Various

“ Hygienic Economy of Food.—For people in good health, there are two important rules to be observed in the regulation of the diet. One is to choose the foods that “agree” with them, and to avoid those which they cannot digest and assimilate without harm; and the other is to use such sorts and quantities of foods as will supply the kinds and amounts of nutrients needed by the body and yet to avoid burdening it with superfluous material to be disposed of at the cost of health and strength. ”

“ The molecules of A in the neighbourhood of any point will, by their motion, spread out in every direction until they come into collision with other molecules of either kind, and this spreading out from every point of the medium will give rise to diffusion. If we imagine the velocities of the A molecules to be equally distributed in all directions, as they would be in a homogeneous mixture, it is obvious that the process of diffusion will be greater, ceteris paribus, the greater the velocity of the molecules, and the greater the length of the free path before a collision takes place. ”

“ The cooking of food and other modes of preparing it for consumption have much to do with its nutritive value. Many materials which, owing to their mechanical condition or to some other cause, are not particularly desirable food materials in their natural state, are quite nutritious when cooked or otherwise prepared for consumption. It is also a matter of common experience that well-cooked food is wholesome and appetizing, whereas the same material poorly prepared is unpalatable. ”

“ In spite of all its imperfections there is a great charm about the diary of Evelyn, and it would hold a still higher position in the history of literature than it does if it were not overshadowed by what is unquestionably the most illustrious of the diaries of the world, that of Samuel Pepys (1633-1703) . This was begun on the 1st of January 1660 and was carried on until the 29th of May 1669. The extraordinary value of Pepys’ diary consists in its fidelity to the portraiture of its author’s character. He feigns nothing, conceals nothing, sets nothing down in malice or insincerity. ”

“ The central discovery of the transformation theory of the solution of an equation F (x, y, z, dz/dx, dz/dy) = 0 is that its solution can always be reduced to the solution of partial equations which are linear. For this, however, we must regard dz/dx, dz/dy, during the process of integration, not as the differential coefficients of a function z in regard to x and y, but as variables independent of x, y, z, the too great indefiniteness that might thus appear to be introduced being provided for in another way. ”

“ In other words, diffusion is that relative motion of the molecules of two different substances by which the proportions of the molecules in any region containing a finite number of molecules are changed.
In order, therefore, to make accurate observations of diffusion in fluids it is necessary to guard against any cause which may set up currents; and in some cases this is exceedingly difficult. Thus, if gas is absorbed at the upper surface of a liquid, and if the gaseous solution is heavier than the pure liquid, currents may be set up, and a steady state of diffusion may cease to exist. ”

“ Food and its Functions.—For practical purposes, food may be defined as that which, when taken into the body, may be utilized for the formation and repair of body tissue, and the production of energy. More specifically, food meets the requirements of the body in several ways. It is used for the formation of the tissues and fluids of the body, and for the restoration of losses of substance due to bodily activity. The potential energy of the food is converted into heat or muscular work or other forms of energy. ”

“ Sums and Integrals.—The relation between a sum and an integral is usually expressed by the Euler-Maclaurin formula. The principle of this formula is that, if um and um+1, are ordinates of a curve, distant h from one another, then for a first approximation to the area of the curve between um and um+1 we have 1⁄2h (um + um+1) , and the difference between this and the true value of the area can be expressed as the difference of two expressions, one of which is a function of xm, and the other is the same function of xm+1. ”

“ The digestive system includes every organ, function and process concerned with the utilization of food-stuffs, from the moment of their entrance into the mouth, their preparation in the canal, assimilation with the tissues, their employment therein, up to their excretion or expulsion in the form of waste. Each portion resembles a link of a continuous chain; each link depends upon the integrity of the others, the weakening or breaking of one straining or making impotent the chain as a whole. ”

“ In the case of a very dilute solution, the coefficient of diffusion of the dissolved substance can be defined in the same way as when the diffusion takes place in a solid, because the effects of diffusion will not have any perceptible influence on the solvent, and the latter may therefore be regarded as remaining practically at rest. But in most cases of diffusion between two fluids, both of the fluids are in motion, and hence there is far greater difficulty in determining the motion, and even in defining the coefficient of diffusion. ”

