THE BINARY STARS. 319 



are able to see it. Many careful observations and measurements 

 of the movements and positions of this companion to Sirius have 

 now been made, and it has been found almost exactly to fulfil 

 Bessel's prediction. It has been ascertained that it completes its 

 revolution round its primary in about forty-nine years ; also, as the 

 distance of Sirius from us is approximately known, the actual 

 distance in millions of miles which separates the pair can be cal- 

 culated when their mean angular distance from one another in 

 seconds of arc has been accurately measured. Now, taking the 

 distance of Sirius from us at loo billions of miles, an apparent 

 mean angular separation between him and his companion of one 

 second of arc would represent an actual distance between them of 

 about 484 million miles. 



When a number of careful measurements of the relative posi- 

 tions and angular separation of two stars have been made extend- 

 ing over a sufficient lapse of time, it is possible to map out the 

 shape of the orbit which each is pursuing as seen from the earth, 

 and to estimate approximately their mean angular distance from 

 each other expressed in seconds of arc. There are some slight 

 discrepancies in the various estimates of the mean angular dis- 

 tance separating Sirius and his companion as given by different 

 observers ; but it seems probable that this cannot differ much from 

 seven seconds of arc. If, then, the mean distance separating 

 Sirius and his companion is seven seconds as seen from the earth, 

 then, as one second at the distance of Sirius represents, as I have 

 said, 484 million miles, seven seconds will indicate an actual mean 

 distance between the pair of 3388 million miles, or rather more 

 than thirty-six times the distance from the earth to the sun. We 

 are, therefore, able to make a comparison between Sirius and his 

 companion on the one hand, and the sun and the planet Neptune 

 on the other. 



Now, Neptune is about thirty times as far from the sun as the 

 earth is, and we will imagine that another planet existed in the 

 solar system at the same distance from the sun as that which sepa- 

 rates Sirius and his companion. Now, taking the earth's distance 

 from the sun as unity, Neptune's would then be represented by 

 the number 30, and the distance of our imaginary planet would 

 then be 36. We know that Neptune completes the circuit 



