74 DISPLACEMENT INTERFEROMETRY BY 



X io~ 3 (since the load of the bifilar is 2m if m is the mass of each ball) and 

 put M=io 3 grams, w = i gram, 2R= 10 cm., /" ' = 30 cm., 



7=- -2 AAT = 4.8Xio- 6 Xd 2 XAW, nearly 



3oXio 3 Xi 10 



or 



If d is estimated as 3 cm., then AN = 0.0016 cm. With the given interfer- 

 ometer and reasonable estimates as to the other magnitudes, one should 

 therefore obtain nearly 40 achromatic fringes (even with the bifilar as 

 stated) for the attractions of i kg. 



There would be no gain, in case of the bifilar, by increasing the mass m 

 at the ends of the needle; for the modulus of the bifilar increases as m, which 

 would therefore cancel the m in the denominator of the expression for 7. 

 But if the system is floated in water, m may be increased with advantage 

 indefinitely, while the load of the bifilar is kept constant by providing a 

 corresponding float. If this bifilar load is w', we therefore have 



d- II' cos * 



~ ni s 

 Mml" g L 



v = ~ ni s -- AA 

 " g 



Inserting the data of the apparatus of the next section, 



M=iog. w = 3og. m' = 2 

 cm. 2 - L = $o cm. 2 = 45 2.R=iocm. 



3oXio 3 X3o 50 10 



or 



AW = 0.01 7 cm. 



per attracting kilogram. With a reasonable size of float there is no difficulty 

 in increasing the attracted mass m to over 60 grams and the attracting 

 mass (with a slight increase in d) to 10 kg., so that values of AN of the order 

 of a millimeter are not out of the question. 



The difficulty with the method lies in the simultaneous increase of the 

 period of vibration of the needle, and this seems fatal; but I thought it worth 

 while, nevertheless, to give the method a trial. 



42. Observations. Floating system. Figures 52 and 53 represent the 

 floating needle submerged in the narrow trough AB provided with two win- 

 dows of plate glass w w', through which the interfering beams enter and leave, 

 nearly at right angles to the co planar mirrors n and n' attached to the needle. 

 This consists of a tube of aluminum, about 30 cm. long and 6 mm. in diameter, 

 with balls at the ends m and m', pairs of 30 grams to 60 grams each being 

 admissible. The two hooks h and i carry the floats F, F', test tubes as much 



