ATTRACTION. 81 KLL. 27 '> 



If the eone W tin Miqut cone the base of which is any plane 

 figun inn on a par- 



at the vertex varies as the thickness of the fru 

 Consider two thin parallel lamina; at different 



tex of such a cone, then the attra* 

 - lamin.i- on the par: lie vertex will be the same. 



.ike any . ly small clement of area on the surface 



laniinfB, and let a conical surface be formed by 

 iit lines which pass through the perimeter of this area and 

 .ch the attracted parti - conical surface will 



lements in the two lamina) which are bounded by similar 

 plane figures. Now, supposing the lamina* of the same thick- 

 ness, the masses of the elements will vary as the squares of 

 distances from the attracted particle, and thus they will 

 equal attractions on this particle. The same result holds 

 cry corresponding pair of elements in the two lamina?, 

 and two lamina* exert on the particle at t 



ire eoual in amount and iirec- 



llows that the attraction of a frustum 

 varies as its thickness* 



210. We have hitherto considered the attracting body 



to be of uniform . but considerable variety may lie 



introduced into the questions by various suppositions as to 



iw of d ^up|>ose, tor instance, that in the case 



ular lamina in Art. 207 the density at any point 



of the lamina is <f>(r . r U the distance of that point 



tre; <f>(r) must then U- put instead of p \\ 

 207 a i be placed u integral sign. Therefore 



the attraction of the lamina will be 



f**( r 



"rr -v 



.o^+O 1 



<6 (r) - - , where <r is a constant, the result is 



2TTCK<T 



/V* 



c(* + *)' 



.Ml d the resultant attraction of an autaMage of 



let constituting a liomoge*amt tpkerital tkell of wry 

 ~ MicX-iiew on a particle oultfJe Ike tML 



18-2 



