ON THK SI'KCII'IC IM'SISTANVI: OK MKltCi'KY. 355 



outer diameter of the tube. In the case of the last tube mentioned above we had 

 <fj = I'G, d* = 6 mm., and LORENZ'S term '35 rf,/r/., hss the value "09, so that, according 

 to him, f..r this tube, the correction should be 73 d } . Our experiments would make 

 (his to be too small, though there is some evidence for a rather smaller coefficient 

 th.m '82. At the same time, it is hardly sufficient to justify any change, and we shall 

 therefore add to the observed length of the tube a quantity 8L equal to '82 of the 

 ili.nneter of the tube. 



The correction to the length / is not quite so simple. It arises from the fact that 

 the ends of the column are not plane surfaces at right angles to its length, but 

 portions of a curved surface which is spherical only if the tube, which was placed in a 

 horizontal position, be so narrow that the effect of gravity may be neglected. The 

 length I is the extreme length of the mercury column measured from end to end, ninl 

 the volume found from it is therefore too great by the amount contained between the 

 mercury and two vertical planes touching the mercury column at the extremity of 

 each meniscus respectively. 



This volume may be expressed in the form 7ra 2 o7, where a is the radius of the tube 

 and 8J a correction to be subtracted from the length. In cases in which the end of 

 the mercury is spherical the calculation of 67 is simple. 



Let ACB, fig. 1, represent a section of the mercury meniscus by a vertical plane 

 through the axis of the tube ; let CD be the axis of the tube, meeting AB at right 

 angles in D ; let the angles of contact at A and B, between the mercury and the 

 glass of the tube, be 6 ; and let O be the centre and b the radius of the mercury 

 bubble. 

 Then 



OA = b, DA = a, 

 and 



Angle DAO = 0. 



The length of the mercury column was determined by reading microscopes, as will 

 be explained below, and in all cases the readings for both A and C were taken so that 



2 z 2 



