While the above results conform fairly well to the law of the temperature coefficient, it is evident that the imbibition of water plays so large a part in the process of elongation of the root or stem that the phenomenon is rather a physical than a chemical one: and on this account, as Blackman has remarked, the data commonly given for the rate of growth in plants are apt to be {114} irregular, and sometimes (we might even say) misleading[144]. The fact also, which we have already learned, that the elongation of a shoot tends to proceed by jerks, rather than smoothly, is another indication that the phenomenon is not purely and simply a chemical one. We have abundant illustrations, however, among animals, in which we may study the temperature coefficient under circumstances where, though the phenomenon is always complicated by osmotic factors, true metabolic growth or chemical combination plays a larger role. Thus Mlle. Maltaux and Professor Massart[145] have studied the rate of division in a certain flagellate, _Chilomonas paramoecium_, and found the process to take 29 minutes at 15° C., 12 at 25°, and only 5 minutes at 35° C. These velocities are in the ratio of 1 : 2·4 : 5·76, which ratio corresponds precisely to a temperature coefficient of 2·4 for each rise of 10°, or about 1·092 for each degree centigrade. By means of this principle we may throw light on the apparently complicated results of many experiments. For instance, Fig. 28 is an illustration, which has been often copied, of O. Hertwig’s work on the effect of temperature on the rate of development of the tadpole[146]. From inspection of this diagram, we see that the time taken to attain certain stages of development (denoted by the numbers III–VII) was as follows, at 20° and at 10° C., respectively. At 20° At 10° Stage III 2·0 6·5 days Stage IV 2·7 8·1 days Stage V 3·0 10·7 days Stage VI 4·0 13·5 days Stage VII 5·0 16·8 days Total 16·7 55·6 days That is to say, the time taken to produce a given result at {115} 10° was (on the average) somewhere about 55·6/16·7, or 3·33, times as long as was required at 20°. [Illustration: Fig. 28. Diagram shewing time taken (in days), at various temperatures (°C.), to reach certain stages of development in the Frog: viz. I, gastrula; II, medullary plate; III, closure of medullary folds; IV, tail-bud; V, tail and gills; VI, tail-fin; VII, operculum beginning; VIII, do. closing; IX, first appearance of hind-legs. (From Jenkinson, after O. Hertwig, 1898.)] We may then put our equation again in the simple form, {116} _x_^{10} = 3·33. Or, 10 log _x_ = log 3·33 = ·52244. Therefore log _x_ = ·05224, and _x_ = 1·128.