Proceedings of the British Association. Ill 



Mrs. Somerville, and others, been shown as analogical, and the iden- 

 tity of the electricities being established, Mr. Goodman proposed to 

 exhibit the connecting link between the phenomena of caloric and 

 electricity, to the properties of which (the former) the voltaic fluid, 

 most nearly approaches. The term existencies is here employed by 

 the author in contradistinction to the ordinarily received opinion that 

 caloric, light, &c. are only effects or phenomena resulting from the 

 motion of material bodies. 



* On a Principle in the Theory of Probabilities,' by Prof. Young. 

 — Let p 1 ' p 2 » p 3 ' . . pw be the respective probabilities of happening of n 

 independent events : then the following general principle will have 

 place, viz : — 



p 1 -|-p 2 -}-p 3 -f-. # +pn=the prob. of one of the events at least hap- 

 pening. 



-f the prob. of two at least happening in con- 

 junction. 



-f the prob. of three at least. 



+the prob. of all happening together. 



This general principle, Mr. Young observed, has not hitherto been 

 noticed. It affords an intelligible interpretation of the sum of the 

 probabilities of any number of independent events ; and it is, more- 

 over, useful in enabling us very readily to determine certain com- 

 pound probabilities when others are already known. 



' On Diverging Infinite Series/ by Prof. Young. The general 

 principles sought to be established in this paper are. 1. Whenever 

 an infinite series becomes divergent for particular numerical values, 

 what has generally been called the generating function of the series 

 requires a correction which cannot be disregarded without increasing 

 an error infinite in amount. 2. And that so far from such series be- 

 ing, as usually affirmed, always algebraically true though sometimes 

 arithmetically false, considered in reference to the generating func- 

 tion ; on the contrary, they are always algebraically false, though 

 sometimes arithmetically true — true, namely, in those cases, and those 

 only, for which the algebraic function omitted becomes evanescent. 



Prof. M'Cullagh communicated some remarks on an attempt 

 lately made by M. Laurent to explain on mechanical principles the 



