hersey: an integrating device 619 



in which 



K =2C (9) 



Any number may be chosen for K, and the templet cut accord- 

 ingly. It is desirable that K be a multiple of 10, provided this 

 does not make the device inconveniently large or small. It is 

 immaterial where the extremities are cut off. Further expedi- 

 ents for simplifying the work, such as the use of templets of 

 graded sizes, or auxiliary base lines for the (x, y) curve, will sug- 

 gest themselves upon examining each particular problem. 



The equilateral hyperbola has the property that the rectangle 

 formed under any point has a constant area. This property has 

 been utilized in various ways for determining the areas of plane 

 figures. One such device is known as Beauvais' hyperbolic tri- 

 angle. 1 The present contribution is nothing other than a gen- 

 eralization of the hyperbolic triangle so that it will determine 

 any function, and not simply areas. 



The statical moment and moment of inertia have been cited 

 as functions which can be evaluated by the new device. Another 

 function, which the writer has met both in barometric altitude 

 calculations and in studying the effect of pressure on viscosity, 

 is the integral of the reciprocal of the ordinate of an empirical 

 curve, 



■*■ dx 



5' 



>xi y 



The templet needed for stepping off this integral is simply an 

 inverted triangle. 



To integrate any function F{x) which can be written f[^{x)], 

 it is necessary only to evaluate J*f(y)dx along an auxiliary curve 

 y = <f>(x). The result will be J*F(x)dx. For example, let it be 



J™X2 

 | e~ x 'dx. Here 

 ji 



F 0) = e~ x * 



4>{x) = x* (10) 



/ (y) = e~y 



1 Engineering News, 66: 340, 628. 1911. 



