26 Selim Lemstrüm. 



Hence, in order to prevent damage by frost on 10 hectares during a frosty 

 night, when the température goes down to - 6" near the ground, a quantity 

 of heat is required corresponding to 8,4 kg of coal; if the température is to 

 he kept at O", 23,4 kg, and if formation of ice is to he prevented, 130 

 kg coal. 



2:0. We treat the suhject in such a manner that we calculate the work 

 which is vvanted to effect a mixture of the layers of air, so that their tem- 

 pérature will constantly be, for instance, at 1" above the freezing-point. 



Presuming that a température of 0° does not reaeh the upper parts of 

 plants till 4 hoiu's hefore sunrise, we have to remove, constantly during the 

 fonr remaining hours, a quantity ot air a certain distance upwards, in order 

 to mix it with the wann air there. And 



{1,293 dh 1,293 dh.. ,, a(/ — t) 



— T- — X.293 (Ifl ' -:- 



l + at 1 + at 1 + a{t + 1) 



is the quantity to be removed during every infinitely short time dr from 

 every m^. 



If we now présume that dh is 0,ooi m that this layer of air is to be 

 removed 3 m upwards a second, and that t'—t^'6^,o, we shall get the fol- 

 lowing : 



1,293 . 0,001 . -^ '- — ' — 3 X number of seconds. 



1 + 0,003665 . 4 



The result in 4 hours will be in 10 hedar es 

 60,545 kg.m. = 140,7 Gal. 



In this way a layer of air of a thickness of 14,4 m has been removed 3 

 m. higher up, the diiference of température being 3°. 



Hence, it is in either case a little heat, that is required to work the ne- 

 cessary effect. In the latter case, especially, the quantity of heat is so small 

 that it does not amount to more than 0,2 kg of coal. 



The quantifies of heat calculated above are now to be returned to the plants, 

 in order to keep their température near O" with formation of ice, or without 

 it, or at — 2°, with formation of ice. 



Whatever method we may apply, for this purpose, it must be of a nature 

 to allow this to be done gradually, i. e. that the added quantifies of heat form 

 a sura of infinitely small quantifies, or an integral. The commiinication of 



