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Herschel's observations relative to Venus labours of its observatory ; Marcus Au-, and Saturn, and Miss Caroline Herschel's guftas Pictet Turtin (born on the 23d account of a new comet, being the sixth July, 1752), who is entrusted with the she has discovered ; this, however, was fuperintendence, hopes to render it ferfeen at Paris, by citizen Meilier, on the viceab'e to the caule of astronomy, and 17th of September.

he has come to Paris, expressly for the P. Piazzi, an astronomer of Palermo, in purpose of procuring new inftruments. Sicily, has published the description of a The profesors Tralles, of Berne, and tuperb inftrument, a circle of five fect Hafiler, have measured triangles and diameter, constructed by Ramsden, and bases at Arau, in the canton of Soleure, also an account of the observa!ions inade in order to connect the chart of the can. with it. These a e contained in a tons of Berne, Bafle, and Soleure, with volume in folio, entitled : Della specola that of France. Froin their obserrations, astronomica de' regi ftudi di 1 alermo, libri we learn, that the latírude of the steeple quatro 'de' Giuseppe Piazzi, C. R. regio of Berne is 46° 56' 55"; and that it is profefore d'Astronomia, &c.In this im- firuared 20' 25" to the east of Paris. portan't work, we find the exaEt latitude M, Schroeder has constructed a 25of the Observatory of Paiermo to be 380 feet telescope at Lilienthal, vear Bremen, 644"; rand its longitude 44' 3" cast of which equals his expectations; and M. Paris. One surprised to discover in Schrader, of Kiel, in Holftein, another this work, that, in a country lying so far of 26 feet. - M. de Hahn, an opulent to the fouthward, ihe sky, lo serene and individual of Mecklenburg, has received agreeable to mankind, mould be but limle a zo feet telescope from Mr. Herschel, of favourable to the astronomer, during cight a fuperior qualiiy, which he has fixed at months in the year.

Citizen Dangos, liis house, at Kemplin, near Hamburgh ; who has resided a long time at Malta, the fmall mirror is omitted, according to which is in latitude 36°, has made a Herschel's method; this was proposed in similar remark respecting it.

France, so early as 1728, by Lemaire. The astronomers of Milan have See, “ Recueil des Machines approuvées par finished the triangles for their grand l'Académie." TOM. VI. meridian as far as Genoa, and measured M. Bode, the celebrated astronomer of the base ; but they have not as yet re- Berlin, who publishes an ephemeris anceived the large séctor, with which they nually, has just added a supplementary hope to be able to measure the celestial volume, which is said to contain observa

rions of considerable importance : this Doctor Slop, astronomer at Pifa, has circumstance has induced me to study continued his observations from 1782' to German, and also to request, that a 1986, with the calculations dependent professor of that language may be added on them; and M. Klügel, professor at to the establishment of the college of Halle, has published in the Memoirs of Prance. the academy of Gottingen, some en. The obfervations of P. Fixlmillner, quiries relative to the perturbations of from 1776 to 1791, have lately appeared, planets. Mr. Wurm, of Nurtingen, in under the title of " Alia Astronomica Creo Wirtemburg, has entered into a laborious " mifanenfia,” but we have lost the auexamination of the diameters of planets, thor. Placidus Fiximillner

was born a subject relative to which there is much May 29, 1721, athe castle of Achleuthe, uncertainty : for example, the diameter near the abbey of Benedictines, at Crema of Saturn is 11" according to M. Bugges, munster, in Austria. He studied phi13" according to M. Zach, and 20“ ac- lofophy at Saltzburgh, in 1735, and be. cording to Herschel.

came attached to mathematics; but on M. Barry, astronomer, at Manheim, his entering into the order of Benehas, until of late, carried on his observa: dictines, he was diverted for several rions with zeal and affiduity ; but the years from his favourite pursuits, by bombs and bullets of the French army theology and canon law Luckily, howa have nine different times struck the ob. cver, in 1761, being then in his 4oth fervatury, which is one of the most re- year, he was permitted to cultivate altro. markable and elevated objects belonging nomy, on account of the tranfit of Venus to that city : on this account the inliru. across the fun : alone, and buried in the ments were all dismounted, and sent be- folitude of a remote province, at a dis. yond the mountains of Suabia.

