produced by small bodies passing near the earth. 411 

 These equations uive 



2?V 

 1 — cos 2a= 



and substituting in the integral of the preceding article we get 



/*p" „ , 2q*r* , 27tm'ng*r*. </V+ »"V ,\ 

 pm~ t 27tp7iv'm -^-f- — —*<*P= r log » « , <* —» ( 4 ) 



where _p" and // are suitable limits of the integral, m is the 

 earth's mass in pounds, and p is the velocity in feet per second 

 communicated to the earth per second. 



6. The value of p' is that value of p which permits the 

 meteoroid to just touch the e rtb's atmosphere without enter- 

 ing it. Assuming that the radius of the earth including the 

 atmosphere is r' (which may be assumed =r + 100 miles), put- 

 ting p' for p and r' for_p in equations (1) and (2), we have 



v r'=vp'. 

 Hence p'V=2grV + r"v% (5) 



and g i r i +p' 2 v i =(gr' + r'vy 



Putting also d for the density of the meteoroid matter if dis- 

 tributed through the space occupied by the group, the earth's 

 density being regarded as unity, and observing that md=- 

 far'nm') we obtain from (4) 



' 2v 2 8 {gr' + r'vy 



^lo g # (6) 



by putting u for the earth's velocity in its orbit, v=xu, p"=~Pr', 

 and j¥=gr 2 /r / u 2 = *069. The term /3 4 /PV may be dropped as 

 of no account unless x is very small. Substituting numbers 

 we get 



6'83tf f P 1 ,., 



^=^ l0 § ' j ^69 I • < 7 > 



If the velocity of the meteoroids be that of a comet in a para- 

 bolic orbit cc 2 = 2 and 



p= 3 -41 S (log P- -034). 



If their velocity be that of the earth in its orbit 

 sc 2 =I, and p=6'83tf(logP— -068). 

 In formulas (6) and (7) /> expresses the acceleration given to 



