158 SECTIONAL ADDRESSES. 



had become so definite that it came to be considered quite a useful thing 

 for a chemist to acquire some knowledge of the higher mathematics, and 

 the appearance in Britain of a textbook of higher mathematics for students 

 of chemistry and physics rendered great service by introducing the kind 

 of mathematics that was likely to be of value in application to these 

 subjects. 



What has happened in physics and chemistry may be reasonably 

 expected to happen in biology so soon as it is able by improvement in 

 the accuracy of its methods, and by progress in the formulation of its 

 problems, to employ mathematics with profit in the manipulation of data 

 and in the construction of those generalisations which are landmarks of 

 progress in all the sciences ; indeed we are, I think, now witnessing the 

 commencement of such a phase in the development of our own subject. 

 The many facets of physiological inquiry make it incumbent on all of us 

 to possess some knowledge of one or more related subjects, and I know 

 of no more promising collateral subject which a young physiologist could 

 take up at the present time, as an alternative to chemistry or biology, 

 than the study of mathematics. But those who do take it up should do 

 so for the purposes of utilising it in their own experimental work, not 

 merely for the purpose of surveying results obtained by others, and still 

 less in order to ' lend an air of verisimilitude to an otherwise bald and 

 unconvincing narrative.' Mathematics is a most valuable aid to reasoning, 

 and it can be of no real use to physiology except when it leads to clarifica- 

 tion of thought both of an author and of his readers.. Under any other 

 circumstances its introduction into biological literature is, I think, of 

 extreme danger, because of the superstition, common alike to those who 

 write and those who read, that anything expressed in mathematical form 

 must be accepted as correct without any further question. 



Mathematics and mathematical physics have been of considerable 

 use to physiology in increasing the accuracy of its experimental data, 

 and this in two ways. First, by bringing the accurate experimental and 

 intellectual methods of physics to bear on the construction and use of the 

 numerous physical instruments which it employs. It has been said by 

 Prof. A. V. Hill that many of the early investigations on muscle were in 

 reality studies of the properties of levers, and it is certain that similar 

 remarks apply to only too many investigations in which the properties 

 of the apparatus used have not been suitably investigated. As illustra- 

 tions of the value of mathematical-physical study of apparatus one may 

 mention the classical investigations of Frank on hsemodynamical recording 

 apparatus, the fundamental treatment of string galvanometers and similar 

 instruments by Einthoven, the correction of capillary electrometer records 

 by Keith Lucas, and the vast improvements in galvanometer systems 

 effected by Downing and Hill. 



Even when the apparatus at the disposal of the physiologist is un- 

 exceptionable, however, it is often the fact that, owing to the nature of 

 the subject, results are not susceptible of repetition with the same ease and 

 certainty as are those of chemical or physical experiments. The variability 

 of the results is due in such cases to what are called accidental circum- 

 stances, a term which in reality means circumstances over which we have 

 no control, owing either to our ignorance of their nature, or else to our 



