made use of in the calculation be confounded with' that difference. But these are precisely the occasions most favourable for the observations with which these particular occultations may be compared; and by which (as I have said) the errors of the tables are corrected, and the geographical longitude determined.

§ 16. It is true that the conditions here required, for ascertaining the flattening of the poles, cannot be very frequently obtained: but, if we look out for them with the diligence that the importance of the

disc, provided the earth were a perfect sphere: together with the corresponding durations provided the earth were an oblate spheroid, having the axis compressed. Latitude of the place 60": height of the moon 10°.

In the APPENDIX I have given other tables, showing the differences that would arise from varying the latitude of the place, the height of the moon, and the quantity of the earth's compression : whereby the reader may be better able to judge of the maximum of difference which would arise under the most favourable circumstances. B.

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object demands, we shall perhaps meet with them more frequently than we imagine. For, I may venture to assert that there does not pass a month without the occurrence of an occultation of some star whose position is well known: and there is no occultation that will not afford, to some part or other of the earth's surface, the conditions required*. If only once out of twenty times they should occur, in a place where there is an astronomical observatory, the question as to the compression, and also as to its quantity, would be very soon determined.

17. For the solution of such questions, for which immense sacrifices have hitherto been made

* Since this was written, the positions of most of the zodiacal stars have been determined with a degree of accuracy sufficient for the purposes detailed in the memoir. The labours of Cagnoli himself, of Piazzi, Harding, Zach, and Bessell have contributed much to this end: so that we may now safely assert that scarcely a night passes "without the occurrence of an occultation of some star whose posi"tion is well known." Nearly forty years ago Messier made the following remark, at the close of a numerous list of observed occultations: "We see by this collection of occultations how many new ones "I have observed, in the first quarter of the moon, on the dark "limb; which are distinguished with the greatest precision. They "are frequent, and much preferable to the observations of Jupiter's "satellites, or lunar eclipses, for determining the longitude. It were "much to be wished that the conductors of our Ephemerides should announce, for the first part of each lunation, the immersions of "stars of even the 7th, 8th and 9th magnitude, which are as readily "observed as those of the 1st, 2nd and 3rd magnitude." Connaissance des Tems, Année viii. page 319. B.

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(for instance, in the measurement of the degrees of the meridian) it surely is not requiring too much that the trifling expense should be incurred of enabling astronomers to travel to places more favourably situated for making observations of such occultations. This would be an undertaking worthy of a sovereign who wishes to distinguish himself as a patron of science. We should, by such means, gradually arrive at a knowledge of the relative length of the terrestrial radii, in a great number of places: and, it is most probable that we might thereby be enabled finally to deduce the true and exact figure of the earth.

§ 18. Although it appears, from the different measurements of the degrees of the meridian, that the figure of the earth is not regular, still it is possible that the irregularities do not belong so much to the figure, or the radii, as to the nature of the upper strata, the different density of which may occasion the concealed error in the perpendicularity of the instruments: an error which (as I have elsewhere shown) may be quite sufficient to reconcile all the disagreements between the measurements hitherto taken*. Consequently the varia

Independent of the deviations arising from the causes here alluded to, the plumb-line has been sometimes known to be attracted towards the sides of the glass vessel, containing the weight, as powerfully as gold-leaf towards an electrical tube. The remark ap

tions in the parallax in different latitudes might very well proceed with as much regularity as appears to exist in the variation of gravity, and in the length of the pendulum.

§ 19. It is in the power of every principal Academy materially to assist in such a discovery, by two methods. First, in regard to times past, to collect together, from all quarters, the observations of occultations stated to have been made in a given interval; for instance, in the last ten years: and to employ some calculator to select and compute all those which are proper for showing the variation of curvature at different places. Secondly, with respect to the future, to insert in the Ephemerides

pears to have been made by M. Flaugergues. "Astronomers ought "to avoid using a glass vessel for the water in which the weight of "the plumb-line is suspended; for, I have observed twice, in one “year, a singular deviation in the plumb-line occasioned by the at“traction of the ball of the plumb-line towards the side of the vessel "in which it was suspended. This ball was drawn towards the side "with as much rapidity as gold-leaf is attracted by an electrified tube: " and I was obliged (in order to destroy the effect of this spontane"ous electricity, so as to enable me to take equal altitudes) to put a coating of sealing-wax upon the ball. But, since I have substi"tuted a metal vessel, this singular phænomenon has not again oc"curred." Connaissance des Tems, Année xiii. page 413. Although such a powerful impulse as this may not often have occurred, yet it is possible that slight deviations from the perpendicular may frequently have arisen from the cause here alluded to; and which may account for some anomalies which have been remarked in the observations made in the course of the surveys. B.

accurate notices of those places or districts where it would be most important that any occultation should be observed (particularly of the principal stars), in order that it might serve to apprize, and excite the attention of such astronomers as might be favourably situated themselves, or contiguous to more advantageous situations. It appears to me that such notices would be more important and useful than those of the phases of solar eclipses, about which the calculators of Ephemerides are in the habit of taking so much trouble.

END OF THE MEMOIR.