[ ^4 ] 



ceflion of an attached and folitary annulus are equal, whereas the 

 former is double that of the latter ; this error therefore counter- 

 balances the former. 



■ Mr.Emersom has given two folutions of this queftion, which 

 are both erroneous, one in his Mifcellanies, the other in his 

 Fluxions. In the former he adopts the fame principles with 

 Newton, in fuppofing the preceffion of a folitary moon, a de- 

 tached rigid annulus, and an attached annulus to be equal. In 

 the latter he determines the diredion in wiiich a body would 

 move in confequence of a uniform motion imprefTed on it in 

 one diredion, and a uniformly accelerated motion in another, 

 to be the diagonal of a parallelogram, whofe two fides reprefent 

 the fpaces defcribed from quiefcence, in the fame time, by the 

 two forces ; which, as Mr. Milner has juflly obferved, produces 

 an error of one half in the conclufion. For let A D be the 

 fpace defcribed by the uniform motion (fig. 5.), while the body 

 would defcribe A B by the accelerated motion ; fince the time 

 is indefinitely little, the accelerating force may be confidered as 

 conflant, and therefore the body will in fad defcribe the parabola 

 AGC; and the diredion of the motion at C will be the tangent 

 EC; but the angle DEC = DAC + ACE= 2DAC nearly, 

 becaufe the tangents A E, C E, are very nearly equal (Ham. Con. 

 Cor. I. Prop. 3. Lib. 2. and Prop. 3. Lib. 3.); that is, the 

 true angle of deviation DEC, is very nearly double the angle 



of 



