The London, Edinburgh and Dublin philosophical magazine and journal of science . he string,and the transverse motion of each element of the string dueto the mutual action between the current in it and themagnetic field is in a third direction approximately perpen-dicular to each of the other two directions. In this paper the string will be treated as if it wereimmersed in a magnetic field the lines of which are parallel,but the force may vary in intensity from point to point alongthe string. As particular cases two different field dis-tributions are considered, first, the uniform field which m
The London, Edinburgh and Dublin philosophical magazine and journal of science . he string,and the transverse motion of each element of the string dueto the mutual action between the current in it and themagnetic field is in a third direction approximately perpen-dicular to each of the other two directions. In this paper the string will be treated as if it wereimmersed in a magnetic field the lines of which are parallel,but the force may vary in intensity from point to point alongthe string. As particular cases two different field dis-tributions are considered, first, the uniform field which mostnearly represents the galvanometer as at present constructed,and second, the best distribution for simplifying the resultingmotion of the string. The open space at the centre occupiedby the microscope and the ends of the string which projectbeyond the field are not specifically considered, as it will boapparent how these irregularities may be allowed for in anapproximate way when the data are known. Let PQ, fig. 1, be the element of any string of length els, Fig. 1. T(+^T(. and confined to a plane. The element is acted upon by thetension Ta at P and the opposite tension Ti+dTx at Q, andthe resultant of all external forces Fds in the plane of thestring acting at any angle %. If the element of the string is at rest these three forces arein equilibrium, and resolving along the tangent, we find 5+FcosX = 0, (1) and along the normal ^-FsinX = 0, ...... (2) dswhere r = -jn = the radius of curvature at String Galvanometer of JEinthoven. 209 The mechanical force exerted upon an element of thestring ds, due to the mutual action of the current I and thefield H, is always perpendicular both to the field and thedirection of the elementary current, that is, it is in thedirection of the normal to the curve assumed by the string, IT and its value is HIds. Hence in (1) and (2) ^ = -; HItakes the place of F, and we have /7T —--1 = 0, and Tx = a constant throughout the (3)as and length
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Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
