404 Intelligence and Miscellaneous Articles. 



rical envelope ; and it is observed (p. 238) that a similar treatment 

 will apply to the vibrations of air between two concentric spherical 

 envelopes ; but when the difference between the radii is very small 

 in comparison with either, the problem reduces itself to that of a 

 spherical sheet of air. The case in which the velocity-potential \p 

 is symmetrical with reference to the poles, is treated first ; and it is 

 shown that it can be represented by a series w r hose general term is 



P.04 ( A„ cos ^M^±} ) + B„ siu <">/"("+ 1) ) , 

 L c c J 



where n is an integer even or odd, and P.„(/*) Legendre's function. 

 If now t=(), \l is an arbitrary function of the latitude, and we see 

 ti»t ^A +A 1 V 1 (^i-. . . + A n P n ( i u) + . . . 



This is, of course, only a particular case of Laplace's Series. But 

 by similar reasoning on the general value of \p Laplace's Series is 

 established. At each step of the process the case is considered in 

 which the radius of the sphere becomes infinite, and we pass physi- 

 cally to the case of a plane layer and analytically from Laplace's 

 to Bessel's functions. " The vibrations of a plane layer of gas are 

 of course more easily dealt with than those of a layer of finite cur- 

 vature ; but I have preferred to exhibit the indirect as well as the 

 direct method of investigation, both for the sake of the spherical 

 problem itself with the corresponding Laplace's expansion, and 

 because the connexion between Bessel's and Laplace's functions 

 appears not to be generally understood " (p. 265, vol. ii.). 



This discussion is, as we have already remarked, of purely ma- 

 thematical interest ; and, indeed, from the nature of the case, by far 

 the largest part of the work is addressed to mathematicians. Here 

 and there, however, are discussions of which the interest is purely 

 physical, such as, in the present volume, that on Whispering Gal- 

 leries (p. 115), that on the Eefraction of Sound by Wind (p. 123), 

 and others. But our limits will not allow us to do more than 

 mention their existence. 



LXI. Intelligence and Miscellaneous Articles. 



A FEW MAGNETIC ELEMENTS FOR NORTHERN INDIA. 

 BY R. S. BROUGH. 



XTAVING recently had occasion to measure the dip of the needle 

 and the strength of the horizontal component of the earth's 

 magnetic force at Calcutta, Jubbulpore and Allahabad, with a view to 

 ascertaining to what extent the indications of an arbitrarily cali- 

 brated galvanoscope uncorrected for the local value of the earth's 

 magnetism, would be trustworthy, I think it desirable to put the 

 results on record. 



The horizontal intensity was measured with a Kew-pattem port- 

 able unifilar masrnetOmeter: and the observations have been corrected 



for temperature, torsion and scale error. 



