546 
Mr. Wildeore on 
and the fluent of 
-f. zc 
cv 2 - f. zc 2 
ba 2 xf. ZC-bs z Xa 2 -c 2 
2.a ^ tf-fxa -c z xi. ZC x cof. ZCV n -col. ZC 
alfo =. the feftor 
QZV = §VQ= the fluent of Bx — , the former being that 
« 7Y 2 9 , \ 
of A x — Then, fuppofmg ftill the motion to begin when 
y ^ o, or ZCnCW, the arch QR. muft be the meafure of the 
angle defcribed by C about Z in the time t ; and the whole arch 
RQV = the meafure of the angle defcribed during the time that 
ZC from being = CW becomes = CV, that is, during one- fourth 
of the time in which the track on the fpherical furface makes 
one revolution or pafles once under Z. Confequently, if on ZR 
there be taken the right line ZC = the fine of CW, and on 
CV, ZC 7/ “ f. CV, and upon the intermediate radii as ZQ their 
correfpondent values of f. ZC, a curve drawn through all 
thefe points C, C x/ , &c. will be the orthographical pro- 
jedtion (upon a plane 90° from Z) of that which is the locus of 
C in abfolute fpace, or upon the immoveable fpherical furface; 
fuch locus touching the circle whofe radius ZC= f. CW at C, 
and that whofe radius ZC // = f. CV at C 7/ . And the time of 
moving from C where ZC = f. CW to C" where ZC /7 — f. CV 
will be equal to that of a femirevolution a femivibration of 
the bar above found ; and every fucceeding part of the curve as 
C", C /x/ 9 C ;/// , defcribed in the fame or an equal time will be 
perfectly equal and fimilar to C, C 7/ . If the angle 
CZC 7/// be a divifor of 360% the path will return into itfelf ; if 
not, it will croft itfelf fomewhere as^at C v ? and fo on for 
ever. 
O £ N £ H A L 
