Refolution of attractive Powers. 187 
mentioned finite terms together with the arc of a circle, whofe 
radius is s/ a — t? and tangent b, unlefs n— f=— 1, in 
which cafe the fluent Y involves that circular arc, and alfo the 
logarithm of y'+iby o'. If n — \ denotes a fraction whofe 
denominator is 2, both the fluents can be exprefied by the 
finite terms together with the log. of -f ^/( y 2 ^iby + a). 
If the fluents be given, when n is a given quantity, and n — { 
not a whole affirmative number, from them can be deduced 
the fluents of any fluxions refulting by increafing or dimi- 
nifhing n by a whole number, unlefs in the above-mentioned 
cafe of n — i=— 1. If £ — o, and confequently the line Vf 'is 
perpendicular to the given line ab 9 the fluent Y will be ex- 
preffed by the finite terms, unlefs n — f = — 1, in which cafe 
it will be as \ log. (y* + tf 2 ) when properly corrected. 
Thefe fluxions Y and V may be transformed into others, 
whofe variable quantity is P x~u the diftance from P, by fub- 
ftituting in the fluxions for y and y their refpeCtive values 
^/{u — a + F)=t=b and ■■ 5 ~ - , and confequently for 
v ' y[u —a -j-P ) x 
s /(y i z±z 2 by + a 2 ) its value u. 
PROBLEM II. 
\ 
Fig. 3. Given the attraction of each of the parts of a given 
furface in terms of their diftance from a given point P, and an 
equation exprefling the relation between an abfcifs Ap — x, and 
its correfpondent ordinates pm =.y of the furface; to find the 
attraction of the furface on the given point P. 
Firft, by the preceding propofition find the attractions Y 
and V of any ordinate m p mf in the directions of the ordinate 
pm and of the line Pj b\ and from the equation exprefling the 
relation 
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