APPENDIX 3. 245 



from the volume of one litre to the volume of v 

 litres under constant temperature. If v increases 

 by the infinitely small quantity dv, r will increase 

 by the quantity dr, which, according to the nature 

 of motive power, will be equal to the increase dv 

 of volume multiplied by the expansive force which 

 the elastic fluid then possesses; let p be this ex- 

 pansive force. We should have the equation 



dr = pdv (1) 



Let us suppose the constant temperature under 

 which the dilatation takes place equal to t degrees 

 Centigrade. If we call q the elastic force of the 

 air occupying the volume 1 litre at the same tem- 

 perature t t we shall have, according to the law of 

 Mariotte, 



- = " whence p = -. 

 Ip v 



If now P is the elastic force of this same air at the 

 constant volume 1, but at the temperature zero, 

 we shall have, according to the rule of M. Gay- 

 Lussac, 



whence 



P 267 



