326 Mr. Landen s s InveJUgation of 
the polar track upon, the moveable fpherical furface will be 
exadlly, or very nearly, a leffer circle whofe radius is m. 
When C is =: o, or very fmall in companion with D, and 
D nr is greater than Ca z , the track of the pole in the immovea- 
ble fpherical furface will be exactly, or very nearly, a leffer 
circle whofe radius is = -7^ — — and then the polar 
i/„ 4 a , a T~2l 2 % r 
v 4 cm + c + a I . n 
•track upon the moveable fpherical furface will be exaftly, or 
wery nearly, a leffer 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 (whilft the common cen- 
ter of both furfaces remains at reft), in the manner deferibed 
in my Paper in the Philofophkal ’Tranfaciions for the year 
1 777 ; the velocity of the point of contaft: being equal to the 
value of v computed above, which velocity when B is — o, or very 
/mall in companion with D, and Dm z is lefts than C a 1 , will be 
exa&ly, or very nearly, = p-~ i X ; and when C is — o, or 
very fmall in companion with D, and Dm' is greater than C a 2 f 
that velocity will be exactly, or very nearly, = X * 
The polar track upon the moveable fpherical furface 
will always roll along the convexity of the track in 
the immoveable fpherical furface; the convexity or con- 
cavity of the former being turned towards the convexity 
of the latter, according as D nr is greater or lefs than Ca\ 
Which track in the immoveable fpherical furface, when it 
is not circular, will touch a certain circle as often as y, during 
the motion, fhall become — o'; and likewife another parallel 
circle 
