220 INJUEY, RECOVERY, AND DEATH 



the tissue was killed by heat: the conductivity of 

 the expressed juice was compared with that of sea 

 water. As no significant difference was found we may 

 consider that the conductivity of the cell sap does not 

 change sufficiently in these solutions to alter 

 our calculations. 



Let us now consider the changes in protoplasmic resis- 

 tance which occur in toxic solutions. When tissue is 

 placed in NaCl 0.52 M the net resistance falls rapidly. 

 The death curve may be obtained by means of the 

 formula^^ 



/ Ka \/'—KaT —KmT\ _KmT 



Resistance = 2700 i _ j ( e —e j+90e -^^^+10 



in which T is the time of exposure, Ka and Km are con- 

 stants, and e is the basis of natural logarithms. We find 

 by means of this formula that in a solution of NaCl 0.52 M 

 (for which Ka= .018 and Km= .540) the net resistance 

 after 10 minutes is 87.76% of the normal ; after 30 minutes 

 it is 64.26, and after 60 minutes it is 41.62. Knowing the 

 net resistance we can calculate the protoplasmic resist- 

 ance, as explained above. After 10 minutes the proto- 

 plasmic resistance is 117.12% (corresponding to the net 

 resistance of 87.767o). Since it is desirable to express all 

 resistances as per cent, of the resistance in sea water we 

 divide 117.12 by 140 (which is the protoplasmic resistance 

 in sea water) and obtain 83.66%. Proceeding in this way 

 we find that after 30 minutes the protoplasmic resistance 

 is 56.22% and after 60 minutes 33.74%. In order to fit the 

 formula to these values we must change the constants, put- 

 ing Kap=0.0234: (in place of Ka= 0.018) and Kmp= 0.702 

 (in place of Km=^0-5A). It is therefore evident that in 



'* For the explanation of this formula see page 61. 



