20 EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 



Thus the compensation would be, per degree of e, at 



10 io 5 dp= +147 io s dx= 76 



15 + 88 46 



20 O 



25 - 94 - 49 



30 259 129 



Hence, for the whole range of 20 degrees, the compensation would not exceed 

 x = 0.2 per degree of e, or about x=i cm. for e = 5. This estimate is thus of 

 the same order as the above, since the eccentricity of i cm. there postulated 

 makes e = #2 radian or 5 degrees, roughly. 



Finally, inasmuch as considerable alteration had been made at the pendu- 

 lum during the preceding experiments (addition of damper, etc.), it seemed ad- 

 visable to redetermine <p, using, however, the micrometer method, instead of 

 the more elaborate pendulum method. The following values of x were 

 found for successive turns of 6 each of the micrometer screw: 



The screw being a ^-inch screw with 20 threads to the inch, its pitch may be 

 put 0.125 cm. If z is the displacement of the lower pivot for each partial turn 

 of 6, y the distance apart of the pivots, and C the constant to be found, 



a = z/y = Cx radians, or, in seconds of arc, 0=0-31 



The value of C found for the pendulum used in the case above was C= 

 0.515. The difference is larger than was expected; but with the center of 

 gravity but 12 cm. from the axis, the addition or removal of the weights at 

 the end of the beam 60 or 70 cm. from the axis is of marked consequence. It 

 is also surprising that the displacement method is so consistent in its results, 

 as nothing more than an ordinary clock-dial with a pointer was used at the 

 micrometer. These results could easily be much improved. In other words, 

 the present direct displacement method for C=<p/$D, and the above direct 

 momental method for h, are not only much more simple, but on the whole 

 more reliable than the laborious vibration methods. With M they suffice 

 completely for the evaluation of the torque, T = Mghtpd. 



12. Further observations. A final series of observations was now made 

 with the new apparatus, recording under good conditions, in the absence of 

 artificial heating. The trough for the float, supported entirely free from the 

 horizontal pendulum, was provided with a thermometer, which was read off 

 at the same time as the inclination observation. The direct measurement 



