592 



A. A. MICHELSON AND HENRY G. GALE 



as the originals, and represent fairly well the average quality of 

 the films. 



A graphical solution is excellent for detecting erroneous points 

 and serves well to give the ratio of the observed to the calculated 

 amplitude, but for determining the phase-difference of the two 

 curves it is not so satisfactory. A least-squares method was there- 

 fore used to secure the ratio of amplitudes, R, and the displacement 

 in phase A0 of the observed with respect to the calculated tide. 

 The following example illustrates the method of reduction. It is for 

 the semi-diurnal tide, first month, E-W. For convenience the solar 

 periods were divided into twelve parts instead of ten, but in other 

 respects the method of reduction is the same. 



In Tables I-VI the numbers in the columns under M denote 

 the different approximate lunar months; under N is given the 

 number of periods used. For the solar tides missing portions of 

 the observed curves were sketched in, following the computed tides, 

 thus giving a total of 730 periods for the year, but for the semi- 



FIRST MONTH, SEMI-DIURNAL, E-W OBSERVED 



21 . 1292 , „ 42. t;^7^ , „ 



a = ^^=+4.2258 /3 = ^— ^=+8.5075 



tan <i, = -=2 ,01^2 

 C = l/a=+/3^ 



£=1/90.2350 



c = 9-499 



y = 9.499 sin (^+63°35') 



