273 



The approximate values of 8 may be derived by dropping its square 

 and neglecting its effect on the sign of the velocity. The errors intro- 

 duced by these approximations are, it may be observed, much less 

 than those resulting from the same approximations in deri\'ing the 

 initial values of z. The resulting equation may be written: 



(8/3 tt) tan <^d5/adi+25{±[sin (at-\-^) + Zi\} 



+ (8/37r) tan (pbzJadt-iSlZir) sin (ai+iS) 



± [sin (ai + iS) + 2i]2 = (32 A) 



in which the positive sign is to be used when the primary current, 

 corrected by Zi, is positive, and negative when it is negative. 



By using the same increment, Aat°, as in the first determinartion of z, 

 equation (32A) becomes: 



6(5-5o)+25[sin (at+^) + Zi]-R=0 (33 A) 



in wliich b has the value previously determined, sin (at-\-l3)-\-Zi 

 is the numerical value of the velocity as first corrected and: 



-R= (8/37r) tan (^d^i/da^- (8/37r) sin (ai+/3) ±[sin iat+^)^ZiY (34A) 



The first term in this expression for R may be evaluated hj placing 



(8/3x) tan 0d2i/daf= (8/37r) tan 0A2i/(7rAa^7l8O) = 6A£i 



in which Azi is the average of the increments of Zi for the preceding and 

 ensuing increments of af+/3. 



It may be observed that R is the residual by wliich the first member 

 of equation (28A) differs from zero when the first approximation to 

 a value of z is substituted therein. 



From equation (33A): 



5=(5o-i?/6)/[l+2[sin {at + ^)+z,]/b] (35A) 



The values of 8 for successive values of at-{-^ may be computed 

 from equation (3 5 A) by the same process as that employed in comput- 

 ing z from equation (3lA). 



A second correction may be applied, by the same procedure, if the 

 corrected values of 22=^1+^ give residuals of more than negligible 

 magnitude when substituted in equation (34A). 



24. The increments Aat° used in computing the correction factors 

 shown in table X, paragraph 261, ranged from 2)2°, for small values of 

 0, up to 10° for the small values of i/B when (j)=80°. 



