278 NEWTON S PKINCIPIA. 



motion will be sensible at other points of the room, as 

 well as directly in front of the orifice. Thus Newton s 

 expectation was confirmed, though he was ignorant of the 

 condition on which it depended. But if the length of the 

 waves are indefinitely small compared with the size of the 

 orifice, and this is the case in the Undulatory Theory of 

 Light, then it is found that, excepting directly in front 

 of the orifice, the definite integral is altogether insensible, 

 the condensations and forward motions of one wave being 

 superimposed on the rarefactions and backward motions of 

 another in such a manner that there is no sensible disturb 

 ance. Such waves must be considered as being propa 

 gated in rectilinear directions. 



The first step in the theoretical explanation of the sounds 

 produced in pipes was made by Newton. He remarks that 

 Sauveur found by experiment that an open pipe about five 

 Paris feet in length gives a sound of the same tone with a 

 viol string that vibrates a hundred times in a second. 

 Therefore, he argues, there are near one hundred pulses in 

 a space of one thousand and seventy Paris feet, which a 

 sound runs over in a second of time ; therefore one pulse 

 fills up a space of about 10 T 7 Q Paris feet, that is twice the 

 length of the pipe. From whence it is probable that the 

 lengths of the pulses in all sounds made in open pipes are 

 equal to twice the length of the pipes. Newton did not 

 examine any further into the subject, but leaves it for 

 others to carry out the theory. Lagrange and Bernoulli 

 were the first to give more minute explanations of the 

 leading facts. Since that time, Euler, Lambert, Poisson, 

 have developed the subject still further. 



The theory is to a great extent included in the equations 

 to the motion of sound in a tube which we have already 

 given. It can be shown from these that the motion is 

 made up of two waves continually travelling along the tube 



