of Gravity and Cohesion jointly, without wind. 375 



notation of (16), (17) in it. It becomes 



W z = l + T' n (19) 



This has a minimum value, 



w 2 = 2V/T'^ 

 when 



(20) 



In applying these formulae to the case of air and water, we 

 may neglect the difference between g and g', as the value of er is 

 about g^o ; and between T and T', although it is to be remarked 

 that it is T' rather than T that is ordinarily calculated from ex- 

 periments on capillary attraction. From experiments of Gay- 

 Lussac's it appears that the value of T' is about '074 of a 

 gramme weight per centimetre ; that is to say, in terms of the 

 kinetic unit of force founded on the gramme as unit of mass, 



T' = ?x-073. 



To make the density of water unity (as that of the lower liquid 

 has been assumed), we must take one centimetre as unit of length. 

 Lastly, with one second as unit of time, we have 



£ = 982; 

 and (18) gives 



IV 



= ^/982Q+'074xn) 



for the wave-velocity in centimetres per second, corresponding 

 to wave-length — . When - =v / '073 = *27 (that is, when the 



wave-length is 1*7 centimetre), the velocity has a minimum value 

 of 23 centimetres per second. 



The part of the preceding theory which relates to the effect of 

 cohesion on waves of liquids occurred to me in consequence of 

 having recently observed a set of very short waves advancing 

 steadily, directly in front of a body moving slowly through water, 

 and another set of waves considerably longer following steadily 

 in its wake. The two sets of waves advanced each at the same 

 rate as the moving body ; and thus I perceived that there were 

 two different wave-lengths which gave the same velocity of pro- 

 pagation. When the speed of the body's motion through the 

 water was increased, the waves preceding it became shorter, and 

 those in its wake became longer. Close before the cut -water of 



