322 Profs. H. du Bois and H. Rubens on Polarization of 



the total number of reflexions taken into account. Summing 

 this series, we get l/m' = l— {2n+n— l)/n\n + l), or, if t is 

 assumed =00, \\m' =z(n — l)/(?i + 1) ; whence 



rc=(m' + l)/(m'-l). 



It will be observed it is only on the assumption of there being 

 an infinity of interior reflexions that we get 1/m' = 1 — 1/m. 



In concluding this paper I venture the tentative suggestion 

 that the jjl values l + y/2 found in this investigation mark a 

 transition stage in JFresnel's Reflexion formula. The hypo- 

 thesis would be that when //. lies outside these limits, some 

 modification of the general formula has to be introduced such 

 as is found to be well enough marked in the case of metallic 

 reflexion. 



XXXII. On Polarization of Undiffracted Long-waved Heat 

 Rays by Wire Gratings. By H. DU liois and H. Rubens*. 

 Notation. 



a, a', constant of grating. 



b, b', slit-widths. 



d, diameter of wire. 

 13, angle of inclination. 

 V? polarization azimuth. 

 II 2 , transmissibility ratio. 



Q, central transmissibility. 



Qs, transmissibility (X polar, rays). 



Qp, transmissibility (|[ polar, rays). 



Qm, mean transmissibility. 



R s , reflecting power (J_ polar, rays). 



I. Introduction. 



§ 1. npWENTY years agoj one of us investigated, among 

 JL others, three silver wire gratings (45 /j. < d < 180 /x) 

 corresponding to the interval 



20<b'/X<100, 



which produced in the visible region a partial polarization of 

 the undiffracted central image at right angles to the wires. 

 The apparent slit-width b' may be decreased and the polari- 

 zation increased by inclining the grating up to 50°; the effect 

 proved to be nearly independent of the thickness of the wire; 

 further, it increased from the violet to the red up to about 

 13 per cent. No appreciable differences of phase were 

 evident. Unindented rulings (>l/x) made on films of 

 deposited platinum also polarize perpendicularly, but much 

 less and with smaller dispersion. In addition, the reflected 



* Communicated by the Authors. 



t H. du Bois, Verh. d. Phys. Ges. Berlin, x. p. 71 (1891) j Wied. Ann. 

 xlvi. p. 548 (1892), xkiii. p. 546 (1893;. 



