that the only true method of investigating the movements of the
heavenly bodies would be to carry on a protracted series of
measurements of their places. This, which now seems to us so
obvious, was then entirely new doctrine. Tycho at once commenced
regular observations in such fashion as he could. His first
instrument was, indeed, a very primitive one, consisting of a simple
pair of compasses, which he used in this way. He placed his eye at
the hinge, and then opened the legs of the compass so that one leg
pointed to one star and the other leg to the other star. The compass
was then brought down to a divided circle, by which means the number
of degrees in the apparent angular distance of the two stars was
determined.

His next advance in instrumental equipment was to provide himself
with the contrivance known as the "cross-staff," which he used to
observe the stars whenever opportunity offered. It must, of course,
be remembered that in those days there were no telescopes. In the
absence of optical aid, such as lenses afford the modern observers,
astronomers had to rely on mechanical appliances alone to measure the
places of the stars. Of such appliances, perhaps the most ingenious
was one known before Tycho's time, which we have represented in the
adjoining figure.

[PLATE: TYCHO'S CROSS STAFF.]

Let us suppose that it be desired to measure the angle between two
stars, then if the angle be not too large it can be determined in the
following manner. Let the rod AB be divided into inches and parts of
an inch, and let another rod, CD, slide up and down along AB in such
a way that the two always remain perpendicular to each other.