1853.] OF THE ROYAL INSTITUTION. 247 
Secondly, in the observations from which are determined the 
elements that are to be combined with theory. Upon the same 
principle by which it was shewn that the track of shadow in one 
eclipse depends upon the track of shadow in another eclipse, it will 
be easily seen that the track of shadow in a distant eclipse will 
depend upon the observed elevation of the moon in the beginning of 
the modern period of comparatively accurate astronomy; (for that 
elevation determines the place of the node; and an error in the 
elevation produces an error in the computed place of the node for 
that time; and this exhibits an error in the annual motion of 
the node; and that error carried through the long period to a 
distant eclipse produces a very great error in the place of the 
node there, and consequently in the track of the shadow). Ifa 
ladder of centuries be constructed, each stave corresponding to a 
century, the extent of tolerably accurate and well-reduced ob- 
servations of the moon (1750 to 1830) is represented by only 
4 of an interval of staves. Thus it appears that an error of two 
seconds in Bradley’s observations (the angle which a finger-ring 
subtends at the distance of a mile, and which is smaller than can be 
perceived by the unassisted eye) would destroy our conclusions with 
regard to the distant eclipses in question. The fault in the principle 
of the Greenwich instrument used for observing the elevation of 
the moon (namely a quadrant, the use of which was for many 
years the bane of astronomy), and the slovenly way of using it 
in Bradley’s time (no attention being given to the taking the 
elevation of the moon at the precise instant of her passing the 
meridian, though her elevation then changes rapidly) might well 
allow of this error. The Lecturer stated that both in the careful 
examination of the principles on which instruments are constructed, 
and in the rigorous attention to the proper rules for their use, it 
might be hoped that great improvement would be found in modern 
times. 
In consequence of these causes of uncertainty, it becomes very 
desirable, in the investigation of the eclipse of Thales, to correct 
the elements of the moon’s motions by some other well deter- 
mined eclipse. Omitting the eclipses since the year 1200 A.D., and 
two in the second century B.C. which are somewhat discordant, 
there are two eclipses of peculiar value. One is the eclipse at the _ 
battle of Stiklastad at which Olaf king of Norway was killed, A.D 
1030, August 31; in which the precise spot is known, and the pre- 
cise position of the moon is known (the breadth of the shadow being 
very smal], inasmuch as, when the eclipse commenced on the earth, 
it was annular). The only objection is, that if there is any uncer- 
tainty in the secular change of mean motions, the adjustment of the 
mean motions to represent the eclipse of Stiklastad will still leave a 
large uncertainty on an eclipse about 1600 years before it. Using 
the illustration of the ladder of centuries, it is like fixing the ladder 
at the bottom and at a point at one third of its height, which fasten- 
