i88 M.-.thcmatUal Corrtfpoiidtnet, ScientiJJc Ki-ws. 



Again, becaufc i (—7—) 's the temperature of tlie body at the end of »i nVmutes, afld 



i {—■!—} its temperature nt tlic end of n miautes, cither of thefe forms will cxprcfs the 



temperature of any bo<ly at the end of any given time, from its firft beginning to cool ; and 



their difference k (-^y — i (— ^)" or h X (^#— )' — i^^)" is the heat which the 



body would lofe between tlie times 111 and w ; h and d being {bund as above. 



In like manner, fince /; {—,-)" = ", or (^^-^^ " = — , we fliall have m log. -^1- = 

 h h h h 



log. — , or m (log. h — (/ — log- h) = log. a — log. /• ; and confequently m = ""' '' ~ °^" 



' log. /j—cJ—log.b 



= time which a body takes in cooling) till it arrives at the obfcrved temperature n. 



And if it be required, as in the quertion, to find the degree of heat to whicli any body 



has been expofed, we fliall have, in this cafe. It = number of degrees between 

 that temperature and the heat to which the body has been raifcd in the time m. Hence 



li — hr = number of degrees the body has been heated, which call t ; then h — i r" 



— t ; from wliich equation h is found = ■ , where r, m and / are known terms. 



m 

 I — r 



Tiiefe formula: will be found of confiderable ufe in feveral branches of chcmiftrv, and 



are capable of a number of praflical applications, which are left, for the prefenc, to the coa- 



llderation of the reader. 



l^EW MATHEMATICAL QUESTIONS. 

 Question VII. By JV. T. of Bath. 

 AS a proper fequel to Queftion III, it is propofed to determine the odds againft the dealer 

 and his partner, at the game of vvhiil, having between them all the thirteen trumps. 



Question VIII. By S. S. of Reading. 

 Given a -^- b = c, to determine the value of x, either by logarithms or a converging 

 feries. 



SCIENTIFIC NEIFS. 



Letter from Sir BeN^JAMIN THOMrSON, Kt. Count of Riimford, F. R. S. to the Right Hon. 

 Sir Joseph Banks, Bart. K. B. P. R. S. announcing a Donation to the Royal Society for 

 tie Furpofe of inflituting a Prize Medal *. 



x\T the annivcrfary of the Royal Society, held the 30ch of November ivpf^, the Pre- 

 Gdent acquainted the Society that Count Rumford had transferred one thoufand pounds 



* From the Tranfufticns for 1797. 



tliree 



