4 SEE— DETERMINATION OF THE [Januarys. 



3. It will l)c shown below that the most remote stars are sepa- 

 rated from us by a distance of at least 1,000,000 light-years, and 

 as this space is a thousand times that to which the spectroscopic 

 method may be applied, it follows that there is no way of fatliom- 

 ing these immense distances except by the improvement of the 

 method of Ilerschel. 



And just as in my " Researches on the Evolution of the Stellar 

 Systems," \'ol. II., 1910, p. 638, I had been able to adduce sub- 

 stantial grounds for returning to the vast distances calculated by 

 Herschel. so also during the past year I have been able to add to 

 the proof there brought forward, and will proceed, to develop it 

 in the present paper, 



§2. Hersciiel's JNIetiiod Depending on the Space Penetrating 



Power of Telescopes. 



In his celebrated star gauges Herschel employed a twenty- foot 

 reflector of 18 inches aperture, and calculated the space-penetrating 

 power of such an instrument from the ratio of the aperture of the 

 telescope to that of the pupil of the eye. The comparative distance 

 to which a star would have to be removed in order that it may appear 

 of the same brightness through the telescope as it did before to the 

 naked eye may thus be calculated. Herschel found the pow-er of this 

 20-foot reflector to be 75 ; so that a star of 6th magnitude removed 

 to 75 times its i)rcscnt distance would therefore still be visible, as a 

 star, in the instrument. 



Admitting such a 6th magnitude star to give only a hundredth 

 part of the light of the standard first magnitude star, it will follow 

 that the standard star could be seen as a sixth magnitude star at 

 ten times its present distance ; and if we then multiply by the sjiace 

 penetrating power, we get 750 as the distance to which the standard 

 star could be removed anrl still excite in the eye, when viewed 

 through the telescope, the same impression as a star of 6th magni- 

 tude does to the naked eye. Thus if Alpha Centauri be distant 4.5 

 light-years, it would be visible in Herschel's telescope at a distance 

 of 3-375 light-years. This is about the distance ascribed to the 



