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 greateft attraction, but that of the quantity of ho- 
mogeneous matter being given. This is the moft general ftate 
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 moft 
general form. 
Tuoucu 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 utmoft generality. 
Among the following inveftigations, 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 f{pecific 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- 
{tribution of denfity in the mountain, was to be introduced into 
the calculations, the ingenious methods employed by Dr Hurt- 
ron 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, 
7 oa 
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