114 



A. A. MICHELSON 



The resulting mean of all observations, for this method of 

 grouping, is that the observed amplitude of the oscillation for the 

 E.-W. Hne is o. 709 of that calculated on the assumption of absolute 

 rigidity; while for the N.-S. line it is 0.510. The acceleration of 

 phase of the observed oscillations relative to the calculated is +0^059 

 for the E.-W. hne and —0^007 for the N.-S. Hne. The graphs of 

 the final means of all the observations and the calculated values 

 are reproduced in Figs. 13 and 14. 



The curves correspond very closely with the following formulae: 



E.-W. y=—asm— {t—T)-{-h 



N.-S. 3^=— a cos -Tp (^ 



^)+h 



Accordingly the ratio of the observed to the calculated ampli- 

 tude for E.-W. is 0.691, and for N.-S. is 0.516, while the phase 

 accelerations are 0^1 1 and 0^02 respectively. 



These last results are slightly different from the preceding. 

 The preference is for the latter as regards amplitude ratios, but 

 these give relatively too much weight to the large oscillations in 

 deducing the phase-difference, and for these the former results are 

 preferred. 



Multiplying the second set of values obtained for the amplitude 

 ratios by the factors given above, 1.028 for E.-W. and 1.014 for 

 N.-S., the final results are: 



Amplitude Ratio 



E.-W... 0.710 



N.-S 0.523 



Phase Acceleration 



E.-W...... +0.059 hour 



N.-S -0.007 hour 



