TIDAL OBSERVATIONS. 505 
Almanac Office. It is to be hoped that arrangements may be made to 
allow him to give his whole time to a continuance of the work during 
the ensuing year, with assistant calculators working by aid of printed tables 
according to methods which by the experience now gained may be put into 
the form of convenient practical rules. Thus, while Mr. Roberts may work 
out proper methods for short or irregular series of observations, others may 
be employed to deduce results from tide-gauge diagrams of other British 
ports, and from the admirable series of recorded heights (every quarter hour) 
for Brest and other French ports which have been shown to me in the 
Hydrographic Office in Paris through the kindness of MM. Liouville and 
Delaunay, and Admiral Paris, and which may be had, it is hoped, on 
application by the Committee. 
[Conclusion of Report up to Aug. 19, 1868.] 
Supplementary Report by Mr, Rozerts. 
28. In the determination of the lunar monthly and solar annual (elliptic) 
tides, the lunar fortnightly and solar semiannual (declinational) tides alluded 
to above (§$ 25), and the luni-solar fortnightly shallow-water (synodic) tide 
(§ 24), let h be the height above the mean of the solar daily averages purified 
of lunar-diurnal and semidiurnal influence, then 
h=+A cos ot +B sin ot 
+C cos 2ot +D sin 2ot 
+C’ cos 2(o—n)¢ +D’sin 2(o—n)¢ 
+E cos nt +F sin n¢ 
+G cos 2nt +H sin 2n¢ 
Multiplying the value of h for each day by the respective values of cos ct, 
sin ot, cos 2at, sin 2ot, &c., calculated from 1864, Jan. 8'11"30™ as era of 
reckoning, for which <=0, and adding, we form the following equations :— 
feet. 
f+ 1r7o= 4181754 + 152B 4+ 27440 + 3:31D +4 2:75C' + 3'96D' 
7 + 418E — o54F + 424Q@ — iH 
+558 = + 524 +183:25B — 338C + 1°73D — 4020’ + 1'99D' 
| + 673E + o25F + 686G + o5oH 
P4317 = + 244A — 3°38B 41837170 + o88D + 0650’ + og2D! 
, — r5oH — oroF — 2151G — o19H 
+ 507 = + 331A + 173B + o88C +4181°33D + o'920' — o'72D' 
’ + 305H — oo8F + 306G — o17H 
—150o2 = + 275A — 4o2B + o65C + o(92D +183:19C’ + o'97D! 
—- r6égsH — or1F — 1170G — o22H 
— 924 = + 396A + 1'99B + o'92C — o72D + 970’ +181°81D! 
a ei , + 325HE — o1roK + 3266 — o20H 
— 641 = + 418A + 673B — 150C + 305D — 168C’ + 3:25)! 
A ‘ +182'43H + otooKk — o14G + o0oH 
—2218 = — os4A + o25B — o10C — o08D — o1rC’ — orr0D! 
+ oooH +182°57F — ocooG — ono 
39 = 424A + 6@86B — 17510 + 3:06D — 1700’ + 3:26D! 
Fr pe ; — oH — oookF +182'43G + oooH 
+1304 = — wi1A + o50B — o19C — o17D — 0°22C' o'20D! 
+ oooH — oooFk + ooG +182°57H 
‘These equations, solved by successive approximations, give the following 
values of the coefficients :— 
1868. 2M 
