EFFECT OF TEMPERATURE ON GROWTH. 749 



different from the lowest at which a gourd can grow, &c. It has also been shown 

 that growth, like other phenomena, is more active the higher the (constant) tem- 

 perature above the inferior limit, but that there is a certain temperature at which 

 growth reaches its maximum activity, and above which any further rise of temper- 

 ature causes a diminution of its rapidity. There is not, in the mathematical sense 

 of the term, any proportion between the rapidity of growth and the height of the 

 temperature, and the more accurately the relation between the two has been investi- 

 gated, the more difficult is it to express this relation by any mathematical formula. 

 It cannot, on the other hand, be doubted that it is of the utmost importance for 

 any future theory of the mechanical laws of growth to ascertain the extent to which 

 growth depends on temperature, at least in a few particular cases. 



The difficulties of investigations of this kind are however much greater than is 

 generally thought ; and the results obtained hitherto, valuable as they are, go no 

 further than what is stated above, and give us no deeper insight into the way in 

 which that particular mode of jnotion of the molecules which we call heat is con- 

 nected with that mode of motion which causes growth. 



Restricting ourselves to the results at present obtained, it will be seen that they 

 have a great practical value in addition to their theoretical significance. A know- 

 ledge of the cardinal points of temperature, I'l'z. its superior and inferior limits and 

 the particular temperature at which the maximum of action takes place, is indis- 

 pensable to investigations of various kinds, in order to get at a correct interpretation 

 of the phenomena. On this account a few of the more trustworthy observations 

 may be given here. 



In order to determine the cardinal points of temperature to which allusion has been 

 made, observations are of value only when conducted at a nearly constant temperature ; 

 the means deduced from very variable temperatures may, as I have shown, lead to 

 very erroneous conclusions. It is however by no means easy to maintain a sufficiently 

 constant temperature for a whole day even by artificial heating or cooling. Special 

 difficulty is met with in the determination of the inferior limit or specific zero, since the 

 observation must extend over a considerable time — in the case of germination, several 

 weeks — to be certain that growth does not take place. It would be possible, by means 

 of the apparatus already described, to determine in the course of a few hours whether 

 growth still takes place in an internode at a very high or at a very low temperature, and 

 at what temperature it is the most rapid, if it were not extremely difficult to regulate the 

 temperature of the plant in the apparatus with sufficient exactness. The auxanometer 

 will however be very useful even in this case. The observations on this point hitherto 

 made, at least those which have any physiological value, have been on germinating seeds, 

 as the temperature and moisture of the soil in which they grow can be more easily 

 regulated than of the air in the case of internodes. Special facilities are offered by the 

 roots of seedlings, as they do not emerge from the soil, and are more easily measured, 

 from their simpler and more regular form. The following figures refer only to the roots 

 of seedlings, the hypocotyledonary portion of the stem being also, in the case of Dicoty- 

 ledons, included in the root. That exactly the same figures are not always obtained by 

 different observers is the result of differences in the mode of observation, the amount of 

 water, the nature of the soil, the inaccuracy of thermometers, &c. 



The first point to determine is, whether germination — /'. e. the growth of the embryo 

 at the expense of the reserve materials in the seed — takes place only at certain temper- 

 atures, and at what temperature it takes place most quickly. Observations of my own 

 gave the following results : — 



