26 Further Remarks on Dr. Bradley’s Theorem 
157: ::1:,? = 0-002070064 the expansion for that 
part of the scale reckoning from 55° to 212° 
Thirdly: Mr. Dalton found that when the air was heated from 
50° to 1334 only, it expanded from 1000 to 1167 parts; con- 
sequently as 78-5 : me “ame — = 0:0021273885 the expan- 
sion for each degree of the scale from 55° to 1331°, 
Fourthly: The same ingenious experimentalist found that for 
an accession of heat from 183} to 212° the increase of bulk was: 
a 1000 to 1158 parts; we have therefore as 78°5: ae a 
sons = 0:00201273885, the rate of expansion reaching from 
1333 to 212: and by bringing these together for the purpese 
of more easy comparison, we find that 
From 65° to 133}, the rate of expansion is 0°002127589 
32 to 212 ee oe ee 0:002083333 
55 to 212° aes ae we 0002070064 
1334 to 212... es 0-002012739 
The greatest rate of expansion in n this statement is 0: 0021273589, 
and the temperature corresponding is lower than either of the 
others, viz. from 55 to 1334. The least rate is 0°002012739; 
and its corresponding temperature is from 133} to 212, which 
is the highest of all the four. Of the other two, that from 32 
to 212 includes a lower part of the scale than the one reaching 
from 55 to 212; and we find the rate of expansion is propor- 
tionally greater. It therefore appears, that the rate of expan- 
sion for the low temperatures is greater than that for the high 
ones; and consequently m, the coefficient of 6, in that part of 
the foregoing theorem w hich depends on the heat of the atmo- 
- ought to be variable according to the dif- 
: 1 
sphere, viz. - 
1 
™m 
ferent heights of the mercury in the thermometer. 
Although the above table shows pretty clearly that the rate of 
expansion is greater in the low temperatures than in the high, 
yet there is not asufficient number of them, nor are they made at 
the proper intervals to enable us to compute the exact law of this 
rate, for all degrees, from the freezing to the boiling point, which 
for the subject under consideration is very much to be desired. 
These are the determinations of the chemists. Let us now 
endeavour to discover how far they are corroborated by the ob- 
servations of the astronomer. 
In the last communication which Mr. Groombridge has fur- 
nished us with, on the subject of refraction (Phil. Trans. for 1814), 
if we arrange the values of z, determined by that gentleman, 
according to the different states of the thermometer, omitting 
those 
