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THE

LONDON, EDINBURGH, anv DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

CONDUCTED BY

SIR DAVID BREWSTER, K.H. LL.D. F.R.S.L. & EH. &e. SIR ROBERT KANE, M.D., F.R.S., M.R.LA. WILLIAM FRANCIS, Pu.D. F.LS. F.R.A.S.'F.C.S. JOHN TYNDALL, F.R.S. &c.

“Nec aranearum sane textus ideo melior quia ex se fila gignunt, nec noster vilior quia ex alienis libamus u apes.” Just. Lies. Polit, lib.i. cap. 1. Not.

VOL, XXTII.—FOURTH SERIES. JANUARY—JUNE, 1862.

LONDON.

TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET, Printers and Publishers to the University of London ;

SOLD BY LONGMAN, GREEN, LONGMANS, AND ROBERTS ; SIMPKIN, MARSHALL AND CO.; WHITTAKER AND CO.; AND PIPER AND CO., LONDON :— BY ADAM AND CHARLES BLACK, AND THOMAS CLARK, EDINBURGH; SMITH AND SON, GLASGOW ; HODGES AND SMITH, DUBLIN; AND PUTNAM, NEW YORK,

* Meditationis est perscrutari occulta; contemplationis est admirari perspicua..... Admiratio generat queestionem, queestio inyestigationem, investigatio inventionem.”—Hugo de'S. Victore.

9

\

—“ Cur spirent venti, cur terra dehiscat, Cur mare turgescat, pelago cur tantus amaror, Cur caput obscura Phoebus ferrugine condat, Quid toties diros cogat flagrare cometas ; Quid pariat nubes, veniant cur fulmina ccelo, _ Quo micet igne Iris, superos quis conciat orbes Tam vario motu.” ee J. B. Pinelli ad Mazonium.

CONTENTS OF VOL. XXIII.

(FOURTH SERIES.)

NUMBER CLI.—JANUARY 1862. Page

Archdeacon Pratt.on Chinese Astronomical Epochs ...... 1 Prof. Marcet on the Comparative Effects of Nocturnal Radiation from the Surface of the Ground and over a large Sheet of

RMSE Uae Fes thee US lee ve tee eh Wes as toe bP ie 9

Prof. Maxwell on Physical Lines of Force ............0-- 12 The Astronomer Royal on the Direction of the Joints in the

Faces of Oblique Arches ...... Phd die ood M. G. Kirchhoff on the Relation of the Lateral Contraction to

the Longitudinal Expansion in Rods of Spring Steel. (With

MCU i il WOR we pick Milas SEW oie te oie eats 4S sersst pe 2S The Rev. S..Haughton’s Notes on Mineralogy. 47 Prof. Potter on the Fourth Law of the Relations af oe “Blastic

Force, Density, and Temperature in Gases .......-...0'.0 52 Prof. Roscoe on the Solar Spectrum, and the aay of the

Chemical Elements ...... sidan 63 Sir R. I. Murchison on the inapplicability of ‘the new term

“Dyas” to the “‘ Permian” one of Rocks, as proposed by

[ON Ci 7a ers re Seer eee een ere ia 65

Notices respecting New Books:—Mr. R. Potts’s Euclid’s Elements of Geometry, designed for the use of the ae Forms in Public Schools and ‘Btudentsa in the Universities. 70

Proceedings of the Royal Society :—

The Rev. H. Moseley on the Motion of a Plate of Metal on an Inclined Plane, when dilated and contracted; and on the descent of Glaciers. . d 72 On the Conductibility of Saline Solutions, by M. Marie-Davy. 79

NUMBER CLII.—FEBRUARY.

Drs. Russell and Matthiessen on the Cause of Vesicular Struc-

eR ME MIRE Sees HA oth tub: wh 5 san cr cand aaa & ei Wee Baus ee 8] Prof. Maxwell on Physical Lines of Force ..........++00+- 85 Mr. A. H. Church on the Composition, Structure, and Forma-

lame woeciaive. (With 2 Plate.) . «3. «iene ise devas s+ sive 95

Prof. Regnault on the S inaees Heat of some Simple Bodies. CTE EL ERR aa ea ik delta ie ewe) pee Ce

IV CONTENTS OF VOL. XXITI.—FOURTH SERIES.

