It is assumed that the glaciation of Northern Europe during the great Ice Age was due to a shift of the pole associated with appreciable variations of solar radiation.

The shift of the pole brought Europe into sufficiently high latitudes to permit of the formation of an ice-sheet; but the large variations of climate during the Ice Age, as shown by the interglacial epochs, were due to the oscillations of the solar energy.

If two complete cycles of solar radiation occurred during the Pleistocene Period, it is possible to account for four advances of the ice in the Alps as demonstrated by Penck and Brückner, but the interglacial epochs were not all warm. The Günz-Mindel and the Riss-Würm interglacial epochs occurred at the maximum of the solar radiation and were, therefore, warm interglacial epochs; but the Mindel-Riss interglacial epoch occurred at a minimum of solar radiation and was, therefore, a cold interglacial epoch.

At a maximum of solar radiation—that is, during a warm interglacial epoch—the climate of North-West Europe was warm and very wet, with a relatively small annual variation of temperature. As the intensity of solar radiation decreased, the mean temperature fell and the annual variation of temperature increased. At the same time the amount of precipitation decreased. The fall of temperature occurred sufficiently rapidly compared with the decrease in precipitation to cause the glaciers of the Alps to advance and for an ice-sheet to form over Scandinavia. As the solar radiation still further decreased, the lack of precipitation caused the glaciers of the Alps to retreat. At the minimum of solar radiation there was a cold interglacial epoch with low mean temperature, a large annual variation of temperature and very low precipitation; in fact, a truly continental climate.

With these changes of climate went a corresponding change in the flora, the sequence being: park land, forest, tundra, grass with sparse trees, and steppe. In this way it has been found possible to determine a sequence of climates and of fauna and flora for the whole Pleistocene Period, which is supported by the geological and archæological evidence available. In particular it is possible to arrange the sequence of human culture, the geological strata of East Anglia, and the history of the ice in the Alps into the scheme of climate change.

The two maxima of solar radiation were accompanied by increased precipitation in all parts of the world, so accounting for the two pluvial periods which are known to have occurred during the Pleistocene Period.

Theories regarding the chemistry of the contraction process in striped muscle have been revolutionised during the last year. The Hill-Meyerhof theory was based on the assumption that the contraction process was due to the liberation of lactic acid by the break-down of glycogen, a non-oxidative reaction, and that the recovery process consisted in the oxidation of part of the lactic acid and the resynthesis of glycogen from the remainder. Meyerhof now believes (1, p. 305) that contraction is produced by the break-down of creatin-phosphoric acid (phosphagen), and that the energy produced by carbohydrate break-down is utilised to resynthesise phosphagen.

We consider in this paper the persymmetric determinants

where

p(x) being a function which is not negative in the interval (a, b) (finite or infinite); we suppose further that the integrals

exist for s = 0, 1, 2,….

The object of this paper is the application of a theorem stated by the writer in the paper “Sur un déterminant de Hankel” to many determinants of the type (1), referred to by Sir Thomas Muir in his paper “The theory of persymmetric determinants from 1894 to 1919.”

In Statistical Methods for Research Workers R. A. Fisher (1) has given a numerical method of curve fitting by means of orthogonal polynomials. It is proposed here to show how the properties of these polynomials and a general formula for them may be developed from the properties of their terminal differences, thus providing general proofs of the properties utilised in the numerical method.