Apeil 19, 1907] 



SCIENCE 



609 



muth for the 6f-iiieh Repsold meridian 

 circle. Collimator marks, according to 

 published statistics, as well as from theory, 

 do not seem to be sufficiently stable for 

 the study of azimuth changes unless sup- 

 plemented by frequent observations of cir- 

 cumpolar stars. The method I have em- 

 ployed for bringing a mark in focus is 

 simple, direct and vastly preferable to the 

 use of a long focus lens; since the marks 

 may be located at such distance that any 

 probable change in the place of the pin 

 will not sensibly change the direction. 



In photographic work, when it is desired 

 to bring objects lying in different planes 

 to a common focus the aperture of the lens 

 is reduced. Accordingly, I made some ex- 

 periments and found when the aperture 

 of the object-glass of the Repsold meridian 

 circle, of 6-foot focus, was reduced to one 

 inch, all objects at about 1,000 feet and 

 beyond were brought in good focus. 



A concrete pier 2 feet square and rising 

 2^ feet above the surface of the ground 

 was erected at a distance of 1,140 feet. 

 On the top of the pier was bolted a cast- 

 iron box, 15 inches wide, 10 inches high 

 and 10 inches deep. Inside the box is an 

 adjustable brass plate with a hole 0.15 in 

 diameter, behind which is placed a 50-volt 

 16-candle lamp. Electricity is supplied 

 from a storage battery, at the observatory, 

 which had been installed for rotating the 

 dome and illuminating the instruments. 

 During daylight, when the sun is not 

 shining, the mark appears like a sixth- 

 magnitude star; at night brighter. 



In order that an object at a finite dis- 

 tance may suif er no change of direction, the 

 hole in the cap which covers the object-glass 

 must be in the optical axis. Any deviation 

 will cause a displacement proportional to 

 the focal length of the telescope divided by 

 the distance of the object. At 1,000 feet 

 one inch subtends an angle of 17". 1. 



Hence very great precision in the fit of the 

 brass cap is unnecessary. In order to know 

 whether the hole in the cap is in the optical 

 axis, the cap may be revolved 180 degrees, 

 or the mark may be observed with the full 

 aperture of the object-glass. In the latter 

 case there is seen a well-defined disk of 

 light about 90" in diameter. 



In 1861 and for a number of years fol- 

 lowing, at the Dudley Observatory, I had 

 a mark at the distance of six miles. After 

 a rain the mark could be observed with 

 great precision. The unsteadiness of a 

 terrestrial mark does not depend directly 

 on the distance. 



TJie Significance of the Star Ratio: George 



C. COMSTOCK. 



The number of visible stars increases 

 very rapidly as we extend the count to 

 fainter and fainter magnitudes, and any 

 rational attempt at their enumeration must 

 involve a limit, or limits, of brightness at 

 which that enumeration shall cease. The 

 rate of increase in the number of stars as 

 this limit is made to move down the scale 

 of mag-nitudes is called the star ratio, and 

 the numerical value of this ratio in differ- 

 ent parts of the sky and at different points 

 in the scale of stellar magnitudes has been 

 made the subject of research by many 

 astronomers. From these investigations it 

 appears that in general the number of stars 

 is increased more than threefold and con- 

 siderably less than fourfold for each in- 

 crease of one magnitiide in the limit to 

 which the enumeration is extended. The 

 ratio appears to be a little greater in the 

 Milky Way than in extra-galactic regions 

 and possibly a little greater for the brighter 

 magnitudes than for the fainter ones, 

 although it seems probable that the last 

 relation is confined to the region outside 

 the galaxy. 



The point of major interest in the dis- 

 cussion is, however, that in general the rate 



