I THINK it necessary to mention that my Assistant, Mr. David Kinnebrook, who had observed the transits of the stars and planets very well, in agreement with me, all the year 1794, and for great part of the present year, began, from the beginning of August last, to set them down half a second of time later than he should do, according to my observations; and in January of the succeeding year, 1796, he increased his error to 8/10ths of a second. As he had unfortunately continued a considerable time in this error before I noticed it, and did not seem to me likely ever to get over it, and return to a right method of observing, therefore, though with reluctance, as he was a diligent and useful assistant to me in other respects, I parted with him. The error was discovered from the daily rate of the clock deduced from a star observed on one of two days by him, and on the other by myself, coming out different to what it did from another star observed both days by the fame person, either him or myself; To reduce his transits to mine, subtract half a second from the beginning of August 1795 to the end of the year, and 8/10ths of a second in the month of January 1796: or, to reduce mine to the tenor of his, add the same quantities to them. The joint excellence of the clock, transit instrument, and method of observing, when properly attended to, have been the means of first discovering this error, and then ascertaining the quantity of it. The clock, originally made by Graham, has been successively improved by Arnold and Earnshaw, and the pendulum hung from the pier detached from the clock work: the transit instrument made by Bird has been improved, by substituting an achromatic object-glass instead of the common one, and by putting the finest wires, of the thickness of the 1/1000 part of an inch, in the focus, instead of those placed there before of double the thickness; by applying a magnifying power of 80 to it instead of the former of 50; and, instead of a fixt compound eye-glass, using a moveable single one, which renders the observation equally exact at all the five wires. The method of observing, introduced by Bradley, of noting the proportional distance of the star from the wire at the two beats immediately preceding and following the transit across the wire, has been carefully used, and thence the transit set down to the tenth of a second. I cannot persuade myself that my late Assistant continued in the use of this excellent method of observing, but rather suppose he fell into some irregular and confused method of his own; as I do not fee how he could have otherwise committed such gross errors. However, this unfortunate instance shews the necessity of first duly understanding, and then closely adhering, to this method of observing. Though we cannot, with all our exertions, attain to perfect exactness, for, as the celebrated Mayer says on a similar occasion, non est hominis fed altioris andaginis tam exigua et evanefcentia temporis momenta inter se dissinguere, this should not discourage us from endeavouring to come as near to it as is in our power, and then, though we cannot observe certainly to one tenth of a second of time, we shall rarely commit an error of two tenths; but the mean of all the five wires, or of the central wire, and any pair of wires equidistant from them, may be expected to approximate still more to the truth. The great thing is to aim always at the truth, and avoid any partial method of observing, either in excess or defect; that our errors may not have a tendency to fall constantly one way: and then the independent observations of two observers will have a better chance of agreeing together, and with the truth; The difficulty of attaining the desired exactness arises from various causes; sometimes from the great faintness of the object, sometimes from its over brightness, a tremor or undulation owing to a bad state of the air, or the quick motion of the star through the field of the telescope occasioned by the great magnifying power, and sometimes from flying clouds.
We should observe with all our attention, when the star comes near the wire, and fix (as if we could mark down) the apparent places of the star in the field of the telescope at the two beats of the clock before mentioned, and thence estimate and note down the proper second and tenth answering to the transit across the wire. If we are not quick in fixing the place of the star at the beat, we shall be apt to assign to it too backward a place in the telescope, and consequently to reckon the time of the transit too great, as my late Assistant did. Sometimes, especially when the star was very distinct and steady, I have, by the observed rate of its motion during the foregoing second or seconds, carried my eye on, and anticipated the place the star was to occupy at the succeeding beat of the clock, and only corrected it if necessary (which was seldom the case) by the actual observation. A good ear seems, in this kind of observation, to be almost as useful as a good eye.
If the star is faint, it may be necessary to fix our eye more particularly upon it than the wire, for fear of losing it; where the star is bright, we should divide our attention more equally between them, regarding the varying interval between them as the object.
It may be thought that when the star is very near the wire at the beat of the clock, its transit may then be more accurately ascertained than at any other time, on account of the quantity to be estimated being less. This would be the case did not the breadth of the wire bear a considerable proportion to the space described by the star in a second, and at the fame time otherwise disturb our judgment of its approach to the line bisecting the wire. To assist my imagination in these cases, I use the following method :—Because the stars generally observed, being near to or not very remote from the equator, move over half the breadth of the wire in about 1/10th of a second of time, I allow 1/10th of a second for the interval between the beat of the clock, at which a small star is in external contact with or partly cut off by the wire and the time of its being bisected or centrally hid behind the wire; and 9/10ths of a second if it be a large star. This rule will probably insure the time of the transit within 1/10th of a second. Those who observe with less perfect or shorter telescopes, which exhibit the stars larger, or whose wires cover a larger space in the heavens, will have a different allowance from mine to make in estimating the fraction of a second, when a star touches, or is partly hid by the wire at the beat of the clock, which their own judgment must dictate to them.