84 



SOLUTIONS AND PROTOPLASM 



[Ch. Ill 



The curve shown in Fig. 10 is constructed from the second 

 and third lines of this table. The table shows that, within the 

 limits of 2.8% and 0.9% concentration, the curve is a logarith- 

 mic one, i.e. as the ordinates increase the abscissae increase 

 as the logarithms of the ordinates. In line 4 are given 



the (Beiggs') loga- 

 rithms of the num- 

 bers in line 3, and 

 in line 6 these loga- 

 rithms are each mul- 

 tiplied by a constant, 

 1.7, which gives a 

 series of numbers 

 closely similar to 

 that of line 2. The 

 relation between 

 density and resist- 

 ance period can thus 

 be expressed by the 

 equation 



50 



40 



30 



20 



10 



50 



« 



30 



20 



10 



.9 1.3 



1.9 



3.5 3.S 



3.7 



Fig. 10. — Curve showing relation between the per- 

 centage of salt in mixtures of fresh and salt water 

 (abscissae) and the mean resistance periods in hours 

 of various organisms plunged therein (ordinates). 

 Constructed from the table. (After data of Go- 

 GOKZA, '91.) 



I)=k. log. R, 



in which D stands for 

 density ; i2, for re- 

 sistance period ; and 

 ^ is a constant whose 

 value depends upon 

 the system of loga- 

 rithms employed. 

 This formula may be 



transformed into the equivalent: R=e^, in which e is the 

 base of the Napekian system of logarithms. Since the 

 osmotic pressure is proportional to the concentration (p. 71), 



it follows also that i2 = e*' where stands for the osmotic 

 pressure and k' for a new constant. The same relation holds 

 when we compare the reciprocals of the relative resistance 

 periods — or the relative rapidity of killing — and the abso- 

 lute diminution of concentration. 



