240 Mr William Galbraith on the Tides. 
These conditions cannot always be obtained, and=then it becomes 
necessary to effect that by computation which cannot be had directly 
from observation. 
To compute the actual rise of the spring-tide above the mean level 
of the sea— 
Let f be the effect of the sun, and /’ that of the moon, on the 
waters of the ocean, then will the whole effect be 
WP eGe Wel EGLO tae aes 
Now, if 7 be the semidiameter of the sun, and d the declination ; 
ge the semidiameter of the moon, and 6 the declination, at the time of 
syzygy, then f=a cos? d, and f’ = b cos? 4, and, thersfote, 
Bg con? a bse0s7 00.10! .. Oyu ST a 
in which a is the aggregate effect of the action of the sun’s mass, 
combined with his real distance, indicated by his semidiameter, and 
b that of the moon in similar circumstances, while cos? d and cos? 6 
give the effects of the distance from the plane of the equator mea- 
sured by their declinations. 
To facilitate this operation, I have computed the logarithmic values 
of a and b, contained in the following table. 
Example 1. On the 3d of August 1849, I found the unit of 
height wu (see page 16) of the tide at Broddick, in Arran, to be 4°34 
feet, when the moon was full, at 15" 52™ p.m., Greenwich mean time, 
what would be its value if the sun and moon were at their mean dis- 
tances and on the equator ? 
By the Nautical Almanac begs i. ? 
To this time the sun’s semidiameter,r= 0 15 47°5 
declination, d=17 19 S8S6N. 
the moon’s semidiameter, p= 0 15 1°4 
declination, 6=15 28 20°7S. 
Hence, from the table for 7 and g, we have, 
Moga testa cbs ee Oro LZ Mno a oe eee 
d =17 19 86 cos? =9:95971 S=15 28 20°7 cosy = 9-96794 
f = 02143 log 9°33100,f’= 0°6157 log 9°78934 
f= 06157 
F= 08300 
1:0000 = mean height of spring-tides. 
1—F= 0°1700 = defect. 
Hence, the preceding value of u is too small by 0-17 x4:34= 
0°7378 foot; therefore, the true value of wis 4°34+40-74=5-08° 
feet, when the sun and moon are on the equator, and at their mean — 
distances from the earth. 
Example 2. On the 29th of December 1849, the moon was full at_ 
2h p.m., required the unit of height on that day, and the excess of tig 
rise above 5:08 feet in the Frith of Clyde ? 
