1.] FOKCE AND ENEKGY. 23 



The same distinction solves another question that perplexed Faraday's 

 Faraday. Gravitation is a force ; electricity is a force ; all forces l^i^stion 

 whatever are correlated ; what is the special correlation between gravity 

 these two 1 Faraday devised experiments in order to discover ^^d elec- 

 some such special correlation, but did not obtain any result. 



The answer to the question is, however, very simple, and easy Answer, 

 to illustrate by experiment. Gravity is a force, and electricity 

 is a form of energy : the force of gravity may produce the energy 

 of motion of a falling body, and part of that energy of motion 

 maybe transformed into the energy of electricity. If the weight 

 of falling water works a water-mill, and this works an electrical 

 machine and produces electricity from it, there is a perfect ex- 

 perimental illustration of the relation between gravitation and 

 electricity ; for the electricity, like the heat, which is produced 

 by friction, is not a mere concomitant of the friction ; it is a 

 part of the energy of motion, which has been transformed. 



The same verbal ambiguity was at the root of the controversy, Contro- 

 now long ago settled, as to the measure of the force of a moving 7^'?/ ^^ 

 body ; — whether the force was proportionate to the mass mul- measure 

 tiplied simply into the velocity, or to the mass multiplied into °^^^' 

 the square of the velocity. All are now agreed that the energy Energy of 

 of motion, to which the power of doing work is due, is propor- "^0^1°" 

 tionate to the mass multiplied into the square of the velocity. 

 For instance : supposing the mass, or weight, of a projectile to 

 be given, its power of penetrating is proportionate to the square 

 of the velocity. JBut the force of a moving body is proportionate 

 to the mass multiplied simply into the velocity : in other words, 

 to its momentum. The proof of the last statement is this. As and mo- 

 already stated, equal forces acting in opposite directions neutralize 

 each other. Now, it is found by experiment as well as by theory, 

 that equal momenta in opposite directions neutralize each other ; 

 that is to say, two bodies coming into collision with equal 

 momenta in opposite directions (supposing of course that they 

 are of lead or some other inelastic substance, so as not to re- 

 bound) will destroy each other's momenta and. bring each other 

 to rest. 



In such a case, the energy of motion that disappears is of 

 course transformed into heat. 



It follows from the statements given above as to the measures 

 of momentum and of energy of motion, that if two bodies are 

 in motion whereof one has a hundred times the velocity of the 



