ANALYSIS TO THE DYNAMICAL THEORY OP THE TIDES. 177 



Butif CftP^OOe*"** denote the height of the 'equilibrium' tide resulting from 

 a disturbing potential ylP*,, (/u.)e ;(A1+8 * ) , we have 



Therefore 



Li - KJ " Li - K* l 



and on introducing the numerical values for h, y 2 , 14 K we obtain 



q= - 1-9476 @f. 

 Thus we have : 



log (C;/;) = n 0-32760 log (CV5) = 1'9646 



log(C/i) = T'91025 log(C?4/i)= 5-6560 



log (d/<B%) = u T-13442 log (Cie/CEl) = )'- 6-228 ; 

 log (C? /@?) = 2-1346 



and therefore if we suppose the exponential or trigonometrical factor to be involved 

 in (JCH, so that the height of the equilibrium tide is expressed by CToP? (^), the height 

 of the corresponding dynamical tide is given by 



= 5 [- 1-9476 P; - 2'12617 Pj + 0'81331 PS 013628 Pj 



+ 0-01363 P? 0-000922 Pf, + 0'000045 Pf, - 0'000002 PI, ; + ...] 



For points lying on the equator we have p = 0, and it may be shown that in this 

 case 



ps .-/ v .,|3-5---(^+l) 



~ ( ~> 2.4... (2ft -2)' 

 whence we deduce 



log P| = 0-47712 log PI O = 1 -4325 



log PI = n 0-87500 log P; 3 = n 1'5464 



log P^ = 1-11810 log P? 4 = 1-643 



log PI = n 1-2941'J log P? 6 = n 1-73. 



Thus the values of the successive terms of the series within the square brackets 

 for points at the equator are 



- 5-8428 + 15-9463 + 10'6746 + 2'6829 + 0'3690 + 0'0324 + 0'0020 + O'OOOl, 



which, on addition, give 23'8645. But the height of the corresponding equilibrium- 

 VOL. cxci. A. 2 A 



