378 



REPORT — 1844. 



over which these vibrations range to be equally invariable. At a velocity oi 

 100 feet per minute, they may sometimes be observed advancing only over 

 the first two inches before the point ; then suddenly the vibrations will spread 

 out, not increasing in magnitude but in number to thirty or forty, extending 

 along many inches in advance of the disturbing point, and covering ten or 

 twelve square feet with an extension of the representation in Plate L VII. Then 

 suddenly without apparent cause, they will subside and become visible only 

 as a thin narrow belt, comprising the two or three waves nearest the disturb- 

 ing body, and as suddenly will again spread out over the surface of the water. 

 The play of this beautiful symmetrical system of confocal hyperbolas is a 

 phsenomenon not inferior in beauty to some of the exquisite figures exhibited 

 by polarising crystals. I have found that the purity of the water had much 

 to do with the extent and range of this phasnomenon ; that any small particles 

 loading at a few points the capillary film was sufficient to derange the propa- 

 gation of these waves, and prevent their distribution over a wide range ; but 

 I have not found that the agitation of the water at all affected the formation 

 of these waves. 



It is perliaps of importance to state that when these forced waves were 

 being generated, I have suddenly stopped or withdrawn the disturbing point, 

 that the first wave immediately sprang back from the others, showing that it 

 had been in a state of compression — that the ridges became parallel, and 

 moving on at the rate of 8| inches per second, disappeared in about 12 

 seconds. 



The manner in which the divergence of the ridge passes through the 

 point of disturbance is shoM'n in the annexed diagram. A B is the path of 

 disturbance, the disturbing point being in B ; a rod B A is 25 inches long ; 

 B C is the diverging wave ridge ; a graduated rod A C projects from A B at 

 the point A, 25 inches behind B, on which are observed the distance of the 

 wave from A along A C, registered in Col. b, Table XXIII. 



If a body move with a given velocity along a 

 known line A B, the side A C being measured at 

 right angles to the line of direction A B, and 

 cutting, in C, the line B C which represents the 

 ridge of the wave proceeding from the moving 

 body B ; it is required to find the velocity of the 

 wave in the line A D perpendicular to its ridge. 



, . T, /-< . ■ 1 X 1 J • T> sm A X i 

 As the triangle A B C is right-angled, sm a=- . — =i^; 



v 6--|-c'^ 



and since the triangle A B D is right-angled, x= 



sin B X c 

 sin D ' 



hence, the time being the same as that in which A B is described, the ve- 

 locity is at once obtained. 



Table I. contains some observations which were made with a view to the 

 investigation of the ratio subsisting between these velocities. The sides and 

 angles are indicated by the same letters whicii are used in the diagram. 



c, its velocity, and h being given ; x, its velocity, and B were calculated by 

 means of the preceding formulas. 