tance from cities, zoademies, and the The revolution at Geneva, in 1794, learned; or, in other words, from all ob. has not interfered, in the least, with the jects which sustain courage, and excite



1796. ]
Lalande's History of Astronomy, 1794

555 emulation, this amiable man dedicated his my Abridgement of Aftronomy in his life to the most abstruse parts of the vernacular tongue. Since the death of fçience. He was very serviceable to me Tindu, M. Jumelin, a physician, M. when I published my tables of Mercury, Chevalier, and M. Racord, a pilot on and was one of the first who calcu- board a French brig, have made a few lated the orbit of the planet Herschel, observations at Constantinople; but in for which he also constructed tables. order to fix, pretty nearly, the exa&t The various orders of friars, hitherto position of the eastern part of the Black useless to mankind, have an oppor- Sea, at the same time with the south of tunitv, in those countries where they the Caspian, citizen Beauchamp has been are still permitted to exist, to be of some sent into Persia, at my solicitation, and he little service to the world, by following has been appointed conful at Malcate, in the noble example of the convent of Arabia, which will enable him to furnish Cremfmunster.

us with still more important materials. Astronomy has experienced other losses, On the 7th Ventose (25th of February) during the present year;, in particular, was executed the ci-devant Barop de we have reason to regret Bailly, Du Se- Marivetz, who had been employed in a jour, and Saron. On the 14th Brumaire work, called “ La Physique du Monde," (14th Nov.) died the citizen Flecheux, published between 1780 and 1787, in 7 author of an ingenious planisphere, and vols. 4to. His youth was spent amidst the of a geocylic machine (Macbine Géocy- dissipations of a court, and he had not tique) for representing the parallelism of applied himself to literature until a period the earth’s axis: he was 55 years old. of life, when old habits are renounced On the 21st Brumaire (11th November) with great difficulty, Vols. II. and III. Perihed Silvain Bailly, hose éloge 1 are dedicated to astronoiny. have already published. On the 3d Ni.. Citizen Saron, in his 64th year, fell vose (23d December) Philip Lesne, my alfo a victim to that tribunal of blood, selation and pupil, died of a disease which spared neither science nor virtue. contracted while serving his coụntry, His sole crime appears to have been, the ia the markes of La Vendée. His death possession of a large fortune; in addition is a great loss to astronomy. On the 8th to this, he was formerly first president of Nevoje (28th December) P. M. T. the late parliament of Paris. He was reLebrun luffered on a public scaffold. ceived into the Academy, in 1779, and was He lived

for some time at the observatory, extremely useful to us, more especially in but he soon embarked in other pursuits, the calculation of comets ;, all those oband rose to the head of the Foreign de served for several years, were calculated partment. He, however, brought up by him, and that, ton, with a most afto. his younger brother, Achilles Tondu, nishing facility. He procured instruments to attronomy; in consequence of which at a great expence, and lent them to he accompanied the ambassador, Choi- men of science, with an exemplary seul Gouffier, to Conftantinople, and died 'generosity. there, in 1787, ouly 28 years


