Joule of Manchester was the first to verify Mayer's law quantitatively. By an experiment analogous to that of Rumford, he transformed work into heat, arranging his apparatus so that he might measure the amount of heat produced and the work expended. On dividing the quantity of work that had disappeared by the quantity of heat which had been disengaged, he found that 424 kilogramme-metres of work had been expended for each calory of heat produced.
Hirn of Colmar measured the ratio of work to heat in the steam engine. He found that for each calory of heat which had disappeared there were produced 425 kilogramme-metres of work.
This number 425 has therefore been accepted as representing in calories and kilogramme-metres the transformation of work into heat, and of heat into work.
Further measurements on the transformations of other forms of energy, chemical energy and electrical energy, have shown that Joule's law of equivalents is general, and that the quantity of mechanical work represented by any form of energy remains undiminished after transformation, whatever the nature of that transformation.
Energy presents itself to us under two forms, potential and actual. Potential energy is slumbering energy, energy localized or locked up in the body. In order to transform potential energy into actual energy, there is required the intervention of an additional awakening, stimulating, or exciting energy from without. This stimulating energy may be almost infinitesimal in amount and bears no quantitative relation to the amount of energy transformed. It is the small amount of work required to turn the key which liberates an indeterminate quantity of potential energy.
Actual energy, on the other hand, is energy in movement, awake and alert, ready to be transformed into any other form of energy without the intervention of any such external stimulating force.
The passage of a given quantity of energy from the potential into the actual state is effected gradually, and during the time of transformation the sum of the actual and the potential energy remains constant.
A weight suspended by a cord possesses a quantity of potential energy equal to the product of its weight into the height through which it can fall. This energy is locked up in a certain space, it cannot be transformed without the intervention of some external energy to cut the cord. During the falling of the weight, at the middle of its path, half of this slumbering energy has become kinetic, and is represented by the vis viva of the weight, while the other half is still potential and is equivalent to the work which the weight will accomplish during the second half of its fall. At any moment the sum of these two energies, the sleeping and the waking
energies, represents the total potential energy of the weight before it began to fall.