DR. ANDREWS ON THE GASEOUS STATE OE MATTER. 
423 
purpose a dividing and calibrating engine was employed, which was devised some years 
ago by myself. It was provided with a short steel screw of remarkable accuracy, specially 
constructed for this dividing engine by Teoughton and Simms. The results of the cali- 
bration were [plotted on a large scale, and the small errors arising from the abrupt 
passage between the calibrated lengths of the tube were estimated by a simple method, 
for which I am indebted to my friend Professor James Thomson. The thermometers 
employed were the same to which I formerly referred. They were all calibrated and 
divided by myself, and their agreement throughout the whole range between 0° and 100° 
was almost perfect. The shifting of the zero-points has not been considerable, but it 
was carefully observed from time to time. 
The capacity c 0 of the glass tube at 0° C. in cubic centimetres was calculated by the 
following equation, in which w is the weight of the mercury, t the temperature at 
which the observation was made, and f (0-000158) the apparent dilatation fori 0 C. of 
mercury in glass : — 
c 0 =w 
l +fl 
13 - 596 * 
• 0 ) 
The value of c 0 , as given by this expression, may be used without notable error for 
temperatures differing only by a few degrees from 0° C., but at high temperatures a cor- 
rection is required for the expansion of the glass vessel. If the readings had been 
made by means of fine divisions etched on the tube, this correction would correspond 
to the cubic expansion of the glass; but when, as in my method of working, catheto- 
metric readings are made from the extreme end of the internal cone above to the 
bounding surface of the mercury below, the correction will be the difference between 
the cubic and linear expansion of glass, or for small differences of this order it will be 
two thirds of the cubic expansion. If c t be the capacity at the temperature t , k the 
cubic dilatation of glass for 1° C. (0-0000272), we shall have, under the conditions stated 
above, 
Ct= G o(l+t^) (2) 
Combining equations (1) and (2), we obtain a general expression for c t , 
( 3 ) 
The original volume of gas at 0° and 760 millimetres was calculated by the usual 
formula. 
1 . P 
1 -\- at 7^0 
( 4 ) 
where v t is the capacity of the tube in cubic centimetres, a the coefficient of expansion 
at the ordinary pressure of the atmosphere (0-00367 for air and 0-00371 for carbonic 
acid), t the temperature of the observation, and jp the height of the barometer reduced 
to 0° C. and the latitude of 45°. 
3 n 2 
