pseeigis ts ey ms starr eeeSe “ REPORT OF THE Pt BRITISH ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE; HELD AT CAMBRIDGE IN OCTOBER 1862. LONDON: JOHN MURRAY, ALBEMARLE STREET. 1863. PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET. CONTENTS. Ossects and Rules of the Association..................020e00es a Places of Meeting and Officers from commencement .............. x DUSTEMAPACCOUN Gs Soeln ke. Tel h es Re ee eee ae. ee Xxiv Members of Council from commencement ................000005 XXV Officerstand’ Council; 1861=62 acre. Hes e i. ek oe Ps XXVili Seeeeee ar Secisonal Committees... .... esa k eens tues uj ce eee Xxix BER MRITITIE MGHIUOES o.oo o5. 6 5 vc oo sient eiadiniale Mincgin biased obo aleneel XXX Report of the Council to the General Committee ................ Xxxi Report of the Kew Committee, 1861-62 ..........cccc ce seeeee Xxxii Report of the Parliamentary Committee........ 0... cc ce cee sees XXX1x Recommendations of the General Committee for Additional Reports MEREEPGHEONER: UIE SCICTIOS 5 o.5's ac ja vorycls e's cece uacis cece ce a XXx1x MILT TIES NOHO GEATICS + 6 ors.ac ci 5(255 «ive or :03K «Tas einreieipiytle + 69,0 040% xii General Statement of Sums paid on account of Grants for Scientific DLE AE SETS go eee Coa any nn esc ee ee xly Extracts from Resolutions of the General Committee ............ xlix Arrangement of the General Meetings .................. 000005 1 Address of the President, the Rev. R. Wrxuis, M.A., F.R.S., &. .... li REPORTS OF RESEARCHES IN SCIENCE. Report on Observations of Luminous Meteors, 1861-62. By a Com- mittee, consisting of James GuaisHer, F.R.S., F.R.A.S., Secretary to the British Meteorological Society, &c.; R. P. Gree, F.G.8., &c.; E. W. Brayzey, F.R.S., &c.; and A. HerRscHeL ..........000+:- 1 On the Strains in the Interior of Beams. By Gzorex Bippetn Arry, Bro Pe eurrionier Oval) o'r. cris 5 sting ase sfan' oh Goo al in ak are ene 82 P Report on the three Reports of the Liverpool Compass Committee and sy other recent Publications on the same subject. By ArcHispaLp SmitTH, M.A., F.R.S., and Frepertck Joun Evans, R.N., F.R.S........... 87 vi CONTENTS. Report on Tidal Observations on the Humber. Presented by Jamss OxtpHam, C.E.; Jonn Scorr Russert, C.E., F.R.S.; J. F. Bareman, en arith si ele OMAR T BOMEPSON 5 osc evs so. . 2 2 Pease 101 On Rifled Guns and Projectiles adapted for Attacking Armour-plate Defences, By T. Asron, M.A., Barrister-at-Law.............--- 103 Extracts, relating to the Observatory at Kew, from a Report presented to the Portuguese Government by Dr. JactyrHo Anronto DE Sovza, Professor of the Faculty of Philosophy in the University of Coimbra. (Communicated by J. P. Gasstor, F.R.S.) .......6.0 22 ee eee ees 109 Report on the Dredging of the Northumberland Coast and Dogger Bank. Drawn up by Henry T. Menyett, on behalf of the Natural History Society of Northumberland, Durham, and Newcastle-on-Tyne, and of the Tyneside Naturalists’ Field Club .............-.-+2+-005- 116 Report of the Committee appointed at Manchester to consider and report upon the best means of advancing Science through the agency of the Mercantile Marine. By Curnserr Contrnewoop, M.B., F.L.S....... 122 Provisional Report of the Committee, consisting of Professor A. Win- tiamson, Professor C. Wurarstone, Professor W. THomson, Professor W. H. Mirtrr, Dr. A. Marraressen, and Mr. Freemre Jenkin, on Standards of ‘Blectriegl Resistance ;:.:: 355522: .. 250") 2 SS soe 125 Preliminary Report of the Committee for Investigating the Chemical and Mineralogical Composition of the Granites of Donegal, and the Mine- Falstassociated with them: «icc. < ste ae eh ee tees. Oe BO es 163 On the Vertical Movements of the Atmosphere considered in connexion with Storms and Changes of Weather. By Henry Hennessy, F.R.S., M.R.LA., &c., Professor of Natural Philosophy in the Catholic Uni- Versity of Treland .2.) s16..%). ols ie aieisinie sles» lee eivisis's ole) -ielsidinialayale eleva 165 Report of a Committee, consisting of the Rev. Dr. Luoyp, General Sazryg, Mr. A. Ssxarn, Mr. G. Jounstonzr Sronry, Mr. G. B. Arry, Professor Donxiy, Professor Wu. Toomson, Mr. Carrey, and the Rev. Professor Price, appointed to inquire into the adequacy of existing data for carrying into effect the suggestion of Gauss, to apply his General Theory of Terrestrial Magnetism to the Magnetic Variations........ 170 On Thermo-electric Currents in Circuits of one Metal. By Frremine Umewen. (Ulibe Wye. 21 Soleil. ak ee ee See 173 On the Mechanical Properties of Iron Projectiles at High Velocities. By DW oAUAGEB AGING DEI E: REV IPT Vals ajeyaye:'+: anche) -ounye a Bo Shhads feet 178 Report on the Progress of the Solution of certain Special Problems of Dynamics. By A. Cayzey, F.R.S., Correspondent of the Institute.. 184 Report on Double Refraction. By G. G. Sroxes, M.A., D.C.L., Sec. B.S., ‘ Lucasian Professor of Mathematics in the University of Cambridge .. 253 CONTENTS. vii Page Fourth Report of the Committee on Steamship Performance. (Plate IIT.) 282 On the Fall of Rain in the British Isles during the Years 1860 and 1861. Sy G. J. Symons, MIBIMS! 4(BlatesH A) Sof. cicero ne 293 On Thermometric Observations in the Alps. By J. Barz, M.R.I.A., RRB Qin, | FREE nents Seem erene ecw ae 363 Report of the Committee for Dredging on the North and East Coasts of Scotland, By J. Gwyn Jerrrrys, FRG.) oi ea ce eee eee 371 Report of the Committee, consisting of the Rev. W. Vernon Harcourt, Right Hon. Joseph Napier, Mr. Tire, M.P., Professor Curisrison, Mr. J. Heywoop, Mr. J. F. Bareman, and Mr. T. Wesster, on Tech- pre nical and Scientific Evidence in Courts of Law ..-..........02e00% 373 An Account of Meteorological and Physical Observations in Eight Bal- loon Ascents, made, under the Auspices of the Committee of the British Association for the Advancement of Science at Manchester, by Jamxs GuatsHER, F.R.S., at the request of the Committee, consisting of Colonel Syxes, Mr. G B. Arry, Lord Wrorrrstey, Sir D. Brewster, Sir J. Herscuet, Dr. Luoyp, Admiral FirzRoy, Dr. Lrr, Dr. Rosryson, Mr. Gassror, Mr. Guatsuer, Dr. Tynpatx, Mr. Farrparrn, and Dr. W. MEER eR SS Pee Ped te Sort toe dees alah wae ls wits RS 376 Report on the Theory of Numbers.—Part IV. By H. J. Srepnen Smiru, M.A., F.R.S., Savilian Professor of Geometry in the University of IE ho. oe ats Bhat Cy re wha 9 SS ered ea eile BL aya IK Aneene yney 503 APPENDIX I. Errata in Report of Observations of Luminous Meteors, 1861-62 .... 5 bo “I Vill CONTENTS. NOTICES AND ABSTRACTS OF MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. MATHEMATICS ann PHYSICS. MATHEMATICS. Address by G. G. Stoxss, M.A., F.R.S., Lucasian Professor of Mathematics in the University of Cambridge, President of the Section. .............. Rey. F. Basnrortu on Capillary Attraction ...............0ssesseccrece Professor BoouE on the Differential Equations of Dynamics............... Rey. Dr. Boor on an Instrument for describing Geometrical Curves; invented Litied 8 lor!) (cs eran Hermon occ oC Apo ann o sco Oe Professor A. CAYLEY on a certain Curve of the Fourth Order.............. —_—_———- on the Representation of a Curve in Space by means of eq epnerand Monoid Surtice ©. \.. .t)ci.'s ss « vials ru a 5 wana elu tale ciate) talaeeneene Mr. W. Esson on the Curvature of the Margins of Leaves with reference to BRPEMESERTOWAMN soc ccs aidin'e' 010 ee o's vawbrd bbe Hucaleewie ety «alee eee ene Sir Wit11am Rowan Hamixton, Quaternion Proof of a Theorem of Reci- PROCHLZOL Curves in Space: ....... xfs cidsleldcacch doe So oCiet ote ta) /alete teeta teteteamenent Rey. Ropert Har ey on a certain Class of Linear Differential Equations . . Mr. T. A. Hirst on the Volumes of Pedal Surfaces ...........00eeee eee Professor WILLIAM JOHN Macquorn RaAnxKINE on the Exact Form and Mo- tion of Waves at and near the Surface of Deep Water .............20055 Mr. W. H. L. Russet on Recent Discoveries made in the Calculus of VATED OLS isi ovasarevecaye}s cieljoleis aic'a/a's « /s) iusiay. oie eichepegenNieeel Reine ote) Siete Mr. C. M. Witticu on some Models of Sections of Cubes .............005 ASTRONOMY. Mr. Isaac AsHe’s Cosmogonical Speculations .........0- eee eeeeeeeeees Mr. W. R. Brrr on a Group of Lunar Craters imperfectly represented in Lunar IU EETIS fens ose rate tel aeictercimpevale areleisi sys eisis nie + oie avs\a"a alleles ste ete chee eet Rey. Professor CHaLiis on the Augmentation of the Apparent Diameter of a Body by its Atmospheric Refraction. ............02+2ccresscececeves on the Zodiacal Light, and on Shooting-Stars .......... Professor HENNESSY on some of the Characteristic Differences between the Configuration of the Surfaces of the Earth and Moon ............++++:- Mr. Witri1am Lassext on a Brilliant Elliptic Ring in the Planetary Nebula, Pee SGN DOT GS! osc s cee eee occa Ss eee Page sill CONTENTS. ix ; Page \ Rey. R. Marn, Observed R.A. and N.P.D. of Comet I. 1862 ............ 15 on the Dimensions and Ellipticity of Mars.................. 15 Mr. J: NasMyrH on some Peculiar Features in the Structure of the Sun’s Sur- BERNE 5S FAY, TANG: YATRA BDO ~ Bales Jere tabtasel RIGA GEER aeRG oabTOg eaters te 16 Mr. Norman Pocson’s Observations on Three of the Minor Planets in 1860. (Communicated: by {Dr} Wisi.) | jo<:5 decease epeyetotalers, Were) ofa faite ofele wren co o's 16 Mr. W. Oeripy on the Excentricity of the Earth, and the Method of finding the Coordinates of its Centre of Gravity ......... ...0005. ange oil mabye 17 M. J. Scxvanrcz on the probable Origin of the Heliocentric Theory ........ 17 Rey. Professor Setwyn on Autographs of the Sun. ......... 0. .e cece eee 17 Mr. W. Sporriswoope on the Hindé Method of Calculating Eclipses ...... 18 M. C. J. Viti on some Improved Celestial Planispheres ................ 18 Lieut ann Hear. Mr. A. CLavupeErT on the Means of following the Small Divisions of the Scale regulating the Distances and Enlargement in the Solar Camera.......... 18 M. A. Des CriorzEAvx sur la Relation entre les Phénoménes de la Polarisation Rotatoire, et les Formes Hémiédres ou Hémimorphes des Cristaux & un ou REAP OS) CONAGTOS 5 ieteyshele Porsxayelojae pays dopeheiauelaseabealerald Coin 1 ayeqeie: BS oust ibe 19 Mr. James Croix on the Cohesion of Gases, and its relations to Carnot’s Function and to recent Experiments on the Thermal effects of Elastic Fluids ERNE SAE TESIN hades cs n0 ctor Notes thai Arar eMeke as eed ence tay le rahavafac a. eettoycnsca avd eke cvela le 21 Rey. J. Din@ie on the Supernumerary Bows in the Rainbow.............. 22 Dr. EssELBAcH on the Duration of Fluorescence .........c0cececeececees 22 Mr. J. M. Menzies on an Optical Instrument which indicates the Relative Change of Position of Two Objects (such as Ships at Sea during Night) which are maintaining Independent Courses ............... 0c eee eens 22 Rey. J. B. ReaprE’s Experiments on Photography with Colour............ 22 Mr. J. SmirH on the Complementary Spectrum. ............ ccc eeeeeeees 23 Mr. Cuarites ToMLinson on the Motion of Camphor, &c. towards the Light 28 Execrricity, MaGnertism. Mr. James Croxt on the Mechanical Power of Electro-Magnetism, with spe- cial reference to the Theory of Dr. Joule and Dr. Scoresby ............4. 24 Dr. EssEtBAcH on Electric Cables, with reference to Observations on the Minlta- Alexandr, LelopTApli 2 (is toaMs. saa dele File: hs avers slatel ald nde ort 26 ———_———— on an Experimental Determination of the Absolute Quantity of Electric Charge on Condensers... 0.0. cei ee ei dee dnce eens cubeuee 27 Mr. G. M. Guy on an Electromotive Engine ............... 0c sees ee eeaes 27 METEOROLOGY. Mr. Isaac AsHe on Balloon Navigation ........0.: cc cecceseceseeeeeeeees 27 on some Improvements in the Barometer .............+.. 28 Mr. Joun Bax on the Determination of Heights by means of the Barometer 28 Rey. Professor CHALLIS on the Extent of the Harth’s Atmosphere ........ 29 x CONTENTS. Mr. F. Gatton on the “ Boussole Burnier,” a new French Pocket Instrument for measuring Vertical and Horizontal Angles. .....--+seeseee seen eens ——- on European Weather-Charts for December 1861.......... Dr. GrapsToNE on the Distribution of Fog round the Coasts of the British AUS Renae ded orrspns state wie teis bee Stl Shi s= ‘aay Dla" ae are ape ju arbre wysieye Sow wi ayer aye (lofeh> Seekomnaegal Mr. J. GuatsHEeR on a New Barometer used in the last Balloon Ascents .... Mr. J. Park Harrison on the Additional Evidence of the Indirect Influence of the Moon over the Temperature of the Air, resulting from the Tabulation of Observations taken at Greenwich in 1861-62. .......... 0 eee eeeeneees Professor Hennessy on the Relative Amount of Sunshine falling on the MMorrid) Aone Of Ghee HATED versie a)sseha) o/6\0 ») 'eis'se-aiayope/aiaia ¢(ors\e 0\0.0) > a ole eleteimil aes Mr. E. J. Lowe on the Hurricane near Newark of May 7th, 1862, showing the force of the Hailstones and the violence of the Gale .........++00005 Mr. Ropert Mauuet’s Proposed Measurement of the Temperatures of Active Volcanic Foci to the greatest attainable Depth, and of the Temperature, state of Saturation, and Velocity of Issue of the Steam and Vapours evolved Mr. T. L. Puant on Meteorology, with a Description of Meteorological Instru- TITIES se) oleh ays) ofetetolleeivln/alishateie sy2- 6, dlays oi) slgiaiel ets (e/e’a «la: 6i5, aiulwleim sletolp iets otaleteeneys Rey. T. Ranx1n’s Meteorological Observations registered at Huggate, York- RRR WEP Pore tWolesa inca avarslaevasetesisiele sere) colons) ove 6tain\a\ nin fo ue (elsYahslr Wiel aint opahateteeite Mr. S. A. Rows11’s Objections to the Cyclone Theory of Storms.......... Mr. G. J. Symons on the Performance, under trying circumstances, of a very small Anefoid Barometer... .......s ccc ccs s esters setsreeecevemecee Professor James THOMSON on the Disintegration of Stones exposed in Build- ings and otherwise to Atmospheric Influence ...........seee ener eeeeees CHEMISTRY. Address by Professor wW. H. Miter, M.A., F.R.S., President of the Section Mr. Groner BowvieR BucxrTon on the Formation of Organo-Metallic Ra- dicals by Substitution 6.2... cee wee elec dvee esc ce veins soialawilns Mr. DuGaLp CAMPBELL on the Action of Nitric Acid upon Pyrophosphate of IER OSIBIM aye: nlels winie «elscals efe\s 5,0 + 51s afer) + c)o\e Woln)s\e ele folalais ojetsi~'al+ otetet= eieemmy oie M. A. Drs CLorzEAvx sur les modifications temporaires et permanentes que la Chaleur apporte 4 quelques propriétés optiques de certains, corps cristallisés Mr. J. P. Gasstor on the Mode of preparing Carbonic Acid Vacua in large (IRR HESE Gl EIS Ay RIOR ASL SO CHER CROMER ao SITE meno or yaae ab o/k ¢ tees Dr. J. H. GLADSTONE on the Essential Oil of Bay, and other Aromatic Oils. . on the Means of observing the Lines of the Solar Spec- trum due to the Terrestrial Atmosphere ...........cessseeevccerereces Mr. A. Vernon Harcourt on a particular Case of induced Chemical Action DreGHantEy on Schonbein’s'Antozone 25. ./ci.% sacs odie) oie ole oe Cer Mr. W. H. Harris on the Adulteration of Linseed Cake with Nut-cake ... Mr. CHartes Herscu on a Simple Method of taking Stereomicro-photographs Ni By. 0 Low on-his'OzonesBOxe *s\ 51.70% «seule oc o' cea tee crore ete A a teats Observataons’on Ozone. of. Se es wee oes sere eee Dr. Morrar on the Luminosity of Phosphorus ..............00000: 436%: WV. OpriIng on Herrous AGid 2758. ob se ek ao Bale a tata oils Ge Page 30 30 31 31 31 31 32 33 34 35 35 35 36 - CONTENTS. Dr. “ trnG@ on the Synthesis of some Hydrocarbons ...........00e000: on the Nomenclature of Organic Compounds.............. Mr. J. W. Osporne on the Essential Oils and Resins from the Indigenous Pe PraHUOMO LN CLON Mar men Selves ereie's.c cre treceasiettecre iss Aaya ci ePers a so 6 ———_—_—__——_ Details of a Photolithographic Process, as adopted by the Government of Victoria, for the publication of Maps................0005 Dr. B. H. Pav on the Manufacture of Hydrocarbon Oils, Paraffin, &c., from LEETT o 6 Sod Oho peop GBIBAC EE ected Hep Oem e bre OS Hain Deer Ctib Okara arin © Dr. T. L. Pxtpson on the Artificial Formation of Populine, and on a new PEE MPPCRIEC ONO coos cas r,s ce Se eaten Seah sy cohen ee Righe ——____————— on the Existence of Aniline in certain Fungi which be- Lome blie in contact withithe: Air, &is%. says. 3% 5016 0) ofe ole werd f ola eleverers ———_—— Analysis of the Diluvial Soil of Brabant, &c., known as giematrnon sd la ELCSOAy On -2 cash gicbayerchsae chy oletere'e lore de Aapensiea vas he oe oe Professor H. E. Roscoz on Hypobromous Acid......... eee eeeeee eee ee : Mr. T. Surron’s Description of a rapid Dry-Collodion Process ............ GEOLOGY. Address by J. Brrte Jukes, M.A., F.R.S., President of the Section........ Professor ALLMAN on an Karly Stage in the Development of Comatula, and its RSP EeENUEG OO TCAl FUOLAMONG) sc. esha cae vie sive cele neyd cred aiencis ve baw ee veiree Professor ANSTED on Bituminous Schists and their Relation to Coal........ —————- on a Tertiary Bituminous Coal in Transylvania, with some remarks on the Brown Coals of the Danube. .............:cceeeeeeeees Captain Gopw1n-AvsTEN on the Glacier Phenomena of the Valley of the REPROD So oa Scio gtd 0.y Dee Pa. AAG oe ea ss oS oes Ook ee ee ee Dr. A. Carre and Mr. W. H. Barry on a New Species of Plesiosaurus from the ReeeenCmE TVANCDY, Y OMMBNIEA. fewsis Ws aitis splame dds fee Cae ee cre cen een Mr. W. T. Branrorp on an Extinct Volcano in Upper Burmah .......... Rey. T. G. Bonney on some Flint Implements from Amiens............-. Rey. J. CRompron on Deep or Artesian Wells at Norwich...............+ Dr. DavBeEny on Flint Implements from Abbeville and Amiens............ on the last Eruption of Vesuvius. .....6.s.eceessescceseess Mr. W. Boyp Dawxrns on the Wokey Hole Hyena-den................. Rey. J. DrnexeE on Specimens of Flint Instruments from North Devon...... Mr. Doveury on Flint Instruments from Hoxne ..............00e cece eee Mr. F. J. Foor on the Geology of Burren, co. Clare ............cce ee eeeee Dr. Frirscw on some Models of Foraminifera. ........... 00. cee e cece eee Professor Harkness on the Skiddaw Slate Series........... 0.0000 cues My. J. Gwyn JEFFREYS on an Ancient Sea-bed and Beach near Fort William, MeeteceNTOSS=S NING es ere musheieter sear ele rae A wae LI ED LER TT Tr cree Dr. W. Lauper Linpsay on the Geology of the Gold-fields of Otago, New NEEL, 5 oy a2) ssa elias a's aS - ASEMGSE aysiae uae Sly curd dovnacessninsoun xii CONTENTS. Page Dr. W. Lauper Linpsay on the Geology of the Gold-fields of Auckland, New ASIEIIG I5i3 3.6.4 dibio gd. O00 OG Ub DOSED AD ODO COD OODE ID AOR ONOnE TO. a0 05 80 Mr. Cuartes Moore on the Paleeontology of Mineral Veins; and on the Secondary Age of some Mineral Veins in the Carboniferous Limestone.... 82 ————_—_—_—, Contributions to Australian Geology and Paleontology 83 Mr. C. W. Pracu on the Fossils of the Boulder-clay in Caithness.......... 83 ——_—_ on Fossil Fishes from the Old Red Sandstone of Caithness 85 Mr. W. PenGeEtty on the Correlation of the Slates and Limestones of Devon and Cornwall with the Old Red Sandstones of Scotland, &c. ............ 85 Mr. T, A. Reapwin on the Gold-bearing Strata of Merionethshire.......... 87 Mr. C. B. Rosr on some Mammalian Remains from the Bed of the German LD CEATI Pr ey let iasis yo FRG AEE Sidhe ods 5 « ayecs del diel elete lover eo he Cetera 91 Mr. J. W. Satter on the Identity of the Upper Old Red Sandstone with the Uppermost Devonian (the Marwood Beds of Murchison and Sedgwick), and of the Middle and Lower Old Red with the Middle and Lower Devonian.. 92 Mr. 8. P. Savitxe on a Skull of the Rhinoceros tichorhinus... 0.60.40 ev eves 94 My. H. Sretry on a Whittled Bone from the Barnwell Gravel ............ 94 Rey. Gizpert N. SmirH on a Successful Search for Flint Implements in a Cave called “The Oyle,” near Tenby, South Wales ............+eeeees 95 Mr. H. C. Sorsy on the Cause of the Difference in the State of Preservation Oiacuicrenuy mds OL H Ossi SHES f. <0 sls s.010+ ore core # otehe sim «sree oaleyninlaiepy ste 95 ———_——_——— on the Comparative Structure of Artificial and Natural lieneae JG Wee enpa oan aoor oad ton oooh oHOmranOMO GOB Or ats. 6 oc oae 96 Rey. W. 8. Symonps on Scutes of the Labyrinthodon, from the Keuper Bone- Breccia of Pendock, Worcestershire ....... 0c cs eee eee ee ec eeeeenes ANOS Mr. A. B. Wynne on the Geology of a Part of Sligo... 1... cece eens eenes 96 ZOOLOGY anv BOTANY, tncitupine PHYSIOLOGY. Borany. Mr. James Buckman on the Ennobling of Roots, with particular reference to PERERTSIID cscs is so ausitals v0 + agen Tey) weds eine eee ee ea satiate 97 , Experiments with Seed of Malformed Roots ........ 97 Dr. DauBEny’s Reply to the Remarks of M. F. Marcet on the Power of Selec- fionvascribed tothe Roots-of Plante’. t).taa. ree hs ble ss feo eltetenmea at 98 My. F. J. Foor on a Botanical Chart of the Barony of Burren, co. Clare.... 98 Mr. Joun Gress on the Inflorescence of Plants......... 00. cece eee eee eee 98 Dr. W. Lauper Linpsay on the Toot-poison of New Zealand ............ 98 Rey. W. S. Symonps on the Occurrence of Aspleniwm viride on an Isolated Travertine Rock among the Black Mountains of Monmouthshire.......... 100 ZooLoey. Professor ALLMAN on the Generative Zooid of Clavatella........ceceeeeeee 100 on an Early Stage in the Development of Comatula...... 101 on the Structure of Corymorpha nutans 2.2.2... e ees 101 on some new British Tubularid@ ... 0. cece ccc cee seieislOl i re CONTENTS. xii Page Mr. A. D, Bartiett on the Habits of the Aye-aye living in the Gardens of the Zoological Society, Regent’s Park, London ................00. 000s 103 Dr. Grrpert W. Cuixp on Marriages of Consanguinity .................. 104 Dr, CLELAND on Ribs and Transverse Processes, with special relation to the Peery artitie Vertebrate Skeleton.) 1020.0. Ui te sO. yeas nese eee ee 105 Dr. CoLLinGwoop on Geoffroy St.-Hilaire’s Distinction between Catarrhine BHCe bal apel ING! QUAGTOMANRS fe). iste vil ols tale diene «ei a.ct ties se velar vajew es 106 Dr. J. E. Gray on the Change of Form of the Head of Crocodiles; and on pucrerenadiles Of India and Afiica ss. 0. ef ee RIE ores OES 106 Rey. T. Hrycxs on the Production of similar Medusoids by certain Hydroid Polypes belonging to different Genera ....... ete c tee wencveesewasavers 107 Mr. J. Gwyn JEFFREYS on a Species of Limopsis, now living in the British Seas; with Remarks onthe Genus ..........c.csecererestcevesccsces 108 ——_——_____——— 0n a Specimen of Astarte compressa having its Hinge- MEMENOUF heist iale Pasta he odd Oa ead neds neces ddde ddien ae dae weun 108 Professor W. Kine on some Objects of Natural History lately obtained from the Maem the AtANHC .) ooo cece rca hecddededeccdasdessucesetauen 108 Mr. Joun Luspock on Spherularia Bombt.... ccc eee eens 109 on two Aquatic Hymenoptera.............-.:eseeeees 110 Rey. W. N. Moresworrn on the Influence of Changes in the Conditions of Existence in Modifying Species and Varieties........0... 6.00 c cece eee 111 Professor R. Owrn on the Characters of the Aye-aye, as a test of the Lamarckian and Darwinian Hypothesis of the Transmutation and Origin of MMT RTP ts! o' veterans ban cy ten cha oh alalahsrabelalarshatshatalatelalshabrgi eh alpten shot a! ater chase dt DME 114 ———_————— on the Zoological Significance of the Cerebral and Pedial PME UIMERID) .ic.cld discs oaicturts 2 cbtve Tees ayaa eoee eas a fable oh aie qoaiees 116 ——_—————_—— on the Homologies of the Bones of the Head of the Poly- EMEEICCRE re eee loi SRR Se ok 8ae 5 MMA he ee aree NASA Hea paIeas « 118 Sir J. Ricnarpson on Zoological Provinces ...........0..ccceeeeeeueeas 118 Professor RoLLEsTON on certain Modifications in the Structures of Diving RMR ITE Ses oes cer ne ORAS SHEE SAL gS Sic PENA R RT Meares « 118 Mr, James SaMUELSon’s recent Experiments on Heterogenesis, or Spontaneous (LL are il or te ie I nl a ai hin) diner sty oie h Ms, Oh 119 PHYSIOLOGY. Mr. Isaac AsHE on the Function of the Auricular Appendix of the Heart .. 120 on the Function of the Oblique Muscles of the Eye........ 120 Mr. Tuomas AsHworrTH on the Scientific Cultivation of Salmon Fisheries .. 121 Professor Bear, an Attempt to show that every living Structure consists of Matter which is the Seat of Vital Actions, and Matter in which Physical and Chemical Changes alone take place .............ccccceceecceveees 122 Dr. Joun Davy on the Coloured Fluid or Blood of the Common Earthworm PLA SEPT esria)) s\sfer dais cinhotirvayslss edlds a aasadeediand sald Metal dL «labs 124 on the Vitality of Fishes, as tested by Increase of Tem- EMRE 009 2he Shale VS se A GMa BAT ao eae HM eeHwAsl cme LPT OM aE AE 125 : — on the Question whether the Oxide of Arsenic, taken in very minute quantities for a long period, is Injurious to Man ................ 125 on the Coagulation of the Blood in relation to its Cause.... 125 XIV CONTENTS. Page Mr. James Dow on the Loss of Muscular Power arising from the ordi- nary Foot-clothing now worn, and on the Means required to obviate this GOSS Bes veretclcteyclay ete oye. nee) aiehavefaliabaleleleie. oi e\c)a_e je Inia) sls, s¥are » vlclslginie @ie. NOR oRaieMalaaes 125 Mr. Ropert GARNER on Pearls; their Parasitic Origin ......+++++esseees 126 ——_—_____—— on an Albino Variety of Crab; with some Observations on Crustaceans, and on the Effect of Light... ......s:sseeeeeeeeeeeeens 126 —__—________——- on the Skull-sutures in connexion with the Superficies of the Brain ..........% ise GEE OOOO NE PODOOINS opie CATE Eno on eae . 126 Dr. Grorce D. Gres on the Physiological Effects of the Bromide of Ammo- WEIDER ities cise A eieicls ticis siolr oe eds Od. + she. oyna miakeahie a lolae) ete nee 128 —_____—_—__——_ on the Normal Position of the Epiglottis as determined by the Laryngoscope .......0 eee ee cence erence nent en eteenerannacs 128 Dr. Groner Harvey on Secret Poisoning ..........2ceececseenserececes 129 Mr. James Hinron’s Suggestions towards a Physiological Classification of PAGETUTT ASO cee s a ci esele.c10:0)sre.= oi+/, «,000:0, 0, 0.0.6, o)eyesel by iavoreioneesta,© oso(e =e anmaneT aR 130 Dr. Cartes Kipp on Simple Syncope as a Coincident in Chloroform Acci- artis A BOD nD nee doc DEC DU OU ODORAUTS DOLD OL H3uch. yao 2c0 Fos or 130 Mr. J. W. Osporne’s Observations made at Sea on the Motion of the Vessel withereterence tO Sea-SiCkNess scsi). 2/e He + os «010 ble leisiele) viel vi ejelelotenelel eile) ake 183 Mr. T. Reynoxps on Tobacco in relation to Physiology ........+.s+e00008 134 Dr. Grorcre Rosrnson on the Study of the Circulation of the Blood. ...... 134 Professor RoLLESTON on the Difference of Behaviour exhibited by Inuline and ordinary Starch when treated with Salivary Diastase and other converting PEE ois ow. 0 s.0,0,0,0,070 08 0 0,0,026,018,0,9 910, See ee Pe Ree er 135 Dr. Epwarp Situ on Tobacco-Smoking: its effects upon Pulsation ...... 135 GEOGRAPHY anp ETHNOLOGY. Sir,R. Atcock on the Civilization of Japan ....... 0055 ce-sn-ceruneee ns 136 Professor ANSTED on the Climate of the Channel Islands.................. 138 Dr. Cuantes T. Bexr’s Journey to Harran in Padan-Aram, and thence over Mount Gilead into the Promised Land. ............s.cceeccccccvcesers 141 Rev. T. G. Bonney on the Geography of Mont Pelvoux, in Dauphiné ...... 145 Mr. J. CRawFurp on Colour as a Test of the Races of Man............... 143 —_—_—__——-——-. on Language as a Test of the Races of Man ............ 144 Mr. Ropert Dunn on the Psychological Differences which exist among the typical Races of Mam... .....i:sici crereyielel- isis) tien egeln(eh iil dle loyal 4) ipl > nlecee a enoreae 144 M. Jutes Gérarp’s Exploration dans l'Afrique centrale, de Serre-Leone 4 LARS Barred bin Sita ne GRR A GeO aS HU O DO do Some OADO No np ould Ss - o-o0- 146 Dr. Livinestone, a Letter from, communicated by Sir Roderick Murchison . 146 Mr. W. Matuews, jun., on Serious Inaccuracies in the Great Survey of the Alps, south of Mont Blanc, as issued by the Government of Sardinia...... 147 Rey. Dr. Mixx’s Decipherment of the Pheenician Inscription on the Newton bone, A Derdeenshire oaks Peis tae!- supe lalearals (Oe. 'e's «\s}t muster eenel a> Gekeemenr ieee 147 Signor Prrrorri on Recent Notices of the Rechabites............000eeees 147 Chevalier Ignazio Vita on Terrestrial Planispheres Mr. AtFrrep R. WALLACE on the Trade of the Eastern Archipelago with New Guinevnnd rte lslantsstys.$. Sed OL Ay 148 CONTENTS. XV Page Mr, Tuomas WriGut on the Human Remains found in the course of the Ex- FeV EATSt Ly NW LOR OLEY:. Lystacexhal ete e Sesele Sars lekayale ol AMM vo loveharare Sata lohduars lava ‘s 149 STATISTICAL SCIENCE. Mr. J. C. Buckmaster on the Progress of Instruction in Elementary Science among the Industrial Classes under the Science Minutes of the Department PE NTE PATI Lae Crop tastes wich sie cetera ein chee ele. eters cece 150 Mr. Davin Cuapwick on the Cotton Famine, and the Substitutes for Cotton 150 Rey. G. FisHer on the Numerical Mode of estimating Educational Qualifica- tions, as pursued at the Greenwich Hospital School .................... 153 Mr. James Heywoop on Endowed Education and Oxford and Cambridge Fel- IN etal ctor at eater aisin a hoo Lacy RSS Roan eee re ame eT 153 Mr, Epwin Hix on the Prevention of Crime............. cece cece ceeenes 154 Mr. W. 8. Jevons on the Study of Periodic Commercial Fluctuations ...... 157 , Notice of a General Mathematical Theory of Political Eco- LOLLY - sags Soglirao once peae dn So roon Comoe Mion 0.0 6 © ese Onan nie eens 158 Mr. Henry DunninG Macteop on the Definition and Nature of the Science SemePa ere HI CERUPE CCITIEIEEY. our xc Vv Malek nh dic! ois eiein, « iaes eiainlchaleyaysamedcie @miciarwieke aged. 3 ee 159 Mr. Herman Menrtvate on the Utility of Colonization .................. 161 Rey. W. N. Motesworrtu on the Training and Instruction of the Unemployed in the Manufacturing Districts during the present Crisis ................ 162 Mr. Freperick Purpy on Local Taxation and Real Property ............ 162 —— on the Pauperism and Mortality of Lancashire .... 165 Mr. Henry Roserts, Statistics showing the Increased Circulation of a Pure and Instructive Literature adapted to the Capacities and the Means of the emnamsOaeE ONT ARON 2s 24a sos wshiee dass Sipdvd Nese dder sap da aes eues 172 Dy. Epwarp Smiru, Statistical Inquiry into the Prevalence of numerous Conditions affecting the Constitution in 1000 Consumptive Persons ...... 174 fee. §. 1HouNTON on the Income Tax ....... 0... sc cers ccsecascuees 175 Mr. Cuartes M. Wiixicu on Expectation of Life ................0000 0: 178 MECHANICAL SCIENCE. Address of WiLi1AM Farrparrn, Esq., LL.D., F.R.S., President of the Section 178 Mr. E. E, Aten on the Importance of Economizing Fuel in Iron-plated sR ee oN ais sales tt ole ee cin Sie ss enn. eldip. yA tes dita’ 182 Professor D. T. ANsTED on Artificial Stones ...........0c:ccecescaecnces 183 Mr. CuarLEes ATHERTON on Unsinkable Ships .............ccceceeeeeees 183 Mr. Joun Coryron on Vertical-Wave-Line Ships, Self-Reefing Sails, and RES IRE ED ora a3 5s. Par os Sees oe alin aie atts ite oh hens v.50 68 184 Dr. F. Grimapr on a New Marine Boiler for generating Steam of High Pres- LLUR. sbrcovcton se cOronBoapomnennide ice cMbe rie Sort oes Bee ar ren 186 Mr. J. SEwELL on the Prevention of Railway Accidents ................ 186 Mr. W. THoroxp on the Failure of the Sluice in Fens, and on the Means of securing such Sluices against a similar Contingency ..................4- 186 Mr. L. WriiraMson on the Merits of Wooden and Iron Ships, with regard to Eosniot repairs and security for Wife i... css eeie ee esis sme veigsieee seed ces 187 XV1 CONTENTS. Mr. R. W. Woortcomss on Oblate Projectiles with Cycloidal Rotation, con- trasted with Cylindro-ogival Projectiles having Helical or Rifle Rotation. . APPENDIX II. Professor SYLVESTER on the Solution of the Linear Equation of Finite Dif- ferences IMits most General HOLM. oo... sc o.e ec ciee outs ove epviels gto auasaiel olen Messrs. J. B. Lawes and J. H. Girserrt on the Effects of different Manures pune Mixed Herbage of Grass And 5.0 )o. 6. cs. es oe os ie oe eee eee Rey. W. Emery on the Past and Present Expenses and Social Condition of Aran erat tay MENG UIEHUIOIE oye ict cysts tet aeal e7 0s a0 "0. Side o: eve shero tlie ce as o-otaket] eRe List of Papers of which the Abstracts were not received ..........00eee008 188 191 OBJECTS AND RULES OF THE ASSOCIATION. ——__~>——_ OBJECTS. Tue Assocratron contemplates no interference with the ground occupied by other institutions. Its objects are,—To give a stronger impulse and a more systematic direction to scientific inquiry,—to promote the intercourse of those who cultivate Science in different parts of the British Empire, with one an- other, and with foreign philosophers,—to obtain a more general attention to the objects of Science, and a removal of any disadvantages of a public kind which impede its progress. RULES. ADMISSION OF MEMBERS AND ASSOCIATES. All persons who have attended the first Meeting shall be entitled to be- come Members of the Association, upon subscribing an obligation to con- form to its Rules. The Fellows and Members of Chartered Literary and Philosophical So- cieties publishing Transactions, in the British Empire, shall be entitled, in like manner, to become Members of the Association. The Officers and Members of the Councils, or Managing Committees, of Philosophical Institutions, shall be entitled, in like manner, to become Mem- bers of the Association. All Members of a Philosophical Institution recommended by its Council or Managing Committee, shall be entitled, in like manner, to become Mem- bers of the Association. Persons not belonging to such Institutions shall be elected by the General Committee or Council, to become Life Members of the Association, Annual Subscribers, or Associates for the year, subject to the approval of a General Meeting. COMPOSITIONS, SUBSCRIPTIONS, AND PRIVILEGES. Lire Memeers shall pay, on admission, the sum of Ten Pounds. They shall receive gratuitously the Reports of the Association which may be pub- lished after the date of such Pane They are eligible to all the offices _ of the Association. Awnvat Susscripers shall pay, on admission, the sum of Two Pounds, and in each following year the sum of One Pound. They shall receive gratuitously the Reports of the Association for the year of their admission and for the years in which they continue to pay without intermission their _ Annual Subscription. By omitting to pay this Subscription in any particu- lar year, Members of this class (Annual Subscribers) lose for that and all future years the privilege of receiving the volumes of the Association gratis : but they may resume their Membership and other privileges at any sub- sequent Meeting of the Association, paying on each such occasion the sum of One Pound. They are eligible to all the Offices of the Association. Associates for the year shall pay on admission the sum of One Pound. They shall not receive gratuitously the Reports of the Association, nor be eligible to serve on Committees, or to hold any office. 1862, b XVlll RULES OF THE ASSOCIATION. The Association consists of the following classes :— 1. Life Members admitted from 1831 to 1845 inclusive, who have paid on admission Five Pounds as a composition. 2. Life Members who in 1846, or in subsequent years, have paid on ad- mission Ten Pounds as a composition. 3. Annual Members admitted from 1831 to 1839 inclusive, subject to the payment of One Pound annually. [May resume their Membership after in- termission of Annual Payment. | 4, Annual Members admitted in any year since 1839, subject to the pay- ment of Two Pounds for the first year, and One Pound in each following year. [May resume their Membership after intermission of Annual Pay- ment. | 5. Associates for the year, subject to the payment of One Pound, 6. Corresponding Members nominated by the Council. And the Members and Associates will be entitled to receive the annual volume of Reports, gratis, or to purchase it at reduced (or Members’) price, according to the following specification, viz. :— 1. Gratis.—Old Life Members who have paid Five Pounds as a compo- sition for Annual Payments, and previous to 1845 a further sum of Two Pounds as a Book Subscription, or, since 1845, a further sum of Five Pounds. New Life Members who haye paid Ten Pounds as a compo- sition, Annual Members who have not intermitted their Annual Sub- scription. 2. At reduced or Members’ Prices, viz. two-thirds of the Publication Price.—Old Life Members who have paid Five Pounds as a composition for Annual Payments, but no further sum as a Book Subscription. Annual Members who have intermitted their Annual Subscrip- tion. Associates for the year. [Privilege confined to the volume for that year only. ] 3. Members may purchase (for the purpose of completing their sets) any of the first seventeen yolumes of Transactions of the Associa- tion, and of which more than 100 copies remain, at one-third of the Publication Price, Application to be made (by letter) to Messrs. Taylor & Francis, Red Lion Court, Fleet St., London. Subscriptions shall be received by the Treasurer or Secretaries. MEETINGS. The Association shall meet annually, for one week, or longer. The place of each Meeting shall be appointed by the General Committee at the pre- vious Meeting ; and the Arrangements for it shall be entrusted to the Officers of the Association, GENERAL COMMITTEE. The General Committee shall sit during the week of the Meeting, or longer, to transact the business of the Association. It shall consist of the following persons :— 1. Presidents and Officers for the present and preceding years, with authors of Reports in the Transactions of the Association. ; 2. Members who haye communicated any Paper to a Philosophical Society, which has been printed in its Transactions, and which relates to such subjects as are taken into consideration at the Sectional Meetings of the Association,. ail RULES OF THE ASSOCIATION. xix 3. Office-bearers for the time being, or Delegates, altogether not exceed- ing three in number, from any Philosophical Society publishing Transactions. 4, Office-bearers for the time being, or Delegates, not exceeding three, from Philosophical Institutions established in the place of Meeting, or in any place where the Association has formerly met, 5. Foreigners and other individuals whose assistance is desired, and who are specially nominated in writing for the Meeting of the year by the Presi- dent and General Secretaries. . 6. The Presidents, Vice-Presidents, and Secretaries of the Sections are ex-officio members of the General Committee for the time being. SECTIONAL COMMITTEES, The General Committee shall appoint, at each Meeting, Committees, con- sisting severally of the Members most conversant with the several branches of Science, to advise together for the advancement thereof. The Committees shall report what subjects of investigation they would particularly recommend to be prosecuted during the ensuing year, and brought under consideration at the next Meeting. The Committees shall recommend Reports on the state and progress of particular Sciences, to be drawn up from time to time by competent persons, for the information of the Annual Meetings. COMMITTEE OF RECOMMENDATIONS, The General Committee shall appoint at each Meeting a Committee, which shall receive and consider the Recommendations of the Sectional Committees, and report to the General Committee the measures which they would advise to be adopted for the advancement of Science. All Recommendations of Grants of Money, Requests for Special Re- searches, and Reports on Scientific Subjects, shall be submitted to the Com- mittee of Recommendations, and not taken into consideration by the General Committee, unless previously recommended by the Committee of Recom- mendations. 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ZOST 109099G 38] 0} (ONILAGN UALSAHONVWI J° qUULIDIUIUIUIOD) 1 98T Joquiaydag WF Woy TNNOOOV S.UAVOSVAWL TIVUANAYD GTHL “AONGIOS AO LNUNYONVACGV FHL YOOX NOILVIOOSSV HSILIYVE MEMBERS OF THE COUNCIL. XXV II, Table showing the Names of Members of the British Association who have served on the Council in former years. Aberdeen, Earl of, LL.D., K.G., K.T., F.R.S. (deceased). Acland, Sir Thomas D., Bart., M.A., D.C.L., F.R.S Acland, Professor H. W., M.D., F.R.S. Adams, Prof. J. Couch, M.A., D.C.L., F.R.S. Adamson, John, Esq., F.L.S. Ainslie, Rev. Gilbert, D.D., Master of Pem- broke Hall, Cambridge. Airy,G.B.,M.A., D.C.L., F.R.S., Astronomer Royal. Alison, ProfessorW. P.,M.D.,F.R.S.E.(dec‘), Allen, W. J. C., Esq. Anderson, Prof. Thomas, M.D. Ansted, Professor D. T., M.A., F.R.S. Argyll, George Douglas, Duke of, F.R.S, | L. & E. Arnott, Neil, M.D., F.R.S. Ashburton, William Bingham, Lord, D.C.L, Atkinson, Rt. Hon. R.,Lord Mayor of Dublin. Babbage, Charles, Esq., M.A., F.R.S. Babington, Professor C. C., M.A., F.R.S. Baily, Francis, Esq., F.R.S. (deceased). Baines, Rt. Hon. M. T., M.A., M.P. (dec4), Baker, Thomas Barwick Lloyd, Esq. Balfour, Professor John H., M.D., F.R.S. Barker, George, Esq., F.R.S. (deceased). Beamish, Richard, Esq., F.R.S. Beechey, Rear-Admiral, F.R.S. (deceased). Bell, Professor Thomas, V.P.L.S., F.R.S. Bengough, George, Esq. Bentham, George, Esq., Pres.L.S. Biddell, George Arthur, Esq. Bigge, Charles, Esq. Blakiston, Peyton, M.D., F.R.S. Boileau, Sir John P., Bart., F.R.S. Boyle, Right Hon. D., Lord Justice-General (deceased). Brady,The Rt. Hon. Maziere, M.R.1.A., Lord Chancellor of Ireland. Brand, William, Esq. Breadalbane, John, Marquis of, K.T., F.R.S. (deceased). Brewster, Sir David, K.H., D.C.L., LL.D., F.R.S. L. & E., Principal of the Uni- yersity of Edinburgh. Brisbane, General Sir Thomas M., Bart., K.C.B., G.C.H., D.C.L., F.R.S. (dec*). Brodie, Sir B. C., Bart., D.C.L., V.P.R.S. (deceased). Brooke, Charles, B.A., F.R.S. Brown, Robert, D.C.L., F.R.S. (deceased). Brunel, Sir M. I., F.R.S. (deceased). Buckland, Very Rey. William, D.D., F.R.S., Dean of Westminster (deceased). Bute, John, Marquis of, K.T. (deceased). Carlisle, George Will. Fred., Earl of, F.R.S. Carson, Rey. Joseph, F.T.C.D. Cathcart, Lt.-Gen., Earl of, K.C.B., F.R.S.E. (deceased). Challis, Rev. J., M.A., F.R.S. Chalmers, Rev. T., D.D. (deceased). Chance, James, Esq. Chester, John Graham, D.D., Lord Bishop of. Christie, Professor S. H., M.A., F.R.S. Clare, Peter, Esq., F.R.A.S. (deceased). Clark, Rev. Prof., M.D., F.R.S. (Cambridge.) Clark, Henry, M.D. Clark, G. T., Esq. Clear, William, Esq. (deceased). Clerke, Major S., K.H., R.E., F.R.S. (dec*). Clift, William, Esq., F.R.S. (deceased). Close, Very Rev. F., M.A., Dean of Carlisle, Cobbold, John Chevalier, Esq., M.P. Colquhoun, J. C., Esq., M.P. (deceased). Conybeare, Very Rey. W. D., Dean of Llan- daff (deceased). Cooper, Sir Henry, M.D. Corrie, John, Esq., F.R.S. (deceased) Crum, Walter, Esq., F.R.S. Currie, William Wallace, Esq. (deceased). Dalton, John, D.C.L., F.R.S. (deceased). Daniell, Professor J. F., F.R.S. (deceased). Darbishire, R. D., B.A., F.G.S. Dartmouth, William, Earl of, D.C.L., F.R.S. Darwin, Charles, Esq., M.A., F.R.S. Daubeny, Prof. C. G. B.;M.D.,LL.D., F.R.S. DelaBeche, Sir H. T., C.B., F.R.S., Director- Gen. Geol. Surv. United Kingdom (dec*). De la Rue, Warren, Ph.D., F.R.S. Derby, Earl of, D.C.L., Chancellor of the University of Oxford. Devonshire, William, Duke of, M.A., D.C.L., FE.RS. Dickinson, Joseph, M.D., F.RB.S. Dillwyn, Lewis W., Esq., F.R.S. (deceased). Donkin, Professor W. F., M.A., F.R.S. Drinkwater, J. E., Esq. (deceased). Ducie, The Ear] of, F.R.S. Dunraven, The Earl of, F.R.S. Egerton, Sir P. de M. Grey, Bart., M.P., E.R.S Eliot, Lord, M.P. Ellesmere, Francis, Earl of, F.G.S. ( dec"). Enniskillen, William, Earl of, D.C.L., F.R.S. Estcourt, T. G. B., D.C.L. (deceased). Fairbairn, William, LL.D., C.E., F-R.S. Faraday, Professor, D.C.L., F.R.S. Ferrers, Rev. N. M., M.A. FitzRoy, Rear-Admiral, F.R.S. Fitzwilliam, The Earl, D.C.L., F.R.8. (dec*), Fleming, W., M.D. Fletcher, Bell, M.D. Foote, Lundy E., Esq. Forbes, Charles, Esq. (deceased). Forbes, Prof. Edward, F.R.S. (deceased), Forbes, Prof. J. D., LL.D., F.R.S.,Sec. RS.E., Principal of the University of St. An- drews. Fox, Robert Were, Esq., F.R.S. | Frost, Charles, F.S.A. Fuller, Professor, M.A. Galton, Francis, F.R.S., F.GS. Gassiot, John P., Esq., F.R.S. Gilbert, Davies, D.C.L., F.R.S. (deceased), Gladstone, J. H., Ph.D., F.B.S. XXV1 Googe The Very Rey. H., D.D., Dean of ly Gourlie, William, Esq. (deceased). Graham, T., M.A., D.C.L., F.R.S., Master of the Mint. Gray, John E., Hsq., Ph.D., F.R.S. Gray, J onathan, Esq. (deceased). Gray, William, Esq., F.G.S. Green, Prof. J oseph Henry, D.C.L., F.R.S. Greenough, G. B., Esq., F.R. 5. (deceased). Griffith, George, M.A, E.C.8 Griffith, Sir R. Griffith, Bt., ELD, M.R.LA. Grove, W. R., Esq., MA, E.R.S Hallam, Henry, Esq., M. A, FRS. (dec). Hamilton, W. J., Esq., FRS., Sec. G.S. Hamilton, Sir Wn. R., UL. D., Astronomer Royal of Ireland, MRE.LA., E.R.AS. Hancock, W. Neilson, LL.D. Harcourt, Rev. Wm. Vernon, M.A., F.R.S. Hardwicke, Charles Philip, Earl of, F.R.8. Harford, J. S., D.C.L., F.R.S. Harris, Sir W. Snow, F.R.S. Harrowby, The Earl of, F.R.S. Hatfeild, William, ete F.G.S. (deceased). Henry, W. C., M.D., F.R.S. Henry, Rev. P. S., D.D., President of Queen’s College, Belfast. Henslow, Rey. Professor, M.A., F.L.8. (dec?). Herbert, Hon. and Very Rev. ‘Wm., LL.D., F.L.S., Dean of Manchester (dec?), Herschel, Sir John F. W., Bart., M.A., D.C.L., E.R.S. Heywood, Sir Benjamin, Bart., F.R.S. Heywood, James, Hsq., F.R.S. Hill, Rev. Edward, M.A., F.G.S8. Hincks, Rey. Edward, D. iy M.R.1.A. Hincks, Rev. Thomas, B.A. Hinds, 8., D.D., late Lord Bishop of Norwich (deceased). Hodgkin, Thomas, M.D. Hodgkinson, Professor Eaton, F.R.S. (dec*). Hodgson, Joseph, Esq., F.R.S. Hooker, Sir William J., LL.D., F.R.S8. Hope, Rev. F. W., M.A., F.RS. Hopkins, William, "Esq., M. A., LL.D., F.R.S. Horner, Leonard, Esq., F.R. S., Pres.G.S. Hovenden, V. F., Esq., M.A Hugall, J. W., Esq. Hutton, Robert, Esq., F.G:S. Hutton, William, Esq., F.G.S. (deceased), Ibbetson ,Capt.L. ie Boscawen, K.R.E.,F.G.S8. Inglis, Sir R. H., Bart., D.C. Ly MP. (dec). Inman, Thomas, M.D. Jacobs, Bethel, Esq. Jameson, Professor R., F.R.S. (deveased) Jardine, Sir William, Bart., F.R.S.E Jeffreys, John Gwyn, Hsq., ERS. Jellett, Rev. Professor. Jenyns, Rey. Leonard, F.LS. Jerrard, H. B., Esq. Jeune, Rey. F., D.C.L., Master of Pembroke College, Osford. Johnston, Right Hon. William, late Lord Provost of Edinburgh. Johnston, Prof. J. F. W., M.A, EBS. (deceased). REPORT—1862. Keleher, William, Esq. (deceased), Kelland, Rey. Prof. P., M.A., F.R.S. L. & E. Kildare, The Marquis ‘of. Lankester, Edwin, ML D., E.B.S. Lansdowne, Hen., "Marquisof, D.C.L. Ba B.S. Larcom, Major, RE., LL.D., F.R.S Lardner, Rey. Dr. (deceased). Lassell, William, Hsq., F.R.S. L. & E. Latham, R. G., M.D., ERS. Lee, Very Rev. John, D.D., E.R.S.E., Prin- cipal of the University of Edinburgh (deceased). Lee, Robert, M.D., F.R.S. Lefevre, Right Hon. Charles Shaw, late Speaker of the House of Commons. Lemon, Sir Charles, Bart., F.R.S. Liddell, Andrew, Esq. (deceased). Liddell, Very Rev. H. G., D.D., Dean of Christ Church, Oxford. Lindley, Professor John, Ph.D., F.R.S. Listowel, The Earl of. Liveing, Prof. G. D., M.A., F.C.8. Lloyd, Rey. B., D.D., Provost of Trin. Coll., Dublin (deceased). Lloyd. oe H., D.D., D.C.L., F.B.S. L.&E., LA. Tendebocae Lord, F.R.S. (deceased). Lubbock, Sir John W., Bart., M.A., F.R.S. Luby, Rev. Thomas. Lyell, Sir Charles, M.A., LL.D., D.C.L., E.R.S. MacCullagh, Prof., D.C.L., M.R.I.A. (dec*). MacDonnell, Rev. R., D.D., M.R.1.A., Pro- vost of Trinity College, Dublin. Macfarlane, The Very Rey. Principal. (dec*). MacGee, William, M.D. MacLeay, William Sharp, Hsq., F.L.S. MacNeill, Professor Sir John, F.R.S. Malahide, The Lord Talbot de. Malcolm, Vice-Ad. Sir Charles, K.C.B. (dec*). Maltby, Edward, D.D., F.R.S., late Lord Bishop of Durham ’(deceased). Manchester, J. P. Lee, D.D., Lord Bishop of. Marlborough, Duke of, D.C.L Marshall, J. G., Esq., M.A., F.G.S. May, Charles, Esq., FRAS. (deceased). Meynell, Thomas, Esq., F.LS. Middleton, Sir William F. F., Bart. Miller, Professor W. A., M.D., Treas. and V.P.R.S. Miller, Professor W. H., M.A., For. Sec.R.8. Milnes, R. Monckton, Esq., D.C.L., M.P. Moggridge, Matthew, Esq. Moillet, J. D., Esq. (deceased). Monteagle, Lord, F.R.S. Moody, J. Sadleir, Esq. Moody, T. H. C., Esq. Moody, T. F., Esq. Morley, The Earl of. Moseley, Rey. Henry, M.A., F-.R.S. Mount-Edgecumbe, Ernest Augustus, Earl of. Murchison, Sir Roderick L.,G@.C.St.8.,D.C.L., TLD, E.R.S. Neild, Alfred, Esq. Neill, Patrick, M.D., F.R.S.E. Nicol, D., M.D. MEMBERS OF THE COUNCIL. Nicol, Professor J., F.R.S.E., F.G.S. Nicol, Rev. J. P., LL.D. Northampton, Spencer Joshua Alwyne, Mar- quis of, V.P.R.S. (deceased). Northumberland, Hugh, Duke of, K.G.,M.A., F-.R.S. (deceased). Ormerod, G. W., Esq., M.A., F.G.S. Orpen, Thomas Herbert, M.D. (deceased). Orpen, John H., LL.D. Osler, Follett, Essq., E.RBS. Owen, ieee Richd.,M.D.,D.C.L.,UL.D., F Oxford, Samuel Wilberforce, D.D., Lord Bishop of, F.R.S., F.G.S. Palmerston, Viscount, K.G., G.C.B., M.P., F.RS. Peacock, Very Rev. G., D.D., Dean of Ely, ERS. (deceased). Peel, Rt.Hon.Sir R., Bart.,M.P.,D.C.L.(dec*). Pendarves, E. W., "Esq., ERS. (deceased). Phillips, Professor J ohn, M.A., LL.D.,F.R.S. Phillips, Rev. G., B.D., President of Queen’ 8 College, Cambridge. Pigott, The Rt. Hon. D. R., M.R.1.A., Lord Chief Baron of the Exchequeri in Ireland. Porter, G. R., Esq. (deceased). Portlock, Major- -General,R.E.,LL.D., F.B.S. Powell, Rev. Professor, M.A., FRS. (dec*). Price, Rey. Professor, M.A., FERS. Prichard, J. C., M.D., F.R.S. (deceased). Ramsay, Professor William, M.A. Ransome, George, Esq., F.L.8. Reid, Maj.-Gen. Sir W., K.C.B., R.E., F.R.S. deceased). Rendlesham, Rt. Hon. Lord, M.P. Rennie, George, Esq., F.R.S. Rennie, Sir John, F.R.S. Richardson, Sir John, C.B., M.D., LL.D., E.R.S. Richmond, Duke of, es G., F.R.S. (dec*). Ripon, Earl of, F. RG Ritchie, Rev. Prof., LL. D, F.R.S. (dec*). Robinson, Capt., RA Robinson, Rev. J., D.D. Robinson, Rey. T. R., D.D., F.R.S., F.R.AS. Robison, Sir John, Sec.R.S.Edin. (deceased). Roche, James, Esq. Roget, Peter Mark, M.D., F.R.S. Rolleston, Professor, M.D., F.LS. Ronalds, Francis, F.R.S. Roscoe, Professor H. E., B.A., F.R.S. Rosebery, The Earl of, KT, D. C.L., E.B.S. Ross, Rear-Admiral Sir J. C, R.N., DCL, ERS. (deceased). Rosse, Wm., Earl of, M.A., F.R.S., M.R.1.A. Royle, Prof. John F, M. D., FRS. (dec*). Russell, James, Esq. (deceased). Russell, J. Scott, Esq., F.R.S. pee, Major. Generlttdwara R.A.,D.C.L., L.D., President of the Royal Society. Sandon William, E sq., F.G.S8. Scoresby, Rev. W., D.D., F.R.S. (deceased). eee: Rev. Prof. Adam, M.A., D.C.L., XXV1i Selby, Prideaux John, Esq., F.R.S.E. Sharpey, ae M.D., Sec.R.S. Sims, Dillwyn, E Smith, Lieut. “Oologel C, Hamilton, F.R.S. (deceased). Smith, Prof. H. J. 8., M.A., F.RB.S. Smith, James, F.R.S. L. & E. Spence, William, Esq., F.R. S oes: Spottiswoode, W., M.A Stanley, Edward, D. Ds F. - os late Lord Bishop of Norwich (deceased). Staunton, Sir G. T., Bt., M.P., D.C.L., F.B.S. St. David’s, C. Thirlwall, D. He “Lord Bishop of. Stevelly, Professor John, L Stokes, Professor G.G., M.A. ar 0. L.,Sec. B.S. Strang, John, Esq., EAD Strickland, Hugh E., Hsq., F.R.S. (deceased). Sykes, Colonel W. H., M.P., F.R.S. Symonds, B. P., D.D. ; Warden of Wadham College, Oxford. Talbot, W. H. Fox, Esq., M.A., F.R.S. Tayler, Rey. John James, B.A. Taylor, John, Hsq., F.R.S. (deceased). Taylor, Richard, Esq., F.G.S. Thompson, William, Esq., F'..S.(deceased). Thomson, A., Esq. Thomson, Professor William, M.A., F.R.S. Tindal, Captain, R.N. (deceased). Tite, William, Esq., M.P., F.R.S. Tod, James, Esq., F.R.S.E. Tooke, Thomas, F.R.S. (deceased). Traill, J. S., M.D. (deceased). Turner, Edward, M.D., F.R.S. (deceased). Turner, Samuel, Hsq., F.R.S., F.G.S. (dect). Turner, Rey. W. Tyndall, Professor John, F.R.S. Vigors, N. A., D.C.L., F.L.8. (deceased). Vivian, J. H., M.P., F.R.S. (deceased). Walker, James, Hsq., F'.R.S. Walker, Joseph N., Esq., F.G.S8. Walker, Rev. Professor Robert, M.A., F.R.S. Warburton, Henry, Esq.,M.A., P.R. S. (dec*). Ward, W. Sykes, Esq., F.C. s. Washington, Captain, R.N., F.R.S. Webster, Thomas, M.A., FRS. West, William, Esq., F.R.S. (deceased). Western, Thomas Burch, Esq. Wharncliffe, John Stuart, Soak E.R.S.(dec*). Wheatstone, Professor Charles, F 8. Whewell, Rev. William, D.D., F.R.S., Master of Trinity College, Cambridge. White, John F., Esq. Williams, Prof. Charles J. B., M.D., F.R.S. Willis, Rev. Professor Robert, M.A., F.R.S. Wills, William, Hsq., F.G.S. (deceased). Wilson, Thomas, Esq., M.A. Wilson, Prof. W. P. Winchester, John, Marquis of. Woollcombe, Henry, Esq., F.8.A. (deceased ). Wrottesley, John, Lord, M.A.,D.C.L., F.R.S. Yarborough, The ‘Earl of, D. CL. Yarrell, William, Hsq., F..S. (deceased). Yates, James, Esq., M.A, FE-.R.S. Yates, J. B. , Esq., FSA. ‘FRGS. (dee). OFFICERS AND COUNCIL, 1862-63. TRUSTEES (PERMANENT). Sir RopERIcK I. MurcuHison, K.C.B., G.C.St.S., D.C.L., F.R.S. Major-General EDWARD SABINE, R.A., D.C.L., Pres. B.S. Sir PHILIP DE M. GREY EGERTON, Bart., M.P., F.R.S. PRESIDENT. ' THE REV. ROBERT WILLIS, M.A., F.R.S., Jacksonian Professor of Natural and Experimental Philosophy in the University of Cambridge, VICE-PRESIDENTS. The Rey. the VICE-CHANCELLOR OF THE UNIVERSITY OF CAMBRIDGE. The Very Rey. the DEAN or ELy, D.D. The Rey. W. WHEWELL, D.D., F.R.S., Master of Trinity College, Cambridge. ake dey. =} SEDGWick, M.A., F.R.S., Woodwardian Profossor of Geology in the University of ambridge. The Rey. J. CHALLIS, M.A., F.R.S., Plumian Professor of Astronomy in the University of Cambridge. G. B. Atry, Esq., M.A., F.R.S., Astronomer Royal. G. G. STOKES, Esq., M.A., F.R.S., Lucasian Professor of Mathematics in the University of Cambridge. J.C. ADAMS, Esq., M.A., F.R.S., Lowndesian Professor of Astronomy and Geometry in the University of Cambridge, and President of the Cambridge Philosophical Society. PRESIDENT ELECT. Sir WILLIAM G. ARMSTRONG, F.R.8. . VICE-PRESIDENTS ELECT. Sir WALTER C. TREVELYAN, Bart., M.A. NicHoLas Woop, Esq. Sir CHARLES LYELL, LL.D., D.C.L., F.R.S., F.G.S. Rev. TEMPLE CHEVALLIER, B.D., F.R.A.S. HvuGH TAYLor, Esq. WILLIAM FAIRBAIRN, Esq., LL.D., F.R.S. Isaac LOWTHIAN BELL, Esq. LOCAL SECRETARIES FOR THE MEETING AT NEWCASTLE-ON-TYNE. A. NOBLE, Esq. Aueustus H. Hunt, Esq. R. C. CLAPHAM, Esq. LOCAL TREASURER FOR THE MEETING AT NEWCASTLE-ON-TYNE. THOMAS HopGKIN, Esq. ORDINARY MEMBERS OF THE COUNCIL. DE LA RUE,WARREN, Esq., F.R.S. | Hurron, ROBERT, Esq., F.G.8. | SyKES, Colonel, M.P., F.R.S. FitzRoy, Admiral, F.R.S8. Hoae, JOHN, Esq., M.A., F.L.S, | Tire, WILLIAM, Esq.,M.P.,F.R.S. GALTON, FRANCIS, Esq., F.R.S. LYELL, Sir CHARLES, F.R.S. WHEATSTONE, Professor, F.R.S. Gassiot, J. P., Esq., F.R.S. LANKESTER, Dr. E., F.R.S8. WEBSTER, THOMAS, Esq., F.R.S. GLADSTONE, Dr., F.R.S. MILLER, Prof. W.A., M.D.,F.R.S. | WiLLiamson, Prof. A.W., F.R.S. Grove, W. R., Esq., F.R.S. PRICE,Rey.Professor,M.A.,F.R.S, HEYWOOD, JAMES, Esq., F.R.S. | SHARPEY, Professor, Sec.R.S. EX-OFFICIO MEMBERS OF THE COUNCIL. The President and President Elect, the Vice-Presidents and Vice-Presidents Elect, the General and Assistant-General Secretaries, the General Treasurer, the T'rustees, and the Presidents of former years, viz.—Rey. Professor Sedgwick. The Duke of Devonshire. Rev. W. V. Harcourt. Rev. W. Whewell, D.D. The Earl of Rosse. Sir John F. W. Herschel, Bart. Sir Roderick I. Murchison, K.C.B. The Rey. T. R. Robinson, D.D. Sir David Brewster. G. B. Airy, Esq., the Astronomer Royal. General Sabine, D.C.L, William Hopkins, Esq., LL.D. The Earl of Harrowby. The Duke of Argyll. Professor Dau- beny, M.D. The Rey. H. Lloyd, D.D. Richard Owen, M.D., D.C.L, The Lord Wrottesley. William Fairbairn, Esq., LL.D. GENERAL SECRETARIES. WILLIAM HopkKIns, Esq., M.A., F.R.S., St. Peter’s College, Cambridge. JOHN PHILLIPS, Esq., M.A., LL.D., F.R.S., Professor of Geology in the University of Oxford. Museum House, Oxford. ASSISTANT-GENERAL SECRETARY. GEORGE GRIFFITH, Esq., M.A., Deputy Panter of Experimental Philosophy in the University of ord. GENERAL TREASURER. WILLIAM SPoTTISWOODE, Esq., M.A., F.R.S., F.G.8., 19 Chester Street, Belgraye Square, London, 8.W. LOCAL TREASURERS. William Gray, Esq., F.G.8., York. | Robert P. Greg, Esq., F.G.S., Manchester. Prof. C. C. Babington, M.A., F.R.S., Cambridge. John Gwyn Jetireys, Esq., F.R.8., Swansea. William Brand, Esq., Edinburgh. Robert Patterson, Esq., M.R.L.A., Belfust. John H. Orpen, LL.D., Dublin. | Edmund Smith, Esq., Hull. William Sanders, Esq., F.G.S., Bristol. | Richard Beamish, Esq., F.R.S., Cheltenham. Robert M‘Andrew, Esq., F.R.S., Liverpool. | John Metcalfe Smith, Esq., Leeds. W. R. Wills, Esq., Birmingham. John Forbes White, Esq., Aberdeen. Professor Ramsay, M.A., Glasgow. | Rey. John Griffiths, M.A., Oxford. AUDITORS. J. P. Gassiot, Esq. Robert Hutton, Esq. Dr. Norton Shaw. OFFICERS OF SECTIONAL COMMITTEES. XX1X OFFICERS OF SECTIONAL COMMITTEES PRESENT AT THE CAMBRIDGE MEETING. SECTION A.—MATHEMATICS AND PHYSICS. President.—G. G. Stokes, M.A., F.R.S., Lucasian Professor of Mathematics. Vice-Presidents.—Professor Adams, F.R.S.; Rev. Professor Challis, F.R.S.; Rey. Dr. Lloyd, F.R.S. ; Rey. Professor Price, F.R.S. ; General Sabine, President R.S. ; Rey. Dr. Whewell, F.R.S.; Lord Wrottesley, D.C.L., F.R.S. Secretaries.—Professor Stevelly, LL.D., Professor H. J. S, Smith, F.R.S., and Pro- fessor R. B. Clifton, F.R.A.S. SECTION B.—CHEMISTRY AND MINERALOGY, INCLUDING THEIR APPLICATIONS TO AGRICULTURE AND THE ARTS. President.—W. H. Miller, M.A., F.R.S., Professor of Mineralogy in the University of Cambridge. Vice-Presidents.—C. G. B. Daubeny, M.D., F.R.S.; J. P. Gassiot, I'.R.S.; J. H. Gladstone, Ph.D., F.R.S.; Rev. W. Vernon Harcourt, F.R.S.; Dr. Joule, F.R.S. Secretaries—W. Odling, M.B., F.R.S.; Professor H, E. Roscoe, Ph.D., B.A. ; H. W. Elphinstone, M.A., F.L.S. SECTION C.—GEOLOGY. President.—J. B. Jukes, M.A., F.R.S. Vice-Presidents.—Rev. Professor Sedgwick, F.R.S.; Sir Charles Bunbury, F.R.S. ; R. A. C. Godwin-Austen, F.R.S.; Professor Ansted, F.R.S. Secretaries.—Professor T. Rupert Jones; Lucas Barrett, F.LS., F.G.S8.; H. C. Sorby, F.R.S. SECTION D.— ZOOLOGY AND BOTANY, INCLUDING PHYSIOLOGY. President.—Professor Huxley, F.R.S. Vice-Presidents.—Professor Balfour, F.R.S.; Rev. Dr. Cookson, Master of St. Peter’s College; J. Gwyn Jeftreys, F.R.S.; Rev. Leonard Jenyns, M.A., F.LS,; Edwin Lankester, M.D., F.R.S. Secretaries,—Alfred Newton, M.A., F.L.S,; E. Perceval Wright, M.D., F.R.C.S.1. SUB-SECTION D.—PHYSIOLOGICAL SCIENCE, President.—G. E. Paget, M.D. Vice-Presidents.—John Davy, M.D., F.R.S.; G. M. Humphry, M.D., F.R.S. ; Pro- fessor Owen, LL.D., F.R.S.; Professor Rolleston, M.D., F.R.S. Secretaries—Edward Smith, M.D., F.R.S.; G. F. Helm. SECTION E.—GEOGRAPHY AND ETHNOLOGY. President.—Francis Galton, M.A., F.R.S. Vice-Presidents.—Rey. J. W. Blakesley, M.A.; J. Crawfurd, F.R.S.; William Spottiswoode, M.A., F.R.S., General Treasurer of the British Association 3 Rey. George Williams, B.D. Secretaries.—Dr. Norton Shaw ; Thomas Wright, M.A.; Dr. Hunt; Rey. J. Glover, M.A. ; and J. W. Clarke, M.A, SECTION F.—ECONOMIC SCIENCE AND STATISTICS. President.—Edwin Chadwick, C.B. Vice-Presidents—Colonel Sykes, M.P., F.R.S.; William Tite, M.P., F.R.S.; Thomas Webster, F.R.S.; James Heywood, F.R.S. Secretaries—Edmund Macrory, M.A.; H. D. Macleod, B.A. Xxx REPORT—1862. SECTION G.—MECHANICAL SCIENCE, President.—W. Fairbairn, LL.D., F.R.S. Vice-Presidents—James Nasmyth, F.R.A.S.; Professor J. M. Rankine; Dr. Ro- binson, F.R.S.; Jobn Scott Russell, F-R.S. ; Professor James Thomson, M.A. ; Charles Vignoles, F.R.S. Secretaries.—P. Le Neve Foster, M.A.; William M. Fawcett, M.A, CORRESPONDING MEMBERS. Professor Agassiz, Cambridge, Massa- | Professor De Koninck, Liége. chusetts. M. Babinet, Paris. Dr. A. D. Bache, Washington. Dr. D. Bierens de Haan, Amsterdam. Professor Bolzani, Kasan. Dr. Barth. Dr. Bergsma, Utrecht, Mr. P. G. Bond, Cambridge, U.S. M. Boutigny (d’ Evreux). Professor Braschmann, Moscow. Dr. Carus, Leipzig. Dr. Ferdinand Cohn, Breslau. M. Antoine d’Abbadie. M. De la Rive, Geneva. Professor Wilhelm Delfts, Hezdelberg. Professor Dove, Berlin. Professor Dumas, Paris. Dr. J. Milne-Edwards, Pars. Professor Ehrenberg, Berlin, Dr. Eisenlohr, Carlsruhe. Professor Encke, Berlin. Dr. A. Erman, Berlin. Professor A. Escher yon der Linth, Zurich, Switzerland. Professor Esmark, Christiania. Professor A. Favre, Geneva. Professor G. Forchhammer, Copenhagen. M. Léon Foucault, Paris. Professor HE, Fremy, Paris. M. Frisiani, Ilan. Dr. Geinitz, Dresden. Professor Asa Gray, Cambridge, U.S. Professor Henry, Washington, U.S. Dr. Hochstetter, Vienna. M. Jacobi, St. Petersburg. Prof. Jessen, Med. et Phil. Dr., Griess- wald, Prussia. Professor oe Kekulé, Ghent, Belgium. M. Khanikoff, St. Petersburg. Prof, A, Kolliker, Wurzburg. Professor Kreil, Vienna. Dr. A. Kupffer, St. Petersburg. Dr. Lamont, Mamnich. Prof, F, Lanza. M. Le Verrier, Paris. Baron yon Liebig, Munich. Professor Loomis, New York. Professor Gustay Magnus, Berlin. Professor Matteucci, Pisa. Professor P. Merian, Bdle, Switzerland. Professor von Middendorff, St, Petersburg. M. VAbbé Moigno, Paris, Professor Nilsson, Siveden. Dr. N. Nordenskiold, Finland. M. E. Peligot, Paris. Prof. B. Pierce, Cambridge, U.S. Viscenza Pisani, Florence, Gustav Plaar, Strasburg. Chevalier Plana, Twin. Professor Pliicker, Bonn. M. Constant Prévost, Paris, M. Quetelet, Brussels, Prof. Retzius, Stockholm. Professor W. B. Rogers, Boston, U.S. Professor H. Rose, Berlin. Herman Schlagintweit, Berlin. Robert Schlagintweit, Berlin. M. Werner Siemens, Vienna. Dr. Siljestrom, Stockholm. Professor J, A. de Souza, University of Coimbra. M. Struvé, Pulkowa. Dr. Syanberg, Stockholm. M. Pierre Tchihatchef. Dr. Van der Hoeven, Leyden, Professor E. Verdet, Paris, M. de Verneuil, Paris. Baron Sartorius yon Waltershausen, Gottingen. Professor Wartmann, Geneva. REPORT OF THE COUNCIL. XXX1 Report of the Council of the British Association, presented to the General Committee, Wednesday, October 1, 1862. 1. The Council were directed by the General Committee at Manchester to maintain the Establishment of the’ Kew Observatory, and a grant of £500 was placed at their disposal for the purpose. They have received at each of their Meetings regular accounts of the proceedings of the Committee of the Observatory, and they now lay before the General Committee a General Report of these proceedings during the year 1861-62. (See Report of Kew Committee for 1861-62.) 2. A sum of £40 was placed at the disposal of the Kew Committee for the employment of the Photoheliometer ; and a further sum of £150 for the pur- pose of obtaining a series of photographic pictures of the Solar surface, with the cooperation of the Royal Society. The Report of the Kew Committee will make known the results of these recommendations. 3. The Report of the Parliamentary Committee has been received by the Council for presentation to the General Committee today, and is printed for the information of the Members. (See Report of Parliamentary Committee.) 4. The Council have to regret the absence from this Meeting of the General Secretary, Mr. Hopkins, through indisposition, which they sincerely hope will soon be removed. 5. The ‘Classified Index’ to the Transactions of the Association, which was authorized to be prepared under the direction of Professor Phillips, is completed in one of the main divisions ; the remainder will be printed with- out delay, and will be delivered to the Members who have subscribed for it before the end of the present year, 6. At that date it is the request of Professor Phillips to be allowed to withdraw from the office of Assistant General Secretary to which he has been appointed, by Annual Election in the General Committee, for nearly thirty- two years. Having for two years received the useful aid of Mr. G. Griffith, M.A., of Jesus College, Oxford, he has expressed to the Council his conviction of the fitness of that gentleman to undertake the duties which have been so long entrusted to himself. 7. The Council having considered the subject, and having ascertained from Professor Phillips that he would be happy to cooperate with Mr. Hopkins as Junior General Secretary in the next year, recommend that the arrangement here suggested be carried out by the General Committee. 8. The Council received in April, 1862, a communication from Mr. John Taylor, Jun., and Mr, Richard Taylor, requesting that, on account of his great age, their father, Mr. Taylor, might be relieved of all further duties as General Treasurer and Co-Trustee of the Association. . The warmest thanks of the Council were given to Mr. Taylor for his kind attention and most valuable services rendered to the Association in two im- portant offices, as one of the Trustees and sole General Treasurer, and their regret that any cause should render it necessary for him to desire to be re- lieved from the duties which he has so efficiently performed for the great advantage of the Association, almost from its foundation. . 9, Sir Philip de Grey Egerton, Bart., was then requested to accept the office of Trustee of the British Association; and Mr. W. Spottiswoode to undertake the duty of General Treasurer to the Association. + These Gentlemen haye kindly consented to act, and have entered on their uties, 10. The Council have been informed that Invitations will be presented to XXXii REPORT—1862. the General Committee at its Meeting on Monday, October 6, from Neweastle- on-Tyne, Birmingham, Bath, Nottingham, and Dundee. 11. That the Vice-Chancellor of the University of Cambridge and the Rev. Professor Challis be elected Vice-Presidents for the next year. October 1, 1862. WILLIAM Farrparrn, President. Report of the Kew Committee of the British Association for the Advancement of Science for 1861-1862. The Committee of the Kew Observatory submit to the Association the following Report of their proceedings during the past year. Deeming it desirable that the instrumental arrangements and scientific processes at use in the Observatory should be represented at the International Exhibition, application was made to the Commissioners for space. This was granted in the nave of the building, where the following instru- ments are at present exhibited :— 1. A set of Self-recording Magnetographs. 2. An instrument for tabulating from the traces furnished by the Mag- netographs. 3. A Unifilar. 4. A Dip Circle. 5. A Self-recording Anemometer. 6. Barometers. 7. An instrument for testing Thermometers, also a Kew Standard Ther- mometer. 8. Sun Pictures, taken by the Kew Heliograph. The Committee have the pleasure to inform the Association that a Medal has been awarded to the Kew Observatory for excellence and accuracy of construction of instruments for observing terrestrial magnetism; and that two Medals have likewise been awarded to Mr. R. Beckley, Mechanical Assistant at Kew, for his Registering Anemometer, and for his Photographs of the Sun. It is proposed that application be made to the Government Grant Com- mittee of the Royal Society for the expenses incurred through this exhibition. At the time when the last Report was made to the Association, the Staff at Kew were occupied with the verification of a set of magnetic instruments belonging to Prof. De Souza, of the University of Coimbra, a gentleman who was present at the Mecting at Manchester. The examination of these was shortly after completed, and the instruments, consisting of a set of Self- recording Magnetographs, a tabulating instrument, a Dip Circle,and a Unifilar, have since been safely received at Coimbra. The following letter was addressed to the Chairman by Prof. De Souza shortly before his departure :— * London, 26th October, 1861. «* My pear Srr,—I cannot leave England, where I have been exceedingly favoured by the Committee of the Kew Observatory of the British Associa- tion, without expressing to you my hearty thanks for the help I have expe- rienced from the Committee in the construction and verification of the Magnetic and Meteorologic instruments for the University of Coimbra, as well as for the valuable instruction which I have received, guided by the Director of the Kew Observatory, and the kindness which the British Asso- REPORT OF THE KEW COMMITTEE. XXXill ciation has shown me in their magnificent Meeting. I shall never forget the help afforded to me in so many different ways, and I desire earnestly to put it in immediate contribution towards the advancement of science. “The Observatory of Coimbra must have in its library, as a memorial, the valuable collection of Transactions of the British Association, and I hope that you may be so kind as to put me in the way of obtaining these volumes. «‘T remain, dear Sir, «« Sincerely yours, “J. P. Gassiot, Esq.” ‘«« JactntHo A. DE Souza.” The request of this letter has been complied with by the Council of the Association, and a complete set of the Transactions has been dispatched to Coimbra. The Director of the Lisbon Observatory has since requested the Committee to superintend the construction of a set of self-recording Magnetographs. The Committee, in complying with his request, have made arrangements for the instruments at present exhibited in the International Exhibition, and these will afterwards be mounted at the Kew Observatory for inspection and verification. A Differential Declinometer for the Government Observatory at Mauritius has been verified and forwarded to Prof. Meldrum, who has received it in safety. Gini, Rokeby, of the Royal Marines, already favourably known by a me- teorological register very carefully kept at Canton during its occupation by the British troops, has received instruction at Kew in the use of magnetical in- struments, and has been furnished with a Dip Circle, a Unifilar, a Bifilar, and a Differential Declinometer, of which the constants have been deter- mined at the Observatory. Lieut. Rokeby proposes to employ these instru- ments at the Island of Ascension during his term of service at that station. He has also been furnished by Admiral FitzRoy with a complete equipment of the meteorological instruments supplied by the Board of Trade. The importance of Ascension as a magnetical station has long been recognized. Situated very nearly on the line of no magnetic dip, the determination of the periodical variations and of the secular changes of the three mag- netic elements cannot fail to possess a high value; and as a meteorological station, a rock in the mid-ocean, within 6° of the Equator, presents an almost unrivalled locality for an exact measure of the amount of the lunar atmo- spheric tide, and of the variations in direction and force of the trade-wind. The Admiralty, apprised of Lieut. Rokeby’s meritorious purposes, have sane- tioned the appropriation of the officers’ quarter at the summit of the Green Mountain, known as the “ Mountain House,” as an observatory; and the department of the Board of Trade, under Admiral FitzRoy’s superintendence, has authorized the expenditure of £50 in providing the additional accommo- dation required for the instruments. Lieut. Rokeby has arrived at Ascension. with the instruments uninjured, and writes in strong terms of the support he receives from Captain Barnard, the commander of the troops on the island. On June 19th the Chairman received a letter from the Astronomer Royal, in which he stated that he was very desirous of comparing the Greenwich records of the vertical-force magnet with those at Kew; and that, if agree- able to the Committee, he would request Mr. Glaisher to endeavour to arrange a meeting with Mr. Stewart for that purpose. The Chairman immediately replied, offering every facility, and Mr. Glaisher has since visited the Observatory, where the comparison has been made. 1862. ¢ XXxiv REPORT—1862. The usual monthly absolute determinations of the magnetic elements con- tinue to be made, and the self-recording magnetographs are in constant operation under the zealous superintendence of Mr. Chambers, the Mag- netical Assistant. - Major-General Sabine, Pres. R.S., has laid before the Royal Society a paper entitled ‘ Notice of some conclusions derived from the Photographic Records of the Kew Declinometer in the years 1858, 1859, 1860, and 1861.” The exceedingly good definition which the labours of the late Mr. Welsh procured for the magnetic curves, has also enabled the Superintendent, Mr. Stewart, to discuss the disturbance-curyes by a peculiar method, depend- ing on such definition; and he has presented a paper to the Royal Society “On the forces which are concerned in producing the larger magnetic dis- turbances.” The Committee are at present engaged in investigating the best means of multiplying copies of these curves, and exhibit to the Association two prints from such—one kindly taken by Sir Henry James by his process, and the other taken by that of Mr. Paul Pretsch. The expense incurred by Mr. Pretsch has been defrayed by £25 obtained from the Government Grant through the Royal Society. The Chairman of the Balloon Committee haying applied to the Super- intendent for the instruments used by the late Mr. Welsh in his ascents, these were delivered over to Mr. Criswick on the 12th of March last, haying been previously verified at the Observatory. The Meteorological work of the Observatory continues to be performed in a satisfactory manner by Mr. George Whipple, and each Member of the Staff of the Observatory seems much interested in the duties he is called upon to discharge. During the past year 184 Barometers and 282 Thermometers have been verified; and, to give an idea of the amount of this kind of work which has been accomplished since first the subject was commenced in the year 1854, it may be stated that no fewer than 1185 Barometers and 6429 Thermometers have been verified up to this date. Rear-Admiral FitzRoy having been informed of the existence at the Ob- servatory of a Barograph invented and used by Mr. Ronalds, the following letter was addressed by him to the Chairman :— (Copy.) “Board of Trade (and Admiralty) Meteorological Department, 2 Parliament Street, London, 8.W., 7th April, 1862. *‘ Srr,—I have the honour to address you as Chairman of the Kew Com- mittee of the British Association for the Advancement of Science, on behalf of this branch department of the Board of Trade and the Admiralty. “T am authorized to request that you will allow us to endeavour to benefit by your regular photographic self-registration of the Barometer at the Kew Meteorological and Magnetical Observatory during at least one com- plete year of continuous record, by causing this office to be furnished with copies of photographic tracings, or their results, in full detail. «The objects specially in view here, are :— “Such accurate and indisputable continuous delineation of atmospheric pressure, or (rather) tension, as can only be obtained by perfectly reliable means; and “Such details of occasional oscillations, or pulsations (so to speak), as can best be obtained photographically. —— Z_ REPORT OF THE KEW COMMITTEE. XXXV «For practical daily purposes, a self-registering Barometer, on the Milne principle, may be sufficient ; but for elaborate analysis of atmospherical con- ditions and changes, in connexion with the numerous influences operating, some occasionally, some frequently, others always, in the air and its ever- restless currents, such an apparatus as that now available at Kew would appear to be indispensable. « Besides ordinary meteorological peculiarities, the direction of magnetic earth-currents, the occurrence of magnetic storms, the differing electrical conditions of various currents of air, the phenomena of earthquakes, and their ‘lightnings’*, seem to be more or less in certain relations to atmo- spheric tension, and therefore to require a close and unbroken barometrical registration. Towards some additional expense incurred by the Kew Ob- servatory in complying with this request, I am authorized to say that this department will contribute, on principle similar to that of verification of instruments. ‘«‘T have the honour to be, “c Sir, ** Your obedient Servant, (Signed) “ Ropert FrrzRoy, BR. Adm,” «P.S. Probably two scales of tracing, analogous to ‘Sailing Charts’ and ‘Particular Plans,’ would be convenient.” “ John Peter Gassiot, Esq., F.R.S., Chairman of the Kew Committee of the British Association.” To which the Chairman shortly afterwards replied in the following terms :— (Copy-) “Kew Observatory, 23rd April, 1862. “Srr,—I have the honour to acknowledge receipt of your letter of 7th inst., addressed to me as Chairman of the Kew Committee of the British Association. On behalf of this Committee, I may state in reply that it will afford us much satisfaction to furnish your department with Photographic Self- registrations of the state of the Barometer at Kew Observatory. “Tam informed by Mr. Stewart, our Superintendent, that we have in our _ possession an instrument well calculated, with some slight alterations, to _ produce the results you desire. _ “It possesses a compensation for temperature ; -besides which, it will be _ placed, when finally in action, in a room where the daily range of tempera- i ture is not more than half a degree Fahrenheit. «This instrument is not yet, however, in working order, and two months may perhaps elapse before it is quite ready. As you seem to think it de- sirable to obtain occasionally curves on an enlarged scale, it will be matter for _ our consideration whether this can be managed, and how. You will be duly informed of our resolution; but, in the mean time, I may state that it would be somewhat more than two months before such additional curves could be ready. In conclusion, without binding ourselves to any specified time (which, indeed, would not be desirable in a matter of this nature), I beg _ to assure you that we shall do all in our power to hasten the desired result ; and, as we hope to have things ready in the course of two or three months, 7 * Secchi and Palmieri, 1862. 3 ¢ : XXXVI REPORT—1862. we shall then also be prepared to reply to you with respect to remuneration for the additional work which the Observatory would thus undertake. «JT have the honour to be, “e Sir, “ Your obedient Servant, (Signed) “J. P. Gassror.” “ Rear-Admiral FitzRoy, F.R.S., §¢.” The Mechanical Assistant being engaged at the Exhibition, it was found impossible to complete the alterations alluded to quite so soon as anticipated ; but a curve was procured about the middle of August, which was sent to Admiral FitzRoy, and approved of by him. The Barograph has since received some further alterations, with a view to increase its stability and general efficiency. These are now completed, and the instrument will be henceforth kept in constant operation. One of the curves from this instrument is presented to the Association. Arrangements were made for recording photographically, by means of the Heliograph, the transit of Mercury which took place on the 12th of Novem- ber last, but the weather proved unfavourable. This instrument was also in readiness for the partial eclipse of the sun which took place on the 31st of December last; but, owing to the unfavourable state of the sky, only two imperfect pictures were obtained. A very good series of sun-pictures was ~ obtained by Mr. Beckley during the months of November and December. The Heliograph was sent from Kew at the beginning of January to Mr. De la Rue’s Observatory, and Mr. Beckley attended at Cranford to assist in erecting and adjusting it to focus; but the weather was so unfavourable during the remainder of that month that no pictures of the sun could be obtained. It had somewhat improved about the 7th of February, when the first photograph was taken, and since then others have been obtained by Mr. Reynolds (Mr. De la Rue’s assistant) on every day on which this has been possible. Altogether, up to the 12th of September inclusive, 177 pho- tographs have been taken on 124 days, namely :— Number of Number of pho- In the Month of working days. tographs procured. Bebra Ary? or. h akais ' 40 ee 13 IMPAT CHE ae 5 ccsles-nehs\os),- | ee anes Se a yi PARE ae Sactttes stone 5, 0 6 AT eteatdx: scars 31 Utes sib scsca? Neus e126 it <1 Mie otcoass crete 26 RIEEO s Ftai'dca rh ab giss)'si nt eet | rere ae 28 ERT er ieee, sche Oy oi als haul 27 AMI EUS res ner kis Se OS at ae nae 26 Up to September 12 . es ae ie 9 124 177 from February 7th to September 12th inclusive there are 218 days ; so that on the average one photograph was procured for 1-77 day. Nearly half of the pictures have been obtained by taking advantage of breaks in the clouds, and many have been taken through haze. In several of the photographs, owing to the unpropitious state of the atmosphere, there is a want of that beauty and perfection which the Heliograph is capable of affording; but all the pictures are sufficiently perfect for measurement by means of Mr. De la Rue’s Micrometer. Many of these are extremely perfect, and all would have been so had the state of the atmosphere permitted. — REPORT OF THE KEW COMMITTEE. XXXVil During the month of August Dr. Sabler, Director of the Observatory of Wilna in Russia, resided at Cranford, and received instruction in Astrono- mical Photography. A Photoheliograph is being constructed for him under Mr. De la Rue’s superintendence by Mr. Dallmeyer, and a Micrometer by the Messrs. Simms. This Heliograph will embody all the optical and mechanical improvements suggested by the experiments with the Kew instrument ; and it is expected that the Wilna apparatus will be in operation in the spring of 1863. In the event of the Kew Heliograph being worked continuously, Sir John Herschel’s suggestion that daily records of the sun should be taken by means of photography will therefore be carried out both in England and Russia; if this were done in one or two other localities, a considerable amount of information would be obtained respecting physical changes con- tinually occurring on the sun’s surface. The experience obtained during the past year has been such as to lead Mr. De la Rue to recommend that photographic records should be continued for a series of years at some public Observatory. The Committee have had in consideration whether this could be done at Kew without interfering with the other work, and have come to the conclusion that the Heliograph might be worked at an annual expense of £200, which sum would cover the cost of an additional Assistant, who might at the same time do the other photogra- phic work of the Observatory. The old dome formerly used for the Heliograph is so inconyeniently situ- ated as to be quite unfit for such work, and it will be necessary to make some addition to one of the present out-buildings in order to contain the in- strument. The cost of this structure is estimated at £100. The Committee strongly recommend that the General Committee of the Association take such steps as they may consider advisable for carrying this desirable object into practical effect. The self-recording Electrometer of Prof. W. Thomson continues in con- - stant operation. Mr. Francis Galton having made arrangements in the Observatory Park for testing sextants, the Observatory is now prepared to receive such instruments for examination, and to issue certificates to such as may fulfil the conditions of any of the following classes :— A. Sextants of the highest order of workmanship for lunar observations and general service, on shore as well as at sea. B. Sextants for naval surveys and for the determination of altitudes with as much precision as is available at sea. C. Quadrants or sextants to be used without telescopes, for the determina- tion of altitudes with an exactness equal to the requirements of general navigation. The charges for examination under classes A and B will be 5s., under class C, 1ls.; and the minute constant errors of instruments under class A will be determined, when desired, at an additional charge of 5s. Fight sextants have been verified at Kew since the last Meeting of the British Association. The Observatory has been honoured with a visit from the following distin- guished men of science, who had visited this country in consequence of the International Exhibition :— Professors Dove, Magnus, and Quincke, of Berlin ; Professor Férchhammer, of Copenhagen; Professors Bunsen, Kirchhoff, and Eisenlohr, of Heidelberg ; Professors Kraft and Pisko, of Vienna; Professor Govi, of Turin; Professor Donati, of Florence ; Professor Bolzani, of Kasan; Professor Lapschine, of 1862. REPORT XXxXVlil “NOLLOH “a ZORT ‘aquaydog’ YLT 9 % BIR TT 0 guNOWE JaZLeNb v pue sxvak 0.9 ysvE OY} LOJ Sydrd904 puodsaq aanjrpuddxa jo souvreq yuosord oy} Suryey L£ €& 64 +seeeegraqaenb aay Jo Suysisuoo ‘TggT ‘vad snoraord oy} Toy 90ST 19AO GANyIpUddxa JO ssadx9 94} Pappe oq snUt YOM OF, IL 81 201F seenadtnsneccnssceentensenesesnaystoganes oni suheicowssaranepasnrnnscrins® (Sinsivnopecuse ee tBraeetasensihs sre iccs jo wins ayy kq paareoar asoyy paoxa papuadxe syunowe 01} Wey} Puy [ ‘aur 07 poytasard sroyONOA Oy} YITA Ff poredoo puv yuNodoe aAoge ayy paurWeXo aAvy J PE 2) GR 9 T OOLF OFS, aT "ee" ZOBT “19G0}9O YIOT OF PUBT JO Joy 0 cl P Reem teeta meee wee een ane wy.) oq IL 4T 02 IL 2 9g sesuadxe Aqjad pue aren Tne : "a7 ‘Krappueyg ‘sasuedxy asnozy 0 Sl 2F : seteserseeerereeeees SBE) PUR §[0D Be 20S “9S8n4sog pure ‘syoog ‘ArauoNNg ‘Suu 09 8 see TLOSBIA pure ‘ajuadieg ‘1oduouUOdy > OL FF ttresererees eo ‘S007, ‘s[eUazEy ‘snjyereddy On al S02 eee eworenree “SZT 4v ‘Z98T ‘Toqula} Gog lee fe Y}6z Surpua ‘syaaa gg “ToyeE “I, weeeeeeee ‘SOP 4e ‘S981 ‘yaquiaydag iam le ie Surpua ‘syoan g¢ ‘Aopjoog “y Peeerr rr ee Z98T ‘yaquiaydag 0 0 08 ise Surpue ‘s1ogaenb anoj ‘ayddiq A “9 see e neem ereeeenne 9 T ‘a0 040 4 0 0 00 deine ignaaet te essettua ‘9 pet ee eee eeeeraseeeeeneeeresesersrQQgiig(, 0 0 Of Ss Buryaarsy Ayjod roy pomoyye ‘0971, eee ewww were ZISL £79049: ST 0 0 006 a are ‘saoqzenb snoz tia "g OF —!'d2p ‘salves LG GE teeters gunogae yee] Wor oouRle ps F D'S F¥ “SENGWAVd et ee eS eS ee eee 9 LT O9LF QO BBL “erereeeseesesttseseeseseconsenecnennessnvereeseeseseeeegOUBlUE] 006 seneseeeeeerenpsensescceneeccesresseeeeesroee NOD TAOA sem jue oyviedes v yorym xoy sngeteddy Suryent ur Aepyjoog “xy Aq popuodxe auiry 10j siseeseneeeersseeneeeees STQAQMOMNION} PALPULJS LOF POLICE ee eee sued mol 0 81 &I tresereeeeveree Kare rTMIpW OU} ULOIT 0 IL 8 °°" epeay, JO pavog ot} Woy ‘pS F —SPIUVINYSUT JO WOYLOYIIVA 9I[} LOF 0 0 O09 TT Tamnsvory, [e1IUEH OY} WoIy paatoooy Bee “ ve oo oo lol oO es “ “SLdI MONA "SORT “TL 129000 92 TORT “pF waquajdoeg mouf woymwossy Ys aya fo saynunuog may ay) fo syunovpy é He RECOMMENDATIONS OF THE GENERAL COMMITTEE. XXXix Kharkof ; Professors Clausius and Wartmann, of Geneva; Captain Belavenetz, Russian Navy ; and Captain Skariatine, Russian Marines. A reference to the annexed financial statement will show that, aithough the expenditure has exceeded the income, the Observatory has been conducted with the utmost regard to economy.; and the Committee recommend that for the ensuing year a sum of £600 should be granted, which, with other amounts to be received, will, it is expected, meet the necessary requirements. Joun P. Gasstor, Kew Observatory, Chairman. Sept. 29th, 1862. Report of the Parliamentary Committee to the Meeting of the British Association at Cambridge, October 1862. The Parliamentary Committee have the honour to report as follows :— The Bishop of Oxford, in furtherance of the resolution adopted at Liverpool in 1854, must be deemed to have vacated his seat in this Committee, but we recommend that he should be re-elected. Your Committee have also to report that Mr. James Heywood has not found it necessary to call upon them to interfere in the matter referred to them at Manchester by the General Committee. Wrorrestry, Chairman. Sept. 14, 1862. RECOMMENDATIONS ADOPTED BY THE GENERAL COMMITTEE AT THE CamBrivce Mrerine 1n Octoser 1862. {When Committees are appointed, the Member first named is regarded as the Secretary of the Committee, except there be a specific nomination. | Involving Grants of Money. That the sum of £600 be placed at the disposal of the Council, for main- taining the Establishment of Kew Observatory. That the sum of £100 be placed at the disposal of the Council, for the pur- pose of making an addition to the out-buildings at Kew Observatory, to receive the Photoheliograph, now in the hands of Mr. De la Rue. That the cooperation of the Royal Society be requested for the purpose of completing and proving the instruments devised for obtaining Photographic registration of the physical aspect of the Sun. That the Committee, consisting of Professor Williamson, Professor Wheat- stone, Professor W. Thomson, Professor W. H. Miller, Dr. A. Matthiessen, and Mr. Fleeming Jenkin, appointed at the Manchester Meeting, be requested to continue their Report on Standards of Electrical Resistance, and to extend it to other Electrical Standards; and that Dr. Esselbach, Sir C. Bright, Pro- fessor Maxwell, Mr. C. W. Siemens, and Mr. Balfour Stewart be added to the Committee; and that the sumof £100 be placed at their disposal for the purpose. That the Committee to report upon Standards of Electrical Resistance, be xl REPORT—1862. authorized to distribute gratuitously provisional Standards of Electrical Re- sistance, should it appear to them advantageous to do so; and that the sum of £50 be placed at their disposal for the purpose. That as all the Balloon Observations hitherto made under the authority of the British Association (owing to unavoidable circumstances) have been con- fined to the autumnal period of the year, these operations should be repeated at other periods of the year, especially during the east winds of spring, with a view to test the normal character of the observations already made ; That Colonel Sykes, Professor Airy, Lord Wrottesley, Sir D. Brewster, Sir J. Herschel, Dr. Lloyd, Admiral FitzRoy, Dr. Lee, Dr. Robinson, Mr. Gassiot, Mr. Glaisher, Dr. Tyndall, Mr. Fairbairn, and Dr. W. A. Miller be a Balloon Committee; and that the sum of £200 be placed at their disposal for the purpose. That the sum of £70 be placed at the disposal of the Balloon Committee, to meet the deficiency in the Grant of £200 made at Manchester. That a sum not exceeding £25, the amount of expenses necessarily in- curred by Mr. Glaisher in the prosecution of the Balloon experiments, be repaid to him. That the Committee on Luminous Meteors and Aérolites, consisting of Mr. Glaisher, Mr. R. P. Greg, Mr. E. W. Brayley, and Mr. Alexander Her- schel, be reappointed ; and that the sum of £20 be placed at their disposal for the purpose. That Mr. Fleeming Jenkin be requested to continue his Report on Thermo- Electrical Experiments ; and that the sum of £15 (being the balance of the Grant made to him last year) be placed at his disposal for the purpose. That the Committee, consisting of Professor Hennessy, Admiral FitzRoy, and Mr. Glaisher, be requested to continue their inquiries relative to the con- nexion of Vertical Movements of the Atmosphere with Storms ; and that the sum of £20 be placed at their disposal forthe purpose. That Dr. Matthiessen be requested to continue his Experiments on Alloys ; and that the sum of £20 be placed at his disposal for the purpose. That Dr. A. Dupré be requested to continue his Experiments upon the action of Reagents on Carbon under Pressure; and that the sum of £10 be placed at his disposal for the purpose. That the Balance of Grant of £8 made at the Manchester Meeting to Mr. Alphonse Gages, of Dublin, be placed at the disposal of that gentleman. That the Committee, consisting of Mr. R. H. Scott, Sir Richard Griffith, and the Rev. Prof. Haughton, be requested to complete their Report on the Chemical and Mineralogical Composition of the Granites of Donegal and the associated Rocks; and that the sum of £5 be placed at their disposal for the purpose. That Mr. H. C. Sorby and Mr. C. H. B. Hambly be a Committee to make Experiments on the Fusion and Slow Cooling of various Igneous Rocks ; and that the sum of £30 be placed at their disposal for the purpose. That Professor Huxley and Sir Philip de Grey Egerton be a Committee to aid Mr. Molyneux in his Researches into the Characters and Distribution of the Organic Remains of the North Staffordshire Coal-field ; and that the sum of £20 be placed at their disposal for the purpose. That Mr. Mallet be requested to conduct Experiments to ascertain the Temperatures of the Volcanic Craters of Vesuvius and of the Temperature and Issuing Velocity of the Steam evolved at the Mouths,—the Experiments, if possible, to be extended to other Volcanic Vents in the Mediterranean Basin ; and that the sum of £100 be placed at his disposal for the purpose. RECOMMENDATIONS OF THE GENERAL COMMITTEE. xli That a Committee, consisting of Dr. Cobbold and Mr. J. Lubbock, be re- = quested to prosecute their Investigations respecting the Reproduction, » Development, and Migration of the Entozoa; and that the sum of £25 be placed at their disposal for the purpose. That Professor Huxley and the Rey. Mr. Macbride be a Committee to con- duct Experiments on the Artificial Fecundation of the Herring ; and that the sum of £20 be placed at their disposal for the purpose. That Mr. J. Gwyn Jeffreys, Mr. Joshua Alder, the Rev. A. M. Norman, and Mr. H. T. Mennell be a Committee for exploring the Doggerbank and other portions of the Sea-coast of Durham and Northumberland by means of the Dredge ; and that the sum of £25 be placed at their disposal for the urpose. 4 That Mr. J. Gwyn Jeffreys, Professor Allman, Mr. John Leckenby, Pro- fessor Wyville Thomson, and the Rev. Thomas Hincks be a Committee for exploring the Coasts of Shetland by means of the Dredge; and that the sum of £50 be placed at their disposal for the purpose. That Mr. J. Gwyn Jeffreys, Professor Allman, Professor Dickie, the Rev. Dr. Gordon, and Mr. Robert Dawson be a Committee for exploring the North-east Coast of Scotland by means of the Dredge ; and that the sum of £25 be placed at their disposal for the purpose. That Mr. J. Gwyn Jeffreys, Mr. Robert M‘Andrew, Mr. G. C. Hyndman, Professor Allman, Dr. Kinahan, Dr. Collingwood, Dr. Edwards, Professor Greene, Rey. Thomas Hincks, Mr. R. D. Darbishire, and Dr. E. Perceval Wright be a Committee to superintend all the Dredging Committees of the Association ; and that the sum of £10 be placed at their disposal for the pur- ose. E That the Committee, consisting of Dr. Edward Smith and Mr. Milner, be requested to continue their inquiries on the Influence of Prison Punishment and Dietary upon the Bodily Functions of Prisoners; and that the sum of £20 be placed at their disposal for the purpose. That Dr. Gibb be requested to inquire into the Physiological Effects of Bromide of Ammonium ; and that the sum of £8 be placed at his disposal for the purpose. That Dr. Carpenter, Professor Huxley, and Mr. Rupert Jones, assisted by Mr. Parker, be a Committee to aid in the Construction of a Series of Models showing the External and Internal Structure of the Foraminifera; and that the sum of £25 be placed at their disposal for the purpose. That Professor Allman and Dr. E. P. Wright be a Committee to complete a Report on the Reproductive System of the Hydroida; and that the sum of £10 be placed at their disposal for the purpose. That Mr. Thomas Webster, the Right Honourable Joseph Napier, Sir W. G. Armstrong, Mr. W. Fairbairn, Mr. W. R. Grove, Mr. James Heywood, and General Sabine be reappointed, for the purpose of taking such steps as may appear expedient for rendering the Patent Law more efficient for the reward of the meritorious inventor and the advancement of practical science ; and that the sum of £30 be placed at their disposal for the purpose. That the Committee on Steamship Performance be reappointed, consisting of the Duke of Sutherland, The Earl of Gifford, M.P., The Earl of Caith- ness, Lord Dufferin, Mr. W. Fairbairn, Mr. J. Scott Russell, Admiral Paris, The Hon. Gaptain Egerton, R.N., The Hon. L. A. Ellis, M.P., Mr. J. E. McConnell, Mr. W. Smith, Professor J. Macquorn Rankine, Mr. James R. Napier, Mr. Richard Roberts; Mr. Henry Wright to be Honorary Se- cretary ; and that the sum of £100 be placed at their disposal. xlii REPORT—1862. That a Committee, consisting of Messrs. W. Fairbairn, Joseph Whitworth, James Nasmyth, J. Scott Russell, John Anderson, and Sir W. G. Armstrong, be requested to cooperate with a Committee appointed by Section B, viz. Dr. Gladstone, Professor W. A. Miller, and Dr. Frankland, for the purpose of investigating the application of Gun Cotton to warlike purposes; and that the sum of £50 be placed at their disposal for the purpose. That the Committee for Tidal Observations in the Humber, consisting of Mr. J. Oldham, Mr. J. F. Bateman, Mr. J. Scott Russell, and Mr. T. Thomp- son, be reappointed, to extend their observations to the Trent and the York- shire Ouse; and that the sum of £50 be placed at their disposal for the urpose. 4 That Sir John Rennie, Mr. John Scott Russell, and Mr. C. Vignoles (with power to add to their number), Mr. G. P. Bidder, Jun., as Secretary, be a Committee to inquire and report as to the effect upon the Tides in the Nene and the Ouse by the opening of the Outfalls below Wisbeach and Lynn to the Wash; and that the sum of £25 be placed at their disposal for the ose. That the Committee for investigating the causes of Railway Accidents, consisting of Mr. W. Fairbairn, Mr. J. E. M*Connell, and Mr. W. Smith, be reappointed; and that the sum of £25 be placed at their disposal for the purpose. Applications for Reports and Researches not involving Grants of Money. That Mr. Johnstone Stoney be requested to continue his Report on Molecu- lar Physics. That Mr. James Cockle be requested to prepare a Report on the History of the Theory of Equations. That a Committee be appointed for the purpose of carrying into effect the objects of the Report on Scientific Evidence in Courts of Law. That Dr. Gray, Dr. Sclater, Mr. Alfred Newton, and Mr. Wallace be a Committee to report on the Acclimatization of Domestic Quadrupeds and Birds, and how they are affected by migration. That Dr. Gray, Professor Babington, and Mr. Newbold be a Committee to report on the Plants of Ray’s ‘ Synopsis Stirpium,’ for the examination of the original Herbaria of Ray, Richardson, Buddle, Plukenet, and others. That Dr. Collingwood, Mr.J.A.Turner, M.P., Mr. James Heywood, Mr. John Lubbock, Mr. J. Gwyn Jeffreys, Mr. R. Patterson, Mr. P. P. Carpenter, and the Rey. H. H. Higgins be a Committee to inquire into the best mode of pro- moting the advancement of Science by means of the Mercantile Marine. That Mr. Consul Swinhoe and Dr. Sclater be a Committee to report on the Zoology of the Island of Formosa. That Dr. Edward Smith be requested to prepare for the next Meeting of the British Association a Report on the present state of our knowledge upon Nutrition, and especially its relation to Urea. That the Rev. W. Vernon Harcourt, Right Hon. Joseph Napier, Mr. Tite, M.P., Professor Christison, Mr. J. Heywood, Mr. J. F. Bateman, Mr. T. Web- ster (with power to add to their number) be a Committee for the purpose of giving effect to the Report of the Committee on Technical and Scientific Evidence in Courts of Law. o- iprchstrincementth, -, erin: nh tent mena ile. ek te _ Sykes, Col.—Other expenses of Balloon Ascents RECOMMENDATIONS OF THE GENERAL COMMITTEE. xh - Involving Applications to Government or Public Institutions. That a Deputation, consisting of Mr. E. Chadwick, C.B., Mr. J. Heywood, Mr. Marsh, M.P., Dr. Farr, Mr. Tite, M-P., Mr. 8. Gregson, M.P., and Col. Sykes, M.P., be requested to wait upon the Secretary of State for the Home Department and the Registrar-General, and represent to them the import- ance of haying prepared Mortuary Statistics in respect to Classes and Occupa- tions, in such forms as were recommended by the International Statistical Congress, or in such other form as will distinguish the Occupations or the Classes of those who die. That the Committee, consisting of Dr. Robinson, Professor Wheatstone, Dr. Gladstone, and Professor Hennessy, which was appointed at Manchester to confer as to Experiments on Fog Signals, and to act as a Deputation to the Board of Trade, be requested to impress upon the Board the importance of _ inquiries on the subject. Communications to be printed entire among the Reports. That the Extract of Professor De Souza’s Report to the Portuguese Government, regarding the Instruments used at Kew Observatory, be printed entire in the Reports. That Mr. Symons’s Papers on Rainfall be printed entire among the Reports. That the Paper by the Astronomer Royal, on the Strains in the interior of Beams and Tubular Bridges, be printed entire among the Reports. That Mr. Aston’s Paper on Projectiles, with reference to their Penetration, be printed entire among the Reports. That Mr. W. Fairbairn’s Paper on the Results of some Experiments on the Mechanical Properties of Projectiles be printed entire among the Reports. Synopsis of Grants of Money appropriated to Scientific Purposes by the General Committee at the Cambridge Meeting in October 1862, with the name of the Member who alone, or as the First of a Com- mittee, is entitled to draw the Money. Kew Observatory. Maintaining the Establishment of Kew Observatory House for the Photoheliograph at Kew.................... 100 lop) — S Sow oon Mathematics and Physics. Williamson, Prof.—Electrical Standards .................. 100 Williamson, Prof.—For constructing and distributing ditto.... 50 @eeeykes, Col.—Balloon Ascents ...............0.0000.- eee 200 Sykes, Col.—Balloon Committee (deficiency) .............. 70 Beamer Mri MOLCOESE 2. ccs citi Peo Ow eRle dar Dendes 20 Jenkin, Mr.—Thermo- Electricity Carriediforwarde 2: ns ee Cee Ae £1180 bo Or SISOS SOS SNeoe SSS) xliv REPORT—1862. Brought forward...... Hennessy, Prof—Vertical Atmospheric Movements......... Chemistry. Matthiessen, cDr-—ANOyS (ci. eel ee lve Oa REE Dupré, M.—Carbon under pressure ............ 0200 ee eeue Gages, Mr.—Chemistry of Rocks 2.0.06... ..cceeeteee sees Geology. Pepe y te GEA eS , ieee wie 6 ine .\6-6.005°8 Zapa'e vo veel 8 sad whe Porny, air. —Fustor of Rocks sfc sse6¥ sso s es vised ow toa we gdicy, Erot.——Coal Hossilg oo... 2. sos ones a oO ae Oe Mallet, Mr.—Volcanic Temperature...........0..eeeceuees Zoology and Botany. CIDA aga Dap 970/77 0 a al a i etreiy rol ——ACITMOS «2. St cs ca es ce ve Pa cet eens Jeffreys, Mr.—Dredging (Doggerbank)................2: Jeffreys, Mr.—Dredging (Shetland) ..................000- Jeffreys, Mr.—Dredging (N.E. coast of Scotland) .......... Jeffreys, Mr.—Committee for Dredging ................05: min, Or. H.-—Prison Discipline’. .........:.02ss heen Gibb, Dr.—Bromide of Ammonium ..................0e0. Warpenter, Dr.——Morammitera .. 2... 6. sss on ss he eee ast thes peli, Erol —-MyGroids: <0). fsa ve cc hc aces oe ee ewes Bviepsuer, Wx Parems Meine ait. fe. « oic0 iss ses os 9.0 vo sens we Sutherland, Duke of—Steamships ..................0.0. Gladstone, Dr. “GunCotton seeks. oh. oe Pe Oldham, Mr.—Tidal Observations...................0.00- Rennie, Mr.— 40 0 0 Races of Men .......... snecccceece 5 0 0} Coloured Drawings of Railway Radiate Animals ............ eters ee OO SGCUONs orenedce aeion caansapesen ai 147 18 3 £1235 10 11] Registration of Earthquake rs Shocks ...... wuvobeceenedernstievun 30 0 0 1842, Report on Zoological Nomencla- Dynamometric Instruments ...... 113 11.2 LUTE seesseseeeeteeeeeeennees odvase 20 10 OF Anoplura Britanniz ....... AOE . 5212 0] Uncovering Lower Red Sand- Tides at Bristol............0« se... 59 8 OQ] _ Stone near Manchester ...... ow 4 4 6 Gases on Light ........e0ee0e0+ sees 30 14 7 | Vegetative Power of Seeds ...... 5 3 8 Chronometers ........ AES a a 26 17. 6| Marine Testacea (Habits of ) 10 0 0 Marine Zoology..........+++ icerate ke 50)! Marine Zoology-c.sysvetver.caseee a0 Or ORG British Fossil Mammalia ......... 100 0 0 | Marine Zoology.........seseeeeeeeee 21411 Statistics of Education ............ 20 0 0 | Preparation of Report on British Marine Steam-vessels’ Engines... BR “greg Fossil Mammalia counocedevervcce 100 0 0 Stars (Histoire Céleste)............ 59 0 0 | Physiological Operations of Me- Stars (Brit. Assoc. Cat. of) ...... 110 0 0] dicinal Agents ......... coesveres SAO MIOMEG Railway Sections .........++ PERG 1040")! Vital Statisties 035: ci.cnsccescenese 36 5 8 British Belemnites....... Tt eceees 50 0 0 | Additional Experiments on the Fossil Reptiles (publication of Forms of Vessels ..sseessesseee 70 0 0 TUE TOT) jigesenmeene ee Pda aaa rog 6 210 0 0 | Additional Experiments on the Forms of Vessels ..s..s.seeceseesee 180 0 0 Forms of Vessels .....6....+.00- 100 0 0 Galvanic Experiments on Rocks 5 8 6 | Reduction of Experiments on the Meteorological Experiments at Forms of Vessels ..........000+ 100 0 0 ym outhe esse eevuewes carers 68 0 0 | Morin’s Instrument and Constant Constant Indicator and Dynamo- Indicator. we2suetetier Slee 69 14 10 metric Instruments .........+66 90 0 0 | Experiments on the Strength of Force of Wind ............+ arseeest; BLO Oe 0 Materials .,... Se spewe evsotedeese 60 0 0 Light on Growth of Seeds ...... 8 0 0 £1565 10 2 Wxtall statistics sss-ccssshesance sos. - 50 0 0 == Vegetative Power of Seeds ...... mea EU 1844. Questions on Human Race ...... 49530 Meteorological Observations at £1449 17 8 Kingussie and Inverness .,.... 12 0 0 Completing Observations at Ply- 1843, MNQUEH cc .- surwegesveaeeeeerenee 35 0 0 Revision of the Nomenclature of Magnetic and Meteorological oe SERES Saacavtewcsccccetecsececkooe oe Zaew” 0 operation wt. .sosdse. across Peace re Reduction of Resta British Asso- Publication of the British Asso- ciation Catalogue ............006 256 0 ciation Catalogue of Stars...... 35 0 0 Anomalous Tides, Frith of Forth 120 0 0 Observations on Tides on the Hourly Meteorological Observa- East coast of Scotland ......... 100 0 O- tionsat KingussieandInverness 77 12 8 | Revision of the Nomenclature of Meteorological Observations at SLE anee cosvespaicneesenns 1842 2 9 6 RIV MIGUtN ee oerecvescenreene sess 55 0 0 | Maintaining the Establishmentin Whewell’s Meteorological Ane- Kew Observatory ...... consrevee Aili Ady ales mometer at Plymouth ,........ 10 0 0 | Instruments for Kew Observatory 56 7 3 ——— ee ar Cr Seer GENERAL STATEMENT. eS Soe: Influence of Light on Plants...... 10) 0) 0 Subterraneous Temperature in MPOTATIG) oacgecs.cs.scccese S foconre a: MOR 0 Coloured Drawings of Railway SIEQHIOMS sonhs-sscssecenccarqcss sac 15 17 6 Investigation of Fossil Fishes of the Lower Tertiary Strata 100 0 0 Registering the Shocks of Earth- RIAEH Re esecns sacs OO Inquiry into the Performance of Steam-vessels......+ .. 124 0 0 Explorations in the Yellow Sand- stone of Dura Den..........++++ 20 0 0 Chemico-mechanical Analysis of Rocks and Minerals............ 25 0 0 Researches on the Growth of BMMUMirihccisessscscssvessocssecsss, 10° 0 0 Researches on the Solubility of SeMtntttestcissssserccescesterensss, 00 Or O Researches on the Constituents Of Manure o0.....s.s.ecccacseeseee 25. 0 O Balance of Captive Balloon Ac- COUNES, : ceccccccccccersccccoeccsees 113 6 HL241 570 ee et 1861. Maintaining the Establishment of Kew Observatory ............ 500 0 0 Earthquake Experiments,........ 25 0 0 Dredging North and East Coasts OF Scotland......ccccccsscsssocree 23 O O Dredging Committee :— 1860...... £50 0 0 1861 ...... £22 0 at tae Se Excavations at Dura Den......... 20 0 0 Solubility of Salts......... eet 20 OU Steam-vessel Performance ...... 150 0 0 Fossils of Lesmahago ......0... 15 0 0 Explorations at Uriconium ,,.... 20 0 0 Chemical Alloys ........0... 20 0 0 Classified Index to the Transac- FIONS cyeerersserrecccesesceseveeene 100 0 0 xlix G 8d Dredging in the Mersey and Dee 5 0 0 Dip Circlesesuses..scsccsscccstgenese 30 0) 0 Photoheliographic Observations 50 0 0 Prison’ Diet “sc.ccccccvccscresscoeese' 20 0 O Gauging Of. Water, isle Wecadtheas 10 0 O Alpine Ascents ....sccccccsssresssee 6 5 1 Constituents of Manures ....,.... 25 0 O £1111 5 10 ——_—— 1862. Maintaining the Establishment of Kew Observatory sse.ee.000.. 500 0 0 Patent Laws ......... etaiadsensae’ cite) On Mollusca of N.-W. America.... 10 0 0 Natural History by Mercantile Marine? ...0-sesseerses weeccccoees 5 0 0 Tidal Observations .....sse000048 25 0 0 Photoheliometer at Kew ......... 40 0 0 Photographic Pictures of the Sun 150 0 0 Rocks of Donegal............0.08. 25 0 0 Dredging Durham and North- umberland o...,...+008 cosceeees 25 0 0 Connexion of Storms......... eaten a 20) 0170 Dredging North-East Coast of Scotland. ..:cvcbsscvecsensesseusses (6. 9) 6 Ravages of Teredo .........0-.. 311 O Standards of Electrical Resistance 50 0 O Railway Accidents ..........++++. 10 0 0 Balloon Committee ............... 200 0 O Dredging Dublin Bay ............ 10 0 0 Dredging the Mersey ............ 5 0 0 PYISGH DICE oncccsnccseacapenaenseais 20 0 O Gaping of Water.....0...0.2c.095- 1210 0 Steamships’ Performance.,....... 150 0 0 Thermo-Electric Currents ...... 