1886.] Equilibrium Theory of Tides for the Continents. 313 

 Evaluating these integrals on this supposition, we obtain 





1st hypothesis. 



2nd hypothesis. 



% 



+ 0-02119 



+ 0-02110 



i 



+ 0-00778 



+ 0-00775 



€ 



-0 01 890 



-0-01882 



s 



+ '03159 



+ 0-03128 



« 



-0 -04364 



-0*03319 



Q 



0-283 



0-278 



It will be noticed that the values of Q are exactly the same as 

 before. 



From these we deduce 



Nature of tide. 





1st hypothesis. 



2nd hypothesis. 





lat. X 



33° 29' N. 



33° 55' IS". 





lat. X 1 

 long. l Y 



1° 3'S. 

 59 7 E. 



1° 3'S. 

 58 58 E. 





lat. X 2 

 long. l 2 



81° 22' N. 

 10 5 W. 



81° 23' jS\ 

 10 5 W. 



The agreement of these values of the quantities with the values 

 calculated on the previous supposition is not quite so close as I anti- 

 cipated, but it should be remarked that the numerators of the quan- 

 tities ^, C, J, € are the differences of positive and negative 

 quantities of very much greater magnitude, as becomes obvious on 

 proceeding to the numerical calculation ; and thus a comparatively 

 small change in one of the large compensating quantities, due to large 

 tracts of land in different portions of the globe, affects the integrals 



a considerable extent. 



In this connexion I was led to investigate the effect of counting 

 various small islands and promontories as sea, or small bays and 

 straits as land. For instance, a portion of sea in the neighbour- 

 hood of Behring's Straits is included as land, and a corresponding 

 correction must be applied to the integrals. This correction I 

 have estimated as follows : — The area of the sea is estimated in 

 square degrees, by drawing lines on a large map corresponding to 

 each degree of latitude and longitude and counting the squares 

 covered by sea, fractions of a square to one decimal place being in- 

 cluded, though the tenths have been neglected in the concluded sum. 

 This area has then been multiplied by the value of (say) cos 3 X cos 21 



