206 



Prof. J. D. Everett on the General Circulation 



which is sensibly equal to 2cov, if v be small compared with the 

 absolute eastward velocity of the earth's surface wRcosX. The 

 sign of v is positive or negative, according as the relative velocity 

 which it denotes is eastward or westward. 



The excess 2cov may be resolved into 2cov cos X, vertical, and 

 2covsm\ horizontal, of which the latter must be equal and op- 

 posite to the constraining force P. 



III. The value of P in both cases (and therefore also for all 

 intermediate directions) is thus 2co sin X . v, which, if the second 



be the unit of time, is „ ^ . It is the same as the constrain- 

 6850 



v • v 



ing force required for motion in a circle of radius ^ or - — r- r- , 

 ° ^ P 2ft>smX 



which, if the second be the unit of time, is 



sin X 



IV. Let C A be a small arc of a circle 

 of latitude, B C an arc of a great circle 

 touching it in C, N C and N B meri- 

 dians. Then NCB is a right-angled 

 spherical triangle, and 



NA=NC=^- 



X. 



Denote this by a, A B by /3, B C by 0. 

 Then, by spherical trigonometry, 



or 



cos 



cos (« + /S) = cos « cos #, 

 a — sin a. J3— cos of 1— ^-j; 



sin a 



/3 



cos a . — 



0* 



•'• o/Q — tan a — cotan X 



The radius 

 In terms of anv unit 



of the sphere is here the unit of length 



BC 2 

 of length, we have gjg = K cotan X. But B C may be regarded 



B f 12 



as the tangent to a circular arc A C, and -^j^a is tne expression 



<^A. Jl> 

 for the radius of curvature. The force which would produce 

 deflection from C B into C A, in the case of a body moving with 

 velocity v, is therefore the same as the constraining force required 

 to keep it on the circumference of a circle of radius R cotan X. 



Y. Since, for given velocity of circular motion, the constrain- 

 ing force varies inversely as the radius, P is to the force which 

 would produce deflection from CB into CA in the ratio 



