Robertson, Further Explanatory Remarks Concerning etc. 33 



solution of the same products. I have expressly refrained from 

 attempting to apply the autocatalytic formula to the curve of 

 muscular contraction because I am of the opinion that the time- 

 relations in muscular contraction are determined by changes of 

 capillarity and by the elasticity of the muscle-elements rather than 

 by the chemical reactions which underlie and cause these changes 8 ). 

 It must be recollected, yet again, that the autocatalytic formula 

 expresses a relationship between mass and time and that before 

 attempting to apply it to a relationship between length and time 

 we must first ascertain that the observed changes in length are 

 directly proportional to changes in the mass of some chemical 

 product. Now we have no proof whatever that during the course 

 of a single muscular contraction the shortening of the muscle is 

 directly proportional to the mass of carbohydrate which is trans- 

 formed into CO 2 and H 2 or other products. Until we possess 

 such proofs, any attempt to apply the autocatalytic formula to 

 curves of muscular contraction is of very doubtful utility. In ap- 

 plying the formula to growth, on the contrary, we have in the 

 weight of the animal or plant a direct measure of the mass of 

 the products of the chemical reactions underlying the process. The 

 application of the formula to growth in weight is therefore 

 rational. 



B. Moeser, as I have stated, raises the further objection that 

 the autocatalytic reaction-formula expresses only a relation between 

 mass and time and fails to incorporate the influence of tempera- 

 ture, moisture, etc. It is for this reason, he asserts, that the 

 deviations between the autorcatalytic curve and the empirical curve 

 occur. I do not question that this is the case, but it may be 

 pointed out that it is also the case in all chemical reactions. In 

 ascertaining the relationship between mass and time in a chemical 

 transformation we endeavor to keep such factors as temperature, 

 pressure, etc. constant. If the temperature varies, the velocity 

 of the reaction varies, and, in fact Karl Peter and I 9 ) have utilised 

 the fact that growth is accelerated by a rise of temperature in 

 support of the view that the velocity of growth is determined by 

 the velocity of a chemical reaction 10 j. But because an autocatalytic 

 chemical reaction is accelerated by a rise of temperature, it does 

 not cease to be an autocatalysed chemical reaction and to display 

 the characteristic time-relations of an autocatalysed reaction at a 



8) T. Brailsforcl Robertson: "Remarks on the Theory of Protoplasmic 

 Movement and Excitation". Quarterly Jour, of Exper. Physiol. 2 (1909), p. 303. 

 Of. also T. Bernstein. Arch. f. d. ges. Physiol. 122 (1908), p. 129. 



9) K. Peter. Arch. f. Entwicklungsmech., Bd. 20 (1906), p. 130. 

 10) T. Brailsford Robertson. Arch. f. Entwicklungsmech.. Bd. 25 



p. 581. 



XXXIII. 



