218 
MR. H. L. CAL LEND AR ON THE PRACTICAL 
filled afresh with dry air at 103 cm. pressure, corresponding to a zero pressure of 
almost exactly one megadyne per sq. cm. By allowing the mercury to run out till 
the bulb A was emptied, and again measuring the pressure, and assuming the formula 
pv = mk 9, the volume of the bulb up to the Cu-Pt junctions was calculated to be 
V 1 — 6 3'41. A repetition of the same operation on March 8 with the same ah’ 
gave the same value. 
The observations were all reduced, assuming V 0 = 63’29 as the volume of the bulb at 
0° C., and its expansion to be that given by the formula on page 168 (linear expansion 
of glass). The correction for glass expansion amounts to nearly 12° at 600° C., and 
must be considered subject to greater uncertainty than the other elements of the calcu¬ 
lations ; the apparent discrepancies between observations at constant volume and 
pressure may be in part due to errors of this nature. 
The method of approximation used in previous portions of the paper in working out 
the results fails in the case of observations at constant pressure. Latterly I have 
used a Fullers spiral slide-rule, which gives results correct to 1 in 10,000 at least. 
This is so exceedingly expeditious and convenient that the formula may be worked 
out directly with great rapidity. If p be the pressure of the air enclosed, V the 
volume of the bulb, 9 its temperature, and v any other portion of the volume 
which is at temperature 6', the formula of the air thermometer may be stated 
thus— 
jp { Y/0 + t{vl6') } = mk, . I. 
where 2 implies that the summation is extended to all portions of the apparatus 
occupied by the mass of air under observation, and mk depends on the mass of air 
enclosed, and is theoretically constant for each filling. To make the statement more 
definite, we will define 9 to be such a function that the above equation is true, p being 
constant and equal to one atmosphere : 9 is, then, the temperature by normal air 
thermometer at constant pressure, and is nearly equal to the absolute temperature on 
the thermo-dynamic scale. 
From Formula I. we obtain, as the value of 9, 
9 = Y/ { mkjp - t {v/9 ')}.II. 
To illustrate the corrections involved, we will proceed to calculate Observation (5) :— 
Mean value of resistance observed, 54’909 legal ohms. Correction for connecting 
wires, 2’516/2 +’008 = 1’266. II corrected, 53’643. Temperature of box, 16’9. 
Temperature correction = —(54) (IT) (’00023)= —’014. B corrected, 53'629. 
R/R 0 = 27258. Assuming R 0 = 19’674 from Observation (16), 
pt = (R/R 0 - l)/’0033947 = 508’4° C. 
Resistance of capillary tube electrode, R 34 ,= 750. Resistance of the platinum 
portion, ’690. Mean temperature, 340°. 5’2 cm. of this portion of the capillary tube is 
therefore reckoned at air temperature, the remaining 10 cm. at the temperature of the 
