88 IOWA ACADEMY OF SCIENCES. 



A simple and satisfactory model of this kind is here 

 described. On one side of a board KL, Figs. 6 and 7, about 

 40 by 7 inches, and standing on edge upon a second board 

 which serves as a base, are two pulley cones with four 

 (grooved) steps on each ; and these are so proportioned 

 that when a belt or endless cord passes over correspond- 

 ing pulleys in the two cones their relative angular veloci- 

 ties will be in the ratios 1:1, 3:1, 2:3, or 1:2. Upon the 

 axes of these cones, and revolving with them, but on the 

 other, or front, side of the board KL, are two cranks AC 

 and BD. A connecting rod BEC actuated by one crank, 

 AC, slides horizontally upon the shaft B of the other crank, 

 being slotted at the end B for this purpose. Another rod 

 DC actuated by the crank BD has at one end, G, a sleeve 

 which slides in the long slot EG of the other rod. A pen- 

 cil, at right angles to the upright board, and carried in this 

 sleeve, G, traces the curve upon a sheet held or pinned 

 against the front of the board. To press the pencil against 

 the paper a rubber band may be passed around the outer 

 end of the pencil and the end of the rod at G. 



With the belt thrown off the pulleys, it may be shown 

 that the crank AC alone produces harmonic motion in 

 a vertical line ; and that the crank DB produces horizontal 

 harmonic motion. And it is plain that the curve traced 

 when both cranks revolve is the resultant of both these 

 motions. 



If the radii of the pulleys are not exactly in the simple 

 ratios 1 :1, etc., the model is the more instructive as it shows 

 the mechanism of the progressive motion or revolution of 

 the curves produced by tuning forks in the similar case • 

 The fact that the curves are slightly distorted because the 

 right and left motion of G departs from a strictly horizon- 

 tal direction in the upper and lower positions of C does 

 not detract from the usefulness of the model. Tlie longei' 

 the model is in proportion to the lengths of the cranks, the 

 smaller will this distortion become. 



In Fig. 7, the belt is on the two equal pulleys, or the two 

 motions are in unison. If the belt be in the position shown 

 by the dotted line the model produces the curve of the two 



