98 Blake'on the Tecth of Cog-Wheels. 
tres, and when ‘itis deiven the action: is behind: thes same 
“When the e generating curve ea up ial the ares:oftwo 
Re one of which is convex and the other concave to- 
ward the centre of one of the base circles, the diameter of 
these ares being. half that of the base circle toward 
waste centre it is concave, and the describing point being at 
their point of junction, the forms traced are those which are 
recommended for adellow:: teeth which: oan — to act 
~ ESS 2 dees 271 ; 
oe instdnges enidalsi all a 
ers, when the interior epicycloids are igenatived by circles 
less than the base on which they roll, the friction between 
the interior and: its corresponding exterior epicycloid is as 
the DirFEReNcE of their lengths ; and when the generating 
circles of the interior epicycloids are larger than the baseon 
which they roll, the friction is as the sum of their lengths. 
For in nthe! first case, every part< of the shorter curve is ap- 
plied to F zp 1e longe _ Now if the 
on the longer without sliding, it is ap- 
plied to it only to the extent of its | Consequently 
the must slide upon the longer to the extent 
curve slides cetaely over the whole of the wphddes Conse- 
quently the friction is as the sum of their lengths. 
Cor.—Hence the friction is the same, whether the 
action is before the line of centres or behind it 
Scuotium.—The rule for determining the quantity of 
friction between epicycloids, as exhibited in the preceding 
ition, is applicable to all isosagistic curves whatever. 
e tule may be thus stated: The friction’ between - ae 
two’ fellow isosagistie curves is as the difference of th 
parts of them, which are described by:a generating corve 
more, concave thav the circumference of the base’ circle 
pc whose centre it is ae peaerasiny ee ren 
be a 9 ott Ip. gonne hoof tt 2tepol mcs 
wails PEED Invortires. 0091 Sia f 
& Stebut i 
_Semonseae-—When ‘the geuevstiieg cutve isa siattight 
ine, theisosagistie curves: generated | nneghinisent a Abe 
