74 



On a Method of Drawing Hyperbolas, 



Drawing-pins are fixed in the board at the origin and 

 A the vertex of the proposed hyperbola, and the asymptotes 



Fig. 2. 



+ y 



drawn. Then the paper square, P, is laid against one asym- 

 ptote and a third pin inserted at C. This can be done with 

 greater accuracy if the line EC is continued to the end of the 

 paper. It remains to place a straight-edge S against the pins 

 A and C, and to mark the intersection of it with the line ED 

 at D. Then D is a point on the hyperbola, and by shifting 

 the pin C together with the paper square P to a fresh 

 position on the line Ox, another point can be determined in 

 like manner. One great advantage of the method is that the 

 value of y can be found directly for any given value of x. To 

 do so, it is only necessary to place the paper P so that OE = #, 

 and proceed as before. 



Obviously, too, the instrument might be constructed in 

 metal and arranged so as to slide along the asymptote Ox, 

 drawing a continuous curve. It might consist of two brass 

 bars hinged at C, with a cross-bar clamped to one of them in 

 such a way that its distance from C and the angle between it 

 and the bar P could be adjusted. This cross-bar might carry 

 a pencil or writing-point free to slide along it, and pressed 

 by a light spring against the edge of S. A rough model of 

 such an instrument was made at the time by the author, and 



