776 Transactions of the American Institute. 



in the apparatus ai'e essentially the same as in nature, the leading 

 geometrical and dynanimical facts pertaining to the theory of waves 

 are presented with completeness, and in their true relations. The 

 wave theory illustrated is that established by Gerstner, Scott Eus- 

 sell, Kankine, and others, and which teaches that, in such waves, 

 all the particles are revolving synchronously, and in the same direc- 

 tion, in vertical circles. An able analytical exposition of it, by 

 Prof. Rankine, is contained in the Philosophical Transactions for 

 1863.* 



The construction of the apparatus is simple. In front of a plane 

 surface are two series of revolving arms or cranks, the length of 

 the lower ones being half that of the upper. Two elastic wires 

 connect the crank-pins of each series; upright wires also connect 

 each pair of cranks, and pass down through a plate into the base. 

 The cranks all revolve synchronously; they thus keep their relative 

 position, and come into any particular position successively, each 

 IQ its turn. The relative position of the cranks of each series is 

 »uch, that the directions of any two, in regular order, differ by the 

 same fraction of a whole revolution that the distance between their 

 axes is of a whole wave length. In the apparatus, the length of a 

 wave is divided into eight equal portions, and hence, the common 

 difference in the directions of the crank-arms is one-eighth of a 

 circle, as shown in the figure. The positions of the cranks in each 

 vertical set are always alike. The number of cranks, Avhether reck- 

 oned horizontally or vertically, is arbitrary — a matter of conven- 

 ience. Their synchronous revolution is produced by any suitable 

 mechanism, such as toothed wheels, rag-wheels with endless metal- 

 lic ribbon or chain, or cranks and connecting frame. In the original 

 machine, equal toothed wheels, one on each axis, with intermediate 

 idle-wheels, give the required motion. For small machines the 

 third method is used, as m the model for the patent office. 



The crank-pins represent as many liquid particles, and the circles 

 Ijehind the crank-pins their orbits. The transverse wires represent 

 lines of equal pressure, or continuous lines of particles, which at 

 j-est would be horizontal, and so coincide with the lines drawn just 



• It is somewhat singular that this theory, though more than a century old, has, never- 

 theless, but just begun to supplant, in the text-books, that which explains ware motion as 

 a vertical oscillation of neighboring liquid columns, as in the two branches of a U-sLaped 

 tube, a theory commonly credited to Newton ; though Newton, in fact, only used it as a 

 convenient approximative hypothesis for a particular purpose, not as a theory true to 

 nature, remarking in conclusion : " Hocc ita se habent ex Hypothesi quod partes aquse recta 

 aeoeadunt vel recta deacendunt ; sed ascensus et desccnsut tile verius jit per circulum." 



