THE ROTATION OF THE EARTH.
Query, Has Mons. Foucault's pendulum experiment been as yet clearly enunciated? and do I understand it aright, when I conceive it is intended to show the existence of a certain uniform rotation in azimuth of the horizon, but different for different latitudes; which rotation, if made out to exist, is acquired solely in virtue of the uniform diurnal rotation (15° hourly) in right ascension of the equator, identical in all latitudes.
A pendulum, manifestly, can only be suspended vertically, and can only vibrate in a vertical plane; and surely can only be conceived, in the course of the experiment, to be referred to the horizon, that great circle of the heavenly sphere to which all vertical circles are referred.
A spectator at the north pole has the pole of the heavens coincident with his zenith; and there, all declination circles are also vertical circles; and there, the equator coincides with the horizon; whereby the whole effect of the rotation of the earth there (15° hourly) may be conceived to be given to the horizon: whilst, at the equator, the horizon is perpendicular to the equator, which therefore gives no such rotation at all to the horizon. Simple inspection of a celestial globe will illustrate this. Considering the matter thus, at the pole the rotation of the horizon is 15° hourly, and at the equator is 0, or nothing. But the sine of the latitude (=90°) at the pole is unity, or 1; and the sine of the latitude (=0°) at the equator is 0. Therefore, at these two extremes, the expression 15° × sin. lat. actually does give the amount of hourly apparent rotation of the horizon; namely, 15° at one place, and 0° at the other. Now, as I understand the experiment, as given in the public prints, it is asserted that the same expression of 15° × sin. lat. will give the rotation of the horizon in intermediate latitudes; of which rotation I subjoin a table calculated for the purpose.
|
Degrees of Latitude |
Natural Values of Sine of the Latitude. |
Value of 15° × Sin. Lat., or apparent hourly Amount of Rotation of Horizon, in Degrees and Decimals. |
Apparent corre- sponding Times of Horizon, performing one Rotation of 360°, in Hours and Decimals. |
| ° | ° | h | |
| 0 | 0.000 | 0.00 | Infinite time. |
| 1 | 0.017 | 0.26 | 1371.0 |
| 2 | 0.035 | 0.53 | 682.1 |
| 3 | 0.053 | 0.79 | 458.5 |
| 4 | 0.070 | 1.05 | 342.6 |
| 5 | 0.087 | 1.31 | 255.4 |
| 6 | 0.104 | 1.57 | 229.6 |
| 7 | 0.122 | 1.83 | 169.9 |
| 8 | 0.139 | 2.09 | 172.5 |
| 9 | 0.156 | 2.35 | 153.4 |
| 10 | 0.173 | 2.60 | 138.1 |
| 20 | 0.342 | 5.13 | 70.2 |
| 30 | 0.500 | 7.50 | 48.0 |
| 40 | 0.643 | 9.64 | 37.3 |
| 50 | 0.766 | 11.49 | 31.3 |
| 60 | 0.866 | 13.00 | 27.7 |
| 70 | 0.940 | 14.09 | 25.5 |
| 80 | 0.985 | 14.77 | 24.4 |
| 90 | 1.000 | 15.00 | 24.0 |
Now this is the point which, it should seem, ought to be the business of experimenters to establish; it being proposed, as we are informed, to swing, in different latitudes, freely suspended pendulums, over horizontal dials, or circular tables, properly graduated, similarly to the horizons of common globes; and to note the apparent variation of the plane of oscillation of the pendulums with respect to the graduated dials; these latter serving as representatives of the horizon. For the hypothesis is (as I understand it), that the pendulums will continue to swing each of them severally in one invariable vertical plane fixed in free space, whilst the horizontal dials beneath, by their rotation, will slip away, as it were, and turn round in azimuth, from under the planes of the pendulums.
It should seem to be imperative on those who wish to put this experiment to proof, to give all possible attention to the precautions suggested in the excellent paper that appeared on the subject, on Saturday, April 19, in the Literary Gazette, copied also into the Morning Post of Monday the 21st. To my mind, the experiment is beset with practical difficulties; but even should the matter
be satisfactorily made out to those best capable of judging, I cannot readily conceive of an experiment less likely than the above to carry conviction to the minds of the wholly unlearned of the rotation of the earth.
I perceive that B.A.C., in the Times of April 24, avows his determined scepticism as to the virtue of the experiment.
Robert Snow.