538 Lloyd Williams . — Studies in the Dictyotaceae. 
liberation of gametes nearly always takes place about five tides after the 
highest, while in the case of the lower springs there is an apparent 
acceleration, and it occurs about thi'ee tides after the highest. 
2. The above rule for the time of liberation is quite independent 
of the length of the interval from one spring tide to another. Thus in 
the table of higher tides, whether the semilunation includes twenty-five, 
twenty-seven, twenty-nine, or thirty-one tides, maximum liberation is 
effected about the fifth tide after the highest, and, excepting in the 
case of No. 12, there is the same uniformity in Table II. 
3. Though the length of the interval between two highest spring tides 
does not determine the exact time of liberation, it has a direct influence 
upon the length of the period taken by an average sorus to develop ; in 
other words, the length of the optimum line varies directly as the number 
of tides included in the semilunation. Thus in No. 6 the interval between 
the spring tides is twenty-five tides, while in No. 4 it is thirty-one. In the 
former case the optimum line is nineteen, while in the latter it is twenty- 
four. In Col. 5, where this relation is shown in percentages, this is seen 
more clearly. Out of thirteen recorded cases, nine are either 74 or 75%, 
the average of the whole being 76 or, excluding No. 12, 75*4. 
This confirms in a striking way the conclusion arrived at from other 
facts — that the development of the crops is chiefly dependent on the spring 
tides, and that the process goes on but slowly during neaps. 
4. In the following table the crops are arranged according to the 
number of tides in the semilunation. 
Date of crop. 
Length of 
semi- 
lunation. 
Height of 
lozvest neap. 
Length of 
crop 
optimum. 
September 6, 1902 
2 5 
ft. 
12 
in. 
ii 
l 9 
2 
August 17, 1901 
25 
12 
11 
19 
3 
August 8, 1902 
27 
13 
0 
20 
4 
August 27, 1903 
27 
12 
4 
20 
5 
August 28, 1900 
27 
1 2 
21 
6 
September 23, 1899 • • • • 
28 
1 1 
4 
21 
7 
August 15, 1900 
29 
11 
3 
22 
8 
August 20, 1898 
30 
10 
6 
22 
9 
September 3, 1901 
3 i 
10 
10 
24 
10 
August 23, 1902 
3 i 
11 
0 
25 
While it confirms what has been said before, it also brings out another 
fact which must have some influence upon the length of the optimum or 
the rate of development. As a general rule, the longer the interval the 
poorer will be the neap tides, and in consequence the activity of reproduc- 
tion will be correspondingly diminished. 
5. It was at first thought possible that just as the spring tides were 
advantageous for maturation, so there might be some special virtue in neap 
