416 H. A. Newton — Effect of small bodies upon the earth. 



Jc log P=27*8 : for P equal to the radius of the earth's orbit 

 k log P = 68*5 : and for P equal to the distance of a star having 

 a parallax as small as can be measured &logP=168 approxi- 

 mately. 



15. If instead of regarding c as constant we consider a series 

 of groups, some having c<l and some having c>l, tlie total 

 value of p 1 made up by adding the several values for the groups, 

 will have negative values of A partly or wholly cancelled by 

 positive values of A'. 



If c is a continuous variable in a group, integration takes the 

 place of summation. In particular, if c varies through unity, 

 and there is no abrupt change in the number of meteoroids for 

 which <f>l and c<^l, the values of log (c— 1) and log (1— c) by 

 which the values of A and A' become infinite when c=l will 

 near the limit cancel each other. 



16. Turning now to the meteoroids that come into collision 

 with the earth, we may regard, firstly, the earth as at rest and 

 without attraction and the meteoroids moving past with a uni- 

 form velocity v. In a unit of time the earth would encounter 

 the bodies which would fill a cylinder whose radius is r' and 

 length is v. Their mass =ditr n v, and the momentum commu- 

 nicated to the earth is ^r/V. 



If the earth's attraction be now considered, the value of r 

 should become p'" 1 . But by (5) 



p'*v*=2grV -fVV=/V(a; 2 + 2/5 2 ), 

 andp=— /V(> 2 + 2/3 2 ) 



where p includes the effect of the earth's attraction in changing 

 the course of the meteoroids before impact. 



17. If we proceed as in sections 10 and 11 to consider a sys- 

 tem of meteoroids equally distributed both in locus and in di- 

 rection of absolute motion, we find for its effect p 2 on the earth 

 per second in feet per second, 



o,? /»7T 3rW 2 /» c + 1 



. p-— t / s in0cos<™yV0=^-4 / (l-a 2 -c 2 )(2/3 2 +cc>& 

 8rV ^ 16cr ■' ±( c -l) 



This gives for 



3<y»-'V/ , 2c 2 . „. c 2 \ _.. 



*>1 H=l£ (? + * + *) ' =*'* 



where ^ and §/ are functions of c* 



* In his treatment of this question (Astr. Nach. No. 2573) Oppolzer seems to 

 have overlooked altogether the absolute motions of the meteoroids. 



