from a Vibrating Body to a surrounding Gas. 411 



moment moving with equal velocities in opposite directions, or 

 (more generally) when the mode of vibration is such that there is 

 no change of position of the centre of gravity of the volume, 

 there is no term of the order 1. For a sphere vibrating in the 

 manner of a bell the principal vibration is that expressed by a 

 term of the order 2, to which I shall now more particularly 

 attend. 



Putting, for shortness, m 2 c 2 = q } we have 



T _ g 3 -2g a + 9 g + 81 



2_ ? % + l) 

 The minimum value of I 2 is determined by 



2 3 -62 2 -842-54 = 0, 



giving approximately 



2=12-859, mc=3-586, /*J = 13-859, ^ = 12-049, 



I 2 ±=-86941; 



so that the utmost increase of sound produced by lateral motion 

 amounts to about 15 per cent. 



I come now more particularly to Leslie's experiments. Nothing- 

 is stated as to the form, size, or pitch of his bell ; and even if 

 these had been accurately described, there would have been a 

 good deal of guesswork in fixing on the size of the sphere which 

 should be considered the best representative of the bell. Hence 

 all we can do is to choose such values for m and c as are compa- 

 rable with the probable conditions of the experiment. 



I possess a bell, belonging to an old bell-in-air apparatus, 

 which may probably be somewhat similar to that used by Leslie. 

 It is nearly hemispherical, the diameter is 1'96 inch, and the 

 pitch an octave above the middle C of a piano. Taking the 

 number of vibrations 1056 per second, and the velocity of sound 

 in air 1100 feet per second, we have \= 12*5 inches. To repre- 

 sent the bell by a sphere of the same radius would be very greatly 

 to underrate the influence of local circulation, since near the 

 mouth the gas has but a little way to get round from the outside 

 to the inside, or the reverse. To represent it by a sphere of half 

 the radius would still apparently be to underrate the effect. 

 Nevertheless for the sake of rather underestimating than exag- 

 gerating the influence of the cause here investigated, I will make 

 these two suppositions successively, giving respectively c='98 

 and c='49, mc = *4926 and wc=-2463 for air. 



If it were not for lateral motion the intensity would vary 

 from gas to gas in the proportion of the density into the velocity 



