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XXXIV. Beply to Dr. Apjohn's " Additional Remarh," 8)C. 

 m The Annals of Philosophy yo/- September 1822. By 

 John Hekapath, Esq. 



To the Editors of the Philosophical Magazine and Journal. 



J London, Cranford, Sept. 5, 1823. 



Deau Sirs, — an the Annals for June I gave a formula for 

 determining the specific gravity of aqueous vapours in contact 

 with their fluids. The method of my finding this theorem, 

 and the principles I employed, appeared to me so obvious and 

 simple, that I could scarcely believe the formula itself could be 

 new: and certainly did not imagine that my reasoning required 

 extended illustration. Dr. Apjohn having however, in the 

 present month's Annals, called the accuracy of the theorem m 

 question, I perceive I must have miscalculated the obviousness 

 of the principles, and therefore beg to trouble you with a de- 

 monstration of them. 



Let us conceive a quantity of vapour having a specific gra- 

 vity S to be confined at its proper tension t in some vessel 

 over its fluid at the Fahrenheit temperature F. Let us now 

 conceive this vapour and its fluid to be gradually and equally 

 cooled to some other temperature F', conceiving at the same 

 time, what is unquestionably admissible though perhaps not 

 practically possible, that the vessel confining the vapour also 

 gradually changes its capacity, so as always to preserve to the 

 vapour an elasticity just equal to the tension it ought to have 

 corresponding with its temperature ; and let the ultimate ten- 

 sion be t' and specific gravity S'. Then because by the com- 

 monly received principles water neither evaporates nor ab- 

 sorbs any of its superincumbent vapours, v/hiist the elasticity 

 of the vapour equals the tension of the temperature, it follows 

 that the vapour at F' is, the same, and of the same weight as 

 the vapour at F ; that is, the mere contact of the water has 

 produced no effect on the vajiour beyond simple connnunica- 

 tion of temperature. But equal changes of temperature being 

 similarly and under similar circumstances communicated, nm.st, 

 as tar as I can perceive, have the same efftcts from whatever 

 bodies tlie communication comes. The change therefore 

 wiiich hji-s been made in the volume, and consecjuently in tlie 

 specific gravity of the vapour in contact with its fluid, by the 

 diminution of temperature, is just equivalent to that which 

 would have been effected by an equal dimiimtion, if the vapour 

 had not been connected with its fluid. But when vapours are 

 not coimectcd with their fhiids, our i)hilosophers tell us that 

 their changes are, ctrtcris paribus, the same as those of the 

 Vol. GO. No. 293. Sept. 1822. B b gases. 



