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XXXV. The Theory of "Moving Coil" and other kinds of 

 .Ball/stir Galvanometer*. By Prof. Harold A. Wilson, 

 M.A.. D.Sc„ M.Sc, F.R.S* 



A 



FORMULA which is usually given for ballistic galva- 



nometers is 



ht . e 



7T- SID «, 



(t7T & 



{ 1 = 



where Q = quantity of electricity passed througli galvanometer. 

 H = magnetic field controlling the galvanometer-needle. 

 Gr=magnetic field at needle, supposed perpendicular to 



H, due to unit current in the coil. 

 T —time of a complete oscillation of the needle. 

 6 — angle of swing of the needle from rest corrected for 



damping. 



If <j> is the steady angular deflexion due to a current /, then 



i= p-tan </>: so that 



IV sin ft 2 

 7r tan (j> 



The above formulas are of course, strictly speaking, only 

 applicable to ballistic galvanometers consisting of a coil of 

 wire having a single small magnet freely suspended at the 

 centre of the coil, and arranged so that at its equilibrium 

 position the axis of the magnet is in the plane of the coil. 



In the following paper the proper formulae for ballistic 

 galvanometers of several types in general use are obtained, 

 and it is found that in several cases they differ appreciably 

 from the above. 



In Prof. Fleming's 'Handbook for the Electrical Laboratory 

 and Testing Room.' vol. ii., the formula for a moving-coil 

 galvanometer is worked out; but owing to an approximation 

 used in the calculation it is not obtained exactly, and it is 

 afterwards given as applying to both moving-coil and moving- 

 needle galvanometers. 



The first type of galvanometer that will be considered is 

 the moving-coil type with a rectangular coil, cylindrical iron 

 core and cylindrical pole-pieces symmetrically arranged. In 

 galvanometers of this type the magnetic field is approximately 

 radial, so that the couple on the coil due to a steady current 

 is proportional to the current and independent of the deflexion. 

 The controlling couple is due to the torsion of the wire by 

 which the coil is suspended, so that the work required to turn 



* Communicated by the Physical Society : read Mar 2d, 1906. 



