Principles of General Physiology

Krogh (1914, 1), moreover, finds that the velocity of embryonic division in amphibia, fish, insects, and echinoderms cannot, even approximately, be expressed by the van't Hotf formula of temperature effect on chemical reactions. Between normal limits, the relation is a linear one. In a further paper (1814, 2), Krogh finds that there is no optimum temperature for the evolution of carbon dioxide, and that this process also follows a linear law.

Regarded from another point of view, we must remember that these vital phenomena are taking place in heterogeneous systems, that is, in systems consisting of various solid and liquid phases. When not coarsely heterogeneous, they are, at least, colloidal, or ultra microscopically heterogeneous. We have, therefore, several processes in addition to the purely chemical one going on together, viz., diffusion of constituents of the reaction to and from the surface where the reaction occurs, similarly to the action of hydrochloric acid on a plate of marble, followed by condensation on the surface and so forth. As Nernst points out (1911, p. 587), the velocity of the process as a whole will be conditioned by tha.t factor which takes place at the slowest rate. In many cases this is diffusion, as in the experiments of Brunner (1904, p. 56). But it does not seem necessary that this should always be the case. It is conceivable that the chemical factor in the complex may be slowed down, as by a low temperature, so far as to become slower than the diffusion factor. In such a case, the "limiting factor," to use Blackman's expression, would be transferred from the diffusion process to the chemical reaction. I am not aware, however, that any instance of such a change has been met with.

Further discussion of heterogeneous reactions will be found in Chapter X. , when treating of catalytic action. In the present place, attention is directed mainly to the complexity of any given vital process, and to the uncertainty as to what factor is the controlling one in the velocity of the reaction, or which one it is whose temperature coefficient is being measured. Between the limits of 26° and 40°, in which the heart continues to contract normally, the relation is linear. There is no temperature " coefficient."

From the preceding paragraph it will be obvious that, for rapidity of adaptation to outside changes, it is of advantage to the reacting organism that its processes be carried on at a raised temperature. Suppose, however, that a chemical reaction, such as an oxidation, is set in progress. Heat produced accelerates the reaction, and it will tend to become faster and faster, verging on an explosion. Some means of regulation of such reactions is clearly necessary. One obvious way of doing this, in the case of oxidation, is to limit the supply of oxygen. Organisms provided with circulation of blood conveying oxygen have the power of cutting down the supply to their various parts by methods to be described later. In warm-blooded animals the chief source by which the temperature is kept up is muscular contraction, controlled by the nervous system.

Apart from its effect on chemical reactions, a high temperature is also of advantage in its action on physical processes, diminishing the internal friction of liquids such as blood, hastening diffusion, and so on. The confusion that is sometimes made between the effect of heat in increa>inur the rate of a change, and its effect on the position of equilibrium in a reversible reaction, has been already alluded to. We have seen that the rate of any reaction, exothermic or endothermic, is accelerated by rise of temperature. On the position of equilibrium, its effect may differ in individual cases, as may be seen theoretically from the consideration that, of the two balanced opposing reactions, either one may be accelerated more than the other. If, for example, the synthetic reaction in the case of alcohol, acid, ester, and water were accelerated more than the hydrolytic one, the equilibrium would be moved in such a direction that more ester would be present and less alcohol and acid, and conversely.

In actual fact, the effect in question differs in direction in the case of exothermic and endothermic reactions. The law expressing this relationship was deduced thermodynamically by van't Hoff (1884, pp. 161-176). For the reasoning adopted, the reader may consult Mellor's "Chemiial Statics and Dynamics" (pp. 395-401). The " Principle of Mobile Equilibrium," introduced by van't Hoff, may be expressed briefly as follows : Any change of the temperature of a system in equilibrium is followed by a reverse thermal change within the system. By taking separately the three possible cases, the meaning will be made more intelligible.

1. Suppose that a reaction has taken place by which a substance B has been formed from another substance A. If this reaction has been accompanied by the evolution of heat, a rise of temperature will cause an increase in the quantity of A. In other words, the reaction is partially reversed. Since the law holds for physical as well as chemical phenomena, it may easily be remembered by consideration of the condensation of water vapour (A) to liquid (B), which is accompanied by evolution of heat. The law tells us that raising the temperature will increase the quantity of steam (A), as every one knows.

