80 a. CENTAUEI. 



the early measures constituting the difficulty ; and at length 

 came to the conclusion that I could only succeed by discarding^ 

 them altogether. A glance at the diagram will show that those 

 of 1822-24-30 and 31 are mutually inconsistent, and widely out 

 of any rational curve, especially that by Fallows, in 1822, show- 

 ing an elongation of 28""75. The positions about the apparent 

 periastron, 1876 to 1879, also are rather wide of the curve, but 

 that is not to be wondered at, considering the difficulty of 

 measurement of so small an interval (less than two seconds oT 

 arc), answering to one inch at nearly one and three-quarter 

 miles. At that time, except to high telescopic power and fine 

 definition, the pair appeared as a single star. 



The apparent curve of course represents the real orbit in- 

 perspective. "We have then to determine how much it is tilted,, 

 and in what direction ? These questions are determined by the 

 projection of the harmonic circles, in which the radii 1, 1', 2, 

 2', 3, 3', etc., are in harmonic proportion to the corresponding 

 radii of the apparent elliptic path of the star. 



The projection of this circle being itself an ellipse, the 

 direction of its major axis gives the line of nodes (the inter- 

 section of the plane of vision with that of the orbit), and the 

 foreshortening is in the direction of its minor axis, and is in 

 the proportion of its major and minor axes = that is as mm',, 

 is to mn'. The lines nn' and mm' serve as proportion 

 lines, on which are marhed off the spaces above or below 

 the line of nodes, which are set up at right angles to the 

 nodal line. Setting off the points P' A C' and ap. in this 

 way, we get P A C and Ap., the major axis of the real 

 orbit, of which A C is the eccentricity, from v.hich the 

 length of the minor axis O E. is deduced. A few more 

 points sets off similarly from various parts of the curve should 

 lie on the circumference of an ellipse, having P Ap. and O R 

 for its major and minor axes. This came out fairly well. 



I have laid off, about the apparent curve, a very few of the 

 actual observations from which the curve was obtained, with 

 dates, and the symbols of the observers My own observations 

 extend from about 1878 to the present time. The earlier 

 measures were made with a fine photographic reticle scale, in 

 squares of 1 -200th inch linear. The result proves such an 

 instrument quite inadequate for such delicate measurements, 

 the measures being manifestly wild. The later ones, from 

 1882*5 were taken with a nev/ microm,eter of my own, 

 designed specially for such work. A descripK;iou of this 

 apparatus may serve for a future paper if acceptable. The 

 measures by this instrument were very closely consistent, both 

 with themselves and with the curve. The measures embrace 