“ As regards formal excellence it is plain that Dickens labours under the double disadvantage of writing in the least disciplined of all literary genres in the most lawless literary milieu of the modern world, that of Victorian England. In spite of these defects, which are those of masters such as Rabelais, Hugo and Tolstoy, the work of Dickens is more and more instinctively felt to be true, original and ennobling. ”

“ Another way in which two or more mixed gases can be separated is by placing them in the presence of a liquid which can freely absorb one of the gases, but in which the other gas or gases are insoluble. Here again it is found by experience that when equilibrium exists at a given temperature between the dissolved and undissolved portions of the first gas, the partial pressure of that gas in the mixture depends on the temperature alone, and is independent of the partial pressures of the insoluble gases with which it is mixed, so that the conclusions are the same as before. ”

“ If the point under consideration be so far away from the geometrical shadow that a large number of the earlier zones are complete, then the illumination, determined sensibly by the first zone, is the same as if there were no obstruction at all. If, on the other hand, the point be well immersed in the geometrical shadow, the earlier zones are altogether missing, and, instead of a series of terms beginning with finite numerical magnitude and gradually diminishing to zero, we have now to deal with one of which the terms diminish to zero at both ends. ”

“ Irreversible Changes accompanying Diffusion.—The diffusion of two gases at constant pressure and temperature is a good example of an “irreversible process.” The gases always tend to mix, never to separate. In order to separate the gases a change must be effected in the external conditions to which the mixture is subjected, either by liquefying one of the gases, or by separating them by diffusion through a membrane, or by bringing other outside influences to bear on them. In the case of liquids, electrolysis affords a means of separating the constituents of a mixture. ”

“ When the members of the group are of different age, sex, occupation, &c., account must be taken of the effect of these factors on consumption in estimating the value “per man.” Men as a rule eat more than women under similar conditions, women more than children, and persons at active work more than those at sedentary occupation. The navvy, for example, who is constantly using up more nutritive material or body tissue to supply the energy required for his muscular work needs more protein and energy in his food than a bookkeeper who sits at his desk all day. ”

“ A dime is a silver coin of the United States, in value 10 cents (English equivalent about 5d.) or one-tenth of a dollar; hence “dime-novel,” a cheap sensational novel, a “penny dreadful”; also “dime-museum.”
DIMENSION (from Lat. dimensio, a measuring) , in geometry, a magnitude measured in a specified direction, i.e. length, breadth and thickness; thus a line has only length and is said to be of one dimension, a surface has length and breadth, and has two dimensions, a solid has length, breadth and thickness, and has three dimensions. ”

“ If a telescope be employed there is a distinction to be observed, according as the half-covered aperture is between the eye and the ocular, or in front of the object-glass. In the former case the function of the telescope is simply to increase the dispersion, and the formation of the bands is of course independent of the particular manner in which the dispersion arises. ”

“ That the process of diffusion obeys the laws of irreversible thermodynamics (if these laws are properly stated) is proved by the fact that the compensating transformations required to separate mixed gases do not essentially involve anything but transformation of energy. The process of allowing gases to mix by diffusion, and then separating them by a compensating transformation, thus constitutes an irreversible cycle, the outside effects of which are that energy somewhere or other must be less capable of transformation than it was before the change. ”

“ The fats of food include both the animal fats and the vegetable oils. The carbohydrates include such compounds as starches, sugars and the fibre of plants or cellulose, though the latter has but little value as food for man. The more important function of both these classes of nutrients is to supply energy to the body to meet its requirements above that which it may obtain from the proteids. It is not improbable that the atoms of their molecules as well as those from the proteids are built up into the protoplasmic substance of the tissues. ”

“ It is of course possible that energy may have given off 217 from the body in other forms than heat and external muscular work. It is conceivable, for example, that intellectual activity may involve the transformation of physical energy, and that the energy involved may be eliminated in some form now unknown. But if the body did give off energy which was not measured in these experiments, the quantity must have been extremely small. It seems fair to infer from the results obtained that the metabolism of energy in the body occurred in conformity with the law of the conservation of energy. ”

