65 SCIENTIFIC APPARATUS. 



button will have only one of the two oscillations which are 

 combined in the motion of that point ; and the other oscillation 

 would be exhibited by a button constrained to move in a 

 similar manner between the figures III. and IX., so as always 

 to be either vertically above or vertically below the extreme 

 point of the minute-hand. The laws of these two motions are 

 identical, but they are so timed, that each is at its extreme 

 position when the other is crossing the centre. An oscillation of 

 this kind is called a simple harmonic motion ; the name is due to 

 Sir William Thomson, and was given on account of the intimate 

 connection between the laws of such motions and the theory of 

 vibrating strings. Indeed, the harmonic motion, simple or com- 

 pound, is the most universal of all forms ; it is exemplified not 

 only in the motion of every particle of a vibrating solid, such as 

 the string of a piano or violin, a tuning-fork, or the membrane of 

 a drum, but in those minute excursions of particles of air which 

 carry sound from one place to another, in the waves and tides of 

 the sea, and in the amazingly rapid tremor of the luminiferous . 

 ether which, in its varying action on different bodies, makes itself 

 known as light or radiant heat or chemical action. Simple har- 

 monic motions differ from one another in three respects ; in the 

 extent or amplitude of the swing, which is measured by the dis- 

 tance from the middle point to either extreme ; in the period or 

 interval of time between two successive passages through an 

 extreme position; and in the time of starting, or epoch, as it is 

 called, which is named by saying what particular stage of the 

 vibration was being executed at a certain instant of time. One 

 of the most astonishing and fruitful theorems of mathematical 

 science is this; that every periodic, motion whatever, that is to say, 

 every motion which exactly repeats itself again and again at 

 definite intervals of time, is a compound of simple harmonic 

 motions, whose periods are successively smaller and smaller 

 aliquot parts of the original period, and whose amplitudes (after 

 a certain number of them) are less and less as their periods are 



