92
ON SOUND.
And the equation of Article 37 becomes,
1 d2R_d2R [ 2 dR
dl ’ dt dr2, r‘ dr
This equation can be completely integrated by the
process of Article 43. Making m — 2, n — — 1, and as¬
suming the solution to be
CL. r'1 + CL. r~'2 + G_ 3. r"3 + &c.,
we find C_2 and all succeeding coefficients = 0 ; and the
G
value of E is simply —, where G is a function of u
and v.
As in Article 45, the velocity of a particle in the
direction of the radius vector = ; and if the wave be
dr
a divergent wave, G is a function of v only, or of at — r ;
dG _dC dv _ dG _ q, '
dr dv * dr dv ’
and the velocity of a particle, or
dR
dr
Integrating this quantity with regard to t, and making