WAVES AND TIDES. 



WAX. 



: i 



fluid through which the wave U propagated. By the t 

 ware the (articles of the 8uid are railed from their places, transferred 

 forward in the direction of the motion of the ware, and permanently 

 deposited at test in a new place at a oonaiderable distance from their 

 uriginal poaition. There ia no retrogradation, no oscillation ; the 

 motion ia all in the same direction, and the extent of the transfer- 

 ence U equal throughout the whole depth. Hence this wave may 

 be descriptively designated the great primary wave of translation. The 

 motion of translation commences when the anterior surface of the 

 wave U vertically over a given aerie* of particles ; it increases in 

 velocity until the crest of the wave ha* come to be vertically above them, 

 and from this moment the motion of translation U retarded, anil the 

 particles are left in a condition of ]>erfect rest at the instant when the 

 posterior surface of tin- wave 1m terminated its transit through the 

 vertical plane in which they lie. This phenomenon boa been verified 

 up to the depth of 5 feet. 



5. The elementary form of the wave is cycloidnl ; when the height 

 of the ware is small in proportion to its length the curve u the pro- 

 late cycloid, and as the height of the wave increased the form 

 approaches that of the common cycloid, becoming more ami more 

 cusped until at last it becomes exactly that of the common cycloid, 

 with a cusped summit ; and if by any means the height bo increased 

 beyond this, the curve becomes the curtate cycloid, the summit 

 assumes a form of unstable equilibrium, t tiers, and falling over on one 

 side forma a crested wave or breaking surge. 



6. A wave is possible in forms of channel where the depth u not 

 uniform throughout the whole depth. It appears however that where 

 the difference between the depth of the sides is considerable, one part 

 of the wave will continue during the whole period of propagation in 

 the act of breaking, so as to show that in these circumstances a con- 

 tinuous wave is impossible. In other coses the ridge of the wave 

 rises so much higher on the shallower part of the fluid as to produce 

 a given velocity without exceeding the limits of equilibrium, and in 

 those coses the wave becomes possible, and the velocity appears to 

 coincide closely with that which we ol.t.iin by supposing the wave 

 resolved into vertical elements, each having the velocity due to the 

 depth, and theu integrating. It results that : 



In the rectangular channel the velocity is that of gravity due to half 

 the depth. 



In the sloping or triangular channel the velocity is that due to cue- 

 third of the greatest tlcpth. 



In a psnbolk channel the velocity is that due to three eighths or 

 three-tenths of the greatest depth, according as the channel ia convex 

 jr concave. 



The velocity of the great primary wave of translation of a fluid ia 

 that due to gravity acting through a height equal to the depth of the 

 centre of gravity of the transverse section of the channel below the 

 surface of the fluid. 



7. The height of a wave may be indefinitely increased by propnga- 

 tion into a channel which becomes narrower in the form of a wedge, 

 the increased height being nearly in the inverse ratio of the square 

 root of the breadth. 



. If waves bo propagated in a channel whose depth diminishes 

 uniformly, the waves will break when their height above the surface of 

 the level fluid becomes equal to the depth at the bottom below the 

 surface. 



9. The great waves of translation arc reflected from surfaced at right 

 angles to the direction of their motion, without suffering -any change 

 but that of direction. 



10. The great primary waves of translation cross each other without 

 change of any kind, in the same manner as the small oscillations pro- 

 duced on the surface of a pool by a falling stone. 



11. The waves of the sea are not of the first order ; they belong to 

 the second or oscillatory order of waves ; they are partial displace 

 meats at the surface which do not 'extend to considerable depths, and 

 are therefore totally different in character from tho great waves of 

 translation, in which the motion of displacement of the particles of the 

 fluid in the waves of the sea is greatest at tho surface and diminishc.-i 

 rapidly. There are generally on the surface of the sea se\. 

 existent classed of oscillations of varying direction and magnitude, 

 which by their m>i"ii give the surface an appearance of irregularity 

 which does not exist in nature. 



1 :!. When wave* of the cea approach a shore or come into shallow 

 water, thev become waves of translation, and obeying the laws already 

 mentioned, always break when the depth of the water ia not greater 

 than their height above the level. 



13. Waves at the surface of the sea do not move with the velocity 

 due to the whole depth of the fluid ; may they not move with the 

 velocity due to that part which they do agitate, or to some given mrt 

 of it ' 



14. A circumstance frequently observed when (he waves break on 

 th^ chore, has been satisfactorily accounted for by the examination of 

 the constitution of the waves of tho sea. It has been frequently ob- 

 nerved that a certain wave U the largest of a series, and that these large 

 naves occur periodically at equal intervals, so that sometimes every 

 third wave, every seventh, or every ninth wave, is the largest Now as 

 there are almost always several co-existent series of waves, and as one 

 f tbce U a long, gentle " under swell," propagated to the shore from 



the deep sea in the distance, while the other* are short and more super- 

 tici.il waves, generated by a temporary breeze of i. 



iring shore ; so it will follow that when the smaller waves are 

 Jrd, or Ith, or Jth, or in any other given ratio to the 1. - -ill . :' 



we waves in which the ridges of the two series are coincident 

 will be the periodical Urge waves ; and if there be three systems of 

 coexistent waves, or any greater number, their coincidences will 

 |M-n.><lical large recurring waves, having maxima and minima of various 

 orders. 



