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The observations were made between the 11th and 21st of July, and amount to 64. The greatest difference among them hardly exceeds 1"; and the mean of the whole is 29".95 of time, or 7.29".1" in degrees.
The use of the observation of azimuths for the same purposes, is considered at great length. The system of triangles was oriented, that is, its position in respect of the meridian ascertained by azimuths, determined chiefly from the sun's passage over the meridian, or, such as are here called, circum-meridian azimuths. The BARON afterwards recommends the method of ascertaining the azimuths by the polar star, after the manner first employed by GENERAL Roy, and since followed by those who have succeeded him in the conduct of the trigonometrical survey of England. He says, that the excellent repeating theodolites constructed by Reichenbach, are well adapted to these observations; and he gives two examples from azimuths observed at Munich, where the angle was repeated a prodigious number of times with very small variations. It would seem, therefore, that this theodolite carries a telescope with a very accurate vertical motion, though less accurate than that of RAMSDEN's great theodolite. If this advantage is conjoined with the power of repetition, it must no doubt render the theodolite the most perfect instrument that has yet been employed in such operations as we are now treating of.
The measurement of the base, which was to serve as the foundation of the trigonometrical survey, comes next; and occupies a considerable part of the first volume. In all the parts of this very essential work, the greatest care seems to have been taken, and no precaution omitted, that the skill and experience of this very ingenious astronomer could add to the methods invented and executed by those who had gone before him.
In the end of the volume, it appears that the difference of meridians between N. D. des Anges and Planier, determined astronomically, is 15' 35".79; and that the same, determined geodetically, is 15.46". There is a difference here of 10" .67, which, however, docs not at all affect the difference of latitude.
The result of the whole, after every possible check was introduced, is, that the astronomical observations at N. D. des Anges made the latitude of that station less by 2" and a small fraction, than when the same was ascertained by the intervention of terrestrial measurement from the latitude observed at Planier. The same difference of 2" was deduced from the latitudes of three other stations, all so distant as to be out of the reach of the attraction of the ridge of Mimet. No doubt could therefore remain, that these two seconds arose from the zenith of N. D. des Anges
being carried that far south by the attraction of the mountain. It is thus very satisfactory to know, that, even with small instruments, so important a point can be settled as the determination of the attraction of a mountain-the most beautiful and most palpable verification of the law of gravitation which science has yet afforded. The further researches, that lead to a comparison between the density of such a mountain and the density of the earth itself, require a number of additional data, which cannot be ascertained with tolerable accuracy, but in the case of mountains of considerable magnitude, and as much as possible insulated. This, accordingly, the BARON DE ZACH did not attempt; and the only investigation of the kind yet existing, is that which was founded on the experiments made at Schehalien.
Great as the skill and accuracy were with which those experiments were conducted, the attraction of mountains is a subject by no means exhausted; and it were greatly for the interest of science that these experiments should be repeated under as great a variety of circumstances as can easily be attained. The northern part of the island of Great Britain is well accommodated to such observations, and the continuation of the trigonometrical survey which is now extended to that country, affords the best opportunity for carrying such experiments into execution. They would indeed make but a small deviation from the general plan of the survey. Were the method to be followed that was pursued in the survey which is the subject of those remarks, any mountain, or chain of mountains, having a plane of considerable extent, either to the south or to the north, might very well be used for determining the attraction. The observations made in that way, though they do not double the effect, as was done in the case of Schehalien, are so much easier to be made, and may of course be executed in so many more instances, that on the whole they may be reckoned preferable. The survey of the mountainous tract, and the gauging, as we may call it, of the mountains, would require to be continued so far as to reach the limits beyond which no inequality of ground can be supposed to act sensibly on the plumb-line. The Grampian mountains would afford many situations well accommodated to observations of this sort. The opposite sides of a valley also, as, for instance, of Loch Tay, or Loch Ness, might be used in the same way. The two zeniths would there be made to approach one another; and the arch between them, found by celestial observation, would be less than the same concluded by trigonometrical measurement, by the sum of the attractions of the mountains on the south and north, minus that of the intervening water, which, as a lighter substance,
would have less action on the plummet than an equal volume of earth or rock. What related to the nature of the rocks, would be readily ascertained by the skilful mineralogist who is now so properly connected with the execution of the trigonometrical survey. It is a great additional argument in favour of what is here proposed, that a long series of similar operations has prepared observers admirably calculated for the present purpose. Men accustomed to live in the open air, and encamped on the sides or the summits of mountains, to watch the motions of the stars for months together, and to endure all the suffering and disappointment which the vicissitudes of the weather inflict on none so severely as on the astronomer. Men trained in this manner are not often to be met with: so much experience and skill in the nicest observations of science, can but seldom be combined with the hardiness of rural, we might almost say, of savage life. It were therefore to let slip a most favourable occasion for promoting the interests of science, not to take this opportunity of inquiring farther into the attraction of mountains. The instruments are already on the spot, as well as the hardy, experienced and skilful observer who is to use them; so that the same thing can never be undertaken at so little expense to the public, and in a manner so truly economical, and so highly advantageous to science.
