532 EEPOET— 1881. 



where ;ijC,V, refer to displacements parallel to the axis ; /i2C2V2 to displacements at 

 right angles to the axis. 



In dispersive media the values of V are greater for red rays than for violet 

 waves. Hence in substances for which tlie axial conductivity of a medium is a 

 maximum, the diti'erence in the values of V for different rays will have less influence 

 on the value of tlie exponential which represents the intensity of transmission of 

 displacements parallel to that axis than on the value of the exponential which re- 

 presents the intensity of transmission of displacements perpendicular to that axis. 

 Hence in positive crystals (smoky quartz, lomellite, &c.) the dichroism takes the 

 form of greater opacity to red than to violet rays, in the ordinary ray relatively to 

 the extraordinaiy ray. In tourmaline and negative crystals, on the other hand, 

 the opacity is greater for red than for violet in the extraordinary ray, and less for 

 the ordinary ray. The author exhibited several specimens of coloured toiu-maline 

 cut into cubes, all of which were more opaque along the axis than across it ; and in 

 all of which the tint, as viewed along the axis, was browner than across the axis, 

 showing in that direction an increased absorption of violet, and blue, and green rays. 



The author also exhibited specimens of lomellite showing maximum opacity 

 and maximum absorption of blue rays in a direction perpendicular to the axis. A 

 further consequence of the theory is, that in substances in which the electric conduc- 

 tivity has different values along three axes there will be trichroism. 



It also foUows that dichroism is a general property of all colom-ed crystals in 

 which the electric conducti^-ities are unequal in different directions. 



In conclusion it was pointed out that a mechanico-optical illustration of the 

 tehaviovir of positive and negative crystals can be made as follows. A positive 

 crystal may be represented by placing metal wires vertically in a hollow cube of 

 glass filled with jelly or Canada balsam ; while a negative crystal may be repre- 

 sented by horizontal layers of wire gauze fixed in a similar cube. The former 

 conducts electricity best along a vertical axis, and is more transparent along than 

 across that axis. The latter conducts electricity better across the axis than along 

 it, and is more opaque to light along the axis than across it, as tourmaline is. 



10. On the arrangement of Cometic Perihelia ivitli reference to the Sun's 

 march in space. By Henry Muirhead, M.D. 



The author exhibited and described a diagram on which the arrangement of 

 cometic perihelia had been laid down. This has been engraved, and the author's 

 speculations on the mode of occurrence set forth in the ' Proceedings of the Philo- 

 sophical Society of Glasgow,' vol. xiii. p. 43. 



MATHEMATICAL DEPARTMENT. 



1. Second Report of the Committee appointed for the calculation of Tables of 

 the Fundamental Invariants of Algebraic Forms. — See Reports, p. £5. 



2. Report of the Committee on Mathematical Tables. — See Reports p. 303. 



3. Report on Recent Progress in Hydrodynamics. — Part 1. 

 By W. M. Hicks, M.A. — See Reports, p. 57. 



4. Sur un criterium de Steiner relatif a la theorie des sections coniques. 



Par M. Halphen. 



On dt^termine une conique, dans un plan, par trois de ses points et par son 

 centre, et Ton demande de distinguer les cas ou cette conique est une ellipse de ceux 

 on cette conique est une hyperbole. 



Pour r(5pondre a cette question <5lementaire, Steiner a donniS, sans demonstration, 



