423 
BETWEEN 75 AND 150 MILLIMETRES OF MERCURY. 
the half of its proportional amount, since we have to do not with the ratio (h the 
capacities of the two bulbs, but with the ratio of the capacity of the upper bulb to the 
capacity of the two bulbs together. Thus if the volume of the upper bulb be unity 
and that of the lower (1 + a), the ratio with which we are concerned is 2 + a ; I, 
differing from 2 : 1 by the proportional error ^ a. 
To adjust the capacities to approximate equality and to determine the outstanding 
difference, the double bulb was mounted vertically, in connection above with a Topler 
pump and below with a stop-cock, such as is used with a mercury burette. The 
“ marks” were provided by small collars of metal embracing tubing of 3 millims. bore 
and securely cemented, to the lower edge of which the mercury could be set as in reading 
barometers. A measuring flask, with a prolonged neck consisting of uniform tubing 
of 6 millims. diameter, was prepared having nearly the same capacity as the bulbs. 
The mercury required at a known temperature to till the upper bulb between the 
marks was run from the tap into this flask. Air specks being removed, the flask was 
placed in a water-bath and the tenq3erature varied until the mercury stood at a fixed 
mark upon the neck of the flask. Subsequently the mercury required at the same 
temperature to fill the lower bulb between the middle and the lower marks was 
measured in the same way. On a mean of two trials it was found that the flask 
needed to be 2°'4 C. warmer in the second case than in the first, showing that tiie 
capacity of the lower bulb was a little the smaller. Taking the relative expansions of 
mercury and glass for one degree to be '00016, we get as the proportional difterence 
'00038. Thus in the notation already employed, 
: Vo = 2 - -00038 = 1-99962 .(4). 
It appeared that so far as the measurements were concerned this rati(3 should be 
correct to at least -^^oo 5 disturbances due to pressure introduce uncertainty of 
about the same order. 
Comparison of Gonujes. 
A simple method of comparing the gauges is to combine them in parallel so that 
the pressures in the lower chambers are the same, and also the pressures in the upper 
chambers, and then to find what slope must be given to the longer measuring-rod in 
order that its effective length may be equal to that of the shorter rod maintained 
vertical. The mercury can then be set to coincidence with all four ^joints, and the 
equality of the gauges so arranged actually tested. It is afterwards an easy matter 
to calculate back so as to find the proportional difference of heights when both 
measuring-rods are vertical. Preliminary experiments of this kind upon the gauges, 
mounted on separate levelling stands and connected by india-rubber tubing, had 
shown that the difference was about j^art. 
It would be possible, having found by the combination in parallel an adjustment to 
