80 rEPORT—1883. 
It might perhaps be advisable to proceed still further and to purify 
K of the coefficient a (2) and of the function of the latitude, viz. 
cos?\, sin 2\, }—3sin?A, as the case may be. Then we should simply 
be left with a numerical factor as a residuum, which would represent the 
augmentation above or diminution below the equilibrium value of the 
tide. This further reduction may, however, be left out of consideration 
for the present, since it is superfluous for the proper presentation of the 
results of harmonic analysis. 
For the purpose of using the tide-predicting machine the process of 
determining H and « from R and ¢ has simply to be reversed, with the 
difference that the instant of time to which the argument is to refer is 0" 
of the first day of the new year, and we must take note of the different 
value of uw and f for the new year. Thus supposing V, to be the value of 
V at 0” of the first day of the year to which the predictions are to apply, 
and 1, f;, the values of uw and f half a year after that 0", we have 
S=c— (V+) 
This value of R will give the proper throw of the crank of the tide- 
predicter, and Z will give the angle at which the crank is to be set. Mr. 
Roberts states, however, that the subtraction, in the predicter of the 
India Office, of V,+, from « is actually performed on the machine, one 
index being set at « and the other at Vj +. 
We learn also from him that one portion of the term w, has been 
systematically neglected up to the present time: namely, that part which 
arises in the form v—é or its multiples. If in the schedules above we 
were to write £=» throughout we should arrive at the rule by which the 
tide-predicter has hitherto been used. 
The above statement of procedure is applicable to nearly all the tides, 
but there are certain tides, viz. K,, Ky, which have their origins jointly 
in the tide-generating forces of the moon and sun; also the tides L and 
M, which are rendered complex from the fact that the tidal analysis only 
extends over a year. 
Treatment of the Sidereal Diurnal and Semi-diurnal Tides K,, Ky.— 
The expression for the whole K, tide of luni-solar origin must, as we 
see from the schedules B and C, § 3, be of the form 
M cos (¢+4—}x7—v—k)+8 cos (t+h—37—k) ie 3). 
If now we put 
S Ss 
2—M DB NAO SE Hause 
R 1+ (a) + M cos V} | 
tan ye ae | G. 
~ cos y+ S/M } 
these two terms may be written 
R cos (¢+-h—} w—v'—«). 
If h, be the sun’s mean longitude at 0 of the first day, t+h—h, is 
equal to yt, where ¢ is now mean solar time measured from that 6» and 
not reduced to angle. 
Hence if we write 
factho—hty . . . . ee 
