Application to the capillary height method

Application to the capillary height method. Sugden1 has pointed out that, when the contact angle is zero, the ratio r/6 of the radius of the tube to the radius of the lowest point of the meniscus is the x/b of Bashforth and Adams s tables. By (6) 

The first part of the table, which is reproduced by permission from the Journal of the Chemical Society, is accurate to the last figure. 

The tables are used as follows. A first approximation is made to a, by assuming the height of rise to be that given by the approximate formula rh — a the value of rjb corresponding to this value of r/a is looked up, b is found, and so a second approximation to a is obtained from the formula bh = a2 with this-value of a a second approximation to r/b and b is read off from the tables, and the process is repeated until a constant value 

Water has a2 = 14 88 sq. mm. at room temperature hence the first part of the tables, which are as accurate as those of Bashforth and Adams, apply to tubes of radius up to 8 8 mm. For many organic liquids, which have d2 often about 5, the accuracy is the same up to about 5 mm. radius. These tubes are of course far wider than those generally used, except for the purpose of a reference surface with which the height in the narrower tube may be compared. 

Sugden s tables (up to r/a = 2 2) are probably the most accurate approximation existent. Rayleigh s formula (9) for small tubes agrees with these tables up to rja = 0 46, within one part in two thousand. For larger tubes, the approximation given by (9) becomes rapidly worse thus at r/a = 0 7 this formula is about 1 per cent, in error. 

---