188 Of the SOLIDS 



Mathematicians by that circumftance, as well as by their con- 

 nection with experimental inquiries. 



In the problem thus propofed, no condition was joined to 

 that of the greater!: attraction, but that of the quantity of ho- 

 mogeneous matter being given. This is the molt general Hate 

 of the problem. It is evident, however, that other conditions 

 may be combined with the two preceding ; it may be required 

 that the body fhall have a certain figure, conical, for example, 

 cylindric, &c. and the problem, under fuch reftrictions, may be 

 ftill more readily applicable to experiments than in its mofl 

 general form. 



Though the queftion, thus limited, belongs to the common 

 method of Maxima and Minima, it leads to inveftigations 

 that are in reality confiderably more difficult than when it is 

 propofed in its utmofl generality. 



Among the following invefligations, there are alfo fome that 

 have a particular reference to the experiments on Scheh allien. 

 A few years ago, an attempt was made by Lord Webb Sey- 

 mour and myfelf, toward fuch a furvey of the rocks which 

 compofe that mountain, as might afford a tolerable eftimate 

 of their fpecific gravity, and thereby ferve to correct the con- 

 clufions, deduced from Dr Maskelyne's obfervations, concern- 

 ing the mean denfity of the earth. The account of this furvey, 

 and of the conclufions arifing from it, belongs naturally to the 

 Society under whofe direction the original experiment was 

 made ; what is offered here, is an inveftigation of fome of the 

 theorems employed in obtaining thofe conclufions. When a 

 new element, the heterogenity of the mafs, or the unequal di- 

 flribution of denfity in the mountain, was to be introduced into 

 the calculations, the ingenious methods employed by Dr Hut- 

 ton could not always be purfued. The propofitions that re- 

 late to the attraction of a half, or quarter cylinder, on a par- 

 ticle placed in its axis, are intended to remedy this inconveni- 

 ence, 