Mr. T. Tate’s Experimental Researches on the Laws of Evapo- ration and Absorption, with a Description of a new Evapora- meter and Absorbometer; 1. si hee fe fies See eee 126

Mr. J. Cockle on Transcendental and Algebraic Solution.— Supplementary, Papers ix .:c.0c8 2.5 ads pe.sa 2 /tlei Some oe ieee 135

MM. Van Breda’s and Logeman’s Remarks on Ampére’s Expe- riment on the Repulsion of a Rectilinear Electrical Current OMELET oie oe epsiniess oe iene So1ee'd oie his, cle RO eee 140

Mr. G. B. Jerrard’s Remarks on M. Hermite’s. Argument rela- ting to the Algebraical Resolution of Equations of the Fifth Degree Sees Saeed sat te SSW Kis cee eR Pee Reed eee 146

Proceedings of the Royal Society :—

Messrs. A. Smith and F. J. Evans on the Effect produced

on the Deviation of the Compass by the Length and Arrangement of the Compass Needles ............ 149

Lieut. -Colonel Richard Strachey on the Distribution. of _Aqueous Vapour in the Upper Parts of the Atmosphere. 152 Physical Considerations regarding the possible Age of the Sun’s

Heat, by Professor; W.. Thomsoni< i: x.0-08 fees 158 Description of a New Mineral from the Ural, orbit M. Rodosz- » kovski; 2.232% 7». Siete ian ae ove acre, anciee

NUMBER CLIII.—MARCH.

Mr. S. V. Wood on the Form and Distribution of the Land- tracts during the Secondary and Tertiary periods respectively ; and on the effects upon Animal Life which great Changes in Geographical Configuration have probably produced ...... 161 Drs. Matthiessen and Vogt on the Influence of Traces of Foreign Metals on the Electric Conducting Power of Mercury .... 171 Dr. Sehunck on,Sugar,inUrine ».. .... 268 Welesgectts ee ee 179 Mr. F. A. Abel on the Composition of the Great Bhurtpoor. Gun, stationed on the Royal Artillery Parade Ground, Woolwich ; and of some other interesting Cannon . 2... j.isi-s.bscs sade 181 Mr. C. Tomlinson on the Cohesion-Fi igures of Liquids ...... 186 Mr. A. Cayley on the Solution of an Equation of the Fifth Order. 195 Mr. J. Cockle’s Note on the Remarks of Mr. Jerrard ...... 196 The Rev. T. P. Kirkman on the Puzzle of the Fifteen Young WANES 5 oss '05. 54 Mr. T’. Graham on Liquid Diffusion applied to Analysis. 204 Proceedings of the Royal Society :— Major-General Sabine on the Secular Change in the Mag- netic Dip in London between the years 1821 and 1860. 223 Proceedings of the Geological Society :— M. Marcel de Serres on the Bone-Caves of Lunel-Viel, RT CPAME ovis te 5) hai swiss oy cea es 0 on ete Dr. A. Gesner on the Petroleum-springs in North America. 939

CONTENTS OF VOL. XXIII.——-FOURTH SERIES. Vv

age Dr. Dawson on the Discovery of some additional Land Ani- _-matls in the Coal-measures of the South Joggins...... 239 Mr. J. G. Veitch on a Volcanic Phenomenon observed at soberly. silyl Ge Go itestecdt Seasick asa Sade Ree ok. ». 240 Mr. J. H. Key on the Bovey Basin, Devonshire........ 240 Signor G. G..Gemmellaro on two Volcanic Cones at the ig: ce Ee ee oa etre 241

Mr. T. Davidson on some Fossil Brachiopoda of the Car- boniferous Rocks of the Punjab and Kashmir........ 241 The Rev. O. Fisher on the Bracklesham_ Beds of the Isle of Wight Basin ..... 241 Prof. Morris and Mr. G. E. Roberts on n the Carboniferous - Limestone of Oreton and Farlow................-- 243 Mr. E. W. Binney on some Fossil Plants from the Lower Woal-measures of Lancashire. ....2...:.2 0a. cess ee 244 The Rev. S. Hislop on the Plant-beds of Central India .. 244 On a Dew-bow seen on the surface of Mud, by W.J. M. Rankine. 245 Note on the Theory of Spherical Condensers, by J. M. Gaugain. 245 On the Action of Nitrate of Sodium on Sulphide of Sodium at different Temperatures, by Dr. Ph. Pauli_......... apexes 248

~ NUMBER CLIV.—APRIL.

Prof. Magnus on the Passage of Radiant Heat through moist Air, and on the Hygroscopic Properties of Rock Salt...... 249 _ Prof. Tyndall on Recent Researches on Radiant Heat ...... 252 Mr. A. Cayley on the Transformation of a certain Differential Piprsmmnmrenen af: I A CE PO De sale 266 Sir W. R. Hamilton’s Elementary Proof, that Eight Perimeters, of the Regular inscribed Polygon of Twenty Sides, exceed Twenty-five Diameters of the Circle. . 267 Mr.S. V. Wood on the Form and Distribution of the Land-tracts during the Secondary and Tertiary Periods respectively ; and on the effects upon Animal Life which great Changes in Geo- graphical Configuration have probably produced. . « 269 Mr. W. H. L. Russell’s ‘Theorems in the Calculus of Symbols. 282 Mr. T. Tate’s Experimental Researches on the Laws of Evapo- Beummaneerbsorption 3-7/2 09. Lee eh eee 283 Mr. IT’. Graham on Liquid Diffusion applied to Analysis...... 290 Col. Sir H. James and Capt. A. R. Clarke on Projections for Maps applying to a very large extent of the Earth’s Surface.

