^21^ Mr, L A N DE IN'* s Jnvefij^aiwn of 



[ .^ „. + 



X D 7rtny 



, Z ,,Z , .2 2,, /2 2 ' 



when D;»" is ~ Ca", becoities s: r 



^"-'-•''= 



V .ay 



e ^'BC . 7^ 



It is evident,, that ;S^ X,"^ xbyp.log. of~~, the vakie of 



T in that particular cafe, will be infinite when -^ is = ^ ; and this 

 conciuiion agrees with what is faid above refpe6ting the motion 

 of the momentary pole along the great circle CR (fig. 2* 

 and 3.). 



I have not found, that the value of T will, in general, be? 

 afligned by the arcs of the canic Jeciions ; but my Tables * fliew^ 

 that It will be fo affigned when Diir- is=:B^% and in fome 

 other particular cafes* 



We have ftill to inveiligate the track of the momentary 

 pole in the immoveable concave Ipherical' furface, which we 

 muft conceive to furround our moveable convex fpherical fur- 

 face, fuppofing the center of both thofe furfaces to coincide 

 with the centers of gravity of our parallelopipedon : which 

 central point is always in this difquifition fuppofed at reft. 



Let AL be the projedlon of part of a great circle CL, 

 at" right angles to the great circle P/»LN; then will the 



fine of the arc CL be ^ "' ~ ''_^iZ^ ; its cofine — 



, I 



D^v/D«^/zVr - Urn^- Ca'-m^ + Ca^n 





VDW«^-BCflV 



; and, the fluxion of that fine 



being = ^' " ^ ^^^ 5 the fluxion of that arc CCL") will be 



* Mathematical Memoirs, publiflied in ijSc)* 



