On the Measure of Work in the Theory of Energy. 219 



of producing the heat throughout the strata just where it is 

 needed for work. Under it accumulations of strata of like thick- 

 ness and composition would be differently acted upon according 

 to the three conditions: — (1) the amount of motion, one prin- 

 cipal source of heat; (2) the thickness of the series of beds 

 undergoing movement, another source of heat beneath ; (3) 

 the amount of moisture present in the beds. Thus widely 

 diverse metamorphic rocks might be made of the same mate- 

 rial ; and if a region of feebly metamorphic rocks is found to 

 lie side by side with one of thoroughly metamorphic, the strata 

 of the two may have originally been similar and of one and 

 the same geological horizon. 



Metamorphism over large areas is thus one of the direct 

 results of the earth's contraction. Solidification is often only 

 a lower stage in the same process ; and the reddening of sand- 

 stones, as already explained*, is frequently involved with it. 



XXIII. On the Measure of Work in the Theory of Energy. By 

 Robert Moon, M<A. } Honorary Fellow of Queen's College, 

 Cambridge^. 



PROFESSOR MAXWELL gives the following definition and 

 measure of work: — "Work is done when resistance is 

 overcome; and the quantity of work done is measured by the 

 product of the resisting force and the distance throughout which 

 that force is overcome" (Theory of Heat, 1871, p. 87). 



1. It is to be presumed that when the uniform force E acts 

 throughout the time T in a given direction upon a body which 

 is free to move in that direction, the resistance overcome by the 

 force will be that arising from the inertia of the body — in other 

 words, the resistance which the body offers to any change being 

 effected in its state of rest or motion for the time being, and 

 which is always proportional to the force employed in overcoming 

 it. It follows from this, that, under the circumstances referred 

 to, the resistance which is being overcome at each epoch of time, 

 and therefore the work done in equal intervals of time, will be 

 the same throughout the motion. But if the body is at rest to 

 start with, andT is divided into n equal intervals, the work done 



T 



at the end of the first interval -, according to the above measure, 



n ° 



IT 2 



will be ^E 2 ^-; that done at the end of the second interval will 

 2 n l 



* Phil. Mag. for July, pp. 49 & 50. 



t Communicated bv the Author. 



