On the Theory of Probabilities. 1 65 



alike in power unto the end of the current, and then a difference 

 again appears which is complementary to the first. 



There are many variations of these experiments which one 

 would wish to make, if possible, and perhaps by degrees the pos- 

 sibility, or else equivalent experiments in other forms, may occur. 

 If the wire employed were changed from a cylinder to a flat 

 ribbon of equal weight, or to several small wires, all being equally 

 coated with gutta percha and submerged, differences would pro- 

 bably arise in the time of delay with the same current ; and I 

 think that the ribbon, presenting more induction surface than the 

 cylinder, would cause more delay ; but probably any one of these, 

 or of like varieties, would cause the same delay for currents of 

 different intensities. Again, one can scarcely doubt that with 

 different conducting substances, as iron and copper, the delay 

 would vary, as is the case in the transmission of sound and light. 

 That the delay for currents of high and low intensity should be 

 the same for the same wire in any one of such cases may still be 

 expected, but it would be very interesting to know what would 

 be the fact. 



The prosecution of these results and the principles concerned 

 in them, through the various forms they may assume by such 

 like variations of the conductors and also of the currents, offers, 

 as Melloni has observed, most extensive and interesting inquiries: 

 even the power of a current to induce a current in neighbouring 

 wires and conductors is involved in the inquiry, and also the 

 phsenomena and principles of magneto-electric induction. 

 Royal Institution, Feb. 7, 1855. 



XXV. On certain Propositions in Algebra connected with the 

 Theory of Probabilities. By George Boole, LL.D., Pro- 

 fessor of Mathematics in Queen's College, Cork*. 



BEFORE entering upon the immediate subject of this paper, 

 I wish to state the connexion in which it stands with my 

 previous papers on the theory of probabilities, published in this 

 Journal. 



If the reader will refer to what I have said in the conclusion 

 of my second paper, published in the August Number of this 

 Journal for 1854, he will find that the claims of the doctrine 

 which 1 have put forth are made to rest upon its satisfaction of 

 the following requirements : — 



1st. That the principles upon which its methods arc founded 

 ihould be of an axiomatic nature. 



* Communicated by the Author. 



