Popular Science Monthly/Volume 14/April 1879/Why Do We Eat our Dinner?
|←Early Traces of Man|| Popular Science Monthly Volume 14 April 1879 (1879)
Why Do We Eat our Dinner?
By Charles Grant Blairfindie Allen
|The Origin of Upland Lakes→|
By Professor GRANT ALLEN.
EARLY last year a paragraph went the round of the papers to the effect that a large female anaconda-snake, in the reptile-house at the Zoölogical Gardens, after a fast of a twelvemonth, had at length been induced to kill and swallow a duck. This very touchy and vindictive lady, it appears, had taken such grave offense at her capture in her South American home, and at her subsequent compulsory voyage to Great Britain, that she sulked persistently for a whole year, and invariably refused the keeper's most tempting offers of live rabbits or plump young pigeons. Month after month she lay passive in her cage, with her heart beating, her lungs acting, and all her vital functions proceeding with the usual slow regularity of snake-life; but not a mouthful of food did she attempt to take, and not a single fresh energy did she recruit from without to keep up the working of her animal mechanism. As I read this curious case of a genuine "fasting girl" in my "Times" one morning, the thought struck me forcibly—"Why, after all, should we expect her to feed? Why should she not go on for ever without tasting a morsel? In short, why should we eat our dinner?" And I set myself to work at once to find out what was the general opinion of the unscientific public upon this important though novel question.
Singularly enough, I found that most people were content to eat their dinner in a very unreasoning and empirical way. They had ways been accustomed to dine daily from their childhood upward, they felt hungry at the habitual dinner-hour, and they sat down to their five courses with an unquestioning acceptance of the necessity for feeding to prevent starvation. But when I inquired why people who did not eat should starve, why they should not imitate the thrifty anaconda, and take one meal in a twelvemonth instead of three in a day, they appeared to regard my question as rather silly, and as certainly superfluous. Yet I must confess the query seems to me both pertinent and sensible; and it may be worth while to attempt some answer here in such language as can be understanded of the people, without diving into those profound mysteries of formulæ and equations with which physicists love to becloud the subjects of their investigation.
A still more startling case than that of the anaconda will help to throw a little light upon the difficult problem which we have to solve. An Egyptian desert-snail was received at the British Museum on March 25, 1846. The animal was not known to be alive, as it had withdrawn into its shell, and the specimen was accordingly gummed, mouth downward, on to a tablet, duly labeled and dated, and left to its fate. Instead of starving, this contented gasteropod simply went to sleep in a quiet way, and never woke up again for four years. The tablet was then placed in tepid water, and the shell loosened, when the dormant snail suddenly resuscitated himself, began walking about the basin, and finally sat for his portrait, which may be seen of life-size in Mr. Woodward's "Manual of the Mollusca." Now, during those four years the snail had never eaten a mouthful of any food, yet he was quite as well and flourishing at the end of the period as he had been at its beginning.
Hence we are led to the inquiry—What is the actual function which food subserves in the human body? Why is it true that we must eat or we must die, while the snake and the snail can fast for months or years together with impunity? How do we differ from these lower animals in such a remarkable degree, when all the operations of our bodies so closely resemble theirs in general principle?
Everybody has heard it said that food is to men and animals what fuel is to a steam-engine. Everybody accepts this statement in a vague sort of way, but until the last few years nobody has been able really to explain what was the common feature of the two cases. For example, most people if asked would answer that the use of food is to warm the body, but this is really quite beside the question: because, in the first place, the use of fuel is not to warm the steam-engine, but to keep up its motion; and, in the second place, many animals are scarcely perceptibly warmer than the medium in which they live. Again, most people show in every-day conversation that they consider the main object of food to be the replacement of the materials of the body; whereas we shall see hereafter that its real object is the replacement of the energies which have been dissipated in working. Indeed, there is no more reason why the materials of an animal body should waste away of themselves, apart from work done, than there is for a similar wasting away in the case of a mineral body such as a stone. When an animal does practically no work, as in the instance of our desert-snail, his body actually does not waste, but remains throughout just as big as ever. So we must look a good deal more closely into the problem if we want to understand it, and not rest content with vague generalities about food and fuel. Such half knowledge is really worse than no knowledge at all, because it deludes us into a specious self-deception, and makes us imagine that we comprehend what in fact we have not taken the least trouble to examine for ourselves.
