ipo Dr. Waring on the 
increments of the bafe AB contained between the two conti- 
guous furfaces EF and ef: from the points E and c of the 
curve draw ED and ed perpendicular to the axis AB, and E3 
perpendicular to the arc ¥e of the given curve at the point E, 
and meeting the axis AB in S ; then will the evanefcent iolid 
TLFfe ~p x PE X FD x¥f = px FD x PS x Dd (becaufe F/= 
x \/( 3 " +/) “ s X zz =^yy> where z and y denote 
respectively the abfcifs PD, and its correfpondent ordinate DE 
of the given curve. 
The increment of the attraction of the furface EF on the 
point P in the direction PD will be as the increment of the 
furface X PE x D d) X ^ 
X force of each particle =p x PD X 
Ddx given force of the particle; but the fluent of the fluxion 
PD x Dd contained between the points E and F is = lPE 2 - 
1 PD = I ED 2 , whence the attraction of the evanefcent folid 
E Fje is as \p xED x Fy^xF : (v/V+jO force of each given 
particle at the diftance (PE = ^/(x z +jy 2 )) = ip x ED 2 x — X D d 
PE 
X F : (%/ z +/) = \py x 
-t-yy 
v'(S+/) 
X F : (y/(% 2 +/)) ; the fluent 
of which, properly corrected, is as the attraction of the folid 
on the point P ; p denotes the circumference of a circle, whofe 
radius is i. 
Cor . i. The fluxion of this folid is \pyz ~ Y which deduced 
from the preceding principles —p X (\/( s +JF) — z ) X (zz^yy) 
2 = V, and confequently their fluents between two values of z> 
which correfpond to two values of jy = o, will be equal to each 
other* 