(With a Plate.)...... Rotates ta aa, eat Prof. Tyndall on the Regelation of Snow-gr anules .......... 312 Prof, Challis on the Principles of T heoretical PIySIESS 2st & 2'sis 313

_ Notices respecting New Books :—Mr. W. Odling’s Manual of -Chemistry, Descriptive and Theoretical .............00: 322

vi CONTENTS OF VOL. XXIII.—-FOURTH SERIES,

Page Proceedings of the Royal Society :— Mr. M. Simpson on the Synthesis of Succinic and Pyro- tartaric’ Acide isis ote OL SS Re See ee 326 Mr. B. Stewart on Internal Radiation in Uniaxal Crystals. 328 Proceedings of the Geological Society :— Messrs. Whitley and Wyatt on some further Discoveries of Flint Implements ..... riches Mr. W. B. Dawkins on a Piyenaden 7 near - Wells Biore 332 Messrs. Palmieri and 'Tchihatcheff on the Recent man OF Vesuviusies elie 00 I ee 332 Mr. E. Hull on the Distribution of Sedimentary Strata.. 333 On the Probable Cause of Electrical Storms, by Dr. J. P. Joule. 334 On the Influence of Heat on Phosphorescence, by M. O. Fiebig. 335 On the Resistance to the Conduction of Heat, by J.M. Rankine. 336

NUMBER CLV.—MAY. M. V.. Regnault on some Apparatus for determining the Densi-

ties of Gases and Vapours. (With a Plate.) . 337 Mr. G. J. Stoney on the Correction for the Length of ‘the Needle in Tangent-galvanometers....... 345

Prof. Chapman on the Position of Lievrite i in the Mineral Series. 348 Mr. A. Cayley on a Question in the Theory of Probabilities... 352 Mr. J. Croll’s Remarks on Ampére’s Experiment on the Repul-

sion of a Rectilinear Electrical Current on itself......... . 865 Mr. T. Graham on Liquid Diffusion applied to Analysis...... 3868 Mr. R. T. Lewis on the Changes in the Apparent Size of the

MOM ering is isje aisu fre) 5s le cleave Mawinelee pared «ine 8 oie) ete eee 380

Mr. S. V. Wood on the Form and Distribution of the Land-tracts during the Secondary and Tertiary Periods respectively ; and on the effects upon Animal Life which great Changes in

Geographical Configuration have probably produced...... 382 Mr. B. Stewart on the Occurrence of Flint Implements in the DYE. +, 0.6. d16 io) sy0 ie. 4 bide ¥'se sigalg Uo othe AEE ope O94

Proceedings of the Royal Institution : Rear-Admiral FitzRoy on Meteorological Telegraphy.... 395 Proceedings of the Royal Society ;— Prof. J. Thomson on Regelation \% .\siis sick: eee 407 Proceedings of the Geological Society :— The Rev. W. Lister on the Drift containing Arctic Shells in the neighbourhood of Wolverhampton... ......+.+: 412 Mr. J. Smith on a Split Boulder in Little Cumbra...... 412 Mr. T. F. Jamieson on the Ice-worn Rocks of Scotland.. 412 Prof. Ramsay on the Glacial Origin of certain Lakes in - witzerland Boers igi ge tbie al aictdcwlone gerd Uae eet 413 On the Phosphorescence of Rarefied Gases, by M. Morren .. 415 On the Spectra of Phosphorus and Sulphur, by M. J. M.-Seguin. 416

. CONTENTS OF VOL. XXIII.—FOURTH SERIES. yi

NUMBER CLVI.—JUNE.

hae | Page

Prof. Clausius on the Conduction of Heat by Gases ........ 417 Prof. Challis on the general Differential Equations of Hydrody-

ie EIN ora oo oo ac sen ins! ps6 Bije sn'e ing! Haters) 4 kul 436

Archdeacon Pratt’s Calculation of the Undulation of an Unstif- fened Roadway in a Suspension Bridge as a heavy Train passes over it; and Remarks upon the effect of a suspended fron Girder in deadening the Undulation..........:..... 445

Mr. R. Sabine’s remarks on a Paper by Dr. A. Matthiessen, F.R.S., and C. Vogt, Ph.D., ‘‘On the Influence of Traces of Foreign Metals on the Electric Conducting Power of Mercury. 457

Messrs. J. H. and G. Gladstone on Collyrite, and a native Car-

aeeOnrAtminag and LIME: . . « seco cou; oc ute ace ergs «a csuene 461 Prof. Schonbein on the Allotropic States of paren) and on = Nitriucation: ."..”,. . 466

Mr. G. B. Jerrard’s ‘Supplementary Remarks on M. Hermite’s Argument relating to the Algebraical Resolution of Equa- fmermamCc PE REN ICETCC e's orale. ube asin - pin tym secs 44h OR 469

