Notices respecting New Books. 379 



This expression simplifies, and may be written 

 m(a — 0) sin m6' 



C sin 



Jo." 



m\ ma 



J m (kr')U m (kr)dm, ( a > # > #/); 



and as there is now no pole at the origin in the m-plane, we 

 may take the path (C) instead of ((7). 



Hence we obtain our solution in the form of an infinite 

 series, by the use of Cauchy's residue theorem, this solution 

 being given, for all values of 6 in the space 0<6<a, by'the 

 equations 



u= 47r Z sin— sin— & IW#r) J™(kr% r>r f . . (1) 



a a a ~ ~ 



u=— 2 sin— Ofw™&U**{krt J«r(*r), r<V. . (2) 



a. oc a a a 7 



This result agrees with that given by Macdonald*, and 

 may be compared with the solution of the same equation in 

 the w-fold Riemann's space, given by Sommerfeldf. 



This method may be extended to the corresponding three- 

 dimensional problem, and it can also be employed in the 

 cases where the diffraction is caused by a Sphere or Circular 

 Cylinder. Several interesting results in these cases have 

 been already obtained by me, and I hope to publish a full 

 discussion of these problems at a later date. 



Glasgow. January 1903. 



XXXVI. Notices respecting New Books. 



The Meteorology of tlie Ben Nevis Observatories. Part II. Containing 

 the Observations for the Years 1888 . . . 1892, ivith Appendices. 

 Edited by Alexander Bitch an, LL.D., F.R.S., and Eobeet 

 Traill Omond ; forming Volume XLII. of the Transactions of 

 the Eoyal Society of Edinburgh. 1902. Pp. xiv+552. 



A PREVIOUS volume (vol. xxxiv.) of the Edinburgh ' Transac- 

 ■£*- tions ' gave particulars of the earlier meteorological observa- 

 tions taken on the summit of Ben Nevis and at its base, at the 

 Public School, Fort William, from December 1883 to the end 

 of 1887. The present volume brings down the complete obser- 

 vational record to the end of 1892. During the final years of 

 this period the Port William data are from the Observatory 

 opened there in July 1890, which possesses a superior set of 

 self-recording instruments. 



* Loc. cit. p. 190. f Loc. cit. p. 356 (13). 



