Progress of Astronomy during the Year 1879. 441 
an entirely new application of known processes. The method 
employed by Pontécoulant and others may be said to be the re- 
peated application of the following processes. A lengthy series 
of cosines or sines, with algebraical coefficients, is multiplied | 
by a similar series of cosines or sines with different algebraical 
coefficients, this multiplication being succeeded by reduction of 
the various coefficients to their simplest terms. In the lunar 
theory as developed hitherto, the great difficulty to subsequent 
workers is the impracticability of verifying the final results, and 
though in the case of Delaunay’s theory this is quite possible, still 
the task would be one of enormous labour, One of the principal 
differences between Mr. Neison’s system and those of his prede- 
cessors is, that this difficulty is overcome, and that the amount of 
computation has been reduced as far as possible. Every argument 
is represented by a fixed symbol, which indicates not only its 
origin, but the method by which it enters the theory. Every 
step is performed with these general symbols, and when the final 
result is obtained, it presents the solution as an explicit function 
of these general symbols. The values of these symbols are then 
substituted for them, the resulting coefficient is reduced to its 
simplest terms, and the complete value is obtained. 
Mr. Neison has reduced 1464 meridian observations of the 
. moon, made at Greenwich between 1862 and 1876, in order to 
determine the correction to Hansen’s coefficients of the annual 
equation, the mean longitude, and the terms depending on the 
distance and twice the distance of the sun from the perigee of the 
lunar orbit. He remarks, that the parallactic term, depending 
on the distance of the sun from the perigee of the lunar orbit, is 
well adapted for determining the solar parallax, being free from 
the liability to systematic error, which interferes so much with 
the use of the parallactic inequality. Hitherto, however, the 
result has not been quite satisfactory, viz. 91. The results 
obtained in the paper show that Hansen’s coefficient of the 
annual equation requires to be augmented by 0'°73.* 
A new theory of the recurrence of eclipses is contained in an 
important paper by Professor Newcomb, “On the recurrence of 
* Mr. Neison is continuing his researches on the lunar theory, and has ready for 
publication a second memoir containing the further development of the theory, by giving 
to each term its particular value, 
