1884.] on the Distances of the Fixed Stars. 97 



The recent researches referred to in the title of this evening's 

 lecture are some investigations which, in conjunction with a young 

 American friend, Dr. Elkin, who was my guest for two years, I have 

 recently carried out at the Cape of Good Hope. 



The instrument employed was a heliometer — my own property — 

 the good qualities of which I had previously tested at Mauritius in 

 1874, and at the Island of Ascension in 1877. 



[The lecturer. here described the heliometer, and illustrated the 

 method of its use.] 



I have said that the angle between the stars is measured in 

 terms of the scale of the heliometer, but the scale-value, in 

 seconds of arc, may change by the effects of temperature and from 

 other causes. 



Bessel in his researches on the parallax of 61 Cygni, determined by 

 independent means the effect of temperature on his scale-value, and 

 applied corresponding corrections to his observations. But he also 

 took the precaution to employ two stars of comparison situated at 

 right angles to each other with respect to the principal star, so that 

 the effect of parallax would be at a maximum for one comparison star 

 at the season of the year when it was at zero for the other, and vice 

 versa. 



But in the course of previous researches I found that there were 

 sources of error other than mere change of the temperature of the air, 

 viz. differences of temperature in different parts of the instrument, 

 and changes in the normal focus of the observer's eye, which exercised 

 a very sensible influence on the results. It was necessary to devise 

 some method by which these should also be eliminated. 



There is a very simple means of doing this. Instead of taking 

 two comparison stars at right angles, take two comparison stars 

 situated nearly symmetrically on opposite sides of the star whose 

 parallax is to be determined — such, for example, as the stars a and 

 p in Diagram II. Now observe these distances in the order a, (3, 

 /?, a, on each night of observation ; so that on each night the observa- 

 tions at both distances are practically made at the same instant. 

 Then, whatever causes have combined to create a systematic error in 

 the measurement of one of- these distances, precisely the same causes 

 must create precisely similar systematic error in the measurement of 

 the other distance. Thus if, by the regular or irregular effects of 

 temperature or by changes in the normal condition of the observer's 

 eye, we measure the distance a too great, so for the simultaneous 

 observations of the distance /3 we shall, from precisely the same 

 causes, measure that distance too great also. 



But the difference of the distances will be entirely free from all 

 errors of the kind ; and if the distances are not quite equal, it is very 

 easy to apply a correction on the assumption that the sum of the 

 distances is a constant. 



In Diagram II. the circle represents a radius of 2° surrounding 

 the star a Centauri. The distance of the component stars a^ and ag 

 Centauri in the diagram is enormously exaggerated for the sake of 



YoL. XI. (No. 78.) H 



