Baines. — On the Injluence of the Earth's Botation on Pdvevs. 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 stee^oer, 

 and to place the deepest part of the stream nearer the left bank. This 

 will cause 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 

 a 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 moving on the earth's 

 surface in any dkection : — 



Let 2^ be the position of the body on the great 

 circle A A', the inclination of whose plane to the plane 

 of the equator is a, the motion of the body being 

 towards A'. Let A' be the axis of a-, C the axis 

 of z, that of y being perpendicular to the plane of 

 the paper. 



Let 6 be the angular velocity of the earth round 

 the polar axis P P' ; 0^, 63, the angular velocities round the axes of cc and 

 s respectively. 



Then 0^ = 9 sin a, 63 = cos a 

 Let X = r cos <{>, y =^ r sin (p 

 r being the radius of the earth, and (p being measured from the axis of cc 

 towards that of y. 



2^ D being a spherical triangle, and the angle D a right angle, 

 sin p D ^= sin a cos f = sin Lat. 



The equations of motion of a particle, referred to axes moving in any 

 manner about a fixed origin, are — the mass being unity, — 



« = J - 'je, + .9. 

 . = I _ .a, + .^3 



-v^ da 

 ^'-Ift- 



- Vds + W02 



Y _ di) _ 

 dt 



- ivd, + nd^ 



^_dw_ 

 dt 



- «02 + vdi 



