154 U. S. COAST AND GEODETIC SURVEY 
uniformly changing elements and determines the speed and period of 
the constituent, and the w which is a function of the moon’s node with 
slow variations and which is treated as a constant for a limited series 
of observations. Because of the very small change in the element p, 
it may for practical purposes also be treated as a constant with a mean 
value of 282° for the present century. 
The constituent speeds are obtained by adding the hourly rates of 
change in the elements appearing in the V of the arguments. The 
hour angle (7’) of the mean sun changes at the rate of 15° per hour. 
The pourly rate of change for each of the other elements will be found 
in table 1. 
For an explanation of the constituent coefficients (C) see page 24. 
The coefficients of the solar terms include the solar factor S’ (para- 
graph 118), and coefficients of the lunar terms involving the 4th power 
of the moon’s parallax include the factor a/c (paragraph 108); in 
order that all terms may be comparable when used with the common 
basic factor U. It is to be noted that in the present system of coef- 
ficients for the terms of the principal tide-producing force there is. 
included a factor ‘‘2’’ which was formerly incorporated in the general 
coefficient. For the terms involving the 4th power of the parallax 
there is a corresponding factor of ‘3”’ in order that all terms may be 
comparable in respect to the vertical component force. 
In general the coefficients have been computed in accordance with 
the coefficient formulas of the text, but exceptions were made for the 
evectional and variational constituents p,, v2, 2, and po, the coeffi- 
cients of which are based upon computations by Professor J. C. 
Adams who was associated with Darwin in the investigation of har- 
monic analysis and who carried the development of the lunar theory 
to a higher order of precision than is provided in this work. (See 
pp. 60-61 of the Report of British Association for the Advancement of 
Science for year 1883.) 
The node factor (f) is explained on page 25. The last column of 
table 2 contains references to the formulas for the node factors of the 
various constituents. 
Table 2a. Shallow-water constituents.—In this table there are listed 
the overtides and compound tides which are described on page 47. 
Table 3. Latitude factors —This table includes numerical values of 
the latitude (Y) functions which appear in the text as factors in 
formulas representing component tidal forces and the equilibrium 
height of the tide. Tle combination symbol at the head of each 
column is taken to suggest the formula to which it applies. Thus, 
the letters v, s, and w refer respectively to the vertical, south, and 
west components of the force, the letter » being applicable also to the 
formulas for the equilibrium height of the tide which have the same 
latitude factors as the corresponding terms in the vertical component 
of the force. The first numeral ‘3’ or ‘4” indicates whether the 
formula is from the development of the principal force involving the 
cube of the parallax or from the development involving the 4th power 
of the parallax of the tide-producing body. The last digit “0,” 
“1,” “2.” or “3” refers to the species of the constituents and indicates 
whether they are long-period, diurnal, semidiurna]l, or terdiurnal. 
In several cases the same latitude factor is applicable to a number of 
different groups as indicated at the head of the column in the table. 