Let us begin, then, by clearly realizing what is the use of fuel to the steam-engine. Obviously, you say, to set up motion. But where does the motion come from? "From the coal," answers the practical man, unhesitatingly. "Well, not exactly," says the physicist, "but from the coal and the air together." All energy or moving power, as we now know, is derived from the union of two bodies which have affinities or attractions for one another. Thus, if I wind up a clock, moved by a weight, I separate the mass of lead in the weight from the earth, for which it has the kind of affinity or attraction known as gravitation. This attraction then draws together the weight and the earth; and, in doing so, the energy I put into it is given out as motion of the clock. Similarly with coal and air: the hydrogen and carbon of the coal have affinities or attractions toward the oxygen of the air, and when I bring them together at a high temperature (of which more hereafter) they rush into one another's embrace to form carbonic acid and water, while their energy is given off as heat or motion of the surrounding bodies. We might have whole minefuls of coal at our disposal; but if we had no oxygen to unite with it, the coal would be of no more use than so much earth or stone. In ordinary life, however, the supply of oxygen is universal and abundant, while the supply of coal is limited; and so, as we have to lay in coals, while we find the oxygen laid in for us, we always quite disregard the latter factor in our fires, and speak as though the fuel were the only important element concerned. Yet one can easily imagine a state of things in which oxygen might be deficient; and in a world so constituted it would have to be regularly laid on in pipes, like gas or water, if the people wished to have any fires.
All energy, then, is derived from the separation of two or more bodies having affinities for one another. So long as the bodies remain separate, the energy is said, in the technical slang of physics, to be potential; as soon as the bodies unite, and the energy is manifested as motion, it is said to be kinetic. But these words are rather mystifying to ordinary readers, and frighten us by their bigness and their abstract sound; so I shall take the liberty of altering them for our present purpose to dormant and active respectively, which are terms quite as well adapted to express the meaning intended, and not half so likely to land us in an intellectual cul-de-sac, or to envelop us in a logical fog. When we take a piece of coal and a lot of free oxygen, we possess energy in the dormant state. But though the oxygen has strong attractions for the carbon and hydrogen, they can not unite, because their atoms do not come into close contact with one another, and because the two last-named substances are bound up in the solid form of the coal. We might compare their condition to that of a weight suspended by a string, which has strong attractions toward the earth, but can not unite with it till we cut the string. Just analogous is our action when we apply a match to the coal. The heat first disintegrates or disunites little atoms of the hydrocarbons which make it up, and sets them in a state of rapid vibration among themselves. This vibration brings them into contact with the atoms of oxygen, which at once unite with them, causing a fresh development of heat, and a liberation of all the dormant energy, which immediately assumes the active form. The carbonic acid and water (or steam) thus produced fly up the chimney, carrying with them the little bits of unburned coal which we call smoke; and a current of fresh oxygen rushes in to unite with the fresh atoms of hydrogen and carbon which have been disengaged by the energy liberated from their fellows. So the process continues, till all the coal has been converted into carbonic acid and water—of course by the aid of a corresponding quantity of oxygen—and all the energy has been turned loose as heat upon the room in which we sit and upon the air outside.
In the case of an ordinary fire, where warmth is the single object we have in view, we only think of the heat, and disregard the other aspects of the process. But it is clear that an enormous amount of motion has also been set up by the energy of the free coal and oxygen, as exemplified by the draught up the chimney, and the numerous currents of air produced by its action within and without the room. Now, in a steam engine we deliberately make use of this motion for our own purposes by a specially devised mechanism. We allow the fire to heat and expand the water in the boiler, thus transferring to its molecules the separation which formerly existed between the atoms of the coal and the oxygen. Then we make the expanded water or steam push up the piston, and we connect the piston in turn with a crank which sets in motion the wheels, and so passes on the active energy to the mill, train, or ship which we desire to move, as the case may be. Thus the dormant energy of the coals and oxygen is liberated in the active state by their union, and is finally employed to effect movement in external bodies by the intermediation of the boiler. Even then the energy does not disappear: for energy, like matter, is indestructible; but it merely passes by friction as heat to that wonderful surrounding medium which we call ether, and is dissipated into the vast void of space, no longer recoverable by us, though quite as really existent as ever.
