58 U. S. COAST AND GEODETIC SURVEY 
175. In the primary summations there are obtained 24 sums for each 
page of tabulations, representing the 24 constituent hours of a con- 
stituent day. In general each sum will include 7 hourly heights, and 
the average interval between the first and last heights will be 6 con- 
stituent days. A few of the sums may, however, include a greater 
or less number of hourly heights within limits which may be a day 
greater or less than 6 constituent days. 
176. Let the constituent for which summations have been made by 
use of the primary stencils be designated as A and the con- 
stituent which is to be obtained by use of the secondary stencils as 
B. For convenience let it be _ first assumed that the 
heights included in the sums for constituent A refer to the exact 
A-hours. This assumption is true for constituent S but 
only approximately true for the other constituents. It is now pro- 
posed to assign each hourly page sum obtained for constituent A to 
the integral B-hour with which it most nearly coincides. 
Constituent A and constituent B-hours separate at a uniform rate, and 
the proposed assignment will depend upon the relation of the hours 
on the middle day of each page of tabulations. The tabulated hourly 
heights on each full page of record run from zero (0) solar hour on the 
first day to the 23d solar hour on the seventh or last day of the page. 
The middle of the record on each such page is therefore at 11.5 solar 
hours on the fourth day, or 83.5 solar hours from the beginning of the 
page of record. 
177. Let a and 6 represent the hourly speeds of the constituents A 
and B, respectively, and p and p, their respective subscripts, and let 
nm equal the number of the page of tabulation under consideration, 
beginning with number one as the first page. 
The middle of page m will then be 
[168(n—1) 4-83.5] or (168n—84.5) solar hours (244) 
from the beginning of the series. 
Since one solar hour equals a/15p constituent A-hours (formula 
240), the middle of page n will also correspond to 
(168 — 84.5) ;5 constituent A-hours (245) 
from the beginning of the series. 
As there are 24 constituent hours in each constituent day, the 
middle constituent A-day of each page will commence 12 constituent 
A-hours earlier than the time represented by the middle of the page, 
or at 
[1682 — as 12] constituent A-hours (246) 
from the beginning of the series. 
178. The 24 integral constituent A-hours of the middle constituent 
day of the page will therefore be the integral constituent A-hours 
which immediately follow the time indicated by the last formula. 
The numerical value of this formula will usually be a mixed number. 
Let f equal the fractional part, and let m be an integer representing 
the number of any integral constituent hour according to its order in 
the middle constituent day of each page. For each page m will have 
