Researches in the Theory and Calculus of Operations. 251 



A prolonged application of calorific force is requisite to 

 originate vibratory molecular movement in the solid body 

 S; and, in so doing, the introduced force actually combines 

 with and enlarges the dimensions of the substance, and thus 

 disappears from thermometrical admeasurement (latent heat 

 of Black). Having reached the liquid state in L, a further 

 supply of calorific force will be consumed in further en- 

 larging the amplitude of the molecular vibrations, and as 

 before, becomes latent in maintaining the further enlarged 

 substance in the aerial state A. 



All bodies continually interchange calorific vibrations, 

 producing a mutual change of bulk, the warmer body de- 

 creasing, the cooler increasing till the temperature is equal- 

 ised between them. The calorific force is repulsive in the 

 form of spherical emanation ; the atomic radii increase in 

 the body which receives a greater accession of calorific im- 

 pulses than it returns, and decrease in the one which imparts 

 a greater amount than it receives. When equilibrium of 

 temperature is reached, the interchange remains equal 

 (Poisson, Fourier). 



8 . Heat increases the bulk of matter, which is an increase 

 in the three dimensions of space, by the conversion of in- 

 tension into extension, or increasing elasticity at the expense 

 of density. Now 1° a force of the first degree, a uniform 

 velocity, generates a force of the degree zero, a phenomenon 

 which increases uniformly in time, and therefore may be 

 measured by a straight line, a magnitude of one dimension. 

 2° A force of the second degree generates force of the first 

 degree (velocity) uniformly, which generates a phenomenon 

 increasing as the square of the time, and so is measurably 

 a square, a magnitude of two dimensions. 3° A force of the 

 third degree generates force of the second degree increasing 

 uniformly, which generates force of the first degree (velo- 

 city) increasing as the square of the time, which last gene- 

 rates a phenomenon increasing as the cube of the time, and 



