86 DISPLACEMENT INTERFEROMETRY BY 



one-tenth fringe, so that the limiting angle here is to be a few thousandths 

 of a second, even if <p= i, which may also be reduced. By making 2R= 100 

 cm. one should therefore be able to reach o.oooi second per tenth-fringe 

 breadth if <p is i. 



Similarly, if AN reads to icr 4 cm., <p= i, 



. 



Acv = 0.017 5 - = 1.2X10 ' radian 



10 



or 0.025 second of arc, with the opportunity of passing to 0.0025 if R is a 

 meter. 



Finally, on using the ocular micrometer for moderately sized fringes of 

 say one scale part (o. i mm. fringes in the ocular) , the case is equally promising. 

 A comparison of the two displacements AN at M' and Ae of the fringes in the 

 ocular showed 



A = O.I 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 cm. 

 ioAW = i 35 75 120 155 190 225 265 305 cm. 



Fluctuations are due to the motion of the pendulum. Thus the mean 



value is . , r 



AN Ae 



-=0.0038 or- -=265 



Ae AN 



Hence 



. ,, 

 = <pAe cos i 7(265 X2K) 



If Ae= io~ 2 (one scale part) and zR= 10 cm., etc., as above, 



io- 2 Xo.7i 



Aa = 0.01- - = 2.7X10 8 radian 



265X10 



or 0.005" per scale part of the ocular micrometer. A few tenths of this may 

 be estimated on the scale. The sensitiveness would be 10 times greater if 

 2R were a meter. 



50. Observations. The interferometer was installed with rather smaller 

 fringes than instanced above and therefore with less sensitiveness, as the 

 inclination of the pier in a heated laboratory would probably run into sec- 

 onds of arc in the lapse of time. For this reason R was also satisfactory 

 at its small value of 2R= 10 cm. The angle </> was directly measured, as the 

 inclination of the line joining the points of the pivots to the plumb-line. Under 

 these circumstances the constants given at the head of the table suffice. 

 Since Aa = o.9 Ae seconds, roughly, the tenth millimeters of the ocular scale 

 are about o.oi second of arc in relation to Aa and the fringes were of about 

 the same size. There would have been no difficulty in making them much 

 larger and therefore more sensitive, as they were clear and strong. As it was, 

 there should have been no difficulty of estimating within io~ 2 second. 



The end of the compound pendulum was damped in lubricating oil. This 

 is probably too viscous for refined work, but the purpose here is merely to 

 try out the method. 



