THE ORBIT OF NEPTUNE. 45 



1862 with those of Greenwich, it would seem that the meridian circle of Pulkowa 

 gives declinations an entire second farther south than those of the great transit 

 circle ; so that had the Pulkowa instrument been employed on fundamental stars, 

 their declinations would have been 2" less than Wolfers'. On the other hand, the 

 Cambridge (Eng.) mural circle places the fundamental stars even farther north 

 than Wolfers, and the Washington mural nearly as far north. 



It is foreign to our present purpose to speculate upon the causes of these dis- 

 crepancies ; we are concerned only with their existence and amount. Their 

 existence renders it absolutely necessary to correct the declinations as well as the 

 right ascensions in order to reduce them to a common standard ; and no obser- 

 vations have been used unless data for these corrections could be obtained. 



This rule necessitates the entire rejection of nearly all the vast mass of obser- 

 vations on which Walker's theory was founded. In the case of the micrometric 

 comparisons, no sufficient data seem to exist for determining the positions of the 

 comparison stars ; the results are, therefore, heterogeneous in their character. 

 However valuable they might have been when made, it will not be admissible, 

 to combine them with the fifteen years of meridian observations made since. 

 Micrometric observations were almost given up after 1850, and the planet was left 

 to be followed by the meridian instruments of the larger observatories. The 

 superior accuracy of this class of observations may be inferred from the fact that 

 the comparatively small error in Walker's radius vector is made evident by them 

 even during the period of construction of Walker's theory. 



A similar remark applies to the meridian observations. Four years of obser- 

 vations made at a great number of observatories may be indiscriminately combined 

 on the supposition that the systematic as well as the accidental errors will destroy 

 each other, particularly if each series extends through the entire period. But, as 

 few or none of these series made at observatories able to publish any thing but 

 their results are continued later than 1849, it will not do to assume that the mean 

 of their systematic errors, as fixed by the standard we have assumed, would vanish. 



The observations which fulfil the conditions we have indicated are made at 

 observatories, as follows : 



Ancient observations. 

 Paris, by Lalande, May 8 and 10 1795. 



Modern observations. 



Greenwich, 1846 to 1864. 



Cambridge, 1846 to 1857. 



Paris, 1856 to 1861. 



Washington, 1846 to 1850. 



Washington, 1861 to 1864. 



Hamburg, 1846 to 1849. 



Albany, 1861 to 1864. 



22. Reduction of Lalande s two observations of Neptune, May 8-10, 1795. 

 The first of these observations is found in the Comptes Rendus, tome 24, p. 667. 

 The second is in the Histoire Celeste, p. 158, and is the eighth star of the firsf 



