JOURNAL 



OF THE 



WASHINGTON ACADEMY OF SCIENCES 



Vol. io APRIL 4, 1920 No. 7 



MATHEMATICS. — A graphical method for plotting reciprocals.'^ 

 F. K. Wright, Geophysical Laboratory, Carnegie Institu- 

 tion of Washington. 



In the search for a mathematical function which shall represent 

 satisfactorily the data obtained from a series of experiments 

 it is convenient in certain instances to plot the reciprocals of 

 one of the variables and from the curve thus obtained to deduce 

 the form of the desired equation. Thus a rectangular hyperbola 

 under these conditions becomes a straight line from the equation 

 of which that of the hyperbola can be written down directly. 

 The obvious procedure is either to compute the reciprocals of 

 the given data or to use paper so ruled that the ordinate-scale 

 js the reciprocal scale i/y. 



A second method may, however, be employed which does not 

 require special computations. The principle of the method is 

 illustrated in figure i. Ordinary cross-section paper is used; 

 the ordinate-scale (F-scale) remains unchanged; the X-scale 

 (not necessarily x but any function of x which it may be desired 

 to use) is transferred from the X-axis (OD) to the horizontal 

 line at unit distance {FA, y = i) from the axis; a series of radi- 

 ating lines is drawn from the origin through the divisions of the 

 X-scale, each radiating line {x\) corresponding to the A'-scale 

 division which it intercepts. The intersection of one of these 

 diagonal lines (x'l) with the ordinate (^^'i) is the point P' in pro- 

 jection, just as the intersection of the ordinate (yi) and the ab- 

 scissa (xi) in ordinary projection fixes the position of the point 



' Received February ii, 1920. 



185 



