BarxEs.—On the Influence of the Earth's Rotation on Rivers. 95 
river-bed of shingle and sand rolled along by the current. The effect of 
this is plainly to make the right shore more shelving and the left steeper, 
and to place the deepest part of the stream nearer the left bank. This 
will eause the velocity and consequently the erosion to be greater at the 
left bank. The right shore being more shelving will be more favourable to 
the deposition of sediment during the subsidence of floods. The continual 
building-up of the right bank explains how a river cuts away on its left 
bank harder material than that of which the right is composed ; while the 
latter, instead of being cut away, is being added to. "The wearing away of 
& high terrace instead of a low flat on the opposite side of the river is 
similarly explained. 
The principal facts in connection with the changes of river courses are 
thus accounted for, which a minute difference in the erosive power at the 
opposite banks of rivers, caused directly by a difference of level, appears 
inadequate to explain. 
To find the deflecting force acting on a body eins on the earth's 
surface in any direction :— 
Let p be the position of the body on the great 
circle 4 A’, the inclination of whose plane to the plane 
of the equator is a, the motion of the body being 
towards A’. Let OA’ be the axis of 2, OC the axis 
of z, that of y being perpendicular to the plane of 
the paper. 
. Let 0 be the angular velocity of the earth round 
the polar axis P P'; 0,, 0,, the angular velocities round the axes of x and 
& respectively. 
Then 0, = 0 sin a, 0, = 0 cos a 
Let z = r cos 4, y = r sin $ 
r being the radius of the earth, and $ being measured from the axis of x 
towards that of y. 
O p D being a spherical triangle, and the angle D a right angle, 
sin p D = sin a cos ¢ = sin Lat. 
The equations of motion of a particle, referred to axes moving in any 
manner about a Pana: origin, are—the mass being unity,— 
1.9 A — vhs + ow, u = Z _ ybs + d: 
dv di 
T c C TN v= 2 — 26, + 20, 
dw dz 
Et to Oy + n, w= — 20, + yO 