“ Men vied with each other in celebrating Diane’s beauty, which, if we may judge from her portraits, has been slightly exaggerated. She was a healthy, vigorous woman, and, by dint of great pains, succeeded in retaining her beauty late into life. It is said that even on the coldest mornings she would wash her face with well water. Diane was a patroness of the arts. She entrusted to Philibert de l’Orme the building of her château at Anet, and it was for her that Jean Goujon executed his masterpiece, the statue of Diana, now in the Louvre. ”

“ The protein of animal food has, however, some advantage over that of vegetable foods in that it is more thoroughly, and perhaps more easily, digested, for which reason it would be economical to pay somewhat more for the same quantity of nutritive material in the animal food. Furthermore, animal foods such as meats, fish and the like, gratify the palate as most vegetable foods do not. For persons in good health, foods in which the nutrients are the most expensive are like costly articles of adornment. People who can well afford them may be justified in buying them, but they are not economical. ”

“ Although the matter can be fully treated only upon the basis of a dynamical theory, it is proper to point out at once that there is an element of assumption in the application of Huygens’s principle to the calculation of the effects produced by opaque screens of limited extent. Properly applied, the principle could not fail; but, as may readily be proved in the case of sonorous waves, it is not in strictness sufficient to assume the expression for a secondary wave suitable when the primary wave is undisturbed, with mere limitation of the integration to the transparent parts of the screen. ”

“ No farmer, however elegant, will, any longer choose to study agriculture in hexameters, or even in Tusser’s shambling metre. The sciences and the professions will not waste their time on methods of instruction which must, from their very nature, be artless, inexact and vague. But in the morning of the world, those who taught with authority might well believe that verse was the proper, nay, the only serious vehicle of their instruction. ”

“ For example, when a soluble salt is placed in a liquid, the process which occurs at the surface of the salt is called “solution,” but the salt which enters the liquid by solution is transported from the surface into the interior of the liquid by “diffusion.”
Diffusion may take place in solids, that is, in regions occupied by matter which continues to exhibit the properties of the solid state. Thus if two liquids which can mix are separated by a membrane or partition, the mixing may take place through the membrane. ”

“ In spite of some excellent criticisms dispersed here and there, and in spite of one or two stories that are not without a certain effective realism, it must as a whole be pronounced savourless, forced, and as leaving unmoved those springs of laughter and of tears which are the common fountain of humour. ”

“ Most physicists admit, as Planck does, that it is impossible to obtain an ideal semi-permeable substance; indeed such a substance would necessarily have to possess an infinitely great resistance to diffusion for such gases as could not penetrate it. But in an experiment performed under actual conditions the losses of available energy arising from this cause would be attributable to the imperfect efficiency of the partitions and not to the gases themselves; moreover, these losses are, in every case, found to be completely in accordance with the laws of irreversible thermodynamics. ”

“ Pecuniary Economy of Food.—Statistics of economy and of cost of living in Great Britain, Germany and the United States show that at least half, and commonly more, of the income of wage-earners and other people in moderate circumstances is expended for subsistence. The relatively large cost of food, and the important influence of diet upon health and strength, make a more widespread understanding of the subject of dietetics very desirable. ”

“ Table III.—Estimates of Heats of Combustion and of Fuel Value of Nutrients in Ordinary Mixed Diet.
The amount of energy which a given quantity of food will produce on complete oxidation outside the body, however, is greater than that which the body will actually derive from it. In the first place, as previously shown, part of the food will not be digested and absorbed. In the second place, the nitrogenous compounds absorbed are not completely oxidized in the body, the residuum being excreted in the urine as urea and other bodies that are capable of further oxidation in the calorimeter. ”

“ We rely, in fact, upon the theory of monogenic analytical functions (see Function) , a function being determined entirely by its development in the neighbourhood of one set of values of the independent variables, from which all its other values arise by continuation; it being of course understood that the coefficients in the differential equations are to be continued at the same time. But it is to be remarked that there is no ground for believing, if this method of continuation be utilized, that the function is single-valued ”

