12. Since the sidereal day is thus the standard of our measures of time, it becomes desirable to refer to it, constantly and exactly, the instruments by which time is measured, in order that we may secure ourselves against errour. For this purpose, in astronomical observatories, observations are constantly made of the transit of stars across the meridian; the _transit instrument_ with which this is done being adjusted with all imaginable regard to accuracy[5\3]. [Note 5\3: On the precautions employed in the measure of time by astronomers, see Herschel's _Astronomy_, Art. 115-127.] 13. When exact measures of time are required in other than astronomical observations, the same instruments are still used, namely, clocks and chronometers. In chronometers, the regulating part is an oscillating body; not, as in clocks, a pendulum oscillating by the force of gravity, but a wheel swinging to and fro on its center, in consequence of the vibrations of a slender coil of elastic wire. To divide time into still smaller portions than these vibrations, other artifices are used; some of which will be mentioned under the next head. 14. (IV.) _Conversion of Space and Time._--Space and time agree in being extended quantities, which are made up and measured by the repetition of homogeneous parts. If a body move uniformly, whether in the way of revolving or otherwise, the _space_ which any point describes, is _proportional_ to the _time_ of its motion; and the space and the time may each be taken as a measure of the other. Hence in such cases, by taking space instead of time, or time instead of {153} space, we may often obtain more convenient and precise measures, than we can by measuring directly the element with which we are concerned. The most prominent example of such a conversion, is the measurement of the Right Ascension of stars, (that is, their angular distance from a standard meridian[6\3] on the celestial sphere,) by means of the time employed in their coming to the meridian of the place of observation. Since, as we have already stated, the visible celestial sphere, carrying the fixed stars, revolves with perfect uniformity about the pole; if we observe the stars as they come in succession to a fixed circle passing through the poles, the intervals of time between these observations will be proportional to the angles which the meridian circles passing through these stars make at the poles where they meet; and hence, if we have the means of measuring time with great accuracy, we can, by watching the _times_ of the transits of successive stars across some visible mark in our own meridian, determine the _angular distances_ of the meridian circles of all the stars from one another. [Note 6\3: A _meridian_ is a circle passing through the poles about which the celestial sphere revolves. The meridian _of any place_ on the earth is that meridian which is exactly over the place.]