324 Dr. A. A. Rambaut. On the Orbit of the Part of the 



The former varies with, the zenith-distance of the radiant and its 

 elongation from the " apex," or the point of the heavens towards which 

 the earth is moving at the time. It has always the effect of displacing 

 the radiant towards the observer's zenith, and hence has been called 

 by Schiaparelli the " zenith-attraction." The amount of this displace- 

 ment (rj) is given by the expression, 



w-u 



tan -hrj = tan -kz. 



21 w + u 2 



in which z is the apparent zenith-distance of the radiant, u is the velo- 

 city of the meteors relatively to the earth before the influence of the 

 earth's attraction has become sensible, while w is the accelerated 

 velocity with which the meteor encounters the earth. 



This displacement, which has been too frequently overlooked by 

 meteor observers, may, as pointed out by Schiaparelli, amount in 

 extreme cases to as much as 25° 38'. In the case of the Leonids, how- 

 ever, it happens that the elongation of the radiant from the " apex " is 

 so small (in the case before us not exceeding 11° at anytime) that the 

 effect of the zenith-attraction never amounts to half a degree, its 

 greatest value being 29'. 



For computing the value of w we have the expression 



w 2 = u 2 + 2gr, 



r being the earth's radius, and g the acceleration of gravity at the 

 surface, or, expressing the velocities, as is convenient, in terms of the 

 mean velocity of the earth in its orbit, 



= «2 + 0-141587. 



In computing the value of 2gr in the above expression the Sun's 

 parallax has been taken to be 8" "80, and the ratio of the earth's mass to 

 that of the Sun equal to 1/331,100. 



We thus have for computing w 



w = u + [8-84999] x i - [7-39895] x 1 , 



the figures in brackets being the logarithms of the coefficients. 



For determining u we may with quite sufficient precision adopt 

 Adams's orbit of 1866. Also if U denotes the velocity of the earth at 

 any time expressed in terms of its mean velocity, and R its distance 

 from the Sun, then, 



