produced by small oodles passing near the earth. 415 



If a widely extended group of small bodies evenly dis- 

 tributed through space have absolute velocities all equal to 

 each other but directed towards points evenly distributed over 

 the surface of the celestial sphere, and if the earth moves in a 

 right line through them ; 



(a) A portion of the bodies will come into the earth's atmo- 

 sphere and affect the earth's motion in the manner of a direct 

 collision ; 



fb) The rest will pass by and exert an effect by reason of 

 gravitation. 



If the earth's velocity be less than that of the bodies the total 

 effect of the action of the bodies of this second class (b) upon 

 the earth's motion will be an exceedingly minute retardation 

 of the earth's motion, even though the extent of the group 

 is infinite. The outer limit of the group, when large, disap- 

 pears from the expression. 



If, however, the earth's velocity be greater than thai of the 

 bodies the total effect of the action of the bodies of this second 

 class upon the earth's motion will consist of two parts : 



First,' a very minute acceleration of the earth's motion, 

 depending for its amount upon the absolute velocity of the 

 bodies ; 



Second, a retardation of the earth dependent for its amount 

 upon the assumed extent of the group. If the action of 

 those bodies which would pass nearer to the earth than a 

 distance P be considered this second part of the action is pro- 

 portional to the logarithm of P. 



That the quantities dA and dA! are very small is later to be 

 shown. 



13. The change in the form of the expression for p t as c 

 increases through unity, and its likeness to the abrupt change 

 of the potential of a point relative to a thin spherical shell as 

 the point passes inside the shell is worthy of notice. 



The values of A and A' being independent of P, are depend- 

 ent upon the inferior limit of the integral (4), which should 

 manifestly be a function of c and d. 



14. In the two forms for p v viz., 



c<l /o^tf^logP— A) 



c>l p 1 = £A' 



the values of A, A 7 , and k log P, can be computed for assumed 

 values of c and P. Thus we get for A and A 7 



c 



A 



c 



A 



c 



A! 



c 



A' 



0-4 



0-6 



0-7 



1-3 



1-1 



2-6 



1-4 



0-2 



0-5 



0-7 



0-8 



2-1 



1-2 



0-9 



1-5 



o-i 



0-6 



0-9 



0-9 



4-3 



]-3 



0-4 



1-6 



o-i 



For a distance P equal to the radius of the moon's orbit 