5 0 0 £1293 16 6 Extracts from Resolutions of the General Committee. Committees and individuals, to whom grants of money for scientific pur- poses have been entrusted, are required to present to each following meeting of the Association a Report of the progress which has been made; with a statement of the sums which have been expended, and the balance which re- mains disposable on each grant. Grants of pecuniary aid for scientific purposes from the funds of the Asso- ciation expire at the ensuing meeting, unless it shall appear by a Report that the Recommendations have been acted on, or a continuation of them be ordered by the General Committee. In each Committee, the Member first named is the person entitled to call on the Treasurer, William Spottiswoode, Esq., 19 Chester Street, Belgrave Square, London, 8.W., for such portion of the sum granted as may from time In grants of money to Committees, the Association does not contemplate the payment of personal expenses to the members. In all cases where additional grants of money are made for the continua- tion of Researches at the cost of the Association, the sum named shall be deemed to include, as a part of the amount, the specified balance which may remain unpaid on ‘the former grant for the same object. | to time be required. | | 1862, d 1 REPORT—1862. General Meetings. On Wednesday Evening, October 1, at 8 p.m, in the New Assembly Room, Guildhall, William Fairbairn, Esq., F.R.S., resigned the office of President to the Rey. R. Willis, M.A., F.R.S., who took the Chair, and delivered an Address, for which see page li. On Thursday Evening, October 2, at 8 p.m., in the New Assembly Room, Guildhall, Professor Tyndall, F.R.S., delivered a Discourse on the Forms and Action of Water. On Friday Evening, October 3, at 8 p.u., a Soirée, with Experiments, took place in the New Assembly Rooms. On Monday Evening, October 5, at 8 p.m., Dr. Odling, F.R.S., delivered a Discourse on Organic Chemistry. On Tuesday Evening, October 6, at 8 p.m., a Soirée, with Microscopes, took place in the New Assembly Rooms. On Wednesday, October 7, at 3 p.m., the concluding General Meeting took place, when the Proceedings of the General Committee, and the Grants of Money for Scientific purposes, were explained to the Members. The Meeting was then adjourned to Newcastle-on-Tyne*. * The Meeting is appointed to take place on Wednesday, August 26, 1863. ADDRESS BY THE REV. R. WILLIS, M.A., F.R.S., Jacksonian Professor, &c, GENTLEMEN OF THE British Assocration,—I have the honour to announce to you that we are now opening the Thirty-second Meeting of the British Asso- ciation, and are for the third time assembled in this University. At its first coming hither in 1833 its organization was scarce completed, its first Meeting having been devoted to explanations, discussions, and allotment of work to willing labourers ; its second Meeting, to the reception of the first instalment of those admirable preliminary Reports which served as the founda- tion of its future labours, and to the division of scientific communications to the Sectional Committees. But it was at Cambridge that the original plan of the Association bore fruit, by the receipt of the first paper which contained the results of experiments instituted expressly at the request of the Association. The success of the Association was now confirmed by the number of compositions and annual subscriptions paid in, and by the help of these funds a most important measure was introduced, namely, the practice of granting, in aid of philosophical researches to be undertaken by individuals or committees at the request of the Association, sums of money to meet the outlay required for apparatus or other expenses, which could not be asked from persons who were otherwise willing to devote their time to the advancement of science. It was at Cam- bridge that the importance and authority of the Association had become so manifest, that the first of its applications for Government assistance towards scientific objects was immediately complied with by a grant of £500 to reduce the Greenwich Observations of Bradley and Maskelyne. At the third Meeting improvements were made in the distribution of the Sciences to the Sections, and a Section of Statistics added. The only change in this respect that was subsequently found necessary was the establishment of a separate Section for Mechanical Science applied to the Arts, in 1837. The employment of alpha~ betical letters to distinguish the Sections had been introduced in 1835. I have said enough to claim for the Cambridge Meeting the honour of com- “ha the development of the Association; and I may be permitted to quote m our fourth Report the gratifying assurance, that so obvious was the utility of the proposed undertaking, that, in its very infancy, there were found several distinguished individuals, chiefly from the University of Cambridge, who volunteered to undertake some of the most valuable of those Reports which appeared in the first volume of the Proceedings. » With a mixture of regret and shame I confess, that although my name is enrolled in the honourable list of those who undertook Reports, it will be d2 hii REPORT—1862. sought in vain amongst those who promptly performed their promises. Yet I may be permitted to say that I still hope to be enabled at some future time to complete the Report on Acoustics, of which I delivered merely an oral sketch at the second Meeting of the Association, in 1832. The Association quitted Cambridge to pursue, with its matured organization, and with continually increasing stability and influence, the career of brilhant and useful labours in every branch of Science that it has never ceased to run during the two-and-thirty years that have elapsed since its foundation. It revisited Cambridge after an interval of twelve years, in 1845; and now, after a lapse of seventeen years, we have the high gratification of welcoming once more the Association to this scene of its early meetings. This appears a fitting occasion for a concise review of the leading principles and prominent labours of the body. Scientific Societies, as usually constituted, receive and publish papers which are offered to them by individuals, but do not profess to suggest subjects for them, or to direct modes of investigation, except in some cases by offering prizes for the best Essay in some given branch. This Association, on the contrary, is not intended to receive and record individual originality. Its motto is, suéGESTION AND COOPERATION, and its purpose is thus to advance science by cooperation, in determinate lines of direction laid down by suggestion. To give form and authority to this principle, the admirable conception of suggestive Reports was in the first place developed; a collection that should constitute a general survey of the Sciences as they stood at the foundation of the Association, each branch reported by some member who had already shown his devotion to the cultivation of it by his own contribution to its advance- ment, and each Report passing in review its appointed subject, not for the purpose of teaching it, but of drawing forth the obscure and weak places of our knowledge of it, and thus to lay down the determinate lines of direction for new experimental or mathematical researches, which it was the object of the Association to obtain. The requests for these Reports were zealously responded to, and so rapidly that at the second Meeting ten were received, and at the third eight others. In this manner in fiye or six years the cycle of the Sciences was well nigh exhausted ; but the series of such Reports has been maintained in succeeding years, even to the present time, by the necessity of supplemental Reports, to point out not merely the advances of each science already treated, but the new lines of direction for inquiry that develope themselves at every step in advance. The Reports thus described were entitled “On the progress and desiderata of the respective branch of Science,” or “ On the state of our knowledge re- specting such Science,” and must be considered as merely preparations for the great work for which the Association was formed. They constitute the suggestive part of the scheme: the cooperative mechanism by which each new line of research recommended in the Reports was to be explored, was energetically set in motion by the annual appointment of Committees or indi- viduals to whom these especial investigations were respectively assigned, with adequate sums at their disposal. These Committees were requested to report their labours from year to year, and thus a second set of documents have been produced, entitled “‘ Reports of Researches undertaken at the request of the Association,” which are entirely distinct from the “suggestive Reports,’ but immediately derived from them, and complementary to them, ADDRESS. lit Such is a concise view of the system at first laid down by the wisdom of our founders, and which, with some modifications, has produced the inestimable contents of our printed volumes. In practice the ‘‘suggestive Report” is often a paper contributed by some able investigator to some meeting of the Association, which produces a request from the body that he will pursue his researches with their sanction and assistance, and write a Report comple- mentary to his own suggestions. Again, although we did not profess to receive and publish individual re- searches, the number of these received at each meeting is very great; the merit of some of them so eminent, that they are authorized to be printed entire amongst the Reports; and the Notices and Abstracts of the remainder, which at first occupied a small proportional part of each volume, now occupy nearly half of it. I will now direct your attention to the principal objects to which our funds have been directed. To appreciate the value of an investigation by the money it costs, may ap- pear at first sight a most unworthy test, although it be a thoroughly British view of the subject. But there are undoubtedly a great number of most important inquiries in science that are arrested, not for want of men of zeal and ability to carry them out, but because from their nature they require an outlay of money beyond the reach of the labourers who ardently desire to give their time and thoughts to them, and because the necessity and value of the proposed investigation are wholly unappreciable by that portion of society who hold the purse-strings. But it is in the cases above alluded to of expensive investigation that the direct use and service of our body has been made the most manifest. The British Association holds its own purse-strings, and can also perfectly under- _ stand when they should be relaxed. Nay, more, by its influence and cha- racter, established by the disinterested labours and successful exertions of more than thirty years, it may be said to command the national funds; for the objects in aid of which Government assistance has been requested, have been so judiciously chosen, that such applications have very rarely been un- successful, but have been, on the contrary, most cordially acceded to. Indeed it may be observed, that from the period of the foundation of the Association the Government of this country has been extending its patronage of Science and the Arts. We may agree with the assertion of our founder, Sir David Brewster, in supposing that this change was mainly effected by the interference of this Association and by the writings and personal exertions of its members. For the above reasons it appears to me that by a concise review of the principal objects to which the funds of our body have been applied, and of _ those which its influence with the Government has forwarded, we obtain a measure of the most important services of the British Association. But in considering the investigations carried out by committees or indi- vidual members by the help of the funds of the Association, it must always be remembered that their labours, their time and thoughts, are all given gratuitously. One of the most valuable gifts to Science that has proceeded from our Association is the series of its printed Reports, now extended to thirty volumes. Yet these must not be supposed to contain the complete record even of the labours undertaken at the request and at the expense of the body. Many of these have been printed in the volumes of other societies, or in a separate form, Several, unhappily, remain in manuscript, excluded from the public by the great expense of publication, liv REPORT—1862. Tam the more induced to direct attention to this’great work at present because I hold in my hand the first printed sheets of a general Index to the series from 1831 to 1860, by which the titles and authors of the innumerable Memoirs upon eyery possible scientific subject, which are so profusely but promiscuously scattered through its eighteen thousand pages, are reduced to order, and reference to them rendered easy. This assistance is the more necessary because so many inyestigations have been continued with inter- missions through many years, and the labour of tracing any given one of them from its origin to its termination through the series of volumes is extremely perplexing. For this invaluable key to the recorded labours of the Association we are indebted to Professor Phillips, and the prospect of its speedy publication may be hailed as a great subject of congratulation to every member of our body. In eyery annual yolume there is a table of the sums which have been paid from the beginning on account of grants for scientific purposes. The amount of these sums has now reached £20,000; and an analysis of the objects to which this expenditure is directed will show that if we divide this into eighteen parts, it will appear, speaking roughly, that the Section of Mathematics and Physics has received twelve of these parts, namely two-thirds of the whole sum, the Sections of Geology and Mechanical Science two parts each, while one part has been given to the Section of Botany and Zoology, and one divided among the Sections of Chemistry, Geography, and Statistics. The greater share assigned to the first Section is sufficiently accounted for by the number and nature of the subjects included in it, which require innu- merable and expensive instruments of research, observatories, and expeditions to all parts of the globe. If we examine the principal subjects of expenditure, we find, in the first place, that more than £1800 was expended upon the three Catalogues of Stars, namely, the noble Star Catalogue, which bears the name of the British Asso- ciation, commenced in 1837, and completed in eight years, and the Star Catalogues from the observations of Lalande and Lacaille, commenced in 1835 and 1838, and reduced at the expense of the British Association, but printed at the expense of Her Majesty’s Government. £150 was applied principally to the determination of the Constant of Lunar Nutation, under the direction of Dr. Robinson, in 1857, and to several other minor Astronomical objects. At the very first Meeting at York, the perfection of Tide Tables, Hourly Meteorological Observations, the Temperature of the atmosphere at increasing heights, of Springs at different depths, and observations on the Intensity of Terrestrial Magnetism, were suggested as objects to which the nascent organi- zation of the Association might be directed. Its steady perseverance, increasing power and influence as successive years rolled on, is marked by the gradual carrying out of these observations, so as to embrace nearly the whole surface of the globe. Thus, under the direction of Dr. Whewell, a laborious system of observations, obtained by the influence and reduced at the expense of the Association, who aided this work with a sum of about £1300, has determined the course of the Tide-wave in regard to the coasts of Europe, of the Atlantic coast of the United States, of New Zealand, and of the east coast of Australia, Much additional information has been since collected by the Admiralty through various surveying expeditions; but it appears that much is still wanting to complete our knowledge of the subject, which can only be obtained by a vessel specially employed for the purpose. More than £2000 haye been allotted to Meteorology and Magnetism, for the construction of instruments, and the carrying out of series of observations ADDRESS. ly and surveys in connexion with them. To this must be added a sum of between £5000 and £6000 for the maintenance of Kew Observatory, of which more anon, The advance made in these important sciences, through the labours of the Committees of the British Association, may be counted among the principal benefits it has conferred. To the British Association is due, and to the suggestion of General Sabine, the first survey ever made for the express purpose of determining the positions and values of the three Isomagnetic Lines corresponding to a particular epoch over the whole face of a country or state. This was the Magnetic Survey of the British Islands, executed from 1834 to 1838, by a Committee of its members, General Sabine, Prof. Phillips, Sir J. Ross, Mr. Fox, and Mr. Lloyd, acting upon a suggestion brought before the Cambridge Meeting in 1833. It was published partly in the volume for 1838, and partly in the Philosophical Transactions for 1849. This was followed by a recommendation from the Association to Her Majesty’s Govern- ment, for the equipment of a naval expedition to make a magnetic survey in the southern portions of the Atlantic and Pacific Oceans. This recom- mendation, concurred in by the Royal Society, gave rise to the voyage of Sir James Clark Ross in the years 1839 to 1843. In a similar manner was sug- gested and promoted the magnetic survey of the British possessions in North America, authorized by the Treasury in 1841; the completion of the magnetic survey of Sir James Ross, by Lieutenant Moore and Lieutenant Clark in 1845, in a vessel hired by the Admiralty; the magnetic survey of the Indian Seas, by Captain Elliot, in 1849, at the expense of the Directors of the East India Company ; and the magnetic survey of British India, commenced by Captain Elliot in 1852, and completed between 1855 and 1858 by Messrs. Schlagint- weit. Finally, in 1857 the British Association requested the same gentlemen who had made the survey of the British Islands in 1837, to repeat it, with a view to the investigation of the secular changes of the magnetic lines. This has been accomplished, and its results are printed in the new volume for 1861*. The Association also, aided by the Royal Society, effected the organization in 1840 of the system of simultaneous Magnetical and Meteorological Obser- yatories, established as well by our own Government as by the principal foreign Governments at different points of the earth’s surface, which have proved so eminently successful, and have produced results fully equalling in importance and value, as real accessions to our knowledge, any anticipations that could have been formed at the commencement of the inquiry?. - General Sabine, whose labours have so largely contributed to these inves- tigations, has given to the University an admirable exposition of the results during the present year, in the capacity of Sir Robert Rede’s Lecturer. In 1854, in consequence of representations originating with the British. Association, our Government created a special department, in connexion with the Board of Trade, under Admiral FitzRoy, for obtaining Hydrographical and. Meteorological observations at sea, after the manner of those which had been for some years before collected by the American Government at the instance and under the direction of Lieut. Maury. Observations on the wind have been carried on by means of the various self-registering Anemometers of Dr. Whewell, Mr. Osler, Dr. Robinson, and Mr. Beckley, which instruments have been improved, tested, and thoroughly brought into practice by the fostering care of our body; and by the aid of its funds, experiments have been made on the subterranean temperature of deep mines; and on the temperature and other properties of the Atmosphere * Vide volume for 1859, p. xxxvii. + Report, 1858, p. 298. lvi REPORT—1862. at great heights by means of Balloon Ascents. Four of these were made in 1852, in which heights between nineteen and twenty thousand feet were reached. But in the present year Mr. Glaisher has attained an altitude of nearly thirty thousand feet. We may hope that some account of this daring achievement, and its results to science, may be laid before the Association at its present Meeting. Earthquake shocks were registered in Scotland by a Committee of the Association, from 1841 to 1844; and Mr. Mallet commenced, in 1847, a most valuable series of Reports on the Facts and Theory of Earthquake Phenomena from the earliest records to our own time, which have graced our volumes even to the one last published. One of the most remarkable and fruitful events in our history, in relation to Physical observations, is the grant by Her Majesty, in 1842, of the Obser- vatory erected at Kew by King George the Third, which had been long standing useless. It gave to the Society a fixed position, a depository for instruments, papers, and other property, when not employed in scientific inquiry, and a place where Members of the Association might prosecute various researches, This establishment has been, during the twenty years of its existence, gradually moulded into its present condition of a most valuable and unique establishment for the advancement of the Physical Sciences. After the first few years its existence was seriously perilled, for in 1845 the expediency of discontinuing this Observatory began to be entertained ; but upon examination, it then appeared that the services to science already rendered by this establishment, and the facilities it afforded to Members of the Association for their inquiries, were so great as to make it most desirable to maintain it. Again, in 1848, the burthen of continuing this Observatory in a creditable state of efficiency pressed so heavily upon the funds of the Asso- ciation, then in a declining state, that the Council actually recommended its discontinuance from the earliest practical period. This resolution was hap- pily arrested. In 1850 the Kew Committee reported that the Observatory had given to science self-recording instruments for electrical, magnetical, and meteorolo- gical phenomena, already of great value, and certainly capable of great further improvement; and that if merely maintained as an Ewperimental Observatory, devoted to open out new physical inquiries and to make trial of new modes of research, but only in a few selected cases to preserve continuous records of passing phenomena, a moderate annual grant from the funds of the Associa- tion would be sufficient for this most valuable establishment for the adyance- ment of the Physical Sciences. In this year it fortunately happened that Lord J. Russell granted to the Royal Society the annual sum of £1000 for promoting scientific objects, out of which the Society allotted £100 for new instruments to be tried at Kew, —the first of a series of liberal grants which have not only very greatly con- tributed to the increasing efficiency of the establishment, but haye ensured its continuance. It now contains a workshop fitted with complete tools, and a lathe and planing machine, &c. by which apparatus can be constructed and repaired, and a dividing engine for graduating standard thermometers, all presented by the Royal Society. The work done, besides the maintenance of a complete set of self-recording magnetographs, established in 1857, at the expense of £250, by the Royal Society, consists in the construction and verification of new apparatus and in the verification of magnetic, meteorolo- gical and other instruments, sent for that purpose by the makers. For ex- ample, all the barometers, thermometers, and hydrometers required by the ADDRESS. lvii Board of Trade and Admiralty are tested, standard thermometers are gra- duated, magnetic instruments are constructed, and their constants determined for foreign and colonial observatories, and sextants are also verified. An example of its peculiar functions is given in the very last Report (1861), where it appears that an instrument contrived by Professor William Thom- son, of Glasgow, for the photographic registration of the electric state of the atmosphere, has been constructed by Mr. Beckley in the workshop of this Observatory, with mechanical arrangements devised by himself, and that it has been in constant and successful operation for some time. Those who have experienced the difficulty of procuring the actual construction of appa- ratus of this kind devised by themselves, and the still greater difficulty of conveniently carrying out the improvements and alterations required to per- fect it when brought into use, will agree that the scientific importance and utility of an establishment cannot be overrated, in which under one roof are assembled highly skilled persons not only capable of making and setting to ’ work all kinds of instruments for philosophical research, but also of gradually altering and improving them, as experience may dictate. The creation of this peculiar Observatory must be regarded as one of the triumphs of the British Association. As far as the Association is concerned, its maintenance has absorbed be- tween five and six thousand pounds, the annual sum allotted to it from our funds having for each of the last six years reached the amount of £500. The construction of the Photoheliograph may be also quoted as an ex- ample of the facilities given by this establishment for the developing and perfecting of new instruments of observation. A suggestion of Sir John Herschel in 1854, that daily photographs of the sun should be made, has given birth to this remarkable instrument, which at first bore the name of the Solar Photographic Telescope, but is now known as the Kew Photoheliograph. It was first constructed under the direction of Mr. De la Rue by Mr. Ross. The British Association aided in carrying out this work by assigning the dome of the Kew Observatory to the instrument, and by its completion in 1857 in their workshops by Mr. Beckley the as- sistant; but the expense of its construction was supplied by Mr. Oliveira, amounting to £180. This instrument was conveyed to Spain under the care of Mr. De la Rue on occasion of the eclipse in 1860, who most successfully accomplished the proposed object by its means, and it was replaced at Kew on his return. But to carry on the daily observations for which it was con- structed requires the maintenance of an assistant, for which the funds of the Association are inadequate, although it has already supplied more than £200 for that purpose. Mr. De la Rue, in consequence of the presence of the Heliograph at Kew being found to interfere with the ordinary work of the establishment, has kindly and generously consented to take charge for the present of the instrument ‘and of the observations, at his own Observatory, where celestial photography is carried on. But it is obvious that the continuation of these observations for a series of years, which is neces- sary for obtaining the desired results, cannot be hoped for unless funds are provided. I cannot conclude ‘this sketch of the objects in the Physical Section to which the funds of the Association have been principally devoted, without alluding to Mr. Scott Russell’s valuable experimental investigations on the motion and nature of waves, aided by £274. If we now turn to Geology we find £2600 expended, of which £1500 were employed in the completion of the Fossil Ichthyology of Agassiz, and upon lyili REPORT—1862. Owen’s Reports on Fossil Mammalia and Reptiles, with some other researches on Fossils. The remainder was principally devoted to the surveys and measurement, in 1838, of a level line for the purpose of determining the permanence of the relative level of sea and land, and the mean level of the Ocean; and to the procuring of drawings of the geological sections exposed in railroad operations before they are covered up—a work which was carried on from 1840 to 1844, when the drawings were deposited in the Museum of Practical Geology, and the further continuance of it handed over to the geological surveyors of that establishment. £2300 have been devoted to the carrying out of various important experi- mental investigations in relation to the Section of Mechanical Science. Of this sum £900 were paid between 1840 and 1844, in aid of a most important and valuable series of experiments on the Forms of Vessels, prin- cipally conducted by Mr. Scott Russell, in connexion with the experiments on Waves. ‘This investigation was ready for press in 1844, but it is greatly to be regretted that the great expense of printing and engraving it has hitherto prevented its publication. Nearly the same sum has given to us various interesting and instructive experiments and facts relating to steam-engines and steam-vessels, carried on by different Committees from 1838 to the present time; amongst which may be especially noted the application of the Dynamometric instruments of Morin, Poncelet, and Moseley, to ascertain the Duty of Steam-engines, from 1841 to 1844. Experiments on the Strength of Materials, the relative strength of Hot and Cold Blast Iron, the effect of Temperature on their tensile strength, and on the effect of Concussion and Vibration on their internal constitution, carried on principally by our late President and by the late Mr. Eaton Hodgkinson, at different intervals from 1838 to 1856, have been aided by grants amounting to £400. The remainder of the sum above mentioned was principally devoted to the experimental determination of the value of Railway Constants, by Dr. Lardner and a Committee in 1838 and 1841. The Section of Botany, Zoology, and Physiology has absorbed about £1400, of which nearly £900 have been applied to Zoology, partly for the expense of Dredging Committees for obtaining specimens of Marine Zoology on our own coasts and in the Mediterranean and other localities—whose useful labours have been regularly reported from 1840 to 1861—but principally for zoolo- gical researches in different districts and countries. ’ In Botany may be remarked the labours of a Committee, consisting of Professors Daubeny and Henslow and others, formed in 1840, to make expe- riments on the preservation of Vegetative Powers in Seeds; who continued their work for sixteen successive years, reporting annually, and assisted by a sum of £100. The greatest age at which the seeds experimented upon was found to vegetate was about forty years. Another Committee, with Mr. Hunt, was engaged during seven years, from 1841, in investigating the influence of coloured light on the germination of seeds and growth of plants. These are specimens of the admirable effect of the organization of our Asso~ ciation in stimulating and assisting with the funds the labours of investi- gators in new branches of experimental inquiry. It would occupy too much time to particularize a variety of interesting researches in the remaining sections of Chemistry and in the sections of ADDRESS. - lix Statistics, Geography, and Ethnology, to which small sums have been as- signed. The newly issued Report of our Manchester Meeting is admirably calcu- lated to maintain the reputation of the Association. Besides a number of excellent Reports which are the continuation of researches already published in our yolumes, it contains elaborate and important Reports by Mr. Stewart on the Theory of Exchanges in Heat; by Dr. Smith and Mr. Milner on Prison Diet and Discipline ; by Drs. Schunck, Angus Smith, and Roscoe on the progress of Manufacturing Chemistry in South Lancashire ; Mr. Hunt on the Acclimatization of Man; Dr. Sclater and M. Hochstetter on the Apteryx of New Zealand ; Professor Phillips and Mr. Birt on the Physical Aspect of the Moon. Professor Owen contributes a most interesting paper on the Natives of the Andaman Islands. The President of the Royal Society re- ports the Repetition Magnetic Survey of England ; and Mr. Fairbairn, our late President, reports on the Resistance of Iron-Plate Pressure and Impact. _ The Transactions of the Sections occupy nearly as much space as the Reports, and are replete with valuable and original matter, which it would be impossible to particularize. Many of my predecessors in their Addresses have alluded to the most striking advances that have been made in the various sciences since the last Meeting; I will mention a few of these in Astronomy, Chemistry, and Mechanics. : In Astroyomy, M. Delaunay has communicated to the Academy of Sciences of Paris the results of his long series of calculations in the Lunar Theory, destined to fill two volumes of the Memoirs of the Academy, The first volume was published in 1861; the printing of the other is not yet begun. This theory gives the expressions for the three coordinates of the moon under an analytic form, and carries those for longitude and latitude to terms of the seventh order inclusive, that of Plana extending generally only to terms of the fifth order. The addition of two orders has required the calculation of 1259 new terms for the longitude, and 1086 new terms for the latitude. It was by having recourse to a new process of calculation, by which the work was broken up into parts, that M. Delaunay has been able to advance the calcu- lation of the lunar inequalities far beyond the limits previously reached. The Earl of Rosse has given to the Royal Society (in a paper read June 20, 1861) some further account of researches in Sidereal Astronomy carried on with a Newtonian telescope of six-feet clear aperture. These researches are prefaced by an account of the process by which the six-feet specula were made, a description of the mounting of the instrument, and some considera- tions relative to the optical power it is capable of. A selection from the observations of nebulz is given in detail, illustrated by drawings, which con- vey an exact idea of the bizarrerie and astonishing variety of form exhibited by this class of cosmical bodies, Argelander, the eminent director of the Observatory at Bonn, is carrying on with great vigour the publication of his Atlas of the Stars of the Northern ‘Heavens within 92° of Polar Distance. A large portion of this enormous work is completed, and two volumes, containing the data from observation for the construction of the Charts, were recently published. These volumes contain the approximate places of 216,000 stars situated between the parallels of 2° south declination and 41° north declination. Simultaneously with the construction of Star-charts, among which those of M. Chacornac of the Paris Observatory deserve particular mention, addi- tions have been made to the number of the remarkable group of small planets lx REPORT—1862. between the orbits of Mars and Jupiter, their discovery being facilitated by the use of charts. The last announced, which is No. 74 of the Series, was discovered on the morning of Sept. 1 of this year, by M. Luther of Bilk, near Diisseldorf, whose diligence has been rewarded by the discovery of a large number of others of the same group. The present year has been signalized by the unexpected appearance of a comet of unusual brightness, which, although its tail was far from being as conspicuous as those of the comets of 1858 and 1861, exhibited about its nucleus phenomena of a distinct and remarkable character, the records of which may possibly at some future time aid in the discovery of the nature of that mysterious action by which the gaseous portion of these erratic bodies is so strangely affected. On an application made by the Council of the Royal Astronomical Society, Government has granted £1000 for the establishment, during a limited period, under the superintendence of Captain Jacob, of an Observatory at a consi- derable altitude above the level of the sea, in the neighbourhood of Bombay. The interesting results of the ascent by Professor Piazzi Smyth a few years since of the Peak of Teneriffe, for the purpose of making astronomical and physical observations, suggested to the President and Council of the Society the desirableness of taking this step. In Cuemisrry, the greatest advance which has been made during the past year is probably the formation of compounds of Carbon and Hydrogen by the direct union of those elements. M. Berthelot has succeeded in producing some of the simpler compounds of carbon and hydrogen by the action of carbon intensely heated by electricity or hydrogen gas; and from the simpler com- pounds thus formed he is able to produce, by a succession of steps, compounds more and more complex, until he bids fair to produce from inorganic sources all the compounds of carbon and hydrogen which have hitherto been only known as products of organic origin. Mr. Maxwell Simpson has also added to his former researches a step in the same direction, producing some organic products by a synthetical process. But these important researches will be fully laid before you in the lecture on Organic Chemistry which Dr. Odling has kindly promised for Monday evening next. Dr. Hofmann has continued his indefatigable researches on Poly-ammo- nias, as well as on the colouring matters produced from coal-tar. M. Schle- sing proposes a mode of preparing chlorine by a continuous process, which may perhaps become important in a manufacturing point of view. In this process nitric acid is made to play the same kind of part that it does in the manufacture of sulphuric acid, the oxides of nitrogen acting together with oxides of manganese as carriers of oxygen from the atmosphere to the hydro- chloric acid. The methods of dialysis announced last year by the Master of the Mint, and of spectrum analysis are now in everybody’s hands, and haye already pro- duced many interesting results. In Crvit or Mucuantcat Enetnerrtne there is nothing very new. The remarkable series of experiments carried on at Shoeburyness and else- where have developed many most interesting facts and laws in relation to the properties of iron, and its resistance to projectiles at high velocities, which will doubtless be fully laid before you at some future period; but in the present imperfect state of the investigation, and in consideration of the purpose of that investigation, prudential reasons forbid the complete publi- cation of the facts. My able predecessor in this Chair, who has taken so pro- minent a part in these experiments, has given an account of some of the ADDRESS. Ixi results in a communication to the Royal Institution in May last, and also in the new volume for 1861; and is, as he informs me, engaged with a long series of experiments on this subject, which, with his experience and ability, cannot fail to develope new facts, and will, in all probability, ultimately de- termine the law of penetration. In London we may direct attention to the commencement of the Thames Embankment and to the various works in progress for the concentration of the Metropolitan Railways; especially to the proximate completion of the Underground Railway. The lamentable disaster in the Fens of last summer has been most ably subdued, but the remedial measures adopted are not fully completed, and the interests involved are of so great a magnitude and com- plexity, that it is scarcely possible for this event to be discussed on the pre- sent occasion with due impartiality. The magnificent collection of machinery in the Great Exhibition shows a great advance in construction; but this is not the proper occasion to enter in detail into the various contrivances and processes which it displays. Before I conclude I have the painful duty of reminding you that since our last meeting we have had to deplore the loss of that most illustrious patron of science and art, His Royal Highness the Prince Consort, the President of our Association at Aberdeen and the Chancellor of this University. In the latter capacity he afforded us many opportunities of observing his scientific attainments and genuine zeal and love for all branches of knowledge: his gracious kindness and respect to men of science and literature have left an impression upon us that can never be effaced. I must also ask a tribute to the memory of our late Professors of Chemistry and Botany, both of whom have done in their lifetime excellent good service to science, and especially to the British Association ; Professor Cumming by contributing one of the invaluable primary Reports upon which our proceedings were based, as well as other communications; Professor Henslow by various Reports, some of which I have already alluded to. We have had also to lament the loss of that able scientific navigator, Sir J. Clark Ross. It remains for me to express my sense of the high and undeserved honour conferred upon me by the position in which you have placed me, and in the name of the University to welcome you hither, and wish you a prosperous and fruitful meeting, alike conducive to the progress of science and impulsive to its cultivation in the place of your reception, 4} Sept booth a'as sokim henson ae, aerbaead-ai peters: WE aoe baee-od soak wore ony rial seot@irs eiakt ate is Se aaca tenia dbve Sree ents nan Sqo ken Os a ae ek ae oll cog S wal ait Seema t dteseysons sr = al sai seis: Soot gata re conf asl « : tb-aarra st! iss Sn post oe ot brut tm oe vegeta wf sli: ot) eigen -) ere a GaGa tic nanale depend. ¢ we ipa griphon = abt taeB3l eo cm ot vroctere Lesiragewri ei aint.b wisi oh ig cel scone gat 7 fie tenga we oe hans +H pean riafitt ale ineteed Beadadey eee oP ree derstx 224} 20h oldiomny “Hfonvunte dl tude otra fees &: err aott wal) are 4 | EON aa MeonkT al Gr Get fiukevaste Da 2 Ban ; ph semen weg 6 Fl tert ad eisctittial> taal toe et ie) re Levpelip ait Sb glam ay: dope pec pie heey ialinesad 2% sundti ny Sie aes = a n95-0 deccht Ste smeritinee. be tests liAatedk waa seh 1. chuleaes ori. Boy ese f Pei sieail! i “Pie: Saath te wel. oat anvils bebe aiil tan ie sabinticl. $S drendiethy 001 li aeyarinild Torah aia tigt . iG freshers “vi ty solinsonth), att bie resol Am noikainmend: 3 1) ote. qubriseda be Ai ines bang chain, oie botreiia od tte ie agree to actiegest! Lin wok bat. som. ecenieth sd if soar vesirterwat il bola. oases Be deine ot tpg: wa 2088 " Rey. 24 #4 Bo eile hes ae tadty { c i ; Jaen i wnah is ny bee teggeiee adi cde sodiaiie ih a? } dase » aber aoe 94-1 aQis eat aiieigt phar he ek aR cmb £ :oltareepl. tate gett ab ena aeepe ? tee 5195 eeeren th pvlcematy phinitoegs abaitren iota. + sgeokdn Le ion =o esta Nast sible aaa wan 28 aie Hee ante bed sik 0 AO cant Sods oral derail: ePaper = > a eat ded} sh set AQinaky ar oiepotee abefxy = anecteast borfuenlns han cial - ait iy carte. GAS mee Gish ora oseiy aren Ber doiaert aitingg sat ei rain b ate eel i frivs sonic: lope: aqui od? of : Dae oss pitts oe taalg aka : itiig aera ae | 2 a te a Zz : ‘in (2 ilrageet tay ae 4 AD ot Sets. a ee ae aoe a boyeur dg “Rx Lal S30 eed Sara 6 ba tod ta A092 CLC) REPORTS ON 4 _ THE STATE OF SCIENCE. AOKALIG 20, o ~~. * _ CT ST be za f . oe | f ,wRs 4 af @ . ] ‘ SW a F) i Bi. aye tes ri a = "A, 4 As ley ae » .. ' tae + So * eae Fr J REPORTS ON THE STATE OF SCIENCE. Report on Observations of Luminous Meteors, 1861-62. By a Committee, consisting of James GuatsHer, F.R.S., F.R.A.S., Secretary to the British Meteorological Society, &c.; R. P. Gree, F.G.S. &c.; E. W. Brayuey, F.R.S. &c.; and A. HerscHE.. Tae Committee are indebted to Members of the Association and to other ° observers for a larger number of observations bearing upon individual meteors than has fallen to their lot to assemble during previous years. They may be counted as follows:—(A) Meteor 1, July 16th, eight accounts; (B) meteor 2, July 16th, thirteen accounts; (C) meteor, August 6th, three ac- counts; (D) meteor, November 12th, eight accounts ; (E) meteor, November 19th, eleven accounts; (F) meteor, December 8th, twenty-eight accounts ; (G) meteor, February 2nd, 1862, eleven accounts; (H) meteor, February 23rd, 1862, five accounts. Of the small shooting-stars, double observations only are found. The discussion of these observations follow the Catalogue in Appendix I. Eight accounts of one and thirteen of the second of the meteors visible on the evening of July 16th, 1861, show those of the Duke of Argyll and Mr. Frost to have been distinct meteors, succeeding each other with an interval of more than an hour. The accounts are embodied in the present Catalogue, and the results discussed in Appendix I. Of the meteor August 6th, a further account from excellent observers in London, has afforded a good determination ; the accounts and their interpre- tation are presented in the Catalogue and Appendix I. Numerous accurate observations of shooting-stars of the 10th August, period _ 1861, too voluminous for separate insertion in the Catalogue, haye been col- lected and examined for accordances, and the accordant observations only entered in the Catalogue, together with individual observations which ap- _ peared of particular interest from among the entire number; the resalts of the accordant observations are tabulated in Appendix I, 1862, onan ~ x, 2 REPORT— 1862. A CATALOGUE OF OBSERVATIONS | . aE: | Place of J Position, or Date. Hour. bservation. Apparent Size. Colour. Duration. pee bm 1861.|h m July 16| 9 30 p.m.)/Weston - super -|Large as Venus at Duller than 3or 4 seconds; Exploded when W Mare. (Also) max. Venus at; moving altitude 45°. seen in Dor- max. bril-) slowly. setshire.) liancy. 16| 9 58 p.m. Whitehall, Lon-/Very large ball, but Very brilliant. Slower than Began almost E don. not quite full. meteors and disappeare/ = usually behind the © move ; houses on th ‘“leisurely.”| west side Whitehall. 16\Exactly 10/Gainford, Darl-|Like Jupiter, seen’.,.......+++....-/Motion not/From 10° below p-m. ington, York-| in a good tele- rapid. Aquile, throug shire. scope, but not! the E. to N.E, exactly spherical. from altitude 30) to about altitue 20°, VGheas23 seseeeese|Greenwich and |Kensington. Alrea\dy inserted, |p. 10 ofReport) for 1861 .......++4 16\Soon after |Derby ...........-/ Like a rocket ...... ? ssesceceveeeeee{ndured very|Went N. ........ 10 p.m. long, about 16}10 p.m., or 15m. after 10 p.m. 16\Between 10 p-m. and half-past. 16/About10 40 p-m. 16) ? Southborough, Tunbridge- of the ob-| Came from o wells. server walk-| a wing of # ing (at call)} house; isa 13 orl4yds.| pearedsome lit from another} distance aboy room, saw} the horizon. the spark which was cast off at the close. Whitburn, near|Like ball of quick-| ? ....pcsseeeeee, 2 ceeeeceeseeeees|DUC Euseeyeseee sens Sunderland, silver, or an i Durhan. enormous star. 4 Furness Abbey,/Threw a strong) ?.,.......+...../Moved very|/From behind ah Lancashire. light. slowly ; south of : ; “gracefully”| Abbey; Nort ward through I lost behind tree Penmaen-Mawr, |Very large ......... Ear rcree, es s+... Very slow in/Over the hills | Conway, N. | its motion,! and S. of Pel Wales. “quiet and} maen-Vach ; di ? TORR EEO Ree etter eneee ? ccsesecseeeeeee/A COmpanion|From §.B. to 15 seconds. deliberate.’’} appeared behit Penmaen-Va “ : A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 3 OF LUMINOUS METEORS. Direction; noting also Length of | whether Horizontal, Path. Perpendicular, or Inclined. ppearance; Train, if any, and its Viale. Remarks. Observer. — —_—_ | ite train 8° in length] ? .....,seee../Appeared im the N.We..|,;ccoresssersssceccessceceeses ‘Personal _ac- attended the nucleus. counts to W. Burst into sparks which Ii. Wood. continued 3. seconds, advancing 10° before they disappeared. x a blunted or spread|. tail 14 or 20 times longer than the head. | ssseseneeeereee/DOWnwards at an angle/Point of observation Charles Reed. of 25° to the horizon.| was facing the Na-, tional Gallery, near the top of Parliament Street. hortly before disappear-|About 90°../First horizontal, then!....... Pate Fase roisk veevaees Mrs. E. Addison. ing threw off a part of declining slightly. its substance, which followed it closely like a lesser luminary till both were suddenly extin- guished in a sudden and peculiar manner in clear sky. A track of light endured for some se- [of Argyll. TERE LCE akhabeqenanlea cigceande OUNCEERC Ares enddetclegecencccccctuccedegdades alte Howe ; Duke ppeared in "mid-air, 60° coprecceo{HOFiZONtAl, OF VELY|.qeeeyecesececeagedecpueoneces John Borough. like a Roman candle slightly "declining at ball ; but the train which last. pursued it did not look exactly like sparks. ajestic,” Left a track of light behind it, but 2 seseseseeeee/Came over from the|Open bayrwindow faced|Mrs. Davies. right of the house,| N.N.E no sparks till just before descending as a rocket ‘it disappeared, when one in the form of an arch. : was cast off from re ? sesseyeoees. Quite horizontal; from|.:....sssececscesseeseraeeseee{Me Me left to right. He) eecsbeswais Horizontal, Or —Very|c. than any Clear bluish...|About 14 sec. planet. 16)114 p.m....|Sittingbourne, |Threw a brilliant/As it neared) ? Kent. light when high) the horizon in the heavens,| it assumed expanding and) a_ beautiful increasing in| blue colour. brightness as it neared the ho- rizon. 16)114 p.m. ...|Banburv .,.......|Like a toy balloon../Bright —clear| ? blue white. and 1G}11 30 p.m.|Frome .,,eccveeres| 2 sevesesserereneseeers 16|113 p.m, ...|EastIsleyDowns,|Large as a full) ? ...seccevcseeee Position, or Altitude and Azimuth. Duration. seseesereeeeees/EVODably burst in view in the zenith. First seen high in the heavens, going S.W. Lost in haze of the horizon. sessssseesseees(O” above 6 Pegasi; 3° above 8 Aqui- le; 2° above Serpentis. Here houses inter- vened. Deve loped the ta in the last 30° of the visible track. seesseeereseess(Disappeared a few degrees above the horizon. { Appeared near the Newbury, moon, and more meridian ; disap- Berks. light. peared behind cloud. VGLIZ p.m. ...|BrentwoOd seseee|i2 cchcnsscoccecsscocace| 2 debeeceosrssese] © susovcuuveunten|t. aurecusen sah dvartem 1G\114 p.m, |Cheltenham.,....|? vcscsccesessceesseeee! ? secesesseeeeees{Half aminute;From about 45° or soon steady and altitude to about after. | equable. 30° altitude. | 16/11 32 p.m.|Flimwell, Hurst|Like Capella in the,White in (3seconds from Passed in zenith Green, Sussex.| zenith. Lit up} zenith and] zenithtoex-| between # y Dra- the clouds like) upon the} plosion. conis ; burst crescent moon) clouds. about 7 Ophiuchi. at 45°. 16/11 33 p.m.'Sandown, Isle of|Large signal-rocket) ? ......sesseee0 Wight. 16/11 33 p.m./TavistockSquare,/A sudden lumino-! ? ...... Euston Road,| sity overhead. London. seetee From the zenith, near a Lyre, td a few degrees from the S.W. horizon. ’ 4 seconds from/|First seen 15° south zenith to| ofzenith; passed disappear- downwards di- ance. rect through Scorpio, and dis- appeared _ near the horizon. tate A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 5 Appearance ; Train, if any, and its Duration. No sparks or train. Left a long clear white streak for some little time. Disappeared in haze of the horizon. At the point; of disappearance the stream of light was visible for 5 minutes Track very bright, endured, : 3 minutes; like a half circular mark of phos- phorus upon a wall. Track of luminous matter ; lasted 4 or 5 minutes; curiously contorted by degrees, as if by currents of air. Large body of sparks thrown off at _ disappearance. first emitted sparks; after- wards a bright train which endured some minutes. ? PERTH POP eee reer reeeeeseees Burst with few sparks./90° Track at the last visible some minutes. Length of | whether Horizontal, Direction ; noting also Path. Perpendicular, or Remarks. Observer. Inclined. 15° to 20°\Course from N. to S..../By letter to W. HJ. Ellis. a > > high. Wood, Weston-super- Mare. covsecsevece|WEFtiCAl eseeeseene sostecs|ae Ceegvevcasscesse sssveeseeee/ E's R. Cooper, SOPe Oeste Passed over from E.to|The curved tail was|John Griffin, S.W. clearly seen byacom-| M.D. panion called out of a house by the observer. Brightest in the Milky Way. > Cenemplgasvewdll 2. wasidacstasBaccwies Pern Heer esevcccesccsccescsoveoeeee| William Dunn. seeseseseseeees/LOOK a SOuth-westerly|Saw at least 4 meteors, L. Lousley. course. of more or less bril- liancy, from 10310 12 p-m. Rebevagersccel Watescsacuetee Bans skecsens ta The time distinguishes|J. L. P. this meteor from that of 10 p.m. Sageeeees From tlie Sis t0'S. Wis: |secccscccedareceseresescscose (Jamies Philps. Inly momentary; sparks|90° sseceeees Nearly vertical to S.W./Overcast W. and S.W.,|F. Howlett and seen in the zenith; white, and extending half D’s diameter to either side of the nucleus; not in front or behind. No track seen to remain. Most brilliant track ; visi- ble for 5 minutes, Bright train visible several “Minutes. The lower _ portion took a crescent form, the horns drifting 15° or 20° S. into the Milky Way in 5 minutes before disappearance. by W. or S.W. exceptnear the zenith,| A.S. Herschel. where the meteor was lost at altitude 70°, ? seseeeeeeeee Nearly vertically down-'The track at first|/W. M. Frost. wu wards. straight ; soon curved opposite to the rising wind. Portions drifted fading into the Milky Way. serseseeeees Vertically, S.W. «+++... Probably originated in'T, Crumplen and Andromeda. J. Townsend (Assistants to Mr. Slater’s Observatory, Euston Road). sa a 1861. July 16 16 16 16 Hour. hm 11 34 p.m. 11 38 p.m. 11 40 p.m. About } to 12 p.m. Aug. 4 rs a * =x) 8 8 8 810 11 p.m. About 10 p-m. 11 37 p.m. Midnight ... 10 10 p.m. 11 21 p.m. 11 22 p.m.| 10 21 pm. 10 31} p.m. 10 313 p.m. REPORT—1862. Place of West End,Hamp-|Ist maget..cccssssese| 2 seceverdesvenes stead, Manchester, Considerably _ex-|Vivid__bluish- Lat. 53° 29"5,| ceeding 2 in| white. Long.2°15’W,| _ brilliancy. > © C8C Feet ee eTeee Estimated not to have ex- ceeded 2 seconds, Trafalgar Square,|Equalled in size the| ? ....+.+.sdeeeess London. great meteor, 11.33 p.m., July 16. Deal . cscocsseceeeJONd MAG+ ...20000. U, eseccvendsvvesc Greenwich Ob-|2nd mag.x ......... Blue ....sccoceee servatory. Thid-..2,,, ight. .ppeared to burst ......... ‘ SEPT R Ramee eet eeesereeersee eft a bright track, cigar- shaped. jourse bent up rather suddenly in the middle, with two maxima of brightness. he meteor in its course appeared to be extin- uished, and then sud- enly rekindled. Left a rain of about 20°, which sted a few seconds. [o train or sparks . eft a small track :........ eft MO MACK ..22..0iceceees. eft a small track i.....00. Direction ; noting also Length of | whether Horizontal Path. Perpendicular, or ‘ Remarks. Inclined. About 140°/About B. to W., almost|The sparks in the first half of the course did overhead. not pass away imme- diately. was intlined 18° to the horizon. magnificent splendour through the sky. ? bode ectane oe E. to W. beateeeree POP Oe rel secre beeereereses tel eaeereres Ses Msecad Passed directly over-|A edmplete view from head. first to last. : ve BGG, Won dsceenasiea seeeeee(One or two smaller meteors during the night in same direc- tion. ssaerte selseees|seeecereceeedscvcesevseeeseses/NiX ShOOting-stars ré- corded from 11.15 to 12.15 p.m. About 20°..;Towards the left; 15°|....c.ccsssees from horizontal ; down. 20° .setse.../L0 right ; 50° from Ver-|.....-éseveseesees tical ; down. See seeeeneserens Se eereeeesee Only about/To left; 30° from hori-|Gave the impression of 3° or 4°.| zontal; up. a path of considerable length, nearly in the line of sight. Bea sEta-ss\ecscuence? Ostia y cossacigenas The same _ gentlemen observed the meteor July 16th, 11.33 pani. 10° .22......|S. preceding ..,........./Six meteors recorded, 10.11 p.m. No trains. BOccnsaatcucss Shot UPWAtGSns <2: tes sesu)-cassaPaudessscees Sadeawaceaee US ascticces To right; 15° from hori-|...... Sadedys lekcesccssvaster- wa _ zontal; down. : 30° ........./To right, 10° from ver-|At Greenwich, two ob- tical ; down. servers recorded 14 shooting-stars from10 7 Observer. — William Taylor ; Miss J. W. Taylor. 60° to 70°../At its centre the path|Presented a sweep 0 David Walker, M.D. Communicated by W. H. Wood. John A. James. Bristol News- paper. Rev. F. Howlett. Id. T. Potter. Joseph Baxen- dell, Observa-| " tory,Stock St.,| - Manchester. | . T. Crumplen and J. Townsend. Herbert M‘Leod. W.C. Nash. Id. W. C. Nash and J. Howe. to 11 p.m. REPORT—1862. Position, or Place of ! E = : Date.| Hour. Obie Apparent Size. Colour. Duration. oe ae 1861.;h m s » Aug. 810 32 5 (Cambridge Ob-2nd mag.x ......... 2 seccsvesecseee(RAPIA soveee..-(Centre 11° E. from p.m. servatory. S.; altitude 40°. BILO 4 VS) MWbidicccccccsccccses A bright star, Ist} ? ...... secseeees| RIEL “aveeecees 17° S. from E.; p.m. mag. altitude 61°. 810 35 p.m.|[pswich ....,..../Much brighter than) ? sesccssecssssee| 2 seseeeseseeseee EXactly N., half- any star. way between the Pole star and horizon. (The place may be relied on.) 8110 35 p.m.|Aylesbury (Hart-|A flame of light ...]? sseccssseseeees|Only for alIn the head or well Observya- moment. sword of Perseus. tory). 8/10 40 p.m.|Birkenhead(Sea-| ? ...s.scsecscssecsscee| 2 cesceeeeeeeeeee| 2 sesssseeeeeeeee/DUe H.; altitude combe). 1723 8/10 45 p.m./Aylesbury (Hart-\A fine shooting-star|Prismatic 4 seconds...... |Near Polaris ......} well Observa- colours seen. tory). 8/10 49 34 |Cambridge Ob-|Ist mag.x .sseseces| 2 ceeeeeceseereee| 2 eeeeeenveeerees Contre 67° W. from p.m. servatory. | S.5 altitude 55°. 8/10 50 p.m.|Birkenhead (Sea-|Ist mag....sessseees| ? sersereee seeee-{L second ......, Centre 30° E. from combe). S.; altitude 13°. 810 50 25 |Trafalgar Square,|Ist mag.x........06+- ‘Fine blue light|Rather slow.../From 3° N. o p-m. London. Mizar to 13° below x Bootis. 810 51 p.m.Greenwich Ob-|A splendid meteor..| ? ...... sesseeese(2 tO 3 Seconds Appeared near B servatory. Draconis, and passed to Arc- turus. 910 11 26 (Cambridge Ob-|lst mag.x .........| ?» 2 cccosecsceseoes/ centre 3° Ni. from p.m. servatory. E. ; altitude 39°. 9/10 14 p.m.|Birkenhead (Sea-'Ist mag.x ses..sse.| 2 eeseerseseeeeee Nearly 2 secs.|Centre 45° E. from combe). S.; altitude 6°. 910 27 45 |Ibid. .eeseuseess.(I8t mage seccreeeel 2. .eos..{L second .,....\Centre due S. ; alti- p.m. tude 37°. 9/10 45 p.m.|Deal ............ Ist MAg.% seeeseees| 2 - eseees| 2 vesscocscepecas/ DEDWEEML! ANG Ophiuchi. 9|10 47 p.m.Greenwich Ob-|Very bright 2 .ecseeeoeeee.../Momentary ...|Near Polaris ..... servatory. 910 47 p.m./Birkenhead (Sea-|Ist mag.*............| ? sassseeeeee--/2 Seconds ...\Centre due N.E.; combe). altitude 20°. 910 52 45 |[did. «...sseoeees[1St MAH. .ceeecccnee] ? seseeeeeeeseees/ Nearly 1 sec. [Centre 5° E. from p-m. S.; altitude 7°. 9/10 57 45 [Tbid. ........006-/St Magee. ..ccceeeees| 2 eceeeseeeeeeees 24 Seconds .../Centre 55° E. from p-m. 10) 0 25 am. Ibid. Shooting-stars..,... > Bec tthans sevens] 2 S.; altitude 21°. coieenccvecnss.|Leee altitude 40°. cosvstbsecoees(oentre S.S.E.5 altiam tude 10°. 10)10 8 p.m.|[bid. ......06.00 Brilliant meteor; | ?...... barbegded| 2 sectetNaee ...../Between Aquila Ist mag.* \ and Capricornus, 10)10 18 pimiTbids aéasiiessiis| 186 mag.*;.as bright) ? ......ccciseees) 2 csossssdisdecss|Under Aquila sssiss as Venus. 10/10 21 p.m.|[bid. ssssseassee 6th mage oo... BAS sisscins thasiai > sseasabeaes w«+.(Centre E.S.E. ; al , titude 3°. QOIO23 pam.|Tbids .s.scécssscsfOR@ MGA oisesedeel 2 \eacaszcceboacns| Pi cacdebetecenes Centre S.W.; 3° below « Lyre. | 10/10 233 p.m./Greenwich Ob-|Small ...seccssceceee| 2 cesceseceiecees Rapid; 1 se-Passed from Her- servatory. cond. culis towards the) bulbs 8.W. horizon, 10/10 24 p.m./Cranford Ob- 3rd Magee .scsciss:| 2 saeaadsccieess.| 2 sccsecioes «..../Same track as | : servatory. 10:23 p.m. 10,10 24 p.m. Greenwich Ob-Small ............... P piseraiaiieens Rapid; 1 se-\Passed from a servatory. cond, Cygni to « Her- culis. 10,10 25 p.m.\Cranford Ob- (2 brilliant meteors.| > .........:.....{ 2 sesecetsseeesee| Near Cygntis sss. servatory. } 10|10 26 pan. Ebid. ssgésaiaaesclOth MAg.% sisessee. 2) geriacdded.cocd| 2 ccncdedeccesscsHGentEe E.S.E.,; ned horizon. 10 10 27 p-m. Ibid. Sbaedeeceins Ist mag.* Bar edeeee ? ee ctbedevtesvee ? Prerrreriri tii it Centre E.8.E., Pegasus. 1010 27 p.m. Greenwich Ob-|2nd mag.* ........./Bluish ...... ../2 seconds,...;.|Passed from a few servatory. degrees above @ Andromede _ to} between a and 6 Pegasi. 10/10 28 p.m.|Cranford Ob- |5th mag.* ......... P desdeacschtaees oiavescedbnoswers Centre E.N.E. ; al- servatory. titude 15°. 1010 29 p.m.|[bid. .....sseeeee Ist mag. ; brilliant D dadssadssccoeo|,2,anedtadeasdoatef PORE BO 1186 15° as Venus. altitude; centre S:S.E. | A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. ll rm ; Direction ; noting also ppearance ; Train, if any,| Length of | whether Horizontal ; and its Duration. | Path. Perpendicular, or . ea Observer Inclined. © track left s.ssis....... fali@eeetedi cccess PITTI ete «|W. De la Rue. _—_—_— TO HACK besicdcccscscsa| P casiccciccss ; sdsedseeedecaareaiassaseddess|Ed. — a bright track......... Bd? seeceeeee . At Greenwich, two ob-|Id. : : = servers recorded 33 shooting-stars from -~ 10 to 1) p.m: At Cambridge; three observers recorded 30 e shooting-stars ffom efta track is..cc.c0.0s. a ~ | 10 toll pm. Id. 3 At Cranford, one ob- ° sefver recorded 29 shooting-stars from 10 to1l p.m. ‘ : At Birkenhead, one ob- t no track «.. ? > setver recorded 16d. shooting-stars from 10 to 11 p.m. HO AFACKE sisasdicecccccs| 2 saadddececac(TO right ; 6° from verti« At Deal, one observer [d. cal; down. recorded 9 shooting- EN Rececaideel 2 ccsdedecsods| 2 veenesss | es veseeee.| Stars from 10.20 to/W. C. Nash. ll pm At Trafalgar Square, ft no track ..........226..| ? seessesseees/ LO right ; 6° from verti-| London, two observ-|W. De la Rue. cal; down. ers recorded 12 shoot- MOPACK. .5.0040...0000. 40° ..es00s4./TO right 325° from yer-| ing-stars from 10 to|W. C, Nash. I tical ; down. 11 p.m. PEAQKG do. cktsiccacceas| 2 saxtbdcccess \ saacdccaaeeacesccessicaassses.|W. DE la Rue. HO track sés..iceceeeess De ealadiacitdles. « > dalea .” Wesdda deccedecesccseccvedssabes Id. —“—. f UMMM locdocdacecucess| 2) scccedsccese ‘Snail Beced deatinddsedesaccaceden i.s{Id. Pee s a track 5° im length....15° s.sjceee/To rights mearly hori-)...+.ssesesssesercesteersees|We 6, Nashi a zontal. BPMPSEACK .00ccdescas0000| ? ccceedsonees — se eRe S adweseahes W. De la Rue. . es . bright track marked its 15° ......00. saeidsvacccacsdcsacceciaacecca\ hd. course throughout (15°). 12 REPORT—1862. Place at ; . Position, or Date.| Hour. Observation. Apparent Size. Colour. Duration. eee 1861.|; h m s : ; Aug.1010 323 p.m./Greenwich Ob-2nd mag.* ....06...| ? seseoeessseeeeefl Second ....../From y Urse Maj servatory. joris to the N. horizon. 10,10 32 32 |Cambridge Ob-|3rd mag. seeeee| 2 caseeeeeceeseee/ SLOW MOtion...|Centre 13° S. fron} p-m. servatory. W. ; altitude 20° 1010 32 47 |[bid. ......+..++-/1st mag.x P cesvcecscecceee| > cosvaccevecsseeiOentre same as the p-m. last. 10:10 39 p.m.|Cranford Ob- (6th mag.* ......... 2 cseececaereee| > coeecccssersve (Centre B.S.H.3 al seryatory. titude 4°. 1010 40 p.m.'Trafalgar Square, Very luminous [Blue light ...| ? ...eceee.sed° below x Ursay London. meteor. Majoris. 1010 42 p.m./Cranford Ob- /4th mag.* .......+. o apesseccencvets D raeoce stat enevees Centre S.E.; alti servatory. tude 9°. 1010 503 p.m.|Greenwich Ob-j3rd mag.* ......... CE DRED reeks 1 second ......|From « Cygni to @ servatory. Lyre. 4 1010 51 p.m.|[bid. .ee.cseeeeee Sree E aaraocecann Daaevarneeqescene 1 second ......|From « Cygni to ff Delphini. 10,10 51 1 (Cambridge Ob-|3rd mag. .........| 2 ceeceeeeseaeee Rapid ....s00. Centre 26° W. fro p-m. seryatory. S.; altitude 46° 10)10 56 p.m.|Trafalgar Square,|2nd mag.% .......44| 2 cescsceeneseee| 2 seseee erty e 1° E. of « Herculis London. 10/10 57 20 [Deal .....cce00e UGG AG Hose ads Beans eehc cdavesbali2 iasssuecneeeren B to & Bootis ...+04 p-m. 1010 57 30 Ibid. ...... weet. UGE MAGN © sdk Made eescecsene PWR ee icc eoeee « to y Urse Ma p-m. joris. 1010 57 30 |Trafalgar Square,|Very brilliant Blue light ...|Fast motion.../2° above Bene p-m. London. meteor. nasch to 2° above Arcturus, 1010 58 p.m.Greenwich Ob-|Very bright......... P aeecnsddaerns 2 seconds...... From a Pegasi. servatory. Passed Delphi nus to a Aquila. 10/10 59 p.m.|Birkenhead(Sea-|Ist mag.% ......... ? sscsseeseeeeeee Moved 1 sec,../Centre 26° E. from! combe). S.; altitude 30°) 10|/From 10 to/Haverhill ....../Shooting-stars......!......4. Peadsnaspo|ccesvsuuanesseste In all quarters..... 11 p.m. 10/From 11 toIbid............. ves| SNOOUIMNE=BUATS. cus eal veces sce sasoraes|savesvesevcontshie In all quarters of 113 p.m. the sky. 10/11 45 p.m.|Birkenhead (Sea-| ? .........cecseeeeeeee Davehs Sbueitives aie idewtaewete wee Ther cee ceed sede crn combe). 11} 1 3 a.m./Weston - super -|Mars ......csseseeee Like the elec-| ? .....s.sse.s00s Centre 40° W. fron Mare. tric light. N. ; altitude 18° 11/8 40 p.m.|Hawkhurst, Kent/Ist mag.x ......... Ee peels ee | Rapid ......... Centre 22° W.from S.; altitude 39° 11) 8 45 p.m.|Trafalgar Square,/Grand and lumi-|? ...........00.. Rather slow.../15° below Merak.. London. nous, even in strong twilight. 11| 8 53 p.m.!Hawkhurst ...... UUPILER e-ere ox cess De eorpeet occur Slow motion.../Centre 22° W. fron S.; altitude 37° A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 13 Direction ; noting also whether Horizontal, Perpendicular, or Inclined. pearance; Train, if any,| Length of and its Duration. Path. Remarks. AT RAM ches dawa li fons sa sirewiecsin|; 2x'v vende vomoveedewocssoseceee ibe Wate e aes wet eee ROMO TEACK vedsnevccorducsl ? ce 0ccccoener| VETtICAL Ss GOWN) veevesvedlesvessewsees Bene eeeeresereeree SPMIEMEM et ecsesocceeses| 2 evcvscccscoe| LO lefts 45° from Verti-|.ssccucecseccsvecovsasesccess cal; down. eft no track eee eereereeeees as caeeewanaeits tte et itee POee ee eee eeeeeeeee! arked track’8° in length] ? ...,,.ss0e0.] 2 seeeeceereeeceereveeeseeeeelesesesssesennes eaacsvasventess OfE MO ELACK ...cccccssccece| 2 + cee Poosene HOOP O Mee eeesererereeeeseneeee® ee Observer. W. C. Nash. Rev. J. L. Challis. Td. W. De la Rue. T. Crumplen and J. Townsend. W. De la Rue. EME MO TACK ve..cecseceeces|(20°) vooee.(LO Tights; 30° from.........0..00+ exgaps coadaess|Weice, NBR vertical; down. ft MO trACk ....,,ceevereee|(3O°) seeee.| Vertical ; GOWN «....0ce0].cceee pease Vesenoncesneuseecs|la RLOWE, eft no track ..... Basnvesces| ! sscaenscects| LOGIE GO” ION VENEHI),, vcssecccccncessossesess ..|Rey. J.L. Challis. cal; down. it no track eee terneseteees ie weet eteeeees Stationary PTTL OP seem eer rece set eters etaetees ie Crumplen and ’ J. Townsend. en a track See eeeeedareres 20° eRe e Ree TREO eee POR e eet Eee tee eeeeete® venneee Pee eebeeeeeeeseeeseenes Herbert M‘Leod. SMEs ct recdsesse| LO: cov cccess|s=+es0esssennere Pcl eee eaewesapees ane dc Id. eft a track 20° long ......|..sssecesceesseleees Sen oe cee isvas|-seaeves akeapedeey seveveeeeees/ 1» Crumplen and - J. Townsend. eautiful track; 30° in |(45°) ....../To right; horizontal ...!.......... Sueeroiedie ..|J. Howe. length. yy ack endured 1 second...!20° ,,,......|To left; 37° from hori-|.......ssseeceesesssseseseeeee/Ds Walker, M.D. ¥ zontal ; down. MIN GTEIu A Cees eetvcevtsestel.ccvetceoveveve Mostly divergent from|Two observersdelineated|W. W. Boreham Cassiopeia. the courses of 70| and J. Hobler. meteors in the hour. BEMBSHGyW ees hee Coverebinsavs[secdsdscaveseas Diverging from Cassio-/Two observersdelineated Id. peia. 45 meteors. MECMCMEVEH COVSICEL-| 2... c5:cvese] 2 avccsscnbececacsesscesccasslossecye sito Naat tacs sss D. Walker, M.D. ‘ably in its path before it durst. of 3° 15’ broad;|10° ......,.,,/Inclined westward 30°|From 1.25 a.m. to 1.40)W. H. Wood. lasted 4 seconds. to the vertical. a.m., meteors fell too fast to be registered. 0 train or sparks ......... 10° ...,...../To right; 30° -from|Strong twilight ......... A. S. Herschel. : vertical ; down. TRssevnnseetssecenectenessenes 2 sesssdccoerelasse seeeeceeevonsecesconscenes Too cloudy for hetter/T. Crumplen and ; observation. J. Townsend. ght enduring track......'20° ..,.....,{To left; 30° from verti-|.....s.cecsscscssseeseeeseeees A. S. Herschel. cal; down. 14 REPORT—~1862. eee == Position, or Date. }- Tour. Place of Apparent Size. Colour. Duration. Altitude and Observation. PP Astin, 1861./ h m gs Aug.11) 9 27 p.m.|Flimwell, Hurst|Jupiter,.....:e:sssros| 2 seseerseesereee| 2 eeeeees sauieane Centre 30° : Green, Sussex. Sars E.; altitud Py OO Ragan: [hids....cscasscsace Jupiter....,.. RTA g eee Very slow .. leon. near + Cygi ; to » Pegasi. 11, 9 30 p.m. Hawkhurst, Kent|Jupiter............... Diensaead Lasacacl 2 sccvctsgacesuae Centre 30° § F omit ; altitud 1110 0 p.m.|/Flimwell, Hurst/4th mag.* ......... weusbasnaccegel faeces becseteeee Sibth 3 (y Equ Green, Sussex. and y Delphin to Equilat. wit! (9 and « Del ' phini). f 13/30 15 p.m./Ibid................ DOPIKER. 0 ss ouceeccdes|'S eeevenrs FR Moderate Down; W. margi! speed. of E. branch ¢ Milky Way. From 3 (6 X Aquile to ¢ Sa ‘ a gittarii, | 11/10 17 4 |Hawkhurst,Kent/Venus, or some-|Bright bluish|2 seconds; |Down the Milk p-m. what larger in) in first two-| slow motion.| Way from Aqu first two-thirds} thirds, then to Sagittarius. of course. dull red, ' 11/10 20} p.m. Ipswich ......... |Vivid meteor .,,.,./It was a palish Moved very |In a line throug meteor, not| slowly; 23) 6 Urs Majori a brilliant; seconds, just above white one. Urs Majoris. 11/10 22 p.m.'Hawkhurst,Kent/Brighter than /Pure white ,,./14 or 1} sec, Gentre 83° N. Venus. It cast! ; altitude 16° a shadow, 1110 27 p.m.Ipswich ......... Very bright ...... WHIRIGE “Jigs scecs|coveveas Pavaveeus Ceased at y Pegas a! 1110 28 p.m. Flimwell, Hurst/Jupiter............... Dv acexehne dydiese Rapid |....s W. Airy. lasted 5 or 6 seconds. rizontal ; down. Tiltiant white track ....,.|,.ccccsssoccseclecscesees Sepasevsewewe ddneewasltndere tree tetera Rey. F. Howlett. © train or sparks ........./5°........+.../To right; 30° from yer-|’) ...... wintienn1ediivasth te be Weed. tical ; down. be a : 2 Three meteors fell n or sparks ......... MATA so caaacl io: nedgerkspeneimeann aaa simultaneously. Id. train or sparks ptrteeaee 15° ttteeeeee Vertical ; down sareeee THERE One eenneeeenenenenees Id. ower and redder at last ;'5°............ To right ; 30° from Ver-|.....sssssseseeeseeeseeeeeeees(Ae S. Herschel. turning to left, and tail tical; down. ceasing. eee BET a i czanenaals auyalicah states From Cassiopeia .,.......|Two observers counted|W. W: Boreham 8 46 meteors in one| and J. Hobler. hed : P hour ; clear sky. » 39° : ac Leen eneeneeneongns 5 en6° ,,. beeen pene hori- Two meteors pursyed| H. Wood. ee 5° or 6° ...'To left ; 30° from hori-| f ‘He same apparent jq. zontal; down. path. a long track visible/20° ......... Vertical; towards 45°)........... Rees stut de ere Ee A. 8. Herschel. 9 seconds. W. from S. MINTS WG8SG CG) 0050 000ecbesltasevsenyeceece From 8 Cassiopeiz to 16).....,.......ceeossecsesseceee Rey. F. Howlett. 9 Cap. Meduse. Pete ee eeeenee stetdas ‘ ? Deve eereeees ? Po es eee eens Td. i DCCC CO OOO oo one Monon nnn rene From 3 (a 7) AMGTO= |i ie caves eves Wee eeeecesenneeee Id. med to 3 (6, 7) Ce- } phei. 16 REPORT—1862. Date.| Hour. one. Apparent Size. Colour. Duration. 1861., h ms | Aug.11)11 23 p.m./Hawkhurst, Kent 2nd mag.* ., 4] 2 Reed evew eens] SLOWesaswvannew 11/11 23 10 Ibid. ..... Sonenes( SIR QNAE cesta vy Dw spevens Suoveon| | ssenbuurnaiene p.m. PATI S 20) UGS) svessenesvee 2nd MA.” \sccvceva| Savvvesasbserees| f. ccescvescuaunnn p.m. ‘ab 38 p.m. Weston - super -)Ist mag.* Mare. 1111 41 10 |Hawkhurst, Kent/2nd mag.* seovsees| 2 sevcecsencseeee| exceedingly swift. csssseves| White .....++..|Momentary ... p.m. 12} 0 1 20 (Ibid. ..... sereees(2nd mag.* .,...++.,|Brilliant white|Very slow a.m. motion. 12) 0 31 20 Ibid. ............/1st mag.* .,,,.....|Brilliant white/Slow motion... a.m. EZRA TS: (Thid. sscswsitescs 3rd mag* ..seeee 2 WNielevssscenve| o oes a.m. PAiete ol NGI. aasseseontes Ist MAg.*, ..ccsessee| 2 sevccesevenesee{RAPIG vreesvese a.m. Le Ge | ts Ee Sxd MAG .corcceve| 2 severees fone P swiniebaeave need a.m. U2) 1 SUy am Phid. — ...c.c0sas 4th mag.* .,....... Sere EY Moderate speed. 12) 1 3ldam[bid. we 4th mag.*. dis.i..s. PAM vskvsnees Moderate speed. 12) 1 3lyam.lIbid. .....see 2nd mag* ......... Pt A isnened ‘Moderate speed. 12) 1 314} a.m.|Ibid. .....5...... 2nd mag.* ......... Perstsecdeteseees ‘Moderate |_ speed. 12} 2 6 a.m.|[bid. | ......0008 Ist mag.*....scceeeee SPRUE Joastvnes \Fast motion ... Me G 8 Wide a reccexvares 4th mag* ..sscesee] 2 saeeeeee becvsl’? sacsvbh-cseaae a.m. 12) 2 14:30 |Ibid. v.50... and mae <.2ccueee Peer ort, Rapid ......... a.m. : 12/2 14.40 |Ibid. ............ Twice the width of White ......... Rapid ...... a.m. the moon; _ir- regular circle. Sept. 6 8 0 p.m./Blackheath ...... =2nd mag* ....., \Bluish white.. 1 to 2 secs. (approxi- mate time). 26/10 O p.m.Greenwich ...... Srd Mag. ...cevcereee Bee ee 2 secveuestee ‘ .|Centre 30° N. fror ..|Centre 23° E. fro ..|Centre ...|From a point I ...|Appeared 4 (¢ at Position, or Altitude and Azimuth. ( E. ; altitude 33° Good observa tion. j Centre due E. ; titude 40°. Centre 23° S. fror E.; altitude 30° Centre 29° S. fro E.; altitude 26°F From % to 3 (6 , Lyre. Centre 40° W. fron S.; altitude 36° Centre 7° E. fron N. 3 altitude 45° N.; altitude 57° Near 8 Cephei Centre 27° y Cygni to¢ Cygni Centre 40° § from W.; tude 653°. altitude 80°. E. from 8. 117 altitude 52°. | E. from 8S. 45! altitude 44°. | Out of y Peg Centre due altitude 56°. Just below the Centre 8° E. fre S.; altitude 27 3°? for below the last. | 4 joris. fi ¢) Ursee Majori = 2 A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. VW | . . . | Direction ; noting also ppearance ; Train, if any, Length of | whether Horizontal, and its Duration. Path. Perpendicular, or Remarks. Observer. Inclined. a bright track visible/8°..,..... .../To right; 20° to 25°/A slow meteor with en-/A, S. Herschel. some seconds. from vertical; down.| during track. 0 track or sparks; {25° ......... To left; 38° from hori-/Remarkable for direc-|Id. straight course. zontal; up. tion, length, and smallness. 0 track or sparks ........./10° ...... ...|Lo right ; 30° from ver-|Ordinary appearance ...\Id. tical ; down. ‘ might track throughout,|15° or 16°..|To right; 15° from ver-!.........606 Vertoase cose ..-|W. H. Wood. 15’ broad; enduring 2 tical ; down. seconds. tismmawnite? track [7°,...........{eccseees ddudenasowayeuseusanea|ieasedcestessceree ers seseeees/A. S. Herschel. throughout; endured 3 seconds. io sparks ; no track”...... Nt anes See Ronletie 5° from iVeralivecsdesticcderssucevssdeavce (Id. tical; down. Curved| to left at last. vight track; endured)............... Osletiys:do>. AOMy Wer-Wieeeu. sh dee pcdeeadl cee adece ck Id. 3 seconds at centre. tical; down. ‘Oo track; the light ap-|?............ Cpa ate on deh Staats steed ae Mie Wc rovierecIevads MPN est Id. peared to sparkle. ck brightened up when/10° .,....... Molett* horizontal, ;,chasscchessssccess pisenaaveatee Id. nucleus had vanished; Visible 3 seconds, od observation of track, 15° ....,.... To right ; 35° from ver-'...... ReanceCaamenannceaverds Id. which brightened up tical ; down. after meteor was flown. Pee eee eee eee cee eee eee 15° eee eeeee SOOPER EERE OED HERE ERED HHH HEHEHE HHT EH eee ween eee ee Id. Aros Seana vaes Arad | eae Ore '30° from horizontal .,.|Three meteors to left ;\Id. downwards ; appeared together. 8 oS ote 2 60° from horizontal ...!..... pate rsaaaey canessncmebepe ld. PPP eee ene eeesereeeeeeseeeeeees 10° weet eeeee 30° from horizontal SEO COP Oee neem ener eet eenreees eee Id. ft a HACK ss eeseesseeevees, TAT ss To right s\ Va? from ho=). PERO e mm e ett teeee| © Oe bebe wereree) © tee sage. | WVIICG, os veteeces ..scss|Bluish white... cosseseeel Second .,....[From 8 Cygni Abeta rewelewnneceeatee Position, or Altitude and Azimuth. Duration. Appeared a fey degrees aboy Ursa Major, passing between the stars « and 8, disappearing behind a cloud at about 10° o 15° from t constellation. — 1 second ,.....\From 6 Delphin across @ Aqui tod Aquile. 1 to 2 seconds|Moved in a south. erly direction few degrees below __ the Pleiades. Momentary.../From « Persei Z Aurige. From about centre of Came: lopardus ; passe diagonally across Ursa Major from a to y, and dis: appeared a few degrees _ below the latter star. 1 second ....../From » across 9 | Draconis. F From the Pleiade: to y Tauri. 1 to 2 seconds|Across Capella; about 20° in a northerly diree- tion. ‘ From y Pegasi, halfway to @ Pegasi. Passed rapidly fron s Persei to Arietis. f 1 second ..,...\From y Andro- medz to K ~ ..|.. Perseis 1 second ....../From jp Andro- mede to 0 Cas-: siopeiz. 1 second 1 second 1 second é Aquile. RACY VEEETIC® 30° from zenith t wis seoseeee[Fell from zen towards the S. | From y to B C phei. 1 second .,....|Across _Cassiopeii to y Cephei. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 19 Direction ; noting also Length of |} whether Horizontal Path. Perpendicular, or ‘ Remarks. Observer: Inclined. Appearance ; Train, if any, and its Duration. —————. — EINES 55 0 Lif 0EM LjereessfernceRllayes t46eeeeeeeeseees|Rather cloudy .........++./J. MacDonald. cae een wesseaGbavebevenscenecccescess|cceudgnanaectcscsvncccascechec| We Cs N&Bh. I ir Beene Honecer Co sereasesusoecac seesslececedeveeceseccsce eossseeese/ 1G. BORE) Va ee cadevesihuassudeccsvestvccclens ata dwadessess eavensesccapae Id. About 45° A very brilliant meteor../Id. TOPO RM eee ee eee et ee ereeeesene sepeett Svto N, ghiorizontally:.i|\\icitecssteccenectuceeeseopel Ld: seer eeeeeeeeraaseee Pore ee ee tane Id. ° PERO O Rete shh b eee etbetseene 15 SOP Pee a eT ROb Ebb et tee e re nenee AER Rew ereleneee Hoenn eeee iaesasegeeeaker LG any TS asses! 8 xrcctuiind. WP aibivengh cade ccsndtsassestfoes F PeCnnenee seeteceseseeys-(J~ Coupland, Ws aslsivaeissouveces BEER Favs weeetes AOD be aeeerenee Sobre beneceee 3 MacDonald. o Pec eee Seer seers erie 12 sbbibece. mech@ibwarudcersssaaeanest=. W. C. Nash. nall train TUR Tredersibiveoee Bbaseacclessces 's 3 i..{Id. 20 : REPORT—1862. T4, Position, or Apparent Size. Colour. Duration. Altitude and Azimuth. Place of Date. Hour. Observation. 186].! h m | Oct. 10|10 16 p.m./Greenwich .,,...,=2nd mag.* «+... Blue .....+0..{1 second ......;Across « Lyre towards N.W. horizon. =2nd mag.* ...+6 White ........./1 to 2 seconds|From Z to 6 Cygni.. =2nd mag.% see IWUBREG Secscccsalccenvenckessnyaen Fell from a fe degrees aboy the Pleiades, | passing through them; disap- pearing about 15° below. Seeeee fr eeeeeeeeneeees 1 second ......|Passed rapidly fron s Aurige to é | Ceti. Small .......s0+esees| Bluish White...)..cccceeeeere «Shot up from the) | southern ho- | 1010 20 pm. Ibid. ..... qieenas 11} 9 25 p.m.|Blackheath ...... 11| 9 30 p.m.|Greenwich ......|=Ist mag.* 11) 9 30 p.m.|Blackheath ...... rizon. y Small avs cacatevosertlice sesssssseeeeeesl Second ,,....|Passing from E. t W. a few di grees above the Pleiades. | =2nd mag.* ......|Blue «ee.,.+06/1 second ...+0.| Passed from ne + Herculis aero! w Draconis. =Ist mag.x..+... .. Bluish white...|L to 2 seconds From ¢ Arietis y Trianguli. oo] = 1st MAg.%.sosessee|eovsesssseereessee(2 0 3 Seconds|Across @ Gemino rum. 23) 7 28 pam.|Ibid. .....ese00e/-—=2nd magex ...e,/Blue ......404/1 second .....-|From Equuleus 6 ‘ wards the horizon. PEO TAZ “PAN LDids “svssoccanceh 14| 8 20 p.m.'Greenwich ...... 14/10 26 p.m. Ibid... 22/10 21 p.m. Ibid. sees. 23) 7 28 p.m. Ibid. ........s00/=2nd mag. ....../Bluish white....1 second ....../From « Equulei B Aquilie. B88 959 Spi Ebid.-.veccssevecwes =3rd mag.*. ......|White ....... 1 second ......|Passed rapidly fre 3 Cygni to Lyre. Very bright .......00|sseseessssersseeee 8 or 9 seconds|From centre — Pleiades to I of Aldebaran. Nov. 2,10 47 p.m.|/Birkenhead ....,. 6 7 O p.m.|Greenwich ...... = gt map Mrccccccas|-oocseucener socenelssrcoescvcsoees see) HOM ArOM the ZEx towards the for about 12° = 20d MAES coscselscsseescwnns veeeeel2 Seconds...,..|From the neig bourhood of C€ pella, and pass to y Urse } joris. Small cisccscossseceslecseesssesereeseeel2 SeCondS,..,,.|From the. nei bourhood of ¢ | | 7, § 45 p.m.|Blackheath ...... 7| 8 49 pam.|Ibid. csssecceoese pella, in the rection of Alde baran for abi bo. ; if Ng A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 21 0 eee eee ee _—_—o Direction; noting also : pearance; Train, if any,|) Length of | whether Horizontal, ‘ r and its Duration. ‘ Path. Perpendicular, or Remarks Observer. - Inclined. None ..... ROPER tre a at ates siraviteseoana te mectoacc re teste a ett | W9oeyvavauckthhavertoeees ak W.C. Nash. WORDED AUIIOVs Gece uc cecsceese j15° aesinasteve{ivapet unanseavebivstacerecdats | dondua dat ehantelysehees saake es Id. EUPLUs chit eancesscceoss |e Uicaiat Aare a Rae mianesaieamencustoarese rae at Bes bee pee sose(J. MacDonald, Small train eee dente neeresses 40° stveeseesleacces Oe ee eee revere errr rrr rrr rr rer rrr W. C. Nash. } LG EE Breve eaten Aetcceet ae Gavanduosncedex arte srasdaet crates pausaveyeneeat J. MacDonald. MEIER OT Gree scene secesegn Mosscaaveae VELQEIZONEAL can ssavesccadilstastetealessoecdercondwaeulae MPU MEEUTO SES os cscovesess: PUR Core Rent cere a sare ere ing | aceaeeanedsencs odiwentcodapae W. C. Nash. ME sanade “ud eee eucde| LOnm aboaveth|- nu vexosteabcatenavetrsss2xtty Moon shining brightly..|Id. BUGIREAMI oe. +0...0ss00- SO ruslekncias os GO NSE i esse evecctenane|Soddcevccs danas Veciha Vee sndn a Id UPPER SS fe ccscevsseces EOP etie ra setsl taanzcneseet sannseanareceet ne The next meteor fol-i[d. lowed this one at an interval of a few seconds, _ springing from nearly the same place. AU esssves. Seeneaseceeness AD ira Aauesrs Lass cag sanatesartny voccsadeohs Cloudy after this timed. ; for the remainder of the evening. GAIN 442....... peeeci enix a lxangksinve castes sesaacc ts stalarcterre unis rrr oes LUGE E yg RR Ae ee ssitahwenpad +» |D. Walker. about 3 seconds and burst, leaving the frag- ments luminous for a short period. [ SSAC ess tes cneaecnsee. Woe ccauetees|seaceves cau tecwacosteens nual acaiie eceanepeseniascavesencet J. MacDonald. Toss veces clecocseosecsense Inclined upwards oes NEL a scccsocscetnctt tts sect lld: eg Renae (th eeeesecccececeeccares Ox Se eeeeeerleerereeneeee Peewee eeneee PERO le eee eee eee ener eee eee ene eeons Id. ‘ 22 Place of Date. Hour. Observation. .1861.| h m Wov. 8} 8 5 p.m. Exeter ...........- a | | 10) 9 22 p.m. Greenwich 1010 34 1010 38 1011 1 EBD) 0 10 36 11 1110 52 12,5 45 p-m. p-m. p-m. p.m. p-m. p.m. p-m.) p-m. ‘Ibid. . [bid. ‘Hay, S. Wales... . Weston - super - Ibid. eeeereeeneee Ibid. Ibid. Ibid. Mare. Southern Hay, Exeter. Barlaston, Stone REPORT— 1862. Apparent Size. Colour. Larger than & Ro-|.....ssssseeeeeees man candle-ball. eens seereeeneseeeee DIUC — eeneesees = 2nd mag.* Pear-shaped; 30’ |A fine blue by 15’ at first, but 20’ by 10’ at middle of its course. | Nearly the size of] ? ....cc..sessse the moon. Larger than any Roman candle- ball. Elongated as long Greenish as the moon’s| white. diameter. Deep blue Saleoeeee 1 to 2 seconds From the ... About 5 secs... From near the body) Sel Pees ans aetestes From the tail of th Position, or Altitude and Azimuth. Duration. —_—_— a seeseeseeees|9.5.E., over Torbay or mouth of the Exe. From alti- tude 30° or 40° Momentary ... and a Draconis. }) From ce Tauri a point a littl above 2” Gemi-} norum, From between Tauri and 1 Ge-|| minorum to Aurige. Passed from y Ge-|| minorum in westerly direc. tion, across th upper part of Orion. Fell from a fey degrees W. Ursa Major | about 10° fron Aldebaran. . 1 second ...... 1 second 2 seconds...... Lyn constellation ; disappeared a few degrees beloy Polaris. From « Eridani to-} wards the S. ho rizon. of Cygnus. Alti tude 60° or 70° horizon, W. 3 seconds...... From 3° above Great Bear. From 20° W. S. altitude 40°. to 40° W. of S._ altitude 8° or || Fell slower than a shooting - star. 9°. | A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 23 Direction ; noting also ippearance ; Train, ifany,) Length of | whether Horizontal, and its Duration. Path. Perpendicular, or Remarks. Observer. Inclined. rst into a bright light|............... Fell vertical ............ Another light was seen|G. A. Lance. when first seen; left in the W. an hour here a transitory track ; later. dropped to objects on the horizon fading away; skittle-shaped. I train ...... + Seer NOD eS vcr aca]e4scancsnadearsssonses abasdénd]eBseshes grok cone marta debe W.C. Nash. dasevsene GaaeMeAiaanen cof hf mich vedvec|«aaudcuvoouissetsesvocccsescus|scoss§evesacencsaceassuciveshos|LGe eee eet eteee POPPER eee eee eee ee 15° eee eee wel eeee PRR e mee Tee SERPH EEE He eee eee Id. RUMEN Ua xankE aan asaase 25° ..ss.ecefFLOrIZONtAlly, HE. tO. Wass)eccscheassssescssecccscsccsbaol LQ. SESSUMNI Es y sb sersevvor]occxsncnposassolvecccossecehoscscssssessecsasle eo cobeeseecveres Gaaaveena +se+\J. MacDonald. PemBMabes Sescdsobusinses| ZO) sesbssdss|iveadieoe sons, eseneepvnnsundksyenala’ PTT TTT W.C. Nash. weeks Epbseseoseeeeees--./L0° to 15° |Almost perpendicular...|....cssscccccse.cscsecssovepeol LG iddy sparks emitted be- hind. Pursued by a long pale streak of light. (60° to 65°)|To right; from 20° to|Flashed overhead like Rev. T. W.Webb. 8° or 10° from verti-| sudden moonlight, cal; at last down. but did not continue so bright as it ad- vanced. Moon ten days old. ew strong moving50° ......... Eel 6 §25, scegue vedo: Probably started from) W. H. Wood. hadows. Left a bright the head of Draco. rack 50°, which lasted ) seconds eared to burst :........ Denese xenans Longitudinally west- |.........sseeeeees sanhuneudee= A. J. Cumming. ward. rgest and brightest at|A short Inclined downwards inCloudy ...............++ G. Wedgwood. the head, tapering to a] course. a Slightly curved line, eddish tail. not straight. Date. 1861. Noy.12) 5 49 p.m.|Manchester (12 ab=60' ; bd=13'; Nucleus yel-\34seconds .../From S.S.E. alti 24 Place of Hour. Observation. —_——— h m miles 8.E.). ce’ =10'. lowish flame, tude 35°; to conical part nearly S. altic brilliant tude 8°. blue. 12) 5 50 p.m.[Bristol............/Brighter than the)Vivid blue ...]? ..ssesee-/Very nearly overs moon. head. 12) 5 50 p.m.|Stone, near |Oval shape, nearly|Pale brilliant/About 6 secs. |First seen a lit Aylesbury. = tothe moon.| blue. N. of Pole-st (y Cephei), to 15° above hor zon, W.S.W. J 12) 6 3 p.m.\Oxwich, South|As large as a |Steel-blue ...|? cccsssseseeeee/From 6° or 7° Local time.| Wales. 15|10 14 p.m.'Greenwich ......!=Venus ....s0.../A greenish tint 4 or 5 seconds From the zenith 15:10 15 p.m.|Shooter’s Hill, Woolwich. p-m. chester. N.W.ofExeter. REPORT—1862. Apparent Size. cricket-ball. Aldebaran or Mars|Mars for half forhalf its course, then flaming; diameter 5’ ; last 3°= Mars. 19 5 30 p.m. Sherwood,7miles|Much larger than any of the fixed stars, Colour. predominated. 5 About 10 15 Styall, near Man- Oval nucleus 8’ long’ Bluish .,,.«...- | its course,| dull; then steel - blue, brilliant. Last. 3°= Mars, and faded away. Position, or Altitude and Azimuth. Duration. —— and W. of Pleias des to same) height at th opposite side of the heavens. | Started 3° S. of Pennard Castl from Oxwich Rectory. a northerly rection. Owi to the dense ha the path of meteor amol the stars cou not be traced. 34 seconds by'From 1 Hey. € chronometer.| meleopardi B Urs Minor Began to fla at the Pole-s Blue, bursting like a Ro- man candle. 3seconds......\From S.E. by altitude 42°; S.E. by S. tude 18°: burs with sparks (?). 7 Or 10 SeCONS|...+eeasevereeeeres A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 25 ppearance ; Train, if any,| Length of and its Duration. Path. eee ee sharply defined ;/25° sparks or) breaks; no permanent tail left; no disruption at disappearance. enon eee | a track of golden) ?.., light. o sparks or tail; burst(90°) ...... into large fragments; much scattered; no noise heard. eee een an candle-ball, with\(130° to red sparks and fire ; tail} 140°.) 8° or 10°, tapering into detached sparks. Tilliant train throughout|50° ......... the whole of its course. About 1 second before the meteor disappeared, it threw off a small luminous fragment ap- parently 4th the size of the whole body, which suddenly disappeared after travelling 1° cr 2°. No noise was heard. o track left; when nu-/40° ..., cleus flamed blue, red sparks were emitted all round = % diameter of moon, Direction ; noting also whether Horizontal Perpendicular, or ; Remarks. Inclined. To right ; from: 43° t0j.coce....cccccsecssccdevsesoeel 61° to the horizontal; down. > ) aNc” iar? A Figure of the meteor compared with the moon, As nearly as possible!.........ssscssceseesees rece S.S.W. (Inclined! .csisesessevcssens Very foggy. Flashed an intense light, as if it broke out from behind a cloud before it was seen; loose clouds. Mounted as it approach-|Appeared level with the ed, moving apparently| eye, and stationary at level with the sea. first; very bright. N. Observer. — R. P. Greg. Rev. W. M. Burch. William Penn, S. G. L. srecscesescesereee(All exceedingly hazy/W. C. Nash, night. Moon and one! or two principal stars seen. Afinelunarhalc. Almost vertical ; down../The flaming nucleus ir- regular in figure, but not elongated; hazy sky; full moon; halo. (No other the heavens from 93 to 11 p.m.) To right; 35° fromThe position carefully vertical; down. taken from memory. .|From y Ursz Majoris.../The meteor appeared to drop between us and the opposite hill; we felt certain it dropped meteor was visible in, \A. S. Herschel. \R. P. Greg. ArthurCumming. in the valley. 26 Date. Hour. 1861.| h ms Nov.19} 9 15 to 9 35 p.m. 19\/Between 9 &10 p.m. 19/9 35 pm. REPORT—1862. Place of Observation. Apparent Size. Ipswich .........,Large as the moon,|A _ bright stream of but very much brighter. Norwich .........,A bright body as) ?... large as the moon. Whitstable ...... A splendid meteor.. Colour. Duration. . fire, 19 9 35 pm. 9 38 23 p-m. Guestling Hill...|Half diameter of the moon. servatory. meter of the moon, 19] 9 40 p.m./Woodford ...... At first stationary ;/Pale whenunder-| seconds. neath the moon, then =Venus. When under the moon = of moon’s diameter. blue. Tee eereeeres a Roman candle-ball. 2 ..sseseeeeeeess(Durst into 3 pai Position, or Altitude and © Azimuth. It did not move|Approached on very fast, but like a spent rocket ; like the S.E., burst ing into 3 pie when = almost overhead. - nearly overhea | | secessese| 2 ccseeassesvesee/The grand exploy sion took plac close underneat! | the Great Bear. | Rose from a banl of clouds 30° from S.; disap peared a_ littl left of Witte: ham, 20° £E from N. Passe ) | | | | 4° or 5° undei the moon, whicl had altitude | about 40°. 19|Disappeared|Greenwich Ob-|One-half the dia-|?....... is cex Nearly 10secs.|Appeared between y Orionis and Aldebaran (from behind great dome of equat real). Passed 6 or 8° below Pollux, and dis- appeared 15° further N. 4 green |At least 10)At first stational for 2 seconds at a point i Cetus. Ad vanced _nort ward under the moon at half its altitude, | and finally disap- peared without noise. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 27 pearance; Train, if any, and its Duration. ew shadows. Broke into 3 pieces or streams of ire, which soon disap- peared; as large as a nan’s fist. st into 3 parts; one or} ? ,,, wo appeared to fall, nd the other seemed ploded with an appear-|,,, nce of 6 to 8 balls of ire, SRP R EO eRe meee were renee seeeees train of prismatic olours;. fragments addy brown. Threw ut fragments, and arted into two before 2aching and in passing ander the moon. When i three ee the last things Gificent meteor ; car- ed a splendid coloured ain with sparks, and ‘last broke into 3 or 4 d vanished. d forth suddenly near e moon like oxyhydro- nm lime-light; then veloped a fiery tail, cleus becoming blue. ‘Oke into 3 or 4, like aS on a string, just e disappearance. strong moving, Length of Path. secrete tees Direction ; noting also whether Horizontal, Perpendicular, or Inclined. S.E. towards the N...... Remarks. Observer. About 80 or 90 seconds Mr. Felgate; G. after the explosion, three distinct reports like heavy ordnance or distant thunder were audible, Webb; G. Pulham; Ro- bert Bixby ; Frank May- hew; John Steel; Charles Lawrence (communi- cated by Biddell). G. From S. Baby W. towards/A full minute afterwards|Rev. G. Gilbert. zontally across sky. Horizontal .., Pe eteke ...../Lnclined downwards 15° from hori- or 20° zontal. heard a loud report. A eeceeseeree Bese membres esesees Be ad egae Horizontalivstyeecceesckks|Seoeck wek see eeaea eee Messrs. James Pearce. James Rock and C. Savery, M.R.C.S. —_—S Oe 1861. 19) 9 40 p.m./Tunbridge .,....\One-third the size!White with a'/From 10 to 15/First seen as oy Place of Observation. Apparent Size. h m of full moon, REPORT—1862. Colour. bluish shade. Duration. seconds. 19| 9 45 p.m.|Heavitree,Exeter/Light very bright|Bright white.../Moving by no 19 19 19 and steady; oc- means quick- casionally thicker ly aa in some parts straight line. than others; like an unusually large star. 9 45 p.m.|North Foreland |A body _ nearly|..............005. Moved slowly, equalling the continuing moon, but far in sight 10 brighter. to 12 secs. Evecsbeucesb ne Dover .......40004|Much larger and|Ball of yellow) ? ceccccesecesees brighter than | fire, pure Roman candle-| and pale. ball. 2 edocs eee-/Wrotham — Hill,/Threw a great light] ? ...... vaueedson| te eves cuatnenened Kent. on the opposite side from the moon, > ‘From the Position, or | Altitude and | Azimuth. — te ray 7 First seen S. of some distam before it came} the moon. # ploded plain, Langley Poi Pevensea é bour. Passed a more than {| below the moo Came out from 1 sky, and disa peared with noise; unife altitude of 1 to 29°. q From 60° altit S.E. ; passed E. of the zeni towards true } burst N. by altitude 12° 15°, by At the Tan Stembreok, Dover, th meteor d peared _ behi the Castle part of the hi vens; travell many miles } fore it came the moon. | Passed under t moon and ¥ lost to hehind hills. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 29 ; Direction ; noting also earance; Train, if any,| Length of | whether Horizontal, and its Duration. Path. Perpendicular, or Remarks. Observer. Inclined. ods CSoe ene OC eee 2 ssscveveeeee| 2 eavccesestetevsseererseess-/Companion of observer|W. Blackstone. thought that his coat was on fire. Observer thought it lightened. ly the top of the moon was visible, the lower part being outshone by he meteor. When the explosion took place, 7 balls of fire about the size of an orange formed themselves info a sort tail. rew shadows half as|..,..........+.|Nearly due S. to N.;|Brightness did not vary.|W. Mitchell; deep as those of the| horizontal ; altitude A hissing noise was| John Harmer moon; rocket-like tail 30°, heard as it passed. (communicated 8 or 10 feet long. Di- byC.V. Walker). vided into two parts on passing the moon; burst into 10 or 12 fragments, which were ed. € appearance was that/About 2th|Direction from S.W. to/Appeared to drop some-|R, T, Abraham. of a light running along| of the N.E. ; ‘horizontal. thing as it went along. outstretched line,| circle of the light ofarocket.) the ho- rizon (=60°). @ ried a tail 3° long; Full70° ...\Curving towards the About two minutes after|James Chapman. violet at the head; earth. extinction, a short apering to a flickering dull but loud report point ; flame coloured; was heard ; distinctly } or 3 seconds before but closely double. dursting a globular body eparated from the head halfway along the ail, and there con- ainued. Exploded into nany fragments, which ell some distance. adows in the streets) ....4......../The meteor was Ob-|ssscsssseeesessseeseseeeeeees] Edmund Brown. noyed rapidly. - Served to explode near Maldon, in Essex. eee the Fro eae¥ sees seeonile caseese ssssesseseveeeeeees/ Lhe air smelt of sulphur| James Douse. gan to vomit fire o he most brilliant hues. 30 REPORT—1862. Place of Anpftepe’s Col Durati Poston, or Date.| Hour. : pparent Size. olour. uration. titude and — Observation. Azimuth. 1861.| h m a Nov.19| ? ......eeee..,Wrotham Hill,|Four times the size|Brilliant white) ? ..........+-04 Appeared. S.S.E Kent. of one of the passed 43 widt planets; threw underneath shadows on the moon. Burst wif} fields. bright —colou near the N. | 24) 7 40 p.m.|Broxbourne ...\Somewhat larger White with |13 second .../Appeared 5° W. 24) 8 10 24/10 2 26) 5 42 27| 9 32 3011 11 Dec. 1; 1 50 1} 8 263p.m.|London .........,=a@ Lyr®.........4.. j@ Lyre i... ‘Moderate Appeared nea’ 1) 8 37 than Sirius. bluish tinge. B Cygni; dis peared 4° E. a Aquile on t equator. p.m.|Weston - super -/=Sirius ......+0.... Brilliant blue..|2 seconds .../Appeared in Ple Mare. des ; disappeare near « Ceti. | p-m.|Greenwich ......|=2nd mag.* ...... Bluish white..|1 second ....../Started near Orionis; pa towards the hi rizon through Orion, and dij appeared a litt to the left of) Orionis. Pisrn EDIDas is tatocevas re Small ......+e+.+...-/Bluish white ..|1 second ....../ Passed through Pleiades in direction of debaran. ; p-m.|Greenwich Ob-/=2nd mag.* ,..... White },(...,.. 1 second ......|From y Geminor servatory. to a point tween « ané Orionis. Pa EIA.” os... -0 ee =2nd mag.* ...... 1) UY Bago 1 to 2 seconds|Shot between « | 6 Geminorun = Ist mag.x......... Bluish white ..|.......ssecsecees Moved below | Major tow N. horizon. — Airis LIC ay cavweeesst =5th mage sseoe(Blue ........- 0:7 second ... Nearly in the p of the meridi and about | from the horiz p-m.|Greenwich ....../Small but bright.../Blue ......... About half aa Orionis to + second. onis. p.m.|Wakefield ......| Very brilliant ...... Bluish white ..|......s020008 ...../From overhe eastward ; di! peared behin railway emb ment. | speed. Draconis. p-m. Greenwich ......)=2nd mag.* ....../Blue ..,.......2 seconds......|From 4 Lyre within 10° of W. horizon, © A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 31 Direction ; noting also per ance ; Train, if any, Length of | whether Horizontal ~ and its Duration. : Path. Perpendicular, or ’ Remarks. Observer, | Inclined. od-red ; tail like a} ?.......0.00 Horizontal when under-|Clear sky; no smell of|\James Douse, aon sword. neath the moon. sulphur. - Oo . es in about 9° in length...) ? ...... paaevdlacdetseees sae Bacceiees svestous cedecesscenererssceees seeeeeee/H. S. Eaton. a Risiveeneunvs-|MBCMNO |} ccigesscescenene ..|Many came from this|W. H. Wood. : locality fer several evenings. This was the largest and brightest. Prerererrrrirrrreryy tener 15? one ete errno eee e eran eee tees tarseas THF eFeE ETE eeeeeaeeneeessee peer WY C. Nash, Eta aan coh =pe0080s 8° potsar|sccccssccestseescencesecaesso=|MtAthler CLOUGY o6....cseda.[0a MacDonald. wee eeeetereereraenensnene 18° OOo prance COC eeerersssserenenece pecveces A fine bright night oneeee W.C. Nash. MET sBWNSG¥6s .<) 005s. 5° to 7°.../Inclined path, S.to N...|A fine bright night ...,../[d. trresesnesersereeressnes|seeeeceeeesseee/Lnclined towards N. .../A fine bright night...... Id, train; disappeared|4°_ ..,......| Towards the W., at anjIt was very small and/H. C. Criswick. ddenly. angle of 45° to the! rapid. horizon. Mihaess ss densacsverseces ROS vcegscsclacaeeaans msaenashewienss senor Rapid motion ....... sreee|W. C. Nash. long train behind)...............|Nearly vertical ....,.. ../The sun shining at the no explosion was time. a short tail ............/20° ...,...../Directly from Polaris...|Remainder of flight in-|Herbert M*Leod. tercepted by houses. PRD meal EH EHP Hee Ores eee ee tee bere neta h CORPSES OTT E EEE TESTES TSH ED . C. Nash. ‘of some length .,,..,/20° 52 REPORT—1862. Position, or — Place of i ; ; Date.|. Hour. Observation. Apparent Size. Colour. Duration. ent 1861.) h m Dec. 1) 8 50 p.m.|Greenwich .,,.,.,= 2nd Magex «..+++eeveevees Seuetie ..(1 second jFell perpendi about. larly from point a_ litt aboye and to W.) Lot + Um Major. 1|9 8 p.m.|Blackheath Hill, Size of Sirius.......The colour ofj1-5 second .,.|From between Greenwich. the un- Pleiades and clouded Algol; neare moon. the latter. 1} 9 14 p.m.|Walthamstow ...,\Somewhat smaller Pale yellow...!3 seconds .,,.|From 4 (Aldebar than Polaris. and « Orion fos he We Castor. 1| 9 15 p.m. Weston - super -|/Diameter 2’.,,...... saaaneraseel ses..-/Very slow; /Appeared bet Mare. 5 seconds;) y Orionis speed slack-| « Orionis, a ening stead-) burst 4° abe ily, until « Orionis, almost sta- tionary. 2) 9 45 p.m.\Barlaston, near Larger than Venus,Greener than Rapid motion..\From altitude Stone, Salop. | butnotso bright.) the greenest due E, rays of stars. 3) 5 20 p.m.|Blackheath ...,,.;=Ist mage ...... Bilge tices sees ‘Less than From direction 1 second. Cassiopeia to Pegasi. 4,2 5 a.m.|Birkenhead (Sea-|Bright meteor ......| ? sesr+..ss.+-.9 Seconds...... From centre combe). quadrate sta 7\At night .,. 8} 8 15 p.m. 8} 8 15 pm. exactly. 8 About 83 p.m. Preston .isseeees Lancaster......+.- St. Bees, 14 mile inland, DiNSi a etiiet actos Large meteor «..... Almost as large BENE caine tanh the moon. Ball of fire 5 inches) ? .esssseoserens Bridlington Quay. 3 seconds in in diameter, ? perfect | state; 6 | seconds in all. Asillarge. «.08...ShE)sscssesseecdoeesat 2 es tvieecam moon. Ursa Major within 10° of horizon. ? scdievncesnce HIDES iS LRN or 30° a littl of N.W. | SF eeeeees eee ee eee A CATALOGUE OF OBSERVATIONS GF LUMINOUS METEORS. 33 .ppearance ; Train, if any,! Length of and its Duration. Path. after having travelled about 3° or 4°, it broke into five portions, three of the portions being as large and bright as the meteor when first seen. ing, and then diminish- ing. shaped in falling ; train 10°; half disap- ared in the flight; ragments _ proceeded streamers after ursting; 5°, diverg- ight disappearing uddenly at maxi. um, with a red gently ACen eeeeeeetrerer scseeeeeesenend ilar to that of the] ? score ight following. SN OOEe Cee eee tere reeereteseees ee & steer v the last half of its) ? ......00.. lurse shot out a usand most bril- t stars; diminished size, and vanished at) PUHCETEEE EERE TROT He ER OO OTTO ES senses oneretee i+ ew to size of Venus;20° ,,,...... Fell vertical ..,...00 oa TL pr cceeeneeeteveseeevesesleaeeeeeeensases ¢ Direction ; noting also whether Horizontal, Perpendicular, or Inclined. the path, which was short, appeared to be a horizontal line. TUTTO OTe eee Fear er eeeeeeFeHieueeters Remarks. ae ee eee not very large, was exceedingly bright ; after breaking up, it was visible for about 0-S5sec.; no noise was heard. See POe ee eee ener eeereeeererees SEO EEEOP ORTHO TSE ETOP eee eee ee eeee ene eet eeDEDeeuteneeenes ‘Perpendicular PROTO OTe ee eee eae tear ee ees eeereseseter ? SEROTEH OH eee POT OHTA E EES e ee Hees eeheeterereeeerreeereneeder From the Pole - star/Hissing sound _ like downwards to due W. From overhead down- wards, N.W. into the Irish Chan- nel, between St. Bees -pegBad fee and the Isle of Man. quenching iron during the passage of the meteor ; two minutes later, a sound like the discharge of a heavy gun. ,|Appeared to descend): ,, :,:..ccscccesvessscuseccpes PRO ee ene reer essere Oeeerere Observer. sasecescecscessesseese(de MacDonald. ere was no train; but7° ....,,.../[t took a course due S.;/This meteor, although/H. C. Criswick. ght unsteady, brighten- aivonucecedueuns A serpentine COULSON G cel eta ccnancientguvsnstecccsadebs| Ete Ss. Eaton. ew brighter and pear- PPTTTITETITITITILLL LILI reir ii ii 2 W. H. Wood. W. C. Nash. D. Walker, M.D, Communicated by R. P. Greg. Correspondent, * Lancaster Guardian.’ ‘Isaac Sparks. S., Correspond- ent,‘ Manchester Guardian.’ D 34 REPORT—1862. : Position, or Place of ~ * F Date. Hour. ‘ Apparent Size. Colour. Duration. Altitude and Observation. PP ‘Agimuth. 1861.;h m Dec. 8} 8 15 p.m.|Hull..........0.+../9ize varied; light/White, then |2 seconds....../From 10° to 1 exceeded that of} blue. above the moo the moon. whence move to 20° above horizon. 8) 8 15 p.m./York (Holgate)...|Half the size Of a|....ccccssessseees|erereees seeeeeeaee lean eeesereneessonstes cricket-ball. 3 8| 8 15 p.m.|Southport ......|Almost as large as\Blue light; |?...... seeeseeee(Erom about t the moon; bright} colour pale ; Pole-star to as noon-day. blue. tude 25° or 305 a little W. o N.W. 4 | 5 i 8} 8 15 p.m.|Manchester.,....|Longest diameter|Pale blue,..,..| ? sccovseeseee-{HrOM a point ned equal that of the the Pole-star t moon. the horizon, | westerly. 8| 8 15 p.m.|Liverpool....... ..([Like the moon as}......e.s00 sateen Rapid flight:s|..csesccccsvsescooeelll seen at the time. 3 seconds. ax) BiaS 15 . HI. |THid... rrsaresovenslyacrshonadescavenvascnns|APMME Auatalibce|clascassieesdecaeclmeali reece lightning. : SiS elO im.|Prestwich, Man-| 2 Siseseccasenesteushuli Peabeweercnecnsclinisesnctraeeeree: 2 ngneess te ceuheeenee chester, 8 8 18 p.m.|Dundee ....,....|One-third diameter|Bright white,|10 or 15 secs. |About the altituc of the moon, like molten of Sirius or metal. Orionis; abo the horizon — the time. 8) 8 20 p.m.|St.Bees,Cumber-|Brilliant meteor Or| ? ......cscceess-| 2 eesssesvseeeees{From altitude 4 land; 3 miles} shooting-star. due S. dow inland. wards. 8, 8 20 p.m.|Castletown, Isle|Considerable fire-| ? .....sceeeeeee-(SeVeral _ secs.|Horizontally of Man. ball; lighted up remained S.W. the scene in a stationary. | N.E. ¥ very remarkable e manner, A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 35 \ppearance ; Train, if any, and its Duration. irst a bright light of ? large size, then faded with a few sparks as if going out, immediately enlarged, _ elongated, brilliant blue, leaving’ red sparks behind shading into the blue. ‘lowing red envelope; tail ending in green; very even and somewhat permanent. farted into 7 or 8 frag-| ments, like red - hot, cinders. al shape followed by|}......sscseses long broad train; the! flame repeated itself three or four times. It we three distinct ashes of light upon the ground and sky. mg tail showing all the prismatic colours. OER E PEDO eee e onto en eneereetenes aes lare._ visible closed shutters as if it lightened. spearhead-like crescent moon ‘five days old, with a short shaft ; was followed by red star-like balls clustered behind. reddish bolt issued from behind filmy clouds like a flash. The bolt or meteor afterwards sepa- - into a number small and_ brilliant — fireball was snditenty arrested in its progress, remained stationary for several seconds, and burst without noise, through) ? Doane Peeneereenee eer teres seeeee Direction ; noting also Length of | whether Horizontal, Path. Perpendicular, or Inclined. ? Bete ieantosne Motion westerly ......++- Remarks. Observer. .|Moon bright in a cloud-|Baker Edwards, less sky. Ph.D. Cast shadows in the moonlight ; moon six days old. HOt oeeeee Hissing noise like |L., Correspond- quenching iron ac-| entto‘Manches- companied the ap-| ter Guardian.’ pearance. Two mi- nutes later, a sound was heard like the discharge of a heavy gun ? FO CPO eee eee ee eee eee eee er len nny Thee eeeeeeeneeeenteeeeene J. st Slugg. Ran rather low and FOEOER Hae Tee Seer eee THOS OSES ES see eee ones ebenrenene® horizontally. MOvedN GE: 0'SoW.i9:|scageresvessevsereserssanuneue Correspondent to ‘ Liverpool Mercury.’ Rises causnsawopeansvoeveneslisscopiesveabincerccnceeemeas R. P. Greg Sailed slowly from E. t0]...,......s0ssssecaccssssnsere ‘Scotus,’ Corre- W., with a little dip spondent to towards the horizon. ‘ Manchester Guardian.’ Downwards at 45° to\No sound could be'John Jenkins. the horizon. heard. .--/Moved horizontally till it stopped and burst. Moon clouded at the|Correspondent to moment. ‘Mona Herald.’ 36 REPORT—1862. D Place of Col D Eitan, nd ate.| Hour. : Apparent Size. olour. uration. Ititude an Observation. eet | | 1861.; h m | Dec. 8) 8 20 p.m. Liverpool seccerlccrseceeceeececesececeee/DIWISH + BTCCR| seseeeseeeeseseee LHe Spark sprang} light. from a little a proceeded with scintillations to} the er then came suddenly extinguished. 8 23 p.m.|Birkenhead (Sea-|...seecssssssseeeesereas|eseenseneeeenes ../Darted down-|Appeared 8° or 9° combe). wards; not, E. of Cassiopeia 4 seconds. burst 35° to 40° above the ho« rizon, some- where about N.N.W. by W. 8 25 p.m.|Stone,nearAyles-|Double of Venus ;/Red flush, then 5 seconds,,....|From & Cephei to bury. § of a minute of| a purple a Cygni (the are. flush, and) stars doubtful). then a blue, flush of light. | 8 25 p.m.|Silloth, Cumber-|Nearly size of full Palish blue .. . 5 or 6 seconds,|From altitude 50° land. moon. rapid. in the S.; dis: appeared a little to the N. by W. co ies) ao oo 8 30 p.m.|Dungannon, Ire-Strong glare in| ? sessssereeeees Lasted a few From altitude 30° land. moonlight. seconds. due E. 8) 8 30 p.m.|Ulverston......c04] ? seseeessessrereeeeeee| 2 eeeeeeeeteeenes) 2 ceesereeererene o ctesssccses sceseeseeseveee(Descended from to render distant altitude 50°N. W objects visible. to altitude 10) N.W. by W. 8] ? .sseeeceeeee| Manchester ...... Large as } Of the] ? ...csccccseores ? .ccdeesbgevers (Onl turmings ae moon. the meteor fall ing perpendicu larly N.N.W, A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 37 Length of Appearance; Train, if any, Path. and its Duration. irst a reddish spark; in... combustion at the meri- dian ; increased in in- tensity to apparently a large sheet of flame; extinguished suddenly. ight slackened at burst-| ? ssesssseeee ing, but explosion the most briiliant; frag- ments violet. tar-like, and very bril-| ? liant for two seconds, then burst, and con- tinued like a rocket, followed by coloured fragments. blazing track followed it, and immediately following were many smaller globes or bulbs of fire; several bright rene eae e ee enee Direction ; noting also whether Horizontal, Perpendicular, or Inclined. er | a Romero eeeneiee FeO ede e cere eeeee sere etresens Inclined 22° towards the horizon. Inclined at a great angle to the horizon. ‘Descended slightly ...... Observer. a Several and meteors night. shooting-stars|J.BakerEdwards, this}; Ph.D. Sky hazy; small halo|/D. Walker, M.D. about the moon. Cloudy night, moon con-|W. Penn. cealed; attention caught by crimson flush like lurid light- ning. Seen in clear sky Rey. F. Redford. Light clouds ; moon and|-+- stars more or less visible, red. ge ball of fire withl.............../Fell down towards the' coloured sparks and earth. long train. MATE yecsis cass essassseses Di eecsavetars|lus-tO! Watvsckecesse eececies ave out like a stream Of}............04 Fell from near the crimson fire, expand- zenith straight down ing like a trumpet, and in the northern sky. then bursting without noise. BLe LBmInChes LONG|ss.ssucmwe-0.00)ereceravessoovoeevasberssaces issued above, then! ceased, and issued at the side, till bursting with sparks. red balls left behind)? ....... sepvel Er oadavacsy fas Peeeeneueseness tail followed, and stars)......s0sse+e+ about the latter portions| fell from it. light scemed uniform) ? ........+0.- and ceased suddenly. straight line, but the movement was irre- gular. Soe Ralaaard 2 ivssesesssvesLell Vertical. ..... eeeceaqes Appeared to moye in a'No noise or explosion... FOP POO reer eee eee eaereeeesenniee Cees reateseneeerens weer eeereee S.E. to N.W. «.........-.,After walking 200 yards|Communicated a loud noise was| byAlbertGreg. heard like a gun. W. R. Milner. Arthur Neild. 38 REPORT—1862. D Place of a : ate.| Hour. Observation. Apparent Size. Colour. Duration. 1861.|h m Dec. 8| ? «e..eseeeee,Bowdon, Man-|Nearly as large asLight blue ...\3 seconds ......|From a little N.W.8 chester. the moon; brighter than the sun. Bie fenceneseaber Liverpool........-|Very brilliant, |..ssesseeeeeeeeeee giving out con- siderable glare. 8] 2 ...+0eee00+-(Llandudno ...... Light exceeded that|Many coloured 2 or 3 SecOnds)...+++.sssseeeeeseeeee of the moon, more like that of the sun. 8] ? eves..s0s../Settle, Yorkshire|At the flash, Ob-| ? w..ccsceccesene server turned to examine the moon. 8] ? ..eceeeeeee-| Newcastle - on -/Very _ brilliant Picaavdacedeceres 5 OFG SCCONAS..| ? ..occecsevese ssooue Tyne. meteor. 8 Inthe even-\Cartmel, Lan- |?.. Hatwovst| Pils siaveccccecce| © covecgncstdiene ing. caster. 8] ? ..sseeeeese-/Douglas, Isle of|Like full moon let/Startlingly [Visible 10 Man. loose in the sky.| palecolour.| seconds before it burst. Beles. psevies Langdale .cseeesse] ? ccssessseeseenssveoee! 2 ossal 2 seceverneaWetne Slav aaanescsnas Holcombe « Eillilitieeumecsyscscesseus peel tccrenaxcsds 2 suegauddebeenn Bury. IIe oxvvease rape Islington, Lon-|Larger and brighter|..,..6..s000+++04+ esccveesdasvddtsee don. than the largest star. “| Possancceenere Twickenham .,.|Most brilliant | ? ...ecccosssceee| 2 seeceseeeevenee meteor; eclipsed the light of the moon. , 24 p.m.Greenwich ......,;=3rd mag ....../Blue .........|Halfa second.. 810 45 p.m. /Birkenhead(Sea-|Meteors and ShOOt-)..........ssssseeeleeerernees evevecee to combe). ing-stars. ll 5 pm 4 5 15 p.m./Glasgow .......+- Fine meteor......... 2 osbaee medevers 9 seconds...... 9, 5 30 p.m./Hawkhurst, Kent/Brighter than Ist! ? .....scceceseee 2% or 3 secs. ; mag.*; large and bright meteor. 9 9 35 p.m./Greenwich ? seesceeseesevee(Lt appeared to come slow motion. Nedewe Small. -ccscecsicccccsdlscticcvcwes soetdss{ABECONG seve Position, or | Altitude and Azimuth. of the zenitl described an a towards the W. cesesecsevevssees- (At the altitude of rocket. out of the moor ? seereeccceeeceseseass SHO OeR eee teerereneeeneas 4 | Disappeared behind woods N.W. .| Disappeared behiné a cloud near tk horizon. From altitude 50' or 45° W. q “ From the Pole-sta Across y Aurigz the direction o the Pleiades. — Between Ursa Maj and Orion, S.E. | In the S.W. sky 4 Across 6 Ursa» | Minoris; extin o] halfway betweer, 6B Urse Minor and Z Urs Mi joris. Appeared from | behind a clout | moving _ parallel | to the horizon. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS, 39 ; - Direction ; noting also ppearance ; Train, if any,] Length of | whether Horizontal : and its Duration. Path. Perpendicular, or” Remarks. Observer. Inclined. ee | AS | SRN RN SE oy a long broad train} ? .....secccee| 2 ceccesseeesessseeeeerseeeee/A FuSHing sound heard] ? behind. during the passage. arried a luminous train,|.,..............Moved S.E. to N.W. .../sssccescensssesseeeeesesseeees{ Correspondent to s Liverpool Mercury.’ utline very irregular,|...........006+[s sevsccccsescoscescorssevssene/(OlCar NIGH srsesessssseeee|1» So G., Corre- oval shaped ; tail formed spondent to of consecutive bulbs of * Manchester fire. Guardian.’ Dall Of fre .csccccsecoesee| 2 socsssssseee] 2 eeteceesscevoeeseeseseesees Sky free from clouds ...|W.H. Cockshott. ? ssssersesserssessscssesessess| 2 seseeeseses| © ceeseeeeeretesesseeseeseeee/Many shooting-stars |Correspondent seen this evening at} to ‘ Northern Newcastle. Advertiser,’ R. Hawthorn, > ssssesesssvecnsesssceuenceeess| 2 coseseseaeee] © seeeterersevseeeeteevsesees Report very. loud; {Communicated alarmed the inhabit-| by Albert Greg. ants. urst in sparks ike a). ..ssecescuesss|teereeteerseceerenseeenss +++++/People greatly alarmed ;|Samuel Simpson. rocket. no noise heard, > > censsnsensessssssecceesessasee| 2 cessesavaee] 2 eneeeeseeeeeeceseseeeeeeees sesssesesessssessereesseeveees/ JON Richardson. € six or seven falling] ? .......5....|Lhey fell vertically ......|cccccscserecsscsscssseesccevelde We Wraith. stars. eable in colour, |40° ..,......|+ tocveseeeese tevesseseeeesees/BY memory, at same|James Foote. 8 7 pursued by a vari- spot following day. coloured tail several degrees in length; no explosion, no sparks. inated the whole)....... seveeeee{LOOK & nOrth-Westerly|......ssseerscscsessseeesseeee/H. G. P., Corre- country. direction. spondent to * Manchester Guardian.’ Mitheassist..55% CEPA het cx Oe beviees BNA ehoncpdldeee Sette sees Pe iat vecssvesccescercessesesnstes| Was Nash BeabSetscdese+ccacessuacvs|ssecssoccevesss|tesessess.coosecteseeveosegeve(More fell here at) this|D; Walker, M.D. time than at the highest time of last August or November. ee Besse tenccores| F seccseeeecee| © casesetsesseneeeseesererenslicscesener eee ceeeeeeereeeeenee Communicated by R. P. Greg. isappeared without ex-|...,.....,.....{A8 if from Cassiopeia ...|.... sadeccccccsccscnessiveeeelJul's We Herschel. plosion. teteseesrrneeveneeesesensseeees LO” seseeeens Parallel to the horizon....Rather cloudy _ ........|J. MacDonald. 40 | Date.| Hour. Place of REPORT—1862. ° | Oblervatiod. Apparent Size. Colour. | 1861.|h ms Dec. 9 9 40 p.m. Greenwich .,.,..,=2nd mag.# «..++./Blue — sessysere 910 50 p.m. Ibid. ssscseeeeeee] = 2nd Mage weeee/BlUC seeeeseee 10 9 45 p.m. Weston - super -|=2nd mag.x, @ |Dull or smoky Mare. Urse Majoris. blue. 10/10 30 p.m.? Ibid. seecaseseee =Capella............/Bright blue... 11} 9 12 p.m. Royal Observa-|/=Ist mag.k.seeeee/BlUC sreeeeers tory, Green- wich. L111 11 p.m.|Dbid. ..ssseeeaee =2nd mag.* ......{Blue wees ILI1 23 p.m.|Ibid. sesssceseee =2nd mag.* ......|Bluish white... I1J11 28 p.m.l[bid. ....sceveee =3rd mag.F .1.... White cackssuss 1310 0 p.m.| Weston - super -|=§ Aurigz......... Smoky blue... Mare. 1811 37 p.m.|Birkenhead (Sea-|=1st mag.* ..,.../Bluish .....++. combe). 23! 7 O p.m.jRoyal Observa-|=2nd mag.* ...... White ......... tory, Green- wich. 24) 7 0 p.m.|London ........./Mostly 2nd and/White and to4 a.m. 3rd mag. None! yellow; so large asVenus.| steady lights. 24,9 O p.m./Woodford ..... Shooting-starser..,,| ? csseeee secceess 2410 to 11 /Hitchen ........./Small stars .....0...] ? esses Seatensis p.m. 24/11 38 34 |Deal .......... ..|=@ Andromede .,.|White ......., p.m. 2519 O p.m./Royal Observa-|=2nd mag.x ......Jceceeseee eee tory, Green- wich. 2511 45 46 [Deal ...s00....|Between @ and Blue... p-m. Cygni. Duration. 2seconds ..., 1 second Position, or Altitude and Azimuth. Fell from the} neighbourhood } of Orion toward over 20° space. Across @ Majoris. Less than 1 second. Nearly 2 secs. 1 to 2 seconds 1 second ...... 1 second ...... 1 second ...... Less than 1 second. 3 seconds ... 1 second More _ swift after mid- night than before; mo- derate. ..|L to 2 seconds 1 second ...+. (Un the S. seccascencill Appeared near Urs Minoris disappeared neat ” Draconis. Appeared azimuth 40°, altitude 20° N. of W. From ¢ Aurigze to point a few de~ grees below the moon. | From a point a few) degrees above a Orionis to y Ori-) onis. Fell perpendicu- larly from 6 Ge minorum towards horizon. ‘From @ Tauri to- Appeared by Cae pella. Centre immediately below 6 Persei. From the direction of Cassiopeia to a Urse Ma- joris. Chiefly near the radiant — before midnight, after- wards in 4a quarters. From near o to below « Andro- mede. Shot in a northerly direction —_ ee tween # and B Geminorum. Between « Cygni and y Draconis, below « Cygni. — L A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 41 RN Direction ; noting also | arance ; Train, if any, Length of | whether Horizontal ; é and its Duration. Path. Perpendicular, or ; Remarks. Observer. Inclined. etestinndswdges'es doses pairs ZO ei csecenays|ITCLINEAT «5.755. dddpasweved| -oceosouspqasscapeopstaeversee( (Oe MacDonald: MeNSRNSARGecvradacesecesiD ovens eeenecs iN. to S., inclined POeeEVICOOUUTIVIOS Peery erry TT Terre W. Cc. Nash. Hess; light alternated)......,........ sssseeeessssenssesseseeesseees/AS if a rapidly revolving W. H. Wood. en times a second. light. BPR Eds best coseaces se Se eee Slightly inclined N. of/The only two meteors|Id. W. seen ; night fair. MAST: Bik ies reseed AOS. Ei coger HS sEO WG sas owns pe capaupee A fine meteor ...,........ W. C. Nash. . |e reese BO secseeeee E. to W., inclined ....../Generally cloudy.,.......[d. MME Re sas scnesnc0ces[D°.sccccessecs Perpendicular ...... oaeees| VELY CLOUDY, sairssaveneees. (ECs SR ass duasss06s-|eccsses Sactes od E. to W., horizontally...| Very cloudy..........s.05. Id. ess ; decreased (8°............ WartOnBee Ge deccvecevece Night unfavourable...... W. H. Wood. pidly until lost to ical OO .--/16° to 18° Horizontal from E.to W.|No other visible for 30D. Walker, M.D. minutes. Be ss0%s Mibeendsceescesss-|20° seesessee fSaaswvennc om susecuetesatores. teneeesssescaeeteesssssseseees| We O. Nash, é left trains; coursesi3° to 40°,)...... pbheN s sata stances +29 to 30 per hour atjA. S. Herschel. ight. very va- 10 p.m.; fewer after- rious. wards, “ae ranenvesseseererees) 2 ceesesseeces| 2 sesseeessssssseeseeeseeesas(SeVeral shooting-stars|John Hill. within a short period. il small shooting-|....,.......... General direction from)....sssesceccsessseuess seseeee|W. Penn, S without tails. Bellatrix to « Ori- onis. : AMIDE 53, ssor0nesnubcrdlauts vs4orvasvascd sccsdesloteentessd tees, Herbert M°Leod. nd. ee poses » hi Almost horizontally, S.|.......ccecccccceeseees seeeee| We C. Nash. to N. > NEE About 2°.,./Straight down........ce00/.. peswimuexsts ppeneosctdeeduade i\Herbert M°Leod. 42 REPORT—1862. Hinge ae ; Position, or Date.}| Hour. Obsersat Apparent Size. Colour. Duration. Altitude and servation. | Azimuth al 1861.| h ms Dec.26)11 27 23 (Deal....s0.00.008.-/=y Draconis ..,,...|White .,......:/1 second ......|Appeared _bety p.m. : % and Z Dracon disappeared tween y and | Draconis. 27| 7 55 p.m. Belfast Lough...) =Ist mag.x..