45 



component hour. Since the period, in mean solar hours, of a com- 

 ponent whose speed is a, is 360°/a, the length of the component hour 

 of a diurnal component is 360/24a=15/a solar hours, and 1 solar 

 hour is a/15 component hours. For semidiurnal components, 1 solar 

 hour is a/30 component hours. 



85. Tabulation of component hours. — A tabulation of the mean 

 lunar hours corresponding to mean solar hours will illustrate the 

 process of preparing such a tabulation for any component. Since 

 the speed of the lunar day (and of the Mi component) is 14°.492, 052,1 

 per hour, 1 solar hour is equal to 14.492,052,1/15 = 0.966,136,8 lunar 

 hours. In the tabulation at the end of this paragraph, the left-hand 

 column lists the mean solar hours each day. The next column gives, 

 in parentheses, the corresponding lunar hours, to three places of 

 decimals, for the first 15 hours of the first calendar day, and the third 

 column, the corresponding nearest whole lunar hour. Succeeding 

 columns give these whole lunar hours on the following calendar days. 

 It will be observed that the values of the corresponding lunar hom's 

 diminish hourly by 1.-0.966,136,8 = 0.033,863,2. Between the four- 

 teenth and fifteenth mean solar hours the cumulative diminution 

 passes half a unit, so that in whole numbers the fourteenth lunar hour 

 corresponds to both the fourteenth and fifteenth mean solar hours. 

 Obviously from the fifteenth solar hour on, until the progressive 

 diminution passes 1.5, the corresponding lunar hours are 1 hour less 

 than the solar hours. After 1.5/0.033,863,2 = 44.296 hours, i. e., 

 beginning with the twenty-first hour of the second day, the corre- 

 sponding lunar hours drop back another unit, and may be found by 

 subtracting 2 from the solar hour (or adding 22 if the remainder 

 would be negative), and so on. To fill out the tabulation it is neces- 

 sary only to find the solar hours at which the lunar hours drop back a 

 unit. These occur at intervals of 1/0.033,863,2 = 29.53058 hours begin- 

 ning with 0.5/0.033,863,2=14.76529 hours. They are, therefore, the 

 integers following : 



14.76529, or 1st day— 15 hours. (-1) 

 44.29586, or 2d day— 21 hours. ( — 2) 

 73.82644, or 4th day— 2 hours. ( — 3) 

 and so on. 



The hours beginning at which successive numbers are to be added or 

 subtracted to give the nearest component hour of each of the har- 

 monic components are tabulated in Manuals of Harmonic Analysis 

 of Tides under the heading "Tables for the Construction of Primary 

 Stencils; " from which the data for the AI group of components, up 

 to the twenty-ninth day, is extracted. 



