HARMONIC ANALYSIS AND PRHDICLION OF TIDES 155 
The following formulas were used in computing the latitude factors. 
The maximum value (irrespective of sign) with corresponding latitude 
is also given for each function. 
Vp B32 Si) Oe eee maximum—1 when Y=+90°. 
WY sats) PP) Gee aes aR dati maximum-+1 when Y=+45°. 
330, Vss2, and Yi, same as V4; 
WA COsn) ree Len ee maximum-+1 when Y=0. 
Y 4g SAME as Y 439 
Ware cose Yee ee maximum+1 when Y=0 or+90°. 
cus ciia, 1 a ee eee inet maximum +1 when Y=+90°. 
Wa cos ee oe erty? maximum-+1 when Y=0. 
Yo=sin Y (cos?¥Y—2/5)_-- maximum +0.4 whenY= +90°. 
Y,u=cos Y (cos’Y—4/5)_-_ maximum—0.2754 when Y=-+58.91°. 
Yao Same as Y yay 
Vac Y cos*Y. 2 maximum +0.3849 when Y= -+35.26°. 
Y 543 same as ees 
AE Cos ye. eR AIS maximum- 1 when Y=0. 
Y.u=sin Y (cos?¥Y—4/15)__ maximum +0.2667 when Y=+90°. 
Yy2=cos Y (cos?¥—2/3)__. maximum—0.2095 when Y=-+61.87°. 
Ve (COs 4/5) aes maximum—0.8 when Y= +902. 
Table 4. Mean longitude of lunar and solar elements.—This table 
contains the mean longitude of the moon (s), of the lunar perigee (p), 
of the sun (h), of the solar perigee (p,), and of the moon’s ascending 
node (NV), for January 1, 0 hour, Greenwich mean civil time, for each 
year from 1800 to 2000, the dates referring to the Gregorian calendar. 
These values are readily derived from table 1, the rate of change in 
the mean longitude of the elements for the epoch January 1, 1900, 
being applicable without material error to any time within the two 
centuries 1800 to 2000 covered by table 4. The same rate of change 
may also be used, without introducing any errors of practical impor- 
tance, to extend table 4 to dates beyond these limits. In extending 
the table, care should be taken to distinguish between the common 
and leap years, and for the earlier dates due consideration should be 
given to the kind of calendar in use. (See p. 4 for discussion of 
calendars.) It will be noted that each Julian century contains 36,525 
days, while the common Gregorian century contains only 36,524 days, 
with an additional day every fourth century. 
Table 5. Differences to adapt table 4 to any month, day, and hour.— 
These differences are derived from the daily and hourly rate of change 
of the elements as given in table 1, multiples of 360° being rejected 
when they occur. The table is prepared especially for common years, 
but is applicable to leap years by increasing the given date by one 
day if it is between March 1 and December 31, inclusive. The cor- 
rection for the hour of the day refers to the Greenwich hour, and if 
the hour for which the elements are desired is expressed in another 
ane of time the equivalent Greenwich hour must be used for the 
table. 
Table 6. Values of I, v, &, ’, and 2v"’ for each degree of N.—Referring 
to figure 1 (page 6), note that by construction are 87’ equals arc 
8. Then in the spherical triangle 2 7A, the three sides are N, », 
and (N—£), and the opposite angles are respectively (180°—J), 7, and w. 