15. The tide- wave appears to be the only wave of the ocean which 

 belongs to the first order, and appears to be identical with the great 

 primary wave of translation ; its velocity diminished and increases with 



t!i of the fluid, and appears to approximate closely to the 

 .':'. to half the depth of the fluid in the rectangular channel. 

 and to a certain mean depth which i that of the centre of gravity of 

 the section of the channel. It is, however, difficult t.. <1< t< i mine tho 

 limit* within which the tide-wave retains its unity ; where portions of 

 the same channel differ much in depth at points remote from each 

 other, the tide waves appear to separate. 



16. The tide appears to be a compound wave, one elementary 

 bringing the first part of flood tide, another the high water, and so on ; 

 these move with different velocities according to the depth. On ap- 

 proaching shallow shores tho anterior tide-waves move more slowly in 

 the shallow water, while the posterior waves moving more rapidly, 

 diminish the distance between successive waves. The tide-wave be- 

 comes thus dislocated, its anterior surface rising more rapidly and its 

 posterior surface descending more slowly than in deep water. 



17. A tidal bore [Bonu] is formed when the water is so shallow at 

 low water that the first waves of flood tide move with a velocity so 

 much less than that due to the succeeding port of the tidal wave, as to 

 be overtaken by the subsequent waves ; or wherever the tide rises so 

 rapidly, and the water on the shore or in the river is so shallow, that 

 the height of the first wave of the tide, is greater than the <ii ; 



the fluid at that place. Hence in deep water vessels are aafe from the 

 waves of rivers which injure those on the shore. 



18. The identity of the tide wave and the great wave of tr 

 tion, shows the nature of certain variations in the establishment of 

 ports situated on tidal rivers. Any change in the depth of the 

 produces a corresponding change between the moon's transit ami the 

 high water immediately succeeding. It appears from the observations 

 in this report that the mean time of high water has been rend' r 

 minutes earlier than formerly, by deepening a portion of about 12 

 miles in tho channel of a tidal river, so that a tide-wave which 

 formerly travelled at the rate of 10 miles an hour, now travels at the 

 rate of nearly 15 miles an hour. 



19. It also appears that a large wave, or a wave of high water of 

 spring tides, travels faster than a wave of high water of neap tides, 

 showing that there is a variation on the establishment, or on the 

 interval between the moon's transit and the succeeding high water, due 

 to the depth of the fluid at high water, and which should, of course, 

 enter as an element into the calculation of tide tables for an itil.md 

 port on the sea shore. The variation of the interval will vary with the 

 square root of mean depth of the channel at hijjh water. 



" These results give us principles," the committee on waves uonelude, 

 " 1, for the construction of canals ; 2, for the navigation of canals ; 3, 

 for the improvement of tidal rivers; 4, for the navigation of tidal 

 rivers; 5, for the improvement of tide tables." But an equally 

 valuable application, not however foreseen when these results ha. . 

 obtained and examined, unless by Mr. Russell himself, was to the 

 improvement of naval architecture. Of this, a brief account has 

 already been given in the article 8nir-Buiu>iN. 



After the publication of the report by the committee on waves, 

 which contained the experimental investigation of which we hr, 

 given the principal results, the phenomena of waves engag< 

 attention of eminent mathematicians, who endeavoured to deduce 

 from first principles the curious facts which V . 

 associates had olwrved, so as to reconcile theory with , 

 Among these were the Astronomer-Royal (a summary of wh..e eon- 

 elusions has been given in this article), Mr ,<l Professor 

 Kellaud, who also succeeded in obtaining from analysis many of the 

 very singular experimental results. Their re; puMUbed 

 in the Transactions of tho Cambridge Philosophical S 

 those of tho Royal Society of Edinburgh; and Professor Kellan 

 gave a view of the actual state to which tho theory of v. , 

 been brought in tho Report of the tenth meeting of the British 

 Association. 



The theory of wav i as forming a part of abstract) 



mechanics, as well as in certain applications, has been considered also 

 in the articles Aco : VIP.UATION; and UNDur.A- 



Tuiiv TIIKOHV OF LIGHT. An excellent familiar explanation of tho 

 subject, especially an regards the coincidence and int. 

 waves, will be fouii'l in Professor Tyndall's 'Glaciers of the Alps/ 



WAX. There are several varieties of this substance, but the term 

 used by itself means Bi:i:' WAX, under which heading will be 

 an account of the manner in which it is secreted, its cl 

 n( it ut ion, and the means employed in preparing it for commercial 

 purposes. 





