In yielding himself up, however, to his love of astronomy, he found that he had several difficulties to overcome. He belonged to a class in society elevated, in the opinion of that age, above the pursuit of knowledge, and jealous of the privilege of remaining igno rant with impunity. Tycho Was of a noble family in Denmark, so that it required all the enthusiasm and firmness inspired by•the love of knowledge, to set him above the prejudices of hereditary rank, and the opposition of his relations. He succeeded, however, in these objects, and also in obtaining the patronage of the King of Denmark, by which he was enabled to erect an observatory, and form an establishment in the island of Huena, such as had never yet been dedicated to astronomy. The instruments were of far greater size, more skilfully contrived, and more nicely divided, than any that had yet been directed to the heavens. By means of them, Tycho could measure angles to ten seconds, which may be accounted sixty times the accuracy of the instruments of Ptolemy, or of any that had belonged to the school of Alexandria.
Among the improvements which he made in the art of astronomical observation, was that of verifying the instruments, or determining their errors by actual observation, instead of trusting, as had been hitherto done, to the supposed infallibility of the original con struction.
•0ne of the first objects to which the Danish astronomer applied himself was the forma lion. of a new catalogue of the fixed stars. That which was begun by Hipparchus, and continued by Ptolemy, did not give the places of the stars with an accuracy nearly equal to that which the new instruments were capable of reaching ; and it was besides desirable to know whether the lapse of twelve centuries had produced any unforeseen changes in the heavens.
'The great difficulty in the execution of this work arose from the want of a direct and easy method of ascertaining the distance of one heavenly body due east or west of an other. The distance north or south, either from one another or from a fixed plane, that of the equator, was easily determined by the common method of meridian altitudes, the equator being a plane which, for any given place on the earth's. surface, retains always the same position. . But no plane extending from north to south, or passing through poles, retains a fixed position with respect to an observer, and, therefore, the same way of measuring distances from such a plane cannot be applied. The natural substitute is the measure of time ; the interval between the passage of two stars over the meridian, bearing the same proportion to twenty-four hours, that the arch which measures their distance perpendicular to the meridian, or their difference of right ascension, does. to four right angles.
An accurate measure of time, therefore, would answer the purpose, but such a measure no more existed in the age of Tycho, than it had done in the days of Hipparckus or Ptolemy. These ancient astronomers determined the of the fixed stars by re ferring their places to those of the moon, the longitude of which, for a given time, was known from the theory of her motions. Thus they were forced to depend on the most
irregular of all the bodies in the heavens, for ascertaining the positions of the most fixed, those which ought to have been the basis of the former, and of so many other determine,. tions. Tycho made use of the planet Venus instead of the moon, and his method, though more tedious, was more accurate than that of the Greek astronomers. His catalogue con.
• tabled the places of 777 fixed stars.
The irregularities of the moon's motions were his next subjects of inquiry. Tlie an cients had discovered the inequality of that planet depending on the eccentricity of the orbit, the same which is now called the equation of the centre.' Ptolemy had added the knowledge of another inequality in the moon's motion, to which the name of the eveotion has been given, amounting to an increase of the former equation at the quarters, and a diminution of it at the times of new and full moon. Tycho discovered another inequality, which is greatest at the octants, and depends on the difference between- the longitude of the moon and that of the sun. A fourth. irregularity to which the moon's motion is subject, depending wholly on the sun's place, was known to Tycho, but included .timong the sun's equations. Besides, these observations made him acquainted with the changes in the inclination of the plane of the moon's orbit ; and, lastly, with the irregular mo. don of the nodes, which, instead of being always retrograde at the same rate, are sub . ject to change that rate, and even to become progressive according to their situation in respect of the sun. These are the only inequalities of the moon's motion known be. • fore the theory of Gravitation, and, except the two first, are all the discoveries of Tycho.
The atmospherical refraction, by which the heavenly bodies are made to appear more elevated above the horizon than they really are, was suspected` before the time of tip M astronomer, but not known with certainty to exist. He first became aequainted with it by Lading that the latitude of his observatory; as determined from at the solstices, and from observations of the greatest and least altitudes of the cireampolar stars, always differed about four minutes. The effect of refraction he supposed to be 84' at the horizon, and to diminish from thence upward, till at 45° it ceased altoge. Cher. This last supposition is erroneous, but at 45° the refraction is less than 1, and probably was not sensible in the altitudes measured with his instrament4 or not die. tinguishable from the errors of obseriation. An instrument which he contrived on par. pose to make the refraction distinctly visible, shows the scale on which his observatory was furnished. It was an equatorial circle of ten feet diameter, turning on an axis pa. mllel to that of the earth. With the sights of this equatorial he followed the sun on the day of the summer solstice, and found, that, as it descended towards the horizon, it rose . above the plane of the instrument. At its setting, the sun was raised above the horizon by more than its own diameter.