+....../ Yellow .,..../2 seconds...,..18° above the : -rizon, near Aurigz. 27| 8 57 p.m. Ibid. ......+++-..|Twice size of Venus|Yellow ....../64 seconds .../\Centre at 8 D conis. 27/10 34 p.m. Weston - super -|=Rigel ..........-.|Bright blue...|Near 2seconds|At appearance Mare. tween 6 and Draconis. 2710 34 p.m.|[bid. .......00ses/=SiTiUS ....++,.0+e-| Bright blue...|2 seconds...... Near d Leonis. 27\11 8 p.m. Ibid. ............8 Urs Majoris |Very dark ...\Less than (Between 6 ané ; (foot). 1 second. Draconis. 31| 7 37 p.m.|Ibid. ............,Larger than Sirius)Very bright |Nearly 3 secs. |Near ¢ Cygni .« 1862. Jan. 2/12 43 311 48 311 49 ll] 7 5 11|About7p.m.|Edgware Road,\Considerably larger|Similar to |SlOW...seseeeeee|eeseeneceeeeeeres and less than} blue. Venus. a.m.|Birkenhead (Sea-]= Venus .....+++... Yellow ......|3 seconds ... rode ree combe). Aldebaran. P-M.|Ibid. seeeceeeesee] —=PFOCYON eevee .. Bluish ........./1¢ second .,./Centre at ha (y Orionis Aldebaran). Pm.TbIds sesss6...060 = Ist mag.x.........|Bluish ...,,,.../4 second ......|Centre almost way (a Ori andyGeminor p-m.|Euston Square, |BrighterthanVenus More yellowSlow move-|Appeared belo London. than Venus,| ment, moon; di in strong peared 3° contrast. Procyon. Kilburn. than Venus. Venus. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 43 | eR a p earance; Train, if any, ahd its Duration. lless FETE Oe Osos eeeeeseee ite tail 16° long ; dis- ppeared nearly simul- aneously with meteor. “Sparks; short evan- cent tail of flame- € character or ap- rance. lar sparks behin lin its descent, which $ particularly slow. Length of Path. eeeeenee Pee eeeeeereeres see eerees oteeeeee .....{[nclined (most) west eeeeee ..|Vertical ; down ...... Direction ; noting also whether Horizontal Perpendicular, or Remarks. Observer, Inclined. isverbebeseveucttevovocncdedcleseiusssdeleddesscecsvisereees| Herbert McLeod, Almost horizontal: jiveih bers ssvevesevseveeccteveiaes D. Walker, M.D. To left ; 52° from hori-|..... hesecavererien ssesyeeet as Id. zontal; down. A little inclined west Position at disappear-|W. H. Wood. ance near the two stars 80 Herculis. of perpendicular to horizon. Inclined north side of perpendicular. side of perpendicular, let fall from its ap- pearance. Path parallel to 3 and y Cygni, from the former towards the latter. Over % Cygni. was an interval of three seconds of time between this and another meteor. They merged from the head of Draco. This meteor in its transit passed exactly midway between a and y Cygni; de- creased before dis- appearance; the sky became overcast for the night; such was the case on the 28th, 29th, and 30th. To right; 45° from ho-|...... SUERSE OUTED 008 eebabad rizontal ; down. To right; 30° from ver-|...... Mo rks eect tical ; down. PP ee ee eee eee Pee eee CeCe eee eee ee ey) The latter half of the|\Observing Venus and path appeared curved.| the moon; clear evening. An) inclined) direction|.:...0dss.ccsee0+.<0eetetes st. from beneath the moon. Near y Leonis............ Id. Near 61 Cygni............ Id. There|[d. D. Walker, M.D. Id. Id. W. R. Birt. C. Herb. Bright. Position, or | Altitude.and _ Azimuth, peared 4° abor} peared near Bootis. 44. REPORT— 1862. Date Hour eee Apparent Size Colour Duration. , : Observation. PP ps ; 1862.;/h m : Jan. 11] 9 43 p.m.|Weston - super -;=Sirius ...... souees Mivid blue... |i2iseevccne Mare. 11/11 48 p.m.|Ibid, ......e+++;=Jupiter .,..+....|Bright yellow |3 seconds, slow notion. 12/0 1 am.|Ibid. ..... seseeee=& (foot) of UrsalA very dark/Less than Major. colour. I second. 25159 O pim:|Ibid, csscasseser- =—Capellassecse-stves Rigel vognersars 2 rips aeane 23\09 “0: p.m.|Ubids” Sianscesss se = Capella. siscssives Reddishyellow 14 second...... Pal9 14. p-m-|[bid. = Vealker, M.D). saceenecesccsscescesveveveeses(As S- Herschel. track left; no sparks.../8°....... ++ee/Parallel to y, « Cassio-|Clear night ............ peel kae peiz. kled ; no track left ...|7°.....,......|Directed from ¢ Persei...|Only two shooting-stars|Id. from 10 to 11 p.m. ee eee 20° fapebiicerteubscsesacapeiae ahewbaweee wablinesis Coeevocrccnevcesegccsesns W. Penn. track left; sparkled ;11° ., ent downwards, and ower at last. rseree/LO left ; 20° from hori-|Fine passing clouds... zontal; down, ...|A. S. Herschel. BEEP ras yarasce-10°;.aopshecs.|LOvlett-s horizontal: AOR: 29°. Radiant Polaris ., From Polaris ............ ———_— OUT Se lemme es Remarks, 51 Observer. FOTO eee renee ee eeere OURO e ee eee eter eee ere Hees seeeee . One meteor in an hour.. eneeee Radiant Polaris ......... SOOO U eRe e eee ee eeeeeeeenes ene Tailed star; Ist mag- nitude; blue; 10° in 3 seconds; tail as- cended and dissipated like steam. eee eeneee eee eeeeeesesees oe eikd, D. Walker, M.D. Id. Id. Robert jun. Craig, W. H. Wood. D. Walker, M.D. Id. W.C. Nash. Id. A. S. Herschel. D. Walker, M.D. A. 8S. Herschel. Id. W. H. Wood. Id. APE eee eee ee ewereraee Fell from zenith to-|, wards the western horizon. FromyPolaris: .. .. «sserseus =one-eighth of |Pale red ,.....'2} secs., SloWasslieapnscdsesesseeeSeean moon. Apr. 3/11 25 p.m.[slington, Lon-|=4th magx......0./White ....5+.0°7 second .,./Centre 1° S. don. pq Camelopa dali. 4,8 10 p.m. mechan - super -|=Ist mag.* .,..../Blue sseeeee../ SECON ese From Sirius... Mare, Al OS pPm|Lbid, ....ssesces-| = 1SH MAL.¥.ss0r000-(DIUC. sesanenee 4 second ,.....\From Jupiter .. bar of light remained about 20 seconds after the first appearance of the meteor. rlike meteor; became suddenly extinct, leav- ing a bar of red light 25° in length, fluctuating between red and orange, and lasting 8 seconds until disappearance. 0 explosion; long di- stinct train of light, disappearing slowly like smouldering twine. 1 turning round, two bars of white light were seen, which en- dured fifteen seconds. aded sooner than the north. vo flashes like lightning, then ran along the ho- izon in one long broad ine, which wrens POPC ewer oeserees track left ........00. Dl eeee Overcast with haze ...!., covered with thick aze, tee eeereeeees eee tere tenes Sere eeeeeens Sebo reese ens Perpendicular to ho- rizon. ...{Perpendicular to ho- Direction ; noting also ppearance ; Train, ifany,) Length of | whether Horizontal, 18 and its Duration. Path. Perpendicular, or Remarks Inclined. O track left; no sparks...J15° .....06../EYOm Polaris .sssecessssseccessescssvvescnsneeresees ne Light train ..,.00.4,..seeeeeeleceeseeeeeeeees An the N., fell from thel..... svaiiebgn@utienlen tes essai behind the houses. horizon. pressed 2° or 3°. ..(From E. to W. by S. ....,/Slightly inclined to the|Jupiter horizon. position, especially to the S. ? sesseseeeees/A little inclined ...,...../Sky obscured at 10 p.m. cal; down. Perpendicular horizon. Directed from .o Urse Majoris. rizon. zenith, disappearing E. to W,, at an angle of|The tail faded gradually, about 80° with the E. to W., nearly hori-lcsccecsscccoosscnsesscovarves zontal; west end de- To left; 30° from verti-|, to the}.. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. no change. streeeeecevesererssussereesess Studley Martin. appeared shine brighter when the bars disappeared than he did before. Parallel to the horizon,|/The stars seemed to go| James yet in a descending inclining out on that side of the hemisphere, and did not recover their brightness for half an hour, One star in an hour;/A N.W.; cloudless. Fell one per hour -|A. S. Herschel. to/T. Juman. W. H. Wood. Id. Id. W. H. Wood. Id. 53 Observer. J. MacDonald. Correspondent to ‘ Liverpool Mercury.’ W. H. Wood. Caswell and Son. Sebo merece eeeeaenes . S. Herschel. 54 Date. Hour, 1862.| h m Apr.14| 7 42 p.m. 17/10 10 p.m. 20) 8 30 p.m. 23) 8 56 p.m. 23] 9 50 pm. 23/10 35 p.m. 10 26 p.m. 25 2510 30}p.m. 2610 52 p.m. 26/10 524 p.m. 27| 8 42 pm REPORT—1862. Place of ‘ | Observation. Apparent Size. Colour. Clerkenwell, 8 to 10 times as|White ....... -- London. bright as Jupiter. Hitchen .....0...|FiN€ MetCOL...cervesleccsecsesebererers Greenwich Hill..|Larger than Jupiter) ? ....,.se000... Weston - super - Larger than Ist |White .,,...... Mare. mag.* Thid. ssessseeeeee|Nearly as large as|Deep yellow... Jupiter. St. John’s Wood,|Brilliant body of mri colour- London. light. 11 33} p.m. 10 30 p.m. Position, or Duration. Altitude and Azimuth. 3 seconds...... From 10° or 12 over Jupiter altitude 32°, by W. 3 seconds,.....|From4}(a Ursa Ma joris and Pola to centre of C¢ rona Borealis. | ...|Between p and _ Camelopardali. 16 Draconis y Draconis, — close and para to « and y Dr conis. f »|From Arcturus 18/ Bootis. 2 seconds Slow ; 14 sec. Slow ; 2 secs. Between N. and ; altitude 45°. | | 7 seconds...... Weston - super - =Ist mag.*......... Brilliant blue..|4 second ...... At appearance ni Mare. 41 and 42 melopardali. Islington, Lon-|=Pollux .......660.. Pollux ..........0°4 second ...|From 1° S. don. Camelopardus. Weston - super -|=Spica Virginis ...|Spica Virginis |} second ......,At appearance Mare. 66 Virginis. Ibid.) > dieswieins = Spica Virginis ...|Spica Virginis |? second ......|66 Virginis .... MIO sessezeders VENUS ....-c0cses| VENUS 400-400. 1 second ......|From #1 Cy passing bety the head sta Lacerta. | Birkenhead (Sea-\-=Jupiter .........,Blue .........,24 seconds ...\Close to jp He combe). culis. | Greenwich ......,=2nd mag.* ...... Reddish ......! 1 to 2 seconds From the direeti | of Urse M | towards _ the » horizon =p Arcturus. pearance; Train, if any, and its Duration. $$. —— Year-shaped; no track visible through clouds; faded gradually, and disappeared quietly; very slight train. rocket. tationary; varied little in brightness. ursued by faint phospho- rescent train. 0 track; disappeared and reappeared three or four times. ket-like, but kite -| shaped; left a few Sparks for half a second on dying out. OTE seceesceccevcceressecees 0 track;. no sparks; a train like & sky-|..ccccssssccss Direction ; noting also whether Horizontal Perpendicular, or . Remarks. Inclined. fe ator ar | _ Lowmight:;.. 20° frommhoe|Nivcscacosescoeeeeevane.ves rizontal ; down. Seen ee eee eernarees eee eeetenee SOHO OR eee ee eter ete teesees SOOO O ROTO ee EF Cease Eee HOSE TUTE E EE OH ee eeae 9° ~ brightest in the middle. tin visible three seconds; urst at last with strong light; pink, and bright as Venus. MBSE DSS c ce ccicctcccccccesccees s 5° came suddenly ex- tinguished. 15° ........./To left; 30° from verti-|..........00 Pet Re Tree G 15 eeetrsaeeees or 3° 4... see eeeeeeeee seen eeeeenes ° Horizontal, W. to E., inclining downwards at last. Inclined west of +...... Toleft ; 35° to 40° from vertical ; down. Ditto, west side of vertical, at an angle of 75°, Inclined 65° west of + Inclined Bate ee eee erewenee A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. Strong twilight; quite overcast ; rain falling. PORROO eee mete rene ener eteaetee POPE OO eee eee eee e terete ees HERO OP Hee et orerereseeeeees FERRET CORO e ee ee ee et eeeesaees | [TSE PPR ene eneees Pee eeeneneeens Increased in brilliancy... Only one other star in the hour; very faint ; cloudless. TOPCO eee e rere eeeeenseneee eae FARR E ee Oe eee e esses eteeeees Appeared first as a cal ; down. second magnitude star, and _ gradually increased until equal Venus, when it be- Observer. T. Crumplen ; A. S. Herschel. Communicated by W. Penn. W. Airy. W. H. Wood. Id. Id. A. S. Herschel. W. H. Wood. Id. Id. .|\D. Walker, M.D. W. C. Nash. Position, or Altitude and Azimuth. | Dropped from 4 near Polaris iff a N. by E. die rection toward§ the horizon. | 5° beneath 3 (6 and! y Herculis). 4% Centre 3 (y Ser pentis and Herculis). Centre 2° below 7 Serpentis. From Z (Crateris to y (Corvis). From Ursa Major. to 14° S. @ Cassiopeiz. From 4 (4g p) L Camelopa dali. Ky 56 REPORT—1862. Date.| Hour. ms tne oe Apparent Size. Colour. Duration. 1862. h m | | Apr.27, 8 51 p.m.,Greenwich ...... =2nd mag.* ...... Yellow seeesseee second ,..... 2710 10 p.m. Birkenhead (Sea- = Venus ....... wove [Blue — ..seeeeee/4 SECON cesses combe). | 27/10 50 p.m.|Ibid. ............ = Jupiter.......0....) Whitish ....../4 second ...... 27:11 25 p.m.|Ibid. .. Sy Wipe ebereceece- [Bluish ...000... % second ...+.. 2810 46 p.m. Weston - super -|=2nd mag.* ....... Blue «.-sss0e ld second «., Mare. oa 9 53 pan(Ubid, cesvecsoens| lat Mapes... White .....000- 1 second, fast.. 2911 6 p.m.Islington, Lon-|=Capella............ ;Capella......... \0°9 second ... don. ZOW 33. p.m. Ebi... s.csearcene =o Urs Majoris..!o Urs Majoris 0-1 second ... 2911 37Ep.m.|[bid. .s.sseseeoee =o Ursx Majoris../oUrsz Majoris|0'2 second ... 29/11 55 p.m.Ibid. .....- .eeeee/Half as bright as)White, then)4°5 seconds; Jupiter. red. exceedingly slow. May 21/10 27 p.m.| Weston - super -|=2nd mag.* ......;Blue ......4 1} second ... Mare. 24/10 10 p.m.iIbid. .......0000 =Ist mag.x «..... Yellow ........./2 seconds...... 25/10 40 p.m. Ibid. .....es.e00.,= Ist mag.# 4.0... Blue ..|14 second ... 25/10 55 p.m.|[bid. ......eeeee- Nab ig | vwacesss mle aem.|EDIds © sp eccescsases =Ist mag. sess. Yellow ...... Dl 22) terns |EDids. cecesveneaes = 2nd mag.* ...... BUC... .wcsverees mL 24> arm IEDId. cs ccswenes =2nd mag ...... Blue .eesseoee 3) LT 35 fam, |[ DIG... ccsasesesees =Capella.........0.. Blue ..e.sseee 3) 1 44 am. |[bid. ....00.0...,=2nd mag.x ..e../Blue © seececeee 210 15 p.m.|Greenwich .,,...;=3rd mag.x ......, Blue ...seeee 310 47 p.m.|Weston - super -|=2nd mags. ...... Blue: ~sssapsees Mare. ..../L second ,,..../From y Serpent ./24 seconds .../R. A. 20 minu .-/x Second ....../8 Pegasi .. From % Pegasi.s 1 second .,....|From 0 Pegasi. | 4 second ......;Head of Capi cornus. % second ,,....|¢ Pegasi .. 4 Second .,..../y Serpentis . % second ......)y Aquarii ss..6u % Second ...... 19 Aquarii ... D.S. 3° to B 23 hours 207) nutes, D. S. 3 % second ...... Markab ....... SECOUG.. .vess|accocsstewes cae 4 second ...... Markab ....008 Ll second ...... a Andromede ¢ Scheat. .|(36) Ursee Maj to horizon. From « Pegas a Aquarii. a Pegasi «eevee $ second .... 1 second ,..... } second A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 61 Direction ; noting also jearance; Train, if any,| Length of | whether Horizontal, and its Duration. | Path. Perpendicular, or Remarks, Observer. | Inclined. 1 ee oda MEeoutGs 208 | ete vane aren beheaded qiteaeapunbene: ..../W. C. Nash. POTEET H REPRE eee ete eeee 27° eeteeee Pee eee OPO POOR UOC OCU COCCOOCCO OO OCOCOCO CE TT eee eee eben eeeeee eeeereee Id, PMN nraetdadaederentietel LO! des ceca. Sarees emun eased Tree Sbeveaveveved suns wecviveveatiIG. | See PEME docvcvaceds| 2D gveeseacl,« vied Woah cavercendt vat eaere seuss TR ES (Id. MMA on gRiatidgh sve ry0s00e+|20.cesseccelecneccscccsecsescccooccesess ail ve dees coteeter ects ob vceceses Id. SR Tetasiraclte)” CO20° fo... cn cceaccocessscaseeuvs|oncseeteertovcseeienscteseaten {Ads Puen eeeencrenens teeeeles PORE PO Ree e eee ceeeeee Peeeereeeere seeecceers JA red thick tail curled iW. H. Wood. off from nucleus and| disappeared within the latter. en peCdece}scceseeclLO° .cessvees Horizontal ...... dessuseeereross eccaascashiccsses vases Id. TERE vccpcrcesoee/LO” ,.csevees MOWATOSSic cesecesseseee> Great numbers left un-|Id, recorded between 105 42" and 115 45™, RUM eisvbysonsosse( LB dvvieede. Horizontal, westward...|Tail endured 23 seconds Id, SEM ccshecccsses|LO°” cienveces ELOTIZONEAL, Siicasaddeieacchvesspescangameadessseenetees Id. OS Se eee MOP es capeenss Horizontal, S............. /Tail endured 2 seconds..\Id. SPR eee eee eee ee etee be) STEPH eee eee eee eee ee ee Peeeeeeretene Sah does EREUR sc cbesecsees MOS a éhecas. Near at! wen 6-7 31 The method and apparatus employed for the above determinations, together with the precautions taken to ensure correct results, have already been describedt. We have made only three observations between 0° and 100°, for it was found that they gave almost exactly the same formule for the correction of the conducting power for temperature as if we had taken seven or more observations between 0° and 100°. Each of the above values for the conducting power, at those temperatures, is the mean of three or more observations. It was easy to obtain the desired temperatures as a mean of several observations, after very little practice. I have no doubt that, in the course of our experiments, we shall be able to find-an alloy, the conducting power of which will decrease between 0° and 100° even less than that of silver- platinum. The experiments are being continued, and I hope, before the next meeting of the Association, to be able to lay before you results which will throw more light on the subject, as well as to propose an alloy with a minimum variation in its conducting power due to change of temperature, which may be made commercially in a cheap manner of the common com- mercial metals, and possessing those properties which are essential that it should have. Apprnpix B.—On the Electrical Permanency of Metals and Alloys, By Dr. Marrmessen, F.2.S, Having, in conjunction with Prof. Thomson, been requested by your Com- mittee to make some experiments on this subject, we thought it advisable for one of us to undertake some preliminary experiments in which all possible disturbing causes were isolated. The chief of these are, oxidation by the oxygen of the air, as well as by acids produced by the oxidation of the oil or grease with which a wire is almost always covered when drawn, as the holes in the draw-plates are generally oiled or greased; stretching during the process of covering and winding ; and after being wound on the bobbin, elon- gation by expansion or contraction, owing to variations of temperature, &c. These, I think, have been obviated in the following manner :—The wires were carefully wound round a glass tube in order to bring them into a smaller compass, and after taking them off, they were placed inside wide glass tubes, and soldered to two thick copper wires, these having been previously passed through corks which fitted into the ends of the glass tube ;. through each of the corks a small glass tube passed, drawn out in the middle to enable it to be * Phil: Mag. Feb. 1861. + Phil. Trans. 1862, pt. 1. t Ibid. 140 , REPORT—1862. drawn off easily, and sealed hermetically bya lamp. The wire being soldered to the thick copper connectors, and the corks fitted into the tube, dry carbonic- acid gas was led through it for the space of about six hours, for the purpose of drying it perfectly, as well as of displacing the air contained in it; after which the small glass tubes were melted off at the points, when they have been previously drawn out. Tin caps, filled with melted marine glue, were then fitted over the corks and the ends of the tube, to prevent diffusion of the carbonic acid and air through the corks. The whole of the tin caps outside, as well as those parts of the copper-wire connectors which dipped in water of the bath in which they were placed whilst being tested, were covered with a thick coating of marine glue. The wires experimented with were as follows :— 2, Silver: annealed -........, f Cut from the some piece; pure 3. Silver: hard-drawn ....:... ees from the same piece, but different 4, Silver: annealed ,...../... {from 1 and 2; pure. . Copper: hard-drawn ...... : é io annealed . grccitier syn orgie mag baka bat 1 7. Copper: hard-drawn ...... Cut from the same piece, but different 8. Copper: annealed.......... from 5 and 6; pure. 9. Gold: hard-drawn ........ C ‘ 10. Gold: annealed.....:....:. mi from the Same pices _ pure. 11..Gold: hard-drawn.......... Cut from the same piece, but different 12., Gold :,annealed.... .«.¢.2.-+s+ from 9 and 10; pure. 13. Platinum: hard-drawn 14. Platinum: hard-drawn F 15. Gold-silver alloy : hard-drawn | Cut from same piece. Made by Messrs. 16. Gold-silver alloy; hard-drawn { Johnson and Matthews. 17. German silver: annealed .... Cut Homie, same, misee "giles 1am 18. German silver: annealed.... Tapped ims sdomper connectors, and 19°C danaey wil var AGE aIad used as normal wire with which the f ; rae rest were compared. ‘*** | Cut from the same piece ; commercial. The reason why duplicates were made in each case was that, in case any of them should by any cause get damaged, the experiments might be continued with the duplicate. When being tested, they were placed in a large bath containing from 40 to 50 litres of water. By testing the wires at 20° it was found easy to keep that temperature in the bath, during the experiments, to 0-1° or 0:2°. Up to the present time, that is to say, four months since they were first tested, the conducting power of the wires 1, 3, and 5 has altered, owing to becoming, in all probability, partially annealed. Wire 8 has also altered mate- rially, having decreased in conducting power 3:5 per cent.: this decrement may be possibly due to bad soldering. The differences found with the other wires are so very small, that it is impossible to say whether they have altered or not; for 0:1° or 0-2° will account for them. It was, therefore, thought better to wait for another two or four months before giving an opinion as to whether they alter or not; for as the wires are in tubes and only surrounded by carbonic acid, we can never be absolutely sure that the wire has exactly the same temperature as the bath, more especially when it is considered that each time the con- nexion with the battery is made the wire becomes somewhat heated. If, two or four months hence, they still show no difference in their con- ducting powers, it is proposed to expose the one set to variations of tempera- ON STANDARDS OF ELECTRICAL RESISTANCE. 141 ture such as may occur (for instance, from 0° to 40°), and then, should no change occur in their conducting powers, to lead a weak current through them, say, for a month; for it has been asserted that a current passing through wire causes a permanent change in its conducting power. If after these experiments the conducting power of the wires remains un- altered, the different forms of resistance-coils, made from those wires, which have shown themselves permanent will then be tested in order to prove which is the best form of coil for the British Association unit. Apprnnix C.—On the Reproduction of Electrical Standards by Chemical Means. By Professor Wiitrauson, F.2.S., and Dr. Marrutessen, F.R.S. In the following Report we have discussed, more especially from a chemical point of view, the relative merits of the different propositions which have been made to reproduce standards of electric resistance, and haye treated them under three heads :— I. Those reproduced by a given length and section or weight, at a given temperature, of a pure metal in a solid state. Il. Those reproduced by a given length and section or weight, at a given temperature, of a pure metal in a liquid state. Ill. Those reproduced by a given length and section or weight, at a given temperature, of an alloy. The points on which we shall speak will be— 1. On their preparation in a state of purity. 2. On their homogeneity and their molecular condition. 3. On the effect of annealing on their conducting power. 4. On the influence of temperature on their conducting power. I. Those reproduced by a given length and section or weight, at a given temperature, of a pure metal in a solid state. As type of this class we have chosen copper, for it has been more exten- Sively used as unit of electric resistance, both by scientific as well as by practical men, than any other metal or alloy ; but what we are about to say regarding copper will hold good in almost every case for all pure metals in a solid state. 1. On its preparation in a state of purity.—As traces of foreign metals materially affect the conducting power of most pure metals, it is of the utmost importance that those used for the reproduction of units of electric resistance Should be absolutely chemically pure. The difficulty in obtaining absolutely pure metals even by chemists is very great. Thus, for instance, Becquerel* found the conducting power of pure gold at 0° equal to 68-9, compared with that of pure silver at 0° equal to 100; whereas, under the same circumstance, - Matthiessen and von Bose found it equal to 77:9,—showing a difference of about 12 per cent. in the values observed for the conducting power of gold, prepared pure by different chemists. This difference may be due to the silver not being pure, or to all of them being more or less pure. Now when we consider that these standards are required by electricians and other physicists who have little or no acquaintance with chemical manipulation, and that the cost of the preparation of absolutely pure metals by scientific chemists would be very expensive on account of the time and trouble they require, we think that this fact alone constitutes a very serious drawback to their use * Ann, de Chim. et de Phys, (1846) t. xvii. p. 242, + Phil. Trans. 1862, pt. 1. 142 REPORT—1862. as a means for the reproduction of standards of electric resistance. From the experience which one of us has had on this subject, it is more than pro- bable that if pure metals be-prepared by different chemists in the ordinary way of business, variations in their conducting power would be found equal to several per cent. Thus, copper supplied as pure by a well-known assayer had a conducting power equal to 92, whereas pure copper conducts at the same temperature 100*, Again, the pure gold of the assayer conducts only 65-5, whereas pure gold at the same temperature would have a conducting power equal to 737. In order to show that the conducting power of com- mercial metals varies to a great extent, we give in the following Table (X.) the values found for that of the different coppers of commerce ; and it will be evident from it,.that to take a given length and weight or section of a com- mercial metal as unit, as has often been done, is very wrong, and can only lead to great discrepancies between the results of different observers. Taste X.t (All the wires were annealed.) Conducting power. BUTE COP POLY Pela: -hssras Sig oi0.a8~ so8. aye ois 100-0 at 15:5 Lake Superior native, not fused ........ 98°8 at 15°5 Ditto, fused, as it comes in commerce.... 92°6 at 15-0 MVOC ES LUA < evens ite iss aoekec ste Riagals ob, 20muate 88-7 at 14-0 IBesiselected ss Seth Br acca aes tinea 81-3 at 14:2 Bright copper wire. lw jwene iledle 72-2 at 15°7 Toush Coppers: . «cepa eo beware Hey 71:0 at 17°3 Dem 5 FAS 5. a nicne ali ated dutin tae 59-3 at 12:7 iO WN 5 a sa derahaats, a2 NS his Dame me 14-2 at 14:8 Similar variations will be found with most other metals, and we shall give examples of these further on. 2. On its homogeneity and its molecular condition.—It is well known that the wires of some metals require much more care in drawing than in others: thus, copper and silver, if not annealed often enough during the process of drawing, will often become quite brittle, and break off short when bent. Now, if the fracture be closely observed, it will be seen that the wire is hol- low; in fact, wherever it is broken, cavities will be found, and sometimes of a millimetre or two in length; so that such a wire may almost be regarded as a tube with a very fine bore. The reason of this is simply that in not an- nealing the wire often enough, the internal part of it becomes hard and brit- tle, whilst the outside remains annealed, from the heat evolved by its passage through the holes of the draw-plates ; after a time, however, the inside, being very brittle, will give way, whilst the outside is still strong enough to bear the force used in drawing it through the draw-plates. These places in the wires are easily discovered on drawing the wire finer; for then at these points the wire slightly collapses, owing to the quicker elongation of the weak points by the force used in drawing. Silver and copper are the only metals which have been experimented with in this manner ; we are therefore unable to say whether it may occur with the other metals. However, although no such wires could be used for experiments, yet what has been shown possible to occur to such a marked extent when purposely trying to obtain such results, may occur * Proceedings of the Royal Society, vol. xi. p. 126. + Phil. Trans. 1860, p. 176. t Report of the Government Submarine Cable Committee, p. 335. ON STANDARDS OF ELECTRICAL RESISTANCE. 143 to some slight extent, especially when great care is not used, and when the wires are drawn by different persons. This may explain why, with some metals and alloys of the same preparation, conducting powers are often obtained which vary several per cent. For instance, W. Thomson* found the conduct- ing power of several alloys of copper which he had had made and tested to alter considerably on being drawn finer; some of them were faulty from the cause we have just mentioned, and, on their being drawn finer, these places showed themselves, and were then cut away. It has also been showny that when copper wire is heated to 100° for seve- ral days, a permanent alteration takes place in its conducting power: thus, with the first wire experimented on, it increased almost to the same extent as if it had been annealed. With the second wire the increment was not nearly so large as with the first, and with the third it hardly altered at all. That this is not due to one or the other of the wires being faulty in the just- mentioned manner is proved, 1st, By the close agreement in the conducting powers. 2nd, By the close agreement between the differences in the values found for the conducting powers of the hard-drawn and annealed wires. They were— 1st wire 2nd wire 3rd wire at 0°. at 0°. at 0°. Hard-drawn ........ 99-5 100-0 100°3 mmealed ss... voy. 101°8 102-1 102:2 The values given for the hard-drawn wires are those which were observed before the wire was heated at all. 3rd, That the same occurs with pressed wires: thus, with bismuth it was found that the pieces of the same wire behaved differently ; wire 1 showing, after 1 day’s heating to-100°, an increment in the conducting power of 16 per cent., whereas wire 2 increased, although a piece from the same length of wire, 9 per cent. Again, take the case of tellurium, and taking the conducting power of each bar at first equal to 100, we find that the conducting power of bar 1 had decreased after 13 days’ heating to 4, where it then remained constant, that of bar 2 after 32 days became constant at 19, and that of bar 3 after 33 days at 6. The cause of these marked changes in the conducting power must therefore be looked for in the molecular arrangement of the wires or bars employed. In the case of copper, they may be, and probably are, due to the partial annealing of the wires ; for we find that wire 1, although the conducting power increased after having been kept at 100° for several days almost to the same extent as if it had been annealed, yet, on annealing it, it only gained as follows (the results obtained with wires 2 and 3 are added) :— 1st wire 2nd wire 3rd wire at 0°. at 0°. at 0°. Hard-drawn ............ 99°5 100-0 100°3 After being kept several j - ‘ days at 100° re RM RW Tsk sy cl ene pe After annealing.......... 101'8 102-1 102-2 The above shows that, in all probability, the annealing plays here a part, but not the whole, in the change ; for otherwise why do the wires behave dif- * Proceedings of the Royal Society, vol. xi. p. 126. t Phil. Trans. 1862, pt. 1, 144 ; REPORT—1862. ferently? This point will be fully discussed in another Report which will be laid before your Committee, and in which it will be shown where the hard- drawn wires become partially annealed, and annealed wires partially hard- drawn, by age. It is a curious fact that a change in the molecular arrangement of the particles of wire of some metals which may be considered homogeneous has very little effect on its clectric conducting power. Thus pure cadmium*, which when cold is exceedingly ductile, becomes quite brittle and crystal- line at about 80°, and returns again to its ductile condition on cooling, shows no marked change in its conducting power at that temperature ; in fact, it behaves asif no such change had taken place. Again, when iron wire is heated in a current of ammonia it becomes perfectly brittle and crystalline, without altering its conducting power to any marked extent. That a wire which changes its molecular condition in becoming crystalline does not necessarily materially alter in its conducting power, is an important as well as a very interesting point, and has also been proved in the case of German silver. 3. On the effect of annealing on the conducting power.—When hard-drawn wires of silver, copper, gold, &e., are heated to redness and cooled slowly, they become much softer, and on testing their conducting powers they will be found to have increased thus :— Silver. Copper. Gold. According to Taking the hard-drawn WATE) 2). Sidr Her! 100-0 100-0 100-0 The annealed will be.. 107-0 102-6 101-6 Beequerely. iid cee itr aot 1090 1023 1020 | a von Boset. Ditto wed saaidatsliia. « 110-0 106-0 — fS&emens$§. Now there is a certain difficulty in drawing a wire which is hard-drawn ; and if annealed wires be used for the reproduction of standards, the molecular condition, or perhaps the process of annealing, has an influence on the incre- ment of the conducting power. Thus, according to Siemens|', the difference in the conducting power between hard-drawn and annealed silver varies be- tween 12:6 and 8 per cent., and that of copper between 6 and —0°5 per cent. ; according to Matthiessen and von Bose@, that of silver varies between 10 and 6 per cent., and that of copper between 2-6 and 2 per cent. Again, the annealed wires of pure metals are so soft that they would easily get damaged in covering them with silk or winding them on the bobbins, so that in using them the utmost care would have to be employed in order to prevent their getting injured. 4. On the influence of temperature on the electric conducting power.—It has been shown that the conducting power of most pure metals decreases, between 0° and 100°, 29-3 per cent.: pure iron has been found to form an exception to this law, its conducting power decreasing between those tempera- tures 38:2 per cent. If pure metals be therefore used as standards, very accurate thermometers are necessary, as an error of 0-1° in comparing two standards would cause an error in the resistance of about 0-04 per cent. Now there is great difficulty in obtaining normal thermometers; and we must * Phil. Trans. 1862, pt. 1. t Ann. de Chim. et de Phys. 1846, t. xvii. p. 242, {+ Phil. Trans. 1862, pt. 1. § Phil. Mag. Jan. 1861. || Phil. Mag. Jan, 1861. *| Matthiessen and Vogt’s unpublished researches. ON STANDARDS OF ELECTRICAL RESISTANCE. 145 bear in mind that supposing the zero-point of the thermometer is correct to- day, we are not at all justified in assuming that it will be so in six months time ; so that we ought to redetermine the zero-point of the thermometer be- fore using it for the above purpose. Again, it has been proved that the in- fluence of temperature on the conducting power of wires of the same metal is not always the same*. Thus, for the conducting power of annealed copper wires the following values were found :— d, No. 1. No. 3. 0 100-0 100-0 20 92°8 92-4 40 86°3 85-6 60 80:4 79-6 80 751 74:4 100 70:5 70-0 showing therefore that if standards of pure metals be used, the influence of temperature on the conducting power of each would have to be ascertained. It must also be borne in mind that it is not at all easy to maintain a stand- ard, even in a bath of oil or water at a given temperature, for any length of time. II. Those reproduced by a given length and section or weight of a pure metal in a liquid state. The only metal which has been proposed to be used in a liquid state for the reproduction of units of resistance is mercury. We shall only have to speak of its preparation in a state of purity, and on the influence of tempe- rature on its conducting power. For a tube, carefully filled with mercury, will certainly form a homogeneous column, and its molecular condition will always be the same at ordinary temperatures. On its preparation in a pure state—Although this metal is one of the most easily purified, yet the use of it as a standard is open to the same objec- tions, although in a less degree, as have been advanced against the use of pure metals in a solid state when speaking of their preparation. We there stated that metals prepared by different chemists conducted differently. Now although the same manipulator may obtain concordant results in purifying metals from different sources, yet that by no means proves that the results of different observers purifying the same metal would show the same concor- dance. Thus we find that the values obtained by one experimenter} for the resistance of mercury, determined in six different tubes, varied 1:6 per cent. This difference, he says, is not greater than was to be expected. The resist- ances found were as follows :— Tubes. ie II. ITI. IV. aVic VI. Experiment... 101652 427-28 555-38 217-73 194:70 11423 Calculated .... 1025°54 427-28 555-87 216-01 193-56 1148-9 Again, the values found for the conducting power of different preparations of pure hard-drawn gold, by the same observer ¢, were found equal to * Phil. Trans. 1862, part 1. + Phil. Mag. Jan. 1861. The same experimenter (Dr. Siemens) states, however, in a later paper (Pogg. Ann. cxiii. p. 95), that he is able to reproduce standards of resistance by means of mercury with an accuracy equal to 0:05 per cent., but does not indicate what other precautions he takes (see remarks on the above, Phil. Mag. Sept. 1861). { Phil. Trans. 1862, p. 12. 1862. L 146 REPORT—1862. 78:0 at 0° 78-2 at 0° 76:8 at 0° 79-5 at 0° 78:3 at 0° 76:7 at 0° 77:0 at 0° 78:0 at 0° 77:3 at 0° These values agree together as well as might be expected, considering that 0-01 per cent. impurity would cause these differences. Now the values obtained by different observers vary between the numbers 59 and 78. If we now take the case of copper, the values found by the same experi- menters* for different preparations of the pure hard-drawn metal were— 99-9 at 0° 99-4 at 0° 99-8 at 0° 101-0 at 0° 99:4 at 0° 100-3 at 0° 99-8 at 0° 99-9 at 0° 100-0 at 0° 99-9 at 0° They were drawn by themselves, and all, with one exception, electrotype copper. It is well known how differently the so-called pure copper conducts when prepared by different experimenters. In the following Table, in order to show these facts more clearly, we have given the conducting powers of the metals, taking that of silver equal 100 at 0°. Silver, copper, gold, and pla- tinum were hard-drawn. All values given, except where the contrary is mentioned, have been reduced to 0°, Siemens. Lenz. Becquerel. | Matthiessen. Silver Peele. 2 100 100 100 100 Copper ..vessecseess 96-9 73-4 95:3 999 iy A keae. dsereeck a fhistores 585 66°9 780 PERT eee Ae ae Ce eee 26°3 23°7 WANG ecetversereceseW ta Leeeseee © Ln peesies 25°77 29°0 EDEN cecauerogssrsgessf) le pestes 22°6 15:0 12°3 WTO feycseseses|) cesses 13°0 131 14°4 at 20°4 HCC RIES, th of an inch, when a new degree of approximation to equality, with an error of not more than 0-01 per cent., will have been reached. Then the coils A,, C, are changed for a fresh pair, A,, C,, with a resistance equal to about 10,000 inches of the wire WX: one-tenth of an inch on WX will then represent an error of only 0-001 per cent. By a repetition of this process, quite independently of any absolute equality between the pairs A, O, A,, ©,, A,, ©,, &c., a gradual approximation to any required extent may be ensured. The delicacy of the galvanometer used, and the nicety of the means available for increasing or diminishing the resistance of R, form the only limits to the approximation. A slight want of equality between any pair of arms will simply bring the point U a little to one side or the other of the centre of WX, as the final adjustment with that pair is made, but will not affect the truth of the comparison between R and S. Each pair must, however, be so nearly equal that the addition of part of the short wire, WX, to one side will be sufficient to correct the other; otherwise the adjustible point U would not bring the index to zero, even when at one end of the wire. This arrangement, besides rendering us independent of the accuracy of any two arms, has some incidental advantages of considerable practical importance. At éach test it gives a measure of the amount by which the new coil to be adjusted must be lengthened or shortened. The test is at first comparatively rough, or adapted to errors of one or two per cent., and only gradually increases in delicacy as the desired equality is more and more nearly approached. It is not necessary that the resistance of WX should remain absolutely constant, since it is only used (numerically) to give a rough approximation to the percentage of error. It is desirable that the battery should remain in circuit as short a time as possible; the circuit is therefore broken between 1 and 2, figs. 7 and 8, by a key, K, with which _ contact should be only momentarily made, when all the other connexions are complete. The direction of the jerk of the galvanometer-needle to one side or the other need alone be observed ; no permanent deflection is required with this arrangement as a guide to the amount of error. This is a considerable advantage, inasmuch as it avoids heating the wires, and saves time. The om’ of the coils on themselves might lead to some false indications, 862, M 162 3 REPORT—1862. unless special precaution were taken against it, as pointed out by Professor W. Thomson*. To avoid this source of error, the galvanometer circuit is broken between 3 and 4, figs. 7 and 8, at K,, and should only be closed after the battery circuit has been completed at K and equilibrium established throughout all the conductors. Before passing to a detailed description of the apparatus as actually con- structed, some remarks are required as to the means of making temporary connexions. All connexions which require to be altered may be the means of introducing errors, inasmuch as the points of contact are very apt to offer a sensible but uncertain resistance. In measuring small resistances, the resistance at the common binding-screws is found to create very considerable errors. Binding-screws have therefore to be ayoided at all points where an uncertain resistance could cause error. Mercury-cups, made as follows, have been found in practice very suitable for temporary connexions, and have been adopted in the apparatus. The bottom of each cup is a stout copper plate, with its surface well amalgamated, forming one of the two terminals to be joined. A stout copper wire, 1 inch in diameter, with a flat end well amal- gamated, forms the other terminal. When the amalgamation is good, and care is taken that the wire shall rest on the plate, this form of connexion offers no sensible resistance. The amalgamated wire is easily kept bright and clean by being dipped from time to time in a solution of chloride of mercury and wiped. The copper plate should also be removed from the cup, cleaned, and re-amalgamated occasionally, All permanent connexions should be soldered. The apparatus itself, as actually constructed, will now be described (figs. 1 to 6). It consists of a wooden board, about 12 in. x 7 in., containing the mercury-cups, the adjusting wire, WX, the key, K, and the terminals to which the battery and galvanometer are connected. The letters in the figures 1 to 6 correspond exactly to those used in the diagrams 7 and 8; and the apparent complexity of the connexions can thus be easily disentangled. cc,, aa, are two pairs of mercury-cups, into which the terminal wires on the bobbin, C, A, dip. This bobbin contains the two coils, C and A, forming the arms of the balance. rr, and ss, are mercury-cups, into which the terminals of the standard and coil to be adjusted are placed. These mercury- cups are so connected with the four cups, d,d,, f,f,, that when d is con- nected with d,, and f with f,, by a couple of wires in a small square of wood, D, then A, C, 8, and R are connected as in fig. ’7; but when D is turned round, so as to connect d with f, and d, with f,, A, C, R, and S are connected as in fig. 8. D is called the commutator. The same end might be effected without a commutator by simply interchanging R and §; but it is frequently incon- venient to do this. All these connexions are made by short stout copper bars, dotted in fig. 2. The wire WX, the sliding brass piece H, carrying a spring for the contact at U (fig. 4), and the scale E, by which the position of H is observed, will be readily understood from the drawing. The sliding piece, H, is connected with the proper points by the helix of copper wire, A, and the serew, I. GG, and BB, are common binding-screws, to which the wires from the galyanometer and battery are attached. K is the key, by depress- ing which, first, the battery is thrown into circuit, and then the galvano- meter. It consists of three brass springs, 1, 2, 3 (fig. 5), each insulated one from the other, and connected by three screws, 1, 2, 3 (fig. 2), with the necessary points of the arrangement. A fourth terminal, 4 (figs. 2 and 6), * Vide Phil. Mag, August 1862. ON TEE GRANITES OF DONEGAL. 163 is immediately under the free end of the springs, and is armed with a small platinum knob or contact-piece. The three springs are also all armed with platinum contact-pieces, all in a line one above the other (fig. 6). When the finger-piece, T, is pressed down, 1 and 2 are first joined, and then 3 and 4; 3 is insulated from 2 by the vulcanite, Q. All the connexions per- manently made, under the board, are shown in fig. 2. Those which have no sensible resistance are stout copper bars, and form the bottoms of the mer- cury-cups: those of which the resistance is immaterial are made of wire, insulated by gutta percha, and are simply shown as dotted irregular lines in fig. 2; they will be found, on comparison, to correspond with the thin lines on fig. 7. It will also be found that all those parts shown by thick lines in the diagram are made by thick bars or rods and merecury-cups. _ Three sets of arms, C A, C, A,, C,A,, are provided; the shortest pair is first used, and U adjusted by the slide, H, till the galvanometer does not de- flect when T is pressed down. The commutator, D, is then turned round, and U adjusted afresh. The coil, R, is then altered according to the two positions of U, and this process repeated, using the second and third pair of arms as required, until the desired approximation between Rand § has been obtained. An astatic galvanometer, with a very long coil, will, for most purposes, give the best results; and one or two elements will be found a sufficient battery. The construction of R and S$ recommended, and the pre- cautions to ensure perfect equality of temperature, will form part of next year’s Report. The apparatus, although specially designed for the production of equal coils, is applicable to ordinary measurements of resistances by comparison with a set of resistance-coils; for this purpose the terminals of the resist- ance-coils should be put in the place of the standard 8, and any conductor of which the resistance is to be measured in the place of R. If a comparison by equality is to be made, the wire WX can be used as already described ; it is, however, frequently desirable to make a comparison with one arm ten- fold or a hundredfold greater than the other, by which means measurements of resistances can be made ten or a hundred times greater or smaller than could be done if equality alone between R and 8 were measured ; for this pur- pose the three pairs, A C, A, C,, A, C,, are made exactly decimal multiples one of the other, and then, by taking A and C,, or A and C,, &c., in the cups aa, and ¢¢,, the required decimal ratio is obtained. The resistance of the wire WX would, however, falsify this ratio, and it is eliminated by a simple copper rod, which is placed for the purpose between the two cups ¢e,, and maintains the whole wire WX at sensibly one potential. The commutator also is useless in measurements of this kind, and should be left untouched in the position shown in fig. 1. The apparatus exhibited was manufactured for the Committee by Messrs. Elliott Brothers, of London, and gives excellent results, Preliminary Report of the Committee for Investigating the Chemical and Mineralogical Composition of the Granites of Donegal, and the Minerals associated with them. In accordance with the resolution of the General Committee at the Man- chester Meeting, the Committee, consisting of Sir R. Griffith, the Rev. Prof. Haughton, and Mr. Scott, proceeded to investigate “ the chemical and mine- M 2 164, REPORT—1862. ralogical composition of the granites of Donegal, and the minerals associated’ with them.” In furtherance of this object, Mr. Haughton and Mr. Scott re- paired, last Easter, to the northern part of the county, as they had visited the S.W. portion of the district in the summer of 1861. They were accompanied on their tour by Mr. Jukes, Local Director of the Geological Survey of Ireland, who gave them the valuable benefit of his experience and assistance throughout the tour. The exploration commenced at Moville, on the E. shore of Innis- howen, whence a section was carried along the N. coast of that peninsula nearly as far as Malin Head. This section exhibited a great thickness of “primary rocks, consisting of quartzite and mica-slate, accompanied by several beds of limestone, and a number of beds of igneous rocks, which appeared to de contemporaneous with the sedimentary rocks. These are best exhibited at a place called the Mintiaghs or Bar of Inch, where there are several alternations of quartz-rock and syenite exhibited in an escarpment of several hundred feet in height. This locality is situated about five miles N. of Buncrana. From Buncrana, the granite of Urrismenagh, near Dunaff Head, was visited. From Milford an excursion was made to the extremity of the promontory of Fanad, lying between Lough Swilly and Sheep Haven, in order to visit the granite of this district. This patch of granite is not a continuation of that which traverses the country in a N.E. and 8.W. direction, as it lies to the N. of that axis and exhibits a slight difference in composition from the granite of the central axis. From Milford the route lay to Dunfanaghy ; anda section was made across the northern end of the granitic axis of the county at Glen, in which its gneissose character was very strongly exhibited. This was marked in a most decisive manner between Lackagh Bridge and Creeshlagh, where the rock might be observed changing from gneiss, by almost insensible gradations, on the one hand into granite, and on the other into hornblende slate and crystalline syenite. The latter is most highly crystalline at Horn Head, where it contains large quantities of titaniciron. On the return-journey from Dunfanaghy to Letterkenny, it was determined to make two sections across the granite ; so that Mr. Haughton and Mr. Scott took the road from Creesh- lagh through the Gap of Barnesbeg, while Mr. Jukes took that by Owencarrow Bridge, about four miles higher up the valley. It having now been found necessary to compare the facts observed with those which were to be observed in other countries, Sir R. Griffith repaired to Scotland in the month of July. Mr. Haughton traversed the centre of Scotland, and paid a visit to Sweden, Finland, and Russia. Both these gen- tlemen discovered facts strongly confirming the views propounded at the Manchester Meeting, of the similarity of the geological structure of Donegal to that of the Scandinavian peninsula and of Scotland. For this latter fact the Committee had been prepared by the examination of a series of specimens of Scotch granites which had been furnished to them by Sir R. I. Murchison, in accordance with his kind promise made at the last Meeting. While these tours were in progress, Mr. Scott repaired, for the third time, to Donegal, and spent the month of July in the re-examination of ‘several points connected with the geology of the southern district. He visited the granite of Barnesmore, near the town of Donegal, which is essentially non- gneissose, and is penetrated by numerous pitchstone dykes, some of which are amygdaloidal. Numerous minerals were discovered here, which were in some cases new to the district. In the neighbourhood of Glenties, a consi- derable quantity of andalusite was found in the mica-slate—a mineral which is replaced near Barnesmore by kyanite, and in the Rosses, near Dungloe, by a white variety of kyanite. ON THE VERTICAL MOVEMENTS OF THE ATMOSPHERE. 165 ‘ From Dungloe, as head-quarters, the structure of Crohy Head was carefully examined, and also the island of Arranmore, which differs materially in its structure from the mainland of Ireland, from which it is only distant three miles. The southern portion of this island is nearly entirely composed of white granite, penetrated by numerous dykes of syenite and of felspathic porphyry. The strike of these rocks is nearly E. and W., while that of the flagey quartz-rocks on the northern shore of the island approaches N. and S. During the course of this tour, two more sections were made across the granite of the main axis, exhibiting the same facts which had been observed before, viz. numerous beds of limestone and of altered slate lying in the granite, stratified nearly conformably with it. These were observed in the centre of Glenveagh, close to Ballaghgeeha Gap, on the pass through the Poisoned Glen from Dunlewy. At Glenleheen, where the same occurrence of non-granitic rocks had been observed in the previous year, four beds of limestone and several beds of slate were discovered. Almost all these beds of limestone contained garnet, idocrase, and epidote in quantity ; and at Glen- leheen itself, scapolite, a mineral whose occurrence in the British Islands has escaped the notice of modern English mineralogists, was discovered. Inas- much as the specimens brought home by the members of the Committee from their several tours are very numerous, it is not possible for them to present their complete report at this Meeting. They hope to embody in it some valuable information relating to the granitic rocks of Canada, which Dr. T. Sterry Hunt has kindly offered to supply to them. They have to express their thanks to him and to Mr. Harte, C.E., county surveyor of the western district of the county, who, with the Rev. Frederick Corfield, has afforded them most efficient assistance. They have succeeded in procuring some of the granite of Rockall, through the kindness of the officers of H.M.S. Porcupine, who furnished it to Mr. Harte, and wil] include its analysis in their paper. On the Vertical Movements of the Atmosphere considered in connexion with Storms and Changes of Weather. By Hunry Hennessy, F.RS., M.R1IA., &c., Professor of Natural Philosophy in the Catholic University of Ireland. Tue labours of the Committee, consisting of Admiral FitzRoy, Mr. Glaisher, and myself, who were appointed, at Manchester, for the purpose of studying the vertical disturbances of the atmosphere with the aid of instruments, have, for the present, been restricted to the work of a single observer. This has arisen from the circumstance that the money-grant appropriated to the Committee has sufficed only to defray the cost of erecting a single instrument. As this instrument is likely to afford opportunities for observing the vertical motions of the atmosphere more completely than has been hitherto possible, it is to be hoped that similar apparatus will before long be in the hands of the other members of the Committee. The fact that all the preliminary work has thus necessarily devolved on the writer of the present Report will suffi- ciently account also for its provisional nature. Hitherto the only kind of atmospherical currents which have formed the subjects of definite observation by instruments are those whose existence is manifested by the movements of ordinary wind-vanes and anemometers. But as these instruments indicate horizontal movements exclusively, ordinary 166 REPORT—1862. winds as well as storms are almost always conceived as currents flowing in perfect parallelism to the earth’s surface. It is true that no physical theory of the motions of the atmosphere can be attempted without some considera- tions which involve the necessity of vertical and oblique motions among the masses of air, as well as horizontal motions; but while direct comparisons of the latter among themselves have continued for many years to be made in different parts of the world, we possess scarcely any such data relative to non-horizontal movements as would enable us to make them subjects of exact inquiry. ihe only writer who, as far as I am aware, has hitherto endeavoured to deduce any well-defined results from observation relative to the vertical movements of the atmosphere is M. Fournet, and his studies were almost ex- clusively directed to the elucidation of the phenomena of some remarkable local winds that frequently prevail among the Alps and in the valley of the Rhone*. A local phenomenon in Ireland + induced me to study the vertical motions of the air in a more general way than was necessary for the explana- tion of this phenomenon itself; and my first step was an attempt at devising a vane capable of showing the existence and direction of non-horizontal currents. This was a non-registering instrument, and the results obtained were therefore somewhat unconnected; but they seemed to establish some important relations between vertical currents and other atmospherical dis- -turbancest. Among these, I may be permitted to notice the phenomena which preceded the disastrous gale of February 9, 1861. For many days, at the close of January and beginning of February, the weather was remarkably fine, and no vertical currents were observed; but on the 7th very distinct evidences of vertical disturbance came under my notice, while the air had as yet no remarkable horizontal motion. On the 8th, at 2 p.w., my attention was called to the vane by its shifting round through N. towards N.E., with decided and frequent downward plunges of the disk exposed to the vertical action of the air. It appeared as if showers of cold air were descending ; for the thermometer showed at the same time a rapidly falling temperature. While vertical convection had become already highly developed, the horizontal motion of the air was not as yet greater than that of an ordinary brisk breeze. Next day, during the storm, although the disk of the vane was in constant oscillation from the undulatory motion which my observations had already shown to be a necessary accompaniment of all high winds passing over terrestrial obstacles, no marked prevalence of upward or downward motions could be observed corresponding to the plunges of the disk noticed on the preceding day. The mercury in the barometer had been falling with great regularity during four days before that on which I had noticed the first decided indications of vertical disturbance. On that and the next day, as well as on the very day of the storm, the barometric column was rising, while the temperature was steadily falling. Here the rise in the barometer was accompanied by north-easterly winds, and the air at the earth’s surface was thus rapidly mingled with cooler masses descending from above, as shown by the vane; so that the increased pressure was due to the increased density of the entire aérial column above the barometer. _ * See Annales de Chimie et de Physique, tome lxxiy. p. 337; and a réswmé of his results in a note to M. Martin’s translation of Kaemtz’s Meteorologie, p. 35. + Proceedings of the Royal Irish Academy, vol. iv. p. 279. } Atlantis, vol, iii,” p, 166; Phil. Mag. for May 1860; and Proceedings R. I. A. for May 1861, p. 232, ON THE VERTICAL MOVEMENTS OF THE ATMOSPHERE. 167 Among the phenomena attending the more tranquil conditions of the air, I had noticed in my earlier observations, during the summer of 1857, that upward currents generally prevailed by day, while downward currents became more prominent at night. This alternation was manifestly connected, as shown by the horizontal vane, with the action of land and sea breezes ; for at this time the observations were made at a point situated about two miles from the sea-shore. By day, the convection due to the heating of the lower stratum of air in contact with the ground could not take place by equal upward and downward exchanges of masses of air, because the place of the ascending warm air was partly supplied by the lateral influx of colder sea air, which, in its turn, would become sufficiently heated to ascend and give place to a fresh lateral influx. By night, the colder air from the land flowed towards the sea, and its place was filled by descending currents from above. At the same time the warmer air from the sea probably tended to occupy the place of these currents, and thus to equalize the temperature of the upper and lower strata of air so as to lessen the energy of the convective movement over the land. Before the termination of the Meeting of the Association at Manchester, I had resolved, with the concurrence of Mr. Glaisher, the only other member of the Committee then present, to cause a registering instrument to be con- structed which would record the existence of non-horizontal atmospheric motions. The following is a description of the anemoscope which I ultimately decided upon as most suitable in its construction for the purposes we have in view. Fig. 1 is a vertical section of the portion of the apparatus which is exposed to the wind, and fig. 3 an elevation of the same portion. Aisa cast-iron pillar which supports a cup, 2, containing frietion-balls made of gun- metal; on these a disk, g, rests, and this is firmly attached to a box from which an arm projects at one side, and is terminated by the cone, P, which acts as a counterpoise for the opposite and working arm of the anemoscope. A short arm, n, shown in fig. 3, supports a wheel, d, in one side of which teeth are cut; the other side is firmly attached to a hollow light copper box, B, which forms the tail. This box is a truncated pyramid, and while its vertical sides are exposed to the horizontal action of the wind, its upper and lower surfaces are exposed to its vertical action. This tail is balanced by a coun- terpoise, 7, which is connected by a bent arm with the axle of the wheel, d. The teeth of this wheel catch those of the pinion, e (fig. 1), and this catches in the rack, f. The rack is attached to a shaft, c, which descends through the hollow supporting pillar and communicates with the registering apparatus. In fig. 2 the most essential part of the arrangements for registering the indications of the upper part of the instrument are shown. The shaft, c, passes through brass guides, and carries a small circular projecting piece, s, which catches in a notch made in the bit, v, attached to the pencil-carrier, p. This pencil-carrier is capable of upward and downward motions only, and the rod to which it is attached passes through guides. The carrier is, more- over, supported by an ivory friction-wheel, ¢, which turns when the piece, s, revolves beneath it. From this brief description, it is apparent that the cone, P, will always indi- cate the direction of the wind in azimuth, like ordinary vanes. At the same time the vertical component (if any) of the wind will raise or depress the tail, B. In the former case it is manifest that the wheel, d, will cause e to turn, so as to raise the rack, f, and in the latter case the effect will be to lower the rack. It follows, therefore, that the shaft, c, and consequently the pencil- carrier which it moyes, must rise or fall according as the vertical motion of 168 REPORT—1862. the air is upward or downward. A spring within the pencil-carrier con- stantly presses the pencil against a sheet of paper placed in front of it. This paper is for the present carried on a flat board, which is moved by a clock. The registering sheets are ruled with vertical hour lines and with horizontal lines which assist in estimating the angle of inclination to the horizon made by the disk during the action of an upward or downward impulse from the air. This follows because the tail and the wheel, d, revolve on the same centre, and each tooth in d describes an are similar to that described by the axis of the tail. An equal number of teeth in ¢ are raised or lowered, and thus the rack and the shaft, c, move through spaces proportional to ares de- ‘scribed by the teeth of the wheel, d, and the axis of the tail, B. The board ON THE VERTICAL MOVEMENTS OF THE ATMOSPHERE. 169 which carries the registering paper can be detached by loosening a clamping- screw which fastens it to the support turned by the clock, so that the sheets can be removed and replaced with speed and facility. The entire apparatus was constructed by Mr. Spencer, of Aungier Street, Dublin; and he has executed the portion connected with the indication of horizontal moyement in such away, that the addition of a registering apparatus for this part of the instrument will not only be easy, but will render the entire combination a complete indicator of the absolute direction of the wind. The results of the instrument in its present state are exhibited on the regis- tering sheets as nearly vertical pencil lines, some above and some below the neutral line, to which each sheet is carefully adjusted. The anemoscope is at present so placed as not to be overtopped by any building ; for it stands on the roof of one of the highest houses in Dublin, in a quarter remarkably open, and close to the south suburbs. Owing to a variety of delays and obstacles in finishing the apparatus, it was not brought into action until the 31st of August, and thus I am able to report only on the results furnished by little more than the records of a single month. These records appear to indicate that vertical oscillations prevail more during the mid-day hours than at other periods; for although ten sheets show no definite predominance at any specific period of the day, and two predominance of vertical movements towards midnight, twenty-one show that these move- ments are most frequent at the hours about noon. From a journal of the weather which was kept at the same time, it appeared that on bright days, when the air had little horizontal motion, gentle upward movements pre- vailed at mid-day. Such phenomena are distinctly manifested by the sheets for September the 5th, 6th, 7th, 8th, and 9th, and all of these were bright sunny days. Before the 5th, the weather had been changeable and unsettled: but on comparing the two sheets comprehending from noon of the 3rd to noon of the 5th, I noticed that the amplitude of the oscillations of the anemoscope progressively and regularly diminished; and it occurred to me that this might indicate a tendency towards convective equilibrium of the atmosphere, and more settled weather. The weather continued fine until the 13th, when there was both high wind and rain, accompanied and preceded by energetic oscillations of the anemoscope. If the general circulation of the atmosphere takes place, as seems to be now completely established, by a twofold motion, one of translation, whether cyclonic or lineal, and the other undulatory, it follows that the pulsations of the latter movement may be influenced by aérial disturbances. The frequency, regularity, intensity, prevalent direction, and more or less intermittent character of these pulsations must depend on varia- tions of pressure, density, moisture, and temperature, as well as on the rippling motion of the air. It is natural, therefore, to expect, what our limited number of observations seem already to indicate, namely, that the sudden and abrupt commencement of such pulsations is usually a precursor _of other disturbances, while their gradual and regular diminution in energy would show a tendency in the air to approach a state of convective equili- brium, and might, therefore, be safely relied upon as a forerunner of fine weather. This point is illustrated by the remarks of the late Professor Daniell relative to the rapid oscillations of the water-barometer during high winds, and their gradual diminution preceding a return to a calmer state of the air*, Although the atmospheric pulse is undoubtedly compounded of the -undulatory movements resulting from the flow of an elastic fluid over the * Phil. Trans. 1832, p. 573. 170 REPORT—1862. irregularities of the earth’s surface, with the effects of convection, in such a way as would render the separation of these effects extremely difficult, yet the careful study of this pulse in connexion with other phenomena may he reasonably expected to add to our power of forming correct conclusions regarding the coming changes of the weather. Report of a Committee, consisting of the Rev. Dr. Luoyn, General Sa- ping, Mr. A. Suirx, Mr. G. Jonnstone Stoney, Mr. G. B. Arry, Professor Donxin, Professor Wm. Tuomson, Mr. Cayizy, and the Rey. Professor Pricr, appointed to inquire into the adequacy of existing data for carrying into effect the suggestion of Gauss, to apply his General Theory of Terrestrial Magnetism to the Magnetic Variations. Iw order to explain the views of the Committee upon the question submitted to them, it is necessary to refer briefly to the leading points of Gauss’s theory. If du denote the quantity of free magnetism in any element of the earth’s mass, and p the distance of that element from the point (2, y, 2), and if we make aes -\%4 pP the partial differential coefficients of V with respect to the three coordinates, x, y, z, respectively, are equal to the components of the earth’s magnetic force in the direction of the axes of coordinates. V is a function of «, y, and z, or of their equivalents wu, A, and r,—r being the distance of the point from the centre of the earth, and u and ) the angles corresponding to the north polar distance, and the longitude, on the sphere whose radius=r. This quantity may be expanded in a series proceeding according to the inverse powers of 7, whose coefficients, P,, P,, P,, &e., are functions of w and X» alone; and it is readily seen that, at the surface of the earth, the three com- ponents of the magnetic force are x=-(7 Fi 4+Fs4 be. ), dus dws du EA a A og & rr Crm eee ena Z=2P,+3P,+4P,+ &e., and are therefore given when P,, P., P,, &c. are known. The form of these functions is deduced from the well-known partial dif- ferential equation nm (n+1)P,+ Y=— ad? hie yal al ed du ne sin? u dd* : n being the number indicating the order of the function. It is found that the first, P,, contains three unknown coefficients ; the second, P.,, five; the third, P,, seven, &c. Hence, if the approximation be extended so as to in- clude terms of the fourth order, there will be 24 coefficients to be determined. Each given value of X, Y, or Z, on the earth’s surface, furnishes an equation => > Pn + cot u du ON GAUSS’S THEORY AND TERRESTRIAL MAGNETISM. 171 among these unknown coefficients; and for each place at which the three elements are known we have three such equations. Hence to obtain the general expressions of X, Y, Z, to the fourth order inclusive, it is theoretically sufficient to know the three elements at eight points on the earth’s surface. But, owing to the errors of observation, and to the influence of the terms neglected in the approximation, the number of determinations must, in prac- tice, be much greater than the number of unknown coefficients. The foregoing conclusions are based upon the hypotheses that magnetic attraction and repulsion vary according to the inverse square of the distance, and that the magnetic action of the globe is the resultant of the actions of all its parts. It is likewise assumed that there are two magnetic fluids in every magnetizable element, and that magnetization consists in their separation. But for these hypotheses we may substitute that of Ampére, which supposes the magnetic force to be due to electric currents circulating round the mole- cules of bodies. This theory may be applied to the changes of terrestrial magnetism, whe- ther regular or irregular, provided only that the causes of these changes act in the same manner as galvanic currents, or as separated magnetic fluids. We have only to consider whether the data which we possess are sufficient for such an application. It has been already stated that, for the general determination of X, Y, and Z, we must know their values at eight points (at least) on the earth’s sur- face, these points being as widely distributed as possible. The same thing holds with respect to the changes 6X, dY, 6Z; and to apply the formule so determined, and to compare them with observation, corresponding values must be known for (at least) one more point. In the case of the irregular changes these observations must, of course, be simultaneous. The regular changes must be inferred from observations extending over considerable periods ; and there is reason to believe that these periods must be identical, or nearly so, for all the stations, since the changes are known to vary from month to month and from year to year. The regular variations of the three elements X, Y, Z, or their theoretical equivalents, have been obtained by observation, for nearly the same period, at Greenwich, Dublin, and Makerstoun, in the British Islands; at Brussels and Munich, on the Continent of Europe; at Toronto and Philadelphia, in North America ; at Simla, Madras, and Singapore, in India ; and at St. Helena, the Cape of Good Hope, and Hobarton, in the southern hemisphere. Of these thirteen stations, however, the three British must be regarded, for the pre- sent purpose, as equivalent to one only, on account of their proximity; and the same thing may be said of the two North American stations and of the two stations in Hindostan. This reduces the number of available stations to nine, the minimum number required for the theoretical solution of the pro- blem in the degree of approximation already referred to, and considered by Gauss to be necessary. It is true that we may add to these the stations at which two only of the three elements have been observed, viz. Prague and St. Petersburg, the three Russian stations in Siberia, and Bombay. But even with this addition, the number is probably insufficient for the satisfactory determination of the unknown coefficients; for it is to be remembered that the places, few as they are, are not distributed with any approach to uni- formity, and that very large portions of the globe are wholly unrepresented by observations. For the reason already stated, this defect in the existing data cannot be now repaired by supplemental observations at new stations, unless the series 172 REPORT—1862. at all were so far extended as to embrace the whole period of the cyclical changes. The simultaneous observation of the irregular changes is limited nearly to the same stations. In their case, too, there is the further imperfection, as respects the present problem, that the changes observed on “ term-days” are for the most part inconsiderable, while those on days of great magnetic disturbance have seldom been observed continuously for any considerable time at all the stations. For the foregoing reasons the Committee are of opinion that the data which we at present possess respecting the changes of terrestrial magnetism, whether regular or irregular, are not sufficient for the application of Gauss’s theory, if, as above assumed, the approximation is to be extended so as to include terms of the fourth order (P, to P, inclusive). It is deserving of considera- tion, however, whether an inferior degree of approximation may not afford some valuable information. The affirmative side of this question has been so earnestly advocated by one of the members of the Committee, that it has been thought advisable to append his letter on the subject to this Report. (Signed by order of the Committee) H. Lioyp. Letter from Professor W. Tuomson to Rev. Dr. Lioyp. “‘ Roshyen, Strontian, Sept. 24, 1862. «‘ My prar Sr,—I am sorry to have been so long prevented from writing to you on the subject of the Committee’s Report on the expression of the Variations of the Terrestrial Magnetic elements in series of Laplace’s functions. “T perfectly agree with the conclusions stated in the draft report of which you sent me a proof, so far as they relate to a complete expression of any class of variations of the elements, or of any individual variation, by means of which its amount in other localities than those of observation could be de- termined with any considerable approach to accuracy. But, on the other hand, the amount of knowledge from observation, shown in the report to be available, would, I believe, be sufficient to allow us to estimate, possibly with considerable accuracy, and certainly with a sufficient approach to accuracy for highly important application, the first terms in the harmonic (Laplace’s) series. I would therefore advise that some such method as the following should be adopted. «‘ Choosing any particular variation, for instance the diurnal or the secular, for which the data from observation are most abundant, find either by trial and error, or any other proper algebraic method, an expression by terms of the first order (three coefficients for each) for the three elements which most nearly represent it. (The method of least squares would give a precise de- finition of what would be the most near representation, on this principle ; but ruder and quicker methods might suffice in first trials.) Then, judging by the results, try similarly for expressions in series of two terms (3+ 5, or eight coefficients in all, in each expression). After trials of this kind it would be easy to judge within what limits may be the probable errors of the estimated first terms from the true first terms, and possibly even to arrive at some probable knowledge regarding the true second terms of the harmonic ex- pressions. «« A very moderate degree of success in such operations as these would allow us to decide whether the origin (magnetic or electrodynamic) of the variation is within the earth’s surface or outside. igs ON THERMO-ELECTRIC CURRENTS IN CIRCUITS OF ONE METAL. 173 -“T hope, then, a result of the Committee’s action may be to carry out an attempt of this kind for every class of variations for which the data give even the narrowest foundation. It might be applied, I believe, with success, as regards the main conclusion, to every case in which each of the three compo- nents has been well determined for even only THREE stations widely apart from one another. «Tt seems probable that an individual deflection of a magnetic storm cannot be identified in localities at very great distances from one another. This must certainly be the case if an individual deflection, and individual flash or flicker of aurora, are simply related to one another, because the individual auroras are certainly local in the sense of being only seen at once over a very limited area of the earth, being in fact actually situated at some distance of not more than 150 miles (which I believe is the highest estimate) from the surface. Hence it is probable that it will be found whether the seat of the disturbing action, producing an individual deflection in a magnetic storm, is above or below the surface, by comparing observations made at stations within a few hundred miles of one another, and endeavouring to identify a single disturb- ance in the three components at all the localities. If the three components could thus be determined at three localities so wide apart as to show con- siderable differences in the amounts, but yet not so wide as to render the identification of the disturbance difficult, the question whether the seat of the disturbance is in the earth or the air would be answered with high proba- bility. “JT remain, yours very truly, (Signed) ‘© WititAm THomson.” On Thermo-electric Currents in Circuits of one Metal. By Fuizrmine Jenxin, Esq. Lasr year I had the honour of directing the attention of the Association to the fact, that an electric current of considerable intensity may be obtained in a circuit of one metal by the application of heat to one or the other side of an interruption in the wire composing the circuit. The experiment is most simply performed by looping together the two ends of two perfectly similar wires connected to the terminals of a galvanometer, and heating one of the loops to a white or red heat in a spirit-lamp, or Bunsen’s burner. If the one loop rests very lightly on the other a current will be obtained, which in the copper wires will flow from the hot to the cold loop across the joint with sufficient intensity to deflect a moderately sensitive galyanometer, even with a resistance in circuit equal to 1000 miles of No. 16 copper wire. The electromotive force of the combination is about one-tenth that of a Daniell’s cell. With two iron loops a permanent current in the opposite direction is obtained, flowing from cold to hot across the joint, but the elec- tromotive force in this case is very much smaller. When the loops are drawn tightly together the current ceases, but reappears as soon as the strain is slackened. _ I was at the time unable to show the connexion between these singular currents and other electrical phenomena, but I am now, in consequence of further experiments undertaken for the Association, able to point out that connexion. 174 REPORT—1862. The currents were clearly not due to chemical action on the wires; for, in the first place, currents of considerable strength were obtained from two per- fectly homogeneous platinum wires, flowing from hot to cold across the loose contact ; and in the second place, the direction of the current was different in copper and iron, whereas the chemical action undergone by the wire was alike in the two cases. The researches of Becquerel, Pouillet, Buff, Hankel, and Grove were ex- amined, to see whether the electricity produced during combustion, or the properties of flame, would account for the currents, but it was found that all the electrical effects produced by flame could be divided into two classes : first, phenomena depending on the relative position of the two wires in the flame ; and secondly, phenomena depending on the voltaic couple formed by the metals used, and the hot vapour acting as an electrolyte between them. My results were independent of the position of the wires in the flame, and could not be accounted for by supposing these wires to form a voltaic couple, inas- much as though in some cases, where wires of two metals were looped together as described, the current flowed from the metal most attacked across the imaginary electrolyte to the other wire, in other cases it flowed in the oppo- site direction. It remained to be seen whether the currents might not have a thermo- electric origin. Last year I imagined that the effect observed might be di- rectly due to discontinuity, but that idea was dispelled by some experiments with loose contacts between wires of different metals, which have thrown great light on the question. Loops of iron, silver, platinum, gold, and copper wires were combined two by two in all the possible arrangements, and the currents measured which were obtained when one or the other or both loops were heated with loose and tight contacts between them. A Table was thus formed, which is appended to the present paper. The resistance of the circuit was so large (2050 x 10°, Weber’s absolute aoe that the inherent resistance of the joint and of the different short wires used in each experiment could be neglected, and the deflections ob- tained on a reflecting galvanometer could be taken as approximatively pro- portional to the electromotive force of each combination. The common thermo-electric currents produced by the metallic contact between dissimilar wires almost vanish in comparison with those produced by the loose contacts. T need not present a complete analysis of the Table, but will speak only of the combination of iron and copper with which the most remarkable results were obtained. When the usual tight metallic contact was made between these two wires and the two loops equally heated, the current first flowed from copper to iron across the joint, and then as the temperature rose ceased altogether, and finally, at a red or white heat, flowed from iron to copper. The maximum deflection obtained in either direction was three divisions. These deflections showed the celebrated inversion discovered by Cumming. If the pressure between the loops was relaxed, the current ceased alto- gether ; but when the loops were moved, so that the copper became red-hot while the iron was cool, a current flowed from the copper to the iron, or from hot to cold across the joint, giving a deflection of 100 divisions; whereas if the iron was heated red-hot and the copper cooled, a current giving 90 divi- sions flowed in the opposite direction, or from iron to copper, but from hot to cold as before. Thus in these two cases the loose-contact currents given when one or the other loop was heated, flowed in the opposite direction be- ON THERMO-ELECTRIC CURRENTS IN CIRCUITS OF ONE METAL. 175 tween the metals, but in both cases from hot to cold across the joint, and were in each case about thirty times as great as the currents given by the thermo-electric difference between the metals. It was found on examining the Table, that wherever copper appeared in con- junction with any other of the metals named, the direction of the loose-con- tact current could invariably be determined by the following rule :—When the copper was the hot wire, the current flowed from the copper to the other metal across the joint; but when copper was the cold metal, the current flowed from the other metal to the copper, or in both eases from hot to cold. Exactly the contrary was found wherever iron appeared in conjunction with any of the five metals but copper; the current then always flowed from cold to hot. Two copper wires alone gave the largest deflection, of about 220 diyisions ; and two iron wires alone gave the next largest of those obtained where single metals only were used, but of course in the opposite direction to the deflection from copper. It was then perceived that all these results would be explained if, the thin coating of oxide on the copper wire might be regarded as a conductor with a hot and cold junction, and endowed with thermo-electric properties far more positive than the iron, while at the same time the coating of oxide on the iron wire would have to be regarded as far more negative than the copper. It was, however, difficult to suppose that two bodies so similar in some re- spects as the oxides of copper and iron should be at opposite extremities of the thermo-electric scale, but the following direct experiment left no doubt on my mind. A little spiral was made of platinum wire, and a small quantity of oxide of copper laid upon it, and held in a flame till white-hot ; another platinum wire was then dipped in the melted mass, when a strong current was at once ob- served from the hot to the cold wire, as if a loose contact had been made between two copper wires. When either of the oxides of iron was tested in a similar manner, a strong current was obtained from the cold to the hot platinum wire, as if a loose contact had been made between two iron wires. I do not yet know positively what the substances are which, interposed between silver and platinum and gold wires, give rise to the loose-contact currents, but I feel no doubt that these are as much thermo-electric currents as those given by the oxides of copper and iron, and are produced in a circuit composed of the metal and a very thin hot film, of which the two surfaces are unequally heated. There are, however, some good reasons for doubting whether electrolytes can be included in a true thermo-electric series, and I consulted many autho- rities with reference to this point. Seebeck himself includes many electrolytes in his thermo-electric scale, and places acids below bismuth, a result con- firmed lately by Gore (in 1857); he also places certain salts above antimony, a result subsequently confirmed by Andrews of Belfast in 1837. This gentleman observed that the tension produced by the salts between the wires was about equal to that between a platinum and silver plate in dilute sulphuric acid, and that the metals used as electrodes did not influence the deflection. He considered the current certainly due to a thermo-electric action. Faraday in 1833 discovered what Becquerel subsequently called pyro-elec- tric currents ; the currents were in different directions with different substances used, and some, if not all, were of the same nature as those I have described. Leroux and Buff obtained currents where glass acted as the electrolyte. Leroux considered them thermo-electric, and Buff chemical effects. Buff also attributes some of the electrical phenomena connected with flame to a 176 _ REPORT—1862. 4 thermo-electric action in which unequally heated air or gas forms part of the circuit. The currents obtained when a hot and cold platinum wire are dipped into dilute sulphuric acid and other liquids are well known; and finally (in 1858), Mr. Wild published a laborious research, in which he seems to prove the development of thermo-electric currents not only at the junction between metals and various solutions, but also between two different solutions. Thus, although none of the above observers seem to have tested the oxides, there seems little reason to doubt that they may be classed with other elec- trolytes, and may give rise to currents in the same manner. On the other hand, I cannot yet consider it definitively proved that any of the currents obtained from electrolytes are due to a true thermo-electrie action—that is to say, to an absorption of heat only, especially as Mr. Wild could find no trace of the Peltier heating and cooling effect at the junctions of his solutions. Further research, showing the source of the power developed, is most de- sirable. While consulting the literature connected with this subject, I found that Gaugain had to some extent preceded me in the discovery of the loose-con- tact currents, in a paper published in the ‘ Comptes Rendus’ in 1853. He comes to the same conclusion as I had done independently, that they were due to the unequally heated film of foreign matter, and places oxide of iron below platinum, and oxide of copper above gold and zinc, but below iron, instead of very much above it as I find. He does not appear to have ob- served the exceedingly high electromotive force to be obtained from these bodies, no doubt owing to the use of a short galvanometer coil of thick wires, such as is commonly used for thermo-electric researches. He introduces a carburet of iron, of which I find no trace, with more positive properties than oxide of copper, to explain some of his results. He gives very few data on which to found his theory, but simply mentions his conclusions, and appears to have made no direct experiment whatever with the oxides. Owing to these circumstances his experiments seem to have attracted little attention. I have endeavoured to contrive a convenient apparatus by which to study the properties of the oxides, but have not hitherto met with much success, owing to the great difficulty in maintaining a constant difference of temperature between the surfaces of the very thin film, which can alone be used with success. Next year I hope to obtain further results in elucidation of these quasi thermo-electric currents from electrolytes. I now wish to add a few remarks on the currents which occur when true metallic contact is made between a hot and cold end of a wire of one metal. The existence of these currents was placed beyond all doubt by Magnus’s careful experiments, but their connexion with other thermo-electric phenomena has hitherto remained entirely without explanation. Wild has suggested that they might be due to a thermo-electric couple formed with hot air or gas at the moment of junction; but experiments which I have made show this explanation to be founded on a mistaken conception of the duration of the current, which is by no means instantaneous, but lasts at least five minutes with copper or with iron wires, very gradually decreasing in intensity from a maximum to zero. Another explanation, viz. that the deflection is due to a sort of discharge of a statical effect produced by the unequal distribution of heat, is also nega- tived by the same consideration, as well as by the fact that a tension of suffi- cient magnitude to produce such a charge could not possibly have escaped observation by direct measurement. Professor W. Thomson has shown conclusively, in his ‘ Dynamic Theory of i oem , j ue a iy , Ve er ee te } Ser y he “shakes » os ef ' , i . on 9 Siu J 1) bi - » 5 n tS". pu al | use ’ bee “ore Wy tity é j ) ae | er 44 FR) ee — mania Ad yey aie SOD, » vale nak Wow Bf -.- ae TUN + ee, | ) — 10 Tight contact s»——>-2 Heated in middle. Maximum Heated at right side, Loose contact s=-——>— 12 Tight contact 21 Heated in middle, Ist maximum —<——eme 2 2nd do. (hotter) »=»——>-5 Heated at right side, Loose contact 2»——>10 or 15 Tight contact <——ewe 10 Heated in middle. Maximum —<——_e« 10 land do.(hotter) ==> 4 Heated at right side, Loose contact 2»——>- 15 Tight contact »=»——>2 Heated in middle. Ist maximum —<——eme 4 Heated at right side, Loose contact —<——eme 100 Tight contact 2==——s—weak Heated in middle. 1st maximum ~<——eue 3 2nd do. (hotter) s»-——=- 3 SrLver. 2nd do.(hotter) —<——eme 5 Heated at right side. Loose contact »»——>—8 Tight contact 2==——>weak Heated in middle. Ist maximum 2=»—>—2 Heated at right side. Loose contact 2=»——>—weak Tight contact 2=»——>weak Heated in middle, Maximum Heated at right side. Loose contact ~<——«me 100 to 150 Tight contact <——euac 10 Heated in middle, Maximum es 12 Heated at right side. Loose contact —<<——me 10 Tight contact ~——eme weak Heated in middle. Maximum —<——eme 1 Maximum Heated at right side, Loose contact —<——eme 190 Tight contact <——eme2 Heated in middle 2 -12 Tight contact 2=»——>10 Heated in middle, Maximum == 10 Heated at right side, Loose contact #==——>—-15 Tight contact 2-15 Heated in middle. Maximum z= 12 Heated at right side, Loose contact —<——eme 5 Tight contact .......... 0 Heated in middle. Maximum oes eee 0 Heated at right side. Loose contact 2=»——>~10 Tight contact s=»——>10 Heated in middle, Maximum 210 Maximum Heated at right side. Loose contact 2=——> 15 to 20) Tight contact 2»——>weak Heated in middle. lst maximum 2=— 3. 2nd do.(hotter) <——eme 4 Copper. Heated at right side. Loose contact —<<——eme 90 Tight contact 2» weak Heated in middle, Ist maxinum 2=»—>-3 2nd do. (hotter) <———eme 3 Heated at right side, Loose contact 2=——>— 10 | Tight contact 2=»——s—weak Heated in middle, Maximum 2—>2 Heated at right side. Loose contact —«——eme 5 Tight contact ~<——eme 10 Heated in middle, Maximum —<—_—_e 10 Heated at right side. Loose contact —<——me weak Tight contact »=»——>weak Heated in middle. Maximum Maximum Heated at right side. Loose contact —<——eme 170 Tight contact ———eme weak Heated at right side. Loose contact ~<——eme 80 Tight contact 2=»——> 10 Heated in middle. a—=—15 Heated in middle. weak Heated at right side. Loose contact <——eume 210 Tight contact 2=»-——>weak Heated in middle, Maximum 2=»——>-2 Heated at right side. Loose contact —<——me 250 Tight contact ~<——me uncertain Heated in middle, Maximum —<—_ee 15 Heated at right side. Loose contact ~<——me 280 to 300, Tight contact me weak Heated in middle, Maximum —~<——eme weak Maximum Heated at right side, Loose contact <——eume 220 Tight contact ~-——eee weak Heated in middle, saw ean tie 0 | ON TH Heat,’ tha clusively ossibly gi Theless If is maintai the two en recommen the hot on wires does siderable ¢ perature. that wires they have the conduc when kept some may suppositior the theory Another in a partia by the sud between a with the c does not 5' Tan, hi next year theories is experimen Dr. Matthi electrical y presence of The nan side and to entered in columns ¢ formed the show the d subdivision heated and deflection together. The thir current, wh held tightly The fom current in t last entries The first en an uncertail An exam 1862, ON THERMO-ELECTRIC CURRENTS IN CIRCUITS OF ONE METAL. 177 Heat,’ that if the condition of metal at a certain temperature depended ex- clusively on that temperature, no distribution or movement of heat could possibly give rise to a current of electricity in a circuit of one metal; never- theless I find, as above stated, that in a circuit of one metal wire a current is maintained for five minutes at a time, gradually vanishing to nothing when the two ends of the homogeneous wire have been for some time in contact, but recommencing if one wire is cooled for a minute and then again applied to the hot one. One explanation of this might be that the condition of the wires does not solely depend on their temperature, but is influenced to a con- siderable extent by the time during which they have remained at that tem- perature. Nor is this a gratuitous assumption: Dr. Matthiessen has proved that wires of several metals do not attain a constant conducting power until they have been kept for some time at a constant temperature; he finds that the conducting power of bismuth increases, while that of tellurium decreases when kept for a time at 100°. Quite similarly, some metals may rise and some may fall in the thermo-electric scale after being heated for some time, a supposition which is necessary to account for the metallic contact currents by the theory I suggest. Another possible explanation of the metallic contact currents may be found in a partial hardening on the one side and annealing on the other, caused by the sudden contact of the hot and cold metal. If this be so, the current between annealed and unannealed wires of the same metal would correspond with the contact current between two homogencous wires, in a way which it does not seem to do. 1 am, however, now engaged in investigating this subject, and hope before next year to be able to give facts which may decide whether either of these theories is tenable. There is great difficulty in forming any conclusion from experiments hitherto made, inasmuch as none of the observers, except Dr. Matthiessen, have used chemically pure metal, and it is found that the electrical properties of a metal are affected to an extraordinary degree by the presence of impurities in very small quantities. Explanation of the Table. “The names of the metals of which the loops were made are entered at the side and top of the Table. The experiments made with each combination are entered in the subdivision at the intersection of the horizontal and vertical columns corresponding to the two metals. The metals named at the top formed the right-hand loop, those at the side the left-hand loop. The arrows show the direction of the current across the joint. The first entry in each subdivision shows the deflection observed when the right-hand metal was heated and the wires held loosely together. The second entry shows the ee when the same metal was heated but the wires drawn tightly together. The third entry gives the maximum deflection, and the direction of the current, when the middle of the joint is gradually heated and the two wires held tightly together. The fourth entry (where given) shows the maximum deflection from a current in the opposite direction when greater heat was applied. The two entries show the common well-known metallic thermo-electric effects. The first entry shows the new loose-contact effect. The second entry shows an uncertain combined effect of metallic and imperfect contact effects. a example will perhaps make this clearer, When copper and iron were * N 2 REPORT—1862. used and copper loop heated, a loose contact produced a current from copper to iron across the joint, giving a deflection of 100 divisions. A tight contact gave nothing decided. When the iron loop was heated (the copper cold) the loose contact produced a current from iron to copper across the joint, giving a deflection of 90 divisions. A tight contact in this case gave a weak current in the opposite direction. When the joint was heated in the middle, as the temperature gradually rose, a maximum deflection of 3 divisions was first reached, showing a current from copper to iron across the joint; and as the heat increased still further this current was reversed, and finally, at a white heat, gave a maximum deflection of 3 divisions with a current from iron to copper. On the Mechanical Properties of Iron Projectiles at High Velocities. By W. Farrsarrn, F.R.S. A VALUABLE series of experiments were made at Manchester upon portions of plates fired at by the Iron Plate Committee at Shoeburyness. These experi- ments comprised the determination of the resistance to punching, to a tensile strain, to impact, and to pressure. They show that the tenacity varied from 11 to 29 tons per square inch in the iron plates, and from 26 to 333 tons in the homogeneous iron plates. The average strength of the iron plates between 14 and 3 inches thick varied from 234 to 243 tons per square inch, and this, or about 21 tons, may proba- bly be insisted upon as a measure of strength in future contracts for iron lates. a The elongation of the plates under a tensile strain may be taken as a mea- sure of the ductility of the material ; it varied in the thicker iron plates from 0-91 to 0-27 per unit of length, and averaged 0:27 inch in the homogeneous metal plates. The maximum observed was 0:35. The most important results in connexion with the question of the resist- ance are, however, those obtained by combining the tensile breaking weight with the ultimate elongation, as first indicated by Mr. Mallet in a paper read before the Institution of Civil Engineers. By finding in this manner the product of the tenacity and ductility, numbers are obtained which, though not identical with those expressing the resistance of the plates in the experiments with guns at Shoeburyness, are yet in close correspondence with them, The average value for Mr. Mallet’s coefficient in the thicker iron plates was about 6500 lbs., and in the steel or homogeneous plates 8300 lbs. But the resist- ance of the iron plates increases with the thickness, whilst that of the homo- geneous metal diminishes. The correspondence of these numbers is indicated in the Report addressed to the War Office and the Admiralty ; but a more extended series of experiments are yet wanting to determine the true value of the coefficient as a guide to be insisted upon in the manufacture of iron plates. 9000 foot-pounds is the maximum for iron given by the *results already obtained ; but an extended series of experiments might develope new features of resistance and new improvements in the manufacture. The experiments on punching afford an explanation of the greatly increased perforating power of the flat-headed shot overthat of the round-headed projectiles. They also lead to a formula for the ordinary cast-iron service shot, which appears to give with approximate accuracy the law of the resist- ON THE MECHANICAL PROPERTIES OF IRON PROJECTILES. 179 ance of plates of different thicknesses to missiles of various weights and velo- cities. These investigations led to inquiries into the state of the manufacture of plates calculated to resist heavy and powerful projectiles directed against the sides of an iron-plated ship, and, moreover, to determine the exact thickness of plates that a vessel was able to carry. Again, they had reference to the quality of the plates and their powers of resistance to impact. There were three conditions necessary to be observed in the manufacture: 1st, that the material should be soft and ductile; 2nd, that it should be of great tenacity ; and, lastly, that it should be fibrous and tough. All these conditions apply to the manufacture of plates, and they also apply, with equal force, to the projectiles in their resistance to pressure and impact. In the experiments at Shoeburyness, it was found that the ordinary cast- iron service shot were not adapted for penetration, as they invariably broke into fragments when discharged against a sufficiently thick armour-plate. In most cases when delivered at high velocities, they had the power of damaging and breaking the plates ; but owing to their crystalline character and defective tenacity, a considerable portion of the power was expended in their own destruction. To some extent the same law was applicable to wrought-iron shot, as part of the force, from its greater ductility, was employed in distorting its form, and depriving it of its powers to penetrate the plate. Cast and wrought iron are therefore inferior as a material for projectiles intended to be employed against iron-plated ships and forts. With steel hardened at the end the case is widely different, as its tenacity is not only much greater than that of cast and wrought iron, but the process of hardening the head prevents compression and its breaking up by the blow when the whole of its force is delivered upon the plate. Steel, although much superior to cast or wrought iron in its power of resistance in the shape of shot, is, nevertheless, suscep- tible of distortion and compression, and in every instance when employed against powerful resisting targets the compression, and consequently the dis- tortion, was distinctly visible. There is another consideration besides the material which enters largely into the question of the resisting powers of shot, and that is form. It will ‘be recollected that, some years since, the late Professor Hodgkinson instituted a series of experiments to determine the strength of iron pillars, and the results obtained were in the following ratios ;— Ibs. Ist. That pillars of about 20 to 30 diameters in length, with 3000 two flat ends, broke with)... 06 5. 0000 S00. e 0. 2nd. Pillars with one end rounded and one flat broke with © 2000 And 3rd. Pillars with both ends rounded broke with...... 1000 being in the ratio of 1, 2,3. Now in order to ascertain the effects of form on cylindrical shot, a series of experiments were instituted to determine the force of impact and statical pressure produced upon shot of different shapes, and from these experiments the following results were obtained. The description of shot experimented upon was cast-iron of the cylindrical form, with flat and round ends; and it is interesting to observe that the re- sults correspond with those where both ends are rounded and one end only rounded, as obtained by Mr. Hodgkinson on long columns; but in the short Specimens with both ends rounded the results are widely different, as may be seen by the following Table. n2 180: REPORT—1862. No. of | Crushing | Ultimate Pressure Pressure Experi- | weight in | compression |per squareinch|persquareinch Remarks. ments. lbs. in inches. in lbs. in tons. 1 73,428 122,115 54°51 2 68,062 125,787 Both ends flat. WMEATOMIE ecw | | webene 123,951 Areas 5674 and *7088. 3 35,540 62,636 4 40,916 57,725 One end rounded. ECR 1) sscece |) eimauwrece 60,180 Areas *7088 and ‘7088. Lt 5. 38,260 53,978 6. 37.580 53,030 Both ends rounded. Mean 37,920 Areas *7088 and °7088. From the above experiments, it is evident that the round-ended shot loses more than one-half its power of resistance to pressure in the direction of its length ; and this may be accounted for by the hemispherical end concentrating the force on a single point, which, acting through the axis of the cylinder, splits off the sides by a given law of cleavage in every direction. On the other hand, the flat-ended specimens have the support of the whole base in a vertical direction ; and from these we derive the following comparative results :— Taking the resistance of the flat-ended shot at 54°82 tons per square inch, and that with hemispherical ends at 26:86, we have a reduction from the mean of the flat-ended columns of 27:96 tons, being in the ratio of 100: 49; or, in other words, a flat-ended shot will require more than double the force to crush it than one with one of its ends rounded. Now, as the same results were obtained at Shoeburyness, in the appearance of the fractured ends, when similar shot was fired from a gun, we arrive at the conclusion that the same law is in operation whether rupture is produced by impact or statical pressure. In the experiments on cast-iron shot, the mean compression per unit of length of the flat-ended specimen was ‘0665, and of the round-ended +1305. The ratio of the compression of the round- to the flat-ended was therefore as 1:96: 1, or nearly in the inverse ratio of the statical crushing pressure. It has been correctly stated that it requires a considerable amount of force to break up shot when delivered with great velocity against an unyielding object, such as the side of an iron-cased ship, or a target representing a por- tion of that structure; and it may be thence inferred that the force expended in thus breaking up the shot must be deducted from that employed in doing work on the plate. This is confirmed by experiment, which shows that though the whole of the force contained in the ball, when discharged from a gun at a given velocity, must be delivered upon the target, the amount of work done, or damage done to the plate, will depend on the weight and the tenacity of the material of which the shot is composed. Tf, for example, we take two balls of the same weight, one of cast iron and the other of wrought iron, and deliver each of them with the same velocity upon the target, it is obvious that both balls carry with them the same pro- jectile force as if they were composed of identically the same material. The dynamic effect or work done is, however, widely different in the two cases, the one being brittle and the other tough: the result will be, that the cast iron is broken to pieces by the blow, whilst the other either penetrates the plate or, what is more probable, flattens its surface into a greatly increased area, and ON THE MECHANICAL PROPERTIES OF IRON PROJECTILES, 181 inflicts greatly increased punishment upon it, In this instance the amount of work done is in favour of the wrought iron: but this does not alter the condition in which the force was first delivered upon the target; on the con- trary, it is entirely due to the superior tenacity of wrought iron to that of cast iron, which yields to the blow, and is broken to pieces in consequence of its inferior powers of resistance. The same may be said of steel in a much higher degree, which delivers nearly the whole of its vis viva upon the plate. In the foregoing experiments it will be observed that the resistance of cast- iron flat-ended shot to a crushing force is about 55 tons per square inch, whilst in the two following we find that the round-ended specimens, of the same material, gaye way and were crushed with a pressure of only 263 tons— rather less than one-half the force required to crush the flat-ended ones, It is a curious but interesting fact (provided the same law governs the force of impact as dead pressure) that the round-ended projectile which strikes the target should lose, from shape alone, one-half its powers of resistance. This may be accounted for as under. Take, for example, a cylinder of cast iron, a, with a rounded end forcibly pressed against the steel plate A,-until it is crushed by a fixed law of fracture ob- servable in every description of crystalline structure; that is, the rounded end or part s forms itself into a cone, which, acting as a wedge, splits off the sides cc in every direction at the angle of least resistance, and these, sliding along the sides of the cone, are broken to pieces on the surface of the plate. At Shoeburyness the same results were observable in all the experiments with spherical and round-ended shot, each of them following precisely the same law. In every case where the shot was broken to pieces, the fractured parts took the same direction, forming a cone or central core similar to that shown at s, as exhibited in my own experi- ments on statical pressure with the round-ended cylindrical shot. The law of fracture of cast iron has been carefully investigated by the late Professor Hodgkinson in his paper on the strength of pillars, to which we haye referred. It is there clearly shown that the resistance of columns when broken by compression is in the ratio of 1, 2, and 3; the middle one, with only one end rounded, being an arithmetical mean between the other two. Now these important facts, according to all appearance, bear directly upon the forms necessary to be observed in the manufacture of projectiles, as we find cylindrical shot with round ends loses one-half its powers of resist- ance to a pressure or a blow which tends to rupture or to break it in pieces. My own experiments given above do not exactly agree with those of Pro- fessor Hodgkinson—the ratio of resistance in a column with one end rounded, and that of a column with both ends flat, being as 3: 1-5, instead of as 3: 2 as in his experiments,—a discovery probably explained by considering that he employed cast-iron pillars from 20 to 30 diameters in length, whereas my own were only two diameters long. Professor Hodgkinson has, indeed, ex- pressed an opinion that the difference of the strengths of the three forms of pillars becomes less according as the number of times the length of the pillar exceeds the diameter decreases, which is the reverse of the results obtained in the foregoing experiments. But on this I may observe, that the conclusion 182 : a REPORT—1862. is founded on a very limited number of experiments on wrought-iron columns of 15 to 30 diameters long as compared with others of 60 diameters, which, in my opinion, has been prematurely assumed as a general law. With wrought iron especially, the crushing-up of the rounded ends would soon bring pillars of that form into the condition of flat-ended pillars when the breaking weight approached the ultimate strength of the material—a conclusion confirmed by observing that the experiments in question are exactly those in Mr. Hodg- kinson’s table in which the breaking weights of the pillars are greatest. However this may be, the experiments I have given show that short cylinders with flat ends have twice the strength of similar cylinders with one end rounded. From this it would appear that the law for short cylinders is not the same, but altogether different from that obtained by Mr. Hodgkinson for long cylinders. The discrepancies which appeared to exist between my own experiments and those of Professor Hodgkinson induced me still further to inquire into the law which seems to govern short bolts of columns of two diameters in length. To account for those discrepancies, the experiments were extended to columns with both ends rounded; and what renders them interesting is, that in short columns with both ends rounded the powers of resistance are nearly the same as those with one end flat and one end rounded, and moreover they appear to follow a different law from that of Professor Hodgkinson’s long columns, which, in most cases, broke by flexure. The difference in strength between short columns with both ends rounded and those with one end flat and one end rounded is almost inappreciable, as will be seen by comparing their values as under :— Tons per square inch. Columns of two diameters long with flat ends crushed with 54:82 Columns with one end rounded and one flat 4 3 26:86 Columns with both ends rounded........ S 3 23°88 So that the difference between them may be taken as the numbers 55, 27, and 24, or, in other words, in the ratio of 1: ‘49 with one end rounded and one end flat—that with both ends flat representing unity—and as 1 : :44 with both ends rounded ; a comparatively slight difference between those with one end flat and the others with both ends rounded. With regard to the dynamic effect, or work done, by round-ended shot as compared with flat-ended ones, it has already been shown that with dead pres- sure the indentations produced on wrought-iron plates by a round-ended shot are nearly 33 times greater than by those with the flat ends, and that the work done is twice as great in the case of the round ends as compared with that by the flat ends. This may be accounted for by rounded shot striking the plate with its; pointed end, and the force of the blow being given by a comparatively small area; the vs viva or the whole force is thus concentrated and driven into the target to a depth consider- ably greater than if spread over the whole area of the projectile. The flat-ended cylindrical shot, which indicates such powerful resistance to pressure, is gene- rally fractured by one or more of its sides being forced downwards in the direction of the line a, and hence its superior resist- ance when the whole area of the cylinder forms the base as the means of support. ON THE MECHANICAL: PROPERTIES OF IRON PROJECTILES, 183 The difference of form does not, however, lessen the quantity of mechanical force (the weights being the same), as each ball has the same work stored in it when delivered from the gun at the same velocity, and the blow upon the target ought to be the same in effect but for the difference of shape in the case of the round ends, which break to pieces with one-half the pressure. It is difficult to estimate the difference of force or work done upon the target by the two balls; it. is. certainly not in the ratio of their relative tenacities (the metal being the same), but arising from form, as the one would strike the target with its whole sectional area in the shape of a punch adapted for perforation, whilst the other, although much easier fractured, would effect a deeper indentation upon the plate. The same law of defective resistance is observable in wrought iron and steel as is indicated in cast iron, but not to the same extent. On com- paring the mean of twenty-six experiments on wrought iron with those on cast iron, it is evident that the difference between the two is considerable in their respective powers of resistance to compression. In the experiments on cast iron the specimens were invariably broken into fragments, and those of wrought iron, although severely crushed, were not destroyed. The same law, however, appears to be in operation in regard to the flat- and the round- ended specimens, although less in that of wrought iron, as both forms were squeezed so as to be no longer useful, the ratios being as 75 : 50 nearly, or 100: 67-4. The round-ended shot, as might be expected, supported con- siderably more than one-half the pressure applied to the flat-ended one before it was finally distorted, whilst the cast iron was broken with less than one- half the pressure required to crush the flat-ended specimens. . From these and the experiments on impact, there cannot exist a doubt as to the damaging effects of wrought-iron projectiles. The experiments on steel indicate similar results to those on cast and wrought iron, as may be seen from the mean of nineteen experiments given in the following summary of results :— No. of Breaking Ultimate Pressure Pressure Ad weight in {| compression | per square per square Remarks. Experiments. Ibs. in inches. inch in lbs. | inch in tons. L 145,756 04 269,419 120°27 Flat-ended. 10 114,980 “21 202,643 90°46 Round-ended. Here the same law of defective resistance is present in the round-ended cylinders as in those of cast iron, and doubtless the same ratio would have been obtained, provided the apparatus had been sufficiently powerful to have fractured the flat-ended specimens; we may therefore conclude that, instead of the above ratio of 100 : 75, it would-have been 100 : 50 or thereabouts. From these facts, and those on wrought iron, we are led to the conclusion that the power of resistance to fracture of a cylindrical shot with both ends flat is to that with its front end rounded as 2: 1 nearly. _ The experiments of which the above is an abstract were extended to lead, as well as cast and wrought iron, and steel; but those on lead were of little value, as the compression was the same whether the ends were rounded or flat. This is accounted for by the extreme ductility of the metal and the facility with which it is compressed. As regards the wrought-iron specimens it may be observed that no definite results were arrived at, excepting the enormous statical pressure they sustained, equivalent to 78 tons per square inch of 184 . REPORT—1862. sectional area, and the large permanent set which they exhibit. These com- parative values are as follows :—- Statical resistance in Dynamical resistance in tons per square inch. foot-pounds per square inch. Cast iron, flat ends........-+. = OD:D2. sbisscielategeleh Xe 7768 Cast iron, round ends ...... =26°8i7iqa.oasians lamar 821:9 Steel, round ends .......-+. ==O0°AG/latieinthia tak 2515:0 From the experiments on the wrought iron, the flat-ended steel specimens, and the lead, no definite conclusion was arrived at, the material being more or less compressed without the appearance of fracture. The mean resistance of the cast iron is 800 foot-pounds per square inch, whilst that of steel is 2515 foot-pounds, or more than three times as much. The conditions which appear to be derivable from these facts, in order that the greatest amount of force may be expended on the iron plate, are therefore :—Very high statical resistance to rupture by compression. In this respect wrought iron and steel are both superior to cast iron; in fact, the statical resistance of steel is more than three times that of cast iron, and more than two and a half times that of wrought iron. Lead is inferior to all the other materials experimented upon in this respect. Again, resistance to change of form under severe pressure and impact is an important element in the material of shot. In this respect hardened steel is infinitely superior to wrought iron. Cast iron is inferior to both. In fact, the shot which would produce the greatest damage on armour-plates would be one of adamant, incapable of change of form, and perfect in its powers of resistance to impact. Such a shot would yield up the whole of its vis viva on the plate struck, and, so far as experiment yet proves, those projectiles which approach nearest to that condition are the most effective. Report on the Progress of the Solution of certain Special Problems of Dynamics. By A. Cayuny, F.R.S., Correspondent of the Institute. My “Report on the Recent Progress of Theoretical Dynamics” was pub- lished in the Report of the British Association for the year 1857. The present Report (which is in some measure supplemental thereto) relates to the Special Problems of Dynamics: to give a general idea of the contents, I will at once mention the heads under which these problems are considered ; viz., relating to the motion of a particle or system of particles, we haye Rectilinear Motion ; Central Forces, and in particular Elliptic Motion ; The Problem of two Centres ; The Spherical Pendulum ; Motion as affected by the Rotation of the Earth, and Relative Motion in general ; Miscellaneous Problems : The Problem of three bodies. And relating to the motion of a solid body, we have The Transformation of Coordinates ; Principal Axes, and Moments of Inertia ; ON THE SPECIAL PROBLEMS OF DYNAMICS, 185 Rotation of a Solid Body ; Kinematics of a Solid Body ; Miscellaneous Problems. As regards the first division of the subject, I remark that the lunar and planetary theories, as usually treated, do not (properly speaking) relate to the problem of three bodies, but to that of disturbed elliptic motion—a problem which is not considered in the present Report. The problem of the spherical pendulum is that of a particle moving on a spherical surface ; but, with this exception, I do not much consider the motion of a particle on a given curve or surface, nor the motion in a resisting medium; what is said on these subjects is included under the head Miscellaneous Problems. The first six heads relate exclusively, and the head Miscellaneous Problems relates princi- pally to the motion of a single particle. As regards the second division of the subject, I will only remark that, from its intimate connexion with the theory of the motion of a solid body, I have been induced to make a separate head of the geometrical subject, “‘ Transformation of Coordinates,” and to treat of it in considerable detail. I have inserted at the end of the present Report a list of the memoirs and works referred to, arranged (not, as in the former Report, in chronological order, but) alphabetically according to the authors’ names: those referred to in the former Report formed for the purpose thereof a single series, which is not here the case. The dates specified are for the most part those on the title- page of the volume, being intended to show approximately the date of the researches to which they refer, but in some instances a moxe particular speci- fication is made. I take the opportunity of noticing a serious omission in my former Report, yiz., I have not made mention of the elaborate memoir, Ostrogradsky, “Mémoire sur les ¢quations différentielles rélatives au probléme des Isopéri- métres,” Mem. de St. Pét. t. iv. (6 sér.) pp. 385-517, 1850, which among other researches contains, and that in the most general form, the transformation of the equations of motion from the Lagrangian to the Hamiltonian form, and indeed the transformation of the general isoperimetric system (that is, the system arising from any problem in the calculus of variations) to the Hamil- tonian form. I remark also, as regards the memoir of Cauchy referred to in the note p. 12 as an unpublished memoir of 1831, there is an “ Extrait du Mémoire présenté 4 l’Académie de Turin le 11 Oct. 1831,” published in _ lithograph under the date Turin, 1832, with an addition dated 6 Mar. 1833. The Extract begins thus :—*« § I. Variation des Constantes Arbitraires. Soient données entre la variable ¢,. . . m fonctions de ¢ désignées par 2, Ys 2 oija Ch autres fonctions de ¢ désignées par u, v, w,. . 2n équations différentielles du prémier ordre et de la forme dat _ dQ dy dQ dz dQ dt ai dl deo diss. ie du dQ dvy_ dQ dw dQ &e.” ay hes dt da’ dt dy” “dé dz without explanation as to the origin of these equations; and the formule are then given for the variations of the constants in the integrals of the foregoing system ; this seems sufficient to establish that Cauchy in the year 1831 was familiar with the Hamiltonian form of the equations of motion. Bour’s “‘ Mémoire sur l’intégration des équations différentielles de la Mé- canique,” as published, Mém. prés, de Inst. t. xiv. pp. 792-821, is substan- 186 REPORT—1862. tially the same as the extract thereof in ‘ Liouville’s Journal,’ referred to in my former Report ; but since the date of that Report there have been published in the ‘Comptes Rendus,’ 1861 and 1862, several short papers by the same author; also Jacobi’s great memoir, see list, Jacobi, Nova Methodus &c. 1862, edited after his decease by Clebsch; some valuable memoirs by Natani and Clebsch (Crelle, 1861 and 1862) relating to the Pfaffian system of equations (which includes those of Dynamics), and Boole “ On Simultaneous Differential Equations of the First Order, in which the number of the Variables exceeds by more than one the number of the Equations,” Phil. Trans. t. clii. (1862) pp. 437-454. Rectilinear Motion, Article Nos. 1 to 5. 1. The determination of the motion of a falling body, which is the case of a constant force, is due to Galileo. 2. A variable force, assumed to be a force depending only on the position of the particle, may be considered as a function of the distance from any point in the line, selected at pleasure as a centre of force; but if, as usual, the force is given as a function of the distance from a certain point, it is natural to take that point for the centre of force. The problem thus becomes a particular case of that of central forces ; and it is so treated in the ‘ Principia,’ Book I. § 7; the method has the advantage of explaining the paradoxical result which presents itself in the case Force O¢ (Dist.)—?, and in some other cases where the force becomes infinite. According to theory, the velocity becomes infinite at the centre, but the direction of the motion is there abruptly reversed; so that the body in its motion does not pass through the centre, but on arriving there, forthwith returns towards its original position ; of course such a motion cannot occur in nature, where neither a force nora velocity ever is actually infinite. 3. Analytically the problem may be treated separately by means of the a 1ax\2 equation qea* which is at once integrable in the form (a) =049/3 Xdzx. 4. The following cases may be mentioned :— Force o Dist. Thelaw of motion is well known, being in fact the same as for the cycloidal pendulum. Force ¢ (Dist.)-2, =, which is the case above alluded to. ‘ a Assuming that the body falls from rest at a distance a, we have x=a (1—cos ¢), where, if n= ¢ is given in terms of the time by means of the equation B nt=p—sin ¢. If the body had initially a small transverse velocity, the motion would be in a very excentric ellipse, and the formule are in fact the limiting form of those for elliptic motion. 5. There are various laws of force for which the motion may be determined. Tn particular it can be determined by means of Elliptic Integrals, in the case of a body attracted to two centres, force OC (dist.)-2: see Legendre, Exercices de Cal. Intég. t. ii. pp. 502-512, and Théorie des Fonct. Ellip. t. i. pp. 531- 538. I : ‘ee escbhe fo ak ee ON THE SPECIAL PROBLEMS OF DYNAMICS. 187 Central Forces, Article Nos. 6 to 26. 6. The theory of the motion of a body under the action of a given central’ force was first established in the ‘ Principia,’ Book I. §$ 2 & 3: viz. Prop. I. the areas are proportional to the times, that is (using the ordinary analytical 1 hy notation), °d@=hdt, and Prop. VI. Cor. 3, Pa Sy py ate apt") so that : Mu P a3 tu—a>5=0. do hew 7. It,is to be noticed that, given the orbit, the law of force is at once determined ; and § 2 contains several instances of such determination ; thus, Prop. VII. If a body revolve in a circle, the law of force to a point § is a force Agp: py (P the body, PV the chord through §). Prop. IX. If a body move in a logarithmic spiral, force q (dist.)-3. Prop. X. Ifa body move in an ellipse, force to centre @ dist., and as a parti- cular case, if the body move in a parabola under the action of a force parallel to the axis, the forcé is constant. The particular case of motion in a parabola had been obtained by Galileo. And § 3. Props. XI. XII. XIII. Ifa body move in an ellipse, hyperbola, or parabola under the action of a force tending to the focus, force q@ (dist.)—2. 8. But Newton had no direct method of solving the inverse problem (which depends on the solution of the differential equation), ‘Given the force to find the orbit.” Thus force q& (dist.)—2, after it has been shown that an ellipse, a hyperbola, and a parabola may each of them be described under the action of such a force. The remainder of the solution consists in showing that, given the initial circumstances of the motion, a conic section (ellipse, parabola, or hyperbola, as the case may be) can be constructed, passing through the point of projection, having its tangent in the direction of the initial motion, and such that the velocity of the body describing the conic section under the action of the given central force is equal to the velocity of pro- jection ; which being so, the orbit will be the conic section so constructed. This is what is done, Prop. XVII. ; it may be observed that the latus rectum is constructed not very elegantly by means of the latus rectum of an auxiliary orbit. _ 9. A more elegant construction was obtained by Cotes (see the ‘ Harmonia Mensurarum,’ pp. 103-105, and demonstration from the author’s papers in the Notes by R. Smith, pp. 124, 125); depending on the position of a point C, such that the velocity acquired in falling under the action of the central force from C directly or through infinity* to P the point of projection, is equal to the given velocity of projection. as 10. But Newton’s original construction is now usually replaced by a con- struction which employs the space due to the velocity of projection considered as produced by a constant force equal to the central force at the point of pro- jection. st ; Al. Section 9 of Book I. relates to revolving orbits, viz., it is shown that a body may be made to move in an orbit revolving round the centre of force, * Tn the second case C lies on the radius vector produced beyond the centre, and the body is supposed to fall from rest at C (under the action of the central force considered as repulsive) to infinity, and then from the opposite infinity (with an initial velocity equal to the velocity so acquired) to P. 188 REPORT—1862. by adding to the central force required to make the body move in the same orbit at rest, a force q (dist.)-3. This appears very readily by means of the differential equation (antée, No. 6), viz. writing therein P+-cu’ for P, and then 6', 2! in the place of o/1—S, its original form, with 6!, h’, in the place of 6, 2 respectively. 12, It may be remarked that when the original central force vanishes, the fixed orbit is a right line (not passing through the centre of force). It thus appears by § 9 that the curve u=A cos (n6+B) may be described under the action of a force q (dist.)-3. A proposition in § 2, already referred to, shows that a logarithmic spiral may be described under the action of such a force. 13. But the case of a force & (dist.)—3 was first completely discussed by Cotes in the ‘ Harmonia Mensurarum,’ pp. 31-35, 98-104, and Notes, pp. 117 -173. There are in all five cases, according as the velocity of projection is 1. Less than that acquired in falling from infi- nity, or say equal to that acquired in fall- ing from a point C to P, the point of pro- jection. 2, Equal to that acquired in falling from infi- w/ 1— a respectively, the equation retains nity. 3, 4, 5. eats than that acquired in falling from infinity, or say equal to that acquired in falling from a point C’, through infinity, to P; viz. PQ being the direction of pro- jection,and SQ, C'T perpendiculars thereon from § and C' respectively, 3. SQTQ; the equations of the orbits being 1. w=Ae™+4+Be~™, A and B same sign, so that rad. vector is never infinite. 2. u=Ae” or Be~™, logarithmic spiral. 3. u=Ac™+Be7-™, A and B opposite signs, so that rad. ector becomes infinite. 4. u=A0+B, m=0, reciprocal spiral. 5. u=A cos (n0+B), m=ny —1. 14, The before-mentioned equation, Cu P apt — ee 0, is in effect given (but the equation is encumbered with a tangential force) in Clairaut’s “ Théorie de la Lune,” 1765. Itis given in its actual form, and ex- tensively used (in particular for obtaining the above-mentioned equations for Cotes’s spirals) in Whewell’s ‘ Dynamics,’ 1823. The equation appears to be but little known to continental writers, and (under the form wv" +u—a’r?>R=0) it is given as new by Schellbach as late as 1853. The formule used in place of it are those which give ¢ and @ each of them in terms of r; viz. ? , r ; ON THE SPECIAL PROBLEMS OF DYNAMICS. 189 dt= il RT {hr (C—2f Pdr)}* ja hdr r{—h-+7°(C—2f Par)}" which, however, assume that P is a function of r only. 15. Force & (dist.)-2._ The law of motion in the conic sections is implicitly given by Newton’s theorem for the equable description of the areas, For the parabola, if « denote the pericentric distance, and f the angle from pericentre or true anomaly, we have pace Me (tan 2f+ 3 tan® if). Nv For the ellipse we have an angle g, the mean anomaly varying directly as the time (g=nt if nave ; an auxiliary angle u, the excentric anomaly, az connected with g by the equation g=u—esin u; _and then the radius vector r and the true anomaly f are given in terms of w by the equations r=a (1—e cos w), and e086 gin pM Ie sin and «tan afm 1 tan de, —e co —— —— —— = f l—ecosw 1l—e cos u 16. It is very convenient to have a notation for and f considered as func- tions of ¢,g, and I have elsewhere proposed to write r=a elqr(e, 9), f=elta (e, 9), read elqr elliptic quotient radius, and elta elliptic true anomaly. 17. The formule for the hyperbola correspond to those for the ellipse, but they contain exponential in the place of circular functions (see post, Elliptic Motion). 18, Euler, in the memoir “Determinatio Orbitz Comete Anni 1742,” (1743), p. 16 et seq., obtained an expression for the time of describing a para- bolic are in terms of the radius vectors and the chord; viz. these being f, g, and k, the expression is Time arrAl (r+94%)'— (r+0-z)'T, which, however, as remarked by Lagrange, ‘ Méc. Anal.’ t. xi. (3rd edit. p. 28), is deducible from Lemma X, of the third book of the ‘Principia.’ But the theorem in its actual form is due to Euler. 19. Lambert, in the ‘ Proprietates Insigniores, &e.’ (1761), Theorem VII, Cor. 2, obtained the same theorem, and in section 4 he obtained the corre- sponding theorem for elliptic motion ; viz. the expression for the time is at —¢'—(sin ¢—sin » Paige 9—o g $ 190 REPORT—1862, = sin 3@=3A pie, sin} g'=3q JU The form of the formula is, it will be observed, similar to that for motion in a straight line (anié, No. 4), and in fact the motion in the ellipse is, by an ingenious geometrical transformation, made to depend upon that in the straight line. The geometrical theorems upon which the transformation depends are stated, Cayley “On Lambert’s Theorem &c.” (1861). 20. The theorem was also obtained by Lagrange in the memoir “ Re- cherches &c.” (1767) as a corollary to his solution of the problem of two centres; viz. upon making the attractive force of one of the centres equal to zero, and assuming that such centre is situate on the curve, the expression for the time presents ‘itself in the form given by Lambert’s theorem, 21. Two other demonstrations of the theorem are given by Lagrange in the memoir “Sur une maniére particuliére d’exprimer Te temps &e.”’ (1778), reproduced in Note V. of the second volume of the last edition (Bertrand’s) of the ‘Mécanique Analytique.’ As M. Bertrand remarks, these demonstrations are very complete, very elegant, and very natural, assuming that the theorem is known beforehand. Demonstrations were also given by Gauss, ‘‘ Theoria Motus ” (1809), p. 119 et seq.; Pagani, « Démonstration @un théoréme &e.” (1834); and (in con- nexion with Hamilton’s principal function) by Sir W. R. Hamilton, “On a General Method &c.” (1834), p. 282; Jacobi, “Zur Theorie &e.” (1837), .' p- 122; Cayley, ‘ Note on the Theory of Elliptic Motion” (1856). 22: Connected with the problem of central forces, we have Sir W. R. Hamilton’s ‘ Hodograph,’ which in the paper (Proc, R. Irish Acad, 1847) is defined, and the fundamental properties stated; viz. if in an orbit round a eentre of force there be taken on the perpendicular from the centre on the tangent at each point, a length equal to the velocity at that point of the orbit, the extremities of these lengths will trace out a curve which is the hodograph. As the product of the velocity into the perpendicular on the tangent is equal to twice the area swept out in a unit of time (vp=h), the hodograph is the reciprocal polar of the orbit with respect to a circle described about the centre of force, radius =/h. Whence also the tangent at any point of the hodo- graph is perpendicular to the radius vector through the corresponding point of the orbit, and the product of the perpendicular on the tangent into the corresponding radius vector is =h. | wn If force q& (dist.)—2, the hodograph, qua reciprocal polar of a conic section with respect to a circle described about the focus, is a circle. 4 23. The following theorem is also given without demonstration ; viz.if two — circular hodographs, which have a common chord passing or tending through a common centre of force, be both cut at right angles by a-third circle, the times of hodographically describing the intercepted arcs (that is, the times of — describing the corresponding elliptic ares) will be equal. 24, Droop, “‘On the Isochronism é&e.” (1856), shows geometrically that . the last-mentioned property is equivalent to Lambert’s theorem; and an analytical demonstration is also given, Cayley, ‘A demonstration of Sir W. ‘R. Hamilton’s Theorem &e.’’ (1857). See also Sir W. R. Hamilton’s ‘ Lee- tures on Quaternions’ (1853), p. 614, 25. The laws of central force which have been thus far referred ~ are force ar, os: Cie ; and it has been seen that the case of a force P+ depends ON THE SPECIAL PROBLEMS OF DYNAMICS. 191 upon that of a force P, so that the motions for the forces Arts and B +5 y* are deducible from those for the forces Ar and 5 respectively. Some other laws of force, ¢. g. S+Br, Stat o+e, are considered by Legendre, «Théorie des Fonctions Elliptiques” (1825), being such as lead to results expressible by elliptic integrals, and also the law Ll for which the result in- r volves a peculiar logarithmic integral. But the most elaborate examination of the different cases in which the solution can be worked out by elliptic integrals or otherwise is given in Stader’s memoir “De Orbitis dc.” (1852), - where the investigation is conducted by means of the formule which give ¢ and @ in terms of r (ante, No. 14). 26. In speaking of a central force, it is for the most part implied that the force is a function of the distance: for some problems in which this is not the case, see post, Miscellaneous Problems, Nos. 86 and 87. It is to be noticed that, although the problem of central forces may be (as it has so far been) considered as a problem in plano (viz. the plane of the motion has been made the plane of reference), yet that it is also interesting to consider it as a problem in space; in fact, in this case the integrals, though of course involved in those which belong to the plane problem, present them- selves under very distinct forms, and afford interesting applications of the theory of canonical integrals, the derivation of the successive integrals by Poisson’s method, and of other general dynamical theories. Moreover, in the lunar and planetary theories, the problem must of necessity be so treated. Without going into any details on this point, I will refer to Bertrand’s memoir “Sur les équations différentielles de la Mécanique ” (1852), Donkin’s memoir “On a Class of Differential Equations &c.” (1855), and Jacobi’s pos- thumous memoir, “ Nova Methodus &c.” (1862). Elliptic Motion, Article Nos. 27-40. 27, The question of the development of the true anomaly in terms of the Mean anomaly (Kepler’s problem), and of the other developments which pre- sent themselves in the theory of elliptic motion, is one that has very much occupied the attention of geometers. The formule on which it depends are mentioned anté, No. 15; they involve as an auxiliary quantity the excentric anomaly wu. 28, Consider first the equation g=u—esin u, ‘which connects the mean anomaly g with the excentric anomaly wu. _ Any function of u, and in particular wu itself, and the functions ee nu may be expanded in terms of g by means of Lagrange’s theorem (Lagrange, ‘ Mém. de Berlin,’ 1768-1769, «Théorie des Fonctions,” c. 16, and “Traité de la Résolution des équations Numériques,” Note LE): 29. Considering next the equation tan af=/ tie tan 2 u, which gives the true anomaly in terms of the excentric anomaly, then, by / replacing the circular functions by their exponential values (a process em- 192 REPORT—1862. ployed by Lagrange, ‘Mém, de Berlin, 1776), f can be expressed in terms of uw; viz. the result is fH=ut2r sin u+2d. 3 sin 2u+2)°. 3sindu+&e., where rest a Awad (=). Hence if u, sin uv, sin 2u, &c. are é 1+/1-é expressed in terms of the mean anomaly, f will be obtained in the form =g-+a series of multiple sines of g, the coefficients of the different terms being given in the first instance as functions of ¢ and \; and to complete tho development \ and its powers have to be developed in powers of e. The solu- tion is carried thus far in the ‘Mécanique Analytique’ (1788), and im the ‘ Mécanique Céleste ’ (1799). 30. We have next Bessel’s investigations in the Berlin Memoirs for 1816, 1818, and 1824, and which are carried on mainly by means of the integral h 2r ont cos (hu—k sin u) du, 20 and various properties are there obtained and applications made of this im~ portant transcendant. 31. Relating to this integral we have Jacobi’s memoir, “ Formule trans- formationis &c.” (1836), Liouville, ‘Sur l’intégrale “cos i (w—a sin uw) du” 0 (1841), and Hansen’s “ Ermittelung der absoluten Stérungen” (1843) ; the researches of Poisson in the ‘ Connaissance des Temps’ for 1825 and 1836 are closely connected with those of Bessel. 32. A very elegant formula, giving the actual expression of the coefficients considered as functions of ¢ and X, is given by Greatheed in the paper “ Inyes- tigation of the General Term &c.” (1838) ; viz. this is fag teen {eer gn Teen sin "9 r where, after developing in powers of A, the negative powers of must be rejected, and the term independent of A divided by 2. This result is ex- tended to other functions of f, Cayley “On certain Expansions &c.” (1842). 33. An expression for the coefficient of the general term as a function of ¢ only is obtained, Lefort, ‘‘ Expression Numérique &c.” (1846). The expres- sion, which, from the nature of the case, is a very complicated one, is obtained by means of Bessel’s integral. This is an indirect process which really comes to the combination of the developments of f in terms of w, and w in terms of g; and an equivalent result is obtained directly in this manner, Creedy, ‘General and Practical Solution &c.” (1855). 34, We have also on the subject of these developments the very valuable and interesting researches of Hansen, contained in his ‘ Fundamenta Nova, &ec.’ (1838), in the memoir “Ermittelung der absoluten Storungen &e.” (1845), and in particular in the memoir “ Entwickelung des Products &e.” (1853). cos 35. But the expression for the coefficient of the general term .- 79 in any of these expansions is so complicated that it was desirable to have for the coefficients corresponding to the values r=0, 1, 2,3, ... the finally reduced expressions in which the coefficient of each power of ¢ is given as a numerical ON THE SPECIAL PROBLEMS OF DYNAMICS. 193 ™ cos » sin ¥. ? a general symbol, the expansion being carried as far as e”, were given, Lever- rier, ‘ Annales de l’Observatoire de Paris,’ t. i. (1855). 36. And starting from these I deduced the results given in my “Tables of the Developments, &c.” (1861); viz. these tables give (e=2-1), a | Ae wv"), Sete o 2 Cae 51 saa oi") nh j=l to j=7, (Ce) (Je GY) (Ci) Go) Go) tain saa wat all carried to e”. 37. The true anomaly f has been repeatedly calculated to a much greater extent, in particular by Schubert (Ast. Théorique, St. Pét. 1822), as far fraction. Such formule for the development of (Z —1 where 7 is . Yi . . : ase, The expression for — as far as e” is given in the same work, and that a for log - as far as e*° was calculated by Oriani, see Introd. to Delambre’s ‘Tables du Soleil,’ Paris (1806). 38. It may be remarked that when the motion of a body is referred to a plane which is not the plane of the elliptic orbit, then we have questions of development similar in some measure to those which regard the motion in the orbit ; if, for instance, z be the distance from node, ¢ the inclination, and a the reduced distance from node, then cosz=cos @ cos x, from which we may derive z=#-+ series of multiple sines of 2. And there are, moreover, the questions connected with the development of the reciprocal distance of two particles—say (a? + a'*—2aa! cos 0)~?—which present themselves in the pla- netary theory; but this last is a wide subject, which I do not here enter upon. I will, however, just refer to Hansen’s memoir, ‘‘ Ueber die Entwicke- lung der negativen und ungeraden Potenzen &c.” (1854). 39. The question of the convergence of the series is treated in Laplace’s memoir of 1823, where he shows that in the series which express r and f in . . : . cos . oe multiple cosines or sines of g, the coefficient of a term sin 7 where 7 is very great, is at most equal in absolute value to a quantity of the form slg): A and X being finite quantities independent of 7, whence he concludes that, in order to the convergency of the series, the limiting value of the excentricity is e=X, the numerical value being e=0°66195. 40. The following important theorem was established by Cauchy, as part of a theory of the convergence of series in general; viz. so long as e is less than 0:6627432, which is the least modulus of e for which the equations T : pues u, 1=ecos can be satisfied, the development of the true anomaly and other developments in the theory of elliptic motion will be convergent. This was first given in 1862, 0 194, REPORT—1862. the “Mémoire sur la Mécanique Céleste,”’ read at Turin in 1831, but it is reproduced in the memoir * Considérations nouvelles sur les suites &c.,” Mem. d’Anal, et de Phys, Math. t. i. (1840); and see also the memoirs in ‘ Liou- ville’s Journal’ by Puiseux, and his Note i. to vol. ii. of the 3rd ed. of the ‘Mécanique Analytique’ (1855), There are on this subject, and on subjects connected with it, several papers by Cauchy in the ‘Comptes Rendus,’ 1840 _et seq., which need not be particularly referred to. The Problem of two Centres, Article Nos. 41 to 64, 41. The original problem is that of the motion of a body acted upon by forces tending to two centres, and varying inversely as the squares of the distances ; but, as will be noticed, the solutions apply with but little variation to more general laws of force. 42, It may be convenient to notice that the coordinates made use of (in the several solutions) for determining the position of the body, are either the sum and difference of the two radius vectors, or else quantities which are respectively functions of the sum and the difference of these radius vectors*. If the plane of the motion is not given, then there is a third coordinate, which is the inclination of the plane through the body and the two centres to a fixed plane through the two centres, or say the azimuth of the axial plane, or simply the azimuth. 43, Calling the first-mentioned two coordinates r and s, and the azimuth yp, the solution of the problem leads ultimately to equations of the form dr _ ds _ Adr, pds pdr | ods VE WS “VRS “HVE WS where R and § are rational and integral functions (of the third or fourth degree, in the case of forces varying as (dist.)—®) of 7, s respectively (but they are not in general the same functions of r,s respectively); \ and p are simple rational functions of 7, and » and o simple rational functions of s; so that the equations give by quadratures, the first of them the curve described in the axial plane, the second the position of the body in this curve at a given time, and the third of them the position of the axial plane. In the ordinary case, where R and § are each of them of the third or the fourth order, the quadratures depend on elliptic integralst ; but on account of the presence in the formule of the two distinct radicals /R, /§, it would appear that the solution is not susceptible of an ulterior development by means of elliptic and Jacobian functionst similar to those obtained in the problems of Rotation and the Spherical Pendulum. 44, It has just been noticed that when R, S are each of them of the fourth order, the quadratures depend on elliptic integrals; in the particular cases mdr __ nds VR VS * Tf v, wu are the distances of the body P from the centres A and B, @ the distance AB, é, the angles at A and B respectively, and p=tan } % tan 4, gq=tan 3 +tan } y, then, in which the relation between 7, s is of the form >» Rand § being as may be shown without difficulty, v+u=a ioe o—uaazyt so that p and q are a a ofv-+u and »—w respectively ; these quantities p and q are Euler’s original coordi- nates. + The elliptic integrals are Legendre’s functions F, B, 1; the elliptic and Jacobian functions are sinam., cosam., Aam., and the higher transcendants 0, H. ON THE SPECIAL PROBLEMS OF DYNAMICS. 195 the same functions of +,s respectively, and m and n being integers (or more generally for other relations between the forms of R, S given by the theory of elliptic integrals), the equation admits of algebraical integration ; but as the relations in question do not in general hold good, the theory of the algebraical integration of the equations plays only a secondary part in the solution of the problem, It is, however, proper td remark that Kuler, when he wrote his first two memoirs “On the Problem of the two Centres” (post, Nos. 45 and 46), had already discovered and was acquainted with the theory ly nd of the algebraic integration of the equation TR Wa (R, 8, m, 2, ut supra), although his memoir, “ Integratio zequationis da dy VA+Bo+Co*+Da%+Ea* VA+By+Cy?+Dy'4 Ey” N. Comm. Petrop. t. xii. 1766-1767 ?, bears in fact a somewhat later date. 45. Having made these preliminary remarks, I come to the history of the problem. It is I think clear that Euler’s earliest memoir is the one «De Motu Corporis ce.” in the Petersburg Memoirs for 1764 (printed 1766). In this memoir the forces vary as (dist.)-?, and the body moves in a given plane. The equations of motion are taken to be oe =2y (—+=), u ay 2u( Ay By ” —¥ = 97 [| —_ 4 de vy wp which, if ¢, » are the inclinations of the distances v, u to the axis respectively ~ (See foot-note to No. 42), lead to dv? +d? 4gdt? ¢ te B be “="), vou a v'u* de dn=2gadt (A cos £+B cos n+D), where D, E are constants of integration. Substituting for v, wtheir values in terms of y, and eliminating dt, Kuler obtains . dfsinn P+/P?—Q? dy sin Z “4 Q 3 where A cos n+ B cos +D cos ¢ cos n+Esin ¢ sin 7»=P, A cos +B cosy+D =Q. And he then enters into a very interesting discussion of the particular case =0 or B=0 (viz, the case where one of the attracting masses vanishes, which was of course known to be integrable); and after arriving at some paradoxical conclusions which he does not completely explain, although he remarks that the explanation depends on the circumstance that the integral found is a simgular solution of a derivative equation, and as such does not satisfy the original equations of motion,—he proceeds to notice that an inquiry into the cause of the difficulty led him to a substitution by which the variables were separated. 46. But in the memoir * Probléme, un Corps &e.” in the Berlin Memoirs - for 1760 (printed 1767), after obtaining the last-mentioned formule, he gives 02 196 REPORT—1862. at once, without explaining how he was led to it, the analytical investigation of the substitution in question, viz. in each of the two memoirs he in fact writes dgsinn+dysin ¢ eee dz sin n—dy sin f tand¢=f, tandn=g, fy=p, he that is p=tanlZtand,; g=tan }f+tan }y; and in terms of these quantities p, q, the equation becomes dp _ dq VP VQ P=( A+B+4+D)p+2Ep*+(—A—B+D)p’, Q=(—A+B—D)q+2E¢+( A—B—D)¢’, so that P and Q are cubic functions (not the same functions) of p and q respectively ; and the equation for the time is found to be where dtr 2g _ pdp gdq aNa (—pyvP' (1+9)7VQ’ which are the formule for the solution of the problem, as obtained in Euler’s first and second memoirs. 47. In his third memoir, viz. that “‘ De Motu Corporis &c.” in the Petersburg Memoirs for 1765 (printed 1767), Euler considers the body as moving in space, the forces being as before as (dist.)—2._ Assuming that the coordinates 4, z are in the plane = Ssateammed to the axis, there is in this case Zz 1 the equation of areas y 77 —* “a =const.; and writing y=y’'sin yy, z=y’ cos yy, that’ is, y'= /y?+z2, and y the azimuth, the integral equations for the motion in the variable plane (coordinates #, y') are not materially different in form from those which belong to the motion in a fixed plane, coordinates «, y (see post, No. 56, Jacobi); and the last-mentioned equation, which reduces l itself to the form y” Ht =const., gives at once dy in a form such as that above alluded to (anté, No. 43), and therefore ~ by quadratures. The variables employed by Euler in the memoir in question are u+u,v—u (say 7, s) and y, v, u being, as above, the distances from the two centres, and y the azimuth of the axial plane. The functions of v,s under the radical signs are of the fourth order; this is so, with these variables, even if the motion is in a fixed plane ; but this is no disadvantage, since, as is well known, the ease of a quartic radical is not really more complicated than that of a cubic radical, the two forms being immediately convertible the one into the other. 48. Lagrange’s first memoir (Turin Memoirs, 1766-1769) refers to Euler’s three memoirs, but the author mentions that it was composed in 1767 with- out the knowledge of Euler’s third memoir. The coordinates ultimately made use of are v+u, v—u (say 7,s) and y, the same as in Euler’s third memoir, and the results consequently present themselves in the like form, ON THE SPECIAL PROBLEMS OF DYNAMICS. 197 49. If the attractive force of one of the centres is taken equal to zero, then the position of such centre is arbitrary, and it may be assumed that the centre lies on the curve, which is in this case an ellipse (conic section) ; the expression of the time presents itself as a function of the focal radius vectors and the chord of the arc described ; which, as remarked, anté, No. 20, leads to Lambert’s theorem for elliptic motion. 50. The case presents itself of an ellipse or hyperbola described under the : ; k dp arts ’ action of the two forces, viz. the equation VE WS will be satisfied byr—a=0, if r—a@ be a double factor of R, or by s—f@=0, if s—B be a double factor of S, a case which is also considered in the ‘ Mécanique Ana- lytique ;’ and see in regard to the analytical theory, t. ii. 3rd ed. Note III. by M. Serret, and “‘Thése,” Liouv. 1848. It is remarked by M. Bonnet, Note LV. and Liouy. t. ix. p. 113, 1844, that the result is a mere corollary of a general theorem, which is in. effect as follows, viz. if a particle under the separate actions of the forces F, F’, . . . starting in each case from the same point in the same direction but with the initial velocities v, v', &e. respectively, describe the same curve, then such curve will also be described under the conjoint action of all the forces, provided the body start from the same point in the same direction, with the initial velocity V= /v?+v7+4.. 51. Lagrange’s second memoir (same volume of the Turin Memoirs) contains an exceedingly interesting discussion as to the laws of force for which the problem can be solved. Writing U,V, u,v in the place of Lagrange’s P, Q, p, g, the equations of motion are x, (wx—a)U 4 (a— a)V_ 0, dt? u v Uy , (y—5)U | (y—6)V_ Ger Sagem et Te dz, (z—c)U (z—y)V_ de Tiare) Babies wih Int where w= (x—a)’+(y—b)'+ (zc), v= (w7—a)’+(y—B) + (e—y)’, and putting also f (= /(a—a)’+ (6— 8)’ + (c—y)’) the distance of the centres, and then w’=/x, v’=fy, eet (~,y are of course not to be con- founded with the coordinates originally so represented), Lagrange obtains the equations Pax (w+y—D¥ poet ke SO +f (Xde+Ydy)=0, & —1)x Aces eee +f (Xdu+Ydy)=0, which he represents by Px gp tM=0, iy 3 de +N=0; 198 REPORT—1862. and he then inquires as to the conditions of integrability of these equations, for which purpose he assumes that the equations multiplied by mda+ndy and pdx +vdy respectively and added, give an integrable equation. 52. A case satisfying the required conditions is found to be B Y=2 PA = =, Y=2a4+—= x eae i Vf ve or, what is the same thing, U=2au+2, Vedat 2 ; that is, besides the forces a os which vary as (dist.)—2, there are the forces 2au, 2av, varying directly as the distance, and of the same amount at equal distances; or, what is the same thing, there is, besides the forces varying as (dist.)—2, a force varying directly as the distance, tending to a third centre midway between the other two, a case which is specially considered in the memoir; it is found that the functions in r, s under the radicals (instead of rising only to the order 4) rise in this case to the order 6. 53. Among other cases are found the following, viz. :—= 7. Veen t Sw tie, 5 5 Vau+2 a vw 2°, Vaan +h ut", V=tu+5 v, f where B=e, or else ce=PSd=2(e. In regard to the subject of this second memoir of Lagrange, see post, Mis- cellaneous Problems, Liouville’s Memoirs, Nos. 100 to 105. 54. In the ‘Mécanique Analytique’ (1st ed. 1788, and 2nd ed. t. ii. 1813), Lagrange in effect reproduces his solution for the above-mentioned law of force (say U= Zt 2yu, Vas +2). There are even in the third edition a few trifling errors of work to be corrected. The remarks above referred to, as made by Lagrange in his first memoir, are also reproduced (see ante, Nos. 49 and 50). 55. Legendre, “Exercices de Calcul Intégral,” t. ii.(1817), and “Théorie des Fonctions Elliptiques,” t. i. (1825), uses p* and q’ in the place of Euler’s p, ¢; the forces are assumed to vary as (dist.)—2, and in consequence of the change Euler’s cubic radicals are replaced by quartic radicals involving only even powers of p and q respectively ; that is, the radicals are in a form adapted for the transformation to elliptic integrals; in certain cases, however, it becomes necessary to attribute to Legendre’s variables p and q imaginary values. The various cases of the motion are elaborately discussed by means of the elliptic integrals; in particular Legendre notices certain cases in which the * In the ‘ Mécanique Analytique,’ Lagrange’s letters are *, qg for the distances r-+-q=s, *—q=w: the change in the present Report was occasioned by the retention of p, q or Euler’s variables. ON THE SPECIAL PROBLEMS OF DYNAMICS. 199 motion is oscillatory, and which, as he remarks, seem to furnish the first instance of the description by a free particle of only a finite portion of the curve which is analytically the orbit of the particle ; there is, however, nothing surprising in this kind of motion, although its existence might easily not have been anticipated. 56. § 26 of Jacobi’s memoir “ Theoria Novi Multiplicatoris &c.” (1845) is entitled ‘Motus puncti versus duo centra secundum legem Neutonianum attracti.” The equations for the motion in space are by a general theorem given in the memoir “ De Motu puncti singularis ” (1842), reduced to the case of motion in a plane: viz. if w, y are the coordinates, the centre point of the axis being the origin, and y being at right angles to the axis, andif the distance ay dt? 2 there is added a term ra which arises from the rotation about the axis. Two of the centres is 2a; then the only difference is that to the expression for integrals are obtained, one the integral of Vis Viva, and the other of them an integral similar to one of those of Euler’s or Lagrange’s. And then 2’, y’ being the differential coefficients of w, y with regard to the time, the remain- ing equation may be taken to be y'dv—a‘dy=0, where wx’, y' are to be expressed as functions of w, y by means of the two given integrals. This being so, the principle of the Ultimate Multiplier * furnishes a multiplier of this differential equation, and the integral is found to be y'du—x'dy ay (#@—y")+ (Ca +y)ay © the quantity under the integral sign being a complete differential. To verify a@ posteriori that this is so, Jacobi introduces the auxiliary quantities X’, \" defined as the roots of the equation \°+A(a*+y’?—a’*)—a’y’?=0, which in fact, if as before u, v are the distances from the centres, leads to u+-v=2V PN, u—v=2V aX", so that \’,” are functions of w+v, w—v respectively ; and the formulz, as ultimately expressed in terms of X’, X”, are substantially of the same form with those of Euler and Lagrange. 57. The investigations contained in Liouville’s three memoirs “ Sur quel- ques cas particuliers &c.” (1846), find their chief application in the problem of two centres, and by leading in the most direct and natural manner to the general law of force for which the integration is possible, they not only give some important extension of the problem, but they in fact exhibit the pro- blem itself and the preceding solutions of it in their true light. But as they do not relate to this problem exclusively, it will be convenient to consider them separately under the head Miscellaneous Problems. 58. In Serret’s ‘ Thése sur le Mouvement &c.’ (1848), the problem is very elegantly worked out according to the principles of Liouville’s memoirs as follows: viz. assuming that the expression of the distance between two con- secutive positions of the body is i ds? =(mdp? +ndy*)+Xr"dy’, where m, n are functions of , v respectively, and if the forces can be repre- sented by means of a force-function U, then the motion can be determined, * Explained in Jacobi’s memoir “Theoria Novi Multiplicatoris &e.,” Crelle, tt. xxvii. XXvill. xxix. 1844-465. : : 200 REPORT—1862, provided only , AU, = are of the forms A=gu—Oy, AU=yp—Wy, A =op— Ty, where the functional symbols ¢, @, &c. denote any arbitrary functions what- ever. 59. It is then assumed that p, vy are the parameters of the confocal ellipses and hyperbolas situate in the moveable plane through the axis, viz. that we have “Stra: ammo 2 oe pe b? ? 2 2 wv y b—pr =i (the origin is midway between the two centres, 2b being their distance ; 3u, 4v are in fact equal to the sum and difference u+v, u—v of the two centres respectively) ; and that the position of the moveable plane is deter- mined by means of y, the inclination to a fixed plane through the axis, or say, as before, its azimuth. In fact, with these values of the coordinates, the expression of ds* is 2 2 l 2 if 5 nae lin es 2 which is of the required form. And moreover if the forces to the two centres yary as (dist.)—?, and there is besides a force to the middle point varying as the distance, then U= ee at Fe —b*), p+y pov whence (observing that A=,?—»*) AU is of the required form, The equa- tions obtained by substituting for U the above value give the ordinary solution of the problem. 60. Liouville’s note to the last-mentioned memoir (1848) contains the demonstration of a theorem obtained by a different process in his second memoir, but which is in the present note, starting from Serret’s formule, demonstrated by the more simple method of the first memoir, viz., it is shown that the motion can be obtained if the two centres, instead of being fixed, revolve about the point midway between them in a circle in such manner that the diameter through the two centres always passes through the projection of the body on the plane of the circle. It will be observed that the circular motion of the two centres is neither a uniform nor a given motion, but that they are, as it were, carried along with the moving body. 61. In Desboves’s memoir “Sur le Mouvement d’un point matériel &e,” (1848), the author developes the solution of the foregoing problem of moving centres, chiefly by the aid of the method employed in Liouville’s second memoir. And he shows also that the methods of Euler and Lagrange for the case of two fixed centres apply with modification to the more complicated problem of the moving centres. 62. The problem of two centres is considered in Bertrand’s “‘ Mémoire sur les équations différentielles &c.” (1852), by means of Jacobi’s form of the ON THE SPECIAL PROBLEMS OF DYNAMICS. 201 equations of motion, viz., the problem is reduced to a plane one by means of the addition of a force as (ante, No. 56), 63. Cayley’s “ Note on Lagrange’s Solution &c.” (1857) is merely a repro- duction of the investigation in the ‘ Mécanique Analytique ;’ the object was partly to correct some slight errors of work, and partly to show what were the combinations of the differential equations, which give at once the integrals of the problem. 64, In § II. of Bertrand’s ‘“‘ Mémoire sur quelques unes des formes &c.” (1857), the following question is considered, viz., assuming that the dynamical equations ie dU Wy dU | df de’ dO dy’ have an integral of the form a=Px?+Qe'y'+Ry?+8y'+Te' +K (where « is the arbitrary constant, and P, Q...K are functions of w and y), it is required to find the form of the force-function U. It is found that U must satisfy a certain partial differential equation of the second order, the general solution of which is not known; but taking U to be a function of the distance from any fixed point (or rather the sum of any number of such functions), it is shown that the only case in which the differential equations for the motion of a point attracted to a fixed centre of forces have an inte- gral of the form in question is the above-mentioned one of two centres, each attracting according to the inverse square of the distance, and a third centre midway between them, attracting as the distance. The Spherical Pendulum, Article Nos. 65 to 73. . 65. The problem is obviously the same as that of a heavy particle on the surface of a sphere. I have not ascertained whether the problem was considered by Euler. Lagrange refers to a solution by Clairaut, Mém. de l’Acad. 1735. The question was considered by Lagrange, Méc. Anal. Ist edit. p. 283. The angles which determine the position are y the inclination of the string to the horizon, ¢ the inclination of the vertical plane through the string to a fixed vertical plane, or say the azimuth. And then forming the equations of motion, two integrals are at once obtained; these are the integrals of Vis Viva, and an integral of areas. And these give equations of the form — dt=funct. (p) dp, dg=funct. (W)dy ; so that ¢, » are each of them given by a quadrature in terms of , which is the point to which the solution is carried. It is noticed that may have a constant value, which is the case of the conical pendulum. 66. In the second edition, t. xi. p. 197 (1815), the solution is reproduced ; only, what is obviously more convenient, the angles are taken to be y, the inclination to the vertical, @, the azimuth. It is remarked that will always lie between a greatest value a and a least value f, and the integrals are transformed by introducing therein instead of y the angle o, which is such that cos L=cos « sin?a+ cos f cosa, 202 REPORT—1862. by which substitution they assume a more elegant form, involving only the radical V 1+ (cos /3— cos a) cos 2, where & is a constant depending on cos a, cos 3; and the integration is effected approximately in the case where cos }—cos @ is small. M. Bravais has noticed, however, that by reason of some errors in the working out, Lagrange has arrived at an incorrect value for the angle &, which is the apsidal angle, or difference of the azimuths for the inclinations a and: see the 3rd edition (1855), Note VII., where M. Brayais resumes the calculation, and he arrives at the value @=7(1+ 3a), a and 3 being small. Lagrange considers also the case where the motion takes place in a resist- ing medium, the resistance varying as velocity squared. 67. A similar solution to Lagrange’s, not carried quite so far, is given in Poisson’s ‘ Mécanique,’ t. i. pp. 385 et seq. (2nd ed. 1833). A short paper by Puiseux, ‘‘ Note sur le Mouvement d’un point matériel Tv 5 68, The ulterior development of the solution consists in the effectuation of the integrations by the elliptic and Jacobian functions. It is proper to re- mark that the dynamical problem the solution whereof by such functions was first fairly worked out, is the more difficult one of the rotation of a solid body, as solved by Jacobi (1839), in completion of Rueb’s solution (1834), post, Nos. 186 and 197. 69. In relation to the present problem we have Gudermann’s memoir “ De pendulis sphericis dc.” (1849), who, however, does not arrive at the actual expressions of the coordinates in terms of the time; and the perusal of the memoir is rendered difficult by the author’s peculiar notations for the elliptic functions*. rk 70. It would appear that a solution involving the Jacobian functions was obtained by Durége, in a memoir completed in 1849, but which is still un- published ; see § XX. of his ‘Theorie der elliptischen Functionen’ (1861), where the memoir is in part reproduced. It is referred to by Richelot in the Note presently mentioned. 71. We have next Tissot’s ‘Thése de Mécanique,’ 1852, where the ex- pressions for the variables in terms of the time are completely obtained by means of the Jacobian functions H, ©, and which appears to be the earliest published one containing a complete solution and discussion of the problem. 72. Richelot, in the Note ‘“‘ Bemerkungen zur Theorie des Raumpendels ” (1853), gives also, but without demonstration, the final expressions for the coordinates in terms of the time. Donkin’s memoir “On a Class of Differential Equations &e.’”’ (1855) con- tains (No. 59) an application to the case of the spherical pendulum. 73. The first part of the memoir by Dumas, “ Ueber die Bewegung deg Raumpendels,” &. (1855), comprises a very elegant solution of the problem of the spherical pendulum based upon Jacobi’s theorem of the Principal Func- tion (1837), and which is completely developed by the elliptic and Jacobian functions. The latter part of the memoir relates to the effect of the rotation of the Earth ; and we thus arrive at the next division of the general subject. sur une sphére ” (1842), shows merely that the angle ® is > * The mere use of sn., cn., dn. as an abbreviation of the somewhat cumbrous sinam., cosam., Aam. of the ‘Fundamenta Noya’ is decidedly convenient. ON THE SPECIAL PROBLEMS OF DYNAMICS. 203 Motion as affected by the Rotation of the Earth, and Relative Motion in general. Article Nos. 74 to 85. 74, Laplace (Méc. Céleste, Book X.c. 5) investigates the equations for the motion of a terrestrial body, taking account of the rotation of the Earth (and also of the resistance of the air), and he applies them to the determination of the deviations of falling bodies, &c. He does not, however, apply them to the case of the pendulum. 75. We have also the memoir of Gauss, ‘‘ Fundamental-gleichungen, cc.” (1804): the equations ultimately obtained are similar to those of Poisson. I have not had the opportnnity of consulting this memoir. 76. Poisson, in the “‘Mémoire sur le mouvement des Projectiles &c.’’ (1838), also obtains the general equations of motion, viz. (omitting terms involving n*), these may be taken to be : x dy . dz > Fa X+2n op sin-+ 5,05 3) ay dw . GPa bs Ee (see p. 20), where the axes of w, y,z are fixed on the Earth and moveable with it: viz., z is in the direction of gravity; x,y in the directions perpendicular to gravity, viz., y in the plane of the meridian northwards, w westwards; g is the actual force of gravity as affected by the resolved part of the centrifugal force ; 3 is the latitude. There are some niceties of definition which are carefully given by Poisson, but which need not be noticed here. 77. Poisson applies his formule incidentally to the motion of a pendulum, which he considers as vibrating in a plane; and after showing that the time of oscillation is not sensibly affected, he remarks that upon calculating the force perpendicular to the plane of oscillation, arising from the rotation of the Earth, it is found to be too small sensibly to displace the plane of oscillation or to have any appreciable influence on the motion—a conclusion which, as is well known, is erroneous. He considers also the motion of falling bodies, but the memoir relates principally to the theory of projectiles. 78. That the motion of the spherical pendulum is sensibly affected by the rotation of the Earth is the well-known discovery of Foucault ; it appears by his paper, ‘‘ Démonstration Physique &c.,”” Comptes Rendus, t. xxxii. 1851, that he was led to it by considering the case of a pendulum oscillating at the pole ; the plane of oscillation, if actually fixed in space, will by the rotation of the Earth appear to rotate with the same velocity in the contrary direction ; and he remarks that although the case of a different latitude is more compli- cated, yet the result of an apparent rotation of the plane of oscillation, dimi- nishing to zero at the equator, may be obtained either from analytical or from mechanical and geometrical considerations. Some other Notes by Foucault on the subject are given, ‘Comptes Rendus,’ t. xxxy. (1853). 79. An analytical demonstration of the theorem was given by Binct, ‘Comptes Rendus,’ t. xxii. (1851), and by Baehr (1853). Various short papers on the subject will be found in the ‘ Philosophical Magazine,’ and elsewhere. 80. In regard to the above-mentioned problem of falling bodies, we have a Note by W. 8., Camb. and Dub. M. Journ. t, iii. (1848), containing some errors 204 REPORT—1862. which are rectified in a subsequent paper, ‘“‘ Remarks on the Deviation of Falling Bodies,” &c. t. iv. (1849), by Dr. Hart and Professor W. Thomson. 81. The theory of relative motion is considered in a very general manner - in M. Quet’s memoir, “ Des Mouvements relatifs en général &e.”’ (1853). Sup- pose that w, y,z are the coordinates of a particle in relation to a set of move- able axes; let é', n', Z’ be the coordinates of the moveable origin in reference Pe’ dn CZ to a fixed set of axes, and treating the accelerations “*, “7, “% dt? dt?” dt’ were coordinates, let these, when resolved along the moveable axes, give u', v', w': suppose, moreover, that p,q, 7 denote the angular velocities of the system of the moveable axes (or axes of x, y,z) round the axes of x, y, and z respectively ; w’, v', w', p, g, 7 are considered as given functions of the time, and then, if as if they x dz ad di dr pet Dot Oa eet Sn ee fo ' is det (05; rh) dt Yat a (Py le ae 4 a dal _@Y , of dx dz Vig De yaa pothe siee vee (F 2G) +7 zat (92 —Ty)—P (PYG) Tes _&z dy _ dx dp __ dq a Se 7 F wa at2 (0G in)tyd oR te pe) —9 (TY JE ws it is shown that the equations of motion are to be obtained from the equation Im[(u—X)ca+(v—Y)éy+(w—Z)éz|=0, where éw, ¢y, éz are the virtual velocities of the particle m in the directions of the moveable axes. This equation is in fact obtained as a transformation of the equation nl (té_x Py a | Le onl (3 x) e+(oe Y)in+(3e )e =e which belongs to a set of fixed axes of &, », Z. 82. The equations for the motion of a free particle are of course u=X, v=Y,w=Z. In the case where the moveable axes are fixed on the Earth, and moveable with it (the diurnal motion being alone attended to), these lead to equations for the motion of a particle in reference to the Earth, similar to those obtained by Gauss and Poisson. The formule are applied to the case of the spherical pendulum, which is developed with some care; and Foucault’s theorem of the rotation of the plane of oscillation very readily presents itself. The general formule are applied to the relative motion of a solid body, and in particular to the question of the gyroscope; the memoir contains other in- teresting results. 83. The principal memoirs on the motion of the spherical pendulum, as affected by the rotation of the Earth, are those of Hansen, “ Theorie der Pen- delbewegung &c.”’ (1853), which contains an elaborate investigation of all the physical circumstances (resistance of the air, torsion of the string, &c.) which can affect the actual motion, and the before-mentioned memoir by Dumas, “ Ueber der Bewegung des Raumpendels &c.” (1855), The investigation is conducted by means of the variation of the constants; the integrals for the undisturbed problem were, as already noticed, obtained by means of Jacobi’s Principal Function, that is, in a form which leads at once to the expressions for the variation of the constants; and the investigation appears to be carried out in a most elaborate and complete manner. 84. In concluding this part of the subject I refer to Mr. Worms’s work, — *The Rotation of the Earth’ (1862), where the last-mentioned questions — ON THE SPECIAL PROBLEMS OF DYNAMICS, 205 (falling bodies, the pendulum, and the gyroscope) are, in reference to the proofs they afford of the rotation of the Earth, considered as well in an experi- mental as in a mathematical point of view. The second part of the volume contains the theory (after Laplace and Gauss) of falling bodies, that of the pendulum (after Hansen), and that of the gyroscope (after Yyon Villarceau) ; and the whole appears to be a complete and satisfactory résumé of the experi- mental and mathematical theories to which it relates. 85. We have also Cohen “ On the Differential Coefficients and Determinants of Lines &c.” (1862), where the equations for relative motion are obtained in a very elegant manner. The fundamental notion of the memoir may be con- sidered to be the dealing directly with lines, velocities, &c., which are variable in direction as well as in magnitude, instead of referring them, as in the ordi- nary analytical method, to axes fixed in space. The memoir is a highly in- teresting and valuable one, and the results are brought out with great facility ; but I cannot but think that the great care required to apply the method cor- rectly is an objection to it, if used otherwise than by way of interpretation of previously obtained results, and that the ordinary method is preferable. I may remark that the theory of relative motion connects itself with the lunar and planetary theories as regards the reference of the plane of the orbit to the variable ecliptic, and as regards the variations of the position of the orbit; but this is a subject which I have abstained from entering upon. Miscellaneous Problems. Article Nos. 86 to 111 (several subheadings), Motion of a single particle, 86, Jacobi, in the memoir “ De Motu puncti singularis” (1842), notices (§ 5) the case of a body acted on by a central force which is any homogeneous function of the degree —2 of the coordinates ; or representing these by 7 cos ¢, y sin g, then the force is caky where ® is any function of the angle ¢. In i fact, after integrating by a process different from the ordinary one the case of a central force a he remarks that the method in fact applies to the more general law of force just mentioned. 87. Jacobi, in the memoir “ Theoria Novi Multiplicatoris &c.” (1845), con- siders (§ 25) the case of a body acted on by a central force P a function of the distance, and besides by forces X and Y, which are homogeneous functions of the degree —3 of the coordinates (#, y); viz. the equations of motion are in this case Ma Px de Tp FM Cpaoury ge hy and there is an integral rat "aly 2 farteY —y? ps . 3(ay'’—a'y) —f (wY—yX) a const (the function under the integral sign is obviously a function of the degree 0 in (a, y), that is, it is a function of Y) if X, Y are the derived functions of xe a force-function U of the degree —2 in (w, y), then there is, besides, the in- tegral of Vis Viva, and thence a third integral is obtained by means of the 206 REPORT—1862. theorem of the Ultimate Multiplier. It may be noticed that in the last-men- tioned case the force-function is of the form =? so that if we represent also the eentral force by means of a force-function R (=function of r), then the entire foree-function is aot The case is a very interesting one; it in- cludes that considered § iv. of Bertrand’s “ Mémoire sur les équations différen- tielles de la Mécanique” (1852), where the force-function is of the form =5 Motion of three mutually attracting bodies in a right line. 88. The problem is considered by Euler in the memoir “De Motu rectilineo &e,” (1765), the forces being as the inverse square of the distance; and a solution is obtained for an interesting particular case. Let A, B,C be the masses, and suppose that at the commencement of the motion the distances CB, BA are in the ratio a: 1, and that the velocities (assumed to be in the same sense) are proportional to the distances from a fixed point. Then, if be the real root (there is only one) of the equation of the fifth order C0 (14+8a+3a7)=Ad’ (a’4+38a+3)+B(a+1*y(a’—1), the distances CB, BA will always continue in the ratio a:1. It may be added that the distances CB, BA each of them vary as *—a*, where a is a constant, and 7 is, according to the initial circumstances, a function of t de- fined by one or the other of the two equations r+ Nee a BI t=n'e¥ P—@—n'a? log a) aoa til t=n3eV 2—r?+n'a7sin— -. a 89. The bodies are considered as restricted to move in a given line; but it is clear that if the bodies, considered as free points in space, are initially in a line, and the initial velocities are also in this line, then the bodies will always continue in this line, which will be a fixed line in space. But if the distances and velocities are as above, except only that the velocities, instead of being along the line, are parallel to each other in any direction whatever, then the bodies will always continue in a line, which is in this case a moveable line in space (see post, No. 93). 90, Euler resumes the problem in the memoir of 1776 in the ‘ Nova Acta Petrop” The distances AB, BC being p and gq, then PP. pre Ny Be at Gus dO pg? tng)” CE SPU PAE) Gt 0 and in particular he considers the before-mentioned case of a solution of the form p=nqg; and also the particular problem where one of the masses vanishes, C=0; in this case, introducing (instead of p, q) the new variables u, 8, Where g=up, dq=sdp (a transformation suggested by the homogeneity — of the equations), and making, moreover, the particular supposition that the integral of the first equation is (Zy—-—= (viz, making the constant ON THE SPECIAL PROBLEMS OF DYNAMICS. 207 of integration to vanish), he obtains between s and w the equation of the first order ds A B which, however, he is not able to integrate. 91. Jacobi has given in the memoir “ Theoria Noyi Multiplicatoris ” (1845) ($28, entitled “De Problemate trium corporum in eadem recta motorum. Sub- stitutio Euleriana. Theoremata de viribus homogeneis’’) a very symmetrical and elegant investigation of the same problem, The centre of gravity being assumed to be at rest, the coordinates «, a,, x, of the three bodies are in the first instance expressed as linear functions of the two variables u, v (being, as Jacobi remarks, the transformation employed in his memoir “Sur I’élimination des 2, 2 Neeuds” (1843), post, No. 114), CY and - come out respectively equal to a au homogeneous functions of the degree —2 of these variables u and v, and the integral of Vis Viva exists, The subsequent transformation consists in the introduction of the variables 7, $, 8, n, Where w=r cos $, v=r sing, s= V7 ees 5 r 7= VP Se this gives a system of equations independent of x; viz., dg: ds; dn=n: 38°+n°?—®: —3sn+@', where @ is a given function of ¢, and ©’ is the derived function. If these equations were integrated, the equation of Vis Viva gives at once r= ; 2 (®—2(s*+n°)); and finally the time ¢ would be given by a quadrature, 1 ; V o—3(s°+ 7° if one integral were known the other would be at once furnished by the general theory, There is a simplification in the form of the solution if h (the constant of Vis Viva) =0. It is remarked that the method is equally appli- cable when the force varies as any power of the distance; and moreover that when the force varies as (dist.)~*, then the solution.depends upon one qua- drature only. 92, The concluding part of the section relates to the very general problem of a system of n particles acted on by any forces homogeneous functions of the coordinates (this includes the case of n particles mutually attracting each other according to a power of the distance), and this more general investiga- tion illustrates the method employed in regard to the three bodies in a line. Tt may be remarked that in the general theorem for the » particles “sint vires &c.,” the constant of Vis Viva is supposed to vanish. The system of three equations has the multiplier M= hehte Particular cases of the motion of three bodies. 93. In the case of three bodies attracting each other according to the in- verse square of the distance, the bodies may move in such manner as to be constantly in a line (a moveable line in space); this appears by the memoir, Euler, “Considérations générales, &c.” (17 64), in which memoir, however (which it will be observed precedes the memoir De Motu rectilineo &c.” (1765), referred to No. 88), Euler assumes that the mass of one of the bodies is so small as not to affect the relative motion of the other two. Calling the bodies the Sun, Earth, and Moon, and taking the masses to be 1, m, 0, then a result obtained is, that in order that the Moon may be perpetually ; 208 REPORT—1862. in conjunction, its distance must be to that of the Sun as @:1, where m(1—a)’=3a’—3a'+a’, or a= 3/ im nearly. It appears, however (ante, No. 88), that the foregoing restriction as to the masses is unnecessary, and, as will be mentioned, the problem has since been treated without such restriction. Euler investigates the motion in the case where the initial carcumstances are nearly but not exactly as originally supposed; this assumes, however, that the motion is stable—z.e. that the bodies will continue to moye nearly, but not exactly as originally supposed, which is at variance with the conclusions of Liouville’s memoir, post, No. 95. I have not examined the cause of this discrepancy. 94, In the ‘Mécanique Céleste’ (1799), Book x. ¢. 6, Laplace considers two cases where the motion can be exactly determined. 1°. Force varies as any function of the distance. It is shown that the motion may be such that the bodies form always an equilateral triangle of variable magnitude—the motion of each body about the centre of gravity being the same as if that point were a centre of force attracting the body according to a similar law. 2°. Force qx (dist.)". The motion may be such that the three bodies are always in a right line (moveable in space), the relative distances being in fixed ratios to each other. In particular, if force q (dist.)~?, then m, m', m' being the masses, the quantity z which determines the ratio of the distances mm’, m'm is given by O=mz?[(1+2)?—1]—m' (142) (1—2)—m" [(1+2)°—27]=0, which is, in fact, the formula in Euler’s memoir “ De Motu rectilineo &c.’’ 95. Liouville’s memoir “Sur un cas particulier &c.” (1842) has for its object to show that if the initial circumstances are not precisely as supposed in the second of the two cases considered by Laplace, or, what is the same thing, in Euler’s memoir ‘ Considérations générales &c.,” then the motion is unstable ; the instability manifests itself in the usual manner, viz. the expres- sions for the deviations from the normal positions are found to contain real exponentials which increase indefinitely with the time. 96. It may be proper to refer here to Jacobi’s theorem, ‘ Comptes Rendus,’ t. iii. p. 61 (1836), quoted in the foot-note p. 15 of my Report of 1857, which relates to the motion of a point without mass revolving round the Sun, and disturbed by a planet moving in a circular orbit, and properly belongs (as I have there remarked) to the problem of two centres, one of them moveable and the other revolying round it in a circle with uniform velocity. The theorem (given without demonstration by Jacobi) is proved by Liouville in his last-mentioned memoir, and he remarks that the theorem follows very simply as a corollary of the theorem by Coriolis, “On the Principle of Vis Viva in Relative Motions,” Journ. de l’Ecole Polyt. t. xiii. p. 268 (1832). There is, however, no difficulty in proving the theorem; another proof is given, Cayley, “ Note on a Theorem of Jacobi’s &c.” (1862). Motion in a resisting medium. 97. I do not consider the various integrable cases of the motion of a par- ticle in a resisting medium, the resistance varying with the velocity according to some assumed law, the particle being either not acted on by any force, or acted upon by gravity only. Some interesting cases are considered in Jacobi’s memoir “ De Motu puncti singularis” (1842), §§ 6 and 7 (see post, No. 108). ON THE SPECIAL PROBLEMS OF DYNAMICS. 209 98. In the case of a central force varying as (dist.)—2, the effect of a resist- ing medium (R O¢ v”) is considered in reference to the lunar theory, in the ‘Mécanique Céleste,’ Book VII. ¢. 6. Formule for the variations of the elliptic elements are given in the ‘ Mécanique Analytique,’ t. ii. (2nd edition). But the variations of the elliptic elements are fully worked out by means of grec and Jacobian functions in Sohncke’s valuable memoir “Motus Corporum ve.” (1833). 99. The effect of the resistance of the air on a pendulum has been elaborately considered by Poisson, Bessel, Stokes, and others; as the dimensions of the ball are attended to, the problem is in fact a hydrodynamical one. The effect on the spherical pendulum is considered in Hansen’s memoir Theorie der Pendelbewegung &c.” (1853). The effect on the motion of a projectile is considered in Poisson’s memoirs “Sur le Mouvement des Projectiles &c.” (1838). Liouville’s memoirs “ Sur quelques Cas particuliers ou les équations du mouvement dun point matériel peuvent s’intégrer” (1846-49). 100. In the first memoir (§ 1) the author considers a point moving in a plane or on a given surface, where the principle of Vis Viva holds good (or say where there is a force-function U). The coordinates of the point, and the function U, may be expressed in terms of two variables a, 3, and it is assumed that these are such that ds*=)(da’ +d’), where ) isa function of a and 6. That is, we have T=3)(a!+4") ; and the equations of motion are d.dal_ 1dd- 0, am , dU di Oda” ae \t ay Ne deeee ot re ae Bap tO + ae One integral of these is A(a!?+B")=2U 40; and by means of it the equations take the form d.ral 1dr dU dt Papeete d.rp!_1 dro dU a ax gp CUtO+ 5, These equations, it is easy to show, may be integrated if (2U+C)\=fa—F@£, and they then in fact give Na?=fa—A, AN pP= A—FB, where A is an arbitrary constant. And we then have da dp Vja—A VA—FP which gives the path, and the expression for the time is easily obtained by means of a quadrature. It is not more general, but it is frequently convenient to employ instead of a, B, two variables » and y, such that a 2 2 as ds*=)(mdp?+ndy’), 2 210 REPORT—1862. where m is a function of p only and n of y only, while \ contains p and y. The geometrical signification of the equation ds*=)(da* +d"), or of the last- mentioned equivalent form, is that the curves a or \=const., B or p=const., intersect at right angles. ; xs ; The foregoing differential equation of the path, writing fu, Fv in the place of fa, F3 respectively, may be expressed in the form Spoosi+Fysin=A, where 7, 90°—7 are the inclinations of the path at the point (A, ») to the two orthotomic curves through this point. 101. The before-mentioned equation (2U+C)A=fa—FB may be satisfied independently of C, or else only for a particular value of C. In the former case the law of force is much more restricted, but on the other hand there is no restriction as regards the initial circumstances of the motion; it is the more important one, and is alone attended to in the sequel of the memoir. * In the case in question (changing the functional symbols) we must have A=ga—aP, AU=fa—FG; so that the functions denoted above by fa, FB now are 2fa+4+Cga, 2F3+CaB ; the equation of the trajectory is da r dp V 2fa+Cpa—A VA—2F84+Cap and for the time the formula is he ga da ap dj3 V 2fa+Coa—A WV A—2FB+CapB It is noticed also that taking B, e to denote two new arbitrary constants, and writing e= JdaW 2fa+Cpa—A+ fap Vv A—2FB+ Cap, the equation of the trajectory and the expression for the time assume the forms dO _ ° ante! as is known @ priori by a theorem of Jacobi’s. If the forces vanish, the path is a geodesic line; and denoting by a the ratio of the constants A, C, we have da dp Vga—a Va—ap wap t= qet® and moreover ds=daNn ga—a+dpVa—¢p, which are geometrical properties relating to the geodesic line. 102. Passing to the applications: in the first place, if a, 6 are rectangular coordinates of a point in plano, then writing instead of them 2, y, we have ds’ =da* +-dy*, which is of the required form; but the result obtained is the self-evident one, that the equations may be integrated by quadratures when U is of the form funct. a—funct. y. But taking instead the elliptic coordinates p, v of a point in plano,—viz., as ON THE SPECIAL PROBLEMS OF DYNAMICS. 211 employed by the author, these are the semiaxes of the confocal ellipse and hyperbola represented by the equations ae y? Pa y we we Gb? ? pal prays ? —very interesting results are obtained. The equations give Bx? =r, By? = (y2—2*) (P—»?), and thence dy? dy’? which is of the proper form, and the corresponding expression of U is eh, Fu—Fv : ee Ens 5a so that the foree-function having this value (fu, Fy being arbitrary functions of » and » respectively), the equations of motion may be integrated by qua- dratures. 103. In particular, if Sfu=getg'p+k(e—o'p’), Fry=qgv—q'y +k(v*—6b*r’), then Ven Feb +I 4 byt). pty poy But »+yv, w—y are the distances of the point from the two foci, and pe+r?—b?(=2"+7’) is the square of the distance from the centre, so that the expression for U is Bie ‘site ao el and the case is that of forces to the foci varying inversely as the squares of the distances, and a force to the centre varying directly as the distance— the case considered by Lagrange in the problem of two centres. But this is merely one particular case of those given by the general formula. The cases g=0, g'=0, k=0 (no forces), and g=0, g!=0 (a force to the centre) lead to some interesting results; it is noticed also that the expression funct. Signa aia! cama 8 ote) Tr that it may be thereby ascertained (without transforming to elliptic coordi- nates) whether a given value of the force-function is of the form considered in the theory. In § 3 the author considers the expression dz? +dy?=X(da? +d’), d being in the first instance any function whatever of @ and (§; and he shows that the expressions of xv, y are given by the equation x+y —1=V(ae+BV —1), w being any real function. If, however, it is besides assumed that d is of the required form=fa—F{, then he shows that the system of elliptic coordi- nates is the only one for which the conditions are satisfied. §§ 4,5, 6, and 7 relate to the motion of a point on a sphere, an ellipsoid, a surface of revolu- tion, and the skew helicoid respectively ; and the concluding § 8 contains only a brief reference to the author’s second memoir. 104. Liouyille’s second and third memoirs may be more briefly noticed. In the second memoir the author starts from Jacobi’s theorem of the V f P2 for the force-function may be written U= 212 REPORT—1862. fanction, viz., assuming that there is a foree-function U independent of the dé de’ de ~ dy’ aa ) all that is required is to find a function © of w, y, z containing three arbitrary constants A, B, C (distinct from the constant attached to @ by mere addition) satisfying the differential equation 2) +(8) (2) a0 for then the required integrals of the ais of motion are dO_ 4, 40 ite ! TRA Spee GG=e+ A!, B!, ©! being new arbitrary constants. Liouville introduces in place of x, y, z, the elliptic coordinates p, yw, v, which are such that x y z ele + i. 2 2 Fe 2 ay y i alin 2 2B e he pear d eo 7 y° 2 1 YBa er or, what is the same thing, wall, ia VERE VENT Ve —B Pers VP —e EV e— 0 ae oN e—b? and he then finds that the resulting partial differential equation in p, p, may be integrated provided that U is of the form pa) fe +(p°— v7) Fut (p* =v av (e°—p*) (p?—v*) (u’—y*) f, F,; w being any functional symbols whatever: viz., the expression for Q is 2 +A+B 2+ 2Cp* e=ld Wee Pp lv z ls -\% Be)” +4 area Fu + A+ Bu? + 2Cp (WH P)(C— eh)” +a is es Qa + A+B? +207 (6°—»’) (¢’—yv’) In the case where U=0 we have a particle not acted on by any forces, and the path is of course a straight line. The peculiar form in which these equa~ tions are obtained leads to very interesting results in regard to the theory of Abelian integrals, and to that of the geodesic lines of an ellipsoid. The formule require to be modified in certain cases, such as c=6 or 6=0. The case 6=0 leads to the theory developed in the first memoir in relation to ON THE SPECIAL PROBLEMS OF DYNAMICS. 213 the problem of two centres. The case is indicated where b=0, c=0, the ratio 6: c remaining finite. The case is briefly considered of a particle moving on a given surface. 105. The third memoir purports to relate to a system of particles, but the formule are exhibited under a purely analytical point of view ; so much s0, that the coordinates of the points (3 for each point) are considered as forming a single system of variables «,, #,,...#;, The partial differential equation is de do doe —— ) =2(U (se) +(e)" +() RU which is transformed by introducing therein the new variables p,, p,... p; analogous to the elliptic coordinates of the second memoir, The memoir really belongs rather to the theory of the Abelian integrals (in regard to which it appears te be a very valuable one) than to dynamics. Memoirs by Jacobi, Bertrand, and Denkin, relating to various Special Problems. 106. I have inserted this heading for the sake of showing at a single view what are the special problems incidentally considered in the under-mentioned memoirs which are referred to in several places in the present Report. 107. Jacobi, “ De Motu puncti singularis ” (1842).—I call to mind that the memoir chiefly depends on the theorem of the Ultimate Multiplier (the theory in its generality being developed in the later memoir “ Theoria Novi Multiplicatoris &c.,” 1844-45). § 4 is entitled “‘ The motion of a point on the surface of revolution,” which, the principle of the conservation of areas holding good, is reduced to the problem of the motion on the meridian curve, and thus depends upon quadratures only. §5 is entitled “On the motion of a point about a fixed centre attracted according to a certain law more general than the Newtonian one” (ant2, No.85). § 6. ‘On the motion of a point on a given curve and in a resisting medium ” (resistance=a-+ be™, or=a-+ bv”); and § 7. “On the Ballistic Curve,” viz., the forces are gravity and a resistance=a-+ bv”. 108. In Jacobi’s memoir “ Theoria Novi Multiplicatoris &e.” (1845), § 25 is entitled «« On the motion of a point attracted towards a fixed centre” (see ante, No. 87); § 26. “On the motion of a point attracted towards two fixed centres according to the Newtonian law” (ante, No. 56); § 27. ‘ On the rota- tion of a solid body about a fixed point” (post, No.193); § 28. “On the problem of three bodies moving in a right line; the Eulerian substitution; theorems on homogeneous forces” (ante, No. 91); ‘and § 29, «The principle of the ultimate multiplier applied to a free system of material. points moving in a resisting medium ; on the motion of a comet in a resisting medium about the sun.” 109. And in Jacobi’s memoir “ Nova Methodus &c.” (1862), besides § 64 and § 65, which are applications of the method to general dynamical theorems, we have § 66, containing a simultaneous solution of the problem of the motion of a point attracted to a fixed centre and of that of the rotation of a solid body (post, No. 206), and § 67, relating to the motion of a point attracted to a fixed centre according to the Newtonian law. 110. Bertrand’s “ Mémoire sur les intégrales différentielles de la Mécanique” (1852).—¢ III. relates to the motion of a point attracted to a fixed centre by a force varying as a function of the distance; §IV. to the case where the forces arise from a force-function U= aa “) (or, what is the same thing, y . 214 " REPORT—1862. = ) (ante, No. 87); § V. to the problem of two centres (ant2, No.62), and § VI. to the problem of three bodies (post, No. 117). 111. Donkin’s memoir “ On a Class of Differential Equations &c.” (1855). Part I. Nos. 27 to 30 relate to the problem of central forces (in space), No. 31 to the rotation of a solid body, and $ III. to the same subject, viz. Nos. 40 and 41 to the general case, Nos. 42 to 44 to the particular case A=B; and Nos. 45 to 48 to the reduction thereto of the general case by treating the forces which arise from the inequality of A and B as disturbing forces. Part II. Nos. 59 and 60 relate to the spherical pendulum ; Nos. 72 and 73 to “ Transformation from fixed to moving axes of coordinates,” say to Relative Motion ; and Nos. 84 to 96 to the problem of three bodies ( post, No, 120). The Problem of Three Bodies, Article Nos. 112 to 123. 112, A system of differential equations, such as dx,_dv, dn 44 x, 2 Xn41 (n equations between n+1 variables), may be termed a system of the nth order, or more simply a system of n equations. Let (u,, u,...-U,4,) be any functions of the original variables (w,, v,,....w,4,), the system may be transformed into the similar system du,__du, du, U, oes SP Th and if it happens that we have e.g. U, identically equal to zero, then the system becomes 0 (ee _M, du, +) off.) n+l so that we have an integral u,=c, and then in the remaining equations substituting this value, or treating wu, as constant, the system is reduced to one of (m—1) equations. Or again, if it happen that we haye in the trans- formed system m equations (m We The results ultimately obtained are of a very remarkable and interesting form, viz. H=funct. (p,, P,, Ps, Pys UG» Yo» Ya» Ya) 18 equal to the value it would have for motion in a plane, plus a term admitting of a simple geometrical interpretation, and he thus arrives at the following theorem as a résumé of the whole memoir, viz., ‘In order to integrate in the general case the problem of three bodies, it is sufficient to solve the case of motion in a plane, and then to take account of a disturbing function equal to the product of a constant depending on the areas by the sum of the moments of inertia of the bodies round a certain axis, divided by the square of the triangle formed by the three bodies.” 123. It may be remarked that the only given integral of the system of eight equations is the integral of Vis Viva, H=const., and that using this equation to eliminate one of the variables, and omitting ‘the equation (=dt), we have, as in the solutions of Jacobi and Bertrand, a system of six equations between seven variables. As the equations are in the standard dynamical form, no investigation is needed of the multiplier M, which is given by Jacobi’s general theory, and consequently when any five integrals of the six equations are given, the remaining integral can be obtained by a quadrature. In the case of three bodies moving in a plane, the solution takes a very simple form, which is given in the concluding paragraph of the memoir. =0; Transformation of Coordinates, Articles Nos. 124 to 141. 124. It may be convenient to remark at once that two sets of rectangular coordinates may be related to each other properly or improperly, viz., the axes to which they belong (considered as drawn from the origin in the positive directions) may be either capable or else incapable of being brought into coincidence. The latter relation, although of equal generality with the former one, may for the most part be disregarded ; for by merely reversing the direc- tions of the one set of axes, the improper is converted into the proper relation. 125. In the memoir “ Problema Algebraicum &c.” (1770) Euler proposes to himself the question “ Invenire novem numeros ita in quadratum disponendos , B, D, E, F GAEL E ut satisfiat duodecem sequentibus conditionibus,” &c., viz., substituting for A, B,C, &e. the ordinary letters cm a Faith note fe a; B eS ae: the twelve conditions are a® +a? +a’?=1, ap+a'p' +a" Bl ’ Be +B" +6R=1, By+By'+B"y"=0, yore ty =, yaty'al+y'a'=0, a +P +7 =1, aa! +B6 +y of al? +” +y?=1, aia" § pip" +y vay "==(), Zp PML, aa” +3" +y"y =0 ON THE SPECIAL PROBLEMS OF DYNAMICS. 219 And he remarks that this is in fact the problem of the transformation of coor- dinates, viz., if we have X=ax + By + 2; Y=c'r +B'y +y'z, 7, =a"e+B"y+ yz; then the first equations are such as to give identically XP 4 Y?4 2247+ y?+427, 126. Assuming the first six equations, he shows by a direct analytical process that a*=(B'y"—f"y')’, or z= +(6'y'—B"y'); or taking the positive sign (for, as the numbers may be taken as well positively as negatively, there is nothing lost by doing so) a='y'"—" y', which gives the system Zz ey ey,» B =y & ya to =o) 0 8, a =f Y me M4 2 py Ke pr: e 2 aes B xe B , a=By—By, B'=ye—yYa, y"=a B'—a' fp, and from these he deduces the second system of six equations. The inverse system of equations X=ar+a'y+a"z, Y=6er+ p'y+ B"z, Z=yetyyty"2 is not explicitly referred to. 127. He then satisfies the equations by means of trigonometrical substitu- tions, viz., assuming a=cosé, then @?+a@'*=sin?Z, which is satisfied by a =sin { cosy, a =sin £ sin n, &c., and he thus obtains for the coefficients a set of values involving the angles Z, n, 0, which are the same as those men- tioned post, No. 130. And he shows how these formule may be obtained geo- metrically by three successive transformations of two coordinates only. The remainder of the memoir relates to the analogous problem of the transforma- tion of four or more coordinates. 128. I have analysed so much of Euler’s memoir in order to show that it contains nearly the whole of the ordinary theory of the transformation of coordinates ; the only addition required is the equation =+1, where the sign + gives a=('y—"y’, &c. (ut supra), but the sign — would give a=—(P'y"—f"y'), &e. 129. The distinction of the ambiguous sign is in fact the above-mentioned one of the proper and improper transformations ; viz., for the sign + the two sets of axes can, for the sign — they cannot, be brought into coincidence: this very important remark was, I believe, first made by Jacobi in one of his early memoirs in Crelle’s Journal, but I have lost the reference. As already mentioned, it is allowable to attend only to the proper transformation, and to consider the value of the determinant as being =+1; and this is in fact almost always done. 130. Euler’s formule involving the three angles are those which are ordi-- narily made use of in the problem of rotation and the problems of physical astronomy generally. It is convenient to take them as in the figure, viz., 0, the longitude of node, 220 REPORT—1862. @, the inclination, 7, the angular distance of X from node, and the formule xe N 7 of transformation then are coe TEE Ih in et x uy’ Z x | cos7 cos@—sinr sin@ cos@ |—sinz cosO—cosr sin@ cosg| sin @ sing y | cosr sin@+sin r cos@ cos |—sinr sin@-+cosr cos cos ¢ | —cos 0 sin z sin 7 sing cos T sin @ cos @ The foregoing very convenient algorithm, viz., the employment of | Be | o-Y | Z | esai\ discal y | @ p' y’ aime AL 9? at to denote the system of equations vw=aX +BY +yZ, y=aX +BY +72, z= "X+pB"Y+ y'Z, is due to M. Lamé. | 131. But previously to the foregoing investigations, viz.,in the memoir “ Du Mouvement de Rotation &e.,’’? Mém. de Berlin for 1758 (pr. 1765), Euler had obtained incidentally a very elegant solution of the problem of the transforma- tion of coordinates; this is in fact identical with the next mentioned one, the letters 1, m, 2; X, p, v being used in the place of Z, 2’, 6"; n, n,n". 132. In the memoir “Formule generales pro translatione &c.” (1775), Euler gives the following formule for the transformation of coordinates, viz., if the position of the set of axes XYZ in reference to the set wyz is determined by ON THE SPECIAL PROBLEMS OF DYNAMICS. 221 aX, yX, zX=90°—Z, 90°—Z', 90°—2", x Z° Y¥Xa, YXy, YXz=n, 7’, 7", then the formul of transformation are x ¥ Z eee w |sing |cos{ sinyn |cosf cos7n y |sinZ’ |cosZ’ sinn’|cosZ' cos! Zi ¥ z | sin 2” | cos Z” sin n"| cos Z" cos n” = O§ with the following equations connecting the six angles, viz., if —A*= cos (9!—7") cos (n!'—n) cos (n—n!), then —A 7 —A ae OT 1 a Re = tam ofa = e05 (n'—n") + o08 (1"—n) : cos (7—7') 133. It is right to notice that these values of £, Z', £2” give the twelve equations a*+2°+ y°=1, &c., but they do not give definitely a=p'y"'—B'y', &e., but only c= +(B'y’—f"y’); that is, in the formule in question the two sets of axes are not of necessity displacements the one of the other. In the same memoir Euler considers two sets of rectangular axes, and assuming that they are displacements the one of the other (this assumption is not made as explicitly as it should have been), he remarks that the one set may be made to coincide with the other set by means of a finite rotation about a certain axis (which may conveniently be termed the Resultant Axis), This considera- tion leads him to an equation which ought to be satisfied by the coefficients of transformation, but which he is not able to verify by means of the fore- going expressions in terms of @, Z', 2", n, n', n". 134. I remark that Euler’s equation in fact is a—l, B »Y =0, @ 6, p'—l,y' al’ : " F y'—1 or, as it may be written, 4 i B 7 —(B'y"—B"y')—(y"a—ya")—(aB'—a'B)+a+B'+y"—1=0, a ; in which form it is an immediate consequence of the equations a 5 B : Y, —ie a='y"'—Bp'y', &e., ats oe y" which are true for the proper, but not for the improper transformation. 135. In the undated addition to the memoir, Euler states the theorem of the resultant axis as follows :—Theorema. Quomodocunque sphera circa centrum suum convertatur, semper assignari potest diameter cujus directio in situ translato conyeniat cum situ originali;” and he again endeayours to ob- tain a verification of the foregoing analytical theorem. 136. The theory of the Resultant Axis was further developed by Euler in the memoir “ Nova Methodus Motum &c.” (1775), and by Lexell in the me- 222 REPORT—1862. moir “ Nonnulla theoremata generalia &c.” (1775): the geometrical investi- gations are given more completely and in greater detail in Lexell’s memoir. The result is contained in the following system of formule for the transfor- mation of coordinates, viz., if a, 3, y are the inclinations of the resultant axis to the original set, and if ¢ is the rotation about the resultant axis, or say the resultant rotation, then we have x Y | Zz ae ot SeeeT Wee cos’«+sin?acosp cosacos3(1—cos¢)-+-cosysing cosacosy(1—cos¢) —cosBsing cosycosa(1 —cos¢)-+-cosBsing|cosycos8(1 —cos¢) —cosesing \cos?y +sin?ycosp I Euler attempts, but not very successfully, to apply the formule to the dynamical problem of the rotation of a solid body: he does not introduce them into the differential equations, but only into the integral ones, and his results are complicated and inelegant. The further simplification effected by Rodrigues was in fact required. 137. Jacobi’s paper, “ Euleri formule &c.” (1827), merely cites the last- mentioned result. 138. I find it stated in Lacroix’s ‘ Differential Calculus,’ t. i. p. 533, that the following system for the transformation of coordinates was obtained by Monge (no reference is given in Lacroix), viz., the system being as above, %, ’ p ? ¥ ’ Fs B', Mh? a, B", y's and the quantities «, f’, y’ being arbitrary, then putting l4+a+/'+ y'=M, 1+a—p'—y"=N, so that M+N+P+Q=4, we have ; 23 =VNP+ ¥ MQ, 2y' =VPQ4+ VMN, 2a" = VYQN+ V MP, 2g’ VNP_V MQ, 26’=VPQ— VMN, 2y =VON— VME. These are formule very closely connected with those of Rodrigues. 139. The theory was perfected by Rodrigues in the valuable memoir “ Des lois géométriques &c.” (1840). Using for greater convenience X, p, v in the place of his 3m, 4n, 4p, he in effect writes tan 3 cosa=), tan 3¢ cos B=p, tan 36 cos y=, and this being so, the coefficients of transformation are 14+N—W—r, 2(Au+r) » 2r\.—p) : 2(urA—v) > 1—’+pe—r*, 2A(uv+r) - 207A +p) >» 2ru—A » 1—-Nv—p’ +’, x y \cosBcosa( 1 —cos¢) —cosysing|cos?8+sin*Bcosp cosBcosy(1—cos¢) +cosesing Zz > ON THE SPECIAL PROBLEMS OF DYNAMICS. 223 all divided by the common denominator 1+)?+ y?+¥ 7. Conversely, if the coefficients of transformation are as usual represented by 2 B Bay? Me s »B, Y's hers ce y'; then d’, nu’, v”, A, w, v are respectively equal to 1+a—,'—y", 1l—a+p'—y", 1l—a—f'+y", Fig aap eo) pi es each of them divided by 1+a+f'+y’". The memoir contains yery elegant formule for the composition of finite rotations, and it will be again referred to in speaking of the kinematics of a solid body. 140. Sir W. R. Hamilton’s first papers on the theory of quaternions were published in the years 1843 and 1844: the fundamental idea consists in the employment of the imaginaries 2, 7, k, which are such that P=Pp=P=—1, jk=—kj=i, i=—tka=j, y= —p=k, whence also (w+iat+jy + kz) (w' +22! +7y' + kz') = ww'—xu' —yy'—2z2' fi(we'+w'e+yz2'—y'2) 4j(wy' +w'y + 20'—z2'2) +kh(w2' +w'z+axy'—ay) ; so that representing the right-hand side by W+iX4+jY+kZ, we have identically W4XC4+ V4 2=(w?+a*+y?+2) (w?+u?+y?+2"), It is hardly necessary to remark that Sir W. R. Hamilton in his various publications on the subject, and in the ‘ Lectures on Quaternions,’ Dublin, 1853, has developed the theory in detail, and has made the most interesting applications of it to geometrical and dynamical questions ; and although the first explicit application of it to the present question may have been made in my own paper next referred to, it seems clear that the whole theory was in its original conception intimately connected with the notion of rotation. 141. Cayley, ‘‘ On certain Results relating to Quaternions” (1845). —It is shown that Rodrigues’ transformation formula may be expressed in a very simple manner by means of quaternions ; viz., we have tx jy +ke=(1 ++ juthvy)-\iX4+7Y +kZ) (1+i4+jut+hy), where developing the function on the right-hand side, and equating the coeffi- cients of 7,7, k, we obtain the formule in question. A subsequent paper, Cayley, ‘‘On the application of Quaternions to the Theory of Rotation’”’ (1848), relates to the composition of rotations. Principal Aes, and Moments of Inertia. Article Nos. 142-163. 142, The theorem of principal axes consists herein, that at any point of a solid body there exists a system of axes Ox, Oy, Oz, such that Syzdn=0, Jzxdm=0, JS xydm=0. 224. REPORT—1862. But this, the original form of the theorem, is a mere deduction from a general theory of the representation of the integrals A xdm, ay ydm, fzdm, Syed, fzxdm, fp aydm for any axes through the given origin by means of an ellipsoid depending on the values of these integrals corresponding to a given set of rectangular axes through the same origin. 143. If, for convenience, we write as follows, M= f dm the mass of the body, and A! = fxd, B’ =fy'dm, C=fzdm, EF’ =f yzdm, G’ =faxdm, H’ =f xydm, and moreover A=f(y’+#) dm, B=/{(@ +") dm, O=/(2*+y’) dm, =—fyzdm, cc —fzxdm, H=—/f«ydm*, so that A=B'+C', B=C'+A', C=A'4+ BY, F=—F’, G=—G', H= 3) then the ellipsoid which in the first instance presents itself for this purpose, and which Prof. Price has termed the Ellipsoid of Principal Axes, but which IT would rather term the “‘ Comomental Ellipsoid,” is the ellipsoid (A’, BY, C, F’, G’, H (a, y, z=) =Mk, where k is arbitrary, so that the absolute magnitude is not determined. But it is more usual, and in some respects better to consider in place thereof the « Momental Ellipsoid” (Cauchy, ‘Sur les Moments d’Inertie,” Exercices de Mathématique, t. ii. pp. 93-103, 1827), (A, B, C, F, G, HYa, y, 2) =Mht, or as it may also be written, (A'4+B40)aety+e)—(A4 B, C’, F, Gg, H'{«, Y; z) =MM, which shows that the two ellipsoids have their axes, and also their circular sections coincident in direction. 144. And there is besides this a third ellipsoid, the ‘ Ellipsoid of Gyra- tion,” which is the reciprocal of the momental ellipsoid in regard to the con- centric sphere, radius &. The last-mentioned ellipsoid is given in magnitude, viz., if the body is referred to its principal axes, then putting A>=Ma’*, B= M0”, C=Mc’, the equation of the ellipsoid of gyration is 2 2 2 wv y z lee ee a ee) | —+ats The axes of any one of the foregoing ellipsoids coincide in direction with the principal axes of the body, and the magnitudes of the axes lead very simply to the values of the principal moments A, B, C. 145. The origin has so far been left arbitrary: in the dynamical applica- tions, this origin is in the case of a solid body rotating about a fixed point, the fixed point; and in the case of a free body, the centre of gravity. But the values of the coefficients (A, B, C, F, G, H), or (A7 3’, OC 2 Ga corresponding to any given origin whatever, are very easily expressed in * | have ventured to make this change instead of writing as usual F= f' yzdm, &e.; asin — most cases F=G=H=0, the formule affected by the alteration are not numerous. P44 2 ON THE SPECIAL PROBLEMS OF DYNAMICS. 225 terms of the coordinates of this origin, and the values of the corresponding coefficients for the centre of gravity as origin; or, what is the same thing, any one of the ellipsoids for the given origin may be geometrically constructed by means of the ellipsoid for the centre of gravity. The geometrical theory, as regards the magnitudes of the axes, does not appear to have been any- where explicitly enunciated; as regards their direction, it is comprised in the theorem that the directions at any point are the three rectangular directions at that point in regard to the ellipsoid of gyration for fhe centre of gravity*, post, No. 159. The notion of the ellipsoids, and of the relation between the ellipsoids at a given point and those at the centre of gravity, once established, the theory of principal axes and moments of inertia becomes a purely geo- metrical one. 146. The existence of principal axes was first established by Segner in the work ‘Specimen Theorie Turbinum,’ Halle (1755), where, however, it is remarked that Kuler had said something on the subject in the [Berlin] Me- moirs for 1749 and 1750 (post, No. 167), and had constructed a new mecha- nical principle, but without pursuing the question. Segner’s course of inves- tigation is in principle the same as that now made use of, viz. a principal axis is defined to be an axis, such that when a body revolves round it the forces arising from the rotation have no tendency to alter the position of the axes. It is first shown that there are systems of axes a, y, z such that of yzdm =0, and then, in reference to such a set of axes, the position of a principal axis, say the axis of X, is determined by the conditions oh: XYdnm=0, wh XLdm=0, cos a cos viz. the unknown quantities being taken to be t=——, -= (a, 3, y> cos y cos y being the inclinations of the principal axis to those of a, y, z), and then putting A= =f x’dm, &c. (F=0 by hypothesis), Segner’s equations for the de- termination of t¢, 7 are ; G'?+(C'—A’) i—G'—H'r=0, (C'—B') r—G'tr+Ht=0, the second of which gives scr URES SS yang and by means of it the first gives G?—G'(A'’—B')?+ {(B’—C')(C'—A')—G?—H} + G' (B'—C') =0, which being a cubic equation shows that there are three principal axes; and it is afterwards proved that these are at right angles to each other. 147. To show the equivalence of Segner’s solution to the modern one, I remark that if w= f° X?dm, we have (Nowra oe B.. t+@—wrtF =0, Gig che cba an Ayes whence * The rectangular directions at a point in regard to an ellipsoid are the directions of the axes of the circumscribed cone, or, what is the same thing, they are the directions of the normals to the three quadric surfaces confocal with the given ellipsoid, which pass through the given point. ‘The theory of confocal surfaces appears to haye been first given by ay Note XXXTI. of the ‘ Apergu Historique’ (1837). - Q 226 REPORT—1862, P:Pi:lirit:tt= BC —F?— (B4C)u4+w, : C'A'—G? — (C'+A')u4+wye : A'B'—H?— (A'+ B)u4+wv’, : GH'—A'F’ +F' u, : H'F’—BG' +G' u, : P'G'—C'H' +H'u, or putting therein F’=0, @i:F:lirrt:¢= BO —(B'+C')u+uv' : CA'—G?—(C'+A')u+uv? >: A'BI—H?—(A'+ But? 3) (GH! ; —B'G'+G'u ; —C’H'+H'u by means of which Segner’s equations may be verified. I have given this analysis, as the first solution of such a problem is a matter of interest. 148. There is little if anything added to Segner’s results by the memoir, Euler, ‘‘ Recherches sur la Connaissance Mécanique des Corps” (1758), which is introductory to the immediately following one on Rotation. 149. Relating to the theory of principal axes we have Binet’s “‘ Mémoire sur les Axes Conjugués,” &c. (1813). The author proposes to make known the new systems of axes which he calls conjugate awes, which, when they are at right angles to each other, coincide with the principal axes; viz. consider- ing the sum of the molecules each into its distance from a plane, such distance -being measured in the direction of a line, then (the direction of the line being given) of all the planes which pass through a given point, there is one for which the sum in question is a minimum, and this plane is said to be con- jugate to the given line, and from the notion of a line and conjugate plane he passes to that of a system of conjugate axes. The investigation (which is throughout an elegant one) is conducted analytically; the coordinates made use of are oblique ones, and the formule are thus rendered more com- plicated than they would otherwise haye been; in referring to them it will be conyenient to make the axes rectangular. 150. One of the results is the well-known equation (A’—0)(B'—e)(C —0)—F"(A’—0) —G"(B' 0) —H(C' —0) + 2F G'H'=0; which, if @,, y,, 2, are the principal axes, has for its-roots fw,*dm, [y,’dm, zdm. And the equations (1), p. 49, taking therein the original axes as rect- angular, are , K' (s— 3) cosa+ ®' cosp+ 6’ cos y=0, 4B’. cosa+ (38'—5; Joos B+ FF cos y=0, +6' cosa+ df’ cos p+ (€'—5) cos y=0, where @', 15’, €’, df’, @', ®' denote the reciprocal coefficients @'=B'C’—F? ON THE SPECIAL PROBLEMS OF DYNAMICS. 227 &e., and K’ is the discriminant =A'B'C’—A'F?—B'G?—C'H?+2FG'H : this is a symmetrical system of equations for finding cos « : cos GB: cos y, less simple however than the modern form (post, No. 154), the identity of which with Binet’s may be shown without difficulty. 151. Another result (p. 57) is that if the original axes are principal axes, and if Ow, Oy, Oz are the principal axes through a point the coordinates whereof are f, g, h, and if ©,'= (say) ef x,*dm, then we have Mie ae UY ee A 6,/—A''6,/—B 1 6/—0 Mf (in which T have restored the mass M, which is put equal to unity), so that if 0,’ have a given constant value, the locus of the point is a quadric surface, the nature whereof will depend on the value of 6,. The surfaces in question are con- ig ze i! focal with each other [and with the imaginary surface =a a a 2 2 which is similar to the ellipsoid +h to=e which is the reciprocal of the comomental ellipsoid A'a?+B'y?+C'z?=Mz#* in regard to a concentric 2 2 2 sphere, radius /]. The author mentions the ellipsoid vt+e + a =F (see p. 64), and he remarks that his conjugate axes are in fact conjugate axes in respect to this ellipsoid, and consequently that the principal axes are in direction the principal axes of this ellipsoid: it is noticeable that the ellipsoid thus inci- dentally considered is not the comomental ellipsoid itself, but, as just re- marked, its reciprocal in regard to a concentric sphere. 152. Poisson, ‘ Mécanique’ (1st ed. 1811, and indeed 2nd ed. 1833), gives the theory of principal axes in a less complete form than in Binet’s memoir; for the directions of the principal axes are obtained in anything but an elegant form. 153. Ampére’s Memoir (1823).—The expression permanent awis is used in the place of principal axis, which is employed to designate a principal axis through the centre of gravity. The memoir contains a variety of very interesting geometrical theorems, which however, as no ellipsoid is made use of, can hardly be considered as exhibited in their proper connexion. The author arrives incidentally at certain conics, which are in fact the focal conics of ‘peo eek pt oru) | 154, Cauchy, in the memoir “Sur les Momens d’Inertie ” (1827), considers the momental ellipsoid (A, By eG: HY, y, z)=1, and employs it as well to prove the existence of the principal axes as to determine their di- rection, and also the magnitvdes of the principal moments; the results are a in the simplest and best forms; viz. the direction cosines are given 7 the ellipsoid of gyration (G+ for the centre of gravity. (A—@) cosa +H cos B+G cos y=0, H cos a-+(B—6) cos B+F cos y=0, G cosa+F cos 3-+(C—6) cos y=0, where (A—0)(B—0e)(C—0)—(A—6) F’—(B—@) G?—(C—6) H’4+ 2FGH=0, © being one of the principal moments. 155. Poinsot, “Mémoire sur la Rotation” (1834), defines the “Central a2 228 REPORT—1862. Ellipsoid’’ as an ellipsoid having for its axes the principal axes through the centre of gravity, the squares of the lengths being reciprocally proportional to the principal moments; and he remarks in passing that the moment about any diameter of the ellipsoid is inversely proportional to the square of this dia- meter. It is to be noticed that Poinsot speaks only of the ellipsoid having its centre at the centre of gravity, but that such ellipsoid may be constructed about any point whatever as centre, so generalized, it is in fact the mo- mental ellipsoid Aw*+By’+Cz=Mk*; and moreover that Poinsot defines his ellipsoid by reference to the principal axes. 156. Pine, “On the Principal Axes, &c.” (1837), obtained analytically in a very elegant manner equations for determining the positions of the prin- cipal axes; viz. these are (A'—0') cosa +H’ cos 3-+G’ cos y=0, H’ cos a+(B'—60’') cos B+ FE" cos y=0, Gs cosa+F" cos 8 +(C'—0’) cos y=0, where (A'—0')(B'—0')(C'— 9')—(A'— 0’) F?— (B'—0') G?—(C'— 0) F? ++ 2F'G'H'=0; viz. these are similar to those of Cauchy, only they belong to the comomental instead of the momental ellipsoid. 157. Maccullagh, in his Lectures of 1844 (see Haughton), considers the momental ellipsoid (A, B,C) Hh, G; HY2, Ys 2) = Mk (A, B, C, F, G, H ut supra), which is such that the moment of inertia of the body with respect to any axis passing through the origin is proportional to the square of the radius vector of the ellipsoid; and from the geometrical theorem of the ellipsoid having principal axes he obtained the mechanical theorem of the existence of principal axes of the body; at least I infer that he did so, although the conclusion is not explicitly stated in Haughton’s account ; but in all this he had been anticipated by Cauchy. And after- wards, referring the ellipsoid to its principal axes, so that the equation is Aa’ + By’? +C2?=Mk", he writes A=Ma’*, B=Mé*, C=Me’, which reduces the equation to a°w*+ b°y*+¢2°=k*, and he considers the reciprocal ellipsoid 2 2 w2 a2 2 aw atts= 1, or, what is the same thing, <+% $o=5 which is the ellip- soid of gyration. 