Now it is known by the theory of elliptic functions that

Whence P, Q, R, being the moments of the disturbing forces about the

present axes,

P

1

0-0

1

2

+m cos x4xlt

+
dt dt

"Experiments, made at Watford, on the Vibrations occasioned by

Railway Trains passing through a Tunnel." By Sir JAMES SOUTH, LL.D., F.R.S., &c., one of the Visitors of the Royal Observatory of Greenwich. Received June 17, 1863*.

In the year 1846 an attempt was made to obtain the consent of the Lords of the Admiralty to run a railway through Greenwich Park, distant only 860 feet from the Royal Observatory, which would in the opinion of many competent judges have been most injurious to that Establishment. Such consent their Lordships refused; but as I was assured on high authority that this attempt was to be repeated, and that too with the fullest confidence of success on the part of its projectors and supporters, I determined to make experiments which might bear more decisively on the question of railway tremors, as affecting that Observatory, than those previously made by myself and others.

For this purpose it seemed indispensable that the station selected for making them should geologically resemble that of Greenwich, and that the astronomical means employed to detect the existence and determine the intensity of the tremors should be, optically, at least equal to the telescope of the Greenwich Mural Circle.

As much importance was attributed by the advocates of this railway to the supposed power of a tunnel to render the vibrations imperceptible, it was also desirable that it should be one of the conditions of these trials.

Having but little more than a popular knowledge of geology, I relied on my old and valued friend the late Mr. Warburton, who had recently been President of the Geological Society, to guide me in the choice of a station; and it was on his authority that I fixed on the Watford Tunnel and its immediate vicinity.

There, under a light gravelly soil of 18 or 20 inches deep, lies a bed of gravel of considerable but variable thickness, sometimes compact, at other times loose, and immediately under it chalk with occasional flints.

The tunnel, of which the bearing is 41° 19' to N.W. of the meridian, and by my measurement is 1812 yards long, passes principally through chalk; its arch is about 24 feet in diameter, the crown of it being about 21.5 feet above the rails. The thickness of the brickwork is about 18 inches; the mean thickness of the chalk above the crown of the arch about 50 feet, whilst that of the gravel, though subject to great irregularity, may perhaps be regarded as 14 feet. If so, we have outside the tunnel above the horizontal plane of the rails 87 feet of chalk, flint, gravel and soil, constituting an assemblage of which the power of transmitting tremors must be comparatively feeble.

There are five shafts in the tunnel, four of which are circular, 8.5 feet diameter, and one quadrangular, about 26 feet by 34.

* Read June 18, 1863: see Abstract, vol. xii. p. 630.

The tunnel runs under the park of the Earl of Essex; and though I had not the honour of a personal acquaintance with the Noble Earl, nor any introduction to him, yet on learning my objects he transmitted to me by return of post, from Carlsbad, a carte-blanche to erect my observatory wherever I pleased, though it were in the very heart of his choicest game preserves. To him therefore is mainly due whatever benefit may accrue to science or to the Royal Observatory from the experiments recorded in this communication.

The point I selected was 302 yards distant from the centre of the line; and the perpendicular from it on the axis of the tunnel meets that at a point 567 yards from the southern or London end of the tunnel, 1245 yards from the Tring or north end, and 594.5 from the fourth shaft. This is the centre of the Observatory which I erected there: it is of wood, as small as is consistent with the necessary accommodation, both for portability and that it might be less agitated by the wind.

It is quadrangular, 12 feet by 10, and its length is in the meridian; the eaves are 8.5 feet, and the ridge of the roof 10 feet above the floor, this last being 4 inches above the ground, which is nearly level with that over the tunnel. The roof is covered with tarpaulins very well secured, so as not to be torn by a gale of wind. In the south and west sides are four windows, which can be opened or shut at pleasure, to light the Observatory by day, or to see powder or other signals at night. In the roof is no opening; but in its northern side there is one which can be shut as required: it is little larger than what is absolutely necessary to allow the reflected rays from the Pole-star to pass uninterruptedly to the observer's eye through its whole revolution.

At its centre, parallel with its sides and resting on the undisturbed gravel 4 feet below the surface, is a mass of brickwork laid in excellent Roman cement, 8 by 3.5 feet at bottom, 7 by 3.5 at top, its length running east and west. On this stand two piers of similar brickwork, 18 inches by 14, and 46 inches higher than the floor: they are capped by two Portland stones of similar horizontal section 8 inches thick. In the interior faces of these stones are firmly fixed the Y-plates, which carry the Ys on which the instrument's pivots rest.

