CHEMICAL AND PHYSICAL NOTES. 129 
equal fractions of heat in equal times. In the second place it loses 
heat by contact with the air, and the rate at which this loss takes 
place depends on the rate of renewal of successive envelopes of 
fresh air, and this diminishes as the temperature of the thermo- 
meter approaches to that of the air in which it is cooling. This 
explains why the term of cooling when the thermometer is only one 
or two degrees warmer than the air is greater than when it is five 
to fifteen degrees warmer. If differences of temperature amount- 
ing to 10° or 15° C. are used, the terms of cooling found are very 
concordant. 
In the case detailed in the Table XI., p. 127, the observations 
were made at equal intervals of ten seconds, and the mean loga- 
rithmic difference (d/) was found to be 0°0669, and the logarithm 
of the fraction remaining after the lapse of the first interval (log. y,) 
was 1°9331, whence y, = 0°8572. Now the fraction $ is expressed 
by the circulating decimal 0-857142, therefore y, = $, and in each 
interval of ten seconds the loss of heat is + of the amount which was 
present at the beginning of it. Therefore, if in each succeeding in- 
terval of ten seconds the same amount of heat were lost, the whole of 
the excess of heat would disappear in seven such intervals, or in 
seventy seconds. Therefore, the arithmetical result which we arrive 
at from observations made at intervals of ten seconds is that the 
term of cooling of the thermometer is seventy seconds. 
But if 0°0669 is the logarithmic difference for ten seconds, then 
0°00669 is the logarithmic difference for one second, 0°000669 for 
one-tenth of a second, 0°0000669 for one-hundredth of a second, and 
soon. The resulting terms of cooling derived from these different 
intervals and logarithmic differences, and the method of arriving at 
them, will be apparent from the following table : 
TaBLe XII. 
Length of interval (seconds) . .d@ 10 1 O1 0°01 
Logarithmic difference . . . . dl| 0°0669 | 0°00669 | 0-000669 | 0-0000669 
Log. first fractional excess . log. y, | 1°9331 | 1:99331 | 1-999331 | 1-9999331 
Fraction remaining at end of ex 09572 | 0-984714 | 0-99846 | 0-999846 
interval . . . som ak UR 
Fraction lost in first interval .1— y, | 0°1428 | 0°015286 | 0°00154 | 0°000154 
Reciprocal of fraction lost E q 65°4193 649°35 6193-5 
Term of cooling, in secs., d 6 =R) 70 65°4 64°9 64°9 
