JOURNAL 



OF THE 



WASHINGTON ACADEMY OF SCIENCES 



Vol. VI JANUARY 4, 1916 • No. 1 



MATHEMATICS. — A simple device for the graphical solution 

 of the equation A=BC. F. E. Wright, Geophysical 

 Laboratory. 



The equation A = BC, in which the letters may represent 

 numbers, or powers of numbers, or functions of variables as sines, 

 cosines, tangents, logarithms, exponentials, etc., is essentially 

 a simplified form of the equation of proportion, A:B = C: D 

 (rule of three) and is so common in physical and technical prob- 

 lems that different graphical methods have been suggested for its 

 solution. A brief discussion of these methods was given several 

 years ago b}^ the writer 1 and the conclusion was reached that, "in 

 all cases it is essential: (a) that the graphical means employed 

 represent the relations adequately and as free from distortion as 

 possible, and (b) that they be easy of application. The first 

 principle requires that in any graphical representation the rela- 

 tive accuracy over the entire field be uniform and comparable 

 to that which obtains in nature." In order to apply this prin- 

 ciple effectively to the solution of a given equation it may be 

 necessary to increase the uniformity in the plotting scale by tak- 

 ing some function of the values in the equation such as the 

 logarithmic function or by raising the values to some power. 



1 Graphical methods in microscopical petrography. Am. Jour. Sci., Ser. 4, 

 36:509-542. 1913. See also R. A. Harris: On uses of a drawing board and scales 

 in trigonometry and navigation. Science, N.S., 18: 108-112. 1903. A diagram 

 or chart for finding the sun's azimuth. Science, N.S. 22: 469. 1905. C. Runge. 

 Graphical Methods. New York. 1912. 



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