In what way, however, has all this to do with the reason for eating our dinners? Simply this: Men and other animals may be regarded from the purely physical point of view as a kind of conscious locomotive steam-engine, with whom food stands in the place of fuel, while the possible kinds of movement are infinitely more varied and specialized. I do not mean to advance any of those "automatic" theories which have been so current of late years. Whether they are true or false, they have nothing to do with our present subject. I only want to put in a plain light an accepted scientific truth. Men differ enormously from steam-engines in their possession of consciousness, wills, desires, pleasures, pains, and moral feelings; but they agree with them in the purely physical mechanism of their motor organs. A man, like a steam-engine, can not move without his appropriate fuel; and if the fuel is not supplied, the fire goes out and the man dies. The exact manner in which the materials are utilized for keeping up this vital flame is the question to which we must now address ourselves.
Food-stuffs and coal agree essentially in the chief characteristics of their chemical constitution. Both consist mainly of hydrogen and carbon, and both possess energy in virtue of the fact that their affinities for oxygen are not satisfied. Water contains hydrogen, and carbonic acid contains carbon; but we can get no motion out of these, because in them the oxygen has already united with the atoms for which it had affinity, and the separation necessary for dormant energy has ceased to exist. But in bread, meat, potatoes, or coal, the hydrogen and carbon remain in their free state, ready to unite with oxygen whenever the chance is presented to them. All alike obtained their energy in the same way. The rays of sunlight falling upon the leaves of their original trees or plants separated the oxygen from the water and carbonic acid in the air, and built up the free hydrocarbons in their tissues. The energy which they thus drank in has remained dormant within them ever since: in the case of the bread for a few short months, in that of the coal for countless millions of geological cycles. But, however long it may have rested in that latent form, whenever an opportunity occurs the atoms will reunite with oxygen, and the energy will once more assume the active shape. There is really only one serious difference between coal and food, and that is that most foods contain another element, nitrogen, as well as carbon and hydrogen; and this nitrogen is an absolute necessity for the animal if it is to continue living. But there are good reasons for suspecting that nitrogen is not itself a fuel, being rather analogous in its nature to a match, and having for its business to set up the first beginnings of a fire, not to keep the fire going when it has once been lighted. So that this apparent difference of kind is really seen to be unimportant when we get to the bottom of the question.
The various matters which an animal eats consist of pure food-stuffs and of useless concomitant bodies: just as coal consists of pure fuel and of the useless mineral matter known as ash. When an animal eats his dinner, the process of digestion and assimilation takes place, and has the ultimate result of separating the pure food-stuffs from the useless concomitants. The latter bodies are rejected at once; but the food-stuffs are taken up by his veins, incorporated with the blood (which consists of food in different degrees of combustion), and used for building up the various portions of his body. Supposing the animal were a mere growing object like a crystal, with no work to perform and no consequent waste of material, the process would stop here, and the creature would wax bigger and bigger from day to day, without any alteration in place or redistribution of assimilated matter. But the animal is essentially a locomotive machine, and the purpose for which he has taken in his food is simply that he may use it up in producing motion. For a while he stores it away in his muscles, or lays it by for future use as fat; but its ultimate destination in every instance is just as truly to be consumed for fuel as is the case with the coal in the steam-engine.
The food, however, only gives us one half of the necessary materials for the liberation of dormant energy. Oxygen is needed to give us the other half. This oxygen we take in whenever we breathe. Animals like fishes or sea-snails obtain the necessary supply from the water by means of gills; for large quantities of oxygen are held in solution by water, and the needs of such comparatively sluggish creatures are not very great. With them a little energy goes a long way. Air-breathing animals like ourselves, on the other hand, need relatively large quantities of the energy-yielding gas in order to keep up the constant movements and high temperature of their bodies. Such creatures, accordingly, take in the oxygen by great inhalations, and absorb it in their lungs, where it passes through the thin membrane of the capillaries, or very tiny blood-vessels, and so mixes freely with the blood itself. Thus we have food, supplied to the blood by the stomach, the exact analogue of the coal in the engine; and oxygen, supplied to the blood by the lungs, the exact analogue of the draught in the engine. Whenever these two substances—the hydrocarbonaceous foods and the free oxygen—reunite, they will necessarily give out heat and set up active movements.