158. Thomson, ‘On the Principal Axes of a Solid Body” (1846), shows analytically that the principal axes coincide in direction with the axes of the momental ellipsoid (A, B, C, F, G, He, y, z) =Mi'; but the geometrical theorem might have been assumed: the investigation is really an investigation of the axes of this ellipsoid. And he remarks that the ellipsoid (A', Be Eas He, Ys z) =Mke (the comomental ellipsoid) might equally well have been used for the purpose. 159. He obtains the before-mentioned theorem that the directions of the principal axes at any point are the rectangular directions in regard to the ene : fe ger aan | ellipsoid of gyration (G+ 3 +9-3) determining the moments of inertia at the given point (say its coordinates are £, n, ¢) he obtains the equation for the centre of gravity. And for ON THE SPECIAL PROBLEMS OF DYNAMICS, 229 Ee ae ee 2 2 2 ASP 2 2 2 BSE 2 2) 72 C=P’ Str +o +e Ste tote On tO + where the three roots of the cubic in P are the required moments. Analyti- cally nothing can be more elegant, but, as already remarked, a geometrical construction for the magnitudes of these moments appears to be required, 160. Some very interesting geometrical results are obtained by consider- ing the “equimomental surface” the locus of the points, for which one of the moments of inertia is equal to a given quantity IT; the equation is of course x 4 yy a 2 1 ie oA a See ety topo" Pry tepoo™ ee and which includes Fresnel’s wave-surface, In particular it is shown that the equimomental surface cuts any surface i a ee A+6'B+0'C+o-M confocal with the ellipsoid of gyration in a spherical conic and a curve of curvature ; a theorem which is also demonstrated, Cayley, “ Note on a Geo- metrical Theorem, &c.” (1846). 161. Townsend, “On Principal Axes, &c.’’ (1846).—This elaborate paper is contemporaneous, or nearly so, with Thomson’s, and several of the conclusions are common to the two. From the character of the paper, I find it difficult to give an account of it; and I remark that, the theory of principal axes once brought into connexion with that of confocal surfaces, all ulterior deye- lopments belong more properly to the latter theory. 162. Haton de la Goupilliére’s two memoirs, “Sur la Théorie Nouvelle de la Géométrie des Masses” (1858), relate in a great measure to the theory of the integral of wydm, and its variations according to the different positions of the two planes x=0 and y=0; the geometrical interpretations of the several results appear to be given with much care and completeness, but I have not examined them in detail. The author refers to the researches of Thomson and Townsend. 163. I had intended to show (but the paper has not been completed for publication) how the momental ellipsoid for any point of the body may be obtained from that for the centre of gravity by a construction depending on the “square potency ” of a point in regard to the last-mentioned ellipsoid. The Rotation of a solid body. Article Nos. 164-207. 164. Itwill be recollected that the problem is the same for a body rotating about a fixed point, and for the rotation of a free body about the centre of gravity; the case considered is that of a body not acted on by any forces. According to the ordinary analytical mode of treatment, the problem depends upon Euler’s equations Adp + (C—B) grdt=0, Bdq+ (A—C) rpdt=0, Cdr + (B—A) pqdt=0, for the determination of p, g,7, the angular velocities about the principal 230 REPORT—1862. axes; considering p, g, 7 as known, we obtain by merely geometrical consi- derations a system of three differential equations of the first order for the determination of the position in space of the principal axes. 165. The solution of these, which constitutes the chief difficulty of the problem, is usually effected by referring the body to a set of axes fixed in space, the position whereof is not arbitrary, but depends on the initial cireum- stances of the motion; viz. the axis of z is taken to be perpendicular to the so-called invariable plane. The solution is obtained without this assumption both by Euler and Lagrange, although, as remarked by them, the formule ‘are greatly simplified by making it; it is, on the other hand, made in the solution (which may be considered as the received one) by Poisson; and the results depending on it are the starting-point of the ulterior analytical deve- lopments of Rueb and Jacobi; the method of Poinsot is also based upon the consideration of the invariable plane. 166. D’Alembert’s principle, which affords a direct and general method for obtaining the equations of motion in any dynamical problem whatever, was given in his “ Traité de Dynamique”’ (1743); and in his memoir of 1749 he applied it to the physical problem of the Precession of the Equinoxes, which is a special case of the problem of Rotation, the motion of rotation about the centre of gravity being in fact similar to that about a fixed point. But, as might be expected in the first attempt at the analytical treatment of so difficult a problem, the equations of motion are obtained in a cumbrous and unmanageable form. _ 167. They are obtained by Euler in the memoir “ Découverte d’un Nou- veau Principe de Mécanique,” Berlin Memoirs for 1750 (1752) (written before the establishment of the theory of principal axes), in a perfectly elegant form, including the ordinary one already mentioned, and, in fact, reducible to it by merely putting the quantities F, G, H (which denote the integrals JI yzdm, &c.) equal to zero. But Euler does not in this memoir enter into the question of the integration of the equations, 168. The notion of principal axes having been suggested by Euler, and their existence demonstrated by Segner, we come to Euler’s investigations contained in the memoirs “‘ Du Mouvement de Rotation &c.,” Berlin Me- moirs for 1758 (printed 1765) and for 1760 (printed 1767), and the “ Theoria Motus Corporum Solidorum &c.” (1765). In the memoir of 1760, and in the “ Theoria Motus,” Euler employs s, the angular velocity round the in- stantaneous axis, but not the resolved velocities & cos a, & cos 3,8 cos y (=p, 4, 7): these quantities (there called w, y, z) are however employed in the memoir, Berlin Memoirs (1758), which must, I apprehend, have been written after the other, and in which at any rate the solution is developed. with much greater completeness. It is in fact carried further than the ordinary solutions, and after the angular velocities p, g, r have been found, the remaining investigation for the position in space of the principal axes, conducted, as above remarked, without the aid of the invariable plane, is one of great elegance. 169. In the last-mentioned memoir Euler starts from the equations given by d’Alembert’s principle ; viz. the impressed forces being put equal to zero, these are dm (ve ‘at)= 0, &e., or, what is the same thing, using u,v, w to denote the velocities of an element in the directions of the axes fixed in space, these are € ON THE SPECIAL PROBLEMS OF DYNAMICS. 231 dw dv dm{ y ——2z— }=0 z (y ae edt i a du o)=°, iy Fn at dv dy\ _ Sdm (« aF —vf) =0. It is assumed that at any moment the body revolves round an instantaneous axis, inclinations a, 3, y, with an angular velocity s ; this gives u=b(zcos B—ycos y) = gz —ry, U=8(v COS y—Z COS a) = 1X —pz2, w=s(y¥ cos a—w cosh) =px—qy, if 8 cos a, 8 cos 3, 8 cos y are denoted by p, g, 7. The values of du, dv, dw are obtained by differentiating these formule, treating p, 7, 7, %, y, 2 as yariable, and replacing dx, dy, dz by udt, vdt, wdt respectively; in the resulting formule for ydw—zdv, &c., w, y, ¢ are considered as denoting the coordinates of the element in regard to axes fixed in the body and moveable with it, but which at the moment under consideration coincide in position with the axes fixed in space. The expressions for 3 (ydw—zdv) dm involve the integrals A= ef" (y? +2") dm, &c., where the coordinates refer to axes fixed in the body; and if these are taken to be principal axes, the expression for 3 (ydw—zdv) dm is =Adp+(C—B) qrdt, which gives the three equations Adp+ (C—B) qrdit=0, Bdq + (A—C) rpdt=0, Cdr + (B—A) pqdt=0, already referred to as Euler’s equations. 170. Next, as regards the determination of the position in space of the principal axes: if about the fixed point we describe a sphere meeting the principal axes in w,, y,, z,, and if P be an arbitrary point on the sphere and PQ an arbitrary direction through P, the quantities used to determine the positions of x,, y,, 2, are the distances w,P, y,P, z,P (=1, m, ”) and the incli- nations «,PQ, 7,PQ, z,PQ (=A, p, v) of these ares to the fixed direction PQ (it is to be observed that the sines and cosines of the differences of A, p, v are given functions of the sines and cosines of /, m, n, and, moreover, that cos*/-+ cos’m+cos*x=1, so that the number of independent parameters is three). The above is Euler’s definition ; but if we consider a set of axes fixed in space meeting the sphere in the points X, Y, Z, then if the point X be taken for P, and the arc XY for PQ, it is at once seen that the angles used for determining the relative positions of the two sets of axes are the same as in Euler’s memoir “ Formule Generales, &c.,” 1775 (ante, No. 132), where the formule for this transformation of coordinates are considered apart from the dynamical theory. Euler expresses the quantities p, g, 7 in terms of an auxiliary variable u, which is such that du=pqrdt; p,q, r are at once obtained in terms of u, and then ¢ is given in terms of w by a quadrature. Euler employs also an auxiliary angle U, given in terms of u by a quadrature. And he obtains finite algebraical expressions in u, cos U, sin U for the cosines or sines of l,m,n; s(the angular distance IP, if I denote the point in which the instan- taneous axis meets the sphere), ¢ (the angle IPQ) and A—9, p—9g, v—¢. 232 REPORT—1862. The formule, although complicated, are extremely elegant, and they appear to have been altogether overlooked by subsequent writers. 171. Euler remarks, however, that the complexity of his solution is owing to the circumstance that the fixed point P is left arbitrary, and that they may be simplified by taking this point so as that a certain relation G—3B°=0 may be satisfied between the constants of the solution; and he gives the far more simple formule corresponding to this assumption. This amounts to taking the point P in the normal of the invariable plane, and the resulting formule are in fact identical with the ordinary formule for the solution of the problem. The expression invariable plane is not used by Euler, and seems to have been first employed in Lagrange’s memoir “ Essai sur le Pro- bléme de Trois Corps,” Prix de l’Acad. de Berlin, t. ix. (1772): the theory in reference to the solar system has been studied by Laplace, Poinsot, and others. 172. Lagrange’s solution in the memoir of 1773 is substantially the same with that in the ‘Mécanique Analytique.’ Only he starts from the integral equations of areas and of Vis Viva, but in the last-mentioned work from the equations of motion as expressed in the Lagrangian form by means of the Vis Viva function T (=23(«?+y"+2")dm). The distinctive feature is that he does not refer the body to the principal axes but to any rectangular axes whatever fixed in the body: the expression for T consequently is T=3(A,B,C,F,G, HY, q,7)*, instead of the more simple form T=3(Ap’+ Bqg’+Cr’), which it assumes when the body is referred to its principal axes. And Lagrange effects the integration as well with this more general form of T, as without the simplification afforded by the invariable plane; the employment, however, of the more general form of T seems an unnecessary complication of the problem, and the formule are not worked out nearly so completely as in Euler’s memoir. It may be observed that p, ¢, 7 are expressed as functions of the instantaneous velocity w(—= p?+q°+7"), and thence ¢ obtained by a quadrature as a function of w. 173. Poisson’s Memoir of 1809.—The problem is only treated incidentally for the sake of obtaining the expressions for the variations of the arbitrary constants ; the results (depending, as already remarked, on the consideration of the invariable plane) are obtained and exhibited in a very compact form, and they have served as a basis for further developments ; it will be proper to refer to them somewhat particularly. The Eulerian equations give, in the first place, the integrals Ap? + Bq? +Cr* =h, Ap? + B+ Crs’ ; and then by means of these, », g being expressed in terms of 7, we have ¢ in terms of r by a quadrature. 174. The position in space of the principal axes is determined by referring them, by means of the angles 6, ¢, c, to axes Ow, Oy, Oz fixed in space ; if, to fix the ideas, we call the plane of wy the ecliptic (Ox being the origin of longitudes), and the plane of the two principal axes «, y, the equator, then we have 0, the longitude of node, g, the inclination, c, the hour-angle, or angular distance of Ox, from the node, and a, 3, y the cosine inclinations of Ow,, a’, 6’, y' those of Oy,, and a”, 6", y” ON THE SPECIAL PROBLEMS OF DYNAMICS. 233 those of Oz, to Ow, Oy, Oz respectively are given functions of 0, ¢, c (the values of a’, 8", y' depending upon 6, ¢ only), we have pdt=sin ¢ sin ¢ d#+cos t dd, gdt=cos c sin ¢ d@—sin ¢ d¢, rdt=dc-+cos dé. 175, A set of integrals is Apa +Bqg6 +Cry =k cos X, Apa’ + Bgh' +Cry' =k cos p, Apa" + Bq6"'+Cry'"=k cos y, equivalent to two independent equations, the values of \, p, v being such that cos*A+cos*z+cos*y=1; but the position of the axis of z may be chosen so that the values on the right-hand sides become 0, 0, &; the axis of z is then perpendicular to the invariable plane, the condition in question serving as a definition. And the three equations then give Ap=ka"', Bo—-p", Cr=ky", where the values of a”, 6”, y’ in fact are a"=sinc sing, B’=coscsing, y’=cos¢; we have thus c, ¢in terms of 7. And the equation rdt=dz + cos ¢@0 then leads to the value of d@, or @ is determined as a function of r by a quadrature. 176. The constants of integration are h, &, 1 (the constant attached to 2), g (the constant attached to 6); and two constants, say a the longitude of the node, and y the inclination of the invariable plane in reference to an arbitrary plane of wy and origin « of longitudes therein. I remark in passing that Poisson obtains an elegant set of formule for the variations of the constants h, k, g, 1, «, y, not actually in the canonical form, but which may by a slight change be reduced to it. 177. Legendre considers the problem of Rotation in the ‘Exercices de Calcul Intégral,’ t. ii. (1817), and the “Théorie des Fonctions Elliptiques,” t. 1. pp. 366-410 (1826). He does not employ the quantities p, q, r, but obtains de novo a set of differential equations of the second order involving the angles which determine the position of the principal axes with regard to the axes fixed in space: these angles are in fact (calling the plane of the fixed axes x, y the ecliptic) the longitude and latitude of one of the principal axes, and the azimuth from the meridian through such principal axis of an arbitrary axis fixed in the body and moveable with it. The solution is developed by means of the elliptic integrals. From the peculiar choice of variables there would, it would seem, be considerable labour in comparing the results with those of other writers, and there would be but little use in doing so. 178. Poinsot’s ‘Théorie Nouvelle de la Rotation des Corps.””—The ‘Extrait? of the memoir was published in 1834, but the memoir itself was not published in extenso until the year 1851. The ‘ Extrait’ contains, however, not only the fundamental theorem of the representation of the motion of a body about a fixed point by means of the momental ellipsoid rolling on a fixed tangent plane, but also the geometrical and mechanical reasonings by which this theorem is demonstrated ; it establishes also the notions of the Poloid and Serpoloid curves ; and it contains incidentally, and without any developments, a very important remark as to the representation of the motion by means of the rolling and sliding motion of an elliptic cone. The whole theory (includ- ing that of the last-mentioned representation of the motion) is in the memoir 234 ; REPORT—1862. itself also analytically developed, but without the introduction of the elliptic and Jacobian functions: to form a complete theory, it would be necessary to incorporate the memoir with that of Jacobi. 179. The following is an outline of the ‘ Extrait ’:— The instantaneous motion of a body about a fixed point is a motion of rotation about an axis (the instantaneous axis); and hence the finite motion is as if there were a cone fixed in the body which rolls (without sliding) upon another cone fixed in space. The instantaneous motion of a body in space is a motion of rotation about an axis combined with a translation in the direction of this axis: this remark is hardly required for Poinsot’s purpose, and he does not further develope the theory of the motion of a body in space. The effect of a couple in a plane perpendicular to a principal axis is to turn the body about this axis with an angular velocity proportional to the moment of the couple divided by the moment of inertia about the axis. ' And hence by resolving any couple into couples perpendicular to the prin- cipal axes, the effect of such couple may be calculated ; but more simply by means of the central ellipsoid (momental ellipsoid a?a?+67/°+¢e2°=k", if A, B, C=Ma?, MB?, Mc’), viz., if the body is acted on by a couple in a tangent plane of the ellipsoid, the instantaneous axis passes through the point of con- tact; and reciprocally given the instantaneous axis, the couple must act in the tangent plane. 180. Considering now a body rotating about a fixed point, and taking as the plane of the couple of impulsion a tangent plane of the ellipsoid, the instantaneous axis is initially the diameter through the point of contact; the centrifugal forces arising from the rotation produce however an accelerating couple, the effect whereof is continually to impress on the body a rotation which is compounded with that about the instantaneous axis, and thus to cause a variation in the position of this axis and in the angular velocity round it. The axis of the accelerating couple is always situate in the plane of the couple of impulsion. 181. Hence also 1°. Throughout the motion the angular velocity is proportional to the length of the instantaneous axis considered as a radius vector of the ellipsoid. 2°. The distance of the tangent plane from the centre is constant ; that is, the tangent plane to the ellipsoid at the = of the instantaneous axis is a fixed plane in space. Or, what is the same thing, the motion is such that the ellipsoid remains always in contact with a fixed plane, viz., the body revolves round the radius vector through the point of contact, the angular velocity being always pro- portional to the length of this radius vector. It is right to remark that in Poinsot’s theory the distance of this plane ‘from the centre depends on the arbitrarily assumed magnitude of the central ellipsoid; the parallel plane through the centre is the invariable plane of the motion. 182. The motion is best understood by the consideration that it is implied in the theorem that the pole of the instantaneous axis describes on the ellip- soid a certain curve, ‘‘the Poloid,’ which is the locus of all the points for which the perpendicular on the tangent plane has a given constant value (the curve in question is easily seen to be the intersection of the ellipsoid by a concentric cone of the second order) ; and that the instantaneous axis describes on the fixed tangent plane a curve called the Serpoloid, which is the locus of the points with which the several points of the poloid come successively in con- = oa | es ON THE SPECIAL PROBLEMS OF DYNAMICS. 235 tact with the tangent plane, and is a species of undulating curve, viz., the radius vector as it moves through the angles 6 to 0,+2II, 0,+ 20 to 6,+4I1, &c. as- sumes continually the same series of values. This is in fact evident from the mode of generation ; and it is moreoyer.clear that the serpoloid is an algebraical or else a transcendental curve according as II is or is not commensurable with 7. [Treating the poloid and serpoloid as cones instead of curves, the motion of the body is the rolling motion of the former upon the latter cone, which agrees with a previous remark. | There is a very interesting special case where the perpendicular distance from the tangent plane is equal to the mean axis of the ellipse. 183. Poinsot remarks that the motion is such that [considering the plane of the couple of impulsion as drawn through the centre of the ellipsoid] the section of the ellipsoid is an ellipse variable in form but of constant magni- tude, and that this leads to a new representation of the motion, viz., that it may be regarded as the motion of an elliptic cone which rolls on the plane of the couple [the invariable plane] with a variable velocity, and which slides on this plane with a uniform velocity. 184. The theory of the last-mentioned cone, say the “rolling and sliding cone,” is developed in the memoir, Liouville, t. xvi. p. 303, in the chapter entitled “ Nouvelle Image de la Rotation des Corps.” If a, 6, c signify as before (viz., A, B, C=Ma’, Md’, Mc’), and if h be the distance of the centre from Poinsot’s fixed tangent plane (hc), then the invariable axis describes in the body a cone the equation whereof is (a? —h’) a +. (0? —h’) 7? +(C—h’?) 2=0 ; the cone reciprocal to this, viz. the cone the equation whereof is a? y 2 oe Bet eae is the “rolling and sliding cone.” The generating line OT of this cone is perpendicular to the plane of the instantaneous axis OI, and of the invariable axis OG ; and the analytical expressions for the rolling and sliding velocities follow from the geometrical consideration that the motion at any instant is a rotation round the instantaneous axis OI: that for the sliding velocity is the instantaneous angular velocity into the cosine of the angle LOG, which is in fact constant ; that for the rolling velocity is given, but a further explanation of the geometrical signification is perhaps desirable. 185. I may in this place again refer to Cohen’s memoir “On the Differential Coefficients and Determinants of Lines &c.” (1862), the latter part of which contains an application of the method to finding Euler’s equations for the motion of a rotating body. 186. Rueb in his memoir (1834) first applied the elliptic and Jacobian func- tions to the present problem. Starting from the equations Ap* + Bq? +Cr*? =h, A’p? + BP? +Cr’=P*, and — —Bdq (A—C) rp" it is easy to perceive that by assuming y=a proper multiple of sin £, the ex- * 1 is Poisson’s &, the constant of the principal area ; it is the letter afterwards used by Jacobi ; Rueb’s letter is gy. In quoting (infra) the expressions for p, g, 7, I have given them with Rueb’s signs, but it would be too long to explain how the signs of the radicals are determined. { dt 236 REPORT—1862. dé oS eect Le ae elt Be | — Vise ae ? o that writing —=am u, the integral equation is nt—e=vw, or u is an angle varying directly as the time (and corresponding to the mean longitude, or, if we please, to the mean anomaly in the problem of elliptic motion). And then p, q, r are expressed as elliptic functions of vu. The value of the modulus &, and that of n (nt—e=u ut supra) are pe Mee nS c ABC ? jas (A—B)(P—Ch) ABC ; p= digufetath, cos am w, fh o== — Y BLB_C sll am wu, —P+Ah cC.A—C 187. Substituting for p, g, r their values in terms of u, we have dé, and thence @ (the longitude of the node of the equator on the invariable plane) in the form pression for dt takes the form ndi= and then = Aam wu, 1 , : a | 0=—7z, u+ill(u, ia) (i= —1), which by Jacobi’s formule for the transformation of the elliptic integral of the third class becomes lores -7 O(u—ar) =] —— Zi i ee . ( resp (ai) ut 3 log @(u-paiy which Rueb reduces to the real fc_ 6=—n'u+tan-! W, W being given in the form of a fraction, the numerator and denominator whereof are series in multiple sines and multiple cosines respectively of mu 188. Rueb investigates also the values in terms of u of the cosine inclina- tions of the instantaneous axis to the axes fixed in space; and he obtains a very elegant expression for the angle ¢, which is the angular distance from « of the projection on the plane of wy (the invariable plane) of the instantaneous axis; viz., this is g=tan( ABn A amu a : ~ (A—B)/ sin am w cos am wu and there is throughout a careful discussion of the geometrical signification of the results. 189. The advance made was enormous; the result is that we have in terms of the time sinc sin ¢, cost sin ¢, cos ¢ (the cosine inclinations of the inva- riable axis to the principal axes), and also 0, the longitude of the node. The cosine inclinations of the axes of x and y to the principal axes could of course be obtained from these, but they would be of a very complicated and un- ti ON THE SPECIAL PROBLEMS OF DYNAMICS. 237 manageable form; the reason of this is the presence in the expression for 0 of the non-periodic term —n'u. It will presently be seen how this difficulty was got over by Jacobi. 190. Briot’s paper of 1842 contains an analytical demonstration of some of the theorems given in the ‘ Extrait’ of Poinsot’s memoir of 1834. 191. In Maccullagh’s Lectures of 1844 (see Haughton, 1849; Maccullagh, 1847) the problem of the rotation of a solid body is treated in a mode some= what similar to that of Poinsot’s; only the ellipsoid of gyration ~ nt+S=1 7 if A, B, C=Ma’*, Mb’, Mc’) is used instead of the momental ellipsoid. Thus, reciprocal to the poloid curve on the momental ellipsoid we have on the ellipsoid of gyration a curve all the points whereof are equidistant from the centre ; such curve is of course the intersection of the ellipsoid by a concen- tric sphere, that is, it is a spherical conic; and the points of this spherical conic come successively to coincide with a fixed point on the invariable axis. This is a theorem stated in Art. VI. of Haughton’s memoir: it may be added that the several tangent planes of the ellipsoid of gyration at the points of the spherical conic as they come to coincide with the fixed point, form a cone reciprocal to Poinsot’s serpoloid cone. It is clear that every theorem in the one theory has its reciprocal in the other theory; I have not particularly examined as to how far the reciprocal theorems haye been stated in the two theories. 192. Cayley, “ On the Motion of Rotation of a Solid Body ” (1843).—The object was to apply to the solution of the problem Rodrigues’ formule for the resultant rotation ; viz., if the principal axes, considered as originally coin- ciding with the axes of «, y, z, can be brought into their actual position at the end of the time ¢ by a rotation 6 round an axis, inclined at angles f, g, h to the axes of w, y, z, and if \=tan $0 cos f, »=tan 46 cos g, v=tan 36 cosh, then the principal axes are referred to the axes fixed in space by means of the quantities \, », v. And these are to be obtained from the equations kpdt=2( dd+ vdu—pdy), « gdt=2(—rvdi\+ du+ddr), crdt=2( pdr—ddu+ dy), where k=1+)°+ p°++ ’, and p, q, 7 are to be considered as given functions of ¢, or of other the variable selected as the independent one. But for effecting the integration it was found necessary to take the axes of z as the invariable axes. 193. The solution by Jacobi, § 27 of the memoir “Theoria Novi Multi- plicatoris” (1845), is given as an application of the general theory, the author remarking that, as well in this question as in the problem of the two fixed centres, he purposely employed a somewhat inartificial analysis, in order to show that the principle (of the Ultimate Multiplier) would lead to the result without any special artifices. The principal axes are referred to the axes fixed in space by the ordinary three angles (here called q,, q,, q,), and the solution is carried so far as to give the integral equations, without any reduc- tion of the integrals cohtained in them to elliptic integrals. The solution is, howeve¥, in so far remarkable that the integrations are effected without the aid of the invariable plane. 194. Cayley, “On the Rotation of a Solid Body &c.” (1846).—It appeared desirable to obtain the solution by means of the quantities A, HB, v, without the assistance of the invariable plane, and Jacobi’s discovery of the theorem of the 238 REPORT—1862, Ultimate Multiplier induced me to resume the problem, and at least attempt to bring it so far as to obtain a differential equation of the first order between two variables only, the multiplier of which could be obtained theoretically by Jacobi’s discovery. The choice of two new variables to which the equa- tions of the problem led me, enabled me to effect this in a simple manner ; and the differential equation which I finally obtained turned out to be inte- grable per se, so that the laborious process of finding the multiplier became unnecessary. 195. The new variables Q, v have the following geometrical significations : Q=1 tan 30 cos], where / is the principal moment (A*p*+ B*q’+C'r’=P), 6 (as before) the angle of resultant rotation, and I is the inclination of the resultant axis to the invariable axis; and y=? cos? 3J, where if we imagine a line AQ having the same position relatively to the axes fixed in space that the invariable axis has to the principal axes of the body, then J is the incli- nation of this line to the invariable axis. It is found that p, g, 7 are func- tions of v only, whereas \, x, v contain besides the variable Q. In obtaining these relations, there occurs a singular relation Q?=xv—l, which may also be written 1+ tan’ 30 cos*, I=sec* 30 cos’ 3J, where the geometrical significa- tions of the quantities I, J have just been explained. The final results are that the time ¢, and the arc tan-1 are each of them expressible as the integrals of certain algebraical functions of v. There might be some interest in comparing the results with those of Euler’s memoir of 1758, where the principal axes are also referred to an arbitrary system of axes fixed in space ; but I was not then acquainted with Euler’s memoir. The concluding part of the paper relates to the determination of the varia- tions of the constants in the disturbed problem. 196. Cayley, “ Note on the Rotation of a Solid of Revolution ” (1849), shows the simplification produced in the formule of the last-mentioned memoir in the case where two of the moments of inertia are equal, say A=B. 197. Jacobi’s final solution of the problem of Rotation was given without demonstration in the letter to the Academy of Sciences at Paris; the demon- stration is added in the memoir, Crelle, t. xxxix. (1849). The fundamental idea consists in taking in the invariable plane, instead of the fixed axes vy, a set of axes xy revolving with uniform velocity, such that the angular distance of the axis of « from its initial position is precisely = —n'w ; and consequently if 6’ be the longitude of the node of the equator on the invariable plane, mea- sured from the moveable axis of # as the origin of longitude, we have PL lat log ee (i= v— =I); lis =5; into a loga- rithmic function) in passing to the trigonometrical functions sin 6’, cos 6’ the logarithm disappears altogether; and we have in a simple form the expres- sions for the actual functions sin 6’, cos 6’, through which 6’ enters into the formule, and thus, Jacobi remarks, the barrier is cleared which stands i in the way when the expression of an angle is reduced to an elliptic ‘integral of the third class. 198. For the better expression of the results, Jacobi joins to the functions H, 0, considered in the “ Fundamenta Nova,” the functions 0,vw=0 (K—vw), H (uw) =H(K—zw) ; so. that and in consequence of this form of the expression for @’ ON THE SPECIAL PROBLEMS OF DYNAMICS. 239 -, Hu k He _ Ou Vi sin amu= Ou? Jt cos amu, VE Aamu= On’ and then considering the cosine inclinations of the principal axes to the invariable axis and the revolying axes in the inyariable plane, these are all fractions which, neglecting constant factors, have the common deno- minator Qu; a’, 8’, y' (as shown by Rueb’s formule) have the numerators Hu, Hu, and ©,w respectively; and a, a have the numerators H (w+ia) +H (u—ia), B, 3’ the numerators H, (wu—7ta) +H, (w+ia), y, y' the nume- rators © (w+ia)+0 (w—ia) “respectively: there are also expressions of a similar form for the angular velocities about the axes of a and y; that about the axis of z (the invariable axis) haying, as was known, the constant value . The memoir is also very valuable analytically, as completing the systems of formuls given in the “ Fundamenta Nova” in reference to elliptic integrals of the third class. 199. It is worth noticing how the results connect themselves with Poinsot’s theorem of the rolling and sliding cone, the velocity of the rolling motion depends only upon the position, on the cone, of the line of contact, so that the same series of velocities recur after any number of complete revolutions of the cone; that is, the total angle described by the line of contact in conse- quence of the rolling motion, consists of a part varying directly with the time (or say varying as w) and a periodic part; the former part combines with the similar term arising from the sliding motion, and the two together give Jacobi’s term nw. } 200. Somoff’s memoir (1851), written after Jacobi’s Note in the ‘ Comptes Rendus,’ but before the appearance of the memoir in Crelle, gives the de- monstration of the greater part of Jacobi’s results. 201. Booth’s “Theory of Elliptic Integrals &c.” (1851) (contemporaneous with the publication of Poinsot’s memoir of 1834) contains various interest- ing analytical developments, and, as an interpretation of them, the author: obtains (p. 93) the theorem of the rolling and sliding cone. The investiga- tions inyolye the elliptic integrals, but not the elliptic or Jacobian functions. 202. Richelot’s two Notes (Crelle, tt. xlii. & xliv.) relate to the solution of the problem of rotation given in his memoir “Eine neue Losung &c.” (1851). This is an application of Jacobi’s theorem for the integration of a system of dynamical equations by means of the principal function S (see my “Report” of 1857, art. 34). Retaining Richelot’s letters ¢, y, 0, which signify i, the longitude of the node, 0, the inclination, , the hour-angle, the question is to find a complete solution of the partial differential equation _1f(av dV\' sing dV F 0-551 (% cos 0455) sin @ do cos of » 1 { (dV dV\ cos¢ dV. ; ' ton (ap cos +57) seat ay 80 0 1 /dV\? dV +26 (as) tat} that is, a solution inyolying (besides the constant attached to V by a mere 240 REPORT—1862. addition) three arbitrary constants; these are ¢,, Y,, p. Writing in the first place V=W-+tt,+yy,, the resulting equation for W may be satisfied by taking W, a function of ¢ and 0, without y or ¢; and it is sufficient to have a solution inyolying only a single arbitrary constant. This leads to a solu- tion which is as follows,— = 6 V=tt een tan cee ad aah it Wy, y, oe V 12-02 % ) $,0 +p) tan Sa tants | | ev p—y,7—8,7 eve =o aes 6+) J J Ow an (Gy 140" e424) where ¢, and 6, are certain given functions of ¢,, J, p, and of @ and ¢. The solution of the dynamical problem is then obtained by putting the differential ts » TB? a dV equal to arbitrary constants L, a, G respectively ; the eagle are be ee more simple than might be expected from the very complicated form of the function V. The foreg: going results (although not by themselves very intelligible) will give an idea of the form in which the ana- lytical solution in the first instance presents itself. 203. Richelot proceeds to remark that the solution in question, and the resulting integral equations of the problem, may be simplified in a peculiar manner by the method which he calls “‘ the integration by the spherical tri- angle.” For this purpose he introduces a spherical triangle, the sides and angles whereof are coefficients —- v,r\, ph; N, A, M, and then assuming N constant, M=x—9@ ((-3) sin? (9+») sin’A+ (<-3) cos” (@+v) sin’A = eth , where p and ¢, are constant, the solution is V=t,t—p(p—A) cos N—pM+p [cos Ad(¢+yr) ; and that this expression leads to all the results almost without calculation. 204. I have quoted the foregoing results from the Note (Crelle, t. xlii.), having seen, but without having studied, the Memoir itself: the results appear very interesting and valuable ones; but they seem to require a more com- plete geometrical development than they have received in the Memoir ; and I am not able to bring them into connexion with the other researches on the subject. 205. The solution, §3 of Donkin’s memoir “On a Class of Differential Equations &c.” (part i. 1854), is given as an illustration of the general theory to which the memoir relates; it contains, however, some interesting geometrical developments in regard to the case (A=B) of two equal moments of inertia. I have not compared the results with those in my Note of 1849. ; 206. The solution of the rotation problem, § 66 of Jacobi’s memoir “ Nova Methodus &c.” (1862), has for its object to show the complete analogy which exists between this problem and the problem of a body attracted to a ON THE SPECIAL PROBLEMS OF DYNAMICS, 241 fixed centre. The section is in fact headed “Solutio simultanea “Gara de motu puncti versus centrum attracti atque problematis de rotatione &c.” and Jacobi, after noticing that Poisson, in his memoir of 1816 (Mém. de l’Inst. t.i.), had shown that the expressions for the variations of the elements in the two problems could be investigated by a common analysis, remarks, «Sed ipsa problemata duo imperturbata hic primum, quantum credo, amplexus sum.” The solution is in fact as follows:—Suppose that in the one problem the position of the point in space, and in the other problem the position of the body in regard to the fixed axes is determined in any manner by the quantities 9,, 9,,9,- Let di , dq, di ly ag and expressing the Vis Viva function T in terms of ¢,, 9,5 Ys 1's Jo's Yq» let LT i BE rg AL dy? dg?” dg, and let H be the value of T expressed in terms of ¢,, 9,5 3s Py» Pos Py» 80 that H=a is the integral of Vis Viva (this is merely the transformation to the Hamiltonian form). And let H,=a,, ¢=«a,', p=a," be the three integrals of areas (H, H,, ¢, are functions of the variables only, not containing the arbitrary constants a, a,, a,',a,"). Then, expressing H, H,, H, (=VH'+9'+¥) in terms of p,, 75 Ps 91> Qo» Jo and by means of the equations H=7, a H.=¢; (where a,= Va,7+a,"+a,'") expressing p,, p,, p, in terms of 4, J.) %» We haye p,dq,+p,dq¢,+p,dq, a complete differential ; and putting § (cae +p.dq, +p.ty,)=V, then (a, a,, a,, b, b,, 6, being arbitrary constants) we have H=a, H, =a, Hy =4,, a dp, 4 Y((Ba TET G ries dq, + Pa aly, = t+, dV d dp ree ee Pea = Ps dy, + pe ay,)= it Les a dp, 4, \— r= ( (Pa da, + da, qg,+ da, a4,)=by as the complete fal: of either problem, the last three of them being the final integrals. And it is added that if in either problem we have H+. instead of H, the expressions for the variations of the elements assume the canonical forms da_ dQadb_ da dt db’ dt da’ The solution is not further developed as regards the rotation problem, but it is so (§ 67) as regards the other problem. ee It must, I think, be considered that a comprehensive memoir on the R =Ps) 242 REPORT—1 862. Problem of Rotation, embracing and incorporating all that has been done on the subject, is greatly needed. Kinematics of a solid body. Article Nos. 208 to 215. 208. The general theorem in regard to the infinitesimal motions (rotations and translations) of a solid body is that these are compounded and resolved in the same way as if they were single forces and couples respectively. Thus any infinitesimal rotations and translations are resolvible into a rotation and a translation ; the rotation is given as to its magnitude and as to the direction of its axis, but not as to the position of the axis (which may be any line in the given direction): the magnitude and direction of the translation depend on the assumed position of the axis of rotation; in particular this may be taken so that the translation shall be in the direction of the axis of rotation ; and the magnitude of the rotation is then a minimum. I remark that the theorem as above stated presupposes the establishment of the theory of couples (of forces) which was first accomplished by Poinsot in his ‘Elémens de Statique,’ 1st edit. 1804; it must have been, the whole or nearly the whole of it, familiar to Chasles at the date of his paper of 1830 next referred to (see also Note XXXIV of the Apercu Historique, 1837) ; and it is nearly the whole of it stated in the ‘ Extrait’ of Poinsot’s memoir on Rotation, 1834. 209. Chasles’ paper in the ‘ Bulletin Uniy. des Sciences’ for 1830.—The corresponding theorem is here given for the finite motions (rotations and translations) of a solid body as follows, viz. if any finite displacement be given to a free solid body in space, there exists always in the body a certain inde- finite line which after the displacement remains in its original situation. The theorem is deduced from a more general one relating to two similar bodies. It may be otherwise stated thus: viz., any motions may be represented by a translation and a rotation (the order of the two being indifferent) ; the rotation is given as regards its magnitude and the direction of its axis, but not as to the position of the axis (which may be any line in the given direction); the magnitude and direction of the translation depend on the assumed position of the axis of rotation ; in particular this may be taken so that the translation shall be in the direction of the axis of rotation; the magnitude of the trans- lation is then a minimum. : It may be noticed that a translation may be represented as a couple of rotations; that is, two equal and opposite rotations about parallel axes. 210. It is part’of the general theorem that any number of rotations about axes passing through one and the same point may be compounded into a single rotation about an axis through that point ;. this is, in fact, the theory of the “ Resultant Axis ” déyeloped in Euler’s and Lexell’s memoirs of 1775. 211. The following properties are also given, viz., considering two similar solid bodies (or in particular any two positions of a solid body) and joining the corresponding points, the lines which pass through one and the same point form a cone of the second order; and the points of either body form on this cone a curve of the third order (skew cubic). And, reciprocally, the lines, intersections of corresponding planes, which lie in one and the same plane envelope a conic, and such planes of either body envelope a developable surface, which is such that any one of these planes meets it in a conic [or, ee is the same thing, the planes envelope a developable surface of the fourth order}. And also, given in space two equal bodies situate in any manner in respect to each other, then joining the points of the first body to the homologous points of the second body, the middle points of these lines form a body capable : : ON THE SPECIAL PROBLEMS OF DYNAMICS, 243 of an infinitesimal motion, each point of it along the line on which the same is situate. 212. The entire theory, as well of the infinitesimal as of the finite motions of a solid body, is carefully and successfully treated in Rodrigues’ memoir “ Des lois géométriques &c.” (1840). It may be remarked that for the purpose of compounding together any rotations and translations, each rotation may be resolved into a rotation about a parallel axis and a couple of rotations, that is, a translation; the rotations are thus converted into rotations about axes through one and the same point, and these give rise to a single resultant rotation given as to its magnitude and the direction of the axis, but not as to the position of the axis (which is an arbitrary line in the given direction) ; the translations are then compounded together into a single translation, and finally the position of the axis of rotation is so determined that the translation shall be in the direction of this axis; the entire system is thus compounded (in accordance with Chasles’ theorem) into a rotation and a translation in the direction of the axis of the rotation. The problem of the composition depends therefore on the composition of rotations about axes through one and the same point; that is, upon Euler’s and Lexell’s theory of the resultant axis. But, as already noticed, the analytical theory of the resultant axis was per- fected by Rodrigues in the present memoir (see ante, ‘ Transformation of Co- ordinates,’ Nos. 139-141, as to this memoir and the quaternion representation of the formulee contained in it). 213. It was remarked in Poinsot’s memoir of 1834 that every continuous motion of a solid body about a fixed point is the motion of a cone fixed in the body rolling upon another cone fixed in space. The corresponding theorem for the motion of a solid body in space is given Cayley, “On the Geometrical Representation &c.” (1846), viz. premising that a skew surface is said to be “‘ deformed” if, considering the elements between consecutive generating lines as rigid, these elements be made in any manner to turn round and slide along the successive generating lines :—and that two skew surfaces can be made to roll and slide one upon the other, only if the one is a deformation of the other—and that then the rolling and sliding motions are perfectly determined—and that such a motion may be said to be a “gliding” motion: the theorem is that any motion whatever of a solid body in space may be represented as the gliding motion of one skew surface upon another skew surface of which it is the deformation. 214. The same paper contains the enunciation and analytical proof of the following theorem supplementary to that of Poinsot just referred to, viz. that when the motion of a solid body round a fixed point is represented as the rolling motion of one cone on another, then “the angular velocity round the line of contact (the instantaneous axis) is to the angular velocity of this line as the difference of the curvatures of the two cones at any point in this line is to the reciprocal of the distance of the. point from the vertex.” 215. There are a great number of theorems relating to the composition of forces and force-couples, which consequently relate also to infinitesimal rota- tions and translations. See, for instance, Chasles, “ Théorémes généraux ce.” (1847), Mobius, “ Lehrbuch der Statik” (1837), Steichen’s Memoirs of 1853 and 1854, &c. Arising out of some theorems of Mobius in the “ Statik,” we have Sylvester's theory of the involution of six lines: viz. six lines (given in position) may be such that properly selected forces along them (or if we please, properly selected infinitesimal rotations round them) will counter- balance each other; or, what is the same thing, the six lines may be such that a system of forces, although satisfying for each of the six lines the con- R2 244, REPORT—1862. dition moment=0, will not of necessity be in equilibrium ; such six lines are said to be in involution, and the geometrical theory is a very extensive and interesting one. Miscellaneous Problems. Article Nos. 216 to 223. 216. As under the foregoing head, “‘ Rotation round a fixed point,” I have considered only the case of a body not acted upon by any forces, the case where the body is acted upon by any forces comes under the present head. The forces, whatever they are, may be considered as disturbing forces, and the problem be treated by the method of the variation of the elements ; this is at any rate a separate part of the theory of rotation round a fixed point, and I have found it convenient to include it under the present head; the only case in which the forces have been treated as principal ones, seems to be that of a heavy body (a solid of revolution) rotating about a point not its centre of gravity. The case of a body suspended by a thread or resting on a plane comes under the present head, as also would (in some at least of the questions connected with it) the gyroscope. But none of these questions are here considered in any detail. Rotation round a fixed point—Variation of the elements. 217. The forces acting on the body are treated as disturbing forces. Formule for the variations of the elements were first obtained by Poisson in the memoir “ Sur la Variation des Constantes Arbitraires &c.” (1809). The variations are expressed in terms of the differential coefficients of the disturb- ing function in regard to the elements, and, as the author remarks, they are very similar in their form to, and can be rendered identical with, those for the variations of the elements in the theory of elliptic motion. 218. Cayley, “On the Rotation &c.” (1846).—The latter part of the paper relates to the variations of the elements therein made use of, which are different from the ordinary ones. 219. Richelot, “Eine neue Lésung &e.” (1851).—The form in which the integrals are obtained by means of a function V, satisfying a partial differen- tial equation, leads at once to a canonical system for the variations of the elements; these formule are referred to in the introduction to the memoir, but they are not afterwards considered. 220. Cayley, “ On the Rotation of a Solid Body” (1860).—The elements are those ordinarily made use of, with only a slight variation occasioned by the employment of the “ departure” of the node. The course of the investigation consists in obtaining the variations in terms of the differential coefficients of the disturbing function in regard to the coordinates (formule which were thought interesting for their own sake), and in deducing therefrom those in terms of the differential coefficients in terms of the elements. Other cases of the motion of a solid body. 221. In regard to a heavy solid of revolution rotating about a fixed point not its centre of gravity, we have Poisson, “‘ Mémoire sur un cas particulier &c.” (1831), and the elaborate memoir Lottner, “ Reduction der Bewegung &c.”’ (1855), where the solution is worked out by means of the Elliptic and Jacobian functions, 222. As regards a heavy solid suspended by a string, Pagani, “‘ Mémoire sur l’équilibre Ke.” (1839). 223, As regards the motion of a body resting on a fixed plane, ON THE SPECIAL PROBLEMS OF DYNAMICS. 245 Cournot, “‘ Mémoire sur le Mouvement &c.” (1830 and 1832). Puiseux, ‘‘ Du Mouvement &c.” (1848). To which: several others might doubtless be added; but the problems are so difficult, that the solutions cannot, it is probable, be obtained in any very complete form. In conclusion, I can only regret that, notwithstanding the time which has elapsed since the present Report was undertaken, it is still—both as regards the omission of memoirs and works which should have been noticed, and the merely cursory examination of some of those which are mentioned—far from being as complete as I should have wished to make it. To have reproduced, to any much greater extent than has been done, the various mathematical inyestigations, would not have been proper, nor indeed practicable; at the same time, more especially as regards the subjects treated of in the second part of this Report, or say the kinematics and dynamics of a solid body, such a reproduction, incorporating and to some extent harmonizing the original researches, but without ignoring the points of view and methods of investi- gation of the several authors, would be a work which would well repay the labour of its accomplishment, é List of Memoirs and Works. Ampére. Mémoire sur quelques propriétés nouvelles des axes permanens de rotation des corps, et des plans directeurs de ces axes. 4to. Paris, 1823. . Mémoire sur la Rotation. Mém. de l’Institut, t. v. 1834. Mémoire sur les équations générales du mouvement. Liouv. t. i. pp. 211-228 (1836). (Written 1826.) Anon. Note on the problem of falling bodies as affected by the earth’s rota- tion, C. & D. M. J. t. iii. pp. 206-208 (1848). Remarks on the deviation of falling bodies to the east and south of the perpendicular, and corrections of a previously published paper on the same subject. C. & D. M. J. t. iv. pp. 96-105 (1849). Baehr. Notice sur le mouvement du pendule ayant égard 4 la rotation de la terre. 4to. Middelbourg, 1853. Bertrand. Mémoire sur l’intégration des équations différentielles de la Mécanique. Liouv. t. xvii. pp. 393-436 (1852), Note sur le Gyroscope de M. Foucault. Liouy. t. i. 2 sér. (1856) pp- 379-382. Mémoire sur quelques unes des formes les plus simples que puis- sent présenter les équations différentielles du mouvement d’un point materiel. Liouv. t. ii. 2 sér. (1857) pp. 113-140. Bessel. Analytische Auflésung der Keplerschen Aufgabe. Berl. Abh. 1816-17, pp. 49-55. (Read July 1818.) Ueber die Entwickelung der Functionen zweier Winkeln u und w’ in Reihen welche nach der Cosinussen und Sinussen der Vielfachen von uund w' fortgehen. Berl. Abh. 1820-21, pp. 56-60. (Read June 1821.) Untersuchung des Theils der planetarischen Stérungen welche aus der Bewegung der Sonne entsteht. Berl. Abh. 1824, pp. 1-52, Binet. Mémoire sur la théorie des axes conjugués et des momens d’inertie , Journ, Polyt. t. ix. (cah. 16) pp. 41-67 (1813). (Read May ——. Note sur le mouvement du pendule simple en ayant égard 4 ]’in- 246 A REPORT—1862. fluence de la rotation diurne de la terre. Comptes Rendus, t. xxxii. (1851) pp. 157-160 & 197-205. Bonnet. Note sur un théoréme de Mécanique. Liouv. t. ix. p. 113 (1844), and Note iv. of t. ii. of the last edition of the Méc. Anal. pp. 329-331 1855). ‘iil Theory of Elliptic Integrals. 8vo. Lond. 1851. Bour. Mémoire sur le probléme des trois corps. Journ. Polyt. t. xxi. (cah. 36) pp. 35-58 (1856). Bravais. Mémoire sur l’influence qu’exerce la rotation de la terre sur le mouvement d’un pendule 4 oscillations coniques, Liouy. t. xix. pp. 1-50 (1854). Note sur une formule de Lagrange relative au mouvement pendu- laire. Note vii. of t. ii. of the last edition of the Méc. Anal. pp. 8352-355 (1855). Briot. Thése sur le mouvement d’un corps solide autour d’un point fixe. Liouy. t. vii. pp. 70-84 (1842). Cauchy. Sur les momens d’inertie. Ex. de Math. t. i. pp. 93-103- (1827). Résumé d’un mémoire sur la Mécanique Céleste et sur un nouveau calcul appelé des limites. (Read at Turin Oct. 1831.) Exer. d’Anal. &e. t. ii. pp. 41-109 (1841). Cayley. On certain expansions in multiple sines and cosines. .Camb.. M. J, t. iii. pp. 162-167 (1842). . On the motion of rotation of a solid body. Camb. M. J. te iii. pp. 224-232 (1842). . On certain results relating to quaternions, Phil. Mag. t. xxyi. (1845) p. 141. On the geometrical representation of the motion of a solid body. C. & D. M. J. t. i, pp. 164-167 (1846). . On the rotation of a solid body round a fixed point. C.&D.M.J. t.i. pp. 167-173 & 264-274 (1846). . Note on a geometrical theorem in Prof. Thomson’s memoir on the principal axes of a solid body. C. & D. M. J. t. i. pp. 207-208 (1846). . On the application of quaternions to the theory of Rotation.- Phil. Mag. t. xxxiii. (1848) p. 196. Note on the motion of rotation of a solid of revolution. C.& D.M.J,- t, iv. pp. 268-271 (1849). Sur les déterminants gauches. Crelle, t. xxxvili. (1849) pp. 93-96. Note on the theory of Elliptic Motion. Phil. Mag. t. xi. (1856) pp. 425-428. 5 A demonstration of Sir W. R. Hamilton’s theorem of the Iso- chronism of the Circular Hodograph. Phil. Mag. t. xiii. (1857) p. 427. . Report on the recent progress of Theoretical Dynamics. Rep.~ Brit. Assoc. for 1857, pp. 1-42. . On Lagrange’s solution of the problem of two fixed Centres. ° Quart. Journ, M. J. t. 1. pp. 76-82 (1858). Note on the expansion of the true anomaly, Quart. M. J. t. ii - pp. 229-232 (1858). ON THE SPECIAL PROBLEMS OF DYNAMICS. 247 Cayley. Tables in the theory of Elliptic Motion, Mem. R. Astr, Soc. t. xxix. (1860) pp. 191-306. A Memoir on the problem of the rotation of a solid body. Mem. R. Astr. Soc. t. xxix. (1860) pp. 307-342, On Lambert’s theorem for Elliptic Motion. Monthly Not. R. Astr. Soc. t. xxii. pp. 238-242 (1861). : Note on a theorem of Jacobi’s in relation to the problem of three bodies. Monthly Not. R. Astr. Soc. t, xi. pp. 76-79 (1861). Chasles. Note sur les propri¢tés générales du systéme de deux corps sem- blables entr’eux et placés d’une maniére quelconque dans l’espace, et sur le déplacement fini ou infiniment petit d’un corps solide libre. (Read Feb. 1831.) Bull, Univ. des Sciences (Férussac), t. xiv. pp. 321-326. . Théorémes généraux sur les syst¢émes de forces et leurs moments. . Liouv. t. xii. pp. 213-224 (1847). Clairaut. Théorie de la Lune déduite du seul principe de l’attraction réci- proquement proportionnelle aux carrés des distances. 4to. St. Pét. 1752, . and Paris, 1765. is Cohen. On the Differential Coefficients and Determinants of Lines, and their . Application to Theoretical Mechanics. Phil. Trans. t. 152 (1862), pp. 469-510. Cotes. Harmonia mensurarum sive analysis et synthesis per rationum et _ angulorum mensuras promot ; accedunt alia opuscula mathematica. 4to. . Camb. 1722. Cournot. Mémoire sur le mouvement d’un corps rigide soutenu par un . plan fixe. Crelle, t. v. pp, 183-162 & 223-249 (1830); Suite, t. viii. pp. 1-12 (1832). Creedy. General and practical solution of Kepler’s Problem. Quart. M. J. t. i. pp. 259-271 (1855). ; D’Alembert. Traité de Dynamique. Paris, 1743. —. Recherches sur la précession des équinoxes et sur la nutation de _ Taxe de la terre. Meém. de Berl. (1749). ey Desboves. Thése sur le mouvement d’un point matériel attiré en raison inverse du carré des distances yers deux centres fixes. Liouy. t. xiii. pp. 369-396 (1848). Donkin. On an application of the calculus of operations to the transforma- tion of trigonometric series. Quart. M. J. t. ii. pp. 1-15 (1858). On a class of Differential Equations, including those which occur in Dynamical Problems. Part I. Phil. Trans. t. exliy. (1854) pp. 71-113; Part. IT. t. exlv. (1855) pp. 299-358. Droop. On the Isochronism of the Circular Hodograph. Q.M. J. t.i. (1856) pp. 374-378. Dumas. Ueber die Bewegung des Raumpendels mit Rucksicht auf die Rotation der Erde. Crelle, t. 1. pp. 52-78 & 126-185 (1855). Durége. Theorie der elliptischen Functionen. 8vo. Leipzig, 1861. (§ xx. reproduces some results on the spherical pendulum obtained in an unpub- lished memoir of 1849.) ; Euler. Determinatio Orbitz Comets anni 1742. Misc. Berl. t. vii. (1743) pal. Theoria motuum planetarum et cometarum. 4to. Berl, 1744. 248 REPORT—1862. ‘Euler. De motu corporis ad duo virium centra attracti. Nov. Comm. Petrop. t. x. for 1764, pub. 1766, pp. 207-242. Probléme: un corps étant attiré en raison réciproque carrée des dis- tances vers deux points fixes donnés, trouver les cas ot la courbe décrite par ce corps sera algébrique. Mém. de Berl. for 1760, pub. 1767, pp. 228-249. De motu corporis ad duo centra virium fixa attracti. Nov. Comm. Petrop. t. xi. for 1765, pub. 1767, pp. 152-184. Considerationes de motu corporum ceelestium. Nov. Comm. Petrop. t. x. for 1764, pub. 1766, pp. 544-558. De motu rectilineo trium corporum se mutuo attrahentium. Nov. Comm. Petrop. t. xi. for 1765, pub. 1767, pp. 144-151. . De motu trium corporum se mutuo attrahentium super eadem linea recta. Nov. Acta Petrop. t. iti. (1776) p. 126-141. Problema algebraicum ob affectiones prorsus singulares memora- bile. Nov. Comm. Petrop. t. xv. (1770) p. 75; Comm. Arith. Coll. t.i. pp. 427-443. Formule generales pro translatione quacunque corporum rigi- dorum, Noy. Comm. Petrop. t. xx. 1775, pp. 189-207. Nova methodus motum corporum rigidorum determinandi. Nov. Comm. Petrop. t. xx. (1775) pp. 208. Recherches sur la précession des équinoxes et sur la nutation de Vaxe de la terre. Mém. de Berl. t. v. for 1749, pub. 1751, pp. 326-338. (Euler mentions, t. vi., that this was written after he had seen D’Alem- bert’s memoir.) Découverte d’un nouveau principe de Mécanique. Mém. de Berl. t. vi. for 1750, pub. 1752, pp. 185-217. Recherches sur Ja connaissance mécanique des corps. Mém. de Berl. for 1758, pub. 1767, pp. 1382-153. . Du mouvement de rotation des corps solides autour d'une axe variable. Mém. de Berl. for 1758, pub. 1765, pp. 154-193. . Du mouvement d’un corps solide lorsqu’il tourne autour d’une axe mobile. Mém. de Berl. for 1760, pub. 1767, pp. 176-227. Theoria motus corporum solidorum. 4to. Rostock, 1765. Foucault. Démonstration physique du mouvement de rotation de la terre au moyen du pendule. Comptes Rendus, t. xxxii. (1851) pp. 135-138. Gauss. Fundamental-Gleichungen fur die Bewegung schwerer Korper auf der rotirenden Erde, 1804. Theoria motus corporum ceelestium. 4to. Hamb. 1809. Greatheed. Investigation of the general term of the expansion of the true anomaly in terms of the mean. Camb. M. J. t. i. pp. 228-232 (1838). Gudermann. De pendulis sphericis et de curvis que ab ipsis describuntur sphericis. Crelle, t. xxxviil. pp. 185-215 (1849). Hamilton, Sir W. R. A theorem of anthodographic isochronism. Proc. R, Irish Acad. 1847, t. ui. pp. 465-466. Lectures on Quaternions. 8vo. Dublin, &. (1853). Hansen. Fundamenta Nova inyestigationis orbitee vere quam Luna per- lustrat. 4to. Goth, 1838. —. Ermittelung der absoluten Storungen in Ellipsen yon beliebigen Excentricitat und Neigung. Gotha, 1843, pp. 1-167. ON THE SPECIAL PROBLEMS OF DYNAMICS. 249 Hansen. Entwickelung des Products einer Potenz des Radius-Vectors mit dem Sinus oder Cosinu seines Vielfachen der wahren Anomalie in Reihen die nach den Sinussen oder Cosinussen der Vielfachen der wahren excen- trischen oder mittleren Anomalie fortschreiten. Abh, d. K. 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Sur une maniére particulicre d’exprimer le temps dans les sections coniques décrites par des forces tendantes au foyer et réciproquement proportionnelles aux carrés des distances. Mém. de Berlin for 1778; and Note Y. of t. ii. of the 3rd edition of the Méc. Anal. pp. 332-349, Recherches sur le mouvement d’un corps qui est attiré vers deux centres fixes. Premier Mémoire, ot l’on suppose que l’attraction est en raison inverse des carrés des distances. Anc. Mém. de Turin, t. iv. (1766- 1769) pp. 118-215. , . Second Mémoire, ot l’on applique la méthode précédente a différentes hypothéses d’attraction. Anc. Mém., de Turin, t. iv. (1766— 1769) pp. 215-243, Lagrange. Nouvelle solution du probléme du mouvement de rotation d’un corps. Meém. de Berl, for 1773. 250 : REPORT—1862. Lambert. Insigniores Orbitze Cometarum Proprietates. S8vo. Aug.1765. — Laplace. Mécanique Céleste, t. i. 1799; t. ii. 1799; t. ili, 1802; t, iv. 1805 ; t. v. 1823. . Mémoire sur le développement de l’anomalie vraie et du rayon vecteur elliptique en séries ordonnées suivant les puissances de l’excen- ~ tricité. Mém. de l’Inst. t. vi. (1823) pp. 63-80. Lefort. Expressions numériques des intégrales définies qui se présentent quand on cherche les termes généraux des développements des coordonnés d’un planéte dans son mouvement elliptique. Liouy. t. xi. pp. 142-152 (1846), Legendre. Exercices de Calcul Intégrale, t. ii. (containing the dynamical ~ applications) 1817. Traité des Fonctions Elliptiques, t. i. (1825) (but the dynamical applications are for the most part reproduced from the Hvercices). Leverrier. Annales de l’Observatoire de Paris, t. i. (1855). Lexell. Theoremata nonnulla generalia de translatione corporum rigidorum. Noy. Comm. Petrop. t. xx. (1775) pp. 239-270. Liouville. Sur Vintégrale #5 “cosi(u—awsinu)du. Liouv. t. vi. pp. 836-37 0 = - (1841). - corps. 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London, 1687. Pagani. Démonstration d’un théoréme de Lambert. Crelle, t. xv. pp. 350- _ 352 (1834). Mémoire sur l’équilibre d’un corps solide suspendu 4 un cordon flexible. Crelle, t. xxix. pp. 185-204 (1839). Painvin. Recherches du dernier multiplicateur pour deux formes spéciales et remarquables des équations différentielles du probléme de trois corps, _ Liouy, t. xix. pp. 88-111 (1854), Poinsot. Mémoire sur la rotation. Extrait, 8vo, Paris, 1834, Extrait d’un mémoire sur un cas particulier du probléme de trois Zur Theorie des Foucaultschen Pendelversuchs. Crelle, t. lii. pp. ON THE SPECIAL PROBLEMS OF DYNAMICS. 251 Poinsot. Théorie nouvelle de la rotation des corps. Liouv. t. xvi. pp. 9- 130 & 289-236 (1851). ——-—. Théorie des cones circulaires roulants. Liouv. t. xviii. pp. 41-70 (1853). Questions dynamiques s sur la percussion des corps. Liouy. t. ii. (2 sér.) pp. 281-329 (1859). : Poisson. Traité de Mécanique. 1 ed. Paris, 1811; 2 ed. Paris, 1833. 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J. t. i. pp. 209-227, and t. ii. pp. 19-42, 140-171 & 241-251 (1846-47). Walton. Instantaneous lines and planes in a body revolving round a fixed point. C.& D. M. J. t. vii. pp. 111-113 (1852). Whewell. A Treatise on Dynamics. 1 ed. Cambridge, 1823. Worms. The Earth and its Mechanism—being an account of the various proofs of the rotation of the Earth, with a description of the instruments used in the experimental demonstrations : to which is added the theory of Foucault’s Pendulum and Gyroscope. 8vo. London, 1862, ON DOUBLE REFRACTION. 2538 Report on Double Refraction. By G.G.Stoxss, M.A., D.C.L.,Sec.R.S., Lucasian Professor of Mathematics in the University of Cambridge. I recrer to say that in consequence of other occupations the materials for a complete report on Physical Optics, which the British Association have re- quested me to prepare, are not yet collected and digested. Meanwhile, instead of requesting longer time for preparation, I have thought it would be well to take up a single branch of the subject, and offer a report on that alone. I have accordingly taken the subject of double refraction, having mainly in view a consideration of the various dynamical theories which have been adyanced to account for the phenomenon on the principle of transversal vibra- tions, and an indication of the experimental measurements which seem to me most needed to advance this branch of optical science. As the greater part of what has been done towards placing the theory of double refraction on a rigorous dynamical basis is subsequent to the date of Dr. Lloyd’s admirable report on ‘ Physical Optics,” I have thought it best to take a review of the whole subject, though at the risk of repeating a little of what is already con- tained in that report. The celebrated theory of Fresnel was defective in rigour in two respects, as Fresnel himself clearly perceived. The first is that the expression for the force of restitution is obtained on the supposition of the absolute displacement of a molecule, whereas in undulations of all kinds the forces of restitution with which we are concerned are those due to relative displacements. Fresnel endeayoured to show, by reasoning professedly only probable, that while the magnitude of the force of restitution is altered in passing from absolute to rela- tive displacements, the Jaw of the force as to its dependence on the direction of vibration remains the same. The other point relates to the neglect of the com- ponent of the force in a direction perpendicular to the front of a wave. In the state of things supposed in the calculation of the forces of restitution called into play by absolute displacements, there is no immediate recognition of a wave at all, and a molecule is supposed to be as free to move in one direction as in another. But a displacement in a direction perpendicular to the front of a wave would callinto play new forces of restitution having a resultant not in general in the direction of displacement; so that even the component of the force of restitution in a direction parallel to the front of a wave would haye an expression altogether different from that determined by the theory of Fresnel. But the absolute displacements are only considered for the sake of obtaining results to be afterwards applied to relative displacements; and Fresnel distinctly makes the supposition that the ether is incompressible, or at least is sensibly so under the action of forces comparable with those with which we are concerned in the propagation of light. This supposition re- moves the difficulty ; and though it increases the number of hypotheses as to the existing state of things, it cannot be objected to in point of rigour, unless it be that a demonstration might be required that incompressibility is not in- consistent with the assumed constitution of the ether, according to which it is regarded as consisting of distinct material points, symmetrically arranged, and acting on one another with forces depending, for a given pair, only on the distance. Hence the neglect of the force perpendicular to the fronts of the waves is not so much a new defect of rigour, as the former defect appear- ing under a new aspect. Lhave mentioned these points because sometimes they are slurred over, and Fresnel’s theory spoken of as if it had been rigorous throughout, to the injury of students and the retardation of the real progress of science ; and 254 - -REPoRT—1]1862. sometimes, on the other hand, the grand advance made by Fresnel is depre- ciated on account of his theory not being everywhere perfectly rigorous. If we reflect on the state of the subject as Fresnel found it, and as he left it, the wonder is, not that he failed to give a rigorous dynamical theory, but that a single mind was capable of effecting so much. The first deduction of the laws of double refraction, or at least of an ap- proximation to the true laws, from a rigorous theory is due to Cauchy*, though Neumann? independently, and almost simultaneously, arrived at the same results. In the theory of Cauchy and Neumann the ether is supposed to consist of distinct particles, regarded as material points, acting on one another by forces in the line joining them which vary as some function of the distances, and the arrangement of these particles is supposed to be dif- ferent in different directions. The medium is further supposed to possess three rectangular planes of symmetry, the double refraction of crystals, so far as has been observed, being symmetrical with respect to three such planes. The equations of motion of the medium are deduced by a method similar to that employed by Navier in the case of an isotropic medium. The equations arrived at by Cauchy, the medium being referred to planes of symmetry, contain nine arbitrary constants, three of which express the pressures in the principal directions in the state of equilibrium. Those employed by Neumann contain only six such constants, the medium in its natural state being sup- posed free from pressure. In the theory of double refraction, whatever be the particular dynamical conditions assumed, everything is reduced to the determination of the velocity of propagation of a plane wave propagated in any given direction, and the mode of vibration of the particles in such a wave which must exist in order that the wave may be propagated with a unique velocity. In the theory of Cauchy now under consideration, the direction of vibration and the reciprocal of the velocity of propagation are given in direction and magnitude respec- tively by the principal axes of a certain ellipsoid, the equation of which con- tains the nine arbitrary constants, and likewise the direction-cosines of the wave-normal. Cauchy adduces reasons for supposing that the three constants G, H, I, which express the pressures in the state of equilibrium, vanish, which leaves only six constants. For waves perpendicular to the principal axes, the squared velocities of propagation and the corresponding directions of vibration are given by the following Table :— Waveanormal 0. au ary. a we y Zz we L R Q Direction of vibra- y R M P Zz Q P N For waves in these directions, then, the vibrations are either wholly normal or wholly transversal. The latter are those with which we have to deal in the theory of light. Now, according to observation, in any one of the prin- cipal planes of a doubly refracting crystal, that ray which is polarized in the principal plane obeys the ordinary law of refraction. In order therefore that the conclusions of this theory should at all agree with observation, we must * Mémoires de I’ Académie, tom. x. p. 293- + Poggendorff’s Annalen, vol. xxv. p. 418 (1832). ON DOUBLE REFRACTION. 255 suppose that in polarized light the vibrations are parallel, not perpendicular, to the plane of polarization. Let 1, m, n be the direction-cosines of the wave-normal. In the theory of Cauchy and Neumann, the square v* of the velocity of propagation is given by a cubic of the form v+a,v+a,v°+a,=0, where «,, a,, @, are homogeneous functions of the Ist order as regards L, M, N, P,Q, R, and homogeneous functions of the orders 2, 4, 6 as regards l,m, , involving even powers only of these quantities. For a wave perpen- dicular to one of the principal planes, that of y z suppose, the cubic splits into two rational factors, of which that which is of the first degree in v”, namely, v—m R—n? Q, corresponds to vibrations perpendicular to the principal plane. This is the same expression as results from Fresnel’s theory, and accordingly the section, by the principal plane, of one sheet of the wave-surface, which in this theory is a surface of three sheets, is an ellipse, and the law of refraction of that ray which is polarized perpendicularly to the principal plane agrees exactly with that given by the theory of Fresnel. For the two remaining waves, the squared velocities of propagation are given by the quadratic (v?—m* M—n’* P) (v?—m? P—n? N)—4in? n? P?=0; «2... (1) but according to observation the ray polarized in the principal plane obeys the ordinary law of refraction. Hence (1) ought to be satisfied by v?—(m? +n*) P=0, which requires that (M—P) (N—P)=4P?, on which supposition the remaining factor must evidently be linear as regards m?, n?, and therefore must be v—n? M—n? N, since it gives when equated to zero v?=M, or v?=N for m=1, orn=1. And since the same must hold good for eack of the principal planes, we must have the three following relations between the six constants, (M—P) (N—P)=4P*; (N—Q) (L—Q)=4Q’; (L—R) (M—R)=4R?... (2) _ The existence of six constants, of which only three are wanted to satisfy the numerical values of the principal velocities of propagation in a biaxal crystal, permits of satisfying these equations; so that the law that the ray polarized in the plane of incidence, when that is a principal plane, obeys the ordinary law of refraction is not inconsistent with Cauchy’s theory. This simple law is, however, not in the slightest degree predicted by the theory, nor even rendered probable, nor have any physical conditions been pointed out which would lead to the relations (2); and, indeed, from the form of these equations, it seems hard to conceive what physical relations they could express. Hence an important desideratum would be left, even if the theory were satisfactory in all other respects. : - The equation for determining v* virtually contains the theoretical laws of double refraction, which are embodied in the form of the wave-surface. The wave-surface of Cauchy and Neumann does not agree with that of Fresnel, except as the sections of two of its sheets by the principal planes, the third sheet being that which relates to nearly normal vibrations. Nevertheless the first two sheets, being forced to agree in their principal sections with Fres- nel’s surface, differ from it elsewhere extremely lttle. In Arragonite, for instance, in a direction equally inclined to the principal axes, assuming Rud- 256 REPORT—1862. berg’s indices* for the line D, I find that the velocities of propagation of the two polarized waves, according to the theory of Cauchy and Neumann, differ from those resulting from the theory of Fresnel only in the tenth place of decimals, the velocity in air being taken as unity. Such a difference as this would of course be utterly insensible in experiment. In like manner the directions of the planes of polarization according to the two theories, though not rigorously, are extremely nearly the same, the plane of polarization of a wave in which the vibrations are nearly transyersal being defined as that containing the direction of propagation and the direction of vibration, in har- mony with the previously established definition for the case of strictly trans- versal vibrations. Hence as far as regards the laws of double refraction of the two waves which alone are supposed to relate to the visible phenomenon, and of the accompanying polarization, this theory, by the aid of the forced relations (2), is very successful. I am not now discussing the generality, or, on the con- trary, the artificially restricted nature, of the fundamental suppositions as to the state of things, but only the degree to which the results are in accordance with observed facts. But as regards the third wave the case is very different. That theory should point to the necessary existence of such a waye consisting of strictly normal vibrations, and yet to which no known phenomenon can be referred, is bad enough; but in the present theory the vibrations are not even strictly normal, except for waves in a direction perpendicular to any one of the principal axes. In Iceland spar, for instance, for waves propagated in a direction inclined 45° to the axis, it follows from the numerical values of the refractive indices for the fixed line D given by Rudberg that the two vibrations in the principal plane which can be propagated independently of each other are inclined at angles of 9° 50’ and 80° 10’, or say 10° and 80°, to the wave-normal. We can hardly suppose that a mere change of inclination in the direction of vibration of from 10° to 80° with the wave front makes all the difference whether the wave belongs to a long-known and evident pheno- menon, no other than the ordinary refraction in Iceland spar, or not to any visible phenomenon at all. It is true that before there can be any question of the third wave’s being perceived it must be supposed excited, and the means of exciting it consist in the incident vibrations in air, which by hypothesis are strictly transversal. Hence we have to inquire whether the intensity of the third wave is such as to lead us to expect a sensible phenomenon answering to it. This leads us to the still more uncertain subject of the intensity of light reflected or refracted at the surface of a crystal—more uncertain because it not only depends on the laws of internal propagation, and inyolves all the hypotheses on which these laws are theoretically deduced, but requires fresh hypotheses as to the state of things at the confines of two media, introducing thereby fresh elements of uncertainty. But for our present purpose no exact calculation of intensities is required; a rough estimate of the intensity of the nearly normal vibrations is quite sufficient. In order to introduce as little as possible relating to the theory of the in- tensity of reflected and refracted light, suppose the incident light to fall per- pendicularly on the surface of a crystal, and let this be a surface of Iceland spar cut at an inclination of 45° to the axis. For a cleavage plane the result would be nearly the same. Let the incident light be polarized, and the vibrations be in the principal plane, which therefore, according to the theory * Annales de Chimie, tom. xlviii. p. 254 (1831). ON DOUBLE REFRACTION. 257 now under consideration, must be the plane of polarization. The incident vibrations are parallel to the surface, and accordingly inclined at angles of 9° 50’ and 80° 10’ to the directions of the nearly transversal and nearly nor- mal vibrations, respectively, within the crystal. Hence it seems evident that the amplitude of the latter must be of the order of magnitude of sin 9° 50’, or about a5 the amplitude of vibration in the incident light being taken as unity. The velocity of propagation of the nearly normal vibrations being to that of the nearly transversal roughly as /3 to 1, as will immediately be shown, it follows that the vis viva of the nearly normal would be to that of the nearly transversal vibrations in a ratio comparable with that of ¥3xsin? 9° 50' to 1, or about 4, to 1. Hence the intensity of the nearly normal vibrations is by no means insignificant, and therefore it is a very serious objection to the theory that no corresponding phenomenon should have been discovered. It has been suggested by some of the advocates of this theory that the normal vibrations may correspond to heat. But the fact of the polarization of heat at once negatives such a supposition, even without insisting on the accumulation of evidence in favour of the identity of radiant heat and light of the same refrangibility. But the objections to the theory on the ground of the absence of some un- known phenomenon corresponding with the third ray, to which the theory necessarily conducts, are not the only ones which may be urged against it in connexion with that ray. The existence of normal or nearly normal vibra- tions entails consequences respecting the transversal which could hardly fail to have been detected by observation. In the first place, the vis viva belong- ing to the normal vibrations is so much abstracted from the transversal, which alone by hypothesis constitute light, so that there is a loss of light inherent in the very act of passage from air into the crystal, or conversely, from the erystal into air. About th of the whole might thus be expected to be lost at a single surface of Iceland spar, the surface being inclined 45° to the axis, and the light being incident perpendicularly, and being polarized in the prin- cipal plane; and the loss would amount to somewhere about ;/-th in passage across a plate bounded by parallel surfaces, by which amount the sum of the reflected and transmitted light ought to fall short of the incident. And it is evident that something of the same kind must take place at other incli- nations to the axis and at other incidences. The loss thus occasioned in mul- tiplied reflexions could hardly have escaped observation, though it is not quite so great as might at first sight appear, as the transversal vibrations produced back again by the normal would presently become sensible. But the most fatal objection of all is that urged by Green* against the supposition that normal vibrations could be propagated with a velocity com- parable with those of transversal. As transversal vibrations are capable (according to the suppositions here combated) of giving rise at incidence on a medium to normal or nearly normal vibrations within it, so conversely the latter on arriving at the second surface are capable of giving rise to emergent transversal vibrations; so that not only would normal vibrations entail a loss of light in the quarter in which light is looked for, but would give rise to light (of small intensity it is true, but by no means imperceptible) in a quar- ter in which otherwise there would have been none at all. Thus in the case supposed above, the intensity of the light produced by nearly normal vibra- * tions giving rise on emergence to transversal vibrations would be somewhere about the (.\,)* or the 51, of ,the incident light. In the case of light trans- * Cambridge Philosophical Transactions, vol, vii. p. 2. 1862, _ 8 258 “ ~ REPORT—1862. mitted through a plate, the rays thus produced would be parallel to the inci- dent, or to the emergent rays of the kind usually considered; but if the plate were wedge-shaped the two would come out in different directions, and with sunlight the former could not fail to be perceived. The only way apparently of getting over this difficulty, is by making the perfectly gratuitous assumption that the medium, though perfectly transparent for the more nearly transversal vibrations, is intensely opaque for those more nearly normal. Lastly, Green’s argument respecting the necessity of supposing the velocity of propagation of normal vibrations very great has here full force as an objection against this theory. The constants P, Q, R are the squared reci- procals of the three principal indices of refraction, which are given by obser- vation, and L, M, N are determined in terms of P, Q, R by the equations (2), by the solution of a quadratic equation. In the case of a uniaxal erystal everything is symmetrical about one of the axes, suppose that of 2, which requires, as Cauchy has shown, that L=>M=3R, and P=Q; and of the equations (2) one is now satisfied identically, and the two others are identical with each other, and give 4p? AS? gyorg For an isotropic medium we must have L=>M=N=3P=3Q=8SR, and the three equations (2) are satisfied identically. The velocity of propagation of normal must be to that of transversal vibrations as 73 to 1, and cannot therefore be assumed to be what may be convenient for explaining the law of intensity of reflected light. The theory which has just been discussed is essentially bound up with the supposition that in polarized light the yvibfations are parallel, not perpendicu- lar, to the plane of polarization. In prosecuting the study of light, Cauchy saw reason to change his views in this respect, and was induced to examine whether his theory could not be modified so as to be in accordance with the latter alternative. The result, constituting what may be called Cauchy’s second theory, is contained in a memoir read before the Academy, May 20, 1839*. In this he refers to his memoir on dispersion, in which the funda- mental equations are obtained in a manner somewhat different from that given in his ‘ Exercices,’ but based on the same suppositions as to the constitution ‘of the ether, In the new theory Cauchy retains the three constants G, H, I, expressing the pressures in equilibrium, which formerly he made vanish, the medium being supposed as before to be symmetrical with respect to three rectangular planes. The squares of the velocities of propagation, and the corresponding directions of vibration for the three waves which can be pro- pagated in the direction of each of the principal axes, are given by the fol- lowing Table. Waye-pormal., ii. isha acess x | y Zz igh x L+G R+H | Q41 Direction..of. vibras. |, ee ee eee eee ath. iz, -4s Zea tate ate | M+H | PI | SF wand le bue Q+6 | P+H | N+I * “Sur la Polarisation rectiligne, et la double Réfraction,” Mém. de cy 8 tom. xviii. p. 153. ON DOUBLE REFRACTION. 259 - Aceording to observation, in each of the principal planes the ray polarized in that plane obeys the ordinary law of refraction, and therefore if we suppose that in polarized light the vibrations, at least when strictly transversal, are perpendicular to the plane of polarization, we must assume that R+H=Q-+I, P+I=R+G, Q4+G=P-+H, which are equivalent to only two distinct rela- tions, namely Pi 6=0— BS Rar et oaks UR Sens Seles (3) For a wave parallel to one of the principal axes, as that of #, the direction of that axis is one of the three rectangular directions of vibration of the waves which are propagated independently. For such vibrations the velocity (v) of propagation is given by the formula v=m (R+H)+n°(Q+1), which by (3) is reduced to v=R+H=Q+4+1, so that on the assumption that the velocity of propagation is the same for a wave perpendicular to the axis of y as for one perpendicular to the axis of z when the vibrations are parallel to the axis of «, the law of ordinary re- fraction in the plane of yz follows from theory. For the two remaining waves which can be propagated independently in a given direction perpendicular to the axis of w, the vibrations are only approxi- mately normal and transversal respectively. In fact, for the three waves which can travel independently in any given direction, the directions of vibra- tion are not affected by the introduction of the constants expressing equili- brium-pressures, but only the velocities of propagation. The squares of the yelocities of propagation of the two waves above mentioned are given as be- fore by a quadratic; and in order that the velocity of propagation of the nearly transversal vibrations may be expressed by the formula PaO MOM criss yada a deeb da (4), in conformity with the ellipsoidal form of the extraordinary wave surface in a uniaxal crystal, and the assumed elliptic form of the section of one sheet of the waye-surface in a biaxal crystal by a principal plane, the quadratic in question must split into two rational factors, which leads to precisely the same condition as before, namely that expressed by the first of equations (2) ; and by equating to zero the corresponding factor, we get v’=(P+H) m*+(P+4+]) x’, which is in fact of the form (4). Applying the same to each of the other principal axes, we find again the three relations (2). Hence Cauchy’s second theory, in which it is supposed that in polarized light the vibrations (in air or in an isotropic medium) are perpendicular to the plane of polarization, leads like the first to laws of double refraction, and of the accompanying polarization, differing from those of Fresnel only by quantities which may be deemed insensible. This result is, however, in the present case only attained by the aid of two sets of forced relations, namely (2) and (3), that is, relations which there is nothing @ priori to indicate, and which are not the expression of any simple physical idea, but are obtained by forcing the theory, which in its original state is of a highly plastic nature from the number of arbitrary constants which it contains, to agree with observation in some particulars, which being done, theory by itself makes kmown the rest. As regards the third ray by which this theory like its pre- decessor is hampered, there is nearly as much to be urged against the present theory as the former. There is, however, this difference, that, as there are only five relations, (2) and (3), between nine arbitrary constants, there remains 82 260 REPORT—1862. one arbitrary constant in the expressions for the velocities of propagation after satisfying the numerical values of the three principal indices of refrac- tion, by a proper disposal of which the objections which have been mentioned may to a certain extent be lessened, but by no means wholly overcome. I come now to Green’s theory, contained in a very remarkable memoir “ On the Propagation of Light in Crystallized Media,” read before the Cambridge Philosophical Society, May 20, 1839*, and accordingly, by a curious coinci- dence, the very day that Cauchy’s second theory was presented to the French Academy. Besides the great interest of the memoir in relation to the theory of light, Green has in it, as I conceive, given for the first time the true equations of equilibrium and motion of a homogeneous elastic solid slightly disturbed from its position of equilibrium, which is one of constraint under a uniform pressure different in different directions. In a former memoiry he had given the equations for the case in which the undisturbed state is one free from pressuret. When I speak of the true equations, I mean the equations which belong to the problem when not restricted in generality by arbitrarily assumed hypotheses, and yet not containing constants which are incompatible with any well-ascertained physical principle. It is right to mention, however, that on this point mathematicians are not agreed; M. de Saint-Venant, for instance, maintains the justice of the more restricted equations given by Cauchy §, though even he would not conceive the latter equations applicable to such solids as caoutchoue or jelly. In these papers Green introduced into the treatment of the subject, with the greatest advantage, the method of Lagrange, in which the partial differ- ential equations of motion are obtained from the variation of a single force- function, on the discovery of the proper form of which everything turns, Green’s principle is thus enunciated by him :— In whatever manner the elements of any material system may act on each other, if all the internal forces be multiplied by the elements of their respective directions, the total sum for any assigned portion of the mass will always be the exact differential of some function.” In accordance with this principle, the general equation may be put under the form ; P ad a? , \\\ pdx dy dz Ge but oe subse é v)=({ feo dy dz bo . (8), where w, y,z are the equilibrium coordinates of any particle, p the density in equilibrium, u,v, w the displacements parallel to a, y, z, and » the function in question. @ is in fact the function the variation of which in passing from one state of the medium to another, when multiplied by da dy dz, expresses the work given out by the portion of the medium occupying in equilibrium the elementary parallelepiped da dy dz, in passing from the first state to the second. The portion of the medium which in the state of equili- brium occupied the elementary parallelepiped becomes in the changed state an oblique-angled parallelepiped, whose edges may be represented by dx (1-+s,), dy (1+s,), dz (1+s,), and the cosines of the angles between the second and third, third and first, and first and second of these edges by a, 3, y, which in ease the disturbance be small will be small quantities only. It is manifest that the function @ must be independent of any linear or angular displacement of the element dx dy dz, and depend only on the change of form of the element, * Cambridge Philosophical Transactions, vol. vii. p. 120. + “On the Reflexion and Refraction of Light,” Cambr. Phil. Trans. vol. vii. p. 1. Read Dec. 11, 1837. { They are virtually given, though not actually written down at length. § Comptes Rendus, tom. liii, p. 1105 (1861). ON DOUBLE REFRACTION. 261 and therefore on the six quantities s,, s,,s,, a, 3, y, which may be expressed by means of the nine differential coefficients of uv, v, w with respect to x, y, z, of which therefore @ is a function, but not any function, since it involves not nine, but only six independent variables. If the disturbance be small, the six quantities s,, s,, 8,,a, 3, y will be small likewise, and ¢ may be expressed in a convergent series of the form $=Pot bi thot Gste: +s where ¢,, ¢,, $,, ¢,, ce. are homogeneous functions of the six quantities, of the orders 0, 1, 2, 3, &c.; and if the motion be regarded as indefinitely small, the functions ¢,, , . . . will be insensible, the left-hand member of equation (5) being of the second order as regards u,v, w. ,, being a constant, will not appear in equation (5), and g, will be equal to zero in case the medium in its undisturbed state be free from internal pressure, but not otherwise. The function ¢,, being a homogeneous function of six independent variables of the second order, contains in its most general shape twenty-one arbitrary con- stants, and ¢, which is of the first order introduces six more, so that the most general expression for g contains no less than twenty-seven arbitrary constants, all which appear in the expressions for the internal pressures and in the partial differential equations of motion*. The general expressions for the internal tensions in an elastic medium and the general equations of equilibrium or motion which were given by Cauchy, and which are written at length in the 4th volume of the ‘ Exercices de Mathé- matiques,’ contain twenty-one arbitrary constantswhen the undisturbed state of the medium is one of uniform constraint, and fifteen when it is one of freedom from pressure. In the latter case, Green’s twenty-one constants are reduced to two, and Cauchy’s fifteen to only one, when the medium is isotropic. Green’s equations comprise Cauchy’s as a particular case, as will be shown more at length further on. It becomes an important question to inquire whether Cauchy’s equations involve some restrictive hypothesis as to the constitution of the medium, so as to be in fact of insufficient generality, or whether, on the other hand, Green’s equations are reducible to Cauchy’s by the introduction of some well-ascertained physical principle, and therefore contain redundant constants. Tn the formation of Cauchy’s equations, not only is the medium supposed to consist of material points acting on one another by forces which depend on the distance only (a supposition which, at least when coupled with the next, excludes the idea of molecular polarity), but it is assumed that the displace- ments of the individual molecules vary from molecule to molecule according to the variation of some continuous function of the coordinates ; and accordingly the displacements w’, v', w' of the molecule whose coordinates in equilibrium are w+ Ax, y+Ay, z+ Az are expanded by Taylor’s theorem in powers of. ' : l : ' Aw, Ay, Sz, and the differential coefficients 7 &e. are put outs‘de the sign of summation. The motion, varying from point to point, of the medium taken as * The twenty-seven arbitrary constants enter the equations of motion in such a manner as to be there equivalent to only twenty-six distinct constants, the physical interpretation of which analytical result will be found to be that a uniform pressure alike in all directions, in the undisturbed state of the medium, produces the same effect on the internal move- ments when the medium is disturbed as a certain internal elasticity, alike in all directions, and of a very simple kind, which is possible in a medium unconstrained in its natural state. The twenty-one arbitrary constants belonging to a medium unconstrained in its natural state are not reducible in the equations of motion, any more than in the expressions for the internal tensions, to a smaller number. 262 _- REPORT—1862. a whole, or in other words the mean motion, in any direction, of the molecules in the neighbourhood of a given point, must not be confounded with the motion of the molecules taken individually. The medium being continuous, so far as anything relating to observation is concerned, the former will vary gontinuously from point to point. But it by no means follows that the motion of the molecules considered individually should vary from one to another according to some function of the coordinates. The motion of the individual molecules is only considered for the sake of deducing results from hypotheses as to the molecular constitution and molecular forces of the medium, and in it we are concerned only with the relative motion of molecules situated so close as to act sensibly on each other. It would seem to be very prebable, a priori, that a portion by no means negligible of the relative displacement of a pair of neighbouring molecules should vary in an irregular manner from pair to pair; and indeed if the medium tends to relieve itself from a state of constrained distortion, this must necessarily be the case; and such a re- arrangement must assuredly take place in fluids. The insufficient generality of Cauchy’s equations is further shown by their being absolutely incompatible with the idea of incompressibility. We may evidently conceive a solid which resists compression of volume by a force incomparably greater than that by which it resists distortion of figure, and such a conception is actually realized in such a solid as caoutchouc or jelly. I have not mentioned the hypothesis of what may be called, from the analogy of surfaces of the second order, a central arrangement of the molecules, that is, an arrangement such that each molecule is a centre with respect’ to which the others are arranged in pairs at equal distances in opposite directions, because the hypothesis was merely casually introduced as one mode of making eertain terms vanish which are of a form that clearly ought not to appear in the expressions relating to the mean motion, with which alone we are ulti- mately concerned. The arguments in favour of the existence of ultimate molecules in the case of ponderable matter appear to rest chiefly on the chemical law of definite proportions, and on the laws of crystallography, neither of which of course can be assumed to apply to the mysterious ether, of the very existence of which we have no direct evidence. If, for aught we know to the contrary, the very supposition of the existence of ultimate molecules as applied to the ether may entail consequences at variance with its real constitution, much more must the accessory hypotheses be deemed precarious which Cauchy found necessary in order to be able to deduce any results at all in proceeding by his method. There appears, therefore, no sufficient reason @ priort for preferring the more limited equations of Cauchy to the more general equations of Green. ‘.. Green, on the other hand, takes his stand on the impossibility of perpetual motion, or in other words, on the principle of the conservation of work, which we have the strongest reasons for believing to be a general physical princi- ple*. The number of arbitrary constants thus furnished in the case in which the undisturbed state of the medium is one of freedom from pressure is, as has been stated, twenty-one. Professor Thomson has recently put this result in a form which indicates more clearly the signification of the con- stantst, and at the end of his memoir promises to show how an elastic solid, * Whether vital phenomena are subject to this law is a question which we are not here called upon to discuss. _+ “Elements of a Mathematical Theory of Elasticity,” Phil. Trans. for 1856, p. 481. Read April 24, 1856, . Z ON DOUBLE REFRACTION. 263 which as a whole should possess this number of arbitrary constants, could be built up of isotropic matter. Green supposes, in the first instance, that the medium is symmetrical with respect to planes in three rectangular directions, which simplifies the investi- gation and reduces the twenty-seven or twenty-one arbitrary constants to twelve (entering the partial differential equations of motion in such a manner as to be there equivalent to only eleven) or nine. It may be useful to give a Table of the constants employed by Green, with their equivalents in the theo- ries of Cauchy and Neumann, the density of the medium at rest being taken equal to unity for the sake of simplicity. The Table is as follows :— Green ABC GHI LMN PQR Cauchy GHI LMN P QR PQR Neumann 000 DCB AAA, AAA; so that Green’s equations are reduced to Cauchy’s by making = L=P, M=Q, Neko aogier «0 a For a plane wave propagated in any given direction there are three velocities ef propagation, and three corresponding directions of vibration, which are determined by the directions of the principal axes of a certain ellipsoid U=1, which he proposes to call the ellipsoid of elasticity, the semiaxes at the same time representing in magnitude the squared reciprocals of the corresponding velocities of propagation; and Green has shown that U may be at once obtained from the function —2% by taking that part only which is of the second order in u,v, w, and replacing u,v, w by 2, y, 2, and the symbols of Lod ; é differentiation > ala by the cosines of the angles which the wave-normal makes with the axes. This applies whether the medium be symmetrical or not with respect to the coordinate planes. Green then examines the conse- quences of supposing that for two of the three waves the vibrations are strictly in the front of the wave, as was supposed by Fresnel, and consequently that the vibrations belonging to the third wave are strictly normal. This hypothesis leads to five relations between the twelve constants, namely G=H=I=yp suppose, P=p—2L, Q=p—2M, R=p-—2N; . (7) and gives for the form of the fundamental function du du dw —2 @=2A—+2B —+2C —_ Sheu aa dy e dz +41 (ce) +(@5) +(az) | + | Ga) +a) +) | +l) Ge) +e) } ror) +N{ (74g) 4% dt ee a ee eee) from which the equations of motion, the expressions for the internal pressures, and the equation of the ellipsoid of elasticity may be at once written down. - The simpler case in which the medium in its natural state is supposed free 264 REPORT—1862. from pressure is first considered*. Green shows that the ellipse which is the section of the ellipsoid of elasticity by a diametral plane, parallel to the wave’s front, if turned 90° in its own plane, belongs to a fixed ellipsoid, which gives at once Fresnel’s elegant construction for the velocity of propagation and direction of the plane of polarization; but it is necessary to suppese that in polarized light the vibrations are parallel, not perpendicular, to the plane of polarization. The general case in which the medium is not assumed to be symmetrical with respect to three rectangular planes, and in which therefore ¢ contains twenty- one arbitrary constants, is afterwards considered; and it is shown that the hypothesis of strict transversality leads to fourteen relations between them, leaving only seven constants arbitrary. But the function obtained on the assumption of planes of symmetry contains no fewer, for the four constants relating to these planes would be increased by three when the medium was referred to generalaxes. Hence therefore the existence of planes of symmetry is not an independent assumption, as in Cauchy’s theory, but follows as a result. In this beautiful theory, therefore, we are presented with no forced rela- tions like Cauchy’s equations; the result follows from the hypothesis of strictly transversal vibrations, to which Fresnel was led by physical considera- tions. The constant , remains arbitrary, and it is easy to see that this constant expresses the square of the velocity of propagation of normal vibra- tions. Were this velocity comparable with the velocity of propagation of transversal vibrations, theory would lead us still to expect normal vibrations to be produced by light incident obliquely, though not by light incident perpendicularly, on the surface of a crystal, and the theory would still be exposed to many of the objections which have been already brought forward. But nothing hinders us from supposing, in accordance with the argument contained in Green’s former paper, that p is very great or sensibly infinite, which removes all the difficulty, since the motion corresponding to this term in the expression for —2 % would not be sensible except at a distance from the surface comparable with the length of a wave of light. Hence, although it might be said, so long as x was supposed arbitrary, that the supposition of rigorous transversality had still something in it of the nature of a forced relation between constants, we sec that the single supposition of incompressi- bility (under the action of forces at least comparable with those acting in the propagation of light)—the original supposition of Fresnel—introduced into the general equations, suffices to lead to the complete laws of double refrac- tion as given by Fresnel. Were it not that other phenomena of light lead us rather to the conclusion that the vibrations are perpendicular, than that they are parallel to the plane of polarization, this theory would seem to leave us nothing to desire, except to prove that we had a right to neglect the direct action of the ponderable molecules, and to treat the ether within a crystal as a single elastic medium, of which the elasticity was different in different directions. In his paper on Reflexion, Green had adopted the supposition of Fresnel, that the vibrations are perpendicular to the plane of polarization. He was naturally led to examine whether the laws of double refraction could be explained on this hypothesis. When the medium in its undisturbed state is exposed to pressure differing in different directions, six additional constants are introduced into the function ¢, or three in case of the existence of planes * The results obtained for this case remain the same if we suppose the medium in its undisturbed state to be subject to a pressure alike in all directions, ON DOUBLE REFRACTION. 265 of symmetry to which the medium is referred. For waves perpendicular to the principal axes, the directions of vibration and squared velocities of propagation are as follows :— Green assumes, in accordance with Fresnel’s theory, and with observation if the vibrations in polarized light are supposed perpendicular to the plane of polarization, that for waves perpendicular to any two of the principal axes, and propagated by vibrations in the direction of the third axis, the velocity of pro- pagation is thesame. This gives three, equivalent to two, relations among the constants, namely, A—L=B—M=C—N=y suppose, (9) which are equivalent to Cauchy’s equations (3). The conditions that the vibrations are strictly transversal and normal respectively do not involve the six constants expressing the pressures in equilibrium, and therefore remain the same as before, namely (7). Adopting the relations (7) and (9), Green proves that for the two transversal waves the velocities of propagation and the azimuths of the planes of polarization are precisely those given by the theory of Fresnel, the vibrations in polarized light being now supposed perpendicular to the plane of polarization. As to the wave propagated by normal vibrations, the square of its velocity of propagation is easily shown to be equal to ; p+AP+ Bm? + Cn’ ; and as the constant p does not enter into the expression for the velocity of pro- pagation of transversal vibrations, the same supposition as before, namely that the medium is rigorously or sensibly incompressible, removes all difficulty arising from the absence of any observed phenomenon answering to this wave. The existence of planes of symmetry is here in part assumed. I say in part, because Green shows that the six constants, expressing the pressures in equilibrium, enter the equation of the ellipsoid of elasticity under the form K («*+y’+2*), where K is a homogeneous function of the six constants of the first order, and involves likewise the cosines 7, m,n. Hence the directions of vibration are the same as when the six constants vanish; the velocities of propagation alone are changed; and as the existence of planes of symmetry for the case in which the six constants vanish was demonstrated, it is only requisite to make the very natural supposition that the planes of symmetry which must exist as regards the directions of vibration, are also planes of symmetry as regards the pressure in equilibrium. We see then that this theory, which may be called Green’s second theory, is in most respects as satisfactory (assuming for the present that Fresnel’s construction does represent the laws of double refraction) as the former. I say in most respects, because, although the theory is perfectly rigorous, like the former, the equations (9) are of the nature of forced relations between the constants, not expressing anything which could have been foreseen, or 266. REPORT—1862. eyen conveying when pointed out the expression of any simple physical relation. The year 1839 was fertile in theories of double refraction, and on the 9th of December Prof. MacCullagh presented his theory to the Royal Irish Academy. It is contained in “ An Essay towards a Dynamical Theory of Crystalline Reflexion and Refraction”*. As indicated by the title, the determination of the intensities of the light reflected and refracted at the surface of a crystal is what the author had chiefly in view, but his previous researches had led him to observe that this determination was intimately connected with the laws of double refraction, and to seek to link together these laws as parts of the same system. He was led to apply to the problem the general equation of dynamics under the form (5), to seek to determine the form of the function ¢ (V in his notation), and then to form the partial differential equations of motion, and the conditions to be satisfied at the boundaries of the medium, by the method of Lagrange. He does not appear to have been aware at the time that this method had previously been adopted by Green. Like his predecessors, he treats the ether within a crystallized body as a single medium unequally elastic in dif- ferent directions, thus ignoring any direct influence of the ponderable mole- cules in the vibrations. He assumes that the density of the ether is a constant quantity, that is, both unchanged during vibration, and the same within all bodies as in free space. We are not concerned with the latter of these suppositions in deducing the laws of internal vibrations, but only in inyesti- gating those which regulate the intensity of reflected and refracted light. He assumes further that the vibrations in plane waves, propagated within a crystal, are rectilinear, and that while the plane of the wave moves parallel to itself the vibrations continue parallel to a fixed right line, the direction of this right line and the direction of a normal to the wave being functions of each other,—a supposition which doubtless applies to all crystals except quartz, and those which possess a similar property. ‘ ’ In this method everything depends on the correct determination of the form of the function V. From the assumption that the density of the ether is unchanged by vibration, it is readily shown that the vibrations are entirely transversal. Imagine a system of plane waves, in which the vibrations are parallel to a fixed line in the plane of a wave, to be propagated im the crystal, and refer the crystal for a moment to the rectangular axes of a", y', z', the plane of ay’ being parallel to the planes of the waves, and the axis of y' to the direction of vibration ; and let « be the angle whose tangent is 2, With respect to the form of V, MacCullagh reasons thus :— The function V can only depend upon the directions of the axes of a’, y', z' with respect to fixed lines in the crystal, and upon the angle which measures the change of form produced in the parallelepiped by vibration. This is the most general supposition which can be made concerning it. Since, however, by our second supposition, any one of these directions, suppose that of w', determines the other two, we may regard V as depending on the angle « and the direction of the axis of a! alone,” from whence he shows that V must be a function of the quantities X, Y, Z, defined by the equations dn dé dz dé di dn Se dy nae ey This reasoning, which is somewhat obscure, seems to me to involve a fallacy. * Memoirs of the Royal Irish Academy, vol. xxi. p. 17. ON DOUBLE REFRACTION. 