TWENTY-FOURTH ANNUAL MEETING. 31 



the square of its velocity units. Now clearly, unless a body have motion, it can have 

 no velocity, and if it have no velocity it certainly can have no energy; for if we sub- 

 stitntute zero for V in the above formula it works out that E =0; that is, when the 

 body is at rest it possesses no true energy. But it may be objected that the for- 

 mula is for "kinetic" energy, and hence will not apply to " potential" energy. Will 

 some one. then, kindly supply us with a mathematical formula applicable to this very 

 peculiar form of "capacity for work" (the usual definition for energy). The for- 

 mula so given must be reducible to the general formula for energy (E = 2 M V-) else 

 evidently it can represent nothing in common with true energy whatever. But, who- 

 ever makes this formula, let him remember that, as soon as V becomes zero, E also 

 becomes zero. Clearly, then, the only energy is energy of motion — kinetic energy. 



How then explain those illustrations of "potential" energy so common to mod- 

 ern text-books on physics, such as placing a weight on a shelf, throwing a stone up- 

 ward till it comes to rest, or the "storage of solar energy" in coal, or the winding 

 of a spring, or any of the many other illustrations that might be cited? 



We will take the case of the throwing of a stone upward into space, as it is the 

 one most usually presented. As commonly given, it is about as follows: 



If a boy cast a stone upward, the moment it leaves his hand it is possessed of 

 a certain amount of kinetic energy imparted by the boy's strength exerted in the 

 act of throwing. But the stone loses motion gradually, and after a few seconds 

 comes to rest; then instantly begins to return to earth, and finally strikes with the 

 energy it had on starting. The kinetic energy the stone had on leaving the hand is 

 gradually converted to "potential" energy, until, when it reaches the maximum 

 height, it will have no kinetic energy, for it is at rest; but will have an equivalent 

 "potential" energy. It will have a certain "advantage of position," for if it is al- 

 lowed to fall to earth it will be capable of performing as much work as was done 

 upon it in placing it in that position. Thus the books explain it. 



Now let me ask how much "potential" energy that same stone would have when 

 it comes to rest, had it been thrown horizontally over the smooth ice of a frozen 

 lake. Unquestionably it will have no energy, for the energy of motion imparted to 

 the stone as it was cast over the ice is gradually converted to heat energy, as it meets 

 atmospheric resistance and impinges against the ice. 



So exactly in the case of throwing the stone upward. Jt starts with considera- 

 ble energy of motion, a part of which, owing to atmospheric resistance is turned 

 to heat; but the greater remainder is gradually overcome by the continually-acting 

 counter force of gravity; so that, when the stone has reached the maximum height, 

 the total reaction has just equaled the total action. There has been no storage of 

 energy whatever in the stone. Where, then, is the energy the stone had when it be- 

 gan its ascent? The law of conservation of energy demands that it must exist 

 somewhere. We noticed that it was gradually leaving the moving body, for the ve- 

 locity was uniformly diminished. Whither did it go? It is not in the stone in any 

 of the forms familiar to us as heat, light, electric or life energy; nor is it there as 

 energy of motion, for the stone is now at rest. Where, then, can it be? It exists as 

 energy of gravitational force, not in the stone, but in that rarest of mediums, the 

 "fourth state of matter," the luminiferous ether, whose vibrations constitute the 

 force of gravity. 



To say that the stone was possessed of a certain amount of " potential " energy 

 before it was started upward, by virtue of which it would be possible for it to rise, 

 overcoming atmospheric resistance and gravity, would be no more absurd than to 

 declare it possessed of "potential" energy when once it had reached the highest po- 

 sition in its path, by virtue of which it could fall to earth and do exactly the equiva- 



