

SIMPLE-HARMONIC WAVES. DIFFRACTION 239 



now vary inversely as the square of the wave-velocity. Again, 

 the emission of energy is, by 77 (17), 



W = lirpkWcA* = lirpnW/c?.A*, (4) 



and so varies (for the same gas) as the fourth power of the 

 frequency. The emission in different gases will (for the same 

 frequency) vary inversely as the fifth power of the wave- 

 velocity, if we assume ( 59) that the latter varies inversely as 

 the square root of the density. For instance it will be about 

 1000 times less in hydrogen than in oxygen. 



In order further to illustrate the effect of the lateral motion 

 of the gas, near the surface of the sphere, from the hemisphere 

 which is at the moment moving outwards to that which is 

 moving inwards, in weakening the intensity of the waves 

 propagated to a distance, we may calculate what the emission 

 would be if this lateral motion were prevented. For this 

 purpose we may (after Stokes) imagine a large number of fixed 

 partitions to extend radially outwards from near the surface. 

 In any one of the narrow conical tubes thus formed, the motion 

 will be of the same character as in the case of symmetrical 

 spherical waves. Now a uniform radial velocity C cos nt over 

 the surface of a sphere would be equivalent to a simple source 

 4-Tra 2 C cos nt, and the corresponding emission per unit area 

 would be %tfa?pc C*, by 76 (15). If we now put G= A cos 6, 

 and integrate over the surface, we get the total emission in our 

 system of conical tubes. The result is 



W ' = 1-rrlcWpcA*, (5) 



since the average of cos 2 6 for all directions in space is J . If 

 we compare this with (4), we see that the effect of the lateral 

 motion is to diminish the emission in the ratio J& 2 a 2 . 



When, as for example in the case of a plate or a bell, the 

 surface is divided by nodal lines into a number of compart- 

 ments vibrating in opposite phases, the opportunity of lateral 

 motion is increased, and the emission of energy correspondingly 

 weakened. For facility of calculation Stokes took the case of 

 a spherical surface, with various symmetrical arrangements of 

 nodal lines. In the problem of the oscillating sphere we have 

 one such line, viz. the great circle 6 = \ TT, and the emission, as 