Mr. A. Cayley on a Question in the Theory of Probabilities... 470

Dr. Atkinson’s Chemical Notices from Foreign J ournals sdee gee he

‘Procéedings of the Royal Society :—

M. A. Schrauf on the Determination of the Optical C Con- Srasiessor Orystallized. Substances 252 2)... .;. sc cies se 478 Sir W. S. Harris on some new Phenomena of Residuary Charge, and the Law of Exploding Distance of Electrical meecumulation on Coated, Glass.,...cn0¢+ o<06 ++ ee0 «20 484 Proceedings of the Geological Society :— ~Prof. Harkness on the Sandstones, and their associated

Deposits, in the Valley of the Eden, &c.............- 492 Mr. A. Geikie on the Date of the Last Elevation of the Sema Vvalley of scotland: 0. oc. ee woe ce we ae Oe 493

Note on the Electricity developed during Evaporation and du- ring Effervescence from Chemical Action, by Professor Tait eter Vanilvn, sq. 20. 2b. pe. ees cece elcwe ss be 494

On Chinese Astronomical Epochs, by Archdeacon Pratt. sicieae to0

NUMBER CLVII.—SUPPLEMENT TO VOL. XXIII.

Mr. J. J. Waterston’s Account of Observations on Solar Radia- PRamme UAE IALC.). i. 3%) ss Siara'aiy'c scales sain 02 eee spe 497 Prof. Clausius on the Conduction of Heat by Gases ........ 512 Mr. W. Baker on the Metallurgy of Lead ...5......-+ee: 534 MEV. Regnault on an Air-Thermometer used as a Pyrometer in measuring High Temperatures. (With a Plate.)........ 537 M. H. Karsten on the Oxidation of Gaseous Hydrocarbon-com- pounds contained in the Atmosphere ..........-- me eM

vill CONTENTS OF VOL, XXIII.—FOURTH SERIES. Page M. A. de Ja Rive on the Aurore Boreales, and on Phenomena which attend them, ..s. .. . o's ase cvs 0 se bine lyl a gle Cig nen Proceedings of the Royal Society :— Mr. P. Griess on a New Class of Organic Bases, in which

Nitrogen is substituted for Hydrogen .............. 553 Mr. P. Griess on the Reproduction of Non-nitrogenous Acids from Amidic, Acids .. . .,.< ia. ss esse 595

Proceedings of the Geological Society :— Mr. J. W. Kirkby on some remains of Chiton from the

Mountain Limestone of Yorkshire’.<\.). 3-2 <. soeneeee 958 Prof. Owen on some Fossil Reptilia from the Coal-measures of the South Joggins, Nova Scotia ............ “Gta ie OO

The Rev. W. B. Clarke on the occurrence of Mesozoic and Permian Faune in Eastern Australia ........0.-+ 02 908

Mr. A. Tylor on the Foot-print of an Jguanodon lately found at Tastings ..2)0.c)em- Sate ale! 0)s ibe See a ie 559

On the Connexion between Earthquakes and Magnetic Disturb- ances, -by. Dr.J,, Lamont “a. Sa kane wei 6 one reteset On the Freezing of Saline Solutions, by Dr. Ridorff........ 560

On the Composition of Minerals containing Niobium, by Prof. FL. ROSe os ss... +5, « = 0, Te-eolee.s, sete nies) « orotate ks eye rr FAUX, oie 0 win 0:0 ¥ s0ss' o's 95046 @ viol so twlaha Bebe hie erolis ieee 564

ERRATA IN VOL. XXII. Page 200, line 9 from top, for =100 read = 226.

PLATES.

I, Illustrative of M. G. Kirchhoff’s Paper on the Relation of the Lateral Contraction to the Longitudinal Expansion in Rods of Spring Steel, and of MM. \ n Breda and Logeman’s Paper on the Repulsion of a rectilinear Electrical Current on itself.

IJ. Illustrative of Prof. Regnault’s Papers on the Specific Heat of some Simple Bodies; on new Apparatus for determining the Densities of Gases and Vapours; and on a new Pyrometer. . III. Illustrative of Mr. A. Church’s Paper on the Structure and Composi- tion of Beekite.

IV. Illustrative of Colonel Sir H. James and Captain Clarke’s Paper on Projections for Maps.

V. Illustrative of Mr. J. J. Waterston’s Paper on Solar Radiation.

THE LONDON, EDINBURGH ann DUBLIN

PHILOSOPHICAL MAGAZINK

AND

JOURNAL OF SCIENCE.

[FOURTH SERIES.]

JANUARY 1862.

I. On Chinese Astronomical Epochs. By Archdeacon J. H. Prarz, M.A.

To the Editers of the Philosophical Magazine and Journal.

GENTLEMEN,

‘YN the absence of authentic history, astronomy sometimes lends

valuable aid in enabling us to fix dates by independent means, if certain facts have been handed down to us regarding the posi- tions of the heavenly bodies. There are two eras in Chinese history which it has been attempted to fix in this manner :—one, the reign of the emperor Tcheou-kong, said to have lived about 1100 3.c.; the other, that of the emperor Yao, many centuries earlier, about 2357 B.c. The traditions regarding these persons are vague and altogether uncertain. My object in the present communication is to show what degree of reliance can be placed on the astronomical determinations. However perfect the methods may be which modern science puts into our hands, the results to which they lead us can be of no value if the data are not sufli- cient and also trustworthy.

