148 
MATHEMATICS: O. E. GLENN 
this being an absolute universal covariant of T\ for all values of the relative 
velocity V. 
A binary form fim(t, x) in t and x, whose coefficients are constants or 
arbitrary functions of the quantities left fixed by T%, has a finite system of 
non-absolute invariants corresponding to the forms in the system f or f m belong- 
ing to R (1, T, A), and a finite system of absolute concomitants analogous to 
the system for/ m in the domain R (l, T, 0). To obtain the concomitants of 
fim(t, x) one may either particularize those of f m under T, making the substi- 
tutions which reduce T to 2\, or, the invariants under Einstein's transforma- 
tions can be developed ab initio by the methods described above for T, the 
arguments of the expansion of f\ m being now £ = ct + x, 77 = ct — x. These 
invariantive functions represent invariant loci in four dimensional space if 
the time t is interpreted as a fourth dimension. All are free from v. 
A . paper in which the above theory and applications are developed in detail 
and which includes tables of the relativity invariants computed for the general 
fim in the case of the non-absolute systems, and for the orders 1 to 3, inclusive, 
in the case of the absolute systems, is to appear in the Annals of Mathematics. 
1 Boole, Cambridge Mathematical Journal, 3, 1843, (1). 
2 Elliott, London, Proc. Math. Soc, 33, 1901, (226). 
3 0. E. Glenn, New York, Trans. Amer. Math. Soc., 18, 1917. (443) 
4 Hilbert, Leipzig, Math. Ann., 36, 1890, (473). 
5 Einstein, Leipzig, Ann. Physik, 17, 1905. Lorentz, Einstein, and Minkowski, Das 
Relativitdtsprinzip, 1913, p. 27. R. D. Carmichael, The Theory of Relativity, 1913, p. 44. 
