EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 11 



of arc, and they agree in order of values with the data of the steel pendu- 

 lum attached to the pier. Values of a, however, made at the same time, 

 do not show the same run of variation, which may be reasonable, as the 

 present pendulum is erected on the concrete subfloor of the laboratory. It 

 was supposed that some change of inclination would result from the pos- 

 sible shifting of the lower pivot in its socket after the jar following an 

 explosion, but there is no certain evidence of this. The chief purpose 

 of these experiments is thus the comparisons which they will offer with 

 the cases of the following paragraphs where the pendulum is partially 

 supported on a float. 



6. New apparatus, with float. Horizontal pivots. A thin cylindrical 

 sheet-copper float was now prepared, about 10 cm. in diameter and 10.3 cm. 

 high, weighing with appurtenances 175 grams. It was attached symmetri- 

 cally to the axis, and the method of submergence is shown in fig. 7, where K 

 is the float and C the water- vat. Three vertical brass wires about 2 mm. in 

 diameter, 120 in horizontal angle apart, pass from the disk i through the 

 surface of the water. The buoyancy was found to be 627 grams by direct 

 measurement, whereas the remainder of the pendulum weighed 697.5 grams. 

 The effective weight was thus only 70.5 grams. Subsequently, to increase 

 the moment of inertia and to move the center of gravity further from the axis 

 (in the interest of greater permanence at the pivots), an additional weight 

 was attached at the end of one arm, bringing the total weight to M = gji 

 grams and the effective weight M V to 169.2 grams. The center of gravity 

 of the solid pendulum was moved outward from 8.1 cm. to 13.1 cm. from the 

 vertical axis. Moreover, the value of the factor is now M/(M V) = 5.74. 

 Inasmuch as the greater part of the weight was supported by the float, the 

 pivots were here tentatively placed horizontally, the lower fitting into a coni- 

 cal hollow of glass-hard steel with its axis horizontal; but the results shown 

 below are quite unfavorable to this adjustment of pivot. 



To find the moment of inertia with respect to an axis through the center 

 of gravity, the pendulum was swung in its erect position, from a wire of known 

 modulus of torsion. In this way the moment of inertia was found to be 

 i.6ioXio 6 and the minimum radius of gyration 20 = 40.71 cm. Hence, the 

 square of the effective radius of gyration was i* = i\-\-h = 1,830. The period, 

 in case of insignificant damping, was determined as T = 2o seconds. Finally, 

 since the pendulum is supported at the axis and not at the center of gravity, 

 the new or flotation center of gravity is thus h' = Mh/(M V). The inclina- 

 tion <f> of the axis, or (p = ^irH' i /T 2 gh, on inserting the values given, reduces 

 to (^ = 0.014 radian, or about 0.80 degree. This is larger than necessary, but 

 it was thought wise not to diminish it. The change of the angle of inclina- 

 tion, being a = <pd, for the deflection 6, is thus determined. For a given <p 

 it is independent of the presence or absence of the float, which therefore 

 does not conduce to enhance the precision of the quantity a, except in dimin- 

 ishing the friction of the pivots. 



