156 Intelligence and Miscellaneous Articles. 



In the most general case Sturm's theorem leads to the con- 

 clusion that all the rays which constitute an extremely delicate 

 pencil, reflected or refracted a certain number of times by plane 

 surfaces, meet two indefinitely small straight lines contained in two 

 rectangular planes. 



Excepting the case of the minimum of deviation, therefore, a 

 simple prism always gives an aberration which can be represented 

 by that of a cylindrical lens, convergent or divergent according to 

 the case, the axis of which is parallel to the refracting edge ; this 

 aberration can be corrected by means of a cylindrical lens suitably 

 arranged. Direct-vision prisms are often affected by an aberration 

 of the same kind, so that clean images can only be obtained in two 

 directions, parallel or perpendicular to the refracting edge, by dif- 

 ferent degrees of drawing-out of the telescope of the spectroscope*. 



I ascertained this aberration by substituting for the slit a reticule 

 formed of two rectangular strokes traced on a coat of silver and 

 illuminated by monochromatic light. I have been able to correct it 

 by intercalating between the dispersing-prism and the telescope a 

 system of two cylindrical lenses, plano-convex and plano-concave, 

 of the same curvature : if the two curved parts are in contact, the 

 system constitutes a medium with parallel faces ; on being separated 

 to a suitable distance they operate like a cylindrical lens whose 

 focal length, variable at pleasure, can be calculated as a function of 

 the distance between the two lenses. 



The employment of prisms with total reflection introduces, into 

 the polarized ray which they reflect, a difference of phase between 

 the two principal components, and gives at the emergence an 

 elliptically polarized ray. I have measured this difference of phase 

 in the apparatus I use; the ellipticity produced by it may de- 

 tract from the accuracy of the photometric measurements obtained 

 by means of a rotating JSTicol. This elliptical polarization by total 

 reflection can be completely suppressed by substituting for the 

 simple prism two prisms with total reflection, superposed, in con- 

 tact, whose two right sections are rectangular, or a single prism 

 suitably cut, producing the effect of the two prisms of which I have 

 just spoken. 



With this disposition, the slit may be placed vertical, which is 

 more convenient. After the two total reflections undergone by the 

 light in this prism, the plane of polarization has rotated 90°, and 

 all difference of phase between the two principal components has 

 vanished, the reflected ray preserves the rectilinear polarization. 



These principles can be utilized in the construction of spectro- 

 photometers, and, I expect, will permit more rigorous measure- 

 ments to be obtained. — Comptes Rendus de TAcademie des Sciences, 

 1881, No. 1, t. xcii.pp. 36, 37. 



* A prism affected with such an aberration would give images of the 

 solar protuberances sharp in one direction only; the measurements of 

 their heights might therefore be affected with an error if the aberration 

 of the prism were not suitably corrected. 



