THE PERIODICITY OF FRESHWATER AL,GAE 
129 
in which M is the length of vegetative period, c is a constant, cr is 
the specific surface, and t is the average temperature. The constant 
has been found to have a value of 6.5, and the formula may be written 
(TtM = 65. Figure 3 presents the interrelations of the three var- 
iables. Table I pfresents some of the average dimensions and other 
figures upon which the curve was constructed. 
Table I 
In this table the species of Spirogyra are arranged in the approximate order of 
their fruiting, when germination occurs about March I. Following are the average 
dimensions; time of reproduction; approximate temperature of the whole vegetative 
period; the specific surface; the order by diameters; order by volumes; order by 
specific surfaces; finally the calculated length of the vegetative period, using the 
empirical formula atM = 65. 
Spirogyra 
Average 
Dimen. 
Reprod. 
Temp. 
Veg. 
Per. 
cr 
Order 
Diam. 
Order 
Vol. 
Order 
M 
{atM 
= 65) 
tenuissima 
Apr. 
5°C. 
days 
12 X 120 
•350 
I 
2 
25 
37 
inflata 
18 X 140 
Apr. 
5° 
.236 
2 
4 
24 
55 
communis 
22 X 65 
Apr. 
5° 
.212 
3 
I 
23 
61 
catenaeformis . . . . 
26 X 70 
Mav 
6° 
.182 
4 
3 
22 
59 
Juergensii 
28 X 90 
May 
6° 
.165 
5 
5 
21 
67 
Weberi 
28 X 150 
May 
6° 
.156 
5 
12 
20 
69 
Grevilleana 
30 X 90 
May 
6° 
.155 
6 
7 
19 
70 
Lagerheimii 
30 14 120 
May 
6° 
.150 
6 
9 
18 
72 
varians 
36 X 75 
May 
6° 
.138 
8 
6 
17 
78 
areolata 
34 X 200 
May 
7° 
.127 
7 
17 
16 
73 
fallax 
36 X 150 
May 
7° 
.124 
8 
13 
15 
74 
protecta 
36 X 200 
May 
7° 
.121 
8 
19 
14 
76 
decimina 
40 X 100 
May 
7° 
.120 
10 
10 
13 
77 
reflexa 
38 X 150 
Mav 
7° 
.118 
9 
16 
12 
78 
fluviatilis 
40 X 140 
May 
7° 
.114 
10 
15 
II 
81 
porticalis 
42 X 130 
May 
8° 
.110 
II 
14 
10 
74 
condensata 
52 X 60 
May 
8° 
.110 
13 
8 
10 
74 
dubia 
46 X 90 
June 
8° 
.104 
12 
II 
9 
78 
stictica 
46 X 240 
June 
8° 
•095 
12 
20 
8 
85 
novae-angliae .... 
55 X 220 
June 
9° 
.082 
14 
21 
7 
88 
diluta 
78 X 90 
June 
9° 
•073 
16 
18 
6 
98 
majuscula 
60 X 300 
June 
9° 
•073 
15 
24 
5 
98 
submaxima 
86 X 150 
June 
10° 
.059 
17 
22 
4 
no 
maxima 
120 X 120 
June 
10° 
.050 
19 
23 
3 
130 
setiformis 
100 X 200 
July 
11° 
.050 
18 
25 
3 
130 
crassa 
150 X 150 
July 
11° 
.040 
21 
26 
2 
147 
ellipsospora 
140 X 250 
July 
12° 
.036 
20 
27 
I 
150 
Additional evidence is given for the correctness of this supposition 
in the fact that in several cases for which I have sufficient data con- 
cerning large and small forms of the same species, the dates of fruiting 
