4 io SCIENCE PROGRESS 



interaction mathematically and find that it is between 2 and 3, 

 say 2'4 — but we are no better off. An interaction of an order of 

 2*4 is meaningless. The order may turn out to be 4 — but again, 

 does this mean that the interaction is really one of the fourth 

 order ? In practice we find that we seldom have the ideal cases 

 of the text-book, which have been picked out on account of their 

 apparently straightforward nature. Even when a change appears 

 simple and straightforward, as in the case of the hydrolysis of 

 cane sugar examined by the polarimetric method, the constancy 

 of the velocity coefficient may be to a great extent an accident, 

 due to the balance of opposing effects of the products of change 

 on the rate of hydrolysis. 



Far too little importance is attached, as a rule, to the value of 

 graphic methods in dealing with problems of mass action. The 

 complete mass action equation for the hydrolysis of an ethereal 

 salt at any one temperature with constant concentration of 

 catalyst is 



dx 



w = K, (a - x) (b - x) - k, {c + x) (d + x), 



where a, b, c, d are the initial molecular concentrations of ethereal 

 salt, water, alcohol and acid and x is the amount of change after 

 time t. On integration this gives an ugly, great equation, 



in which 



i_ K - 1 (Q- P)[Q + P-2(K- i).r] 

 «j - t • P 10g (Q + P) [Q - P - 2 (K - i).r] 



K = -p Q = [K (a + b) + (c 4- d)\ P = v'Q 2 - 4 (K - i)(Ka6 - cd). 



It is cumbrous to use and leaves ample opportunity for errors 

 of calculation. In this case and in many others, notably in those 

 of enzyme action, the experimental errors are unavoidably of 

 considerable magnitude, far greater, probably, than the error of 

 drawing a curve for the course of change and obtaining the rate 



dx 



of change -jj directly by finding the values of the tangents to the 



curve at different points, say for 10, 15, 20, etc., per cent, change. 

 This should be done not by drawing tangents as usually 

 suggested but by means of a black silk thread. It is impossible 

 to drazu a straight line. By using a tight, black silk thread and 

 reading off the values on the squared paper, we eliminate errors 

 due to drawing and a crooked ruler ; we can see both sides of 