As an additional reason for including the inquiry into the attraction of mountains in the plan of the trigonometrical survey, we must be permitted farther to state, that there are several circumstances in the experiments at Schehalien, which should render the repetition of them extremely desirable.
Though nothing could easily be added to the accuracy of the astronomical part, of which we have just now seen the strongest and most impartial evidence, yet equal praise cannot be bestowed on the trigonometrical survey, by which the magnitude and figure of the mountain were determined. The theodolite employed was but an imperfect instrument; it gave the angles to minutes only; it was furnished with telescopes of a very moderate magnifying power; and, though the work of RAMSDEN, was in all respects inferior to the instruments now employed for like purposes. Mr BURROWES, into whose hands this part of the work was committed, was new in the employment; and, though skilled in mathematicks and astronomy, had no experience in the sort of work he was employed now to conduct. As to all, therefore, that relates to the density of the earth, and the conclusions grounded on the figure and magnitude of the mountain, it must not be supposed that the same precision is to be found as in the determinations purely astronomical.
VOL. XXVI. NO. 51.
We are enabled to state this with the more confidence, that circumstances have led us to study the detail of this survey with a more minute attention, than has probably ever been done by any one except Dr HUTTON, who has so ably conducted the computations grounded on it. In this examination we have remarked, that when the solid content of the mountain is reduced into columns of equal attraction, according to Dr HUTTON'S method, owing to some imperfection in the survey, the lengths of those columns cannot always be accurately ascertained; and, particularly when they come nearly to the level of the observations, that it is often uncertain whether they rise above that level, or fall short of it, and, of consequence, whether a certain quantity is to be applied as an augmentation or a diminution of the whole attraction.
There were even faults in the plan, no less than in the execution of the experiments. The observatories were placed too high on the sides of the mountain; they were about half way up; so that between a sixth and a seventh of the total effect of the attraction was lost. The sections were vertical, and carried at random, some entirely, but many of them only partially across the mountain, instead of being conducted horizontally round it, and connected together by two vertical sections at right angles to one another.
In the distance to which the survey extended, no principle seems to have been adopted as a guide, except a very insecure one, that at the distance of a mile and a half, or two miles, the action of a mountain of ordinary size could not sensibly affect the direction of gravity. The knowledge obtained from the experiments at Schehalien afford a much better, and more secure principle for fixing the limits within which the attraction of a great mass of matter may be supposed to produce a sensible effect.
Add to this, that at the time of these experiments, no attention, or next to none, was bestowed on the structure of the mountain, and the distribution of the materials which compose it. This omission, accordingly, gave no inconsiderable degree of vagueness to the conclusions deduced concerning the density of the earth.
It is true, that two gentlemen, * zealous to contribute to the accuracy of this interesting inquiry, endeavoured, not long ago, by a mineral survey of Schehalien, to remedy this defect, and to ascertain, with some degree of precision, the specific gravity of the rocks which compose that mountain. They succeeded,
The Right Hon. Lord Webb Seymour and Professor Playfair.
perhaps, as far as the nature of the thing will now admit; but certainly much less, than if a mountain of simpler structure had been the subject of examination, or if the mineral survey had been undertaken along with the trigonometrical, when the instruments of observation were on the spot, and all the stations distinctly recognised.
These circumstances, though they go no farther than to render the limits within which the accuracy of the results are contained, more distant than they would otherwise have been, are certainly to be held as good grounds for wishing to have the same experiments repeated, with an attention to all the improvements that have been made since the time when they were instituted. The opportunity, then, that now presents itself, we hope will not be overlooked, when the instruments, as has been said, are prepared, and when observers are at hand, zealous to engage in the work, instructed in all the resources of their art, and accustomed to overcome all the difficulties of their situation. Such an enterprise would form a very noble conclusion of the present survey; and would distinguish it from all others yet made, as much for the variety and importance of the objects contained in the plan of it, as for the perfection of the execution. It is already infinitely to the credit of the country, and those entrusted with the government of it, that during the long and expensive war in which the nation has been involved, this great work of science has been carried on as in the midst of profound peace. peace. We may therefore hope, that the termination of an arduous contest, and the restoration of tranquillity to the world, will permit this national work to be completed with an extent and accuracy worthy of the spirit with which it has been begun and carried on.
ART. III. Popular Reflections on the Progress of the Principles of Toleration, and the Reasonableness of the Catholic Claims. By a PROTESTANT. Newcastle. 1814.
HE history of Toleration is still a desideratum, and an important one; for it affords very useful lessons both to Statesmen and Divines, as well as to private Christians of all denominations, besides some matter of curious speculation to philosophers. We shall therefore make no apology for offering a few observations on this subject, which have been suggested by the perusal of the work before us. We understand it to be the production of a learned clergyman in Northumberland, minister