60 U. §. COAST AND GEODETIC SURVEY 
primary stencils, it will generally be found convenient to use two 
stencils for each page of the compiled primary sums, although in some 
cases it may be found desirable to use more than two stencils in order 
to separate more clearly the groups to be summed. The actual 
construction of the secondary stencils is similar to that of the primary 
stencils. A preliminary set of forms is filled out with constituent B- 
hours as derived by differences from table 33 applied to the constit- 
uent A-hours. The odd and even constituent B-hours are then 
transferred to separate forms and the spaces indicated cut out. The 
openings corresponding to the same constituent b-hour are connected 
with ruled lines and numbered to accord with the constituent hour 
represented. The page numbering corresponding to the page num- 
bering on the compiled primary sums and referring to the pages of 
the original tabulated hourly heights is to be entered in the column 
provided near the left margin of the stencil. 
182. In using the stencils each sheet is to be applied to the page of 
compiled primary sums having the same page numbering in the left- 
hand column as is given on the stencil. The primary sums applying 
to the same constituent B-hour are added and the results brought 
together in a stencil sum form, where the totals and means are ob- 
tained. A table of divisors for obtaining the means may be readily 
derived as follows: In a set of stencil sum forms corresponding to 
those used for the compilation of constituent A primary sums the 
number of hourly heights included in each primary sum is entered 
in the space corresponding to that used for such primary sum. The 
secondary stencils for constituent B are then applied and the sums 
of the numbers obtained and compiled in the same manner as that 
in which the constituent B height sums are obtained. The divisors 
having been once obtained are applicable for all series of the same 
length. 
183. In the analysis the means obtained by use of the secondary 
stencils may be treated as though obtained directly by the primary 
summations except that a special augmenting factor, to be discussed 
later, must be applied. The closeness of the agreement between the 
hourly means obtained by use of the secondary stencils and those 
obtained directly by use of primary stencils will depend to a large 
extent upon the relation of the speeds of constituents A and B. The 
smaller the difference in the speeds the closer will be the agreement. 
184. To determine the extreme difference in the time of an indi- 
vidual hourly height and of the B-hour to which it is assigned by 
the secondary stencils, let an assumed case be first considered in 
which the tabulated heights coincide exactly with the integral A-hours, 
and that on the middle day of the page of tabulated hourly heights 
one of the integral B-hours coincides exactly with an A-hour. At the 
corresponding A-hour, one A-day later, the B-hour will have increased 
by 24 we constituent B-hours. Rejecting a multiple of 24 hours, 
1 
this becomes n4(P"—1), so that at the end of one A-day after the 
1 
coincidence of integral hours of constituents A and B the constituent 
A hourly height will differ in time from the integral constituent B-hour 
to which it is to be assigned by 2a( -1) constituent B-hours. 
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