photography. This enabled him to get the best result with stars of
different brightness. The telescope not having been invented, he
could not use a telescopic-sight as we now do in gunnery. This not
only removes the difficulty of focussing, but makes the minimum
visible angle smaller. Helmholtz has defined the minimum angle
measurable with the naked eye as being one minute of arc. In view of
this it is simply marvellous that, when the positions of Tycho's
standard stars are compared with the best modern catalogues, his
probable error in right ascension is only +/- 24", 1, and in declination
only +/- 25", 9.

Clocks of a sort had been made, but Tycho Brahe found them so
unreliable that he seldom used them, and many of his position-measurements
were made by measuring the angular distances from known stars.

Taking into consideration the absence of either a telescope or a
clock, and reading his account of the labour he bestowed upon each
observation, we must all agree that Kepler, who inherited these
observations in MS., was justified, under the conditions then
existing, in declaring that there was no hope of anyone ever improving
upon them.

In the year 1572, on November 11th, Tycho discovered in Cassiopeia a
new star of great brilliance, and continued to observe it until the
end of January, 1573. So incredible to him was such an event that he
refused to believe his own eyes until he got others to confirm what he
saw. He made accurate observations of its distance from the nine
principal stars in Casseiopeia, and proved that it had no measurable
parallax. Later he employed the same method with the comets of 1577,
1580, 1582, 1585, 1590, 1593, and 1596, and proved that they too had