126 THE ANTARCTIC MANUAL, 
amount. Therefore we have the following rule: If the initial excess 
of the temperature of the thermometer above the temperature of the 
air is ¢, and in any interval of time d @ it falls to (¢ ~ dé), then after 
any number x of such intervals (d 6) the logarithm of the fraction of 
bev oh Z ; and by multiplying 
excess temperature remaining is 2 log. ( 
the number corresponding to this logarithm by ¢, the excess of tem- 
perature of the thermometer after 7 intervals of time, each equal to 
d 0, is given. 
The law which has just been explained is Newton’s law of cooling, 
often called the logarithmic law. It is worthy of remark that New- 
ton looked upon this law ag axiomatic and self-evident the moment 
it is stated, and he did not think that it required experimental de- 
monstration. It did not escape question, notably by Amontons; and 
Lambert, in vindication of Newton, although he had held that the 
law was self-evident, carried out a beautiful series of experiments, 
which are detailed at length in the third part of his classical work 
on Pyrometry* and the measurement of heat. They completely bore 
out Newton’s law. 
The method of making the experiment has just been described, 
and as it is important that every one should be familiar with the 
practice of it, we give an actual example. (See Table XI.) 
The experiment here recorded was made under very favourable 
circumstances in the month of September in a large room the tem- 
perature of which was sensibly the same as that of the air outside, 
namely 20°°2 C., and this remained quite constant for a much longer 
time than was required for the experiment; indeed, it hardly varied 
at all during the day. The results are instructive, because they give 
a good idea of the kind of agreement between observation and theory 
which we have a right to expect. The temperature was observed at 
every ten seconds. The initial excess of the temperature of the ther- 
mometer over that of the air is 80°, and log. 8:0 = 0-9031. After 
the first interval of cooling the excess is 6°8°, and log. 6°8 is 0°8325. 
Taking the initial excess as unity, the fractional excess, or the heat 
remaining after the first interval of ten seconds, is 7 and its loga- 
rithm is 0°8325 — 0°9031 = 1°9294 = log. y,. After the second 
interval of ten seconds the excess is 5°8, and log. 5-8 = 0°7634. 
The fractional excess after the second interval is es and its loga- 
rithm is 0°7634 — 0°9031 = 1-8603. 
“ «Pyrometrie oder vom Maasse des Feuers und der Warme,’ von Johann Heinrich 
Lambert. 4to. Berlin, 1779. 