267 If the form of V were known, the rectilinearity of vibration and the constancy in the direction of vibration for a system of plane waves travelling in any given direction would follow as a reswlt of the solution of the problem. But in using équation (5) we are not at liberty to substitute for V (or g) an expression which represents that function only on the condition that the motion be what it actually is, for we have occasion to take the variation 6V of V, and this varia- tion must be the most general that is geometrically possible though it be dynamically impossible. That the form of V, arrived at by MacCullagh, is inadmissible, is, I conceive, proved by its incompatibility with the form deduced by Green from the very same supposition of the perfect transversality of the transversal vibrations ; for Green’s reasoning is perfectly straightforward and irreproachable. Besides, MacCullagh’s form leads to consequences abso- lutely at variance with dynamical principles*, But waiving for the present the objection to the conclusion that V is a function of the quantities X, Y, Z, let us follow the consequences of the theory. The disturbance being supposed small, the quantities X, Y, Z will also be small, and VY may be expanded in a series according to powers of these quantities ; and, as before, we need only proceed to the second order if we regard the disturbance as indefinitely small. The first term, being merely a constant, may be omitted. The terms of the first order MacCullagh concludes must vanish. This, however, it must be observed, is only true on the supposition that the medium in its undisturbed state is free from pressure. The terms of the second order are six in number, involving squares and products of X, Y, Z. The terms involving YZ, ZX, XY may be got rid of by a transformation of coordinates, when VY will be reduced to the form ny Sits: Ves e(O RP REO! vl oe V0) the constant term being omitted, and the arbitrary constants being denoted by — 2@, —3b°, —2¢°. Thus on this theory the existence of principal axes is proved, not assumed. If MacCullagh’s expression for V (10) be compared with Green’s expression for ¢ (8) for the case of no pressure in equilibrium, so that A=0, B=0, C=0, it will be seen that the two will become identical, provided f 2 first we omit the term p = ed = in Green’s expression, and secondly, we treat the symbols of differentiation as literal coefficients, so as to confound, ; du dw dv dw : ‘ , = instance, du da a dake, The term involving p does not appear in the du dv, dw dosages ee therefore does not affect the laws of the propagation of such vibrations, although it would appear in the problem of calculating the intensity of reflected and refracted light ; and be that as it may, it follows from Green’s rule for forming the equation of the ellipsoid of elasticity, that the laws of the propagation of transversal vibrations will be precisely the same whether we adopt his form of g or V (for the case of no pressure in equilibrium) or MacCullagh’s. Indeed, if we omit the term p ae +74E)> the partial differential equations of expressions for transversal vibrations, since for these da dz motion, on which alone depend the laws of internal propagation, would be Just the same as the two theoriest. Accordingly MacCullagh obtained, though * See Appendix. « + See Appendix. MacCullagh’s reasoning appears to be so far correct as to have led to correct equations, although through a form of V which may, I conceive, be shown to be inadmissible. 268 REPORT—1862. independently of, and in a different manner from Green, precisely Fresnel’s laws of double refraction and the accompanying polarization, on the condition, however, that in polarized light the vibrations are parallel to the plane of polarization. It is remarkable that in the previous year MacCullagh, in a letter to Sir David Brewster *, published expressions for the internal pressures identical with those which result from Green’s first theory, provided that in the latter the terms be omitted which arise from that term in ¢ which contains yp, a term which vanishes in the case of transversal vibrations propagated within a crystal. It does not appear how these expressions were obtained by MacCullagh ; it was probably by a tentative process. The various theories which have just been reviewed have this one feature in common, that in all, the direct action of the ponderable molecules is neglected, and the ether treated as a single vibrating medium. It was, doubtless, the extreme difficulty of determining the motion of one of two mutually penetrating media that led mathematicians to adopt this, at first - sight, unnatural supposition ; but the conviction seems by some to have been entertained from the first, and to have forced itself upon the minds of others, that the ponderable molecules must be taken into account in a far more direct manner. Some investigations were made in this direction by Dr. Lloyd as long as twenty-five years ago}. Cauchy’s later papers show that he was dissatisfied with the method, adopted in his earlier ones, of treating the ether within a ponderable body as a single vibrating medium}; but he does not seem to have advanced beyond a few barren generalities, towards a theory of double refraction founded on a calculation of the vibrations of one of two mutually penetrating media. In the theory of double refraction advanced by Professor Challis$, the ether is assimilated to an ordinary elastic fluid, the vibrations of which are modified by resisting masses; and his theory leads him at once to Fresnel’s elegant construction of the wave surface by points. The theory, however, rests upon principles which have not received the general assent of mathematicians. In a work entitled “ Light explained on the Hypothesis of the Ethereal Medium being a Viscous Fluid”||, Mr. Moon has put in a clear form some of the more serious objections which may be raised against Fresnel’s theory ; but that which he has substituted is itself open to formidable objec- tions, some of which the author himself seems to have perceived. In concluding this part of the subject, I may perhaps be permitted to express my own belief that the true dynamical theory of double refraction has yet to be found. ; In the present state of the theory of double refraction, it appears to be of especial importance to attend to a rigorous comparison of its laws with actual observation. I have not now in view the two great laws giving the planes of polarization, and the difference of the squared velocities of propagation, of the two waves which can be propagated independently of each other in any given direction within a crystul. These laws, or at least laws differing from them only by quantities which may be deemed negligible in observation, had previously been discovered by experiment; and the deduction of these laws by Fresnel from his theory, combined with the verification of the law, which his theory, correcting in this respect previous notions, first pointed out, that * Philosophical Magazine for 1836, vol. viii. p. 103. + Proceedings of the Royal Irish Academy, vol. i. p. 10. t See his optical memoirs published in the 22nd volume of the ‘Mémoires de l’ Académie.” § Cambridge Philosophical Transactions, vol, vill. p, 524. || Macmillan & Co., Cambridge, 1853. ON DOUBLE REFRACTION. 269 in each principal plane of a biaxal crystal the ray polarized in that plane obeys the ordinary law of refraction, leayes no reasonable doubt that Fresnel’s construction contains the true laws of double refraction, at least in their broad features. But regarding this point as established, I have rather in view a verification of those laws which admit of being put to the test of experiment with extreme precision ; for such verifications might often enable the mathe- matician, in groping after the true theory, to discard at once, as not agreeing with observation, theories which might present themselves to his mind, and on which otherwise he might have spent much fruitless labour. To make my meaning clearer, I will refer to Fresnel’s construction, in which the laws of polarization and wave-yelocity are determined by the sections, by a diametral plane parallel to the wave-front, of the ellipsoid * Cv +b y+e27=1 : (11), where a, b, c denote the principal wave-velocities. The principal semiaxes of the section determine by their direction the normals to the two planes of polarization, and by their magnitude the reciprocals of the corresponding wave-velocities. Now a certain other physical theory which might be pro- posed leads to a construction differing from Fresnel’s only in this, that the planes of polarization and wave-velocities are determined by the section, by a diametral plane parallel to the wave-front, of the ellipsoid yf we a Z gtpteele ee ee et es (12), the principal semiaxes of the section determining by their direction the normals to: the two planes of polarization, and by their magnitudes the corresponding wave-velocities. The law that the planes of polarization of the two waves propagated in a given direction bisect respectively the two supplemental dihedral angles made by planes passing through the wave- normal and the two optic axes, remains the same as before, but the posi- tions of the optic axes themselves, as determined by the principal indices of refraction, are somewhat different; the difference, however, is but small if the differences between a’, b,c? are a good deal smaller than the quantities themselves, Each principal section of the wave surface, instead of being a circle and an ellipse, is a circle and an oval, to which an ellipse is a near approximation t. The difference between the inclinations of the optic axes, and between the amounts of extraordinary refraction in the principal planes, on the two theories, though small, are quite sensible in observation, but only on condition that the observations are made with great precision. We see from this example of what great advantage for the advancement of theory obseryations of this character may be. One law which admits of receiving, and which has received, this searching comparison with observation, is that according to which, in each principal plane of a biaxal erystal, the ray which is polarized in that plane obeys the ordinary law of refraction, and accordingly in a uniaxal erystal, in which every plane parallel to the axis is a principal plane, the so-called ordinary ray follows rigorously the law of ordinary refraction. This law was carefully verified by Fresnel himself in the case of topaz, by the method of cutting plates parallel to the same principal axis, or axis of elasticity, carefully * Tt would seem to be just as well to omit the surface of elasticity altogether, and refer the construction directly to the ellipsoid (11). + The equation of the surface of wave-slowness in this and similar cases may be readily obtained by the method given by Professor Haughton in a paper “ On the Equilibrium op _o of Solid and Fluid Bodies,” Transactions of the Royal Irish Academy, vol. xxi. p. 172. s 270 -REPORT—1862. working them to the same thickness, and then interposing them in the paths of two streams of light proceeding to interfere, as well as by the method of prismatic refraction ; and he states as the result of his observations that he can affirm the law to be, at least in the case of topaz, mathematically exact. The same result follows from the observations by which Rudberg so accu- rately determined the principal indices of Arragonite and topaz*, for the principal fixed lines of the spectrum. Professor MacCullagh having been led by theoretical considerations to doubt whether, in Iceland spar for instance; the so-called ordinary ray rigorously obeyed the ordinary law of refraction, whether the refractive indices in the axial and equatorial directions were strictly the same, Sir David Brewster was induced to put the question to the test of a crucial experiment, by forming a compound prism consisting of two pieces of spar cemented together in the direction of the length of the prism, and so ent from the crystal that at a minimum deviation one piece was tra- versed axially and the other equatorially?. The prism having been polished after cementing, so as to ensure the perfect equality of angle of the two parts, on viewing a slit through it the bright line D was seen unbroken in passing from one half to the other. More recently Professor Swan has made a very precise examination of the ordinary refraction in various directions in Iceland spar by the method of prismatic refraction t, from whence it results that for homogeneous light of any refrangibility the ordinary ray follows strictly the ordinary law of refraction. It is remarkable that this simple law, which ought, one would expect, to lie on the very surface as it were of the true theovy of double refraction, is not indicated @ priori by most of the rigorous theories which have been ad- vanced to account for the phenomenon. Neither of the two theories of Cauchy, nor the second theory of Green, lead us to expect such a result, though they furnish arbitrary constants which may be so determined as to bring it about. The curious and unexpected phenomenon of conical refraction has justly been regarded as one of the most striking proofs of the general correctness of the conclusions resulting from the theory of Fresnel. But I wish to point out that the phenomenon is not competent to decide between several theories leading to Fresnel’s construction as a near approximation. Let us take first internal conical refraction. The existence of this phenomenon depends upon the existence of a tangent plane touching the wave surface along a plane curve. At first sight this might seem to be a speciality of the wave-surface of Fresnel; but a little consideration will show that it must be a property of the wave surface resulting from any reasonable theory. For, if possible, let the nearest approach to a plane curve of contact be a curve of double curva- ture. Leta plane be drawn touching the rim (as it may be called) of the surface, that is, the part where the surface turns over, in two points, on opposite sides of the rim; and then, after having been slightly tilted by turning about one of the points of contact, let it move parallel to itself towards the centre. The successive sections of the wave-surface by this plane will evidently be of the general character represented in the annexed figures, 1 2 3 + 5 6 ti en ) ° Ww eS * Annales de Chimie, tom. xlviii. p. 225 (1831). + Report of the British Association for 1843, Trans. of Sect. p. 7. { Transactions of the Royal Society of Edinburgh, vol. xvi. p. 375. ON DOUBLE REFRACTION. 271 and in four positions the plane will touch the surface in one point, as repre- sented-in figs. 1, 2,4, 5. Should the contacts represented in figs. 4 & 5 take place simultaneously, they may be rendered successive by slightly altering the inclination of the plane. Hence in certain directions there would be four possible wave-velocities. Now the general principle of the superposition of small motions makes the laws of double refraction depend on those of the propagation of plane waves. But all theories respecting the propagation of a “series of plane waves haying a given direction, and in which the disturbance of the particles is arbitrary, but the same all over the front of a wave, agree in this, that they lead us to decompose the disturbance into three disturbances in three particular directions, to each of which corresponds a series of plare waves which are propagated with a determinate velocity. If the medium be incompressible, one of the wave-velocities becomes infinite, and one sheet of the wave surface moves off to infinity. The most general disturbance, subject to the condition of incompressibility, which requires that there be no ‘displacements perpendicular to the fronts of the waves, may now be expressed as the resultant of two disturbances, corresponding to displacements in parti- cular directions lying in planes parallel to that of the waves, to each of which corresponds a determinate velocity of propagation. We see, therefore, that the limitation of the number of tangent planes to the wave-surface, which can be drawn in a given direction on one side of the centre, to two, or at the most three, is intimately bound up with the number of dimensions of space; so that the existence of the phenomenon of internal conical refraction is no proof of the truth of the particular form of wave-surface assigned by Fresnel rather than that to which some other theory would conduct. Were the law of wave-velocity expressed, for example, by the construction already mentioned having reference to the ellipsoid (12), the wave-surface (in this ease a surface of the 16th degree) would still have plane curves of contact with the tangent plane, which in this case also, as in the wave-surface of Fresnel, are, as I find, circles, though that they should be circles could not have been foreseen. _ The existence of external conical refraction depends upon the existence of a conical point in the wave-surface, by which the interior sheet passes to the exterior. The existence of a conical point is not, like that of a plane curve of contact, a necessary property of a wave-surface. Still it will readily be con- ceived that if Fresnel’s wave-surface be, as it undoubtedly is, at least a near approximation to the true wave-surface, and if the latter have, moreover, plane curves of contact with the tangent plane, the mode by which the exterior sheet passes within one of these plane curves into the interior will be very approximately by a conical point; so that in the impossibility of operating experimentally on mere rays the phenomena will not be sensibly different from what they would have been had the transition been made rigorously by a conical point. There is one direction within a biaxal crystal marked by a visible phenomenon of such a nature as to permit of observing the direction with precision, while it can also be calculated, on any particular theory of double refraction, in terms of the principal indices of refraction; I refer to the direction of either optic axis. Rudberg himself measured the inclination of the optic axes of Arragonite, probably with a piece of the same crystal from which his prisms were cut, and found it a little more than 32° as observed in air, but he speaks of the difficulty of measuring the angle with precision. The inclination within the crystal thence deduced is really a little greater than that given by Fresnel’s theory ; but in making the comparison D2 REPORT—1862. Rudberg used the formula for the ray-axes instead of that for the wave-axes, which made the theoretical inclination in air appear about 2° greater than the observed*. A very exact measure of the angle between the optic axes of Arragonite for homogeneous light corresponding to the principal fixed lines of the spectrum has recently been executed by Professor Kirchhoff +, by a method which has the advantage of not making any supposition as to the direction in which the crystal is cut. The angle observed in air was reduced by calculation to the angle within the crystal, by means of Rudberg’s indices for the principal axis of mean elasticity ; and the result was compared with the angle calculated from the formula of Fresnel, on substituting for the con- stants therein contained the numerical values determined by Rudberg for all the three principal axes. The angle reduced from that observed in air proved to be from 13! to 20! greater than that calculated from Fresnel’s formula. This small ditference seems to be fairly attributable to errors in the indices, arising from errors in the direction of cutting of the prisms employed by Rudberg. The angle measured by Kirchhoff would seem to have been trust- worthy to within a minute or less, It is doubtful, however, how far we may trust to the identity of the principal refractive indices in different specimens of the mineral. Chemical analysis shows that Arragonite is not pure carbonate of lime, but contains a variable though small proportion of other ingredients. To these variations doubtless correspond variations in the refractive indices; and De Senarmont has shown how the inclination of the optic axes of minerals is lable to be changed by the substitution one for another of isomorphous elements. More- over, M. Des Cloizeaux has recently shown that in felspar and some other minerals, which bear a high temperature without apparent change, the inclination of the optic axes is changed in a permanent manner by heats$ ; so that even perfect identity of chemical composition is not an absolute guarantee of optical identity in two specimens of a mineral of a given kind. The exactness of the spheroidal form assigned by Huygens to the sheet of the wave-surface within Iceland spar corresponding to the extraordinary ray, does not seem to have been tested to the same degree of rigour as the ordinary refraction of the ordinary ray; for the methods employed by Wollaston || and Malus 4 for observing the extraordinary refraction can hardly bear comparison for exactness with the method of prismatic refraction which has been applied to the ordinary ray ; and observations on the absolute velocities of propagation in different directions within biaxal crystals are still almost wholly wanting. This has long been recognized as a desideratum, and it has been suggested to employ for the purpose the displacement of fringes of interference. It seems to me that a slight modification of the ordinary method of prismatic refraction would be more convenient and exact. Let the crystal to be examined be cut, unless natural faces or cleavage planes answer the purpose, so as to have two planes inclined at an angle suitable for the measure of refractions; there being at least two natural faces or cleavage-planes left undestroyed, so as to permit of an exact measure of the directions of any artificial faces. The prism thus formed having been mounted as usual, and placed in any azimuth, let the angle of incidence or * Annales de Chimie, tome xlviii. p. 258 (1831). + Poggendorff’s Annalen, vol. cviii. p. 567 (1859). { Annales de Chimie, tome xxxiii. p. 391 (1851). § Annales des Mines, tome ii. p. 327 (1862). || On the Oblique Refraction of Iceland Spar, Phil. Trans. for 1802, p. 381. ‘| Mémoires de l'Institut; Say, Etrangers, tome ii, p, 308 (1811), ON DOUBLE REFRACTION. 273 emergence (according as the prism remains fixed or turns round with the tele- scope) be measured, by observing the light reflected from the surface, and like- wise the deviation for several standard fixed lines in the spectrum of each refracted pencil. Let the prism be now turned into a different azimuth, and the deviations again observed, and so on. Each observation furnishes accurately an angle of incidence and the corresponding angle of emergence; for if ¢ be the angle of incidence, 7 the angle of the prism, D the deviation, and y the angle of emergence, D=¢+y—i. But without making any supposition as to the law of double refraction, or assuming anything beyond the truth of Huygens’s principle, which, following directly from the general principle of the superposition of small motions, lies at the very foundation of the whole theory of undulations, we may at once deduce from the angles of incidence and emergence the direction and velocity of propagation of the wave within the prism. For if a plane wave be incident on a plane surface bounding a medium of any kind, either ordinary or doubly refracting, it follows directly from Huygens’s principle that the refracted wave or waves will be plane, and that if g be the angle of incidence, g! the inclination of a refracted wave to the surface, V the velocity of propagation in air, v the wave-velocity within the medium, sin ¢_ sin q! 4 boknienas ae Hence if g', )! be the inclinations of the refracted wave to the faces of our prism, we shall have the equations 0 Ba 6 = Voegeli eis ied wl, oe 218) Pi Wee, Toe ee eee iy Ord (14) Sher dane Get eee en The equations (13) and (14) give, on taking account of (15), : — ee ‘J v sin SFY os PSY RV sin 5 cos HEY hii meray. pn CO argh es Cone. v cos 5+ aint =V cos 5 ain ao » « (17) whence by division da Oe a gM Gu tan —z = tan 5 tan = cot as ig haa (18) The equations (15) and (18) determine g’ and y', and then (16) gives v. Hence we know accurately the velocity of propagation of a wave, the normal to which lies in a plane perpendicular to the faces of the prism, and makes known angles with the faces, and is therefore known in direction with reference to the crystallographic axes. A single prism would enable the observer to explore the crystal in a series of directions lying in a plane perpendicular to its edge; but as these directions are practically confined to limits making no very great angles with a normal to the plane bisecting the dihedral angle of the prism, more than one prism would be required to enable him to explore the crystal in the most important directions; and it would be necessary for him to assure himself that the specimens of crystal, of which the different prisms are made, were strictly comparable with each hac It would be best, as far as practicable, to cut them from the same ock. The existence of principal planes, or planes of optical symmetry, for light r 274 REPORT—1862. of any given refrangibility, in those cases in which they are not determined by being at the same time planes of crystallographic symmetry, is a matter needing experimental verification. However, as no anomaly, so far as I am aware, has been discovered in the systems of rings seen with homogeneous light around the optic axes of crystals of the oblique or anorthic system, there is no reason for supposing that such planes do not exist. APPENDIX. Further Comparison of the Theories of Green, MacCullagh, and Cauchy. In a paper “On a Classification of Elastic Media and the Laws of Plane Waves propagated through them,” read before the Royal Irish Academy on the 8th of January, 1849*, Professor Haughton has made a comparative examina- tion of different theories which have been advanced for determining the motion of elastic media, more especially those which have been applied to the expla- nation of the phenomena of light. Some of the results contained in this Appendix have already been given by Professor Haughton ; in other instances I have arrived at different conclusions. In such cases I have been careful to give my reasons in detail. Consider a homogeneous elastic medium, the parts of which act on one another only with forces which are insensible at sensible distances, and which in its undisturbed state is either free from pressure, or else subject to a pressure or tension which is the same at all points, though varying with the direction of the plane surface with reference to which it is estimated, Let w, y, z be the coordinates of any particle in the undisturbed state, «+, y+v, z+w the coordinates in the disturbed state, and for simplicity take the density in the undisturbed state as the unit of density. Then, according to the method followed both by Green and MacCullagh, the motion of the medium will be determined by the equation ge du d*u dw (Wc but ae uta iw) de dy dz= (\\e du dy dz, . (19) where @ is the function due to the elastic forces, To this equation must be added, in case the medium be not unlimited, the terms relative to its boundaries. The function ¢ multiplied by dw dy dz expresses the work given out by the element dx dy dz in passing from the initial to the actual state if we assume, as we may, the initial state for that in which ¢=0. According to the sup- position with which we started, that the internal forces are insensible at sensible distances, the value of ¢ at any point must depend on the relative displacements in the immediate neighbourhood of that point, as expressed by the differential coefficients of uw, v, w with respect to #, y,z. For the present let us make no other supposition concerning ¢ than this, that it is some function (—f) of those nine differential coefficients; and let us apply the equation (19) to a limited portion of the medium bounded initially by the closed surface 8. We must previously add the terms due to the action of the surrounding portion of the medium, which will evidently be of the form of a double integral haying reference to the surface 8, an element of which we may denote by dS. Hence we must add to the right-hand side of equa- tion (19) Ed§, the expression for E having yet to be found. * Transactions of the Royal Irish Academy, vol. xxii. p. 97. ON DOUBLE REFRACTION. 275 Denoting for shortness the partial differential coefficients of —q with respect to , ap ee by 7 7a) tq) &e., we have du\ . du du 5 ae rice Ta)? da tf (783 dy* du dou Jas aes (i) we +#(%) ay whence =| dee dy dz =|\\r(z FS du a de dy aer(\rG f' i) \ae a ti ee. =({+( i) du dy dz + Wr (=) a ) au dz dx \r(z A ) bu dx dy Wr aE bu dy dz+ &e. (du du a:)+ fav -\\\{ sa af (G+ 3, dys \a 7) +8" af (a)+ av af r(x) +60} de dy dz. We must now equate to zero separately the terms in our equation involving triple and those involving double integrals. The result obtained from the former further requires that the coefficient of each of the independent quan- tities éu, dv, dw under the sign lie yanish separately, whence Pu du du du\ ) dt =i z x) +5 tay f a) +z: Tez i ) du d du du, d (dv “ dé ~ dx t(a)+% t(G;,)+ Taz r(z) “ue rahe Pw id ,f(dw\ d ,(dw\ d (dw ; we ata 1 (da) + ay (ay) +a Fae) equations which may be written in an abbreviated form as follows :— Cu ” dg| uv oe do} Cw_ do EA a At ele Eat nF Nd where the expressions within crotchets denote differential coefficients taken in a conventional sense, namely by treating in the differentiation the symbols aq@dd da’ dy? dz as if they were mere literal coefficients, and prefixing to the whole term, and now regarding as a real symbol of differentiation, whichever of these three symbols was attached to the w, v, or w that disappeared by differ- entiation. The equating of the double integrals gives {feas—(['r( =) du dy dz ala a) du dz da+c&e, =(j| [i “+m mf" i; +f =z ae) ut (oe. dv+[&e.] au | as * These agree with Professor Haughton’s equations (5), : T 276 REPORT—1862. where J, m, » are the direction-cosines of the element dS of the surface which bounded the portion of the medium under consideration when it was in its undisturbed state. This expression leads us to contemplate the action of the surrounding medium as a tension having a certain value referred to a unit of surface in the undisturbed state. If P,Q, R be the components of this tension parallel to the axes of w, y,z, they must be the coefficients of du, év, Sw under the sign \ so that [du (du du rav(t) +n) (2) (de (de [, Q=/f (52) +mp() +nf(Z) es ad rae ae (22) [dw (dw (dw naif) +" (Gy) +9 (ze These formule give, in terms of the function ¢, the components of the tension on a small plane which in its original position had any arbitrary direction. If we wish for the expressions for the components of the tensions on planes originally perpendicular to the axes of «, y, z, we have only to put in succession /=1, m=1, n=1, the other two cosines each time being equal to zero. If then P.,, ie T_, denote the components in the direction of the axis of w of the tension on planes originally perpendicular to the axes of x, y, z, with similar notation in the other cases, we shall have du __ pf dw cl afdy AG) TMG) TF(z)| (de _ pf{du __ pp {dw | v,=f (7) T,=f =) T= (ae) > 7 (23)* dw , (dv du rz) Tafa) (G). The formul hitherto employed are just the same whether we suppose the disturbance small or not; and we might express in terms of P_, Te &e. (and therefore in terms of ¢), and of the differential coefficients of u, v, w with respect to a, y, and z, the components of the tension referred to a surface given in the actual instead of the undisturbed state of the medium, without supposing the disturbance small. As, however, the investigation is meant to be applied only to small disturbances, it would only complicate the formule to no purpose to treat the disturbance as of arbitrary magnitude, and I shall therefore regard it henceforth as indefinitely small. On this supposition we may expand ¢ according to powers of the small quantities ~, &e., proceeding as far as the second order, the left-hand member of (19) being of the second order as regards u, v, w. The formule (22) or (23) show that ¢ will or will not contain terms of the first order according as the undisturbed state of the medium is one of uniform constraint, or of freedom from pressure. In Green’s first theory, and in the theory of MacCullagh, ¢ is supposed not to contain terms of the first order. Accordingly in considering the poimt with respect to which these two theories are at issue, I shall suppose the * These agree with Professor Haughton’s equations at p.100, but are obtained in a different manner, ON DOUBLE REFRACTION. 277 medium in its undisturbed state to be free from pressure. The tensions P, Q, R, P,, &c. will now be small quantities of the first order, so that in the formule (22) and (23) we may suppose the tensions referred to a unit of surface in the actual or the undisturbed state of the medium indifferently, and may moreover in these formule, and in the expression for ¢, take a, y, z for the actual or the original coordinates of a particle. Green assumes as self-evident that the value of g for any element, suppose that which originally occupied the rectangular parallelepiped dw dy dz, must depend only on the change of form of the element, and not on any mere change of position in space. Any displacement which varies continuously from point to point must change an elementary rectangular parallelepiped into one which is oblique-angled, and the change of form is expressed by the ratios of the lengths of the edges to the original lengths, and by the angles which the edges make with one another or by their cosines. If the medium were originally in a state of constraint, @ would contain terms of the first order, and the expressions for the extensions of the edges and the cosines of the angles would be wanted to the second order, but when ¢ is wholly of the second order, those quantities need only be found to the first order. 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Gin. 1a. fi P Jai | Cubic omits of bears in ne fret) 7 aire rer) sa00 ms | | 25 1 1185 vo im | ws | | aol Qeamtity af cole that com be stewed is henen, ed of what dencriptiee 6 ~™ “ oe | o 108 4 150 lone 2) BS lene | ~ if =U Qaseiny of ele that con be stiwed in ether parts ) Nowe | New Newe | Neue | New 701008 Nuee None | | | Moos 00 Leen | Cobie ents of wher parte = Nee Nowe | Xoo | Nene | aia | Nooo \ | a0 Wit sea of les ws ial a esa ba cst apie ‘ rr a | Fs peabagtes F les Nar ‘ is . | | i | Fa | it | Deengtina of acre perzeiles a Critithe | Mamsatay’ shifting Mado Grifhtho | Grifitha [emg wih Meola { Oridithe Uf nim odnehel Gitte | Grifithe Geiss Grifhithe Grilhche | Gritinds Lea ce Thar of screw yempetior — ten. 14h hin. on. wit on sft thin ate un. Ten. om. EN. in | 18h. sia, | 24. Gin. Ton. Un. | Laugh oth Kno of ba e 3 on wn | 30. din se | snide Mi tin, im f an, Af. sin 2n.tin. | aioe. | eee ‘nk si iL %. Fab. = ———— 14M wed 270 17M. 97a. S0M.211 sn. Si. 27h. 60 Sin., 27 Hin, A SON. ian. 2011, 10M. 6 iM in a Ga, Ca: Ain. an, = “aS | as yim. Brees oe : of ease : | | | Tir in Mesa fer Eacomsomiting the propeller - = J | (Cloteli om shaft and T heal\cloteh SST lltth om el Te ttc ah wT a hath oo ‘at The Cae on Sa ted FB on cal aM and T besd\ntech un halt aod Tele | = ~ - - F ‘on propeller poplar ‘on prope or lice er oa proper Mews for brining the proper =} | | | isch cn che Wakao ble we ttre piel nelle et'ond wate } Tudile ucek unl eke ean hte Iedcal Lengo = Sa | epee mda gg St sin ih mnt aha ete Sel risTa vara Bren aur rs) moa env urs ‘What i the rate of peed bt whan ot Fight deve Normater 29,1800 (Feb 18 1861, Light Motlsaly 31,3660, Lich Avewst 7.1601. | duly 1s Joly 16,1651 [Aug. 7180 abt, 11701) Jety a1; 1008 Jas 7, 1608 March, 1502 Fearany ayasan |) Peezaler 18 190) <1 steremiter'a 1861 W354 kote 1e074 koote tacoed by meaecrl Eataney, aed wher? 2 cts Sor 7 Tah Ui itrio bec i Ta vase tam may | HEAR He, re fee ph a ay an " porn irda arote Laan ith koots | Hebhuoioknes Yehrazuew ante | Hart Eas hte eae kocte outer 17,1801 Mankss 180) i | i | VESSELS FITTED YOR CARRYING CANGO—TAULE 1h ale eed. Arwecumalsion fr § ils ive ar ter, a} j i ke i ijilt i des be Jana i ? Xl 41s, 3 i2i2 5 =< 13 f2nes : Frey wo] woe is z ete 3 4 : = 1 i i SI 4 Finty ao | 404 os z 2 Feee ; i iy je 5 TF | zt pias jit r Rinfy eee cin | 0] AO ua = 5 We : ea: = js pn tes | j ies : ,. ae 4434) 4 35 vit | SrJchu Eathore | 490] 498 oo : 2 > “ : ¥, | 4 ES H < a ae A all ae oe i t3eg4 24rt fie ¢ aeseht eeeel ah ; al srahan mations Saf a | a ma ot a |zag = o4 iz ae} Se. Sak a 8,73" ose EEL ifsa = 12 | Mecehaote os | 40 a7 z egig 3. i H £2 2 wah 4 j Ba a | seehl2 tf 7 18) teeduate 2... 33 | son or = \ae8 z a = = oH 35 Hae eae | is = | tnperatrice 3 | 403 2 = 2 3 i jas can | 73 erie si | . 28 | Toacer = ™s “7 a o a ‘ - Fa ! 22 | Cuantea of Durhas uo oy E 0 = - , 1 a | | Lady Mice Lambton 1 oe om w é z i | i + i: | Wu Teeket 09 ra = 5 2. fea i i ion ae ai di | Wa Aldbun ins es au D 3 eis < = =, ! t 2 Wan, Aldbate .., 198 7 | L 2 fee avy = Elz F as dgut itsag jp ieeaete eles | mr} as 104 00 1 Ee Fee 233 me es 1 hae to a} FeeEy e| as ts “ S 2 iG RON Be Zz : a3 ii fret 3 H wo} os E, fe: 22 2 t | H 2 won| 10 40 7 = a}: = = . hi bt i 7 35 : o ™ a0 er a on 4g aes, 5, | a Pare eS | | 0, 2 Lo 22252 ed Sab. Tad0R ssi ERESERRSEEE Baie El Meroe | “ Salers Neveu Net tee WITN. Vay ALTON GLE) PASH. A. 28n 1660, bm) A TAN cin P20 ALE in, mer, Som, & The | Mucataay, Sons, A Hed Nit complete fir wa J. Teun sol Son, ve a 1500 New New | New Nowe | Nowe 0 “> aay Woromsatal Hemet Tiorsmatal Direct | Horivintal trout 2 2 | 4 | 2 hacer #0} trank, 30 = ba in, | aft, Sn an Metall Metallic et ten Vert 17Ibs 0 tan Beet. 10) | feren 5 toes few. Sur Bh | | 12 toea fewh, Sar. Hh, 11 tame hows, B¢. 10fUla 23 tous Sew Sy 16m 10 tens Newt. SL tees Sees Mew ar 31h WO tems Beek, 38 tom. 31 teas BO YO}. 184 some Mew] ATO Mann Ah wh gn 14 met 5 =| Oetidee a1, 18009 Mahle Femmes ks ce) STA rvulutions Df revalat Deeg asia Teele Tetaker Ire In dtitey, Sone & Tookl | Mumtay, Stan, A Pict ve ve J See Nose | 6 « 1. below draaght, F, 16m Cat lin, mu 67. Hin. 2} itera tn. Truss Net fered i ta. Min. Tra ae ten. Gin "Reet ca proper more ise kee | ‘teber 3), 1800. erred Th cena of eomaney ton of coal Lang averngn FE Some vers) quarters, sued woerely Knnertad Lo abaw © © spprvniiity, the No, of days nl the ship sarviee aa tne | cy | inet be many rama inte with the nymat of aie! | es rN Dr Ue ae ive a8 Theis 13 6 ‘GRASP we the rear pp eum tthe her Sebel koee= RESULTS ODTAINRD NY AM. G. MURDOCH, Gilstar frunon Dita | Prince Anbu Sewn | Severs, Thames | Taro Jars Tysmsoeth Tyee Tyorwonth Copatra Avista Tushlane Mithoarve Methecrne Prinoe of Wolo. Same of Fy 1a 3 | om | 360 vss | | ons | 701 | 7 oo 0 1 ou on 1 eb Duly ely a ar Ela 1s 10 lar ro » r 4s | a3 6 | 307 | oro | 13 iw | ino nw sr | | | | | | tety re J — 70 | 8 wl | oan | Tons. | Tone | Kata | Kaets| SERVICE DURING TG RUSSIAN WAR, 1855-4, UNDER ‘Tire prRRCTIONS OF ADMIRAT SIR FREDERICK W. GREY, KCN, rhow ve Vingyts VITRRD KOH CAIRYING SICK AND WOUNDED—Ne, 7 NEPORT SELS EMPLOYED IN TE 32 | Arcmmotatia or | 4 seta ae aa 48 a | | plilel fy Abele Brel a) pe | A i 2}2 AG i i pales sto Wade 8 wae ‘ s4i89 | eat a2 ¢ | Je ao | | nro | \\so7" 30 si¢0 Weern VeSSEIS PITTED FOR CARNYING OFPICRTS panne of i 0 i a u | H H i ial aire « «| eer | fom ay +| ou 1| stardiasri00 [a 0 0 a| Jonas is }a 0 0 4) Ost 161885 | 210 a | By an ius | 210 Dee si,186 |2 0 | oe 315 | Mfareb a1, 18:0 D | March 31,1858 | 2 0. ©) Apritt,1us0 |9 0 0) May 0.1060 Renter Rover emer, cariar deigiyn a0 bottom foal Sere —Tele Tae enolate oped that #4 C0 VESSPIS PITTED FOR CARRYING ¢ =r | ae laly Moving bials] ; So z ;2 tik i gaa eae | hs heal 1 | au Jada o 3 | 100 | a100 16 x |im | os 6 se fea (| ane 5 oo | mm | | ra] rom [a] 6s | op | oa 7 \ wa | amo | 33 oe | icon > aa] soc = 33 | soma x ra] won * ta] tee Pi ts | cos o 0 | ssi 6 to | ow o 0 | ass ry ro | osm % ‘a | one ® pay mn os | Two H om) oes on ti | cine 2 4 wo sts os auch ws Cw AVALIY No. 0, Expense of | ism 10 ofa mon “| ‘ lust oo) 5 6 fis 0 0} 6 jiu oo) 6 6 6 wo 0} 7 6 4 4 | we &o] 6 12 8 0 6 VsRELs PITTED FOI CAIRYING CATTLR—No to. AND TROOPS—No. R i : te | | Ag | Armonmataiea or ec ee 4 | | : j Sareea | oe mal 5 il or Marine Shp 1 Mii i 4} | £ Rewie pl dle se £ | Pla) 7] t Vay py e L els) i i c a|2| 3) Esl} pas |) a" a | | | ale f Pm ern | |e |u| so | ra) redecte } £8 4) £8 S| septtantags [505 1) 70 vet riniatsempbred tie quarter toni. | a @ |100| i010 0 Orin | Merch tae 12 0 0! 62 4 | 100) oe 4 0 0.18 2 | Jove 3, 1856 6} | | av | o aunts 0} #1 0; Sept an ins [2 0, 0 Teloonl prwre | La . oh | V0 4) Nev 2h 8 [118 ON ecm carry 1600 troope arter privsipally | on ™ lim 40 110 0 | Stes 1239 0 ere Mt eR eS | oa} ™ 140 40 i ess, 185 | 210 0} $3 | oma » H ° Deea,1s |2 0.0 | Paid os |” mwa o a 160) Sosa [210 2 | » | corso | 0 120 Oxta,1hes |2 0G Show ot hicshiprnforel e sezount of foul Litem. | ix sisr0 o} 41010 | Doe 31, 1h TT 6) Paid oft, os | mov0 | eis 0) 916 0| Deeain 6 | edaced porer | ws =e A118 Rews17, IE 2A ala Be Vou por sassy Mrmerly 5 redanal Jia 0 10010 | Oren Sys oy tas fois 0} ese By yam 19 0 ow 6) 1 Lis 0 wr x | eo] ot. 0 o avin ee rs a | mo a} 1310 210 0 o7 | oo 6 dia 5-0 | Movy adopind fee this sree than any other o * i ie aa al n Au 0 1k 0) Ap liis.6 rr | a2 iio 0/374) Ape 1 | Maloond power 0 ‘« tied mal 8 7 0| Apeioyan 0 | Ktuced power | 0 3 | oo m2 0 13.5) Ap 0 10s a | 120) as 0 ou) ay “ | © 0 | mo) 1 0 111 fi w @ | Go| 100110 0 ras Arapert mat 3] knots be head to. Mareb, 1 , is 1 6 6) eoton1ate | 210 0 ‘ 100 18 110) vehon ine |910 0 ing 1600 ean $0 asta Bo ) ou 0 ° 70 4 ° oa | m0 0} ots Ja oo vi 10 ut 20 tou j2 60 J for earring carga. Iteary water © on | anes a | «0 u67 0 0 180 jn 60 or a4 ote | os lira a 6 iis a} Aptsyiee |e 5 0 a ee) ae uo! oot 1s 0 aver} guys, aia | Trae of Co Kata re ee Nor 4 18s ° Oot 14, 1855 March 13, 1858 46 | Oona, 188s Oct, W184 | 7 0 0} twa, Tlie 311 | Oet.ai 1 Poll power. 1 s| omni Teatro 40} Joly 20,1005 Fall over 26) Drm, 1s Nalucnl powsr 3} Apt, 3908 Ratoend pe. O) Ve dT, Lees 6 | Sephet3, 1600 Alteration of rls yor foo eunatoced Feb 3, 1824, 0 6 | St ty ins | 2 15 2) Septe99, 1880 | 220 0 | Relostion iv rate per tou epnuenced Mareh 1, 1850.) 17 7} Ovt 17, te ? Pull power. Oct 11,1688 2 7 | Poll owt Fall omer 0 6 Dee 10,18 |2°7 0 4 6 Alieraion of role per to exminencing 11th Joo. Teed Very expentive Cause ot sate Tedical spent Telucel set Hployel thie quarter preepally (a tring, Haden errr. Pall power, | Sets | pe Tatieted Powe, | SOC Mam: | “Dp PROC ELLER. RATIO OF VESSEL z | we to | Indicated | Inaicated Data of Tria. | Where tried. ; ~ - 4 e elle ° opm 3 El Neco nso ¢ Tower | | Howe Wind No. 7. to No, &, with = beary ewell. Wiod No. & Wiod No, 4 ta No. 3. Light wind and smooth water. Upper edge of acrew 2 ft. Lia. oat ‘Light wind and smooth water. Vewel Wind So, 5. ave Wind So a ware Wied No, 2 to No. Smooth Wolo ge 7 Wind No, 2 w No lobert Napler and Sons jobert Napler and Sons iff ¥ Ere ttt iit PERE ie A lg ! ji No ii it F Has gee ded FFzZFF i 4 a ka : ii Fit y i if on F z §; i fH ie g - ren, ant Sal Aiusphrye, Tenwamt, and Dykes ‘Trial not at roearured hoot, bat between Pymonth and KAldysose. ied Neh, Baoodwale forizontal, Trunk ..-ns:ssinee | Wind No, 9.to Na. 4, Saif boiler power. vontal, Bingle Tran! a fe a Wind No 2. toa x : Wind So 2 Half taller power. ‘Trunk. ‘Wind No 4, Horizontal, Trunk. Wind No. 4. Half boiler power. i browne with Wied Na. 4 with « moderate swell. 1 mean of two rane aly. love pritoat exrsua¥ to No 3, Waders prin Wind No.2. The priming ofthe boiler i now under command 2 to Na's Light breeze. Smooth wate. ‘Thal not ata measured knot, bat between Plymoath and Eddy ateoe. | Very light breese. Smooth water Wind No. 4. Cais. Very light breete and «msooth water. ZtoNo.4, Vewel viggnt Stores ea Board. 4. Moderate swell. ae jad Ne 4. Moderate swell. Half boiler power. Horizontal —ocnvnesnru Steam evald only with diffealty be maintained to 20 Tia. | Vertical, Oscillating, Geared... Wiod No 3. Wied Na 3 to So. & Calm. Sea wmeots. Tiali boiler power: Calin. Sea emooth. Wisd So 3 Na. Wind Na 2. to No & Wind Sa 4. Iisit beiker power. & A "Hligh baters remored freca the abl | Preah Qewwna, ith a tttteawell, Do da. Hail Sollee power. io. 4. te Na & ng from Na 4 toa 2 The ape is the cea of tw ees a Totten foal Soa "Vewel sot mast, THA wot enmerl salam Tiler did rot evperae a very oo py Sot SI Ve eS ad So 2 SS 2 Ser een ‘coo No & Sea umocth Peanbleded bum Siew VESSEL TABLE 4.—RESULTS OF THD TRIALS OF H.M,s SCREW SHIPS, OFFICIALLY TABULATED BY THE ADMIRALTY IN 1850, PROPELLE! RAIIO OL by the spurew heels is 0 padidlenw dt boarding an enewy's her clear of obetrs par (0 stale, that the operati ily as tbe common paddle. wheel Wee have the boaour Us ba, BU, 9 this view the Malller was ordered Letween twa vessels could take It. 60. 4) Tengthened fur the insertion 0 1 previonly (ried in paddie-w het Ther i Use Baler U jtireeal mancer aod filed with engines of the a 1 wus Goad enim, and the 6 the Areliimades and lar engine as nat a nln iNew at of propolslon Is ded, Ib Land's dad, a eA vensels wet the whole of their valle tb has the The rus was as ‘before, from Dover 1) Calsla,19 Fallen 7 to 2%, and ler vperd Live 9 Uo $f kot “Arebimedes ran tbe Gistanee 1a salle set, Arvhimaties en 2, and speed 10 knots, abe tnd sea fa heavy io this respect han yet boca afforded for in - bly taferioe Lo that of the Whigeum In light aire winds, by oaly eceasion on which te sy Tor sore the rain ey Per bi a My oan at 18 Clene vesaris the propelling perwer of Ue screw le rou) oat riortty, sllete Spe wrathes the oa Gan wetcanry pater fa the vewpect, Coe It bn xiao plain, (roms te secomh trish that Ji U ot Son Witz © ber ae atvanlane over $0 Be ‘The iattier was wext tried agalnet the Vervrius tn secu. « decided superiority over the paddle-wherl ad sDeg her competitor. liefore joining the #quadran un 1d althoragh the : i Mefore Joining th Aron un failed What ta strony. 61. wlhono pOWUr, Ke compared tras empoyed a tow the Sree abd Terror to he Orkcer nang aa [aiistueliog of hie Sohn Prank. thfore this time hemwezer fle state {or the instrveta of the ofbears of the tioyal Nava) Colege, U Archimedes, a #he hour having tern reallacd, and the Vairy built fur the use of ‘Nine to Calais io 2 boure 1 wuinate, pean a eomparaisvely Rign role of pent ornid be obtaibed, yet they could scarcely be re Fes Be pei et enacting tn el tr wes sh St pin Se ha hep sesh oan Ba el Hi hn ed ov ig toe ccenanmy Rory Ae po for discon pected wilh (ibe Toelluation of the sup does not di a of the screw facilitates the It ls obvious that in the Widgeon and Archimedes, whieh differed material parison could not be made between the p OF the serew abd that of th arly sluwed, eapectally when the pecallr Gtness of the screw tor wor purp nd, that the experiment mig ructed oo the sare in October, 162, to the beginning of 14 els {0 Cilils Sosihd, Se'm perfoet ealin, wiib the sca atthe serew tig lt be adiyaatageoualy redured from lwo half Karns to about one-Lllrd strokes Yar ilnute, and Ler speed was from tov huts per hour, The the weight, farlitated the yperation of shipping ‘ : iinvwcen, aad the whole tne oceupled by the tuiter un Mer part of the veaacl. Tetfore this I men aliowe th Mh ber der the eattrpand of test: Admiral 1 a iivinte ti to their lordahips his slleraton, we abstain from giving aay (hal the valoe of 3, Bmith'« tnvention will cent, even it it common paddie-mbeel. A teasel oF as bot, Ir ‘and io aby we lah the prupeling, power of th the sbips lying elose neat obedient Rervant The Secrelary of We Admirstly Pit, ist SarrER both ia site and form, an exact com le that thes y be experienced. Tn bot be orereom ipaddte- sve} would 4 jecring, and accompliaber the was taken Loto evoaideration, th be eooclusive, ao far an a trial fue the Aleelo, the after-part. belbg power, and oo & plan which had been nd from them it itwas I thferior ta the Vietoria aod ie and showed In respect of eater than that ot af the experi y shows 1. LLOYD. ait of the trials clearly heady ind, he 1a mile fat “data om whieh fan taatp wection havin 6 bee Inarive cojiovers {nthe Country were therefore ealed on to propose that coustruetion and arrangement of engine which Se that of auy of the vessels then ip pro they mgt wverally think the bert adapted the dimensions of the propeller, and thesumter ofrevolutions (t wauld b ty this alteration, unequivocally show ojuired to make, bring furaisbed for tele uldanee, and the ueceaaity of keeping the whole of the machlaery below tbe Eyoutruction, excopt those reader 0 water line being’ Insiat Beyond these necessary conditions the manufarturecs were left unfettered, hd they, as roved in the form of thelr Tigh be expected, seluig new and wide feld open for thelr exertions, submatted a (reat variety of dealguy the reault The great lmportanes, or rather tho nocesalty, of futroduri Of thireveal expefienee and meeanleal abllty atloned in tho mn whieh a high speed in regarded These Veakgua difered widely from one abot lier xome wero with and some without gearing, and many of them appeared alsa (udlspensabla, fr without it the objet of bi to pmacns real merit. OF these, selections were made, giviog to Wearly alt the m d,s aultable form, although nok, as in the farm fearrying Inlo effeet une at le {wo rimines of the same deserip ‘experience Nad the tuggestoa of the Harbour fomunlaslon, eight pairs for w tatuming double the quantity of feck and to belugse-of- battleships and foar frigates. The good performance o fvealtored thelr originnt tnd coals’ and reductog by oe-balf the apace whieh they cceupy a destloation from mero Goating batterios to seagoing ships, calculated {0 serve. Wi «la conjunction with ulated 10 produce seriou inconyen) fleet. Of the frigate bicek ships, ono only out of the four has been. ordered to be fitted, and wilh «mallcr engines than number of days. Probably sueh cai thom originally lotended for her. Shu bs iu order stilt further fewas lille differeuce ef speed taal experline ‘The expenditure anid 0 by mont of the manufactorers alBelent experience hax ould bo adopted, but stron ‘Ore screw vou Ainuer the varying Yeloeiy of Dower. if for exaimp out by the eu mee the of appleatioo, thero tring a What Aime no kind of engine wih would effectually answer the purrowe All th emacot ‘the plans whieh they severally: props A acquired {a this novel application Tithe year to tenilere werw accepted fue fftexn. pairs of wcrvw engincs for tu opportunity of tying the Yen's head fo wiad ia heavy Weather, | was much greater in the Niger th I the bollérs and engines, and been made or the Of all certainly, bono of them can be regarded i failures ; Hl tbe pecuniary lo bability thal gearing Increasing: ‘balk and weight. of tbe m Aan iii however, whlel hy fruntarounly some private ve Fvantageous! el cecanloned the malls rateot ia coafunetion with stearic pointing oat riya vuole gl with aca Voy byes have already bev exten requirements, ‘out by attaching ina tem ‘ve of greater mportas than ts perb pa com from 0 Kt ary any alterat before the aerew apertun forms calculated to Totely nceesasry for obtaining the required ypeed, 1 3, by 2 cansiderst Yo render her after-tody aa full eto teas (hag 4 knots caused dnd all ‘the vessels then in course of B, were (0 a greater oF less exicat 1 the actlon of the serew, eanpot U ‘evident Ubat Io nuch cases a proper (Teren when a moderate spe! ou fhe great wante of power 2 deetaion which secme (o Hava been judicious, whea It fe borao tn talnd tbat Wie evils oceauloued by the advollon of the coat UF forgunmple akin, witch If of the proper {applsatoa oftizaa-powen zane aN foro, would be propelled at 7} Kool ls propelled ak 6 Kuots aly, akout one-half Of tho engioe power le thrown awa thue wasting half the original cost of aratlve value of the screw, er, nod to be fitted with engines of the sare power, Th Way bo ahorily stated. In flue weather, whe equal engine power W wheo vantake was in favour of (he a uunportant point whieh hitherto remain Ale-wheel vearel, the B {Heae of the views thus carried out "The following table contains some parvealars of the alterations which from tine to twe have b will be aren that the serew engines ordered frou ing lustrameale relat oe gresicr or leas degree may wopelie, as adapted teach of them Pact eae Prhre formule by whieh the ealealations aro ae the square of ter ve trom the dilfer as, Kinda of servw engi inxloty folt by all, ex be full fh neautted for the eof & Ko ng alr pumps, &¢., Dears = const ot fan auxiliary. scarcely necensari Somernd Hove, Mop 1830, ing. the ailvantace of dls Throwing away” the capability of eareyiok jrations "ax these’ induced the Boant fo one pleted. Neueis torte improved, with « view of Insuring advantages which were Heltbrr doubtful nor of auall m Sppeared to outweigh the expense of maklog the neeeasary alteraloas of all tie nerow cogincs matte ta thel is Tito tn ets fo Sor Puanaees of Toveaigator tad Keaarehy Tt di ruallioy bot this: dlsdradilaga irdee trax the ithe numbers lo tho last column cf (he table, and Iu the column next Dut one preceding {a che Daailak, vat thie Glenda redo excellence {8 respect of speed, of the forus of the yarlogs sbips, conjolntly with the'relaive efile ‘sad bollers Wearing at experieuce clearly f ich have been ond Pot the reault thereby p 10 that the realaLance of carcent expense of weight of including Erebus a5} ri, show approximately the "S vy of the the cube t pe in, orerrOMINE cement None of tees ‘are ot ao far from the Tetmeen the performances wEtaen cf double Ube power, a usaf ber afterbedy — —=—s Ayenbe soggy" ecuiry any s0xop¥ qyyA OyAEIOD pare ssi) sour Loan youspuo Zoye3 yoems yo pIOOIZE wo wT io nme veo wen ys wrOruDoRDD acreom e kanpepenes pasrwwon ya reas. 1) tz pazopinu you poole Aye oapedon ound enn, CaojaMpetes pauapEwO9 YOK TO szayen. am 30 300 "0 Fy -w 1 medoud Jo wpa “5°08 ON Proxy PULA “22erd uy Yuyoy feo epeMUL aa. 6 ron SUK@OMET “Be] nomi £4 pong uranyp goytuw (ema “ERE VENGn y Ayposnipy “spoqeainge 4911 JO OR BAITS OM aOJOR [PEA ADITVOIF OMY aAOUP soNHUD OMY om URI) PIFY OU OM) KawU pw LoMed ayy o[qnop Jo saunSur Kq ua\up | a8 { YH ps I y ‘ ’ F ai 29 dis im | Hy) TW (3 | as | 1 P : ° \ » 108 1 as | '3 | tee | tc : lal we | wo} ao | 2 ‘ ‘ \ c Mixed 1 | 1 » t ne |. A. Mentiplay : ‘ 2 j A ‘ 1 7 107 o , Mo 10h 1 5 Dhue TANLE 2)—DIME AND ARSTRACT OF PRRFORMANOPS OF THE PACIPIC STEAM NAVIGATION COMPANY'S NEW : TA ODLE WHEEL SPESMBHIPS “TEU” AND “TRtOA — ata ; all o ale eur] | aa es f ip | aa | a oy ; » ‘ ut | Iudeated March Sl ; 10 | 0 | ea |oan | aot | 6703 | yout suing. as | 73 a3 ? J.0r : : at =r ‘ ; ew: | tare March 70h oon] TT wa | | ms | zoe | ua | sos Se ansj seas cre antl a 0 2o))| asa, | Alston » | | | S : vo | 182) | March Atrat nt | aa | ges | aera | ret | an | von | ats Goal ne 1a} |;10 io | 1254] D. Brow, ary | Fa ire tell aateal | rt ae malluas’ 9 c : | Z | ue | am) = H to Valp yo | 2 | oe | 1400 my v0 v i ey 410 | ao | 1400 ALOR artes aioa ila ah gst lca wm | x ws | goat | clean Welch, good oo | 100 8 1905 | J. Wilkie | 7 : 100} a0} ay o | sw |icier | 6 0 t| 4s | 3077 | 300.) 105 ae) | ¢ 1 |. #00) : ee ‘ lle : | ere a =) naa | ath | ang | 040 | eo Jctan....] Quek toming inter a1. | gon all |i {ul Tot}| J. crite e : Pe , {Callan to Vatparion | ayy as | 140 re + 000! of uo) | 18 0 8 | | | | | : — | aaynan | 3a ean. | au | vos | | | tt na | an | a | ur | A.atenit © Ti wil) be pereslved that the above resulla yive sometbing under albe per (odlcated Ju r. ‘The Derm auil Tteu bave surface condeaaers,_ ani | | , 72 | 40 | 180 } oe att ea nad from bese toro steamships somewhal surpass ite perforiuatoms of olliers in the sere ‘Company with) the same daseription of | amyaon | Airsto Jas | air | ator | 754 | ana | dos | 4947 | Crean Mise 194 | 19 : Pete fea) feed farsi ret Mand, Kier, eC dine eine Tae } May gon | | | | goo | 10 St is eee . , tala Loge of Site yotig slow at Hight trvugh he Btrats of Magellan, cup] a] 8 | ase ; 3 ed. erie Tait miannaxss|\‘8000 |)-20\}) aes] anon roy | set } 4010 | Ordinary — | sthnitin J) opt heal eee {roo | as | a] ars) a. Wit Pera om te ra fon lagi Ao Viveryool was lly 14 kota have seated rom tho Clch Ligh, on the Cy, to he ak aff Dive i 1 | | | ) Teal S F of 170 nautical molles, in 12 hours 16 wninotey, the Aleplacement being about 100 tons. ‘Tho rea of the rnidahip section. being OKO aquare eae | (| 4 wh | ae | ar | 6 ait ieee, Indicated horsepow fawning a fel awa be oa or hs yay varying font 0 ne | | ie ca | mw] 10 | 9} ‘ reste of seat nthe bellers a pereatl by the uptakes tn plters at the Perv, two In oumber, are of the ordinary tabular eon albany ||(rani|| saul "oon {ou hang ||) -momo. {ony | ten Goal, tnt tiny tty | us A ae RT| gc , . Mrarte with Elder's Vatent Moperbeatiog uptakes, ‘The fre arate surfa unre forty the total heating surface about OOOO feat, Who eyituders, July 1h | Yesmantan “ a | as 1 1 | a] t A. Wyil = gore | 0 Lae wher, are stench jackeltd, and the stent te cut off ath stroke In the arwall cylinder, ‘Ihe large cylinders aro 0B inches, and the sinall ches 44 ¢ r=} = =e “ on Bercle ad Tn eee len om et ran roms Creencok to Liverpool wa 19 knots per hoor s the ioilatel lors-power about 800; dlgplaceent of hall about 700 + Ty he ease othe Toate padi enn eer gars 4 Ne dca olla of taka which the lem a; and pug am wwe e” © re Ube A whats 4, Mpg thon mquare fee ranght forward 70 aft B fee he roidahip section an average froy verpool to Valpa Poon oe nT Ones ae ee ok «consumption of stares” shor ie expenditure: yt oe os ‘ i) square feet, the draoght Aft. Git a Hast the pressure of the efeac io boiler m6 (0 dolls, ‘There is one round tubular boller, The Pee i obtalaing thle oo Rianne that propomal bp air, Charion Atherton, and recommended fy thin Goranifice Ieper Ree ee oa ws Gal worked on ead 1 ibe nyeare o€ UNA eaDE ye mean Wieplacement wd (he ; Seite rata aurfuce Le 0 aqonre'fes, Ue Lotal Weallg surtnce SHA) fee, Meloding the uperbeating uptabes, The cylinders (atenun Jacke\tel) are e* Th Perwolh slope in obtaoing th nla Tet repos 7 Mividlug the prodoct bythe connurpaig at Rel tae ea tae, mpage Oe em US no ee S 2 Ha ot Merectmd of OF, and'two of Bulan. diameter, and OM. Gins, stroke, The description of coals Wed wo Fach Yopage ie Bete pureory alte ———————— RIAL AND ROYAL, AUSTRIAN LLOYDS’ STEAMSIIIP COMPANY TABLE 18 09 YRSSELS OP THE IMP ROYAL (WEST INDIA) MAIL PACKET COMPANY ING TO THE VARIOUS SITIPS INCLUDED IN THE RETURN FURNISHED NO TADLE S BELON OF THE BNC WEEN JUN P DIAGRAMS PROM INDICATOR, ES FROM SOUTHAMPTON T Max. 2 7a Ve a | ise 72 | eat] 177 | 16 | 196 | o71 | ato | asa | axa | 176 | T ° : 26 7 316} veo} x11 | eos | 1176 | 273. | Fair wind, sll at (St. Thomas to Sonthan =/ ’ Arcessa Carolin = 9 ‘ 4 4 4 | ov om 2h) irr | 180 ov} 30 Tubal F = wés)| = = 10 ac | Trot tt] o£) | oe | Stl Ss | \ i ieee | 5 me. tng sdf Fakes} Healy De ovser estore 4s a =) oe Aa | | Pe | eh | te) Seek) AS | os) a syrious a1vaa | ata | ioe | ic or | ssa} = 10 | 200 7 : | Head wind and ; ee al - Jinn —_ = el | TABLE Q6—ANSTRACT LOG OF THR APRICAN ROYAL MATL STEAMER “MACGREGOR LAIRD” A. J. Mf. CROFT, COMDIANDEE Finer Vorior #xou Ltyanroot ro Manerns | = " D : g qT T | ee =i] = = = = Les WITH FM's GUN DOAT “TORK | matt v Crea ieee || ces eal tan ' pe 2 Xoo tous pat Stoke¥oom, ail 5 es ; ee ‘ | rag Des m x : 7 ; | | Aprit 26 y | aw so 60 76 7 256 + # Fresh beed wind throaghout. ‘There are 5 tons of cost’ | heed E | i | tfesarare Alloyed here for coming into the river = : F ; | 7 SW $ aos a 2 0 Modorate head winds nt tiwes carrying fore and aft sails sot j 7 : A | |» SAW.and variable, | 8 | 001 17 7 9 0 Da do, do lve pl “ 5 z £3 é ’ { 3 ag 3 | Remarhe, | | « 38 Easterly 8 130 60. 101 7 24 Pore and Af. |) Strong gale from the exstirard, with very heavy « | belied a > | : EE € | | 14 Square 5 Fy steady, cuss the state i " AL OW : g ! i 4 am a | | ~ | ui 8 paso | soo 1 0 r 7 13 ore ant Aft = : 4 ; § : 3 ES a || | | » 2 | 8 26) W208 3 : et. : J nu) at OSquare. | ¥ Moderate and variable, and at times bead wind ie ie Le ; ee ane | ; 5 rie al nine ws | ws | 60] oso ‘ 8 7 i : " 2 2Z ; £ 3 | @ | ss | } a 1 Hae ee ares 20 all Preah breere: sails sot the greater part of the day : : = bs | } al | 3 ay \ 3 | | | AULs.x, ow the Lat, auchored in Funchal Roals, Madeirs, | _ ~-aine] or p nat ra “a2 is : : i 7. “ : sires esse arise | | are | | Pie twa Bade laa one screw, the ss ot Afrca and beck, a datance of aboui 930 miley, wna performed on 640 tone of OIA. hla veel could, herefure, steam to Australia and bach, er rownd ihe won . Without goaling, at the rate = - anv Sis f ano “| {ont ars cpl sl tae aml |j nie AS pepe any Dooensions, c. oF THE SOHAW Staaxen “Maconsoon Laren : bit aid « ey _|f 30 eerie bow ramming} © | ‘The forward Viade set at 90" In advance of wath 245 Fest Total fre grate surface oy tan won 5 iaep | 70s | a7e96| o70e | rane | 10 | 16%, | 28M [Rear crnmc naa aebiar # in Aganes) ot zane 0 Diplasentok ou Veone Bd Batts Fdwuary 4 ps deeds j n le after blade set at 46° \n advance of fore sera ‘008 = Lehi S085 Ton ireaye H : ms | ara | s7000| emo | scase)| secu | 198. | so | Mie after ade wek at 48" In advance of Deh 0; Miship Section —Area ee = Pa ward blade a ‘900 LP. Nowiod =| Draught or W at ie: - 7 im | sr ose | fehatllt aan east tice exo |{ The afler blade vet at 21° in Kigines 20 ht of Water Amida 17 Foot 2 Ineb uss | osm | ary | 20% aio |{ Te afer a SN A ates camel Ba ada Weiebt - 17 Pot 2 Toe = - “ } 1 7 | 17406) ores | pos | wos | 17%) | Of 8006 | Maced parallel, similar to French serew, geared Sf, Sin. strokes two eylinders C2inn diameter, Averago Speed during the Passage 06 Km V0 tl aad Sacto hac tee le is | x foil to a ter Burtace C tubes fin Do. Consumption of C nea’ Account ‘Onman a al 7" to) | sess | sore | wom | asso | reir | tty | tbh | 260) | 0196 | Varad parallel, similar to French screw, Aizitler hee Gee Day Rarolaions pec Misia eine tae ns, 10 Che aia: | | Madea placed to form « 600 Nerew j coarse A y 660 Do. Preemnre of St are BL, bei | | 119 | 93 | reoce| wore | eco | 2010 | 14 | 48m | aay | wren |f ptten ie trance Inioator Horse-power om voy bout | Do. Presrare of Steasa ‘SAlbe, om | 124 | sera Forward: blade at 46° I advance of afer Hollers, tubular, two in number; total beating surface, | Do, Vac nt. y : alle, nearly, : = ee se] | 1H | ear | 10060) war | rene | 7942 | 104, | om | wim Tilade. Including anperbeater s,...s000 ie "4200 feet, 1 Distance run per One Ton of Coale sc... 26 Mite, ADSTRACT OF ENGINEER'S L0G OF THE PADDLE ENGINES, SCREW RNOINES. GREAT EASTERN.” SECOND YOYAGE TO NEW YORK, MAY, 1602 coding at | Gaseeat eines ean Day {fc liebe > — | 1 | Ibe an aria | & T | wu | — akom i) At 0 ra, pllok lft sat 0.16 full epee. aay er Y n I {ght windsy wea smooth, May 4 in wei0| shag | iP | eam wind) my ‘ io t ‘ in | Strong beam windy aip rolliog heavily aay a | a | ion an th Birong SW. gale; tallepesd Al hour Mar 8 ' ‘ uv Teme fog slandlog by engines 10 boary, May 1 1 iis i Ay i Eneines Hopped to lake soundings; nlanilog by « aay i i a | is rer ql : AVLL30 wa arivod Bt Liebe SMp Tota ‘ mn uw foam | a Dewslty of water int racuaw In paddle enptnes, 25) ditto in sevew, $8. The ifertors wark{ox w Gull, Bifective diameter of whcel, lft. = 147222, each rerolation, Screw, Ht, plteb 5 furward, ZN. Ofla.; aN, aif tine No perveplsd AMSTRACT OF ENGINEER'S LOG OF TIE “GREAT RASTERN.” PINST VOYAGE PROM LIVERPOOL TO QUENEC, JUNE TO JULY, 1601 = a ae ites sg bis aan vee re ge «| PAnpLe eXonves SCREW ENOINES. Gasenae Newser, | I ita tives tan ee 170 A120) 900 | 10h] Sie pra W.| & a7 Ww Thiek f fan rom 10 rae Ul # ae ABSTRACT OF ENGINEER'S LOG OF THE “GREAT BA STERN.” VOYAGE PROM QUEBEC TO LIVERPOOL. PADDLE ENGINES, CREW ENGINES Gasexse Rewsnee AL A45 Ase came lo anchor at 7.45 dat off Ube Quarantine Ground. | ssa | 3352 | atos | 509 Actual Lime steaming fom Quebee 8 days £2 hours copings GSA horsepower) tolal, & Fire, 18 vacua Uh paihe exglaen, 28) dit ‘power wlcam guazes dafeetive s ccale GML) elfontive diaineler, Asth, = 1a070M, ery bad) vo pereepllbie wear ath revotaticny screw, sin pit ANSTRACT OF ENGINEER'S LOG OF THE “GREAT EASTERN." TIURD VOYAGE TO NEW YORK, 1602. ‘extreme Glauneter wa vffevtive, via, Gift. = 151M. each revolution) from the Ath May (o the 17th May lnk were a7, ations SH Hata bas tte of term tatoos 48) Guay at saer To ere ip rocune tn pate Sogn, 38 racaum Ineces es hasty of pala ehean SoA eet. sama Hoh sh Seg Mchisructer canes heeded Tatiog SLT ON. tn formed, ancy feeeson ort tule hes 180 va euty lp ar corer aoa seems Gters aly Gna of coal hy yale eugney i0 iann ive uy env eigtey 15 tansy Wt aly einen, 35; 0 KE New York, 1M. Gio. forward, 230) alt Conumptlon, #71 Was. 2 | rapove exoues, | 5 Bairratiae on j = |a ng of Buin ae 4 is a 4. | 47 33|? * s\% ee bela ael>s| 4 3 s/2)R/2 3 =2 | i H “4|23) 3 3 # & | Gayeeie Rewaaes, 2 24 Felas E| Bs Hy M Ema i MW 433 E 3/4 8 4 rile i 2/8 yale lalile 2 5" Fale /2 |a a13/¢ iA | la a la 2/2 \4 | Ibe | eg. | deg. ‘ f sax 9°98] | ataas pa alcharge plots full peed at 399 na H Sou | 1/1] 2 | dion heed nt 0 3 | 3] 8 | Stone bead wiod i i)2| 5 heal wind deo fogs standing by engines HH i a/i]o heal win 1b | dors | i 212 2 | sre 4 beary head sea enz\oes raving 16] naan ara | a7] 1] 1] 3 | Denset bergs| standing by eoginok 1h | dnt 0 | taf | Jaa | aus | aon aia 1 | tal ts Het) ral bere 10 "| agra | 117 | sob} 148 | Burro | ara | Ar} | ass | a74 | 370| son | a2 | weeds, | axoaWe,| WebpAdS, | 3 [2°] 9°] Dawe for: stonpol engines twice to take sown May 17 5.] Aivoae | a0 | Za | toy | agoo | 977 | Anh | ts | Ex | a | 310 | 300 0 | 0 | 0 | Atay rr took pilot on board) at 7.30 03 areived off Sandy Mook, tal ars | us| ah tis ego | anor] es rs sn [nfo | “AMidl (ims staring, diye 18 Koay 45 laste ATSTRACT OF ENG ERR'S LOG OP THE "GREAT EASTERN,” SECOND VOYAGE PROM NEW YODE To Livenroon, SAY AND JUNE, 1802 SCREW EX Prerrancevtrs ore RR J fee aed ten ee FROM LIVE PADDLE ENGINES. | scKe Cert | | | vas | 10 | 3 | iss | | staawe) a yaoi | 113 410 | ao 3» W s sr Bat 10.685 | 113 Aio | ass | 335 3 | 1239 rae be 1748 | Uw 70 | 330 47 | 351 | o> | a | Dense fog us)» bla | 360 B50 | Sos | ALON. oe ALS) ae tack Point, ‘ieaumed easy extreme diameter of paid York 2h FIFTH VOYAGE FROM NEW YORK TO LIVERPOOL, JULY AND AUGUST, 1 Grete Buses, At & pt, started paddle and sere engines s-head Mall speed Joly 25 | | | Attuba stopped euctocs to Gichareed pile of Momtaik Point, July ar) avin sia | wiiw| AL1LAO Fw. eartod engines wheal ful spend. July =| tao | a ia Satw Light head wind soa coche Joly <| 390 | os |srow Tight bead wind foals roaming rery mall for acvew boilers Jaya 5) 12400] oo onw Atg SF iow, stopped rostars odf Cape Kase, “ALAS fall peed. Sui at 2"] 1a0ut | 00. fs Sak Light teats studs fore aod af sale wt Ang. 4.) 1g. fatten | 35 Tit | sm | aun | 3 | 30 | wan Gieht beam winds fore and af ell we Aug. 2 01] taaue | 10 tora | asm | 17} | woa | aun | aga | Sot | 0 | 8 210 Aug. 3 °°} ine | 109 ‘siamo | 343 | 104 | Yon | 2a | Sar | sur | a0 | sro N:| arazW Aug. €:) bik | 0a |S |e ik) ish | B/S] 38] ini Wig 3 Sc] Aube | wae Sia | a3 toh | 1m : Rag 8) Jets | | St | Sho] a | ‘or \t 54 Link stopped tain to tle pict oa Bean AL10 nas. stopped Faddlseagtoes, walling for tlde. Screw engines working eauy all nigel few York to Liverpool. Actual time steaming fro 3 Total ft | 07 | 30h fino fuss eu ent ensity of water {a bollers 1 is ran per Box, 1704; fi jer ceot,; averare dally coasciaplis wa Ja padile engines, 24; vacuum. tn > locrme New York 300. Sin. forward, 297. Kn, all: america oo arrival ak coal Vy paddle engine, 130 toa; Uilte by acrew engines, 165 tods, Uotal dally Indleated horve-power of paddle enziner, —: indicated horve power of screw of paddle wéels S01; eifvtive dlameter 4sit. = JE0S0(. earth pevoluilon= plleh of enews ALL. Liverpool, 24 Gln. forward, 23/, Gin. ait; lp Of paddle whieele 11-2 per cook j lp of Ferew, 17 eonrutaption, 305 tans, ‘AGE FROM LIVENPOOL TO NEW YORK, AUGUST, 1882. ABSTRACT OF ENGINEER’ SIXTH YO PADDLE F SCKEW &NOLY | 2 jeel2 3 lid fi S]gilz lee 2 /¢ Germus Rn, 5: 2) 25)2 5129 2 ? Br S5|=3|33|32 4/8 BR SElgs/S |= E E /Es/2 | < < Ble jé | = =f! = aS i eee Eid she = ——— | te. [Tena ton] x. | x. |. | Inchon dog.|dee.| [fA 28% rat. Startod engines scat slow. AL 320 x. full ypomh. | Auzat soi] gos | 18h | es | Sao | 27a | sa | 2d ara} | 6 ‘AL TLAL roe: stopped comines to Giarhange julot olf Dell Muay AL | Aurwt ts] lass | oso) 340 | 174 | te0 | 20 | 39 | aa | a esiw, sr] 0 U Sore tll spat War kina Augort 10| tyesn | 4 3a | 17h | x | Soe | 3a | Son | tk 217 Ww oa] 5 | oppo Plier erew egos 48min to replace 3 brs bolts } Auguat 20| 1x2 | 0 30 | 15 | tos | aon | gag | | a Saw | oat | Strung 51: lea say Head om ‘August 31) 13980 | oo. aa [74 | 71 | aux | az | 0 | 25 TW, are | | Wo by W. ale az heary bead wea coals goed, Augunt 33) 1h0s0 | aio | taf | tr | aun | Say | sere Saw a3 | 3 ‘7s snd Beaty head sea rong Aigust 33| insas | 10s 330 | 1} | ea | om | 3 | | Se jaa wi) wk zal 7 Serong NW. ple and berg an auksseeten August 34) 14453 | 100 sotoon | 340 | 164 | Ys | 313 | a0 = | sea. we 2 Rh aL TO raf Cape soe 7m full poo Ahizust 35) stra | ana | 3 tase | 348 | 124 | tom | a1 | Bry | | as Saw swinwiw) sa | 4 | Stns fr wind wal heey bead tne Aogust 26) Its | 1191) 350 | ar | tex | ona | ser | ap | ew. SW. tyW, | 030) A > | Strong Deed wind, Auguit 27) Woo | 113 aby | inp | ts | ant) 240 | tie lreing byjthe land. AUZIS Ae; Hopped engines off Moatank to Lae pilot on tesard ak ‘3150 allot ll partir of wines taken apo th tne Total juss | 190 | st /tase Janis | 963 | ar iron (ss bron je a7 - anchee at 12 wenn Aine cy Sr ear as ped 3 boars ‘Arial we seaming froma Liverpool to New York 10 dap LDeul(y of walee fo balers, If 5 veewusn tn pall enstoen vane heres engin 2°5; exlnrme diameter of pad wheel, 4; ellevtivs Ulammeter 40, = 1AYTAN. cock vevetstlen leh of ota rn per oar TE10 y e Laeatae usin a Toe STTy ed padlie whevty IF yer eeu) ap oCeerew, 18 peroeal average Gaty onrumpUio of oala hy Pade engines 169 Neon ante 2 Veavins Dy serew evigine 10) (uss otal Vally coKsUsopll0n of eoala 90} tien ee nishe form: Engit and To the Man The Me Tous, th heen fully 2 The t 5, his valua A E Committ E In conc 4G OF THE SAILING YACHT "DRATRIX, LYS THE RUN FROM SOUTHAMPTON TO CIVITA VECCIIIA, ¥ pproductiv —— = - —--—______ Inppointec pamela peed J Xcote, | DA if the machi Is Under what Sw Area of Sa : near will bo p! land they : Dire eight] Diretion.| 7 n t y tog. {Por torwd| An pe a co Dayorstoath. | Hor. | § a hy | 2 4 a c NNW : Whole wal 0 ‘ ‘ ! starboard NE. 12 mil March 4 oI ich Fy NW 4 . Reefer mien, forcaail, ataywal * 146 | 6} 10 paca Ushant 1 Hn from which I tak slisbu Mareh 01 STL W r nl | ar aih ? sais NW SW 8 29 | anid reefe stays 36 6) 1 | “Laying to, with strong gale and heary sea ew March 7 1 |o «Hansa, : uv He aawil aeaW SW. to NW 3 5 3 s 6 0] 1 la hier: aunt : Seer EW, to NAW a 250 1 » | 0| 10 aati quall ‘Dimen sa ere |e - Ww evs | so00 | 7 reefed foresail, jib, apd st my 1 1 6 0 s ip3 ft. G ix ae & Scare cutee Ite } 780 fe i ( 8 AGiadship =P les ses W. | lare Wat 8 on 85 | Whole fore and aft ’ it 6.6] 10 Atta Eng ts If W y 77 | Whole «ail and square aai o| 4 At | Mareb 1 ta be aan ‘ 3 16 | Wholo fore and d square an 7 7a |o 6| 10 10. 12 mies. noting ho M os = . - 7 A malnaail, f ti Aan F § ar; Bam. abreast Bucrease’ ess in S| S78E ‘ 3 : : {x Rwater, ci de 5 = W F 1 | 13 1 Cape de Ga re a : P \ o| w 2 ) wo | 100 |6 6| 10 Frew Rites a 4 i 2 109 om jo a rT ¥r tubes in = . Bs = vs ws » os |o o| 1 At dinia ENE. 10 the tube = paaelliciiee Va 4 | vou owas | 2925 | o@ \6 0) 10 | o| x At 3 Civita V Boile arch 2 = = id Weigel mem So te surface ¢ l THE SATLING YACHT ®DEATRIX,” LYS, ON THE 5 War Daromet | te. J 3 ‘ g — lb caret} Under wha nal Area of Ball et. | stiNe | Mouth | s 3 ' D i T Oyealcn! 5 r Ai I? : Yards feet. | 234 js ex.| S250¥ Rous a sro | 3 6| 10 | 1 2 1 0 1 201 1200 0! w |o6| 0] and fino pleasant weather. a 4 8 >70 | 29 . a /6 o| 10! t and variable, with a cloudy sky an 8 2 oe | Whole sail to double rrefe | 2 I ? with mall of wind and rain. 7 Ww 2735 | 2080 | Whole sail without gallantopsail | Tait 6| 10 | Fresh breeze and fine weath 1 2760 | 29°00 Whole sail to three reefed roainsails . | 1000 t 43 | 60 | 6 0| 10 | Strong breeze and heavy ea; pitched away jibboom. 4 ¢ 0+ f w | o|6 0) 10 | Fresh and equally weather, " soos | 297 Whole fore and afte x | w |o o| 10 t d fine weather. | 1 | calm } 070 | gordo | 19 miles F, | Whole sail and gallant topaxi 26 | a1 |6 0) 10 | Tightnirsw with an easterly current of 12 miles. ses'| saa’ |l Us pla’ ne ; ri 5 |6 0) 10 | Light aire and calms, with an easterly current. Rex aly exo | zoos | 10 moles E. | Whole sail & sail,squaretopsail| 140 03 | 78 | 6 G| 10 | Light airs and calms, with foe pleasant weather. 3 2ACG pam. brought up in Gibraltar Bay, At 11 ao | $7 weigh at noon off Cabreta Point, ; = | Preah breeze East o| NE Fore, aft, and square aail 1050 6 0! 10 x} oe siw, [{Frab bres? | spon : : 5 ok and i shes oe Virat part, freab breezes latter, ight airs a 5 vs w. |{ Fresh brews? | Round ‘ F e P 1 1 10 | 1 p es Later, ight 9 |a719N,| N.62W. | Strong breeno’ | Norther o v. | s076 Whole fore avd aft to clone reefed 1060 to 508 6 6| 10 | Firvt part, light airs; Iatter part, stroog b 10 3 [33 ON,| N.48W. | Fresh breezes | o | NW , 2070 Single reefed fore and aft 600 to 800 » | 100 | 0 6| 10 | Fresh breesew nnd strong breetes, with fine weather i Pease Fresh be West “4 ove Whole fore and ~ 18s | 186 | 0 6] 10 | Frosh breezes, with » heary swell from the re \n Stravg breese “| 05 | o04 Whole wail to clone reefed 0 220 | 235 | 6] 10 | stroug br th Bear 47 v2.8. | | 1 Ww. | 00 | 2007 Cline wooo | 22s | 6} 10 | Strong broenes with beary rqualls ; ail balan NW i w. | svar | os7 Doob 000 0.850} 188 | 208 | a] 10 | Strong breedcs ant squalls weather, ‘ \ 4 F VAL O pan, caine. through tbe Needles Pasa | sx | y vir | 2 8501 J “brought up in Lymington Creek poe a — Norm —The dlisensions of the Hhealsls™ are ae follows —Length, M4. 30.5 dry Keel for founaze, FN. Sin.; breadth, 18. 1840.5 dept, YOM) | ut ON STEAMSHIP PERFORMANCE. 289 _ nished; also to those who are at present engaged in recording the per- _ formance of Her Majesty’s ships at sea, especially to the Royal Naval _ Engineers,—than whom a more thoroughly practical, highly intelligent, _ and yaluable body of scientific officers does not exist in this or any other country,—for the assistance they have so readily afforded. To the yarious Steamship Companies and Steamship Owners, and their Managers and Engineers, who have supplied returns. The Meetings of your Committee during the year have been held at Stafford ouse, through the kindness of his Grace the Duke of Sutherland, and have fully attended. thanks of the Association are again due to Mr. W. Smith, C.E., for uable aid. His offices have also been freely at the service of the tee. conclusion, your Committee believe that their labours have already been ductive of considerable advantage, that the objects with which they were jointed are being rapidly attained, and that, by continuing their labours, machinery they have succeeded, after considerable trouble, in organizing e productive of the utmost benefit to those engaged in steam navigation, i they have reason to believe that the future collection of the returns will & comparatively easy task. (Signed) SUTHERLAND, Chairman, _ _ Offices of the Committee, bury Street, Strand, London, W.C. ABLE 25.—WNotes on thé North German Lloyd Company’s Steamship > and her Performances on Trial, November 1st and 2nd, 1861*, ed by Messrs. Caird and Oo., of Greenock. sions, fc.—Length on load water-line, 330 ft.; beam, 42 ft.; depth, in. (four decks). Displacement at 202 ft. draught of water, 4400 tons, section at 204 do, =692 sq. ft. s.—The cylinders are 80 in. diameter; stroke, 42 in. Condenser—Has brass tubes 1 in. external diameter, with a surface of 6568 square feet. ater Pumps for supplying Condenser with Sea Water.—Two double- izontal pumps, 21 in. diameter, and a stroke of 18 in., which can be dto24in. It being found that this capacity of pump supplied too much ight holes, 13 diameter, were bored through each pump-piston. On trial, there was still sufficient water, and the pumps worked much without any noise. The sea-water was forced through the brass m condenser, and the steam was condensed on the external surface of ers.—There are sixteen furnaces in the four main boilers, with a grate face of 350 square feet, and a total heating surface of 9400 square feet. duxihary Boiler.—There are two furnaces, with a grate surface of 25 feet, and a heating surface of 460 square feet (not in use on trial- uperheater has a heating surface of 2000 square feet. resswre.—Safety-valveswere loaded to a pressure of 30 lbs. per square inch. he Propeller is three-bladed, 17 ft. diameter, with an increasing pitch ying from 29 to 32 ft. Lrip—On the 1st November, 1861, the ‘Hansa’ was tried be- 862 * The indicator diagrams of this vessel will be found in the Appendix. 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OPP ere | BS | so mn 8 Fe a mn Be Shad SBRessBs | ae | #8 | 's 5 rs a Pevesee| on | ee | = | * Es ce gRevec| Ee | Be fe | BEeeeee | | 3 S #S23vK0A BATINIISUOD 9914} UO ‘ADTAIOS BUIES OY} UT S[ASSIA : XR roo XIg WIM porvdurod sv ‘yorq pur eiIpuexery 07 uojdwEYjnog wor , UBIO, , oN} JO vag Je BOULUTIOZIA,g OY} JO sy[NsoI 94} SUIMOYS UN}OxT ‘hunduog woynhranyy wary 1D},UAW PUD MmNsSUuAT— BT ATLV, ON STEAMSHIP PERFORMANCE. 991 _ tween the Cloch and Cumbrae lights, a measured distance of 13-66 knots, which she accomplished in 61 minutes 50 seconds, equal to a speed of 13-25 knots per hour; revolutions from 47 to 50 per minute, with a steam-pres- sure in boilers varying from 26 to 29 Ibs. per square inch, Draught of water being 201 ft. Consumption of Coal, §c.—On November 2nd the ‘ Hansa’ was taken out again, and the steam kept at a pressure varying from 26 to 29 lbs. per Square inch, the revolutions of the engines ranging from 48 to 50 per minute; and it was found that 8616 Ibs. of coals, which were weighed on deck and lowered to the stoke-hole, kept the steam up at the pressure above named for 136 minutes. This is equal to a consumption of 3801 lbs. of coal per hour, or about 2lbs. per horse-power. The coals used were from the best Welsh pits (Aberdare). Lhe Temperature of the Steam in the boilers was 272°; on leaving super- heater, 340°; on entering cylinder, 280°. There being the facility for mixing the steam in this case, the steam from three boilers was supplied superheated; and the steam from the fourth passed direct to the cylinder. This was found to be necessary from the superheated steam being too dry for the packing and faces. the Appendix. The result of this will be seen from the diagrams in Feed-water —The temperature of feed-water about 80°, and the water to: make good the waste that occurred by blowing off steam, d&c., was supplied to the large boilers direct from the sea. ENGINEER’s Pocket Loa. The following are the particulars asked for in the “ Engineet’s Pocket Log” issued by the Committee on Steamship Performance, Engines by Running between and Length of yoyage—knots or statute miles. The steamer, Built by In the year Greatest speed under steam alone, in knots or statute miles. Average duration of voyage, deducting stoppages. Shortest time in which the voyage has been made, Longest time taken to perform the voyage. Kind of cargo carried. Tons of cargo by weight. Tons of cargo by measurement. Supply of coals taken. Is this for the double run? Consumption of coals on one voyage. Quality of coals used. Oil—gallons per 24 hours. Tallow—pounds per 24 hours. Number of engineers, Number of firemen. Number of trimmers. TABLE OF DISPLACEMENTS AND IMMERSED SECTIONS, FROM 1 FT. TO 28 FT, Tonnage, builder’s measurement. Tonnage, register. Weight of engines, Weight of boilers without water. Weight of water in boilers. Weight of screw. Weight of screw-shafts, Vessel—length over all. Beam. Depth. Length at load-line, . Breadth at ditto. Draught at ditto. tA The mean girth under water, as found by taking the mean of the girths, as measured on the “ body-plan” of the vessel, of the immersed parts of a series of equidistant frames or cross sections. Length of bows from “ dead flat.” Length of stern from “ dead flat.’ Numnber.of masts. How rigged. From top of bulwarks to load water-line, Length of engine-room. Length of boiler space. Length of vessel taken up as coal-holes in addition to above. : Distance from engine to screw propeller. Diameter of screw propellers. Average pitch. Pitch at circumference. Pitch at boss, i : u2 292 Length fore and aft at boss, Length fore and aft at point of blades. _ Greatest width of blade. Width of blade at boss. Number of blades. Screw is covered at aforesaid draught. Is it a common screw ? Is it a Griffith’s screw ? Are the blades curved ? State if there is anything peculiar in the configuration of the screw. Paddle-wheels—Diameter over floats. Length of floats. Breadth of floats. Thickness of floats. Number of floats. Centre of shaft above water-line. Dip of floats. Tf feathering floats. Diameter between centre of floats. Length of crank-arm on float. Centre of feathering excentric to centre of shaft. Ditto inches higher than centre of shaft, or inches lower than centre of shaft, Description of engines. Description of valves. If geared, what is the multiple of gearing ? Or number of teeth in wheel and ditto in pinion. Number of cylinders. Diameter of piston. Diameter of trunk. Length of stroke. Does trunk extend through both ends of cylinder ? Valves set to cut-off at Number of steam-ports at each end. Length of each. Breadth of each. Slide-valve travel. Steam-covyer at top. Steam-coyer at bottom. If a V on end of valve, its breadth. Ifa V on end of yalve, its depth. Steam lead at top. Steam lead at bottom. Exhaust-lap at top. Exhaust-lap at bottom. Exhaust-clearance at top. Exhaust-clearance at bottom. Is there link-motion ? Is there a separate expansion-valyve ? Grades of cut-off measured from beginning of stroke. Cut-off generally in use. (NorE.—If the engines are on the high- and low-pressure principle, fill up as much of the preceding as is applicable, stating which cylinder is referred to, and also fill up the following.) Description of compound engines. Number of high-pressure cylinders. Diameter of piston, REPORT—1862. Diameter of trunk, Length of stroke. Does trunk extend through ? Steam is cut off at from beginning. Exhaust opens at Exhaust shuts at Area of steam-ports. Number of low-pressure cylinders. Diameter of piston. Diameter of trunk. Length of stroke. Does trunk extend through ? Steam is admitted at Steam is cut off at Exhaust opens at Exhaust shuts at Area of steam-ports. (Notr.—As some of these quantities may be unknown, it will suffice to give particulars of valves, cover, lead, and travel, so that the cut-off can be found from them.) Valves of compound engines. Condensers —contents of each, including tubes, if any. Number of condensers Number of air-pumps, Diameter of air-pump. Diameter of its trunk, if any. Does trunk extend through ? Stroke of air-pump. Have the air-pumps foot-valves ? Are they double-acting ? Description of condenser. If surface condenser, can it be also used as a jet condenser ? Total number of tubes, Material. Thickness. Length of each between tube-plates. Inside diameter of tubes. Through what length of tubes does the water circulate ? Circulating-pumps, how many ? Are they double-acting ? Diameter of each. Diameter of trunk, if any. Length of stroke. Diameter of suction-pipe to each pump. Diameter of discharge-pipe from each pump. Diameter of suction-valye on ship’s side. How much is it opened ? Boilers—number of pieces. Total number of furnaces. Total length of firebars over ends. Width of each furnace. Thickness of bars at top. Width between bars at top. Total air-space through bars in one furnace. Area over bridges. Bottom of ash-pit to top of dead plate. Top of dead plate to crown of furnace at front. eee height of crown of furnace above ars. ON THE RAINFALL IN THE BRITISH ISLES. From back tube-plate to back of fire-box. From crown of furnace to top of fire-box. Number of air-holes in furnace fronts and door. Diameter of each. Is there a slide on these ? From top of fire-box to crown of boiler. From top of fire-box to top of steam-chest. Size of steam-chest. Steam room in each boiler in cubic fect, With water-level, inches above fire-box crown. Are the boilers dry-bottomed ? Number of tubes for each furnace, in height. Ditto in width. Ditto, left out for stays. Length of tubes. Inside diameter of tubes. Material. Chimney—diameter at uptake. Number of chimneys. Height from fire-bars to top of chimney. Superheater. Is there a superheater ? At what temperature is the steam used ? Temperature of smoke in chimney. Saltness of water in boilers. Is there a feed-heater ? Temperature of the feed water. Temperature of the hot-well. Vacuum maintained. What is the difference between the inches in the vacuum-gauge and the inches on the ship’s barometer taken at the same time ? Pressure of steam in boilers. When at full speed, what is the difference between the steam-gauges at the boilers and near the cylinders ? Is there a good command of steam ? Is there flame in the smoke-box ? Reyolutions of engines per minute. Please enclose indicator diagrams, and mark each one thus, or in some other intelligible way :— AT/G|S|V|R/K|D Cc Ship’s Rushby | Name Park and 14/23 45/12/13) 74 Date 298 which reads thus:—Aft engine top of piston; Grade of expansion 3; Steam- gauge 14; Vacuum-gauge 23; Revolu- tions of engine 45; Speed of vessel, in knots, per hour 12; Mean draught 18 ft.; Rushby Park Coals, per hour, 73 ewts. If the speed of vessel be given in statute miles, write M instead of K. Instead of AT write AB, FT, FB, as the case may be. If convenient, after V in- sert a which reads, Barometer 29 in. You are also requested to fill up as many lines of the following Tables as you have an opportunity of doing. TABLE OF PERFORMANCE UNDER TRIAL, UNDER STEAM ALONE,UNDER SAILALONE, AND UNDER STEAM AND SAIL COMBINED, Number of Trial. Date. Place. Ship’s course Direction of wind. Force of wind. State of sea. Duration of trials. Area of sail set. Description of sail set. Average speed per hour. Consumption of coal per hour. Quality of coal. Indicated horse-power. Diagrams enclosed, No. Draught of water. Pitch of screw. Screw covered. Grade of expansion. Steam-gauge. Vacuum-gauge. Barometer. Revolutions per minute. Number of furnaces at work. Nore.—Trials Nos. are under steam only, and Nos. under steam and sail combined, On the Fall of Rain in the British Isles during the Years 1860 and 1861. By G. J. Symons, M.B.M.S. Brrore entering on the consideration of the rainfall during the last two _ years, it will be well to offer a very few preliminary remarks on the various causes which affect the amount of rain collected, and also briefly to state in what manner the information given in the following Tables has been verified. _ The first requirement is obviously that the gauge should be rigorously accurate, and placed in a suitable position ; but it is equally obvious that the satisfactory fulfilment of these conditions can only be determined when every 294 REPORT—1862. gauge has been visited and tested by some person well acquainted with the subject, and provided with the necessary apparatus. This examination, involving as it does the testing of more than 500 instruments, scattered far and wide over the British Isles, from Galway on the west to Norwich on the east, from the Shetland Isles to Guernsey, cannot be completed for several years, and is, moreover, not indispensable; for adjacent stations will generally enable us to determine if any large error attaches to either the instrument or its position. For the present, then, it is a matter, not of choice, but necessity to take the readings as recorded by the observers ; and as the majority of the gauges already tested have borne the examination satisfactorily, it is presumed that this may be safely done. In the next place, it is almost needless to say, that unless the height of the rain-gauge above the ground and above sea-level be known, the records are not comparable with other stations; for every foot of elevation above the round is believed materially to diminish the amount collected, and every increase in the height above the sea-level to increase it. These particulars are therefore given wherever they are known; but the values must be re- ceived, subject to revision when the stations have been visited and the elevations accurately determined. It is, of course, almost impossible to secure perfect accuracy in such an extended series of returns as are combined in the following Tables, but I - believe they are very nearly perfect. The information was sent to me by the observers in reply to circulars issued at the close of each year; the returns, as received from them, were classified into counties and districts, examined, all errors being sent back for explanation, and copied into the following Tables, which have finally been checked against the observers’ MS. returns. The excessiye rainfall in the Lake District of England haying caused considerable interest, not to say incredulity, it may be well to add a few words in entire confirmation of the perfect veracity of the returns, The gauges were mostly erected in 1844 or 1845, by Dr. Miller of White- haven, whose known accuracy might alone be a sufficient guarantee; but, besides this, there is the personal experience of those who, like myself, have studied the rainfall of that district, as alone it can be properly studied, dwelling amid the mountains and watching the effect of each summit on the drifting clouds, whether driven by a heavy gale or merely floating on a gentle breeze. To make certain that the gauges were as accurate as when originally erected, I recently lent my friend Mr. G. H. Simmonds the necessary ap- paratus; he has carefully tested several of the gauges, and, so far as the calculations are concluded, we find them strictly accurate. The stations have been arranged on the plan employed in the Reports of the Registrars-General of England and Scotland, except that the ordinary county boundaries are maintained, and that the stations in each county are arranged in the order of latitude from south to north. In Ireland, the arrangement is merely according to latitude. : The counties comprised in each district are enumerated in the following List, so that the fall at any station may be referred to in the general Tables with the greatest facility. ENGLAND AND WALES. Division I. Middlesex.—Middlesex. » I. South-eastern Counties.—Surrey, Kent, Sussex, Hants, Berks. », III. South Midland Counties.—Hertford, Bucks, Oxford, North- ampton, Bedford, Cambridge. ; » IY. Eastern Counties.—Essex, Suffolk, Norfolk. ON THE RAINFALL IN THE BRITISH ISLES. 295 : Division y, | | - VI. ¥/ ” yil sae Hi ELD fs IX » x Division XII. wri qa 2 ARTY. : XV. P| eee it. VEL Ec RVI oat, ST ‘Division XX. South-western Counties.—Wilts, Dorset, Devon, Corn- wall, Somerset. West Midland Counties,—Gloucester, Hereford, Shrop- shire, Stafford, Worcester, Warwick. . North Midland Counties.—Leicester, Rutland, Lincoln, Notts, Derby. . North-western Counties.—Cheshire, Lancashire. . Yorkshire.—Yorkshire. . Northern Counties.—Durham, Northumberland, Cum- berland, Westmoreland. . Monmouthshire, Wales, and the Isles.—Monmouth, Gla- morgan, Pembroke, Cardigan, Anglesey, Carnarvon, Flint, Guernsey, Scilly, Man. ScorLanp. Southern Counties.—Wigtown, Kirkcudbright, Dumfries. South-eastern Counties.—Selkirk, Peebles, Berwick, Haddington, Edinburgh. South-western Counties.—Lanark, Ayr, Renfrew. West Midland Counties.—Stirling, Bute, Argyll. East Midland Counties.—-Kinross, Fife, Perth, Forfar. . North-eastern Counties.—Kincardine, Aberdeen, Elgin. . North-western Counties.—Ross, Inverness. . Northern Counties.—Sutherland, Orkney, Shetland. IRELAND, Treland.—All the Counties whence returns have been received. i The fall at a few of the stations has been laid down on the accompanying Map, with the double object of illustrating the relative fall in different parts of the British Isles, and the relation, in each locality, between the fall in 1860 and 1861. This has been done in the following manner :—Darkly shaded dises uniformly represent the fall in 1861; lightly shaded, that in 1860. The radii of the circles are half the scale given on the Map; the diameters therefore increase as the fall; and hence the increased diameter of the circles immediately points out the places of heaviest fall. The relative frequency _ and extent to which either the darkly or lightly shaded circles extend beyond the others shows which year had the heavier fall; and the breadth of the _ annulus shows by how much it exceeded the other. _ Inselecting the stations for insertion in the Map, preference was given to those less than 200 feet above mean sea-level, and at which the gauge was _ within a few feet of the surface of the ground. It was not found consistent with good geographical distribution to adhere rigidly to these requirements the general Tables. The fact, however, that the mean height of the selected gauges above the ground is, in England, 1 ft. 4 in.; in Scotland, 1 ft. 11 in. ; i in every case, but the exact height may be readily ascertained by reference to ~ and in Ireland (omitting Cork), 7 ft. 7 in.; and above the sea, 131,177, and ment of these conditions. The paucity of stations in Ireland necessitated the { 108 ft. respectively, shows that a near approach has been made to the fulfil- - + use of rather elevated gauges; in the case of Cork, the Map shows the fall _ at the ground computed from the fall observed 50 ft. above it, as otherwise it would not have been comparable. It is remarkable, and perhaps suggestive, that in 1860 the excess in - South Britain was counterbalanced by a deficiency in Scotland; and that in 296 REPORT—1862. 1861 the equipoise was maintained, but in the reverse order, England being comparatively dry, and Scotland (especially the western coast) subject to almost unprecedented rains. It is also most noteworthy that, if the returns from all the stations in England, Scotland, and Ireland are combined, the fall is nearly identical in the two years. In 1860, the average fall at 390 stations was 39-784 inches; and in 1861, 38-466 inches. The singularity of this result is fully shown by Table I., which gives the average fall in each district for each year, and the excess or defect in each district of 1861 over 1860. Tasxe I.—Average fall of Rain in 1860 and 1861, and difference between the two years. Number Division. of 1860. 1861. |1861-1860. Stations. in. in. in. England:— I. Middlesex ................00005 7 32°553 | 20°763 | —11°790 > II. South-eastern Counties ...| 46 36°710 | 25°913 | —10°797 i III. South Midland Counties ...| 20 go'22r | 21°505 | — 8°716 + IV. Eastern Counties ............ 16 31912 | 20411 | —II'Sor c V. South-western Counties ...| 48 46:040 | 34°403 | —11°637 53 VI. West Midland Counties ...|. 22 34°259 | 25°838 | — 8-421 x, VII. North Midland Counties...) 32 32°059 | 23°598 | — 8'461 ” VIII. North-western Counties ... 31 43°081 | 39448 | — 3°633 YY TX; Yorkshire sive. .e...c8ss 32 38°895 | 30°680 | — 8215 r X. Northern Counties ......... 24 50°941 | 52°357 | + 1°416 = XI. Monmouthshire, Wales, &c. 6 48550 | 41110 | — 7°440 Scotland :—XII. Southern Counties............ 4 49°075 | 55087 | + G6:o12 Fe XIII. South-eastern Counties...... 12 30°332 | 30°862 | + 0530 Sp XIV. South-western Counties ... 16 40°573 | 52°701 | +12°128 < XV. West Midland Counties ... 12 52°278 | 63°377 | -+-11'099 is XVI. East Midland Counties ...} 30 42°980 | 50°535 | + 7°555 +) XVII. North-eastern Counties...... 8 37°799 | 35°880 | — I'g10 »5 XVIII. North-western Counties ... 7 44°623 | 67°306 | +22°683 ¥ XIX. Northern Counties ......... 5 34°128 | 38°746 | + 4°618 Treland : — XX. Ireland ...........c0ceceeeeeee- 12 38°692 | 38°813 | + otr2z General average ............... 390 39°784 | 38466 | — 1°318 Hmnpland. pase -seestasns ook 284 38°656 | 307548 | — 8108 PCOUANG sacar steve sarees sees 94 41°472 | 49°312 | + 7°840 relanidh ies. Chasen seeceo. 12 38°692 | 38°813 | + otr21 The next point for consideration is the relation which subsists between the fall in the two years, 1860 and 1861, and the average of a long series of years. A large number of the gauges having only been in use for ten or Tasxe II.—Difference between mean Rainfall, as obtained from long series of years, and from the ten years, 1850 to 1859. . Total | Mean of | Mean of p Division.| Name of Station, 2 prige Pt number | the whole | ten years, ii baie cra koi years.| period. | 1850-59, | Per cen inches. inches. II. | Greenwich............... 1815-61 47 25°42 23°16 9 V. | Exeter, St. Thomas’s...) 1814-61 48 32°80 3115 5 Vile | Orletong- Avie. ..22. 02 1831-61 31 29°18 28°82 I VIII. | Bolton-le-Moors ...... 1831-61 31 46°92 44°10 6 TX al elallitax vt osesenceee yore 1829-61 33 32°38 30°71 5 XV. | Rothesay ............... 1800-61 62 48°31 45°97 5 MoT ML AQ paavib uy NOT \X FUAOGS () JSOMP LOLs A DT “sU0wUAs*p 7 Ag rw. “7 T99T ie Appin O98T 22 TRL Mp Moys sosrp papvys Apybry s7TymUuLOOT 08 O8 OL 09 OF OF OF OF OT O + ~— tt SAIPULVIP LOL apOIy ; le OTH mor ne ae Sr spunea ay wo TEED ug et rig AMOS Koveaag one] 19. oor ME TEL np Mone ene pene rrynn.cot ov ot ra yey Poe gy 207 oe orovy Abacus PIN 4 WRRAMAAS Yo ered oy odie 9 pruaresdas oe oeny me “T98LY OORT “a oH: VEAL % Me PY, ee D = a nee | | a : ON THE RAINFALL IN THE BRITISH ISLES. 297 fifteen years, it was found necessary to adopt, as a standard of comparison, | be eel the fall during the ten years, 1850 to 1859. The fall during this period appears from Table II. to be very suitable for the purpose, as the amount during it was generally within 5 per cent. of the average fall during the last fifty years. Tables III. and IV. give the results obtained by comparing the fall in 1860 and 1861 with this standard, and show (1) that at almost every station the fall in the two years was greater than the average, (2) that the excess was slight in Mid-England, larger in the South-west of England, the South-west of Scotland, the West of Ireland, and largest of all in the English Lake District. Tarte I11.—Excess of the Mean Rainfall for 1860 and 1861, above the average of the ten years, 1850-1859. Division. Station. Excess. || Division. Station. Excess. Chiswick VIII. | Stonyhurst Enfield Coniston IX. | Redmires Standedge Well Head Southampton Abbott’s Ann Patrington Wheldrake Middleton fork Bishopwearmouth Seathwaite Baverstock ..........0.. weak GOodamMoor .....cccecceeee Tavistock Exeter, St. Thomas’s Exeter Institution Castle Toward Kilmory Pittenweem ... Deanston Castle Newe Sandwick Bressay IEEDY .c0-.ss=0ace Caccvccsan: Liverpool Bolton-le-Moors Preston (Howick) Preston(House of Correc- TION )) Seessecscss sescsencee O BNOWH HAP RNIN DHAUN Tanre TV.—Average Excess in each Division. Division. | Excess. || Division. | Excess. || Division. | Excess. || Division. | Excess. inches. inches. inches. inches. I. +3'00 Vas + 3°67 > Ra arene XVI. +2733 Il. +2°40 VII. + roo 3.2 1 ee ae XVII. +7°00 Ii. +1°50 || VIII. + 7oo|} XIII. ooo || XVIII. |... Vis +300 IX, + 3°67 XIV. +2°50 XIX. +3°co Vy. +4'88 Xx. -++18°00 XV. +6°00 XX, +825 298 REPORT—1862. TABLES OF MONTHLY RAI . ENGLAND AND WALES. Division I.—Minpresex, Mippissex, ! I 1860. Chiswick. | Whitehall. | Gnildhall. | Guildhall. | ®%0hn’s | Camden Wet oP Se ee ae =. sage | Ground..|. di: 6 ft. 0 in, |7 ft. 0in. | ft. 0 im. | Of. 4 in, | ewe. (Sea-ievel.| oo... 51 ft. 123 ft. | 161 ft. | 100 ft. above in. in in. in. ARUARY 5) 0033s scenersseas 2°18 1°74. 1°61 4°34 I ve | HODrary ..... | @*senpies 2°07 2°34 2°64, 75 1°96 boy Xo nn ere eee 1°47 1°27 2°49 1°56 24 BGO | eweseeeee | teers sees 3°88 4°01 3:11 3°14 37a BR | cwecreese | oeep sees 5°85 5°43 Bar 7'02 719 BM cen. | ssep'senes 2°05 1°82 2°49 2°40 3°42 4°40 4°86 3°87 5°28 \ 7:34 { 4°31 4°47 5°26 3°10 2°90 2°25 2°66 b foe) 3°45 4°02 160 163 LI 1°68 2°03 2°62 2°40 2°75 2°60 2°80 2°36 2°76 2°78 3°01 3°54. 2°39 2°40 2°35 1°86 2°70 2°53 2°40 tp 2°69 ATO | wweeeeeee | cee eenees 34°37 34°57 34°75 38°14 40°O7 Division I1.—Sourn-Easrern Counties (continued). Kent. Sussmx. Hunton Linton : ; Welling, Greenwich Aldwick, Park, Tunbridge. | Maidstone. |RexleyHeath.| Observatory.|| Bognor. Stapleberst. Staplehurst. 0 ft. 8 in. | 0 ft.6 in. | O ft. Oin. | 4 ft. Oin. | 6 ft. 0 in. 0 ft. 5 in. || 0 ft. 0 in, Peed 200 ft. ? 125 ft. 60 ft. 150 ft.? 155 ft. sens in. in. in. in. in. in. in. 3°37 2°87 2°04 2°97 1°60 180 . 2°23 1°16 1°40 37 1°60 105 I"Io 764 1°93 2°61 2°55 2°71 1°89 1°90 102 2°52 2°34. 2°75 3°04. I'24 1°00 2°20 *03 3raz 2°79 3582 by ange 3°13 453 5°09 5°06 5°36 5°63 580 =| 5"60 r7i 2°07 2°49 1°58 2°53 2°80 2°65 2°80 3°54 3°52 3°69 3°25 3°70 3°23 259 | 3°36 2°48 2°89 2°48 3°10 2°30 1°60 qi 175 1°63 1'50 1°60 1°96 2°64 2°67 2°44 2°59 2°36 2°50 2°24. 2°40 2°38 2°39 2°27 2°10 2°80 2°20 30°38 33°66 31°43 33°65 28°72 32°00 29°40 300 REPORT—1862. ENGLAND AND WALES. Division IT.—Sovrn-Easrern Covuntizs (continued). Sussex (continued). Thorney Chichester | Shopwyke, Glynde, | Bleak Hou 1860. Worthing. ome Museum. | Chichester. Lewes. Hastings Feeieht OF | Ground... 0 ft. Oin. | Oft. 6 in. | Of. Gin. | 1f.3in. | a. 4 ft. 0 ir boro. { Sea-level.| 10 ft. 10 ft. 20 ft. (ee me ee 80 ft. above : in. in. in in. in in RIAUUALY: socepcscassssscess 4°66 2°25 3°71 3°58 5°08 4°36 Hebruary 62. csescereeee "65 °78 95 gt 1°29 76 IM Eate li veisscn ts aesen sete e= 1°70 1°74 2°16 2°01 2°08 2°23 PADIM piccecrevresednsen ses 1°82 1°70 big i rns 1°98 I'95 ERY mee sastesses cater s= 3°41 2°81 3°55 3°85 3°65 3°46 SIMIC cc coneseeasenecuec=te 4°98 611 5°07 5°00 4°78 3°15 STUY yeaa cebvecec borates pa 1°84, 3°18 3°43 2°90 3°50 2°72 PAUIBUBE ..<50ccccecnsdaces 3°70 3°10 3°87 4°21 541 3°49 Heplember ......sccs-<0.- 3°02 3°30 4°17 3°75 4°53 4°92 MOCEGHEP. wscpcsccdue| “Hara” (O* ereris 9 thas) me Exeter. y ih =e , A aie Ground ..| 0 ft. 0 in. | 40 ft. Oin.| 13 ft. 7 in. | 20 ft. 0 in.| 3ft. Oin. | 0 #t. 6 in. above | Sea-level.| 160 ft. 170 ft. 155 ft. 160 ft. 50 ft. 200 ft. 27 in. in. in. in. in. in January, ..Uoc..- ara-<:|h om eass 3°98 AD Ole =. bSp. 5711 424 Hebroaiy *f.. <- sates iio eee 87 190) BIE eaten te: 1°36 124 March) \-.csoo-ssqueaeeerl icee mee 2°70 R700 WMP scree: 3°48 315 April sc; fectieccensesuceee atin orem 1°74 LR he os aoenth 1°25 2°14 ILS depp asecrrs-eel|\ yee 2°88 Cy te | nee Se 4°57 3°38 June 5. nc-teveeeseoeee ss haa 6°92 6°48 7°09 8°04. 614 DULY ccseecueeee eeeaee elt eee 1°63 "72 1°65 1°90 1°84. ANT ETE SS orton nas 3°86 3°55 3°32 3°33 2°26 467 September ......... a 1°95 1°65 1°56 1°75 1°78 3260 a Me sesoseree aise ae 122 rab 1B 76u Tee “ber: oh 3°33 3°60 3°96 3°53 4°68 3°07 December. j2s.-.seae --| 7°40 5°52 5°26 4°58 6°13 6"10 SERIA 5 ssicccinmagn | aes eee 36°26 | 36°08 | Beare 42°17 | 453 @ POPS TT Ve Torquay. 1 ft. O in. 150 ft. in. 4°56 I°0o 2°11 I'03 Hoar 6°67 e °59 3°21 2°48 1°48 4°06 45°96 36°36 ON THE RAINFALL IN THE BRITISH ISLES, ENGLAND AND WALES. Division V.—Sourn-Westurn Counties (continued). Drvonsuire (continued). Highwick, Newton Dartmoor. Bushel. 1 ft. 6 in. | 40 ft. O in, 300 ft.? 1580 ft. in. in. 6"10 773 1°42 1°94 3°78 4°58 1°63 1°16 4°27 759 8°87 10°36 1°53 3:12 4°40 6°89 2°37 5°23 2°29 3°93 4°74 5°55 6°62 5°80 48°02 63°88 Teignmouth. 1 ft. 1 in. 60 ft. Tiverton. 3°79 8°92 2°38 6°32 3°49 3°38 2°46 9°79? . 55°41? Huntsham Court. 584 ft. in. 7°08 2°87 4°13 3712 5°21 10°52 3°24. 8°17 3°ia 3°99 3°45 7°42 62°32 1 ft. lin. | 3 ft. O in. DevonsuireE (continued). Castle Hill, South Molton. 160 ft. 57°46 Division V.—Sourn- Western Countixs (continued). * Observations discontinued, position being unfayourable, 307 Teignmouth. ieee Dawlish. ria 0 ft. 3 in. | 45 ft. Oin.| O ft, 8 in. | O ft. 6 in, 25 ft. 298 ft. 62 ft. 100 ft. in. in. in. in. 3°85 6°44 3°74 692 12 1°49 1°24 1°63 3°27 2°75 3°88 4°72 1°26 1°57 2:22 1°34. 2°05 4°48 2°78 3°96 8°27 $10 9°35 9°09 198 2°84 1°33 1°94 3°69 6-40 2°80 5°06 2°50 2°41 3°67 1'99 2°04, 2°38 1°66 2°53 2°50 3°42 2°00 5°62 7°62 5°71 6°21 4°52 40°35 47°99 40°88 49°82 | CoRNWALL. Tehidy Barnstaple. |, Helston, Penzance. Park, | Redruth. 0 ft. 6 in. || 5 ft. Oin. | 3 ft. 0 in. | O ft. O in. 31 ft. 110 ft. 94 ft. 100 ft. in. in. in. in, 5°29 6°04. 7°83 7°25 1°50 1°74. 1°89 1°80 4°01 2°46 3°02 2°40 2°76 Ii7 VI4 1700 3°42 3°69 3°63 4°20 7°00 4°87 5700 5°75 3°64. 1°86 1°68 1°80 7°89 4°43 5°29 4°68 3°54 2°78 3°52 3710 4°01 2°71 3°86 3°40 2°64 4°24 3°99 5°25 4°44, 6°97 8°40 8°00 50°14 42°96 49°25 48°63 x2 308 REPORT—1862. ENGLAND AND WALES. Division V.—Sourn-Wesrern Counties (continued). Cornwat (continued). 1860. Height of Rain-gauge Ground.. as Sea-level. tenn een ween weeeeee seat eee nereseneres teen e teen ewes eeeeses PAUIGRISES 5. dd. ~00- cote os September October Truro. 40 ft. O in. 56 ft. Sipe |fome "sk" ae Div. V.—S.-W. Co. (cont.). Somerset (continued). 1860. Aten eee een reee Height of Rain-gauge above Ground.. Sea-level. January ee eee ere Senter eeteeeae Bath. 50 ft. O in. 150 ft. GLOUCESTER. Tngstne es Clifton Clifton. Cirencester. Pie iiee 56 ft. 0 in.| O ft. 6 in. | 50 ft. Oin. | 1 ft. Oin. | 3 ft. 6 in. 98 ft. 192 ft 242 ft. 446 ft. 50 ft.? — in. | in. in. in. in. i 6"10 4°94 4°27 4°52 302 1°41 “99 “74 1°20 “49 3°05 2°92 2°34 0 227 "99 @ 2°46 1°69 1°32 I'00 *g90 3°17 3°54 3°21 3°85 2°69 7°22 7°10 6°44 5792 499 2°34. 1°87 1°63 1°75 oi 3 | 6°04 5°68 5°15 5°03 3°74 2°30 2°43 2°22 G46 2°66 3°39 3°03 2°68 2°00 1°33 2°56 2°83 2°33 3700 2°3r 2°92 3°78 3°19 3°05 2°22 42°96 40°80 35°52 36°94 =| © 27°99 Bodmin. | “pngaga™ 3 ft. 0 in. | 3 ft. O in. 300 ft. 800 ft. in. in. 776 7°68 1°73 2°13 4°17 520 1°55 2°09 3°47 5°14. 8°49 10°70 2°22 2°98 7°58 917 3°60 4°23 3°51 5°08 3°94 4°40 3°31 8°25 56°33 67°05 | Pencarrow, Bodmin. 4 ft. O in. 230 ft. in. 6°68 2°48 3°91 1°57 3°02 7°43 2°58 6°98 4°74 3°44 4°93 3°85 51°61 Treharrock House, Wadebridge. 3 ft. O in. 200 ft. ? in. 5°57 149 3°04. 1°38 2°90 6°03 2°86 6°26 3°91 3°38 3°39 598 46°14 St. Petroc Minor, Padstow. 0 ft. 2 in. | 96 ft. | in. 5°22 1°47 3°59 108 3°24 5°89 3°04, 5°52 3°18 3°89 4°52 6°86 47°40 Division VI.—Westr Mripranp Covntizs. ENGLAND AND WALES. Gloucester. Taunton. 1 ft. 3 in. 50 ft. Long Sutton. O ft. O in. 170 ft.? ON THE RAINFALL IN THE BRITISH ISLES, Frome (North Hill). 0 ft. 3 in. Division V.—Sovrn-Western Counties (continued). 309 Mells, Frome. 8 ft. 0 in. 300 ft. in. 4°89 1°50 2°34. 2°93 3°24 8°65 2°42 SoMERSET. Bridgewater. Street. 6 ft. 6 in. | 5 ft. 0 in 45 ft. 70 ft. ? in. in. 1°25 4°67 1°32 793 1°32 2°55 2°09 1°80 3°22 3°50 5°65 5°38 2°60 3°11 33 4oo 1°30 2°05 145 2°42 3°00 2°46 2°78 3°28 29°53 36°15 Twigworth, Gloucester. 3 ft. 6 in. 50 ft. SHROPSHIRE. Haught itti Rocklands. peg ‘Hall, Shrewsbury. iipeae er, | : Shifnall. ’ son birt 0 ft.6in. | 4ft.6in. | 4ft.4in. | 5 ft. 0 in. Seeicenesn 1000 ft. ? 450 ft. 192 ft. Sscdeo ic in. ‘in. in. in. in. 4°75 3°94 2°61 1°00 4°90 66 1°82 °38 2°20 1'02 3°02 1°46 2°12 2°80 a7 1°37 2°00 *78 *60 1°45 3°27 2:31 2°87 1°00 4°04. 712 7°04 5°45 1°10 6°51 1°70 1°97 2°59 rs 1°88 4°95 5°86 5°78 3°15 4°59 2°35 2°82 1°74 4°10 1°37 27 1°63 1°59 1°40 2°35 3°52 157 1°63 1°50 2°43 5°39 5°45 3°69 "80? 4°13 40°77 37°87 31°23 20°80? | 37°90 Hengoed, Oswestry. 4 ft. 8 in. eoaweeeee 45°51 | 310 REPORT—1862. ENGLAND AND WALES. Division VI.—West.Miptanp Countiss (continued). STAFFORD. WonrcEstTEr. Warwick. | Orleton, Stoneleigh at ) 1860. Leek. Worcester. | Tenbury. poms Rugby. Biswinehs : pacieht of | Ground... 25 ft. Oin.|| sss. O ft. 9in. | Off. Sin. | 2 ft. 4in. | 4 ft 6 in. Pecer tp bertevel,| cesses |] Sate oe 200nn. : |] Geatea 315 ft. | 340 ft. above in in. in. in in in. OMNUAMY, -'3.30>e ne qversw =. 4°50 2°79 3°45 2°25 2°56 3°78 IH DYUATY (in... tee -See-- | 2°30 57 "4 |) « Io2 84 81 Marehe ..5t2.2..0sreees ih 4583 I'92 og | Il aang 1°89 2°01 AULA sec tens os tkteeeres ae 87 1°20 E232 58 121 1°08 INTAES: fu. acaenee'c dieemenes | 4°I4. 3°94 2°17 3°60 2°96 2°40 pUNOC Se ...- bc. Poe | 636 || 9g*go0 mos 5°70 5°36 6:26 Afri hy oie aoe Pee 2°62 aT Lory, |, seiko 1°40 1°45 VAUBUBE ...ssc.ccaesseoucs 4°88 4°70 S77 ill varae 3716 6°39 September ........1.02+5. 3°02 2°81 2°53 | 2°58 2°51 2°44 CLONER 5s cts< efgx |< 264. 2°56 December «......J:<-5--- | 2°35 | 2°13 2°84 1°90 1°99 Ratals ‘-..<2-.285< | 36°21 | 34°03 38°64. 48°61 46°84. 7 ON THE RAINFALL IN THE BRITISH ISLES. 313 4 ENGLAND AND WALES, Division VII.—Norra Mipranp Countizs (continued). ‘ DERBYSHIRE. E Darby. Chatsworth Combs Combs Chapel-en- Gardens. || Chesterfield. | Norwood. Moss. Reservoir. le-Frith, | Woodhead. 5 ft. O in. | 6 ft. Oin. | 3 ft. Gin. | 3 ft. 6 in. | 3 ft. 6 in. | 3 ft. Gin. | 3 ft. Bin. | 3 ft. 6 in. 179 ft. 404 ft. 248 ft. 238 ft. 1669 ft. 710 ft. 965 ft. 939 ft. in. in, in. in. in. in. in. in. BOT | cvteesaee 4°16 3°59 4°39 5°28 4°34 5°46 te), .2u823.. "64 "63 "93 a7 1°16 2°89 ol ae 2°36 1°97 3°96 7°24. 5°62 8:28 *76 1'27 "69 “31 1°46 1°87 1°50 Zr 3°70 1°78 3°35 WOg 410 4°29 3°70 5°32 5721 4°69 4°26 3°48 9°23 7°00 6:02 1122 1°89 "87 1°20 1°85 3°60 3°93 3°39 3°38 6-23 5°68 4°45 3°94 8-88 714 6°34 6°72 254, 2°60 2°05 2°02 3°52 3°27 2°68 3°81 2°52 3°13 1'72 2°05 6°15 6°02 4°93 7°30 51 3°05 2°30 2°70 4°01 3°51 2°91 Gor 2°52. 2°60 2°36 2°63 77 3°45 2°40 2°85 SE Pe cere 29°54 27°66 53°00 54°17 44°99 66°35 Division VIII.—Norta- Western Covuntiss (continued). 4 Cusine (continued). LANCASHIRE. s ack H use,| Hill End, | Matley’s | Observatory,| Sandfleld Old Sale, fai ale Top. Mottram. woes Newton. Eweriook ae eh Peet tor Manchester. 3 ft. 6 in, | 3 ft. 6 in. | 3 ft. 6 in. || 30 ft. Oin.| 2 ft. Qin. | 3 ft. Oin. | 2 ft. 3 in. 680 ft. 399 ft, 396 ft. patie |) tae. 106 ft. 134 ft. in. in. in. in. in. in. in. SB S000: 2°97 2°35 1'70 3°26 3°58 3°38 Racer 48 *60 *50 Itt 87 "90 4°52 4°57 3°50 1°86 2°98 3°47 3°09 153 1°34 1°29 77 “71 31 m05 3°99 3°99 2°41 1°88 2°78 2°69 2°53 761 6°47 6°79 3°13 5°38 6:04 6-46 2°99 2°78 2°16 1°54. 1°80 1°66 2°02 5°29 5712 4°48 6°03 6°50 5°17 5°45 271 2°76 2°18 a7 2°17 2°38 2°42 4°50 4°26 4°07 2°44 3°82 3°43 3°34 2°67 2°39 2°51 118 1°95 211 2°38 1°69 1°80 1°60 174 2°94 2°93 3°22 seteenee 38°93 33°94 24°53 35°40 3614 36°24 B14 oe: REPORT—1862, ~~ ENGLAND AND WALES. Division VIII.—Norra-Westenn Counties (continued). Lancasuire (continued). Market-st., | Piccadilly, e Waterhouses, The Folds, Belmont, 1860. Mancha Masse letes: Fairfield. Oldham. Rokaurle- Bolton. rr | er a | ET Height of | qround..| 3 ft. 0 in. | 46 ft. Oin.| 6 ft. O in, | 3 ft. 6 in. | 2 ft. Oin. | 0 ft. 0 in. ave Pne. { Sea-level.| 1... . | 194ft | 312%. | 345 ft. | 200f. | 800ft. JAWUARY oa pscesedebederces sbeery Marely ~ ..cs.cccdedsdeces» AYU sc. 050 scostedderen: WT Oe enter ecce OUBE Klee decor eeeeerss DORNER. vv goin ne Gee ees: PRU BUA, 5 tno0evaugetesse= September WGEABEN a decses Gpideiess November .... December Totals Division VIII.—NorrH-Western Counrttizs (continued). LAncasHireE (continued). | 1860. 4 Bleasdale, Caton, Holker, | Wra Castle,| Coniston : Garstang. Lancaster. Cartmel. | Windermere. Park. Sheffield. qicisht of | Ground. 4 ft. 6 im. | 2 ft. 4 in, | 4 ft. 8 in, | 4 ft. 9 in, |4 ft, 11 im. 8 ft 6 i above. { Seaclevel.| 600 ft. 120 ft. | 155 ft. 250 ft. 154 ft. 188 in. DANUALY 3°10 2°80 39 2°65 oar "20 May ocn.s.0..0sssponsneee 3°20 6°20 1°43 5°45 1°60 1°30 GIRL Og isle. ce ono saat 8°50 9°40 3°69 9°55 5710 4°50 DULY. ocp.-.cseseeceseneees 5°70 2°10 2°49 2°80 2°85 2°70 IAUIPUBE... «..00<0.senepansar 6:20 7°50 2°74. 6°70 3°50 3°20 September ..........-.0.- 2°30 5°80 3°33 3°95 1°09 *90 RO CLOBER) on a.e-00>sanpseeire 5°70 | 14°10 2°98 11°06 4°30 3°30 NOVEMBER 25.0.0 onsngs ss 2°70 4°30 2°39 4°38 4°30 415 December ............-.- 6°70 | 5°80 3°18 4°25 3°90 4°00 Matale .s.ccascngs 53°80 | 95°20 | 28°70 75°64 37°85 33°55 ON THE RAINFALL IN THE BRITISH ISLES, SCOTLAND. Division XVI,—Easr Mrpranp Countizs (continued), Firs continued). Perri. Pittenweem. Aberfoyle. Ledard. eepanrcee, Deanston. |Ben Lomond. Britas of re Sft.Oin. | Oft.6in. | Oft.Gin. | Oft. 4in. | Oft. Oin. | 0 ft. Gin. | Oft. Gin. | Oft. Oin. 75 ft. 60 ft. 1500 ft. 100 ft. 120 ft. ? 1800 ft. 270 ft. 150 ft. ? in. in. in. in. in. in. in. in. 3°93 5°20 3°40 3°60 3°70 9°50 8°50 4°00 108 180 2°10 |} tad 2°95 0700 4°10 5710 2°48 4°40 1°50 3°00 3°90 12°70 6'20 4°80 87 "20 2°00 *60 65 2°00 1°90 "70 95 3°40 5°50 1°55 3°15 8-00 3°79 3°30 3°35 6°80 14°00 435 3°55 II'0o 8*10 5°50 roo “40 400 2°40 2°85 440 3°20 2°55 2°04 3°80 9°40 4°10 5°40 10°40 5°20 5710 “48 3°20 6°40 1°30 | “70 5°60 3°30 2°00 2°55 6°20 10°50 4°30 4°99 14°70 8:00 5°60 3°30 2°10 640 320 06©6| «= 280 3°60 2°90 3°20 4°33 2°90 8-30 3°70 2°75 160 479° 3°25 | 27°36 40°40 73°50 34°10 37°30 83°50 59°80 4510 Division XVI.—Easr Mipranp Covnrtzs (continued). Perri (continued). Forrar. : ~ ame Reonk' Palace. Teen Stanley. Aree Dundee. Barry. Craigton. ft. 3in. | 2 ft. Gin. | Oft. 3in. | 1ft.Oin. | Oft. Gin. || Oft.Oin. | Oft. 3in. | Oft. Oin. 66 ft. 80 ft.? 792 ft. 200 ft. 300 ft. 60 ft. 35 ft. 440 ft. in. in. in. in. in. in. in. in. 3°55 2°90 8'20 2°30 2°90 3°75 3°03 3°50 2°17 1°00 7°90 2°20 *g0 1°28 “94 1'73 2°74 2°88 8°30 2°50 2°10 1°93 2°23 2°55 "56 22 1'20 *38 *30 S64 "41 "80 152 “98 4°90 1°35 1°70 1"'IO "13 1°05 711 5°50 6-40 6°37 5°40 5°65 4°38 5°30 3°59 2°67 2°70 3°13 3°10 3°10 2°62 3°80 3°45 1°32 6°60 2°50 3°10 3°00 2°65 - 3700 1°16 “80 4°70 66 1°80 85 1°50 1°co 3°14 2°00 15°80 1°50 1°50 2°00 2°43 2°67 m5 | 3°23 3°59 3°40 4°90 5°20 4°63 6°37 } 4°64 5°25 2°50 482 | 4°80 6°52 3°85 5°80 |— | eee = al 37°88 28°75 | 72°70 Zit 32°50 34°71 28°85 37°57 826 +. 7 > REPORT—1862, > - a SCOTLAND. Division XVI.—Easz Mipianp Countizs (continued), Forrar (continued). KINCARDINE 1860. Kettins, | Hillhead: | Seichen, | Arbroath, | 2useum, Montrose. Brechin. picight of | Ground... 1 ft. in. | 0 ft. 0 in, | Ot. 0 in, | 2 ft. 0 in, 0 ft. 6 in, bee | Sealevel.| 218 ft. | 500f%. | 550ft. | 65 ft. 210 ft. above in. in in. in in. JADUALY ...002+-wageene 0. 3°41 3°48 3°51 3°41 3°60 Bebyuary |,..>-= 2°31 2°50 2°65 1°96 2°70 PATINEL. Soo duce ss xa. #2 "45 84 93 78 1°20 IN ai o's a ss'v i ahitegn ss < I'21 1°17 1°61 1°18 2°30 UNO yea tates ve Bay nae se 6°77 5°68 6:00 4°75 610 PONS Js «ose wus ettdeapeas > 3°12 3°00 3°00 1°87 3°10 PURO. «sles ca's adap vans 3°48 3°07 3725 2°96 4°10 September ......csecess-. 35 95 gt 1°04 “50 Oaiabar . is... genes 2°16 2°85 2°80 2°51 2°80 November .......¢..2.++ 512 6°45 6°70 4°33 580 December .........+.-++: 6:07 5°68 5°77 4°64 6°60? Motals dase: 36°39 37°43 38°80 30°48 41°50? | Division XVIII.—Norra-Wesrern Counties, Ross. | INVERNESS. | 1860 Stornoway, Beaufort Culloden Portree, Raasay Isle of Lewes. Tale of] a. | Castle. House. Isle of Skye. House. Reiners | Gromdy 0 ft. 3in; | Of. Gin, | 44. 6 in, | 34. Oin, | Of. 1m, | 4f, Om shows Sea-level.| 70 ft. 15 ft. 40 ft. 104 ft, 60 ft, 80 ft, in in in. in. in in 2°79 1°90 2°03 1°30 9°95 3°90 2°15 180 2°25 122 II'05 4°40 5°80 4°00 4°64 3°14. I1'75 6"g0 2°60 68 1'24 1°50 5°20 2°40 4°10 7o "92 1'00 5°56 4°15 2°44 1°88 3°19 2718 3°96 3°25 1°46 3°90 1°85 181 2°77 2°65 5°03 3°28 3°08 2°93 4°15 4°40 3°98 4°80 1°20 1°23 8:20 6°50 3°44. 3°40 4°67 2°46 17°86 13°70 2°30 3°90 1°41 1°53 2°86 2°40 December )....3.02<.-<3- 171 2°13 "96 121 5°58 2°95 in ON THE RAINFALL IN THE BRITISH ISLEs. 