493 M. Verdet on the Optical Properties developed in 



and since the resistance of a layer of wires is proportional to the 

 length, and in the inverse ratio of the square of the diameter, 

 \vc should have 



On the other hand, since the sum of the electromotor forces 

 developed in a layer is proportional to the length of the wire, we 



may set/= -4 By substituting these values, the preceding ex- 

 pression becomes 



kffd 2 

 kh + Ld 4 ' 



and its maximum is given by the relation 



kh-Ld 4 = 0. 



As, however, -g expresses the resistance of the bobbin, we see 



that this resistance ought to be equal to that of the galvanometer. 

 The extremities of the wire of the helix were connected with 

 those of a galvanometer constructed according to the system of 

 M. Wilhelm Weber. It is known that the object of the arrange- 

 ments adopted by this physicist, is to allow the deviations of the 

 needle to be reduced to a very small amplitude, the smallness of 

 these deviations being compensated by exactitude of measure- 

 ment. To this end, the needle of the galvanometer is suspended 

 by means of a frame of copper to a vertical mirror placed above 

 the frame of the galvanometer, and itself suspended at the lower 

 extremity of a silk thread without torsion, which supports the 

 whole apparatus. At some distance from the mirror, and almost 

 in the same horizontal plane, is placed a scale divided into milli- 

 metres, above which is a small telescope ; by means of the tele- 

 scope the image of the scale reflected in the mirror is read off, and 

 by conveniently removing the scale and the telescope, it may be 

 arranged that the image of the division on the scale immediately 

 under the axis of the lunette, coincides with the vertical cross-wire 

 when the magnetized needle is in the position of equilibrium. 

 The axis of the telescope is thus normal to the mirror ; as it is 

 also perpendicular to the divided rule, it is easy to see, that if the 

 needle and the mirror, which are invariably connected, are de- 

 flected through any angle, the image of the scale seen in the 

 telescope will suffer a displacement equal to the tangent of double 

 the angle through which the mirror is to be turned, this tan- 

 gent being drawn to a circle whose radius is equal to the distance 

 from the mirror to the scale. Hence it is the same if the axis 

 of the telescope be not perfectly normal to the mirror, provided 





