the meridian be observed, as indicated by the instrument. Then, if the interval between the inferior and superior passage be equal to the interval between the superior and infe rior, the adjustment to the meridian is perfect; but if the interval between the inferior and superior passage be less than the interval between the superior and inferior, the circle described by the line of collimation deviates to the eastward of the true meridian, from the zenith to the north point of the horizon, and to the westward, from the zenith to the south point of the horizon; while if the interval between the inferior and superior passage be the greater, the deviation is in the contrary directions.

Let & be the observed difference of the intervals from twelve hours, or half the difference between the two intervals in seconds, the polar distance of the star Polaris, and L the latitude of the place, then, z representing the deviation from the meridian in time, the value of z will be given by the logarithmic formula,

log. z= = log. +log. sec. L+ log. tan. ø — - 20.

2

EXAMPLE.

Place of observation, Cambridge, latitude 52° 12′ 36′′.
Polar distance of Polaris, 1° 39′ 25′′ 05.

Difference of intervals from 12 hours 7m 22° -4423.

*

To determine the value of a revolution of the azimuthal screw, s, the time of passage of an equatorial star across the middle vertical wire must be noted one day; and then, turning the screw, s, once round, the time of passage must be noted again; and the difference of these times will be the value in time of a revolution of the screw. Suppose the difference thus observed to amount to two seconds, then the value of one complete revolution of the screw, s, is two seconds, and the value of the motion of the adjusting screw being thus obtained, must be reduced to the horizon, by increasing it in the ratio of cosine of latitude to radius, and may then be ap plied to correct the error of deviation as found above.

*The time here spoken of, and throughout the description of this instru ment, unless otherwise expressly stated, is sidereal, and not mean time.

A second method, founded on the same principles as the preceding, consists in observing the pole star, and another star, which crosses the meridian near the zenith of the place of observation. The time of passage of such a star, Capella, for instance, when near its superior transit, across the middle wire of the telescope, will differ but very little from the time of passing the true meridian, if the deviation of the instrument from the meridian be but small. Assume the two times to agree exactly, and the difference between the times of superior transit of Capella and Polaris will be the difference of the observed right ascensions of these two stars. From this difference subtract the difference of the computed, or catalogued, right ascensions of the two stars, and call the result D; and the deviation will be given by the formula,

log. z = log. D + log. sin. + log. sec. (L + π) ;

being the polar distance of Polaris, and L the latitude of the place of observation. From Capella not having been exactly on the meridian, when on the middle vertical wire, the value of D, as above obtained, is only an approximation to the error of the observed right ascension of Polaris, and the deviation computed from it will be only approximately correct; but, by repeating the operation, the adjustment may be completely perfected.

D is actually the value of the sum of the errors of the observed right ascensions of Capella and Polaris, and hence the value of z will be correctly given, by so considering it, instead of supposing as above, that this error for Capella is zero. The true deviation then is given by the formula, log. z = log. D+ log. sin. +log. sin. '+log. cosec. ('

log. sec. L;

being the polar distance of Capella. Using this last formula, the method may be applied to Polaris, and any star distant from the pole, or to any two stars differing from each other not less than 40° in declination. If, however, the transit of one star is observed above, and of the other, below the pole, the formula will be

log. z =

log. D+ log. sin. + log. sin. '+log. cosec. ('+ ) + log. sec. L. Considerable advantage may be obtained by selecting two stars that differ but little in right ascension, as there is then the less probability of error from a change in the rate of the clock, or in the position of the instrument, on which account such methods are to be preferred in temporary observatories, where the stability of the instrument is not to be depended upon for any length of time.

In all the preceding formulæ, the deviation from the meridian is given in time; but, to convert it into angular measure, if desirable, we have only to multiply by 15, and the seconds of time will be converted into seconds of a degree.

When the instrument is by any of the methods explained above brought into the meridian, a distant mark may be set up in the plane of the meridian, by which the adjustment to the meridian may afterwards be tested.

METHOD OF OBSERVING WITH THE TRANSIT.

The adjustments having been completed, in making observations with the instrument, the instant of a star's passing the middle vertical wire will be the time of the star's transit; but the time of the star's passing all the five wires must be noted, and the mean of the times, taken as the time of transit, will be a more accurate result than the time observed at the middle wire only.

