529 



tlie central bore we have a conslant field of an inlensify H^ ; over 

 the length 4 corresponding to the length of the strongest part, the 

 field is also homogeneous and has a density H^, whilst the string 

 continnes l^ejond this part over a distance 1^ where the densitj' of 

 the field falls to nought. The entire length of the string is conse- 

 quentlj 2 {J^ -\- /., -f- 1^). Now we integrate successively over the parts 

 l^ /j and /j, and find for the lateral pressure: 



over /j : iTj = IHJ^ 



over 4 : z^z^ = I {HJ^ + HJ^) 



over I, : z.z^z, = I {RJ^ + HJ,) 



in which the underscoring indicates that we have no longer to do 



witli a variable, bnt with a constant. The line answering to these 



integrals for the lateral pressure is represented by II. 



For the form of the string we obtain after a second integration : 



1 / 

 in part L : A = H.L' 



in part h-^^^^f^ !Ml + !Lb^-^ ^^ \^^^^ 

 and in part ^^ = /' = ^ } ^ ^' + ££A + 2 ^i^L + IMl^^ + HJ,J, 



HA-l^ + hh-V hl^ \-H,(\l,^ + IJ, 



-A 



In the points between /, and /., and between ^ and l^ the line 

 given by the last expression shows a gradual change of direction 

 and not an abrupt one. This is proved by the fact that the value of 



— at the end of /, is equal to -- at the commencement of /.,, if / 

 dl ' ^ dl - 2 



be made = 0. This equality of the differential coefficients holds 



likewise for the transition of 4 into 4 . 



Though perhaps we might obtain a better approximation for the 



shape of the string by supposing 



that the intensity of the magnetic 



field varies according to a line 



of the form represented in fig. 6, 



we can already obtain some 



X practical result with the simple 



y 



f 



p-^. p expression, graphically repre- 



sented in fig. 5. 

 Let us first take the case that the string is not longer than the 

 height of the field, in other terms that L = 0. 



