PAPER BY PROF. HELMHOLTZ. 99 



in consequeDce of the delay become curved, whereby the convexity of 

 their arcs is tnrued toward the shore; in consequence of this they run 

 upon the shore and break to i^ieces there. 



In the next paragraphs I will show in what respects the movements 

 and forms of water-waves must be changed in order to be applicable 

 to the air. These relations are indeed not to be rigidly transferred 

 from water-waves that break upon the shore to the air, and even the 

 siropler theory hitherto developed, which neglects the influence of the 

 air, gives no complete explanation on this point. 



But the conditions are not very different from those cases in which 

 we can make a strict application, and I therefore believe there is no 

 reason to doubt that waves of air which in the ideal atmospheric circu- 

 lation symmetrical to the axis could only progress in a west east direc- 

 tion, must, when once they are initiated in the real atmosphere, turn 

 down toward the earth's surface and break up by running along this in 

 a northwesterly direction (in the northern hemisphere). 



Another process that can cause the foaming of the waves at their 

 summits is the general increase in velocity of the wind. My analysis 

 also demonstrates this : it shows that waves of given wavelength can 

 only co-exist with winds of definite strength. An increase in the differ- 

 ential velocities within the atmosphere indeed often happens, but oue 

 can not yet give the conditions generally effective for such a process. 



1 will here also mention another point that ma,y give rise to consid- 

 erations against my explanation. Water-waves forced up to a great 

 height always have narrow, strongly curved ridges and broad, flat, 

 curved troughs. Analysis shows that this feature is independent of 

 the nature of the medium. Atmospheric waves have, on the other 

 hand, rounded heads when they become visible to us as bands of cirri. 

 But we must remember that according lo the proposition first formu- 

 lated by lleye, air that has formed cloud or mist is lighter than it was 

 before. Therefore what we see as mist rises up and increases the size of 

 the summit of the wave more than would be the case iu transparent air. 



VI. CONSEQUENCES DEDUCED FROM THE PRINCIPLE OF MECHANICAL 



SIMILARITY. 



If we confine ourselves to the search for such rectilinear waves as 

 advance with uniform velocity without change of form, we may, as be- 

 fore remarked, represent such a movement as a stationary one, by 

 attributing to both the media a uniform rectilinear velocity equal and 

 opposite to that of the wave. It is well known no change is thereby 

 introduced into the relative motions of the different parts of the masses. 

 In this way the bounding surface of the two media appears as a sur- 

 face fixed in space; above it the upper medium flows in one direction; 

 below it the other medium in the opposite direction. At a great dis- 

 tance from the bounding surface both movements become rectilinear 