To the other losses sustained during a ter having made a variety of remarks tyranny of nine months, I may fairly extremely useful t9 geographers, respect. add that of Lavoisier, who perished on ing the country as far as the mouth of the 19th Floreal (May 8th), and Wallo, the canal that communicates with the who fell on the ninth Toermidor (J sy Black Sea. The Turķs would not pere 27th:). mit the French to make observations at We have also to regret M. NiewTrebisonde, and Sinope; the Englig land, of Leyden, who had composed an and Russians also opputed this plañ : be interesting work on Nautical Aftronomy, lides this, we about the same time loft which the Dutch stood in great need of, the two beft-informed musulmans be- as this branch of foience is too much longing to the whole empire One of neglected in their country. He had spent them was the Yisir Halil Pacha, decolo a whole summer in the grand observatory láted at Tenedos. He had formed a belonging to M. Zach, at Gotha, and school for the artillery and engineers, we expected great things from his zeal and-caused our clemen:ary creatiles to be and skill. tranflated for their instruction. The The last mi fortune of this kind, in other was the Vice-Admiral Capitana, the course of 794was in the person of Bey, whose head was struck off in Oc- citizen Achilles Peter Dionis du Sejour, tober 1787; he was in possession of ex. of the ci-devant Academy of Sciences, celicnt instruments, and had "published the Academies of London, Stockholm,

4 B 2


age, af

and Gottingen, and councellor of the tacked by a malignant fever, which his great chamber of the Jare parliament of constant uneasiness since the death of ci. Paris. He was born in this capital, rizen Freteau, rendered more dangerous. January 11:1, 1734, and studied at the He died on the 5th Fructidor (22d Aug.) college of Jesuits, from 1743 to 1750. in the 60th year of his age, at his country He was admitted in the Academy as an house, ar Angerville, near Fontainbleau, associate in 1765, at which time, his which had formerly belonged to the brethren in the parliament pretended he famous Lord Bolingbroke. could only fit as an honorary member; His fimpiicity was correspondene to but he despised the suggestions of vanity, his learning and virtues, for there was and deemed himself honoured by belong. nothing in his drois or ma, ners, that ing to a body of learned men, under announced the poffeffion of great knowany denomination

ledge, an exalted fituation, or a large On this occasion, he undertook a series fortune. of labours, which he followed up during thirty years, with equal assiduiry and MATHEMATICAL CORRESPONDENCE. success; this was the application of the

To ibe Editor of the Monibly Magazine. algebraic analysis to all the branches of astronomy, and especially to eclipses. SIR, Afronomers have always neglected ana: T *HE letters of your correspondents lyses too much; the observations and A. SEARCH and No CONJURER, re.. calculations necessary to produce resulis, vived fome early imp etfions made on my demanding so much time, that they mind, in the course of my youthful studies ; would have litele or no leisure for ab. and I was excited to re-examine the ftract speculations. Du Sajour is the difficulties, which I had encountered in first who addi&ted himself entirely to this a fcience, in the endeavour to obtain the branch of science, and he made an im. comprehension of a mode of real ning, portant application of it, in determining by which such wonders are faid to be the longitudes of a great number of towns perforined. by means of the eclipses of 176 and In the course of this pursuit, Mr. 1769.

FREND's Algebra was lately put into In consequence of a Mimoir, written my hands; and I found myielf in the by me, respecting the comers tvhich had situation of those persons, whom he doaffrighted alt France in 1773, ne drew scribes in his preface, as having waded up a Treatise on this subject. He pub- “ through a few chapters of Moclaurin's liihed it in 1775, and exbivited a mode. Alyebra; but frightened, and with of calculating the orbit of a comet, by “ good reason, at Cardan's Rule," and, means of three obfervations; this is one contequently, unable to proceed farther of the most difficul: problems in aftro.' in that part of my mathematical studies. nomy. In this work, he demonitrated, There was no great difficulty, indeed, how difficult it was to conceive the en. in comprehending Cardan's process : but counter of a comer with the earth, in when I came to the application of it to the order of probabilities, or even in practice, I do not know whether it fucpossibilities--for he went so far as that. ceeded once in the equations which I 1 know that such an affertion ought to formed at random ; and I was told hy be accompanied by restrictions, but it the initiated, that it would not do unless was necessary to dispel terror, ônd nothing two impoffible' roots were in the equa. could be more useful than a pubication rion how to make these impotlible roots, of this kind, in order to comfort the or ro discover whether they were in any public.

propused equation, I was totally at The disappearance of Saturn's ring, Joss. which ha pens once every fifteen years,

As the rule was demonstrated to me, induced Di Sijour to publish a volume * was made equal to atub and then ! in 8vo, in 1776, on this subject. In was told, that as only one fuppofition 1786 and 1739, he completed two large had been, another might be made 4ro volumes of his works, under the rjele namelv, that 3ab might be equal to'qi of “ Traité Analytique des Mouvemens Mr. Frend denies this, and says, thật apparens ues Corps celeftes."

