82 REPORT—1883. 
the argument of the K, tide is 2¢+2h—2y”, and f is the factor for 
reduction. 
The numerical value of = both for K, and K, is *46407. 
It appears that in using the tide-predicter Mr. Roberts has been 
hitherto using a process which is obviously incorrect, although the incor- 
rectness has probably only led to very small errors. He has divided the 
R of the K, tide into two parts proportional to the O and P tides 
respectively, as deduced for the same year by the harmonic analysis for 
those tides. This process is incorrect in one respect, and not absolutely 
satisfactory in another. It is incorrect, because}it is equivalent to the 
treatment of v as zero in the formula 
R?=M?+8?+2MS cos 1; 
and it is unsatisfactory, because the theoretical ratio of O to P is 
> (1—e?) sin J cos? 47 
7, (1—Ze,”) sin w cos? 4’ 
whereas the ratio of the lunar to the solar K,‘is 
7 (1+ $e?) sin 2I 
7, (1+2e,?) sin 2u 
Again, he has divided R of K, into two parts proportional to the 
M, and §, tides. This is again incorrect. The incorrectness arises from 
a similar treatment of v as zero, and because the ratio of M, to 8, is 
7 (1—$e*) cost 52 
7, (L—$e,?) cost Sw’ 
whereas the ratio of the lunar to the solar K, is 
+ (1+ 3e?) sin? TF 
7,(1+e?) sin? w 
Moreover, the S, tide is probably liable to meteorological disturbance. 
The Tide L. 
Reference to the theoretical development in § 3 shows that this tide 
requires special treatinent. 
In schedule B (i.) it appears that it must be proportional to 
cos! 3IV 1—12tan? 4! vos 2(p—é) 
x cos [2/+2(h—v)—2(s—£)+(s—p)-R+7] . (51) 
where 
sin 2 ae 
tin in 2 (p—é) 
x cot? 4 J—.cos 2 (p—é) 
In this expression we must deem F to form a part of the function 2, 
for which a mean value is to be taken. This is, it must be admitted, not 
very satisfactory, since p increases by nearly 41° per annum. ’ 
