PAPER BY PROF. HELMHOLTZ. 123 



form velocity. For the surface Hi we put fl, for tbis velocity, for the 

 surface H2 we take {—a-i) since we give the latter a motion in the oppo- 

 site direction to that which would be given to it in the normal cases 

 where the wind outruns the wave. 

 We have at once 



— h = f(2' ^ 



and in the higher layers of the fluid 



where Jh is a constant to be determined by the equation (le). 

 Similarl^^ 



4-2+ (P2 i= —C2 (^*4-2/') + /'2 



For plane boundary surfaces when for these as above assumed 

 ^'i = ;/-2=0, and also ^=0, we should also have hi and li^ both equal to 

 zero, and the living force in this case becomes 



When on the other hand billows have arisen, Li is smaller for a con- 

 stant valiie of cii and therefore also of fi, since, as we have seen then a 

 uegative value of SLi results from an increase in the altitude of the 

 wave. We can therefore under these circumstances put 



Li=^a{- {Hi—ri). A 



wherein rx has a positive value that depends on the form and height 

 of the wave, but not on /Zj. If we imagineriTi increased by the quan- 

 tity D Hi and the quantity Xi correspondingly increased by I> Li then 

 iu the strip thus added to the field the velocity is uniformly equal to ay 

 and therefore 



DLi=%a\.DHi 



A + i>ii='J-«' [(5'i + I>^:)-r,].A. 



Therefore the same value of ?-j also holds good for the greater alti- 

 tude independent of the value of D Hi. 

 The formula (4) gives directly 



\\ = -\i{Hi-ri) (4«) 



Compared with galvanic conditions, pi measures the total flow or the 

 intensity of the current; h is the difference of potential between the 

 boundary surfaces. Hence {Hi—Vx) is the conductivity which is pro- 



