GRAVITY AND CENTRIFUGAL FORCE 329 



hypsometric or barometric formula 



_Mg_ 



p = Poe «^ ' (4) 



which gives us pressure as a variable depending only on height. 



The most famous application of this equation is in the study 

 of variations in pressure of the earth's atmosphere with height, 

 Galileo first pointed out that the atmosphere created pressure, 

 and P^rier proved that the pressure varied with height by 

 means of his famous ascent of the Puy de Dome, barometer in 

 hand. Laplace^ deduced the correct formula for the varia- 

 tion of pressure with height in his celebrated Mecanique Celeste 

 and Gibbs showed that it took its place as part of the gen- 

 eral thermodynamic scheme. As an example, substituting 

 the numerical values M = 29 gm/mol, g = 980 cm/sec^, 

 72 = 8.31 X 107 erg/mol deg, T = 300°K, we find that at 

 a height of 5000 meters the pressure has dropped to 56.5% of 

 its value at the earth's surface. 



It was also appreciated at rather an early date that the con- 

 centration of solute in a solution should vary with the height 

 because of the influence of gravity. In the early part of the 

 last century Beudant^ claimed experimental evidence of this 

 effect. Gay Lussac,^ however, definitely proved that it was 

 too small to be observed. He placed cylinders of various solu- 

 tions in the cellar of the Paris observatory, and after a year's 

 time analyzed the top and bottom portions, finding no differ- 

 ences in concentration. Many years later Gouy and Chaperon^ 

 showed by calculations that for solutes of ordinary molecular 

 weight the effect is negligibly small. 



Though ordinary solutions failed to show the effect, the advent 

 of colloidal solutions opened up new possibilities in this dir- 

 ection. Einstein^ pointed out that a colloidal suspension should 

 obey the same kinetic laws as an ordinary solute, and a starthng 

 experimental confirmation was provided by Perrin.^ He al- 

 lowed a suspension of gamboge to come to equilibrium after 

 settling for some time and then actually counted the number of 

 particles of a given radius (i.e., similar molecular weight) 

 occurring at different levels. In order to test his result it is 



