iVZi 



If we liave drawn the line \f{Z)(U and we join any divisional 



point witli M, we find llie slope of tlie chain on tlie place of tlie 



load, corresponding to the divisional point. So e.g. in figure 4 the 



slope at 3„ will be represented by the line EM. To calcnlale the 



slope with regard to the l^'-axis, we deduce from the congruence 



of the triangles SET and MEO, that the increase of height TE 



EO 

 which we may indicate as AA, is = — V ST. 



As EO represents the integral latei-al pressure, consequently 

 \f{Z)dl and OM the total longitudinal tension P, whilst >S7' repre- 

 sents the length LI of the chain of which the slope has been calcu- 

 lated, we can write, passing to infinitely small differences 



dl r 

 dh = -j/{Z)dl 



or integrating: 



h = ^j(^dljf{ll)dl^ 



We may apply this reasoning to the string galvanometer. We find 

 then that the lateral pressure whicii we called f{Z), is proportional 

 to the intensity of current in the string [ and to the field-intensity 

 H at every point which may be written f[IH), or as 1 is constant 

 over the length of the string, If{H). 



For the galvanometer we get the expression : 



iM' 



t{H)dl 



if the coordinate-system has its origin in the point N. If we take 

 the point N^ i. e. the middle of the not-deviated string, this expres- 

 sion becomes: 



K = ^ \jdi (^J/mdi^ - j^di (^Jf{H)di\ j 



o 



in which the definite integral has simply the meaning of the maximal 

 deflection iViY, of the string at the existing intensity of current 

 and tension. 



If we keep to a coordinate system originating in JSf, we arrive at 

 the conclnsion that the shape of the string is related to the local 

 intensity of the magnetic field , in such a way, that we obtain an 

 expression for the shape of the string by integrating twice succes- 

 sively the expression for the magnetic field. 



