UPPER THERMAL DEATH POINTS 433 



taken somewhat arbitrarily, as the time required to produce 

 injuries from which approximately half of the individuals failed 

 to recover. The actual death of the animals, accor(iing to the 

 temperatures employed, may occur in from a few minutes to 

 twenty-four hours or more after restoration to normal conditions. 

 Undoubtedly such differences are in certain respects significant, 

 but for purposes of immediate comparison they may be disre- 

 garded and the degree of injury which is just sufficient ultimately 

 to lead to death, regardless of the time required, may be accepted 

 as the most satisfactory available criterion. It may be mentioned 

 that the starfish gastrulae obtained from a single lot, of eggs 

 show little individual variation; the fatal exposure is very nearly 

 the same for all. In this respect they differ from Paramecium 

 in which the individual differences are large. 



It will be noticed in table 1 that the time required to produce 

 fatal injury at any temperature bears a fairly definite relation 

 to the time required at other temperatures. Thus, at 34°, for 

 example, about twice as long a time is required as at 35° and 

 about one-half as long a time as at 33°. Expressed in mathe- 

 matical symbols, 



^ = Qi = 2 



where L denotes the length of life, 6 the temperature, and Qi 

 the temperature coefficient for a change of one degree. Values 

 of Qi are given in alternate columns of table 1. The general 

 average of all of the values of Qi is 2.1. This value agrees closely 

 with that found, for example, by Loeb ('08) for the eggs of 

 Strongylocentrotus and Moore ('10) for Tubularia crocea. 



These results may also be stated in another form (table 2). 

 The amount of injury (I^) inflicted at the temperature d by an 

 exposure of unit time (one minute) can be expressed in quanti- 

 tative form by taking as unity the amount of injury just 

 sufficient to produce death. Thus at 38°, in the series selected 

 for table 2, where an exposure of twenty-three seconds is necessary 

 to cause death, l38» = 2.6; in the same way 134° =0.14; and the 

 other values are given in column 2 of table 2. The mathematical 



