On C. S. Lyman's new form of Wave-apparatus. 15 



fore I propose the time defined by this proposition as only near 

 the truth." This important qualifying clause seems to have been 

 quite overlooked by those who have professed to give Newton's 

 theory of waves. 



The modern theory, which teaches that in wave-motion all the 

 particles of a liquid are revolving synchronously in vertical circles, 

 though so broadly hinted at by Newton himself as the true one, 

 in the words italicized above, has nevertheless been developed 

 for the most part only within the present century. It was first 

 clearly stated and ably advocated by Gerstner in 1804. More 

 recently it has been satisfactorily established as accordant with 

 observed facts and the laws of mechanics, by the experimental 

 researches of Weber and Scott Russell, and the mathematical in- 

 vestigations of Stokes, Rankine, and others. A concise exposi- 

 tion and demonstration of the theory may be found in a paper 

 by Professor Rankine, in the Philosophical Transactions for 1863. 

 Though but just beginning to find its way sparingly into the 

 text-books, it has become the generally accepted theory among 

 men of science; and having in reality supplanted the old hypo- 

 thesis as an expression of scientific truth, there is no good reason 

 why it should not also supplant it in the lecture-room. 



In teaching this theory, however, it is often found difficult to 

 make pupils understand how the infinitude of simultaneous revo- 

 lutions, which it supposes, can take place without mutual interfe- 

 rence, and in such a way as to produce the observed phenomena. 

 It was to obviate this difficulty, and illustrate, as far as practicable, 

 the modus operandi in question, that the piece of mechanism was 

 devised which is the subject of this article. It presents to the 

 eye not merely the surface contour of a wave with its undulatory 

 motion (which to some extent other forms of wave-apparatus also 

 do), but, besides doing this in a more exact and satisfactory 

 manner, it exhibits the motions also that are at the same time 

 taking place below the surface in the whole mass of liquid 

 affected. This completeness of illustration is due to the circum- 

 stance that in the apparatus the elementary motions are the same 

 essentially as in actual waves ; hence the leading points, geome- 

 trical and dynamical, of the theory of waves are presented natu- 

 rally and in their true relations. 



The construction of the apparatus will be readily understood 

 from a brief description and the accompanying woodcut. 



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 given position 



