ENERGETICS 37 



MATHEMATICS IN PHYSIOLOGY 



This is the most appropriate place to refer to the view taken by some, that 

 the introduction of mathematics into biological questions is mischievous. 



Huxley's (1902, p. 333) comparison of mathematics to a mill, which only 

 gives out in another form what was put into it, is often quoted. At the same 

 time we must not forget that this new form is much more useful than the 

 original one. 



Plato remarks, "If arithmetic, mensuration and. weighing be taken away 

 from any art, that which remains will not be much" ("Philebus," Jowett's 

 translation, 1875, vol. iv. p. 104). Stephen Hales devoted himself to quantita- 

 tive measurements in physiology and denned his point of view thus (1727, 

 p. 2) : " Since we are assured that the all-wise Creator has observed the most 

 exact proportions, of number, tveight, and measure, in the make of all things, 

 the most likely way to get any insight into the nature of those parts of the 

 creation, which come within our observation, must in all reason be to number, 

 weigh and measure. And we have much encouragement to pursue this method 

 of searching into the nature of things, from the great success that has attended 

 any attempts of this kind." The Biblical passage referred to will be found in 

 the beautiful 40th chapter of Isaiah, verse 12: "Who hath measured the 

 waters in the hollow of his hancl, and meted out heaven with the span, and 

 comprehended the dust of the earth in a measure, and weighed the mountains 

 in scales, and the hills in a balance?" 



If it be admitted that our physiological methods are limited to those of 

 physics and chemistry, further remarks are unnecessary. The value of mathe- 

 matics in physics is plain, to every one, and its value in chemistry becomes 

 continually more obvious. As Arrhenius (1907, p. 7) points out, the expression 

 of experimental results in a formula shows their relation to known laws in a 

 way which is otherwise very difficult or impossible to attain. One is enabled 

 to see whether all the factors have been taken into account and even an 

 empirical formula may assist in deciding whether irregularities are due merely 

 to experimental error or to some unsuspected real phenomenon in the process. 



For example, the action of trypsin on a protein might be expected to follow the course of a 

 uni- molecular reaction (see Chapter X. ). Actually we find that the velocity constant calculated 

 by the appropriate formula shows a continual diminution as the reaction proceeds. This 

 fact leads us to look for the cause. In experiments on the influence of alkali we find that the 

 activity of trj'psin is, within limits, in proportion to the degree of alkalinity of the digest. 

 We naturally look for diminution of alkalinity in the course of tvypsin digestion and find that 

 the production of amino-acids, especially the strongly acid di-carboxylic ones, is capable of 

 producing a considerable change in the direction in question. 



Possibly it may seem hard to add an extra burden to the already large 

 equipment necessary for the physiological investigator. The reader will, no 

 doubt, have been struck by the wide range of natural knowledge which has to 

 be taken into account. At one moment we may be concerned with the move- 

 ments of protoplasm in a vegetable cell, or the composition of the primeval 

 ocean, and at the next, the work done in compressing a gas, the chemical 

 properties of amino-acids, or the constitution of dyes. 



In connection with the wide range of knowledge implied in the various problems with 

 which physiology is concerned, it is interesting to remember that oxygen was discovered by a 

 physiologist, Mayow, as we shall see in Chapter XXI., and many facts belonging to other 

 sciences have also been brought to light in physiological investigations. " On the other side, 

 we may note that the function of the heart was practically discovered by an artist, Leonardo ; 

 the arterial pressure by a clergyman, Hales; the capillary circulation by a "bedell," Leeu- 

 wenhoek ; intravenous injection by an architect, Wren ; the nature of animal heat by a chemist, 

 Lavoisier ; the function of the green plant by a clergyman, Priestly ; and so on. 



A moderate amount of mathematics will probably have to suffice for most 

 of us, enough to be able to understand and use the fundamental equations. 

 But, since, as often insisted on already, vital phenomena are essentially changes, 

 it will be obvious that the infinitesimal calculus, which deals with changing 

 quantities, must be included, at least in its elements. It might indeed with 

 advantage be allowed to take the place of much of the geometry and trigonometry 



