376 



Prof. F. L. 0. Wadsworth on 



horizontal edge of the triangle, as in fig. 6. The point e at 

 which the blade of the ruler intersects the side be of the 



FfG. 6. 



triangle will be one of the points on the required curve, the 

 others of which may be found by sliding the triangle along 

 the axis of x, always keeping the two edges of the parallel 

 ruler in contact with the three points o, c, and f. This method 

 is somewhat simpler mechanically, but not quite so rapid and 

 convenient as either of the preceding. 



It is evident that there are six other possible solutions to 

 be obtained by combining the sides ac, ae (fig. 1) with each 

 pair of adjacent sides. But these solutions are unsatisfactory 

 graphically, because simultaneous values of x and y will be 

 represented by lines inclined to each other at an angle dif- 

 ferent from the angle between the axes. If the angle at a is 

 made equal to the angle between the axes, we have one of the 

 three solutions already considered. 



The use of two similar triangles in the graphical, and more 

 particularly the mechanical tracing of curves, is of wide ap- 

 plication. By their aid we may always express the product 

 or quotient of two variable quantities geometrically as the 

 length (tensor) of one of the sides. Other applications of 

 this principle will be found in a recent paper of the author's 

 on the mountings of concave grating spectroscopes*. 



* "Fixed Arm Concave Grating Spectroscopes," F. L. 0. Wadsworth. 

 Astro-Physical Journal, vol. ii. p. 370 (Dec. 1895). 



