THE^AID OF THE ACHROMATIC FRINGES. 



35 



at the interferometer and thermometer near the period of maximum tempera- 

 ture, after which the coil would begin to cool. These observations should 

 have been made by two observers ; but by confining the work to temperatures 

 not more than 20 above atmospheric temperature, it was found possible to 

 take both readings in succession without serious error. 



A large number of experiments were made both in terms of the ocular 

 micrometer, Ac (see inset, fig. 38; here the temperature increments must lie 

 within 2) and by the Fraunhofer micrometer AN at the mirror of the inter- 

 ferometer. These very soon showed the reason of the anomalous contraction 

 referred to ; for it was found that all the expansions were apt to begin with a 

 contraction immediately after the heating current had been closed. Hence 

 it is due to the initial expansion of the coil itself. As this was fastened at its 

 two ends to the heavy wooden table, it seemed clear that the consequent 

 flexure of the table was the ultimate cause of the interferometer discrepancy. 

 The end C of the coil (fig. 37) must therefore be left free to expand, as well 

 as the tube T. 



Hence a modification of the apparatus was made by allowing the end C 

 of the coil to recline on a large grooved wheel, which by slight rotation would 

 admit of any expansion of the kind in question. With this improvement the 

 anomalous contractions vanished and the work thereafter proceeded smoothly. 



Of the results obtained I shall give only the example in figure 39, which 

 shows the readings AN of the micrometer in lo- 3 cm., at the different tempera- 

 tures (21 to 35) given by the abscissas. The locus is fairly linear, but the 

 rate of expansion is slightly greater on cooling than on heating, as shown 

 by the arrows. 



If a is the coefficient of linear expansion we may write 



a At = Al/l = (r cos i/bl)AN 



so that 



r cos i AN 



bl ' At 



where the increments Al, At, AN, of length temperature and micrometer dis- 

 placement (the latter brings the achromatic fringes back to a fiducial mark 



