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 epicydoidal line, intercepted betiveen its middle point 

 and the position of its generating point, hears 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 betiveen its middle point and the posi- 

 tion of its generating point, is 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-elastic 

 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, vvas first suggested by a suc- 

 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. 



Art. V. — On Sugar from Potatoe Starch; by S. Guthrie. 



FOR THE AMERICAIV JOURIfAL. 



Mr. Editor. — From the accounts of making sugar from potatoe 

 starch, to be found in most of the recent works on chemistry, I was 

 led to believe that in remote inland districts, where the potatoe 

 grows abundantly, potatoe sugar might be made advantageously, both 

 to the population of the district, and to the manufacturer himself. 



