524 



REPORT — 1891. 



time will be this number multiplied by the number of units in tbe surface 

 of ^, or 





Airr^fj nv cos xj/ sin i/^cZi/' = Trnvr^ 



28. Distribution of 'parabolic comets as to perihelion distance. — This 

 supposition of equable distribution of the goals of comets as they cross 

 the spherical surface ^ involves also a law of distribution of comets as to 

 perihelion distance. The number of comets that enter the sphere in a 

 given time whose motions make with the normal angles between if/ and 

 vf/ + dij/ is proportional to sin i}/ cos {j/dij/. If N be the number of comets 

 that enter ^ in a given period of time with an angle with the normal 

 less than ij/, we may write cZN ^ h sin \j/ cos il/dif/, where Jc is some constant. 



Fig. 14.— a>=70°. 



Fig. 15.- 



:110° 



o 



But if 2 is the perihelion distance of a comet which at the distance r from 

 the sun moves at an angle with the radius equal to \\i, then q = r sin^ \p, 

 and dq ^ 2r sin i/r cos i/ftZi/'. But comets that enter j) with angles to the 

 normal between i/^ and \p + d^ have perihelion distances between q and 

 q + dq. Hence N" may also represent the number of comets that in the 

 given period of time pass their perihelia, and whose perihelion distances 



are less than q. 



comets be grouped according to their perihelion distances the number of 



Therefore -y- is a constant, and we conclude that if 

 dq 



comets whose perihelion distances are less than q is proportional to q. 



