CHAPTER II
THE LIGHT FROM THE STARS
Stellar Magnitudes and Luminosities.
34 . The ancients thought of the stars as luminous points immovably
attached to a spherical shell which covered in the flat earth much as a
telescope-dome covers in the telescope, so that when one star differed from
another in glory, it was not because the two stars were at different distances
from us, but because one was intrinsically more luminous than the other.
Hipparchus introduced the conception of “magnitude” as measuring the
brightnesses of the stars, and Ptolemy, in his Almagest, divided the stars
into six groups of six different magnitudes. The 20 brightest stars formed
the first magnitude stars, while stars which were only just visible to the e} T e
were the sixth magnitude stars. Thus Ptolemy regarded the differences of
visible glory as being represented by five steps, each step down being repre
sented as an increase of one magnitude.
35 . According to the well-known physiological law of Fechner, the effect
which any cause produces on our senses is proportional to the logarithm of
the cause. If we can just, and only just, appreciate the difference between
10 and 11 , we shall not notice any difference at all between 20 and 21 , but
shall just be able to detect the difference between 20 and 22 , or between
5 and 5^. Our senses do not supply us with a direct estimate of the intensity
of the phenomenon which is affecting them, but of its logarithm. It is then not
surprising to find that what Ptolemy regarded as equal differences of bright
ness were actually equal differences in the logarithms of the amounts of light
received. Sir JohnHerschel remarked in 1830 that Ptolemy’s “ first magnitude”
stars were just about 100 times as bright as his sixth magnitude stars, so that
his five steps correspond to a difference of 2 in the logarithm of the amount
of light received, and actually it is found that each one of his five intermediate
steps corresponds very closely to a uniform difference of 0‘4 in the logarithms
of the light received, and so to a light ratio of 10 0 * 4 or 2*512.
Accurate measurements of apparent brightness are now expressed on the
scale introduced by Pogson* in 1856, on which each step of one magnitude
represents a light ratio of exactly 2*512. It is, of course, necessary to admit
fractional magnitudes, a tenth of a magnitude representing a light ratio of
ITOf (an easy number to remember), and a hundredth of a magnitude a light
ratio of 1*0093.
* Catalogue of 53 known variable stars, Radcliffe Observatory, 1856.
+ More exactly the number is D0965.
