186 WKITINGS OF JOSEPH HENRY. [1855- 



of heat, as well as late writers on the subject, has proposed to 

 calculate it by multiplying the number of days in which 

 the plant is passing through its growth by the mean tem- 

 perature of each day ; while M. Quetelet, of Brussels, who 

 has made more experiments on this subject than any other 

 person, thinks that the heat ought to be measured, not by 

 the simple product of the sum of the temperatures of the 

 several days but by the sum of the squares of the tempera- 

 tures of these days. He deduces this rule from the consider- 

 ation that if heat be due to vibration, the impulses from 

 it ought to do work in proportion to the square of the inten- 

 sity, and not simply in proportion to the intensity. For ex- 

 ample, a cannon ball moving with twice the velocity will 

 penetrate a wall four times as far, — moving with three times 

 the velocity, nine times as far, — and so on, in proportion to 

 the square of the velocity. In accordance with this, let S 

 represent the amount of heat required to produce the full 

 development of the plant, and t and t' be the mean tempera- 

 tures of the several days; then will S={tf + {tj + {t"f, &c. 

 It follows as a consequence of the law of the square of tem- 

 peratures that alternation of temperatures within certain 

 limits may produce greater effect than a uniform tempera- 

 ture. For example, if on three consecutive days the tempe- 

 ratures w^ere 70°, 60°, and 80° F., and on three other days, 

 70°, 70°, 70°, though the average heat is the same, the effect 

 of the former will be slightly greater than that of the latter; 

 since the sum of the squares of the first is 14,900 while that 

 of the latter is 14,700. 



From a priori considerations there can be no doubt that 

 to produce a given amount of organization a definite amount 

 of power must be expended ; but we are unable to say in the 

 present state of science how much of the power which may 

 disappear is lost in producing other than useful effects. Also, 

 in the foregoing investigation it might reasonably be sup- 

 posed that the mean heat of the day, in part, should be de- 

 rived from the heat of the sun, and not alone from that of 

 the air. The upper surface of a plant will be heated by the 

 direct rays of the sun, while the lower will be exposed in the 

 shade to the heat of the air. It has therefore been proposed 