When the sun is the object observed, the time of the center of his disc passing the middle wire is the time of transit; but, as it would be impossible to estimate the center with accuracy, the time of both his limbs coming into contact with each wire in succession is to be noted, and a mean of all these times will be the time of transit required. This mean may be conveniently taken, by writing the observed times of contact of the first and second limbs underneath each other in the reverse order, when the sums of each pair will be nearly equal *.

The time of either limb passing the center wire is recorded in full, but for the other wires, the seconds only are recorded, as the sums of the several pairs only differ by decimals of a second. Half the sum of the times at the middle gives, then, the correct time of transit as far as the seconds, and the decimals are found by removing the decimal point one place to the left in the sum 13.2, which is equivalent to dividing by 10. Then the time of transit, or mean of observations in the above example, is 12h 0m 1s.32. This example is taken from observations made with a large transit; and, if with a smaller * This is Dr. Pearson's method.

instrument the sums of the several pairs of observations should differ by more than a second, it will be necessary to take the sums of both figures of the seconds, and the division by 10, performed as above, will give the last figure of the seconds, as well as the decimals.

In taking transits of the moon the luminous edge alone can be observed, from which the time of transit of the center must be deduced by the aid of Lunar tables.

In observing the larger planets, one limb may be observed at the first, third, and fifth wires, and the other at the second and fourth, and the mean of these observations will give the transit of the planet's center.

It will sometimes happen that from the state of weather, or from some other cause, a heavenly body may not have been observed at all the wires; but, if the declination of the body be known, an observation at any one of the wires may be reduced to the central wire, so as to give the time of transit, as deduced from this observation. If an observation be obtained at more than one wire, the mean of the times of passing the center, as deduced from each wire observed, is to be taken as the time of transit. The reduction to the center

wire is given by the formula,

RV cosec. T,

or log. R= log. v + log. cosec. ;

in which R represents the reduction, the polar distance of the body observed, and v the equatorial interval from the wire, at which the observation has been made, to the central wire. The equatorial intervals for each side wire must, therefore, be carefully observed, and tabulated for the purpose of this reduction. The formula R=V cosec. π is only an approximate value of the reduction, and with large instruments capable of giving results within 0"-05, a further correction is necessary for bodies within 10° of the pole. The whole reduction in this case is given by the formula,

The time of any star's passage from one of the side wires to the center wire being observed, the equatorial interval from that wire to the center is obtained by multiplying the observed interval by the sine of the star's polar distance; and the equatorial intervals being deduced in this manner from a great many stars, the mean of the results may be considered as very correct values of the equatorial intervals required

No star very near the pole should, however, be taken for this purpose.

USE OF THE PORTABLE TRANSIT.

The large transits in permanent observatories are used to obtain, with the greatest possible accuracy, the right ascensions of the heavenly bodies, from which, and the meridian altitudes observed by a mural circle, an instrument consisting of a telescope attached to a large circle, and placed in the plane of the meridian, nearly all the data necessary for every astronomical computation are obtained. For such purposes the small portable transit is not adapted; but it is competent to determine the time to an accuracy of half a second, to determine the longitude by observations of the moon and moon culminating stars, and to determine the latitude by placing it at right angles to the meridian, or in the plane of the prime vertical*.

The transit of the sun's center gives the apparent noon at the place of observation, and the mean time at apparent noon is found by subtracting or adding the equation of time, as found in the Nautical Almanack, to 24 hours t. The difference between the mean time, thus found, and the time of the sun's transit, as shown by a clock or chronometer, is the error of the clock or chronometer for mean time at the place of observation.

The time shown by a sidereal clock when any heavenly body crosses the meridian should coincide with the right ascension of that body, as given in the Nautical Almanack. The difference between the time shown by the sidereal clock, at the transit, and the right ascension of the body, taken from the almanack, will, therefore, be the error of the clock, +, or too fast, when the clock time is greater than the right ascension, or too slow, when it is less.

THE PORTABLE ALTITUDE AND AZIMUTH INSTRUMENT.

The bending of an unbraced telescope renders it unfit for the determination of altitudes; but by placing the telescope

The prime vertical is the great circle which passes through the zenith and the east and west points of the horizon.

The astronomical day commences at noon, and conta.ns 24 hours, the hours after midnight being called 13, 14, &c., and the day ends at the next noon. The equation of time is given in the Nautical Almanack for apparent noon at the meridian of Greenwich, and the correction to give the equation of time at any other meridian will be found by multiplying the difference for one hour, as given in the almanack, by the longitude of the place, estimated in time.