On a Theorem relating to Curved Diffraetion-gratinas. 47 



magnets thus formed were placed on a block between springs 

 which held their ends firmly in contact, thus giving a closed 

 iron circuit. A magnetizing current being passed through 

 the primary, the induction through the secondary coils on 

 reversing the primary current was measured, and found to be 

 the same for both coils. Then a piece of copper 05 millim. 

 thick was interposed between each of the opposed pairs of 

 faces of iron ; and the induction near the end was found to be 

 only 0*73 of the mean induction. 



The effect produced with a long iron rod would naturally be 

 of the same kind as with the ring described above, except 

 that the leakage of induction would take place to a greater 

 extent. 



Another point is, that in experiments with a closed iron 

 ring the lines of induction lie entirely within the iron, and 

 hence the magnetic permeability //, ( = l + 47r&)is determined 

 directly ; but when a rod is employed, the lines of induction 

 pass for the greatest part of their course through air, and 

 what is measured is the average permeability of an air-iron 

 circuit. Now air having always a smaller permeability than 

 iron, the result is to bring out the magnetization-coefficient 

 again too low. 



Hence it would hardly seem necessary to adopt M. Mas- 

 cart's suggestion that " a special phenomenon is produced 

 in the case of closed rings which exaggerates the effect of 

 induction." 



VI. On a Theorem relating to Curved Diffraction-gratings. 

 By Walter Bailt, M.A* 



IN a paper read before this Society in January 1883 f, I 

 showed that if a plane be taken perpendicular to the lines 

 of a curved diffraction-grating, and the normal to the centre 

 of the grating be taken as the initial line, then the equation 



COS 2 COS 1 /-in 



r c d 



in which c is the radius of curvature of the grating and d is 

 an arbitrary constant, gives a curve having the property that 

 if a source of light is placed at any point of the curve, the 

 curve is the locus of the foci of all diffracted rays whether 

 reflected or transmitted. 



When d is greater than c, r may be infinite. Let (/> be the 



* Communicated by the Physical Society : read May 8, 1886. 

 t Phil. Mag. March 1883, p. 183. 



