144 THE AMERICAN MONTHLY [May, 



Tlie mean temperature at which the maximum Asterio- 

 nella growths have been observed in Lake Cochituate is 

 50° F., the temperatures of the different growths, liow- 

 ever, varying from 35° to 67°. The temperature of the 

 water affects the diatoms indirectly by producing stag- 

 nation, as has already been pointed out. 



The question of the rate of increase of diatoms is an 

 important one. It has generally been assumed that the 

 increase takes place in accordance with the law of geo- 

 metrical progression, i. e., starting with a single cell, 

 this cell after a certain time divides into two, each of 

 which after another interval of time divides into two 

 more, and so on, so that after n intervals of time, the 

 number of cells would be ar" , where a=l, and r=2. 



There are some writers, following Otto Muller, who 

 have claimed that the increase takes place more slowly 

 than this, because, they say, when a cell divides, the 

 smaller of the resulting cells does not have the same 

 power of leproduction as the larger on account of lack- 

 ing the necessary thickness of connective band. 



My observations seem to show that the diatoms do in- 

 crease substantially in accordance with the law of geo- 

 metrical progression, and that the ratio varies between 

 1.3 and 2.0 per week, the average ratio for ten growths 

 of Asterionella covering a period of thirty-five weeks 

 being 1.58. The corresponding ratio for Tabellaria was 

 1.56. We may say, in a general way, that during a vig- 

 orous growth these diatoms increase at the rate of about 

 50 per cent each week. 



A growth of Synedra in Basin No. 2 of the Boston 

 Water Supply, lasting ten weeks, had a slower rate, the 

 average ratio being 1.3 per week. In this growth the 

 Synedra multiplied more rapidly at first than they did 

 later on. The ratio for the first half was 1.4, and for the 

 second half, 1.2. 