Eighteen inches north of the brick massive, but in the same plane with its base, is the centre of the base of another pier, brought up also in Roman cement, 24 inches from N. to S., 18 from E. to W.; and it rises 12 inches above the floor. The upper surface is perfectly horizontal, and serves to support a vessel which contains mercury. Both this pier and the massives are insulated from the floor, and touch the ground only at their bases. The mercury-vessel was 18 inches by 43, with its length in the meridian.

The transit-instrument of the Campden Hill Observatory is far too precious to be exposed to the risks of such an expedition; I therefore had one constructed which might be considered an excellent substitute. The objectglass (which under favourable circumstances will bear a power of 1000) is 87 inches focus and 4·75 aperture. The transverse axis is 31 inches; and

the Y has sufficient azimuthal motion to enable me to follow the Pole-star in its whole course, so that at any hour (if clear) I could have the reflected image of the star in the mercurial vessel ready to testify against the tremors caused by a train.

Supported by timber passing into the ground, but unconnected with the floor and convenient to a writing-desk which occupies the S.E. angle of the building, stands a journeyman clock. It is set by my excellent gold pocketchronometer, Molyneux No. 963, and rarely deviates from that more than one- or two-tenths of a second in three or four hours. The clock of the Watford Station was compared with the chronometer, going and generally returning, for the purpose of identifying particular trains.

These details will, I hope, suffice to prove that every precaution was taken to obtain accurate results, and that those which I did obtain may be fairly considered as identical with what would have been found in a first-class observatory under the same circumstances of locality and traffic.

I was at my post to commence observations on December 22nd, 1846; but that and the three following nights were starless. The 26th was fine, but, owing to the irregularity of the trains, and the want of well-organized signals, I could only satisfy myself that all was in good working order, and that the trains caused great disturbance. For thirteen following nights I was at my post, but in vain; all was dark, with the thermometer from 22° to 31°.

On January 11th, 1847, it cleared, and I observed seven trains with decisive results, being able to announce their presence before it was known to my assistants, who were on the watch outside the observatory.

The Pole-star's image as reflected from the mercurial surface, when no train was near, appeared

As a very small, perfectly steady disk, thus

which as the train approached broke up into a quintuple, thus.

As the disturbance increased, the form became linear at right angles to the length of the mercury-vessel, thus

(1.)

(2.)

.... (3.)

When the train was considerably advanced in the tunnel, a cross formed, thus-.

And when near the perpendicular from the observatory, three parallel lines of disks appeared, thus-.

(4.)

(5.)

still parallel to No. 3. As the tremors became more distant, these transformations of the image take place in a reverse order, until the star resumes its original disk-like form.

These results were strongly conspicuous even in a fully illuminated field, and equally so whether the magnifying power was 60, 200, or 750. The phenomena are very striking, from the contrast between the smaller images, which are blue, while the larger ones are reddish, and from the sudden way in which they break out.

The nights of the 13th and 14th were fine, and so thoroughly confirmed my previous observations that I felt it my duty to lose no time in informing the late Lord Auckland, then First Lord of the Admiralty, of the preceding details and of my conclusions from them, that a tunnel did not prevent great tremors from being propagated from it when a train was traversing it, certainly to the distance of 643 yards, and probably much further.

The impression which these facts made on his Lordship he expressed in the following letter.

Copy of a Letter from the Earl of Auckland to Sir James South. "Admiralty, January 26th, 1847. "SIR, I have to return you many thanks for the very interesting report which you sent to me of your experiments upon the distance to which the vibration caused by steam-carriages within a tunnel extend; and I cannot but admire the enterprise and ability with which these experiments were conducted. They would be quite conclusive if the question of carrying a tunnel through Greenwich Park were again to be agitated. "I am, very faithfully yours,

"To Sir James South, &c. &c."

"AUCKLAND."

The reserve with which I spoke of that further distance arose from the circumstance that I was not in possession of the exact measurements of the tunnel and the position of its shafts. I had twice applied for them in vain to the railway authorities, and was obliged at last to execute the measures myself*. This consumed some time, and the observations were not completely resumed till February 24, 1847.

The process was this. About 600 yards before the entrance of the tunnel a rocket was fired as a signal for attention. At the instant that the engine passed the south end of the tunnel, one of Lord Essex's game-keepers fired one barrel of his gun, and the other about a second after, which was necessary to distinguish this from the shots of poachers, who were often at

* This delay was not occasioned by any want of courtesy on the part of the Directors or other officers; from whom, especially from Mr. Creed, their Secretary, I received the heartiest cooperation. He not only directed all the officers along the line to aid as far as possible my investigations, but pressed on me free passes for myself and my assistants. I was also indebted to Captain Bruyeres for the character of the trains, and to Mr. Stubbs, the Superintendent of the Watford Station, for the zeal with which he followed out the Secretary's instructions at much personal inconvenience.