90 



MATHEMATICAL AND PHYSICAL SCIENCE. 



[Diss. VI. 



(417.) 

 Naval ar- 

 chitecture, 



(418.) 

 Resisted 

 motion of 

 projectiles, 



(419.) 

 Experi- 

 ments on 

 waves in 

 water. 



(420.) 

 Observa- 

 tions of 

 MM. We- 

 ber on the 

 form of 

 waves. 



dulum mentioned in Art. (246), and the agreement 

 appears satisfactory. With reference to Coulomb's 

 experiments on oscillating disks there remains some 

 doubt whether the theory applies satisfactorily to 

 viscid fluids such as oil. 



On the very difficult and still empirical subject of 

 naval architecture as regards forms of least resist- 

 ance, I shall not here speak; but one very interesting 

 case of the resistance of fluids in canals will be noticed 

 in the course of this section Arts. (422), &c. 



The theory of military projectiles has perhaps re- 

 ceived no improvement so considerable during the 

 last 100 years as by the previous experiments of 

 Robins, and the invention of the Ballistic Pendulum 

 referred to in the preceding Dissertation ; though the 

 experiments of Borda in France, and of Hutton in 

 this country, have of course increased the technical 

 precision of artillery. Poisson has considered, in a 

 mathematical way, some of the simpler cases of pro- 

 jectiles moving with a moderate velocity. 



II. Experiments on Waves. MM. WEBER Mr 

 RUSSELL. Whilst the theory of the dilated and com- 

 pressed waves which constitute sonorous vibrations 

 in elastic fluids was being successfully investigated 

 by Lagrange and Laplace, the case of waves in water, 

 due to a disturbance of hydrostatic pressure only, 

 was attacked by the same mathematicians with far 

 less success. It is generally allowed that the more 

 recent and abstruse researches of Poisson and M. 

 Cauchy, though very valuable as improvements in 

 pure mathematics, have been also singularly barren 

 of valuable results admitting of the very desirable 

 confirmation of direct experiment. The greatest of 

 all hydrodynamical problems, that of the Tides, is, as 

 has been seen in the second section of the chapter on 

 Physical Astronomy, Art. (69) &c., so excessively 

 complex as to be the last, instead of the first, which 

 analysis might have been expected to resolve. 

 When, on the other hand, we see the light which has 

 been thrown even upon it by experiments on a com- 

 paratively small scale, we learn to value them in 

 proportion to their rarity. 



The brothers ERNST HEINRICHWEBER and WILHELM 

 WEBER, known for many ingenious experiments in 

 physics, and particularly in magnetism, are the authors 

 of a useful book on waves. 1 They made experiments 

 on the velocity of waves in glass troughs, by means of 

 which they determined in several cases the velocity 

 of the wave with different depths of fluid ; they also 

 ascertained mechanically the form of the wave, which 

 they found to be that of the curve of sines. But the 

 most important of the Webers' experiments is pro- 

 bably the determination of the motion of individual 

 particles of the water, which they ascertained by 

 watching from the exterior of the glass trough the 



curve described by minute floating particles as the 

 wave passed over them. The usual form of the trajec- Trajectory 

 tory is an ellipse having the greater axis horizontal, the icl ^ * )a 

 whole ellipse being described when the wave includes 

 a ridge followed by a depression of the surface ; but 

 if there be only an elevated wave propagated, then a 

 semi-ellipse is described in the direction in which 

 the wave moves, and the particle returns to rest in a 

 new position ; if the wave be a hollow one the con- 

 verse takes place. The limits of oscillation diminish 

 with the depth of the fluid, particularly the vertical 

 limits ; consequently at some depth the motion of 

 the particles is nearly in a short straight line. The 

 rapidity of the degradation of the individual motions 

 depends on the relation between the length of a wave 

 compared to the depth of the fluid : where the wave 

 is very short compared to the depth of fluid, the el- 

 lipses near the surface become circles, and the mo- 

 tion rapidly disappears beneath ; when the length of 

 the wave is great compared to the depth of fluid, 

 the motion of the particles is nearly the same from 

 top to bottom. The conclusions of theory are on the 

 whole confirmed by these experiments. 



The experiments of Mr JOHN S^COTT RUSSELL, so (421.) 

 far as we shall notice them, refer to two closely con- R p ',' 

 nected subjects : the transmission of waves, and experi- 

 the resistance of water to vessels propelled through ments on 

 it as affected by waves. They are principally to be waves - 

 found in the Edinburgh Transactions, vol. xiv., and 

 the British Association Report for 1837- The velo- 

 city of waves in troughs of different depths and sec- 

 tions was ascertained by allowing the wave to be re- 

 flected at either end of the trough, which does not in 

 any way affect the time of its propagation, and gives 

 great facility for accurate observation, as the distance 

 travelled over may thus become large, at the same 

 time that all casual and interfering waves are gra- 

 dually eliminated. The instant of the passage of 

 the wave was ascertained by reflecting the light of a 

 candle vertically upwards from its horizontal sum- 

 mit. The length of the trough was 20 feet, but 

 since the wave was made to traverse it as often as 

 60 times, a distance of 1200 feet was really ob- 

 served. The waves were single or "solitary" 

 waves, either " positive" produced by a gush of 

 water from behind a sluice, or " negative" by with- 

 drawing water suddenly. Mathematicians seem not 

 agreed as to whether or not the " solitary" waves of 

 Mr Russell are to be treated as a species apart. 2 

 Unquestionably it has long been known that a par- 

 tial wave either positive or negative may be propa- 

 gated without any farther disturbance of the fluid. 

 Theory also shows that the velocity of a wave long in 

 proportion to the depth of the water is nearly as the 

 square root of the depth ; but it does not clearly ap- 



1 Wellenlehre auf experimente gegrundet, oder iiber die Wellen trap/barer Flussigkeiten mit anwendung auf die Schall und Licht- 

 wellen. Leipzig, 1825. 



2 Compare Mr Airy in the article " Tides and Waves," Encycl. Metropolitana ; Prof. Stokes in British Assoc. Report for 1846, 

 and Mr Earnshaw in Cambridge Trans., vol. viii. 



