1895.] Cubic Surfaces containing 27 real straight lines. 11 



In this case take as an arbitrary point that at which 16 meets 

 4, we get a quadratic which determines the points at which 5 and 

 17 meet 4. 



Similarly all the other lines may be found. 



When the position of all the lines is fixed, the form of the sur- 

 face can be found by taking sections through any straight line on 

 the surface. 



These sections are conies, the straight line forming part of the 

 complete cubic section. Many points on these conies are known 

 as being the intersection of the planes with lines already found. 



The rules for the geometrical construction given in Vol. VIII., 

 Pt. iv., page 241 maybe deduced from the analytical method given 

 above. For it has been shewn that the position of the lines 4, 12, 

 2, 13, 14, 15, 9, 7, 8, and the point at which 16 meets 4 may be 

 placed in arbitrary positions, and that this construction determines 

 all necessary constants. 



When this has been done the facts used to determine the 

 remaining lines are 



(1) If three straight lines form a triangle this triangle is a 

 section of the surface. 



(2) Any two triangular sections meet each other in three 

 points in one straight line, e.g. 3, 5, 7 and 13, 14, 15 are sections, 

 3 meets 13, 5 meets 14, 7 meets 15, and the three points of inter- 

 section are in one straight line. 



(3) If we find four points on the surface in one straight line, 

 this line lies wholly on the surface. 



(3). Expansion produced by Electric Discharge. By Miss 

 Martin. 



Acting under Professor J. J. Thomson's directions, I have 

 lately endeavoured to find some explanation of certain pheno- 

 mena first mentioned, I believe, by Herr G. Meissner (Abh. d. 

 Gesell. der Wissensch. zu Gutt. 1871, Bd. xvi., p. 98). In the course 

 of some experiments " iiber die elektrische Ozonerzeugung und 

 fiber die Influenz-Elektricitat auf Nicht-Leitern," Meissner ob- 

 served that if a gas contained in a space between the plates 

 of a condenser were subjected to a sudden rise or fall of potential 

 the volume of the gas underwent a momentary increase. His 

 apparatus consisted of two concentric glass tubes about 50 cm. 

 long, both rounded off at the lower end and having no connection 

 with each other in any way except that the inner tube was held 

 in place at the upper end by a ring of wax. Between the two 

 tubes was a space of 3 — 5 mm. The outer surface of the outer 

 tube, and the inner surface of the inner were coated with tinfoil 



