470 Scientific Proceedings, Royal Dublin Society. 
plying the distance in seconds of are by the ratio between the 
power used and a certain standard power. In observations of 
distance any apparent displacement caused simply by personal 
peculiarities is supposed to produce an effect inversely pro- 
portional to the magnifying power ; if » be the reciprocal of the 
power, the equation in distance is therefore « = p (a’+v B'+v" 
y +...). The mean results have also been compared with W. 
Struve’s Mensuree Micrometricee. .Though the discovery of new 
double stars has only been considered a secondary object, nearly 
200 new pairs have been detected during the progress of the work 
at Cincinnati. The measures are all given in full detail and 
occupy 151 pages; the mean results are given separately. The 
whole forms a carefully prepared volume printed with the 
elegance usual in American publications. 
The systematic errors in measures of double stars have been 
investigated by Professor Thiele in a paper: “Castor, Calcul du 
mouvement relatif et Critique des observations de cette étoile 
double” (Copenhagen. 1879). The author has chosen Castor 
partly because the orbital motion is slow and can be represented 
by a simple formula of interpolation, partly because it has been 
very frequently measured by almost all observers of double stars. 
First, three normal places were formed which represented the 
distances and position angles observed since 1815, and an angle of 
position from Bradley’s and W. Herschel’s measures. From these 
and the ratio of the sector to the time formule for computing 
distance and position angle as functions of time by means of the 
eccentric anomaly were derived and an ephemeris computed from 
1718 to 1900. With this ephemeris all individual observations 
by every observer were compared and the mean error determined 
for every observer within such a period during which he might 
be supposed not to have changed his way of measuring. Every 
observer is now followed from one period to another and the 
changes in the mean error determined, whereby variations in his 
systematic error would reveal themselves. 
Dr. Seeliger has made an elaborate examination of Madlet’s 
measures (A.N. 2288). Ma€dler’s distances appear to be con- 
siderably less accurate than O. Struve’s, while his position angles 
do not appear to have larger mean errors than than those of QO. 
Struve, The results of a direct comparison between Madler’s 
