by 15, will give the equatorial value of it in time. This multiplied by the cosine of any star's declination will give the effect of the error of collimation on the time of the star's transit.

The error of collimation is best measured by means of a movable vertical wire, to which motion is given by a micrometer screw, as described in another place.

Should no distant terrestrial object be visible from an observatory, owing to intervening objects near at hand, a small telescope in the building having its object glass turned towards that of the transit instrument may serve as a collimator. The rays of light proceeding from the wires at the focus of the object glass of the small telescope strike this object glass, are refracted by it, and emerge in parallel lines; they then strike the object glass of the transit instrument, and are conveyed to the focus of parallel rays, which is the astronomical focus; so that in looking through the eye end of the transit instrument the wires of the small telescope will be distinctly seen. Care should be taken to throw the light of a window or lamp in at the eye end of the small telescope. A similar contrivance may be employed for a meridian mark.

But the transit instrument may be made its own collimator, by placing a vessel of mercury underneath, and turning the object end of the telescope downwards. If the axis be horizontal, and the instrument truly collimated, the wires being illuminated by an orifice in the side of the eye piece, the rays of light will pass from them to the object glass, emerge in parallel lines, strike the surface of the mercury vertically, be reflected back in the same lines, and converge to the focus of the object glass at the same points which they left, so that the reflected image of the wires will be seen coinciding with the direct image. If not, there is either error of collimation or of level, or both. If the axis had previously been made horizontal by the striding level, it is the latter, and the diaphragm containing the wires must be moved till there is coincidence between their direct and reflected images; or a movable wire may serve to measure the interval between them. This interval is double the collimation error, because the angle of incidence is equal to the angle of reflection, the former being on one side the vertical, the latter on the other. If, therefore, the direct image of the wire be brought to the vertical by the screws of the diaphragm by a movement over half the distance between the direct and reflected image, the reflected image will be brought there too.

The striding level need not be used at all, if the instrument be reversed in the ya, in using the collimating eye piece with a basin of mercury; for in one position of the instrument the angle obtained by taking half the distance between the direct and reflected image of the wires is the sum, and in the reverse position is the difference of level error and error of collimation. The well-known algebraic formula, "to half the sum add half the difference for the greater of the two quantities, and from half the sum subtract half the difference for the less," will serve to determine those two errors separately. To know which is the greater, the level or collimation error, we have this rule:-If the reflected image in both positions appears on the same side of the direct, then the level error is the greater of the two, but if on different sides, the collimation error is the greater. All this will appear evident if the student make a diagram with a line to represent the supporting axis with level error exaggerated, a

line perpendicular to this at the middle, to represent true line of collimation, another line from the same middle point oblique to represent the erroneous line of collimation, a horizontal line below to represent the surface of the mercury, and from the point where the erroneous line of collimation meets it, a vertical and also a line making the same angle with it as does the erroneous line of collimation. In reversing the instrument the only change will be in the erroneous line of collimation, which will now make the same angle on the other side of the true.

The following example will serve to illustrate all the foregoing rules for applying the corrections to an observation with the transit instrument.

Multiplying this result by 3" the known value of a division of the level scale, we have 135 as the value of i the inclination of the supporting axis.

The correct siderial time being ascertained by the transit of a star of known right ascension, the correct mean solar time may be found from this, as follows:

The Nautical Almanac gives on p. XXII. of each month the mean time of transit of the first point of Aries, which is the zero of siderial time, and may be called from analogy the siderial noon. 1.* By means of this and the table of time equivalents, explained at p. 147, the mean solar time corresponding to any given siderial time, may be obtained by the following rule.

Mean solar time required = mean time at preceding siderial noon + the equivalent to the given siderial time.

EXAMPLE.

To convert 7* 11′′ 10'20 siderial time (the true time of meridian transit recorded above) March 8th, 1850, into mean solar time for the meriIdian of New York.

Mean time at preceding siderial noon, viz. March 8th,

056m 3074

To obtain the mean time of siderial noon at any place having a different longitude from Greenwich, it is necessary to subtract 98565 multiplied by the hours and fractions of an hour, by which the place differs in long. from Greenwich if the place be west, and to add this product if the place be east of Greenwich. As the daily gain of siderial time on solar is about 3m 56, this divided by 24 or 9-8565 will be the hourly gain or the hourly motion of the sun backward from west to east.

+ This is obtained by multiplying 9.856 by 4.94 the difference of longitude between New York and Greenwich. This correction may be applied here instead

The mean solar time may be obtained by direct observation of a meridian transit of the sun, which is made by taking the transit of each limb of the sun, that is to say observing the times when the sun's disc is tangent to the wires, both upon its western and eastern side, and taking a mean of the times as the time of transit of the sun's centre.*

Or more accurately by applying as a correction additively or subtractively to the observed time of transit of the limb the time occupied by the sun's semidiameter in passing the meridian, which is given for every day in the year in the Nautical Almanac, p. I. of each month.

To convert mean solar time into siderial the rule is as follows.

To convert 85" 4162 mean time at New York, into siderial time. Sider. time at preced. mean noon, Gr. viz., March 8th, 23' 3" 1998 Correction for long. N. Y.

+ 48 68

Sum sid. time required 7" 11" 1006+

The reasons for the above rules are sufficiently evident.

PROBLEM.

93. Given the latitude of the place, and the declination of a heavenly body, to determine its altitude and azimuth when on the six o'clock hour circle.

of to the mean time of siderial noon. Strictly the equivalent of 4863 in solar intervals should be applied, or 48.68 may be applied to the given siderial time additively before taking out the solar equivalents.

* A colored glass over the eye piece is necessary in observing the sun.

The sum amounting to more than 24, of course 24 must be rejected from it, as after reaching 241 the siderial time begins at zero again.