292 Equilibrium of a Gas under its own Gravitation only. 



care, by aid of good drawing-instruments, u x calculated from 

 u by quadratures will be found to agree so closely with u , 

 that u itself wi]l be seen to be a good solution. If any dif- 

 ference is found between the two, u x is the better : u 2 is a 

 closer approximation than u x ; and so on, with no limit to the 

 accuracy attainable. 



Mr. Magnus Maclean, my official assistant in the University 

 of Glasgow, has made a successful beginning of working-out 

 this process for the case u=lQ where «#=co ; and has already 

 obtained a somewhat approximate solution, of which the pro- 

 duce useful for our problem is expressed in the following 

 table. 



d 2 u 

 Numerical Solution of -V-» + x 

 ax 1 



0. 











Mass within dis- 



Distance from 

 centre 



=r=l/x. 



Eeciprocal of 

 distance from 



Temperature 



Density 



tance r from 

 the centre 



centre 

 =a?=l/r. 



=u. 



=u 2 ' 5 . 



—du/dx 



= \ dxu 2 ' 5 x~ 4 . 



Jx 







oo 



16-00 



1024 



•00 



•100 



10 



14-46 



795-2 



•28 



•111 



-9 



14-14 



751-6 



•38 



•125 



8 



13-71 



695-8 



•52 



•143 



7 



13-10 



621-2 



•731 



•167 



6 



12-20 



520-0 



1-056 



•200 



5 



10-92 



394-1 



1-566 



•250 



4 



9-00 



243-0 



2-336 



•333 



3 



6-15 



93-81 



3-436 



•500 



2 



2-25 



7-595 



4-366 



•667 



1-5 











4-49 



The deduction from these numbers, of results expressing in 

 terms of convenient units the temperature and density at any 

 point of a given mass of a known kind of gas, occupying a 

 sphere of given radius, must be reserved for a subsequent 

 communication . 



One interesting result which I can give at present, derived 

 from the first and last numbers of the several columns of the 

 preceding table, is, that the central density of a globular 

 gaseous star is 22-J- times its average density. 



my laboratory in 1874, in a series of skilfully executed drawings repre- 

 senting a large variety of cases of the capillary surface of revolution, 

 which have been regularly shown in my Lectures to the Natural Philo- 

 sophy Class of the University of Glasgow. These curves were recently 

 published in the Proc. Roy. Instit. (Lecture of Jan. 29, 1886), and 

 ' Nature,' July 22 and 29, and Aug. 19, 1886 ; also to appear in a volume 

 of Lectures now in the press, to be published in the 'Nature' series. 