“ The simplest model of a perfect gas studied in the kinetic theory of gases (see Molecule) differs from the above illustration in that the bodies representing the molecules move in space instead of in a plane, and, unlike billiard balls, their motion is unresisted, and they are perfectly elastic, so that no kinetic energy is lost either during their free motions, or at a collision.
The mathematical analysis connected with the application of the kinetic theory to diffusion is very long and cumbersome. ”

“ But for the great majority of people in health, 220 suitable combinations of the ordinary sorts of wholesome food materials make a healthful diet. On the other hand, some foods are of particular value at times, aside from their use for nourishment. Fruits and green vegetables often benefit people greatly, not as nutriment merely, for they may have very little actual nutritive material, but because of fruit or vegetable acids or other substances which they contain, and which sometimes serve a most useful purpose. ”

“ Food which is attractive to the eye and pleasing to the palate quickens the flow of saliva and other digestive juices and thus aids digestion. The third is to kill, by heat, disease germs, parasites or other dangerous organisms that may be contained in food. This is often a very important matter and applies to both animal and vegetable foods. Scrupulous neatness should always be observed in storing, handling and serving food. If ever cleanliness is desirable it must be in the things we eat, and every care should be taken to ensure it for the sake of health as well as of decency. ”

“ Only part of the energy liberated by the combustion of the coal is available for driving the engine, the rest takes the form of heat imparted to the condenser. The colder the condenser the more efficient is the engine, and the smaller is the quantity of waste.
The amount of unavailable energy associated with any given transformation is proportional to the absolute temperature of the auxiliary medium. When divided by that temperature the quotient is called the change of “entropy” associated with the given change (see Thermodynamics) . ”

“ It can be shown, from the fact that η1 is a quadratic polynomial in y1, that no differential equation of the second order can allow more than 8 really independent infinitesimal transformations, and that every homogeneous linear differential equation of the second order allows just 8, being in fact reducible to d2y/dx2 = 0. Since every group of more than two parameters has subgroups of two parameters, a differential equation of the second order allowing a group of more than two parameters can, as a rule, be solved by quadratures. ”

“ Quantities of Nutrients needed.—For the proper nourishment of the body, the important problem is how much protein, fats and carbohydrates, or more simply, what amounts of protein and potential energy are needed under varying circumstances, to build and repair muscular and other tissues and to supply energy for muscular work, heat and other forms of energy. The answer to the problem is sought in the data obtained in dietary studies with considerable numbers of people, and in metabolism experiments with individuals in which the income and expenditure of the body are measured. ”

“ If round the origin of waves an ideal closed surface be drawn, the whole action of the waves in the region beyond may be regarded as due to the motion continually propagated across the various elements of this surface. The wave motion due to any element of the surface is called a secondary wave, and in estimating the total effect regard must be paid to the phases as well as the amplitudes of the components. It is usually convenient to choose as the surface of resolution a wave-front, i.e. a surface at which the primary vibrations are in one phase. ”

“ The formation of a sharp image of the radiant point requires that the illumination become insignificant when ξ, η attain small values, and this insignificance can only arise as a consequence of discrepancies of phase among the secondary waves from various parts of the aperture. So long as there is no sensible discrepancy of phase there can be no sensible diminution of brightness as compared with that to be found at the focal point itself. ”

“ The larger the aperture the smaller are the angles through which it is necessary to deviate from the principal direction in order to bring in specified discrepancies of phase—the more concentrated is the image.
In many cases the subject of examination is a luminous line of uniform intensity, the various points of which are to be treated as independent sources of light. If the image of the line be ξ = 0, the intensity at any point ξ, η of the diffraction pattern may be represented by
the same law as obtains for a luminous point when horizontal directions are alone considered. ”

“ In fluid media, whether liquids or gases, the process of mixing is greatly accelerated by stirring or agitating the fluids, and liquids which might take years to mix if left to themselves can thus be mixed in a few seconds. It is necessary to carefully distinguish the effects of agitation from those of diffusion proper. By shaking up two liquids which do not mix we split them up into a large number of different portions, and so greatly increase the area of the surface of separation, besides decreasing the thicknesses of the various portions. ”