327 SCOTLAND. Division XVII,—Norra-Easrern Counties (continued). Kincarpine (continued). ABERDEEN, Exer. rien | Feces, | pegbat: | Banchory: || peocmas, | Aberdeen. |Castle News:|| ° Elgin. ft. 3in, | O ft. Sin, | 1 ft. 6 in. | 0 ft. 4 in. || 4 ft. Oin. | 0 ft. 4in. | 1 ft. Oin. | O ft. Oin, 450 ft. 200 ft. 200 ft, 95 ft, 1110 ft. 100 ft, 915 ft, 125 ft. in. in. in. in. in. in. in. in. 412 3°40 3°50 4°20 2°78 4°75 2°67 1°67 2°44 2°80 2°20 2°50 2°40 2°10 3°92 1°35 2°95 2°60 2°88 2°30 3°04, 2°45 ale 2°65 165 I'Io 1°56 1°50 1'22 1°30 2°01 1°38 1°35 1°00 1°57 I‘IO 1°85 1°30 2°43 1°57 6°38 5°30 4°34 3°40 5°70 3°60 5°69 2°36 2°75 3°00 2°66 “79 1°67 125 3°06 2°66 4°83 3°80 5°93 2°90 4°94 3°40 474 3°22 73 "40 "96 1*00 1-09 1°55 1°06 2°24, 3°20 2°30 1°85 2°60 2°80 2°50 2°53 2°67 6°35 5°20 5°76 5°50 118 4°90 3°42 1°81 6:06 650 5°85 6:20 4°69 5°60 6°39 | 2°13 42°81 37°40 38°16 33°90 33°36 34°70 40°49 25°71 Division XIX,.—Norruern Covnrizs. Div. XX. cont.) TRELAND Se SurHeR.anp. ORKNEY. SHETLAND. nued) . Balf Royal h Maddy. Duneghin Scourie, ae ast, Sandwick. Bressay. Institution, ft. O in. | O ft. 4 in. | 0 ft. 2in, | 0 ft. 2in. | 0 ft. 6 in, | 2 ft. Oin. || 0 ft. 9 in, 150 ft, Oin. 20 ft, ? 6 ft. 20 ft. 30 ft, ? 50 ft, 78 ft. 20 ft. 80 ft. in. in. in. in. in. in. in. in. 410 I'90 2°50 2°60 2°20 3°00 4°70 5°39 2°35 2°70 3°80 2°50 1°30 1°81 2°30 1°36 6°00 3°00 5°10 3°80 2°60 3°40 4°70 2°54, 150 1°30 180 1-00 2°40 1'23 1'I5 105 3°40 I"90 2°70 3°40 1'90 2°28 2°55 3°32 100 3°50 2°80 2°80 I-40 1°69 1°50 445 3°20 190 2°10 I"40 “18 1°00 *90 1°06 405 3°80 3°20 5°30 4°00 4°88 3°50 2°37 4°60 1°30 4°10 4°30 1°99 4°65 3°70 1°66 870 4°00 690 6°70 4°99 5°49 5°60 1'29 | I'g0 2°30 1°40 2°50 3°00 3°53 3°40 2°83 1°35 1°80 I'g90 5°80 2°40 5°02 2°80 4°09 in = — ——_ — _——_—_ | |S | —_ _. _———. i “65 29°40 38°30 | 42°10 | 28°18 37°96 36°80 3I°91 828 REPORT—1862. IRELAND. Division XX. (continued). QuUEEN’s WATERFORD. Care. gtr! rei Spc | Sn ees tne a a ss feat me 1860. Waterford. | Portlaw. Boe Killaloe. Bortesiinis: Height of | Ground.| 4 ft.0 in. |20 ft, 0in.| 1 ft. 6 in. | 5 ft.0 in. |) 9 ft in aln-gauge ¢ Sea-level., 60 ft. 50 ft.? | 185 ft. 128 ft. 245 ft. above in. in. in. in. in. JANUALY ......50ccneeeeree 6°05 7°50 5°22 7°07 4°37 February ......+-..00+++ 1°34 1'92 1°33 3°01 1°30 Marelr ...is.500sdsveese 1°31 2°84 1°97 4°85 2°76 Arora Sachs oscasesevoe = 2°19 1°44 1°45 2°12 2°38 May. ..0..csecssevascceses S045 3°92 2°38 4°52 3°09 ANT O Me ct cwesecs eum sees 9 6°54 5°68 5°72 5°84. 4°73 Duly- 2....2psccsseeesvere- 2°44 1°97 2°02 2°24. 2°78 Aupust ......00ceeneree-- 5°39 712 5°85 7°38 5°30 September ...........++++ 2°29 2°09 2°62 2°62 1"40 October: .. sh. 0s0Varcsces- 2°77 2°99 2°78 4°58 2°24 November ........--+++++ 3°54 5°40 3°28 2°64. 2°52 December ......+0++++++ 3°65 3°34. 2°94 1°89 197 Totals ...:-...4:-- 40°86 46°71 37°56 48°76 34°84 ENGLAND AND WALES, 1861. Division I.—M1pp.EsEx. ee a MippteEsex. 1861 Chiswi A 2 Chiswell St. John’s . swick. Guildhall. Guildhall. Street. Wood. Bsewv eh | ewig) She 5 ft. O in. |7 ft. O in. 50 ft. O in.) O ft. 0 in. SAUCE / Sea-level.| ......-+- 51 ft 12S) | aN 161 ft. above in. in. in. in. in. JANUALY «...e2seereeeeeees 82 "45 "40 1°41 55 February .......0.-..++- 1°41 1°58 1°53 1°58 180 Mayol >< sderssnenanesene 1°89 2'07 1°94 2°17 2°22 April <..cchcctearpneons.- 1°44 1°30 Ton 1°30 1°26 Mayes: ssauceseaneeaer =F 1°31 1°26 1°13 1°30 1°36 GUNG Ses sedscnccemeeotess 2°35 2°49 2°32 3°04 163 DULVe. sicccseececuseee wees 1'90 2°47 2°20 2°71 2°87 (AUISUBL %s.eoc-coscmeaerere *50 *69 “60 "92 "39 September ..........-.--- 1°78 1°63 1°44 1°57 2°06 \Octanern .4--.sseseqne= =o 1'04 “86 “68 "92 97 ; i 4°84 4°55 WIckLow.)) Fassaroe, |) Bray. $f 0 inl 250 ft. ? Lal ° xi ee) 575% Camden Town, 9) on. 4a 100 ft. | « ON THE RAINFALL IN THE BRITISH ISLES, IRELAND. Division XX. (continued). 329 Sa - Dusty. Mayo. Sui¢o. BE.rast. SS _ || Queen’s Ti Galway. |) Dubie” | Glasnevin. | Monkstown. Lough Corrib, Marknce™” College, "Belfast ” | — | —— i. ea ia al a I| Oft.Oin. || 28 ft. O in. | 6 ft. 0 in. | O ft. 6 in. |) 20 ft. O in. || 16 ft. 3 in. || 9 ft. Oin. | 4 ft. Oin. 40 ft. 96 ft. 65 ft. 90 ft. | GO ft.? 145 ft. 58 ft. 12 ft. — —-— —— a | Lh Oh C™—_ in. in. in. in. tise in. in. in, 6°85 3°05 3°54 463. || = 7°92 5701 6°46 5°47 3°98 "29 “69 “50 3°66 2°83 2°52 2°48 117 1°64 1°95 1°94 3°99 4°13 3°14 3°79 3°10 1°52 2°23 2°08 | 1°76 1°94 2°07 2°21 3°68 I'g0 3°67 215 | 4°55 5°20 2°66 3°69 3°45 429 3°38 5B. | sae 6:20 5°79 6:07 205) 1°70 2°67 2°04 1°67 2°48 2°31 2°64. 5°00 4°53 4°18 5°10 440 || 687 4°61 4°78 1°72 1°68 1'99 1°99 1°92 1°38 121 1'29 3°84 180 1°87 204 | 47 3°76 2°78 2°57 2°04 1°88 2°31 2°28 It | 2°37 1°71 1°57 2°48 2°42 2°60 3°33 2°58 1°57 2°97 3°37 9°36 26°70 3108 33°26 43°44 43°74 38°23 39°84 ENGLAND AND WALES, 1861. aie ; Division II. Division I.—Mrpprxsex (continued). ken! Comme Monviesex (continued). Surrey. Hackney. | “Hoed” | "Hond” | Tottenham. | pucernge, | Wises, | Ham, | Kittens, ft. 6 in. | 0 ft. 4 in. | 36 ft. 4 in.| 0 ft. 3 in. | 0 ft. 0 in. | 30 ft. 0 in.} 0 ft. 4 in. | 4 ft. 8 in. 40 ft. 270 ft. 306 ft. GOGH |i «..8t aa 140 F631 |) fosehoa 580 ft. in. in. in. in. in, in. in. in. “44 "45 28 48 "64 "62 "95 186 1°87 1°17 1'77 4°96 1°84. 2°80 2°05 2°30 2°33 1°48 2°14 2°26 2°41 3°20 772 1'26 98 "84 69 93 ‘91 °97 I'7o 1°24 83 1°25 118 I'07 32 1°62 . 178 1°82 1'26 1'75 1°83 I'l4 2°93 3°53 2°42 2°72 2°02 2°48 2°23 3°07 3:11 4°84 | *58 1'02 "44. 76 "74 rir *66 "99 | 166 '77 1'29 I'g0 1°86 1°54 2°41 2°94 | 84 104 "4. I'o0o "86 1°59 1°62 1°59 (5°30 3°46 2°35 4°44 5°23 3°58 5°27 6-09 (142 1°65 112 1°37 1°83 125 1'09 1°74 T’o2 | 20°63 13°96 20°18 | 21°41 | 20°02 2415 30st} | 862, Z _ ee 330 a! REPORT—1862. ENGLAND AND WALES. Division II.—Soura-Easrern Counties (continued). Surrey (continued). cs ET Deepdene. Denbies Brockham, | The Holmes Weybridge 1861. Dorking. Dorking. Betchworth. | Betchworth. | Cobham. eath. —————————— aan saan EL Ground..| 2 ft. 0 in. | 25 ft. 0 in.| 0 ft. 6 in. | 0 ft. 6 in. | 0 ft. 6 in, | 0 ft. 6 in. Sea-level.) ..:...... 600 ft. 300 ft. 300 ft. 110 ft. 120 ft. Rain-gauge Height of above DANUBYY oh jsecencehetses: 83 “08 42 1'47 31 4.5 February 4....0scc.e+0s: 2°92 62 2°40 2°37 2°03 1°98 Maroht <..iecccctetsesess 3°43 3°24. 2°63 2°60 2°04. 2°25 SANDE! fy. cc hons csganetes ss 7 2°17 83 87 82 80 MaQ™ G.cu.pesenceeret os’ 1°30 "42 1°31 1°36 I'l4 1°38 June ...... fais Seyeee ta 2°68 3°60 2°38 2°22 3°89 2°41 SULE Hi: cegteecestueeee 3°35 2°10 3°64 3°42 1°92 2°65 AUBUB ras ctvadesrtests ses 1:05 1'00 “or 54 53 50 September .,..........0: 2°77 2°19 2°63 2°75 1°54. 1°65 OCCODER vectsadectsesss..- 1°38 2°14 1°33 1°63 "89 85 November ,...........+6- 5°45 5°33 4°92 5°24 4°47 4°73 December ...........65+ i | a | | | Division II.—Sovrn-Eastern Counties (continued), Kent (continued). Welling, Greenwich | Greenwich | Greenwich Aldwick, : 1861. BexleyHeath. Observatory. | Observatory. | Observatory. || near Bognor. Worthing. Rain-gauge ¢ goa tevel.| 150%. | 155%. | 177 ft. | 206 ft. 20 ft. above Haight of | roms 6 ft. Oin, | Of. 5 in, |22 ft, 4 in, | 50 ft, 8 in. || 0 ft. 6 in, in. in in. in in in DANWALY sa sencoreseOrtens: ‘47 60 "30 20 ip fe) February ......css.c000. Ig! 1°80 1°40 1'00 1'I7 Maro « ..5s..ce0niediens 2°14 2°20 1°60 I°Io 1°71 | ADU? cccvihscesseeeeene 83 "80 "80 80 58 | Ma Re yin. ccsheaa dtenenes 2°00 1°60 1°50 1'20 1°61 SUNG? QE icccyicserd “aoe AEE 1°90 1°80 1'70 1°30 2'O4. JUL a rhe saaygeevsenepens 2°24 210 I'90 1°70 2:82 AUGUBL coc spscoseeVeceses "7 ‘60 "40 "30 48 T'04 September ,......; fas: 1'25 1°50 bb Ce) *90 2°77 3°98 October .........5 Weis c . : ‘60 "29 ° 1°85 ON THE RAINFALL IN THE BRITISH ISLEs. ENGLAND AND WALES. 331 Surrey (continued). cr. Wandsworth.| Battersea. ) 0 f. Oin. | 5 f. Oin. | 0 ft, Oin. | 18 ft. 58 ft, 13 ft. in. in, in, fee ee wees * Dover. Kent. Hunton Court, Linton Park. Staplehurst. Division II,—Sovrn-Easrern Counties (continued). Tunbridge. 0 ft. 0 in, 125 ft. Maidstone. 4 ft. 0 in, 60 ft. in. "48 1°87 Division IT,—Sovrn-Easrern Oounrres (continued). Sussex (continued), tington, High ak Fun Wickham, St. Leonards.| Fairlight | Chichester. Hastings. Yn | LR Thorney | Qhichester | Shopwyke, [Bleak House, Tandy near | Cehester | Ghonmyke, ler rout | Oft. Gin. | O-ft. Gin. | 1 ft. 3in. | 4 ft. Oin. 10 ft. 20 ft. ? ft? 80 ft. 0 ft. 0 in, 212 ft. 10 ft. 0 ft. O in. | 0 ft. 9 in. 498 ft. 1 ft. 0 in, 10 ft. J | | eeeteneee eeneeeeee seen eaeee ——— | |S | 332 REPORT—1862. ENGLAND AND WALES. Division II.—Sours-Easrern Counties (continued). Sussex (continued). 1861. stindon. | Pca’ | Gnichester. | Ghickoster | “parms' | Ucklle seen | Ground..| 1ft. Oin. | 4 ft. Oin. | Oft. Gin. | Oft. Gin. | Oft. Oin. | 6ft. Oin. ete 7 8° (Sea-level.| 190 ft. 316 ft. 250 ft. 284 ft.? | 120ft. 200 ft. in in. in in 75 78 34 23 2°56 2°08 1°25 1°78 3°25 2°96 2°15 2°51 79 “76 35 *69 1'79 1°55 1°24 1°56 2°45 2°34. } ; { 2°88 4°45 4°81 7 2°85 118 73 *84 1°16 3°94 3°94 3°65 377° 2°45 181 1°51 1°85 512 4°99 799 7°50 2°06 1'92 1°75 1°64, 3°°79 28°67 | 27°74 28°35 Division II.—Sovurn-Easrern Countres (continued). Hampsuire (continued). Ordnance 8. | OrdnanceS. | Gas Works, 1861. Fareham. |Office, South-|Office, South- Southampton. Petersfield. | Petersfield. ampton. ampton. picight of | Ground..| 1 ft. 0 in. | 18 ft. 6in.| Oft. in. | 10ft. 05m. | seessson 0 ft. Oin. above © { Sea-level.| 8 ft. 94 ft. 75 ft. DO fie 4 wegen 200 ft. in in. in. in. 81 000 77 96 2°37 1°52 3°2 2°90 3°00 1°83 4°51 4°18 41 "27 "40 61 1°63 1°39 77 1°64. 3°97 3°29 2°85 280 4°07 3°19 5°17 5°31 87 *60 1°33 I'09 3°07 2°90 4°50 428 1'09 7a 1°33 1°64. 6°47 4°61 742 688 2°09 1°16 *53 1°42 lh ie ee . ON THE RAINFALL IN THE BRITISH ISLES, 333. ENGLAND AND WALES. Division I1.—Sourn-Eastern Counties (continued). Sussex (continued), - | Hampsuire. | Phe i | Buxted Park. es, i hg None Crawley. | Ventnor. Osborne. Fareham. Ses 1 ft. Oin. | 1ft.Oin. | Oft.6in. | 5ft.Oin. | 3ft. Oin. | Oft. 10in. | Oft. Oin. peste. 2% 250 ft. 300 ft. ey Sens 300ft. | 150ft. 172 ft. 26 ft. in. in. in. in. in. in. in. in. 61 "47 “61 } a "83 38 59 I'g0 1°82 2°OI 1°77. = { 2°70 2°01 2°10 2°00 3°09 2°60 2°39 } e { Zone Il \ 295n 2°40 2°90 70 61 49 573 $3 |) “a5 45 30 1'76 1°87 1°27 2°13 2°38 | 2°05 1°56 1°80 2°65 2°55 2°16 117 3°49 2°90 2°54. 4°10 3°63 3°09 3°93 4°54 Sere || 25E 3°10 3°70 106 1°05 "94. 36" || “66 66 1"40 4°76 4°38 4°26 } 6°63 | 419 - || 3°27 3°65 3°60 2°28 1°96 1°79 1°97 1°89 "70 140 _ 840 7°76 6°72 2°59 648 | 710 5°74 5°70 181 1"g0 2°13 4°12 2°59 1°36 1"40 1°80 | | mr | ps | rf 32°57 30°25 27°56 28°57 34°25 27°29 25°89 30°60 Division I1.—Sourn-Easrern Counties (continued). Hampsuire (continued). BsrksuIRE. 2 Royal Mili- Lon aay Hichen Selborne. eee ee a, Aldershott. | | ary College, Wallinetond. Witten am, Sandhur: Abingdon. | een 3 ft. Oin. | 4ft. Oin. | 1ft.4in. | 3ft.Oin. | 5 ft. Oin. | 7ft. Oin. | 1£t. Oin a i eS 400 ft. ? 177 ft. 325 ft....|| 246 ft. 200 ft, 170 ft in. in in in. in in in in. "35 il 22 62 56 57 69 "87 2°23 2°12 1°94 Ig 2AGe Ss || | s.2a58 1°73 1°76 3°20 3°24 3°60 2°78 2°36 1°89 2°06 1°97 “48 "36 1°65 "28 “55 68 81 104 | 1°38 1°32 2°64 2°57 Thy 1°69 1-07 iz | 2°28 1°78 3°15 2°05 1°62 2°06 2°47 2°76 | 4°97 3°72 3°21 Zur 3°22 2°96 Sia ae | ‘To2 95 2°35 "47 75 "45 ‘78: "99 2°52 2°90 1°57 2°35 2°68 2°15 1°73 - 1°55 194° 1°37 1°g2 - *96 roo | 1°18 I'l4.- 1‘20 541 3°75 5°16 3°82 461 || 3°60 3°95 3°20 273 | 1°95 2°09 ° 1°58 L°17e 2 | 1°20 1°70 169 : 7°01 25°07 30°40 22°50 22° 5amrem| | 2.0806 20°76 334 ‘ REPORT—1862. ENGLAND AND WALES. Division II1I.—Sovrm Mipranp Counties. HERTFORDSHIRE. Field’s Weir, | Gorhambury, Hemelhiem -| Berkhamp- 1861. Watford. | Hoddesdon. | St. Alban’s. stead, si stead. Royston. Raingne | min 5 ft. 6 in, | 2f.0in, | 2.9 in. | 8 ft. Oin. | 1 ft. 6 in. | Of. 7 in. above Sea-level.| 250 ft. SARUM, | Bites. 250 ft. 370 ft. 267 ft. in in. in. in in in DANUALY, 2...i.0..echtrae 38 85 "4.6 50 84. 1°30 Bebruary .i....<0séee.s 1°89 2°35 2°32 2°00 24 2°06 Marla | hs sscdso05sQuaettes 2°20 3°10 2°38 2°31 2°64 I'gt (ADE ri -.25.d:02018ealnes: 65 1°28 “98 80 go 83 IMBYj[ovinesdscaecQbstdvss 76 1°40 105 g1 88 97 PUTO, ising esecdeos-o gus cr 2°73 1°95 2.75 2°45 2°07 I'g0 Wal yeievanescronteee (EIeve. 3°37 2°00 3°16 3°92 4°13 3°29 AMIZUSE co. .0d0000:Ghdta se *60 55 *go 55 1'02 66 September ...........6.. 2°04 1°80 1°86 1°75 2°28 1°03 October. ..-.c.... UVitse. "75 “go 1'25 1°25 4 1°08 November .........6..... 3°34. 4°60 3°77 3°36 3°94. 3°42 December’ ....... sii. 1°48 1°20 1°25 1°40 1'73 1°36 ane eS Eee Sea eeaeee ee ee eteneem ee ef ee Totals .... ssi ae 20°19 21°98 22°13 21°20 24°10 19°81 Division I1I.—Sovra Mrpranp Countis (continued). NoRTHAMPTONSHIRE. BEDFORDSHIRE. | : Marholm, 1861. ply Leloes 5 Oundle, Peter- Aspley. | Cardington. ‘ borough. puiieht of || Ground..|$ ft. 10 in.| Of. 2 in. |20 ft. Oin.| Of. Gin. | Of. Gin. |... | abaTe” PROMOML) commas | Sade 4608.) htnacam | in. in in. Panuary ....)....caiveo< 1°36 93 95 February ..\.....s06s-- 2°52 | 216 1°99 March ......\.....des2 te: 2°06 2°31 1°76 ASTI oye. <-.b.atetgieeses 1°58 1°32 87 MAY ig irivessshon-temenete, 127 1°36 rr ¢ June ........ beac sewaetee: 2°33 3°05 2-14 TULY wecegssccdascts sceva.. 4°13 4°52 3°95 AUPUBE. .....ke0cackenvec- 74 “44 “35 September 1°60 1°53 r'oz October .<.:..4....camver: . 1°33 1'07 "84. November Ee 3°01 2°99 2°65 December 1°33 161 1°38: 29 Totals '..;.< cases 23°75 23°29: 19°02 i" ON THE RAINFALL IN THE BRITISH ISLES, 335 ENGLAND AND WALES. Division III.—Sovrn Miptanp CounttEs (continued). _ BuckIncHAMsHIre. OXFORDSHIRE. Rose Hill, | Observatory, | Observatory, < Oxfo i Oxford. Oxford: Banbury. Banbury. Banbury. a, Aylesbury. 1 ft. 0 in. 4 ft. Oin. || 7 ft. 9 in. | 0 ft. Oin. tae oa 7. 43n. | 4 iO | iia 250 ft. 290 ft. 208 ft. 350 ft. 840 fe | Sassi aan, in. in. in. in in, in 46 "20 "66 53 "50 "54 1°64. I*50 I'90 2°68 2°71 2°75 2°22 1°70 1°68 2°27 2°34. 1°94. 74 86 “69 1°21 1°30 1°37 73 "64 1°36 1°62 1°62 I"40 2°02 Ign 3°12 2°15 2°03 2°00 374 3°31 5°15 3°36 3°26 3°25 ‘78 "46 ‘60 43 37 57 180 1°51 1°94. 2°51 2°43 2°48 1'16 1°03 1°58 1°32 1°28 "99 2'60 2°67 3°07 298 2°74. 2°83 1°54 1°52 1°65 1°53 1°51 1°22 19°43 17K 23°40 22°34 22°09 21°34 Diy. I.—S. Mann Counrms (cont.). Division [V.—Eastern Counties, pron CAMBRIDGESHIRE, Essex. Mid- een “Yeah | Now Beak) Oto | -maytens)’ | angio | Withame! | lashaon, Wisbech. 5 ft. 6 in. sp 6in: | Oft.8in. | ......4.3 0 ft.4 in. | 6 ft. Oin. | 1 ft.6 in. | 1 ft. Oin. 104 ft... 8 ft. AD -fti.- |) ssatieedt 93 ft. 360 ft. 20 ft. 300 ft. in in. in in. in. in in in 98 91 86 "59 *69 103 526 1°72 pe 1°80 1°55 1°77 1°68 1°76 1°50 61 2°32 1°93 1°63 1°55 1°44 2°IO 2°04, 2°48 r81 mm. 92 95 99 ‘60 88 1°35 *52 45 1°06 1°25 1°34. 1°31 I'Ig 1°55 90 129 196 3°22 3°18 2431 1°94 2°20 2°22 "79 3°34 3°62 3°80 4°67 2°57 1°85 3°62 2°40 "28 55 69 "5° 97 "75 63 53 etl? 1°65 1°73 1°37 1°95 1°65 bap b 1'23 | °86 "71 78 “80 99 bi Co) 48 *98 | 2°84 3°65 3°85 3°33 4°09 4°35 4°01 3°06 | 130 re7 1°65 1°38 1°33 1°05 83 “96 336 REPORT—1862. ENGLAND AND WALES. Essex (continued). Division [V.—Easrern Counties (continued). 1861. Paice ad Dunmow, Height of Gedund Raranse | Grd hae 100 ft. ? in. in. JANDALY 0201,.. 002930500. 277 *60 Febraary® s.....5icc... 1°52 2°08 Marching ib...) 6/2... 1°80 1°81 Aprilistesccdhe scouts. "66 “92 Mayagsh.. sd se+ccnass . "95 1°08 JUNC egece eres -kaeh. 1°73 1°87 VULYs Beh.2.s-bsercctuee ? 2°10 ATO. eb eRe... | 3°14 { 38 September ...........;... 1°44 1°45 October’. 4.6 5..cnaik. "58 *46 November ............... 3°47 3°20 December ............... 1'03 1°22 Matals \...ic<'cee. 16°59 17°17 Division IV.—Eastery Counrres (continued), ‘eeeasiMenmnempdemieeiosmeceeeee re See neeEe 2 Norroux (continued). Se ee eee eee 1861. Burnham. | Holkham. x et Ground..| 4 ft. 6 in. | O ft. 0 in. abore © { Sea-level.| 102 ft. | 39 ft. in. in. January ...c....seceeeeee- "99 1°00 February i.....ssie000e. 2°39 2°35 March t...descccaeesurene 2°73 2°25 ADEM ..cccckan ss hemes 1°35 1°65 Mays sisi: soa 1'97 1°70 Uarie aigss:.ct ses eee 1°54 1°30 Dilly piace: sceecs cee 2°78 I'90 AUIS URE sic .pcccnie eee *60 55 September ............... 2°24, 1'g0 October ....1....heewsce, 54. "43 November ............ .. 6°14. 5°50 December” ::.....pacccs: I'S 1°27 {> ., ————— Totals ....¢ss.t<.. 24°78 21°80 SUFFOLK. Bocking, Grundis- Bury St. Westley, rine: butets Ramah, Bay. 3 ft. Oin. || 4 ft. Lin. | 2 ft. Oin. | 1 ft. 6 in 200 ff/2 || +8 e8 eoscscees Sdtaddeve in. in. in. in. 1°36 I"lo 1°31 1°03 2°55 |) ley: 2°69 2°36 259 1°33 195 2°04. WE “40 "82 "74 85 1°26 1°14 I'lo 2°08 Ilr 22 1°57 2°34 2°02 2°20 2°12 "65 "94 “61 "49 1°77 1°53 1°27 the “66 55 “80 °53 3°33 408 3°37 3°64 | “90 1°40 1°22 bis de | 19°81 17°46 19°50 17°71 Division Y. Sovrn-Western Covntres. WIxTsuire. Alderbury, Holkham. Salisbury. Bavyerstock. |Marlborough. 4 ft. O in. | 0 ft. 6 in. 3 ft. O in. 4 ft. 0 in. weeeee 1S Barton Hall, Bury. 1 ft. 0 in, in. . 20°70 VILTSHIRE ontinued). e acme * Cain 348 ft. ON THE RAINFALL IN THE BRITISH ISLES, ENGLAND AND WALES. Division IV.—Eastern Countres (continued). Surrouk (continued). Thwaite. 3 ft. 6 in. 150 ft. in. 1l4 2°79 2°36 1°26 1'25 I'12 4°50 36 1°73 ‘74 4°34 1°53 23°62 Thurston Lodge, Bury. = Nether Hall, Thurston. eee eeeree Division V.—Sourn-WestErn Covunrtiss (continued). a ta re | Little Bridy. Portland. . 2 ft. 0 in. 52 ft. Encombe, Wareham. 1 ft. O in. 150 ft. DorseEr. 0 ft. 4 in. 348 ft. Bridport. O ft. 11 in. 95 ft. ? in. *60 3°92 3°44 “51 337 (ee eee ee ere Norrouk. Diss. Norwich. Egmere. . | 0%. 6 in. | Of. Oin. | 4% 0in 115 ft. 30 ft. 150 ft. in. in. in. ‘60 1°28 I'00 2°40 2°75 2°69 1'70 2°60 2°21 85 “go 1°86 I‘0o 1°34 2'O7 1°20 1°32, 1°45 4°70 4°93 2°82 "80 “48 "66 1°28 2°31 2°99 “45 “49 “72 3°40 Sor 4°97 1°37 1°39 138 19°75 24°80 24°82 Devon- SHIRE. Netherbury. | Forde Abbey. Kingsbridge. O ft. 0 in. | 0 ft. Gin. || O ft. 6 in. 50 ft. ? seated 7 143 ft. in. in. in. 89 1°03 1°90 5°15 4°72 2°20 3°97 3°84 3°94 55 “58 94 1°03 1°36 2°05 5°00 4°26 3°38 4°34 = A . 2°61 3°00 2°13 3°02 3°01 1°88 DULY? "Ss. sas cccdeeeeess. 4°47 4°05 4°67 6°69 4°30 4°62 AUBUBE: ...9...5-40008 0s. 1'95 2*10 *39 1'05 63 85 September ............... 3°36 4°60 2°53 2°59 1°97 1°97 OCHRE is... foetes 1°96 1°55 1°40 1'72 2°16 1°23 November ,.....5.,.3:... 3°49 3°95 1'98 2°75 2°22 aE December ......,cc15000. 2°18 2'05 I's 1°96 I'rs 1'22 Motala ...%2.¢4.. 30°90 36'40 23°42 29°81 22°64. 20°82 Division VII.—Norra Miptanp Counrrss (continued), Licoty. 1861. | Sythe | Grantham. | Boston, |SanthAKymo] Celeb, | cial paneht of | Ground..| 4 ft, 3in. | Off. Oin. | 14. 0in, | Of. Oin.| ......... 3 ft. 6 in, abe © { Sea-level.| ......... WO aa Dif: *| emer 26 ft. above ! in in. in in. in in JANUBLY 0.0 40ss00deeeecess "20 "67 "93 1°09 °35 30 | February. ......0e. ds: I"70 1'79 2°12 1°70 1°53 145 Marche... tous ste mes 2°10 1°83 1°65 I'50 1°37 1:02 Aprile .t. Sodecsattemerct ne 74, 1°26 1°23 1°57 78 rg ] Maye. ..sccu seen "20 1°23 1°55 1°62 63 80 JUNG" 2. 5,. dct teees 2°83 2°29 2°49 3°55 3°49 3°20 JSulye S.. 5.43; cates 3°70 4°35 3°74 4°33 4'02 2°96 AMIBUBE «sh sccc Meee: a3 “48 "15 39 ‘09 35m September ,.............. 1°70 1°40 1°38 1°08 117 113 @ October ...5,..0.Recvanee 92 I‘Or go 76 66 82 November ............... 2°90 2°92 2°84 2°64 2°11 2°61 - December j.../.90...... 1°30 1°28 1"40 1°42 I'l3 Ig Metals)... 294... 19°81 20°51 20°38 21°65 17°33 16°97 oe “4 ON THE RAINFALL IN THE BRITISH ISLES, 343 ENGLAND AND WALES. iy. VIL—W. Mr- ae xp Counrres(cont.) Division VII.—Norra Mipranp Covnrtizs. LEICESTERSHIRE. Rurann. Rothley, - ya Leicester. phere Bouse para Empingham. borough. 1 ft. 3in. | 2 ft. 8in. | 0 ft. 4in. | Oft. 8in. || 4 ft. Oin oiedecte | |. avstners 210 ft. 237 ft. cearerts in. in. in, in. in. "29 "54 1°19 "58 *30 1°70 2°31 1'79 1°68 1°75 2°94 3°11 2°43 2°15 1°87 reir 98 1°31 1'25 "80 116 1°89 1°55 1°56 1°30 2°46 1°99 2°38 2°77 I"lo 2°90 6°25 4702 4°75 2°40 °57 “51 “84 “46 o°05 53 2°39 2°14 1°68 1740 *90 1°60 1°97 1°38 "70 1°51 2°35 2°20 2°62 2°60 1°55 161 1°24. 124 ris 17°62 25°53 22°46 22°12 15°42 Division VII.—Noxrra Miptanp Counties (continued), Linco (continued). . Spri teBurton,| ‘Warket | Gains, | Gardens, | Stockwith. | Brigg. | Grimsby. | Barnetby Gainsboro’. 3 ft.6in, | 3 ft.6in, | 3 ft.6in, | 8 ft.Oin. | 3 ft.6in, | 3 ft. 6in, | 15 ft. O in. 3 ft. 6 in, 96 ft 100 ft. 76 ft. 38 ft. 21 ft. 16 ft. 42 ft. 51 ft. in. in, in in. in. in. in. in, "94 0°00 "19 28 0°00 ‘60 rol "85 2°53 3°50 2"42 2°33 1°88 2°49 1°44 2°61 1°96 1°67 1°40 1°75 1°52 1°44 1°24, 1°47 I'07 1°34 r'02 1°00 82 "gt 1°22, ror +56 2°22 "70 66 "74, 106 83 "82 3°54 2°77 3°07 2°72 2°50 2°NE 2°80 2°64. 3°74 3°22 4°26 4°53 3°83 4°34 3°50 3°38 + 33 °37 *38 53 "49 "46 "23 "42 1°64 2°74. 1°39 1°46 1°62 2°68 1°13 2°11 "94 "74. 108 I'0§ 1°36 1°29 *66 118 2°50 3°97 2°44 2°36 2°48 3°25 3°22 3°36 129 1°50 1°20 1°04, ror 145 "98 1°30 21°24 24°04 19°55 19°81 18°25 22°48 18°26 21°15 344, REPORT—1862. ENGLAND AND WALES. ————— Division VII.—Norru Mipianp Countizs (continued). Lincoun (continued). Norrincuam. | 1861. New Holland. Wigbield Ee ate Welbeck. Worksop. Retford. / picight of | Ground..| 3 ft. 6 in. | Oft. 0 in. |25 ft. 0 in.| 4 ft. 0in. | 3.6 in, | 3ft% 6 in, | above” [ Sea-level.| 18 ft. TE2H, | 1674 |) ager 127 t. 52 ft. { ove in, in. in. in. in, : 85 *69 "4.6 000 °30 2°72 2°48 2°11 3°08 2°27, 3°43 2°84 3°03 2°61 2°17 1°69 1°19 1°56 1°35 I'1g 1°20 93 1°08 1°39 “79 1°70 1°49 4°81 2°22 2°69 3°46 3°34 4°54 3°19 3°45 56 54 "86 23 "29 1°93 I'gt 1°86 1°69 1°47 1°35 1°26 1°16 1°45 1°42 2°03 1°94 2°26 2°06 2°43 1°41 1°40 "43 1'l4 1'26 22°33 20°01 24°16 20°41 19°73 ¢ ve Division VILI.—Norru-WestEern j CounTIES. Division VII.—Norra Minranp Counts (continued). Denrsysuire (continued). CHESHIRE, Bosley Bosley 1861. Chapelen- | Woodhead. | p27 | ph. | Macclesfield. | Macclesfield. le- — 3 ft. 6 in. | 2 ft. 9 in. | 3 ft. 6 in. pugieht of 1 Ground..| 3 ft. 6 in. | 3 ft. 6 in, | 3 ft. 6 in. i ae a 8° F Sea-level.| 965 ft. 939 ft. | 1210 ft. | 590 ft. 500 ft. 539 ft. | | in. in. in. in. in. in. : SANUAIY i ve ctsssapeeerees *29 1'20 *B0 *16 "40 *14 | Hebruaryulctvassconeeees 3°09 6°22 2°14 1°94. 1°97 1°86 Marl: <.sspsseounmmpeest) Jem 9°33 3°90 3°15 5°72 5°13 2: \}0) 911 See Seeceny eanpess|) 1°20 2°50 1'18 1°35 1°41 1°24 i May ....... Sovecceainene: "99 2°13 1'09 1°18 1°22 1°25 ' June . ‘ peal 3 tOm; 4°13 3°12 3°61 3°18 2°84. 4 July ...... oes], Z0 4°60 4°63 4°20 4°33 4°34 AUIZUSt Os sscbuasesnee Sees] | 2Az 3°33 171 2°15 2°47 2°43 September ..,.,...4. egese] | 5°22 4°36 3°03 3°52 4/22 4°28 October: =~. shaca.tabeones 1°70 1'72 1°76 1°36 1°24 1°22 November .,.....s000.-41 4°53 6°13 2°67 3°07 3°35 3°97 December .,.....j00cees 3°10 2°99 2°62 2°07 2°02 1°99 Totals ........ see] 37°19 49°64 28°65 27°76 32°03 30°59 ; ON THE RAINFALL IN THE BRITISH ISLES. 345 ENGLAND AND WALES. Division VII.—Norrx Mintanp Counties (continued). Norrineuam (cont.). DERBYSHIRE. | Bast Retford. West Retford.| Derby. Chatsworth. | Chesterfield.| Norwood. | Combs Moss. etsebe | 2 ft. Oin. | Oft. Gin. || 5 ft. O in. | 6 ft. Oin. | 3 ft. Gin. | 3 ft. 6 in. | 3 ft. 6 in, 3 ft. 6 in. | 50 ft. 50 ft. 179 ft. 404 ft. 248 ft. 238 ft. 1669 ft. 710 ft. | in. in. in. in in. in. in, in. “18 "23 "66 "47 1°06 “48 1°14 "50 2°17 2°17 2°17 485 4°20 3°79 3°57 425 2°12 2°11 3°86 4°90 q7k 3°47 6°27 8°56 1°16 114 1'20 1'29 1°92 1'29 *50 1°57 "719 83 63 1°04. 83 1°06 1-40 1°45 2°76 3°05 124 3°46 2°29 2°89 3°24 3°34 3°57 3°16 4°30 4°45 3°72 3°38 4°55 4°60 aa we "92 ii 33 "56 3°10 3°50 1°52 167° | 2°16 2°81 2°Or 2°26 4°32 6°22 | 1°34 1°33 | saiee 1°39 1°65 1°23 1°66 2°02 2°35 2°OI |’ «ear 3°51 2°09 2°34. 4/08 6°22 128 1'29 1746 ZOA | - 5:67 1°40 4°50 3°41 19°56 - 19°31 2201 31°32 25°48 24°15 33°33 45°64 a Division VIII.—Norru-WestEern Covuntiss (continued). eee CHESHIRE (continued). Kingsley, | Sponds Hill, Thelwall, Aqueduct, | Top Lock, Hill End, Foti piingkon: Whaley. Quarry Bank.| Northwich. Marple. a Mages Oft. Oin. | 3 ft. Gin. | 3 ft. 6 in. | O ft. 8in. | 1 ft. 6 in. | 3 ft. 6in. | 3 ft. 6 in. | 3 ft. 6 in. 208 ft. 1279 ft. 602 ft. 295 ft. 96 ft. 321 ft, 543 ft. 680 ft. in, in. in. in. in. in. in. in. 2.4. "98 "72 ‘22 “26 *31 "20 63 (2°57 2°79 2°67 1°56 2°72, 1°99 1°48 1°83 3°57 6°99 6°72 4°36 4°29 6°39 4°00 6°13 1173 I'S 1°40 1°56 I'71 1°48 1°56 1'27 ‘ror 1°42 1°49 1°03 *70 IIo 85 1°29 2°68 2°04. 2°00 1'79 2°67 3°01 3°66 1°94 425 4°55 4°46 2°89 3°59 4°22 3°84 5°66 2°84 2°93 2°35 212 2°44. 2°45 2°38 2°92 3°84 6°55 6°48 3°26 3°43 4°62 4°91 4°65 aa 1'40 1°40 I'lg 147 1°40 1:26 1°16 2°98 4°19 4°17 3°13 3°66 4°33 4°66 4°82 1°87 2°64. 2°64 2°13 1°99 2°25 2'60 2°10 = | . ALE 37°99 37509 25 The | 28°93 33°55 32/40 34°49 | 346 REPORT—1862. ENGLAND AND WALES. © Division VIII,—Noxrru-Western Counties (continued). CHESHIRE (continued). LANCASHIRE. Matley’s Observatory,| The Brook, | Old Trafford,| Sale, 1861. wee Newton. aiversead | Liverpool. | Manchester. | Mancheste ee i. |S 3 ft. 6 in. | 3 ft. 6 in, | 30 ft. Oin.| 2 ft. Oin. | 3 ft. 0 in, 2 ft 8 if Rain-gauge (Seq-level.| 399 ft. | 306%. || 52f% | aac. 106 ft. | 134 ft. in. in. in. in. in in. JANUALY .ssseescssseseese.] O'OO "42 27 "39 "39 “48 HebFuary ...cc3s0s..00:| 2°78 1°61 1°88 1°56 2°52 2°12 March © .s6s-0088 Waves’ 5°47 4°98 3°08 3°07 4°14 4°40 Apel eesestsce Satheessess : 1'l7 1°16 1°40 1°41 2°43 1°58 Mayet sc cctecssct OU UCEEEE 1'20 "97 "92 1°20 74 86 OUND fasccstecc. bees ares2| 1° SOS 3°77 2°17 2°87 2°41 2°23 JULY foscabesssstietteos 528 4°30 2°95 4°65 3°65 4°02 AUBTBE 221005. 08isees.... 2°67 2°86 1°96 3°41 2°23 2°44 September .....:...064... 3°96 3°99 2°76 4°42 4°05 4°07 October .2:....:282sb..008 98 1°23 1°53 2°42 1'23 rg November ... | 95 4°53 2°75 3°82 3°88 3°49 December .........+ wered| ? >. BOS 1°98 1°48 2°06 ‘eT 1°75 Totals ..i..s0600..] 33°16 31°80 23°15 31°28 29°74 28°58 Division VIII.—Norra-Wesrern Covuntiss (continued). LANCASHIRE (continued). Howick Fishwick, | House of | House of |Holme Sia - 1861. Bury Preston. | Preston.’ | CoPrection, | Correction; |” "Preston. Eats || 0 ft, 6 in, | 24 ft. O in,| 1 ft. Lin, | 58 ft. 6 in. | 1 ft, 6 im Rain-gauge (Sea-level| 400ft.? | 72f. | 154. | 140f | 187 | 143. in. in. in. in. in. in. Tathwlry. i.scc..c8Fssss.:: *20 “72 “52 *67 "62 “63 Pia Be tere 2°65 3°97 2°64 gir 2°96 3°72 = ee cetk 3°50 4°39 4°32 4°30 3°35 GL ry DED fora sves ccc Maeteect 1°75 1°35 112 1°23 1°03 Ee be May's... sseseeeeseoes: "75 1°24 1°16 1°22 1°00 1°13 JUNG $e ccszee.c0eeedeccse 1°35 2°39 1°52 1°73 i ( ies July Oe ee xs eee 4°67 3°82 2'96 3°76 3°35 5 a ee re 3°10 3°38 3°76 3°99 3°33 aah 2h eptember ....... P1Baves 3°15 410 4°40 4°41 3°79 ie! Coeoe villece beeen 2'Io 3°50 3°96 4°12 ed 4°28 aoa Per the 2°55 4°95 4°56 4°94 3°79 LR December ......sssss.e0. 3°90 2°28 240 2°42 1°95 2°63 ‘Totals valeiweres< 29°67 36°59 33°32 35°90 39°75 38°48 o ON THE RAINFALL IN THE BRITISH ISLES. 847 ENGLAND AND WALES, Division VITI.—Norra-Wesrern Counties (continued). LANCASHIRE (continued). Market Piccadill Ww. Belmont, Heaton, : A terhouses,| Bolton-le- » ? Standish, Street, ac Ys Fairfield. ? “ Bolton-le- | Bolton-le- : Machekker. Manchester. Oldham. Moors. Moors: ahoaek: Wigan. ‘fb. 0 in. | 46 ft, Oin.| 6 ft. O in: | 3 ft. 6 in. | 2 ft. Oin. | 0 ft. O in, | 0 ft. Oin, | 0 ft. O in. 5 a 194 ft. 312 ft. 345 ft. 290 ft. 800 ft. 500 ft. 285 ft. —$—— | —___., in. | in. in. in, in. in, in. in. "26 *40 "41 “17 “78 1°20 "70 2'04 2°66 2°77 2°70 2°74 3°85 3°60 2°90 4°09 5°26 5°96 6°16 6°06 692 7°20 5°20 6°17 1°29 1°65 1°45 1°18 1°72 2°10 2°70 2°11 "65 "95 reir I'rs 1°45 1°70 1°40 1°66 2°12 1'97 2°37 2'08 1°56 3°10 2°60 4°45 3°89 4°25 441 4°52 4°99 6°30 4°70 5°72 1°87 2°66 3°38 3°16 4°47 6°50 3°50 3°94 3°95 4°85 4°95 4°38 7°28 9°20 6°40 7°08 1°43 1°70 1°57 88 2°43 2°40 I'90 2°80 3°91 5°14 5°05 4°62 612 8°30 5°20 5°08 2°04. 2°13 2°20 1°85 3°34 4°10 2°70 2°50 29°33 34°43 35°76 32°79 44°91 55°70 39°90 47°63 Division VIII.—Norra-Wesrern Counztiss (continued). LANCASHIRE (continued). Shore, | Observatory,| Bleasdale. Caton Hest Bank. Holker, P apes” Stonyhurst. | Garstang. | Lancaster: | Lancaster. | Cartmel. Cartmel. | Coniston. Sin. | 0 ft. O in. | 4 ft. 6 in. | 2 ft. 4 in. | 2 ft. Qin. | 4 ft. Sin. | 6 ft. Lin. |4 ft. 11 in, 29 ft. 381 ft. 600 ft. 120 ft. 82 ft. 155 ft. 171 ft. 154 ft, 3 in. in}. in. in. in. in. in, 1°60 I'lo 68 1°44. 1°49 2°81 3°53 13°50 3°80 4°00 5°92 4°24 3°83 5°29 3°44 | 9°20 3°75 6°80 5°99 5°76 5°03 5°65 6°26 11°50 Iso 1°40 I'l4 °74. "62 *86 "76 *30 *90 1'40 1°58 I'21 1°05 1'29 *9gI 2°70 "90 2°30 2°63 2°73 2°36 2°78 3°49 4°00 3°20 5°30 7°06 4°36 3°48 5°50 4°63 I1"50 3°75 6°30 7°53 6°50 5°68 TAI 6°87 12°00 380 5°80 641 4°70 4°31 5°35 3°34 10°00 2°00 3°00 4°13 2°52 4°06 3°33 3°36 5,00 5°20 8°60 8°38 7°63 6°77 701 7°62 17'00 2°30 3°00 3°69 2°71 2°63 2°83 3°02 55° 49°00 55°05 44°54 4r3r | sotra 47°23 10220 348 REPORT—1862. ENGLAND AND WALES. Div. VIII.—N.-W. Co. (cont.) Division [X.—YorxsHire. LANCASHIRE (continued). YornsHirE—West Ripixe. Wray Castle,| Station, | The Edge, | Broomball | Redmir oe 1861. Windermere:| Sheffield. | Sheffield.’ | Parke | Sheffield” | ‘Tickhill effield. pidisht of | Ground..| 4 ft. 9 in. | 3 ft. 6 in. | 3 ft. 6 in. | Oft. 4 in. | 3 ft. On, | 0 ft. 1 i abere ” { Sea-level.| 250 ft. 188 ft. | 336 ft. | 337 ft. | 1100ft. | 61 ft. in. in. in. in. in. DANUATY: ssecstecetese0s. 67 “98 “76 27 “SEQ IRebEmairy -\; 2. eres 22%. 4°20 5°39 5°39 5°46 2°86 March ......ssssseesseee 4°44 5°15 5°20 6°65 3°19 PADETS eesiseh escort seeys 2°21 2°48 2°29 3°23 1°66 May ies. hese sap areeter *90 "86 88 I'lo 83 PRAT CPs sop avsc ents coos | 1°60 2°75 2°51 3°89 2°85 MUP As Savcaespascvense Pees 2°89 4°23 3°69 4°40 3°75 A pear cewaereeateams'cs 68 1°07 95 2°06 "41 September ............... 2°32 2°93 2°19 3°02 2°14 OGhGperissetssscacreeeres« 1712 1°42 1°25 1°46 1°03 November .,.......c00+0- 2°87 3°08 2°87 4°04. 2°62 IDeUEM DEL #2 s2ci.Se cess 1°65 1°82 1°70 2°36 1°21 Totals <..,0805.. 25°55 32°16 29°68 37°94. 23°14 Division [IX.—Yorksuree (continued). Yorxsnmee—West Rivine (continued). » Warl Midgel Ovend 1861. Wakeneia, | Well Heed | Hunter's | Wyte’ | “uMeon” | Moor, Halifax. Halifax. Halifax. Height o eee 4%. Oin. | 1 ft. Oin. | 1 ft. Oin. | 1. Oin. | 1 ft. Oim. | 1 ft. Oin a Sea-level.| 115 ft. | 487 ft. | 1250ft. | 1425f. | 1850f. | 1375 ft. in. in. in. in. in. in. JANUASNY, o).0sceeeteaeee=- 23 "19 1'80 1°40 1‘go 1°50 ebYUary \,....catesess= 3°90 3°97 4°60 5°30 5°40 5°30 Warclt "<0, .cccsesmereters 3°56 5°24. 5°10 6°10 7°40 6°60 PAIN tan ya¢ sxsoneuneteas 1°63 1°30 “go 1°20 1°30 1'20 LES) bAreesee conctc osc "70 *78 0°00 “IO 0700 "10 STING, oo sees actos 2°02 1°74 1’00 I'g90 2°30 2°00 UL ecg eee gen saeeememee™ 2°51 5°07 4°30 6°60 6°60 6°50 FANIOUBL 5. c4gscavedensasts "78 1°52 1°80 4°40 4°70 4°10 September ...........5++ 2°53 3°39 4°70 5°30 5°90 5°10 (OCEODE.. «c+ .-s ELOY EIEIO TORUS * sung osoqe ‘ynquoSuery 0 Pe gh es eTasO nT eqounlg Wwe eT 9p [0D © SMPOAH TE 48 'SR 1a WAOYAIIVYPY LOULopy Fo yromumng ‘ooul ~ > Wee “ « ce se is 4 uordoyg orfsary “Aoyy parva Ser ga TT « i4 ce te Aouuog “4 “J, “A0vy “OUIBNT §,10A.T08q 0) Bn a eS a a a ee |e ee a, ee ee 366 ‘opeys oY} UI Ie oy} Jo yey} Suteq ommyzerodurs, [eyTUT oy} “UNS oY} 04 So}NUTM 9eIG} SuLMp posodxo siojowouIeyy, qg-yourg uodn ywoH yuvrpes s,ung oy} Jo yoyo oy} Jo suoyvarosqQ—'T ATTY, wa io] 4 < 2 rm & Zz Lal mn Zz ° _ 5} > ee a n = co) Ss) — a & 2 a ° & x 3 m a A. ° “yout Sy 0-48 « « “ “c “ “ “ 6c ts “ “eoRpAMs Gov LT. ‘W'd OSZT. | T98T “dog g oZP's onbsvue A, op #0g MOTIq, 402 OO z “QourT G-1& GAT ‘Wd OZ'ZL | OO8T ‘aay 82 OOS*Z moe} Tt tt melo TP EBOR, e *sarjouL Pp P.9% 66 “ “s ¢ 3 . . ° ° ° . “gout T 8-28 9-61 “OO NT ogst Ame g 008'9 Ft SCORN OUN ae Caste ‘i *soOUL Z Gg ef sf $ a Ge (Aap ou Tlos:‘epeys) “saqout g 18% “ “ 6 «“ “ = ap oe eee « “ “(Tos Aap uy Te) "your T PBS aL ‘Wd O'T Lest ‘suv 0z | ¢008‘0T * 2 8 cess Maegan JOceRpaRy | SS Tren ae ‘yout T Tt 14 We OF O98T “sny 8 ¢000'6 “es “8 Tmorg eaoge yqnopey é “sayout F 6 ‘ 7 “ “ d Sgt iek uaeemmraue 8 “ “ ‘ “OU T g 4 VOSTE | & m d st tt seudop ep. exjguesT é “ “sayout P 6 & se “6 “ é = oe ogee me poe “ «6 sc “ “yout T G 6.6 “WY O0'OT iT : é Ae: eae 4 woxwod ep 190 a “90 our P P “cc it3 17 ‘ é . . . . . . “yout I I 3 WVOL | O98t “Sav T d 8s OE TT, 2 " "our ot eat. of MOT oc} oP SESE Oe 2) 2 eee ee ee *soTjoUL Pp ch “cc 7 “ ¢ : . . . ; / ; “qour T 8 0 ‘MV O0L | o9st 4mets| 999'6 ae 8)701TV TOP 190 . _ ‘your T g 9 roo 09st Amp 0g 40086 ie eee oe oe sypdung so] i . "SO out ¢g L cs 6 c . . . ~~ 8 j : 5 ; “yout iu 6 OL ‘Wd O'T ogst Ame 92 e91'8 yor fos 8 + gusteg Bp op ToD | “UPTRW LV AL “Tog jo ‘opeyg ur . : “qoop YStpsugy : a 2 ‘qydeq piles: ei Sorts Lh moyL aqeqy ur qyStoR Cod ef OULB NT 8,10AI08qQ ‘QOBFIMS OY} IBoU puL 4B [log oy Jo cinjesrodwoy, oy} Jo suoTpeAtosqQ—T] TTAVy, bt es 2 ee Ee eT ¢ . . e . . . . a $12 L-OP 8-52 “mOON TOSE “Sny Lz gers soumog xnNegy 0-82 0-2P 0-61. ‘WY CFOL | T98T “SXV OT 002'6 ‘ho 5 8 puepoy op eqparg. - 1-08 G.9F 8-92 ‘wad 0% | I98T ‘SUV TT SSPr‘s oe ew wee SOTTO NVI. a 9-L1. OLE 0.02 ‘Wd 08°F 3 = 4000'S oe. Be * semmon eprnaatd, : Z1Z 9-2P F-1Z ‘Wd G'¢ ' he ‘ 0-22 Lh L-61 ‘Wd Ge'ct | T9SL ‘Sy F SSKs - + + saauatkg ‘soumog xnegr $ + 91% LP aes | ‘swoon | Tost 4me6s| ¢0s9 "+ + + s Bowuaqeyopayorpg | * " * * Tv ‘f 368 BEPORT—2862. Height in|SPi"t| No. of ‘Tastz IIJ.—Observations made with Station. English | pfer.|instru-| Position. | By whom placed. | Date of deposit. feet. |cury.| ment. : Mont Blane ,.:....s00ee0e8. | 15,784 | S «| Pennine Alps | Prof. Tyndall. 1859. Aug. 21. Monte Rosa (HoéchsteSp.)| 15,217 | S | 316 a », | Col. Robertson. 1860. July 16. » 99 (Nordend)... | 15,132 | S = a » | Sir T. F. Buxton, | 1861. Aug. Finsteraarhorn ...........- 14,046 | S | 313? | Bernese ,, | Rev. L. Stephen. | 1861. Aug. 5. dae oaeeee ‘5 S | 318? = » | F. F. Tuckett. 1860. July 27. Corridor (Mt. aioe 14,000?| S ... {Pennine ,, | Prof. Tyndall. 1859. Aug 21. Castariicesctrdsceaveses crass 2a;879 |S | 376 5 », | W. Mathews, Jun. | 1861. Aug. 23. Grand Paradis ....-....... 13,300 | S | 367 |Graian ,, | F. F. Tuckett. 1861. July 3. Griyolavacscecsestess|—4A'r mae. |* Ve.ce 2007 69 «= |—25°8 27°90 8. 9. 10. 11. 12, 13. 14, 15. 16. REMARKS. (17) Electrometer, balloon reading 58°; air reading 61°. Palpitation of heart very perceptible. MI (18) Deep blue sky; dark bluish hands and lips, not face. (19) Sand out. Electrometer, balloon reading 58° ; air reading 60°2. Heart less af- fected ; moving northwards. (20) Twenty-eight vibrations of horizontal magnet occupied 433. (21) Electrometer, balloon reading 59°; air reading 58°. Breathing affected. (22) Nodewat —8°-2. Electrometer, balloon reading 58°; air reading 59°. Very deep blue sky; clouds far below ; cold, but not intense. (23) Nodew. All the feelings of sea-sickness. (24) Ozone o. Feeling of illness. Mr. Coxwell says a disagreeable sensation came over him ; cannot tell how. (25) No dew at this temperature. (26) No dew. Through a feeling of illness, I was unable to keep to the instruments long enough to lower the temperature to get a deposit of dew. (27) Electrometer, balloon reading 58° ; air reading 58°. (28) Ozone o; theair is very dry. tn ap in i alc a 390 55 Time a4 ee hm s (1) TI 25 oam (2) | 2u3F 0. (3) | 11 38 oO, a 1139) 0.5, D)) |} “ar 40.-0"}, (6) LMS 0: |; (7) Ir 44 ° ” (8) T0145. .0) bs (9) 436 opm (10) 449 90 » (11) 4 40 30 » 44945 » 441 Oy (12) | 44115 » 441 30 5 442 0, 4 42 30 y Aika ©. \y 443.39 » 4 44 30 5, (13) 445 3° » 4 47 3° » 4 48 30 ,, 449 0 4509 90, 4 50 3° », 452 Oy 4 52 30 ,, 2793))39) 53 454 0 » 4 54 30 », (14) 456 0,, 4 5645 ,, 4 57 30 », 43.59) 0% wy 4 59 30 » me Tere <, ac €. ee (15) Bor Os i. REPORT—1862. Siphon Barometer. Reading corrected and reduced to 32° Fahr. in. 13°I44 16°359 18°944 20°042 20°542 23°442 24°242 Att. Therm. serene aeeee eeneee eeeeee Aneroid Barometer, No. 2. eeeee Height above sea-level. Crystal Palace, July 30, 1862. eteee seeeee teeeee teeeee ween featee eeeeee teeeee totes deeeee tenner eeeeee seeeee seeeee weeeee aeeeee setees weeeee a eneee eeeece seagate 29°96 250 wseaee 29°96 250 eccves 29°87 330 eeasd 29°82 370 seeeee 29°80 390 Seauee 29°65 480 eeeeee 29°55 57°

- cadana cit aaeees 50° ie een eat anecg oh - gases) Wr Sennen 44'0 EAD escaeetNh fecoaan JN gacnau 1) cooace f onades 8: 62 pe 55 58 49 RL TABOR F ssace: | acenes RaRvanMMe Cecmace: sill, aacaeg 36°3 > Eo oy Re RO occ ae ee ee rc es eee er 40°5 MCA L scuevah |S ovcka ih ivaue) fie Seasea eokdis 41'5 5°4 6-2 6°5 RACED ast S.ccseer fb yesann | ff gesace. UP. eeades 41'S MPUSOVM | iecaseg | wecdsg TR Secese | devece congas 41° pie e5 a5 58 5°8 cy _ Mr. Coxwell discharged quickly several bags of ballast; let go the grapnel, and called _ out to me to take hold, when the car struck the earth with great violence, which broke _ Several instruments; then bounded and descended again, and finally the balloon-netting caught in a large tree at 115 50™, at Langham, near Oakham. (9) Thirteenincar. Raised a little for photograph. (10) Left at 45 40™ 10%, (11) Sand out. (12) Wind S.W. (13) Gas cloudy. j (14) Thin fog; horizon hidden ; hazy. (15) Sand out. od 892 ‘ REPORT—1862. Taste I.—Meteorological Observations made in Hight 2. Siphon Barometer. | Dry and Wet Ther- 2g — : E2 | time | ening, | a, azul) MEM Ser Ze andredused | Therma. | N° 2: to 32° Fahr. hm 5 in. ° in. feet. es 3 (1) 5 I 30p-m. senses teense .25°98 4,104 521 46:2 ESPNS Pins ececce || - cones . 25°76 45324. 51°5 46-2 (2) Cire” he: (hey paene peace 25°68 454.03 52-1 46°0 5 7 30 ee oN a eaesve” |) } Scans . 25°47 4,613 49°72 43°71 SEO T ge atti we wcooe apa ceases 25°30 4,783 49°0 43°1 (3) 5) 9939) 33 Ee assemel| isos sds 25°40 4,683 48°5 43°5 OBLONG y | y viedaes a Ue eae 25°35 4,733 48°9 43°5 (4) iit yor Sl eA ee eee 25°20 4,923 48-2 431 5120, eveess paesce 25°20 4,923 48°5 4371 Ser foe | eee S 25°26 4,863 48-2 43°70 Boalt) Ce el re tecere | 25°25 4,873 48-2 43°3 (5) RMOMSO st ii. | scses i ill seowes . 25°20 4,923 47°9 43°70 (6) 5 17 3° 5, eit ope aie 25°00 5,155 49°5 43°1 RRO accwee |) Ire Setseutrge || Seene 23°59 6,747 Gmermsoms |) i ill fastest; |i peeetes 23°40 6,937 (3) (Boo Les ere ei en i oe 23°42 6,917 GUAT Oss el) eieesce |S \L) Peeecons [Mpatdens) JI) pemeeectes 615 OM, : aoa ea We tect 23°63 6,720 GeUgeeon imma eric. | Peete. [Wbesesen Ndr emacs GSS OUR Mee Boosye | loess * 23°95 6,400 6ag250./;, SSP A! oe 24°35 6,000 AG ee Tee 24°55 5,800 “raaey ster 75) | Sa are 24°60 5,750 (4) DRAM eer i sscses. s. |' steers 24°95 5,400 GEZIOM TN fcsseve ) || Resenee 25°40 495° MOU GA Vict osccccums | Posbpes 25°90 4,450 00, Qh A eee ee ee apo itbvehecesna that ene (5) O27) ele SRE We eres al lescaert 26°48 3,870 Gizan a’, ext Sct te || Coe te 26°60 3,750 6250 ,, Sanco Ml e532 27°65 2,700 6 25 30 ,, Ssagsene NP eaecenun [too sea tee, Win ences (6) GRRE CO. bes wt ep ueaccegy, , ta P sedans 29°96 |ontheground| 68:0 ee i omme) eeneee seneee eeeeee weeeee seeeee eaeeee weeeee eeeeee (1) Cumulostratus and cumulus same height ; strati above. seeee | weeeee eeeeee | tte eee weeere | weeeee ee ee er rr ee weeeee seneee (2) Ozone o, by Moffat and Schénbein. (3) Going down Long Reach. (4) Gravesend. (5) Removed instruments; hop-garden under us; came down in potato-field. (6) In this ascent the instruments were carried by a board fixed to the side of the car of the balloon, I standing all the time and looking over the side of the car; Mr. Ingelow was seated on my left hand and read the Aneroid Barometer and Daniell’s Hygrometer; my son was on my right hand. ON EIGHT BALLOON ASCENTS IN 1862. Crystal Palace, July 30, 1862. 395 esr Dry and Wet Thermometers (aspirated). Hygrometers. an ee = Daniell’s. | Regnault’s, Diff. |Dew-point. pace Dry. Wet Diff. |DewW-point. h ; meter. Dew-point. | Dew-point, ° ° Foe ° ° ° ° ° ° 57 32°9 58 32°4 6-4 313 a8 29'0 5s 31°8 Heed dee sodas RASC. | asses 32°0 57 Bee eopives: (i, | codstar- | | cosets | | seceee Sannea 32°0 63 oe Vy eo Besa | | caver | | coches Ayo | i ae : 31°8 56 324 6°5 32°5 6°3 B27 =| Bases P| b sakteuey’ || ( essccens| 4 oschaee MM caeces 31'0 6°4. 32°8 aieaes wuytdess, | becadtar+ |) acasaeteey “eases. 32°0 oe) 34°3 4°7 36-2 5°5 354 50 Baa Wl) 0 4, BOrBo7.. i edvese. |b osees : 9,884 45°0 38-0 I 24 5 WNL 8 asecse. .. i] esaeae,. || © wuweeeue I) | etemmns eee eee Py es a He ZOSOF oi vases » | 21°28 9,884. Te 2AnGOmee ZE37T © || Weeutes |) | wenevel alle cose 462 39°5 (9) ns © <5 1) i irene ZI°SO, ji | céccce™ Pi cgeeaee a Geese By in) te) 1s a rr iduasely [ke jeaeee ete 472 40°5 E260 E2630 *. 22232, ht Possess lh betwee 8442 | ee. VE daseee (10) IeZ7TaO! ,, 22°622 5270 22°90 7,836 510 46°5 De32) 0) |,, 22802 “lL aspers 22°85 7,650 51-2 46-0 cr : + o |, 22:BOZ A Weecsess. |) | svese> 7,650 53°8 47°8 EE ay) if) We eswenste Tl Wowevee || Pestens). (I patcnnems Sodebe Hill. eeteoe (U3) gel ie ae Soares | Boescser i Mgtvcoce™ . [UMeteaceae Proc Pu | Wie 14) 137° 30 |, 24°248 bio Kae mal | tacos: 5,919 56°83 50°5 (15) Lagenrors 24°460 59°70 24°60 5,820 57°70 50°5 ESTO ros Life toy Ce ieee aie AS Pacers sil wieseess eanees 580 51°5 TAT Oy 257083 62°0 25°30 5,028 58°9 52°0 (16) I 41-30-,, 257564. 65"0 — AS53O" AC eesas tease . 142 0, Sal coon 25°60 (17) peat if 25-5 SA al" wextusl eins decent 4,480 ore 53°5 scene ieee a cours Fox Sacuas o°9 54-5 (18) TAM Oe 2Br562 || lescses ditesses - 3,438 61°0 53°5 (19) TpABssO. 1, 26°756 6770 | wsseee 3,219 59°0 54°0 152 0 ,, 25°795 | wees 25°82 45233 53°5 49°2 (20) I 52 30 ,, 25°594. O50 ot Bees .cp 4448 TESOL) | Sicideacee 4] |b sebee ° saree + Ateepas 52°2 48°5 (21) I 3 oO) 25°079 65*0 25°25 5,019 510 47°8 Rs SR (me ee see eg ge tarry (22) I 57 40 # Savdeerh || it exper waves’ ||) coseseate th). oSeauee wmresee I 5 oy 24°394. C255. tees 5,780 OTL TE {oon Seon b Aaa erereyee 0 Weer oD Ape| | eS : wapee * (23) BSS AG TIS ioscan, eedebon es eae | ae ee seeeee 2h DGB. 1 237928 62°0 24°10 6,313 2) iO.) 23°778 62°0 ane 6,491 (1) Birmingham in view ? (2) Wind N.W.; moving S.E.; gorgeous view. (3) Light and shade magnificent. (4) Balloon full; gas cloudy. (5) Turned to descend. (6) Opened valve. (7) Most glorious view possible; cumuli far below, detached. Wolverhampton under us, as a fine model. (8) Plains of clouds in the distance. (9) Opened valve. (10) Rippling of edges of canal beautiful ; calm; Black Country remarkable ; alpine and dome-like clouds; bright on one side, dull on the other; detached cumuli; horizon ap- parently same height as the eye. ¥ ON EIGHT BALLOON ASCENTS IN 1862, 397 se Balloon Ascents. Wolverhampton, August 18, 1862. mometers (free). pe Dry and Wet Thermometers (aspirated). Hygrometers. an eee SSeS Zambra’s Daniell’s. | Regnault’s, Diff. | Dew-point. cei Dry. Wet. Diff. |Dew-point. meter. Dew-point. | Dew-point. ° ° ° ° ° ° °o ° ° Meee sft) asthe . 45°7 5°5 32°0 6°5 29°2 AGRO sssecet st oscscst ili cusccseed|beleelene 30° 55 | 286 | gors seseee | eeeees 38°5 51 24°9 4°5 24°8 7 22°2 6:0 28°6 ADUSEOA ccavesd =! -cochon -$}: | ebnecnboribulsaeane 22° 25°0 7-0 PE MET |) wsoadeP Mh csesee: ||) ‘sawabech"| . Soestewenph ccerevavndie sccdeons WW) Matecte 40°0 3°72 ey ll octecek’ Il) -concse’ 7) seas WM deescole o[C recenan 42°0 ME cewere’ | seccve™” | coctue ©] evened of) coveect= ibs ovceee fle “ejvnses 39°5 Gewese ih) erste! | cesves 50°0 46°5 3°5 4258) Ne Beredon 39°0 teeeee Seteee 54°38 -oacocueel | MRSS | ne 5272 46°3 54 413 Consee 39°0 OO z 8. ae 10. ie 12. 13. 14. 15. 16. (11) The sun shining on shades of Dry and Wet Bulb; valve opened; beautiful resonant sound. (12) Aspirator difficult to work. (13) Clouds very beautiful. (14) Warm to sense. (15) About midway between Wolverhampton and large town,? Walsall. (16) Balloon collapsed. (17) Shouting below, thinking we are de- _ scending ; a reservoir in sight. (18) Shaded the instruments. (19) Protected the Dry Bulb from influence of sun; sand out ; shouting. (20) Beautiful prismatic colours round the balloon’s shadow; passing along high road to Birmingham. (21) Bell heard in Birmingham very distinctly. (22) Sand out. (23) Cumuli same height as car. 398 2 Siphon Barometer. Dry and Wet Ther- 238 Aneroid . £5 Time. Reading Barometer,| Height above Sa iy Att. >. | sea-level. Ze _nompcted Therm. No. 2. Dry. Wet. to 32° Fahr. m s in a in. feet, a a (1) PESO piles ee TVAy Cin 6 8) lon Cooma (eo cee Mle Tee Meco seen) ee hk Cn 2 org | ee en ey ee Mee ees eth IX GD: 55 21°882 G27n- ae 8,771 TE SOMSSMEEEI laefess [iv .Sbotee ZI"Q5 | . tesonmeye It wena, Nees SOMME, | vcoStvs-- fl desace 71438 : (2) Raters Fe AN ie. | «asccacya| || gaeste 26°80 3,003 53°0 49° CELA Ny PE BIO vos ip dss decsen ed vecere 26°10 39703 512 480 (15) Fe MO cen. F| raddabec 4P || oevess 24°82 5,194 4570 43°5 748 0 » fees a Pewtang 24°90 5,106 45°0 43'5 (16) 749 20 » r OT tad ee 24°18 5,900 4370 (17) ABO GOSS): ll ec sas's ae ZASS vhe| Pirdevass 430 7 BRO cy. wetlye deoec tae: |" gecveve 24°88 5,200 43°3 (18) TBM 20a Win © [downsge) | dearest 24°88 5,200 44°2 (19) 7 BOO cas tehdhe dees ceeeed |) haces 24°92 5,160 44°2 TEST BO se5 tas eercwes yak | eceass 25°00 5,080 (20) ee Le ae cue aeererea Le oer ee eR 5570 a. 2. 3. 4. 5. 6. ts (1) One-half of Kennington Oval is lighted ; gas coming out from neck clear. (2) Getting too dark to see the dew on the black bulb of the Hygrometer. (3) Gas clear; great noise below; no wind; see earth; foggy below. (4) Moving slowly near water. (5) Heard Victoria bell. (6) Over Vauxhall Bridge ; sand out. (7) Saw Regent Street and Serpentine. (8) Loud noise below; see the river for miles. (9) Railway whistle ; could distinguish the squares below; looked well lighted up. (10) Going over Westminster ; over Wellington Barracks. (11) Gas cloudy; saw two bridges together over the river. (12) Saw the Strand and Crescent lighted up brilliantly. (13) London looks beautiful ; Houses of Parliament, Charing Cross, and Piccadilly distinct ; dark below. (14) Heard chureh clock strike. (15) In cloud ; London out of sight. : (16) Blue sky ; clouds below a rich red; packed up Wet Bulb. (17) In cloud; too dark to read instruments ; 7" 51”, counted ballast bags, we have four; t 3 ON EIGHT BALLOON ASCENTS IN 1862. 407 Balloon Ascents. Crystal Palace, August 20, 1862. mometers (free), ge Dry and Wet Thermometers (aspirated). Hygrometers. an Zambra’s a : Gridi < Diff. |Dew-point. There Dry. Wet. Diff. |Dew-point. meter. Daniell’s. Regnault’s. Dew-point. | Dew-point, — — |__| EE | ° ° ° ° ° ° ° ° WWwo CYNON OW HWY O DW wn lo} _ 50°5 “a ey muetll|) bseuseos Milfuerenne ecoeee 49'0 mm us og G2 BLO G2 BRU DA U9 48 19 49 42 Mm NMNINI WP NY CONT p oO Lal 7* 52™, gas cloudy; above clouds, beautiful view; London out of sight; 7" 54”, gas cloudy ; can scarcely see to write. (18) The setting sun tinged the clouds with red. (19) In cloud; just see above; earth pitchy dark. (20) Agitated dry-bulb thermometer over side of the car. The hum of London was distinct, and then gradually died away. The balloon, after a time, was allowed to descend below the clouds; the appearance of London, as now viewed through mist, was that of an immense conflagration ; the lights were not, as before, innumerable and distinct points, but large in volume, united, and of wonderful extent; this appearance continued till we again ascended above the clouds, where it was much lighter, but not sufficiently so to enable the instruments to be read; and thus we journeyed till again descending below the clouds, we heard the lowing of cattle, indicating that we were some distance from London ; the balioon was allowed to descend very slowly, for it was quite dark. Mr. Coxwell had sand ready to discharge on the instant, which he did on nearing trees, hedges, &c., and thus we passed over them and dropped gently to the ground, in the centre of a field near Hendon, a little before 10 o’clock. The grapnel was not used, as Mr. Coxwell was fearful of hurting some one, or otherwise doing injury. 408 References to Notes (22) (23) AMAANAAUAANAUNAAAAAAAAPHLPDHDAADDADADRDRAADPEDRRERDREREE Time. wo eceoo0o0o0o0o0o0ce 0c 0000000000 00000 wo wh nv eoo00000000 00000 REPORT—1862. Taste I.—Meteorological Observations made in Eight Siphon Barometer. Reading corrected and reduced to 32° Fahr. seenee Boeeee serene seeeee seeeee senses sense eeeeee ences eeeeee weneee weeeee seeeee eeeeee seeeee seeeee seneee feeere feeene (1) Line of light to the east. : (3) Clouds broken in the east; beautiful lines of light ; gold and silver tints. (4) Balloon spirating; heard voices calling from below. (5) Clouds beautiful; could see the earth in the distance. (6) Very misty ; blocks of clouds above ; cold to sense; voices calling from below: Daniell’s Att. Therm. wesene eeeeee weeeee seetee seeeee teneee weneee eeeeee Aneroid Barometer, No. 2. Height above sea-level, seeeee (2) Thick mist. Dry and Wet Ther- Dry. Wet 60°8 59°5 60°0 58°5 58°9 58°0 59° 597° 59°9 597° 53-2 56°5 578 548 BW ae) 5472 572 53°8 56°83 53°8 55°5 53°5 55° EE jae) 52°2 49°8 49°8 47°2 470 44-2 46°5 43°8 43°38 42°38 43°2 42°2 42°0 412 40°2 40°0 397 a9 7 38°5 37°5 40°7 3770 415 3772 40°5 377° 40°5 36°5 41'0 35°8 37°5 32°5 37°72 32°0 35°0 30°5 35°2 29°8 34:8 29°2 33°0 28°2 32°8 26°0 31°9 26'0 310 26°5 29°8 (31) Hygrometer was broken the night before; 1 had attempted to mend it, but it would not work. (7) Scud below creeping over the earth ; cumuli on same level in the distance; black clouds above ; over Mr. Wolley’s farm. (9) A great many ponds of water in sight; entered the clouds a few seconds afterwards. (10) Lost sight of earth. (8) Heard railway train. (11) Great masses of alpine cloud; beautiful cumulus cloud. ’ ON EIGHT BALLOON ASCENTs IN 1862. 409 Balloon Ascents. Hendon, August 21, 1862. mometers (free). Negretti Dry and Wet Thermometers (aspirated). Hygrometers, and (ee Zambra’s : aes Daniell’s, |Regnault’s. Diff. | Dew-point. bale Dry. Wet. Diff. |Dew-point. meter. Dew-point. | Dew-point. 13 58-4 ° ° ° ° ° ° ° m5) | 572 "9 57°72 o2 58°9 o'o 59°0 17 | 5570 370 52-2) oa) | 5x2 34 | 506 370 51'0 2°0 512 2°0 Sil 24 | 47°4 26 | 444 28 410 27 40°7 I'o 41°5 I‘0 410 08 40°2 oz 39°8 Pm | 397 I'o 360 37 32°3 43 318 35 32°5 4°0 30°9 52 29°2 50 | 25°5 52 24°7 45 | 23°3 54 212 5°6 20°2 4:8 18:6 6°8 12°4 59 IO'r 4°5 14°3 8. 9. 10. 11. 12. 13. 14, 15. 16. (12) In cloud, surrounded by white mist. (13) Sensibly lighter; a light wind. (14) Valley of cloud; in a basin; on reaching its limit saw the sun rising. (15) Like a lake under the sun; immense ocean of cloud ; magnificent view. ti Under the sun a lake; mountains of cloud to the left ; fine cloudscape. (17) Lost sight of sun; earth visible underneath; misty. (18) Deep ravines and shaded parts in clouds; sun again rising in the same magnificent way ; silver and golden tints. (19) Lake and mountain scenery ; clouds near us sweeping boldly away. 3) Moon seen. (21) Cold to the sense; gas clear. (22) Applied water to Wet Bulb. (23) Mr. Glaisher’s pulse 88. 1862, 2k 410 REPORT—1862. Taste I.—Meteorological Observations made in Hight g Siphon Barometer. Dry and Wet Ther- Be . i Paernd Height above 3 z =a Beene Att. aa ae sencleval, Dry Wet 28 and reduced | Therm. to 32° Fahr. hm 5s in ° in. feet ° ° (1) eC eOaais wil denser |! eons ke 19°45 11,616 27°8 (2) 5 22 ° a | Reece, |} Wueese 19°09 12,254. 25°5 (31) (3) 5 23/colag obese. |i soe8ec 18-90 12,421 23°2 (4) 5 24 0 5 scoaccnee) ||! 4.9855 18-90 12,421 23°3 (31) DS zATSOMANL | edie await Mercecs 18°80 12,571 23°0 525 Tors dhess teces 18°70 12,691 23°3 5 26 0 SULT ateleecs Ut Wevece 18°60 12,831 23°5 (29 5) DTEROMMTC | Tcteors Uh Iewones 18°42 13,080 240 (29°) SEZO COURT. \sivece if) losecee 18:20 13,381 24°0 19°5 SeZO SOM lsdeces = ||) fessnee 18°15 1354.56 23°5 18°5 SOONER! (ecascs —!|| Geass 18-00 13,665 25°0 20'°2 Se LOMGMEMON| —isctess 1], wees 17°90 13,680 22'2 162 BESZMIOMPMEEER|: {sds005° ||) we aap 17°38 13,685 21°5 16'0 BBZETOUNG |] ls dseee Brera. (Me scncceae | ie ais 21°0 14°5 SAGO ate al! letecce fi} dinewacs 17°82 13,799 19°5 13°38 5 340 yy sueene fl fess ° 17°78 13,375 19°5 13°2 (5) 5 34 39 5 PL || ber Sonos 17°78 13,875 19°3 12°2 SGA SNOitsy || | teNeesn 1) faueae 17°70 14,027 19°5 12'2 (6) 536 0, doses. Ifieeeses 17°72 13,989 19°9 13'0 5 36 30 5 ‘ype. eects 17°71 14,008 20°0 13°5 eS kO Fos cull) lteeones, 72|Pabesses 17°70 14,027 20°5 14°0 538 o y Se AN Soba 17°65 14,121 21°5 14°9 BSP 430s SUL ee hasss All beaves 17°62 14,178 22.°5 16°5 4 O Oe a tedsree | Rideirecse 17°68 14,064 24°0 180 {Am VOM ELT eis@ssws| onl teesnee 17°68 14,068 24'8 20°O (7) 5 43 9 » | OS AD Sean 17°62 14,178 24°8 20°5 AA OMS Tet eakewe Uit Teseees 17°62 14,178 25°2 20°5 5 44 3° 5 “ ; 17°62 14,178 26°5 19°5 AOL LO Se Me hisses UN aescess 17°58 14,254. 2.6°5 19°7 SAS AS aes Ah pasans: 8? Sone : 17°58 14,254 263 19°9 5/40 Oa Ml Piessc cca aren 17°58 14,254 27°2 20°0 54615 » A en. |" eos 17°58 14,254 27°2 20° 547 © » 4 oe |e sedec 17°56 145355 27'6 20°0 Pca Milne es Se Sespe. 17°57 14,273 26°0 20°5 9 5 48 30 4 Baten OA Beas a 17°58 14,254. 25°5 BESO RO Tap) ol | caeteweet lt Wecenes 17°57 14,273 25°5 19° 5 59 45 9 Peas alld teevees 17°58 14,254 25°2 18°9 (10) Ln sso Coc) MARES aS eR IB Hoe 8 17°56 | 14,318 25°2 18°r Sig SZ MOLE. Min “btotees © Ald Revoc. 17°60 | 14,258 24% 18'8 (11) Big: Olds <1) etesce 1141 besteen 17°62 | 14,228 238 17°5 556 oy Efvise, aad done os 17°62 14,228 23°8 17°38 Bas 0 a0. Seta eg, Adit Pooes “| 17°62 14,228 23°0 17°5 (12) cy Piers Beeews attr 17°62 14,228 23°1 171 5. $7 30 5) = Berassk, | Seaton 17°61 14,243 22°5 17‘I 558 oy Metal sees 1760 | 14,258 2370 16°5 (13) 5 58 30 » dyeitcoa! .4&iv Je 8720m 14,228 234 16°5 5 59 32 55 viniad init 17°62 | 14,228 23°4 16°4 (14) 60 Oy onste seers 17°63 145213 23°5 16°5 (1) Master Glaisher’s pulse 89. (2) Captain Percival’s pulse 88. ‘33 Mr. Coxwell’s pulse go. (4) Mr. Ingelow’s pulse roo. 5) Magnificent peaks of cloud in distance, rising from a base like seas of cotton; gas transparent. (6) Network looks beautiful, perfect symmetry of form. Feet very cold; our boots covered with ice. i j ON EIGHT BALLOON ASCENTS IN 1862, 411 Balloon Ascents. Hendon, August 21, 1862. mometers (free). Neerestt Dry and Wet Thermometers (aspirated). Hygrometers. an ee Zambra’s ‘di Daniell’s. |Regnault’s. Diff. /|Dew-point. Loa Dry. Wet. Diff. |Dew-point. _ meter. Dew-point, | Dew-point. ° ° ° ° ° ° ° ° ° 45 |- 71 50 98 48 63 6:0 23°4 A 20°0 65 30°2 57, 274 6-3 32°4 71 39°2 73 4° 69 36°2 6°5 22°6 6°5 21°5 6°6 29°5 6:0 22°71 6:0 17°5 48 6°5 43 3°72 47 44 2 14°4 6°83 132 64 12°4, 7% 12'4 72 12°4 76 131 5°5 74 6°5 15°4 6-2 15°3 y hp 8 21°3 5°3 12°5 6-3 19°7 6:0 17°7 55 17-0 6:0 20°5 54 17°6 65 24°3 6-9 25°6 7° 27°5 7° |—27°4 8. 9. 10. ll. 12. 13. 14, 15, 16. (7) Ice on Wet Bulb and connecting-thread. (8) Sea of clouds below. (9) Fine echo from balloon. (10) Sun obscured by thin strati. (11) Sea of clouds all round. (12) Stratus sameheight ; cirrus above. (13) Valye twice opened. (14) Beautiful sea of cloud everywhere ; dropped paper, visible two sg ‘ : Eo - 412 REPORT—1862. Tasie I.—Meteorological Observations made in Eight 2 Siphon Barometer. | Dry and Wet Ther- zs ioe asses Glimaee nf! . ER) . P Height above SA Time. Heading Att. Barometer, sea-level. Ze be pat These: No. 2. Dry. Wet. to 32° Fahr. hm is in 4 in. feet = a 6 1: oam. aoe’ bol aaeaaie 17°70 14,108 24°2 16°5 2 3g iS): al EAI oman oe eee 17°90 13,802 24°5 16°5 Be De ocr: I sae | lie ee 17°95 13,715 24°2 16°8 a Gy st - Saad Ge rea ee Ce 1810 135484 23°38 16°5 (1) Oa eyo a a See) ier ee 18°11 13,479 24°2 16°5 (2) GeeA One| kee ON Bsees 18°15 135419 24°2 16°7 DMRS Ot hots | sens 18°23 13,299 25°2 18-2 PRBO EOS e |. secse |, decane 18°30 13,194 25°2 19°2 : 24s “0 ©) i eae Bee Seer 18°35 13,119 25°2 _ Mw OeT adecss . s | Casenee ||) Aeteentecs Il imeddere 24°5 13° (3) GUZEEOMEAN | cdesce | gaeaee 19°07 12,174 30°0 24°0 OMTOEZOM tee) tess | deces I9'I1 12,123 29°8 23°0 ay SO op 1) Re (ie Bee 19'S 12,070 278 22°0 (4) Curdqecomemes| °.h...0) |) Senere 19°28 11,901 27°5 202 GMYAMEDMESS | <:cgccee || viBxsesv 19°30 11,875 27°38 213 ons con aS i Sa ee: See 19°30 | 11,875 27°5 21°5 RISMMO ssf]. \stches “E> beeen 19°30 11,875 27°38 21°5 BIO RO Wg, lr cece, ta aes 19°65 | 11,420 31°5 23°83 617 oy eeeees fi ereeee 19°80 11,225 3270 25°0 Te tae A Ee SE. as: 20:05 | 10,871 33°8 260 OBIS oIG Gyyr a e- theese, | Pui csce 20°20 10,688 34°5 27'1 AP" TOSS YoY gall eee Cera | es Se 20°30 | 10,566 36°5 23-2 619 © 5, saben” El) tesa gee 20°80 95936 37:0 29°2 (5) Hi20 40 ee ey eed 21°00 9,650 37°0 29°5 G22 gO Saye al ees Bll cescese 21°70 8,310 415 310 (6) 6 23 30 5, ee I Ni 22°20 8,196 43°5 32-2 (7) PO aS ee ila, ete Sea | ae Bee 22°33 8,040 43°0 33°0 (8) Gp25 ato El Takes BRS ie 22°65 75655 42°8 32°5 Bias gos. fret. os 22°72 | 75573 | 43°5 | 33°0 (9) Po ee Sate | Nae A, a Se? | 22°95 | 75293 | 445 33°0 (10) G79 Bl oeae, Bie 23°08 7,141 44-2 340 Seon, i) Shs Be: 23°12 71°94 43°0 35°2 (11) Fo et a ee x SR 23°11 7,106 42°8 36-0 (12) GEE OREM |e a Sitar | be. aie 23°20 7,001 43°0 (13) eo ae a Sets Se ee 23°30 6,834 43°0 38°5 (14) SSE SE ae Sian i Se 6,907 42°0 (15) 6 31 30 5, ee ee es 23°40 6,767 42°5 See. . medicce Haars 23°50 6,650 42°0 (OS RS eae | meee Sera y Ge 23°60 6,533 42°0 (16) ae ee eee ee aes SA 24°00 6,058 415 Le ES ae ee OA Se 24°22 5,819 418 Oa ee 5 yuk. es an Se 24°50 59515 41°5 6 34 9 5 = OSS oh we 24°70 5,298 42°2 (17) a ee Ao Be t aS 24°80 | 5,189 43°5 G 8 Pe a 24°90 5,080 44°2 © 26-32 - - h ate, +e te oe 24°92 5,058 438 ae we eas Cane ey es Sa 25°10 4851 452 | tle 25 F = - F rf (1) Valve opened. (2) Valve opened. (3) Dropped large piece of paper with our names written on it. (4) Train heard. (5) Could hear the watch tick when the ear was above it, but not when below. (6) Gun heard. (7) Balloon reflecfion on cloud, surrounded by prismatic colours. (8) Dog barking; railway train heard. a Balloon Ascents. ON EIGHT BALLOON ASCENTS IN 1862. Hendon, August 21, 1862. mometers (free). Diff. ° ° 77 |—29"0 8:0 29°4. 74 1770 73 26°7 77 19"0 75 27°7 7° 17°3 6:0 139 63 159 57 |—138 60 |+ 51 68 |+ 16 58 |+ 18 63 |— 68 by |— 54 60 |— 54 63 |— 44 vue i 55 7O) «|-+ 88 78 17°3 74 14°7 8°3 16°0 78 18-1 75 18°7 10°5 18°0 113 18°7 10° 2I'0 10°3 20°1 10°5 20°5 1r'5 19°6 10°2 22°0 78 25°8 68 27°8 58 30°2 45 3371 1'5 38°7 15 39°72 1'5 38°7 1°5 38°7 17 EVA 20 37°3 x7, S77 7. 379 2°5 38-0 31 We) 2°6 39°72 37 |+372 8. 9. Dew-point.| Thermo- Negretti and Zambra’s Gridiron meter. 10. (9) Clouds approached. (11) In mist. (13) Top of cloud. (15) Fog; mist. Dry and Wet Thermometers (aspirated). Dry. 11. Wet. 12. 413 Hygrometers. Daniell’s. | Regnault’s. Diff. |Dew-point. Dew-point.| Dewe-point. ° ° ° ° 13. 14. 15. 16. (10) Lost sight of sun. (12) Just entering the clouds. (14) Valve opened. (16) Earth visible. (17) Passed through cloud about 2000 feet in thickness, and found the country without a Tay of sun, misty and dark, 414, REPORT—1862. Taste I.—Meteorological Observations made in Eight 2 Siphon Barometer. Dry and Wet Ther- gs Bnereud Height above Bz Time. peeing. CO sea-level, as and reduced exis st to 32° Fahr. hm 5 in ° in feet. a is Bee yeqgomem. | Sstevcs. |) etedsces 25°20 45745 45°70 42°2 ODysaGety: |b aposes, | dees. 25°30 4,639 45°0 42°2 Gia ecw | seteca tl ecces 25°60 45320 6:0 43'2 (1) oe Siok Sie (Eee een | Me nee 25°92 3,980 46°83 43°38 CRA ORs eet Gestsees (| teaedes 26°15 3,751 47°38 44°83 GsAOMO iss’. | yeteves Fl esvess 26-40 3,502 48-2 45°I (2) OPT MEO hy FE! isdcess | a isveus 5 26-60 3,300 49°5 47°2 GWAZ MO Mase FUN trcdacee: 2'| Mssuces 26°80 3,186 50°0 47°8 GRAZ RES ER Coin |) a ctssss: 11 Ceeoete 27°00 2,872 5170 48°2 GEAGIMOM IIE jesse i! Wesere 27°20 2,673 51°5 482 STAR EOm ET eissss |! Seabee 27°70 2,177 53°5 5o°1 GUAGRBO ME | vives | feeeeee 27°98 1,898 54°5 512 OPAROMERET \rdewix’. |) dvoscws 28°20 1,684 55°5 52'0 GRACO Masti” lictewee | | eocons 28°40 9489 56°0 52°5 (3) PANOMNOM@aS LE |'< sects: (4) fucevee 29°42 513 61°8 56°0 Crystal Palace, September 1, 1862 (4) Ame GeO PM rel amerterscen f\lkSecacors Wilh mesces itl ieeavst 630 59°9 8} | ar4o 0% 5, >A felis 4 fb sceee 29°78 250 63°38 59°8 6) AG UO tera e- re | eiccnc ss 29°78 250 65:0 59°8 | 4 52 0 » | COR, ie cepa he SS Ee 270 64°0 59°8 (7) | 453 O » 29°45 | esas - | 29°65 320 63°0 570 4 53 20 5) GE well, Setwae's 29°20 720 611 56°5 4 53 4° 5, Ze BO El) haces. 28°90 996 59°72 54°5 454 S » 28°52 | sseawe 28°55 1,332 572 541 | 14 54: 30g Za DO) "Si. detects 28-00 1,868 552 §2°5 oO 4 55 Char § 2EO' Tl Lseces 27°65 2,214 54°2 51'0 4.59 4°» (10) 457 SO» 2730 | sevens 27°21 25654 52°2 49°5 4 58 3° » 26°99 | weeeee 2692 25940 51°5 47°8 (11) AEQ) TOs 2G'00 | pests. 26°91 2,950 50°5 47°2 (12) Geeks 10 wes 2EISO Tee cesss 26°78 3,080 50°0 46°5 (13) 5 1 30 » ane ee Sr 26°69 39170 50°0 46°5 Le PD ar : j 5) gh aF%, 26°65) y 12) pecaes 26°61 35257 49°5 46°5 (14) Ras Ofte 26°Go =. $2.55 26°60 3,268 49°2 46'0 (15) 55°. eS EAE: Melee cscs 26°46 3,408 49°2 (16) 5 5 40 » Sh ee be cee 26°46 3,40 49°2 448 a7) 5 6 30 » i MW Bae oon 26°41 3458 49°5 448 Sr Oo ae (18) | 5 8 Oy» 26°40 | seesee 26°41 3458 | 495 | 442 3. 4. 5. 6. (1) Biggleswade under us. (2) Shouting heard; people not visible. (3) On the ground, four miles from Biggleswade. In this ascent the Aneroid Barometer was read by Mr. Ingelow. (4) Clouds, stratus, about a mile high. (5) He fee near horizon, which was moderately clear. (6) Wind E.N.E. (7) 4 53™ 40°, over south tower of the Palace, (8) The ie course of the Thames to Richmond i is in sight ; gas cloudy. (9) Mouth of the Thames and its course up to and beyond Richmond in Tight, : ON EIGHT BALLOON ASCENTS IN 1862. 415 Balloon Ascents. Hendon, August 21, 1862. mometers (free). Negrete Dry and Wet Thermometers (aspirated). Hygrometers. an ——— Zambra’s fs di Daniell’s. | Regnault’s. Diff. | Dew-point. i acai Dry. Wet. Diff. |Dew-point. si meter. Dew-point. | Dew-point. 5 8 38°9 ° ° ° ° °o ° ° 2°8 38°9 2°8 40°0 30 40°8 30 41°6 31 42°6 2°3 44°7 22, 45°5 2°8 45°3 3°3 44°8 34 46°7 3°3 48-0 3°5 48°6 3°5 47°8 5°83 511 Crystal Palace, September 1, 1862. eB eS EE ee | 31 evil 4°0 56°5 Seapets} siasseds OO} wpessac [erpocses [Dv eseps . 52'0 52 Bata 42 | 56°3 6°0 BEG UH}. ceesna |), Meese Beal) pidawes STi anges “bel Pobrrsy 23 52°0 4°6 52°5 47 50°3 Sa! 512 27 47°8 3°2 ys i i os a pester) inseam |\™ ‘icepes 45'1 27 | 467 3°7 AAO! |. ceceas voeene seeeee pteneb seses 47°38 30 43°7 | 3°5 AGN || ctecve | ceavee | csctse * eeeeee 4370 : 3°5 42°8 10. 11. 12. 13. 14. 15. _ (10) Palace like a mist ; heard railway whistle, and close over Norwood. (11) Railway whistle heard ; two trains together. (12) Rays of sun lighting up Gravesend. (13) Gas very cloudy; rays of sun perpendicularly downwards; over Mitcham Common. (14) Over Mitcham Common ; people not visible. ; (15) Carriages visible; wind E.N.E. (16) Cumulus in horizon ; apparently at a lower elevation. (17) Palace beautiful. : (18) Over water. 416 REPORT—1862. TasrE I.—Meteorological Observations made in Eight 2 Siphon Barometer. Dry and Wet Ther- 23 fuscia Snail Daa ean i c EE | time, | Reading, | ggg, Barometer, Hcghtabore a actrees | Them. | NO sali (hain to 32° Fahr. | ae a ea hm i =s in. = in. feet. 5 3 (1) 5 9 opm. 26°50 | eeneee 26°50 35368 49°8 44°2 GIO siOu ag |. 226550. 10). eee ses | 26°55 35318 50°0 44°8 GatorgOlns || . 20:48 ||, dewwes 26°51 33358 50°0 44°8 (2) GMOs | || 26530 |} Reece 26°31 3,560 50°0 44/8 (3) 5 iO) 155 2670. Th dessa s 26°19 3,680 48°38 43°5 (4) 5 13 20 5, (5) G5) 10. 43 26°20 {ocee 26°19 3,680 49°2 441 (6) 5 15 40 5, (7) GD AKO. 23 26°25 Tasaae 26°25 3,620 49°2 44/0 te BET O55 26°29 fecuse 26°29 3,580 49°2 44'1 9) 5 17 40 5; (10) 5 19 © 5) 26°28 =| boaeee 26°28 3,590 48°83 | 4371 (11) | § 20,0 4 26°29 | seveee | 26-29 | 3,583 | 478 | 42-8 (12) 523 0 » 25°95 teens | 25°95 32937 472 43°0 5 23 30 5 25°94 posses 25°91 39977 47-2 42°1 BS 2A Os 25°90. | beveee 25°90 3,987 47°0 42°1 (13) 525° 0 5, 25°90 | taveee 25°90 3,987 47°2 42°5 (14) Sze O: 55 26°09 | wees 26°05 3,837 43°1 42°5 Brz6 30. 3, 2G bo see sce 26°15 3,737 48°2 43°5 Bey, FO. 55 26°20 ~ | cevees 26-20 3,687 48°5 43°5 (15) 52a e055 CATES (oT ow bein Sars 26°10 3,787 478 42°5 B29 10.5h | BOG il! ohesens 26'00 3,887 47°2 42°1 (16) E2065" 55) 1 25°88. |! kecess 25°88 4,000 47°2 42°5 (17) 531 0 » 25°75 | teeeee 25°79 4,090 47-2 4271 (18) ee Eade | 25°65 | eeses 25°70 4,180 46-2 41°5 5 33.O 9 | 25769 | evens 25°69 4,190 46-2 415 535 0 4 25°69 SEED 25°69 4,190 46°1 41°5 (19) | 5 36 oy, (20) 5 37 0 » 25°96 | sense . 25°98 39900 4772 42°8 (21) 5 37 30 % ZO2ZO || Neves 26°19 3,690 47°2 42°5 5 42 0 » 26°55 | ween 26°50 3,362 47°5 432 (22) Ly 5 42 © 5 20°82" — Nobis. as 26°82 3,040 48°5 44:2 5 ABZe O's ASR pe eA scorer 26°95 2,910 | 49°2 45°5 5 44 0 » 20°95. il) Eveces 26°95 2,910 49°8 46°1 (23) 5 45 O 5 ZO 2 tl eataees 26°88 25970 49°2 461 (24) 546 0, (25) 5.47 2! 39 1. 2: 3. 4, 5. (1) Wind changed to E. (2) Wind E.S.E. (3) Over corn-fields. (4) Three trains in sight; gas cloudy. (5) Gun heard. (6) Gas escaping from balloon at safety-valve very fast. (7) Apparently on a level with cumuli in distance; train; sun shining in distance. (8) Train seen; old Battersea Bridge near; South-Western Railway under us; near to Maldon; moving in the direction of Richmond Park ; newly made reservoir (of red bricks) under us; dog barking; wind E.N.E. (9) Over embankment of South-Western Railway ; Thames very clear. (10) Crystal Palace visible from the ring. : (11) Seemed to have changed direction ; could see the four black lines of railway. (12) The islands in the Thames near Mortlake very clear. (13) Supposed nearly over Hampton Court. (14) Gas very cloudy. (15) Shouting below. (16) Gas coming out of valve fast like smoke; higher than all clouds near us; could see the mouth of the Thames very plainly ; some said they could see the sea. . Balloon Ascents. ON EIGHT BALLOON ASCENTS IN 1862, Crystal Palace, September 1, 1862. mometers (free). Diff. Lal ANIA IHW ON DANO HYP ON SHeh AAA AAANAAUAAUAAARA OH BHNNG BS Dew-point. 38-2 39°3 39°3 39°3 37°8 38°6 38°4 38°6 37°0 37°3 33°3 36°4 36°6 37°2 36°4 38'4 38-0 36°6 36°4 36°3 36°4 36°1 361 36°0 37°9 37°2 384 39°6 41°6 42°2 42°8 Negretti and Zambra’s Gridiron Thermo- meter. Dry and Wet Thermometers (aspirated). 417 Hygrometers. Dry. eeeeee Sete ee teens Wet. eeeeee seeeee serene Diff. eeeeee senete weeeee seeeee seeeee Dew-point. oeeree seeaee seeeee Daniell’s. | Regnault’s. Dew-point. | Dew-point. 33°1 41°5 8. us 10. 11. 12. 13. 14, 15. 16. (17) Clouds follow the course of the Thames from its mouth up to the higher parts of the river, seemingly following the whole course of the river, and confined to it throughout; quite clear where we are; clouds far below, moving apparently at right angles to us. fs} Thames Ditton under us. 19) Fast train on South-Western Railway ; upper current W. ?; clouds meeting us, moving at right angles to our motion; clouds very low. (20) Clouds passing quickly below us; can scarcely see the earth on one side ; clouds still follow the course of the river. (21) Can see the earth at intervals through the clouds. (22) Clouds meeting us of three different degrees of white—the top bluish white, the middle the pure white of the cumulus, the lower blackish white, and from which rain was falling upon the earth. (23) Train with 29 carriages seen; gas beautifully clear; netting seen through it, and balloon apparently empty. (24) Can see carts ; hear people shouting. (25) Saw a black dog, and heard him bark. 418 Taste I.—Meteorological Observations made in Eight REPORT—1862. 2 Siphon Barometer. Dry and Wet Ther- zs ° : Aneroid | Height above é Zz Time. Regting Att, Barowieich, eg tony 22 and reduced | Therm. a to 32° Fahr. hm =s ° ° in. feet. c 5 48 op.m 2G:08) | 1 eeacas 26°68 3,170 48°2 44°5 5 SO" iON, 26°99 | eevee 26°90 2,950 49°2 44°5 5 VE2T Ola, ieee eeeeee 27°49 25356 50°0 46°5 RP GGMEOM as CF licdcene || opevens 27°40 254.46 50°5 47°2 ORD) cfebn cn ah beer nore tal Reece S 27°40 254.46 50°5 47°38 Ly ery Age i ashed 27°44 254.06 50°0 48°0 (1) B55 POs 5 56 oO » 27°60 beveee 27°55 2,290 51°0 49°2 (2) § 87° los, oo LT ail eo 27°65 23190 512 49'2 PRR URSOMEE |" cscs. | “eaters |) benesp hdl Miecwaes 52°0 50°5 (3) ERS SOMMEC |< 18-10 13,715 25°5 25°0 ReZzOmlOee tr alll teasss mw deweee, |]? Seoese (}) Qieamace 23°2 25°0 T2750 |, 167936 38°0 16°90 15,184 yn PE TE OOD | es i ace . Snes e 17°2 23 x28 0, 16°686 36-0 16°65 ¥5,510°° |) Gaeen 5 Curae (11) BL 2RUAO ert Uh Secpaes buf) saceaa’t il) anagen toeeee 16°5 19"0 X29 oO 3 16°046 B20 || Neaase 16,520 16°5 170 ii 29720)! Seratt Mii teesns . 15°82 ccsase * | sear we Ms 30.2 OOM HY eueeh. 0 al eeneve o PAS aacacn ce ||'> lieouee oo oe weaen (12) 2 9005 ee mt See a. A) aesae vA Serge | Basen 16°0 13°I 230) ZO oh U) seewee if Senne i] Ceenpe 4]. Uswmee . seneee teens 3 x32) 7098 15°38 Z0°0 || Beeuse 17,590 15'0 121 GY ANTS ies Mis aes 55 a NE Seewes’) deren i" teesten evsver f weceee i Ze 0 a 14°651 28°0 14°90 13,890 2.200) T4°553 | eeneee 14°80 19,068 Oy kame aa 14°553 2:7°O)) |) -wanene 19,068 seeeee eeeee Pigg aiO, Laas ceases eeeeee Sesash 15'0 Ir’! I 37 20 9 eum bce Reseda seeeee eeeese | seeee . Boece Seteee I 37 30 i T45AG9. I) esas ° 14°80 19,222 I 37 40 pupae wenesa 14°40 (15) I 37 50 2 Shane Ti Nases 3 Beeset seseee 14°5 10°2 I 38 0 Seseoes O} Su5C EY) dees CH. laesteee— |i, cae ean be Sc I 38 10 < dices. ble. Seabee Rescsc, |) pencsse 13°2 10° I 38 20 ,, 14°947 30°5 sone 19,960 E3825) 35) lo eee, eevee 14°28 20,126 (16) . = a ‘ 33°947 1 38 40 a euase OP waenee 14°00 (1) Misty. (2) In cloud, wholly obscured. (3) Lighter. (4) Much lighter, still in cloud. (5) Gun heard. (6) Dense cloud. (7) Out of cloud. (8) Tried Camera upon beautiful clouds—failed ; the balloon was spirating and ascending too quickly. ON EIGHT BALLOON ASCENTS IN 1862. 421 Balloon Ascents, Wolverhampton, September 5, 1862. mometers (free). ip Dry and Wet Thermometers (aspirated). Hygrometers, an Zambra’s c mas Daniell’s. | Regnault’s. Diff. | Dew-point. be Dry. Wet. Diff. |Dew-point. meter. Dew-point. | Dew-point. ee ee ae = ° ° ° ° ° ° ° ° ° 40 479 44 469 20 Pla, Wi sean 46°0 43°8 22 Ales te Niessen s 42'0 5 Oy) 40°4 44°2 Peer cseces, |! seses 43°3 4r'5 18 39°3 Ria 38°5 15 38°7 12 38°3 40°7 13 ML ale iS cece |) weedese ttle dea 38°0 o's 36°1 sevee | ceeees 360 36°0 foo) 46108 | Gkawcase 35°5 06 28°9 PICO oecekey ||. osecapiee| fccosuillewcsdess (|) passage’ 25°0 ceeeee | ceeeee 26°5 24°5 23°0 1°5 14°5 ee aaee 25°0 o°5 22°3 sence eeeeee 18'0 “al eee 17'9 17'0 24°0 Rens caaces 17'8 arpcre Beers ere sedeoe coeeas 10°5 8. 9. 10. ll. 12. 13. 14, 15. 16, (9) Deep blue sky. (10) The ice not properly formed on Wet-bulb Thermometer. (11) Earth visible in patches. (12) The Wet-bulb reads correctly. (13) Ozone: Moffat 2; Moffat 2; Schénbein o. (14) Mr. Coxwell pants for breath. (15) Mercury of Daniell’s Hygrometer invisible. (16) Ozone: Moffat 3; Moffat second paper 3; Schonbein 1. 422 REPORT—1862. Taste I,—Meteorological Observations made in Eight ” Siphon Barometer. Dry and Wet Ther- E 8 e B Aneroid Height above SA Time. needing, Att. a ris sea-level. as and reduced | Therm. to 32° Fahr, hm in 4 in, feet © a TASSUROP AO. [ON Riss. | |e eeees) | Chsvece, |] U pierce cub soeceec eel eee (1) ESO MAOUG, 13°76 eee tne cee 20,393 8-0 4°5 TOMOM SPS RRS Ai peeaag) erase pl peeen =~ U8 Reece | foemees THROM 55 ie Avesta eo bees He Cheeeeee 10'2 81 (2) DRACEZORSS | hucticss Keseos, |) Ohecrvr) |) Gbeeerte = (mMmoINOne Rakes I 41 20 5, 13°35 26° | weeaee BI,TSe* | va. teens TRATRSO S\N Seees Uo Tevews | obseess) Lo inteens | eeeemere aise @ I 4I 40 ,, (4 141°So 4 eRe Weodae N Oe easneee W OR eee | eee Daas aa aee (5) TAA 0 » T2754.) | Meercee || (es eoee 2.25380 8-1 42 (6) TEACHMOMME 1 cd. =] “Fevecer: | bsexeel Ul: Lbscost cape aR eeeeemna aCe (7) IAS! O) 5 11°954 Bra) |) pecans 23,976 fosre) —40 TO" Olen 11'254, ees he Beceee S5S282 oct Uecwercer ll by ees (8) 1sr 0) 5 10°803 <4 Bade 26,350 —5'0 mere abe os 9753 |) ecsee, Yl Besse 29,000 ZOE «| stsscs seers 11°53 25,318 ZO | wee eee 2° SOs TORQ A! Weeeccsch iy peenes 23,021 2 8 30 » merce, | phe. 12°80 | 22,654 4 = 2 845 » 13°154 BOOT Mbctsy 21,650 seBies) IP Seeeens Zi OMOnny TACOSH.§ ||) bewece. ©]. Saavde 20,018 170 110 2 9 3° » T0974, | Ovesse 16°45 MG;O05 SIH Sleeren el eeerees ZGh4O. 5 EROTA) ebscose [i Bebese 14,938 BELOW OOS tole ees) ie esccck Wit Reseset Ne amieemscs 2am 15°8 21I O yy 17°71 wae )rebeecns 14,012 eta ea ae (lee eee. © Ui beetce on petece UNS citsgaeee ore | lett eee 214 O 5 TOS Wee iesescer tbat ses Ck 1 a | Ri Tae (ie DITA {Oy OPS have oe Becenn| Ub Perens: 1 Peteaes, on dieteceant ree eat ere (9) Pater ol 1s 18455 ei (iat cod 12,900 BAG Os) Mates 1 Fete se Ig't0 | 12,250 26°5 18-2 (10) 216 10 ,, 1O75a_ lsbossas 19°90 | 11,150 2 16 20 4 DOORS ale esha eg 20°25 10,780 (11) 2 16 50 yy 20°653 27°0 20°65 10,070 31t 23°1 2 17 3° »y QISIEL Vokes 21°55 92379 Bato Og. | ia. ae Bicwesr). [he mtepercs 33,0 25°0 ee LOW OF Tl wens Botvas peeeee | ee eeee 342 25°9 2 19 30 5 21°845 31°0 21°90 8,530 PZ ae fol Semel Pee WetBeeewe: 1) (PS epe 35°2 27°O 2 2020 » 22"041 eile S07 8,310 (12) 2 20 30 5 v hg Per Biase: |) peeetee Beal eeaene (13) 2 20 40 yy 22°241 3370 22°20 8,090 40°1 29°2 2 23°50 (14) 222 0 » a Lecce AP eipeecs es tee rs 42°2 31°0 222 10 » é Rus: Seco sereee, yin eaeske (15) 2 22020 22°637 35°70 22°76 7,625 AZIO™ il oases 2 23 3° » ss COR te te cree te CT Pee iscscn- 0) geass 223 50 » 22°932 37°0 23°20 7,260 oencen ih (ese 224 0 yw 23°028 39°70 23°00 7,150 2 25° O » 23°326 40°0 sevens 6,810 42°0 (1) Sand out. (2) Aspirator difficult to work. (3) Ozone: Moffat 4. (4) See with difficulty. (5) Experienced a difficulty in reading the instruments. (6) Aspirator troublesome. (7) Sand out. (8) Lost myself; could not see to read the instruments. (9) Ozone: Moffat 5; Moffat second paper 5; Schinbein 2. : ON EIGHT BALLOON ASCENTS IN 1862. 423 Balloon Ascents. Wolverhampton, September 5, 1862. mometers (free). nee Dry and Wet Thermometers (aspirated). Hygrometers. an | —$—$— —$— $ $ $ $ pn ay Daniell’s. |Regnault’s. Diff. |Dew-point.| Thermo- Dry. Wet. Diff. |Dew-point. meter. Dew-point. | Dew-point. ° ° ° ° ° ° ° ° ° Saeerh Tl odeese 8-0 35. | 227 8°5 nor ae | ee 92 desaee Toten ee oeedes - g0 PRM BGTeEO ME cececa || ccceas |. ceoees | dowves Rese tt \nep tue —I15'0 RRSEAEDID. esas IIo 9°5 73 7 |— 5%3 MI terery W sckeue |||) dvcose | facscz |” scseege [i apecten |) owapeas —I5'0 MMe 4h ccwsee Ja) Wéssce | desess |. stoves eee seniepe —20°0 5. OR | AEB ERS 4°5 3°99 |—26'0 eeweee | eeeeee ft eseee . 2 8 ry 1 ; Revises | a | : 2 ee te es ee ie ye a A eae — 270 cane Soeers || wesate - 50 eeuete — 20 aD sien » |+ 2°0 Babee) |) eapes . 11‘0 66 |—34°7 aie oiaee 18'0 677 |—27°0 Sey TT texcese 23°2 Sees ST, anseee 24°5 ooo pl REE Meee 24.8 180 63 |—19°6 83 | —22°4 8-0 9°3 3°3 11°3 82 | 139 | 3572 eee oeeeed yee eS ’ teecee | weeves . I4°0 II‘9 15°2 aro 173 soe bee eebens 490°0 seneee eevsee | covrrs aeeeee rr soeeee aveeee 20°0 seen teens 40°°0 ssh eee eevee 40°0 - 8 9, 10. 11. 12. 13. 14, 15 16. (10) Wind East. (11) Gun heard. (12) Sand out. (13) Wet-bulb seems to be free from ice. (14) After this observation I pressed the bulb of Wet Thermometer between my thumb and finger, for the purpose of melting any ice remaining on it, or on the connecting-thread. - (15) Ozone: Moffat’s test 6. 424 REPORT—1862. Taste I.—Meteorological Observations made in Eight — 2 Siphon Barometer. Dry and Wet Ther- #3 < : Aneroid | eicht abo Eg Time. Reading | gee, [Barometer ae evel. 3 bok 22 and reduced | Therm. to 32° Fahr, hm? s in. ° in. feet. S 226 opm. 23°473 BTR |" pracewes 6,640 BEZG TO bag | fl peeeers. | |uebaecnes | ||| Sitewsnn ai! Merce GO iiaeenes (1) BEZOTIS ass, Vi Tlwibeee 1. | bdesacs .| -devene Mel ( Tenses 45°2 34°2 Dea AMO uss PiEAO AO deed sh He estmes bon| utoasss. S| ietveseve mln esmcee | 0 eeeataame | ecmeers 2 29 30 5 24°512 AGO" ON scans 5,500 49°2 360 (2) is) eee pal mk eeu entered Beecreerees ME escrarweast) sce (|p onctal PEAT AMO MeAR ET Weieic. (|, caceces” yi) caseene 6 [0 Aiaabans Hehe 4) Saqeco 2 TE Ch I eros | MeecreRP ena fe eooocogh || fsorccso 49°2 35°70 REG2 Oise, 25°401 50°0 25°55 AS52008, Oh eee f ceetene BAGz SOE > vwcesee | vwedase | eevee oll mares 50°5 36-0 ZESs COs: 25°800 EOC (|) etesaes 4,110 BUGAMAOMEe ||| Co Ssesss | S@ensce }| Sgevoes) 1\t Ie begemee 51I 37°0 DEAOUMO Meg! | Cossescc. 6)|| cicvwmee al | ~ceweee Fi] Mienepest” 0 | Beet Ml Secenas 238 0 5, 26°399 50.0 | 26°35 3,484 53°0 45°0 Sasi rOwas || besccn °] agemsien oh Wigeeces. ||) Romane. ob | uememnrnena neta (3) 2 3820 95, 2 3940) bs 277598 BOO |} Ravene 2,260 SBE) Cpr taal ME Sodcceee 4|f -coopecime \| (et. cccsc atiete 54°0 48°0 2°30 AO ves WR ieeeees |) Gesaene 28-10 3 Ook. | Wetec. Bi) aedenee ZGiO2) | ce Ranies A 5772 52°8 Crystal Palace, September 8, 1862, (4) 447 oOp.m. 29°90 | deeeee 29°92 250 67°2 63°0 (5) AicAS AO) 55 29°40 | éeeee ° 29°47 813 66's 63°1 (6) 449 O45, BEBO | || desene 28°80 1,232 63°2 60°5 (7) BehOO) ag ZRF Oil) Wasssee 28°50 1,530 6371 60'2 (8) 4 50 30 4, DEER. Till descns 28°30 1,730 62°8 59°8 (9) BvGT e055 S77: 1 |i asses 27°59 25432 602 57°2 Bn? 30 35 Z7ERe Ui itesenes 27°40 25520 58°38 56°5 (10) AW5230; '59 27°20 aoa 27°10 2,923 56°5 54°2 (11) WA PON) MEE AS Tey) Ie Seen 26°70 35320 55°2 52°5 454 0 5 26°52 | seens » | 26°30 39720 54°0 52 (12) 4 54 3° 55 26°05 cesses | 25°90 4,169 52°0 50°5 (13) 455 ° » 25°86 | eevee . 25°68 4380 51°5 5°°5 (14) 4 55 30 955 4.56 0 5 25°56 covses 25°50 4,560 51°0 49°8 (15) 4 56 I0 5, (16) 4 56 30 5, 25°46 vessee | 25°41 4,650 50°5 49°8 457 © » 25°45 | wwaeee 25°38 A727 50°5 50°0 4 57 3° 55 25°43 seeeee 25°38 45727 50°8 49°8 (17) 4 58 20 55 25°44 sense 25°36 45750 511 49°8 2. 3. 4, 5. 6. 7. (1) Wet-bulb seems to be correct; it has decreased from the reading I drove it to by the action of the heat of my thumb and finger. (2) I do not think Aspirated Wet-bulb is correct. (3) Ozone: Moffat’s paper 7- (4) At 45 47™ 15* eased up; at 45 47™ 28° let go catch. (5) At 4® 48™ 15° over the lake. (6) Gas clear; at 45 49™ 55° scud at lower elevation, not under us. (7) Thames seen clearly; ships seen. (8) Sand out. % b wd = Balloon Ascents. Wolverhampton, September 5, 1862. ON EIGHT BALLOON ASCENTS IN 1862. 425 mometers (free). Meesettt Dry and Wet Thermometers (aspirated). Hygrometers, an ae oe Daniell’s. | Regnault’s. Diff. |Dew-point.) Thermo- Dry. Wet. Diff. | Dew-point. meter. Dew-point. | Dew-point. ° ° ° ° ° ° ° ° ° wovene i} totes 41°5 mxe3 21'S B35 ese 45°5 av eaes ARAL sro: eaaeee tenets 27°0 13°2 21°38 oy | eee 471 44°1 3°0 40°7 29°5 Ruse | oWeines 47°0 142 19°7 Seavert Hf wrbses 48°0 14°5 20°8 I4°l 224 SN cree | akeOE | serch S| weccee- sl jeonee . ebcads veonee B75 80 | «3770 51°5 eee) W | wtesee 5 53°5 60 42°1 54°0 44 48°8 57°5 Crystal Palace, September 8, 1862. 42 612 34 60"4 27 58:2 2"9 578 Bi, 572 30 54°6 2°3 54°4 2°3 S23 2°7 49°9 2°8 43°5 X55 49°0 79 49°5 r2 48°6 } (O'7 49°1 SS) 49°5 H 60 48°8 153 48°6 8. 9. 10. 11. 12. 13. 14. 15. 16. (9) Gas getting cloudy; just see netting ; smell of gas. (10) Gas cloudy. (11) Heard shouting below. (12) Mist; dense fog; gas cloudy ; netting invisible. (13) In a dense white cluud; can just see the earth. (14) Earth not visible. (15) In cloud, thick and white ; dropped a piece of paper, visible 23 seconds. (16) Gas still cloudy. (17) Half out of cloud; blue sky above. 1862, 2F 426 REPORT—1862. Taste I.—Meteorological Observations made in Eight 2 Siphon Barometer. Dry and Wet Ther- 23 pematy OP AOD (el Cds . o q ‘ 4 Height above Be Beta O Ussce ae crease ols taee 26°10 33958 52°5 51°5 (11) BEORZO | Grea eemvaccrs: Mil lanes as) 25°95 4,108 52°2 515 (12) § TO. 40 55 hh G0 a 25752 AO REE SE 25°74 45220 51°5 50°0 (13) 5.11. 1§ (14) Silt Zor, (15) 5 11 25 55 5 II 30 26°66 Gaon 25°52 45440 510 49°8 (16) 5 11 55 55 (17) 5Berz™ ong; 25°40 25°40 4,540 51'0 461 BAIZSEG by. | 1) Drdecsta ipl | etedteees 25°22 4,895 51°0 44°1 (18) BeI2ZGgOpes || fl WH Rasch | tasecee 25°20 4920 5a 44'2 5 13> Or hoy 25°10 teens 25°20 4,920 521 438 BEL Oks Ue teases etl tiireacas 25°20 4,920 53°2 44'I (19) 5 14 40 5, | BPG ELOt by” | Me Revece. bares 25°19 45930 54°2 44'1 5°15 30 55 BASOG © ihebcese. 25°11 5,026 55% 44/1 (20) 5 15 35 » | BUr6d Opi b RM Ete eee 25°00 59175 56°5 4571 (21) 5 16%30)(,, (22) 5 16 45 » (23) CLIT Os, BSG |") |Wiostnss 24°92 5,263 57°2 46°1 (1) Still partly in cloud. (2) Cloud more dense; descending. (3) See the roads on the earth. (4) Can see the earth as through a fine mist. (5) A misty view; horizon obscured all round. (6) Can see Blackheath, the Royal Observatory, Woolwich, and the Crystal Palace. (7) Very black clouds over London. (8) Mouth of the Thames visible. (9) Shouting below; dropped a piece of paper, visible for 2” 458. A beautiful break in the clonds in the west. (10) Over woods. (11) Shooters Hill visible. (12) In slight mist. (13) Just see the earth. (14) Earth invisible. , ON EIGHT BALLOON ASCENTS IN 1862. 427 Balloon Ascents. Crystal Palace, September 8, 1862. mometers (free). eet Dry and Wet Thermometers (aspirated). Hygrometers. an — fombes Daniell’s. | Regnault’s. Diff, |Dew-point.) ppermo- Dry. Wet. Diff. | Dew-point. meter. Dew-point. | Dew-point. ° ° ° ° ° ° | | | } | i 9 10. uM Ie uz 13. 14. 15. 16. (15) Blue sky in zenith, clouds below ; came out of cloud in a hollow or basin. (16) Image of balloon with beautiful prismatic colours on the clouds. ~ (17) Sun shining; clear blue sky. (18) Deep blue sky ; beautiful reflexion of the balloon, with primary and secondary pris- matic rings. (19) Sun warm ; clouds heaped upon others ; we are not much higher than level of top of (20) Gas rather cloudy; see netting pretty well. (clouds. (21) Earth seen through the clouds. (22) Fluffy clouds. (23) Ring cut the spectral balloon about one-third from top. re F 428 REPORT—1862. Taste I.—Meteorological Observations made in Hight Siphon Barometer. Dry and Wet Ther- as ; a oh eee Ae? Ee | mime, | Beading, | ate, /Beometer) eer | Pee} andreduced | Therm. oe sale to 32° Fahr. hm i =°5s in ° in. feet. (1) SEL 7 20M.) i|| Madaces | ||| Moscone 24°95 5,230 57°2 (2) 517 55 » (3) RO ma Ousey sy Aol wishwceets F i|) | Bivaisies 24°78 5,428 58°5 5 190 5, ZETO | seoore 24°82 55338 60'0 (4) SOUR (ailihebiee. Wl|. geoceas 25°05 5,112 58:2 (5) | 52055 » § 21 0 » seen eee 25°05 5,109 ha) § 21 Io ,, 25°36 | cenene 25°02 55145 57°5 (6) BOO Os mba 1rc8 oS il: Foavens 25°00 5,169 EG (7) 5 21 50 » (8) Reobs Sophy 25:03' | || sane 25°08 5,057 56-2 5 22 4o ,, 25°30 | ownene 25°09 5,043 5472 (9) 5 2245 » (10) B2RMEOMM | | cesses |) fesvnes 25°10 5,029 51°8 SiCAMMOMPt || — (9) (10) (11) (12) (13) (14) (15) (1) North Kent train, eight carriages. Time. REPORT—1862, Taste I.—Meteorological Observations made in Eight Reading corrected and reduced to 32° Fahr. a eeeee eeeeee seeeee (3) Nearly over Small Wood. (4) Could plainly see people waving handkerchiefs. (5) Over very large wood. (7) Crystal Palace still in sight. Siphon Barometer, (2) Flock of sheep, like large specks. Aneroid Barometer, No. 2. in. 28°49 28°60 28°65 28°80 28°95 29°10 29°20 29°25 29°30 29°28 Height above sea-level, Dry and Wet Ther- (6) Still over same wood. (8) See dog, and hear him barking and people shouting. a ON EIGHT BALLOON ASCENTS IN 1862, 431 - Balloon Ascents. Crystal Palace, September 8, 1862, _mometers (free). Ramet Dry and Wet Thermometers (aspirated). Hygrometers. = an eee Zambra’s 4 idi Daniell’s. | Regnault’s. saan Dry. Wet. Diff. | Dew-point. , meter. Dew-point. | Dew-point. ° ° ° ° ° ° ° 55°8 : MME 09S A sceweiscd kasaedt ome 5570 56°6 58°0 56°5 59°6 595 53°6 59:2 60'1 60°6 61°0 59°9 ESMR eaenste! CC Rs MGOE!|E lovspese,J|) teadens,..1) cheers 58°5 59°9 392 1°5 58°7 "7 58°5 2°0 583 1°5 58°7 I°5 53°7 14 58°6 12 58-9 14 53°6 rr 59° 13 58°6 rg 586 my 5 58°7 f m ts | 587 * 5 59°2 7 a5 59°2 — 59°0 Ri I vi 59°0 1°3 58°5 '7 582 t ae 57°0 St 8. 9. 10. ll. 12. 13. 14, 15. 16. (9) Over North Kent Railway. (10) Near large limeworks. 3} Gas clear; over Swanscomb Marsh. (12) Bank of river*Thames. 13) People on steamboats energetic. (14) Crossed the river in 2™ 1° from hank to bank to the W. of Gravesend. (15) Over London and Southend Railway. 432 REPORT—1862, Taste I.—Meteorological Observations made in Eight — 2 Siphon Barometer. Dry and Wet Ther- 23 Aneroid . ae Time. Reading Barometer, #cight above BZ Att. ? -level. Zs ited | Teena! | Nome) Toe ee to 32° Fahr. hm i s in ° in, feet. ° a (1) 5 56 55p.m GUSTER Migs \ elie thease a epee 28°40 1,628 60°8 58-2 557 dO. | lh vatesease: , | ||) Pence 28°38 1,639 60°5 58-0 2) 5 58 Cin, 28°40 28°22 1,798 60'0 580 5 5° 15 5 58 40 4 ceases Bll peses Sauipe. ili Wareces 60° 58:2 HEEQMO Ly | | eeevee | te esee 28°11 1,907 3) ; ‘O10 55, 28°37 || eesoee 28°05 1,967 60°5 58:1 ° 4 6 o10 is are. ls Sco 27°98 2,034. 60°0 58°5 : O20 us, 28-55 Ol) kscsae ahs 25034. us 57°8 T ko So, ie anes 27°9 2,034 59° 57:2 6.51030 4 Asc, {ls Sox80 27°90 2,114 59°8 57°5 Gasca cits, A as (ler eee 27°90 2,114 59°8 5772 (4) H ZEMOmes ai) cassee || Geeeete 27°78 25235 59°5 571 3 4 » (5) 6 325 » (6) 6 415 » (7) 4 5 Oust) . il AGawdacs,) Mal) Uhepetnes 27°89 2,122 59°2 5770 ° (8) 6 10 o is ierasned 30°07 1 2 3 4, 5 6. 7 (1) Over meadows opposite Rosherville Gardens ; gas clear. (2) Tilbury Fort examined with a telescope. (3) Over Mucking Flats. (4) Let gas out. (5) Over meadows. Balloon Ascents. ON EIGHT BALLOON ASCENTs IN 1862. 433 mometers (free). Diff. | Dew-point. ae (6) Descending. Tilbury Fort. 1862. Crystal Palace, September 8, 1862. Rees Dry and Wet Thermometers (aspirated). Hygrometers. an pet a Daniell’s. | Regnault’s, Thermo- Dry. Wet. Diff. |Dew-point. meter. Dew-point. | Dew-point. esese | seeeee | eeese | eoeoee (7) Packed the instruments up. (8) Down in Mucking Flats, about 23 miles from Stanford le Hope, and 4 miles from 4.3.4: REPORT—1862, § 4, Avoprep TEMPERATURES OF THE ATR AND DEw-Pornt, with HercHt, IN THE EIGHT Battoon AscENTs. From all the observations of the temperature of the air and of the dew- point in the preceding Tables, a determination was made of both elements with the corresponding readings of the barometer and heights. Some of the numbers in the column for heights have been interpolated when either of these elements have been observed without a corresponding observation of the barometer. The numbers thus found are within brackets. The results are contained in the following Tables. Tasre I1.—Showing the adopted Reading of the Barometer, calculated Height aboye the Sea, Temperature of the Air, and Temperature of the Dew- point in eight Balloon Ascents. Frsr Ascent.—July 17. Time of |Reading of| Height Temp. || Time of |Reading of| Height em obserya- |the ae Sane the ee of the observa- |the Seems shinee the f the of the tion. |reducedto| levelof | %* ew- tion. |reducedto| level of Gad ew- A.M. 32°F. the sea. i | point. A.M. 32°F. the sea. T | point. hm in. feet. o ° hm in. feet. > ° 95% oy 49° | 59°0 | 514 ||10 39 14°63 | 19380 | 36°5 21°6 47 26°01 3835 | 45°° | 35°3 44 14°63 | 19336 | 34°0 | 21°3 49 2522 4467 | 43°0 | 32°0 47 14°13, | 20238 | 31°5 14°6 51 24°14 5802 | 34°8 | 32°% 48 see | (20512) | gr°0 53 22°42 7980 | 32°5 | --- 50 13°64 | 21059 | 23°38 |—12°5 54 20°02 8065 | 31°8 | 27°38 54 13°34 | 21792 | 19°70 |— 82 55 21°58 | 8809 | 29°8 | 21°8 57 12°14 | 23949 | 37°5 |— 4°5 56 20°93 9598 | 2672 | 17°6 |izx o 11°74. | 24746 | 16°0 |— 8'o 58 19°63 11giz | 26°0 | 24°5 it | rrmq | 26177 1670 |— g'o 10 2 19°28 11792 | 26°0 | 244 3 11°64 | 25022 1670 |— 8'5 3 18°63 | 12709 | 26°0 | 20°38 5 11°64. | 25028 | 17°5 4 -eee 1(13088) | 26:2 | 19°9 7 11°64 | 25077 13"0 5 18°14 | 13467 | 280 | 23°7 12 II'95 | 24547 | 23°7 8 17°24 | 14544 | 310 | 23°8 20 12°65 | 23868 | 27°0 II 16°74. | 15704 | 31°6 | 22°7 25 03°IA | 223997 5 aoa 15 16°04. | 16914 | 32°0 | 22°7 37 16°36 16282 | 29°7 9°4 25 14°94 | 18844 | 37°2 | 24°6 38 18°94 | 12376 | 34°2 74 27 14°64 | 19374 | 361 | 23°2 39 20°04 | 10539 | 37°0 29 14°64 | 19415 | 38°2 | 21°8 40 20°54 9882 | 37°8 19°8 30 14°64 | 19415 | 38° | 20°2 44 23°44 6330 35 14°64 | 19485 | 42°2 | 19°5 45 24°24. 5432 Between 10" 50™ and 11" 25™ in the last column, the numbers entered with the sign — before them imply that the temperature of either Daniell’s or Reg- nault’s hygrometer had been lowered to the degree stated, but that no dew was deposited, and therefore that the temperature of the dew-point was at a still lower degree. At 10" 50™ the readings of the Dry and Wet (free) were 24°-5 and 17°-2, giving a dew-point temperature of —26°-6. At 10" 50™ the readings of the Dry and Wet (aspirated) were 23°-0 and 17°-0, giving a dew-point temperature of —20°6. At 10" 54™ the readings of the Dry and Wet (free) were 19°:2 and 11°2, giving a dew-point temperature of —47°5. At 10" 57™ the readings of the Dry and Wet (free) were 16°5 and 9°-5, giving a dew-point temperature of —44°-1; and the readings of the Dry and Wet(aspirated) were 18°5 and 8°-0, giving a dew-point temperature of —69°'9, , a 2 < Ny ON EIGHT BALLOON ASCENTS IN 1862. 435 At 11" 7™ the readings of the Dry and Wet (free) were 19°-0 and 9%0, giving a dew-point temperature of —67°4; and the readings of the Dry and Wet(aspirated) were 18°-2and12°-0, giving a dew- -point temperature of —34°-5 At 11" 25” the readings of the Dry and Wet (free) were 28°-1 and 17°: 5, giving a dew-point temperature of —26%1. From the general agreement of the results observed by Daniell’s Hygrometer to —10°, by Regnault’s Hygrometer to this and lower temperatures, and those of the dew-point as found by the Dry- and Wet-bulb thermometers, there can be no doubt that the temperature of the dew-point at heights exceeding 25,000 feet must have been at least as low as —50°. Reading of the Barom. reduced to 32°F. hm_ sj in. 29°96 29°96 29°87 29°82 . 29°80 29°65 29°55 29°50 29°20 28°85 28°65 28°20 27°65 27°10 . 26°87 26°50 26°40 26°35 26°27 26°25 26°18 26°12 26°08 25°91 25°80 25°73 25°78 25°85 25°90 _ 26°00 25°98 25°76 25°68 SE Yi 25°30 25°40 25°35 25°20 25°20 25°26 25°25 25°20 25°00 Seconp Ascent.—July 30. Height above the level of the sea. feet. 250 250 330 370 390 480 57° 615 890 1189 1389 1829 2379 2452 3161 3543 3640 3690 . 377° 3790 3860 3920 3960 4169 4279 4358 4308 4234 4184. 4084 (4094) 4104 4324 4403 4613 | 4783 4682 4733 4925 4920 4863 © 4873 4920 | 5155. Temp. of the Air. 68-2 68-0 67°2 66°5 66°5 66°0 65°5 65°2 63°38 62°0 62°0 59°8 58°5 54°2 52°5 51°0 50°4. 49°8 50°0 50°6 51'0 52°2 52°5 515 50°0 50°5 50°5 515 51°8 51°8 51°5 52°1 515 52°1 492 49°90 48°5 48°9 ‘43°2 43°5 43°2 48°2 479 .49°3 Temp. of the Dew- point. 50°0 49°7 48°0 479 479 479 473 4571 449 43:2 43°0 43°5 42°6 41°9 40-4 39°8 40°4 41°0 39°7 49°7 40°0 39°7 39°4 40°3 39°7 39°2 39°2 40°3 40°1 40°1 39°9 40°2 40°7 39°8 36°5 36°7 38°1 377 375 3772 373 38°0 376 36°2 Time of /Reading of} Height the Barom.| above the observa- tion. P.M. hm. 5 18 20 21 22 23 24. 30 30 30 reduced to 32° F, — in. 24°93 24°78 24°79 24°95 24-99 24°32 24°78 24°62 24°32 24°47 24°57 24°30 24°22 24°02 23°83 24.00 24°42 24°60 24°53 24°35 24°12 23°82 23°69 23°58 23°50 23°47 = As 23 “40 23°47 23°79 level of the sea. feet. 5220 5379 5360 5200 5200 533° 545° 5830 553° 5380 5280 5903 5983 6183 (6220) 6370 6252 6785 5577 5649 5846 6102 64.66 6642 6752 6826 6856 6896 (6910) 6937 6867 6547 (6603) (6617) (6625) 6637 6747 6937 Temp. of the Dew- point, ce ans 37°3 37-2 38°9 37°2 38°7 35°9 35°8 354 36°2 38°4 35°8 35°8 35°8 34°0 32°7 351 35°9 364. 3571 34°7 33°71 34°3 33°8 35°2 314 32°6 314 29°83 30°3 32°0 31°4 31°6 32°9 32°74. 313 29°0 31°8 31°8 30°8 32°4 32°5 32°7 32°8 Height above the level of the sea, feet. 3870 375° 2700 (2400) on the ground 4448 (4562) 5019 (5273) (5695) 5780 (5913) (5958) 6313 6491 (6580) 7886 (8342) 8571 (8660) 8771 (8771) (8771) (8771) 8771 (9327) (9715) 9902 9695 (9987) 10864. 11748 12364. (12595) 12708 12942 13852 (14290) 14434 16339 (16885) 17157 (17240) 17321 (17380) (17770) (17860) (18039) (18445) 436 REPORT—1862. Seconp Ascent.—July 30 (continued). Time of |Reading of| Height Temp. || Time of |Reading of observa- |the Barom.) above the af the of the || observa- |the Barom. tion. reduced to level of Ase Dew- tion. reduced to P.M. 32°F. the sea. * | point. P.M. 32° F. hm _ s| in. feet. a 5 [hm s| in. Gig Oh 2acKs 5800 | 460 | 34°3 || 6 23 26°48 Ig 30} 24°60 5750 | 46-2 | 3672 24 26°60 20 24°95 5400 | 47°0 | 354 25 27°65 ae 254° 4950 | 4775 | <3 75° 25 Sole pei 22, 25°90 4450 | 47°38 | 38°8 30 29°96 22 30] sees (4160) | 49:0 | 38°6 Tuirp Ascent.—August 18. P.M. | P.M. © 53 0} 29°34 490° E52 39 25°59 56 oO 29°34 490 | 67°8 54°6 53 0] eee I 5 © 28°84 1130 | 62°5 52°5 55 0} 25°08 6 o| 28°55 1419 | 60°0 | 9256". oltamahs sre 6 20! 28°25 1713 | 58-2 53°71 57 40] cece 6 30) «--- | (1795) | 57°2 58 0} 24°39 7 \ Oo) 27-00 2042 55°5 50°5 58 30] sae 8 of 26°67 3347 58 go] wees § 20)... (3466) | 52°5 20 O]''23°93 9 oO} 26°27 3705 50°0 49°6 Io} 23°78 Io o| 25°86 4138 | 49°9 T 30)" (55 TO 25} eee (4440) | 49°8 44°2 9 oO] 22°58 II oO] 25°30 4767 | 48°8 42°2 TO +0|" Astor EX gol *e..5'. (5140) | 48-6 IO 30] 22°18 12 0} 24°60 5509 | 48-2 i} “oP Arat I2 30| 24°60 5510 | 47°8 38°83 II 40] 21°88 13, 20), 2... (6155) | 48-0 35-7 II 50 Fic 14 o} 23°64 6585 | 46°5 Iz 0 0 15 o| 22°69 7706 | 45°7 IZ 20} 1s. 2% 17 oO} 21°69 8935 | 44°0 32°0 13 oO} 21°88 18 45) 20°90 9954 | 43°0 29°6 || 13 40 es 58 55) Ye.s2 |\(torz9)"| Ao°s 286) - SXF GOW Odeste 20 oO} I9790 | 11267 | 38°5 14 0} 20°99 Bo | sl seb Oars) B72 24°9|]} 15 Of 21°14 20 35| 19°80 | 11399 | 36:0 24°8 || 15 30 eee 21 of 19°75 | 11470 | 39°5 | 22°2|| 17 of 20°24 22 0} 20°30 10840 | 41°8 25°2 20 ©} 19°60 24 0} 20°90 9884 | 45°0 26°9 21 oO} 1911 aie 36 (9884) | 45:0 QZ Ole CFeisie 24 15} 20°90 9884. oe 22 30| 18°86 24 50| 21°38 giz0 | 46-2 32°0 23. «0] 18-71 25 Foy tes re (g040) | 45°8 24 Of 1811 25 IO] cove (8960) | 47°2 33°71 BRON Tis Se 26 0] seve (8575) ee 28:2 25 20) 17°61 26 30] 22°21 8342 . 30°5 29 ©} 16:41 27 of 22°62 7836 | 51:0 379 Bu LO Valen 32 o| 22°80 7650 | 49°2 37°0 32 Oo} 15°93 33 Oo} 22°80 7650 | 53°8 36°6 42, Ole Wate oe 34.) Ol Basis Wl (7265) 2 heise 36°0|| 32 20] 15°84 37 30) 24°25 5919 Be ly 232 SON ats oe 38 of 24-46 5820 | 53°8 37°8 | AI Oo} 25°08 5028 | 53°5 a SOR teres 41 30) 25°56 4530 43°5 43 0] 25°58 4480 is feel SY 20k Gee ss 46 O| 26°56 3438 oie 47°5 35 O| eee 48 0} 26°76 3219 | 56:0 36 10] See 52 Oo} 25°79 4233 | 55°0 36 20] “Been (18505) Temp. area of the } ase Dew- r point. ° ° 492 | 395 | | Sol | 41°7 55°5 | 42°2 58-3 | 41-7 68'0 | 47°4 : 3975 50°0 | 40°9 54°8 we 40°! 540 | 41°7 50's | 386 ee 37°5 510 | 39°8 51°0 38°4. 510 | 37°6 pis 39°0 ne 39°0 as 39°5 5°°5 °° 34°9 50°0 50°5 341 43°1 a6 29°3 ie 21°2 39°2 25°6 38°5 38-0 341 ae 23°4 ee 2gsr 27°38 6-0 be iE 50 28°1 ON EIGHT BALLOON ASCENTS IN 1862. Turrp Ascent.—August 18 (continued). 437 Time of |Reading of} Heigh . || Ti Reading of| Height Temp. observa- |the Basch. eters the Tee. obi | pee the ence, Arey the Teme: of the tion. |reducedto| level of oe ©! Dew- | tion. | reducedto| level of 7 ©! Dew- P.M. 32°F, the sea. T+ | point. | PaMe 32°F. the sea. T+ | point. hm _ =°s| in. feet. G of | Bu mae) sie ans feet. is SS 2 36 30) 15°03 18560 | 3 12 30] 12°93 | 22705 | 24°0 36 40] wee. ea 24°8 |— 2°0/| 13 of «-.- |(22160)| +. |— gro 36 50] see. 18650) | 2575 | 13 13} 13°63 | 21977 | 24-0 37 S55} .ce-- | (18935) | © 23 20) 3... >] (22000), | += »|—10'O 38 10} 14°87 | Ig9000 | © £3) goliath K22004)i 2450 38 30/ «+». |(19200) | -. |— 5°0 13 40) 13°58 | 22008 | 24:0 38 40} «... |(19290) | 28°5 18 30] 13°45 | 22107 | 24°0 39 oO} 14°62 | 19461 FQ 2 PSsp es METS) «. |—I0'0 39 Io} .+-- | (19604) 19 30 (21685) | 24°0 39 20] «+++ | (19800) | 261 | I9 40 (21615) | 25°0 39 30} «+e+ | (20000) | 2575 | 19 40 (21610) | 24°8 42 O] «eee | (20350) ++ |— 85]| 32 of} «.-- | (16405) ar foKe) 42 10} 1412 | 20359 | 25°1 33 0} 16°78 15984 45 ©] e+e. | (20665) «- |— 5°0 34. of 17°53 | 13320 | 32°8 II'l 35 esee | (20888) | 23°5 36 o} 18°63 | 12453 | 380 13°3 49 oO} 13°62 | 21111 39 0} 20°02 10624 | 40°7 14°4. 49 50] «+++ |(21200) | 254 |—10°0|; 40 0} 20°72 | Io224 | 45°5 14°4 59 Of 12°83 | 23164 -. |—I2'o 41 30] 21°62 8764. 59 Io] 12°71 | 23215 | 24:2 43a Ol 220907 8144. 59 20] 12°61 | 23377 : — 80 43 10] seats (7910) | 50°5 360-7 59 49) 12°93. | 22705 | 24° |—Io'o 43 30) 22°74 7438 3 0 Of 13°13 | 22295 AG Oly amore (6943) sis 38°6 3 20) 13°13 | 22295 | 24°5 |— 9°0 47 0] wees (6282) 40°0 eeee «see |(22295) | 24°8 |—1I0°0|| 49 0] 24°28 5621 | 50°0 4 30) 13°13 | 22295 24°0 |— 9g'0 50 20] 25°08 4821 52°1 43°9 BP) Ol 2293 | 22705 |. 24-5 51 oO} 25°36 4.521 51°5 448 5 30] -..- | (22705) } .~- |—ro'o CC ke) eo (3900) | 5170 | 48-9 6 Io} .«... | (22705) | 24°0 4 5 Of] wees on the | 67:0 7 | 12°93 | 22705 | 24°70 |— 8:0 ground Fovurrn Ascent.—August 20. P.M. P.M. 6 5 oO} 29°86 250 | 67°38 | 567 || 6 43 oO} 25°68 4256 | 50°0 45°5 26 o}| 29°86 250 | 66:2 | 55:9 43 30| 25°60 4316 | 51-0 45°3 27 0} 29°85 250 | 660 | 56:0 47 ©} 25°55 | 4366 | 505 | 43°7 28 30) 29°66 430 | 65:2 | 54°38 48 0] 25°60 4316 | 50:0 43°8 29 0} 29°62 450 | 64°6 | 54°3 49 | 25°75 | 4116 | 49-2 | 45:7 29 30] 29°48 530 | 64:2 | 53°7 49 30] 25°80 | 4055 | 50°5 | 464 29 40] 29°40 602 | 64:1 | 5373 50 oO} 26°05 3803 51-5 44°9 29 50) 29°33 662 | 63°5 | 52°5 51 30] 26:25 | 3693 | 515 | 44:9 30 oO] 29:28 FOF ei O8°2e| 52°7 52 oO} 26°35 3593 | 51°5 449 31 0} 28°95 1037 || 63:0. | 52°3 55 O| 2628 3663 | 512 45°71 32 30] 28°55 1397 | 61°5 | 51°7 56 of 26:25 | 3693 | 50°9 | 45°4 33 9} 28°45 1497 | 61°5 | 5173 57 30) 26:20 3743 | 503 4572 34. 0] 28:00 giz | 58°5 | 50°5 58 of 2615 3793 | 49°3 44°4 35. 9 27°75 2160 | 57°5 | 491 || 7 © Of 2611 3833 | 50°2 447 35 30] 27°65 2257 | 5672 | 50°0 I 20} 26°08 3863 | 49°8 4474 36 o| 27°40- 2408 | 56:0 | 49°2 2 o| 26°05 3893 | 49°5 44:7 37 OO] wee (2665) | 55:2 | 4971 | 4 Oo} 25°85 4052 | 48:2 44:7 37 10] 27°20 | 2709 | 5571 | 49°0 | 5 9} 25°70 | 4250 | 480 | 438 37 39) 26°95 | 2959 | 54:2 | 48°83 7 0} 25°58 | 4384 | 47°0 | 43°0 38 0} 26°75 | 3159 | 5371 | 489 8 of 2560 | 4354 | 472 | 43°7 39 9} 26°55 | 3359 | 52°8 | 48-2 9 0} 25°68 | 4278 | 481 | 43°9 4I oO} 26°12 3816 | sxx | 46°6 IO 0} 25°50 3405 | 48:2 44°7 41 30) 25°95 3986 50°5 | 464 IZ 0} 26°20 621 | 49°38 43°70 42 oO} 25°82 4116 | 51°0 | 45°9 13 0] 26°45 3468 | sro 45°3 438 REPORT—1862. Fourtu Ascent.—August 20 (continued). Time of |Reading of} Height Temp. || Time of (Reading of| Height Temp. observa- j|the a above the ae of the observa- the Bion. ere the ofa: of the tion. reduced to| level of ‘Air Dew- tion. reduced to| Jevel of ‘Ais Dew- P.M. 32° F. the sea. 5 point. P.M. 32°F. the sea. point. Hig it 9 V5) ake feet. A 6 h.m ss} in. feet. é ° 7 15, . 01? 27:50 2398 53°5 | 48°5 7 29 30| 27°70 2217 559 501 16 0} 27°70 2198 | 54°2 | 48-9 30 0 27°58 2417 . | .55°5 50°2 16 30| 28°03 1871 | 54°8 | 493 92, joanne (2620). | 55°2 51°73 17 0} 28:25 1655 | 55°5 | 49°6 33 0) 27°18 2723 | 542 | 488 18 0} 28-50 EAV7] - 1556'S 0) §a1 34 0} 27°18 2723 | 54°8 49°3 19 0} 28°53 1387 | 57°0 | 50°3 35° 0} «27°22 2683 | 55°2 579 Ig 10} 28°55 1367 | 57°0 | 50°3 36 o| 27°30 2603 | 54°8 43°5 Tg 30] 28°63 B2O7 6 bab Qh ses 37 0] -be (2670) | 54°2 48°38 20 o| 28°64 1277 AUS 7 Stree 40 0| 27°03 23739410535 4671 20 30} 28-62 2397 57°50 SEZ 41 0} 26°80 3003 | 53°0 46:0 22 0] 28°33 1587 57°38 | 510 42 0| 26°10 3723 51-2 44°7 23 0} 28:25 1667 | 572 51°4 47 0 24°82 | 5194 | 45°0 | 41°8 24. 0| 28-01 1907 | 56°8 | 50°5 48 0} 24°90 5106 | 45°0 41°38 25 0} 27°85 | 2067 | 568 | 50°5 49 0, 24°18 5900 | 43°0 25 20) 27°75 2167 | 56:2 | 50°2 52 o| 24°88 5200 . | 43°3 26 o} 27°70 2217 | 56°5 | 5071 55 o| 24°88 5200 | 44°2 26 30} 27°70 2217 | 56°5 | 50°7 56 0] 24°92 5160 - | 44°2 28 o| 27°78 2297 | 56°8 501 Frrrn Ascent.—August 21. A.M. A.M. Ana0) (Olmmest 320 | 60°83 | 58-4 || 5 20 of 19°70 | 11222 | 29°8 3I 0} 29°59 358 | 60:0 | 57°2 21 0} 19°45 | 11616 | 27°8 33. 0} 29°58 367 hi 58'9 .| §7:2 22 0} 19°09 12254 | 25°5 35 oO] 29°45 499 | 5972 | 58-9 23. 0} 1890 | 12421 23°2 36 0] 29°20 728 | 59°0 | 59°0 24 | 18°90 | 12421 | 23°3 39 0} 28°78 1130 «|| 57°38 | 5272 26. Onna bs 12851 23°5 4° o| 28°70 T210. | 59-9. | §1-2 27 o| 18:42 | 13080 | 24'0 41 o} 28°62 1286 | 57°72 | 50°6 29 Of 18:20 | 13381 ZaLO) |= fon 42 o| 28°58 1326 | 56°83 | 51°0 29 30} 18°15 | 13456 | 23°5 |— 9°8 44 o} 28°18 1706 | 55°5 | 512 30 30| 18:00 | 13665 | 25:0 |— 63 45 0] 27°90 2000 | 55°0 | 51°I 31 of 17°90 | 13680 | 22:2 |—23-4 49 0} 26°95 2930 | 52°2 | 47°4 32 30] 17°82 | 13799 | 19°5 |—29°4 51 o| 26-40 3510 | 49°38 | 4474 34 of 17°78 | 13875 | 19°5 |—23°4 52 0} 25°95 3951 | 47°0 | 41°0 34 30] 17°78 | 13875 | 19°3 |—39°4 53 oO} 25°78 4138 | 46°5 | 40°7 35 oO} 17°70 | 14027 19°75 |—30°6 55 0} 25°05 | 4927 | 43°38 | 41°5 36 of 17°72 | 13989 | 19°99 |—36'2 55 30} 24°72 5260 | 43°72 | 41°0 36 30] 17°71 14008 | 20°0 |—22°6 56 of «++. | (5357) | 42°0 | 4o2 37. | 17°70 | 14027 | 20°5 |—a21°5 57 O| 24°45 | 5557 | 402 | 39°8 38 of 17°65 | 14121 | 215 |—19°5 57 30] 24°05 | 5989 | 39°7 | 39°7 38 30] 17°62 | 14178 | 22°5 |—221 5 (0 ofag 58 6510 | 38°5 | 36:0 40 of 17°68 | 14064 | 24:0 |—17°5 3. Of 23°75 6336 | 40°7 | 32°73 42 of 17°68 14068 | 24°38 |—17°5 4 of 23°68 6413 | 41°5 | 31°8 43 0} 17°62 | 14178 | 24°38 |— 3:2 5 ©] 23°20 6967 | 40°5 | 32°5 44 o} 17°62 | 14178 | 25-2 |— 474 7 O} 23°15 7027 | 40°5 | 30°9 44 30] 17°62 | 14178 | 26°5 |—14-4 8 0} 23°10 7087 | 410 | 29:2 45 o} 17°58 14254 | 2675 |—13°2 Io 0} 22°48 7810 | 37°5 | 25°5 45 45] 17°58 | 14254° | 26-3 |—12-4 II oO] 22°Io $281 872° | 24-7 46 of 17°58 | 14254 | 27°72 |—12-4 12 0} 22°00 8406 | 35:0 | 2373 46 15] 17°58 | 14254 | 27°2 |—12-4 14 oO} 21°65 8841 35°2 | 21°2 47 0] 17°56 14335 27°76 |—13°71 15 0} 21740 9150 | 34°8 | 2072 48 of 17°57 | 14273 | 260 |— 7-4 15 30] 217Io 9525 | 33°70 | 18°6 48 30) 17°58 | 14254 | 2575 16 0} 20°65 1oo8s5 | 32°38 | 12°4 5° Of 17°57 | 14273 | 25°5 |—15°4 Bie LOPS 4S UB LOs gS) et. 92,90), 20° 5° 45| 17°58 | 14254 | 251 |—15°3 18 0} 20°30 10472 310 | 143 51 of} 17°56 14318 | 25:2 |—21°8 Time of |Reading of observa- |the Barom. tion. A.M. ON EIGHT BALLOON ASCENTS IN 1862, 439 Firrrn Ascent.—August 21 (continued). Height Temp. || Time of [Reading of| Height Temp. aliove the pane of the observa- |the atota, pete the oe ae Ge the reduced to} level of | % "2° | Dew- || tion. reduced to} level of "ia ©) Dew- 32°F, the sea. ae point. A.M. 32° F, the sea. a point in. feet. é * hm _ si! in feet. ° ° 17°60 14258 | 24°r |—12°5|| 6 24 | 22°23 8040 | 43°0 21'0 17°62 | 14228 | 23°38 |—19°'7]| 25 0 22°65 7655 | 42:8 | 2071 17°62 14228 23°38 |—17°7 25 30) 22°72 7573 43°5 20°5 17°62 14228 | 23°0 |—17°0 27 0! 22°95 7293 | 44°5 19°6 17°62 | 14228 | 23:1 |—20°5 27 30, 23°08 7141 | 44°2 22°0 17°61 | 14243 | 22°5 |—17°6 28 0 23712 7094. | 43°0 25°8 17°60 14258 | 23°0 |—24°3]/ 28 30) 23°11 7106 | 42°38 27°38 17°62 | 14228 | 234 |—25°6|| 29 0| 23:20 7Oo1 | 43°0 30°2 17°62 *| 14228 | 23:4 |—27°5|| 30 0 23°30 6884 | 43°0 ee a 17°63 | 14213 | 23°5 |—27°4 31 0] 23°28 6907 | 42°70 38°7 17°70 | 14108 | 24°2 |—29°0 3¥ 30}. 23°40 6767 | 42°5 39°2 17990 | 13802 | 24°5 |—29°4 32 0] 23°50 6650 | 42-0 33°7 17°95 | 13715 | 242 |—17°0|| 32 15) 23°60 6533. | 42°0 | 38°7 810 | 13484 | 23°8 |—26°7|/ 33 0] 2400 | 6058 | 4r'5 | 3777 18-11 13479 | 24°2 |—I9g°0 33 3°) 24°22 5819 | 41°8 37°3 1815 | 13419 | 24°2 |—17°7 33 39) 24°50 5515 | 41°5 Sed 18-23 | 13299 | 252 |—-173 34 0} 24°70 5298 | 422 | 37°9 18°30 | 13194 | 252 |—11-2|| 35 0} 24°80 5189 | 43°5 | 38'0 18°35 | 13119 | 25°2 |—13°1]] 36 0} 24°90 | 5080 | 44:2 | 37°5 voy (12815) | 24°5 |—13°8 36 30] 24-92 5058 | 43°83 39°2 19°07 | 12174 | 30°0 er 37 Ol 25226 4851 | 45-2 47-2 Ig'll 12122 | 29°8 1°6 37 3°] 25°20 4745 | 45°0 38°9 9°15 | 12070 | 27°8 18} 37.45) 25°30 | 4639 | 45°0 | 38:9 19°28 Imgor | 27°5 |—12°6 38 0] 25-60 4320 | 46°0 40°0 19°30 | 11875 | 27°38 |— 54]! 38 30) 25-92 3980 | 468 | 408 19°30 | 11875 | 27°5 |—107]| 39 of 2615 | 3751 | 47°8 | 41°6 19°30 | 11875 | 27°38 |— 44) 40 o| 26-40 3502 | 48-2 42°6 19°65 11420 | 31°5 4°5 41 0} 26-60 3300 | 49°5 44°7 19°80 | 11225 | 32°0 3-8 42 0} 26°80 3186 | 50° 45°5 20°05 10871 | 33°38 173 42 15} 27°00 2872 51°0 453 zo'20 | 10688 | 34°5 14°7 43 0| 27°20 2673 | 51°5 44°38 20°30 | 10566 | 36-5 160 44 0} 27°70 2177 | 15375 46°7 20°80 9936 | 37°0 18-1 45 9] 27°98 1898 | 54°5 48°0 21°00 9650 | 37°0 18-7 45 30] 28:20 1684. | 5575 48°6 21°70 8810 | 41°5 18'0 46 0} 28:40 1489 | 56°0 47°38 22°20 8196 | 43°5 18°7 || 7 10 oO} 29°42 513 | 61°8 51'r Srxra Ascent.—September 1. p {| P.M. 29°78 250 | 63°0 | 57°3 | 5 5 30] 26°46 3408 | 49°2 40°1 29°78 250 | 63°38 | 565 | 6 30) 26-41 3458 | 49°5 | 39°8 29°78 250 650 | 55°5 8 0} 26-41 3458 | 49°5 | 385 Jobe 270 | 64°0 | 5673 9 oO] 26°50 3368 | 49°8 33°2 29°65 320 | 63°0 | 51°9 Io of 26°55 3318 | 50°0 39°3 29°20 720) ') 61°E) | 6275 IO 30} 26°51 3358 | 50°0 39°3 28°90 996 | 5972 | 503 II 30} 26°31 | 3560 | 50°0 39°33 28°55 TS9Z0 (0572 Aegis 13 0} 26°19 3680 |} 48:8 37°8 28°00 1868 | 55:72 | 47°8 15 0} 26°19 3680 | 492 38°6 27°65 2214 | 542 | 481 || 16 0 26°25 3620 | 49°2 38°4 27°21 2654 | 52°2 | 46°7 17 0} 26°29 3580 | 49°2 38°6 26°92 | 2940 | 51°5 | 44-0 1g 0} 26°28 3599 | 488 | 37-0 26°91 POS ON S59 5 | 4357 20 a} 26°29 3583 | 47°8 37°3 26°78 | 3080 | 50°0 | 42°8 23 0} 25°95 | 3937 | 472 | 38:3 26°69 | 3170 | 50°0 | 42°8 23 30) 25°91 3977 | 472 | 364 26°61 3257 | 49°5 | 43°3 24 0 25°90 | 3987. | 47:0 | 366 26°60 3268 | 49°2 | 42°6 25 OO} 25°90 3987 | 47°72 37'2 440 REPORT—1862. Srxru Ascenr.—September 1 (continued). Time of |Reading of| Heigh Temp. || Time of |Reading of} Height observa- |tke arid ative the ea of the | obserya- |the arcane sles the tion, reducedto| levelof | “4:. . Dew- tion. reduced to| level of P.M. 32°F, the sea. * | point. P.M. 32°F: the sea, hm =~s in. feet. > = |; hm_ gs in. feet. 5 26 o}| 26°05 3837 | 48:1 | 364 || 5 56 oO} 27°55 2290 26 30] 26°15 3737. | 48:2 | 38:4 57 o| 27°65 2190 27 0] 26:20 3687 | 48-5 | 38-0 57+ eee (2040) 28 0] 26-10 3787 | 47°38 | 36°6 58 Oo} 27°95 1890 29 0} 26:00 3887 | 47°72 | 364 58 10} 28°05 1790 30 Oo} 25°88 4000 | 47°2 | 363 58 30] 28-12 abe Sr) Oo]. 2h75 4090 | 47°72 | 3674 59 0} 28:22 1620 32 0} 25°70 4180 | 462 | 361 59 30] 28°30 1540 33. 0] 25°69 4190 | 462 | 3671 || 6 © o} 28°45 1417 35 Oo] 25°69 4190 | 461 | 360 © 30} 28°52 1347 37 9} 25°98 3900 | 47°2 | 37°9 2 0} 2830 | 1567 37 30) 26°19 3690 | 47°2 | 37°72 3 0} 2819 1677 40 0} 26°50 3362 | 47°5 | 384 3 30) 28°05 1817 42 0} 26°82 3040 | 48°5 | 39°6 4 oO} 27°81 2057 43 0} «26°95 2910 | 49°2 | 41°6 On 27875 3117 44 0) 26°95 2910 | 49°8 | 422 5 30" 27°75 3117 45 0} 26°38 2970 | 49°2 | 42°8 6 oO} 27°75 3117 48 0} 26°68 3170 | 48-2 | 404 6 15| 27°79 3077 50 0} 26:90 2950 | 49°72 | 39°5 6 30] 27°80 3067 52 oO] 27°49 2356 | 50°0 | 42°8 8 0} 27°90 2967 53. | 27°40 2446 | 50°5 | 43°7 8 30} 28-00 2867 53 30) 27°40 2446 50°5 | 45°0 9 oO] 28°20 2667 54 9 27°44 2406 | 50°0 | 45°9 Srventa Ascent.—September 5. | P.M. | P.M. D'MIG $GlP fees 490 | 59°5 | 484 |] I 30 15} eee |(16965) | 16:0 0+ i5 Of 25°77 720 | 59°0 | 50°5 30 30] «+e 1(17055) | 16:0 5 20) 28°97 QOD sal 57 e || 5SSE 32 .O} 2540 ai 59° ESS BGO tase (1340) | 56°5 | 47°9 34. O} s+ .0pe|(r8x80) vee |[— 5°5 6 o} 28°38 1480 | 55°5 | 46-9 37 Of 14°55 | 19068 15°6|—2171 Io o| 2619 3660 | 45°5 | 41°5 37 20] «+e. |(19290) | 15°3/— 8-0 DL + OP 5. % 4116 | 44:2 | 404 38 Oo} «sees. | (19735) 14°2 11 30] 25°49 | 4388 | 43°3 | 38-9 38 10] .--. | (19847) | 12°9 IZ 0} 24°99 4920 | 42°0 | 38°7 38 20) 14°05 19960 12 30) 24°89 5011 | 40°9 | 3873 | 38 25) 13°95 | 20126 13 0} 24°30 | 5675 | 39°5 | 36°5 || 38 50] «.-- | (20315) | 8:0/— 5:0 13 30) 24°25 | 5722 | 38:0 | 36-1 39 0} 13°76 | 20393 8°5 14 30) 23°70 | 6330 | 36°5 | 365 || 40 0} «.-- |(20733) | 9'2|— go 16 0} 23°36 6729 40 I5| «++ | (20818) | «2. |—1570 16)-3o)" ee. (6821) | 36-1 | 36-1 40 30] «++ |(20903) | 1-0 17 0} “2g 6914 | 36:0 | 35°7 || 41 20) 13°35 | 21182 sees |—I5'0 17°20) Werle « (7245) exit | 4373 41 50| -.-- | (21407) 4°5 17 40| 22°66 7575 39°5 | 3072 44 oO] 12°75 22380 21" of fap 72 9926 | 32°71 | 26°6 48 o| 11°95 | 23976 070 |—30°0 22 of 20°07 | 10770 | 312 | 26°99 || 50 of 11°25 | 25382 |— 2°0|no dew 24 o| 18°73 12568 | 26°5 | 19°7 51 o}| rt0'80 | 26350 | 25 30) 17°93 |(13875) | 25°5 | 22°3 532 | 9°75 | 29000 50 26 of we-- |(14312) | 2372 ZEIT OND whole's 25318 |— 2°0 27 O| 16°94 | 15184 8 30) 12°55 | 22654 2°0 27 30) =---> 1(15347) | 18°7 8 45) 13°15 | 21650 II‘o 28 of 16°69 | 15510 | 18-0 9 9} 14°05 |} 20018 170 28 30] -... |(16015) | 17°9 9 30] 16°37 | 16015 18-0 29 0} 16°05 16520 | 17°9 9 40} 17°07 | 14938 29 20} «+. |(16640) | 17°8 | 10°5 LO” Of Ow els's DH(14706) 9} Siaaeg oe (16875) | 16-2 II 17°71 14012 < a ON EIGHT BALLOON ASCENTS IN 1862. AAT, Srvenrn Ascent.—September 5 (continued). | Time of |Reading of} Height T 5 | ee 8 f |Readi f| Height T . observa- |the ey tage the nd of the dieerta: shafBaron, above the M5 aa of ‘the tion. reduced to} level of wes Dew- tion. reduced to} level of "4 © | Dew- P.M. 32°F, the sea. * | point, P.M. 32°F, the sea. a point. hm_s s| in. feet. a = hm_s s!/ in feet. zs : va 214 o| 18:06 | 13520 | 24°5 PP GS Hi} 5 Ge (6590) TA. 30|. x... (13210) | 24:8 ZG) UG sate 'ate (6560) | 45:2 | 21°5 15 0} 18-46 | 12900 os (oe) ZO" (Geol ate (5655) | 45°5 | 27:0 16 oO} .... 12250 | 26°5 29 30) 24°51 5500 | 47:0 | 21°38 16 50) 20°65 | 10070 | 31°! Z030|ie serene (5110) | 47°r | 35°1 Ty AONE jess 5< (8800) | 34°2 31 30| | ieerere (4720) | 49:2 | 19°7 1g 30} 21°85 8530 32 o| 25°40 4521 | 48-0 BY IG) va,» <0 (8400) | 3572 92) F0|eeee ade (4315) | 50°5 | 20°8 20 20] 22°04 8310 33 0] 25°80 4110 20 40] 22°24 8090 | 401 | 15°2 SAG el ie eae (4050) | 51-1 | 22°3 on OW tests + (7860) | 42:2 | 17°3 | 3G) lola terras (3795) abo es telegas 23 20) 22°64 7625 | 40°0 | 20°0 38 o| 26-40 3484 | 52°2 | 37°70 23 50] 22°93 7260 | 40°0 39 0o| 27°60 2260 24. | 23°03 7150 39) 2Cle vente Shoe 54°0 | 4271 25.0} (23°95 6810 | 42°0 3. (6), Noles on the | 57°2 | 48°8 26 0} 23°47 6640 ground The reading of Regnault’s hygrometer at 1" 45™ was reduced to —30°, without any deposition of moisture; the temperature of the dew-point was therefore at a lower degree. At 1" 48™ the temperature of the dew-point, as determined by the Dry- and Wet-bulb thermometers, was — 35°, as shown below. At 1" 37™ the readings of the Dry and Wet thermometers (aspirated) were 15°-5 and 11°-3, giving a dew-point temperature of —21°-1. At 1" 37™ 10° the readings of the Dry and Wet thermometers (free) were 15°-0 and 11°1, giving a dew-point temperature of —18°1. At 1" 37™ 50° the readings of the Dry and Wet thermometers (free) were 14°-5 and 10°2, giving a dew-point temperature of —13°-0. At 1" 38™ the readings of the Dry and Wet thermometers (aspirated) were 14°-2 and 10°-5, giving a dew-point temperature of —18°1, At 1" 38" 10° the readings of the Dry and Wet thermometers (free) were 13°-2 and 10°-0, giving a dew-point temperature of —14°-8. At 1° 39™ the readings of the Dry and Wet thermometers (free) were 8°-0 and 4°°5, giving a dew-point temperature of —22°-7, At 1" 40™ 15% the readings of the Dry and Wet thermometers (free) were 10°-2 and 8°1, giving a dew-point temperature of —8°2, At 1° 40™ 30° the readings of the Dry and Wet thermometers (aspirated) were 9°°5 and 7°8, giving a dew-point temperature of —5°3. At 1 44” the readings of the Dry and Wet thermometers (free) were 8°-1 and 4°2, giving a dew-point temperature of —26°-0. At 1" 45™ the readings of the Dry and Wet thermometers (aspirated) were 7°°3 and 4°-5, giving a dew-point temperature of —17°3. At 1" 48™ the readings of the Dry and Wet thermometers (free) were 0°-0 and —4°:0, giving a dew-point temperature of —35%2. At 2" 9" the readings of the Dry and Wet thermometers (free) were 17°-0 and 11°-0, giving a dew-point temperature of —34°-7, At 2" 10™ the readings of the Dry and Wet thermometers (free) were 225 and 15°-8, giving a dew-point temperature of —27°-0. From the general agreement of the results as observed by Regnault’s hy- grometer and those of the dew-point as found by the Dry- and Wet-bulb thermometers, there can be no doubt that the temperature of the dew-point at heights exceeding 30,000 feet must have been as low as —50°. wn wn Annu a as Yb O w w w w P90C0O0000000000 O48 nw Oo. O0 Reading of the Barom. reduced to 32° F, in. 29°92 29°47 28°90 28°70 28°50 27°75 27°55 27°20 26°70 26°30 25°90 25°68 25°50 25°41 25°38 25°38 25°36 25°36 25°42 25°50 25°55 25°60 25°73 25°95 26°10 26°20 26°28 26°38 26°70 26°74 26°78 26°68 26°25 26°10 25°95 *25°74 25°52 25°40 25°22 25°20 25°20 25°20 25°19 25°11 25°00 24°92 24°95 24°78 24°82 25°05 25°05 25°02 25°00 25°08 25°09 25°10 25°11 REPORT—1862. Ereuta Ascent.—September 8. Height above the level of the sea. feet. 250 813 1232 1530 1730 2432 2520 2923 3320 3720 4169 4380 4560 4650 4727 4727 475° 4750 4690 4610 4560 4510 4480 4160 3946 3850 377° 3670 3350 3310 3270 3370 3808 3958 4108 4220 4440 4540 4895 4920 4920 4920 4930 4926 5175 5263 5230 5428 5388 5112 5109 5145 5169 5057 5043 5029 5019 T ate | | Sa Air. ch i point. P.M. ‘s > hi fs 67-2 | 61°2 5 24 30 66°5 | 6074 25 0 G22 711582 25 30 6371 | 57°38 26 0 G2-8u a2 26 20 60°2 |} 54°6 27410 583 | 54-4 27 30 5625) pega s 28 o 552 | 49°9 29 30 54°0 | 48°5 30 30 52°0 | 49°0 an 20 SES | 495 31 30 sro | 48-6 || . 31 45 595 | 4971 32 0 SOs! | 4915 32 30 50°38 | 48:8 33, jo 51°r | 48°6 33 15 5°°5 | 49°F 33 30 50°3 | 48:0 34 0 49°5 | 479 35/9 49°3. |. 47°7 35 3° 49°5 | 46°8 36 © 50°0 | 45°9 36 20 49°8 | 48-2 37 0 595 | 49°71 37 30 50°83 | 48-9 38 30 512 | 48°8 39 0 SES | 50% 39 35 S72 | 599 39 30 52°35 | 5055 O40 53°79 | 50°0 49 30 535 } 49°5 ORS: 53°5 | 49°6 42 0 52 o ) 58.5 43 0 5272 | 50°8 44.0 55 | 48°5 || - 44 30 510 | 48°78 45 0 51°0 | 40°8 45 30 510 | 36-9 46 o SEW 87. 47 0 51t | 35°4 48 0 53°2 | 34°9 48 30 542 | 34°2 aD 9 55°2 | 33°5 noes 56°5 | 34°5 50 0 57% |} 35°9 §° 39 572 | 38-0 51 o 58°5 | 40°5 52 0 60'0 | 4073 54 0 58-2 54 30 57°51| 359 54 45 57°5 | 35°9 55 © ae 5, | 3579 55 10 562 | 38-4 56 0 542 | 41°6 56 io 518 | 4q2 56 40 515 | 44°9 oF KS Time of |Reading of the Barom.| above the reduced to 329 F, in. 25°09 25°30 25°50 25°92 26°69 26°80 27°06 27°25 ‘27°52 27°60 27°68 27°82 27°95 28°05 28°17 28°30 28°40 28°49 28°60 28°65 28°80 28°95 29°10 29°20 29°25 29°30 29°28 29°20 29°18 255 29 *5 29°15 29°20 29°21 29°18 29°15 2915 29°14 29°18 29°18 29°21 29°28 20-48 29°50 20°54 29°46 29°12 29°00 28°90 28°50 28°40 Height level of the sea. feet. 5939 4829 4629 4197 3328 3218 3618 3438 2954 27383 2540 2432 2360 2207 2090 1990 1870 1720 1620 1530 1420 1370 1220 1077 932 842 805 768 782 842 856 887 887 887 842 827 805 842 856 887 887 896 $56 856 826 772 672 553 517 589 ON EIGHT BALLOON ASCENTS IN 1862. 443 Eien Ascent.—September 8 (continued). Time of |Reading of} Height Temp, || Ti i Hei : observa- |the Bardi. above the ee of the aoe rep een eye oar Bre tion. reduced to| Jevelof | %..'