JOURNAL ^ 



OF THK 



WASHINGTON ACADEMY OF SCIENCES 



Vol. VI NOVEMBER 4. 1916 No. IS 



MATHEMATICS.— Note on an integrating device. M. D. Her- 

 sey, Bureau of Standards. (Communicated by Louis A. 

 Fischer.) 



This note offers an approximate method for evaluating the 

 integral 



/ = P f(y) dx (l) 



in which f(y) is stated analytically but in which the relation 

 between y and x is available in the form of a curve only. 



yl yZ 



When f(y) takes the form y, — , or — , the integral becomes, 



respectively, the area, the statical moment, or the moment of 

 inertia, about the .r-axis, of the plane figure bounded by the 

 curve, the z-axis, and the limiting ordinates at x l andrr 2 . These 

 three problems are familiar ones in machine design and naval 

 architecture. They are frequently solved, with sufficient accu- 

 racy for the purpose, by plotting an auxiliary curve of squares 

 or cubes if the case requires it, and then determining an area by 

 cutting up the figure into strips of equal width, and applying 

 some average ordinate rule. The present device is offered as 

 a substitute for the latter method. It is equally accurate and 

 more convenient. The applicability of the device is not limited 

 to these particular functions. 



The device consists of a templet, or plane figure, to be cut out 

 of stiff paper, celluloid, or German silver. In its simplest form, 

 the templet is bounded by two perpendicular lines and a curve. 

 Call the two straight lines respectively the back and the base, 



617 



