[22] See Professor W. F. Barrett, Nature, 1877, vol. 16, p. 12.
[23] This follows from the ordinary formula for the focal length f of a biconvex lens, each surface having a radius of curvature equal to r. For then it can be shown that
f = r/2 · 1/μ – 1
where μ is the index of refracture of the lens material. As shown later on, the acoustic index of refraction of carbonic acid, when that of air is taken as unity, is 1·273. Hence, μ – 1 = 0·273, and 1/μ – 1 = 3₂/³. Hence, f = 2r ₁₁/¹², or f is slightly less than twice the radius of curvature of the spherical segment forming the sound-lens.
[24] We can, in fact, discover the ratio of the velocities from the amount of bending the ray experiences and the angle BAC of the prism, called its refracting angle. It can be shown that if we denote this refracting angle by the letter A, and the deflection or total bending of the ray by the letter D, then the ratio of the velocity of the wave in air to its velocity in carbonic acid gas (called the acoustic refractive index), being denoted by the Greek letter μ; we have—
μ = sin ( A + D/2 ) / sin ( A/2 )
[25] On the occasion when this lecture was given at the Royal Institution, a large phonograph, kindly lent by the Edison-Bell Phonograph Company, Ltd., of Charing Cross Road, London, was employed to reproduce a short address on Natural History to the young people present which had been spoken to the instrument ten days previously by Lord Avebury, at the request of the author. The address was heard perfectly by the five or six hundred persons comprising the audience.
[26] In the case of the paraffin prism the refracting angle (i) was 60°, and the deviation of the ray (d) was 50°. Hence, by the known optical formula for the index of refraction (r), we have—
r = sin i + d/2 / sin i/2 = sin 55°/sin 30° = 1·64
For the ice prism the refracting angle was 50°, and the deviation 50°; accordingly for ice we have—