An introduction to mathematics, by A. N. Whitehead.

TRIGONOMETRY 175
great instrument for the exact measurement
of the times at which stars are due south or
due north. But indirectly this instrument
measures angles. For when the time elapsed
between the transits of two stars has been
noted, by the assumption of the uniform
rotation of the earth, we obtain the angle
through which the earth has turned in that
period of time. Again, by other instruments,
the angle between two stars can be directly
measured. For if E is the eye of the astronoA
B
Fig. 22.
mer, and EA and EB are the directions in
which the stars are seen, it is easy to devise
instruments which shall measure the angle
AEB. Hence, when the astronomer is forming a survey of the heavens, he is, in fact,
measuring angles so as to fix the relative
directions of the stars and planets at any instant. Again, in the analogous problem of