The generators of the water columns tend to become straight in many cases with 

 time; their ultimate inclinations a from the vertical turn out to be a linear function of 

 the pressure. In fact we may write this empirical relation in the form 



a = mp — a (1) 



where a is nearly independent of depth and pressure and m is a function of depth only. 

 For these experiments, we had 



a = 20° (average) 



and 



d (inches) m (degrees /in. Hg) 



0.39 1.51 



0.78 1.24 



1.17 3.11 



1.56 4.60 



Another empirical rule which seems to hold roughly over a large part of the 

 column motion is that the ratio of the diameters w 1 and w 2 of a column at two different 

 heights, z t and z 2 , above the initial water surface is a constant in time. Hence the motion 

 is in a kind of normal mode, at least for large enough times. For a wide variety of cases 

 the profile motion may be expressed by 



t 

 w(z,t) = w In -, (2) 



to 



in which w is a slowly varying function of z, and in fact may often be treated as con- 

 stant. Not much is known empirically concerning t however. Since 



dw 



— « 0, (3) 



dz 



we can infer that the angular slope of a column generator is approximately 



dw d In t 



a = — tan -1 — = tan _1 w — . (4) 



dz dz 



In this way we may relate w In t to z, m( d) , and p. 



352 



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