76 DISPLACEMENT INTERFEROMETRY APPLIED TO 



so for thicker wires (0.05 cm.). The work may, therefore, be done rapidly. 

 Oil damping, even if not otherwise objectionable, was found to be too slow, as 

 a rule. Thermal discrepancies (air convection) decrease when the wires are 

 thicker; but the disturbances from viscosity increase. 



The frame carrying the wire and the torsion-heads must be quite rigid. 

 If the torsion-head works stiffly, the twist of the framework is always percep- 

 tible. This must be scrupulously guarded against. 



67. Measurements. With the original phosphor-bronze wire, a trial showed 

 a double deflection at 5 of 1.7 per milligram. Half of this is available at the 

 mirrors m, m r . The equation of the interferometer may be written b A0 = AN 

 cos i = X/2, b being the breadth of the ray parallelogram, Ad the rotation at the 

 mirrors m, m', corresponding to the displacement of micrometer AN when * is 

 the angle of incidence (45) and X the wave-length. Thus for the double 

 deflection per milligram 



AN = bA9/cos t = ioX(i. 7/2) Xo.oi75/o.7i = 0.21 cm. 



As AN = io~ 4 /2 cm. can be registered on the micrometer, io~ 4 X2.4 mg. may 

 be estimated. Thus, if a weight of 25 mg. is used, the sensitiveness would be 

 within io~ 6 . 



Per fringe the conditions are somewhat better. For here 

 A0 = X/2&=io~ 5 X6/2o = 3Xio- 6 radians 



and this corresponds to 3 X io~ 6 /o.85 Xo.oi75 = 2 X io~ 4 mg., while a fraction 

 of a fringe is still determinable. 



To make this fringe sensitiveness available, the tangent screw-micrometer 

 must be used, as the achromatic fringes serve merely as an index. Here 

 A0 = X/2& at the mirrors corresponds to 2 A0 at the end of the wire. If AS be 

 the displacement of the micrometer at the tangent screw and R= 18.2 cm. the 

 radius of the graduated circle 5, 



A5 = ^X/&=i8.2X6Xio- 5 /io=i.iXio- 4 cm. 

 per fringe. Fractions of a fringe can therefore here be recorded. 



If t is the modulus of torsion and m the mass weighed at the end of the lever- 

 arm, b'= 1 1 cm., mg b' = tAd, and therefore 



t cos i A , , tn\ 



2mbb' 

 for a passage of fringes. 



In case of the phosphor-bronze wire of diameter 0.025 crn -> the values of 

 / in terms of milligrams would thus be 



*= 10X981 Xn/8.5Xo.oi75 = 7.2X10* 

 Hence if Ag corresponds to one fringe, 



7.2Xio 5 X6Xio- 5 



Ag= = 2X10- 



2X10X10X11 



or if a mass of 20 mg. is used 



