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Updated: June 19, 2025
In order to understand these forms and qualities in their purity it is necessary to separate them from their content and thus one gets the point, without dimensions, the line, without breadth and thickness, a and b, x and y, constants and variables, and we finally first arrive at independent creations of the imagination and intellect, imaginary magnitudes.
The magnitudes are six and a half, seven, and ten, distances 0.3", p. 216°, and 22", p. 62°. In the Pleiades we naturally turn to the brightest star eta, or Alcyone, famous for having once been regarded as the central sun around which our sun and a multitude of other luminaries were supposed to revolve, and picturesque on account of the little triangle of small stars near it which the least telescopic assistance enables us to see.
Every number is finite and specific; every line is so likewise, and the infinite or infinitely small signify only magnitudes that one may take as great or as small as one wishes, to show that an error is smaller than that which has been specified, that is to say, that there is no error; or else by the infinitely small is meant the state of a magnitude at its vanishing point or its beginning, conceived after the pattern of magnitudes already actualized.
In trying to describe the great pines and sequoias of the Sierra, I have often thought that if one of those trees could be set by itself in some city park, its grandeur might there be impressively realized; while in its home forests, where all magnitudes are great, the weary, satiated traveler sees none of them truly. It is so with these majestic rock structures.
Observations of the changeable Brightness of the Satellites of Jupiter, and of the Variation in their apparent Magnitudes; with a Determination of the Time of their rotary Motions on their Axes, to which is added a Measure of the Diameter of the Second Satellite, and an Estimate of the comparative Size of the Fourth. Phil. Trans., vol. lxxxviii.
Since Herschel's time, the number of these minor planets known to astronomers has increased to upwards of one hundred. With respect to Jupiter, our astronomer arrived at some important facts in connection with the duration of its rotation. He also made numerous observations on the intensities and comparative magnitudes of its satellites.
But it is now becoming more and more understood that to establish the relations which exist between physical magnitudes, and to represent the variations of these magnitudes by functions which allow us to use the power of mathematical analysis, it is most necessary to express each magnitude by a definite number. Under these conditions alone can a magnitude be considered as effectively known.
There is considerable diversity of opinion on this point. Some say the larger star is pale red and the smaller light blue; others consider the color of the larger star to be greenish, and some have even called it white. The magnitudes are five and nine, distance 6", p. 350°. Auriga contains several noteworthy clusters which will be found on the map.
On the 12th of January, he again observed them in new positions, and of different magnitudes; and, on the 13th, he discovered a fourth star, which completed the four secondary planets with which Jupiter is surrounded.
When the limit of separating power for a telescope of a particular aperture is set at 1" or 2", as the case may be, it is assumed that the stars composing the doubles on which the test is made shall be of nearly the same magnitude, or at least that they shall not differ by more than one or two magnitudes at the most.
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