436 C. Bar us — Certain generic Electrical 



7. Having thus obtained some general notions of the depen- 

 dence oif\0)/f(0) ojif(0), it is in place to inquire more fully 

 into the form of this dependence. I will proceed in a manner 

 similar to that employed in §4, and postulate the hyperbolic 

 equation (x+l) (y+m)=n. Availing myself of the chart, figure 

 1, selecting for preliminary computation a set of coordinates as 

 carefully as possible from it, 



x=ll'1 y=0'00300 



20-0 164 



50*0 050 



I find the constants Z, m, n to be 



l=— 01360, r/i = 0'0002548, \i=0'03764. 



The values found for I, m, n are exceedingly significant. 

 Since x varies between 10 and 70, I is in general much less 

 than one per cent of x. This observation at once suggests the 

 assumption of a simpler form of equation in which 1=0. 

 Again the positive character of m indicates that larger values 

 of aj ° ° would tend still further to simplify the equation (x+l) 

 (y + m)=n. But «J 00 > ag 5 7 follows from the experiments; 

 hence also 



/P)//P)=">*1°*, 



and therefore the postulation of x(y+m)=M is altogether war- 

 ranted. 



To obviate the necessity of a complete recalculation of «, I 

 used the following method of passing from a\ ° ° and a\ 5 7 to a. 

 If the values s s s', s'\ correspond respectively to t, t'. t", and if 



l + at-\-/3t* l + at' + pt' 3 1 + at"+ fit" 2 ' 



it follows that 



_ (s' — s)(st" z -s"t z ) — (s"—s)(st'*—s't*) 



a ~(st'—8't)(8t"*-s"t*) — (st'' — s"t)(8t'*-8't*y 



from which it is easy to deduce a—a\ ° ° in terms of a\ ° ° — a\ 5 7 . 

 Xow st" ' — s"t—D" and st' ' — s't=l)' are already known from 

 the earlier computations ; and when a correction only is sought 

 s"t 2 and s't 2 may here be neglected as compared with st" 2 and 

 st' 3 , respectively, t being small in comparison with t' and t" . 

 Hence 



rt'l ^3 5 7 



a—al 00 = 



■ t "2J t '2 J)'/ J)" 



which equation, since the fraction (t"jt') 2 is constant, is a con- 

 venient form, and much of the correcting may be done men- 

 tally. I may add that the three quantities «J 00 , afjj, aj 57 



