TIDAL DATUM PLANES 5 
Variations in Range 
The range of the tide at any place is not constant, but varies from day to day; 
indeed, it is exceptional to find consecutive ranges equal. In part, this variation arises 
from the effects of wind and weather, but in much the larger part it is of a periodic 
nature, related to the positions of moon and sun relative to the earth. In the change 
in range from day to day, the tide reveals clearly the presence of three variations, 
each associated with a particular movement of the moon. 
The most noticeable variation, as a rule, is that related to the moon’s phase. 
During the phase cycle the tide rises higher and falls lower about the times of new and 
full moon, and rises least and falls least about the times of the moon’s first and third 
quarters. The tides occurring about the times of new and full moon when the range 
is greatest are known as spring tides, while those occurring about the times of the 
moon’s first and third quarters when the range is least are known as neap tides. 
It is to be noted, however, that at most places there is a lag of a day or two between 
the occurrence of spring or neap tides and the corresponding phases of the moon; that 
is, spring tides do not occur on the days of full and new moon but a day or two later. 
Likewise, neap tides follow the moon’s first and third quarters after an interval of a 
day or two. This lag in the response of the tide is known as the “age of phase in- 
equality” or “phase age” and has different values in different localities. For example, 
in New York Harbor the phase age is 26 hours while in Boston Harbor it is 38 hours. 
That is, in New York Harbor spring and neap tides occur a day after the corresponding 
positions of the moon, while in Boston Harbor they occur one and a half days after 
these positions. 
The second variation in range is that associated with the moon’s varying distance 
from the earth. When the moon is nearest the earth or in perigee, high water rises 
higher and low water falls lower than usual, while when the moon is farthest from the 
earth or in apogee, the rise and fall is less than usual. The tides occurring at these 
times are known, respectively, as perigean and apogean tides. 
In the response to the moon’s changes in position from perigee to apogee, it is found 
that, like the response in the case of spring and neap tides, there is a lag in the occurrence 
of perigean and apogean tides. The greatest rise and fall does not come on the day 
when the moon is in perigee, but a day or two later. Likewise, the least rise and fall 
does not occur on the day of the moon’s apogee, but a day or two later. This interval 
varies somewhat from place to place, and in some regions it may have a negative 
value. This lag is known as the “age of parallax inequality” or “parallax age.”’ 
Taking Boston and New York again as examples, it is found that at the former place 
the parallax age is 58 hours, while at New York it is 31 hours. 
The third periodic variation in the rise and fall of the tide is related to the moon’s 
changing declination. When the moon is close to the equator the two high waters of 
a day, and likewise the two low waters, do not differ much; in other words, at such 
times morning and afternoon tides resemble each other. With the moon’s increasing - 
declination, differences between morning and afternoon tides appear, and at the times 
of the moon’s maximum semimonthly declination these differences are most marked. 
The tides occurring when the moon is near the equator are known as equatorial tides, 
while those occurring when the moon is near its maximum semimonthly declination 
are known as tropic tides. Like the response to changes in the moon’s phase and 
parallax, there is a lag in the response to the change in declination, this lag being known 
