531 



From oiir formulae we can obto'm a better insight into the signi- 

 ficance of the average active intensity, in a not homogeneous field. 

 Active intensity means the intensity of a perfectly homogeneous field 

 causing the same deviation h as can be obtained in the not homo- 

 geneous field. We get the expression -. 



Be again H, = 4000 H^ = 20000, /, = 7 mm. and /, = 43 mm., 

 then Hw, the active density, is lo843, whilst the arithmetic average, 



^1 + ^. 

 calculated as H, -]- [H^~H,)-- — - amounts to 17760. 



We niciy add here, that the aN erage active value can also be 

 obtained with sufficient accuracy by dividing the square of the 

 average intensity by the maximal intensity : 



H ' 



ri ■'-'- 1,1 em. 



^ max. 



In the example chosen, this empirical formula results in //«. = 

 15771 instead of 15843, as first calculated, consequently an amount 

 differing by less than 72 "/o ^'om the real \alue. 



The mathematical connection between the shape of the string 

 and the local field-intensity enables us either to calculate or to 

 construct the shape of the string if the local intensity of the field 

 be known with sufficient accuracy. 



I have tried to measure the local field intensity by different methods. 

 Firstly Prof. P. Zeeman had the kindness to try his method depending 

 on the resolution of the spectral lines into doubles in the magnetic field. 

 As in the narrow and high interferricum the spectral tubes filled 

 with Helium or with Hg vapours were destroyed in a few seconds, 

 this method has not given practical results. 



Therefore I had to apply other methods, viz. the bismuth-method, 

 and the method with the magnetic balance of Cotton. 



For the bismuth-method I used thin wires of pure bismuth furnished 

 by the firm of Hartmann-Braun. The measurements were made by 

 means of a wire of 0.17 mm. diameter and a length of 12 mm. 

 with a current of 1 inilliampère. The temperature of the wire was 

 measured repeatedly by measuring its resistance, after the field had 

 been reduced as near as possible to nought. The results were finally 

 calculated by means of the formula : 



7^= 2060 + 8^ + (120.9 -1-- 2 At) A 

 which formula had been calculated from earlier measurements 

 published by Henderson and later measurements of myself. 



