Progress of Astronomy during the Year 1879. 469 
four inches aperture would show sufficiently well, are thus again 
and again being observed with fine refractors of six or seven inches 
aperture or upwards, while a very great number of stars are 
hardly ever if at all looked for. “Omit the observations of 
Dembowski and O. Struve, and our knowledge of nine-tenths of 
the double stars would not be materially advanced in the last 
thirty years.” Mr. Burnham has from the beginning shown that 
he does not follow the ordinary beaten track, and his numerous 
discoveries of close and difficult pairs have proved him to be an 
unusually sharp-sighted and attentive observer. In nine previous 
lists he had given the places of 482 new double stars, mostly 
rather difficult pairs, which few would have discovered with a 
6-inch refractor. The present (tenth) list of 251 new objects 
raises the total number of new double stars discovered by Mr. 
Burnham to 733; of these 251 stars, 75 pairs are less than 1" 
apart. His observations of old double stars embrace chiefly such 
ones which require a large aperture to be brought out well, or 
which have not been recently observed by others. Particular 
attention has also been paid to certain difficult pairs discovered 
by Mr. Alvan G, Clark. 
Mr. Burnham has already in the M.N. for December announced 
his further discovery of the duplicity of fifteen naked-eye stars, 
among which the quadruple system 86 Virginis and the triple 
system B.A.C. 4531 deserve special notice. 
No. 5 of the publications of the Cincinnati Observatory con- 
tains “ Micrometrical Measurements of 1054 Double Stars from 
January Ist, 1878, to September Ist, 1879.” These observations 
are partly made with a view to the preparation of a catalogue of 
all double stars between the equator and 30° south declination, 
partly in order to re-examine such objects as Mr. Burnham has 
found to need re-observing. These latter stars are not limited 
to the southern hemisphere. A few others have been entered in 
the working lists chiefly to aid in the investigation of personal 
equation between the director, Mr. Ormond Stone, and Mr. H. A. 
Howe. A great deal of trouble has been bestowed on the in- 
vestigation of this equation, which for position angle is expressed 
by the formulas =-a+w@+w* y+ ..., where a, P, y, &., depend 
on the observer and the angle with the vertical, while w is the 
reciprocal of the visual angle v, the latter being found by multi- 
