hill of Keylenberg, not more than 200 toises in height; and from which the Brocken itself could not be seen, on account of the curvature of the earth. The light therefore seen at Keylenberg was nothing but the repercussion of the light of the signal from the clouds, of which it is known that there are many instances."

These remarks may be very useful to those who are engaged in similar operations, and particularly in the measurement of the degrees of longitude, or for the measurement of arches perpendicular to the meridian.

All this is followed by a table of the observations made by help of these signals, for determining the difference between the time at Nôtre Dame des Anges, and the Imperial Observatory at Marseilles. 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, circummeridian 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 dif ference 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, does not at all affect the difference of latitude.

It is

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. 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 mountainthe 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 plain 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 con

tinued 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