PHYSICS: C. BARUS 
343 
or about 40 scale parts of the ocular micrometer per degree of tem- 
perature. 
5. Liquids. — It remains to select suitable liquids for experiment. 
For water at 27°, dd/dp = 0.0019; for ethylic alcohol at about 18°, 
dd/dp = 0.017; for ether at 18°, dd/dp = 0.028, pressures being meas- 
ured in atmospheres. Thus for the four tubes specified in §3, the 
respective displacements in the ocular micrometer would be (per 
atmosphere) 
The case of water may be dismissed for here the thermal displacement 
per atmosphere, Ae^', is a small fraction of the elastic displacement in 
the ocular micrometer. But alcohol and ether show satisfactory con- 
ditions. Thus a sudden half turn of the lever of the screw compressor 
producing 100 atmospheres would displace the fringes, in case of tube 
III and ether, 173 scale parts elastically and 114 scale parts thermally, 
together 287 scale parts. Stops of 30 atmospheres would be advisa- 
ble. Tube IV with 63 and 114 scale parts respectively is even more 
advantageous. 
It remains to estimate the diminution of owing to the partition 
of heat between the liquid and the tube. If Ad' is the increment of 
the combined system of liquid and tube the ratio will be 
if c' and p' are the specific heat and density of the solid. These ratios 
X for the tubes and liquids in §3 and the corrected Ae'^ are easily 
tabulated. Tubes of the type I are unsatisfactory. In case of tubes 
of the types II or III the thermal displacement would be but about 
5% of the elastic displacement in case of water; but in case of alcohol 
25 to 35%, and of ether 35 to 55%. In tubes of the type IV the ad- 
vantages of thicker walls and small external diameter have again de- 
creased. The problem of selecting the best tube admits of general 
solution. 
If we combine equations (4) and (8) and put 
I Ae' 
2.7 water: Ae'' = 0.08 
1.1 alcohol Ae" = 0.68 
1.7 ether Ae'' = 1.14 
0.63 
II 
III 
IV 
A=Al/l; B = Ap/3k; C = p'c' / Pc; y = rl-rl/rl 
