Paul Bert (1) (1870) and later Richet (2) (1894) investigated the apnœa in diving produced in the duck (Anas Boschas var. domesticus) by submergence of the head in water.

In 1911 Frances M. Huxley (3), while studying this apnœa, discovered that it is largely a postural reflex and that it could be induced without submergence. She also showed that in this reflex a labyrinthine and a cervical element are involved, and later I (4) showed that in most ducks the former, but in some the latter, predominates and that they are cooperative, acting together.

The importance in Mathematical Physics of the Bessel functions, whose order is half an odd integer, suggests that the corresponding Mathieu functions may be worthy of a closer attention than they have yet received. At the very least it is expedient to pave the way for their computation. In the second paper bearing the above title, asymptotic developments of the characteristic numbers which correspond to these functions were given; it is here proposed, in the first place, to take the more direct line of approach.

As is well known, when the conducting surfaces of a charged condenser are in connection with the electrodes of a discharge tube at low pressure, the discharge of the condenser through the tube may take one or other of two forms; it may be of the continuous type or it may pass as a sudden flash, the most noticeable feature of which, as has been pointed out, is the absence of the definite structure usually regarded as normal in a low-pressure discharge.

I wish to thank the Royal Society of Edinburgh for the indulgent appreciation of which this recognition is a token. It has always been a subject of gratification to me that I have been not unknown to this distinguished company, with its great historic traditions.

A semi-diurnal variation appears to some extent in many meteorological phenomena, in particular in barometric pressure, rainfall, visibility, atmospheric electric potential gradient, and atmospheric pollution, even though the variation of temperature, at least in the lower levels of the atmosphere, is very approximately a purely diurnal variation.

The data examined in this paper suggest that, in the forenoon, insolation affecting the ground and the lower layers, and, in the evening, outgoing radiation affecting clouds and the upper part of the troposphere, each lead to a disturbance of the stability of arrangement of the atmosphere in the vertical direction and to a consequent increased mixing of layers. On the other hand, in the late afternoon and in the later part of the night, as the turbulences arising from the above two effects respectively die down, there is an improvement above normal in the laminarity of flow of atmosphere over the earth. The resultant effect is therefore, on the average, a semi-diurnal variation in the vertical structure and horizontal movement of the atmosphere, which variation is reflected in the meteorological phenomena mentioned above. It is shown in the paper that the various individual effects may be greatly exaggerated, or almost eliminated, or accelerated or retarded, at least in temperate latitudes where a suitable variety of types of upper air structure, from which to select, is available.

In December 1925 a paper was read before the Society by one of us on the salmon of the Moisie in 1922 and 1923. Since that date scales and measurements of 182 fish taken on June 25, 1923, and of 143 fish caught between June 18 and July 12, 1924, have been received from Mr J. S. Adams, Dorchester, Massachusetts, U.S.A. The scales have been read and measured under the microscope, and the results we now place on record.