O. T. Sherman — A Pendulum Study. 179 



(e. g.) the mean of the interval bounded by the first and 

 thousandth transit, the second, and timus Iti d second, etc. 

 Thus including in the second interval by far the great r part 

 of the first interval, but depending on two different observa- 

 tions. This served to insure against accidental errors. These 

 values are then carefully plotted, the number of transits from 

 the beginning being used as the abscissae. The curves thus 

 derived fulfill our expectations as far as we can sharply criti- 

 cise a statement so general. 



Furthermore, curves from the same mounting preserve their 

 general peculiarities for different observations. For different 

 mountings the amplitude is greater with the less stability. In 

 the preceding diagram we represent certain of these curves for 

 the different places of observation. The sharp and quick 

 irregularities are omitted on account of the smallness of the 

 scale. In fact we have not now to deal with them. 

 Since at the time of observation we supposed ourselves 

 dealing with synchronous motion, the curves are not complete. 

 They serve their purpose. The curve for Washington repre- 

 sents the least stability ; that for Disco the greatest. At Disco 

 we give three curves. The first represents the action of the 

 stand when first set up, the parts being dry. The stand was 

 exposed to the weather. Between the first and second series a 

 heavy fog had swollen the parts. Between the second and 

 third a heavy snow storm had still further swollen the various 

 parts. For the first installation the amplitude of the curve is 

 at least 0-0008 of a second ; for the second at least 00003. 

 For the third it is indeterminate. All refer to about the same 

 amplitude of vibration. The curve for St. Johns represents 

 fairly the increased effect of the disturbance with decreasing 

 arc. The same is also shown in the curves for New Haven, 

 and the second curve for Disco. It has not seemed necessary 

 to correct the values here represented for arc. 



We venture to think, then, that while an observer who finds 

 himself compelled to work with a mounting other than he 

 would wish can not consider that his time is increased by a con- 

 stant, yet he is in a position to detect and define the effect of the 

 stand movements at the moment of observation. This would 

 seem the first step toward eliminating the effect. That such 

 an elimination can be made— at least a practical elimination— 

 we hope to show later. We can offer as yet no experimental 

 data of its completeness. 



It is to be observed that the curves derived from this cause 

 r from those produced by the form of the knife edge. 

 It is easily shown that for any smooth, rounding, and practi- 

 cally, for any slightly waving form of the edge, the time of 

 vibration is represented by 



