ease and shortness of his labour will prevent that disgust, which is too often induced by forced and incessant application.
We may add, that some attention to the manner in which the pupils repeat their Latin lessons, has been found advantageous: as they were never put in bodily fear, by the impatience of a pedagogue, they had leisure and inclination to read and recite, without awkward gestures and discordant tones. The whining tones and convulsive gestures often contracted by boys during the agony of repeating their long lessons, are not likely to be advantageous to the rising generation of orators.
Practice, and the strong motive of emulation, may, in [Pg 23] a public seminary, conquer these bad habits. After the pupil has learned to speak ill, he may be taught to speak well; but the chances are against him: and why should we have the trouble of breaking bad habits? It is much easier to prevent them. In private education, as the preceptor has less chance of curing his pupil of the habit of speaking ill, he should be peculiarly attentive to give the child constant habits of speaking and reading well.
It is astonishing, that parents, who are extremely intent upon the education of their children, should overlook some of the essential means of success. A young man with his head full of Latin and law, will make but a poor figure at the bar, or in parliament, if he cannot enunciate distinctly, and if he cannot speak good English extempore, or produce his learning and arguments with grace and propriety. It is in vain to expect that a boy should speak well in public, who cannot, in common conversation, utter three connected sentences without a false concord or a provincial idiom; he may be taught with much care and cost to speak tripod sentences;  but bring the young orator to the test, bring him to actual business, rouse any of his passions, throw him off his guard, and then listen to his language; he will forget instantly his reading master, and all his rules of pronunciation and rhetoric, and he will speak the language to which he has been most accustomed.
No master will then be near him to regulate the pitch and tones of his voice. We cannot believe that even Caius Gracchus could, when he was warmed by passion, have listened to Licinius's pitch-pipe. Much of the time that is spent in teaching boys to walk upon stilts, might be more advantageously employed in teaching them to walk well without them. It is all very well whilst the pupil is under the [Pg 24] protection of his preceptor.
The actor on the stage is admired whilst he is elevated by the cothurnus; but young men are not to exhibit their oratorical talents always with the advantages of stage effect and decorations. We should imagine, that much of the diffidence felt by young men of abilities, when they first rise to speak in public, may be attributed to their immediate perception of the difference between scholastic exhibitions and the real business of life; they feel that they have learned to speak two languages, which must not, on any account, be mixed together; the one, the vulgar language of common conversation; the other, the refined language of oratorical composition: the first they are most inclined to use when they are agitated; and they are agitated when they rise to speak before numbers: consequently there is an immediate struggle between custom and institution.
Now, a young man, who in common conversation in his own family has never been accustomed to hear or to speak vulgar or ungrammatical language, cannot possibly apprehend that he shall suddenly utter ridiculous expressions; he knows, that, if he speaks at all, he shall at least speak good English; and he is not afraid, that, if he is pursued, he shall be obliged to throw away his cumbrous stilts.
The practice of speaking in public, we are sensible, is a great advantage; but the habit of speaking accurately in private, is of still greater consequence: this habit depends upon the early and persevering care of the parent and the preceptor. There is no reason why children should not be made at the same time good scholars and good speakers; nor is there any reason why boys, whilst they learn to write Latin, should be suffered to forget how to write English. It would be a great advantage to the young classical scholar, if his Latin and English literature were mixed; the taste for ancient authors and for modern literature, ought to be cultivated at the same time; and the beauties of composition, characteristic of different languages, [Pg 25] should be familiarized to the student.
Classical knowledge and taste afford such continual and innocent sources of amusement, that we should be extremely sorry that any of our pupils should not enjoy them in their fullest extent; but we do not include a talent for Latin composition amongst the necessary accomplishments of a gentleman. There are situations in life, where facility and elegance in writing Latin may be useful, but such situations are not common; when a young man is intended for them, he may be trained with more particular assiduity to this art; perhaps for this purpose the true Busbyean method is the best.
The great Latin and Greek scholars of the age, have no reason to be displeased by the assertion, that classical proficiency equal to their own, is not a necessary accomplishment in a gentleman; if their learning become more rare, it may thence become more valuable.
