212 



RECENT STUDIES IN GRAVITATION. 



make the couple period, then, a little different from the natural one 

 hundred and twenty second period, and accordingly we revolved the 

 large sphere once in two hundred and thirty seconds, when the sup- 

 posed quadrantal couple would have a period of one hundred and tif- 

 teen seconds. 



Figs. 10 and 11 may help to show how this enabled us to eliminate 

 the disturbances. Let the ordinates of the curves in fig. 10 represent 

 vibrations set out to a horizontal time scale. The upper curve is a 

 regular vibration of range ± 3, the lower a disturbance beginning 

 with range ± 10. The first has period 1, the second period 1.25. 

 Now, cutting the curves into lengths equal to the period of the shorter 

 time of vibration and arranging the lengths one under the other, as in 

 fig. 11, it will be seen that the maxima and the minima of the regular 



vibration always fall at the same points, so 

 that, taking 7 periods and adding up the ordi- 

 nates, we get 7 times the range, viz, ± 21. 

 But in the disturbance the maxima and mini- 

 ma fall at different points, and even with 7 

 periods only, the range is from + 16 to — 13, 

 or less than the range due to the addition of 

 the much smaller regulation vibration. 



In our experiment the couple, if it existed, 

 would very soon establish its vibration, 

 which would always be there and would go 

 through all its values in one hundred and 

 fifteen seconds. An observer, watching the 

 wheel at the top of the revolving axis, gave 

 the time signals every eleven and five-tenth 

 seconds, regulating the speed if necessary, 

 and an observer at the telescope gave the 

 scale reading at every signal — that is, 10 

 times during the period. The values were 

 arranged in 10 columns, each horizontal line giving the readings of 

 a period. The experiment was carried on for about two and one-half 

 hours at a time, covering, say, 80 periods. On adding up the columns 

 the maxima and minima of the couple effect would always fall in the 

 same two columns, and so the addition would give 80 times the swing, 

 while the maxima and minima of the natural swings due to disturb- 

 ances would fall in different columns, and so, in the long run, neu- 

 tralize each other. The results of different days' work might, of 

 course, be added together. 



There always was a small outstanding effect, such as would be pro- 

 duced by a quadrantal couple, but its effect was not always in the same 

 columns, and the net result of about three hundred and fifty period 

 observations was that there was no one hundred and fifteen second 



Fig. 11. — Results of superposition of 

 lengths of curves in fig. 10 equal 

 to the period of the regular one. 



