784 



Physics. — ''Dn the theory of the stri?ic/ i/a/vanotiiet<'r of ^{^iTHOW.ti." 

 By Di'. L. S. Ornstkin. (Couiiiiunicak'd by Prof. H. A.Lohkntz.) 



{Gommunicatt'd in tlie meeting of September 2G, 1914). 



§ 1. Mr. A. C. Crehore has developed some considerations in 

 ilie Phil. Mag. of Aug'. 1914'), on the motion of the string galvano- 

 meter, which cause me to make some remarks on this subject. 



For a string, immersed in a magnetic Held H, and carrying a 

 current of the strength J, the differential equation for the elongation 

 in the motion of the string is 



a^+'^ö^^^ d^^ + V ^'^ 



in which x is the constant dampinu' factor, a'' = — , 1\ is the tension 



Q 

 and Q is the density. The direction of the stretched string has been 

 chosen as the r-axis. For .r == and ,r — / the string is üxed, so 

 // = 0. In deducing the equation the ponderomotive force is supposed 

 to be continually parellel to the elongation //, which is only approxi- 

 mately true, since the force is at every moment perpendicular to 

 the elements of the string (perpendicular to ./ and H) ; but if y 

 may be taken small, then the e(iuation (1) is valid. The approxi- 

 mation causes a parabola to be found for the state of equilibrium 

 witli constant H and ,/, instead of the arc of a circle, as it ought 

 to be; however, the parabola is identical with a circle to the degree 

 of approximation used. 



Dr. Crehore now^ observes, that the equation (1) may be treated 

 after the method of normal coordinates by putting 



1/ = ^ (f ^ nv \^) 



Besides the equation 1, he deduces a set of equations, the "circuit 

 equations", which give a second relation between (fs and J (from 

 {1) there originates in the well-known way an equation for every 

 coordinate ^/,). The obtained solutions will be independent, when 

 the circuit equation is true, and again their sum is a solution of the 

 problem. However, from the deduction of the circuit equation it cannot 

 well be seen whether this is the case, since not entirely exact 

 energetic considerations underlie this deduction. Now supposing the 

 string to be linked in a circuit with resistance R, and self-induction 

 L, the circuit-equation may be easily found by applying Maxwell's 



1) Theory of the String Galvanometer of Einthoven. Phil. Mag. Vol. 28, 19U, p. 207. 



