...power of analysis. A singular law obtains among the mean motions and mean longitudes of the first three satellites. It appears from observation that the mean...three times that of the second, plus twice that of the thin], is always equal to two right angles. It is proved by theory, that if these relations had only...

...are performed exactly in the same number of days. It has been found by La Place that " the epoch (or mean longitude) of the first satellite, minus three times that of the second, plus two times that of the third, is exactly equal to a semicircle, or 180 degrees." From this it follows,...

...Jupiter, the Earth and the Sun, reader the existence of pha»e« to any otuervable extent impossible. times that of the second, plus twice that of the third, is always equal to two right angles. Herschel, on attentively examining these satellites through the telescope, perceived that the intensity...

...power of analysis. A singular law obtains among the mean motions and mean longitudes of the first three satellites. It appears from observation that the mean...they are liable. They extend to the synodic motions (K. 92) of the satellites ; consequently they affect their eclipses, and have a very great influence...

...which latter is about half that of the revolution of the third. Again, the mean longitude of the first, minus three times that of the second, plus twice that of the third, is always equal to 180° : hence it results, that when the first satellite is eclipsed, the other two will always dispense...

...performed exactly in the same number of days. It has been found, by La Place, that "the epoch (ot.mean longitude) of the first satellite, minus three times that of the second, plus two times that of the third, is exactly equal to a semicircle, or 180 degrees." From this it follows,...

...three times the mean motion of the second. And the mean sydereal or synodical longitude of the first, minus three times that of the second, plus twice that of the thin!,, is always equal to two right angles. When the satellites fall into the shadow of the primary,...

...these three bodies approached very near to the relation which renders the mean motion of the first, minus three times that of the second, plus twice that of the third, equal to nothing. Then their mutual attraction, rendered this ratio rigorously exact, and it has moreover...

...attraction, rendered this ratio rigorously exact, and it has moreover made the mean longitude of the first, minus three times that of the second, plus twice that of the third, equal to a semi-circumference. At the same time, it gave rise to a periodic inequality, which depends...

...the time of that of the second ; the second half that of the third ; the mean longitude of the first, minus three times that of the second, plus twice that of the third, is always equal to 180°. Or the angular velocity of the first, added to twice that of the third, is equal to three times...