The expression for ft remains tlien : 



[f we give to /^ -j- /, the length of 50 milHmeters, to H, the 

 value of 4000, to H^ the valne of 20000 gausses, we obtain, if 

 the bore possesses a radius /^ ^ 10 or 7 millimeters, deviations 

 h bearing a proportion as 17.8 to 19.832. This means that the 

 smaller bore of 14 millimeters diameter gives an increase of the 

 sensibility of 11 7o as compared with a perforation of 20 millimeters, 

 the height of the field being in both cases 100 millimeters. 



Since 1909 I have used a galvanometer in which the perforation 

 has been reduced to 13.7 millimeters, for which the firm of Zeiss 

 has constructed a special apochomatic objective. The Cambridge 

 Instrument Cy. has of late likewise reduced the bore of their 

 instruments. 



With the formulae given above we can also approximately calculate 

 the change in the sensibility if the height of the strongest part of 

 the field is shortened whilst the length of the string remains constant. 



Let us write for that purpose: 

 1 



H. 



2 h' i- h ih + h) 



+H,(^-^h' +Lhy 



If L_-\-h *^'e constant, e.g. =50, and if we give to /.successively 

 the values 50, 45, 40, 35, 30, whilst I, remains =7; if further i/. 

 be 4000 and B, = 20000, we obtain for h 26.47, 26.22, 25.47, 

 24.22 and 22.47. This means that a diminution of the height of the 

 field of 10 7o gives only a diminution of the sensibility of 0.8 "/„ ; 

 a diminution of height^ of 20 7^ takes 3.8 7^, one of 30 7„ 8.2 7, 

 away from the sensibility. 



From this we may conclude that it is of no consequence, if the 

 length of the string exceeds the height of the field by 10— 157„. On 

 the other hand with a given length of the string the height of the field 

 may be 10 — 15 7, less, without causing an appreciable loss of 

 sensitiveness. Now it is possible that with a given diameter of the 

 iron-core a diminution of the height of the field might cause a slight 

 increase of the density, by which even the slight loss caused by an 

 excels of length of the string over the height of the field would be 

 entirely compensated. I must add, however, that I have not given 

 any further consideration to this question. 



