23 1 M)\ Landen's tnveftigation^ Sac, 



other bodies in our fyflem) ; It follows ; that it will not conti- 

 luially revolve about either of thofe axes, but will revolve, or 

 endeavour to revolve, about fucceffive momentary axes, as fliewn 

 above. If then its three permanent axes of rotation be called 

 itsfirji-, ft'cond, and third axes ; and the poles of its Jir/i axis be 

 thofe about which its momentary poles are carried according to 

 our theory ; the fecond and ibird axes will be in the plane of its 

 equator, the three being at right angles to each other. There- 

 fore, with refpecl to the above theory, this terreftrial mafs muft 

 be confidered of fuch a form, that its equator, and any fedlion 

 parallel thereto, fliall rather be elliptical than circular. And, 

 denoting its firft, fecond, and third axes by ^, c, d, refpectively,. 

 obfervations evince, that the difference c -^ If will be much 

 greater than the difference J -c. Whence it follows, that (fup- 

 pofing the earth's rotatory motion to be difturbed only by the 

 centrifugal force arihng from the inertia of its own particles) the 

 track of polar evagation with us will be nearly circular, and the 

 radius of the limiting circle very fmall, whether we have regard 

 to the moveable or immoveable fpherical furface referred to 

 above ; but that, in the latter furface, fuch circle will be much 

 lefs than in the former : and it moreover follows, that the con- 

 cavity of the track upon the moveable furface will continually 

 touch and roll along the convexity of the track in the immove- 

 able furface. 



In other planets, the tracks of polar evagation may, from a 

 fimilar caufe, be very different. The theory above explained 

 evidently proves, that their axes of rotation may poflibly vary 

 greatly in portion, merely through the inertia of matter i whilfl 

 Providence has fo ordered it, that the pofition of the axes of 

 rotation of this planet fhall, by that caufe, be but very little 

 altered. 



'^!B 



