le A ai ee) 
. 

Ce wa 9 

has, for example, recommended, but not yet passed, 
the sig, acer of the rules in the case of Holothuria 
versus Physalia (Opinion 76), and is at the moment 
4 sie to adjudicate on the name of the common 
; yu! 
se-fl 
(see NATURE, January 27, 
The 
mmission has also-—ur. 
. IT5). 
thereto by its 
_ devoted secretary, Dr. C. W. Stiles—attempted to 
draw wu 
_ alterable names, Nomina conservanda. 
for various groups lists of agreed and un- 
If, owing to the war and the peace, so thorough 
a worker as Mr. Chapman can have, apparently, 
forgotten or remained ignorant of the Commission’s 
_work, there must be many in the rising generation 
to whom it is equally unknown, If they cannot find 
what they want in the Report of the International 
Congress of Zoologists or, more accessibly, in the 
_ American periodical Science and in the Smithsonian 
“ Miscellaneous Collections,’”’ they may like to know 
_ that the present members of the Commission in this 
country are Dr. Hartert and Dr. Jordan of Tring 
Museum, Dr. W. E. Hoyle of the Welsh National 
Museum, and myself at the Natural History Museum ; 
_also that the Commission is seeking to fill one of its 
_ vacancies with an Australasian representative. 
F. A. BaTHER. 

_ The Formation of Coloured Bows and Glories. 
WHEN favourably situated, a person may see rings 
_of coloured light round the shadow of his own head, as 
_ east upon a neighbouring fog-bank or cloud. These 
coloured rings or glories, as they are called, have been 
_ explained by previous writers as merely coronas due 
to 
light reflected from deeper portions of the cloud ; in 
_ other words, the effect is regarded as of the same 
_ nature as the ordinary corona but due to secondary 
_ scattering. That this explanation cannot be accepted 
icles near the surface of the cloud scattering 
as correct is definitely shown by experimental 
observations made with artificial clouds. 
The experimental arrangement is the same as that 
used by Mecke (Ann. der Phys., vol. 61), and if the 
_ eye of the observer be placed on the same side of the 
cloud chamber as the source, so as to look down very 
nearly along the path of the beam passing through it, 
a succession of colours is seen along its track through 
the cloud. These colours also change as the angle 
of observation is changed; and the smaller the 
ag the greater is the angle from which they can 
seen. The complete system of rings is obtained on 
illuminating the cloud with a beam of sunlight, and 
may be viewed in a perpendicular direction with the 
aid of a plane sheet of glass held at 45° in front of the 
cloud chamber, so that the observer’s head does not 
screen the cloud chamber from the illuminating 
pencil. The observations prove that the phenomenon 
under discussion is shown by every position of the 
cloud, and therefore really arises from primary 
scattering by the droplets of water. 
That the glories or brocken-bows arise in a way 
which is quite different from that of the ordinary 
transmission coronas is proved by the fact that the 
sequence of colours in the brocken-bows and in the 
transmission coronas due to cloud particles of the 
same size are far from being identical. The normal 
corona, due to larger drops, shows a central white 
field with a brownish-red edge, which is surrounded by 
the familiar coloured rings, but in the brocken-bows 
the arrangement is different and varies somewhat 
with the size of the drop. It is sometimes found that 
just round the central spot (which is the image of the 
source of light reflected from the first surface of the 
observing flask) there is a distinct minimum of 
NO. 2780, VOL. I11] 

> - 
ho Set. 
| FEBRUARY 10, 1923] NATURE 183 
_ zoologists, already taken action in several cases. It | intensity exhibiting colour; then the intensity 
increases, the colour being greenish-white bordered 
by a brownish-red edge, and then follows the usual 
succession of coloured rings as in,the coronas. It,is 
sometimes found that round the central spot there is 
aclear maximum, and then a belt ofminimum intensity, 
and then again a maximum ; in other words, there is 
an oscillatory distribution of intensity ; in the central 
field of the brocken-bow only red and green rings or 
belts are present in different intensities, whitish- 
yellow colour being totally absent, while in the 
corresponding coronal. rings the central field is 
yellowish-white or nearly without colour. 
In order to understand how the glories are formed, 
we have to consider the light which travels back 
towards the source from the droplets. This arises in 
two ways: (a) by reflection from the front surface of 
the droplets; (6) by two refractions and one internal 
reflection. When a plane wave falls on the spherical 
particles and is reflected back at its external surface, 
the reflected wave front is strongly divergent, and, as 
a result, it merely adds a little to the general illumina- 
tion of the field and does not give rise to any notable 
diffraction effect. But the wave front (b) formed by 
internal reflection is not so divergent as in (a), and is 
limited by a cusped edge, at which it is doubled back. 
When the droplet is small the path differences 
between back and front of the wave near the cusped 
edge are very small. Hence we may, without 
appreciable error, consider the wave front to be a 
ae spherical cap of appropriate radius. As a 
sufficient approximation, we may assume the centre 
of this spherical cap to be the image of a point placed 
on the axis at an infinite distance, produced by two 
refractions and one reflection. We have to find in 
directions making a small angle with the axis back 
towards the direction of the primary source the 
aggregate effect of this wave cap. The problem now 
is the same as the diffraction produced by a small 
circular opening in the screen on which light is 
propagated in spherical waves from a point source. 
We take as the axis of symmetry the line drawn from 
the source to the centre of the opening, and it is 
required to find the intensity of illumination at any 
point of a plane screen parallel to the plane of the 
opening and at a distance from the later. The 
detailed mathematical treatment of this problem is 
given in Gray and Mathews’s “ Treatise on Bessel 
Functions and their Applications to Physics,” chapter 
xiv., and the result is applied in this case for the 
measurements of the positions of the maximum and 
minimum in the glory-rings) Considering the ex- 
perimental difficulties and’ assumption in the theory, 
the results agree fairly well with the observations. 
B. B. Ray. 
University College of Science and Technology, 
g2 Upper Circular Road, Calcutta, 
December 13. 

The Definition of Limiting Equality. 
In teaching the calculus to students of applied 
mathematics and physics I have found that the de- 
finitions of limiting value and of limiting equality given 
in practically all our text-books are unsatisfactory, 
and in my opinion inadequate. According to these 
books the test of limiting equality of two magnitudes 
is that their difference shall become less than any 
assignable quantity, however small. But this condi- 
tion is satisfied by any two quantities whatever if they 
vanish simultaneously, and it affords no justification 
for the use of statements such as dy=f'(*)dx; on 
the other hand, if the quantities remain finite in the 
