1258 
line at first, but after a short time the pattern changes 
to a series of almost circular cells, each having a well- 
marked, clear centre. No motion is readily detected, 
but by the injection of small puffs of smoke through a 
capillary tube with its open end placed at the centre 
of the clear space, and in contact with the base plate, 
it was easily possible to detect ascent at the centre of 
these cells. 
A structure similar to that found in layers of air of 
depth 6 mm was also obtained in deeper layers at 
very high temperatures. The reason for this is readily 
seen from a consideration of Rayleigh’s criterion quoted 
above. If the difference of density, 7.e., of temperature, 
required to produce cellular motion is to be attained 
by heating the base of the chamber, it is clear that 
when there is a large difference of temperature be- 
tween the top and bottom of the chamber, the mean 
temperature of the chamber will also be raised con- 
siderably. This leads to a rapid increase in the product 
xv, and in shallow chambers it will be impossible to 
satisfy Rayleigh’s criterion for motion. 
The curious structure shown over the greater part 
of Fig. 5 can be formed with quite small differences of 
temperature in shallow chambers, differences which 
are much lower than are required by Rayleigh’s 
criterion. 
A simple expedient made it possible to test the view 
stated above. A chamber was constructed with a glass 
base and a metal top around which was fixed a narrow 
flange, so that liquid air could be poured into the 
vessel so formed. The evaporation of the liquid air 
cooled the top of the chamber, and gave polygonal 
cells readily in chambers of any depth. These could 
be easily seen from below, though the condensation 
- produced inside the chamber quickly frosted the glass 
and shut off any view of the inside of the chamber. 
A final experiment in the production of the simple 
convection cells merits mention. A depth of 12 mm was 
given to the chamber, and it was found possible to lay 
a dense but very shallow layer of smoke over the base 
plate. Almost immediately after the layer was formed 
a series of round holes were punched in the layer of 
smoke by the descent of colder air from above, giving 
a series of circular clear patches over the plate. Within 
a few seconds, convection patterns began to show with- 
in the chamber, placed centrally over the holes in the 
smoke carpet. This circulation carried small streamers 
of smoke upward and inward towards the centre, as 
shown in Fig. 6, and here and there it is possible to 
detect the streamers of smoke which have not yet 
reached the centre. After some minutes the whole 
chamber became filled with convection cells such as are 
normally obtained when smoke is injected into the 
chamber. 
In the laboratory experiments described above, the 
convection cell has both centre and periphery clear of 
smoke. This is presumably to be explained by the for- 
mation of a “dust-free’”’ space in immediate contact 
with the heated base plate. The air which fills the 
centre and periphery of the cells has been drawn from 
this dust-free space immediately above the base plate. 
LABORATORY INVESTIGATIONS 
It should be emphasised that two types of motion 
are found in the course of these experiments. In the 
first type, the genuine Bénard convectional cell of 
polygonal form, the motion is downward in the centre. 
Fie. 6.—Dense layer of smoke over base plate in a chamber 
of depth 12 mm, showing clear holes formed in this smoke layer, 
and subsequent development of convection cells above the 
oles. 
In the second type, shown in Fig. 5, alongside the typi- 
cal polygonal cells over a restricted area, there is some 
difficulty in determining the nature of the motion by 
simply watching it with the naked eye, though it was 
found by injecting small quantities of smoke that there 
was ascent in the centre of the roughly circular struc- 
tures. The motion in these cases will be referred to as 
“convection of the second type.” 
The results derived by Chandra are summarised 
in Fig. 7. The continuous line separating the two 
16 
CONVECTION OF 
TYPE | (CELLULAR) 
CONVECTION 
OF TYPE Il 
DEPTH IN MILLIMETERS 
(0) 0.04 0.08 0.12 0.24 0.28 
AT/z 
Fic. 7.—A summary of Chandra’s observations of limiting 
conditions in air (cf. Fig. 12). 
O16 0.20 
types of convection becomes asymptotic to a horizontal 
line a short distance below the 7-mm level, imdicating 
that only the second type of convection can be ob- 
tained in chambers of depth appreciably less than 
7 mm. 
Motion in Unstable Layers Having a Shearing Motion. 
Depth of Chamber 7 mm or Greater. A modification of 
the apparatus previously described was used to in- 
vestigate the effect of shear on the form of the cir- 
