76 SCIENTIFIC APPARATUS. 



of position. It does not at all depend on the rate at which the 

 change is made, but only on the two positions. If a body moves, 

 and loses kinetic energy, it does an amount of work equal to the 

 kinetic energy lost. If it gains kinetic energy, an amount of work 

 equal to this gain must be done to take it back from the new 

 position to the old one. The amount of work which must be 

 done to take a body from a certain standard position to the posi- 

 tion which it has at present is called the potential energy of the 

 body. The theorem may be stated in this form ; the sum of the 

 potential and kinetic energies is always the same, provided the 

 surrounding circumstances do not alter. Hence the theorem is 

 called the Conservation of Energy. It is one fact out of many 

 that may be deduced from the equations of motion ; it is not suffi- 

 cient to determine the motion of a body, but it is exceedingly 

 useful as giving a general result in cases where it might be difficult 

 or undesirable to investigate all the particulars ; and it is especially 

 applicable to machines, the important question in regard to which 

 is the amount of work which they can do. 



It will have been seen that the science of motion depends on a 

 few fundamental principles which are easily verified, and consists 

 almost entirely of mathematical deductions and calculations based 

 on those principles. It is no longer therefore an experimental 

 science in the same sense as those are in which the fundamental 

 facts are still being discovered. The apparatus connected with 

 it may be conveniently classified under three heads : 



(a) Apparatus for illustrating theorems or solving problems 

 of kinematics, such as those mentioned above for 

 compounding harmonic motions. There is reason to 

 hope for great extension of our powers in this 

 direction. 



(V) Apparatus for measuring the dynamical quantities, such 

 as weight, work, and the elasticities of different sub- 

 stances. These are more fully classified under Mea- 

 surements. 



