HARMONIC ANALYSIS AND PREDICTION OF TIDES 61 
At the end of the third A-day this difference becomes 72 -1) 
1 
constituent B-hours. The same difference with opposite sign will 
apply to the third constituent day before the middle day of the page. 
Now, taking account of the fact that the B-hour on the middle day 
of the page may differ by an amount as great 0.5 of a B-hour from the 
integral A-hour, and that the integral A-hour may differ as much as 
0.5 of a constituent A, or 0.5 pb/p,a of a constituent B hour from the 
time of the actual observation of the solar hourly height, the extreme 
difference between the time of observation of an hourly height and 
the time represented by the B-hour with which this height is grouped 
by the secondary stencils may be represented by the formula 
pb ) pb ] : 
—w~w] Bil = - é 
+ | 722 +0 aa 1 ) constituent B-hours. (253) 
The differences may be either positive or negative, and in a Jong 
series it may reasonably be expected that the number of positive and 
negative values will be approximately equal. 
185. The above formula for the extreme difference furnishes a 
criterion by which to judge, to some extent, the reliability of the 
method. Testing the following schedule of constituents for which 
it is proposed to use the secondary stencils, the extreme differences 
as indicated are obtained. The differences are expressed in con- 
stituent B-hours and also in constituent B-degrees. It will be 
noted that one constituent hour is equivalent to a change of 15° in 
the phase of a diurnal constituent, 30° in the phase of a semidiurnal 
constituent, etc. 
Constituent Ab: peers ss J 8 
Constituent Bae wee ee 0O 28M Ky Ke Re T: Pi 
Difference in hours_____________ 3. 58 1.36 1.20 1.20 1.10 1.10 1. 20 
Difference in degrees__________- 54 41 18 36 33 33 18 
Constitwent: At: seer Se ee ee se L 2MK 
ConstitwentpBese see Ds Pe SST ee i ee MS da MK MN vo Ne 
Differences MOuTSy eee ee ee 1.09 1.18 1.43 1.24 1. 26 1.45 
Difference in degrees_____-_---___--------- 65 35 64 74 | 38 44 
WOnSEUGTE TEARS See ee ae ee ea eee oO 
Constitventyi nest See sels AeA eet Saas eee [t) 2N pl Q 2Q 
Mifferencenunghourse =. ee eke CERNE eRe ey ihe al 1. 02 3.42 3. 79 6. 58 
i 51 57 99 
MD ifferencerinidesrees <2 ie Bs 36 31 
186. In the ordinary primary summation the extreme difference 
between the time of the observation of a solar hourly height and the 
intregal constituent hour to which it is assigned is one-half of a con- 
stituent hour and, represented by constituent degrees, it is 7.5° for 
diurnal, 15° for semidiurnal, 22.5° for terdiurnal, 30° for quarter 
