268 REPORTS ON THE STATE OF SCIENCE. 



moment is a constant percentage of the amount of unchanged sugar 

 present. In symbols : — 



d'-*^ 7 /„ _ s /a = initial amount of sugar. 



X = amount already inverted. 

 t = time which has elapsed since 

 the reaction started. 



dt = >^- (« - ^) 



T where 



or - loge = fc 



t a — X 



This last expression is the simplest type of mass action equation and 



is known as Wilhelmy's Law. The Law was verified with some 



1874. care by Fleury, who pointed out that the inversion is attended 



1862. by an evolution of heat ; also by Lowenthal and Lenssen and by 



1882-3. IJrech, who again showed that the amount of sugar hydrolysed 



is proportional to the amount present. 



The velocity constant k = i - log^ — - — ) in Wilhelmy's Law may 

 be taken as representing the rate at which the sugar is inverted. 



B. — Conditions under which Cane Sugar' is Inverted. 



B 1. — Supposed Spontaneous Inversion by Pure Water. 



Mauuiene imagined that cane sugar could be inverted by water 

 1 Sfii ^lo'ifi, as on leaving a solution standing at room-temperature during 



several months invert sugar was formed. 

 -iciKK Bechamp confirmed this conclusion and showed that zinc and 



calcium chlorides prevented the change. Bechamp soon afterwards 

 ,oKQ proved, however, that if the solution were kept perfectly sterile no 



inversion occurred. Some antiseptic salts, such as mercuric chloride, 

 1864. ai-e said to have an inverting action of their own. 

 ,0-0 Pellet's solutions were probably, like Maumene's, not sterile. 



Inversion on boiling solutions of cane sugar cannot, however, be 

 ■tQn^ explained so simply. Maumene showed that the inversion of 



sugar on the water-bath is accompanied by the formation of an 

 , n^P^ acid. Lound claimed that if heated out of contact with the air or 



in contact with air free from carbonic acid, sugar solutions are 

 not inverted at all. He attributed Maumene's result to the presence of 

 carbonic acid. 

 ■IC.QO Gladstone and Tribe showed that on heating sugar solutions 



the inversion which occurs is accompanied by a darkening of the 

 solution and the formation of a volatile substance which gives the 

 iodoform test. If, however, a zinc-copper couple be present during the 

 boiling no darkening of the solution occurs. 

 icQQ W- -^' Smith also recorded that the change in optical rotatory 



power of a sugar solution on boiling is due partly to inversion 

 and partly to decomposition. 

 , qA.7 More recently Kullgren ' has pointed out that the hydrogen 



ions ■'' of the water and the invert sugar are not sufficient to 

 account for the increase in the inversion velocity at 100° C. as the action 

 proceeds. He demonstrated by titration that an acid is gradually formed 

 from the invert sugar and that the curve could be interpreted if due 

 allowance were made for this formation of acid. 



' Zeits. Phys. Chem., 41. * Vide infra. Section E. 



