On Night-Frosts. 23 



in which, liowever, KÔ has not been fuUy determined nor T— ß, for the lower 

 température of tlie plant, in comparison Avith that of the surroundiug air, is not 

 known witli certainty. As the cooled air, from its greater density, constantly 

 falls downwards, being replaced by warmer air, T-0 cannot attain a greater 

 value, and maj', therefore, duiing the time (h be indicated by (IT. On the other 

 hand, it is probable that this quantity of heat dépends on T. We therefore 

 express this term 



-K:îff'iT,dT)ch 



The last term is evidently 



(1,293 . 0,623 -— - dh (606,5 0,305 dT)) dr in every m^ 

 760 



where dF signifies the sinking of the pressure of aq. vapeur during the time 

 dr; dh an infinitely small increase in height h. 



For the sake of a better surve}' we will siraplif}' the expressions of the 

 preceding foimula and give 



JX f{T, 0) dt =^fqdT,yK: (fZT)'.-'^^ f{T) dr =^f</dT 



dF 

 dr 



Jl,293. 0,623 (606, 5—0,305 d T) — dh . dt — ]'q"dT 



when we shall get 



Q.=.\\q^{q + q"]dr 



Every moment an exceedingly thin layer of air gives its heat to the 

 plants and sinks to the ground, to be replaced by a fresh one, and this pro- 

 cess continues ail night until sunrise. By this time the plants are surrounded 

 by a cooled layer of aii-, the température of which is lowest near the ground, 

 rises at an increasing height and, at a certain height //„, reaches the tempe- 

 rature of 0°. If we neglect the quantity of heat, which has radiated from 

 the air itself and also that from the smface of the eartli, the beat lost by the 

 cooled layer of air from 0" to —i" will amount to exactly the same quantity 

 which must be returned to the plants, to give them the température they would 

 have, if they had been surrounded by air of 0° all the time. 



The calculation of 



may be performed in the foUowing way. 



