54 U. S. COAST AND GEODETIC SURVEY 
height values showing through the openings when the stencil is applied 
to the tabulations. Openings applying to the same constituent hour 
are connected by a ruled line which clearly indicates to the eye the 
tabular heights which are to be summed together. For convenience 
in construction two stencil sheets are prepared for each page of 
tabulations, one sheet providing for the even constituent hours and 
the other sheet for the odd constituent hours. 
162. The stencils are adapted for use with tabulations made in 
any kind of time provided the time used is uniform for the entire 
series of observations. For convenience the tabulations are usually 
made in the standard time of the place. The series to be analyzed, 
however, must commence with the zero hour of the day and this is 
also taken as the zero constituent hour for each constituent. Suc- 
cessive solar hours will fall either earlier or later than the correspond- 
ing constituent hour according to whether the constituent day is 
longer or shorter than the solar day. 
163. For the construction of the stencils it is necessary to calculate 
the constituent hour that most nearly coincides with each solar hour 
of the series. 
Let a=speed or rate of change in argument of constituent sought 
in degrees per solar hour. 
p=number of constituent periods in constituent day; 1 for 
diurnal tides, 2 for semidiurnal tides, ete. 
sh=number of solar hour reckoned from 0 at beginning of each 
solar day. 
shs=number of solar hour reckoned from 0 at beginning of 
series. 
dos=day of series counting from 1 as the first day. 
ch=number of constituent hour reckoned from 0 at beginning 
of each constituent day. 
chs=number of constituent hour reckoned from 0 at beginning 
of series. 
Then 
‘ : 360 
1 constituent period=—— solar hours. (237) 
1 constituent day = solar hours. (238) 
: 15p 
1 constituent hour oa solar hours. (239) 
1 solar hour Er constituent hours. (240) 
Therefore, 
a a 
= = as 241 
(chs)=]7 eae) 7 apes (dos) —1}+(sh)] (241) 
164. The above formula gives the constituent hour of the series (chs) 
corresponding to any solar hour of the series (shs). The observed 
heights of the tide being tabulated for the exact solar hours of the 
day, the (shs) with which we are concerned will represent successive 
integers counting from 0 at the beginning of the series. The (chs) 
as derived from the formula will generally be a mixed number. As 
