A new upper limit of the electron anti neutrino rest mass has been ded
uced from the tritium beta-decay spectrum. A source of molecular triti
um has been investigated with a new solenoid retarding spectrometer. T
he results are m(nu)e2BAR = -38.8 +/- 34.1stat +/- 15.1syst(eV)2/c4 fr
om which we conclude m(nu)eBAR) less-than-or-equal-to 7.2 eV/c2 with 9
5% c.l. Our beta-endpoint corresponds to a H-3-He-3 atomic mass differ
ence of DELTAm(H-3-He-3) = 18590.8 +/- 3 eV/c2 (1sigma).