ON A NEW INSTKUMENT FOR DRAWING ENVELOPES. 



623 



giving the virtual centre for the rotation of the paper. It is obvious that 

 a circle with any radius can be at once obtained by turning the direction 

 of the axis of one pair of wheels relatively to the other, for example, 

 when the axes are placed parallel to each other, an infinite radius is 

 obtained, that is, the curves drawn upon the paper is a straight line. 

 From this it will be seen that the range of the instrument is largely 

 extended, and that instead of using an instrument of a very large size, 

 together with trammels for setting out large wheel teeth, such teeth, 

 even for wheels of thirty or forty feet in diameter or of a rack, can be 

 obtained by using a small and compact instrument. 



The principle of the action is explained by the diagram (fig. 7), in 

 which is shown the upper rollers A and B of each pair of rollers through 

 which the sheet of cardboard passes. The position of the pair of 

 rollers A is fixed, while the frames carrying the pair represented by B can 



Fig. 7. 



turn about a vertical axis. In the position shown in full lines, the centre 

 of rotation is the intersection of the axis of A and B at O, and the fixed 

 point P would therefore draw the arc M P N if the sheet of paper was 

 moved by combination with the two pairs of wheels at A and B. If, how- 

 ever, the pair of rollers B are turned into the position a, 6,, the centre of 

 rotation becomes Oi, and the pencil at P would describe the arc Nj P M,. 

 If, on the other hand, it were turned in the position of a.^ b^, the centre of 

 rotation would be O2, and the arc would now be N., P M.,. It will be 

 noted that the points Oj, O2 are outside the turning paper, and that there 

 is nothing to prevent these centres moving away to an infinite distance in 

 either direction by changing the position of the pair of rollers at B until 

 their axis of rotation is parallel to that of the pair A. 



The accuracy with which the circles are drawn having been thoroughly 

 tested by constructing a simple trammel on this principle, the complete 

 instrument shown in figs. 8 and 9 was constructed. From fig. 9 it 



