Methods of describing Various Curves for Arches. 



73 



King's patent cast iron paddle gates are used for filling and dis- 

 charging the lock. They are inserted in the lock gates adjoining the 

 coin post, between the two lower arms. The form of this gate is 

 represented in Fig. 3 ; — a, is the blade of the gate ; b and c, are the 

 fixtures which are attached to the arms of the lock gate, and in which 

 the paddle gate turns. A short post is placed between the lower 

 arms at the breadth of the paddle gate from the coin post. The 

 paddle gate is hung on the upper side of the lock gate, so that when 

 open, the blade will not project on the lower side. Into the socket 

 in the top of the paddle gate, a large rod is inserted, which extends 

 above the balance beam, and on the top is placed a wrench by which 

 the gates are turned. At d, a portion of figure b is represented sepa- 

 rate, which can be detached, and the paddle gate inserted, or remo- 

 ved as occasion may require. . 



Cincinnati, January 21, 1833. 



_/ 



Art. VIII. — On the methods of describing various curves for Arches; 



by J. Thomson, Civil Engineer, Nashville, Tenn. 



TO THE EDITOR. 



rx 



Sir. — The following observations on the methods of tracing vari- 

 ous curves for arches, are submitted for publication in the American 

 Journal, with the hope that they may be found useful to mechanics, 

 by saving the time and labor of tedious calculation. 



In regard to the method of describing oval arches, the communi- 

 cation of Mr. Miller, in Vol. XXII, No. 2, of this Journal, contains 

 much useful information ; yet the merely practical mechanic, unac- 

 quainted with algebraical calculations, is still uninformed in regard to 

 the method of finding the point D, (fig. 1) or the distance CD, the 

 determination of which is the only difficulty he will encounter. The 

 distance CD, in that communication, is only expressed in indefinite 

 parts, and not by means of a quantity derived from the ratio of AC 



toCB. 



of the arch by the following decimal numbers. 



difference of the rise and half 



Vol. XXIV.— No. I - 



10 