We see no reason why there should not be Latinists as well as special pleaders. We have not laid down any course of classical study; those who consider the order in which certain authors are read, as of material consequence in the education of scholars, may consult Milton, Mrs. We have lately seen a collection of exercises for boys,  which in some measure supplies the defect of Mr.
Garretson's curious performance. We wish most earnestly that dictionaries were improved. The author of "Stemmata Latinitatis," has conferred an essential service on the public; but still there is wanting a dictionary for schools, in which elegant and proper English might be substituted for the barbarous translations now in use.
Such a dictionary could not be compiled, we should think, without an attention to the course of books that are most commonly used in schools. The first meanings given in the dictionary, should suit the first authors that a boy reads; this may probably be a [Pg 26] remote or metaphoric meaning: then the radical word should be mentioned, and it would not cost a master any great trouble to trace the genealogy of words to the parent stock.
Cordery is a collection of such mean sentences, and uninstructive dialogue, as to be totally unfit for boys. Commenius's "Visible World displayed," is far superior, and might, with proper alterations and better prints, become a valuable English school-book.
Both these books were intended for countries where the Latin language was commonly spoken, and consequently they are filled with the terms necessary for domestic life and conversation: for this very reason they are not good introductions to the classics.
We prefer this mode of assisting them with glossaries to the use of translations, because they do not induce indolent habits, and yet they prevent the pupil from having unnecessary labour. Translations always give the pupil more trouble in the end, than they save in the beginning. Valpy's "Select Sentences," would be much more useful if they had a glossary annexed. Ovid's Metamorphoses, with all its monstrous faults, appears to be the best introduction to the Latin classics, and to heathen mythology.
Norris's Ovid may be safely put into the hands of children, as it is a selection of the least exceptionable fables. To accustom boys to read poetry and prose nearly at the same period, is advantageous. Cornelius Nepos, a crabbed book, but useful from its brevity, and from its being a proper introduction to Grecian and Roman history, may be read nearly at the same time with Ovid's Metamorphoses.
After Ovid, the pupil may begin Virgil, postponing some of the Eclogues, and all the Georgics. Plutarch's Lives, for instance, will be useful and interesting. When we mention Plutarch's Lives, we cannot help recollecting how many great people have acknowledged the effect of this book in their early education.
Charles the Twelfth, Rousseau, Madame Roland, Gibbon, we immediately remember, and we are sure we have noticed many others. An abridgment of Plutarch, by Mrs. Helme, which we have looked into, appears the preface excepted to be well written; and we see another abridgment of Plutarch advertised, which we hope may prove serviceable: good prints to a Plutarch for children, would be very desirable.
As an English introduction to mythology, we recommend the first volume of Lord Chesterfield's Letters, as a most elegant view of heathen mythology. But if there be any danger that the first volume should introduce the remainder of Lord Chesterfield's work to the inexperienced reader, we should certainly forbear the experiment: it would be far better for a young man never to be acquainted with a single heathen deity, than to purchase Lord Chesterfield's classical knowledge at the hazard of contamination from his detestable system of morals.
Without his Lordship's assistance, Mrs. Monsigny's Mythology can properly initiate the young pupil of either sex into the mysteries of ancient fables. In Dr. Darwin's "Botanic Garden," there are some beautiful poetic allusions to ancient gems and ancient fables, which must fix themselves in the memory or in the imagination of the pupil. The sooner they are read, the better; we have felt the advantage of putting them into the hands of a boy of nine or ten years old.
The ear should be formed to English as well as to Latin poetry. Classical poetry, without the knowledge of mythology, [Pg 28] is unintelligible: if children study the one, they must learn the other. Divested of the charms of poetry, and considered without classical prepossession, mythology presents a system of crimes and absurdities, which no allegorical, metaphysical, or literal interpreters of modern times, can perfectly reconcile to common sense, or common morality; but our poets have naturalized ancient fables, so that mythology is become essential even to modern literature.
