NEWTON S PRIX ci PI A. 277 



friction is found to consist partly in a diminution of the 

 velocity of propagation, and partly in a more rapid dimi 

 nution of the intensity than would correspond to the 

 increase of distance from the centre of divergence. The 

 diminution of velocity is found on calculation to be so 

 small, that it is less than one foot in 1,578,000 miles. The 

 change of intensity, though not so utterly insignificant 

 as the change of velocity, is found to be still insensible. 

 Such small differences as these may be altogether neglected. 

 It is well known that sound does not always travel in 

 a rectilinear direction. &quot; Sounds,&quot; Newton remarks, 

 &quot; may be heard though a mountain be interposed ; and if 

 they come into a chamber through the window, dilate 

 themselves into all parts of the room, and are heard in 

 every corner, not as reflected from the opposite walls, but. 

 as directly propagated from the window, as for as our 

 senses can judge.&quot; Let us imagine a series of waves to 

 be advancing directly through an orifice, and let the aper 

 ture be divided into small elements. Each element may 

 be considered as the origin of a series of disturbances. The 

 disturbance in any part of the room will be made up of 

 those propagated from all the several elements. Now, the 

 motions being all small, it is a well known principle that 

 the actual disturbance will be the sum of all those that 

 would have been propagated from each separate element 

 on the supposition that there was no other motion at the 

 same time in the medium. Each separate disturbance may 

 be calculated by the known rules according to which any 

 motion spreads itself on all sides. The actual disturbance, 

 on which the sound depends, will be represented by a 

 definite integral. It is needless to go through the work, 

 but the result is, that, provided the length of a wave be 

 not very small compared with the orifice and this is the 

 case in sound, and the waves on the surface of water the 



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