THE AID OF THE ACHROMATIC FRINGES. 27 



15. Observations. The helix C in figure 29 was slender in shape, the length 

 being 37 cm. and the diameter withi i being about 1.5 cm. There were about 

 1 1.2 turns per centimeter per layer and 8 layers of wire, so that the field within 

 may be estimated at H=noi gauss, i being the current in amperes. The 

 current o.oi to over 2 amperes thus corresponded to field from i to over 200 



gauss. 



The rod first selected was of low-carbon shop steel, 43 cm. long. Thus it 

 projected a few centimeters beyond either end of the helix. 



The displacement of fringes observed was characteristic, being (in the smal- 

 ler fields) slow and deliberate on closing the circuit (so that their motion could 

 almost be followed by the eye), but very rapid on breaking the circuit. In 

 the higher fields (200 gauss) there is always much jarring on closing the circuit, 

 as though the rod passed through the whole antecedent cycle of elongations. 

 The fringes are turbulently displaced and only gradually subside. Reading 

 is more difficult. 



The experiments were begun with small fringes (about o.i mm. in the 

 ocular), and the readings Ae were made in terms of an ocular micrometer 

 scale, which was a centimeter divided into o.i mm. Comparing this with the 

 datum AA^ of the displacement micrometer normal to one of the mirrors of 

 the interferometer, the relation was found to be 



A = 2 2 X i o 3 A./V cm., or- = 45X IG~ D 



Ae 



If AJV corresponds to the angular displacement, A0, of the contact lever and 

 to A/ of elongation of the iron rod r in the helix C (fig. 29) we may write as 

 above, 

 (i) 



if i is the angle of incidence (45) at the mirrors of the interferometer and 



b the breadth of the ray parallelogram. 



But 



(2) A/ 



if r is the normal distance of the line of thrust of the rod rr from the axis a 

 of the contact lever. Thus 



. rcosi , rcosi 



(3) A '=~6- 



If / is the length of the iron rod A/// will be the datum required. 

 If the above data are inserted, the coefficient becomes (/ = 43 cm.) 



' ,o^X4.5Xia,-.<rX5.34A. 



. 



so that 



A/ = io~ 5 X2.A cm. 



