506 Profs. Ayrton and Perry on the 



for any given speed. It was also pointed out that a tangent 

 function might also be employed, but that it would not lend 

 itself so readily to calculation. We had, both, in 1878 used 

 a curve to express this relationship, but it was not until 1881, 

 when we met M. Deprez, and learnt of his work, that we had 

 any conception of the many calculations which might be 

 made by graphical methods, using the curve as a fundamental 

 relation. Herr Frohlich uses one term of the above expres- 

 sion: — 



E =^o < 15 > 



He regards p the permanent field as 0, and he has no term which 

 remains proportional to the current. We shall speak of (15) 

 as the Frohlich formula, because it usually goes under that 

 name. It is, of course, an empirical formula, like (14). 



The reasoning which led us to regard (14) as a rational 

 formula, was based on a magnetic theory which need not here 

 be expounded. 



A very great necessity exists for having some such em- 

 pirical formula as (15), but, as is well known, it is quite 

 incorrect when c is small. It is not nearly so incorrect as 

 we might imagine it to be from the statements made by 

 Mr. Kapp (p. 529, Journ. Soc. Tel. Eng. and Elect, vol. xv. 

 1887), who has given in his fig. 3 a most absurdly unsuitable 

 Frohlich curve, or by Dr. Hopkinson (plate xvi. Phil. Trans. 

 1886), whose Frohlich is also not the most suitable. It is 

 obvious that the Frohlich ought not to be expected to agree 

 with the real characteristic near the origin. It ought to be 

 made to agree most perfectly with the working part of the 



characteristic. To effect this purpose let the observed values 

 ■pi 



of —and E be plotted as the coordinates of points on squared 



paper. The straight line which lies most evenly among the 

 points for the working values of E satisfies the equation 



^6 + E=a. 



The measured coordinates of two points on this straight line 

 enable b and a to be calculated. 

 Thus, for example, 



N- 1364 F 



~~ l + 2-7xl(T 4 F 



will be found to satisfy the observations published by the 

 Drs. Hopkinson for the Manchester dynamo from F = 6000 to 

 F = 30,000 with a wonderful amount of accuracy. But for 



