CHEMICAL AND PHYSICAL NOTES. 127 
According to the theory which has been explained above, if the 
thermometer in cooling loses in each equal interval of time exactly 
the same fraction of the excess heat which it held at the beginning 
of the interval, and if the observations are without error, then the 
logarithms of the fractional excess after the second interval ought to 
be 2 x 1:9294 = 1°8588 in place of 1°8603, as above. The differ- 
ence is obviously not great. In order to know what it amounts to in 
the observation of the temperature we have 1°8588 + 0:9031 = 
0:°7619 = 5°78°, which ought to be the excess of the temperature of 
the thermometer over that of the air, if the thermometer follows the 
Taste XI. 
Diff - 
2 8 ‘between Logarithm Logarithm of Logan tain ae 
er aa 3 FS ropes ~ | Logarithm of queens Difference] quotients | calculated] = 3 
Experi- Epoch. 23 S Ther ofthis | gipference |_ Of these | calculated for] difference | 5 
ment. 2 gE mometer | ‘ifference. by initial a o 6 bee bi ee ae 
=] a at of difference. mares 
t— 20-2 log s log yn log 1 log Yc 
n secs, t nas % log s. — 0°9031 |— log yn41] — 2(0°0669)| + log 8 St. 
ere = log y. =dl. = log ye = log st. 
° fo} oO 
0 0 28°2 8-0 0°9031 | 0 0: 0706 0-0000 0:°9031 | 8:00 
1 10 270 6°8 0°8325 | 1:9294 “0691 1-9331 0°8362 | 6°86 
2 20 26°0 5°8 0°7634 | 1-8603 “0644 | 18662 0°7693 | 5°88 
3 30 25°2 5:0 0:6990 | 1°7959 “0706 | 1-°7993 0°7024 | 5:04 
4 40 | 24°45) 4°25 | 0-6284 | 1-7253 | -0661 | 1-7324 | 0-°6355 | 4°32 
5 50 23°85) 3°65 0°5623 | 1°6592 *0709 1:6655 0°5686 | 3°70 
6 60 | 23-3} 38-1 0-4914 | 1°5883 | -0582 | 1:°5986 | 0-5017 | 3-17 
7 70 22°85) 2°65 04282 | 1-5301 0715 | 1°5317 0:°4348 | 2:72 
8 80 22°03 2°3 0°3617 | 1°4586 *0607 1°4648 0:3679 | 2°33 
2 90 22°2 2°0 0-°3010 | 1:3979 1:°3979 0:3010 | 2:00 
law and if the first two observations are exact. The agreement with 
the observed difference, 5°80°, is quite satisfactory. But we know 
that no observations are free from error, which must affect the first 
observations as well as the others. In the table we have the observa- 
tions made at the end of each of nine consecutive intervals of ten 
seconds. In the seventh column of the table we have the differences 
of the consecutive logarithms of the fractional excesses remaining. 
Theoretically these differences ought to be identical. They are not; 
and their variations are irregular. We may therefore take the mean 
difference, which is 0'0669, and with it calculate what ought to be 
