36 PRESIDENTIAL ADDRESS SECTION A. 



that a knowledge of absolute magnitudes is applied to the deter- 

 mination of the distances of stars too far remote for angular 

 measurements. We must therefore as a next step consider star 

 magnitudes. Ptolemy (A.D. 130) in the Almagest, divided the 

 stars into six magnitudes; the brightest he called of first magni- 

 tude and the faintest visible to the naked eye he called the sixth 

 magnitude, and this is the basis of our present classification. The 

 relation between the brightness of two stars differing by one magni- 

 tude has now been defined as y 100 to 1 (log = 0-4), i.e., each 

 succeeding magnitude is 2-512 times as faint as the preceding one. 

 This figure, of which the logarithm is exactly 0-4, has been chosen 

 so as to make a change of 5 magnitudes exactly a change of 100 

 times in brightness. On this exact scale some of the brighter 

 stars are more than 100 times brighter than a standard sixth 

 magnitude star and so the scale has to be extended from 



+ 6. +5 +1, 0, -1, -2, etc. 



A star of zero magnitude is therefore one magnitude brighter than 

 one of the first magnitude and -a star of magnitude — 1 is a 

 magnitude brighter still. The "apparent magnitudes," as we see 

 them, are not the real or "absolute magnitudes" because some 

 stars are comparatively near us and some very distant. 



The law of decrease of brightness with distance is, however, 

 well known. The brightness varies inversely as the square of the 

 distance. 



Star Distances. 



Distance is often expressed as the parallax, i.e., the angle 

 contained between two lines from the star, one passing through 

 the sun, and the other through the earth at greatest elongation 

 as seen from the star. 



No star is known to be near enough to have a parallax of 

 one second of arc, which corresponds to the angle subtended by a 

 foot-rule at a distance of forty miles. There are 1,296,000 seconds 

 of arc in a circle. The unit commonly used in speaking of star 

 distances is the "parsec," i.e., that distance at which a star must 

 be to have a parallax of one second. The unit of distance for 

 magnitude purposes is ten parsecs (parallax =01"). 



From this distance, light travelling at 186,000 miles a second 

 takes 32-6 years to reach us. Distances are often given in "light- 

 years." The following table shows the relationships we have been 

 considering. 



Table I. 



Ratios of apparent magnitude, intensity and parallax for 

 the same star at different distances: — 



