April 7, 192 1] 



NATURE 



^IZ 



Stellar Magnitudes and their Determination.^ 



By H. Spencer Jones, Chief Assistant, The Ro^val Observatory, Greenwich. 



II.- Apparent Magnitudes: (&) Photographic. 



\17 ITH the application of photography to astro- 

 *'' nomy it was inevitable that attempts 

 should be made to determine apparent magnitudes 

 by photography. Visual observations are slow, 

 for every star must be compared individually, 

 and the telescope reset for each. Photography 

 effects a great economy in observing time 

 at the telescope, for when a plate is secured its 

 measurement may be undertaken at any convenient 

 time. The photographic plate, however, is sensi- 

 tive to a different region of the spectrum from the 

 human eye; if a blue and a red star appear of 

 equal brightness to the eye, the former will be 

 recorded as much the brighter bv the photo- 

 graphic plate. The photographic' and^ visual 

 scales of magnitude will therefore not agree with 

 one another. The difference, photographic minus 

 visual magnitude, for any star is called the 

 "colour-index" of that star, providing as it does 

 a measure of the colour of the star ; the redder the 

 star, the larger is its colour-index. 



The determination of photographic magnitudes 

 IS based upon the two following conventions : 

 (1) the light ratio shall be the same as that 

 adopted for visual magnitudes, its logarithm 

 being, therefore, 040; (ii) for stars the 

 spectra of which are of the type Ao in 

 the Harvard classification {i.e. in which the 

 most conspicuous feature is the Balmer series 

 of hydrogen lines), the photographic and visual 

 magnitudes shall be equal. If this holds for stars 

 of, say, the 6th magnitude, it will hold also for 

 stars of all magnitudes, by (i). Stars which are 

 bluer than type Ao have small negative colour- 

 mdices; those which are redder have positive 

 colour-indices, the values for the reddest stars 

 being larger than two magnitudes. 



The accurate determination of photographic 

 magnitudes is a problem which is much more com- 

 plicated than it appears upon the surface, and 

 beset with many difficulties. It consists essen- 

 tially of two distinct problems : the absolute 

 determination of the magnitudes of a suitably 

 chosen series of stars, and the extension of this 

 series to determine the magnitudes of other stars I 

 by comparative methods. Although much work I 

 has been done at Harvard, Mount Wilson, Green- I 

 wich, and elsewhere, there remain discordances ' 

 which require further investigation before photo- 

 graphic photometry can be regarded as having \ 

 been placed upon a definite and satisfactory basis. ' 



The area around the North Pole has been 

 chosen in the northern hemisphere as the most 

 suitable area for the absolute determinations, as 

 It is always available for use for comparative 

 methods. A sequence of stars has been chosen 

 by the Harvard observers, called the " north polar 



' Continned from p. 146. 

 NO. 2684, VOL. 107] 



sequence, which are graded in magnitude so as 

 to provide the necessary basis for comparison, and 

 the magnitudes of these stars have been carefullv 

 determined by the use of various methods. The 

 difficulty of the absolute determination of these 

 magnitudes is increased by the complication intro- 

 duced by the law of photographic action. It has 

 been found that, for a given light intensity, I, the 

 photographic effect produced does not increase uni- 

 formly with the time, so that the same photo- 

 graphic effect is not obtained bv, say, doubling 

 the intensity and halving the time of exposure. 

 In fact, the relationship between the intensity and 

 the time of exposure required to produce a given 

 photographic effect is of the nature I?f = a con- 

 stant, where q is a constant for anv given type of 

 plate, but has different values for different types, 

 although averaging somewhat about o-8. Now 

 most of the methods of determining absolute 

 photographic magnitudes depend upon successive 

 exposures given on the same plate, some means 

 being employed to reduce the intensities during 

 one of the exposures. It is clear that, for all 

 photometric work, the times of the two series of 

 exposures must be exactly equal, and then the 

 comparison of the images obtained from the two 

 exposures only involves the assumption that the 

 intensities which in equal times produce equal 

 photographic effects must be equal. 



If, then, the photographic effects produced by 



I a series of stars in the first exposure are denoted 



i by : — 



i and by the same stars in an equal exposure, in 

 which the brightness has been reduced in a pro- 

 portion equal to a difference of Am in magnitudes, 

 are : — 



then, if t^ = j'^, it follows that the magnitudes of 

 stars r and s differ by Am. In this way, differ- 

 ences of magnitude are determined, as in the case 

 of visual observations with a photometer. The 

 zero of the magnitudes must be chosen in accord- 

 ance with the convention referred to above. 



In practice, of course, it rarely happens that' 

 two stars can be found the photographic intensities 

 of which in the two cases are exactly equal. The 

 procedure usually adopted is to estimate the photo- 

 graphic effects against an arbitrary scale, and 

 then to use the known fact that the two images of 

 any one star correspond to a magnitude difference, 

 Am, in order to determine the values of the scale 

 intervals. The magnitude of every star can then 

 be read off. 



\'arious devices have been used to reduce the 

 intensities by a known amount. One method, 

 which has been extensively used at Gncnwich, is 



