66 * U. S. COAST AND GEODETIC SURVEY. 



Another device to accomplish the distribution of the hourly heights 

 is a set of tracing-paper sheets designed by Doctor Borgen, of Ger- 

 many. These sheets are prepared with lines so arranged that when 

 the sheets are laid on the hourly heights that have been copied in a 

 standard form the heights which are to be grouped under any particu- 

 lar component hour will appear between a pair of lines. A separate 

 set of sheets is necessary for each component. In jjrinciple and in 

 use these sheets are essentially the same as the stencils of the Coast 

 and Geodetic Survey. 



24. STENCILS. 



A system of stencils was devised and prepared by L. P. Shidy, of 

 the U. S. Coast and Geodetic Surve^^, earl^" in the year 1885, for 

 the purpose of effecting the distribution of tabulated solar hourly 

 heights according to the component hours to be represented by the 

 sums.^ Since that time these stencils have resulted in a very great 

 saving of labor. 



For the use of the stencils it is necessary that a standard form be 

 used for the original tabulations of the observed hourly heights (fig. 

 22) . The standard form adopted by the Coast and Geodetic Survey 

 is a sheet 8 by 10-^ inches, with spaces arranged for the tabulation of 

 the 24 hourly heights of each day in a vertical column, with 7 days 

 of record on each page. The hours of the day are numbered con- 

 secutively from O"" at midnight to 23^ at 11 p. m. Each day is indi- 

 cated by its calendar date and also by a serial number commencing 

 with 1 as the first day of series. The stencils (fig. 23) are prepared 

 from the same standard forms, with days numbered serially to cor- 

 respond to the serial numbers of the tabulations. They are thus 

 applicable to any series of observations mthout regard to the calendar 

 dates. A separate set of stencils is required for each component for 

 which sums are to be obtained. For convenience in construction 

 each set of stencils is prepared with two stencil sheets for each page 

 of tabulated heights, one sheet taking account of the odd component 

 hours and the other sheet of the even component hours. To provide 

 for the summation of series up to 369 days in length, each set con- 

 sists of 106 stencils for use on 53 pages of tabulations. When a 

 shorter series is summed, only a portion of the stencils need be used. 



The openings in the stencils are numbered according to the com- 

 ponent hours that correspond most closely with the times of the 

 height values that show through the openings when the stencil is 

 applied to the sheet of tabulations. Openings apph'ing to the same 

 component hour are connected by ruled lines which clearly indicate 

 to the eye the heights which are to be summed together. 



These stencils are adapted to tabulations made in any kind of time, 

 either local or standard, civil or astronomical, provided the time is 

 uniform throughout the series of observations. In the tidal analysis 

 made by the British authorities the records have generally been 

 referred to astronomical time vith the day beginning at noon; but 

 for convenience the tabulations made by the Coast and Geodetic 

 Survey generall}^ conform to the mean civil time ordinarily used at 

 the place of observations. The series to be reduced must, however, 

 commence with the zero hour of the day. If the actual series of 

 observations commences at any other time of day, the heights for 



iEeport of U. S. Coast and Geodetic Survey, 1893, Vol, I, p, 108. 



