98 Mr. Herapath on True Temperature, and the [Aug. 



&c." in order to give philosophers an opportunity of examining 

 the truth of my views on an extensive scale. I shall also 

 myself, as I proceed, compare the formulae with the best expe- 

 riments I have at hand, that it may be seen how correctly the 

 theory I have developed agrees with the results of observation. 

 If, however, in the course of this comparison, it should appear 

 necessary to point out any inaccuracies in the methods or expe- 

 riments of others, philosophers will, I trust, receive my observa- 

 tions with candour, and do me the justice to believe, that 

 though I may differ on certain scientific points from some, I 

 have not the less respect for their labours or their abilities, and 

 have only two objects in view ; — the extension of science, and 

 the investigation of truth. 



V 



On the Temperatures resulting from the Mixture of Bodies which 

 do not act chemically on one another, and on the Cause of the 

 Phenomena attributed to " Calorific Capacity or Specific 

 Heat." 



Prop. I. Theor. I. 



If two portions, W W,, of the same fluid at the true tempera- 

 tures T T, be mixed together, the true temperature t of the mix- 

 ture, when no exitraneous temperature interferes, is equal to 

 T W + T, W, 



w + w, ' 



Because by my theory of heat, the temperature of any body is 

 proportional to themotion, orthe intensity of vibration of one of its 

 particles, the sum of all the motions of the particles of any portion 

 of a body, will be as the temperature and the weightof that portion 

 conjointly. And because no extraneous motion or temperature 

 is supposed to interfere, there can be no acquisition or loss of 

 motion in the two parts taken together by the mixture ; and, 

 therefore, the sum of all the motions of the two parts will be the 

 same before and after the mixture. But the sum of all the 

 motions before the mixture is as T W + T, W„ and the sum of 

 all after the mixture as (W + W,) t ; therefore (W + W,) t = 



TW + T I W,andr = TW + T ' Wl 



Cor 1.— If W = W, 



W + w, 



T + T, 



T = 



2 



Cor. 2. — By Prop. 9 of my preceding paper, the true temper- 

 atures are in the subduplicate ratio of the spaces occupied by 

 the same portion of gas under an invariable compression ; and 

 these spaces, if the temperatures are measured by the air ther- 

 mometer, have the same ratio as the corresponding degrees of 



Fahrenheit + 448. Therefore T : T, :: -/448 + F: V448+F, 

 in which F is the Fahrenheit temperature corresponding to T, 

 and F[ that corresponding to T,. In the same way, if F lt cor- 

 responds to t, we have T : t :: \/ 448 + F : V448 + F,, 



