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On Certain Errors in Lunar Observations . [Odtober, 
I could test the accuracy of my observations by comparing 
the time found by the Lunar with the time shown by my 
chronometer. From these comparisons I discovered that, 
whilst under some conditions I obtained results which were 
corredt to within five seconds of time, under different con- 
ditions I obtained results which were twenty seconds or 
more in error. . , , 
Having used the same sextants in each case, and these 
sextants being in perfedt adjustment, I at first supposed that 
on some nights my eye was better suited for observation 
than it was on other nights, and that “ personal error ” was 
the explanation of erroneous results. 
I found, however, that when I had tabulated these enors, 
there appeared to be a law connedted with them, so I set to 
work to discover, if possible, some other solution of the 
mystery than that of personal error. _ 
On looking over the article on Lunars, in an early edition 
of the “ Encyclopedia Britannica,’ I saw it stated that 
some error existed, but where this error lay was not known. 
But the more perfedt the instrument, and the more accurate 
the observers, the more certain was the error to be mani- 
fested. To search for and find the solution of a paradox is 
always interesting, and although the Lunar observation and 
Geometry generally are now out of fashion, whilst vague 
theories and speculations are popular, I yet trust that some 
readers may take an interest in a novelty, though this is a 
geometrical one. ... f 
I will first endeavour to explain the principle ot the 
Lunar. . . 
The Moon moves by its own independent motion from 
west to east round the Earth, its rate of movement being a 
little more than 13 0 in the twenty-four hours. If, then, the 
Moon was coincident with a star at (say) 9 p.m. on a given 
night, and moved direaiy away from this star, then on the 
following night the Moon at 9 p.m. would be slightly more 
than 13° to the east of this star. The star being fixed, 
whilst the Moon moves, causes the Moon to adt like the 
hand of a clock, whilst the star remains fixed like a mark 
on a disc. . _ .. ^ f ,, 
By measuring and calculating the exadt distance ot the 
Moon, from the Sun or from certain stars, we are provided 
with one item ; the other item being— knowing what the 
exadt distance of the Moon is from the Sun, or star, at 
certain instants of Greenwich time. 
How the distance of the Moon from the Sun, or from 
certain stars, is given in the “Nautical Almanac,” for 
