October 30, 1891.] 



SCIENCE. 



247 



finger-holes occurs, and the only example in which it projects 

 from the side at all is from Point Barrow. Since the publication, 

 however, another specimen comes from Carles inlet, and this is 

 quite puzzling. In Dr. Stolpe's paper you have my Patzcuaro 

 specimen exactly, only mine has no ornament and is a practical 

 every-day implement for killing ducks. The spear-shaft is ten 

 feet long, of slender cane, and has a hole at the after end for the 

 hook of the throwing stick. The gig consists of three iron barbs, 

 for all the world like the Eskimo trident for water-fowl. The 

 problem now is to connect .Alaska with Patzcuaro. 



O. T, Mason. 



Washington, D.C., Oct. 26. 



Molecular Motion in the Development of Water Waves. 



When waves are developed on the surface of water, whether by 

 something thrown into or moving through the water, or by the 

 friction of the wind blowing along the surface, the water consti- 

 tuting the wave rises up and sinks down, but does not move along 

 the surface. When the friction of the wind is the cause of wave 

 production, or when tlie waves are produced by any other force 

 exerting a pull or a push in the water, there is some horizontal 

 movement or current; but this current is not wave-motion proper, 

 and is entirely distinct from it. The undulations in a slack rope, 

 vibrated at one end, are true wave-motion, analogous to that 

 which occui's on the surface of water. 



If we suppose the water to consist of molecules, each having 

 capacity for its own proper motion, and subject to the force ex- 

 erted by the earth's attraction and by the pressure of other mole- 

 cules above it, but free to move with comparatively small fric- 

 tion, the formation of waves becomes very simple. Water under 

 the pressure when the formation of waves is possible, is incom- 

 pressible, and when a solid body is thrown into or moved through 

 the water so rapidly that the displaced particles cannot get out of 

 the way laterally, some of them are forced up, under the well- 

 known law that motion is in the direction of least resistance. If 

 the body is placed in or drawn through the water slowly enough 

 for the displaced particles to push their way horizontally, none of 

 them are thrown up, and the initial wave is not formed. But 

 time is required for this movement, and when the body is thrown 

 into the water, or moved through it rapidly, the displaced parti- 

 cles are forced to rise up against the force of gravitation, the 

 quantity forced up — that is, the size of the initial wave — being 

 determined by the volume of the body and the rapidity of its 

 movement through the water. If the force is impulsive and not 

 constantly acting, the second wave is less than the first, and they 

 go on diminishing until the foi'ce is expended in horizontal mo- 

 tion, and there is an elevation of the surface commensurate with 

 the volume of the immersed body, — the same result precisely 

 that would have been reached without wave-formation if the 

 body had been immersed slowly enough. 



When wind first impinges against the surface of still water, the 

 friction pulls up a little of the water in the form of a minute ini- 

 tial wave, but the force being constantly acting, the wave con- 

 tinues to increase in size until the maximum possible from the 

 given friction is reached. 



The force of cohesion between the molecules of water is less 

 than the pull of gravitation upon them, for if this were not the 

 case, water would stand up like a solid mass, as ice does, instead 

 of spreading out and flowing, in obedience to the force of gravita- 

 tion, and continuing to flow until it reaches some substance in 

 which the force of cohesion is suflicient to counteract the pull of 

 gravitation on its molecules, or until the increased cohesion from 

 congelation accomplishes the same result. 



While the force of cohesion between the molecules of water is 

 not sufficient to prevent them from moving in obedience to the 

 force of gravitation, it is still considerable, and very gi-eat as 

 compared with the force of cohesion between the molecules of air 

 and other gases; and when a portion of the water is forced up 

 against the force of gravitation, the substance continues in mass, 

 and must so continue until subjected to a force sufficient to over- 

 ■come both gravitation and cohesion. 



