446 Mr. Herapath on True Temperature, and the [Dec. 



riment, enables us to demonstrate the laws and the phenomena 

 which have engendered the hypothesis of " Latent Heat and 

 Calorific Capacity." Will any theorem derived from the hypo- 

 thesis of caloric enable us to do this 1 or rather will that doctrine 

 furnish us, from its own principles, with any general and compre- 

 hensive formula of the kind ? If it will, some one, perhaps, will have 

 the goodness to let the world see it ; and to let us know something 

 more of the merits of a doctrine, which I own appears to me to 

 be more entitled to attention from the ability of some of its 

 friends, than for any claims to respect which it has for its innate 

 worth, or for the good it has done towards the extension of 

 science. 



Prop. XVII. Prob. IV. 



The temperature of a given weight of ice, and also of a given 

 weight of water, being known, it is required to find the quanti- 

 ties of water which shall be in the solid and fluid state after the 

 mixture. 



If the water be not enough in quantity or temperature to raise 

 the mixture to 1000, the whole of the water, by the preceding 

 Prop, and Corollaries, will be frozen ; and if it be enough to 

 raise it beyond 1000, the whole of the ice will be melted. These 

 extreme cases are easily found ; for by Cor. 3, Prop. 16, 



1000 — T 



w = 19 W.— T^r. when all the mixture is frozen and its 



22000 19 T 



temperature 1000 ; and w = W . -5- ^rr^n wnen the mixture 



is completely liquid, and its temperature 1000. Therefore if the 

 «iven 10 exceed 19 W . — -— — and fall short of 



22 £ — 19000 



W . — — "Lono > the mixture will be partly liquid and partly 

 solid. 



Again, since by Cor. 4, Prop. 4, t = w B + t0 fr = 



19 W T + 22 10 t 



-, by substituting; for B and b their values found by 



19 w + 22 10 ' J & J 



Cor. 1, Prop. 16, and by supposing there is no solidification or 

 liquefaction arising from the mixture, we shall have 1000 = 



i ^L on the idea that W is the quantity in the solid 



19 W + 22 10' n J 



state, and 10' that in the fluid state, the mixture being at 1000, 

 the temperature of liquefaction. But there being no increase or 

 diminution of matter, W + vf — W + w, and, therefore, 1000 = 



19 W T + 22 w t , , 19 W T + 22 w t - (W + iv) 19000 , 



-7, ana w — 3000 



19 (W + a) + 3 tc" 3000 



quantity of water in the mixture. Consequently W + w — w' 

 is the quantity of ice in the mixture. 