The associations of taste, though arbitrary, are not easily changed in a nation whose literature has attained to a certain pitch of refinement, and whose critical judgments must consequently have been for some generations traditional. There are subjects of popular allusion, which poets and orators regard as common property; to dispossess them of these, seems impracticable, after time has sanctioned the prescriptive right.
But new knowledge, and the cultivation of new sciences, present objects of poetic allusion which, skilfully managed by men of inventive genius, will oppose to the habitual reverence for antiquity, the charms of novelty united to the voice of philosophy. In education we must, however, consider the actual state of manners in that world in which our pupils are to live, as well as our wishes or our hopes of its gradual improvement.
Children may be familiarized to the strange manners and strange personages of ancient fable, and may consider them as a set of beings who are not to be judged by any rules of morality, and who have nothing in common with ourselves. The caricatura of some of the passions, perhaps, will not shock children who are not used to their natural appearance; [Pg 29] they will pass over the stories of love and jealousy, merely because they do not understand them.
We should rather leave them completely unintelligible, than attempt, like Mr. Riley, in his mythological pocket dictionary for youth, to elucidate the whole at once, by assuring children that Saturn was Adam, that Atlas is Moses, and his brother Hesperus, Aaron; that Vertumnus and Pomona were Boaz and Ruth; that Mars corresponds with Joshua; that Apollo accords with David, since they both played upon the harp; that Mercury can be no other than our Archangel Michael, since they both have wings on their arms and feet; that, in short, to complete the concordance, Momus is a striking likeness of Satan.
The ancients, Mr. Riley allows, have so much disfigured these personages, that it is hard to know many of the portraits again at first sight; however, he is persuaded that "the young student will find a peculiar gratification in tracing the likeness," and he has kindly furnished us with a catalogue to explain the exhibition, and to guide us through his new pantheon.
As books of reference, the convenient size, and compressed information, of pocket mythological dictionaries, will recommend them to general use; but we object to the miserable prints with which they are sometimes disgraced.
The first impression made upon the imagination  of children, is of the utmost consequence to their future taste. The beautiful engravings  in Spence's Polymetis, will introduce the heathen deities in their most graceful and picturesque forms to the fancy.
The language of Spence, though classical, is not entirely free from pedantic affectation, and his dialogues are, perhaps, too stiff and long winded for our young pupils. But a parent or preceptor can easily select the useful explanations; and in turning [Pg 30] over the prints, they can easily associate some general notion of the history and attributes of the gods and goddesses with their forms: the little eager spectators will, as they crowd round the book, acquire imperceptibly all the necessary knowledge of mythology, imbibe the first pleasing ideas of taste, and store their imagination with classic imagery.
The same precautions that are necessary to educate the eye, are also necessary to form the ear and understanding of taste. The first mythological descriptions which our pupils read, should be the best in their kind. This princess was so beautiful, that, they say, one of the companions of Juno had robbed her of a pot of paint to bestow on this lady, which rendered her so handsome.
She was beloved of Jupiter, who assumed the shape of a bull to run away with her, swam over the sea with her on his back, and carried her into that part of the world now called Europe, from her name. Chapter on Attention. Darwin's Poetry. Aikin to his son on the morality and poetic merit of the fable of Circe, which convinces us that the observations that we have hazarded are not premature. Botanic Garden. The usual manner of teaching Geography and Chronology, may, perhaps, be necessary in public seminaries, where a number of boys are to learn the same thing at the same time; but what is learned in this manner, is not permanent; something besides merely committing names and dates to the memory, is requisite to make a useful impression upon the memory.
For the truth of this observation, an appeal is made to the reader. Let him recollect, whether the Geography and Chronology which he learned whilst a boy, are what he now remembers—Whether he has not obtained his present knowledge from other sources than the tasks of early years. When business, or conversation, calls upon us to furnish facts accurate as to place and time, we retrace our former heterogeneous acquirements, and select those circumstances which are connected with our present pursuit, and thus we form, as it were, a nucleus round which other facts insensibly arrange themselves.
