70 U. S. COAST AND GEODETIC SURVEY. 



will have the same tabular values, and no distinction is made in the 

 construction of the stencils. Thus, stencils for component M serve 

 not only for component M^ but also for Mg, M4, Mg, etc. 



For the construction of a set of stencils the standard forms 

 designed for the tabulation of the hourly heights may be used. 

 A preliminary set of such forms is prepared with the days of series 

 entered consecutively, beginning with 1, and with each hourly 

 height space designated by the number of the component hour to 

 which the height is to be assigned. The component hours are readily 

 derived by the application of the differences given in Table 31. 

 Each difference applies to a group of solar hours, the first hour of 

 each group being indicated by the table. Under the usual system 

 of distribution each hourly space will be represented by a single 

 component hour number. 



After the preliminary set of forms has been filled out as indicated 

 the odd and even competent hours on each page will be transferred 

 to separate sheets of the form and the spaces marked cut out. In the 

 Coast and Geodetic Survey this cutting is done by a machine with a 

 punch operated by a small hand lever. The openings corresponding 

 to the same component hour are as far as practicable connected by 

 ruled lines, which are numbered to accord with the component hours 

 represented. Black ruling with red numbering is usually adopted. 

 The use of the red numbers to indicate the component hours has 

 the advantage that it emphasizes the distinction between these num- 

 bers and the figures representing the hourly heights which are to be 

 summed. Figure 23 illustrates one of the stencils used for the sum- 

 mations for component M. 



In using the stencils they are placed one at a time on the forms 

 containing the tabulated heights of the observed tides, and all the 

 heights on a page corresponding to each component hour are summed 

 separately, the grouping of the heights being indicated by the ruling 

 on the stencil. 



For component S no stencils are required, since the component 

 hours are identical with the solar hours in accordance with which the 

 observed hourly heights have been tabulated. 



For components like K, P, R, and T, whose speeds differ little from 

 the speed of component S, the lines joining the openings in the stencils 

 will frequently become horizontal. Since the sum of the values in 

 such a horizontal line will have previously been obtained and entered 

 in the margin of the form, the resuming will be saved by having a 

 corresponding opening in the margin of the stencil which will expose 

 this sum. 



25. SECONDARY STENCILS. 



After the sums for certain principal components have been obtained 

 by the stencUs described in the preceding section, which for con- 

 venience will be called the primary stencils, the summations for 

 other components may be abbreviated by the use of secondary sten- 

 cils which are designed to regroup the hourly page sums already ob- 

 tained for one component into new combinations conforming to the 

 periods of other components. Certain irregularities are introduced 

 by the process, but in a long series, such as 369 days, these are for the 

 most part eliminated, and the resulting values for the harmonic con- 

 stants compare favorably with those obtained by use of the primary 



