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.

We can demonstrate the fact, however, in the case of man by the help of certain very interesting measurements which have been recorded by Daffner[148], of the height of German cadets, measured at half-yearly intervals.

Growth in height of German military Cadets, in half-yearlyperiods. (Daffner.)
Height in cent.Increment in cm.
Number observedAgeOctoberAprilOctoberWinter ½-yearSummer ½-yearYear
1211–12139·4141·0143·31·62·33·9
8012–13143·0144·5147·41·52·94·4
14613–14147·5149·5152·52·03·05·0
16214–15152·2155·0158·52·53·56·0
16215–16158·5160·8163·82·33·05·3
15016–17163·5165·4167·71·92·34·2
8217–18167·7168·9170·41·21·52·7
2218–19169·8170·6171·50·80·91·7
619–20170·7171·1171·50·40·40·8

In the accompanying diagram (Fig. [30]) the half-yearly increments are set forth, from the above table, and it will be seen that they form two even and entirely separate series. The curve joining up each series of points is an acceleration-curve; and the comparison of the two curves gives a clear view of the relative rates of growth during winter and summer, and the fluctuation which these velocities undergo during the years in question. The dotted line represents, ap­prox­i­mate­ly, the acceleration-curve in its continuous fluctuation of alternate seasonal decrease and increase.

In the case of trees, the seasonal fluctuations of growth[149] admit {119} of easy determination, and it is a point of considerable interest to compare the phenomenon in evergreen and in deciduous trees. I happen to have no measurements at hand with which to make this comparison in the case of our native trees, but from a paper by Mr Charles E. Hall[150] I have compiled certain mean values for growth in the climate of Uruguay.

Fig. 30. Half-yearly increments of growth, in cadets of various ages. (From Daffner’s data.)

Jan.Feb.Mar.Apr.MayJuneJulyAug.Sept.Oct.Nov.Dec.
Evergreens 9·1 8·88·68·97·75·44·36·09·111·110·810·2
Deciduous trees20·314·69·02·30·80·30·71·33·5 9·916·721·0