14. 



ON THE ORBIT OF 7 VIRGINIS. 

 [From jEdes HartwelliancB, Letter to Admiral Smythe, June, 1851.] 



I HAVE great pleasure in sending you the results which I have obtained 

 respecting the orbit of y Virginia, and I feel the more indebted to you 

 for having called my attention to the subject, inasmuch as the problem of 

 determining the orbits of double stars is one with which I had previously 

 only a theoretical acquaintance. The orbit, given by Sir John Herschel in 

 the Eesults of his Cape Observations, was taken as the basis of the cal- 

 culations, and equations of condition for the correction of the elements were 

 formed by comparing certain selected angles of position deduced from ob- 

 servation with the values calculated by means of Sir John Herschel's elements. 



The positions employed are those given by Bradley's observation in 1718, 

 Sir William Herschel's observations in 1781 and 1803, a normal position for 

 1825 deduced from the observations of 1822, 1825, and 1828, one for 1833 

 from the observations of 1832, 1833, and 1834, another for 1839 from the 

 observations of 1838, 1839, and 1840, and, lastly, a normal position for 1848 

 from the observations of 1846, 1847, 1848, 1849, and 1850. The number 

 of these positions being greater by one than that absolutely necessary for 

 the determination of the elements, I at first omitted the equation of con- 

 dition for 1718 and solved the remaining ones in such a manner as to 

 shew the effect which would be produced in each of the elements by a 

 small given change in any one of the observed angles of position. The 

 result proved that the elements would be greatly affected by small errors 

 in the observed positions for 1781 and 1803, and I therefore called in the 

 observation of 1718 to the rescue, and solved the equations anew, supposing 

 the positions for 1825, 1833, 1839, and 1848 to be correct, and distributing 

 the errors among the other three, according to the rules supplied by the 

 method of least squares, giving double weight to the observations of 1781 

 and 1803. 



