1886.] Equilibrium Theory of Tides for the Continents. 309 



of the equator respectively between latitudes \ Y and \ 2 , the last of the 

 integrals becomes 



2 i (h + h) [ sin ^ + sin 3\J ^ 

 720-2(* 1 + * 2 ) ^sinxj** 



But for (e.g.) 



cos 2 \ cos 21 cos \d\dl 



=i_ £9 sin X + sin 3\j ^ £sin 2zJ 



the actual limits Z 2 and 7 1 must be given, and not merely their differ- 

 ence. 



It is, however, obvious, on inspection of these integrals, that the 

 land in high latitudes affects them but little ; and we shall not lose 

 much by neglecting entirely the Antarctic continent in their evalua- 

 tion. 



This evaluation is reduced by the above process to a series of multi- 

 plications, and on performing them the following values of gt, |p, C, J), 

 and Q are obtained on the two hypotheses. 



(1.) That there is as much Antarctic land as is given in the schedule, 

 which is, however, only taken into account in the last integral (£, and 

 the common denominator 4nrQ of each. 



(2.) That there is no land between S. latitude 80° and the pole. 



The value of Q is given in terms of the whole surface, and repre- 

 sents the fraction of that surface occupied by land ; it must be remem- 

 bered that the Mediterranean Sea is treated as land. Professor 

 Darwin quotes Bigaud's estimate* as 0"266 : — 





1st hypothesis. 



2nd hypothesis. 



& 



+ 0-03023 



+ 0-03008 



$ 



+ '00539 



+ 0-00537 



€ 



-0 '01975 



-0-01965 



§ 



+ 0-02910 



+ 0-02895 



€ 



-0-01520 



-0*00486 



Q 



283 



278 



These results for <g and Q have already been given by Professor 

 Darwin in " Thomson and Tait's Natural Philosophy," and 1 have 

 found them correct. 



* " Trans. Cam. Phil. Soc," vol. vi. 



