On the ^ariy Babylonian Eclii^se of the Sun. 255 
of the moon's mean longitude must be increased by 0-32°, corresponding 
to an increase in the value of the secular acceleration in mean longitude 
of 1-48", thus bringing it up from 6'18" to 7-56". But this would increase 
the latitude of the point where the path of the eclipse crossed the meridian 
of Babylon from 34-4:° to over 38°, so that it would no longer correspond 
with the observed phenomenon. To bring the eclipse into accord with 
the recorded phenomena, it would be necessary to suppose the longitude 
of the moon's node to be also increased by double this amount, or its 
secular acceleration to be increased by about 3", bringing its value up to 
about 9-5", which is fully 2" greater than can be deduced from the more 
modern observations. 
The adopted theoretical elements of the moon's orbit, even when 
amended by increasing the secular motion of the perigee and node, does 
not represent the modern observations since 1660 with the closeness 
which is desirable. To enable these modern observations to be properly 
represented it is necessary to apply small corrections to nearly all the 
elements. The system, of corrections which serves best to bring these 
observations into accord with the tables, if we suppose the theoretical 
value of the moon's secular acceleration in mean longitude to remain 
unchanged, is — 
AZ=-11-6"T +0-00"T^ +00000"T3 
AA=+22-5 +636 +0-0064 
-AB- + 28-8 +0-77 -0-0007 
but if the value of the secular acceleration in mean longitude be deduced 
directly from the observations, as well as the values of the other elements, 
then the system of corrections which best represents the observed places 
of the moon is — 
Ai=-12-7"T +1-25"T= +0-0012"T3 
AA = +22-5 +6-36 +0-0064 
— AB = +40-0 -0-77 -0-0007 
and the modern observations can be represented by any system of correc- 
tions lying between these two, and as far as these observations are 
concerned any such system may be regarded as permissible. 
Professor Newcomb deduced the system of corrections — 
AZ=-10-0"T +1-77"T= +0-0015"T3 
AA = +ll-8 +0-68 -0-0055 
-AB = +23-9 +0-12 -0-0003 
but this system depends on a very large empirical term of long period, for 
whose argument there can be no theoretical justification, and which fails 
to represent the observed values with sufficient closeness. 
Another system has been deduced by Dr. Cowell from the observations 
