ON THE COASTS OP IRELAND. 27 



with opposite signs four times in their diurnal period. If then their phases at the 

 first of those four times be represented by (p and -v// respectively, and their coefficients 

 by f6 and p, we have 



/Asin<p+»'sin'4/=0, /"-sin ((p4-90°)4-j'sin (•4/+90°)=0, 



^sin(9+180°)+vsin(-4.+ 180°)=0, /M»sin (^4-270°)+i'sin (.|.+270°)=0. 

 The solution of these equations is either yi^^z—^y^ ^='4' ; or |a.=j', ^=i|/+ 180°. Con- 

 fining our expressions to the former (by which we lose nothing of generality), we 

 have this result ; that, upon that day, the solar diurnal tide and the lunar diurnal 

 tide are in the same phases at every part of the day. Observing then that a is the 

 angle which is to be added to the moon's hour-angle west, in order to give it the 

 same relation to the phase of lunar diurnal tide which the sun's hour-angle west has 

 to the phase of solar diurnal tide, it will be seen that a must be equal to the excess 

 of the moon's right ascension over the sun's right ascension (altered by 12*^ if neces- 

 sary) on the day on which the diurnal tide vanishes both at high and low water. 



In order to investigate the value of a with accuracy, the following process was 

 used : — If from the table in page 1 7 we form the numbers " day of evanescence at low 

 water — day of evanescence at high water," at Glenarm, or Donaghadee, &c., it will 

 be seen that the four numbers at the same station have values alternately greater and 

 less. This is owing, I conceive, to parallax, or some other cause which is periodical 

 in one revolution of the moon nearly ; and a correction is probably necessary, appli- 

 cable with opposite signs to the alternate values. Thus, comparing the second with 

 the mean of the first and third, half the difference is one value of the correction; 

 comparing the third with the mean of the second and fourth, half the difference is 

 another value of the correction ; and the mean of these may be used. Thus corrected 

 values of the " day of evanescence at low water -— day of evanescence at high water" 

 were obtained. Taking the means of the corresponding corrected values for the six 

 stations from Glenarm to Dunmore East, we have, 



A u * T 1 ^A A^ 4.U 1 • A.T« / and the excess of the moon's ") J*^ ." 



About July . 4-41, the mean value is 076, | j^^ ^^^^ ^^^ ^^^^ j^^ j^ j 20 46 



About July . 17*86, the mean value is 0*73 „ „ ,, 8 33 



About August 1*92, the mean value is 0*47 » ,•> j? 19 58 



About August 14*56, the mean value is 0*00 „ „ „ 7 \^ 



From the regularity of the progress of the numbers in the second and third columns, 

 it appears certain that the value 7^ 13"^ for a must be very near the truth. 



From the reasoning above it will appear that, in the case of simultaneous eva- 

 nescence of diurnal tide at high water and at low water, we have no means whatever 

 of ascertaining the values of joo and (p on that day. Or, if we take the expressions on 

 page 22, we have for diurnal tide at high water, 



a.sin/3.sin{ <l — O -|-A }-[-&. sin { ([ — O+B}, 

 and at low water, 



a.cosj3.sin{ d — 0+A}-f&.cos{ ff — G+B}; 



E 2 



