100 U. S. COAST AND GEODETIC SURVEY 
directly obtained, in order to refer the ¢ to the 0 hour of the Ist day 
of January. For Ssa the corrections will be twice as great. 
283. If the year commences on the first day of any month other than 
January, the corrections will differ a little from the above. Calculated 
in a manner similar to that above, the following table gives the 
correction to be applied to the ¢ to refer to the first day of any month 
at which the series commences... The correction to the ¢ of Ssa will 
be twice the tabular value for Sa. 
Correction to ¢ of Sa Correction to ¢ of Sa 
to refer to begin- to refer to begin- 
ning of month ning of month 
Observations commence— Observations commence— 
Common Leap Common} Leap 
year year year year 
° ° ° ° 
ReSriyy (SAO BL 2 OB Apres 14. 07 A OSE WO Vele eee ne ie ea 15. 56 15. 93 
5X2) 0) ee ge a ee 13. 50 1 4e 45 al PAU CIES: ears Te TS Oe 14. 98 15. 43 
Mars iia oeee fil ee oeen hee eee 15. 89 15893) || Sept): 3 see eee” 2 eed 14, 41 14, 94 
ADT Se RSOeA ee N Ss Se Te 15. 31 5543} Oot. Wes se. ROLES SRR ea ee 14, 82 16. 43 
Misys dere iar 2 ea 15. 72 1593) || NOV LEs-f. Sate oe eet eee 14, 24 14, 94 
Juneyls 22. 8. cee Ee 15. 15 N5X435 | Dec) Leates oe eee 14. 65 15. 43 
284. If the monthly means extend over many calendar years, it may 
be convenient to combine them for a single analysis. In: this case the 
(V,+4u) for January 1 may be taken as the average of the values for 
the beginning of each year included in the observations, and the 
correction to the ¢ to refer to the beginning of the year will be a mean 
of the values given above for common and leap years, weighted in 
accordance with the number of each kind of year included. If only 
a few years of observations are available, it is better to analyze each 
yeat separately in order that the results may serve as a check on each 
other. 
285. The augmenting factors to be used for constituents Sa and Ssa 
when derived from the monthly sea level values are based upon for- 
mula (404) in paragraph 266 and are as follows: 
Sa 1.0115, logarithm 0.00497. 
Ssa 1.0472, logarithm 0.02003. 
ANALYSIS OF HIGH AND LOW WATERS 
286. The automatic tide gage, which furnishes a continuous record 
of the rise and fall of the tide, now being in general use, it is seldom 
necessary to rely only upon the high and low waters for an analysis. 
It may happen, however, that a record of high and low water observa- 
tions is available for a more or less isolated locality where it has been 
impractical to secure continuous records. Such records, if they in- 
clude all the high and low waters for a month or more may be utilized 
in determining approximate values of the principal harmonic con- 
stants, but the results are not as satisfactory as those obtained from 
an analysis of the hourly heights. 
287. An elaborate mode of analysis of the high and low waters is 
contained in volume 1 of Scientific Papers, by Sir George H. Darwin. 
Other methods are given by Dr. R. A. Harris in his Manual of Tides. 
The process outlined below follows to some extent one of the methods 
of Doctor Harris, extending his treatment for the K and O to other 
constituents. 
