June 12, 1SS4] 



NA TURE 



157 



near the ecliptic very elongated ellipses. Obviously, then, 

 those pairs of stars are most "favourable — other conditions being 

 equal — which lie near the major axis of the parallactic ellipse. 

 The dotted ellipse in Diagram II. represents the form of the 

 parallactic ellipse ; that is to say, the form of the apparent path 

 which o Centauri must describe if it is affected by parallax. 

 Of course the size of the ellipse is exaggerated — in fact in 

 the diagram nearly 5000 times — therefore remember that the 

 diagram represents only that which we can compute before we 

 have observed, viz. the shape of the ellipse, or the relations of the 

 lengths of the two axes ; the absolute size has to be determined 

 from the observations. 



The most favourable couple of comparison stars in our drawing 



is that marked a and 0— they are nearest to the major axis of the 

 parallactic ellipse, and they are very symmetrically situated with 

 respect to a Centauri. 



Now turn to Diagram III. Here is exhibited the results of 

 my measures on a very large scale — in a manner similar to 

 that in which the height of the barometer for different hours of 

 the day, or the comparative price of wheat at different seasons 

 of the year or in different years, is now exhibited in the daily 

 papers. Imagine the star o about a mile immediately below any 

 point of that curve, and the star rather over three-quarters of 

 of a mile immediately above the same point, and you would then 

 have a diagram to scale. 1 The middle horizontal line represents 

 the mean difference of these two distances, and each dot or 



HI, —Curves showing the results of the observations of a Centauri relative to the comparison stars a and fi. 



> of Sirius for paralla 



showing results of obs< 



i of e Indi for paralla 



mark on Fig. I of the diagram represents the variation of that 

 distance according to each successive observation. The different 

 kinds of dot represent measures made at different hour angles, 

 or when the relation of the direction of measurement to the line 

 joining the observer's eye is different. These different kinds of 

 personal errors were separately investigated, and they were then 

 allowed for and the observations were corrected accordingly. 



The observations so corrected are represented in Fig. 2, where 

 each black dot expresses the result of the observations of a single 

 night, and the curve is the computed curve resulting from a 

 mathematical discussion of the observations. 



You must be careful to understand that this is not simply the 

 kind of curve which best represents the observations. The curve 

 is limited by purely geometrical conditions to have its maximum 

 on March 7 and its minimum on September 10, and to follow a 



precise form of curve according to a simple law. The observa- 

 tions only determine the range from maximum to minimum, and 

 yet you see how perfectly the maximum of the observations 

 agrees with the maximum of the curve, and the minimum of the 

 observations with the minimum of the curve, and how closely 

 the law is followed throughout. 



The result was that from these observations the parallax of 

 a Centauri was o"747, or practically three-quarters of a second 

 of arc. 



But I was not content with this result alone. I wished furthei 

 confirmation, and selected another pair of stars, o' and &, shown 

 in Diagram II. 



the wall diagram 



represented by about 15 



