22 Selim Lemström. 



The table page 21 enables us to calculate the radiating quantity of heat 

 at any interval, and is, as is seen, lather varying [See Note IIIJ. 



Not being able, by a direct treatment, to calculate the radiating quantity 

 of heat, we must make use of an indirect method. We again call the read- 

 er's attention to the fact that the matter in question is the quantity of beat 

 which radiâtes from the upper parts of the plants, as also, that damage by 

 frost can never occur till the air, which surrounds thèse parts, has reached a 

 température below 0", so damage by frost dépends, inter alla, on the height 

 h of the plants above the surface of the earth. 



We résume the formula of Dulong and Petit, but, in order to simplify 

 matters, we will noAV give it the following, more general, form: 



clQ, = ffJ'Cr, e) dr + k:S{T, e,f) dv 



in which dr signifies an infinitely short tirae. As is known, the latter term 

 lefers to a case when the réfrigération takes place in some gas. The différ- 

 ence between the experiments on which this formula is founded, and Avhat 

 takes place in nature, is, however, essential. In thèse experiments the radiat- 

 ing body was warmer than the air which surrounded it, but, during a frosty 

 night, plants lose heat and grow colder than the suri'ounding air: i. e. in our 

 formula (T - 0) changes from + to -, and at the same time the signification 

 of O must be altered. As it is the layers of air nearest to the plant, that 

 are to be taken into considération here, 6 is their real température and will 

 in this case always be higher than T, i. e. than that of the plant. If we 

 présume such a case to be the matter for our examination, that 6 is already 

 below the dew-point, another term will evidently have to be added to this, 

 depending on the heat which is produced by condensation. The formula will 

 therefore assume the following appearance: 



dQ, = [K, f(T, 6) k: f'{T, d, f) - k: f"{F, 0)] dt 



where K" is a new constant and F signifies the pressure of aq. vapour. 



We will now examine the signification of the last two terms more closely. 



K„' f'(T, 6, if) represents the quantity of heat that the aii- gives to the 

 plant at the unity of time, by conducting and radiathuj. It is probable that 

 those constants, wlüch bad been determined for (TO) positive, will be valid 

 in case it turns negative. Thus, we should get the following term: 



