Notices respecting New Books. 67 



satisfied with any one of them. It may therefore be of some in- 

 terest to give a sketch of the proof adopted by Mr. Ferrers. The 

 principal discussion takes place with reference to Zonal Harmonics, 

 though a proof of the general case is given on pp. 93-95. The 

 method, then, is as follows : — Hejirst obtains an expression for the 

 potential of a spherical shell of uniform small thickness, whose 

 density is A for the part corresponding to the value of jj. from 1 to 

 X, and B for the part corresponding to the value of /j. from X to — 1. 

 He then extends the same method to the case in which the densities 

 are A from /jl=1 to /u=X 1 , B from ;u=X 1 to /x=X 2 , and C from 

 /i=X 2 to fx= — 1. His next step is to take X^X and \ 2 =\-\-d\, 

 and thus arrives at the result that 



i dx{1+ . . . +(2t + l)P i (X)P i 0O+ . . . } 

 has the value unity from /jl = \ to /i = X + c?X, and zero for other 

 values of p. jSTowif we suppose X 15 X 2 , . . . to be continuous values 

 of X ranging from 1 to —1, it is evident that the expression 



£tf\./(A 1 ){l+ ...+(»+WiW+ •■•} + 

 i d\ /(X 2 ) { 1 + . . . + (2i + l)P i (X 2 )P l < / .) +...}+... 



will equal /(X x ) when^u=X 1 , /(X 2 ) when /z=X 2 . . . ; and consequently 

 the whole expression must be /(/*). But it is also plain that 



{/(\)^(^)+/(X 2 )P,(X 2 )+ . . . + }dX=(j( f ,)V i ( f ,)d^, 



and consequently that f(fj) can be expressed as a series whose 

 general term is 



the theorem to be proved. 



Instructions to Meteorological Observers in India, being the First 

 Part of the Indian Meteorologist's Yade Mccum. By Henry F. 

 Blaneord, Meteorological Reporter to the Government of India. 

 Calcutta, 1876. 

 Meteorology of India, being the Second Part of the Indian Meteoro- 

 logist's Vade Mecum. By Henry F. Blaneord. Calcutta, 

 1877. 

 Tables for the Reduction of Meteorological Observations in India. By 

 Henry F. Blaneord. Calcutta, 1876. 



The works above mentioned constitute a complete Meteorological 

 Library, and, although written expressly for India, are by no means 

 restricted in interest to the Indian Peninsula, as they contain re- 

 marks of general application, especially relative to the instruments 

 employed in Meteorological research. In the " Instructions " each 

 instrument, including its varieties, is fully described ; and the reader 

 will find many valuable hints on the use of the Barometer, Ther- 

 mometer, Actinometer, Hygrometer, Bain-gauge, Wind-vane, and 

 Anemometer ; also interesting articles on Cloud and Weather obser- 



F2 



