1882.] 337 fT5jjy_ 



Suppose tliat the linear dimensions of the apertures are infinitesimal 

 compared withp, and let the letters «, &, Cj considered as numerical magni- 

 tudes designate the areas of the apertures a, b^ Cj respectively. Let be 

 the angle between a ray and the normal to the surface from which it radi- 

 ates. Let a sphere of radius p be supposed to be described about some 

 point of bj as a center, and let s be the area of that part of its surface in- 

 cluded Avithin the cone of rays passing from the center to the periphery 

 of the aperture Cj ; 



tlien -^=r^cos^ (1) 



in which r is the distance passed over by the ray from b^ to c^. 



Also p=r cos (2) 



therefore «=Ci cos* (3) 



Now the heat radiated from b^ is directly proportional to the area b^, to 

 the area s and to cos 0, but inversely proportional to 2^' ; hence ♦ 



^ cos d =^ cos* (4) 



is proportional to the heat radiated from b^ through Cj. 



Similarly . —^ (5) 



is proportional to the heat radiated from ff, through r, since it passes c nor- 

 mally. Now the heat passing from b^ to c^ must evidently move in a di- 

 rection to overtake the aperture c„ and to do this it must evidently take a 

 direction such that is defined bj' the equation 



tan = ^'^, or cos^ 6=- . f. . (6) 



Hence by comparing expressions (4) and (5), and substituting from (6) it 

 appears that the heat radiated from a-^ through, c^ is greater than that radi- 

 ated by an equal surface b^ through e^, in the ratio of (v^ + 4'M^)''' to -y*, in 

 case the temperatures of «j ajid b^ are equal. If the temperature of a,-^ were 

 lower than that of b^ this ratio would be diminished ; but by increasing u, 

 the ratio can still be made to exceed unity, thus confirming the observa- 

 tions previously made. Neither is it essential that the radiations all take 

 place at the same velocity. The reflectors can be arranged for some one 

 velocity and they will then send back the radiations to B which have that 

 velocity. 



Perhaps the most simple ideal arrangement for effecting the proposed 

 interference with the radiation naturally taking place between two bodies, 

 is to suppose the apertures distributed around the circumference of equal 

 circles upon three parallel disks fixed upon a common central axis, so that 

 the plane of the paper in the figure becomes the surface of a circular cylin- 

 der, in which case the required velocity -?* can be given to the apertures by 

 simple rotation. Let us, for brevity, call such an arrangement a radiation 

 syren, or simply a syren, as it slightly resembles in its mechanical details 

 the acoustic in.strument called by that name. 