3ab can be equal to g only in particular It was in the midst of labours such as cases ; and brings as a proof, the equa. thefe, notwithstanding every appearance rion *+274–28=0, in which x=1, of a robust conftitution, that he was at consequently, atbai; and, therefore,


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Mathematical Correspondence.

357 Mr. Frend says, that, as a and b are both arcs are also nearly as the above-menless than unity, 3ab cannot be equal to tioned differences, and the arcs themserves 27. If this is really the case, and I fee nearly as the chords : therefore, the no means of contradicting it, the adop- abovementioned differences, when the arcs cion of Cardan's Rule must lead every are small, are as the squares of the arcs, one who depends upon it, into continual quam proxiniè. error, unless

there is some method A mean of the principal measures of pointed out by Algebraifts, which tills a' degree of latitude, taken foce 1736, him, when he may apply the rule to a: by Maupertuis, Callini, Boscowich, Maparticular case, or when it fails. I have son, and Dixon; Bouguer and de la heard, indeed, that there must be two Condamine, de la Caille, &c. in diffeimpoffible roots in an equation, to bring rent parallels, gives 69.076947 English it under Cardan's method : but the pro- miles, or 5526.19576 chains; which cess of finding them out, must make the multiplied by 1.003, being about half rule very tedious and difficult of appli. the ratio of the equatorial diameter to cation

the axis, gives 5542:7 chains, for a mean Again, Mr. Frend objects to the equa- degree of a great circle ; whose, radius tion used in explaining Cardan's Rule, will

, consequently, be 397579 chains. aitabstr=o, and calls it absurd : for, From hence, we have one chain=.64949, says he, three numbers addedt "gether, of a fecond, the difference between cannot be equal to nothing. Doubtless, whose natural secant and radius is = according to his position, which does noc (11)4957156; and this multiplied by admit of negative numbers, the expression 319579 gives .00000157429 of a chain, is absurd: but I should be much or .00124683 of an inch ; from whence obliged to some one of your correspond. the derivation of the rule is easy. ents to inform me, what is the real use The construction of a table from there of these negative numbers; and whether, data, is too obvious for explanation. It if equations can be folved without them, might be calculated for every 100 chains she supposition should be admitted into as far as necessary ; but, as the firft dif. a work of science ? In Mr. Frend's ferences of the terms would not be equal, . book, various equations are solved, with. it would be necessary, if considerable out admitting them: the true folution is accuracy were required, to be prepared brought out by one root, when, accord. with a table of equations of second dif. ing to the common mode, two roots ap- ference constructed upon the common pear; and the learner is to iry which of theorem for iis interpolation; fo that, them is the true one. If this method upon the whole, it seeins better to calmay be pursued throughout the whole culate it for any particular case, from of the science, there secins to me to be Mr. Waddington's rule, which will be fomething gained by simplifying the somewhat nearer the truth if we put principles; but, before I give up en- 1247 for 124, and cut off fix places in. tirely the old mode, I should like to be stead of five." Or it will be the easiest well informed, what loss will be sustained way of any, by using the number 125, in the higher parts of algebra, by reject. which is nearer than Mr. Waddington's, ing the negative quantity for, to lay and being = one-eight of 1000, therethe truth, it frequently puzzled me so fore only cut off rwo figures, and divide much, that, though I can get through a by 8, or take the footh part. quadratic equation, all beyond seems to If we use logarithms, we shall get a me to be enveloped in impenetrable dark- rule which, I think, may be found nefs and mystery:

somewhat Ihorter in its application, viz. I remain, fir, yours,

From double tbe logarithm of ibe distance Fuly 20, 1796. Exotericus. in chains, substract 2.904193, and the

remuinder will be the logarithm of the diffirQUESTION XIIJ (No. IV.).--Answered ence in inches between :be apparent and by 7. Fr.