On the determination of the Era 1100 B.c.

2. M. Gaubil, a jesuit missionary at Pekin, sent to Paris in 1734a MS. of Chinese astronomical observations, which Laplace published in the Connaissance des Tems for 1809. The oldest observations which Laplace considered to be of any value for astronomical purposes (as he there tells us) are two observations of the length of shadow cast by a gnomon at the summer and winter solstices in the time of Tcheou-kong at a place Tching- tcheou, called also Loyang and Hon-an-fou. The latitude of this place was observed by the missionaries in 1712 three times, and found to be 34° 52! 8" by one observation, 34° 46! 15” by the second, and 34° 43! 15" by the third, the last being considered the best. The vertical style or gnomon was 8 feet (pieds) high,

Phil. Mag. 8. 4. Vol. 28. No. 151. Jan. 1862. B

2 Archdeacon Pratt on Chinese Astronomical Epochs.

and the shadows were 1 foot 5 inches (pouces) and 13 feet long, there bemg 10 pouces in | pied. These data give at once, by a table of tangents, 79° 7’ 11” and 31° 18! 42" for the altitudes of the sun. To these Laplace applies corrections for refraction, parallax, and the sun’s semidiameter, and makes them finally 79° 6' 52" and 31° 18/ 48". Half the sum and half the differ- ence of these should give the colatitude of the place of observa- tion and the obliquity of the echptic. They give the latitude = 34° 47! 10", and the obliquity =23° 54! 2”. This latitude is equal to the mean of the three observations mentioned above, but is greater by 4! than the best of the three. Laplace shows, by a formula in Adécanique Céleste, that 23° 51! 58" was the obliquity in 1100 z.c. This differs by 2! 4” from that obtained from the observations, which, at the rate of 48" a cen- tury (the mean decrease of obliquity, see Herschel’s ‘Astronomy,’ art. 640), would throw the date back to 1858 B.c. Laplace thinks the obliquity deduced from the observations as perfect an accordance as could be desired, “seeing the uncertainty which this kind of observations presents, especially because of the iil- defined limit of the shadow (Con. des Tems, 1809, pp. 433,434).

3. Itis the extent of uncertainty arising from this cause which Iwish nowto determine. Let be the height of the style, s and w the Jengths of the shadows at the summer and winter solstices, Zand @ the latitude and obliquity, a and 6 the altitudes of the sun. Then

1 eee: h 1 1 Sead h Oe faa Be A Tis! =) Sioa 2 aha ase 90 i= 5 tan 5 1 5 tan ie ) 5 tan 9 tan oo st h? ae h? dw __1—cos2ads | 1—cos 2B dw ee Oe teh Rees ee ge a a ae Similarly, r5) _ __ l—cos 2a ds i 1—cos 2p 28 Ow Jeeesiray weet eee Se 7 Put a=79° 6 52", B=31° 18! 48", cos 2a= —0:92867, cos280=0-45978' Uo BIOS a OWL, oa OS 0.9 OW ss 61=0°482 5 +0365 S- = 27 6—- + 20 IF and Of = —-27°°6 S + 20°°9 a

h h The recorded lengths of the shadows contain no fractions of an inch. It may therefore be supposed that fractions equal to, or less than half an inch, were thought too trifling to observe ; or the undefined appearance of the shadow made greater niccty impracticable. Put, therefore, ds and dw each equal to half an inch, in excess or in defect, as errors to which the measure of the

Archdeacon Pratt on Chinese Astronomical Epochs. 3

‘shadows is liable. It then appears that the latitude and the obliquity, determined from these observations, will be free from error only within the limits —0°-25 and +025, that is, within a range of 0°5. Now this variation in the obliquity, at the rate of 48" in a century, is equivalent to a range of 30! x 60 --48!'=374 centuries! This astronomical observation, therefore, really gives no independent information whatever regar ding its date. All we can gather is, that if History points out that 1100 B.c. was the era when this observation was made, Astronomy presents na obstacle to this determination.

On the determination of the Era 2357 B.c.

4. An attempt has been made by M. Biot (see Journal des Savants, 1840, 1859) to fix the date of the Emperor Yao by reconstructing the celestial sphere (as he imagines it to have been at that time), and reasoning from the change in the posi- tion of the equinoxes. He fixes the date at 2357 B.c. I will briefly explain his process, and then show in what I think it inconclusive. He states that the ancient Chinese astronomers divided the equator into 28 unequal parts (called stew or man- sions) by declination circles drawn through certain stars chosen for the purpose. M. Biot has evidently bestowed much atten- tion on the subject, and has endeavoured to identify these stars, which the ancient Chinese astronomers are supposed to have used so far back as 4000 years ago! In the next page, in Tables I. and II., I have gathered together some of his results, and in the two following pages some further calculations, the use of which will be explained.

