WRIGHT: SOLUTION OF EQUATION A=B-C 3 



struction is based on the factthatan equation of the typeA = BC 

 can always be expressed in such form that each factor has a value 

 less than unity; for, in case a factor is greater than unity, the 

 equation can be so written that the reciprocal of this factor is 

 taken, which is then less than unity. The graphical solution 

 of the equation by a straight line diagram can be accomplished 

 either by a method of similar triangles or by a method of pro- 

 jection which, however, is also a method based on similar tri- 

 angles. Both methods furnish results of the same order of 

 exactness. Convenient forms of solution by the two methods are 

 illustrated in figures 1 to 4, in which a refers in each case to the 

 solution by similar triangles while b represents the solution by 

 the method of projection. In figure 1 A, B, C are less than 

 unity; in figure 2 A, B, C > 1 ; in figure 3 A, B < 1, C > 1 ; in 

 figure 4 A, B > 1, C < 1. 



In case it is inconvenient to use reciprocal values, it is possible 

 to extend the range of the solution by changing the scale of the 

 base line from 1 to 10, or to 100 or to any power of 10. This 

 amounts simply to the shifting of the decimal point in one of the 

 factors. 



In the first method (figs, la, 2a, 3a, 4a) it is evident that if the 

 values of A, B, C be plotted along the side lines the remainder of 

 the solution is simply a matter of rectangular coordinates; and 

 similarly for the solution by the method of projection. 



The graphical solution on the basis of the above relations is 

 readily accomplished by attaching permanently to a small draw- 

 ing board of the usual size (19" x 26") a sheet of 1 mm. coordi- 

 nate paper, 50 cm. square, at one corner of which a straight 

 edge fits in a fixed socket so that it can be rotated about this 

 corner as axis (fig. 5) . To solve an equation such as sin A = sin 

 B sin C, two sine scales are first prepared by marking off the sine 

 values directly (listed in sine tables) on a narrow slip of 1 mm. 

 coordinate paper; these are then attached to the bottom and right 

 side of the large sheet of coordinate paper as indicated in figure 5. 

 In case B and C are known, set the edge of the rule at the value of 

 B (40° in figure 5), find the abscissa C (41° in figure 5) and pass 

 along its ordinate to the intersection with the edge of the rule; 



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