"IN

"TN a paper, containing an account of the discovery of two fatellites revolving round the Georgian planet, I have given the periodical times of these fatellites in a general way, and added, that their orbits made a confiderable angle with the ecliptic. It is hardly neceffary to mention, that it requires a much longer feries of obfervations, to fettle the mean motions of fecondary planets with accuracy, than I can hitherto have had an opportunity of making; but fince it will be fome fatisfaction to aftronomers to be acquainted with feveral of the moft interefting particulars, as far as they can as yet be afcertained, I fhall communicate the refult of my paft obfervations; and believe that, confidering the difficulty of meafuring objects which require the utmoft attention even to be at all perceived, the elements here delivered, will be found to be full as accurate as we can at this time expect to have them fettled.

"The most convenient way of determining the revolution of a fatellite round its primary planet, which is that of obferving its eclipfes, cannot now be ufed with the Georgian fatellites, as will be fhewn when I come to give the pofition of their orbits; and as to tak

ing their fituations in many fuccef. five oppofitions of the planet, which is likewife another very eligible method, that muft of courfe remain to be done at proper opportunities. The only way then left, was to take the fituations of thefe fatellites, in any place where I could ascertain them with any degree of precifion, and to reduce them afterwards by computation to fuch other fituations as were required for my purpose.

"In January, February, and March, 1-87, the pofitions were determined by caufing the planet to pafs along a wire, and eftimating the angle a fatellite made with this wire, by a high magnifying power; but then I could only ufe fuch of these fituations where the fatellite happened to be either directly in the parallel of declination, or in the meridian of the planet; or where, at least, it did not deviate above a few degrees from either of them; as it would not have been safe to truft to more diftant eftimations. In October I had improved my apparatus fo far as to measure the pofitions by the fame angular micrometer with which I have formerly determined the relative pofitions of double ftars.

"In computing the periods of the fatellites, I have contented my

felf with fynodical appearances, as the pofition of their orbits, at the time when the fituations were taken from which these periods are deduced, was not fufficiently known to attempt a very accurate fidereal calculation. By fix combinations of pofitions at a distance of 7, 8, and months of time, it appears that the first fatellite performs a fynodical revolution round its primary planet in 8 days 17 hours 1 minute and 1, feconds. The period of the fecond fatellite, deduced likewise from four fuch combinations, at the f.me distance of time, is 13 days 11 hours 5 minutes and 1,5 feconds. The combinations of which the above quantities are a mean, do not differ much among themfelves; it may therefore be expected that these periods will come very near the truth; and, indeed, I have for many months paft been used to calculate the places of the fatellites by them, and have hitherto always found them in th fituations where thefe computations gave me reafon to expect to fee them.

"The epochæ, from which aftronomers may calculate the pofitions of these fatellites, are October 19, 1787; for the first 19 h. 11′ 28′′; and for the fecond 17 h. 22′ 40′′ There were at thofe times 76° 43′ north following the planet; which, as will be fhewn in the fequel, is the place of the greatest elongation of the fecond fatellite; where, confequently, its real angular fituation is the fame as the apparent one. And I have brought the firft fatellite to the fame place, as hitherto there has not been time to difcriminate the fituation of its orbit from that of the fecond.

"The next thing to be deter mined in the elements of thefe fatellites, is their diftance from the $788.

planet; and as as we know that, when the periodical times are given, it is fufficient to have the distance of one fatellite, in order to find that of any other, I confined my attention to the discovery of the distance of the second. As foon as I attempted measures, it appeared, that the orbit of this fatellite was feem. ingly elliptical; it became therefore neceffary, in order to afcertain its greateft elongation, to repeat these measures in all convenient fituations; the refult of which was, that on the 18th of March, at 8 h. 2′ 50", I found the fatellite at the diftance of 46",46; this being the largest of all the measures I have had an opportunity of taking. Hence, by computation, it appears, that the fatellite's greatest vifible elongation from its planet, at the mean diftance of the Georgian fidus from the earth, will be 44",23.

