)ETAILED STUDY OF OPERATION WITH NORMAL LOAD 59 



cms, the curve of no-load has a form analogous to the 5 k.w. curve 



this figure. 



It will be noticed that, in practice, it is possible to obtain only a 

 rather limited portion of curve, under load, because the values become 

 more and more unstable as they depart from the minimum current 

 value, either way. 



Theoretical Form of V-Curves. Although, for various reasons 

 considered later, the V-curves always differ slightly in practice from 

 those deduced from the diagram, it is interesting to determine their 

 theoretical algebraical equation. 



If we note that the current / and the power P 2 are given, by eqs. 

 (4) and (8), in terms of E ly E 2 , ?-, and 0, it will be seen that we only 

 need to eliminate <f> between these two equations to obtain the desired 

 relation between E 2 and 7. 



From eq. (4), expanding and 'replacing sin f and cos 7- by their 



v- r 



values and , we have 



E 1 2 =E 2 2 + (Z/) 2 + 2E 2 [ZI cos cos ?+ZI sin < sin r } 

 = E 2 2 + (Z7) 2 + 2 P 2 R + 2XVE 2 2 P-P 2 * 



The equation obtained on squaring to remove the radical sign is 



This equation is of the 4th degree in 7 and in 2 . The V-curves 

 obtained, in rectilinear co-ordinates, taking E 2 as abscissae and 7 as 

 ordinates, are therefore more or less complicated curves of the 4th 

 degree. They may be calculated by points by solving with respect 

 to 7, for example, but the calculation is unnecessarily complicated; 

 and the graphical construction shown in Fig. 31 is preferable. 

 In the particular case where 7> 2 =o the equation reduces to 



i.e., an assemblage of two easily constructed ellipses whose axes inter- 

 sect each other as shown in Fig. 34. The V-curve for no load is there- 

 fore formed of two branches of an ellipse which intersect each other on 

 the axis of amperes. The sections of it which are in the useful portion 

 are almost rectilinear. 



