422 D. J. SCOURFIELD ON LOGARITHMIC PLOTTING. 



The oblique lines ruled across the accompanying plate have 

 been drawn at the above angles, and serve as standards of 

 comparison in estimating the increase represented by any part 

 of a curve shown on the same plate. Changes due to decreases 

 in the numbers are of course represented by lines at the same 

 angles, but inclined in the opposite direction. 



In illustration of the use of logarithmic sectional paper for 

 biological purposes, some figures taken from C. Apstein's " Das 

 Siisswasserplankton " (Kiel, 1896), have been plotted on the 

 plate. The figures in all cases represent the number of indi- 

 viduals present under each square metre of surface of the Grosser 

 Ploner See in Holstein, from the 8th May, 1892, to the 30th 

 April, 1893. The depths range between 34 and 45 metres, 

 but are sufficiently close to one another to allow of direct 

 comparison of the results. The upper curve shows the changes 

 in the total number of Diatoms of all the species numerically 

 recorded — namely, Asterionella gracillima, Melosira varians, M. 

 arenaria, Fragilaria virescens, F. crotonensis, and Synedra delica- 

 tissima. The second curve exhibits the changes in the number of 

 specimens of the Rotifer Anurcea cochlear is ; the third curve the 

 same details for the Copepod Cyclops oithonoides, and the lower 

 curve the same for the Cladoceran Diaphanosoma brachyurum. 

 The three higher curves deal with organisms which are perennial 

 in their appearance, although subject to enormous variation in 

 numbers ; but the lower curve relates to a species which is markedly 

 periodic, dying out altogether in the winter so far as individuals 

 beyond the egg-stage are concerned. The plotting of a curve to 

 represent the facts in this case presents some little peculiarity,, 

 in that, owing to the construction of the logarithmic chart, there 

 can be no zero line, or rather the zero line is infinitely remote. 

 The simplest way to indicate that the species does nevertheless 

 originate a fresh cycle of existence each spring, becoming extinct 

 again each winter, seems to be to assume that the infinitely 

 remote zero line can be brought up close under the base (unit) 

 line, and then from the points indicating the first and last definite 

 figures obtained, to draw lines down to points on the assumed 

 zero line representing the previous and following date of collecting 

 respectively. In the case of Diaphansooma brachyurum this 

 method has been followed, with the exception that, as the species 

 is known to disappear long before the end of the year, an 