Perhaps no two men in the world, who are well versed in these studies, connect their knowledge in the same manner. Relation to some particular country, some favourite history, some distinguished person, forms the connection which guides our recollection, and which arranges our increasing nomenclature. By attending to what passes in our own minds, we may learn an effectual method of teaching without pain, and without any extraordinary burden to the memory, all that is useful of these sciences.
When these have been once completely associated in the mind, there is little danger of their being ever disunited: [Pg 32] the sight of any country will recall its history, and even from representations in a map, or on the globe, when the mind is wakened by any recent event, a long train of concomitant ideas will recur. The use of technical helps to the memory, has been condemned by many, and certainly, when they are employed as artifices to supply the place of real knowledge, they are contemptible; but when they are used as indexes to facts that have been really collected in the mind; when they serve to arrange the materials of knowledge in appropriate classes, and to give a sure and rapid clue to recollection, they are of real advantage to the understanding.
Indeed, they are now so common, that pretenders cannot build the slightest reputation upon their foundation. Were an orator to attempt a display of long chronological accuracy, he might be wofully confounded by his opponent's applying at the first pause,.
Ample materials are furnished in Gray's Memoria Technica, from which a short and useful selection may be made, according to the purposes which are in view. For children, the little ballad of the Chapter of Kings, will not be found beneath the notice of mothers who attend to education.
If the technical terminations of Gray are inserted, they will never be forgotten, or may be easily recalled. For pupils at a more advanced age, it will be found advantageous to employ technical helps of a more scientific construction. Priestley's Chart of Biography [Pg 33] may, from time to time, be hung in their view. Smaller charts, upon the same plan, might be provided with a few names as land-marks; these may be filled up by the pupil with such names as he selects from history; they may be bound in octavo, like maps, by the middle, so as to unfold both ways—Thirty-nine inches by nine will be a convenient size.
Prints, maps, and medals, which are part of the constant furniture of a room, are seldom attended to by young people; but when circumstances excite an interest upon any particular subject, then is the moment to produce the symbols which record and communicate knowledge. Radcliffe, in her judicious and picturesque Tour through Germany, tells us, that in passing through the apartments of a palace which the archduchess Maria Christiana, the sister of the late unfortunate queen of France, had left a few hours before, she saw spread upon a table a map of all the countries then included in the seat of the war.
The positions of the several corps of the allied armies were marked upon this chart with small pieces of various coloured wax. Can it be doubted, that the strong interest which this princess must have taken in the subject, would for ever impress upon her memory the geography of this part of the world?
How many people are there who have become geographers since the beginning of the present war. Even the common newspapers disseminate this species of knowledge, and those who scarcely knew the situation of Brest harbour a few years ago, have consulted the map with that eagerness which approaching danger excites; they consequently will tenaciously remember all the geographical knowledge they have thus acquired.
The art of creating an interest in the study of geography, depends upon the dexterity with which passing circumstances are seized by a preceptor in conversation. What are maps or medals, statues or pictures, but technical helps to memory? If a mother [Pg 34] possess good prints, or casts of ancient gems, let them be shown to any persons of taste and knowledge who visit her; their attention leads that of our pupils; imitation and sympathy are the parents of taste, and taste reads in the monuments of art whatever history has recorded.
In the Adele and Theodore of Madame de Silleri, a number of adventitious helps are described for teaching history and chronology. There can be no doubt that these are useful; and although such an apparatus cannot be procured by private families, fortunately the print-shops of every provincial town, and of the capital in particular, furnish even to the passenger a continual succession of instruction. Might not prints, assorted for the purposes which we have mentioned, be lent at circulating libraries?
To assist our pupils in geography, we prefer a globe to common maps. Might not a cheap, portable, and convenient globe, be made of oiled silk, to be inflated by a common pair of bellows? Mathematical exactness is not requisite for our purpose, and though we could not pretend to the precision of our best globes, yet a balloon of this sort would compensate by its size and convenience for its inaccuracy. It might be hung by a line from its north pole, to a hook screwed into the horizontal architrave of a door or window; and another string from its south pole might be fastened at a proper angle to the floor, to give the requisite elevation to the axis of the globe.
