1822.] Causes of Calorific Capacity/, Latent Heat, S^c, 17 



equation involving only t and known quantities. The value of 

 T being determined from this equation will afterwards enable us 

 to determine that of W, and consequently the weight of the 

 vapour. 



Case 2. — ^When the matter and temperature of the vessel are 

 to be taken into account, we must substitute for them in the 

 equation A in the same manner as we have for the matter and 

 temperature of the body Q. And in the equation B, we must 

 make an allowance in the capacity S for the effect of contraction 

 or expansion on the capacity in changing from the temperature 

 of the vessel to the temperature r. By this means we get two 

 new equations Aj and Bj from which ehminating W^, as before, 

 we obtain the value of t, and thence the other requisites of the 

 problem. 



Cor. — By the same process we can find the effect of the mix- 

 ture of a quantity of water and vapour at one temperature with, 

 another given quantity of water and vapour at another tempera- 

 ture, the capacity, temperature, and matter of the vessel being 

 given. From this we may find how much water at a given tem- 

 perature it would take, when intromitted into a vessel filled with 

 water and vapour of a given temperature, to reduce the temper- 

 ature or tension of the mass from one given quantity to another, 

 as w^ell as many other things of a similar kind. These are, how*^ 

 ever, problems which, though very interesting, we cannot, in the 

 present state of science, exhibit in finite equations ; and for this 

 reason I think it unnecessary here to pursue the inquiry. 



Scholiu7n. 



The theorems contained in this part of the present paper, 

 <jontain all that is necessary to be known relative to the force, 

 condensation, and laws of aqueous vapour in the theory of the 

 steam engine. A moderate share of ingenuity will enable engi- 

 neers to apply the principles I have developed to the resolution 

 of almost, or, perhaps, every problem that can arise or be pro- 

 posed relative to the power and operations of that useful instru- 

 ment. I had at one time thoughts myself of entering pretty fully 

 into the resolution of the more practical cases ; but perceiving? 

 this was a matter of no unusual difficulty, when the physical part 

 was clearly expounded, I have thought it better to employ the 

 little time I have had to devote to these things to a more lumi- 

 nous development of my physical principles, and of the evidence 

 I have had at hand to support them, than to cramp one part of 

 the subject without advantage to the other. 



Sometime ago I had promised myself to close the present 

 paper with the last volume of the Annals; and, for this purpose,, 

 had availed myself of the kind indulgence of the proprietors and 

 editor to occupy in the two or three last numbers larger portions 

 of that work than are usually allowed to single mdividuals. 



New Series, vol. hi. c 



