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of the nobleman just named. They have since been consigned to the care of the University of Oxford; and are now, we have no doubt, in the progress toward publication.
Circumstances, of which he does not inform us, having led him to Marseilles in 1810, and induced him to make some considerable stay in that city, a climate and situation so favourable for observation naturally inclined him to undertake the solution of some of the great problems of practical astronomy. He was provided with a good apparatus; and the research he thought of pursuing was one abundantnice and difficult-the attraction of mountains.
It is to the discoverer of the principle of universal gravitation that we owe the first idea of such attraction, as a thing not only real, but capable of being ascertained by actual observation. Newton, in his Tract De Mundi Systemate, § 22, computes, that a plummet, at the foot of a hemispherical mountain three miles high, and six broad, (at the base,) would be drawn about two minutes out of the perpendicular. This suggestion was sufficient to rouse the attention of astronomers, who could not but remark, that a cause was here pointed out, which, in certain circumstances, might greatly impair the accuracy of their observations. It does not, however, appear that any one undertook to investigate the subject experimentally, till the visit made to the Andes by the French and Spanish
academicians about the year 1738. The sight of the mountains which form so stupendous a rampart along the shores of the Pacific Ocean, could not but remind these astronomers of the influence which such masses might have on the accuracy of the observations by which they were to ascertain the figure and magnitude of the earth. M. Bouguer, a most active and skilful astronomer, proposed to ascertain the fact by actual observation; and began with making a coarse estimate of the effect which might be expected from Chimboraço, the highest of the Cordilleras, elevated more than 3000 toises above the level of the sea, and not less than 1700 above the level of the plain from which it rises. From the dimensions of this enormous mass, he computed that it might draw the plummet out of the perpendicular by 1′ 40′′; a quantity much too large to escape observation.
So skilful and ingenious an observer as Bouguer, could not fail quickly to perceive, that there were more ways than one by which the quantity of this attraction might be experimentally ascertained.
It is obvious that, abstracting from all disturbance of the plumb-line, the altitude of any given celestial body when it passes the meridian is the same in all places under the same parallel of latitude, or in all places due east and west of one another. If, therefore, two stations are chosen, one at the foot of a mountain, suppose on the south side,
and another at a considerable distance to the east or west of the former, the meridian altitude of the same star, if the mountain have no attraction, will be the same at both these stations. But if, at the first station, the plummet be drawn towards the mountain, that is, if the apparent zenith be carried towards the south, the meridian altitudes of the star at the two stations, will differ, by the deviation of the plumb-line from the true perpendicular. If, then, observations are made at two such stations, the questions, whether the mountain has any attraction, and what the quantity of that attraction is, will both be resolved. It will add to the accuracy of the determination, if stars to the south and north of the zenith he observed at both stations. Those to the south will have their zenith distances diminished, and those to the north will have them increased, by the same quantity, when compared with the observations made beyond the influence of the mountain; so that the effect to be measured will be doubled.
Another method proposed by these academicians was, to take two stations, one on the south, and another on the north side of the same mountain, and as nearly as possible in the same meridian. From the zenith distances of the same stars observed at each station, the difference of their latitudes might be very accurately determined. The difference of the latitudes might also be determined
from the distance between the same stations, found from a trigonometrical survey of the ground. The difference of these determinations would give the sum of the deviations of the plumb-line on the opposite sides of the mountain; and, when divided in the inverse ratio of the squares of the distances of the stations from the centre of gravity of the mass, would give the deflection of the plummet at each station. *
A third method supposes one observer to be placed at the eastern foot of the mountain, and an
* The Baron de Zach has fallen into an error in quoting, or rather in interpreting, a rule laid down by Bouguer, for dividing the deflection between the two stations, and allowing to each side of the mountain its due proportion of the effect. The formula of that academician, in the case that the stations are in the same meridian, but at different distances from the centre of gravity of the mountain, requires that the sum of the deviations, or the total deviation observed, should be divided between the stations, in the inverse ratio of the squares of their distances from the centre of gravity of the mountain, as is stated above. The Baron makes it in the direct ratio of the cubes; referring at the same time to Bouguer, whose general proposition, on the contrary, gives the result just mentioned. The theorem of the Baron is obviously wrong; and even the theorem of Bouguer is but a coarse approximation; as, in an irregular figure such as that of a mountain, the attraction does not vary as any power of the distance from the centre of gravity, or from any fixed point whatsoever.
other at the western. If each of these observers regulate his clock exactly by equal altitudes, or by the time when the sun passes over the meridian, the difference of time pointed out by the clocks, or the difference of longitude of the stations, will be greater than if the mountain had not acted on the plummets, and carried the one zenith too far to the east, and the other too far to the west. If this difference, therefore, be determined by signals made at each station, and observed at the other, it will be discovered, whether the differences of longitude so found correspond to the measured distance by which the one observatory is east or west of the other. This method, though perfectly good in theory, would be found more subject to error than that just described, in the same degree that the difference of the longitude of two points is less easily determined than their difference of latitude.
The French academicians made trial of the first of these methods, by placing their instruments on the south side of the great mountain of Chimboraço. They observed the meridian altitude of some stars on the north, and of others on the south side of the zenith; and they repeated the same observations of the same stars a league and a half to the west of the first station, where they conceived themselves to be out of the reach of the action of the mountain. By comparing the observations at