2. If the reaction is endothermic, accompanied by absorption of heat, rise of temperature will cause decrease in the quantity of A, that is, the reaction will go on further. One may say that, as the reaction requires heat to progress, an extra supply will help it on. An illustration, merely to assist the memory, is the case of ether (A). By evaporation spontaneously to vapour (B) it cools, and, if prevented from absorbing heat from its surroundings, it may become so cold that evaporation practically ceases. If heat be supplied, more vapour (B) will be formed, and the liquid phase (A) will diminish.

3. The third case is that of a reaction in which no thermal, change occurs. Here a rise of temperature will have no effect on the relative amounts of A and B. An instructive case to consider in this connection is that of the taking up of a dye by a substance which is stained by it, say paper, or tissue in the process of histological staining. As will be seen in subsequent pages, this process is representative of many of those occurring in living cells. I found (1906, p. 187) that the amount of dye which a piece of paper of a certain size will take up from a given solution of Congo-red, if allowed to remain in it until no further amount is taken up, is lesft at 50° than at 10°. Now, whether this process is one of pure adsorption ( = surface condensation) or also partly chemical, it is no doubt associated with the production of heat. Calling the system, paper in contact with dye solution, A, and the dyed paper, B, van't HofFs law, the first case above, tells us that rise of temperature causes increase in A, as experiment shows.

Although, however, at the higher temperature there is less product formed, yet the rate at which this is formed is greater. The curves of Fig. 29 serve to show this fact. It will be seen that, at the higher temperature, equilibrium was attained in about 100 minutes (curve a), whereas at the lower temperature (curve b), it was not quite complete at the end of the experiment (twenty-four hours). The amount taken up at the lower temperature was rather more than

At the higher temperature, the rate of adsorption is faster, although the total amount adsorbed when equilibrium is reached is less. , 0_ . one half of that originally present in the solution ; at the higher temperature, only one quarter. This experiment will be found (Chapter XXI.) to have some bearing on the way in which oxygen is carried by haemoglobin. The great influence that temperature has on both rate and equilibrium in chemical and physical processes necessitates care in the maintenance of a constant known temperature in investigating them. The means of doing this will be found in the textbooks dealing with practical physical chemistry, such as those Findlay, Ostwald-Luther or Spencer.

The essential characteristic of life is incessant change. To produce change, work must be done. The power of doing work is due to the possession ol Of the two great laws dealing with energy, the first tells us that, while any one kind of energy may be transformed into any other kind, there i gain or loss. The second law deals with the conditions under which these changes take place and the proportion of one kind that can be transformed into another.

Although the total energy cannot be altered, the amount of it available for conversion into other forms and capable of doing work, i.e., the free energy, is not constant, and indeed, in the present state of the universe, so far as we are able to investigate it, free energy always tends to diminish. This fact, a matter of invariable experience, is known as the " Principle of Carnot and Clausius," and is of great importance in the interpretation of many physiological problems.

There are two factors which, multiplied together, give energy. One of these, of the nature of a "strength," is called the "intensity" factor; the other, of the nature of a space or mass, is called the "capacity" factor. As regards the latter factor, energy can be added algebraically, but not as regards the former. In the animal body, energy is derived from chemical combination. This form of energy is readily converted into various other forms, without the necessity of passing through the form of heat.

In the vegetable organism, energy is derived ultimately from the sun's rays. It follows, therefore, that animal energy has the same origin. The maximal work of a chemical process can be calculated by means of a formula due to Nernst ; it depends on the position of equilibrium in the reaction considered as reversible, and is greater the nearer this position is to that of complete change in one direction. That manifestation of molecular forces known as surface energy plays an important part in cell phenomena, owing to the large variations of which it is capable in a small space. This is due to the changes in its capacity factor, surface area, chiefly by aggregation of colloidal particles.

The phenomena peculiarly characteristic of vital changes are those associated with the actual process of transfer or transformation of energy. Many nonvital phenomena show also a special degree of activity in such states. The total energy obtained from a food-stuff by complete oxidation, the " heat of combustion," does not of necessity imply that stuffs of the same heat of combustion are of equal value as sources of available energy. The distinction between free and bound energy must be taken into consideration. The " struggle for existence " is for the possession of free energy.

