Surfaces, Clean and Contaminated. 393 



could be observed in the wave-length. After a little ex- 

 perience with the forks in a given state of adjustment, a 

 momentary glance at the pattern was sufficient to enable one 

 to recognize the condition of the surface. 



The interpretation of the observations depends upon the 

 following formula, due to Thomson : — 



Let U= velocity of propagation, 



X = wave-length, 

 r = periodic time, 

 p = density, 

 T = superficial tension, 

 h = depth of water, 



then (Bassett's ' Hydrodynamics/ vol. ii. p. 177) 



U -t 2- Ut + p\J taUb X ' 

 so that to find T we nave 



T= ^. 2C0th 2_^_^P. 



27TT i X 4-7T 



In the present experiments the effect of the limitation of 

 depth is negligible. We have h = l'S centini., and for the 

 greatest value of X about # 7 centim. Now 



,, 2ttA 1 + «-*«*/* , '" , ... 

 C0th ^T = l- g -M/A = 1 + 2e ^ 



approximately, when h is relatively large ; so that 



coth (2irhj\) = 1 + 2e" 30 = 1, 



with abundant accuracy. Again, in the case of water we 

 have p = 1 ; and thus x 3 ^2 



1,5 St 3 " "~ 5" 



which is the formula by which the calculation of T is to be 

 made. The second term will be found to be small in com- 

 parison with the first, so that approximately T varies as X 3 . 

 A one per cent, error in the estimation of X will therefore 

 involve one of three per cent, in the deduced value of T. In 

 many of the experiments about 15 waves were included be- 

 tween the marks. An error of ^ of a wave is thus 1 in 150, 

 leading to a two per cent, error in T. We may expect the 

 final mean value to be correct to less than one per cent., but 

 we must not be surprised if individual results show dis- 

 crepancies of two per cent. 



An example (August 2) will now be given in which the 

 surface of clean water was greased with oleic acid. The dish 



