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observed by Maraldi was relative only, and due to the projection 
of the satellite on a brighter part of Jupiter’s disc (which we 
know to be subject to partial variations of brilliancy) than that 
the whole or nearly the whole hemisphere of a satellite should 
suffer change in the manner imagined. The fact that the 
satellite appears smaller than the shadow, so far from being 
contrary to the laws of optics, as many have supposed, is directly 
deducible from those laws. The black umbra should indeed be 
smaller, but the complete shadow formed of umbra and pen- 
umbra together, should be larger than the satellite. 
I may notice in passing, that observations having reference 
to the relative brilliancy of celestial objects are at all times 
difficult, but that those made towards the end of the seventeenth, 
and in the earlier part of the eighteenth century, appear 
specially unreliable. Whether from the use of unwieldy focal 
lengths, or from imperfection in the single object glasses, or 
from a want of thorough appreciation of irregularities due to 
atmospheric causes, certain it is that there are recorded a mul- 
titude of observations of this sort in the interval named, which 
have not been confirmed by subsequent observation. 
Soon after his discovery of Jupiter’s satellites, Gfalileo per- 
ceived the use to which the phenomena they presented might 
be applied for the determination of the longitude. He was 
sanguine indeed, as to the use of this method for finding the 
longitude at sea, not being aware, it would seem, of the mecha- 
nical difficulties which render the method unavailable on ship- 
board. With the object of constructing tables of the satellites’ 
motions, he observed them for many years. The Tables he 
formed disappeared unaccountably on the death of his pupil 
Kimieri, to whom he had entrusted them for publication, and 
were accidentally discovered a 'few years ago in a private library 
at Eome. Notwithstanding the amount of labour bestowed 
upon them, the Tables are far from representing with, accuracy 
the motions of the satellites. Gfalileo, indeed, and those who 
followed him in attempting the work of tabulating these motions, 
altogether underrated the difficulty of the task. A long series 
of observations by Hodierna, Borelli, Passim, Maraldi, Bradley, 
and a host of other observers, the rigid theoretical scrutiny of 
the subject by Newton, Walmsley, Euler, Bailly, Lagrange, 
Laplace, and others, and a laborious comparison of the results 
of observation and theory, by Lalande, Wargentin, Delambre, 
and Woolhouse, have been required to bring the theory of the 
system to the exactness and accuracy it has now attained. 
The relations actually presented by the motions of the 
planets are very singular. They are partly exhibited by the 
following Table : — 
