268 



SCIENCE 



[N. S. Vol. XLV. No. 1159 



The results obtained with this apparatus are 

 essentially exhibitional. Thus far SO-minute 

 intervals if x is the mean arc on the screen s 

 and D the mean swing from which, for the 



mag-nification 60, the angles ^ = 9.6° and 11.5° 

 roughly follow. As the x is equivalent to 2 em. 

 per minute for the swing D ^10 em. this im- 

 plies 5 cm. per minute for the usual swing of 

 25 cm. The experiment is therefore striking, 

 but the necessary interferences make it un- 

 trustworthy for absolute values of 0. Under 

 all circumstances care must be taken that the 

 lens vibrates without displacing the image of 

 the pendulum wire (at rest), both at the be- 

 ginning and at the end of the experiment. 



7. Electrical Methods. — The preceding meth- 

 ods are essentially exhibitional, since the meas- 

 urements are made from images out of focus. 

 It seems possible however that by the use of 

 the following electrical device a method of 

 precision might eventually be evolved, though 

 this is not attempted in the present paper. In 

 all these eases the pendulum bob is a massive 

 cylindrical magnet weighing .8 kg., 20 cm. 

 long and 25 cm. in diameter, with its axis in 

 the prolongation of the string and its north 

 pole downward. The bob is to be additionally 

 and sy mm etrically weighted. Its arc of vibra- 

 tion is along PP in Figs. 5 and 6. In case of 

 the former four identical coils R, R', L', L, on 

 a wooden core about 5 cm. square were placed 

 sym m etrically to the line PP and just below 

 the magnetic bob. The currents induced in R 

 and R' are guided to counteract those in L and 

 L' in an otherwise continuous circuit, so that 

 the galvanometer at G indicates the diiferen- 

 tial current. If the system RR'LU is sym- 

 metrical to PP the current in is zero. If PP 

 deviate to PP' the current in RPi.' wiU be in 

 excess. The zero may then be restored by ro- 

 tating RR'LU until PP and P'F coincide. 

 This and other methods were tested, but a 

 more elegant design is given in Fig. 6 in which 

 CC is a long coil with strands of wire wound 



in the direction of the original arc of vibration 

 PP. The coil which I used was about 30 cm. 

 long wound on a square wooden core 5 X 5 sq. 

 cm. in cross section, with 6 layers of 34 turns 

 each of copper wire .8 mm. in diameter. The 

 terminals of the coil lead to the galvanometer 

 (?, an astatic instrument (preferably), with 

 mirror. The coil CC with the pointer p must 

 be capable of revolving around a vertical axis 

 at a, over the fixed graduated circular plate 

 TT for the measurement of the angle 6 in 

 standardizing the instrument. 



It is obvious that so long as the pendulum 

 vibrates in the plane PP, the induced electro- 

 motive force is normal to the strands of wire 

 and the current at is zero. When the vibra- 

 tion is oblique, along P'P' for instance, there 

 is a component electromotive force along the 

 strands and the current at G increases rapidly 

 with 6. If the period of the needle is about 

 equal to that of the pendulum the arra"ngement 

 is quite sensitive and an image of a jSTemst 

 filament reflected from the mirror of the needle 

 soon oscillates across a distant waU. or screen. 



To obtain the current zero, the magnetic bob 

 must oscillate strictly in the vertical plane PP. 

 Any cross vibration or elliptic oscillation at 

 once develops marked ciirrents. Moreover in 

 the course of time it is extremely difficult to 

 obviate the development of these cross vibra- 

 tions. They would arise if the bob rotates 

 around its own axis, since rigorous rotational 

 symmetry is rarely attained. They would also 

 arise in the reaction of induced currents on 

 the magnetic pole. 



The following is a typical experiment among 

 many results. A galvanometer with astatic 

 needles was adjusted by aid of three astisizing 

 magnets placed symmetrically below and on 

 the sides of the needle (strengthening the 

 earth's field) until its period was decreased to 

 4 seconds, nearly identical with that of the 

 pendulum. In view of this relatively strong 

 magnetic field, the needle was practically free 

 from damping resistances. The experiment 

 was very striking, for vrith an arc of vibration 

 D between 20 cm. and 25 cm., the vibration of 

 the image of a Ifernst filament at first 

 {D = 25) increased over 3 cm. per minute. 