In Table I. are given the names of these twenty-eight stars, and their positions at the era, and the consequent widths of the mansions. (The figures in the second column show the magni- tudes of the stars.) In the choice of stars two things surprise one: (1) that their intervals in AR are so very unequal, and (2) that im many instances such unimportant stars are chosen. Thus, while the width of the fifth mansion is more than 30°, the width of the third is less than 3°. Indeed the stars at the beginning and end of the third mansion are so near in AM, that in the column of longitudes for 1750 a.p. the fourth star falls behind the third! For this reason apparently M. Biot goes far back into time past for his epoch, that the line joining the two stars may have as large a projection as possible on the equator of the time, so as to give the greatest advantage to this, at best, very ill-conditioned mansion. The fourth is Galea a narrow mansion, though not quite so narrow as the third. It will be seen that it is the introduction of the star % Orion (instead of some other, perhaps between Nos. 4 and 5) which makes these mansions so narrow.

B2

4 Archdeacon Pratt on Chinese Astronomical Epochs.

TaBLe [. l : a No. of Latitude. Longitude. Dedlination,| , Fight ee a Star at its commence- |. ies patie OB . ment. 1750 A D. 2357 B.C. { 2357 BC. 1 | » Pleiades... 3.44 9) 5631 | + 3 10) S56 sonore 2 BRUNE 2oeck 3,4, 236) 64 58 | + 0 30 8.55 | 18 5 3 NIOrIONs ves A oe: 80 13 | 3 38 97 OO 2 48 4 Oo Orion. 2e.< 2) —23 35 78 52 | —I138 32 29 43 | 3 36 5 pt Gemini ...... Si Oak 91 49 | +12 11 33 19 | 80 35 6 6 Cancer ...... 5,6) 0 47 | 122 15 | +20 28 63 54 6 38 7 Oydra ss... 4, —J]2 25 | 126 49 | + 9 44 10: 321 17 8 a Hydra. 08 2| —22 24 | 143 48 | + 113 87 37 7 39 9 |397,Hydra ...... 5| —26 5 | 152 13) 2 29 95 16 | 16 40 10 a Crater ...... 4| —22 43 | 170 15 | 039 | 1kl 56] 17 27 i y Gonvuse sc. 3 3| —14 29°) 187.15 | + 4) Yo9u2s lan iZ ig @ Virgoresiccnes }) = 2 -2 |/200 21" =E 12 125) Maksse tae 13 K) Nii conssceenes 4, + 256; 211 0} +13 9 | 157 35 8 58 14 ae Mabrays Sse 4) + 0 22 | 221 36 | + 6 46/ 166 383 | 14 5 15 aw Scorpio...... A) 5 26 | 239 27 |-— 5 39.) WsOsssnieeaee 16 o Scorpio...... 3,44 4 0} 24419} 617 | 185 40} 3 5& 17 Hy Scorpio...... Al —¥5 2) | 252.46 | —20> 1 Jotes45yi aige49 18 Y2 Sagittarius 3,4) 6 57 | 267 47 | —18 3 | 206 34 | 9 52 19 @ Sagittarius 3,4| 3 55 | 276 41 | —18 19 | 216 26 | 26 29 20 @Capricornus 3} + 4 37 | 300 33 | —i6 23 | 242 55 | 8 24 21 e Aquarius ... 4| + 8 7 | 308 14 | —14 12 | 251 19 | 11 50 22 8 Aquarius ... 3] + 8 388 | 319 55 | —14 49 | 263 14 | 10 10 23 a Aquarius ... 3) +10 41 | 329 52 | —12 58 | 273 24 | 18 48 24 a Pegasus 2} +19 25 | 349 59 | 2 39 | 292 12 | 16 IT 25 y, PESaSUS -2n6r2 2} +12 36 5 40 | 6 17 | 308 23 9 13 26 Z Andromeda 4) +17 37 17 6| +135 | 317 36 | 15 19 27 [SOATICS coseeecee 3 8 29 |__30 29 | 2 42 | 332 55 | 10 48 238 35 Aries ...... 4, +11 17 | 48 27 | 4+ 4 42 | 343 48 | 14 47 RICAN ee ee ee koe. me bel oat 2 28 Tasre II.

Position of Equinoxes and Solstices, 2857 B.c.

| 1. 4 Pleiades.a... 1 30 behind Vena Dauner So. a Hydra, vat-. 2 23 behind Summer Solstice. 15. 7 Scorpio...... 0 388 before Autumnal Equinox. 22. (3 Aquarius ... 6 46 behind Winter Solstice.

