HARMONIC ANALYSIS AND PREDICTION OF TIDES 59 
successive values from 1 to 24. The integral constituent A-hours 
falling within the middle constituent day of each page of tabulations 
will then be represented by the general formula. 
[(168n—84.5) 735 — 12—f+m] constituent A-hours (247) 
from the beginning of the series. ; 
179. The relation of the lengths of the constituent A- and constit- 
uent B-hours is given by the formula 
1 constituent A-hour= Pi eonstituent B-hours (248) 
1 
The constituent B-hour corresponding to the integral constituent 
A-hour of formula (247) is therefore 
pice De yi ature Le ee : 
[(168n—84.5)> ae 12 tigate egos Une B-hours (249) 
from the beginning of the series. 
The last formula will, in general, represent a mixed number. The 
integral constituent B-hour to which the sum for the constituent A- 
hour is to be assigned will be the nearest integral number represented 
by this formula. Let g be a fraction not greater than 0.5, which, 
applied either positively or negatively to the formula, will render it. 
an integer. 
180. The assignment of the hourly page sums for constituent A- 
hours to the constituent B-hours may now be represented as follows, 
multiples of 24 hours being rejected: 
[(168n—84.5) 5 —12—f-+-m—multiple of 24] constituent A-hour 
(250) 
sum to be assigned to 
[{ (168n—84.5)-2 —12—f-+-m}”° + q—multiple of 24] constituent B- 
hour. P Pi (251) 
The difference between the constituent A-hour and the constituent 
-B-hour to-which the A-hour sum is-to be assigned is 
[f (168n—84.5);55—12—f-+m}| Po —1| +9 —multiple of 24] (252) 
By means of the above formula table 33 has been prepared, giving 
the differences to be applied to the constituent A-hours of each page 
to obtain the constituent B-hours with which they most nearly 
coincide. 
181. For the construction of secondary stencils the forms designated 
for the compilation of the stencil sums from the primary summations 
may be used Because of the practical difficulties of constructing 
stencils with openings in adjacent line spaces it is desirable that the 
original compilation of the primary sums should be made so that cach 
alternate line in the form for stencil sums is left vacant. As with the 
