26 MR. AIRY ON THE LAWS OF THE TIDES 



suits of one substitution in the four equations g, g', g", g'" (the numbers resulting 

 from the tidal observations being G, G', G", G'"), it was then necessary that 



^—^ ^_5! ^—91 



g-G' g-G' g-G' 



By search among the quotients of the substitution, numbers were found approaching 



G' 

 as near as possible to -q, &c. ; then, supposing w unaltered, the variations of the quo- 

 tients were found, which corresponded to changes of 1 in .r, ^ and z ; from these, by 

 solving three linear equations, the corrections to x, y and z were found ; and then a 

 common multiplier for w and x was found by comparing the result of each corrected 

 substitution with the tidal numbers G, G', &c. 



The other method was, to put the equations in the following form : 



M;X(A-l-C.y+D.^)+a^X(B+E.3/+F.2) = G. 



Between two of the equations, w and x were eliminated, and a complicated equation 

 between y and z remained ; another equation of the same character was obtained 

 from the other two of the original equations ; and these two equations were solved 

 by trials. 



By these methods (but principally by the former) the equations were solved for 

 a=0 and a= — 2'' for all the stations as far as Mullaghmore. Beyond that station 

 it was found totally impracticable to solve them. Values of w, .r, y, z were some- 

 times found which seemed nearly to satisfy the equations, but when an attempt was 

 made to correct these values, the corrections became absurdly large, and the cor- 

 rected values gave results much further from the truth than the original results. 

 And for those stations at which the operation was successful, there were special re- 



M 

 suits of inadmissible character. Thus, when a=0, -g was found =4-30 for Kilbaha, 



M 

 and =1-45 for Mullaghmore; when a=--2*', -y- was found =3*40 for Kilbaha and 



=0*82 for Mullaghmore. These discordances seemed to show that a must be posi- 

 tive; but in no case could a solution be obtained with a positive value for a. 



On examining carefully the numbers given by observation, I was led to the follow- 

 ing considerations, which seemed likely to throw considerable light on the subject. 



On inspecting the table in page 17, it will be evident that at the first stations, as 

 far as Old Head, the disappearance of diurnal tide at high water does not occur on 

 the same day as the disappearance of diurnal tide at low water ; the former always 

 occurring earlier than the latter. Biit at the stations from Glenarm to Dunmore 

 East, the disappearance of diurnal tide at high water sometimes precedes and some- 

 times follows that at low water; and may be said, roughly speaking, to occur on the 

 same day. This circumstance fixes absolutely the value of a. For, when the diur- 

 nal tide at high water and that at low water vanish at the same time, the inference is, 

 that at that time the lunar diurnal tide and the solar diurnal tide have equal values 



