the Winding of Voltmeters. 



107 



as ordinate and a as abscissa, and by means of this curve for 

 any value of <j)(a) given we could at once find a approximately. 

 Table II. was then arrived at in the following way: — A 

 value of p was chosen, and 4>(p) written down. Then since 

 0857 <j>(p) is equal to <j>(ri) by (15), n was known from this 

 by the curve for <j)(a); m was next found in the same way 

 from (16). Thus columns 1 and 4 in Table II. contain 

 values of p and n which satisfy (15), and which were ob- 

 tained in this way,, while in columns 1 and 6 we have values 

 of p and m which satisfy (16). 



Table II. 



V- 



<P(p)- 



0-857 <f>(p), 

 or <p(n). 



n. 



11430(2)), 

 or 0(m). 



m. 



2 



1-6124 



1-381 



103 



1-842 



4-35 



1 



1-3764 



118 



0-39 



1-572 



1-78 







1-0397 



08913 



-0-425 



1-189 



0-425 



-1 



0-70295 



0-6026 



-1-370 



0-8035 



-0-69 



-2 



0467 



0-4002 



-2-38 



0-5337 



-1-69 



Now first using the pair of columns 1 and 4, we chose 

 corresponding values of p and n, say 2 and 1*03 ; then, since 

 from (14) 



and 



2 = 2 + l-1436-4ci, 

 l-03=4—a + l, 



we could calculate a pair of values for a and b which satisfy 

 (14) and (15), since d was assumed to be known. Next 

 taking another pair of values of p and n from Table II., 

 another pair of values of a and b was calculated, and so on. 

 Plotting these values of a and b as coordinates of points on 

 squared paper we obtained the curve sss, fig. 1 *, the coordi- 

 nates of every point of which are the values of a and b that 

 satisfy (15) . In the same way we drew the curve t tt for (16) , 

 and the coordinates of the point of intersection Z are the 

 values of a and b which satisfy (15) and (16), and therefore 

 make the error (9) a minimum. 



Thus for example, taking d= — 1, as seems to be the case 

 in our solenoid instrument, we find that, with some approxi- 

 mation to accuracy, 



a=0'19 and b= -0*82 



* This and the two succeeding figures are only about one twelfth of the 

 aize each way of the figures actually employed in the calculations. 