The exact place and mode of their recombination we can not yet be said to fully understand. But even if we did, the details would be sufficiently dry and uninteresting to general readers; and we know quite enough to put the subject in a simple and comprehensible form before those who are willing to accept the broad facts without small criticism.
We may say, then, that the energies of the body are used up in two principal ways—automatically and voluntarily. The automatic activities are produced by the steady and constant oxidation of some portion of the food-stuffs in the blood and tissues. As this oxidation takes place, it sets up certain regular movements, which compose what is (very incorrectly) known as the vegetative life in animals. There are an immense number of these movements always going on within our bodies, quite apart from our knowledge or will. Such are the beating of the heart, with the consequent propulsions of blood through the system; the expirations and inspirations of the lungs, which supply us with the oxygen for carrying on these processes; the act of digestion and assimilation; and many other minor functions of like sort. But just as in the case of the steam-engine, so in the human or animal body, the union of the oxygen with the hydrocarbons, besides producing motion, liberates heat. This heat keeps the bodies of birds, quadrupeds, and human beings, which are all very active in their automatic movements, at a much higher temperature than the surrounding medium; while reptiles, fishes, and other "cold-blooded" creatures, having much less energetic motions of the heart and lungs—which of course betokens much less oxidation of food-stuffs—have bodies comparatively little different in warmth from the air or water about them. We thus see in part why it was that the anaconda and the desert-snail could go so long without food; though we can not quite understand that question till we have examined the voluntary movements as well. It should be added that, though the latter class of actions also produce heat—as we all know when we walk about on a cold day to warm ourselves—yet the temperature induced by the automatic activities of the body alone is generally sufficient under normal circumstances to keep us comfortably warm. Thus, while we are asleep, only the actions of breathing and the beating of the heart continue; but the union of oxygen with the food-stuffs to produce these movements suffices as a rule to make bed quite hot enough for all healthy persons; and if we ever wake up cold after a good night's rest, we may be sure that our automatic activities are not what they ought to be.
The voluntary activities of the body are brought about in a slightly different manner. Directly or indirectly, they depend upon the union of oxygen and food-stuffs within the tissues of our locomotive muscles, the energy so liberated being made use of to bend or extend our bones or limbs in the particular way we desire. The muscles always contain (in a healthy and well-fed person) large quantities of such stored-up food-stuffs; and the blood supplies them from moment to moment with oxygen which may unite with the food-stuffs whenever occasion demands. But the union does not here take place regularly and constantly, as in the case of the automatic organs; it requires to be set up by an impetus specially communicated from the brain. That seat of the will is connected with the various voluntary muscles by the living telegraphic wires which we call nerves; and when the will determines that a certain muscle shall be moved, the nerves communicate the disturbance to the proper quarter, the necessary oxidation takes place, and the muscle contracts as desired. We do not quite know how the nerves and muscles perform these functions; but it is pretty certain that the nitrogen of our foods plays an active part in the process, and that, as I have already hinted, it acts in a manner somewhat analogous to that of a match. We may suppose, to put the matter in a familiar form, that the will sends down a sort of electric spark to the muscle; and that this spark, lighting up the explosive nitrogen, causes an immediate union of the oxygen with the constituents of muscle, and so produces the visible movement.
Of course, voluntary actions, like automatic ones, liberate heat; but this heat is generally somewhat in excess of what is required for comfort, especially in hot weather. Lower animals, however, which have no fires and no artificial clothing, require it more than we do to keep us warm; and even we ourselves in wintry weather always feel chilly in the morning until we have had a good brisk walk to set up oxidation, and consequently liberate enough heat to make us comfortable.
Thus all motion, in the animal as in the steam-engine, depends upon the union of oxygen with food or body-fuel. It is true that in the animal body oxygen can unite directly with carbon and hydrogen without the necessity of a high temperature, which we saw was indispensable in the case of the coal, in order to bring the two sets of atoms within the sphere of their mutual attractions. But the difference is probably due to the different condition of the hydrocarbonaceous substances within the animal body; or else, as others conjecture, to the assumption by the oxygen of that peculiar state in which it is known as ozone. At any rate, the two processes do not disagree in any essential particular, being both cases in which free substances, possessing dormant energy by virtue of their separation and their affinity for one another, unite together, and in so doing liberate their energy as heat and visible motion.
