1821.] Causes of Calorific Capacity, Latent Heat, &;c. 445 



mined it to be. So far, therefore, the theory again coincides 

 with all the experiments I have to produce. 



Cor. 2. — By the preceding cor. it appears, substituting for B 



. , . . . ". 19WT + 88»< , .. . . 



and b their values, that t = — j= — — — — when all the ice is 

 melted, and t = — s — —?r^- when all the water is frozen: 



' (W + tc) 19 



W, T, denoting the weight and true temperature of the ice or 

 snow, and w, t, the same things of the water, r being the true 

 temperature of the mixture. 



(2 9 t — 19 T) W 



Cor. 3. — Hence we have w = — — - — , all the ice being 



(t — t) 22 o 



melted, and w = %- — —- — , all the water being frozen. From 



22 t — 19 t a 



these theorems two curious cases arise, the circumstances of 

 which we can easily determine ; namely, that at a given temper- 

 ature two unequal portions of water may be found, which, mixed 

 with equal weights of snow at a common temperature less than 

 32° Fahr. or two unequal temperatures may be found at which 

 two equal portions of water in like manner mixed with equal 

 weights of snow at a common temperature less than 32° Fahr. 

 will produce a mixture of the same temperature ; that is, 32° 

 Fahr. I can onlv stop to compute the first of these cases. Let 

 us put W = 1, t = 990 (22i° Fahr.), t = 1010 (41$° Fahr.) 



3190 Q 9 



and r = 1000 ; then by the first formula ic = — — = — = 144, 



" 220 2 



and by the second w = 5^ = about — . Therefore, if a given 



quantity of ice or snow at 224° Fahr. be mixed with — of its 



weight of water at 4i§° Fahr. the temperature of the mixture 

 will be the same as if the ice or snow had been mixed with 14^ 

 times its weight of water at the said 414-° Fahr. ; that is, in other 

 words, if 17 oz. of snow at 22'5° Fahr. be mixed with only 1 oz. 

 of water at 41*6° Fahr. any additional quantity of water at the 

 same 41-6° Fahr. not above 245 oz. will only melt the ice par- 

 tially, but not raise its temperature. 



Scholium. 



The numbers' 22 and 19, which we have determined for the 

 baromerins of water and ice, denote also the respective powers 

 of these bodies to affect the temperature of any other body, and, 

 therefore, denote numbers proportional to what are called the 

 " capacities" of these bodies. Now the " capacity of water 

 being 1," Kirwan determined the " capacity of ice to be '9? 

 and irvin -8. The mean of these two is *85. By the ratio of 22 

 to 19, it ought to be •8(3. Thus then our theory furnishes us 

 with a simple formula, which, from the numbers of a single expe- 



