s8© Mr. Knight on the Attraction of such Solids 
this case 
A — 4.x arc (tang. = ■£) — 2aL (1 -j- ~j. 
Cor. i. Draw the right lines pr, pn ; because d- = 
= tang, rpm, the last expression may be put into the form 
A = 4.Z arc. rpm — 42L . sec. rpm. 
Cor. 2. If, in the last value of B in Prop. 2G, we make x in- 
finite, there results B = x' arc ( tang. = r) ; from whence it 
is plain that the first term of the expression for A in the last 
cor. viz. 4a; arc rpm, expresses the action of an infinitely long 
prism, whose base is the triangle rpn, on the point p. 
Consequently, the other term of A, or 42L . sect, rpm, is the 
action of the infinitely long solid whose base consists of the 
parabolic segments parp, pbnp. 
We may next consider the generating plane uvvV, fig. 15, 
to be a rhombus, given in species, and so varying in magni- 
tude, as to touch four similar and equal curves, at those points 
where perpendiculars from the centre of the rhombus fall 00 
its sides. 
Prop. 30. 
Let the guiding curves be semi- circles, to the radius k ; the 
attracted point at the vertex p. 
We saw, in Prop. 2, Cor. 1, that the action of a rhombus, 
on a point placed perpendicularly over its centre, is A = 4 arc 
(tang. 7/ 1 + k 3 ) “b 4 arc (tan g.= fv/ : i+^V) 
— 2?r ; in which we must put x* for a *, zkx — x* for P, and 
we get, for the attraction of the solid, 
A = 4/^ arc (tang. = ^ V <-ik ( 1 -j- r*) x — r.z a ) -j- 4 fx arc 
(tang. 
1 
r'x 
V 2k ( 1 -f> r' 2 ) x — r'V) — 27 tx. 
