1821 .] Causes of Calorific Capacity, Latent Heat, ^c. 451 



given by Count Rumford, who had evidently conducted his 

 experiments with consummate skill and precaution, and neatly 

 with that by MM. Lavoisier and Laplace, I have preferred it 

 for the investigation of the numbers of the present problem. 

 Besides it appears to me, that had Dr. Ure taken into account 

 the matter in his glass basin and condensing globe, he would 

 have brought out a much higher number than he has, if not very 

 nearly the same as Rumford, or Lavoisier and Laplace ; and, 

 therefore, I look on that philosopher's experiment as corroborat- 

 ing the higher numbers of these. 



By a similar train of reasoning to that which I have pursued 

 in Prop. 16, we obtain the equation (w + w') b t' ' = wbt + w'b' ' t' 

 when all the vapour is condensed, and (w + w') b' t' = tvbt -f- 

 «/ b' t' when all the water is converted into vapour; taking w, t, b, 

 to represent the same things as in the cited Prop. 16, namely,, 

 the weight, true temperature, and baromerin of the water, and 

 %o' , t ' , b', the same things respectively of the vapour ; and taking 

 ■/ to represent the true temperature of the mixture. From the 

 first of these equations, we have b : b' :: w' t' : (to + w') r' — w t t 

 and from the second b : b' :: (w + w') •/ — w' t' : w t. 



Cor. 1. — In the case stated by Dr. Thomson, to which I have 

 already alluded, it is said that one part by weight of steam at 

 212° Fahr. mixed with nine parts of water at 62°, gives a mix- 

 ture of 178-6°, the steam being all condensed. Here t = 1030*8, 

 t' = 1142-5, f = 1 172-6", w = 9, and w' = 1 ; and, therefore, 

 b : b' :: w' t' : (w + w') t' - w f :: 1 172-6 : 1142'5 - 9277'2 

 :: 1172-6 : 2147-8 :: 1 : P83W6:: 6 : 11. 



We can now, substituting these numbers, compare the theo- 

 rem with experiment. If we take the case from which we have 

 computed them, the middle temperature will come out 178-8° 

 Fahr. or -2° higher than 178'6° from which the numbers were 

 derived. This difference arises from the numbers 11 and 6 hav- 

 ing a greater ratio than 2147-8 and 1172-6. 



Dr. Ure distilled 200 grains of vapour in 32340 grains of 

 water at 42*5°, and found the result 49°. Here we 'have 



T = 1010-9 and* = 1172-6; and because — = ^ = 161-7, 



a 200 * 



, 161-7 x 10109 x 6 + 1172-6 x 11 ._,_ _ . . , . 



we have t = -. — -r^— « = 1017-9, whichgives 



b x (lt)li + 1) o 



49-3° Fahr. that is, T 3 „ of a degree above what Dr. Ure observed 

 it to be. In this experiment of Dr. Ure, it is to be observed that 

 he does not note the height of the barometer at the time of the 

 experiment, a circumstance which he must be aware would 

 influence the result of the calculation, perhaps indeed almost 

 sufficient to annihilate even the trifling difference which there is 

 between the theory and experiment. My theorem presupposes 

 the barometer to have been at 30 inches. The same omission 

 likewise exists in the following experiments of Count Rumford ; 

 and, therefore, I must assume the same, as in the experiment of 



2g2 



