e 
284 Sugar of Potatoe Starch. 
the point B, the same relation to the radius AC, or the line which 
represents the uniform motion of the center C, it follows that the 
portion of any epicycloidal line, intercepted between its middle point 
and the position of its generating point, bears the same relation to 
the supplemental chord DB, as the distance through which the cen- 
ter of the generating circle passes in describing the whole epicycloid 
to one half of the circumference of the same circle. 
15. In an epicycloid described upon a fixed circle, having an infi- 
nite radius, it appears (13.) that the center of the generating circle 
passes through a distance equal to its circumference, and hence by 
reference to the last Art. it follows, that the portion of the curve 
called the cycloid intercepted between its middle pownt and the post- 
tion of its generating point, 1s equivalent to twice the supplemental 
chord DB, (Fig. 3.) of its generating circle. 
The leading properties of the epicycloid are thus developed by the 
aid of a few of the most common and elementary principles of ge- 
ometry and mechanics. Their practical application to the pendulum, 
—to the motion of carriage wheels,—to the conversion of a rotary 
into a rectilinear motion, and to the mode of determining the form 
of the working faces of cogs of different sized wheels, will readily 
be suggested to those who are at all conversant with the theory and 
practice of mechanics. ‘The same principles may likewise be applied 
in the investigation of the vertical motion of particles in a non-elastc 
undulating medium, and to a new mode of spherical projection. 
In conclusion I would state, that the idea of treating the subject 
of the epicycloid as presented above, was first suggested by a sue 
cessful attempt of a lamented friend, Mr. Elisha Dunbar, late of 
Hartland, Vt. to illustrate, by a similar process, some of the leading 
properties of the cycloid. 
Middletown, Conn. October, 1831. 
ciao: sae a 
Ant. V.—On Sugar from Potatoe Starch ; by S. GuTHRIE- 
FOR THE AMERICAN JOURNAL. ? 
potatoe 
Mr. Editor-—From the accounts of making sugar from pe 
starch, to be found in most of the recent works on chemistry; 
led to believe that in remote inland districts, where the potat 
grows abundantly, potatoe sugar might be made advantageously; 
to the population of the district, and to the manufacturer bims? 
