302 REPORTS ON THE STATE OF SCIENCE, ETC. 
The values of « given in 1921 are not correctly given. In order to reduce to k as 
defined by Darwin 22°-18 should be subtracted from the phase lags for semi-diurnals 
and 11°-09 from the phase lags for diurnals. For a given constituent we denote the 
lag of its phase behind the simultaneous phase of the corresponding equilibrium 
constituent 
(a) at Newlyn, by « 
and (b) at Greenwich, by y 
Thus y=nt+ pL 
where Lis the Longitude in degrees West of Greenwich and p=0, 1, 2, for long period, 
diurnal and semi-diurnal constituents respectively. It may be remarked that y is much 
more useful than « both for analysis and prediction, as we need only use Greenwich 
Mean Time and the ‘ astronomical arguments’ only need to be evaluated for the — 
Greenwich Meridian. This is essentially the U.S.A. practice. 
Newlyn: Latitude : A= 50° 6’1N. 
Longitude; L= 5° 32”6W. 
Tide-gauge record : one year for semi-diurnal constituents, six months for diurnal 
constituents, commencing Oh., Jan. 0-1, 1918, G.M.T. 
Method of analysis : special, as in B.A. Report, 1921. 
Amplitudes : in feet. 
pettes0., 168. 179-5 M, : 5-620 124-7 135°8 §,: -010 329-5 335-0 
: | 22°83 33:9 | P,: -071 102-6 108-2 
160-2 | v,: -226 111-3 122-4 | K,: -200 102-2  107- 
ABD mn 
wow nr 
KOSS 
OO bo 
Noe 
me bo 
He OO 
SH 
me bo 
bo 
ia 
ce 
oo 
to 
mM 
ta 
= 
ey 
o 
(ee) 
«J 
s) 491 165-8 176-9 N,: 1-066 103-1 114-2 | O,: -180 334-2 339-7 
L,: +189 122-7 133-8 | wu,: -197 159-8 170-9 | Q,: -060 281-3 286-8 
de 102. 100-7 111-8! 2N,: -089 89-5 100°6 | 
APPENDIX. 
By J. PRoupMAN. 
(Being part of Adams’ Prize Essay, 1923.) 
In constructing the dynamical equations of the tides it is necessary to introduce 
terms representing the forces of friction of external origin, due mainly to the retarding 
effect of the sea-bottom. 
T. Young (1813), followed by W. Ferrel (1874), made the hypothesis that the 
magnitude of the external frictional force is proportional to the square of the speed 
of the current, and adapted this hypothesis to the consideration of harmonic 
constituents in the way indicated below. Ferrel pointed out, as an important 
result, that one of the effects of friction on the tides produced by a harmonic 
disturbing force was to give rise to another constituent of speed three times as great. 
In his work on tidal friction in the Irish Sea, G. I. Taylor (1918) made the same 
hypothesis as Young, and in extending Taylor’s work, H. Jeffreys (1920) remarks that 
even in the empirical prediction of tides, friction may have to be taken into account. 
Tf u, v denote rectangular components of the current, and F, G the corresponding 
components of external friction, then the hypothesis gives 
F = ku | (w+ v2)! |) 
G = kv | (u2 + v3 |) 5 | ; : (1) 
where k is a constant. 
First suppose that 
u=U,cosct ,v=0 j , ‘ : (2) 
so that 
| (uw? + v?)2 | =u | cos ct |. 
