128 THE ANTARCTIC MANUAL. 
the excess remaining after each interval of ten seconds. The initial 
fractional excess, 7, is 1, and its logarithm is 0. Subtracting 0°0669 
we get 1°9331=log. y,; and again subtracting 0'0669 we get 1°8662 
= log. y.; and so on. The logarithms obtained are found in the 
eighth column of the table. In the ninth column we have the sum 
of log. 8°0, or 0°9031, and the respective numbers in the eighth 
column. They are the logarithms of the calculated thermometric 
excesses. These are given in the tenth column. 
The first and the last entries in this column necessarily agree with 
the observed values in the fourth column. The greatest difference is 
0:08°, so that the actual rate of cooling may be held to agree fairly 
well with the rate which, according to theory, we ought to observe 
if the bulb of the thermometer were a perfectly homogeneous body of 
infinite thermal conductivity and of symmetrical shape, cooling in a 
vacuum enclosed by walls having a definite and constant tempera- 
ture. We know that this description fits neither the thermometer 
nor the room in which it was cooling. The shape of the bulb, whether 
it be cylindrical or spherical, is not symmetrical in the above sense, 
because, for purposes of observation, the thermometer must always 
have a stem, and the part of the bulb where it is united to the stem 
is exposed to different conditions, as regards cooling, from the other 
parts of it. Although the thermal conductivity of the bulb of a mer- 
curial thermometer is not perfect, its degree of imperfection is not 
such as to introduce much error into observations of this kind. The 
temperature of the room, and no doubt that of its walls, was very 
constant, but of course there was no vacuum. 
The instrumental deformity introduced by the necessity of a stem 
for the thermometer must always introduce some deviation from the 
normal rate of cooling, but it is, as thermometers are made, not prac- 
tically of much importance. The disturbing element which takes 
precedence of all others is the air. 
The conditions in which the experiments quoted in the table 
were made were as favourable as they could be, and it would not 
be possible to get air more motionless than it was. But however 
motionless the mass of the air may be, a thermometer, or any other 
object, suspended in it, and having a higher temperature, must produce 
convection currents in its immediate neighbourhood, which will be 
the more energetic the greater the difference of temperature. Hence 
the conditions under which a thermometer cools in air are complex. 
In the first place it cools by radiation to its surroundings, and, set- 
ting aside instrumental imperfections, this takes place independently, 
as it would in a vacuum, according to the logarithmic law, losing 
