138 PROCEEDINGS OP THE AMERICAN ACADEMY 



between mechanical energy and heat, and so should be able to give us 

 the mechanical equivalent. Besides this, we are able to measure a 

 certain amount of electrical energy in both mechanical and heat uuits, 

 and thus to also get the ratio. Chemical energy can be measured iu 

 heat units, and can also be made to produce an electric current of 

 known mechanical energy. Indeed, we may sum up as follows the 

 different kinds of energy whose conversion into one another may fur- 

 nish us with the mechanical equivalent of heat. And the problem in 

 general would be the ratio by which each kind of energy may be con- 

 verted into each of the others, or into mechanical or absolute units. 



Of these different kinds of energy, only the first five can be meas- 

 ured other than by their conversion into other forms of energy, 

 although Sir William Thomson, by the introduction of such terms as 

 " cubic mile of sunlight," has made some progress in the case of radia- 

 tion. Hence for these five only can the ratio be known. 



Mechanical energy is measured by the force multiplied by the dis- 

 tance through which the force acts, and also by the mass of a body 

 multiplied by half the square of its velocity. Heat is*usually referred 

 to the quantity required to raise a certain amount of water so many 

 degrees, though hitherto the temperature of the water and the reduc- 

 tion to the air thermometer have been almost neglected. 



The energy of electricity at rest is the quantity multiplied by half 

 the potential ; or of a current, it is the strength of current multiplied 

 by the electro-motive force, and by the time; or for all attractive 

 forces varying inversely as the square of the distance, Sir "William 

 Thomson has given the expression 



r- flPdv, 



J *J 



where R is the resultant force at any point in space, and the integral 

 is taken throughout space. 



These last three kinds of energy are already measured in absolute 



