32 
MR. DARWIN ON THE BODILY TIDES OF VISCOUS AND SEMI-ELASTIC 
With the notation of the present paper n — 2D. for the fortnightly tide, and D.t is 
the “ mean moon’s ” longitude from her node. 
The following are the results, giving the place of observation, its N. latitude, and 
the years of observations. With respect to Brest and Toulon, R is reduced to feet 
from centimetres, so as to be made comparable with the other results :— 
Ramsgate, 
about 51° 21'. 
Liverpool, 
53° 40'. 
Hartlepool, 
54° 41'. 
1864. 
1857-58. 
1858-59. 
1859-60. 
1866-67. 
1858 -59. 
1859-60. 
1860-61. 
R -0331 
•093 
•037 
•024 
•036 
•052 
■053 
•073 
e 268°-29 
170 °-7 
148°-8 
72°-9 
340°-6 
190°*34 
222°-34 
158°-62 
Brest, 
48° 23'. 
Toulon, 
43° 7'. 
Kurraebee, 
24° 53'. 
Cat Is’.aud, 
Gulf of Mexico, 
30° 23'. 
1875. 
1853. 
1868-69. 
1869-70. 
1870 71. 
— 
R -099 
•051 
•038 
•064 
•035 
•043 
e 80 o- 65 
139°-50 
335 o, 40 
333 u -91 
04 
04 
O 
CO 
OO 
04 
136°-69 
In their present form the observations do not appear to present any semblance 
of law, but when they are rearranged we shall be able to form some idea as to whether 
they are really quite valueless or not for the point under consideration. 
The theoretical expression for the fortnightly tide of an ocean covering the whole 
earth, according to the equilibrium theory, is 
3 T 
— - a sin 2 i(\ — cos 2 9) cos 2DLt. 
10 s 
Where t =~Ct = —, a= earth’s radius, i the averao-e obliquity of the earth’s axis to 
2 c 6 5 a ■ -l j 
the normal to the plane of the lunar orbit during the fortnight in question, 9 the 
colatitude of the place of observation. 
If we take i— 23° 28' the obliquity of the ecliptic, c(=20'9 million feet, we find 
- a sin 2 i— ’207 foot. 
10 S 
So that the fortnightly tide should be expressible by 
•207 (|- —sin 2 (lat.)) cos 2 D.t. 
In Thomson’s corrected equilibrium theory the second factor should be 
— --sin- (lat.) 
O 
