326 PROCEEDINGS OF THE AMERICAN ACADEMY. 



The correction found in this way is to be regarded as an upper limit, 

 the assumption being made that the crack will close up at 15,000 kgm. 

 The correction found by this assumption is somewhat doubtful. A 

 lower limit to the correction can be found by making the assumption 

 as far removed as possible from that made above, namely, that at the 

 upper end the cylinder suffers no change of internal radius. The 

 change of effective area at the upper end is due to enlarging of the pis- 

 ton alone, therefore, and is evidently 1.4 X 10"'^ X p. In this case 

 the change in the effective area is 1.3 X 10"' X p. The upper and the 

 lower limits differ only 1/10 per cent at 10,000 kgm. The correction 

 applied in the following work was taken as the mean of these two 

 limits, 1.8 X 10~^ X p, and the observed gauge readings have been in- 

 creased in this ratio. This happens to be the same as the correction 

 used for the former gauge. 



The experimental evidence used in part of the above approxima- 

 tions requires brief mention. The calculations given above show a 

 more rapid closing of the crack at the end B, so that the tendency of 

 the piston would be to bind at the upper end. This was verified ex- 

 perimentally by the fact that the upper end of the piston was always 

 more brightly polished after a little use than the lower end, and that 

 sticking could be avoided at the higher pressures by making the piston 

 slightly conical. To accomplish this it was sufficient to make the 

 upper end 0.0002 inch less in diameter than the lower. The figure 

 above for the initial width of the crack at the upper end (0.00035 inch) 

 was obtained by combining with the conicality the measured value for 

 the effective area to be described later. 



In actual use care was necessary to be sure that the sticking was 

 really due to closing of the crack, and not to viscosity in the fluid 

 transmitting pressure. In the early experiments, in which the trans- 

 mitting fluid was molasses and glycerine, almost complete sticking was 

 found at pressures as low as 7500. That this was not due to closing of 

 the crack was shown simply by warming the whole apparatus, thus 

 decreasing the viscosity without materially decreasing the size of the 

 crack. It was thus possible to reach. 13,000 with very much less sticking 

 than at 7800 at the lower temperature, and also with much less leak, 

 showing an actual decrease in the size of the crack at high pressures. 

 The liquid finally adopted for use in this work was a mixture of glucose 

 with glycerine and water. Glycerine and water were first mixed in 

 equal parts, and then the glucose thinned with this mixture to a best 

 consistency found by experiment. The advantage is that the pressure 

 effect on viscosity is much less than for the molasses and glycerine mix- 

 ture, so that a mixture of given consistency will work over twice the 

 pressure range of the molasses mixture. 



