From 1879 to 1888 he was engaged on difficult experimental investigations, which began with an inquiry into the corrections required, owing to the great pressures to which the instruments had been subjected, in the readings of the thermometers employed by the "Challenger" expedition for observing deep-sea temperatures, and which were extended to include the compressibility of water, glass and mercury.
In view of the extremely slight compressibility of liquids, atmospheric pressure may be regarded as a coincident condition; also C. M.
In the more general case of the convective equilibrium of a spherical atmosphere surrounding the earth, of radius a, (1-1?-=(n+ I) Po --a 2 dr, (12) gravity varying inversely as the square of the distance r from the centre; so that, k = po/po, denoting the height of the homogeneous atmosphere at the surface, 0 is given by (n+I)k(I -9/6 0) =a(I -a/r), (13) or if c denotes the distance where 0=o, 0 _a (14) 0 r c -a' When the compressibility of water is taken into account in a deep ocean, an experimental law must be employed, such as p - po=k(P - Po), or P/po=I+(p-p0)/A, A=kpo, (15) so that A is the pressure due to a head k of the liquid at density under atmospheric pressure po; and it is the gauge pressure required on this law to double the density.
(17) For sea water, A is about 25,000 atmospheres, and k is then 25,000 times the height of the water barometer, about 250,000 metres, so that in an ocean 10 kilometres deep the level is lowered about 200 metres by the compressibility of the water; and the density at the bottom is increased 4%.
It is often impossible to observe the pressure-coefficient dp/de directly, but it may be deduced from the isothermal compressibility by means of the geometrically obvious relation, BE = (BEÃ†C) XEC. The ratio BEÃ†C of the diminution of pressure to the increase of volume at constant temperature, or - dp/dv, is readily observed.
The compressibility of sea-water is not yet fully investigated.
Buchanan found a mean of 20 experiments made by piezometers sunk in great depths on board the " Challenger " give a coefficient of compressibility K=491 X 107; but six of these experiments made at depths of from 2740 to 3125 fathoms gave K=480Xio 7.
The compressibility is in itself very small, but so great in its effect on the density of deep water in situ that the specific gravity (0 0 /4°) at 2000 fathoms increases by o 017 and at 3000 fathoms by o 026.
The rate of propagation of sound depends on the compressibility, and in oceai water at the tropical temperature of 77° F.
Soc., 1895) has obtained the following results, which have been adopted in legislative enactments in the United Kingdom: -- In this no account is taken of the compressibility of water -- that is to say, it is supposed that the water is under a pressure of one atmosphere.
This determination involves a knowledge of the density and of the compressibility of the solution; the latter property is difficult to measure accurately.
Their table of comparison published in 1906 shows the following agreement: - It seems likely that measurements of vapour pressure and compressibility may eventually enable us to determine accurately osmotic pressures in cases where direct measurement is impossible.
From the known coefficients of compressibility and thermal expansion we find that V may be represented by the linear equation V=1.000+0.0008 A, where A is the lowering of the freezing point below o°.
His chief contribution to physics lay in the experiments by which he proved the compressibility of water and measured it by a piezometer of his own invention (see Phil.