HARMONIC ANALYSIS AND PREDICTION OF TIDES 113 
table 13, using the year of observations, together with item (1), as 
argument. 
315. Form 194, Harmome analysis (fig. 16).—This form is based, 
primarily, upon formulas (295), (296), (303), and (304) and is designed 
for the computations of the first approximate values of the epochs 
(x) and the amplitudes (H) of the harmonic constants. Provisions 
are made for obtaining the diurnal, semidiurnal, terdiurnal, quarter- 
diurnal, sixth-diurnal and eighth-diurnal constituents, but only such 
items need be computed as are necessary for the particular constituents 
sought. For the principal lunar series M,, Mz, M3, My, Me, and Mg, 
compute all items of the form. For the principal solar series S,, S2, Su, 
and S,, items (14), (16), (83), (85), and (37) may be omitted. For 
the lunisolar constituents K, and Kg, items (14), (16), and (23) to 
(37) may be omitted. For the diurnal constituents J,, O,, OO, P:, Qu, 
2Q, and p,, items (5), (6), and (14) to (37) may be omitted. For the 
semidiurnal constituents L,, Nz, 2N, Re, T2, d2, ue, v2, and 25M, items 
(3), (4), (8) to (16), and (23) to (87) may be omitted. For ter- 
diurnal constituents MK and 2MK, items (5), (6), (9), (12), and 
(18) to (37) may be omitted. For quarter-diurnal constituents MN 
and MS, items (3), (4), (8) to (25), and (35) to (37) may be omitted. 
In the bottom portion of the form the symbol of the constituent is 
to be entered at the head of the column or columns indicated by the 
subscript corresponding to the number of constituent periods in a 
constituent day, the remaining columns being left blank. 
316. The hourly means from form 142 (fig. 13) are entered as items 
(1) and (2) in regular order, beginning with the mean for 0 hour. 
Item (4) consists of the last five values of item (8) arranged in reverse 
order. Item (6) consists of the last six values of item (5) in their 
original order. For the computations of this form the following 
tables will be found convenient: table 19 of this publication for 
natural products, Vega’s Logarithmic Tables for logarithms of linear 
quantities, and Bremiker’s Funfstellige Logarithmen for logarithms 
of the trigonometrical functions. In the last table the angular argu- 
ments are given in degrees and decimals. 
317. In choosing between items (44) and (45) the former should 
be used if the tabular value of (41) in the first quadrant is greater 
than 45° and the latter if this angle is less than 45°. In referring 
(41) to the proper quadrant it must be kept in mind that the signs 
of the natural numbers corresponding to (38) and (39) are respectively 
the signs of the sine and cosine of the required angles. Therefore 
(41) will be in the first quadrant if both s and ¢ are positive, in the 
second quadrant if s is positive and ¢ negative, in the third quadrant 
if both s and c are negative, and in the fourth quadrant if s is nega- 
tive and c positive. In obtaining (49) use (46)+(47) for all 
constituents except S, and (46)+(48) for S. The log factor F' for 
item (50) may be obtained from form 244a. 
318. Form 194 is designed for use when 24 constituent hourly 
means have been obtained and all the original hourly heights have 
been used in the summation. If in the summation for a constituent 
each constituent hour of the observation period received one and 
only one of the hourly heights, it will be necessary to take the log- 
augmenting factor from table 20 and add this to the sum of items 
(46) and (48) to obtain item (49), striking out item (47). 
