Notices respecting Sew Boohs. 617 



According to all previous determinations*, the potential 

 drop at the cathode is independent of pressure. If the current 

 is maintained constant while the prepare is varied, the work 

 done at the cathode remains the same. From the experi- 

 ments it follows that the intensity of the glow is the same. 

 Thus it would appear that the fraction of the energy which 

 is converted into visible glow-radiation is constant. Accord- 

 ing to E. Goldstein, the glow arises from diffusely scattered 

 cathode rays. If this is correct, it would follow from the 

 above experiments that, independently of the value of the 

 pressure, a constant fraction of the power per unit of current 

 undergoes conversion into the energy of cathode rays, and of 

 this latter a constant fraction into the energy of the glow. 

 This transformation into the energy of the glow takes place 

 at higher pressures in the immediate neighbourhood of the 

 cathode, at lower pressures over a larger volume of the gas. 



LVI. Notices respecting New Books. 



Quadratic Partitions. By Lt.-Col. Alla:n t Cunningham, E.E. 



Francis Hodgson, London, 1904. Pp. xxiii-f 266. 

 T^HIS important tabulation of various quadratic partitions will be 

 welcomed by all workers in the theory of numbers. The 

 tables were begun in 1897, and were subsequently laid before the 

 British Association Committee of Section A. The printing and 

 publication were finally carried out with the aid of a grant from 

 the Royal Society's Publication Fund. The scope of the Tables is 

 indicated in the opening sentence of the Introduction. The main 

 table occupies 240 pages, about 8/9ths of the book, and gives all 

 primes i p) below 100,0u0, the prime factors of (p — 1), and the terms 

 of the partitions a*+ 6V+2cf 3 A 2 +3B 2 , and ^(L 2 + 27M 2 ). The 

 same table contains up to the limit p3> ^5,000 the terms of the 

 partition t-—"2t"\ and up to the limit p^> 10, 000 the terms of the 

 partitions a*-htf : ^(X 2 -5Y 2 ), f+7n 2 , and |(« 2 -r-w*). Other 

 partitions with different multipliers of the second quadratic term 

 are given in shorter tables, all cases of the multiplier less thau 2:0 

 being included with the exception of 4, 8, 9, and 12. Then follows a 

 series of short tables giving up to certain limits solutions of special 

 forms of the Pellian Equation. AVe have checked the results 

 in many cases, and so far have found no errors. In an Appendix 

 the author indicates to what extent he has bven able to utilise 

 previously existing tables by Lambert, Barlow, Jacobi, and others. 



Introduction ala Geometrie Generate. By G. Leciialas. Gauthier- 



Villars: Paris, 1904. 

 Tins small pamphlet of 55 pages gives with the lucidity charac- 

 teristic of French mathematical works a graceful introduction to 

 the mysteries of hypergeometry. The author is one of the Con- 

 tinental authorities in this line of imaginative geometry, and any- 



* E. Warburg, Wied. Ann. xxxi. p. 579, 1887. 

 Phil. Mag. S. 6. Vol. 9. No. 52. April 1905. 2 S 



