HARMONIC ANALYSIS AND PREDICTION OF TIDES: Ve 
It will be noted that formula (308) depends upon the value of p and 
therefore will be the same for all short period constituents (S excepted) 
with like subscripts. Formula (809) depends upon the speed a of the 
constituent and will therefore be different for each constituent. 
215. When the secondary stencils are used, the grouping of the 
ordinates is less simple than that provided by the primary stencils 
only. Let it be assumed that the series is of sufficient length so that 
the distribution of the ordinates is more or less uniform in accordance 
with the system adopted. 
Suppose the original primary summations have been made for con- 
stituent A with speed @ and that the secondary stencils have been 
used for constituent B with speed 6. Then let p and p’ represent the 
subscripts of constituents A and B, respectively. 
The equation for constituent B may be written 
y=B cos (bt+ B) (310) 
216. In the primary summation for constituent A, the group of ordi- 
nates included in a single sum covers a period of one constituent A 
hour or P solar hours. Expressed in time t, midway of this interval 
and representing the exact integral constituent A hour to which the 
group applied, the average value of the B ordinates included in such 
a group may be written 
oe 
a a 
5p fe cos (b§-+ B) dt 
LO Gh Bet 4 LS DON io 3a /h 15pb 
= rap B | sin (bt+8+ ae )=sin (01+ 6-52) | 
a 15pb 
-(= A sin pee) B cos (bt+ B) 
=F, B cos (bt+ B) (311) 
24a . 15pb 
In which F;, for brevity, is substituted for the coefficient = un 
and gives the relation of the average B ordinate included in the A 
grouping to the true B ordinate for the time ¢ represented by that 
group. The reciprocal of this coefficient will be that part of the 
augmenting factor necessary to take account of this primary grouping. 
If the primary summing has been for the constituent 5, this coefficient 
may be taken as unity since the original 5 sums refer to the exact S 
hour. 
217. When the secondary stencils are applied to the constituent 
A group sums, the groups applying to an exact constituent A hour at 
any time ¢ and represented by that time, will be distributed over an 
“oP : solar hours. 
interval of a constituent B hour, or 
For an integral constituent B hour at any time ¢t within the middle 
day represented by a seven-day page of original tabulations the limits 
, le 
of this interval will be (SF) and (1+4P). For the same page 
