^14 Mr, Landen's Invejiigaiion of 



It is not only obfervable, that the tracks which the varying-^ 

 poles take, in the furface of any revoking body, are fiich that 

 its momentum of rotation may continue the lame whilft its 

 angular velocity continues the fame ; but it may be obferved, 

 that, in any given body, there is only one fuch track which a 

 momentary pole can purfue from any given point. 



If the angular velocity and the momentum of rotation of a 

 revolving body were to vary according to the computations ad- 

 verted to above, it would follow, that a body might acquire an 

 increafe of force from its own motion, without being any way 

 afFc(fled by any other body whatever, as the fame percuffive 

 force, applied at the fame diftance from the momentary axis, 

 would not always deftroy the rotatory motion of the body, 

 which furely cannot poffibly be true. From the principles or 

 laws of motion, which I coniider as undoubtedly true (and 

 which indeed are no other than the common principles of me- 

 chanics), I conclude that a revolving body, not afFe6led by any 

 external impulfe, can no more acquire an increafe in its mo- 

 mentum of rotation, than any other body, moving freely, can 

 acquire an increafe in its momentum, or quantity of motion, in 

 any given direction, without being impelled'by gravity or fome 

 other force. And the truth of this conclufion (which is here- 

 inafter proved by other reafoning) may be eafily inferred from 

 the property of the lever; feeing that the joint centrifugal 

 force of the particles of the revolving body (which is the only 

 difturbing force) has no tendency to accelerate or retard their 

 motion about the momentary axis, but only to alter the por- 

 tion of fuch axis, the direction in which that force a£i:s beiqg 

 always in a plane wherein that axis will be found. 



By the theory explained in this paper, it appears that a pa* 



raUelopjpedon may always be conceived of fuch dimenfions, 



4 that 



