'j2''6 -^^' Landen's Invejltgatlon of 



the polar track upon the moveable fpherical fur face will be 



■exactly, or very nearly, a lelTer circle whofe radius is m. 



When Cis=:o, or very fmall in comparifon vv^ith D, and 

 D/»^ is greater than Qdr^ the track of the pole in the immovea- 

 ble fpherical furface will be exadly, or very nearly, a lefler 



circle whofe radius is = , zzzzz-^, ■ ; and then the polar 



track upon the moveable fpherical fiirface will be exa£lly, or 

 very nearly, a lefler circle whofe radius is n. 



Whatever the curves may be which the momentary 

 pole fhall defcribe in thofe two fpherical furfaces, the track- 

 upon the moveable furface will always touch and roll along 

 the track in the immoveable furface (whilH: the common cen- 

 ter of both furfaces remains at reft), in the manner defcribed 

 in my Paper in the Philofophical 'Tranfadiions for the year 

 17^7 ; the velocity of the point of conta6l being equal to tlie 

 value of i; computed above, which velocity when B is — o, or very 

 fiiiall dn comparifon with D, and Dm" is lei's than Qa^, will be 



exactly, or very nearly, =-t-— tzX-^-; and when C is — o, or 

 very fmall in comparifon with D, and Dw^ is greater than C^', 



di' '111 ni 1 ^ — c~ mne 



lat velocity will be exactly, or very nearly, = 753—5 X -^' 



The polar track upon the moveable fpherical furface. 

 will always roll along the convexity of the track iii 

 the iiTimoveable fpherical furface ; the convexity or con- 

 cavity of the former being turned towards the convexity 

 of the latter, according as Dm" is greater or lefs than C^% 

 Which track in the immoveable Ipherical furface, when it 

 is not circular, will touch a certain circle as often as y^ during 

 the motion, fhair become = ; and likewife another parallel 



circle 



