838 
PROFESSOR O. REYNOLDS ON CERTAIN DIMENSIONAL 
lines of flow depends, cceteris paribus, on the angle between two consecutive lines. 
Thus the divergence of the lines indicates the excess of pressure, the excess being, 
cceteris paribus, proportional to the square of the angle of divergence. 
The shapes of the curves of flow are independent of the density of the gas, but the 
distance between these lines varies inversely as the density ; and since the angle 
between the lilies at distance s increases with s, we see that the excess of pressure along 
the lines of flow increases as the density diminishes, as long as the mean range of the 
molecules is not limited by the size of the containing vessel. When this point is 
reached, there can be no further increase in the mean range, and the excess of pressure 
will pass through a maximum value, and then fall with the density, until the ratio of 
the excess of pressure to the mean pressure becomes constant, which it will be in the 
limit. 
The distribution of the force of impulsion as indicated by the figures. 
121. In fig. 12 the divergence of the lines of flow is much greater towards the edges 
of the plates than in the centre; hence the excess of pressure will lie greater towards 
the edges. In the same way, on the cold side of the plate, the convergence of the lines 
of flow is greatest towards the edges, and here the pressure will be least. 
When the density of the gas is such that the width of the plate is large compared 
with s, the divergence of the consecutive heat-lines at the middle of the plate is small, 
which shows that there would be but little action on this part of the plate. At the 
edges, however, the divergence is greater, and there must always be action at the edges ; 
and the smaller the density of the gas, or the narrower the plate, the more nearly to the 
middle of the plate will the inequality of pressure extend. Thus with a very narrow 
plate, such as a spider-line, we may have the inequality of pressure all over the plate, 
although in the same gas, with a broad plate, the action might only extend to a dis¬ 
tance from the edge equal to the thickness of the spider-line. 
Fig. 13 illustrates the paradox which furnished the clue to this theory. Towards 
the middle of the plate the heatdines are parallel, and consequently the pressure 
would be equal and opposite on both plates, being the mean pressure of the gas; so 
that, if the plates were of unlimited extent, there would be no change in the pressure 
on either plate due to the one being hot and the other cold. 
At the edges, however, the heat-lines diverge from the hot plate ; hence at this 
point this plate would be subject to an excess of pressure, which would tend to force 
the plate back against the mean pressure of the gas on the outside. At the edges of 
the cold plate the heat-lines converge on to the plate ; hence there will be a deficiency 
of pressure, and the tendency will be for the pressure at the back to force the plate 
forward toward the hot plate. Thus the action is not to separate the plates, but to 
force them both to move in the direction of the hotter plate—to cause the hot plate to 
run away, and the cold plate to follow it. 