"It ought to be mentioned, that in the reduction of this measure, I have ufed Meyer's tables for the fun, and the tables published in the Connoiffance des Temps of the year 1787, reduced to the time of Greenwich, for the Georgian planet.

"Very poffibly this diftance might not be taken exactly at the time when the fatellite happened to be at the vertex of the tranfverse axis of its apparently elliptical orbit; but, from other measurements, we have reason to conclude, that it could not be far from that point. For inftance, the 9th of November, at 15 h. 56", by a mean of four good measures, the fatellite was 44",89 from the planet; which, by calculation, reduced to the fame distance of the Georgian fidus from the earth as the former, gives 41",33. And likewife, the 19th of March, at 7 h. 45′ 59′′, the distance

H

mea

meafured 44",24; which, computed as before, gives 42",15. Now, we find, when the places are calculated in which the fatellite happened to be at the times when thefe two measures were taken, that they fall on different fides of the former meafure, and alfo on oppofite parts of the fatellite's orbit; but that nevertheless they agree fufficiently well with the pofition of the tranf verfe axis which we have adopted in the fequel.

"Admitting, therefore, at prefent, that the fatellite moves in a circular orbit about its planet, we cannot be much out in taking the calculated quantity of 44",23 for the true measure of its diftance. And, having afcertained this point, we calculate, by the law of Kepler, and the affigned period of the first fatellite, that its diftance from the planet must be 33",09. I ought however to remark, that, in this computation, a true fidereal period fhould have been used; but, as that cannot as yet he had, the trifling inaccuracy thence arifing may well be excufed, till, at fome future opportunity, we may be permitted to repeat these calculations in a more rigorous manner."

"It remains now only, in order to complete our general idea of the Georgian planet, to investigate the fituation of the orbits of its fatellites. I have before remarked, that when I came to examine the distance of the fecond, I perceived immediately that its orbit appeared confiderably elliptical. This induced me to attempt as many measures as poffible, that I might be enabled to come at the proportion of the axes of the apparent ellipfis; and thence argue its fituation. But here I met with difficulties that were indeed

almost infurmountable. The uncommon faintness of the fatellites; the fmallnefs of the angles to be measured with micrometers which required light enough to fee the wires; the unwieldly fize of the inftrument, which, though very manageable, ftill demanded affistant hands for its movements, and confequently took away a great share of my own directing power, a thing fo neceffary in delicate obfervations; the high magnifiers I was obliged to ufe by way of rendering the spaces and angles to be measured more confpicuous; in fhort, every circumftance feemed to confpire to make the cafe a defperate one. Add to this, that no measure could poffibly fucceed which had not the most beautiful fky in its favour; and we may eafily judge how scarce the opportunities of taking such measures muft be in the variable climate of this ifland. As far then as a fmall number of select measures will permit, which, out of about twentyone that were taken, amounts only to five, I fhall enter into our prefent fubject of the pofition of the fecond fatellite's orbit.

"The following table contains in the first column the correct mean time when the measures were taken, The fecond gives the quantity of thefe measures. In the third columu are the fame measures reduced to the mean distance of the Georgian planet from the earth. The fourth contains the calculated pofitions of the fatellite as it would have ap peared to be fituated if it had moved in a circular orbit at rectangles to the visual ray; and the degrees are numbered from the first observation fuppofed to have been at zero, and are carried round the circle from right to left.