Archdeacon Pratt on Chinese Astronomical Epochs, TaB.eE III, 3 é Right Wid : e Right Width of No. of Declination. acme Seas Declination. ee mansion. mansion. In the year 1729 B.c. In the year 1100 B.c. Me 535) 5.98 | 10 50u1, 1h 21 | 13.28 | 16 53 eens M4) | 1G 131-18 1 4 32.) 24321") F755 = == RR} 34 14 eee + 2 29 42 16 1 58 4 =) Ve 36 37 4 29 §. 35 44 14 5 39 5 +15 24 Ale Otiirc oe +17 48 49 53 eee 6 +22 8 72 30 5 55 +22 51 81 57 5 1s 7 +11 27 78 25 16 34 +1i 23 87 10 15 53 8 Bit oG |) os 59 1-724 14 0 47-| YOae TTS 9 = % Ale 102 23 16 45 = 3 Hh 110 12 16 47 10 eek 119 8 17 41 a 126 59 17 51 11 22) ae | 135 49 16227, iF 144 50 16 31 12 +6 9 153 16 Il 55 + 5 29 161 21 jl 53 13 + 9 42 165 1] 8 43 + 6 1] 173 14 8 Al 14 +3 6 173 54 141 One 181 55 14 .9 15 ==. 19-26 187 55 6 40 52 9G et 5 10 16 =F) 3 194 35 EZ > oe OL Te e 39 17 = 93) Sy 186 7 1S-57 —24 4 04 53 18 32 18 aa Days |) DUG UA 9 26 ASN OM eo 3s 10 13 19 = 2122 | 224 .30)) 25 42 —23 37 | 233 38 26 46 20 17 OE AAS al 9 20 le po! 2O0L24 § 8 21 = | 259 32 12°06 —— iy 45) 268 of i easy; 22 == 271 32 10 0O —14 50 | 280 29 9 47 23 = IPAG 25 “oz Sete —I1 43 | 290 16 gL | QA + 0 27 299 35 16 20 + 0 47 | 307 37 16 24 25 = Be | en a 8 50 a Olas ee 8 25 25 4 21 324 45 15 29 a oy fe; | 332 26 15 30 27 + 0388 | 340 14 10 38 +4 5 347 56 10 54 28 + 8 18 330 52 14 31 +11 51 308 50 14 38 op eS ee eee 248 | TaBLeE LV.

Position of Equinoxes and Solstices.

2357 B.C.

°

\Vernal Equinox ...|] 30 before No. 1. ‘Summer Solstice...;2 23 before No. 8. Autumnal Equinox. |0 38 behind No.15.

2.

Winter Solstice ...

6 46 before No. 2

5 4 7 1

2 5 3 3

3 9 5 2

1729 B.C,

1100 B.C.

behind No. 1.1 10 before No. 28. behind No. 8.250 before No. 7. behind No. 15.1 55 behind No. 14. behind No. 22.1 28 before No. 21.

5

6 Archdeacon Pratt on Chinese Astronomical Epochs.

TABLE V.

: Their differences of Right Ascension, Nos. of mansions compared.

2357 B.C. 1729 B.C. 1100 B.C.

1 and 15 182 8 182 32 182 36

2, 16 176 45 178 24 176 53

Se ae 16] 45 161 53 162 37

Ee Ke 176 51 178 27 179 11

Go 1G 183 7 183 24 183 45

6 is 20 179 1 177 42 178 27

7 4 Of 180 47 181 7 181 22

§ 5. 99 175 37 176 33 177 26

9°. 798 178 8 179 9 180 4

10550724 180 16 180 27 180 38 Re haere 179 0 179 6 179 11 12. YG 172 1 171 29 W715 1c ee 107 175 20 175 3 174 42 PM see 177 10 176 58 176 55

M. Biot attempts to illustrate the correctness of his list of stars, though so irregularly distributed and in many instances so inferior in importance, by stating that there is evidently a law in their selection, and that a narrow mansion in one part of the heavens corresponds to a narrow mansion in the opposite part ; so also with the wider mansions; so that the stars, at the epoch, were situated in pairs on the same meridian.

5. It is by the application of this test, which is to some extent approximately true, that I think I can detect a flaw which destroys the necessity of passing so far back into past time as the twenty- fourth century B.c. In the first of the three columns in Table V., IL have given the differences of MR for 2357 B.c. gathered from M. Biot’s results in Table I. It will there be seen that the pairs of stars deviate from beimg on the same meridian by an average =about 3°, 2f we except the third pair in which the deviation is as much as 18° 15’. There must be some reason for this exception. ‘The fact is, both the limiting stars of that mansion are exceptional; No. 3 being so near Nos. 2 and 4 (as I have already pointed out), and No. 17 having so large a declina- tion. (No.6 hasas large a declination, see Table I.; but that star is close upon the ecliptic, which No. 17 is not, which may be some reason for its use, there being no nearer star.) These two stars, moreover, are both small, being only of the fourth order of magnitude. I conclude, therefore, for these reasons that they have been wrongly determined. If X% Orion is rejected, the necessity for pushing back the epoch so far is removed.

