512 
MESSRS. T. B. THORPE AHD J. W. RODGER ON THE RELATIONS 
have been atfected by this circumstance. The repetition of all above 100° showed, 
however, that the distillation which had occurred was too insignificant in amount to 
influence the results, In all subsequent observations over 100° the thermometer was 
inverted and replaced in the bath just before the observation of temperature. 
Observations of the thermal expansion of j)ropionic acid have been made by Kopp 
(‘Annalen/ 95, 309), by Pierp.e and Pdchot (‘Annales de Chimie et de Phj^s.,’ 4, 
28, 71), and by Zander (‘Annalen,’ 224, 91). As the results are very concordant, 
the mean value of the different expressions has been employed. For the relative 
density we have adopted rZ (0°/0°) = 1'0170, the mean of the values given by Kopp, 
LxVNdolt, Linnemann, and Zander. 
Taking 
7 ^^ = ’014042 = ’003295 (calculated) = ’006802 
= 4°’70 ^3 = 137°’05 (from curve) = 58°’30, 
we obtain the formula 
105-746 
~~ (109-53 + ’ 
which gives the following calculated values :— 
Mean temp. 
Difference. 
Observed (mean). 
Calculated. 
j ° 
4-70 
-01404 
•01404 
•00000 
16-87 
-01151 
.01156 
+ -00005 
28-21 
-00979 
•00987 
+ -00008 
40-04 
-00839 
•00845 
4 - -00006 
52-03 
-00729 
•00731 
+ -00002 
63-63 
-00642 
•00641 
- -00001 
76-70 
-00562 
•00559 
- -00003 
89-56 
-00496 
•00493 
- -00003 
101-01 
-00448 
•00444 
- -00004 
112-98 
•00403 
•004U0 
- -00003 
112-37 
•00405 
•00402 
- -00003 
] 23-67 
•00368 
•00366 
- -00002 
137-05 
•00329 
•00329 
•00000 
