HARMONIC ANALYSIS) AND PREDICTION OF TIDES Hi 
designated by k’ or by the small g._ The relation of the modified 
epoch to the local epoch may then be expressed by the following 
formula: 
x’ or g=x«+pL—aS/15=Greenwich (V,+u)+¢ (320) 
226. The phases of the same tidal constituent in different parts of 
the world are not directly comparable through their local epochs since 
these involve the longitude of the locality. For such a comparison it. 
is desirable to have a Greenwich epoch that is independent of both 
longitude and time meridian. Such an epoch may be designated by 
the capital G and its relation to the corresponding local epoch ex- 
pressed as follows: 
Greenwich epoch (@)=x+pL=Greenwich (V,+u)+aS/15+¢ (321) 
227. The angle x may be graphically represented by figures 7 
and 8. In figure 7, we have a simple representation of a single con- 
is 
8 
ne) 
= ; 
S c - 
€ fy 40 2 
re) n . 
£ = g = o ae? 2 
= oO ® 2¢ ie os = 
e E € © ‘ ae ee 
o 8 e os 5.0 = © a 
Ss £ ££ On toy} ie 2 
S = Denes ed Ee == 
# ee rs 25 os SE ome c 
0 a O re = De are) 
S c c (a © c= S) 
o O Oo o> oD om OO Ee 
ms = SS ~ 0 Oo 8 + vo — 
[= = [= Od —59) Y a2 Lt) 
rs pl ———»><« p(S-L) > < cL ><—¢(S-L) ><—— _ 5 —— > 
| 
<—____——_—_——.— Local V,+u wa cid NS 
i] 
cS — Local epoch (K) > 
r= Greenwich epoch (G) >| 
FIGURE 8. 
stituent. In this figure changes in the phase or angle are measured 
along the horizontal line, positive change toward the right and nega- 
tive change toward the left. The full vertical line indicates the 
beginning of the series, at which time the angle p 0, or at, equals 0. 
At the left of this vertical line, the symbol of a moon (M) indicates 
the zero value of the equilibrium argument that precedes the begin- 
ning of the series. For the principal lunar or solar constituent, this 
will be simultaneous with a transit of the mean moon (modified by 
longitude of moon’s node) or of the mean sun, and for other short- 
period constituents with the transit of a fictitious star representing 
such constituent (p. 23). At the point represented by this moon, 
the angle (V-++wu) has a value of zero. This angle increases to the 
right, and at the beginning of the series has a value represented by 
(V.+u), which may be readily computed for the beginning of any 
series. This interval from M to the time of occurrence of the first 
following constituent high water is the epoch x. This represents the 
lag or difference between the actual constituent high water at any . 
