Physiology of the Spermatozoa of Ferns . 5 51 
As an illustration of this method of calculation let us 
suppose it required to make solutions of the three salts just 
mentioned each isotonic with fy mol (approx. i°/ o ) potassium 
nitrate. The molecular weights of sodium chloride, potassium 
sulphate, and cane-sugar are respectively 58-5, 174*2, and 342. 
One-tenth of the gram-molecules are respectively 5*85, 17*42, 
and 34*2 grams. We shall therefore require fx5*85 gm 
sodium chloride, fx 17*42 gm potassium sulphate, and 
| x 34*2 gm cane-sugar dissolved in 1000 ccs or' more 
simply 0-585, 2*3, and 5*1 gm °/ o of the three substances 
respectively. 
The above method of calculating isotonic solutions gives 
approximately accurate results only when the concentrations 
are neither very high nor very low. De Vries has given 
the higher 1 limit as 3 gm °/ o potassium nitrate (approx. T 3 F mol). 
Another and much more accurate method 2 is based upon 
our knowledge of the specific molecular conductivity of 
electricity in solutions at different concentrations. For my 
purpose, however, as will be clear from the conclusions drawn 
from the results, the method of de Vries sufficed. 
With regard to the chemical aspect of the solutions used 
it should be observed that in a vertical column of any one 
table the solutions are isomolecular. In a vertical row of 
all three tables taken together, however, the solutions in 
Table I contain more molecules 3 than those in II and less 
than those in III. The proportionate number of molecules 
may thus be represented, Table I: II: III:: 100 : 75 :150. 
When making experiments upon the length of life of the 
spermatozoa I found that they swarmed about three times 
as long in hanging drops of tap-water as in similar drops 
of distilled water. Both Pfeffer 4 and Voegler 5 have remarked 
1 De Vries, loc. cit., p. 535. 
2 For an application of this method to physiological work and a comparison 
of its results and those given by the method of de Vries see the paper of Ryssel- 
berghe, 1899, loc. cit. 
3 i. e. taking no account of their dissociation. 
4 Pfeffer, loc. cit., Bd. i, p. 368, Anm. 3. 
5 Voegler, Bot. Zeit., 1891, p. 645. 
