52 
5 idereal A s tvonomy . 
[January, 
contrary, endeavoured afterwards to simplify the calculations, 
and published, in the 61 Memoirs of the Astronomical Society 
of London, ” a method almost entirely graphic, still leaving, 
however, much complication in the final formulae. Suc- 
cessively the astronomers Bessel, Madler, Hind, Smith, 
Villarceau, De Gasparis, Wolf of Zurich, and Klinkerfues 
proposed analytical methods, all of which necessitate the 
longest and most exaCt calculations. A little disheartened 
by these complications, and being convinced that they were 
not necessary to obtain accurate results (the measure- 
ments of double stars not themselves admitting of this 
precision), I tried, in 1874, to solve these problems more 
simply, and to find graphically the absolute orbit from the 
apparent orbit by the assistance of simple trigonometrical 
formulae. 1 have succeeded, and this method is not only 
incomparably more simple, but even more sure, than the 
preceding, although it does not pretend to the same degree 
of precision.* 
The historical series of these labours shows how science 
has progressed in less than a century to the profound 
knowledge of the partial stellar systems, and above all of 
binary systems. 
III. Nature of Double Stars. 
When a star shows itself double in the field of a tele- 
scope, it is not certain on that account that it is a true 
double star of which the components are associated. The 
junction observed maybe merely an effect of perspective, and 
one of the two stars may be in reality very far behind the 
other in space, although found on the same visual ray. In 
* My method does not give the period in thousandths of a year, but the 
principal number is exad. Thus, for example, the preceding methods have 
given, with pretension to the thousandth of a year (which I abstain from re- 
producing), the following periods for a Corona : — 
737 years .. .. Hind. 
608 ,, Maedler. 
420 ,, Klinkerfues. 
240 ,, e . Powell. 
195 Jacob. 
843 ,, Darerck. 
Evidently of these six periods five at least are imaginary. These calculations 
— in which the method of least squares plays the principal part — ad blindly, 
and give mechanically divers results, according to the figures which are mani- 
pulated. Thus no greater precision must be attached to micrometric results 
than they deserve. For y Virginis we have results which vary from 629 years 
to 139. My method gives 175 years, to nearly half a year, and it cannot be 
wrong. But it cannot be applied to couples for which the measurements are 
insufficient. 
