The position of the horizontal axis has been all along supposed to be measured by the level, and this is certainly the most ready method. But the level may happen to be broken, or, unless it comes from a very careful maker, it may be sluggish, or unequally divided. The beautiful levels which accompany Erters instruments, which are covered at the ends with parchment and filled with ether, are very liable to leak, as we know by experience. In such a difficulty, our celebrated surveyor Captain W. F. Owen raised a tall pole, and having put thereupon a distinct mark, adjusted his instrument by moving the elevation screw until the wire passed through the mark seen directly and by reflexion. In another instance, where the level was broken, an observer of some name was unable to supply its place, and a projected set of observa tions failed in consequence. The simplest method is that pursued by Captain Owen, substituting the pole star or other slow-moving star at its culmination for the tall pole. When the axis is thus nearly cor rected, which may easily be done when the star passes the first wire, it is better to observe the star over the rest of the wires half directly and half by reflexion, and to reduce each set to the mean wire. On draw ing the figure it will be seen that any error of level will affect the transit of a star seen directly one way, just as much as it will affect the transit of the same star, seen by reflexion, the other way, or that the difference of the two transits, after each set has been reduced to the mean wire, is twice the error due to inclination : that is, the differ ence of the transits in the two pOsitions is, when the star is above the pole — 2 x i, from which i is determined, and may be used for all the other observations. The observation will succeed very well with any slow-moving star, if the observer has time to shift from one position to the other without hurry ; or he may use two high stars, each observed over all the wires, if they have the same altitude, or if be should happen to know the other errors of his instrument. Indeed, if be has no objection to solve simple equations with four unknown quantities, he may proceed exactly as we have shown in former instances, introducing another term with i and its coefficient, and changing the sign for the observations by reflexion.
Observations by reflexion of Polaris are well suited for another purpose, namely, for examining the value of the level scale by means proper to the instrument itself. Raise the west end until the bubble is nearly at the west end of the scale, and by a mean of half a dozen readings, reversing each time, ascertain the error of inclination. Now observe Polaris exactly as we have before mcntioned,or, if the observer likes better, directly over the 1st, 2nd, 8th, and 7th wires, and by reflexion over the 3rd, 4th, and 6th ; reduce each set to the mean wire, and calculate by the formula already given the true inclination of the axis. On a following night repeat the operation, the illuminated end being on the same pier, only lowering the west end of the axis until the bubble is nearly at the east end of the scale, and get as before two values for the inclination, one from the scale, and another by observa tion. Take a mean, and you will have the true value of the parts.of the scale. If the result varies much in the two experiments, it shows either that the curvature of the level is unequal, or that one pivot is thicker than the other. This may be ascertained by the level alone, as we have shown above, or would be indicated by a difference between the direct and reflected observations when the axis is horizontal by the level, or by comparing the inclination obtained from reflexion in the manner last pointed out, in reversed positions of the instrument, supposing the x's not to change during the experiment. Thus if the
inclination be determined by observing Polaris over the first half of the wires directly and the second half by rcflexion, a value of the inclination will be found. Reverse the instrument, and make the same observations upon another slow-moving star, and you will have a second value of the inclination, which should agree with the former if the pivots are equal; half the difference, if it exists, is the difference in the radii of the pivots. The level however affords a much easier, and, we believe, better measure of inequality ; but it will not show if the pivots be elliptic, which the observations by reflexion would do if stars at different altitudes were observed. If the two teats agree, it is a reason for believing that the pivots are round within the limits of these very searching experiments. But as we believe these observations have never yet been made, it would be useless to expatiate further upon their possible advantages. The late astronomer royal, Mr. Pond, tested the transit at Greenwich by observing a set of stars directly and a second set by reflexion after the axis had been most carefully levelled, and found that on reversing hie sets on a subsequent night he got the same mean interval, as he ought. Professor Woodhouse examined his level scale by observing Polaris over half the wires with one end high, and the other half with the other end high. This is less sensitive than the method we have pointed out, but will do for its purpose very well, if the instrument is examined and verified by a meridian mark between the first and second set of observations, other wise we should be afraid a change in azimuth might be caused by turning the elevating screw, in spite of all the care of the artist to prevent it.
An eye-piece has been introduced into use within the last few years, which, by illuminating the wires in a particular manner, enables the observer, looking downwards into a basin of mercury, to see at the same time the wires and their reflected image : if these be made to coincide, the telescope is vertical, and therefore the axis horizontal. If the micrometer wire be used to measure the interval, the result will be found to be twice the inclination.
The transit may be levelled, as it was in older times, by a plumb line, which, hanging from a frame placed close to the instrument and in front of it, is made to pass over two dots, placed at the eye and object end of the telescope. This is an accurate but intolerably trouble some method. In Groombridge's circle, Troughton used a plumb-line in a tube at right angles to the axis and to the telescope for the same object. The images of the opposite dots at top and bottom were thrown on the line by lenses, and viewed through microscopes, in the way in which he always applied the plumb-line. We do not know whether Mr. Groombridge adjusted the horizontal axis by means of this plumb-line or no, but the artist himself said that be introduced the tube principally to make the axis equally weak all round, finding that it was previously so much stronger in one direction than another as to give him trouble in dividing it. Finally, the axis may be adjusted, or the inclination measured micrometrically, by means of a vertical collimator, which is convenient enough, but, so far as our own experience goes, rather uncertain in its indications, and much inferior in both respects to a good level. A really good level carefully and frequently applied will show the position of the transit axis to about 0".2 or or the inclination correction to and this is a smaller quantity than a considerable number of careful observations will show.