true levels. The difference between the true and Either of the above rules, the last of apparenr level, is the difference between which is nearest the truth, will do till the earth's semi-diameter and the secant the arc becomes so large as to render the

arc of its circumference, whose error of the first hypothesis considerable, length is the given distance. The versed which will not be the case within the fines of circular arcs are as the squares of limits of any ordinary operation of this their chords ; the versed fines of small kind. Should it be necessary to ascer


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tain this difference in a great distance, as To make a table for a number of for instance exceeding 20 miles ; the best distances, being an Herculean task, which method will be to find the secant of the scarcely any of y ur correspondents will arc by the following analogy–Tabular go intó, more especially when it is done radius : 251523000 : : tat ular secant by that able mathematician, Doctor Hutof the arc : fecant required, -.. using ton, in bis. useful Dictionary; and as & table of natural secants extending to many of your readers inay not have an 10 or 12 places, and subtracting from opportunity of consulting that book, the the secant thus found the before-men- following extract may be


useful. cioned radius 251523000, the remainder

Your's, &r. will be the difference of levels required in

I. H. inches.--In this latter case, the follow

Distance, Difference ing table will be found of some use for

Distance, Difference or BC. of Level, or

or BC.

of Level, the reduction of chains into degrees,

CF. minutes, and seconds of a great circle: Yards. Inches : Miles. Ft. In. Degrees.


· Chain
= .000180416


300 0 231




500 0.643
600 0.925




7 .001262915


5 16


2.081 .00162 374



32 6 = 001804164



6 The same answered by Mr. I. H.


9 53 9 Not having ever seen ~ Waddington's 1300 4.344 Land Surveyor's Companion,” I am not


80 3 able to enter into his method of drawing 1500

95 7 the rule given in his question ; but it

1600 6.530

13 II2 7 appears to be obtained by supposing the 1790 7.425 14 130 1 arth radius equal to 3968 miles ; for

802 then

3968 x 2 -=64, and

= 124, Question XIV (No. V). Answered by which is Mr. Waddington's multiplier.

Mr. Fr. But as the earth's diameter is now found

The length of the curve of the cy7955

cloid, which the nail describes in each to be 7958 miles, = 126, which revolution of the 'whcel, being equal to 64

cimes the diameter of its generating will be a nearer multiplier than 124, as circle; and the space passed over by the may be cried from what follows. coach in each revolution (the base of the

Let A represent the BCDE cycloid) being equal to the 'circumcarth's centre. A line

férence of the wheel ;--we thall have equally distant from A, is

3.1416 : 7 :: 4 ; 8.9126, &c. miles called the line of true

in an hour, for the mean velocity of the level; but the line of fight

nail. BCDE is the apparent

The same answered by Mr. Wm. Adam, of and the difference

the Free School, Wooburn, between them is evidently A

It is evident, that the pail in the CF, DG, EH. By the 47th Euclid's ist, coach wheel deferiies a cycloid. Hence, ✓ AB2+BC=AC, then AC-AT= as 3.1415927: 4 :: 7 miles : 8.912610 CF, the difference required. Suppose miles, the mean velocity of the nail re-* BC=2 miles, the earth's radius = 3979,

quired. See the article CYCLOID in

Doctor Hutton's Dictionary. then „AB:A-BC2-AF=.00050263882, which multiplied by 5280=(Feet in one

ERRATA. In No. III, page 214, inftead of Mile) 2.64393297 feet = 2 feet 7.847

Cor: 3 to the problem, fubititute the following: inches. Whence, by the same rule, may the base vary, , the locus of the pomt E will be

C:ss. 3. If the equal fides be constant, and any difference of the true and apparent a cirele, whose centre is C: also the solid under level be obtained.

AE, BE, and CE, will be constant.


5.038 5.784


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