24 MR. AIRY ON THE LAWS OF THE TIDES 



8\nJyi.cosh.w-^smJ}i.smh.x+sindi.cosh---t-\-oi.wj/-{-s\ndi.s'mh — t-^o6.a:if 

 •^smd^.cosh^t-\-oc.wz-\-s\n d2.smh—t-\-K.xz. 



It is to be remarked that, when w, x, y, and z, are ascertained (with an assumed 

 value of a), the following more intelligible results will be extracted from them : — 



S=-y/wJ2ljr^= solar coefficient of the sine of the sun's declination, for solar diurnal 

 tide. 



*=the angle determined by the equation tan5= — ; it is the constant angle which 

 is to be subtracted from the sun's hour-angle west at the time of observation, in order 

 to give the angle on whose cosine depends the height of solar diurnal tide at the 

 instant of observation. 



Then, the lunar diurnal tide 



= (/? . sin ^1+5 . sin d.^ cos A — ^— *4-a=S.(y.sin c^j-fa.sin fl?3).cos A— /—a- -fa ; 

 and, {putting / for the moon's longitude measured from the intersection of its orbit 

 with the equator, I for the sine of its inclination, and ^ for the mean daily increase 

 of longitude from transit to transit =13° 38'}, y.^\VLd^-\-%.^\x\dy=^\{y.^\\\.l^-\-z.'&\xil^) 



— 2^- sin /3+sin l^-\—~'^\xv /j— sin /^y = I(^+v.cos ^.sin 4+^— y.sin S.cos 4) ; or, 



if tan;7=— — tanS, this quantity becomes =I.2-f-3/.cos^.sec;7.sin /2H-'? ; or, making 



)j=w.^, it becomes =I.;z+3/.cosS.sec;7.sin /2+«=^+3/-cos^.sec?;.sinfl?2+«: and therefore 

 the lunar diurnal tide =S.%+?/.co8^.sec;j.sin«/2+n-(^os A — / — *+«• 

 M Effect of moon for eiven declination 



S — Effect of sun for same declination ~ ^ +^- ^^^ ° " ^^^ ^' 



M=S.2+i/.cos^.sec>7= lunar coefficient of the sine of the moon's declination on a 

 certain anterior day, for lunar diurnal tide. 



2+w= the time, in lunar days, earlier than the moon s Greenwich transit next 

 preceding, for which the moon's declination is to be taken as governing the diurnal 

 tide. This is correct for the time of high water, first division, and requires an altera- 

 tion for other times, n is =,-^^^^-7; and tan;j=— -^-tan 13° 38'. 



13 38' ' ' z-'ry 



s—a,— the constant angle which is to be subtracted from the moon's hour-angle, 

 in the same manner as s from the sun's hour-angle. 



The factors of the unknown terms w, x, wy, wz, xy, and xz, in the algebraical ex- 

 pression for the elevation produced by diurnal tide, were computed for high water 

 and low water, first division, at Kilbaha, for every day throughout the observations. 

 These computations would apply equally to the other stations, it being understood 

 that certain constants (which the reader will easily investigate) depending on the 

 longitude of the station and the time occupied by the passage of semidiurnal tide, 

 are to be applied to the angles a and s. The hour-angles used for the moon were 

 found by comparing the moon's time of transit at Greenwich with the time of Kil- 



