1821.] a Method of applying Madaurin's Theorem, 107 



We may from the same principle find the cosec. x in terms of 

 the arc Xy radius unity. 



cosec. X = ^rj-^ = ^. _ 6a» + da:^-/ar»+ Aa»-&c. — Ic "^ ^ ^ "*" 



B j3 + C x'^ + &c. 

 From whence we get 



f (A - h) x"^ : , ; 



\(J)-Cb + Bd-Af+ h)x' 



L&c 



Then by making the coefficients of :r-, x^, x^, x^, &c. respect- 

 ively equal to zero, we have 



lD = Cb'-'Bd + Af-h 



127 

 601800' 

 &C 



The law of continuation being evident, therefore, 

 cosec. a^ = - + _ + -^ + jV^ + ^^^^ + &c. 



Article V. 



On the Solution and Crystallization of Lime. By R. Phillips, 

 FRSE.FLS.&c. 



Mr. Dalton, in his *' iSTew System of Chemical Philoso- 

 phy," has stated the curious fact that lime is more soluble in cold 

 water than in hot, and has given the following table to show the 

 difference which exists in water of various temperatures. 



One part of water of Takes up of lime. Takes up of dry hydrate of lime 

 60" ^W TiT 



130 ^ ^1^ 



019 I 1 



^'■'^ TTTo" "9~5"^ 



" This table," he observes, '' leads us to conclude that water 

 at the freezing temperature would take nearly twice the quantity 

 of lime that water at the boihng temperature takes." 



Mr. Dalton has not attempted to account for the curious fact 

 which he has discovered. Mr. Brande has not mentioned this 



