fuch calculations and aftronomical obfervations; and to this the doctor very properly bears teftimony at the end of his Remarks. In juftice, fays he, to captain Phipps, I think myfelf obliged to inform the public, that the foregoing letter is publifhed with his confent; and that I have his authority to fay, that the calculations which have given occasion to it, namely that of the retardation of the fun's return to the vertical wire, and that of the time which the fun's diameter should take to pass the vertical wire, were both made by Mr. Ifrael Lyons.' We are the more furprised that Mr. Lyons has fallen into thefe errors, when we confider the refpectable rank, as a mathematician, which he has held for many years; and we would willingly fuppofe that they have happened through fome hurry or inattention; for which, however, he is perhaps not entirely excufable in a business of such serious and great importance.

To give a brief account of the nature of these mistakes, and of the experiment which occafioned them, it may be obferved that, in many inftances the figure of the earth having been found not perfectly globular, but rather approaching near to the figure of an oblate fperoid : various means have been used to inveftigate the ratio of the axis to the equatorial diameter of the earth, or the degree of ellip ticity of the meridians, if indeed they are ellipfes among thefe, that which is derived from the confideration of the dif ferent lengths of the pendulum vibrating feconds, or the dif ferent numbers of vibrations performed in the fame time by pendulums of the fame length, in different latitudes, hath long been attended to with much care and precifion; it being judged one of the best methods, as thofe obfervations, when accurately made, give the proportion of gravity between the feveral places of obfervation. As experiments of this kind had never been made in fuch high latitudes as captain Phipps was like to advance to in his voyage; among the many objects of enquiry which he had judiciously proposed to himself, this appeared too interefting to be neglected; and he accordingly provided himself with the most accurate means of obfervation. He took with him, for this purpose, a pendulum formerly made by Mr. Graham, and now refitted up with fome additional contrivances by Mr. Cumming: this pendulum, which was accurately adjufted to vibrate feconds at London when the thermometer ftood at a certain height, the captain fet up in the latitude of 79° 50′; and having carefully obferved its vibrations for above 24 hours together, he hoped to obtain the rate of its going, or the number of vibrations made in a given time, and.of courfe what depended on it by a compa

E 4

rifon

rifon with its first rate in London, after the proper allowance is made for the different ftates of the thermometer. In making fo nice an experiment as this, it is evident that the time, in which the certain number of vibrations of the pen. dulum are obferved to be performed, must be determined with great precifion; this time then he very prudently proposed to determine by two different methods, that fo they might mutually check or confirm each other: the one of these methods was by obferving the number of vibrations performed during one entire revolution of the fun, from a given vertical circle till his return to the fame the next day; and the other by a good watch, which had been obferved to go very regularly. In the latter method, during the 24 hours of obfervation, many comparisons were made of the time fhewn by the watch with the corresponding number of vibrations of the pendulum; all of which agreed very well with each other, and confpired to fhew that the watch went very regularly, and therefore gave the number of vibrations performed in a certain time as fhewn by the watch; or, in other words, its rate of going, as compared with the pendulum, was thus found. Another process was inftituted in order to determine its rate of going with regard to true time; which was effected by means of a number of obferved altitudes of the fun, whereby the time fhewn by the watch was reduced to apparent, and this again to mean or true time by the proper equation: and thus laftly was obtained the number of vibrations of the pendulum performed in a certain given portion of true time, through the means of the watch. In the process by the other method, the pendulum was put in motion when the fun's limb touched the vertical wire of a telescope, fixed for that purpose, and left remaining till the return of the fame limb to the vertical wire again the next day; when the number of vibrations of the pendulum, which had been performed during the revolution, were noted down: then because that, from the given latitude and day of the year, the true time of fuch a revolution of the fan can be accurately calculated; this being done, he thereby obtained the number of vibrations performed in a certain portion of true time, by this method alfo. On comparison, the refults of these two methods were found to agree very nearly together; and it was inferred from them, that, in the latitude of 79° 50', there would be gained between 72 and 73 feconds, in 24 hours, by a pendulum which vibrated feconds in London, after allowance was made for the different temperatures of the air. Unluckily, however, it is now found that the accuracy of thefe obfervations cannot be depended on, as their feeming agreement arifes entirely from Mr. Lyons having used

a falfe

a falfe rule in calculating the time of the fun's return to the vertical wire where the proper rule is used, it gives a conclusion on very different from the other, and induces fuch a rate of going to the watch, as is quite inconsistent both with its rate as determined from the observed altitudes of the fun, and with the rate at which it was regularly obferved to go during the whole of the voyage. It is reafonably fufpected, therefore, that this difagreement of obfervations must have happened through a small change in the position of the telescope between the times of the two obferved contacts; and therefore the other method is the only one from which any conclufion can be drawn in this experiment.

In this letter the doctor fays:

I am inclined to believe that the gain of the pendulum must have been very nearly what you reckon it. But the evidence of this refts entirely upon the comparison with the watch, and the fix altitudes of the fun taken with the aftronomical quadrant for determining the lofs of the watch. For the exact agreement which you think you find between the gain of the pendulum as refulting from the comparifon with the watch, and as deduced from the obfervation of the fun's return to the vertical wire of the equatorial telescope, is imaginary. The appearance of agreement arifes entirely from an error in the computation of the retardation of the fun's return; and when this error is fet right, the watch and the observation will be found to differ confiderably.

