September 30, 1921] 



SCIENCE 



305 



sions existed, the simple case of the solar field 

 being actually six dimensional/ as are also 

 certain other physical solutions obtained by 

 Weyl. 



III. The author has found all solutions of 

 Gik='^ of the orthogonal form Xj^dz^^ -\- 

 X^dx^ -\- X^dx^ + Xidx^ in which the four 

 coefficients are functions of one variable say x^. 

 An example of such a field is 



X --dx - — X i (dx 2 -U dx ~ + dx -) . 



1 1 1^2' 3' i ' 



All cosmological solutions which satisfy the 

 same hypotheses are determined and can be 

 expressed by elementary, algebraic and trans- 

 cendental functions. 



The principal solution is 

 idxi' 



ds^ 



c2(i +xi'y 



a-l^nadxj^ + Il^^adxs^ + Xi''<'tdx. 



■]■ 



where c is arbitrary and a„, a^, a^ obey the re- 

 lations. 



a2 + <*3 + aj = 0, asofa -f asat -{- aia2 = — -g-. 



These fields can all be represented in flat 

 space of seven dimensions. A paper on this 

 subject has been sent to the Mathematischen 

 Annalen. 



TV. If we require the quaternary form ds- 

 to be the sum of two binary forms, that is 

 the sum of the squared elements of two sur- 

 faces, then the only cosmological solution 

 (neglecting the trivial euelidean form) is 



ds2 = X^-2 (dX^2 +.dx^2) 4- x^-2 (dx^2 + dX^2). 



This represents a quartic manifold of four 

 dimensions imbedded in a 6-flat. The 

 finite equations are 



X^2 + x^2 -I- x^2 = 1, x^2 +■ X.2 + X^2 = 1. 



This is apparently the simplest solution of 

 Einstein's equations which has thus far been 

 found, and the first one (beyond the obvious 

 flat and spherical spaces) which in its finite 

 form is algebraic. 



Edward ILvsner 

 Columbia Universitt, 

 New York 



^ See American Journal of Mathematics, Volume 

 43 (1921), pp. 126-133. 



THE PRODUCTION OF ENHANCED LINE SPEC- 

 TRA BY A NEW METHOD 



The ordinary spark spectrum differs from 

 the arc spectrum in that certain lines are 

 weakened, others are enhanced and new lines 

 appear. In general the more violent the 

 stimulus of the source the more intense are 

 the new enhanced lines as compared to the 

 weakened lines. It is customary to refer to 

 the lines which are the more prominent in the 

 spectrum produced by an arc as arc lines, 

 while those which are enhanced by the spark 

 are known as spark lines and constitute the 

 pure spark spectrum. 



Lorenser and Fowler, as well as Sommer- 

 feld and Kossel, have shown that modern 

 theories of atomic structure and radiation 

 leave little doubt that the enhanced lines in 

 the spectrum are due to radiation from atoms 

 that have lost an electron, i.e., ionized atoms; 

 and that arc lines are due to radiation from 

 the un-ionized or neutral atom. The varying 

 facility of producing the enhanced lines of 

 different elements depends, then, on the in- 

 tensity of the forces which bind the electron 

 to its nucleus and on the energy used in tear- 

 ing the electron off. For example, no en- 

 hanced lines of lithium have ever been pro- 

 duced while the enhanced doublet of calcium, 

 H and K, is strong even in the flame spectrum. 



In a study of the enhanced lines of the cal- 

 cium spectrum begun by examining the spec- 

 trum of calcium wires exploded by the An- 

 derson method^ it was found that as the 

 size of the wires used was decreased, while 

 the energy of the stimulus remained the same, 

 the intensity of the enhanced lines increased. 

 This increase in intensity indicated a more 

 complete ionization of the calcium atoms. In 

 seeking a way by which the amount of calci- 

 um in the source could be still further re- 

 duced a new source of light was developed. 



A fine asbestos fiber about three centimeters 

 long was saturated-with an aqueous solution 

 of some salt of calcium. The saturated fiber 

 was fastened in place as the fine wires had 

 previously been fastened and the charge of 

 the high tension condensers thrown across it, 



1 Astro. J., 51, 37, 1920. 



