number of turns and fractions of a turn of the screw necessary to bring the wires to one of the dividing lines of the 5' spaces will show how many minutes and seconds the intersection of the wires stood past this division. To save the trouble of counting the number of turns of the screw, a notched scale is placed vertically a little on one side, at the focus of the microscope, so as to be magnified by its eye-glass. A pin, which points horizontally past the scale, towards the intersection of the wires of the microscope, moves over one notch at each turn of the screw. The zero of the notched scale at which the pin ought to stand at the commencement of the observation, is marked by a hole at the middle of the scale. To recapitulate, the reading of the degrees, minutes, and seconds will be taken as follows: the degrees by the index or pointer, then looking into the microscope, the degree nearest which the pointer stands will be recognised by a round indentation in the metal, near a long dividing line; the half degree is marked by a dividing line of the same length, without any indentation; the quarter degree by a shorter line, and the 5' spaces, of which there are three in each quarter degree, by shorter lines still. If the intersection of the wires stand exactly upon one of these dividing lines, the reading will be so many degrees, halves, quarters, and five minutes; but if the intersection of the wires of the microscope be a little past one of the dividing lines on the limb, the intersection must be brought back to the dividing line by turning the screw which moves the frame containing the wires. The number of turns of the screw necessary for this purpose, indicated by the number of notches passed over on the scale by the pin within, will be so many additional minutes to be added to the reading as it now stands, and the seconds will be obtained from the screw head by noting at what numbers upon it its index stands. The mural being used in the same observatory ordinarily with a transit instrument, by observing the time of transit of the star over the wires of the mural, and comparing the result with the transit observation corrected as explained under the head of that instrument, the hour angle of the star when it crosses the imaginary middle wire will be known; or it can be computed from a high and low star observed with the mural itself, as explained for the transit instrument. From this hour angle the error in the observed altitude of the star arising from the deviation of the instrument from the meridian, may be obtained as follows: REDUCTION TO MERIDIAN OF AN OBSERVATION MADE WITH THE MURAL CIRCLE. But 1-cos P2 sin2(P), see (8) Art. 72. Since PSPS', PSPm very nearly, whence PS-rms'm, and the hour angle SPS' is generally very small. star. in which p is the hour angle in seconds of time, and Ps the polar distance of the The correction or reduction does not become of any sensible magnitude, till the hour angle exceeds 5 seconds. The correction or reduction is always to be added to the apparent polar distance, if the star has a N.P. distance less than 90°, but subtracted if greater than 90°. This may be seen from the diagram, and still better on a globe; the great circle of which the horizontal wire is a portion, intersecting the meridian N. of the diurnal circle of the star, when its N.P.D. is less than 90°, and s. when it is greater. Instead of the polar zero, a horizontal zero has been more commonly used. It is obtained by taking the reading with the horizontal wire bisecting the star, as seen direct on one night, and as seen by reflexion from mereury on the following night; half the difference of the two readings will be the meridian altitude of the star, from which and the latitude the polar dist, or declination may be obtained as explained at p. 150. Within a few years past a third zero, which may be called the nadir zero, has been employed. This is obtained by means of a collimating eye-piece and basin of mercury, placed under the object glass of the telescope, turned vertically downward, as described at p. 161, note. When the direct image of the horizontal wire coincides with that seen by reflexion, the reading will be the nadir zero, and the difference between this and the reading when the telescope points to a star crossing the meridian, will be the distance of the star from the nadir, which is the supplement of its * See (7) Art. 70. + The sine of a very small are differs insensibly in length from the arc itself, and its value may be found by multiplying the sin of 1", taken from the tables, by the number of seconds in the arc. This serves to express the length of the arc in the same terms as the radius, sine, cosine, &c., are expressed, so that these quantities can enter the same formula. See form. (1) Art. 71. zenith distance, from which the polar dist. or dec. may be obtained, as already explained.* *The circle and transit instrument are combined in one, in the German observatories. The instrument which results is called a transit circle or meridian circle. Both observations, to wit, that for the right ascension and that for the declination of the object, are taken simultaneously. TRIAL METHOD OF DETERMINING BOTH LATITUDE AND TIME. Supposing neither the chronometer error nor the latitude to be exactly known, but the altitudes of two stars A and B, differing 90° in azimuth be observed, and assume successively two trial latitudes, computing the chronometer error by each latitude, and by the altitude of each of the stars. Suppose the first assumed latitude for example to be 45° 15', and the resulting chronometer error by star A to be 46.2, and by star B, 50*2; the discordance is 4. Suppose the second assumed latitude to be 450 25', and the resulting chronometer error by a to be 53.4, by B 378-4; the discord now is 16 the opposite way. Then 10' of latitude has changed the discord 20s; therefore a change of 2' of latitude will remove the first discord of 4s, and the latitude is therefore 45° 17'; and since 10' altered the error by a 72, and by в 128, 2' will alter the former by 1.44, and the latter by 2.56, and both agree in giving the error 47.64. |