An idea of the different projections of the sphere, may be easily acquired from this globe in its flaccid state, and any part of it might be consulted as a map, if it were laid upon a convex board of a convenient size. Impressions from the plates which are used for common globes, might be taken to try this idea without any great trouble or expense; but we wish to employ a much larger scale, and to have them five or six feet diameter.
The inside of a globe of this sort might be easily illuminated, and this would add much to the novelty and beauty of its appearance. In the country, with the assistance of a common carpenter and plasterer, a large globe of lath and plaster may be made for the instruction and entertainment of a numerous family of children. Upon this they should leisurely delineate from time to time, by their given latitudes and longitudes, such places as they become acquainted with in reading or conversation.
We enter into this detail because we are convinced, that every addition to the active manual employment of children, is of consequence, not only to their improvement, but to their happiness. Another invention has occurred to us for teaching geography and history together. Priestley's Chart of History, though constructed with great ingenuity, does not invite the attention of young people: there is an intricacy in the detail which is not obvious at first.
To remedy what appears to us a difficulty, we propose that eight and twenty, or perhaps thirty, octavo maps of the globe should be engraved; upon these should be traced, in succession, the different situations of the different countries of the world, as to power and extent, during each respective century: different colours might denote the principal divisions of the world in each of these maps; the same colour always denoting the same country, with the addition of one strong colour; red, for instance, to distinguish that country which had at each period the principal dominion.
On the upper and lower margin in these maps, the names of illustrious persons might be engraven in the manner of the biographical chart; and the reigning opinions of [Pg 36] each century should also be inserted. Thus history, chronology, and geography, would appear at once to the eye in their proper order, and regular succession, divided into centuries and periods, which easily occur to recollection.
We forbear to expatiate upon this subject, as it has not been actually submitted to experiment; carefully avoiding in the whole of this work to recommend any mode of instruction which we have not actually put in practice. We cannot forbear recommending, in the strongest manner, a few pages of Rollin in his "Thoughts upon Education,"  which we think contain an excellent specimen of the manner in which a well informed preceptor might lead his pupils a geographical, historical, botanical, and physiological tour upon the artificial globe.
We conclude this chapter of hints, by repeating what we have before asserted, that though technical assistance may be of ready use to those who are really acquainted with that knowledge to which it refers, it never can supply the place of accurate information. The causes of the rise and fall of empires, the progress of human knowledge, and the great discoveries of superior minds, are the real links which connect the chain of political knowledge.
Gray's Memoria Technica, and the Critic. The man who is ignorant that two and two make four, is stigmatized with the character of hopeless stupidity; except, as Swift has remarked, in the arithmetic of the customs, where two and two do not always make the same sum. We must not judge of the understanding of a child by this test, for many children of quick abilities do not immediately assent to this proposition when it is first laid before them.
The child stares because the word make is in this sentence used in a sense which is quite new to him; he knows what it is to make a bow, and to make a noise, but how this active verb is applicable in the present case, where there is no agent to perform the action, he cannot clearly comprehend. When he has once perceived the combination of the numbers with real objects, it will then be easy to teach him that the words are called , are , and make , in the foregoing proposition, are synonymous terms.
We have chosen the first simple instance we could recollect, to show how difficult the words we generally use in teaching arithmetic, must be to our young pupils. It would be an unprofitable task to enumerate [Pg 38] all the puzzling technical terms which, in their earliest lessons, children are obliged to hear, without being able to understand. It is not from want of capacity that so many children are deficient in arithmetical skill; and it is absurd to say, "such a child has no genius for arithmetic.
Such a child cannot be made to comprehend any thing about numbers. A child's seeming stupidity in learning arithmetic, may, perhaps, be a proof of intelligence and good sense. It is easy to make a boy, who does not reason, repeat by rote any technical rules which a common writing-master, with magisterial solemnity, may lay down for him; but a child who reasons, will not be thus easily managed; he stops, frowns, hesitates, questions his master, is wretched and refractory, until he can discover why he is to proceed in such and such a manner; he is not content with seeing his preceptor make figures and lines upon a slate, and perform wondrous operations with the self-complacent dexterity of a conjurer.
