Of GREATEST) ATTRACTION. 189 
ence, and will probably be found of ufe im all inquiries con- 
cerning the difturbance of the direction of the plumb-line by in- 
equalities, whether in the figure or denfity of the exterior cruft 
of the globe. 
Tue firft of the problems here refolved, has been treated of 
by Boscovien and his folution is mentioned in the catalogue 
of his works, as’ publifhed im the memoirs of a philofophical fo- 
ciety at Pifa. I have never, however, been able to procure a 
fight of thefe memoirs, nor to obtain any account of the folu- 
tion juft mentioned, and therefore am fenfible of hazarding a 
good deal, when I treat of a fubjeét that has paffed through the 
hands of fo able a mathematician, without knowing the conclu- 
fions which he has come to, or the principles which he has em- 
ployed in his inveftigation. In fach circumftances, if my re- 
fult is juft, I cannot reafonably expect it to be new; and I 
fhould, indeed, be much alarmed to be told, that it has not been 
anticipated. The other problems contained in this paper, as 
far as I know, have never been confidered. 
8: I. 
To find the folid into which a mafs of homogeneous matter 
muft be formed, in order to attract a particle givenjin pofition, 
with the greateft force poflible, in a given direction, 
Ler A (Fig. 1. Pl. 6.) be the particle given in pofition; AB 
the direction in which it is to be attracted; and ACBH a fec- 
tion of the folid required, by a plane pafling through AB. 
Since the attraction of the folid is a maximum, by hypothe- 
fis, any {mall variation in the figure of the folid, provided the 
quantity of matter remain the fame, will not change the attrac- 
tion in the direGtion AB. If, therefore, a fmall portion of mat- 
ter be taken from any point C, in the fuperficies of the folid, 
‘and placed at D, another point in the fame fuperficies, there 
Aa 2 will 
