THE FORMS OF ENERGY. 117 



that this expression applies to any kind of matter moving with any 

 velocity. 



In the case of Heat, too, we can fix on a perfectly definite unit say that 

 raising 1 gm. of water from 15 to 16 0. in terms of which may be ex- 

 pressed any quantity of heat in whatever kind of matter, and whatever the 

 temperature of tha't matter. Common experience of the working of the 

 steam-engine, or of other modes of transforming heat into kinetic energy, 

 raises a strong probability that if heat energy is measured simply by 

 the quantity of heat, that is, as so many calories, and not by any more 

 complicated expression, then there is a fixed rate of exchange between 

 it and kinetic energy ; for the greater the amount of work to be done, 

 the greater the amount of fuel required, and roughly in the same 

 proportion. This probability is converted to certainty by the investiga- 

 tion on the rate of exchange between kinetic energy and quantity of heat, 

 carried out by many physicists and especially by Joule, whose celebrated 

 researches on the value of the rate of exchange we shall presently describe. 



But in other forms of energy we have no such general units. In 

 Light, for instance, we may compare the light given by one mono- 

 chromatic red flame with that given by another red flame of the same 

 quality, and we may, more or less easily, fix on a unit of red light of 

 some particular quality. But another, say a green light, cannot be 

 transformed to red to effect comparison with the unit, and so it cannot 

 be expressed in terms of a red unit. But for each quality or wave- 

 length of light, we may show that the quantity of illuminating power in 

 terms of a unit of its own quality is proportional to the quantity of heat 

 developed when the light is absorbed by a surface on which it falls. 

 For both the heat developed on absorption in a given time, and the illumi- 

 nating power vary together, inversely as the square of the distance from 

 the source. Hence, each kind of light, which we may assume to be light 

 energy, is transformed into heat according to a fixed rate of exchange. 

 Again, in Chemical energy we have no general unit. We may say that 

 in each special kind of chemical action, the amount of action is pro- 

 portional to the quantity of substance formed ; but we have no direct 

 common unit connecting the action in one case with that in another, 

 where quite a different compound is formed. But in each case, separately, 

 the quantity of heat developed is proportional to the quantity of the 

 substance formed, so that here also, if we assume that chemical energy 

 is proportional to the amount of substance which may be formed by 

 union, the rate of exchange between chemical energy and heat is fixed. 



In the case of Strain energy, we may always think of the strain as 

 produced by the transformation of kinetic energy, and since the kinetic 

 energy can be regained on allowing the body to unstrain, with, in 

 general, a small loss accounted for by the heat developed in the pro- 

 cesses, we may fairly suppose that the strain energy gained is equal to 

 the kinetic energy lost, and we usually measure it by the amount so lost. 

 Hence, our mode of measurement, itself, assumes a fixed rate of exchange, 

 as in the case of potential energy, and the fact that any discrepancy can be 

 accounted for by other energies appearing, justifies the assumption. 

 We might, perhaps, measure strain energy in terms of that possessed 

 by a standard body with a standard strain, comparing the energy in any 

 other strained body by transferring its energy in a suitable manner to 



