328 Mr. Landen’s lnvejiigaiton of 
caufe all the variation of the velocity about AB ; that velocity 
varies in confequence of the evagation of the pole P ; and that 
evagation is caufed by the motive forces urging the body to. 
turn about AB, AC, AD, conjunBly. Therefore the motive force 
• B^y^ about AB only will not, in general, be equal to 
3 ^ 
uVI Cl^ | * 
— . 1 — — x flux, of eQ> y the value of the whole motive force 
3 , « 3 T 
requifite to caufe the variation of the velocity — , as M. Euler 
reckoned. 
The like objection may, I conceive, be juftly made to his 
other two equations fimilar to that which is here particularly 
adverted to. 
M. D^Alembert’s radical errors, in treating this fubjeft, 
appear to me nearly fimilar to M. Euler’s. 
Other arguments may be adduced to prove, that the equa- 
tions affumed by thofe gentlemen are not well founded. If the 
forces to turn the body about the lines AB, AC, AD were 
each = 0, the velocities about thofe lines muft each remain inva- 
riable ; but it feems abfolutely impoflible that they can ever 
remain fo, whilfi: the angles which thofe lines make with the 
momentary axis are each continually varying. Moreover, ac- 
cording to their conclufions, the tangent at P to the track of 
polar evagation, upon the moveable fpherical furface, will not 
always be perpendicular to the dire&ion in which the pole P 
will be urged to turn by the joint centrifugal force of the par- 
ticles of the revolving body ; whereas it is proved, I prefume, 
beyond a doubt, in my Paper above-mentioned, that the faid 
track will always be interfered at right angles by the direction 
in which the momentary pole fhall, at any inftant of time, be 
urged to turn by the force caufing its evagation. 
4 
If 
