102 



DISPLACEMENT INTERFEROMETRY APPLIED TO 



= 



radian 



2X378 



and the displacement, x, of either end of the needle, therefore, if y is the 

 corresponding scale reading in the telescope, 



All the work was done in the semi-subterranean basement of the laboratory 

 and in the dark, except for the light which came through a ground-glass screen 

 from the lamp at the scale. The room was so damp that electric charges are 

 out of the question. The thermostat indicated temperature changes rarely 

 exceeding a degree per day. 



84. Long-period observations. A number of early readings, taken at inter- 

 vals of about half an hour with the weight M alternately on opposite sides of 

 the needle, are shown in figure 1 18. There is some drift, and if the observations 

 be distributed in triplets, the successive double amplitudes Ay (marked on 

 the curve) make a decreasing series. The mean is Ay = 5. 4. From these, 

 the actual double amplitude of the shot may be computed for each case, the 

 mean value being A* = 0.0786 cm. This is about half the value obtained with 

 the former quartz fiber, but it suffices. The reason for the irregularities and 

 variations of figure 1 18 is at the outset hard to ascertain, even if the needle is 

 never quite at rest. The shot, in other words, undergo something that is 

 analogous to the Brownian motion of motes or very small bodies, except 

 that the cause here may be surmised to be referable to temperature differ- 

 ences and convection currents (dynamic pressure reductions) in the sur- 

 rounding air ; but one is at first very far from understanding all these vagaries 



As the apparatus was arranged, the observer sat in a neutral position (plane 

 of the needle) within about an average meter from the 1 1 ft 



needle-case and controlled the attracting weight M man- 8 

 ually. It is possible that control from a remote distance 

 would be preferable, but I did not at first think so. Later 

 I worked from a distance only; but the results were no 

 better. 



Some time after, the apparatus was taken apart for the 

 determination of the torsion coefficient t of the filament. 

 For this purpose a little vertical brass cylinder was sus- 

 pended from the wire. If T is the period and K the mo- 

 ment of inertia of the cylinder oscillating about its axis, 



The cylinder weighing 1.768 grams and being 0.4735 cm- 

 in diameter has for its moment of inertia K = 0.0495. The period T of this 

 system was almost exactly T = 6 seconds. Hence if the semi-length of theneedle 

 is r = ii cm., the two shots at its end each 0.59 gram, and the mass of the 

 straw shaft 0.58 gram, the moment of inertia of the needle is 190. Thus 

 the period of the needle should be (apart from damping) ^ = 37 seconds or 6.2 



