Of GREATEST ATTRACTION. 180 



ence, and will probably be found of life in 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. 



The firft of the problems here refolved, has been treated of 

 by Boscovich; and his folution is mentioned in the catalogue 

 of his works, as publifhed in 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 fubject that has pafled 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 fuch circumftances, if my re- 

 mit is juft, I cannot reafonably expect it to be new ; and I 

 mould, 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. 



I. 



To find the folid into which a mafs of homogeneous matter 

 muft be formed, in order to attract a particle given in pofition, 

 with the greater! force poflible, in a given direction. 



Let A (Fig. 1. PI. 6.) be the particle given in pofition, AB 

 the dire&ion in which it is to be attracted ', and ACBH a fec- 

 tion of the folid required, by a plane palling through AB. 



Since the attraction of the folid is a maximum, by hypothe- 

 fis, any fmall variation in the figure of the folid, provided the 

 quantity of matter remain the fame, will not change the attrac- 

 tion in the direction 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 



A a 2 will 



