306 Prof. G. H. Darwin. On the Correction to the [Apr. 1, 



Many or all of these points may fall on continents, so that the 

 evanescence or donbling may only apply to the algebraical expres- 

 sions, which are, nnlike the sea, continnons over the whole globe. 

 But now let us consider more precisely what the points are. 



It is obvious that the latitude and longitude X 2 an( i h> being 

 derived from expressions for cos 2 X 2 cos2Z 2 and cos 2 X 2 sin 2Z 2 , really 

 correspond with four points whose latitudes and longitudes are — 



\\ — \i h> ^2> ^2 + 180°; — X 2 , Z 2 +180°. 



Thus there are four points of evanescent semi-diurnal tide, situated 

 on a single great circle or meridian, in equal latitudes N". and S., and 

 antipodal two and two. Corresponding to these four, there are four 

 points of doubled semi-diurnal tide, whose latitudes and longitudes 



are — 



X 2 , Z 2 + 90°; -X 2 , Z 2 + 90°; \ 2 , Z 2 + 270°; X 2 , Z 2 + 270°, 



and these also are on a single great circle or meridian, at right angles 

 to the former great circle, and are in the same latitudes N". and S. as 

 are the places of evanescence, and are antipodal two and two. 



Passing now to the case of the diurnal tide we see that X p Z 1? 

 being derived from expressions for sin 2\ 2 cos l x and sin 2\ 1 sin Z x , really 

 correspond with four points whose latitudes and longitudes are — 



X l5 Z l5 Zi + 180 ; 90°-X i , Z i; -90° + ^, Zi + 180 . 



Thus there are four points of evanescent diurnal tide, situated on a 

 single great circle or meridian, two of them are in one quadrant in 

 complemental latitudes, and antipodal to them are the two others. 

 Corresponding to these four there are four points of doubled diurnal 

 tide lying in the same great circle or meridian, and situated similarly 

 with regard to the S. pole as are the points of evanescence with regard 

 to the N. pole ; their latitudes and longitudes are — 



-\ l5 l x ; X 1? Zi + 180 ; -90°+^, 90°-X 1 , Zi + 180 . 



Lastly, in the case of the long period tide, it is obvious that the 

 latitude X is either N. or S., and that there are two parallels of lati- 

 tude of evanescent tide. In case sin 2 X is less than § , or X less than 

 54° 44', there are two parallels of latitude of doubled tide of long 

 period in latitude f arc sin sin 2 \ }. 



From a consideration of the integrals, it appears that as the con- 

 tinents diminish towards vanishing, the four points of evanescent 

 and the four points of doubled semi-diurnal tide close in to the pole, 

 two of each going to the 1ST. pole, and two going to the S. pole ; also 

 one of the points of evanescent and one of doubled diurnal tide go 

 to the N. pole, a second pair of points of evanescence and of doubling 

 go to the S. pole, a third pair of points of evanescence and of 



