558 Dr. J. H. Vincent on the Construction of a Mechanical 



fringe of light elastic threads, each of which supported a 

 weighty particle. The motion is confined to a vertical plane 

 through the cord, to which it is entirely transverse. If the 

 unloaded cord be regarded as representing the free sether, and 

 tbe loaded cord as the medium, then //,, the refractive index, 

 is given by 



M*?} 



M 2 = . , W 



p z — V 



where p/'27r=n, the frequency of the waves, 



<r,p =linear density of fringe and cord respectively, 

 and lirj s/v = free period of any particle in the fringe. 



Helmboltz's expression for \x when there is only one type of 

 absorbing particle can be written 



*-}££ (ii - } 



where a>/3. 



Tbis equation is of the same form as the first. 



Graph of Helmholtz's Equation. 



Before describing the model which has been constructed, it 

 maybe of interest to refer to the graph of the above equation. 

 Fig. 1 is drawn from the equation 



2 n 2 — a 2 



in which the quantities occurring in the right-hand member 

 are derived from those in equation (ii.) by dividing by 2w. 

 The ordinates are proportional to /^, being the numerical 

 values of ///, where 



/a'=-021/a. 



The constants chosen for a and b are those of the model, 

 while /// has been taken so as to make the theoretical curve 

 coincide with the experimental curve (fig. 2) at one point. 



As n changes from to b, /u, increases from — to oo . 



From n = b to n = a the curve lies beneath the axis of n ; no 

 waves are propagated having a frequency between these limits. 

 The curve cuts the axis of n when n = a. At this point the 

 velocity of propagation is infinite. As n increases, the value 

 of /jl rapidly approaches unity. That is, for high values of n 

 such a medium would have no effect on the waves traversing it. 