A sensible boy is not satisfied with merely seeing the total of a given sum, or the answer to a given question, come out right ; he insists upon knowing why it is right. He is not content to be led to the treasures of science blindfold; he would tear the bandage from his eyes, that he might know the way to them again. That many children, who have been thought to be slow in learning arithmetic, have, after their escape from the hands of pedagogues, become remarkable for their quickness, is a fact sufficiently proved by experience.
We shall only mention one instance, which we happened to meet with whilst we were writing this chapter. John Ludwig, a Saxon peasant, was dismissed from school when he was a child, after four years ineffectual struggle to learn the common rules of arithmetic. He had been, during this time, beaten and scolded in vain. He spent several subsequent years in common [Pg 39] country labour, but at length some accidental circumstances excited his ambition, and he became expert in all the common rules, and mastered the rule of three and fractions, by the help of an old school book, in the course of one year.
He afterwards taught himself geometry, and raised himself, by the force of his abilities and perseverance, from obscurity to fame. We should like to see the book which helped Mr. Ludwig to conquer his difficulties. Introductions to Arithmetic are, often, calculated rather for adepts in science, than for the ignorant.
We do not pretend to have discovered any shorter method than what is common, of teaching these sciences; but, in conformity with the principles which are laid down in the former part of this work, we have endeavoured to teach their rudiments without disgusting our pupils, and without habituating them to be contented with merely technical operations. In arithmetic, as in every other branch of education, the principal object should be, to preserve the understanding from implicit belief; to invigorate its powers; to associate pleasure with literature, and to induce the laudable ambition of progressive improvement.
As soon as a child can read, he should be accustomed to count, and to have the names of numbers early connected in his mind with the combinations which they represent. For this purpose, he should be taught to add first by things, and afterwards by signs or figures.
He should be taught to form combinations of things by adding them together one after another. At the same time that he acquires the names that have been given to these combinations, he should be taught the figures or symbols that represent them. Each operation of arithmetic should [Pg 40] proceed in this manner, from individuals to the abstract notation of signs. One of the earliest operations of the reasoning faculty, is abstraction; that is to say, the power of classing a number of individuals under one name.
Young children call strangers either men or women; even the most ignorant savages  have a propensity to generalize. We may err either by accustoming our pupils too much to the consideration of tangible substances when we teach them arithmetic, or by turning their attention too much to signs.
The art of forming a sound and active understanding, consists in the due mixture of facts and reflection. Reid has, in his "Essay on the Intellectual Powers of Man," page , pointed out, with great ingenuity, the admirable economy of nature in limiting the powers of reasoning during the first years of infancy. This is the season for cultivating the senses, and whoever, at this early age, endeavours to force the tender shoots of reason, will repent his rashness.
As these children advance in arithmetic to square or cube, a number will be more intelligible to them than to a person who [Pg 41] has been taught these words merely as the formula of certain rules. In arithmetic, the first lessons should be short and simple; two cubes placed above each other, will soon be called two; if placed in any other situations near each other, they will still be called two; but it is advantageous to accustom our little pupils to place the cubes with which they are taught in succession, either by placing them upon one another, or laying in columns upon a table, beginning to count from the cube next to them, as we cast up in addition.
For this purpose, a board about six inches long, and five broad, divided into columns perpendicularly by slips of wood three eighths of an inch wide, and one eighth of an inch thick, will be found useful; and if a few cubes of colours different from those already mentioned , with numbers on their six sides, are procured, they may be of great service. Our cubes should be placed, from time to time, in a different order, or promiscuously; but when any arithmetical operations are to be performed with them, it is best to preserve the established arrangement.
One glass, and one glass, are called two glasses. One cube, and one glass, are called what? Two things or two. By a process of this sort, the meaning of the abstract term two may be taught. A child will perceive the word two , means the same as the words one and one ; and when we say one and one are called two, unless he is prejudiced by something else that is said to him, he will understand nothing more than that there are two names for the same thing.
