90 REPORT—1883. 
Initial Arguments. Factors for Reduction. 
Votu - 
sin w cos? $w cos! + 
(= 1) = Olea — 8) +o fin Tee 41 
ey sin w sin? dw cos* 37 
oe (herent: ASE) sin 1 sm? $1 
Q Arg. O—(s,—p,) . | Fac. O 
= ; oo sin 2w(1—$ sin? 7) 
J (he v)+(8,.—po) —4 sin 21 
MS Arg. M, Fac. M, 
2MS Arg. M, Fac. M, 
2SM 27—Are. M, Fac. M, 
MK Arg. M,+Arg. K, Fac. M, x Fac. K, 
2MK Arg. M,—Arg. Ki Fac. M, x Fac. K, 
MN ne M, ss N Fac. M, x Fac. N 
MSf 27—Arg. M, Fac. M, 
(1—3 sin? w) (1— sin aly 
Mm (8,—Po) [poe fib 
es sin? w cost 47 
Mf 2(s,—£) ee 7 
Sa h, unity 
Ssa 2h, unity 
There are two tables, numbered I. and II., given at pp. 304 and 305 
of the Report for 1876 of the Committee of the British Association on 
Tidal Observations. The columns headed « give functions which, when 
their signs are reversed, are the arguments at the epoch. To show the 
identity of these expressions with those in the above schedule [I], we 
must put 
f=—h., g=—Nes D=s.t¢v—~, O=h, w=p.tv—i, w=p). 
For the sake of symmetry these tables contain several entries which 