• The interval between the time when the fun's western limb touched the vertical wire on the 16th day of July, 1773, and the time of the return of the fame limb to the vertical wire on the day following, which your computer hath reckoned 24 h o 495, could be no more than 24 h o 14": for, a fmall change in the fun's declination is to the correfponding change in the hour-angle (not, as your computer ftates it, as the cone of the latitude of the place of obfervation, but) as the cofine of the Jun's declination to the tangent of the angle contained between the circle of declination and the vertical circle.'

He then demonftrates the truth of this rule; and, after giving the true calculation from it, he adds:

• Thus the obfervation gives the gain of the pendulum 37" more than the watch. But as the watch went fo well during the whole voyage, as its lofs in these twenty-four hours was afcertained by fix altitudes of the fun, and as the gain now given by the watch agrees fo nearly with the refult of the fubfequent comparifons at Smeerenberg Point, I have no doubt but that the error lies entirely upon the obfervation of the fecond tranfit. I fuppofe the telescope, from fome unperceived cause, had fhifted its azimuth; which is the more probable, as it does not appear that any means were used to verify the pofition of the intru

ment.

ment. Perhaps the fituation upon the small rocky ifland afforded none *.'

Befides the correction of the rule ufed by Mr. Lyons for the purpose above-mentioned, which is the chief bufinefs of this letter, the doctor gives a like correction of another falfe rule ufed by the fame gentleman in the note, page 161, in calculating the time in which the fun's diameter paffes the vertical wire.

In the conclufion of the letter he alfo remarks on the method used in deducing the ellipticity of the earth's meridians; and, after giving the calculation by Clairault's rule, he adds,

This is the juft conclufion from your obfervations of the pendulum, taking it for granted, that the meridians are ellipses: which is an hypothefis, upon which all the reasonings of theory have hitherto proceeded. But, plaufible as it may feem, I muft fay, that there is much reason from experiment to call it in queftion. If it were true, the increment of the force which actuates the pendulum, as we approach the poles, fhould be as the fquare of the fine of the latitude: or, which is the fame thing, the decrement, as we approach the equator, fhould be as the fquare of the cofine of the latitude. But whoever takes the pains to compare together fuch of the obfervations of the pendulum in different latitudes, as feem to have been made with the greatest care, will find that the increments and decrements do by no means follow thefe proportions; and in those which I have examined, I find a regularity in the deviation which little refembles the mere error of obfervation. The unavoidable conclufion is, that the true figure of the meridians is not elliptical. If the meridians are not ellipfes, the difference of the diameters may indeed, or it may not, be proportional to the difference between the polar and the equatorial force; but it is quite an uncertainty, what relation fubfitts between the one quantity and the other; our whole theory, except fo far as it relates to the homogeneous spheroid, is built upon falfe affumptions, and there is no faying, what figure of the earth any obfervations of the pendulum give.'

There is as little probability of determining the figure of the earth by another method which has been long and often attempted with much care and application, viz. by the different lengths of the degrees of the meridian. For this alfo is founded on the fuppofition, that the earth is a true fpheroid, which there is the greateft reafon to think it is not, because of the unequal denfities of its different parts. Even

Captain Phipps, in a letter to me of the 15th of September, fays, "You were right in fuppofing that the fituation of the telef cope did not admit of any means of verifying its pofitiono

grant

granting it to be a true spheroid, from which figure it certainly cannot be much different, ftill the degree of ellipticity is fo fmall, that the many causes of error attending the obfervations and measurements muft, in all probability, for ever defeat any attempt to determine the problem with a tolerable degree of accuracy. And indeed this is confirmed by the many trials which have already been made; several of which appear to have been performed with all poffible attention, and every cause of error moft carefully guarded against : yet when thefe feveral measures are compared together, and the ellipticity calculated accordingly, they produce fuch different conclufions, fome of them being four, five, or even fix times as great as others, that no dependence can be placed on any of them.

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230'

Upon the whole, as the quantity of ellipticity as computed by fir Ifaac Newton from the diurnal revolution and gravity towards the center, upon the fuppofition of the matter of the earth being homogeneous, is nearly a mean among all the feveral refults derived from different methods, we think the former may continue to be adopted preferably to any of thofe which vary fo widely from one another.

XI. Obfervations upon the prefent State of our Gold and Silver Coins, 1730. By the late John Conduitt, Efq. Member for Southampton, and Mafter of his Majesty's Mint. From an Original Manufcript. Formerly in the Poffeffion of the late Dr. Jonathan Swift. 8vo. 1s. 6d. Becket.

WHO

Hoever may have been the author of this piece, we will venture to pronounce it a very good compofition on the fubject, the arguments being clear, and founded on an extenfive plan. Though it was drawn up about the year 1730, yet the reafoning is general, and applicable to all times, and the perufal of it may prove very useful to every person who would be well acquainted with a fubject which is become so very interesting at this time.

The three principal articles which our author has in view, in thefe Obfervations on the Gold and Silver Coins, are their weights, their proportion to each other, and their exportation. In order to thefe, he first premises a fhort account of the nature of foreign trade and monies. He fays,

• When we cannot pay in goods, what we owe abroad, on account of the balance of trade, or for the fale or intereft of stocks belonging to foreigners, or for foreign national fervices, our

debts