April 7, 192 1] 



NATURE 



175 



difficult is the absolute determination of apparent 

 magnitudes than might be gathered from the 

 above brief account of the theory. 



The magnitudes of stars in other areas are 

 based upon those of the north polar sequence. 

 The procedure involves photographing the area in 

 question and the pole area upon the same plate, 

 giving the same exposures, and then comparing 

 the two sets of magnitudes against an arbitrary 

 scale, using the known magnitudes of the pole 

 stars to standardise the scale. Actually, it is 

 customary to expose on the pole, then to give 

 two exposures on the field, followed by another 

 exposure on the pole. In this way the effect of 

 any uniformly progressive change in the sky 

 during the time occupied in taking the plate is 

 eliminated. A portion of a photograph showing 

 a comparison of the polar area with another area 

 is reproduced in Fig. 5. In this figure the pole 

 stars can be distinguished by the fact that the 

 displacement between the two images is not parallel 



\ 



i 



- I 



i I 



i I 

 1 j 



Fig. 5. — Portion of photometry plate showing pole and field stars. 



to a reseau line. An alternative method of measure- 

 ment is to measure the diameters of the star 

 images in a micrometer. For a wide range of 

 magnitude, the relationship m = a+b in/d, in 

 which a, b are constants, and d is the diameter of 

 the image of a star of magnitude m, is found to 

 hold. The constants a and b can be determined by 

 a least squares solution, using the data obtained 

 from the stars of known magnitude. 



A slightly different method of procedure is to 

 take photographs at some distance out of focus, 

 the plate meanwhile being given slight periodic 

 motions in two perpendicular directions by means 

 of a device invented by Schwarzschild, and called 

 by him a "Schraffierkassette." The central por- 

 tion of the image so obtained is uniformly grey ; 

 the plate is measured in a comparator, the central 

 portion of the image being seen surrounded by a 

 grey field, the density of which can be varied, 

 produced by a plate with a uniformly graduated 

 density. The position of the latter is varied until 

 the tint of the star image matches that of the sur- 

 rounding field. The readings can be standardised 

 NO. 2684, VOL. 107] 



by stars of known magnitude. This method pos- 

 sesses the advantage that it is not appreciably 

 affected by bad definition, whereas when images in 

 focus are being dealt with, bad definition causes 

 woolly edges, and the images are not then exactly 

 comparable with those of the scale. 



Either a reflecting or a refracting telescope may 

 be employed for the determination of photographic 

 magnitudes. Owing to the absorption produced 

 by the object glass of a refractor, there is a slight 

 relative difference, depending upon the colour of 

 the star, between the magnitudes obtained by the 

 two types of instrument. The differences in 

 magnitude can be expressed as a linear function 

 of the colour-index, and the constants of the rela- 

 tionship require to be determined for each instru- 

 ment from a comparison of the results obtained 

 from white and red stars. The phenomenon be- 

 comes of some importance when the scale of mag- 

 nitudes is extended to faint stars, for it has been 

 shown by Scares that the faint stars are, on the 

 average, considerably redder than the brighter 

 stars. The effect of this will be to give systematic 

 errors in the case of a refractor equivalent to the 

 errors that would be introduced by the use of an 

 incorrect light ratio. 



It is of interest to compare the numbers of the 

 brightest stars down to a limiting magnitude of 

 70m in the case of visual magnitudes with the 

 corresponding numbers in the case of photographic 

 magnitudes. The visual estimates were made at 

 Harvard, the photographic at Greenwich. 



The brightest star, both visually and photo- 

 graphically, is Sirius; its spectrum is of type Ao, 

 so that both visual and photographic magnitudes 

 are — i-6m. 



The economy in observing time effected by the 

 application of photography to the determination 

 of magnitudes has resulted in visual magnitudes 

 being determined by photographic methods. This 

 is effected by the use of isochromatic plates in con- 

 junction with a yellow filter, which is found by 

 experiment to give a spectral-intensity curve 

 similar to that of the normal human eye. This 

 can be tested by means of the magnitudes deter- 

 mined visually with a photometer, and the visual- 

 scale can then be continued to magnitudes much 

 fainter than those which have been determined 

 visually. For distinction, it is customary to call 

 the magnitudes so determined " photo-visual " 

 magnitudes ; photo-visual magnitudes of the stars 

 of the north polar sequence have been determined 

 at Mount Wilson down to a limit of i8m, much 