He will see that any two of the cubes may be put together, as it were, in one parcel, and that this parcel may be called two ; and he will also see that this parcel, when joined to another single cube, will make three, and that the sum will be the same, whether the single cube, or the two cubes, be named first.
In a similar manner, the combinations which form four , may be considered. One, and one, and one, and one, are four. All these assertions mean the same thing, and the term four is equally applicable to each of them; when, therefore, we say that two and two are four, the child may be easily led to perceive, and indeed to see , that it means the same thing as saying one two , and one two , which is the same thing as saying two two's , or saying the word two two times.
Our pupil should be suffered to rest here, and we should not, at present, attempt to lead him further towards that compendious method of addition which we call multiplication; but the foundation is laid by giving him this view of the relation between two and two in forming four. There is an enumeration in the note  of the different combinations which compose the rest of the Arabic notation, which consists only of nine characters.
Before we proceed to the number ten, or to the new series of numeration which succeeds to it, we should make our pupils perfectly masters of the combinations which we have mentioned, both in the direct order in which they are arranged, and in various modes of succession; by these means, not only the addition, but the subtraction, of numbers as far as nine, will be perfectly familiar to them. It has been observed before, that counting by realities, and by signs, should be taught at the same time, so that the ear, the eye, and the mind, should keep pace with one another; and that technical habits should be acquired without injury to the understanding.
If a [Pg 45] child begins between four and five years of age, he may be allowed half a year for this essential, preliminary step in arithmetic; four or five minutes application every day, will be sufficient to teach him not only the relations of the first decade in numeration, but also how to write figures with accuracy and expedition.
The next step, is, by far the most difficult in the science of arithmetic; in treatises upon the subject, it is concisely passed over under the title of Numeration; but it requires no small degree of care to make it intelligible to children, and we therefore recommend, that, besides direct instruction upon the subject, the child should be led, by degrees, to understand the nature of classification in general.
Botany and natural history, though they are not pursued as sciences, are, notwithstanding, the daily occupation and amusement of children, and they supply constant examples of classification. The trees that form the grove are each of them individuals; but let their numbers be what they may when they are considered as a grove, the grove is but one, and may be thought of and spoken of distinctly, without any relation to the number of single trees which it contains.
From these, and similar observations, a child may be led to consider ten as the name for a whole , an integer ; a one , which may be represented by the figure 1 : this same figure may also stand for a hundred, or a thousand, as he will readily perceive hereafter. Indeed, the term one hundred will become familiar to him in conversation long before he comprehends that the word ten is used as an aggregate term, like a dozen, or a thousand.
We do not use the word ten as the French do une dizaine ; ten does not, therefore, present the idea of an integer till we learn arithmetic. This is a defect in our language, which has arisen from the use of duodecimal numeration; the analogies [Pg 46] existing between the names of other numbers in progression, is broken by the terms eleven and twelve. In pointing out these analogies to children, they become interested and attentive, they show that species of pleasure which arises from the perception of aptitude , or of truth.
It can scarcely be denied that such a pleasure exists independently of every view of utility and fame; and when we can once excite this feeling in the minds of our young pupils at any period of their education, we may be certain of success. As soon as distinct notions have been acquired of the manner in which a collection of ten units becomes a new unit of a higher order, our pupil may be led to observe the utility of this invention by various examples, before he applies it to the rules of arithmetic.
Let him count as far as ten with black pebbles,  for instance; let him lay aside a white pebble to represent the collection of ten; he may count another series of ten black pebbles, and lay aside another white one; and so on, till he has collected ten white pebbles: as each of the ten white pebbles represents ten black pebbles, he will have counted one hundred; and the ten white pebbles may now be represented by a single red one, which will stand for one hundred.
This large number, which it takes up so much time to count, and which could not be comprehended at one view, is represented by a single sign. All this is fully within the comprehension of a child of [Pg 47] six years old, and will lead him to the value of written figures by the place which they hold when compared with one another.
Indeed he may be led to invent this arrangement, a circumstance which would encourage him in every part of his education.
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