Researches in the Theory and Calculus of Operations. 255 



and gaseous, are functions of the amplitudes of the waves 

 of caloric ; while the temperature, or intensity of heat, in- 

 creases with the velocity of vibration. 



Digression 2. At the commencement, one single wave 

 of expansion from the central force at *0 (fig 45) reached 

 the bounding limit (nodal spherical surface) AA'AiA 1 . 

 Infinitely latent was the central temperature before expan- 

 sion; after expansion, zero absolute throughout the ex- 

 panded sphere. The last throe of the advancing wave filled 

 the spherical BA with the semi-wave measured by the arc 

 EsjA of tenuous substance. Immediate reflection from the 

 nodal spherical surface reduced the tenuous substance to 

 pure ether measured by the returning semi-wave As 2 B, 

 repelling the substance of the shell by condensing it into 

 the next shell BB,' and establishing the complete etherial 

 wave Bs 1 As 2 B. These two steps occupied two instants 

 of time, the first in going from B to A measured through 

 the arc s l5 the second in returning from A to B measured 

 through the arc s 2 . During this second instant of time, 

 another emanating wave advanced from B r through s 3 to 

 B, and will proceed from B through s 2 to A in the third 

 instant; in which last instant also a second return semi- 

 wave goes from A through s 2 to B, and a semi-wave will 

 go through s 4 to W ; forwarding a further condensation 

 from AB and BB' towards the centre, and completing the 

 etherial conducting medium to the extent AB' of two 

 complete waves. In this way the process continues to ap- 

 proach the centre of the system. 



All is conducted by expausion, opposed by compressive 

 reaction. The spherical figures 44 being supposed fixed in 

 place, and the action of the forces to be from centre to cir- 

 cumference, if a compressive force equal in magnitude and 

 direction to ss f be suddenly applied to c, the two forces 

 OV and Or will destroy each other: and O's and Or' pull 



