Energy. 323 



sound, the vibrations of various elastic bodies. The vibrations are 

 transferred from one body to another, each body vibrating according to 

 its peculiar structure as to shape and materials. In order that we may 

 hear these vibrations they must strike upon the tympanum of our ear. 

 They do this by means of the air ; any vibrating body communicating 

 its vibrations to the air, which in turn communicates them to the ear 

 drum. The sensation of hearing is, however, in the brain, and it gets 

 there by the vibrations striking upon the sensitive organs in the internal 

 ear, and being changed there into nerve currents which flow up to the 

 brain and agitate certain brain cells. The nervous current is therefore 

 one of the forms which the energy of vibratory motion takes, or rather 

 it sets up motion in the nerves and then ceases as vibratory motion of 

 air. The measurement of the energy involved in molar motion has 

 been definitely and satisfactorily made by numerous experiments and 

 calculations. The unit of this measure used by physicists is generally 

 the Kilogrammetre. The Kilogram, or 1,000 grams, is a French measure 

 of weight, equal to 15.432^ English grains, or close to two pounds 

 Avoirdupois, and the metre is a measure of length equal to 39-^ 

 inches. The kilogrammetre is the power necessary to raise the kilo- 

 gram one metre high, or the power derived from allowing a kilogram 

 to fall a distance of one metre. 



If we raise a kilogram two metres high there will be two kilogram- 

 metres of energy expended in getting it there ; if we raise it four metres 

 high it will take four units of energy to do it. If we raise it 19. 6 metres 

 (which is equal to 64^- feet) we shall have used 19.6 units of energy to 

 'do the work, and if the body should fall back it would return that much 

 energy. In falling that distance it would consume two seconds of time, 

 and at the instant of reaching the ground it would be moving at a rate 

 of 19.6 metres per second. If the operation be reversed, it is obvious 

 that any force which is used to project the body upward must start it 

 off with a velocity of 19.6 metres per second. But if the velocity with 

 which it is thrown up is only half as great, the hight to which it will as- 

 cend is not the half of 19. 6 metres, but only one-fourth of that hight or 

 4. 9 metres. Consequently to reduce the initial velocity to one-half is to 

 reduce the energy to one-fourth. We therefore perceive that the energy 

 is in proportion to the square of the velocity. The following formula 

 will cover all cases : Let Y = the initial velocity in metres per second 

 and M equal the mass or weight of the body in kilograms. Then the 

 mass multiplied by the square of the velocity and the product divided 

 by 19. 6 ( or M V 2 -=- 19. 6 ) will equal the energy in kilogrammetres. And 

 Y^ -h 19.6 = the hight in metres to which it will go if thrown up. It can 

 be neatly shown how the energy of a body shot upward is changed from 

 energy of motion to energy of position every instant during its ascent 



