442 
MR. J. T. BOTTOMLET OX THERMAL 
pump be started to flow. The dropping of the mercury is scarcely heard to commence 
before the balance is disturbed, and the index spot of the reflecting galvanometer is 
seen travelling along the scale in the direction which shows that the temperature of 
the wire has begun to rise. 
The difference also as to speed of heating and cooling at common pressures and in 
high vacuums is often surprising during experimenting. At common pressures, from 
760 mm. to 10 mm., the times which elapse on starting or stopping the current, 
before the wire assumes a permanent condition (that is, the times for heating and for 
cooling), are not strikingly different ; but at very low pressures, toW mm - or so > the 
heating on starting the current is seemingly instantaneous, while the cooling, when 
the current is stopped, of the fine platinum wire, weighing only a few grains, is so 
slow sometimes as to be almost a tedious process. 
• It has been pointed out by Mr. Crookes, and it is not difficult to understand, how 
it is that a change of pressure between 760 mm. and 10 mm. has so small an influence 
on the carrying power of the air, while a slight change at a pressure of \ mm. or less 
has a great influence. In the first case, the number of molecules is great and the 
length of the free path small; and, although, on diminishing the density, the number 
of carrying molecules is reduced, yet at the lower pressure these molecules meet with 
correspondingly less obstruction in their movements, and have correspondingly greater 
facility for transferring the heat outwards which they receive from the wire. But at 
low pressures and in a small vessel the free paths of the molecules become comparable 
with the distance from the hot wire to the cool envelope, and molecules can move to 
and fro between the wire and the envelope, experiencing but few collisions and 
comparatively little obstruction from other molecules. In this case diminishing the 
number of molecules reduces their aggregate carrying power, but does not correspond¬ 
ingly increase the facility with which they can, as it were, carry their charges to the 
cold walls of the enclosure. 
It is a matter of considerable interest to compare these experimental results with 
the well-known “Law” of Stefan, in accordance with which the radiation from a 
given surface for any particular wave-length at different temperatures is supposed to 
be proportional to the fourth power of the absolute temperature; and the loss of 
energy, therefore, proportional to the difference between the fourth powers of the 
absolute temperatures of the cooling body and its surroundings. It was to test the 
exactness of this law that the experiments of Schleiermacher,'* already referred to, 
were undertaken. To compare Stefan’s Law with the results of my experiments 
(though it is to be remarked that the law as stated refers to pure radiation), I have 
calculated the values of T 4 — T 0 4 for a sufficient number of temperatures, taking 
T 0 = 273 + 15. Choosing then an experimental point on one of the curves traced 
with high vacuum, I laid down the curve y = a (T 4 — T 0 4 ), making it pass through the 
point y = 0, t = 15° C., and through the chosen experimental point. This curve is 
* ‘ Wiedemann, Annalen,’ vol. 26, 1885. p. 287. 
