53 PLANKTON OF WISCONSIN LAKES 



material, but it requires about one million individuals of Euglena. One 

 milligram of dry material contains about 30 million cells of Micro- 

 cystis, while Whipple and Jackson ^^ found that it takes about 2.8 mil- 

 lion cells of Asterionella to weigh this amount. These results show 

 clearly that a relatively small rise in the number of Crustacea is equiv- 

 alent to a very marked increase in numbers in the smaller forms so far 

 as the yield of dry material is concerned. 



The numerical results show a wide variation in the numbers of the 

 different forms, ranging from two or three individuals per liter of 

 water in some forms to several thousand in others, or even to more than 

 30 million in one of the members of the nannoplankton. Such a wide 

 range in numbers makes it impossible to construct diagrams by the 

 usual methods for the purpose of illustrating the distribution of the 

 various organisms, so that it has been necessary to use the spherical 

 type of curve in order to get all of the forms on the same diagram. 

 Lohmann ^^ used this type of curve for the graphical expression of some 

 of his results on marine plankton and he has discussed the method of 

 constructing such curves. He prepared a table, based on a value of 

 1 = 0.25 mm., showing the radii of spheres by half millimeters, which 

 represent numbers from 32 individuals up to 864 million individuals; 

 his table is incorporated in this report as table No. 52 (p. 219). The 



3/'V 



formula for determining the radius in a given instance is R = V 



4.19 

 in which V equals the volume of the sphere, or in this case the number 

 of individuals to be represented by the sphere. In order to simplify 

 the formula, Lohmann has used 4 as a denominator instead of 4.19 

 since the omission of the fraction 0.19 makes only a very small differ- 

 ence, amounting to but 1.5 per cent in a number as large as 800 million. 

 Lohmann *s diagram illustrating the method of construction of the 

 spherical curve is shown in figure 21. The time element is platted 

 along the abscissa, which also serves as the equatorial plane of the 

 series of spheres. The radii of the spheres representing the various 

 numbers of a given form are platted as ordinates at the proper time 

 intervals so that the central point of each sphere is situated at the in- 

 tersection of the radius and the abscissa. A circle of proper radius 

 drawn around this point of intersection represents a cross section of 

 the sphere. In order to complete the curve the outer ends of the radii 

 representing ordinates are connected by lines. Only the radii above 

 the abscissa may be used in constructing a curve, or both those above 

 and those below are connected if a symmetrical figure is desired. 



"Jour. N. E. Waterworks Assoc, Vol. 14, 1899, pp.1-25. 



" Wissensch. Meeresuntersuch. K. Kom., Abt. Kiel, Bd. 10, 1908, pp. 192-194. 



