9 355 



fades out through its increased size, while we just want to leach as faint stars as 

 possible. Partly to throw some light on these considerations I have measured not 

 only the spectra of the first but also of the second and third order. 



On each spectrum only one pointing was made. The gain in accuracy by 

 repeated measurement of the same image is small in comparison with the other 

 accidental and systematic errors. I therefore preferred to increase the accuracy by 

 taking more plates. 



In order to get a good determination of the variation of the effective wave- 

 length and its mean error with the intensity of the image of the same star, also 

 many faint images were measured which are individually of very little use. 



4. Reduction of the Effective Wavelengths to the sanne 



Intensity of the Image. 



The determination of colour equivalents from effective wavelengths rests in 

 the present paper on the supposition that the effective wavelength depends only on 

 the colour of the star and the intensity of the image on the plate. Hence it is 

 supposed that a bright and a faint star of the same colour will give the same 

 effective wavelength when the exposure times are chosen in such a waj', that the 

 images of the two stars show the same intensity, or in other words, that the ex- 

 ponent p in the formula of Schwarzschild mentioned above is independent of the 

 wavelength. The gradation of the scales of exposure time and of intensity may be 

 different for different wavelengths, but the proportion between the two gradations 

 must be independent of the wavelength. That the exponent p is practically inde- 

 pendent of the wavelength has been found in different photographic investigations. 

 As the part of the spectrum here considered is only small, tlie above assumption 

 is plausible. 



This assumption is, however, still supported by the material itself. The intensity 

 of the spectra of the 11""* order are, as mentioned above, 4'37 magnitudes fainter 

 than the spectra of the P' order. If now two exposures of the same star are chosen 

 of such different duration, that the spectra of the P' order of one exposure are of 

 equal intensity as the spectra of II"'' order of the other exposure, then practically 

 the same effective wavelength is found from the spectra of the P' order of the short 

 exposed and the spectra of the II"** order of the long exposed image. It may, of 

 course, be objected that the spectra of P' and 11"'' order have different dispersion 

 and are therefore not to be compared directly, but with spectra of approximately 

 symmetrical figure appreciable errors are not to be expected on account of this 

 circumstance. Another control was made by the aid of the faint diffraction images 

 produced by the grating in connection with three metallic bars, which were placed 

 at right angles to the rubber wires in order to support them at certain intervals 

 and to keep them at the proper distances from one another. These additional spectra, 



D. K, D. Vidensk. SolsU. Skr., nalurv. og mathem. Afd.. 8, R:ekke, IV. 4. ^y 



