588 A. A. MICHELSON AND HENRY G. GALE 



The films were measured by sliding them on a lathe-bed beneath 

 a low-powered microscope. The fringes, estimated to tenths, were 

 counted as they moved up and down, and the numbers recorded 

 for each hour. The difference in the motion at the two ends of 

 each pipe gave the numbers for plotting the observed tides. 



The calculated tides were drawn from the computed shift in 

 fringes, the calculations being made for two-hour intervals. The 

 calculations were made under the direction of Professor F. R. 

 Moulton by Mr. Albert Barnett and Mr. Horace Olsen. The 

 formulae are given in the accompanying article by Professor Moul- 

 ton, "Theory of Tides in Pipes on a Rigid Earth." The value of 

 IX for the water used was found to be i .3408 for X 4358, and this is 

 probably correct to within considerably less than o . i per cent for 

 the range of temperatures used. 



Calculated and observed curves for the period from March 24 

 to April 21, 191 7, are reproduced in Figures 2 and 3. The dotted 

 curve represents the observed and the full curve (displaced verti> 

 cally to avoid overlapping) 0.7 of the calculated values of the 



tides. The ordinates are numbers of fringes, N = — , and 



A 



one fringe Corresponds to 1/1564 mm. 



The observed and calculated curves were plotted on long rolls 

 of co-ordinate paper to the following scale: abscissae, i cm = 

 I hour; ordinates, i cm = 2 fringes. In order to have the ampli- 

 tudes approximately equal, o. 7 of the calculated values were plotted 

 instead of the full ampHtudes. Beginning with 10 : 00 a.m. Novem- 

 ber 20, 1916, the curves, both observed and calculated, were 

 divided into periods of 12 '^'4 2 for the semi-diurnal and 25^82 for the 

 diurnal lunar tides. The principal solar tide, period twelve hours, 

 was started at noon of the same day. In order to avoid a cumu- 

 lative error in the case of the semi-diurnal lunar tide the period 

 12^4206013 was put on a computing machine and added repeatedly 

 to the initial time to get the exact beginning of each new period 

 throughout the year. This process was repeated, using the period 

 25^8193409 for the diurnal lunar tide. 



The observations were reduced in groups of about a lunar 

 month each, by dividing each period into ten equal parts (twelve 



