W. Mason — Netv Harmonic Analyzer. 487 



K dx — ,- sin — dx. (b) 



h a 



Integrating this we have 



K X = — cos — z h ^- (') 



n TT /i 



From tig. 2 is can be seen that Avhen 



1 



£c = 0, i«' = 0, so C 



91 TT 



Substituting this value for C in equation (7 



1 2';^7r.7: , . 



7 (1 - COS —r—). (8) 



n TT K 



This equation merely states that if the instrument 

 curve is so constructed that the abscissae of the tracing 

 point and the abscissae of the curve satisfy equation (8), 

 the tracing point of the instrument will draw an area 

 proportional to the constant desired. To obtain this 

 curve we will refer again to fig. 1. is the angle the arm 

 makes with a horizontal line, L the distance between the 

 pivot and the tracing point, H the distance of the pivot 

 above the axis of integration of the machine, X, Y, the 

 coordinates of the curve with reference to an axis along 

 the axis of integration of the machine, and to one perpen- 

 dicular to it through the point 0, and X', Y', the coordi- 

 nates of the tracing point with reference to the same axes. 

 It will be noticed that X and x are measured from the 

 same axis and when the machine is in operation have 

 simultaneous values ; the same may also be said of X' 

 and o(/. No similar relations exist between Y and y or 

 Y' and y% but as these terms do not appear in the essential 

 equation, this does not matter. From the figure 



• ^ H-X' -^^ H-X 



sin d = — = and 1 = ;: . 



L tan 



Since from equation (8) 



/ -^^z 1 /. 2 n TT X, 

 03 or A = — =^ (1 — cos — ), 



by assuming values of x or X, Y can be calculated and the 

 curve fully determined. 



The only point not determined is what value to use for 

 K. The smaller this value becomes, the smaller the abso- 

 lute error will be, so it will pay us to use as small a value 



