176 JOURNAL OF ECONOMIC ENTOMOLOGY [Vol. 7 



The aim of the present writer has been then, to develop the theories 

 of Director Sanderson and prove or disprove them; to formulate such 

 laws as might be found to govern the action of temperature conditions 

 on insect development, and by so doing, to place the study of tem- 

 perature in this connection on a more definite basis than it has been 

 heretofore. 



This work has been done at the West Virginia Experiment Station 

 under the direction of Director Sanderson, and the full statement of 

 the results, as well as the data upon which they are based, is soon to 

 appear as a bulletin of the New Hampshire Station where the work 

 was started and most of the data taken. 



The study has seemed to prove the following points and we would 

 therefore propose them as tentative laws : 



1. The rate or velocity of insect development is affected by tem- 

 perature, and, other factors being constant, this rate increases in 

 direct proportion to the increase in temperature, u'ilhin the normal 

 liinits of develop7uent. 



2. The curve expressing the increase in rate of development is a 

 true hyperbole. 



3. The Developmental Zero or what has been styled the "Critical 

 point," is at or near the point where the reciprocal curve for the 

 time factor intersects the temperature axis. 



4. The thermal constant for an insect or any stage of an insect is 

 the constant for the developmental curve for such insect or stage. 



5. The effective temperature for conditions of variable temperature, 

 i. e., the ordinary daily variations, is higher than the mean for the 

 period. (This point is not supported by any evidence in the present 

 paper but there is little doubt in the mind of the writer that it will be 

 found to be correct.) 



The first law is not new but has been generally recognized for many 

 years. It therefore needs no discussion. The second one has not, 

 so far as we know, been definitely stated in any published paper. The 

 proof is the shape of the curves plotted from experimental data and 

 the shape of the reciprocals plotted from these curves. One of the 

 properties of an hyperbole is that the reciprocals plot to a straight 

 line. Another is, that the product of the two factors establishing 

 any point on the curve is equal to the product of the factors establish- 

 ing any other point on the curve; in other words, it is a constant.' The 

 shape of the reciprocals from the experimental curves is graphically 

 shown in the figures. On the figures is shown the accumulated tem- 

 peratures for the different points establishing the curves. These 

 theoretically, should be constant. Their near approach to the con- 

 stant, under experimental conditions, is additional proof as to the 

 nature of the curve. 



