That is to say, between the intervals of 10° and 20° C., if it take _m_ days, at a certain given temperature, for a certain stage of development to be attained, it will take _m_ × 1·128^{_n_} days, when the temperature is _n_ degrees less, for the same stage to be arrived at. [Illustration: Fig. 29. Calculated values, corresponding to preceding figure.] Fig. 29 is calculated throughout from this value; and it will be seen that it is extremely concordant with the original diagram, as regards all the stages of development and the whole range of temperatures shewn: in spite of the fact that the coefficient on which it is based was derived by an easy method from a very few points in the original curves. {117} Karl Peter[147], experimenting chiefly on echinoderm eggs, and also making use of Hertwig’s experiments on young tadpoles, gives the normal temperature coefficients for intervals of 10° C. (commonly written _Q__{10}) as follows. Sphaerechinus 2·15, Echinus 2·13, Rana 2·86. These values are not only concordant, but are evidently of the same order of magnitude as the temperature-coefficient in ordinary chemical reactions. Peter has also discovered the very interesting fact that the temperature-coefficient alters with age, usually but not always becoming smaller as age increases. Sphaerechinus; Segmentation _Q_^{10} = 2·29, Later stages _Q_^{10} = 2·03. Echinus; Segmentation _Q_^{10} = 2·30, Later stages _Q_^{10} = 2·08. Rana; Segmentation _Q_^{10} = 2·23, Later stages _Q_^{10} = 3·34. Furthermore, the temperature coefficient varies with the temperature, diminishing as the temperature rises,—a rule which van’t Hoff has shewn to hold in ordinary chemical operations. Thus, in Rana the temperature coefficient at low temperatures may be as high as 5·6: which is just another way of saying that at low temperatures development is exceptionally retarded. ―――――――――― In certain fish, such as plaice and haddock, I and others have found clear evidence that the ascending curve of growth is subject to seasonal interruptions, the rate during the winter months being always slower than in the months of summer: it is as though we superimposed a periodic, annual, sine-curve upon the continuous curve of growth. And further, as growth itself grows less and less from year to year, so will the difference between the winter and the summer rate also grow less and less. The fluctuation in rate {118} will represent a vibration which is gradually dying out; the amplitude of the sine-curve will gradually diminish till it disappears; in short, our phenomenon is simply expressed by what is known as a “damped sine-curve.” Exactly the same thing occurs in man, though neither in his case nor in that of the fish have we sufficient data for its complete illustration.