There is, however, one important distinction of detail between the mechanism of a steam-engine and the mechanism of an animal body, which gives rise to many of the mistaken notions as to the use of food which we noticed above. In the engine, we put all the coal into the furnace, and burn it there at once; while the piston, cylinder, cranks, and wheels are not composed of combustible material, but of solid iron. In the animal body, on the other hand, every muscle is at once furnace, boiler, and piston; it consists of combustible materials, which unite with oxygen in the tissues themselves, and set up motion within the muscle of which they form a portion. The case is just the same as though the joints of an engine, instead of being quite rigid, were composed of hollow India-rubber and whalebone, with iron attachments; were then filled with coal, oxygen, and water, and possessed the power of burning up these materials internally and setting up motions in the India-rubber tubings. Hence the materials in the muscles are always undergoing change. The carbon and hydrogen which have united with the oxygen are perpetually forming carbonic acid and water; and, as
 these have lost or given up all their energy, they are naturally of no more use to the body than the similar carbonic acid and steam which fly up the draught are of use to the engine. Accordingly, they are taken up by the stream of blood as it passes, separated from the useful components of that compound liquid by an appropriate organ, and rejected from the body as of no further service.
But their place in the muscle must once more be supplied by fresh energetic materials; and these materials are brought to it by the selfsame blood which removes the deënergized waste products. And now we begin to see why we must eat our dinners or starve. Every time our heart beats, every time our lungs draw in a breath, a certain amount of matter in the tissues of the muscles which produced those motions undergoes oxidation, and is carried off in the oxidized form to be cast out of the body as waste. Every new pulsation or breath requires a certain new quantity of energetic material, both as food-stuffs and as oxygen; and hence we must supply the one from the stomach and the other from the lungs if we wish to keep the mechanism going. The store of hydrocarbonaceous matters laid by in the body is generally considerable in well-fed persons; for, besides the contents of the muscles themselves, we have usually a large reserve fund in the shape of fat, ready to be utilized when occasion arises. Hence, we can get along for a very short time, if necessary, without food; because we can fall back, first upon the fat-reserve, and then upon the muscles and tissues, for energetic materials. But after a time the ceaseless beating of the heart and movement of the lungs will use up all the available matters, and the blood will cast off the oxidized product and excrete it from the body; till at last no more materials are forthcoming, the whole contents of the tissues have been oxidized and got rid of, and the heart and lungs must perforce cease to act, in which case the unhappy victim is said to have died of starvation. As regards the supply of oxygen, on the other hand, we are very much more restricted in our power of endurance; for we have no large store of this necessary for combustion laid by in our bodies, and if the supply be cut off for a single moment (as by compressing the throat or suffocating with carbonic acid) the heart and lungs must cease at once to act, and death takes place immediately. For of course death, viewed on its purely physical side, means the cessation of that set of activities which results from the union of oxygen with the food-stuffs in the body.
By this time I hope the reader can see quite clearly what is the necessity for eating his dinner. If we are to live, we must keep up the cycle of our bodily activities, and especially those two fundamental ones, the breathing of the lungs and the beating of the heart. In order to do this, we must supply the muscles employed with the two energy yielding substances, oxygen and hydrocarbons. The supply of oxygen must be continuous; in other words, we must never for a moment leave off breathing; but the supply of hydrocarbons may be intermittent, though it must be sufficient on the whole to balance waste. We must not regard the object of food, however, as being merely to build up the matter of the body; we must rather consider it as intended to recruit the energies of the body. The more active any creature is, both in its automatic and its voluntary movements, the greater will be the amount of hydrocarbons consumed or used up in its muscles, and the greater, consequently, the amount of food and oxygen which it will require to make up the loss. The tiny humming-bird will need far more food in a year than the great anaconda with which we began our discourse: because the humming-bird has a rapidly moving heart and lungs, while the cold-blooded snake respires and circulates slowly; and the humming-bird darts about perpetually at lightning-speed from flower to flower, while the snake lies coiled up motionless in its blanket from year's end to year's end, or only comes out sleepily now and then to swallow the food which will keep up its vital actions through another long and lazy fast.
