102 ■ U. S. COAST AND GEODETIC SURVEY. 



sum is to be considered as applying to the middle instant of the period 

 from hour to 23d hour; that is, at the 11.5 hour of the day. If the 

 component month or component year is divided into 24 equal parts, 

 the instants separating the groups may be numbered consecutively, 

 like the component hours, from to 23, with the instant of the first 

 groups taken at the exact beginning of the series. A table riiay now 

 be prepared (Table 34) which will show to which division each daily 

 sum, or mean, of the series must be assigned. 



Letting 



a=the hourly speed of any component, in degrees. 



p=l when applied to a monthly or an annual component, and 



p = 2 when applied to a fortnightly or a semiannual component. 



a = day of series. 



s = solar hour of day. 



Then 



and 



also 



1 component period = — solar hours (411) 



1 component month = ^ solar hours (412) , 



1 component year = solar hours (413) 



Dividing the component month or component year into 24 equal 

 parts, the length of 



1 component division = -^ solar hours (414) 



Therefore, to express the time of any solar hour in units of the com- 

 ponent divisions to which the solar hourly heights are to be assigned, 

 the solar hour should be multiplied by the factor a/15-p. 



Thus, 



Component division = r-^— (solar hour of series) 



= j|^ [24(^-1) +11.51 (415) 



since in using the daily sums, the solar hour of the day to which each 

 such sum applies will always be 11.5 hour. 



By substituting the speeds of the components from Table 3 the 



following numerical values are obtained for the coefficient t^-' 

 ^ 152> 



Mf . . . 0.036,601,10; MSf . . . 0.033,863,19; Mm. . . 0.036,291,65; 

 Sa. and Ssa . . . 0.002,737,91. 



By using the appropriate coefficient and substituting successively 

 the numerals corresponding to the day of series (d), the correspond- 

 ing value of the component division to which each daily sum is to be 



