BRIDGMAN. — A SIMPLE PRIMARY GAUGE. 213 



This force, F + P 2 , acts in addition to the hydrostatic pressure on the 

 inner end of the piston, which is now decreased in radius by 2.1 X 

 10- 7 X R X.P. The new effective radius is therefore 



R + =£ - (2.1 - 1.2) X 10- 7 X Rx P, 



as compared with the original effective radius R + AP/2. The cor- 

 rection on the area is therefore 2 X (2.1 — 1.2) X 10 -7 X P, or 

 0.018 per cent per 1000 kgm. The correction turns out, as was to be 

 expected, independent of the size of the crack. 



If the maximum value given above for the distortion of the cylinder 

 is used, the effective radius will be found to be 



A D 



R . + ~ - 1.7 X 10- 7 X RxP, 



which gives a maximum correction of 0.034 per cent per 1000 kgm. 

 per sq. cm. Experimental reasons will be given later for preferring 

 the lower value for the correction. This value, 0.018 per cent per 

 1000 kgm., was therefore the correction applied in all the subsequent 

 work. 



The Gauge in Practical Use. 



The first essential in making an actual measurement with this gauge 

 is a knowledge of the effective area of the piston. As has been inti- 

 mated above, this could not be determined directly because of the 

 smallness of the parts, and an indirect method was therefore adopted. 

 Briefly, this consisted in subjecting simultaneously to the same hydro- 

 static pressure the small piston and another piston large enough to be 

 measured accurately, and finding the equilibrating weights required 

 on the two pistons. The effective areas are then in the ratio of the 

 equilibrating weights. 



The larger piston was \ in. (0.635 cm.) in diameter, 2 in. (5.18 cm.) 

 long, ground to fit a reamed \ in. hole in a large cylinder of Bessemer 

 steel. As this larger gauge was intended for use only to 1000 kgm., the 

 increased breadth of crack produced by exerting the pressure on the 

 interior only of the cylinder was not great enough to give troublesome 

 leak. Also the correction to the effective cross section due to distor- 

 tion is small enough to be entirely neglected at 1000 kgm. The diam- 

 eter of the \ in. piston could be measured certainly to one part in 

 2500 with a Brown and Sharpe micrometer. The hole in the cylinder 

 was not measured by filling with mercury and weighing, or by any 

 such frequently employed device. It was instead carefully tested 



