On C. S. Lyman's new form of Wave -apparatus. 21 



the velocity of a particle in its orbit, or at the crest of the wave, 



( -'Vi Vt"r" / v /• 



the velocity of propagation of the wave 



V t ~2tt- V 2^ =V ^ R== »' 

 the sine of the angle of steepest slope of surface is 

 . n 2irr r 



S1 „0=_ =1 . 



It will be understood that the normal wave, to which the 

 theory applies, and which the apparatus illustrates, is the wave 

 on deep water, or water a wave's length at least in depth. In 

 shallow water the orbits are no longer circles, but ovals, or ap- 

 proximate ellipses of less height than length, according to the 

 degree of shallowness. 



When waves pass from deep into shallow water, as toward a 

 beach, they become gradually shorter, their total energy is im- 

 parted to a less and less mass of liquid, and the extent of the 

 motion of the particles is proportionately increased. The crests 

 also travel faster than the troughs ; so that the front of each 

 wave becomes by degrees steeper than the back, and at length 

 curls forward and falls over, exhibiting the well-known roll of 

 surf. The formulae for waves in deep water, therefore, require 

 modification to adapt them to waves in shallow water, where 

 depth of liquid and ellipticity of orbit enter as elements. 



It has been necessary, in order properly to explain the appa- 

 ratus and its uses, to give more fully the leading points of the 

 theory of waves than would be required, were the works con- 

 taining it more generally accessible. For these points the papers 

 of Professor Rankine have been chiefly consulted. It is hoped 

 that this outline of the theory, thus incidentally given, will prove 

 not unacceptable to such instructors as may not have at hand 

 the original works, and that this new piece of apparatus may 

 contribute somewhat toward imparting a clearer understanding 

 of the phenomena of waves. 



The apparatus has been pateuted, and is manufactured by 

 Messrs. E. S. Ritchie and Son, the well-known philosophical-in- 

 strument makers, of Boston, Massachusetts. 



