1892.] facilitating the Reduction of Tidal Observations. 357 



is insensible. It is required then to determine the correction to be 

 applied to gi 2 , 2 , and thence those for E, F, e, f . 



Suppose that, when time t is counted from O d O h of month T, the 

 M 2 tide is expressed by M cos [(30 /*)], where /3 = 1 0> 0158958. 



When means taken over 30 days are harmonically analysed the 

 formula (6) gives the contributions to J^ a J 2 . As it is now required 

 to obliterate these contributions, the signs must be changed, and the 

 corrections are 



sn ao- 



(15). 



For reasons which will appear below I now write 



= ^ (T) -0-5258. 

 Then introducing the value of /3 into (15), I find 



: OT ( T >+34-( 



' .. (16). 



sin 29 29' '52 



Let m denote the value of J T > at O d O h of month 0, and let 

 " OT ( T ) = m +& T \ and let Jf 8 denote a certain factor whose logarithm is 

 0-00849, and let M = f R m . 



In the harmonic analysis for the M 2 tide, considered below in 6, we 

 shall have 



A z = m COS %m, BZ = Sl n ? 



Accordingly 



sin ^ m ~ * 2 [_ 2 sin 2 cos 



These values of M C ? S t (T) must now be introduced into (] 



sin b 



the algebraic process need not be given in detail. If we write 



'43'-35?P S (44l'-32) 



* 



: 



tf 

 : 



sin2929'3l"-4 

 VOL. III. 2 B 