The desert-snail, however, can endure much longer without food than even the anaconda, because, like so many other mollusca, it can hibernate. This process of hibernation consists in the inducement of a state during which the heart ceases to beat, respiration is suspended, and the animal can hardly be said to live at all. But when warmth and moisture are once more applied, the heart recommences its action, the lungs or gills quicken their movements, voluntary locomotion ensues, and the creature sets out again on the quest for food. Something analogous occurs in the case of the bear, the dormouse, and other hibernating quadrupeds; but in these instances the vital functions continue much more in their ordinary state, and are kept up by the supply of fat which is dissolved by the blood, and consumed in effecting the necessary automatic actions. The bear, which goes to sleep in the autumn as sleek and plump as a prize pig, wakes up in the spring a poor, lean wretch, with only just flesh enough to cover his bones, and carry him off in search of fresh food. The much more complicated mechanism of the higher animals requires to be kept always in action; it can not cease almost entirely, like that of the snail, and then revive again when circumstances become more favorable. Hence hibernating mammals must lay by fat during the summer to keep their principal organs at work during the long winter fast. Yet, even among human beings, cases of "trance" or "suspended animation" occasionally occur, during which the cycle of vital actions almost entirely ceases to all appearance for a considerable time, and then begins again on the application of some external or internal stimulus—which latter may be not unaptly compared to the slight shaking which we sometimes give a watch or clock to set it going when stopped by a momentary impediment. Persons recovered from drowning, in whom the cessation of action has been quite sudden and has not affected the structure of their organs, are often thus restored by the judicious use of rubbing and alcohol.
The camel presents a more interesting phenomenon in his well-known humps. These protuberances consist really of reserve-stores of fat, which the camel uses, not only for keeping up the action of his heart and lungs, but also for producing locomotion in his frequent enforced fasts among the deserts of Arabia or India. The humps dwindle away as he marches, in a manner exactly similar to that of the bear's fat during his hibernation, only of course much more rapidly, as they have so much more work to perform.
Finally, it may appear strange that the small amount of food we eat should suffice to carry our large and bulky bodies through all the varied movements of the day. But this difficulty disappears at once when we recollect how large an amount of energy can be laid by dormant in a very small piece of matter. A lump of coal no bigger than one's fist, if judiciously employed, will suffice to keep a small toy-engine at work for a considerable time. Now, our food is matter containing large amounts of dormant energy, and our bodies are engines constructed so as to utilize all the energy to the best advantage. A single gramme of beef-fat, if completely burned (that is, if every atom unites with oxygen), is capable of developing more than 9,000 heat-units; and each such heat-unit, if employed to perform mechanical work, is capable of lifting a weight of one gramme to a height of 424 metres; or, what comes to the same thing, 424 grammes to a height of one metre. Accordingly, the energy contained in one gramme of beef-fat (and the oxygen with which it unites) would be sufficient to raise the little bit of fat itself to a height of 3,816 kilometres, or about as high as from London to New York. Again, it may seem curious that the food eaten by the anaconda in South America, and stored up in its tissues, should suffice to keep up the action of its heart and lungs for so many months. But then we must remember that it performed very few other movements, most probably, during all that time; and if we think how small an amount of energy we expend in winding up an eight-day clock, and how infinitesimal a part of our dinner must have been used up in imparting to it the motion which will keep it swinging and ticking for one hundred and ninety-two hours, we can easily understand how the large amount of stored-up energy in the snake's muscles might very well serve to keep up its automatic actions for so long a time.
There are five hundred other little points which this mode of regarding our bodies at once clears up. It shows us why we are warmer after eating a meal, why cold is harder to endure when we are hungry, why we need so little food when we are lying in bed inactive, and so much when we are taking a walking tour or training for a boat-race, why cold-blooded animals eat so rarely and warm-blooded creatures so often, why we get thin when we take too little food, and why we lay on fat when we take too little exercise. But these and many other questions must be passed over in silence, or left to the reader's discrimination, lest I should make this paper tediously long. It must suffice for the present if I have given any of my readers a more rational reason in future for eating their dinners. To be sure, Nature herself has admirably provided that even the most unscientific person should find sufficient internal conviction as to the desirability of dining without the aid of extraneous exhortation; but it is at least some comfort to know that so universal and so unreasoning a practice is not altogether an unreasonable one as well.—Belgravia.
- I am speaking quite metaphorically and popularly, and do not mean to imply adhesion to the electrical rather than to the isomeric theory of nervous conduction.
- I purposely simplify and omit details, so as to give the reader a graphic and comprehensive picture of the central facts. So long as essentials are not distorted, a good diagram is far better for educational purposes than an accurate facsimile.