March 31, 192 1] 



NATURE 



'43 



photometric Durchmusterung of MuUer and Kempf 

 at Potsdam the zero was chosen so that the mean 

 magnitude of 144 selected fundamental stars north 

 of the equator, between magnitudes 4 and 7, 

 should agree with the corresponding value in the 

 "Bonn Durchmusterung." The systems of mag- 

 nitudes derived in these two investigations are not 

 in absolute accordance, as will be seen later. 



For the accurate determination of visual magni- 

 tudes, some form of photometer is necessary. The 

 two types which have provided the best results 

 are the ZoUner photometer and the meridian 

 photometer of Pickering. The former is illustrated 

 in Fig. I, the principle of the instrument consist- 

 ing in the formation of two images in the focal 

 plane of the telescope, one being the image of the 

 star under observation, and the other that of an 

 artificial star the brightness of which can be varied 

 and brought into equality with that of the real 





Fig. I. — The Zollner Photometer. 



Star. The light from a standard lamp, giving a 

 constant illumination, passes through a pin-hole in 

 a diaphragm o, holes of different sizes being used 

 to simulate stars of different magnitudes. The 

 divergence of the rays passing through the pin- 

 hole is increased by a concave lens, m, and it then 

 passes successively through a polarising Nicol, fe, 

 a thin quartz plate, /, cut perpendicularly to its 

 optical axis, a second Nicol, i, and a third Nicol, 

 h. The Nicol i and the quartz plate I are fixed 

 relatively to one another, but the Nicol k can be 

 rotated, so varying the colour of the light falling 

 on the third Nicol. When the colour agrees as 

 nearly as possible with that of the star under 

 observation, k is clamped into position. The Nicol 

 h acts as an analyser, and the system fe, I, i is 

 turned as a whole relativelv to it in order to vary 

 the brightness of the artificial star and bring it 



NO. 2683, VOL. 107] 



into equality with that of the real star. The light 

 then passes through a lens, /, which focusses it 

 in the focal plane of the telescope, after reflection 

 by the plane glass mirror ee', which forms two 

 images of the artificial star of nearly equal bright- 

 ness by light reflected from its front and back 

 surfaces respectively, the former being somewhat 

 the brighter of the two. There are four positions 

 of the rotating system in which equality can be 

 obtained between the brighter of these images 

 and that of the star under observation, and the 

 reading corresponding to each is observed. Some 

 observers prefer to make the observation by ad- 

 justing the brightness of the images of the artificial 

 star so that the real star image is intermediate 

 in brightness between the two images of the arti- 

 ficial star. As differences in brightness only are 

 measured, it is immaterial which procedure is 

 adopted provided it is adhered to throughout. A 

 standard star is then observed in a similar way. 

 If Ij, Ij are the angles through which the polar- 

 ising system is turned in the two cases, from the 

 position corresponding to crossed Nicols, then the 

 ratio in brightness of the two stars is sin^ Ij : sin^ I ,, 

 and therefore their difference in magnitude is 



5 log (sin Ij/sin l^). All the Potsdam observa- 

 tions were made with two photometers of this 

 type, though differing in some details from that 

 illustrated here ; 144 fundamental stars were 

 chosen, which were combined into 432 pairs, and 

 intercompared in order accurately to determine 

 their magnitudes. Every zone star was then 

 compared with an adjacent fundamental star. 



The Zollner photometer is convenient and accu- 

 rate in use. The colour compensation reduces the 

 subjective errors of personality which are liable to 

 occur when two images of diff"erent colours are 

 compared. The colour match can be made much 

 more accurately, however, for yellow and red stars 

 than for white or yellowish-white stars. The prin- 

 cipal objection raised against it is the employment 

 of an artificial star — not on the ground of pos- 

 sible variations in its magnitude, for there are 

 types of standard lamps which give very constant 

 illumination, but owing to the fact that the image 

 of the artificial star may not be exactly similar to 

 that of a real star under all conditions of seeing. 

 It is stated by Miiller that the tendency is to make 

 bright stars too bright and faint stars too faint, 

 but, provided that the diaphragm or the aperture 

 of the telescope is so chosen that the magnitude 

 of the artificial star does not differ greatly from 

 that of the star under observation, the errors pos- 

 sible on this account are very small. One of the 

 Potsdam photometers was provided with three 

 object glasses which were used in conjunction with 

 three diaphragms. It was found best to use an 

 aperture of 30-40 mm. for stars of magnitudes 2 

 to 4, of 60-70 mm. for stars of magnitudes 4 to 

 6, and of 130-140 mm. for stars of magnitudes 



6 to 8. 



The meridian photometer, devised by Pickering 

 and used at the Harvard Observatory for the very 

 extensive photometric work carried on there under 



