1821.] Causes of Calorific Capacity, Latent Heat, fyc. 447 



Cor. — Hence if w' is equal to or greater than W + w, all the 

 mixture is liquid ; and if it come out nothing, or negative, all 

 the mixture is solid. By putting id' = 0, we shall get 



1000 — T 



w = 19 W . M t _ 1900Q ; and by putting uf = W + to, we shall 



get w = W . ~2 t _~ 82000 j which theorems coincide with those 

 deduced in the first part of the present proposition. 



Prop. XVIII. Theor. XIV. 



If a given weight, w, of water at a given temperature, t, be 

 thrown on or mixed with an indefinite quantity of ice at the 

 temperature of its liquefaction, I say that the weight of ice 



melted, no other cause interfering, will be equal to -~ i00 ?22w. 



' ° T- 3000 ^ <iw * 



This theorem I have given without demonstration in the 

 Scholium to Prop. 1 of the present paper, or page 102 of the 

 present volume of the Annals. I might with propriety have 

 deduced it in a cor. to the preceding Prob. but in consequence 

 of its involving the theory of the Calorimeter, the invention of 

 those celebrated philosophers MM. Lavoisier and Laplace, I 

 have made it the subject of a separate proposition. 



In whatever way we conceive the water to be applied to the 

 ice, whether it be scattered over an indefinite portion of it, or 

 communicate in a body with one particular part, it has no 

 influence on the quantity of ice liquefied ; for the quantity 

 melted will be evidently proportional to the amount of tempera- 

 ture the whole water can part with to reduce it to the temperature 

 of liquefaction ; that is, to the excess of the water's temper- 

 ature above 1000, and the quantity of the water conjointly. 

 Hence the temperature of the water will have no effect on any 

 other part of the ice but that which it absolutely liquefies ; and, 

 therefore, we may, in pursuing the consequences of the mixture, 

 imagine the water to be mixed with as much ice only as it really 

 liquefies, and totally disregard its connexion with the rest. Let 

 W be the quantity it liquefies ; then 19000 W + 22 io t is 

 equal to the united temperatures of the ice and water before the 

 mixture, and 22000 (W + w) the same thing after the mixture. 

 But nothing being gained or lost, these quantities must be equal ; 

 that is 22000 (W + w) = 19000 W + 22 w f : whence 



W = 22 w '-ZJO^. Q. e. D. 



3000 ^ 



Cor. 1. — The application of this theorem to the determina- 

 tion of the quantity of ice melted in the calorimeter, I have 

 already given, by calculating the effect which an equal weight of 

 water at the given temperature would have, and then augment- 

 ing or diminishing this effect in the proportion of the barouaerin 

 of water to that of the bodv to be tried: but the theorem mav be 



