270 NEWTON S PRINCIPIA. 



is very slow. (6.) Sound travelling through a dusty 

 atmosphere produces no perceptible motion in it. In re 

 gard to the third species of facts, we know but very little ; 

 it is sufficient for our present purpose that we find in the 

 ear vibrating bodies prepared to receive the sound. These 

 are the more obvious phenomena. They will serve as a 

 guide to the true theory. The true test of that theory 

 will be in its exact explanation of more refined and less 

 obvious phenomena. 



Since sound is caused by a body vibrating in air, before 

 we invent any new theory we should prove that none of 

 the natural consequences of such a motion will account 

 for the phenomena of sound. Now we know that the 

 motion of a tremulous body will disturb the air near it, 

 and that moving air the air beyond it and so on. Thus a 

 disturbance will be propagated on all sides in the elastic 

 medium which surrounds the body. Also we find tremulous 

 bodies in the ear fitted to receive such vibrations. What 

 is more natural than to suppose that these vibrations are 

 themselves what we call sound ? To verify this it is ne 

 cessary to examine strictly the nature of the disturbance 

 in the air caused by a vibrating body. The investigation 

 cannot be given here, but the general result is as follows. 

 Suppose a disturbance propagated from a centre in all 

 directions, then, first, the intensity of the disturbance 

 will decrease as the square of the distance increases. Thus 

 as the disturbance was originally small, the motions at 

 some little distance from the sounding body will be quite 

 insensible to any of our senses except that one which was 

 expressly adapted to receive its impressions. Secondly, 

 the velocity with which any wave travels is independent 

 of the nature of the disturbance, and agrees very closely 

 with the observed rate at which sound travels. 



Thirdly, the nature of the motion of the particles is such 