March

"The light of the fatellites of the Georgian planet is, as we may well expect, on account of their great distance, uncommonly faint. The fecond is the brightest of the two, but the difference is not confiderable; befides, we must allow for the effect of the light of the planet, which is pretty strong within the fmall diftances at which they are revolving. I have feen fmall fixed ftars, as near the planets as the satellites, and with no greater light, which, on removal of the planet, fhone with a confiderable luftre, fuch as I had by no means expected of them. A fatellite of Jupiter, removed to the distance of the Georgian planet, would fhine with lefs than the 180th part of its prefent light; and may we not conclude, that our new fatellites would be of a very confiderable brightness, if they were brought fo near as the orbit of Jupiter, and thus appeared 180 times brighter than at prefent? Nay, this is only when we take both the planets at their mean distance; for, in their oppofitions, a fatellite brought from the fuperior planet to the orbit of the inferior one, would reflect nearly 250 times the former light; from all which it is evident, that the Georgian fatellites must be of a confiderable magnitude.

"If we draw together the refults of the foregoing calculations into a fmall compafs, they will ftand as follows:

The firft fatellite revolves round

the Georgian planet in 8 days 17 hours 1 minute and 19 feconds. "Its distance is 33′′

"And on the 19th of October, 1787, at 19 h. 11′ 28′′, its pofitiort was 76° 43′ north following the planet.

"The fecond fatellite revolves round its primary planet in 13 days 11 hours 5 minutes and 1,5 feconds.

"Its greatest distance is 44′′,23.. "And on the 19th of October, 1787, its position at 17 h. 22′ 40′′, was 76° 43′ north following the planet.

"Laft year its least distance was 34",35; but the orbit is fo inclined, that this meafure will change very confiderably in a few years, and by that alteration we shall know which of the double quantities put down for the inclination and node of its orbit are to be used.

"The orbit of the fecond fatellite is inclined to the ecliptic S 99° 43′ 53,3" }

81 6 4,4 "Its afcending node is in 18 degrees of Virgo {16 degrees of Sagittarius

}

"When the planet paffes the meridian, being in the node of this fatellite, the northern part of this orbit will be turned towards the Eaft

"The fituation of the orbit of the first fatellite does not seem to differ materially from that of the fecond.

H 2

"We fhall have eclipfes of thefe fatellites about the year 198

{

1799 1818 ( when they will appear to afcend through the shadow of the planet almoft in the perpendicular direction to the ecliptic.

"The fatellites of the Georgian planet are probably not lefs than thofe of Jupiter.

"The diameter of the new planet is 3421 miles.

"The fame diameter feen from the earth, at its mean diftance, is

3,90554.

"From the fun, at the mead distance of the earth, 1 14,5246. "Compared to that of the earth, as 4,21769 to 1.

"This planet in bulk is 80,49256 times as large as the earth.

"Its denfity as,220401 to 1. "Its quantity of matter, 17,74 0612 to 1.

"And heavy bodies fall on its furface 8 feet 8 inches in one fecond of time."

R. Franklin, in various

"comes charged plus, the other mi

his Experiments and Obfervations, afferts, that the natural quantity of electric fluid in glafs cannot be increased or decreased; and that it is impoffible to add any to one furface of a plate or jar, unless an equal quantity be, at the fame time, given out from the other furface. This error has been adopted by fucceeding electricians among others, by the late Mr. Henly, who in one of his laft papers, printed in the Philofophical Tranfactions for the year 177 has the following words:

66

According to Dr. Franklin's the"ory, the fame quantity of the e"lectric matter which is thrown up"on one of the furfaces of glafs, "in the operation of charging it, "is at the fame time repelled or dri

ven out from the other furface; " and thus one of the furfaces be

"is, I think, fatisfactorily proved, "&c."

"Beccaria alfo has adopted the fame opinion, faying, “That a "quantity of exceffive fire cannot "be introduced into one surface, "but inasmuch as an equal dofe of "natural fire can quit the other "furface."

"These affertions are, I apprehend, directly contrary to what really happens. Inftead of which, I believe, we may fafely affert, that glafs, and every other known fubftance, may have its natural quantity of electric fluid either increased or diminished to a certain limited degree; which degree hears no proportion to the quantity of matter contained in a body, but is (cæteris paribus) in proportion to the extent of its furface.

"This