^2^ Mr. Landen's hivejiigatton of 



c^ufe all the variation of the velocity about AE ; 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 



— ^ • Bd'^'^J about AB only will not, in general, be equal to 



— • — :-xflux. of ^jG, the value of the whole motive force 

 3 «3T 



requiiite to caufe the variation of the velocity — , as M. Euler 



reckoned. 



The like objeclion may, I conceive, be juftly made to his 

 other two equations fuTiilar to that which is here particularly 

 adverted to. 



M. D'Alembert's radical errors, in treating this fubjedl, 

 aj)pear 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 = o, the velocities about thofe lines mud each remain inva- 

 riable; but it feems abfolutely impoffible that they can ever 

 remain fo, whilft 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 tlie moveable fpherical furface, will not 

 always be perpendicular to the dire£lion 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, Iprefume, 

 beyond a doubt, in my Paper above-mentioned, that the faid 

 track will always be interfefled 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 



