NEWTON S PRINCIPIA. 271 



that at some distance from the sounding body, the directions 

 of oscillation of the particles will pass through the centre 

 of disturbance supposing the propagation symmetrical in 

 all directions, or more generally, whatever be the nature 

 of the disturbance, the vibrations are normal to the front 

 of the wave. In fluids no other vibrations are possible. 



Of course Newton could not investigate completely the 

 motion of sound. That was far beyond the power of the 

 mathematics of his day. But, in a wonderful manner he 

 solved to a certain degree the simpler case of the motion of 

 the air in a tube. The principle he used, and the present 

 mode of reasoning on this subject, are both illustrated in 

 the following analytical view of the investigation. 



Whatever the motion of the air may be, we suppose the 

 tube so small that we need not consider any motion ex 

 cept that which is along the length of the tube, and this 

 motion will be the same for all particles in the same per 

 pendicular section of the tube. Suppose, then, that at the 

 time t, the particle which when the air was at rest was at 

 a distance x from the origin of measurement is at the dis 

 tance z + %. Then an element of air whose length had been 

 dx, is now dx + dg, and as the mass must remain the same, 

 the density which was D is now 



= D l ~ 



p = - ~ TT 



, , ** V dxj 



i T -r~ 

 dx 



The square of may be neglected, for we know that that 

 particular motion of the air which we call sound, whatever 

 it may be, is very small. Also the pressures on the two 

 sides of the element are, when reduced to a unit of area, 



p and p + -j - d x, 



