48 



SCIENCE 



[N. S. Vol. XXXIX. No. 993 



ors of Lord Rayleigh, Wien, and particu- 

 larly Max Planck. In order to explain the 

 . dependence of the distribution of energy in 

 the spectrum upon the temperature of the 

 radiating body Planck was led to consider 

 the emission of energy from a large num- 

 ber of electrical oscillators, which from 

 their power of absorption of energy may 

 be also described as resonators. In order to 

 find the entropy to be associated with these 

 resonators by an application of Boltzmann's 

 definition as a probability, and to define 

 what is equally likely as to the amount of 

 energy possessed by the individual resona- 

 tors Planck found it necessary to assume 

 that this amount of energy could not vary 

 continuously, but must be an integral 

 multiple of a certain very small amount 

 which has been termed the elementarj^ 

 quantum of energy. The results of this 

 quantum hypothesis of the atomic nature 

 of energy has been to send a sort of earth- 

 quake shock through some of the founda- 

 tions of physical theory, and we can not yet 

 judge of the ultimate outcome. These mat- 

 ters were handled so thoroughly by my 

 predecessor that I do not need to do more 

 than mention their importance. 



I have thus mentioned as the chief meth- 

 ods of physical investigation the method of 

 pure dynamics, that of thermodynamics 

 and that of the statistical method. I may 

 add the method of which I have given an 

 example, that of simple analogy, without 

 the backing of any definite hypothesis. I 

 have spoken of Carnot's successful use of 

 this plan, also of Ohm's law as the analogy 

 of Fourier's. A further example is found 

 in the case of chemical reaction-velocities. 

 Without making exact dynamical assump- 

 tions, in many cases it is sufficient to as- 

 sume that the velocity of a reaction is pro- 

 portional, like that of a pendulum moving 

 in a highly resisting medium, to the dis- 

 tance yet to go to reach equilibrium, that is, 



to the amount of substance that has not yet 

 reacted. We thus get an approach to com- 

 pletion proportional to an exponential 

 function of the time. This exponential is 

 of so frequent occurrence in all parts of 

 nature that the reason for it is often over- 

 looked and we see amusing instances of its 

 rediscovery. It seems likely that this 

 method of analogy, perhaps in this very 

 example, may be of considerable applica- 

 tion in biology. Suppose for instance, a 

 portion of jelly inoculated by a needle with 

 a certain bacillus. If the jelly is physically 

 and chemically homogeneous the colony will 

 grow at such a regular rate and with such 

 a symmetrical form that it seems as if a 

 differential equation could be formed, and 

 the analogy with diffusion is very strong. 

 If we could express biological forces or 

 tendencies as we now can chemical ones 

 there is no doubt that we could make long 

 strides in this direction. What is now the 

 outlook for our other methods applied to 

 biology 1. Where we have to do with a dis- 

 tinctly physical phenomenon such, for in- 

 stance, as in the propagation of the pulse- 

 wave through the arteries, we may use the 

 methods of pure dynamics. Or where we 

 have to do with the conduction of the elec- 

 trical current through the tissues we may 

 use the known laws of electricity. But in 

 connection with most of the phenomena of 

 life we are far from having a sufficiently 

 exact notion of the phenomena to apply 

 dynamical principles. On the other hand, 

 the method of thermodynamics may be of 

 great use. No one, I suppose, doubts that 

 the first law of thermodynamics is appli- 

 cable to all physiological phenomena, both 

 animal and vegetable. Whether it may be 

 extended to mental phenomena is not so 

 certain, and can not be settled until we are 

 able to measure the amount of energy in 

 mental processes. Certain experiments 

 seem to show that we are near to this, and 



