^.-' 



*- , 



102 



G. P. Bond on the Rings of Saturn 



If we put F 



s 



r 



the attraction of Saturn on the middle 



of any ring^ we obtain the relation, 



^^ >3- 



m 



r 



F 



r 



From the smallness of the mass of the ring, as well as from 

 its unfavorable distribution, it is easy to see that r^ — r must be 

 very small compared with r^. 



To obtain / and /, I have computed from Laplace^s formula 

 the following values : f^ is the attraction of a single ring upon a 

 particle on its surface, at the extremity of the major axis of its 

 base ; /, and /^ the attractions of the two next adjacent. The 

 interval between —001, 26 = ^i^. The radius of the outer edge 

 of the outer ring being =1. 



■ 



Attractions of Three Narrow Rings. 



a = 001 



•02 

 •03 

 •04 

 •05 

 •06 

 •07 

 •08 

 •09 

 •10 



/o . 



4-0-00661 



679 

 685 

 689 



691 



692 

 693 

 693 

 694 



+ 0'0d694 



0-284 

 •393 

 '460 

 •507 

 •543 



•571 



•594 



•614 



■631 



0646 





+ 



+0 



134 



150 

 154 



157 



160 

 162 

 164 

 165 

 166 

 166 



# 



The attraction of the whole ring, considering its mass to be 

 uniformly distributed, I have next computed by quadratures. 

 Breadth of whole ring =0-335. Radius of outer edge =^1- 



=+4-52Xmasaofring. 



Distance of particle witliin the oiiter edge =0 



M 



«l 



II 



(4 



CI 



<( 



H 



« 



(( 



U 



■< 



« 



u 



u 



u 



M 



« 



a 



« 



u 



u 



ft 



u 



0075 Attraction 



0475 



0875 



1275 



1675 



2075 



2475 



2875 



3275 



U 



a 



a 



u 



u 



U 



a 



H 



2-42 

 1-70 

 116 

 001 



+0 04 



-0*52 



1-32 



-3-53 



' These two tables give the means of finding / and / 

 ficient exactness. For Saturn we have 



with suf- 



iSf 



7 \3 



? 



log. 5? 



9*5567 5 log. mass of ring 



7-4S48 



The density of the ring is assumed = Saturn'^s, unless it be 

 otherwise stated. A change in the density affects only that part 

 of the ring's attraction depending on /^^ f and / . 



