SECTIONAL TRANSACTIONS.—A. 373 
p denote the limiting value, at great heights, of the fraction of the weight 
which is balanced by the pressure gradient. Unless p» is extremely small, the 
density decreases upwards approximately according to an exponential law. But 
if »=0 (i.e. if, at great heights, the whole of the weight is balanced by radia- 
tion-pressure), the density p at height x, for a gas with the properties of ionised 
calcium, is found to be given by p=(const.)/(x+,)*, where x, is the height of 
_ the equivalent homegeneous atmosphere. This gives a comparatively slow 
_ decrease of density with height, in marked contrast with exponential laws. 
_ Comparison with observation shows that for ionised calcium atoms in the solar 
chromosphere » can scarcely be as large as 0.01. 
45. Dr. L. Simserstein.—Determination of the Curvature Radius of 
Space-Time. 
Assuming de Sitter’s space-time, as determined by the line-element 
; ds = cos? co. c*dt?— dr* —R? sin *o(d¢?+ sin 29d?) 
é } , r do 2 
with R written for the curvature radius and o= R and considering both the 
observed star and the observer’s station as ‘ free particles’ in radial, purely 
inertial motion, a formula is deduced for the complete Doppler effect or spectrum- 
shift D = Shy comparing the segments of the observer's and the star’s world- 
lines intercepted by two minimal lines representing light signals sent from the 
star to the observer. The rigorous result is 
D=y [1+ V1— cos%o/y?]-1. ’ SHES? OB) 
where r=Ro is the observer’s distance from the star at the instant of receiving 
its light. The upper sign corresponds to a receding and the lower to an 
approaching star, giving a red and a blue shift respectively. 
In a first approximation at a determination of the radius R from the most 
remote objects of the sky for which both D and r values are available, the 
formula becomes 
Dea 
the co-ordination of signs being as before. No distance estimates being as yet 
available for the spiral nebule, this formula is applied to eight globular clusters 
‘and the two Magellanic Clouds, and gives an arithmetical mean of 
R=6-7x 10" 
astronomical units. 
Formula (1) is extended to any, generally oblique, inertial motions. If r, 
be the shortest distance (perihelion) of the star and v, the corresponding 
velocity, the rigorous general formula reduces practically to 
De=(1—") (7+) Rt ae Lae 
7] \R? ¢ 
Hs This is applied to the previous objects and to ten more clusters and one 
Spiral nebula (the data for which were obtained quite recently), in all twenty- 
og objects, and yields, statistically, the radius 
Baty ar bs CO 
. Dr. H. H. Prasxerr.—The Spectra of Nebulae. 
_ The paper discusses some new observations on the spectra of nebulae. These 
new observations furnish the absolute intensities of the hydrogen and some 
nebulium’ lines as determined by the wedge method in the Orion Nebula, 
artially confirm the previous interferometer results in assigning a low atomic 
eight to ‘ nebulium,’ and finally contain a complete description of the new 
