vices, to be hereafter spoken of. A little consideration will show, however, that, although every transit observed by our astronomer is too early by 08.2, yet, in ordinary cases, this correction is of no account, provided only that it is constant. If he observes the star too early by 08.2, and the comet also too early by that amount, the difference in the times will be absolutely correct. But suppose one observer to note the transit of the star, and another that of the comet: each may have a peculiar habit, so that where one would note 08.2 top early, another might note 08.3 too early, and the difference of their absolute personal equations, 08.1, it would be necessary to apply to the observations of A to reduce them to homogeneousness with those of B. This difference of absolute personal equations is relative personal equation, which, when once truly known, enables us to reduce the observations of one skillful astronomer to what they would have been had another made them.
We say "skillful," because it is only among skillful observers that the phenomenon in question is truly found. In astronomical observations the senses are trained to a fine delicacy, and old observers acquire a constancy of habit which gives to their work a homogeneousness that is wanting in that of younger men.
We have given a brief account of the early method of estimating the time of a star's transit across a spider-line in the field of the telescope by the method of eye and ear; there is yet another method now in common use, which it is necessary to understand before we pass to the consideration of the means of determining personal equation.
This second method is the American or chronographic method; this consists, in the present practice, in the use of a sheet of paper wound about and fastened to an horizontal cylindrical barrel, which is caused to revolve by machinery once in one minute of time. A pen of glass which will make a continuous line is allowed to rest on the paper, and to this pen a continuous motion of translation in the direction of the length of the cylinder is given. Now, if the pen is allowed to mark, it is evident that it will trace on the paper an endless spiral line. An electric current is caused to run through the observing clock, through the pen, and through a key which is held in the observer's hand.
A simple device enables the clock every second to give a slight lateral motion to the pen, which lasts about a thirtieth of a second. Thus every second is automatically marked by the clock on the chronograph-paper. The observer also has the power to make a signal (easily distinguished from the clock-signal by its different length), which is likewise permanently registered on the sheet. In this way, after the chronograph is in motion, the observer has merely to notice the instant at which the star is on the thread, and to press the key at that moment. At any subsequent time he must mark some hour,
