Prof. Boole on the Theory of Probabilities. 175 



processes are completed may have a considerable influence on 

 the nature of the products formed, has, I think, been rendered 

 evident by my experiments on the fermentation of rubian. In- 

 deed I would go further, and assert that the difference in the 

 effect produced by the same ferment, under different circum- 

 stances, is a direct consequence of the greater or less degree of 

 rapidity in the change which its elements may be undergoing, 

 and of the consequent more or less rapid motion communicated 

 to the elements of other bodies. The very simplest experiments 

 in organic chemistry are sufficient to prove, that a body sub- 

 jected to a process of rapid decomposition yields very different pro- 

 ducts to what it does when the same process is slowly conducted. 

 Now the butyric acid fermentation of sugar differs chiefly 

 from the alcoholic in the length of time which it requires for its 

 completion. The numbers and ratios, which I have here (some- 

 what hypothetically, perhaps) placed in juxtaposition, seemed to 

 indicate that the fermentation by which succinic acid is formed 

 from sugar is characterized by still greater slowness ; and that, 

 by sufficiently retarding the action of ordinary ferments on sugar, 

 we may also by means of these succeed in forming succinic acid 

 in saccharine solutions, perhaps even in considerable quantities. 



XXIV. Further Observations relating to the Theory of Probabi- 

 lities in reply to Mr. Wilbraham. By George Boole, LL.D., 

 Professor of Mathematics in Queen's College, Cork"^. 



O EVE RE domestic affliction prevents me from forwarding this 

 ^-^ month the papers mentioned in the conclusion of my letter 

 just published in the Philosophical Magazine. That letter, and 

 the paper by which it was accompanied, have, I trust, in some 

 degree prepared the way for the more fundamental questions to 

 which I hope shortly to be able to proceed. A careful inquiry 

 into the conditions which a true method must satisfy, may greatly 

 narrow the field of discussion, by entitling us to set aside methods 

 which do not satisfy those conditions, and enabling us to esti- 

 mate at their just value objections drawn from any assumed 

 advantage of such methods, or, in fact, from assumptions of any 

 kind in the formation of which such conditions have been ne- 

 glected. 



And I conceive that it may thus narrow the field of inquiry in 

 the present instance, if, having already examined Mr. Wilbrar 

 ham's comparison of the solutions of a certain problem given by 

 Mr. Cayley and myself, I should offer a few remarks, and sug- 

 gest a question with reference to the method proposed by Mr, 

 Wilbraham himself in the conclusion of his letter (Phil. Mag. 

 * Communicated by the Author, ^ 



