of a Mass of Matter. 209 



If heat is to be transformed into work, which is a negative 

 transformation, a positive alteration of disgregation must take 

 place at the same time, which cannot be smaller in amount than 

 that determinate magnitude which we regard as equivalent. In 

 the positive transformation of work into heat, on the other hand, 

 the state of things is different. If the force of heat is overcome 

 by opposed forces, so that a negative change of disgregation is 

 brought about, we know that in this case the overcoming forces 

 may be greater than is required to produce the particular result. 

 The excess of force may then give rise to motions of considerable 

 velocity in the particles of the body under consideration, and 

 these motions may subsequently be changed into the molecular 

 motions which we call heat, so that in the end more work comes to 

 be transformed into heat than corresponds to the negative change 

 of disgregation brought about. In many operations, especially 

 in friction, the transformation of work into heat may take place 

 even quite independently of any simultaneous negative trans- 

 formation. 



The relation in which the third kind of transformation, namely 

 alteration of disgregation, stands to considerations of this nature, 

 is implied in what has been already said. The positive altera- 

 tion of disgregation may indeed be greater, but cannot be smaller, 

 than the accompanying transformation of heat into work; and 

 the negative alteration of disgregation may be smaller, but can- 

 not be greater, than the transformation of work into heat. 



Finally, in so far as regards the second kind of transformation, 

 or the passage of heat between bodies of different temperatures, 

 I have thought myself justified in assuming as a fundamental 

 proposition what, according to all that we know of heat, must be 

 regarded as self-evident, namely, that the passage from a lower to a 

 higher temperature, which counts as a negative transformation, 

 cannot take place of itself — that is, without a simultaneous positive 

 transformation. On the other hand, the passage of heat in the 

 contrary direction, from a higher to a lower temperature, may very 

 well take place without a simultaneous negative transformation. 



Taking these circumstances into consideration, we will now 

 return once more to the consideration of the development by 

 means of which we arrived at equation (II.) in § 5. Equation (2), 

 which occurs in the same section, expresses the relation in which 

 an infinitely small alteration of disgregation must stand to the 

 work simultaneously performed by the heat, under the condition 

 that the alteration takes place in a reversible manner. In case 

 this last condition need not be fulfilled, the alteration of disgre- 

 gation may be greater, provided it is positive, than the value 

 calculated from the work ; and if negative, it may be, when 

 taken absolutely, smaller than that value, but in this case also it 



