FROM A VIBRATING BODY TO A SURROUNDING GAS. 
455 
me— 0’5 further in the direction of high pitch than low pitch, namely, to three octaves 
higher and only one octave lower. 
When the sphere vibrates symmetrically about the centre, i. e. so that any two oppo- 
site points of the surface are at a given moment moving with equal velocities in oppo- 
site 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, mV=f, we have 
^= 2 +l,^=( 2 *-9 r */+(4-?y= 2 -2 + ?+|. 
q 3 — 2q* +9g + 81 
q\q+ 1) * 
The minimum value of I 2 is determined by 
£ 3 — 6£ 2 — 84£— 54=0, 
giving approximately 
£=12-859, mc= 3-586, ^=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 comparable 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 X=12‘5 inches. To represent 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 repre- 
sent it by a sphere of half the radius would still apparently be to underrate the effect. 
Nevertheless for the sake of rather underestimating than exaggerating the influence of 
the cause here investigated, I will make these two suppositions successively, giving 
respectively c=-98 and c=-49, mc=' 4926, and mc= -2463 for air. 
If it were not for lateral motion the intensity would vary from gas to gas in the pro- 
portion of the density into the velocity of propagation, and therefore as the pressure 
into the square root of the density under a standard pressure, if we take the factor de- 
pending on the development of heat as sensibly the same for the gases and gaseous mix- 
tures with which we have to deal. In the following Table the first column gives the 
mdccclxviii. 3 s 
