PETER GUTHRIE TAIT. 167 



but Perkins' estimates of pressure are inaccurate, and no numerical 

 data of any value can be obtained from his results. Regnault in 1847 

 attempted to take into account the compressibility of the piezometer by 

 applying pressure alternately to the outside and the inside of the 

 piezometer, and then simultaneously to both. But this method gives 

 the elastic constants of the piezometer only when dealing with an 

 absolutely incompressible liquid. Amaury and Deschamps measured 

 the change in external volume of the piezometer, but Tait points out 

 that unless the bulbs are truly spherical or cylindrical, of uniform 

 thickness and homogeneous material, errors due to application of pres- 

 sure on the outside or inside alone may be introduced of the same order 

 as the quantity to be measured. A very complete series of measure- 

 ments had been made for water from 0° — 100 °C. by the two Italian 

 experimenters, Pagialini and Vincentini, but only for low pressures. 

 Moreover, though they made careful determinations of the change in 

 the glass due to changes of temperature, they failed to eliminate the 

 effect of pressure on the piezometers, applying pressure to the inside 

 only, and so their results are some forty per cent, too great. Lastly, 

 Amagat made very extensive experiments up to 3,000 atmospheres, but 

 he considered the compressibility of the glass to be of small effect and 

 consequently left it out of account, and the first really satisfactory work 

 on this important subject was that accomplished by Tait and his 

 assistants, the full report of which appears in the 'Challenger Eeports.'* 



The great merit of Tait's work was the careful determination of the 

 pressures used, and the preliminary researches on the compressibility 

 of mercury and of glass, so as to apply the proper corrections to his 

 thermometers and piezometers, together with the fact that his investiga- 

 tions extended to sea-water and to solutions of salt of various strengths. 

 A brief summary of his most important results follows : 



As an approximation for the compressibility of fresh water through 

 the whole range of the experiments (pressure from 150 to 450 atmos- 

 pheres and temperatures from 0° to 15°C), he secured the formula: 



0.0018 6 / & t 2 \ 



36 + p V 400 + 10, 000 J 



where t is the temperature of the water in degrees centigrade and p is the 

 pressure in tons per square inch. 



The point of minimum compressibility of fresh water is about 60°C. at 

 atmospheric pressure, but is lowered by increase of pressure. 



The average compressibility of sea-water is about .92 of that of fresh water, 

 with a minimum compressibility at about 56°C, lowered by increase of pressure. 



The average compressibility of salt solutions for the first p tons of addi- 

 tional pressure beyond atmospheric pressure is, at 0°C. — 



0.00186 

 36 + p + s 



* Vol. II., ' Physics and Chemistry,' London, 1889. 