When the mass lifted up in the formation of tlie initial wave 



falls back (as it must do under the constantly acting force of 

 gravitation), with a velocity too great to be expended in horizon- 

 tal motion, the molecules receiving this impact must rise up as 

 those did which constituted the initial wave, and soon, each wave 

 being the progenitor of that wave which follows it. If the force 

 is impulsive, as when a body is thrown into the water, each wave 

 is the sole progenitor of the wave following; if the force is con- 

 stantly acting, like the friction of the wind, each wave in produc- 

 ing another is supplemented by the constantly acting force which 

 caused the initial wave. 



When the uplifted water falls back on something not so free to 

 move as the molecules of water, — as, for instance, when the 

 water becomes so shallow that the fall is against the bottom, 

 or so thick with grass and water-plants as to impede the free 

 movement of the vrater, — the wave-formation at once begins to 

 diminish and soon ceases entirely. In short, the waves on the 

 surface of the water are the result of the impact of the lif ted-up 

 mass falling back on the free to-move molecules constituting the 

 whole mass with a velocity so great that the force cannot be 

 transmitted horizontally. 



In observing the phenomenon on a lake a few miles wide, it is 

 interesting to note that, even in a high wind, the surface of the 

 water near the windward shore is only a little agitated by small 

 ripples; farther out it becomes rougher, and on the lee shore the 

 waves have reached the highest point possible for the extent of 

 surface and force of the wind. The pressure of the wind on the 

 surface of an inland lake is constantly variable, even over com- 

 paratively small areas, as every one has observed who has navi- 

 gated a sail-boat; and as the friction, which is the wave produc- 

 ing force, varies with the pressure, the waves vary in both length 

 and height. 



When the wind is high the crests of the highest waves become 

 unable to withstand the impact of the force, and are broken into 

 fragments or spray, forming what we call " white-caps." This 

 phenomenon does not depend entirely on the violence of the wind, 

 nor on the height and volume of the waves, but it depends on the 

 relation between these two. If the waves are very large and oval 

 (and this depends on the nature and action of the force producing 

 them), only the most violent wind can cause white-caps, while if 

 the waves are small but narrow and sharp, a comparatively light 

 wind will develop them. In a portion of the water broken up in 

 the formation of white caps, not unfrequently the force of cohe- 

 sion is so far counteracted that the water is carried off in the 

 form of spray; the residue of the white-cap not carried off as 

 spray, instead of sinking down with the main body of the wave 

 as in other cases, flows down the farther side of it. Hence the 

 formation of white-caps tends to diminish rather than to increase 

 the size of the waves. 



It sometimes happens that the impact of the wind against the 

 water elevated above the surface becomes so violent that it is all 

 blown away as spray, and no waves are formed at all. In Janu- 

 ary, 1834, I think it was, this phenomenon occurred on Lake 

 Eustis. in Florida. We took passage on the ''Mayflower,'' a little 

 side- wheel steamer of from thirty to forty tons bux-den, very nar- 

 row and long, and low decked, to cross the lake from east to west, 

 the distance being about seven miles. It was blowing a breeze 

 from the west, which caused waves probably a foot high, and 

 sufficient to cause the little steamer to rock perceptibly. A very 

 black cloud came up from the west, meeting us, and between one 

 and two o'clock in the afternoon, when we were about one-fourth 

 of the way across, a storm of wind and rain burst upon us with 

 intense fui'y. Putting on my overcoat hastily, I at once made 

 my way with difficulty through the wind and rain to the pilot- 

 house, a little coop perched on the front end of the deck, to see 

 that the captain, who was steering, did not lose his presence of 

 mind, and to urge him to hold the head of the boat to the wind, 

 from whatever direction it might come. Fmding him cool and 

 self-possessed, I returned to the cabin, another little coop amid- 

 ships, and found the passengers, eight or ten in number, in great 

 terror. Acting on a suggestion of the captain, I got out the life- 

 preservers, and in less time than it takes ae now to write this 

 sentence, each passenger had on one, ready for the plunge which 

 we all knew would come in a few seconds if the wind struck the 



