96 Transactions.— Miscellaneous. 
Therefore 
x=— 20, — 263 = — 2 0V cos a cos ¢ — r 0? cos? a cos ọ 
Y — — 2% 0, — y6; — y05 = — 2 0V cos a sin $ — r 0? sin 9 
Z= 2% 0, + 20,0; = 29V sin a cos ¢ + r0? sin a cos a cos > 
= 297 sin Lat. +r 0? sin a cos a cos ó 
V being the velocity of the body on the earth's surface. 
The terms in X, Y, Z, not containing V, are the forces parallel to the 
axes, acting on a body at rest on the earth's surface. Their resultant is 
therefore balanced by centrifugal force, and reaction of the earth's surface. 
The terms containing V in X and Y, being resolved along the tangent at p 
to the great circle A A’, cancel, showing that the earth's rotation has no 
effect in accelerating or retarding a moving body. The term in Z, 20 V 
sin Lat. represents a force acting in a tangent to the earth's surface, and 
at right angles to the line of motion of the body, the positive sign showing 
that the constraining force is directed towards the left, the body having an 
equal tendency towards the right which is the deflecting force. 
Let the mean velocity of a stream be three miles an hour (the stream being 
assumed to be everywhere of the same depth, and the velocity to be equal 
at equal depths below the surface), then the deflecting force being propor- 
tional to the velocity, the mean deflecting force acting on the stream is that 
due to a velocity of three miles an hour, and it has been shown that the angle 
of inclination of the surface line of the cross-section to the horizon, is that 
whose tangent is the mean deflecting force divided by the force of gravita- 
tion = f, suppose— 
g 
SEES BAL. iia angular motion of the earth per 
second which is 0:0000729 
V — 8 miles an hour or 4:4 feet per second 
Sin Lat. = sin 45° = 0-707 
Wee Fk uis Ex ee cedit 0-707 x 4&4 . 9.99001408 
g : 
1 
— 71028 
which multiplied by 63360, the number of inches in a mile, gives j$.- inch 
nearly, which is the difference of level at the opposite sides of a stream a 
mile wide. 
