details of their operations, observations, and calculations, were subsequently examined by a committee of men of science, many of whom were foreigners, collected at Paris, who confirmed their results, and by the sanction of such a union of talents, gave such a degree of credit and authenticity to their conclusions as could scarcely be acquired by other means;" and we have no doubt that the author, notwithstanding the advertisement above mentioned, will in future conceive that he is justified in pleading the sanction of the committee of the Royal Society for the publication of his memoir, as equally conclusive of the inaccuracy of the English measurement.

After the preceding compliments to Delambre and Méchain, and similar tributes to Biot, Arago, and Svanberg, he proceeds to his examination of the English survey.

These new measures,' he says, alluding to the three former, were found to confirm, in a remarkable manner, the general results of those which had preceded, and gave very nearly the same proportion for the excentricity and other dimensions of the globe, so that there would not have remained the smallest doubt respecting the figure of the earth being flattened at the poles, had there not been a fourth measurement performed in England, at the same time as that undertaken in Lapland, the results of which were entirely the reverse. This measurement, which comprised an arc of 2° 50′, was undertaken by Lieut. Col. Mudge, with instruments of the most perfect construction that had ever yet been finished by any artist, contrived and executed for that express purpose by the celebrated Ramsden. The details of the observations and other operations of Lieut. Col. Mudge may be seen in the volume of the Philosophical Transactions for the year 1803; and one cannot but admire the beauty and perfection of the instruments employed by that skilful observer, as well as the scrupulous care bestowed on every part of the service on which he was engaged. Bengal lights were employed on this occasion, as objects at the several stations, and their position appears to have been determined, with the utmost precision, by the theodolite of Ramsden, which reduces all angles to the plane of the horizon, and with such a degree of correctness, that the error in the sum of the three angles of any triangle is scarcely, in any instance, found to exceed three seconds of a degree, and in general not more than a small fraction of a second.

Accordingly, the geodetical observations were conducted with degree of exactness which hardly can be exceeded; and even if we suppose for a moment, that the chains made use of in the measurement of the bases, may not admit of equal precision with the rods of platina employed in France, nevertheless the degree of care employed in their construction, in the mode of using them, and the pains taken to verify their measures, were such, that no error that can have occurred in the length of the base, could make any perceptible difference in the sides of the series of triangles, of which the whole extent does not amount to so much as three degrees. ›

• Nevertheless,

Nevertheless, the results deduced by the author from this measure alone, would lead to the supposition that the earth, instead of being flattened at the poles, is in fact more elevated at that part than at the equator, or at least that its surface is not that of a regular solid. For the measures of different degrees on the meridian, as reduced by Lieut. Col. Mudge, increase progressively towards the equator.

The following table of the different measures of a degree in fathoms is given by the author in his memoir :

The singularity of these results excites a suspicion of some incorrectness in the observations themselves, or in the method of calculating from them. The author has not informed us in his memoir, what were the formula which he employed in the computations of the meridian; but one sees by the arrangement of his materials, that he made use of the method of the perpendiculars, without regard to the convergence of the meridians; and although this method is not rigorously exact, it can make but a very few fathoms more in the total arc, and will have very little effect upon the magnitude of each degree. It is therefore a more probable supposition, that if any errors exist, they have occurred in the astronomical observations, but it is scarcely possible to determine the amount of the errors, or in what part of the arc they may have occurred, excepting by a direct and rigorous computation of the geodetical measurement. I, have, therefore, been obliged to have recourse to calculations, which I have conducted according to the method and formulæ invented and published by M. Delambre.'

We cannot enter very minutely into the method pursued by Don J. Rodriguez for the detection of this supposed error, but we intend to give a general view of it. We must first, however, be allowed to make one observation on what we consider to be a want of ingenuousness in the preceding passage: we allude to that part in which the author asserts that, admitting an error, there was more reason à priori to suspect it to lie in the astronomical observations, than in either the geodetical observations or the calculations; and that he therefore merely went over the latter in consequence of their connection with the former, and not with the expectation of detecting any inaccuracy in this part. Now we appeal to any man, who is conversant in these matters, whether, supposing an error to

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exist,

exist, it is not much more likely to occur in the geodetical operations or calculations, than in the astronomical observations; and we have little doubt that such was the author's own opinion in the first instance. The fact is, however, that he had gone over the calculations before he wrote this paragraph, and found all that part extremely correct; and then, in order that it might act least against his own conclusion, he states it as a circumstance which was à priori to be expected. Had the author said, "my first idea was that the error was in the geodetical part of the operations: but, on recomputing them on different principles from those that were employed by Col. Mudge, I find them perfectly correct; and therefore, the error must be in the astronomical observations;" — had he, we say, given the sentence in this form, it would have put us on our guard with respect to admitting the latter inference whereas, by the turn which he has given to it, he in some measure prepares the reader to receive his conclusion, by referring him to the astronomical observations as the most probable source of error.

Let us now take a concise view of Don J. Rodriguez's investigations and conclusions.

For this purpose, without inquiring at present concerning the nature of the particular elements which the author has em ployed in his calculations, it will be sufficient to observe that they are deduced from other measurements, with which the English measurement does not agree, at least in the subdivision of the arc; for, as to the whole arc, they coincide as nearly as we might expect, on the supposition of the earth being a perfect spheroid.

