314 



On the Equilibrium Theory of 7 ides. [Apr. 1, 



for the approximate centre of gravity of the portion, to find an 

 approximate value of the integral //cos 3 \cos 2Zcos Xdl over its surface. 



By drawing the assumed coast line on a map, it will become obvious 

 that such corrections may be applied for the following portions, 

 defined by the latitude and longitude of their centres of gravity; 

 remarking that when there is a portion of land which may be fairly 

 considered to compensate a portion of sea in the immediate neigh- 

 bourhood, no correction has been applied. For instance, it would be 

 seen that part of the Kamschatkan Peninsula is excluded from the 

 coast line, and part of the Sea of Okhotsk is included; but these 

 will produce nearly equal effects on the integrals in opposite direc- 

 tions, and are thus left out of consideration. 



Area in 

 square degrees. 



+ 160 



+ 240 



+ 166 



80 

 68 

 20 

 69 

 43 

 22 

 48 

 65 

 16 

 34 

 49 

 27 

 11 

 43 

 39 



Longitude. 



+ 172° 

 + 150 



85 

 60 

 85 

 75 

 55 

 34 



- 37 



- 47 



- 53 

 -107 

 -102 

 -114 

 -123 

 -118 

 -138 

 -173 



Latitude. 

 + 64° 



+ 71* 

 + 60 

 + 52 

 + 9 

 + 21 

 + 4 

 -11 

 -20 

 -19 

 + 18 

 + 13 

 + 2 

 + 1 

 + 12 

 - 5 

 +36 

 -42 



N.B. — Land-areas are considered positive, sea negative. 



We then find the following corrected values of the integrals : — 





1st hypothesis. 



2nd hypothesis. 





+ -02237 



+ 0-02247 





+ -00230 



+ 0-00231 



€ 



-0-01952 



-0-01961 



i 



+ 0-02665 



+ 0-02676 





-0-01775 



-0-02810 



Q 



0-279 



0-274 



