APPENDIX D.
VERNIER PENDULUM.
Bruce Castle, Tottenham,
June 7th, 1832.
To the Council of the Royal Astronomical Society.
Gentlemen,—In troubling you with the following sketch of an improvement in astronomical clocks, I have a two-fold object. First, to obtain the loan of the necessary instruments, should you consider the plan worth prosecuting; and, secondly, to avail myself of the suggestions of such members of the Society as are more experienced than myself in the minute details of practical astronomy. The objects of the proposed improvement are: To supply an apparatus capable of measuring time to a small fraction of a second, and to make the determination of the exact time a matter of calm and deliberate inquiry, and thus to avoid the errors which must frequently arise from the hurry attending the present method.
In order to accomplish these objects, I propose to make use of the principle of the Vernier, by suspending in front of the clock an additional pendulum somewhat shorter than that of the clock, and so placed that the coincidence of the two when vertical may be determined by means similar to those used by Captain Kater; this additional or Vernier pendulum to be put in motion at the instant of observation by means of a trigger under the command of the observer at the telescope, and its vibrations reckoned till a coincidence takes place between it and the clock pendulum. This pendulum may have a maintaining power and an index to save the trouble of counting. When at rest, the Vernier pendulum must of course be raised to the extent of its oscillation.
The results of experiments commenced with very imperfect instruments about two years and a-half ago, and continued at intervals to the present time, appear to be as follows:—
When a Vernier pendulum, vibrating once in ·9 second, or 10 times in 9 seconds, is employed, its coincidences with the seconds pendulum of the clock may be determined to a single vibration with the greatest ease by the unassisted eye, and thus, of course, tenths of a second are readily estimated.
When a Vernier pendulum vibrating once in ·99 second, or 100 times in 99 seconds, is employed, its coincidences with the seconds pendulum of the clock may also be determined to a single vibration, but not without the aid of a telescope. By these means hundredths of a second are measured without much difficulty.
In order to avoid the inconvenience of having to suspend sometimes one pendulum and sometimes the other, and also to escape the loss of time which, if the hundredths pendulum were constantly used, would arise when the observer wished to estimate tenths of a second only, I propose to adopt the following arrangement:—To employ a single Vernier pendulum of such a length as to vibrate once in 8·99 second, or a thousand times in 899 seconds. This pendulum differs so slightly from the tenths pendulum (making ten vibrations in 8·99 seconds, instead of 9 seconds), that for estimating tenths of a second it is practically the same, while it affords the means of measuring hundredths of a second also. Its operation will be best understood by an example:—Suppose the interval to be measured by means of the Vernier to be ·24 second. At the second and third vibrations of the Vernier pendulum after its release there would be approximate coincidences between it and the clock pendulum, showing the fraction of time to be between two-tenths and three-tenths of a second. The coincidence at the second vibration would, however, be somewhat nearer than that at the third. At the twelfth vibration there would be another approximate coincidence somewhat closer than the first. At the twenty-second vibration there would be a yet closer coincidence. At the thirty-second one closer still, and at the forty-second vibration the coincidence would be the most accurate of the series. Thus it appears that the tenths of a second may be known by counting single vibrations of the Vernier pendulum till a coincidence of some kind occurs, and that the hundredths of a second may be determined by counting the decades of vibrations, or all the coincidences after the first, until the most exact coincidence arises.
By the use of the Vernier pendulum, when connected with an index, all chance of error in reading the clock will, it is conceived, be avoided. Having touched the trigger at the moment of observation, the observer has, as it were, registered the time, and he may examine the clock at his leisure, for it is manifest that a comparison of the index of the Vernier pendulum with that of the clock will at any time determine the moment of observation. It will also be seen that, should the observer omit to notice the first coincidence of the pendulums, no inconvenience except delay will arise, because the same coincidences will occur in a regular series as long as the pendulums continue in motion.
There are a few provisions necessary for extreme accuracy which, in this hasty sketch, it would be out of place to notice. I will just mention, however, that the apparatus contains within itself the means of measuring what may be called the mean error of the observer, or the average interval which, as regards the particular individual, elapses between the instant of observation and the release of the Vernier pendulum.
To subject the plan which I have here attempted hastily to describe to a rigid trial will require instruments of much greater accuracy than those which I can command, and if the Society possess a good clock not now in use, I shall feel extremely obliged if I can obtain the loan of it. An additional pendulum the requisite length, is not, I presume, to be found among the Society’s instruments.
I have the honour to be, Gentlemen,
Your obedient servant,
Rowland Hill.