42 PROCEEDINGS OP THE AMERICAN ACADEMY. 



magnesium, which is illustrated in Plate 1, the line of wave-length 



2790.8,* which forms the most refrangible member of a characteristic 



group, is seen to be reproduced four times. Two of these false spectra 



are in the region between wave-lengths 1800 and 1900 and two in the 



region between 900 and 1000. It is to be noted that of the two groups 



near 1800 the less refrangible is the stronger, while of the groups near 



900 the more refrangible is the stronger. This is in accord with the 



theory, for if the two strong reproductions are considered to be the 47th 



and 23d spectra of the grating of m groups, the two weak reproductions 



are the 46th and 24th spectra, while the real line 2790.8 corresponds to 



the 70th spectra. 



When, however, the wave-lengths as measured in the previous paper 



were compared with those calculated from the fractions f J X 2790.8, 



t§ X 2790.8 , f J X 2790.8 , ^ X 2790.8, the observed facts did not 



seem to agree with the theory as accurately as might be expected. It 



seemed worth while to remeasure the wave-lengths of the false spectra, 



in order to determine if the fault lay in the theory or in the observed 



values. The author was encouraged in this step by the interest which 



Professor Runge took in the matter. In fact the method employed in 



re-measurement was suggested by him. 



The arrangement of the apparatus was as follows : — 



Two slits, A iand B, were placed upon the circle whose diameter was 



the radius of the concave grating. The grating itself was kept fixed iu 



position and the normal to its surface fell 



-^^.^ m'ldway between the two slits. By this 



^\ method the image of A was formed at B. 



\ An arm carrying tlie plate-holder C was 



\ pivoted at the centre of the circle. The 



\ I result of this plan was that the first spec- 



\ / trum obtained when A was used as source, 



\ / was shifted with respect to that obtained 



\ y with B as source by a definite amount. 



."'^ The heights of the two slits were so arranged 



_ . that the A spectrum fell directly over the 



Figure A. ^ , • , 



B spectrum upon the photographic plate. 



The method of procedure was to illuminate A with the light from a 



magnesium spark and to place the plate-holder C in such a position that 



a photograph of the false lines under investigation was obtained. Next 



* Exncr and Ilaschek, K. Akad. der Wiss. in Wien, 106, Abth. II. (1897). 



