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



Call B the baromerin of a given portion of ice, W the weight 

 of it, which we suppose proportional to the quantity of its 

 matter, and T its true temperature. Let b, w, t, denote the same 

 things respectively of a given portion of water, and call t the 

 true temperature of the mixture cleared from all adventitious 

 circumstances. Then WBT + w t bis the sum of the motions 

 or temperatures of all the parts of the bodies before the mixture, 

 and (W B + w b) r would be the same thing after the mixture on 

 the supposition that each body retained its respective baromerin 

 unchanged. Therefore no motion being gained or lost by the 

 mixture, we should have WBT + w b t = WBt + w b t, and 



t = — rrrr: -7— ; the same as we have in Cor. 4, Prop. IV. 



W B + wb ' ' f 



However, because if the ice by the mixture be not melted, the 

 water is most probably converted into ice ; or if the water be 

 not converted into ice, the ice is into water, the baromerin of 

 one of the quantities must be changed, and either (W B + wb)r 

 must become (W B + w B) t, supposing the water frozen, or 

 (W b + iv b) t, supposing the ice melted. In either case the 

 sum of the motions, as we imagine nothing gained or lost in the 

 mixture, will be the same before and after; so that we have 

 W B T + w b t ■ = (W -f- w) B r when the water is frozen, or 

 = (W + w) b t when the ice is melted. In the former case, 

 B : b :: w t : W T — W t — w t, and in the latter B:J::Wt 

 + wt-w*:WT. Hence by knowing W, iv, T, t, and t, we 

 get the ratio of B to b. Q. E. 1. 



Cor. 1. — Br. Black, with whom the present doctrine of "Latent 

 Heat " originated, found, by mixing water at 172° Fahr. with an 

 equal weight of ice at 32°, that the whole of the ice was melted, 

 but no addition made to its temperature. According to this 

 experiment T = t = 1000, t — 1 136'5, and W, w, may each be 

 put equal to \. Therefore B : b :: 2000 - 1136-5 : 1000 :: 

 863*5 : 1000 :: 19 : 22 very nearly. Consequently the baromerin 

 of ice is to that of water as 19 to 22 very nearly ; and the mass 

 of a particle of ice is to that of a particle of water as 22 to 19. 



Notwithstanding philosophers have written so much on the 

 doctrine of " Latent Heat," they appear to be so poor in experi- 

 ments that I have met with but one besides that from which I 

 have computed the preceding numbers with which I can compare 

 the theorems I have investigated ; and that one is to be found 

 in almost every book on the subject. Dr. Black mixed 143 half 

 drachms of water at 190° Fahr. with 119 half drachms of ice at 

 32° Fahr. In a few minutes all the ice was melted, and the 

 temperature of the mixture found to be 53° Fahr. By Table 3, 

 190° Fahr. gives 1 153, and 32° gives 1000. Therefore 



WBT + wbt 119 x 19 x 1000+ 143 x 22 x 1 153 _ 1091. 9 

 T ~~ (W + ic) . b (119 + 143). 22 



which gives 52-6° Fahr. or only -4° below what Dr. Black deter- 



