sin 



On a Model to illustrate Helmholtz's Theory of Dispersion. 557 



through an angle 0, given under ordinary experimental con- 

 ditions by 



sin (iryl sin 0jl)j{iTyl sin 0/\) = ^q. 



Such a rotation reduces the visibility of the prime maximum 

 of the fringes to y 1 ^, or to less than one third of the visibility 

 of the second maximum with a properly adjusted slit. The 

 actual reduction of distinctness does not, however, appear to 

 be nearly so great; and the question arises, over what range 

 of brightness of the field the limit of visibility may be regarded 

 as constant. It might be of interest to test this point, em- 

 ploying Lord Rayleigh's method * of determining the limit of 

 visibility, and controlling the brightness by a revolving disk 

 with transparent and opaque sectors. 



In the case of Lloyd's mirror the relative retardation of the 

 interfering streams from a point distant £ from the central 

 line of a properly placed slit is at a point xy of the screen 

 2x(c + g)/d, where c, d are the distances of the central line 

 from the mirror and screen respectively. 



If then the slit be turned as in the former cases, the visi- 

 bility will be given by the absolute value of 



— <! yfcos#+ -j sin sin $ ] k V sin— \ -jl sin#— -y cos sin (f>) I I 



— - 7 (cos# + -7-sin 0sm(j))k — -yfsin — j-cosO sm<f> jl 



and this is independent of the length of the slit, if 



tan = c sin <j)/d y 

 a relation that holds for the whole field. 



LX. On the Construction of a Mechanical Model to Illustrate 

 Helmholtz's Theory of Dispersion. By J. H. Vincent, 

 D.Sc, AM.C.Sc.f 



Introduction. 



IN a course of lectures recently delivered at the Cavendish 

 Laboratory, Prof. J. J. Thomson described a mechanical 

 model which obeyed the formula given by Helmholtz for the 

 velocity of propagation of waves in a medium capable of 

 absorption. 



Prof. J. J. Thomson's Model. 



The system contemplated consisted of a weighty cord 

 stretched horizontally ; from this cord depended a uniform 



* Loc. cit. 



f Communicated by Prof. J. J. Thomson. 



Phil. Mag. 8. 5. Vol. 46. No. 283. Dec. 1898. 2 Q 



