Changes in the Sea-level. 207 



and leaving out the constant term, we get for the last part of 

 our integral 



-^{« 2 Q 2 4« 3 Q 3 +&c.}. . . . (C) 



And finally, adding (A), (B), and (C) together, observing 

 hat the coefficients of ^[a 2 Q 2 + « 3 Q 3 + &c.J- in (B) and in (C) 



together make up the whole mass of the earth (or — ^- — ) 

 divided by a, equating to zero, and transposing, we get 



^^{* 2 Q 2 + a 3 Q 3 + &c. + a„Q ;; + &c4 



_ 47 r^{^ + ^ 3 +&c.+ ^ 1 +&c.} L(D) 



= ^ 2 {a 2 Q 2 + A 3 Q 3 ^&c. + A w Q^~+&c.}, J 



whence we may successively determine a 2 , u 3> & c -> an ^ obtain 

 the amount of disturbance, 



r — a=fl{a 2 Q 2 + « 3 Q 8 -f &C.J-. 



T 



In the physical problem before us - is so nearly equal to 1, 

 that we must take many hundreds of terms before — would sen- 

 sibly differ from 1 ; and in the meanwhile, Q w being never 

 greater than 1 and converging slowly*, while A w diminishes 

 pretty rapidly, the terms would have become exceedingly small. 



T 



We may therefore write 1 for -, and a for r; and then we get for 



s 



the general term, 



fP l \ Pa 



aci «U-2n-riJ=2 An ' 



I have had calculated for me the first fifty values of A n for a 

 cap of ice extending to N.P.D. 30°, and the values of Q n and of 

 the product A n Q n corresponding to the disturbance at N.P.D. 

 35°, or about that of the north of England. For the divisor 



£ — - I have then taken /o = 6, which I presume to be under 



o <Ln -\~ JL 



the probable value, so as to make the calculation of the disturbance 



if anything too large; and, with the same object, I have used 



* See Murphy, as above. 



