the limit ^ 2V ^ = ^J_^Ii 



dv dv 



Prof. Stokes on the Internal Distribution of Matter, fyc. 239 

 have for the mass required 



Of the differential coefficients within brackets, the last alone becomes 

 infinite when the thickness of the stratum, and consequently the range 

 of integration relatively to A, becomes infinitely small. We have in 



both differential coefficients having their values belonging to the 

 surface. Hence we have ultimately for the mass 



KrdY x _dY\ 



Att\ dv dv J 

 Hence, if ru be the superficial density, defined as the limit of the 

 mass corresponding to any small portion of the surface divided by 

 the area of that portion, 



W A*\dv dv} (3 ) 



which is the known expression. 



In assigning arbitrarily a function V to the interior of S, in order 

 to get the internal density by the application of the formula (1), we 

 may if we please discard the second of the conditions which V had 



to satisfy at the surface, namely that — y-^ = -j- ; but in that case 



dv dv 



to the mass, of finite density, determined by (1) must be added an 



infinitely dense and infinitely thin stratum extending over the surface, 



the finite superficial density of this stratum being given by (3). 



We have seen that the determination of the most general in- 

 ternal arrangement requires the solution of the problem, To determine 

 the potential for space external to S, supposed free from attracting 

 matter, in terms of the given potential at the surface ; and the deter- 

 mination of that particular arrangement in which the matter is wholly 

 distributed over the surface, requires further the solution of the same 

 problem for space internal to S. If, however, instead of having 

 merely the potential given at the surface S we had given a particular 

 arrangement of matter within S, and sought the most general rear- 

 rangement which should not alter the potential at S, there would have 

 been no preliminary problem to solve, since Y, and therefore its dif- 

 ferential coefficients, are known for space generally, and therefore 

 for the surface S, being expressed by triple integrals. 



Instead of having the attracting matter contained within a closed 

 surface S, and the attraction considered for space external to S, it 

 might have been the reverse, and the same methods would still have 

 been applicable. The problem in this form is more interesting with 

 reference to electricity than gravitation. 



" On the Occlusion of Hydrogen Gas by Meteoric Iron." By 

 Thomas Graham, F.R.S. 



Some light may possibly be thrown upon the history of such 



