144 U. S. COAST AND GEODETIC SURVEY 
stants for use in the prediction of the tides and also for certain per- 
manent preliminary computations to adapt the constants for use 
with the U. S. Coast and Geodetic Survey tide-predicting machine 
No. 2. The form is used in a loose-leaf binder. 
422. The constituents are listed in an order that conforms to the ar- 
rangement of the corresponding constituent shafts and cranks on the 
predicting machine. The accepted amplitudes and epochs are to be 
given in the columns provided for the purpose. At the bottom of the 
page a space is provided for indicating the source from which the con- 
stants were derived. 
423. The column of Remarks provides for miscellaneous informa- 
tion pertaining to the predictions. This includes the kind of time in 
which the predictions are to be given, the approximate extreme 
range of tide at the place for determining the proper scale to be 
used, the height dial, the marigram gear, the marigram scale, and 
the datum to which the predicted heights are to be referred. 
424. The extreme range may be estimated from the predictions for 
a preceding year or may be taken approximately as twice the sum of 
the amplitudes of the harmonic constants. The height dial, mari- 
gram gear, and marigram scale which are recommended for use with 
different extreme ranges are given in the table on page 138. 
425. The principal hydrographic datums in general use are as fol- 
lows: Mean low water for the Atlantic and Gulf coasts of the United 
States and Puerto Rico. Mean lower low water for the Pacific coast 
of the United States, Canada, and Alaska, and the Hawaiian and 
Philippine Islands. Approximate low water springs for the rest of 
the world, with a few exceptions. For use on the predicting machine 
the datum must be defined by its relation to the mean sea level, and 
this relation is usually determined from a reduction of the high and 
low waters. 
426. Column A of Form 444 is designed for the differences by 
which the epochs of the constituents are adapted once for all for use 
with the unmodified Greenwich (V,+1)’s of each year. These dif- 
ferences take account of the longitude of the station and also of the 
time meridian used for the predictions, and are computed by the 
formula 
as 
K/ —k=pL—sFe (466) 
in which 
«’ —x=adapted epoch—true epoch. 
p=subscript of constituent, which indicates number of periods 
in one constituent day. For the long-period constituents 
Mm, Ssa, Sa, MSf, and Mf, p should be taken as zero. 
L=longitude of station in degrees;+if west, —if east. 
a=speed of constituent in degrees per solar hours. 
S=longitude of time meridian in degrcees;+if west,—if east. 
The values of the products oe for the principal time meridians may 
be taken from table 35. For any time meridian not given in the 
table the products may be obtained by direct multiplication, taking 
the values for the constituent speeds (a) from table 2. 
427. Column B is designed for the reduction of the amplitudes to 
the working scale of the machine. The scale is unity when the 40- 
