Of GREATEST ATTRACTION. 217 
the height of that column, or of the cylinder, AD = x, AB, 
the radius of the bafe, =r. 
By the laft propofition, the column ftanding on DF, exerts 
on A an attraction in the direction AD, which is = Ap 
x fin v. 
Now Dd=i4, Df=x2z,andDdxDf=x2e. Therefore 
the attraction in the dire@tion AD is ~*= xX finy = «2 fin V, 
x 
and reduced to the direction AB, it is x z finv x cofz. 
Tuts is the element of the attraction of the cylindric fhell 
or ring, of which the radiusis AD or x, and the thicknefs «; and 
ee rem on the {nppotition that z only. is variable, 
mae x pe v Beta, it gives afino{ xcofz —#fin v X fine 
i the attraGion of the’ thell: ‘When z= 90, and finz = 1, 
we have the attraction of a quadrant of the fhell = # finv, and 
therefore that of the whole femicircle = 2 4 fin v. 
Next, if « be made variable, and confequently v, we have 
2 y # fin v for the attraction of the femi-cylinder. 
Nowthe angle: v would have for its fineifthe radius were/a’-++-x", 
and fo fnv= 3 wherefore the above expreflion is 
Nata = f 
24% thi 
Sirs eee dy a) +C; and as this muft ya- 
nifh when x =0, 2a4La+Cx0, and G=—2aLa, fo that 
the 
