100 Lord Rayleigh : Further Applications of BesseVs 



determinations was 15 times as long as that used by 

 Mr. Tucker. 



Most of the determinations were made with solutions 

 made up from ' ; pure fused " calcium chloride, but determi- 

 nations made with solutions made up from " pure crystals " 

 gave identical results. The densities recorded in Table II. 

 were made from the latter solutions. In the same table are 

 recorded the values of the densities obtained by previous 

 observers. 



In conclusion, I should like to express my obligation to 

 Prof. Porter for his kindness in guiding and encouraging 

 me throughout this work. 



IX. Further Applications of BesseVs Functions of high order 

 to the Whispering Gallery and allied Problems, By 

 Lord Rayleigh, O.M., F.B.S* 



IN the problem of the Whispering Gallery t waves in two 

 dimensions, of length small in comparison with the 

 circumference, were shown to run round the concave side 

 of a wall with but little tendency to spread themselves in- 

 wards. The wall was supposed to be perfectly reflecting for 

 all kinds of waves. But the question presents itself whether 

 the sensibly perfect reflexion postulated may not be attained 

 on the principle of so-called " total reflexion," the wall 

 being merely the transition between two uniform media of 

 which the outer is the less refracting. It is not to be 

 expected that absolutely no energy should penetrate and 

 ultimately escape to an infinite distance. The analogy is 

 rather with the problem treated by Stokes J of the commu- 

 nication of vibrations from a vibrating solid, such as a bell 

 or wire, to a surrounding gas, when the wave-length in the 

 gas is somewhat large compared with the dimensions of the 

 vibrating segments. The energy radiated to a distance 

 may then be extremely small, though not mathematically 

 evanescent. 



* Communicated by the Author. 



t Phil. Mag. vol. xx. p. 1001 (1910) ; Scientific Papers, v. p. 619. 

 But the numbers there given require some correction owing to a slip in 

 Nicholson's paper from which they were derived, as was first pointed 

 out to me by Prof. Macdonald. Nicholson's table should be interpreted 

 as relating to the values, not of 2*1123 (n—z)/z^ } but of 1*3447 (n— z)/zb, 

 see Nicholson, Phil. Mag. xxv. p. 200 (1913). Accordingly, in my 

 equation (5) 1*1814^3 should read l'8558«i, and in equation (8) 

 51342 ni should read '8065 w*. 



% Phil. Trans. 1868. See < Theory of Sound,' § 324. 



