TRANSACTIONS OP SECTION A. 545 



The incident energy per unit volume is E, and the limiting pressure on a large 

 sphere is ird l E. Schwarzschild gave 25 as the maximum ratio of pressure 

 to ra 2 E, but the true value is between 2'9 and 3. For a tail of a comet com- 

 posed of particles of the proper density, this increases the maximum possible 

 ratio of pressure to gravitational attraction of the sun from 18"5 to 22 for 

 monochromatic rediation. 



When the ratio of diameter to wave-length increases beyond the critical 

 value corresponding to this maximum, the fall of the ratio p/ira^E towards unity 

 is less rapid than Schwarzchild's figures would indicate, so that there is a closer 

 approximation to the maximum, for a given size of particle, over a greater range 

 of the spectrum. 



When, by the use of Wien's law, the effect of the continuous spectrum on 

 any particle is determined, the maximum pressure is larger, for two reasons — 

 viz. , the increase in the monochromatic maximum and the decrease in its gradient 

 — than that hitherto accepted. The increase is very useful to a radiation pressure 

 theory of the tails of comets in that it removes the necessity for the majority 

 of the particles in these tails to be totally reflecting, and at the same time 

 approximately of the critical size. 



When two particles fairly close together are under the influence of solar 

 radiation, they will mutually repel in certain cases, and the size for which the 

 mutual repulsion will just balance the gravitational action will be much larger 

 than in the case dealt with above. A mathematical determination of this critical 

 size would be of great service in testing an alternative theory of the tails, 

 and appears to be possible. The need for work on these an^i other lines was 

 emphasised in the paper. 



A departure from the spherical shape could greatly increase the maximum 

 pressure in some cases, and that of a disc-shaped particle provides a rough 

 illustration. 



4. Note on the Results of the Hourly Balloon Ascents made from the 

 Meteorological Department of the Manchester University, March 18 to 

 19, 1910. By Miss Margaret White, M.Sc. 



The balloons carried Dines self-recording instruments, and were sent up 

 hourly from 7 p.m., March 18, to 10 p.m., March 19. Twenty were recovered. 



A north wind prevailed at the ground during the greater part of the period 

 over which the ascents extended, but it became more westerly in the afternoon 

 of the 19th. The balloons were found in the Hereford, Worcester, and 

 Monmouth districts, one reaching North Devon. 



While the maximum height reached varied from 9 to 20 kms., the direction 

 of the places of fall was constant within 18°, and this slight change was pro- 

 gressive and in the same direction as the variation in the direction of start. 

 It thus appears that the direction of the upper wind was constant throughout 

 the time of the experiments and did not vary with height. The direction 

 followed was practically that of the isobars shown at the ground. 



The maximum duration of the ascent (obtained from information of the time 

 at which the balloons were picked up or, in some cases, seen falling) in several 

 cases did not exceed two hours, which, assuming a uniform increase of wind 

 velocity with height, indicates a maximum velocity of more than 100 miles per 

 hour. A table giving the direction of start, maximum height reached, and 

 distance in direction of place of fall was shown. 



The curves of variation of temperature with height were given. These do 

 not diverge from the now well-known general type. The average temperature 

 gradients shown for successive kilometres above sea-level are : 0'97, 0'41, 0"41, 0"47, 

 054, 0-58, 0-69, 070, 063, 0-58, 021, -0-11, -0-12, -011, -008, -003, -0-02, 

 —001, —002, —005 degrees Centigrade per 100 metres. 



Isothermal lines over the time of the ascent are plotted at intervals of 5° C. 

 Whereas at the ground level the temperature was remarkably constant through- 

 out the course of the experiments, showing a variation of less than 2° from 

 the mean, the isothermals at the higher levels show a well-marked rise through- 

 out the first fifteen hours, — e.g., a temperature of — 40° C. was at first encountered 

 at a height of six kilometres, and at the end of twelve hours was not met witn 