6. In Tables III., [V., V. I have given the results of calcula- tions I have made for two other epochs, viz. 1100 3.c. and 1729 B.C. (halfway between 1100 B.c. and 2357 B.c.), in order to see

Archdeacon Pratt en Chinese Astronomical Epochs. 7

whether there is any special reason for so remote an epoch as 2357 B.c. being selected. I can see no special reason. (1) Even if X Orion is not rejected, it will be seen that the width of the third mansion is 23! and 58! at those two later dates, and these are not so inferior to 43/, the width in 2357 B.c., as to induce any great preference for that epoch. (2) By com- paring the columns of declinations in Tables 1. and III., it will be seen that the twenty-eight stars lie very much alike with reference to the equators of the three epochs, without any decided advantage for 2357 B.c. In allof them the mid-line is south of the equator; the distance is 28/, 26!, 48’ in the three cases. (3) M. Biot points out that the arrangement of stars chosen by the Chinese is equatorial, and not ecliptical; and he well illustrates this by showing that « Hydree has been chosen, though only of the second magnitude, as the eighth star in pre- ference to the much brighter star Regulus in the same hour- angle, but on the ecliptic and about 24° from the equator. But he departs from this idea when he draws an argument for his ancient epoch from the circumstance that 7 in Pleiades is the jirst of the twenty-eight stars, and that therefore when the system was chosen that star must have been the vernal equinox. The Pleiades, in their sevenfold group, are so conspicuous and marked an object, that it is very easy to understand that, being chosen as one of the twenty-eight determining stars, they should be fixed upon, for that reason, as the point of departure. At the three dates in my Tables, the declination of 7 is only 10’, 53/, 11° 21'; the largest of which is smaller than that of twelve of the twenty-eight stars as laid down by M. Biot for 2357 B.c. In passing backwards to obtain as great a width as possible for his third mansion, he seems to have stopped short at » in Pleiades for no other reason than that, being first of the equatorial series, it might also be the equinox; whereas by going further back he might have somewhat further widened his third mansion. {4} M. Biot also observes that four of the chosen stars, the ist, 8th, 15th, and 22nd (see Table I1.), fall very near the equinoxes and solstices of 2357 B.c., and that this is an argument in favour of that epoch. But my Table IV. shows that in 1100 z.c. four others of the twenty-eight’ stars, also at equal intervals in point of number, viz. the 7th, 14th, 21st, and 28th, were still nearer to the equinoxes and solstices. So that no argument can be drawn from this source in favour of his epoch: rather the contrary. He says that the four stars he names are mentioned in the Chou-king*, an ancient work on

* For what is known of this work Chou-king, or Shoo-king, see Encye. Brit., word China, p. 640: also see History of Astronomy” in Library of Useful Knowledge.’

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8 Archdeacon Pratt on Chinese Astronomical Epochs.

astronomy, as being at the equinoxes and solstices in the time of Yao. As one of the points (see Table II.) is wrong by 46', this commits the Chou-king to.an error of 487 years. Moreover, these traditions are not to be relied upon as facts. We have in Indian astronomy an instance of an ancient conjunction of sun, moon, and planets stated as if an observed phenomenon, whereas it is clear that the idea (which is false in fact) was come at by caleulatmg backwards, and that upon defective data. (5) An- other thing which M. Biot appears to think confirmatory of his epoch is this. He states that the Chinese used to observe with care the motion of the circumpolar stars in the Dragon, the Great Bear, and the Lesser Bear, and two in Lyra; and conjec- tures that the position of the declination-circles passing through them at that epoch influenced the astronomers in the choice of the stars which define the twenty-eight mansions. Eleven, how- ever, of the mansions have none of these circles passing through them, and the angular distances of the others from the nearest stars vary through all degrees of magnitude between 8! and 26'; of these approximate conjunctions on the same meridian twelve take place at the inferior passage of the cireumpolar star. There does not appear to be anything at all remarkable in these approximate relations. Other positions of the pole and other epochs may be no doubt found where even a nearer approxima- tion of the kind exists. (6) Another argument of M. Biot in favour of his epoch is, that a star is spoken of by Chinese astronomers as the Unity of the Heavens,” which name is sup- posed to indicate that it was at the pole of the equator when first so designated: and the French chronologist Freret thinks the star must be « in the Dragon, though M. Biot thinks it may be another star close to it. It is very easy to show that, as the longitude of this star was in 1750 a.p. 153° 54’, it must have been 63°9 x 72=4601 years before that epoch (that is, 2850 B.C.) when it was at the pole, or at its nearest point only a few minutes from it. This is 500 years before M. Biot’s epoch. In this time, however, it would not have moved away more than about 46/, and therefore might still be regarded as the pole- star. But this shows the uncertainty of such means of fixing dates, even by the best astronomical means, if the data are not precise. The star would continue within a distance of 46, taking both sides of the pole, for no less a period than 1000 years. The fact, therefore, of its being regarded as the pole- star, if such errors are allowed (and we see larger errors allowed in this approximation to a system), would not fix the date within 1000 years. ‘There is a tradition that the Chaldee astronomers had observed @ Draconis in the pole. It is quite possible that such a circumstance might be handed down, one so easily observed,

Prof. Marcet on the Effects of Nocturnal Radiation. 9

even