WRIGHT: A NEW DIP CHART 443 



graphy."* In this paper the general principles underlying the 

 construction of graphical plots for the solution of equations are 

 discussed in some detail; of these principles the most important 

 are: (1) Uniformity in relative accuracy over the entire plot, and 

 comparable to that which obtains in nature (distortion as slight 

 as possible); (2) the use of straight lines rather than curves, 

 wherever possible. In the present instance such uniformity is 

 best obtained by plotting the sine and tangent functions directly 

 rather than the angles themselves. The diagram is then a straight 

 line diagram throughout and the distortion present corresponds 

 to that of the equation itself.^ In the new chart all variables are 

 represented in 1° intervals. The relations underlying the con- 

 struction of this chart are shown in figures la and lb in which 

 the sides of the square (MO) are equal to unity. The triangles 

 KOL and MON are similar and the proportion obtains 



KL :K0 = MN : MO = MN. 



In figure la we have by construction 



KO = sin B, KL = tan C, and MN = tan A. 



On substituting these values in the above proportion we obtain 

 equation (1) above. Similarly in figure lb (C < 45°, tan C < 1) 

 we get on substitution 



tan (90 - ^) : sin 5 = tan (90 - C) 



an equation identical with (1). 



Compared with the Hewett chart the present chart has the 

 advantage of greater precision but it is, in one respect, appar- 

 ently less satisfactory, namely, that when the angle C < 45°, 



' Am. J. Sci. (4), 36: 509-539. Plate VIII. 1913. 



5 From the standpoint of the graphical representation of an equation, we 

 may consider the above equation to be an expression of direct relations be- 

 tween the functions themselves rather than between the variables under the 

 functions. Fundamentally, of course, the equation expresses relations between 

 the variables, and the increments are so taken. The procedure here adopted 

 amounts practically to the representation of each function by a scale so chosen 

 that the resulting curves are straight lines. The same principle underlies the 

 construction of the slide rule and other calculating devices; also the use of 

 logarithmic paper. 



