EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 



whence D is equal to 914 cm., which agreed with the direct measurement. 

 The center of the images ("mean") holds pretty well to the scale, shifting 

 but from 13.7 to 16.1, while the distance D is smaller and the total angle 

 (0.8/51.5 radian, about i degree) larger than would usually be employed. 



In the experiments made below, the distance D was frequently above 2,000 

 cm. Since i second of arc is about sXio- 6 radians, the deflection x corre- 

 sponding to 6= i sec. would therefore be 



x = 4 X 2000 X 5 X io- 6 = 4 X io- 2 cm. 



or nearly half a millimeter. A sharp focus F", F'" is thus nevertheless needed 

 if single seconds of 9 are to be read off visually. I frequently made use 

 of what seemed to be the internal diffraction patterns 

 of the slit, fine bright lines in each being used for 

 measurement. 



The angle 6, denoting the deviation of the pendulum, 

 is invariably very large as compared with the angle a, 

 the corresponding change of inclination of the pier to 

 the plumb-line. In fact, fig. 2 , cdg denotes the horizontal 

 pendulum, with the grating at g, pivots at c and d, the 

 center of gravity at G, at a distance h from the axis cd. 

 The latter prolonged intersects the plumb-line through 

 G at e, all in the plane of the diagram. The angle 

 between the axis de and the vertical df is <p in the same 

 plane. When the axis, owing to the tilt of the pier, 

 takes a new position de', the arc ee' is nearly 



h'0=H' a 



When tp is very small, as is necessarily the case, h = h' and HH' very 

 nearly, so that 



hd = Ha and h H<p whence a = <pd 



Thus if de is a rigid stick pivoted at d and fe a flexible inextensible line, the 

 motion is such as if the whole mass of the pendulum were concentrated at e, 

 the diagram being the plane of the couple Mgh = MgH<p. 



As in a = tp6 all angles are given in radians, if the angle <p is of the order of 

 i, the ratio a/6 is but 0.0175. I need merely instance, therefore, if <p = o.oi, 

 since X = 4Da/<f> and D = 2,000 cm. (as above, conditions all of which are 

 easily realized), that per second of arc of a, x = 4 cm. 



The form which the scaffolding eventually took is shown in the diagram, 

 fig. 3, in elevation. All rods were of %-mch iron pipe; so that, if desirable, 

 a current of water could have been passed through the essential braces. FF' 

 is a long rectangle of gas-pipe, 240 cm. from end to end and io cm. high. Its 



FIG. 2. 