The formula for the work done in compressing a gas from a volume v2 to Vj, or from pressure p^ to py viz. — is also applicable to that done in concentrating a solution from one osmotic pressure to another, to the potential of metallic electrodes, and to the case of certain solutes confined by a membrane permeable to one ion only, to mention cases of physiological interest. The properties of the carbon atom make it of especial value in the transformation of chemical energy, so that the body of doctrine known as organic chemistry is of fundamental importance in physiology.

The effect of a rise of temperature on the rate of chemical reaction must be carefully distinguished from that on the position of equilibrium. The former is always increased, while the latter is controlled by van't HofFs "Principle of Mobile Equilibrium." Whether it is changed in the direction of further progress of a reaction, or the reverse, depends on whether the reaction is accompanied by evolution of heat or the contrary. In the former case, a rise of temperature throws the reaction back, while the opposite is the case in the latter. If the reaction is thermo-neutral, no change is produced by alteration of temperature.

The temperature coefficient of complex processes in heterogeneous systems, such as those of living cells, cannot be used to indicate whether such a process is chemical or physical in nature. The following essays of Boltzmann (1905) will be found of interest: — The works of Willard Gibbs can only be attacked with profit by the expert mathematician. IT has been shown in Chapter I. how living cells are made up of a highly complex system of constituents, not mixing together — liquids, solids, and sometimes gases. Some of the solid substances, the "hydrophile" colloids, contain water in such proportion that many of their properties approximate to those of liquids.

Investigation has made it plain that where these different "phases," as \\v have been taught to call them by Willard Gibbs, come into contact with each other at their interfaces, the properties are not the same as in the main mass. One of the most obvious phenomena of this kind is that shown by the surface of contact of liquids with gases, solids, or other liquids immiscible with them. This surface behaves as if stretehed. In B the portion of the film inside the loop has been broken by touching it with a pointed bit of filter paper. The result is that the tension of the film between the ring and the loop causes this Aim to contract as much as possible, thus drawing the loop into a circle, the figure of maximum area.

One of the simplest ways to demonstrate this is due to van der Meusln-ugghe (1866, p. 312). A loop of fine silk is taken and tied to a wire ring. If the whole be dipped into soap solution, so as to produce a film, the loop floats in the film ; the silk thread forming its boundary is quite loose, and can be readily moved into any shape by means of a fine needle wetted with the soap solution (see Fig. 30). The film inside the loop is now broken by touching it with a bit of filter paper cut to a fine point. The loop is immediately drawn to a circular form by the tension of the film surrounding it, and can be felt to resist attempts to change its shape by the needle. The soap, solution should be prepared by the method of Boys (1912, p. 170) from pure sodium oleate, with the addition of about 25 per cent, of glycerol.

The best way of showing that the form taken by a liquid when free is that with the least surface, namely the sphere, is by the use of ortho-toluidine, as described by Darling (1911). This liquid has the same density as water at 22°, but, since it has a higher coefficient of expansion, it is less dense above 22° and more dense below that temperature. If a leaker half lull df water at 22° is taken, and a solution of scxlium chloride of Moot 0'3 per cent, is run in

at the bottom, so as to form a lower stratum of slightly higher specific gravity, ortho-toluidine can be run in at the junction of the two liquids by means of a tap-funnel, and spheres of o to 8 centimetres in diameter can be made. It is interesting to note that the phenomena shown by such suspended spheres of liquid were chiefly investigated by Plateau, the physicist of Ghent, after he became blind owing ioJ;aZ1Tg at midday sun for experiments on vision. His researches were published in

1873. In his work he was assisted by his son-in-law, van der Mensbrugghe, whose name we have already met with. A method of measurement of surface tension is by the use of Searle's apparatus, made by Pye, of Cambridge (Fig. 31). The pull of the tension of a liquid film is made to twist a wire of phosphor-bronze by a known amount, which is compared with that effected by a known weight. "A rectangular glass microscope slide is clipped to one end of the lever, which also carries a scale pan. The counterpoise is then adjusted so that the lever is horizontal when the lower edge of the slide is just immersed in the liquid. The reading on the scale is noted and the liquid removed. The lever will rise considerably. After drying the glass slide, the lever is brought down to its previous position on the scale by adding weights to the scale pan ; in other words, a force is applied to twist the wire to the same extent as the surface tension of the liquid did. If A is the length of the slide in centimetres and T its thickness, the total length of the film is 2(A + T), since both sides of the slide are active. Then M being the mass in grammes added to the scale pan, its weight is 98 1M in dynes, and the surface tension in dynes per centimetre is

