178 ADDRESS DELIVERED BY THE PRESIDENT ON PRESENTING THE [579 
the Earth’s orbit—thus 13 or more observations, when compared with any theory, 
should suffice to correct the errors of that theory. But the observations extending 
only over a short interval, say one month, the coefficients would be so minute as to 
give no trustworthy value of the corrections; the equations only suffice to determine 
a few functions of the elements which, being determined, the equations will be satisfied 
by widely differing values of the elements, if only these values are such as to give 
to the functions their right values. And by fixing a priori the entire number of 
functions in question, and using them in place of the elements of the Earth and 
Mars, the equations will be practically as rigorous as if all the 13 unknown quantities 
had been introduced. By such considerations as these, each observation is made to 
give a relation between only 3 unknown quantities, the correction of the Sun’s parallax 
being one of them. 
The principle appears to be one of extended application, in regard to the proper 
mode of dealing with the constantly recurring problem of the determination of a set 
of corrections from a large number of linear equations; and it is used by the author 
in regard to the equations which present themselves in his theories of Neptune and 
Uranus. 
Returning to the Mars observations, these were made at six Northern and three 
Southern Observatories, the total number being 154 Northern, and 143 Southern, together 
297 observations. There was the difficulty of reducing to a concordant system the 
observations at the different Observatories, since (the whole number of comparison stars 
not being observed on each night) the adopted mean position of each of them was 
not unimportant. But this being carefully discussed and allowed for, the observations, 
extending from August 21 to November 3, 1862, are divided into five groups, and 
from these is deduced a correction to the provisional value 8"’9 of the parallax. The 
author then reproduces or discusses other determinations, from micrometric observations 
of Mars, the parallactic inequality of the Moon, the lunar equation of the Earth, the 
transit of 1769, and Foucault’s experiment on Light—the last result, as not a strictly 
astronomical one, and with no means of assigning its probable error, is left out of 
consideration—and the combination of the remaining ones gives the author’s concluded 
value of the parallax; from which other astronomical constants are deduced. 
“ On the Right Ascensions of the Equatoreal Fundamental Stars and the Correct 
ions necessary to reduce the Right Ascensions of different Catalogues to a mean 
homogeneous System,” Washington Observations for 1870, Appendix III., pp. 1—73. 
This important Memoir is referred to in the Council Report for 1873. The object 
is to do for the right ascensions of the equatoreal and zodiacal Stars what had been 
done by Auwers for the declinations, namely, to furnish the data necessary to reduce 
the principal original catalogues of stars to a homogeneous system by freeing them of 
their systematic differences. The results are contained in two tables of corrections (as 
depending on the R.A. and N.P.D. respectively) to the several catalogues ; and in a 
table of concluded mean right ascensions for the beginning of each fifth Besselian year,