8z 



THE QUARTERLY REVIEW OF BIOLOGY 



But the realization of the statistical nature 

 of the Carnot principle had certain impli- 

 cations for biological theory. If the law 

 of entropy may justly be compared to the 

 law that a large and equal number of black 

 and white grains shaken up will produce 

 a grey powder, then two considerations 

 emerge. Firstly, the sorting out of the 

 grains could be accomplished by a 

 Maxwell demon — in Lewis' terminology, 

 a cheat — acting in the system, and sec- 

 ondly, by prolonging the agitation till a 

 fluctuation of a very rare type led back 

 to the original condition, on the basis of 

 Heraclitus' remark — "If one is suffi- 

 ciently lavish with time, everything possi- 

 ble happens" — surely not due to Hero- 

 dotus as Guye would attribute it. 

 This reminds one of F. R. Japp's refusal 

 (2.7) to believe that if a font of type 

 was shaken up in a bag, the text of 

 Hamlet could possibly result, however 

 long this was continued, and of P. F. 

 Frankland's reply (14) that if the time 

 allowed was infinite, Hamlet must re- 

 sult. What is sure, at any rate, is that 

 the statistical nature of Carnot's prin- 

 ciple does not preclude such a rare 

 fluctuation, nor less rare minor ones tend- 

 ing in the same direction. As Johnstone 

 said, a philosophical consideration of this 

 subject must take into account chances 

 which even an insurance company would 

 at once set aside as of no matter. Now 

 "The fluctuations," says Guye (18), 

 ' 'which can occur in a given element of vol- 

 ume are in general the more important the 

 smaller the number of molecules contained 

 in the homogeneous element of volume 

 considered. The reply to the foregoing 

 question will depend therefore, on the 

 degree of tenuity which is attributed to 

 the structure of the tissues and of the 

 living matter." 



This is, indeed the aspect of the question 

 that has recently been engaging attention. 



A. V. Hill (2.5) came to the conclusion 

 recently that "It is conceivable that the 

 ultimate minute mechanism especially of 

 the smallest living cells, may somehow 

 be able to evade the statistical rules which 

 govern larger systems; it may for example 

 like Maxwell's demon be able to sort 

 molecules, to use the energy of the more 

 rapidly-moving, to employ a uni- 

 directional permeability, and so to avoid 

 the general increase of entropy which 

 appears to be the governing factor in all 

 other material change. Such an evasion, 

 if established, would be of ultimate 

 philosophical, biological, and practical 

 importance; there is no evidence, however, 

 of any value, that it really occurs." 

 F. G. Donnan (iz), on the other hand, 

 has recently made some calculations which 

 if they do no more, at least keep open the 

 possibility; he has attempted to estimate 

 the size of the element of volume within 

 which an evasion of the second law would 

 be likely to take place. He shows how 

 for all ordinary cases the probable fluctu- 

 ations from the equilibrium state would be 

 quite imperceptible, in other words, the 

 chances would be immeasurably against 

 any deviation from Carnot's principle. 

 But for a small cubical particle of side 

 0.1/x consisting wholly of molecules of 

 molecular weight 10,000 the relative 

 thermodynamic probability of an easily 

 detectable fluctuation from the chemical 

 equilibrium state is distinctly high. As 

 Donnan points out, although it is true 

 that most living cells are larger than the 

 imaginary particle in question, some are 

 not, and probably it does not materially 

 differ in size from phases and parts of 

 cells having separate existence as systems 

 to say nothing of the bacteriophage and 

 ultrafiltrable viruses. "It seems, there- 

 fore," he says "very probable that there 

 exist biological systems of such minute 

 dimensions that the laws of classical 