If it be wished to obtain a measurement of the absolute surface tension at a water-air interface, it is best to use tap water, since this is less likely than distilled water is to contain greasy matter, which has a powerful effect in lowering surface tension, as we shall see later. With Searle's apparatus I have found no difficulty in a lecture experiment in obtaining readings of 71 '6 dynes, or 98 per cent, of the correct value, 73. The weight needed in an actual experiment to produce the same torsion of the wire as the pull of the water did was I'll grams, a sufficiently obvious weight.

The effect of surface tension in regulating the size of drops falling from an orifice is also used as a method of measuring the surface tension of liquids. It is sometimes called the " stalagmometer " method, and is due to Quincke. The size of a drop will increase until its weight balances the tension of its surface film, which is holding it up against gravity. As soon as this size is exceeded the drop will fall. In practice, the number of drops in a known volume of the liquid is counted, and this number is, obviously, inversely proportional to the size of the drops, and this again is proportional to the surface tension — the larger the drop the greater the surface tension. Account must be taken of the weight of the drop, that is, the specific gravity of the liquid must be known. The formula is : —

Number of drops of water x density of liquid Number of drops of liquid Another method is founded "on the rise or fall of the level of a liquid in a capillary tube, according to whether it wets the glass or not. This change of level is due to the curved shape of the meniscus or surface separating liquid from air, so that the surface tension has a vertical component which pulls up the liquid against gravity, or presses it down, according to whether the meniscus is concave or convex. The best form of apparatus for this method is that of Rontgen and Schneider (1886, p. 203), especially in the modification described by Schryver (1910, p. 109).

A means of rendering this measurement more accurate was pointed out to me by W A. Osborne. Two capillaries of different but known diameters are taken, and the difference of heights to which the two liquids to be compared rise in the two capillaries is measured. By this device the measurement of the height of the meniscus from the body of the liquid is unnecessary, a somewhat difficult and uncertain one. Since the total height in each case is inversely proportional to the diameter of the capillary, and directly proportional to the surface tension, the difference of the heights of the two liquids is also so proportional. We know the diameters of the two capillaries and the surface tension of one liquid, so that it is easy to calculate that of the other. This method is also recommended by Michaelis and Rona (1909, p. 496).

The precise cause of the existence of surface tension is too complex for discussion here. Briefly, one may say that it is due to the forces of attraction between the molecules of a liquid, producing what is known as the " internal pressure " of Laplace (1845, iv. p. 389). This pressure can be calculated, and amounts to several thousand atmospheres (Stefan, Wied. Ann., 29, p. 055). The molecules in the body of the liquid are exposed to these forces equally on all sides. Those at the surface are exposed to unbalanced forces tending to draw them in (see Fig. 32). The result of this is that the surface of a liquid is always the least possible, or, in other words, is pulling itself together. One may see the necessity of a minimum surface also from the point of view of energetics. Since there are forces drawing the molecules inwards, work is required to bring them to the surface, therefore the greater the surface, the greater the energy contained in it ; but, as we have seen, free energy always tends to a minimum. For further details see Freundlich (1909, pp. 6-14). The explanation of the properties of the free surface, by regarding it as the seat of tension, is due to Thomas Young (1805, p. 82), who speaks of unbalanced molecular cohesive forces at the surface as the cause of the tension.

The values of the surface tension of pure liquids vary greatly. The following numbers in dynes per centimetre will serve to illustrate this : — The molecule 4 is exposed to equal attractive forces on all sides. The molecule B, at the surface of the liquid, on the other hand, is exposed to unbalanced forces, of which the resultant is a pressure in the direction of N. Equilihrium will result when the number of molecules at the surface is the least possible ; that is, the surface area tends to a minimum.