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Of the Attraction of such Solids as are terminated by Planes ; and of 

 Solids of greatest Attraction. By Thomas Knight, Esq. Commu- 

 nicated by Sir Humphry Davy, LL.D. Sec. R.S. Read March 19, 

 1812. [Phil. Trans. 1812, p. 247.] 



The attention of most mathematicians who have treated of the at- 

 tractions of bodies, has been confined to those bounded by continuous 

 surfaces ; and Mr. Knight is not aware that any author, with the ex- 

 ception of Mr. Playfair, has given an example of that kind of inquiry 

 which he here undertakes. 



If a solid be bounded by plane surfaces on all sides, whether regu- 

 lar or irregular, he undertakes to determine its action, both in quan- 

 tity and direction, upon any point placed either within or without the 

 body. 



For this purpose, the solid is first conceived to be divided into its 

 most simple forms, of which the action can be determined separately ; 

 and thence the collective force of the aggregate is subsequently ascer- 

 tained. 



The first section treats of the attraction of planes bounded by right 

 lines (whether triangular, quadrangular, or polygonal), on points how- 

 ever situated. 



The second section extends the same inquiry, first to pyramids, and 

 then to solids, which may be divided into as many pyramids as there 

 are sides. 



And in the third, the attraction of prisms of various forms is inves- 

 tigated. 



Having completed this part of the subject, Mr. Knight next applies 

 the formulas he has obtained to find the attraction of certain complex 

 bodies, which, though not bounded by planes, have a natural connexion 

 with the preceding subject, having their sections in one direction of 

 a right-lined figure, though in another direction their sections be in 

 part curvilinear, such as the portion of a cylinder generated by the 

 motion of a segment of a circle parallel to itself, or parabolic cylinder 

 by similar motion of a portion of a parabola. 



Under the same head, also, the author includes curvilinear pyra- 

 mids, or groined solids cut from the preceding cylinders by a trans- 

 verse motion of a similar or dissimilar curve, so as to have a paral- 

 lelogram for their base. 



v In the section which concludes this communication, the author 

 enters into the consideration of solids of greatest attraction ; for 

 though this subject has been already treated of, in part, by Professor 

 Playfair and by Silvabelle, their investigations relate solely to homo- 

 geneous solids of revolution ; but Mr. Knight extends the investiga- 

 tion to the attractions of those solids treated of in the preceding sec- 

 tions, not only when the density is homogeneous, but also according 

 to different hypotheses of varying density. 



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