With regard to the absolute measured length of the arc in fathoms, it has been verified, as we have seen, by the computation of the whole series of triangles, from Col. Mudge's own data; and therefore no doubt remains as to the accuracy of this part of the undertaking. The whole angular measure of the arc also agrees very nearly with the result which might have been expected, by assuming the earth to be a perfect spheroid, of certain excentricity, and its equatorial radius of given magnitude: but, if the same elements be used in the subdivided arc, the results do not agree; and this disagreement is that which constitutes the singularity of the English measurement. Now Don Joseph Rodriguez, in order to discover the cause of this disagreement, assumes the earth to be a perfect spheroid, of which the compression is somewhere between 3 and and its equatorial radius between certain limits corresponding with these degrees of excentricity. With these elements, he computes what the number of degrees of the above mea

sured

1

sured arc ought to be on the above hypotheses, and finds that it nearly agrees with that which is deduced from Colonel Mudge's observations, which in course ought to have been expected; because he knew, previously to his computation, that the whole arc, compared with that with which he compared those of Delambre and Méchain, would give nearly the same elements, and consequently these elements would give nearly the same results. This coincidence therefore proves nothing with regard to the accuracy of the two extreme observations of the English arc, but merely the near agreement between the results of this measurement and that of Delambre, which in fact was previously known. For the same reason, the disagreement between the observed and computed parts of the subdivided arc is no proof of any inaccuracy in the intermediate observations; it merely shews their want of agreement with the French results, and even with the whole arc of which they form the parts; a circumstance also previously known, and which in fact gave rise to this author's investigations. Hence we may conclude, without any farther observations, that this memoir proves nothing but the author's extreme partiality for French science; because, unless it be admitted as an axiom that the French measures are perfectly correct, and that the earth is a perfect spheroid of rotation, not the least dependance can be placed on the conclusion which the author has drawn from his investigation.

As to the French measurement, we do not dispute its ac curacy; we know and respect the talents of the two able ma thematicians under whom it was conducted; and we wish not to estimate its correctness by elements and hypotheses drawn from the English trigonometrical survey: but, at the same time, we deny the right which Don J. Rodriguez has assumed, of judging of the latter by inferences deduced from the former.

We conceive that we have justly arrived at the above conclusions, without any reference to the particular elements which the author has assumed; let us now, before we finish, bestow a few lines on this subject. In the first place, it must be obvious to every reader that, unless the earth be a spheroid, and very regularly so, as the author has assumed, not one word of his observations, nor one line of his calculations, deserves a moment's attention: the first question, therefore, naturally is, "What is the opinion of philosophers on this subject?" to which we may answer, that nearly all, whose judgment is most to be respected, agree that the earth is not an uniform spheroid, nor even any solid of rotation. They have been led to this conclusion from the discordancy between the different degrees

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degree's of excentricity, drawn from a comparison of different measures; these varying in all degrees between is and both extremes arising out of a comparison of French measures with each other; see La Place, Exposition, p. 56.; also Puissant, Geodesia, p. 187. and p. 222. Yet, in direct contradiction to these authorities, and numerous others that might be brought, Don J. Rodriguez assumes the earth to be a spheroid, and very regularly so, and on this ipse dixit alone he wishes to destroy all confidence in the results of the English measurement.

Another cirumstance, we think, is conclusive as to the credit that is due to the present memoir. According to the writer, it appears that the principal astronomical error must have occurred at the station at Arbury Hill, where the computed and observed latitudes differ little less than 5" which discrepancy he attributes wholly to Col. Mudge. Now it happens unfortunately for Don Joseph Rodriguez, that the latitude of this place is readily verified by means of Blenheim Observatory, which is situated on very nearly the same meridian; and the distance between the parallels of latitude of the two places is only 139,322 feet. This distance gives for the difference of latitude 22' 59'33; and the absolute difference of the two, as determined from the observations made at Arbury Hill by Col. Mudge, and those made for five years at Blenheim, gives for this difference 22′ 59′′ 6; which is a most remarkable coincidence, confirming at once the accuracy of the astronomical observations at this station, and therefore also of necessity manifesting the fallacy of Don Rodriguez's investigations, or at least of the inferences which he deduces from them.

That the English survey presents very singular results, we readily admit; and that philosophers should feel a desire of accounting for them, and other similar anomalies, independently of an irregular formation in our globe, we can easily imagine; because, while a system of uniformity and order is almost every where apparent in the grandest operations of nature, the mind seems unwilling to admit a deviation from it in this particular instance. We must, however, be careful that the judgment is not biassed on this account; the perfect spheroidal figure of the earth is but an hypothesis; and an hypothesis, not completely confirmed by experiment or observation, is always to be admitted with extreme caution. It is this principle, introduced by Bacon, and adopted by Newton, which places modern philosophy so pre-eminently above that of the antients; and it is our duty to preserve it unimpaired.

This consideration will not prevent us from examining, very minutely, any deviations from what appears to be a rational hypothesis; it only guards us against a too precipitate conclusion,

and