° ew- tion. reduced to| level of of the Dew- P.M. 32°F, thesea. ; point. P.M. 32° F. the sea. a point. hm s|-in. feet. a a hm s| in feet. a S 5 57 30} 23°38 1639 | 60°5 | 55°83 || 6 x 30) 27°98 | 2034 | 59°8 | 54° 58 of 28-22 1798 | 600 | 56:2 I 45| 27°90 2114 | 59°8 | 54°8 58 40] 28:11 | (1870) | 60°0 | 56°6 2 ©} 27°90 2114 | 59°8 | 54°9 6 © oO} 28:05 1967 | 60°5 | 56:0 3 40) 27°78 2235 59°5 | 50°0 © 20] 27°98 2034 | 60°0 | 57°1 5 oO] 27°89 2122, | §9'2.1 §57°0 I of 27°98 2034 | Goo | 55°8 IO 0} 30°07 on the ground § 5. Varration or TEMPERATURE OF THE ATR witH Heteur. In order to arrive at an approximate value of the normal variation of tem- perature on each day, it is necessary to make some estimate of the amount of the disturbing causes. For this purpose I placed every reading of temperature in the preceding Tables in the high ascents, or the means of small groups of observations in the low ascents, on diagrams, and joined all the points, and caused a curve to pass through or near them, so that every change of temperature was thus made evident to the eye. In all these projected curves there were parts of evidently the same curve showing a gradual decrease of temperature with increase of elevation, and a gradual increase with decrease of elevation. These parts were connected and assumed to be a close approximation to the truth, and capable of giving approxi- mate values of the normal variation of temperature with height. The departure in the projected curve of observed temperatures from the assumed curve of normal temperatures in these diagrams indicated the places and the amounts of disturbance. The next step was the reading from these curves the tempe- rature at every thousand feet, and in this way the next Tables were formed. The numbers in the first column show the height in feet, beginning at 0 feet and increasing upwards ; the numbers in the second column show the interval of time in ascending to the highest point; the notes in the third column show the circumstances of the observations; the numbers in the fourth and fifth columns the observations and the approximate normal temperature of the air ; and those in the next column the difference between the two preceding columns, or the most probable effect of the presencé of cloud or mist on the temperature, or of other disturbing causes in operation. The next group of columns are arranged similarly for the descent, and the other groups for succeeding ascents and descents. 444A rEePort—1862. Taste I1I.—Showing the Temperature of the Air, as read off the curve drawn through the observed temperatures, and as read off the curve of most probable normal temperature, called adopted temperature, and the calculated amount of disturbance from the assumed law of decrease of temperature. Temperature of the Air. Ascending. Descending. Height, in feet, | Sovelod the oat ck ob Gated [pet Ob ‘ated ° etween Circum- = Adopted ate | between Cirew ad Adopted ate ° seryed Pree effect of cum P dimes. |*N€2S-| temp, | *™P- |‘Gsturb«| times. | *B0°5-| fempe | teMP- (Steeurb ance. ance. July 17. 9 9 ° : 9 ° 26000 16:0 | 16°0 00 | 16"0-| 16°90 oo 25000 1670 | 160 o'0 | 180 | 17°72 |+ 08 24000 16°3 | 16:0 |+ o8 26°0 | 18°5 75 23000 17a9 - | Od 1°8 27°99 | 19°8 8-1 22000 19°5 | 16°2 2°3il = | 28-1 | 21-0 ar 21000 2 24°1 | 16°8 7°3\| + 28°5 | 2275 6:0 20000 r=] a= A271 | 1750 151 3 “3 286 | 23°9 47 19000 a a) eke pian Wie Gre} 22°2 B =e 28°38 | 25°0 3°8 18000 a = 35°2. | 17:8 17°4 3 = 29°0 | 26:2 2°8 17000 « 2 32°7 | 1870 14°7 » ; 292 | 27°38 14 16000 =| 31°9 | 18°5 134 5 29°5 | 2970 1+ 0o°5 15000 S 21-2 1G 5 12°7 | 5 30°5 | 30°5 o'o 14000 3 29°5 | 20°71 9°4.| a ars" | 140s oo 13000 a 26°76) 20°75 52) 8 33°70: | 33°O O70 12000 5 25°9 | 22°3 gO) 8 34°5 | 34°5 oro I1000 = 26:0 | 24°0 20 a iy 360 | 36°0 o"o 10000 aL 26:2 | 26°0 o2|| 6 Gy NBG a aiEs (oho) gooo g 29°70 | 290 [oKe) 4g 2 8000 © 32-0 =| 3270 fone) 5 = 7000 Fa rs | 36°75 | 36°5 ool] * 6000 a & 34°38 | 41°0 6-2 5000 Sa(93953).| 452 59 4000 4355/6 | Sao 6°5 3000 “ 479 | 54°8 gt 2000 oie) | 25h Hees 73 1000 5 = 569 | 6471 Be ° 61°5 | 7o.o |+ 8°5]| July 17.—The departure in this ascent from a regular progression is very remarkable. Below the cloud the decrease of temperature was pretty well uniform ; on passing out of it there was an increase of 6°, and then the decrease was resumed. At 10,000 feet the temperature was 26°, and there was no change in the next 3000 feet; then a very remarkable increase took place, till at 19,500 feet with a temperature of 42° the rise was checked, and then declined rapidly to 16° at 5 miles high. In the descent a disturbance from the regular increase of temperature was met with at the height of 24,000 feet, and continued to 17,000 feet; at 13,000 feet clouds were reached, and no observations were taken below 10,000 feet. The dense clouds which covered the earth caused an apparent loss of temperature of about 81°; and the effect of a warm current of air, which was first met with at the height of 11,000 feet, amounted, at 19,500 feet, to fully 25° warmer than would have been had this intermediate current of warm air not existed. The excess of warmth is shown at the different elevations of 1000 feet in the 6th column of the Table for this day. ON EIGHT BALLOON ASCENTS IN 1862. 445 Tasce IIT. (continued.) Temperature of the Air. Ascending. Descending. Siac macon ; | cal u- | aicu- level of the sea. |Between|q: 4] Ob- | abated tae ‘Between! oircum-| 2%-, | adopted! lated giiat |stances| S204 Meu, fet ol gst Stance] eed (temp. (ie ance. ance. July Shh ° ° ° ° ° ° 7000 ° 50 42-8 | 33 =e 44°0} 44:0 o"o 6000 = d 43°5| 45°5|— 2°0 = z oe 46°0|} 46:0 oo 5000 2s, | Misty.| 48-2] 48:2 oo eS => 47°4| 47°4 oo 4000 4,2, 520] 508 )/4+ 12] Ou | «- 4972| 492] oo 3000 a< 52°7| 53°2|— OS] ga | -* | 541] 54°F) 0 2000 9 tn 59°5| 57°\+ 2°5|| & - Ar 59:21) | 5972 o°o 1000 2 62°9} 62°9 oro} * a 63°72) 63°2 role) ° 707 |) \JO"7 oo = 68:0] 68-0 oo August 18. 12000 | rs ee vs ‘ i) : ee oe . 11000 E S38 | 392| 380l+-r2]| ¢ rc 4r2| 38-0|+ 3:2 10000 x So | 418] 39°5 ZEB” Rin 44°5| 40°0 45 gooo a #2 | 440] 408 3:2|| = = 46°5| 46°3| 47 8000 4% ego) | 45:2:|1 4200 F°0, S ‘ 50°0| 44°0 6:0 7000 Ss z= 46°1| 438 pes) 8 5 54°0| 46:0 4:0 6000 g 29 4772| 45°0 Zp S we 53°5| 48:0 5°5 5000 s | 82] 485] 465) 20] 4% 52°7| 51°0| 1-7 4000 ~ |2e| 499) 492)/+ 97] + . 541] 53°5|+ 06 3000 g I ° 52°8| 52°8 oo|| 7A oe 56°0| 5670 oo Bose 3) See SHES. 5745 oro}| .* 1000 22 | 62:9] 62°9| ool| 8 oe ° mo 79°9| 70°9 foyfe) . On descending, a warm current of air was entered at the height of 24,000 feet, and extended downwards to 16,000 or 17,000 feet, and the calculated effect of this is shown in the 11th or last column on July 17, on the opposite page. July 30.—There were alternately warm and cold currents at different elevations, as the balloon passed down the valley of the Thames; the depar- ture from the curved line which was made to pass through the observed readings when laid on a large diagram, at times was from 1° to 3° in excess, and at other times nearly as much in defect; but in the descent, which was rather rapid, there were no disturbing causes in operation. The amounts of disturbance in the ascent will be seen at each 1000 feet in the preceding Table. On August 18 the temperature of the air decreased as usual on leaving the earth, until at the height of 4000 feet the rapidity of the decrease was arrested, and a warm current of air met with, which continued till the height of 11,500 feet was reached, when the balloon turned to descend, when the same warm current was passed, extending to the same limits ; and was met with again on the re-ascension, at about the same distance from the earth, and found to extend to the height of 14,000 feet, when the regular diminution was resumed, and afterwards continued to the highest point reached: on the second descent, the same warm current of air was again met with, and continued till clouds were reached at the height of 6500 feet, which caused another interruption in the regular increase of temperature, as is usual in entering cloud from above, The temperatures of the air at every 1000 feet, as observed, were 4.46 REPORT——1862. Tasie III. (continued.) Height, in feet, above the mean level of the sea. |Between August 18. 23000 22000 21009 20000 19000 18000 17000 16000 15000 14000 13000 12000 11000 10000 gooo 8000 7000 6000 5000 4000 3000 2000 1000 ° _—_—- le August 20. 5000 4000 3000 2000 1000 ° 5000 4000 3000 2000 1000 ° what times. From 1" 48™ to 24 59™ p.m. From 65 26™ to 65 47™ p.m. From 75 21™ to 85 5™ p.m. Temperature of the Air. Ascending. : Ob- Cc - Adopted stances Soe | tem ° ° v. 24°0| 24:0 a9 24°2| 24°2 . 24°4) 24°4 a 24°6| 24°6 oe 25°7| 25:0 oe 3r0| 260 oe 27°2| 2972 oe 28°83 28°8 ae 30°8| 30°8 . 33°5| 328 on 37°5| 349 a 40°5| 37:0 oe 45°0| 389 a 49°5| 410 ate 50°7| 43°2 a 510] 4572 os 52°38 | 47°8 ' 54°7| 49°8 “5 52:0] 5270 aD 541) 541 | disturb- | ance. | ance. September 8. : 5 # a “ 3 4 é 5000 # g | Above 50°O} S50°0 OO || oO = Above oa 511 4.000 Fa — 52°7 52°7 oo || “3 cloud. ote 50°3 3000 el spond S6"4 56°4. | ooll es In cloud 2000 = 61°0| 61°0 oro |] fur a a 1000 ot |Below} 65:1} 6571 oo] 9, ° Fo |cloud.| 69:0} 690 oro|| * 5000 5 g ic ale 55 °Sche~ wie SF se Ad 51°4 4000 o ee oe . 52°5 | oe 33 oe oe 512 3000 = &, . os oe 34 oe ve 53°9 2000 On an an . a aS ee a 56°5 1000 £4, p ats as oe PB) oe “t 60°2 ° ge oe ele ts - 5 ve oe 64:8 September 8.—The sky was cloudy, and the decrease of temperature was nearly uniform, and there was no marked interruption in the regular decrease of temperature on descending. The next Table has been formed by taking the difference between conse- cutive numbers in the preceding Tables, in each of the several ascents. The disturbances on July 17 were so great and the results so different from those on the other days of experiments, that no use has been made of the results, other than inserting them in the Table. 1862, 25 450 ae REPORT—1862. Taste 1Y.—Showing the Decrease of Temperature July 17. | July 30. | August 18. | August 20. Pac nore State of the Sky. sea. Cloudy. Clear. | Cloudy. Clear. Cloudy. ae Be ae 6S Gels ie Pes 2 sla e)/2¢)2|2¢)e8]4] 421% From To <4 a 2 a 3 a < A < a ft. ft. ° ° ° ° ° ° ° ° ° ° 28000 | 29000 : a wae ac age cee Ses eee 27000|28000] .., aoe eee aaa aR ae ae aan ees eae 26000|27000} ... =O. 7a: on aaa aE ea ogy & eee == eee |25000|26000| oo 12 ods on are sce tae age na «aa 24000 |25000} 0o°o 1°3 sae oat Ke nee oo fa ive eee 23000|24000] ov! 00 | Wee ae ae og sae age ese ase 22000 |23000} o*l 12 re ons nas on o2 o"4 tee one 21000 |22000| 0°6 I5 oe ee eee eee O72 08 eee see 20000|21000] 02 14 aa ave ase eee oz o°8 nas eee 19000 | 20000] 073 Il sla oes wie eee o4 I'0 ane oe 18000| 19000] 05 12 BSc ase - oe Io I'o ae on 17000] 18000] o2 1°6 Hr ae Sen ene r2 170 eee ove 16000} 17000] 05 12 oe ane = eee 16 I'o wee eee 15000 | 16000 I°o i5 A Fe sae ae 2'0 I°o eee we eee | 14000/15000| 0°6 1'0 ae 54 sep tee 2°0 12 eee eee 13000|I4000} 1°4 ita a a ane eve eh 1°8 ee ese 12000] 13000] 0°8 ton eae eae nee “or 2:1 2°5 aee oe II000|1I2000|] 1°7 15 nas — op ae I'9 27 ane 10000] I1000| 2°0 Tool akere cae 1'°5 2°0 IS 28 : ene 9000|Ioo00] 3:0 | ... |] ... cer 1°3 1:8 |) “2:2, |" 28 sue oe 8000] gooo} 3:0 are ee Ar 1'2 2°2 20 24 eee oe 7000} 8000} 4°5 = “on ces 1°8 2"0 2°6 a4 ae eve 6000} 7000} 4°5 27 | 2°6 Ia | 2:6) | 26 3°3 eee tee 5000| 6000} 42 2°7 14 I'5 30 2°2 4°0 ods eae 4000] 5000] 4:8 2°6 18 27 2°5 a1 4:0 ea ae 3° 3000 4000 48 2°4. 49 3°6 2°5 I'9 45 40 2°83 4 2000} 3000/ 5°0 3°83 Sr 47 eee vee gr 50 30 ct 1000] 2000] 43 59 4°0 54 oes -o 49 4°5 ove ©} 000} 5°9 7°38 4:8 8-0 eee a 6°5 49 eee A glance at this Table shows that, without exception, the numbers at the lower elevations are very much larger, in all states of the sky, than those at the higher, and therefore that the changes of temperature are much larger near the earth, for equal increment of elevation, than far from it. Also by comparing the numbers at low elevations with cloudy and clear skies, those with the former are much smaller than those with the latter, and therefore the decrease of temperature with increase of elevation is larger with a clear than with a cloudy sky. By taking the mean of the results at every stratum of 1000 feet, omitting those belonging to July 17, we haye— Ascending. ‘ in every 1000 fect of elevation up to 29,000 feet. | August 21. | Cloudy. | Ascending. Descending. reel . ae 2°2 32 2°8 2°9 28) 3°5 Se 3° 31 | 38 3°38 | 36 38 | 3°5 4° | 40 4° | 40 41 | 46 46 | 50 43 | 54 4°0 6'0 Up to ON EIGHT BALLOON ASCENTS IN 1862. September 1. September 5. September 8, | State of the Sky. | Partially Cloudy. iain Cloudy. Cloudy. a al oS | 2 a ea B= | A: s ae Es} oes 3. | ge | a eg z g 3 3 g 3 < A < a < A ° ° ce) ° ° ie) 08 ace a 0'9 ss ts I‘o aoe ss I‘o aed vee I'l I'l : : R Ee 2° a ee rs 2°I Be “Fe oe 2°0 22 *s dae ae 2°0 2°2 “ see a 2°5 2°3 are onc ee 25 2°0 eee eee Ze 2°8 . see «os 2:3 2, | ieeae mee ae Het |p eon | eee nee one 2°5 2°5 || te * 2°5 2oB I ees ice : Zine | ace” posts sp see 2°8 > Jes dnd | Valuer 5 . ee 24 2°5 * oes - 2°83 3°1 eee rn Sse ar 26 sas F | a5 2°7 eae Gee Bre} Sass 4/0 Boia (lier 3 co Fi eee 4/0 27% Wl Ws0 * aes is ace 3°5 2°8 Me Ae 32 | 2°0 a55 370 37. 27 «lal oie go nme Kan Wl cD | ic: din Gi 47 see oh 3°2 41 = fifi 6'5 72 | 34 |} 39 | 46 | Cloudy. Clear. At heights less than 5000 feet. a Pe Peis ss i. ST OF On 3? 189 feet. 254 feet, 295 feet. 345 feet, 2H2 452 REPORT—1862. These results differ considerably from those found in a cloudy sky, and doubtless the difference between experiments carried on under a cloudless sky at these elevations would differ still more. They do not at all confirm the law of gradation of temperature of 1° in 300 feet. Tur DECREASE OF THE TEMPERATURE OF THE AIR At heights exceeding 5000 feet. feet. feet. i e From 5,000 to 6,000 was 2-8 from 10 experiments, or 1 in 357 feet. 33 6,000 33 7,000 39 2:8 33 33 32> 33 357 3? 39 7,000 9° 8,000 99 2-7 ” 33 3? 99 370 3? bP) 8,000 39 9,000 39 26 33 ” bP) 3”? 384 ? > 9,000 ” 10,000 9 26 ”? 3”) ” 33 384 3”? 3? 10,000 > 11,000 oF 26 3? ”? >> 99 384 >? 3) 11,000 3? 12,000 9 2°6 99 bP. 3? 33 384 ”” », 12,000 ,, 13,000 ,, 25 ,, ” » » 400.--,, 9 13,000 ” 14,000 3) 2:2 2) 33 Lh | 33 455 3 ” 14,000 ” 15,000 ” 21 ” ” ” ” 477 ” 3) 15,000 3”) 16,000 9 21 3) ” bP) 39 477 33 39 16,000 ” 17,000 39 33 Ped 33 527 39 »> 17,000 ,, 18,000 _,, 556 ,, », 18,000 ;, 19,000 ,, 3 93! 370 ile a OE 99 19,000 bes 20,000 9 39 9? 9 39 667 ” » 20,000 ,, 21,000 ,, z 39° day “29 Biple EC 3? 21,000 2? 22,000 9? 2) 39 3) 771 3” 55 22,000 ,, 23,000 ,, »» 23,000 ,, 24,000 ,, » 24,000 ,, 25,000 ,, », 25,000 ,, 26,000. ,, », 26,000 ,, 27,000. ,, »» 27,000 ,, 28,000 ,, ae tee ee ” 28,000 ,, 29,000 _,, 08 ,, ” ” » 1250 ,, These results follow almost in sequence with those found with the partially clear sky, and together show that a change of temperature of 1° takes place in 139 feet near the earth, and that it requires fully 1000 feet, for a change of 1°, at the height of 30,000 feet ; the intermediate heights require a gradually increasing space between these limits to its elevation, and plainly indicate that the theory of a decline of temperature of 1° for every 300 feet of ascent must be abandoned. By adding successively together the decrease due to each 1000 feet, we have the whole decrease of temperature from the earth to the different ele- vations ;— ” ” 6 ADR) 95 ” ” ” 771 ” ” ” ap «OOD ovigy ” ” 9» 1000" ,, ” ” »> 20005 :,, Paracas eical sewers SOF WOWWODOSO S i) io} PH HENNA ERE RARBRARRDHODM DO ft. feet. a feet. From 0 to 1,000 the decrease was 7:2, or 1° on the average of 139 2 2,000 # 12:5 me 160 x 3,000 a alot i. 176 os 4,000 iv 20:5 ss 195 “ 5,000 ds 23-2 4 211 ss 6,000 5 26-0 fe 230 zn 7,000 sf 28-8 P: 243 $5 8,000 s 31:5 af 254 js 9,000 5 34-1 Ft 263 ON EIGHT BALLOON ASCENTS IN 1862. 453 ft. feet. z feet. From 0 to 10,000 the decrease was 36:7, or 1° on the average of 272 id 11,000 u 39°3 es 279 i; 12,000 % 41:9 i. 286 <3 13,000 ifs 44-4 a 293 i 14,000 ¢ 46-6 ia 300 . 15,000 a 48-7 Bs 308 3 16,000 “ 50°8 m8 314 Re 17,000 a 52-7 z 322 As 18,000 ao 54:5 nf 330 Fy: 19,000 - 56:3 Ee 337 4 20,000 i 57°8 = 346 % 21,000 4 59-1 ee 355 2 22,000 on 61:4 i 358 a 23,000 is 62-4 sf 368 as 24,000 ae 63:7 5s 377 M 25,000 <3 64:8 s 386 * 26,000 + 65:°8 i 396 - 27,000 * 66:8 = 404 = 28,000 fe 67-7 3 413 _ 29,000 + 68°5 23 423 3 30,000 70-0 he 428 These results, showing the whole decrease of temperature with different elevations, differ considerably from those which would be found on the sup- position of a decline of 1° of temperature for every 300 feet. The observed decrease in the first 1000 feet, viz. 7°-2, is more than double of that given on this supposition, viz. 3°°3, and the observed values are all greater at the lower elevation ; but the difference between the two becomes less and less, till at the height of 14,000 feet they agree. At greater elevations they again differ, but in the contrary way, the observed values being now the smaller,— the differences between the two increasing with increased elevation, till at 30,000 feet the difference amounts to no less than 30°—the observed values showing a decline of 70°, and theory a decline of 100°. The numbers in the last column show the average increment of height for a decline of 1°, as found by using the temperatures of the extremities of the column alone; and they do not differ much from those found by Gay-Lussae, Rush and Green, and Welsh, at the same elevations. At 14,000 feet the average is the same as that of theory, viz. 1° in 300 feet; and certain it is, in any balloon ascent exceeding 8000 feet, where the average decrement is 1° in 254 feet of ascent, and up to 20,000 feet, where the average is 355 feet, that such results would have been looked upon as generally confirming the above theory, and hence the necessity of including observations before leaving and near to the earth, and extending them to the highest point possible. Respecting the rate of the decrease of temperature with height, it is abundantly evident that much uncertainty would always prevail, how great soever the accumulation of observations of mountain temperature might be, and the only means of determining this important element is by balloon ascents. In the preceding Table it will be seen that the decrease of temperature in the first 5000 feet exceeds 23°, and that even in cloudy states of the sky it amounts to 20°. So large a decrease of temperature taking place, whether the sky be clear or cloudy, within the first 5000 feet of the earth, it became very desirable, and indeed necessary, to ascertain how this change of tempe- 454. REPORT—1862. rature is distributed: for this purpose all the observations of the temperature of the air taken within this distance of the earth were laid down upon large dia- grams; a curved line was made to pass through or near them, and the reading at every 100 feet was taken from these curves, and those at every even hundred were inserted in the following Tables, as well as those from the projected curves as found by joining the observations themselves, and in this way the following Tables were formed :— Taste V.—Showing the Mean Temperature of the Air at every 200 feet up to 5000 feet. Temperature of the Air. Ascending. Height, in feet, j Jovel OF the ncn. [Betw ob-_| ‘ated Hee * }Petween! circum- =, |Adopted| |< what rved t tuniea! stances. com | temp. Meets ance. July 17. @ Jie ° 5000 = 39)3)| 95 ee 4800 2 40°4| 40°4 oro 4600 a) 414) 41°4 o’o 4400 mo 42°4,) 42°4 oo 42.08 AS 4 43 4 o"o 4000 ———— | 445| 4a5 oo 3800 z 45°2| 45°2 o"o 3600 a 46°0| 46°0 o"o 3400 cy 46'9| 469) oro 3200 » 47°38! 47°38 foe) 3000 ax 48°6| 48°6 o"o 2800 ° 494) 494) oro 2600 - 50°3| 50°3| oto 2400 = ro 51°0| 5§1°0 oo 2200 a & Pe GO A Os 7 oo 2000 Ss S 52°5| 52°5 o°o 1800 = 3 53°4| 53°4 o*o 1600 8 iS 54°3| 54°3| oo 1400 ° 55°2| 55°2 o*o 1200 ee 56°0| 56:0 o"o roco 56°9| 56°9 oo 800 a7 7 | Sf? | see 600 58°6| 58° o"o 400 59°51" 59°5 on 200 60°5| 60°5 o"0 ° 61°5| 61°5 o"o July 17.—The results are dependent upon the observations before leaving the earth, joined to those taken at and above 3800 feet; but they accord with others under the same state of the sky, indicating an almost uniformly de- creasing temperature until the thick cloud was reached. July 30.—The fluctuations on this day are better shown here than in the preceding section ; there seem to have been no fewer than four or five dif- ferent strata, on this day, within 7000 feet of the earth, experienced during the ascent and passage of the balloon till the time of descent, which was rapid, and during which the increase of temperature was gradual throughout. ON EIGHT BALLOON ASCENTS IN 1862, 455 Taste V. (continued.) Temperature of the Air. Ascending. Descending. Height, in feet, es Between Ob- | ioe | Betwe Ob ve Bye etween) Cireum- Adopted Bie etween! Circum- ~, |Adoptea| ate ra stances. — temp. paint ee stances. pat te : : ean ance. ance, July 30- ° ° ° ° o °o 5000 Misty | 48°2| 482 oo Se ArT) Aven oo 4800 “js 482] 48°3|/— 06 EA 47°6| 47°6 oo 4600 . 49°7| 493 |+ 04 . 47°9| 47°99] oro 4400 Ac 50°9| 49°38 or te 48°2| 482 oo 4200 ile hr isi) Coe 1°4 oF 48°6| 48°6 oo 4.000 A ee 52°70} 50°38 | 12 ar 49°2| 492 o*o 3800 A 50°6| 51°2|— 06 2 Ss 49°9| 49°9 o"o 3600 an xe 50°F |S 17 1°O = : 50°99} 50°9 o"0 34.00 A es BIG hz" o'7 a ® 52°0| 52°0 o’o 3200 = a Gara tes 258 o6 || ss 53°0| 53°0 o"0 3000 =n es B27 3.2 o°5 a oe 54°1| 54°1 oo 2800 2 of 53°72] 53°38 06 || 3 ¢. 55°2:| 55:2) OG 2600 Fy : 53°7| 54°6|/— og|| B oo 56°3| 5673 fore) 2400 ey 57°) 553|+ 17) a 57 3) ‘5758 9°o 2200 | “¢ 59°0| 56°0 3°0 Ss ee 58°2| 582 fohge) 2000 ™ =e 59°5| 57°0 ro Ne uk se 59°2| 59°2 o"0 1800 ae te 6o'o| = 58°1 I'9 °, Ss 60°0| 60'o oo 1600 g - 6o'9| 59° 1°7 |} eg = 60'9| 60°9 o'o 1400 ¢ : 61'°9| 60'2 r7\| B Se 615) 61°5 o'o 1200 a © 62°70} 61°6/+ o4/]] ~ at) 62°2| 62°2 oo 1000 5 62°9| 62°9] oro se 63°2| 63:2 foXe) 800 oe 64°0| 64'0 o"o ia 64°2| 6472 oo 600 SL 65'2| 65°2 foyve) ve 65°1| 6571 (oe) 400 << 66°3| 66°38 o"o ee 66:0| 66°0 o'o 200 ce 68°6| 68°6 oo pe 67°0| 67°0 o"o ° ae 70°7| 70°7 o°o on 68°0| 68°0 o'o August 18. 2 5000 3 48°5| 485} oo s | 495] 49°55} oro 4800 3 48°83] 48°83 oo Ss 50°2| 5o0'2 oo 4600 Ps 49°70] 49°0 oo 2 51°0| 51’0 oo 4400 & | 492} 492] ovo & | 518) 518] oro 4200 < 49°5} 49°5 ee 5275) 52°55 oo 4000 : 49°9} 49°9 Sole, |= S32) ae oo 3800 BN on 50°4| 504) oo] @ 540} 5470] v0 3600 a |29 335] 509] 50°9 90 5 54°9| 54°9 oo 3400 BA cg geal SL Spor wls5 |. PO ae 557| 55°7| 00 3200 eta SO! 522] 522 ool] w 5675] 56°5 oo 3000 mM 53°0| 53°0| ool] %& 572] 57°72] o0 2800 & 53°7| 53°7| ool] 3 579| 57°9| oo 2600 F 54°6| 54°6 oo|| B = 58°7| 58:7 oo 2400 = 556) 556) ool F 2 | 594] 594] 90 2200 Py 56°6| 56°6 o7o|| op g 60°2| 60-2 oo 2000 Ga 57°5| 57°5 G:0)|||8 ea = 61-0] 61-0 foe) 1800 4, a 584) 584 oo 8 So 61°7| 61-7 [oWe} 1600 4 is 59°5| 59°5| ool] PB 5 62°4| 624] oo 14.00 ° E 60°4| 604 oo B 63°1| 6371 [oXe) 1200 = a 61:7} 63-7 oho) 64°0| 64:0 oo 1000 Q 6279] 62°9 Coho) 64°3| 64:8 (oho) 800 | 6474) 644} oro 65°7| 65°7| 00 600 66:0} 66°0 o°o 66°5| 6675 o"o 400 67°6| 67°6 o"o 67°3| 6773 oo 200 69'2| 69°2 oo 68:1| 68-x oo ° 7o°'9| 709} oo 69°0| 69°0] oo 456 REPORT—1862. TaBieE V. (continued.) | Height, in feet, | above the mean Temperature of the Air. level of the sea. | Between | August 20. 4200 4000 3800 | 3600 | 3400 3200 | 3000 2800 2600 2400 2200 2000 1800 1600 1400 1200 1000 800 600 400 200 ° 5000 4800 4600 4400 4200 4000 3800 3600 3400 3200 3000 2800 2600 2400 2200 2000 | 1800 1600 1400 what times. From 6" 5™ p.m. to 6" 47™ p.m. From 7" 20™ p.m. to 745 47™ p.m. Pp 47 Pp Ascending. Circum- stances. Below cloud. In cloud. Below cloud. Caleu- lated oo | Descending. Caleu- Between Circum-| .OP-, | Adopted lated ; whal serve t times. |St@C&S-| t¢ Pp ve ieee ance, ° ° ° 48°4| 484] oro 48°83) 48-8 oo 4971) 49°71 o"o 49°6| 49°6| oo z 50"2) - 50% oo g 50°9| 50°9| ovo > Sx6) 5a°h oo rq wo 2-2 | 5222 oo 2 52°9| 52°9 fohre) Ley 4 53:3} -.5373 oro 5 eo | 540] 5470] oo % = 54°6| 54°6| oo = = 552} 552 oo “ 2 nv fe) 3 4 B ————— | Height, in feet, above the mean level of the sea. |Between August 21. 5000 4800 4600 4400 4200 4000 3800 3600 3400 3200 3000 2800 2600 2400 2200 2000 1800 1600 1400 1200 1000 800 600 400 200 ° September 1. 42.00 4000 3800 3600 3400 3200 3000 2800 2600 2400 2200 2000 1800 1600 1400 1200 1000 800 600 400 200 ° 3000 2800 2600 2400 2200 2000 1800 1600 1400 ON EIGHT BALLOON ASCENTS IN 1862. - Taste V. (continued.) Temperature of the Air. what times. From 4" 30™ a.m. to 4" 55™ a.m. From 4" 40™ p.m. to 55 32™ p.m. 64 6™ p.m. From 62 1™ p.m. to Ascending. \Cireum- Ob- Adopted) stances.) S274 "temp, | ° ° 43°5| 43°5 442) 442 45°0| 45°0 45°8| 45'8 46°5| 46°5 472) 47°2 47°9| 47°9 48°6| 48°6 49°4| 49°4 50°22 5o°2 ra Slo] 5170 5 Buy, angie) 3 52°4| 52°4 E GSieal| abciees cs 533) 53°8 A 54°5| 54° 552) 552 55°9| 559 56°6| 56°6 523), 57:3 58°0| 58°0 58°7| 58°7 59°4| 59°4 60°2| 60'2 611} 611 61°8| 618 ee 469) 46°9 oo 47°5| 47°5 oe 48°0| 48-0 oe 48°6| 48:6 . 49°3| 49°3 - 49°9| 49°9 on 50°5| 50°5 oe 512 512 oe 52°0 52°09 oe 52°9 §2°9 oe 53°9| 53°9 . 54°7| 547 7 BG Seb . 564) 564 a Sail S7k3 oe 58-3 58°3 oS 592) 592 oe 60°5| 60°5 oe 61°7| 61°7 oe 63:0] 63:0 an 64:2] 64°2 + 65°7| 65°7 Bes] 53°5| 53° gen | 53°6| 53°6 sna 53°38) 53°83 #54| 53°9| 53°9 gig | 540] 540 Bie2| 540) 54:0 a=} 540) 540 BBS | 542) 542 ome} $5°0| 55°0 457 Calcu- lated” effect of * | disturb- ance. oO oo o"o o'o Descending. Calcu- dated | ae Cireum- OBE Adopted |sisturbs ons stances. caidas temp | ance. || ee = = ° 9 © oo 43°5| 43°5 00 4473) 44°3 o'0 | 45°09) 45°0 o'0 || 45°7| 45°7 o'0 46°4| 46°4 oo 2 47°} 47°0 oo|| g 47°7| 47°7 oO | a 48:2 48-2 o°O | A 48°8 48°8 oro |] 49°4| 49°4 oo = wo 50°r| 50°71 ool B | & | 507] 507 oo =F 4 514| 514 oo || © e, 52°3| 52°3 o0|)/ 2 | 532) 53° oo}, : 5470} 54°0 | oO oo 3 549} 549 o'0 2 55°3| 558 ool) B 56°7| 56:7 0°0 | 57°4| 574 oe 58'0| 58:0 o'o | 58°7| 58-7 o'0 | 594] 59°4 eal 60'2| 60°2 00 | 610 61'0 oo | 62°0 62°0 a a oe ste 46°2| 46-2 ool] "+ | 465) 46°5 00 S as 46'9| 469 070 | B . 474| 474 o'o wy o. 47°7| 47°7 ool] us ah 481) 48-1 a Ss aa 48°5| 48:5 ped (item i es gS Moe o°0 = oD 49°7| 49°7 o°o || ie ad 50°2 50°2 ooll # 50 50°8| 50°8 eolt e [hc pee ees 00 5 oe 52°72] 52°2 oo . 53°90} 5370 oo oe CEA Ds) 7h 070 00 (oho) oo oo oo oo oo oo = Bal 53°5| 53°5 : se iges . oro] 95 aie 5470} 54°0 loko} TO o a 54 5 54°5 ool a2 | eFE| sro] see OO}| 3 8 Sines oo] BD | SEs oo | . B a a o'0 | 458 REPORT—1862. TaBz Y. (continued.) Temperature of the Air. | Ascending. Descending. ie ere Bet meen Cireum-| -| |Adopted “ated Between| Circum-| Ob-_ |Adopted “ated — stances. Tehp fat, pod he stances. ee rad pits ance. ance. September 5. a 5 5 = 5 5000 49°7| 40°7 oro sr 4772| 47°72 oo 4800 414| 414 oro * 477| 477 oro 4600 422) 42°2 o"0 ee 481} 481 oo 4400 431] 4371 oo oe 48°7| 43°7 oo 4200 44°0} 44°0 oo - 493} 493 oo 4.000 ‘ 44°38] 44°8 oo oe 50°0} 5070 oo 3800 | 45°6| 456] ool & sie 50°6| 50°6 o'o 3600 es 464) 4674 oo 5 = SE2) 5172 oo 34.00 a A7'2|* AT2 roxte) » “6 518) 518 oo 3200 ny 480} 480 9:0)|| «35 oe 5274] 5274 oro 3000 5, dg 48°3| 43°83 oo 7 oe 53°0| 53°0 oo 2800 = & | 495) 495] |] og ++ | 536) 536] oro 2600 F ic) 50°2] 502 oo|| 8 “4 542| 54°2 o°0 2400 & E 5170} 51°0 oo Ss a 54°8| 54°8 oo 2200 a i} 59) 519 oo m4 = 554] 554 oo 2000 a Fa §2°99| 5279] oro °° 560} 56°0| oro 1800 x 53°38] 53°38 ool| & 2° 56°6| 566 oo 1600 z 54°38) 54°38 oro|] +s oe 57°2|- 57m oo 1400 & 558| 558| oo] B | -. | 5781 578] o' 1200 56°7 |, .56°7 oo > se 584} 584 o'o 1000 57°5| 57°5 roxe) a 59°2| 59°2 foe) 800 584] 584 oo wa 59°7| 59°7 oo 600 59°3| 593 oo ee 60°2| 602 oo 400 60°2|} Go°2 oo e 612} 61-2 oo 200 611} 611 o'o os 62°70} 62°0 oo ° 62°0| 62°0 oo +e 62°8| 62°8 oo On August 18, 20, 21, September 1, 5, and 8, there were no disturbing causes to any amount in operation within 5000 feet of the earth, and therefore the projected and adopted curves are identical. ON EIGHT BALLOON ASCENTS IN 1862. TaBLE V. (continued.) 459 Temperature of the Air. Ascending. Descending. acl ag feet, above the mean Galens Galeu- a Between) Gircum-|_Ob- Adopted lated || Between Circum-| Ob-_ |Adopted Rati what | stances.| Served. |"temp. |°Hect of | what stances. | Served | temp, |“ ae ‘ times. temp. P+ |disturb-|| times. temp. disturb ance. ance. September 8. ° ° ° 5) ° ° 5000 oe 50°0 5 se 5 4800 oe . 504 . oe on 50°3 4600 oe 509] «se o. +. 49°9 44.00 oe BES nas oe oe 49°38 4200 «o F 519 os Bi 50°70 4000 A ae ie 52°7 4 oe 50°3 3800 =| é 53°6 = 5d se 510 3600 me F 54°4 3 oe oe 518 3400 & “és : ize B bie ne 52°3 3200 = a. : 55°7 +. ay: Se 531 3000 So se : 564 ua 2800 £ ae Se 57°4 3 2600 A ae ; 58°7 tS 2400 a oe oe 59°7 B 2200 a oe os 60°4 $ 2000 = t. is 610 n 1800 4. Se ee 61°8 a 1600 Eg op Se 62°5 8 1400 ° ve oe 63°6 i 1200 ad ee es 64°4 F 1000 oe a 65"1 800 oe ee 65°8 600 .. ee 66°5 400 e +e 67°3 200 +e oe 682 ° . ee 69'0 5000 os oe oe . 7s oe oe 514 4800 ee ee oe oe . oe oe 512 4600 ee *. ee ae ac ic «. 512 4400 se ° ee oe s¢ Bi ee 512 4200 e ee ee ee ee os ee 512 4.000 zs se ee os ve ee ee 512 3800 se Re Se ae re a Be “ic 513 3600 ee a ne oe § oe a 514 34.00 “ ee ee ee ee wn se ee 517 3200 ee vs ee os ° S a ee 52°3 3000 oe oe o 2 oe ar PC oe 539 2800 oe oe .- oe ee re ate Br 54°4. 2600 oe -° oe oe oe 8 Sc es 5570 2400 ee ee se ee oe A se ee 55°7 2200 oe ze ee Slo oe = oe os 56-2 2000 ae vs 3 ot ae > ae Ae 565 1800 co | ee o- +e ° 3S oe +. 57°0 1600 0 se oe os “10 8 bee oy 67°75 1400 Ac e ie ve ae = Be te 53:2 1200 er Se as ae we 5 oi ee 59°0 1000 “36 ar ee ee . are ae 60°2 800 a Bis An ° a re ae 610 600 ie : ee i xe ae : 61°6 400 aye : . : oe aye d 62°5 200 we ec . we oe Be AG 63°2 ° erie se ve ae ic ae os 64°8 _ The next Table has been formed by taking the difference between the temperatures at eve 5000 feet. ry consecutive 100 feet, in every ascent and descent, up to 460 REPORT—1862. Taste VI.—Showing the Decrease of Temperature with every Height above the level of the sea. From To feet. | feet, August 18. | July 17.\| | July 30. | | } Cloudy. |} Clear. | Cloudy. |} Clear. | Cloudy. 2 : t = Boa a poe z 212] Ei 3 S 3 2 8 Q n o n < < A < ° ° ° fo} o°6 03 ol o2 O°5 03 oz o'r o°5 1) York | 407% Descending. oO w State of the Sky. Ascending. August 20. Cloudy. to . & = 3 = A < August 21. Cloudy. Ascending. Descending. -a0 ON EIGHT BALLOON ASCENTs IN 1862. 461 Increase of Height of 100 feet up to 5000 feet. September 1. September 5. September 8. Mean. State of the Sky. Partially clear. eral Cloudy. | Cloudy. | E q c Z cae rie ee o | 2 | & os | f | s | B | B || Cloudy.) ereae|| Cleat | chser- 2 = a = 3 a 2 = eros bene 8 3 5 5 g 5 3 3 2 3 2 z Ss || & 3 3 < A 4 < A || < =) A ° ° fe} ° ° ° o ° ° ° oe os O43 OK |, ‘oc o"4 o'r o°%3 10 o°3 se Ss c 073 o'r o'2 o'74 orl 073 10 03 . ae O74 o'2 o'2 o'2 ve on 9 O73 + oe * o'4 o'2 03 o'2 os 0°3 9 03 . oe o'5 o'3 o'2 orl o'r 0% 10 03 . Bia o'4 03 o'2 ol o'r O73 10 o3 . - o°5 Q:3. || 078, |. ox o'o O73 10 03 oe ae o'4 04 || 03 o'r fore) 0°%3 12 03 o%3 o'2 ° o'4 o3 || o4 0% foe) o3 12 0°3 O73 o'2 o'74 0°%3 o'4 O74 oo 03 12 03 03 o'2 o'4 0°%3 o°5 o4 ol o3 12 O73 3 o2 o'4 o°%3 o'4 O'% ov! 0°3 12 03 O73 03 o'4 03 || o4 o'4 o'r 03 12 0°3 O'3 o2 P o'4 0°%3 o'4 o'4 or O34 12 O73 03 o2 | 0'4 03 o°%3 o'4 ov! 03 12 0°%3 o°%3 o'2 || oO} o'3 o°3 O74 o2 o3 12 03 O73 oz o4 0°3 o%3 o'4 o3 O74 12 03 O73 o'2 o4 o3 o'4 o'4 0°%3 o'4 12 03 03 o'2 : o4 o°3 03 é O73 o'4 II 03 O73 o2 o'4 0°%3 o4 0% O74 11 0% o4 o3 o°3 03 oS or 04 iI 03 0'4. 03 o4 o°3 0°5 or2 04 11 o4 o4 O73 0'%3 o3 O'S o'4 o%4 1 O74 o%4 03 : o4 0°3 o°5 - o4 o"4 11 o"4. 0'4 o°3 o4 o3 o°5 04 o'4 II o4 O'4 o°3 04 £3 o°5 03 04 iI 04 o'4, o3 o'4 03 o'4 O73 O74 II o'4 o%4 o3 . 05 03 03 ‘ o"2 o'4 11 o'%4 o's 03 03 o'2 II 275 | 03 | 04 05 3h Ae foe ae wWwwwowwowwnwwnwnwnownwwrs PHRAAHRAHAADAADADA A DOQUUNUNUNWNUNNWHUNH HUW HUWWKHUHWH BW WWWWWWW 462. REPORT—1862. An inspection of this Table shows that the largest numbers are those situated at the bottom, and the smallest at the top of each column in all states of the sky, and therefore that the decline of temperature in equal spaces was largest in that space next the earth, and gradually less with increase of ele- vation. The numbers in the last column of the Table show the average value at each 100 feet, the one in cloudy states of the sky, and the other in partially clear states, with the number of experiments upon which each result is based. FRoM THESE RESULTS THE DECLINE OF TEMPERATURE When the Sky was Cloudy For the first 300 feet was ...... 0°-5 for every 100 feet. From 300 feet to 3400 feet was 0°-4 a et00 4, * S000 &,,; 20S 2? 9 39 3) Therefore in cloudy states of the sky the temperature of the air decreases nearly uniformly with the height above the surface of the earth nearly up to the cloud. When the Sky was partially Cloudy. in the*first S: 2. 100 feet there was a decline of 0°-9 From 100 feet to 300 % Pe Pe 0°-8 for each 100 feet. ” 300 ” 500 ” ”? ” 0°7 ” » 200 5, 900 ” 3 ” 0°-6 » 900 ,, 1800 9 3 » 0°-5 ” 1800 ” 2900 ” ” ” 0°°4 ” ” 2900 ” 5000 ” ” ” 0°3 ” The decline of temperature near the earth with a partially clear sky is nearly double of that with a cloudy sky; at elevations above 4000 feet, the changes for 100 feet seem to be the same in both states of the sky. In some cases, as on July 30, the decline of temperature in the first 100 feet was as large as 1°1. From these results we may conclude that in a cloudy state of the sky the decline of temperature is nearly uniform up to the clouds; that with a clear sky the greatest change is near the earth, being a decline of 1° in less than 100 feet, gradually decreasing, as in the general law indicated in the preceding Section, till it requires a space of 300 feet at the height of 5000 feet for a change of 1° of temperature. These results lead to the same conclusion as before, viz. that the theory of gradation of 1° of temperature for every 300 feet of elevation must be abandoned. As regards the law indicated by all these experiments, it is far more natural and consistent, than that a uni- form rate of decrease could be received as a physical law up even to moderate elevations. § 6. Vartarron or tHE HyGRoMErRIC CONDITION OF THE ATR WITH ELEyATION. All the adopted readings of the temperature of the dew-point in Section 4 were laid down on diagrams of a large scale, and their points were joined; and as it was evident that there were strata of moist air, and that the changes do not follow any regular decrease as in the case of the temperature of the air, it was therefore not considered prudent to adopt any curve with the view of obtaining normal results, but to use the projected curve as simply found by joining the points as stated above. ‘From the readings at every 1000 feet of ON EIGHT BALLOON ASCENTS IN 1862. 463 elevation the next Table was formed ; other readings were taken at angular intermediate points, and these are included in the remarks following the Table. The numbers under the heading of “Tension of Vapour” are formed by using “ Regnault’s Tables,” and the degree of humidity in the next column has been calculated by using the observed temperature of the air correspond- ing to the observed temperature of the dew-point. Taste VII.—Showing the Variation of the Hygrometric condition of the Air at every 1000 feet of Height. Humidity of the Air. Ascending, Height, in feet, above the mean Tempe- - | Degree level of the sea. Between arauine tee ae Fiatie = wha orce 0: a times. | *#nces- wer "| vapour. cm La Sa ga Yabo SER esas 25000 Ea | aa bas 24.000 BSesle'ssi\a's> 23000 25s 4a5=l4% 22.000 pers jp° 21000 ° in. dened , Er, 1670| ‘o89| 48 19000 g 3 24°1| “130) 54 aed a it 23'8 128| 62 17000 iF 3 ee a 16000 A 3 22°8 ig 15000 "4 < 235) 1426) 7 14000 £ 23°9| "128| 78 13000 | 24-0). AS) oe 12000 a 23°8| 128) 92 11000 a 23°3; "125| 89 10000 + ae al Sioned gooo a aot) AES ine ZS 8000 g 27°9| "152| 84 7000 g mj | 30°0| ‘167} 78 6000 ae a5 32°0] 181} 90 5000 ws) 32°0 "181 76 ae 340] "196| 65 3000 a“ 39°6| °243) 73 2000 23 44°7| ‘296) 75 cpa SS | 497| °357| 77 % 55°°| °433] 79 July 17.—At the earth’s surface the dew-point was 55°, which seemed to decrease gradually to the height of about 4000 feet, the ‘relative humidity decreasing from 79 to 65 within the same space; on entering a cloud the rate of the decrease of the dew-point was checked, and for a space of 3000 feet was almost constant, differing but little from 32°, whilst the relative humi- dity increased to 91 at 5800 feet. On leaving the cloud at 8000 feet high, and between that and 9600 feet, both the dew-point and the relative humidity decreased quickly, the former to 17°-9 and the latter to 65. From 9600 feet to 11,500 feet, whilst the temperature of the air remained at 26°, the dew- point increased to 24° 8, and the relative humidity to 95, closely approaching to saturation. From the height of 12,000 feet to 19,000 feet, the amount of water in the air was almost constant, the dew-point undergoing scarcely any 464 — REPORT—1862. variation, but during which time there was a great increase of temperature, and consequently the relative humidity decreased with rapidity from 95 to 39. The balloon then fell from 19,500 feet to 19,200 feet, the temperature of the air decreased to 38°, and the dew-point increased from 193° to 21°, and the humidity increased to 49. After 19,200 feet the dew-point decreased with rapidity to 16° at 20,000 feet, with a humidity of 48; and afterwards with great rapidity to a dew-point of less than —12° at 21,000 feet; and at heights exceeding this the dew-point is unknown, but was certainly lower than —20°, and probably as low as —30° up to 24,000 feet ; from the ob- servations of the dry- and wet-bulb thermometers it seems to have been as low as —50° at 25,000 feet ; therefore the tension of vapour above 20,000 feet must have varied from about 0-015 in. to less than 0-01 in., and the degree of humidity to have decreased to 2, or even less. In this series we can distinctly trace a stratum of moist air in the cloud above 4000 feet, and again between the heights of 9500 feet and 11,500 feet. From 11,500 feet to 19,000 feet the tension of vapour differed but very little from 0°13 inch ; then the amount of water present in the same mass of air was nearly constant for 8000 feet in vertical height; immediately after this there were some irregularities, and above 20,000 feet the air was dry, being almost free from vapour. Tare VII. (continued.) Humidity of the Air. Ascending. Descending. Height, in feet, wpe ire sam Tempe Degree Tempe Degree level of the sea. |Between Circum-jrature of Elastic of [Between Cireum-|rature of Elastic of what stances. |the dew- force of | numi- || bat | stances.|the dew-| ree Of humi- times. point. vapour. dity. times. point. vapour, dity. July 30. g 3 in. 7 FA in. 6000 4.8 33°8| ‘194] 68 || So ose 33°0| 188] 61 5000 go = B72 | 222). 166. |] ae 36°7.| ‘218}. 67 4000 2a 1. a 39°5) 242) 63 || w eer eee 38°5| °233] 66 3000 ee 41-4| °261| 65 a eke 42°3| °270} 65 2000 gu 43°2| °279| 54 || = BP see 41°8| °265| 53 1000 ee 44'2| *290] 51 B B | oo 45°8| °308] 52 ° Fe 530] *403| 54 || § oe 474} °328) 48 July 30.—The temperature of the dew-point in this ascent was constantly varying: on the ground it was 53°, at 1000 feet it was 441°, but at interme- diate points it was sometimes on one side and sometimes on the other, to the amount of 1° or 2° from the curve-line joining these points ; then up to 2400 feet there was a stratum of moist air, and above 3600 feet there were strata of moist and dry air alternately for 2000 feet ; higher than this there was a stratum of dry air from 5600 to 6400 feet, and higher still one of moist from 6500 feet to the highest point reached: these terms, moist and dry, have reference to a curve-line, which was made to pass near every point as laid down from observation ; and the same phenomena generally prevailed during the ure The relative humidity generally increased to the highest point reached, ON EIGHT BALLOON ASCENTS IN 1862, 465 Taste VII. (continued.) Hygrometrical results. Ascending. Descending. =e in feet, above the mean Tempe- . level of the sea. a beatae: iene GH a one aainis Girona ore arene a panes times, | S*nces. ae “| vapour, ero times. | t#nces. perce vapour. noe August 18, ps in. PRP site 11000 eve 26°0| “I41] 59 ret | one 24°5| °132| 51 10000 ae 28'0| °153| 58 as) eee 27°0| °347| 51 goo0o s Ay 31°8| *179| 63 45 28°8| *158] 49 8000 S- ne 33°9| “195| 65 poe | oe 37°0| *220| 61 7000 a4 35°9| °211| 68 wt tee 37°0| *220] 53 6000 a, a 4 38°0| °229] 7I so 8] oe 475) caeei gat 5000 an 4r'o| °257| 75 BS coe 41°5| °265| 66 4.000 Shel | Ree eee *329| 91 : — 46°6| °318| 76 3000 g ™ | cloud 5070} *361| go 2000 ce ee 510] °374) 79 1000 ome 52°5| °396| 72 ° F 57°0| °465] 62 23000 eee |— 8'0}| °029 22000 «. |—I0'0| 026 21000 ee |—ITo| *025 20000 see? i sO] LO2g)|" 22 Ig000 been [= 270 O40) 22 18000 F 1°8| °047] 30 sh vee To} 046] 31 17000 zs 8:0] *062| 27 ie 370] 050] 32 16000 5 1470| ‘082| 42 g = Gol “osaiieag 15000 a) 1g'2| *104] 52 ai g 7'0| *060| 34 14.000 AR 23°8| *128| 61 a g2| *065| 36 13000 S 24°7| °133| 67 % So II°5| °072| 36 12000 E 24'0| *129| 59 as) 5. 14'0| *082] 36 11000 E 28'0| *153| 52 5 i 14°0| *082] 34 10000 ‘y 33°0| 188] 52 Es " 15'2| *086| 28 g000 a B6>x |OC2Ese 53 5 : 22°0| *118] 35 8000 A 39°0| °238) 57 a 34°5| ‘199| 55 7000 R 39°'2| °239| 64 3 37°2| °222| 6% 6000 g 40°8| °255| 59 = Fiawnath’ Ao hin BRS 61 5000 ey A. 42'2| °269| 59 B finclouds) 43:2] *279| 62 4000 act 45°8| °308| 70 46°2!|) sg Egi) 77 3000 see eee peg vie see 49°0| °348] 74 2000 ais opr ee es 4 515] °385] 71 i) * . 1000 S@ | 54°0) 418) 69 ° = Eg 57°0| 465] 66 August 18.—The temperature of the dew-point dohreasba from 57° on the ground to 521° at 1000 feet, increased from 523° at 1000 feet to 534° at 1700 feet whilst passing through mist, decreased to 50° at 2000 feet, and varied but little till 3800 feet was passed; the degree of humidity varying from 62 on the ground to 96 at 3800 feet when in a cumulus cloud. The dew- point decreased rather quickly to 41° at 5000 feet, and with less rapidity to 26° at 11,000 feet, the humidity varying from 96 at 3800 feet to 59 at 11,000 feet. Whilst almost stationary in elevation for some time, at the highest point the temperature of the air increased, whilst that of the dew- point decreased, so that the degree of humidity changed from 59 to51. The balloon then descended: the temperature of the dew-point increased gradually to 31° at 8200 feet, and to 38° at 7800 feet: the humidity was 61 at the lower elevation; the dew-point remained nearly at the temperature of 37° from 7800 feet to 6000 feet, and rose to 48° at 3500 feet—its lowest 1862, 21 4.66 REPORT—1862. Taste VII. (continued.) Hygrometrical results. Ascending. Descending. poe in feet, = above the mean level of the sea. |Between| ,. Tempe-! plastic | Degree || Between| Tempe-| pastie | Dearee what | teu ature OF force of | auChi. || BBE | Stance Ite dew-| {2% Of] tuum. times, A point. vapour, dity. times. point. vapour. dity. August 20, spe c= 5000 x A as fia S Be lesti: 4.000 a 7 46°2| °313| 88 Se 44'2| *290| 84 3000 at 48'9| °346| 84 pb F 46°6| °318| 83 2000 a goo| 361) 75 3S 4g'o| °349| 82 1000 Ere 52 3 "393 e : oy 5r7| °384| 81 ° =| Zo}; ° B Zz” 55 3 = 5000 ||Incloud| 42°3| *270/ 88 4000 ga) -: 44°2| ‘290| 83 gooo (kam ... 46°0| °311| 77 zooo ea &) .. 50°5| °367| 80 . 1000 PS ioe 517} °384| 81 ° La point: the humidity increased from 53 at 7000 feet to 77 at 3500 feet, The balloon then ascended, and the dew-point fell to 37° at 8000 feet, and the humidity from 76 to 61. The dew-point then increased somewhat to 393° at 8500 feet, with a humi- dity of 65: from this elevation the dew-point decreased to 21° at 11,600 feet, with a degree of humidity of 51. The dew-point then turned to increase, and was 252° at 12,400 feet, giving a humidity of 57 at this elevation; it thende- creased gradually to 23° at 14,500 feet, and then rapidly to —83° at 20,100feet: the relative humidity was 59 at 12,400 feet, and 22 at 20,100 feet. Above 20,000 feet a dry stratum of air was entered and no dew was deposited on either of the hygrometers, their bulbs being reduced to a temperature of —10°. In descending, the dew-point increased steadily to 14° at 12,000 feet, remained at this reading till nearly 10,000 feet, then increased rapidly to 343° at 8000 feet, and then gradually and almost uniformly to 57° on the ground: the degree of humidity increased from 31 at 18,000 feet to 36 at 14,000 feet, remained at this value to 12,000 feet, decreased to 28 at 10,000 feet and then increased to 77 at 4000 feet, and was 66:on reaching the ground. In this series a narrow stratum of nioist air was passed through between 1000 and 2000 feet from the earth, and then another on passing through a cumulus cloud at the height of 3800 feet ; above this to 11,000 feet there was a con- stant decrease in the amount of water; the balloon then descended and the vapour increased steadily to 8000 feet, then a stratum of moist air was met with from 1000 to 2000 feet in thickness; from 6000 feet to 3500 feet on descending, and again from 3500 to 7000 feet on ascending, there was an increase and decrease respectively ; between 8000 and 9000 feet and be- tween 11,000 and 12,000 feet dry strata were passed; then for 2000 feet there was but little variation in the humidity of the air, above 15,000 feet there was a rapid decrease in the amount of vapour, till the air became very dry above 20,000 feet. In the descent one stratum only of moist air was passed through, viz. between 13,000 feet and 9000 feet from the earth. August 20.—Between 400 and 600 feet a dry stratum of air was pana then there was but little variation in the temperature of the dew-point, and the air was for the most part humid during the ascent, ON EIGHT BALLOON ASCENTS IN 1862, 467 Tazre VII. (continued.) Hygrometrical results. . Ascending, Descending. eight, in feet, |~ ne Betw x Tempe- . | Degree Tempe- . , | Degree = een! Circum -|rature o Lage of Beaween Circum. |T2ture of plastic - of N ‘ -| force o: i- = i- times, | Stances go vapour, ‘ath Piss stances, rong vapour, ee August 21. ef | ne Sie 14.000 . |—14'0] ‘o22] 318 =7270} ‘OIR| I 13000 =| re Im EoW | 786) 628 2 = —13'0| ‘023]. 17 12000 3 B. |+ 3°70] ‘ogo| 36 B q. oo} 7044] 28 11000 if es) 1o'°0| 068] 43 wn 5. l#13°r| °078]. 43 10000 ee? 2 14°1| *082| 46 os S 1g'0| *103| 51 gooo ra) 3S 20°38} -r12] 56 “3 a 18:0] *o98| 42 8000 2 < Dez ©1361) Ox ~ 19'°0| *103} 38 7000 g 32°0| ‘x81| 71 B In 2'0| ‘18r]. 58 6000 a In 39°0| *238| 97 g |Cloud.| 37-5) +225] 89 5000 a, cloud.| 41°6| °263] 93 4 B 380} *229] 81 4000 of - | 4o'8} ‘ass! 78 o 4o5| ‘252! 78 3000 4 = 46°8 *321| 86 9, = AB'7 | 307 less 2000 f | Os | 5°°9| °373} 88 » S 47°0| °323] 77 1000 £ | Ss | 568) 462) 96 5 & | 49°7| °357| 74 ° ee Goro} 518) 94 |f A | 2. | 56°] *449)] 82 August 21.—The temperature of the dew-point decreased from 60° on the ground to 57° at 400 feet, then increased to 59° from 500 to 700 feet whilst passing through a thick mist, and to 60° at 1000 feet; a decline then took place to 50°8 at 1300 feet, and 50°9 at 2000 feet; from 2000 feet to 3200 feet there was at first a gradual, then more rapid decline to 40°8 at 4000 feet ; on entering cloud the dew-point increased to 41°-6, and on leaving it at about 6000 feet there was a sudden fall of 2°. The relative humidity was 94 on the ground ; the air was saturated for 200 feet from 500 to 700 feet; the humi- dity was 74 at 1000 feet, 79 at 1300 feet, and 97 in the cloud. Above the cloud the dew-point decreased quickly and with but slight irregularities till the height of 10,400 feet, where it was 144°, with a humidity of 48; at 14,000 feet the dew-point was —14°, and the air was dry, the relative humidity being 18. Above 14,000 feet the temperature of the dew-point declined to —20°, with a humidity of 12 only. During the half-hour this height was maintained the temperature of the air increased, whilst that of the dew-point diminished, so that the air became drier. On descending the air continued dry, the dew-point increased from —22° at 14,000 feet to +19° at 10,000 feet, the humidity increasing to 51; there was but little variation in the dew-point in the next 2000 feet, but during this space the temperature of the air increased 7°, so that the relative humidity was irre- gular. At 7500 feet the dew-point was 20°, at 6900 feet it was 42°; on approaching the clouds at the former height the relative humidity was 38, and at the latter it was 88. Whilst passing through the cloud both the temperatures of the air and dew-point declined, the latter to 383°, and the humidity was 89. On descending below the cloud the dew-point increased gradually from 382° at 4000 feet high, then quickly to 45°7 at’ 3000 feet, then fell to 44°-7 at 2500 feet, then increased to 56° on reaching the ground. At 5800 feet the relative humidity was 83, between 2500 feet and 1500 feet it was 76 or 77, and it was 71 on the earth. In this series, till the clouds were passed, there were two or three layers of moist air; but from the time of passing above the clouds, the air was constantly increasing in dryness till the greatest height was attained, and ‘ poss 212 ; 468 REPORT—1862. Taste VII. (continued.) eee ese eR moms Anca piano CS Mi) NS Se Hygrometrical results. Ascending. Descending. Hesn, in feet, above the mean Tempe- Rh) Tempe- «| Degre level of the sea. eee ”) Circum- cane: of aoe “ ra eren Circum- eee of a of : , times. |Stances. poy yapour. ae times. | Stances. pence vapour. = September 1.| © . + in. a . in. 4.000 - 8 37°6| +225] 69 || Su alo 37°0| °220| 70 3ooo «(|E a & 43°2| °279| 76 ||\;Gexl ... 38°7| °235| 69 2000 | Eg Mn 479| °334| 78 |ip'D 8 47°3| °327| 86 1000 Gig 50°3| °365| 72 ||BB ° ead BS re ney he ga¢ 4.000 $:/en¢ 3000 |g g a S22 | 45°38} °308) 75 2ooo |S ae ja | 460) “311] 74 roo. [ESO BE a o | S/o3s September 5. 2.4000 —36°0} ... 16 23000 —28:0| awe 21 22000 —20°5 | ase 32 21000 —I5'0| «. 33 20000 — 5°2| eso 50 aa coe 1[—37°O| eee 8 19000 , [20°] ane 20 ose doe: 7 1—= 351) | Peas 8 18000 BS |-— £9] o- 41 awe ove |= 33°2)|" lowe 9 17000 g g |t 80} *062| 76 Sa eos) f= ZIT eee 9 16000 a * 13°2| °078| 84 mae ose pil 43010) eases 9 15000 a. 3 16°7| *093} 89 os ry |—28°5 . 10 14000 » a 19'2| ‘r04| 88 me o | |=26°51\ reve Io 13000 m 22°5| °120} or ave E 2455 | * ove 10 12000 g£ 22°0| "118| 81 “ee = |—21°O| ... II 11000 5 26°0| ‘I4I| 85 Pe ~ |= S'0] oe. 17 10000 a 26°5| °144| 81 cas s + 3°0/ *050] 27 g000 _ 27°5| °152] 75 ae a 7°5| *061] 29 8000 | 29°5| °163) 71 A i] 12°7| *077| 33 7000 = 35°0| ‘204| 77 “ 3 20°5| *110| 43 6000 36°2| 214] 98 aE s 21:01) PEs Eeag 5000 = 38°5| °233] 91 — 5B 21°5| *115| 36 4000 = 40°8| °255| 86 on mas 22°5| °120) 33 3000 S 43°2| °279| 81 see aes 38°7| *235] 58 2000 45°5| °305| 76 eos ene 42°8| °275] 62 1000 3 49°9| °360| 76 AM s 46:2] +313] 63 ° =a) 56 “eo aa “ie x0 5o'o| °*361| 64 increasing in dampness in the descent to 10,000 feet ; then a dry stratum of air was met with, till on approaching the clouds and passing through them a moist stratum was passed; below the clouds there were but slight variations till the descent was completed. September 1.—The changes of the dew-point in this ascent were more frequent and more abrupt than on August 20; there seemed to be different layers of moist air, varying in thickness from 200 to 300 and 400 feet up to 3000 feet, and above this the variations were smaller in amount and less in number. In the descent a moist stratum of air was met with between the heights of 2000 and 1300 feet. September 5.—The temperature of the dew-point increased from 483° on leaving the eayth to 503° at 700 feet; it then began to decrease, and was ON EIGHT BALLOON ASCENTS IN 1862. 469 Taste VII. (continued.) Hygrometrical results. Ascending. Descending. Height, in feet, above the mean Tempe Degree Tempe De - . _ * e level of the sea. |B ap Circum-|rature of rake of gaits Circum- abe of] Eustace 2 times, | St@nces.|the dew- vapour humi Pi ities stances, |the dew- ce es humi- point. dity. ? point. Pours dity. September 8.| 2 | o | in. Y o | in 4000 q Hliactoua} 48°6| -343| 86 |S 5 [aona! 49:1| +349] 96 3000 Bae . 5r8| °385) 85 oF zooo fA) SB | 559| 447| 83 SEs 1000 te, a 2 595] 509] 82 |h ae ° + 615) °546| 77 S 5000 7 : 33°5} 192] 44 || Ae 45°O| 299] 53 qocoo | dg. SE STE | OF Ne 482) °338) 89 3000 5B Se Bar ee 0, 38 46°0| -311] 75 2000 re on eee Sy 3 540] 418 1000 on wee 5° 58°90 “482 ° Y - a) _ > wn 3 38°-9 between 4300 and 4700 feet, and declined to 362° from 5600 feet to 6800 feet. The relative humidity increased with slight variations from 67 on leaving the earth to 100 at 6800 feet in a cumulus cloud; on passing out of the cloud, the dew-point declined quickly to 303° at 7600 feet, then uni- formly to 263° at 9800 feet: the relative humidity decreased to 69 at 7600 feet, and increased to 81 at 10,000 feet; in the dew-point a slight increase then took place to 27° at 10,800 feet, and then a decrease to 192° at 12,600 feet. The dew-point increased to 223° at 13,000 feet, and the humidity to 91 at this elevation. The dew-point was 103° at 16,800 feet, and the hu- midity was 77. A rapid decrease of the dew-point then took place to —21° at 19,200 feet, and then as rapid an increase to —7° at 19,500 feet and to —3° at 20,100 feet: the humidity declined to 18 at 19,200 feet, and increased to 36 at 19,500 feet, and to 50 at 20,100 feet. Above this point the temperature of the dew-point rapidly declined: at 24,000 feet no dew was deposited on Regnault’s Hygrometer, and at higher points still it must have been less than —50°. In the descent there were no marked irregularities till the balloon was within 8000 feet of the earth, when the dew-point increased and decreased two or three times in the next 4000 feet, after which it declined gradually to the earth. The variations in the amount of moisture in the air on this occasion were few and to small amounts after passing out of the cloud in which the air was saturated. About 1800 feet a dry stratum of air was passed, and after 2000 feet the amount of vapour became smaller, and was exceedingly small in amount at the higher elevations. September 8.—The humidity in this ascent increased from the earth to the clouds with very little variation, but on passing above them the decrease was very great; the two latter results are not used in the formation of the next Table. 470 ; REPORT—1862. Taste VIII.—Showing the Degree of Humidity July 17. | July 30. August 18. | _ August 20. State of the sky. State of Height | é above the Cloudy. a oe y Cloudy. Clear. Clear. Cloudy. Cloudy. level of | « the sea. . | ° . . . to 2 to . th : to 2 to 4 gizgiglfigiz¢ielad [eels bs FI | F=| a cs | i q | a cs 5 zB | 8 ome Mee ern ie ae eee 3 aa 8 3 3 3 8 : 3 2 < aA | 4 A < a 4 a <4 A 4 On August 21 the observations were taken very early in the morning, in fact directly after sunrise, and it will be seen that the degree of humidity at the elevations exceeding 10,000 feet are very much smaller than in any other ascent at the same elevations ; from this it would seem that a diurnal range takes place in this element at this elevation, as in the temperature of the air ; so that in comparing the laws of moisture indicated by one ascent with those of another, the times of the day at which the experiment was made must be taken into account. It is possible, indeed almost certain, that at the height of 14,000 feet and above, the air would become more humid as the day advanced, the vapour rising from the upper surface of the clouds and ascending into the higher regions by the action of the sun. b An inspection of the numbers in this Table shows that the moisture in the air is very different at different times, both in its amount and distribution. The degree of humidity in cloudy states of the sky in the lower strata of i ON EIGHT BALLOON ASCENTS IN 1862, 471 at every 1000 feet up to 29,000 feet. ¥ August 21, | September 1, September 5. | September 8. | Mean, the sky. State of the sky. : 5 | s -| Height Cloudy. a y Cloudy. | Cloudy, ass y Cloudy. |) Cloudy. | Cloudy. B z sha the a S| level of ; : 7 é S sea, =} = o 2 ° o n ° n ° a 5|| 2| 6 gia fa|a/2]2 |) 4 | 44/2] alseise feet. = 29000 28000 | 27000 3 26000 S 25000 oe oe oe a 2 16 ee oe | oe] ee flee}eoi/76/ 1} 24000 sre ar ee AD ate 21 : sie: . ++|--|/211 1] 23000 =e ae ae se se 32 ° ce live | co] oe |Jee{+ +1132] 1] 22000 oe ar “fe or ve 33 Pd ore mor ++/++{/33] 1} 21000 ts oe ae a a 5° cap laces ae ++|++|/36)2] 20000 ois a oe an ah 20 ° Sahl) crenlie rej*+|/21/2] Igooo ae ee oe oe a 41 : ee | oo] oe | oe flee]e +1133] 3] 18000 .. .° . o° 76 ee eoles ee |]- +/+ 1145/3] 17000 oe . . a ae 84 e's oe | oe + |le+]--1153| 3] 16000 ole oo oe an ee 89 oo| v0 ve fies}e*|/58) 3 15000 18 12 . oe 88 : ae. |s~ +e |{Z5] 21143/3] 14000 28 17 . ar AG gr a oe | oo} ee | ve [123] 2114813] 13000 36 28 . sé os 81 oe tet feats ++ 132] 21/48] 3] 12000 43 43 os . oe 85 on ee lice] ee} oe 1143] 21/5215] 1000 46 51 os ee 8x . wes | ete ++ {148} 21/52] 5] tooco 56 42 c an 75 a ielbsts ++ 1149] 21/54] 5 gooo 61 38 . 4c AR 71 ne 5 + 1149] 21/5817 8000 71 58 o° ee 77 . + |63] 2//64) 7 7000 97 89 Se 98 - ++ ||82! 3/68) 6 6000 93 81 pie AP, gt ar ++ 1183] 5/|69] 6 5000 78 78 69 70 we 86 * 86 | 96 | 94.| 89 ||80|10}/76} 7 4.000 86 85 76 69 75 81 85 75 ||80/12//76| 5 3000 88 17 78 86 74 76 ° 83 77\E1\|71) 5 2000 96 74. 72 ee 3 76 oe 82] «| -- | e+ 1177] 81168) 5 1000 94 81x aD : > 76 15.2 4\ (Gi) «+ 1177) 61163] 4 ° the air, as might be expected, is very much greater than in clear states; and above the clouds, at the same height, there are very different degrees in the different experiments. The laws of moisture are indicated by these experiments, as found by taking the means of the numbers under the same state of the sky, and are as ? follows :— With an overcast sky, the degree of . humidity on the earth was ....... ; \ 17 from. 6 experiments. MEADOOMoS ION Ss... Solx aes. deoeR Peg bo 2000Reoaiasnt wiinaes piadawt: youd wenke bibl. SOOO re aecart as seve tele oe ie o brotess 80°; 12 NO Brn! Ray cia sto steers A apne chile SON, VLG EMD iene tats ontats ietn rs cea Sa A SG sorar ev cre yrs ra ate teatcparg aay nator ete ne OI re 4.72 ‘ REPORT—1862. The laws of moisture here indicated are—an almost uniform state of humi- dity of the air to the height of 3000 feet, viz. 77; then a sudden increase to 80 in the next 1000 feet, and to 83 by 5000 feet, which slightly decreased to 82 by 6000 feet. When the sky was partially clear, the degree of humidity On the ground was ........ 63 from 4 experiments. ty ROOD EOCG | Wie sic scralle winnie bon 68°, *¥ BOTs Kogeteerti ss oo «bs ddl «os eS Ss UA Be Se = Se 16 4 5 e SOOO Sa Leoke db etek < Wo ey se BIMOO a toe bayahelt ab cite sb a 68 36 * GOOD sp ret orenn eoatenswpee o> et > Above the clouds the degree of humidity At {000 feet was...'.....4. 64 from 7 experiments. 2). a a ee ee 58, Ses SE. she aia ass wb Ba 35 OF : HELI C ot Os aN ee oe a 52.33 7 is CRUISU os Sadia Iai Pian AE Shea 5 48 , 5 - TLC ed a eo a AS. 3s » OU nn 4 win ores cs AS eg DB 33 CAMOORE St | a chne ocean t et oe pe te & UH (I Cas i easy Ros ee 53s 3; 8 ty TET, Ole 0 Os eae, A ae 45 Ss 3 A FRCUM 1pca< Ales tesaisle aie 3-5. 33 3, 2 Pe Thott) (CRS ie oes ae ae Pi ae i RUE LOS lal aR RC oe 36. 3 2 = 1 0) Le ig RS I a gl Seo oy. ee ee PLDI: oo cl Sate or Bs ote Ba. as 2 i DOO iar {SER sips see Bl s5~ ak 55 POU ce GS b ule oa ba be fs ok - 24,000 25,000 er oN unknown. 28,000 29,000 The laws of moisture here indicate a humidity on the ground, with a par- tially clear sky, less by 15 than in cloudy skies, increasing to 77 by 3000 feet, then nearly constant to 5000 feet, when the humidity abruptly de- creased to 69, and then nearly evenly at the rate of 5 in 1000 feet, till at 9000 and 10,000 feet it is 52; the degree then constantly decreases, till at heights exceeding 25,000 feet the degree of humidity is reduced to less than 10; and it would seem that at the higher elevations there is an almost entire absence of water. These seem to be the general laws; but this regular diminution is evidently often interrupted, and strata of moist air exist at different elevations even up to 20,000 feet, and these may be of considerable thickness. ON EIGHT BALLOON ASCENTS IN 1862. 473 § 7. Comparison oF THE TEMPERATURE OF THE DEW-POINT, AS DETERMINED BY DIFFERENT INSTRUMENTS. Every simultaneous or nearly simultaneous determination of the dew- point by the different instruments or methods was copied out, and then all those determinations between every 1000 feet of elevation were collected together, and in this way the first five columns of the following Table were formed. The numbers in the last six columns were formed by taking the differences between the temperatures of the respective dew-points in the same horizontal line, or those taken at about the same height and elevation. Taste [X.—Showing the Temperature of the Dew-point, as determined at about the same height by different instruments and methods, and compa rison of the results together. Under 1000 feet. Dew-point Temperature of the Dew-point as deter- Temperatures mined by Dry and Wet] 5 Calculated Observed D d Wet (fi by = ae by |) "above that by > | Campirated) | a. Date. 12 Ct i | as [ST eee) So s SA 5 5 || SA a|is K 5 | Eos Be | Ee) we | Se | Fe] -t | S2| 3 | Se [eee BE | 22/26) 28 || 22) 36/26) 32 | 28 |3e° p | ba | eB) Bel pe) eh) S| gE) Bele a =) AS) em) ar~|at | aa / am | ratia d h m feet. ° ° ° ° °o ° ie) ° ° July 30 4 36 | 250 | 50°0 50°0 | o'o 4 423| 890 | 44°9 44°0 Tee Aug. 18 0 56 | 490 | 55°0 | 54°6| 55°0 53°9 +04) oo|+1'1|—0'4|40'7)4+11 zo 6 5] 250 | 56'7 55°5 +12 Sept. 1 440 | 250 | 56'5 52°0 +4°5 453 | 320) 519 52°0 en 5 © 9} 490 | 49°5 | 49°9| 49°°) 45°5 —0'4)+0°5 /+4°0|+0'9 |4+4°4 |+3'5 8 5 43 | 887 | 59°9 58°5 +14 Between 1000 and 2000 feet. 513 52°71 49°3| ++ | 4970 50°3 50°5 50°5| «+ | 4g'0 478 50° 49'0 47°5 566 5570 474 REPORT—1862. Taste IX. (continued.) Between 2000 and 3000 feet. Dew-point Temperature of the Dew-point as deter- Temperatures mined by Dry and Wet | 5 Calculated Ob: d D d Wet (fi A from | by || abovethat by | CREED | Date. Height. 22 = 3 oS : Pa Pal | lip tp g Po 2 | BSS PalES| 2 /5e FS) 2) S| 8 |e [Eee BE) UE) 92) GR) ELISE 22/2614 @ SA g/ 5 bo a | 5 & "Bb ‘S a |8°|4ée| ee | Ae) Ae | ae | ae| ee A dhm feet. ° ° ° ° ° ° ° ° ° July go 4 453 2379 | 42°6] +. | 38'S] 9 oe [+42 251 2900)! 42°21 22 | A2°S |. o- ++ |-03 Aug. 18 1 7 | 2042 | 52°5| 50°6| -- | 48°5|it1°9] -- |+4'0}] -- |4orx 2.20 6 364\iz2R7 | so'o| -. | 51°5|, ow [ae ERG 6 372| 2959 | 48°8| -- | 485] -- || +. |+0°3) Sept. 1 4 §5 | 2214. | 48°3| -- | 45°F) -¢ «+ |+3°0| 4 583] 2940 | 440] «- | 47°8] .. -» |—3°8 5 44 | 2910 | 422} os | 415} es ss |+0°7 5 53 | 2446 | 43°7| e+ | 43°5| -- s+ |-+0°2 | 5 57 | 2190 | 47°1| -- | 46°0| oy ee [Prd 6 4] 2057 | 48:9] -- | 480] .. «+ \-o'9 8 6 of 2034 | 571] ++ | 56°5| eo ee |-0'6 | : PR Re 5 a A ele eee Der | Ea fee Et 8 a bE Between 3000 and 4000 feet. July 30 4 50} 3690 Aug. 18 20 Sept. 1 6 41 emMMAAnAnAnAnnAAnXn II ADDAAADH Leal 377° 379° 3438 3159 3816 3893 3693 3593 3663 3693 3793 3893 3405 3468 3080 3257 3458 3680 3620 3590 3583 3987 3787 3690 3362 3660 363 40'5 41°5 47°8 48°0 ee 472 ON EIGHT RALLOON ASCENTS IN 1862, 475 Tasre IX, (continued.) Between 4000 and 5000 feet. Dew-point Temperature of the Dew-point as deter- Temperatures mined by fe Dry and Wet | 5 Calculated Ob d Dry and Wet (free) oe Te s oan 5s . ryan that by site tat ky a2. Date. Height. Peaubbaameipes } (Ee ge ag eee Ee ee ee ea P.|PS) 2/5822) (58) 8 | 28 [Eee 2 @ 8 B a & a E | éa\ge| 8 | de | en| ae a |A re d h mj} feet, ° ° ° ° ° ° ° © ° ° July 30 4 56 | 4169 | 403] +. | 4I°5| « oo |—1'2 4 563) 4279 | 39°7| «+ | 412) os o |= 25 5 15] 4104 | 40°2| -« | 43°L) oe « |—2°9 5 3.| 4324 | 40°7) ++. | 432) + * [724 5 43) 4403 | 39°38] -«.| 4I°0| .- . |-12 5 73) 4613 | 36°5| -e.| 40°5.| o- +s |—4'0 5 9%| 4683 | 382] -«.| 39°75] oe oe | 14 5 14 | 4863 | 37°3} -+-| 39°5| + + |—22 5 16 | 4873 | 380] «. | 39°0| «- «| +30 5 163) 4923 | 37°6| ++.| 39°5| ++ » |-¥9 6 21 | 4950 | 37°0] +«.| 39°70] «» ee .|—2'0 6 22.| 4450. | 38°8| «..} goo] . es [12 Aug.20 6 42 | 4116 | 45°9| «2 | 44°2| oe oe |41°7 6 48 | 4316 | 43°8| -- | 44°5| «- ee |\—O'7 6 49 4116 | 45°7| «+ | 44°5| «© me +2 7 di 7 5 5 I 5 476 REPORT—1862. Taste IX. (continued.) Between 6000 and 7000 feet. Dew-point Temperature of the Dew-point as deter- Temperatures mined by Calculated Observed || Dry and Wet (free) Dry and 3 from by above that by (aspirated) | 3 - above that by | E > Date leigh 6} & eH » ents P E »,. . “ ~ ° ss , s.|8¢| 2/22/82] 2] 28] 2] 28 /EEE 3s@l/us|2i¢e|38 ll ue |2ie!|]32!238/] 38 [232 asi | ae] 22) 22 || #3) 22| #2) 88] 28 Bam ba Ew) to 2 I me | 's xe |S & |&\de) de | &2| ae) ge| de| de 4 dhm feet. o ° ° ° ° ° ° ° ° ° July 30 5 41 | 6370 | 34°0 36°0 —2°0 5 43 | 6370 | 32°7| «- 34°0| oe - |—13 5 52 | S102 | 33°1|] «> 36°70} «. ee |—2°9 6 © | 6937 | 30°3| -- 32°70 | o- ~ |—917 6 1 | 6867 | 32°0| -- | 31°5] -- os |+-0'5 6 2 | 6547 | 31°4| -- 32°0| os -. |—0'6 6 114) 6937 | 30°0| -- 32°0| -- - |—2°0 6 13 | 6917 | 30°0| «+ | 32°70] oe es |—2°0 6 14 ae 30°8| .. 31s] .. oe tae 6 18 | 6400 | 32°7| -- 31'O| «. oo [917 6 183] 6000 | 32°8| «+ | 32°O| «es +» |+0°8 Sept. 5 117] 6914 | «+ | 36:0] ++ | 35°5|| eo ae on ++ [+05 Between 7000 and 8000 feet. Aug. 18 1 27 | 7836 | 41°8| e. Bia | eeuifiae = -» |+7°8 x 32 | 7650 | 40°) -- | 35°5| 35°0 +5°1/+56| «- | -. [ors I 33 | 7650 | 42°0 oe | 36°6 || -- oe [+574 ne EE ESD sts ndtnS Sn gE Snag EERE! Between 8000 and 9000 feet. July 17 9 55 I 8809] 19°7| -- ee | 24°0]] oe sa [-—4°9 Aug. 18 2 11% ar 42 ci ea he Al a ba Sd | Between 9000 and 10,000 feet. July 17 11 40 | 9882 | 19°9/ 19°7| «- ee {l-+o'2 Aug. 18 1 183| 9954 | 29°2/ -- | 30-4] -- «- |—o'8 I 24 | 9884 | -- | 29°9| 24°0/ «- oe ee «+ I+5°9 Aug. 18 1 22 | 10840] 28°6| .. | 22°0] 25:0} -- |+6°6/+3°6| «2. | -- |—3'0 2 17 | 10864] 27°4| 31°0| ++ | 29°5 || —3°6| «. J|—2r] o« |+1°5 Sept. 5 1 22 | 10774] 28°9| «. oe | 25O]] oe «- {+39 ON EIGHT BALLOON ASCENTS IN 1862. 477 Tasre IX. (continued.) Between 11,000 and 12,000 feet. Dew-point Temperature of the Dew-point as deter- Temperatures mined by } Dry and Wet | 5 Calculated | Observed || Dry and Wet (free) |~77 ® 3 (aspirated) | : from by above that by Lees that by g is « Date. Height. fit 2 Ee Res Rey ». : 5 sags * . = a3 o on we he om 7 i oI = BS 3 B|ES) 2/23 | FE) | 2e| oe | Se eek ~~ m > 2 = a 92) B2)58| 32 | 28 |58 | 22/58 | 28 See aut ss, ) 2H =] aa, | q > an |e p | pe | eB BE] pe) ee) SE) eB! BE |e A A~ |An | ee | a~ | an | ea | Am] ae lA d h m feet. ° ° ° ° ie} ° ° ° ° ° July 17 10 2 11792) 23°9 2570|| . apy) | er Between 12,000 and 13,000 feet. July 17 10 3 12709| .. 19°5| 21°0 | . i ° oe [15 Aug. 18 2 21 | 12364) 22°2| 22°2 - | 29°0]} o°0 “ oo |— 68 3 36 | 12453] 12°6| .- ee | 14°0 . —14 Sept. 5 1 24 | 12568] .. | 14°5 (250) 4A « |—10% July 17 10 4] 13000] 169] .. | 210] 22°0|| .. |—4'r|--5'1 —10 IO 5 |13467| 24°9] .. 22°5 || os - (+24 Aug. 18 3 34 | 13320| .. 9°8 12°5 || o- ie oe as, (27 Between 14,000 and 15,000 feet. | July 17 10 8 | -4544 24°0| 267 | 20'5| 24°0 |-27 +3'5 00 +62 +27 |-3's | Between 15,000 and 16,000 feet. July 17 10 11 15704. 24°6 | 22°7| 22'0| 21°5 +19 |+26|+3°3 to7 +14|-+0-7| Between 16,000 and 17,000 feet. July 17 10 15 16914 Aug. 18 2 31 24°3| 19°8 23°0 —o'7| « 20°8 6°0 +4°5 |+1°3 |+3°5 oe oe —3'2|—1'0 |+2°2 «- |—-6 7 Between 17,000 and 18,000 feet. & Between 18,000 and 19,000 feet. Aug. 18 2 32} 2 345 18°83 24°0 tet +20'2 ae —i- eee oe 3°5 +205 July 17 10 25 | 18844] 24:9] 24°4| 25°1| 24°2 ||--0°5 |—o°2 |-+-0°7 |—0'7 | +-0'2|-+0'9 Aug. 18 2 35 | 18039 — 574) -- Z°O|| oe se =- oe | 84) ZO leew cee | 0 In5l tore (oye) os an —11'5 478 . REPORT—1862, Taste IX. (continued.) Between 19,000 and 20,000 feet. Dew-point Temperature of the Dew-point as deter- Temperatures mined by Dry and Wet | 5 Calculated Observed Dry and Wet (free) (aspirated) 2 4 from by above that by i that by g ee Date. Height. ae ea 6 ae =./8¢| Bled ee| & 28| §| 28 Hoe ge] 38/281 38 | ge |42| 22 |S8 | 3a [S82 sé | Fa | 6) 26] 22 | 26| Be | 28] sale ¥ a| 3 Ba | 8 >| & g & | S| ae] se) &| ae) en | ae | 2 lé d h m feet. ° ° ° ° ° ° ° ° ° ° July 17 10 27 |19374 25°6| 23°2| 22°6| 21°0 ||+2'4/+3:0|4+4'6 |4+0°6 |42°2 |4+ 16 IO 29 |19415 19°5| 214 22°2 ||—I'g| +». |—2°7] -» |—o'8 IO 30 |19415 21°8) 18°3| 2175) 22°2 ||-4+-3°5 |+0°3 |—0'4 |—3°2 |—3'9 |—0'7 IO 35 |19548 16°6| .. 190} 20°0 || «. |—24)—3°4| .. es |—1'0 IO 39 |19380 23°83] .. 20°O| 21'r || -- |4+3°8)/42°7| .. oo |—I'E IO 44 119336 22°1| 22°1| 20°] 20°5 || o'0|+1°6|4+1°6|4+16)/41'6| oo Sept: 5 1 37$)19000+/—13'0| .. ~ 10° an +» |—3°0 wan” : Between 20,000 and 21,000 feet. aie Ee Sept. § 1 goapocco+|—e2] .. |. [as] | [een] | |_| By taking the mean of each column of differences in each 1000 feet of elevation, the next Table is formed. Taste X.—Showing the mean differences between the Temperatures of the _ Dew-point as found by the use of the Dry- and Wet-bulb Thermometers and by Daniell’s and Regnault’s Hygrometers, and comparison of the results as found from the two Hygrometers. Excess of Temperature of the Dew-point as found by Dry and Wet Thermometers (free) || Dry and Wet (aspirated)|| above that found by above that found by Heights between ae a Sols} 8 lal 28 [el 3 Vs] 28 lel 28 42 |2| 22 |2| 22 |] $2 |2] Ze [Sil SE S38 lw as is BS | as |e] 325 oe aS an | 6} & iS) ih S ° = p 3is| 2 |s| SE is] EE] s) BE | 5) BE A Zz) am |4] ea j2t Am 12) mist we feet. feet. < iM shat +41 | 8) -+2°6 |2/|/+0'2 |2) +2°6 |2 --| 4-0°2 | 7 +05 +11 .| —0°6 ON EIGHT BALLOON ASCENTS IN 1862. 479 The numbers in every one of these columns are affected with a change of sign, and, therefore, no certain difference is shown over the determination of the dew-point as found by any method or instrument over that found by any other. By taking the means of all in each group of 5000 feet, giving weight according to the number of experiments upon which each result is based, we have :— From the ground to 5000 feet high the temperature of the dew-point as determined by— Dry and Wet bulb (free) Experiments, Was 0°-4 higher than as found by Dry and Wet (aspirated) ..from 4 », thé samé as found by Daniell’s Hygrometer .......... wine », 22 higher than as found by Regnault’s Hygrometer .. ,, 3 Dry and Wet bulb (aspirated) Was 0°-1 higher than as found by Daniell’s Hygrometer .... ,, 2 Tape es . 3 59 Regnault’s 9 sH¥S 5S ae Daniell’s Hygrometer Was 1°-0 higher than as found by Regnault’s Hygrometer .. ,, 3 From 5000 feet to 10,000 feet the temperature of the dew-point as de- termined by Dry and Wet (free) Was 0°2 higher than as found by Dry and Wet (aspirated) ..from 1 oa Neal a * is Daniell’s Hygrometer .... ,, 29. a. 1°83 a a ps Regnault’s 3 , ee Ae ee Dry and Wet (aspirated) Was 5°-9 higher than as found by Daniell’s Hygrometer .... 5, 2 “4, 0%7-lower 3 35 Regnault’s 5 (FET ee Ue From 10,000 to 15,000 feet the temperature of the dew-point as deter- mined by i Dry and Wet (free) Was 2°-1 lower than as found by Dry and Wet Saag from 3 -5, 2°-0 higher 53 4». _ Daniell’s Hygrometer . . “oe », 07 lower pa is Regnault’s po T atAee% hat i eu Dry and Wet (aspirated) Was 6°-2 higher than as found by Daniell’s Hygrometer .... ,, ,, 14 lower 4 Regnault’s - RAGE “ “ Or Daniell’s Hygrometer Was 2°2 lower than as found by Regnault’s Hygrometer.... ,, 4 A480 REPORT—1862. From 15,000 to 20,000 feet the temperature of the dew-point as deter- mined by Dry and Wet (free) Experiments, Was 1°1 higher than as found by Dry and Wet (aspirated) ..from 7 gy O85 > a a Daniell’s Hygrometer .... ,, 9 9 Sot D 53 = 39 Regnault’s 95 Seer Aas Dry and Wet (aspirated) Was 0°-6 lower than as found by Daniell’s Hygrometer...... g378 AG ae Repnault’s) ~y35.- tte sana api le 2 0 9 3) 9 2) Daniell’s Hygrometer Was 0-4 higher than as found by Regnault’s Hygrometer.... ,, 8 By taking the mean of all, according to the number of experiments, we haye :— From the ground to 20,000 feet the mean temperature of the dew-point as found by Dry and Wet (free) Was 0°-2 higher than as found by Dry and Wet (aspirated) ..from 15 5, 90° by ms - Daniell’s Hygrometer .... ,, 114 tae, ae 5 iy ss Regnault’s =5 vcakebyne ced Dry and Wet (aspirated) Was 0° 9 higher than as found by Daniell’s Hygrometer .... ,, 10 3, 0°6 lower 4 ee Regnault’s si its Sib an, cae Daniell’s Hygrometer Was 0°1 lower than as found by Regnault’s Hygrometer .. ,, 16 From all the results it would seem that the temperature of the dew-point as deduced from the Dry- and Wet-bulb thermometers as ordinarily used has a tendency to give a result a little too high, but to an amount that is less than the probable error of observations, and that, therefore, it is a perfectly trust- worthy instrument to use, even to great altitudes; also, the results by Daniell’s Hygrometer seem to be of equal value with those found by Reg- nault’s Hygrometer, at all elevations. § 8. Comparison oF THE READINGS OF THE MERCURIAL AND ANEROID BaROMETERS AT DIFFERENT HEIcuts, All the simultaneous readings of the Siphon and Aneroid Barometers were extracted from Table I. and inserted in the following Table. ON EIGHT BALLOON ASCEN'TS IN 1862, 481 TasLe XI.—Comparison of the Readings of Mercurial and Aneroid Barometers, in the ascents on July 17 and August 18. , Excess of i : E f | | eatings of | ending o Readings of |esiiny a | Month, day, hour Barometers. Aneroid Month, day, hour Barometers. ‘Anactidine | Siphon ini ge |... | Siphon | | and minute. f above and minute. above Siphon. |Aneroid.| Barometer. Siphon. |Aneroid.| Barometer. in. in, | in. in, | in. m= s} in. July 17, 9 49 0 25°22] 25°32 toro | Aug. 18, 0 56 0} 29°34| 29°51] torr7 | 9 51 24°14] 24°30] +0°16 || 6 0, 28°55) 28°78} +023 | 9 53 22°42 | 22°65! +0°23 8 9 26°67 | 26°90} +0°23 9 54 22°02 | 22°20} +o18 Io o| 25°86) 26°08) +022 9 55 09} 21°58) 21°80] -or22 || 14 0} 23°64] 23°82] +0-18 9 56 20°93| 21°10) +o'17 || 15 22°69 | 22°68| —oro1 | 9 58 19°63 | 20°09| 40°46 | 20 19°90| 20°05 | +ors5 | Io 2 19°28 | 19°60} +0732 | 24. 15) 20°90| 21°28 | +038 s h fo) ° Co) I QO} I ) I ° ° I ° ° I ° ° I oO} ° | I 5 Io 3. o| 18°63| 18°90) +0'27 \ 127 0} 22°62! 22°90] +0°28 Io § oj 1814} 18:40) +026 | I 32 0} 22°80| 22°85] +o'o5 | to 8 of 17°24] 17°52| +0'28 || I 38 0} 24°46] 24°60) +o14 | IO Ir 0} 16°74! 17°10} 40°36 || I 41 0} 25°08! 25°30! +o'22 TO 15 oj 16°04] 16:25] +ora1 || I 52 0! 25°80} 25°82) +o'02 To 25 0} 14°94| 15715) +o'21 || 155 0} 25°08 | 25°25) +017 Io 27 oj 14°64) 15°30) +0°66 || 2 © O} 23°93} 24°10] +017 Io 29 oj 14°64] 15°30| +0°66 2 g Of 22°58| 22°71} +013 IO 30 o} 14°64} 15°30} +0°66 2 17 0} 20°24] 20°50] +0:26 IO 35 | 14°64] 15°00} +0°36 | 2 21 0} 19°11} 19°30| +orrg IO 44 0} 14°63) 15°10] +-0'47 || 2 25 20) 17°61| 17°85} +024 10 47 0) 14°13) 14°70) +0°57 || 2 29 0} 16-41 16°50! + 0°09 IO 50 o} 13°64] 14°20] +0°56 2 32 20] 15°84.) 16:00! +016 IO 54 0} 13°14] 13°60| +046 2 49 50| 13°70} 13°60} —o'ro IO §7 | 12°14| 12°60) +0'46 3 5 | 12°93} 13°20) 40°27 II 3. of 11°64 12°10] + 0°46 3 18 30) 13°45] 13°55) +-o"lo II 7 of 11°65] 12°10} +045 3.25 0} 13°65| 13°72] +0°07 II 12 ©} 11°95| 12°40] +0°45 3.34 +) 17°53] 17°42] —o'11 II 20. o} 12°65} 13°20} + 0°55 3 36 o| 18°63] 18°65] +0'02 II 25 0} 13°14| 13°60} +046 3 39 0} 20°02| 20°05} 40°03 II 38 0} 18°94| 19°00| -++0°06 3.49 0} 24°28) 24°42] +014 II 39 0} 20°04} 20°40] +0°36 II 40 0} 20°54 20°80; +0°26 July 17.—The differences between the readings are shown in the last column, and exhibit an increasing difference, increasing in amount with decreasing readings, till at the highest point the discordance between the readings amounted to half an inch. It is presumed that the aneroid baro- meter was in error to these amounts; but both instruments were broken in the descent, and no more information can be given. August 18.—The differences between the readings of the mercurial and aneroid barometers in this ascent were as constant as could be expected, as the readings could seldom be strictly simultaneous. Upon the whole, the readings of the aneroid are as good as those of the siphon. 1862, Ox 482 REPORT—1862. Taste XI. (continued)—Comparison of the Readings of Mercurial and Aneroid Barometers and Negretti’s new Barometer, in the Ascent on September 5. . Excess of Reading above Readings of Barometers, | Excess of | | NOcteuti"a new Bavometer Month, day, hour Aneroid and minute. : above Negretti’s Siphon of of Siphon. | Aneroid. new Barometer. Siphon Aneroid Barometer. Barometer. | Barometer. hm |g] ‘in, in. in. in. in. Sept. 5, 0 © 0] 2940 29°40 pecans 0°00 25) To) 23°97; 29°10 teseee +0'13 g's gol "2857 28°60 28°72 +0'03 —O'rs rT 6 . ‘o) (28748 | 28°35 28°55 —0'03 —oO'17 IIo o| 26°19 26°20 26°35 +oro1 —o'16 I Ir 30] 25°49 W5*G2 al sees +013 I 13 oO} 24°30 24°45 24°60 -+or1s —0°30 I 14 30] 23°70 23°90 23°99 +0'20 —0'20 © 16 0) ©23736 De Plo) | one +0'04, I 17 40| 22°66 22°71 22°75 +or05 —o'09 TF 2x; of © 20°72 20°60 20°65 —o'l2 0°07 122 0} 20°07 20°17 eoeeee -+o'1o I 25 30] 17°93 18°10 17°90 +017 +0'03 127 oO} 16°94 16°90 16"90 0704 +0'04. I 28 o| 16°69 16°65 teeeee —0'04. 135 oO} 14°65 14°90 sevece +0'25 £20, oO} “F4°k5 T4780 | seeee . +o0'25 I 37 30] 14°47 14°80 teeeee +0°33 2 8 30] 12°55 12°80 speeae +0°25 2 9 30| 16°37 16°45 16°50 +0'08 —0'13 2 9 40! 17°07 seeeee 17°20 sectereee | —=O'TZ 2.2% Gl & Wye MS Fess a aa lie eens toss | —O'L4 2 16 10) 19°75 19°90 Tg"90 +or'1s —O'15 2 16 20| 20°05 20°25 20°25 -+o'20 —0°20 2 16 50} 20°65 20°65 20°70 o'00 —0'05 @ 17 -gq|,) 21°15 21°55 21°30 -+o'40 —oO'ls 2 19 30) 21°85 21°90 21°90 +0105 | —0'05 2 ZO 1:20! 22°04. Sl. Hewes < ZOO 4 eae wwe | 40°04 2 20 40] 22°24. 22°20 22°45 —o0'04, —o'21 2 23 20) 22°64 22°76 22°70 +o12 —o0'06 2 23 50) 22°93 | 23°20 23°00 +0'27 — 0°07 224 O} 23°03 23°00 22°95 —0'03 +0'08 2022 Ol) 25 Ao 25°55 25°30 tors -+o'1o 2 38 of 26°40 26°35 26°35 —0'05 +0'05 3 6 ° RPE 29°02 220! ws |) csneoaeset (| Senn dg etetr The numbers in the last column but two show the differences between the readings of the siphon and aneroid barometers, those in the last column but one the differences between the readings of the siphon barometer and - Negretti and Zambra’s new barometer, and those in the last column the differences between the readings of the aneroid barometer and Negretti and Zambra’s new barometer; these several differences are all small, and are within the probable error of observation, as it is not possible that the read- ings can be made at the same instant. They prove that all the observations made in the seyeral ascents may safely be depended upon, and also that an aneroid barometer can be made to read correctly to pressures below 12 inches. ON EIGHT BALLOON ASCENTS IN 1862. 483 § 9, Exzcrricat Srare or THE ATMOSPHERE. In the ascent on July 17, an electrometer, kindly lent by Professor W. Thomson, of Glasgow, was used. Care (according to the instructions from Professor Thomson) was taken to discharge the electricity from the balloon on leaving the earth, and a charge of negative electricity was given to the instrument, and it read 59°, which we may call the balloon-reading. The instrument leaked a little, and it was necessary at every experiment to re- determine the balloon-reading. The following are the results of the ob- servations :— Map doo | Ra Tee a ge as 1ss00 te. {Bien a At 15,700 fect. . | Groctrcity of the air. 68 At 19,500 feet... rectrivity of the ait 1. 61 118300 i 4 Balloon-reading ¥..... 58 #4,23,000 fret, . Electricity of the air .. 58+ Now as these observations were made under the balloon, and the readings for the air were large negative readings always, it implies that the air was charged with positive electricity, but becoming less and less in amount with increasing elevation, till at the height of 23,000 feet the amount was too small to measure but was of the same kind. It is impossible therefore to say whether at higher elevations there would have been no electricity, or whether it would haye changed to negative. I wish, however, to speak guardedly on this subject, and would regard these observations as indications only. I pledge myself no further than that all the directions given to me by Professor Thomson were followed, and that the readings are correct. On tHe Oxycentc Conpition oF THE ATMOSPHERE. On July 17th the test papers, both by Moffat and Schonbein, continued untinged by colour throughout the whole flight of the balloon, and the same result was found during the ascent on July 30. After these ascents I received the following letter from Dr. Moffat :— “ Hawarden, August 4th, 1862. Dear Mr. GuaisHEr, “Tn the Times of Saturday last I observed, in your report of meteorological observations taken during a balloon ascent from the Crystal Palace on July 30th, that ‘test ozone papers were not coloured, and no ozone was noticed in the ascent from Wolverhampton.’ This is remarkable, seeing that ozone increases in quantity directly with increase of elevation on the earth’s surface. The degree of coloration of test papers varies with the humidity of the atmosphere. Dry air retards the decomposition of the iodine of potassium, and very moist air removes the iodine when decomposition has taken place. It does not ‘appear, however, in the observations, that the degree of humidity on the day of ascent was in any way unfavourable to the decomposition of the iodine, or the development of the brown colour on the test papers. 2x2 A484. REPORT—1862. «The time the balloon was up was short (two hours), and ozone must be in very considerable quantity to produce coloration of the test paper in so short a period of time. Still, according to our present notions of increase of the quantity of ozone with increase of elevation, papers of ordinary sensitive- ness ought to have been coloured during the ascents. The sensitiveness of the papers used in the investigation is of course of the utmost importance. “Today the quantity of ozone indicated by test papers prepared by myself is 4; and two papers from a packet prepared by Messrs. Negretti and Zambra, exposed for two hours in sunshine, did not show the slightest tinge, while a slip prepared by myself, exposed under similar circumstances, gave a degree of coloration equal to the mean of the day. From these results it would appear that the test papers used by you were in fault, This is a question of some moment, and one of great scientific interest; and if future balloon ascents give results similar to those you have reported, then the ground of the development of ozone must be looked for in the atmosphere near the surface of the earth. “T am, yours very truly, “ Jas. Glaisher, Esq.” (Signed) «'T, Morrar.” In consequence of the receipt of this letter I went to Hawarden to Dr. Moffat, and induced him to: make some test papers himself for the balloon experiments. He did so, and they were used on August 18th. I took some of the papers prepared by him, and some of the papers out of the same packets which I had used during the two preceding ascents, as well as some prepared by a formula of Schénbein. When I had reached 10,000 feet the new papers were decidedly tinged; at 17,000 feet they were coloured to the amount of 2, on a scale whose deepest colour is represented by 10; at 20,000 feet to 3. At 22,000 feet the coloration had increased to 4; and here Schénbein’s paper was coloured to 1, and Moffat’s old papers were still uncoloured. Moffat’s new papers gradually increased in intensity, and when 3000 feet from the earth at 2"38™ were deepened to 7. It would therefore appear that in all probability the test papers were in fault in the first ascents; and I may here remark that, in consequence, the preparation of the ozone test papers has been stopped, and that it is my intention, as Dr. Moffat himself cannot undertake the task, to superintend the preparation of the papers myself in future. Time or VrsRAtion oF A Magner. On July 17, at Wolverhampton, there were Ss. Ss. 30 vibrations of a magnet in 42-1; that is, one vibration in 1-403 30 ” ” 42:5; ” ” ATT 30 ¥ 9 42-4; ‘3 3 1-413 Therefore one vibration =1:411 second. At the height of 18,844 feet one vibration = 15-489. At the height of 20,244 feet one vibration = 15-536. Therefore the time of vibration seemed to be somewhat longer. On July 30, at the Royal Observatory, Greenwich, the time of the vibration of the magnet =1:573 second. On July 30, the mean of four sets of observations at the mean height of 5300 feet gave One vibration =1*-572, : ON EIGHT BALLOON ASCENTS IN 1862. 485 being sensibly the same as the result on the same day as determined at the Observatory. On August 18, at Wolverhampton, 38 vibrations —60-0 .*. one vibration —1-580 32 ” 50:3 ” ” 1-572 34s, 54:2 os » | 16595 30 of 47:9 f oY 1:597 4)6-344 Therefore one vibration=1°586 second, 1-586 At 11,000 feet 26 vibrations =41°5 second. Therefore one vibration= 1-590 second. A result differing but little from that on the ground, August 20, at the Royal Observatory, Greenwich, the time of one vibration was 1-580 second. August 20, at the height of 3800 feet one vibration =1:583 second. On September 5, I did not succeed in getting the time of vibration of the magnet at all in the balloon. During this ascent we were almost constantly going round and round—a motion fatal to observations of this nature, and failure at all times was the rule in these experiments. I commenced many series of experiments with the axis of the car in one position relative to the cardinal points of the compass, which I found to be different before the observa- tions were completed, and consequently the observations were of no value. The general result of these experiments is that the magnet vibrates in a somewhat longer interval of time at high elevations than on the earth. The number of experiments, however, is too few to speak decidedly on this point. Heienrs AnD APPEARANCE o¥ THE Croups. July 17. The sky was covered with cumulostratus clouds before starting. At 9" 47™ a.m,, at 4467 feet. Clouds were reached. At 9° 51™ a.m., at 5802 feet. Many clouds all round at a lower elevation. At 9" 53™ a.m., at 7980 feet. Entered a dense cumulostratus cloud. At 9" 55™ a.m., at 9000 feet. Passed out of cloud into bright sunshine and blue sky At 10" 2" a.m., at 11,792 feet. Examined the clouds below, which were noted as being very beautiful in form and arrangement. At 10" 15™ a.m., at 16,914 feet. Cumuli were underneath and far below ; strati in the distance, apparently the same height as the eye. No clouds above: blue sky. At 11" 38" a.m., at 12,376 feet. On descending the shadow of the balloon and car on the cloud below was very large and distinct; entered the cloud directly afterwards. At 11" 40™ a.m, at 9882 feet. In so dense a cloud that the balloon could not be seen. At 11" 45" a.m., at 5432 feet. Came out of cloud, but passed through others which appeared to be rising with great rapidity. 486 . REPORT—1862. July 30. Partially clear before starting, there being cirrocumulus, cumulostratus, cirrostratus, and a little cirrus nearly covering the sky, but very thin in the zenith. At 5® 26™ p.m., at 5830 feet. Cumuli all round at lower elevations ; zenith clear. At 5" 54™ p.m., at 6466 feet. A great mist, surrounding the balloon. At 6° 2" p.m., at 6547 feet. Cumuli and cumulostratus were below. At 6" 7™ p.m., at 6600 feet. Cumuli and cumulostratus appeared at the same level with the car, and strati above. August 18. At 1"p.m. Zenith clear, wind W.N.W. but light, clouds moving N. by W. At 1° 8™ p.m., at 3347 feet. “A cumulus cloud was entered. At 1° 24” p. m, ., at 9884 feet. Detached cumuli far below; plains of clouds in the distance. At 1" 27™ p.m., at 7836 feet. Alpine and dome-like clouds, bright and even on one side, in shade and lumpy on the other; detached cumuli at a lower elevation. At 1" 34™ p.m., at 6000 feet. Clouds have a very beautiful appearance. At 1" 58™ 40° p.m., at 5800 feet. Cumuli apparently same height as the car in the distance. At 2" 22™ 308 p.m., at 12,700 feet. Great mass of clouds to the east. At 2" 25™ 20° p.m., at 14,300 feet. A sea of clouds ; snow-white appear- ance; a few clouds below; cirri still much higher. A deep-blue sky. For note on the appearance of the clouds at 3° 33™ p.m., see Section of Observations, &c., p. 400. At 3" 43™ p.m., at 8144 feet. The shadow of the balloon and car on the cloud below very large and distinct. At 3" 43™ 308 p.m., at 7438 feet. Entered clouds. At 3" 46™ 10° p.m., at 6050 feet. In cloud, can see nothing; passed out of cloud at 6000 feet; a lower stratum of cloud. At 3" 46™ 30° p.m., at 5979 feet. Image of balloon on lower clouds mag- nificent. At 3" 48™ p.m., at 5922 feet. Entered a second stratum of cloud. At 3" 49™ p.m., at 5621 feet. Still in cloud. At 3" 50™ p.m., at 5300 feet. Emerged from the clouds. At 3" 51™ p.m., at 4520 feet. In thick mist. At 3° 55™ p.m., at 3000+ feet. Passed out of mist. August 20. At 6" 30" p.m. Very hazy; cirri prevalent in zenith; cloudy elsewhere. At 6" 32™ 30° p.m., at 1397 feet. In a mist. At 6" 38™ p.m., at 3159 feet. Misty all round, detached seud beneath. At 6" 39” p.m., at 3359 feet. Clouds below as scud. At 6" 43™ p.m., at 4256 feet. Clouds far below, but not under us. At 6" 43” 308 p.m., at 4316 feet. Entered a cloud. At 6" 58™ p.m., at 3793 feet. Clouds were all below. At 7" 5™ p.m., at 4250 feet. In mist; earth invisible. At 7" 25" p.m., at 2067 feet. Fog below. At 7° 47" p.m., at 5194 feet. In cloud; London out of sight. At 7° 49™ p.m., at 5900 feet. Having passed above the clouds, their upper surfaces were of a rich red. ON EIGHT BALLOON ASCENTS IN 1862. 487 At 7° 50™ p.m., at 5500 feet. In cloud. At 7" 52™ p.m., at 5200 feet. Above the clouds again. At 7" 55™ p.m., at 5500 feet. Setting sun tinged the clouds with red; 4 beautiful appearance. At 7" 56™ p.m., at 5160 feet. In cloud again. At 8" 5™ p.m., at 7000 feet. Above the clouds. August 21. The sky was overcast, being covered with dense cirrostratus clouds before starting. ‘ At 4° 40™ a.m., at 1210 feet. In a thick mist. At 4° 41™ a.m., at 1286 feet. Clouds broken; in the east there were beautiful lines of light, with gold and silver tints. At 4° 44" a.m., at 1706 feet. Earth visible in the distance. At 4" 45™ a.m., at 2000 feet. Very misty; blocks of clouds above. At 4° 49™ a.m., at 2930 feet. Scud below, creeping along the earth; cu- muli apparently on same level in the distance ; black clouds above. At 4" 55™ a.m., at 4927 feet. Entered the clouds. At 4" 56™ a.m., at 5300 feet. Lost sight of earth. At 4° 57" 30° a.m., at 5989 feet. Great masses of alpine cloud; entered a beautiful cumulus cloud. At 4" 58™ a.m., at 6000+4feet. In cloud, surrounded by white mist. At 5" a.m., at 6510 feet. Emerged in a valley between two clouds. _ At 5" 1™ am., at 6400+feet. Immense ocean of cloud; magnificent view. At 5" 1™ 20° a.m., at 6350+feet. Under the sun the appearance of a lake ; mountains of clouds to the left; fine cloud-land generally. At 5" 3" a.m., at 6336 feet. Lost sight of sun; misty. At 5" 4™ a.m., at 6413 feet. Deep ravines and shaded parts visible in the clouds ; sun again rising in same magnificent way ; clouds sweeping boldly away. At 5" 34™ 30° a.m., at 13,875 feet. Magnificent peaks of cloud in the distance; like a sea of cotton. At 5° 48™ a.m., at 14,273 feet. Sea of clouds below. At 5" 51™ a.m., at 14,318 feet. Thin strati obscure the sun. At 5" 57™ a.m., at 14,228 feet. Strati apparently same height as ourselves; cirri above. At 6" a.m., at 14,213 feet. Beautiful sea of clouds everywhere. - At 6" 24™ a.m., at 8040 feet. The shadow of the balloon on the clouds below was distinct, and surrounded by prismatic colours. At 6" 27™ a.m., at 7293 feet. Clouds approached on descending. At 6" 28™ 30° a.m., at 7106 feet. In a mist. At 6" 29" a.m., at 7001 feet. Just entering clouds. ; At 6" 35™ a.m., at 5189 feet. Stratum of cloud beneath. - At 6" 36™ 30° a.m., at 5058 feet. | Entered the clouds, and passed below At 6" 38"™+ a.m., at 4000 + feet. } them. September 1. _ The sky was uniformly covered with cirrostratus clouds. At 5" 5™ 30° p.m., at 3408 feet.. Cumuli in horizon apparently at a low elevation. At 5" 16™ p.m., at 3620 feet. Apparently on a level with cumuli in the distance. 488 REPORT—] 862. At 5" 30™ p.m., at 4000 feet. Higher than all clouds near us. At 5" 31™ p.m., at 4090 feet. Clouds have formed over the river from the Nore up to beyond Richmond, following the river in all its windings and bendings, and almost confined to its banks throughout. At 5" 32™ p.m., at 4180 feet. Clouds far below, and moving apparently at right angles to our motion. At 5° 36™ p.m., at 4000 feet. Clouds meeting us, moving at right angles to our motion ; clouds very low. At 5" 37™ p.m., at 3900 feet. Clouds passing quickly below us. At 5° 37™ 30° p.m., at 3690 feet. Clouds still follow the course of the river, being limited to its breadth, and parallel to it throughout its course. At 5" 40™ p.m., at 3362 feet. Clouds meeting us of three different degrees of white: the top bluish white, the middle the pure white of the cumulus, and the lower blackish white; and from these, we afterwards learned, rain had been falling on the earth all the afternoon. September 5. The sky was covered with clouds before starting. At 1" 13™ 305 p.m., at 5722 feet. In cloud, wholly obscured. At. 1" 16™ p.m., at 6729 feet. Still in cloud, very dense. At 1° 17™ 20° p.m., at 6914 feet. Out of cloud. September 8. At 4° 48™ p.m. The sky was overcast, with cirrostratus clouds. At 4" 49™ p.m., at 1232 feet. Scud at lower elevation, but not under us. At 4° 54™ 308 p.m., at 4169 feet. In mist, then in dense fog. At 4" 55™ p.m., at 4380 feet. In a dense white cloud. At 4" 56™ 308 p.m., at 4650-feet. Still in cloud, thick and white. At 4" 58™ 20° p.m., at 4750 feet. Half out of cloud; the crown of the balloon was out of cloud, and the car still within. At 4" 59™ 108 p.m., at 4650 feet. Cloud more dense; balloon descending. At 5" 1™ 30% p.m., at 4400 feet. Misty view ; horizon obscured all round. At 5® 1™ 508 p.m., at 4200 feet. Very black clouds over London. At 5" 7™ p.m., at 3370 feet. Beautiful break in the clouds to the west. At 5" 10™ 308 p.m., at 4108 feet. In slight mist. At 5" 11™ 25° p.m., at 4400 feet. Clouds below. At 5" 12™ 30° p.m., at 4920 feet. The shadow of the balloon and car sur- rounded by primary and secondary prismatic rings. At 5" 14™ 40° p.m., at 4920 feet. Clouds heaped upon each other, appa- rently on a level with the car. At 5° 16™ 45% p.m., at 5260 feet. Fluffy clouds below. At 5° 17™ 308 p.m., at 5230 feet. Clouds rising were whiter than those below ; a slight amount of blue in all clouds. At 5" 17™ 55% p.m., at 5428 feet. Balloon approaching clouds. At 5" 18™ 30° p.m., at 5428 feet. The shadow of the balloon and car on clouds, encircled by three distinct prismatic rings. At 5" 20™ 30% p.m., at 5112 feet. Clouds near us like smoke. At 5" 22™ p.m., at 5060 feet. Beautiful chasm in the clouds. At 5" 22™ p.m., at 5057 feet. Entering clouds. At 5° 22™ 45% p.m., at 5040 feet. Just entering clouds. At 5" 24™ 10° p.m., at 5020 feet. Entering clouds again. At 5" 24™ 305 p.m., at 5039 feet. In cloud. At 5" 25™ 20 p.m., at 4700 feet. Still in cloud. ON EIGHT BALLOON ASCENTS IN 1862. 489 At 5° 26™ 255 p.m., at 3220 feet. Cumuli below as scud. At 5" 27™ 30° p.m., at 3600 feet. A fine white cloud apparently resting on the Thames, like a huge swan. APPEARANCE OF THE SKY. July 17. At 10" 15" a.m., at 16,914 feet. Intense prussian blue. At 10° 39" a.m., at 19,380 feet. Deep blue. July 30. At 5" 31™ 30° p.m., at 5280 feet. Deep blue, dotted with small cumuli; sun shining brightly. At 6" 2™ p.m., at 6547 feet. Deep blue, dotted with cirrocumuli. August 18. At 1° 9" p.m., at 3705 feet. Deep blue. At 2" 25™ 208 p.m., at 14,434 feet. Very deep blue. At 3" 33™ p.m., at 15,984 feet. Very deep blue, dotted with cirrus clouds, August 20, At 7" 49™ p.m., at 5900 feet. Blue. September 1. At 4" 45™ p.m., at 270 feet. Blue sky near the horizon. September 5. At 1 21™ p.m., at 9926 feet. Deep blue. September 8. At 4" 58™ 20° p.m., at 4750 feet. Blue sky above. At 5° 11™ 25° p.m., at 4440 feet. Blue. At 5° 12™ 30° p.m., at 4920 feet. Deep blue. Direction oF THE WIND, July 17. The direction of the wind before starting was S.W. At 10° 27" a.m., at 19,374 feet, we determined, by means of the compass and the inclination of the grapnel hanging below, that we were moving in the direction of N.E., and therefore the wind was from the S.W. At 10" 44™ a.m., at 19,336 feet, we seemed to be moving towards the north; if so, the wind was S. July 30. The direction of the wind before starting was N.W. At 4" 41™ 15° p.m., at 480 feet, the direction of the wind was 8.W. At 5° 17™ 305 p.m., at 5155 feet, the direction of the wind was N.N.W. At 5" 40™ 30° p.m., at 6183 feet, the direction of the wind was N, August 18, The direction of the wind before starting was N.W. At 1° 5™ p.m., at 1130 feet, the direction of the wind was N.N.E. At 1" 17™ p.m., at 8935 feet, the direction of the wind was N.W. August 20. The direction of the wind before starting was 8.W., with very gentle mo- 490 REPORT—1 862. tion. No observations of the direction of the wind were made during this ascent, as the air was almost calm. August 21. The direction of the wind before starting was-S.W. No observations of the direction of the wind were made during this ascent. September 1. The direction of the wind before starting was E.N.E., verging to E. At 5° 4™ p.m., at 3268 feet, the direction of the wind was E.N.E. At 5" 10™ p.m., at 3318 feet, the direction of the wind was E. - At 5" 11™ 308 p.m., at 3560 feet, the direction of the wind was E.S.E. At 5° 17™ p.m., at 3580 feet, the direction of the wind was E.N.E. At 5" 36™ p.m., at 4190 feet, upper current W. September 5. The direction of the wind before starting was N. At 2" 16™ 108 p.m., at 11,150 feet, the direction of the wind was E. September 8. The direction of the wind before starting was S.W. No observations of the direction of the wind could be taken during this ascent. On THE PrRopacation or Sounp. On July 17, when at the height of 11,800 feet above the earth a band was heard playing. On July 30, at 5450 feet a gun was heard with a sharp sound, then a drum beating, and then a band was heard. On August 18, at 4500 feet the shouting of people was heard. - at 18,000 feet a clap of thunder was heard. es at 20,000 feet thunder again heard, below us. * at 20,000 feet a loud clap of thunder was heard. On August 20, at 4000 feet heard the shouts of people. 3 at 4300 feet railway whistle heard. x at 3500 feet heard bell tolling. 5 at 2200 feet heard people shouting. 3 at 3700 feet heard a clock strike. On August 21, at 4900 feet a railway-train was heard. 39 at 8200 feet a gun was heard. x at 3500 feet heard people shouting. On September 5, at 6730 feet, ascending, the report of a gun was heard. 9 at 10,070 feet, descending, the report of a gun was heard. On September 8, at 3300 feet heard the shouts of people. From these results we learn that different notes and sounds pass more readily through the air than others. A dog barking has been heard at the height of two miles ; a multitude of people shouting, not more than 4500 feet. On August 18 we heard at three different times what, in my Notes to the Observations, I have called claps of thunder; but I also remarked at these times that a careful examination of the clouds below us failed to discover any thunder-cloud. On inquiry afterwards as to the fact of thunder being heard on the earth, we found none had been, and it was suggested that the sounds © ON EIGHT BALLOON ASCENTS IN 1862. 491 we heard might have proceeded from Birmingham, where guns were being proved on that day. It-is possible this suggestion may be correct. PHYSIOLOGICAL OBSERVATIONS. On July 17, before starting from Wolverhampton, at my request Mr. Coxwell took the number of his pulsations, and found 74 in one minute; my pulsations were 76 in one minute. At the height of 17,000 feet mine had increased to 100, and Mr. Coxwell’s to 84. On regaining the ground the number of both our pulsations was 76. On August 18, the number of our pulsations were both 76 before starting. At the height of 22,000 feet mine had increased to 100, and Mr. Coxwell’s to 98; and afterwards, at a higher elevation, Mr. Coxwell’s number was 110, and mine 107. On August 21, in the morning ascent no observations were taken of our pulsations before leaving. At the height of 1000 feet the following results were obtained:—Mr. Coxwell’s, 95 in a minute; Mr. Ingelow’s, 80 in a minute; Capt. Percival’s, 90 in a minute. At 11,000 feet :—Mr. Coxwell’s, 90 in a minute; Mr. Ingelow’s, 100 in a minute; Capt. Percival’s, 88 in a. minute; mine, 88 in a minute; my son’s (a boy in his 14th year), 89 in a minute. At 14,000 feet the following were the results:—Mr. Coxwell’s, 94 in a minute; mine, 98 in a minute; Mr. Ingelow’s, 112 in a minute; Capt. Percival’s, 78 in a minute; my son’s, 89 ina minute. The pulsations of Capt. Percival were so weak that he could scarcely count them, whilst those of Mr. Coxwell, he considered, had increased in strength. These results show that the effect of diminished pressure exercises a very different influence upon different individuals, depending probably upon tem- perament and organization. In the ascent on July 17, at the height of 19,000 feet the hands and lips were noted as dark bluish, but not the face. At the height of four miles the palpitations of the heart were audible and the breathing was affected, and at higher elevations considerable difficulty was experienced in respiration. - On August 18, the hands and face were blue at the height of 23,000 feet. On September 5, at the height of about 29,000 feet I became unconscious, and at the height of about 35,000 feet Mr. Coxwell lost the use of his hands. At the height of about 29,000 feet I began to recover, and resumed observing at the height of 25,000 feet. _- From these results it would seem that the effect of high elevations is dif- ferent upon the same individual at different times. On THE DrrrerEent APPEARANCE OF THE GAS IN THE Baxxoon. July 17. Before starting the gas was thick and opaque. At 9° 54™ a.m., at 8065 feet. Valve opened, gas opaque. At 10" 2™ a.m., at 11,792 feet. Balloon full, gas opaque. At 10" 15™ a.m., at 16,914 feet. Gas cleared in balloon from appéarance of smoke to transparency. July 30. Before starting the gas was thick and opaque. At 4" 40™ 308 p.m., at 330 feet. Gas clear and transparent. 492 REPORT—1862. At 4" 45" 308 p.m., at 2379 feet. Gas getting thick again. At 5" 31™ p.m., at 5380 feet. Gas partially clear. August 18, Before starting the gas was cloudy and opaque. - At 1" 18™ 55% p.m., at 9978 feet. Balloon full, gas cloudy. At 1" 21™ p.m., at 11,470 feet. Valve opened. At 1" 25™ p.m., at 9740 feet. Valve opened. At 1" 32™ p.m., at 7650 feet. Valve opened. At 2" 22™ p.m., at 12,364 feet. Balloon full, gas clear, At 2" 25™ 20%4p.m., at 14,434 feet. Gas getting opaque. August 20. Before starting the gas was thick and opaque. At 6" 39" p.m., at 3359 feet. Gas still opaque. At 6" 41™ 305 p.m., at 3986 feet. Gas very opaque, issuing from the neck as smoke. At 7" 4" p.m., at 4052 feet. Gas opaque, issuing from the neck as smoke. At 7 18™ p.m., at 1417 feet. Gas clear; can see netting plainly through the balloon. At 7" 22™ p.m., at 1587 feet. Gas issuing from the neck of the balloon ; still clear. At 7" 25™ p.m., at 2067 feet. Gas clear. At 7" 37™ p.m., at 2603 feet. Gas opaque. At 7" 52™ p.m., at 5200 feet. Gas opaque. August 21. Before starting the gas was thick and opaque. At 5" 35™ a.m., at 14,027 feet. Gas clear; netting plainly visible through the balloon, September 1. Before starting the gas was thick and opaque. At 4" 55™ p.m., at 2214 feet. Gas still opaque. At 5" 1™ 30° p.m., at 3170 feet. Gas very opaque. At 5° 15™ p.m., at 3680 feet. Gas very opaque, issuing from the neck very fast, like smoke. At 5" 26™ p.m., at 3837 feet. Gas very opaque. At 5" 30™ p.m., at 4000 feet. Gas opaque, issuing from the neck like smoke. September 5. Before einai the gas was very opaque. During this ascent no observa- tions of the state of the gas were made. September 8. Before starting the gas was opaque. At 4" 49™ p.m., at 1232 feet. Gas was clear. At 4" 51™ p.m., at 2482 feet. Gas getting opaque ; netting scarcely visible through the balloon. At 4% 52™ 308 p.m., at 2923 feet. Gas opaque. At 5" 15™ 35% p.m., at 5026 feet. Gas partially clear. At 5¢ 23™ 50% p.m., at 5029 feet. Gas opaque, issuing from the neck of the balloon. At 5" 28™ p.m., at 4829 feet. Gas very clear. At 5° 52™ 14° p.m., at 600 feet. Gas clear, ON EIGHT BALLOON ASCENTS IN 1862. 493 GENERAL REMARKS. These eight ascents have led me to conclude, firstly, that it was necessary to employ a balloon containing nearly 90,000 cubic feet of gas; and that it was impossible to get so high as six miles, even with a balloon of this mag- nitude, unless carburetted hydrogen, varying in specific gravity from 370 to 330, had been supplied for the purpose. It is true that these statements are rather conflicting when compared with the statements made by one or two early travellers, who professed to have reached some miles in height with small balloons. But if we recollect that at 32 miles high a volume of gas will double its bulk, we have at once a ready means of determining how high a balloon can go; and in order to reach an elevation of six or seven miles it is obyious that one-third of the capacity of the balloon should be able to support the entire weight of the balloon, in- clusive of sufficient ballast for the descent. The amount of ballast taken up affords another clue as to the power of reaching great heights. Gay-Lussac’s ballast, as before mentioned, was re- duced to 33 lbs. Rush and Green, when their barometers, as stated by them, stood at 11 inches, had only 70 lbs. left, and this was considered a sufficient playing-power. We found that it was desirable to reserve five or six hun- dred pounds; and although we could have gone higher by saving less, still on every occasion it was evident that a large amount of ballast was indis- pensable to regulate the descent and select a favourable spot for landing. Secondly, it was manifest throughout our various journeys that excessive altitude and extended range as to distance are quite incompatible. The reading of the instruments establishes this ; and it has been pointed out what a short time the balloon held its highest place, and how reluctantly it ap- peared to linger even at a somewhat less elevation. This was not owing to any leakage or imperfection in the balloon itself, for its efficiency has been well tested, and it remained intact a whole night without the least percep- tible loss of gas. It has been stated by an aéronaut of experience that strong opposing upper currents have been heard to produce an audible contention, and to sound like the “roaring of a hurricane.” Now, the only deviation we experienced from the most perfect stillness was a slight whirring noise in the netting, and this only when the balloon was rising with great rapidity, and a slight flapping on descending, when the balloon is in a collapsed state. I may also state that the too readily accepted theory as to the prevalence of a settled west or north-west wind was not confirmed in our trips. Nor was the appearance of the upper surface of the clouds such as to establish the theory that the clouds assume a counterpart of the earth’s surface below, and rise or fall like hills or dales. The formation of vapour along the course and sinuosities of the river during an ascent from the Crystal Palace has been already alluded to; this was a very remarkable demonstration. GENERAL ConcLusions. Perhaps the most important conclusions which can be drawn from the experiments at present are :— 1, That the temperature of the air does not decrease uniformly with increase of elevation above the earth’s surface, and consequently the theory of a decline of temperature of 1° in every 300 feet must A9A. REPORT—1862, be abandoned. In some eases, with a clear sky, the decline of 1° has taken place within 100 feet of the earth, and for a like decrease of temperature it is necessary to pass through more than 1000 feet at heights exceeding 5 miles. The determination of the decrease of temperature with elevation, and its law, is most important, and the balloon is the only means by which this element can be determined ; very many more experi- ments are, however, necessary. 2. That the humidity of the air decreases with height in a wonder- fully decreasing ratio, till at heights exceeding five miles the amount of aqueous vapour in the atmosphere is very small indeed. . That an aneroid barometer read correctly to the first place, and probably to the second place of decimals, to a pressure as low as 7 inches. . That dry- and wet-bulb thermometers can be used effectively up to any heights on the earth’s surface where man can be located. . That the balloon affords a means of solving with advantage many delicate questions in physics; and, 6. That the observations can be made with tolerable safety to the observer ; and therefore that the balloon may be used as a philoso- phical agent in many investigations. SX) oO List of Stations where Meteorological Observations were made on the days of the several Balloon Ascents. Height Names of Stations. Latitude. Longitude. above Observer. Sea-level. ah ioe feet. Greenwichiviisy*uusvide ae 51 28N. | 0 0 158 | The Astronomer Royal. pWrottesley ss 5a-casst > 52 37 218 531 | Lord Wrottesley. Wolverhampton .........| 52 37 2 13 | 490 Belvoir Castle ............ | 52 54 © 39 Ww. | 260 | W. Ingram, Esq. Grantham .................. | §2 54 © 39 | x81 J. W. Jeans, Esq. Nottingham ...,,.......... Ralcgyt. Lets, ot 174. | E. J. Lewe. EPAWENOEN 4m ce < 005s c0 seeps SLE 3: 2 260 | Dr. Moffat. DISBEBO GLY «a ge cca open devs 53 25 2150 37. ‘| J. Hartnup, Esq. Wakefeld 22:7. 005.0. fv. | 53 40 I 30 115_ | W.R. Milner, Esq. ee a ee ON EIGHT BALLOON ASCENTS IN 1862. 495 Meteorological Observations made at different Stations in connexion with the Balloon Ascent on July 17. - Roya OsservaTory, GREENWICH. Reading of Temp.| Ten- |Degree| ,,- 3 s S eB Timeof |=; —_ ______| of the |sion of a dg eéle. Raines Obseryation.| Barom,| Thermom. | Dew-| Va- | Humi- Win d Ac | 32 . reduced || point. | pour. | dity. q g8/28 to 32°F.) Dry. | Wet. <0/<490 | | m in. a 5 ° in. 0a.M./ 29°73 | 62°0 | 57°2 | 5371 | "404 | 73 Ww. IO 5, | 29°73 | 62°0 | 57°0 | 52°7 |°399 | 72 | -. 20 5, | 29°73 | 62°0 | 57°0 | 52°7 |°399 | 72 | ++ 29°73 62°0 | 56°4 | 516 "382 69 w. 49 5 | 29°73 | 63°7 | 57°8 | 52°9 | “401 68 see Cirrocumulus, cirrostratus, and cirrus. Cirrocumulus, cirrostratus. CODDDWUUONO w ° s fo] 5 6 Pega Pa Pe {19 ae 5° 5, | 29°73 | 63°3 | 57°5 | 52°6 |-397 | 68 “+ 6 | --- |Cirrus, cirrocumulus, cumulus, TO © 4, | 29°74 | 63°9 | 57°8 | 52°8 |"400 | 67 | w. | 7] >: [stratus. Io 10 5, | 29°74 63°9 575 522 139% ‘- ed z cee IO 20 , |2090° * 5 50°0 | "361 5 one tee . p I10 30 , aang coe 58°0 | 54°6 |-427 | 71 | s.w.| 7 | = Light cloud, fine and bright. To 40 5, | 29°74 64°6 58°2 | 54°7 |°428 yi rae 6 | «- 20 50 » | 29°73 63°9 57°3 pay 386 6s oe | 5 lee jII Oo » | 29° . 7 I°O | °382 S.w. 5S | ee 7 Br 0 ;, Ba 64'2 368 51°5 | -38x eeitae, The hak | Cixrus, Valk g = a Bt 20 4, | 29°73| 65°3 | 58°0 | 52°1 |-389 | 62 ay oi tog Dp? Tatus, and cirrostra- II 30 » | 29°73 | 67°7 | 59°9 | 53°7 |°413 | 61 | s.w.] 8 ; | nS. II 40 ,, | 29°73 | 63°7 | 56°8 | 52°1 |-375 | 63 sr Io | :+- |Overcast entirely. I 50a.M.| 29°73 | 6374 | 58°0 |53°5 |*410 | 71 +++ | 10 | ++ |Cirrus, cirrostratus, and cumu- Noon. | 29°73 | 66'5 | 59°5 |53°9 |"416 | 64 | s.w.| 9 | © lostratus. © Iop.M.| 29°73 | 64°6 | 57°7 | 52°0 |°388 | 63 mo 7 | © 20 5, |29°72 | 66'1 | 59°7 | 54°4 |°424 | 66 ae 5 Cirrus, cirrocumulus, cirro- © 30 5, | 29°72 | 66°7 | 59°5 |53°7 | "413 | 64 | S.w. 5 stratus, and cumulostra- © 40 ,, | 29°72 | 68°8 | 61°2 | 55°3 | -437 | 62 oes 9 tus. y © 50 4 | 29°72 | 65°5 | 58°5 | 52°8 |-4o0 | 64 | ... | 7 TO 5, | 29°72 | 64°7 | §8°3 | 53°0 |°403 | 68 | s.w. 7 I to ,, | 29°72 |65"9 | 59°70 | 53°7 |°413 | 64 Ses 6 I-20 4, | 29°72 | 68:2 | 60°5 | 54°5 | "425 | 61 as G | I 30 5, | 29°72 | 66:4 | 59°5 |53°9 |"416 | 65 | S.w. 8 : | { Light clouds; a splendid 140 ,, | 29°72 | 66:2 | 59°5 |54°1 |"419 | 65 | ... ies day. 5° » | 29°72 | 66°7 | 59°8 | 54°3 |-422 | 64 | ... 5 : 2 © 5 | 29°72 | 63°4 | 57°2 | 52°0 |°388 | 67 | S.w. z a 2 Ic ,, | 29°73 | 63°2 | 57°3 | 52°3 |°3 67 Fah : 2 : Bao, la973 634 | 578 |5ara {agit | 67 |. [9 | hae a and 2 30 4, | 29°73 | 63°7 | 58°0 | 53°3 |-407 | 69 | S.w. | g | o» : . 240 ,, |29°73 | 63°0 | 57°8 | 53°4 |-409 | 71 .-. | 10 | +++ |Dull-looking, clouds in S.W. 2 50 ,, | 29°73 | 62°3 | 57°2 | 52°8 |-400 | 72 +--+ | 10 | +++ |Generally overcast; rain has os 0 >, | 29°72 | 62°4 | 57°8 | 53°9 |"416 | 74 | S.w. | 10 | © [just commenced falling. 53 To 4, | 29°72 | 63°1 | 57°9 |53°5 |"410 | 71 nee IO | «+ 3 20 4, | 29°72 | 62°8 | 57°6 | 53°2 |°406 | 71 ede Io | «-- 3 30 5, |29°72 | 62°4 | 57°2 | 52°7 1°399 | 71 | S.We | IO | ess 3 40 5, | 29°73 oe 564 51°38 |°385 | 72 vee | TO | ove ™ 50°,, | 29° I°7 | 56°7 | 52°4 | °39 72 0 IQ | ee P w 4 Oy 25°73 63°2 | 57°2 | 5271 HE 67 | s.w. | 10 | + tps overcast; rain 410 ,, | 29°73 | 60°5 | 56:0 | 52°1 |°389 | 74 ae IO | + : 4 20 ,, |29°73 | 604 | 57°0 | 54°1 |"419 | 80 ges IO | ++ "4 30 ,, |29°73 | 6071 | $5°r | 50°7 |-370 | 71 | S.W. | 10 | ee 14 40 ,, | 29°72 | 60°0 | 54°9 | 5074 |°366 | 71 ae oO; |= 145 5 © 5 | 29°73 | 60°0 | §5°2 | 510 |°374 | 72 oo TO! [Pere Op.m.| 29°72 | 60°r | §5°3 | 49°r |*349 | 72 | S.W. | TO | « 496 REPORT—1862. Meteorological Observations made at different Stations in connexion with the Balloon Ascent on July 17 (continued). Wrorrestey Hatt. | : Reading of | | Temp. Ten- Degree Direc | seis | Time o | of the sion of led le. | Observation. Barom.| Thermom. | Dew-| Va- |Humi- wnat aa\e = Remarks. reduced | ian point. pour.| dity. 268 £8 to 32°F.| Dry. | Wet <5 /<9 =| hm . in. ° = = in. | 9 40 a.m.) 29°33 | 58°0 | 52°8 | 481 | °336 | 70 | S.w. 9 5° » | 29°33 | 59°2 | 53°9 | 49°2 |°351 | 70 |S.S.W.| ... | . |Fine. 10 © ,, | 29°33 | 604 | 55°0 | 50°3 |°365 | 69 | S.s.w. |10 IO 4, | 29°33 | 59°7 | 53°O | 47°2 | °325 | 63 | S.S.w. |10 20 4, | 29°33 | 59°0 | 53°1 |47°9 |°334.| 67 | S.s.w. Fine 10 30 | 29°32 | 59°8 | 54°3 | 49°5 |°355 | 71 S.S.w. eet) 10 4O 4, | 29°32 | 59°O | 53°9 | 4973 | °352 | 70 S.S.W. | [10 §0 ,, | 29°32 | 6074 | 5570 | 50°3 |°365 | 6g | S.S.W. | ooo \Fine. Ir © ,, | 29°32 | 59°0 | 5372 | 48'1 |°336 | 67 | S.w. } II IO 5, | 29°32 | 58°4 | 53°9 |49°9 |°360 | 71 | S.S.w. [Ir 20 ,, | 29°32 | 62°7 | 56-9 | 52°0 | 388 | 69 | S.s.w. Fine |1I 30 ,, | 29°32 | 59°0 | 53°2 | 48-1 |°336 | 67 | S.s.w. iII 40 ,, | 29°32 | 62°0 | 56-0 | 50°8 |°371 | 67 | S.s.w. |II_ 50 a.m.| 29°32 | 6o'o | s0°0 | 41°2 |*259 | 50 |S.S.w.| ... | ... |Fine. Noon. | 29°31 | 62°2 | 55°8 | 50°3 |°365 | 65 | S.S.W. | | | © 1Op.m.| 29°31 | 6o"r | 53°9 | 48°4 *340 © 20 ,, | 29°31 ; 610 | 54°9 | 49°6 | °356 Fs || bes O 30p.m. 29°31 | 62°2 55°8 | 50°3 365 | 65 | S. | .. | .. )Dull. a ron Ky 4 . o fe = WoLvERHAMPTON. ] ] | 9g 20. a.m.| 29°44 | 59°0 | 5570 | sr "4 379 76 S.W- «a7 . Great masses of cumulostratus 9 52 », |29°42 | 59°0 548 510 |°370 | 75 | s.w. | 8 [clouds. } 9 55 » |29°44 | 59° | 54°8 | 520 *370 | 75 | s.w. | 7 | ... Balloon stationary. I TO © 4, | sees | 59°5 | 54°38 | 50°8 (371 | 72 S.wW. | g | ... |Balloon invisible ; passed be-] TO [ZGiey, ea) eee Goro | 55°0 | 50°6 2369 | 72) |BoOW..beS) base] [hind the clouds. | LOetgs see ie. Sede 59°° | 55°O | 51°4 |°379 | 76 | s.w. | 8 es | 10 20 5, |29°41 | 59°3 | 55°3 |51°7 |°384 | 76 | s.w. | 8 we Io 30 4, {29°41 | 6x°0 | §5°8 | 51°3 |°378 | 71 | S.w. | 7 és Io 40 ,, ei 6x93) \|57:0 1 §3°3: |°407 |. 76-1. S.Weol od) [ens ae masses of cumulostra-| 10. 55? pel Meseneae ORS a6 97°C" S3°T. ("404 | Abe G. Ws lea) Shands i} 11 © 4, |29°41 | 61'4 | 56°8 | 52°8 |-400 | 74 | SW. | 7 | o ee COM ie 62°2 | 56°9 | 52°3 1°393 | 71 | s.w. | 6 | IL 15 ,, 29°44 | 62°5 | §7°0 | 52°3 393 | 69 | sw. | 6 |... |) If 25 a.m. 29°42 | Betvorr Castie. 9 0Oa.m,| 29°54. 69's 563. | 518 |°385 | 71 | s.w. |... | 4 |Fine. 3 Op.m.| 29°53 | 64°0 | 56°5 | 50°3 | °365 | 61 | S.w. |... | 3 |Fair, but cloudy. NotrrmveHam. 9 ©a.m.}29°70 | 58°6 | 54°3 | 50°4 |°366 | 75 w. |6°5 | 2 |Fine. 3 Op.m.| 29°66 | 66'9 | 61-2 | 56°6 |-459 | 70 w. 7 | «. |Fine. to oOp.m,)29°6r | §2°0 | 49°7 | 47°5 |°329 | 85 | s.w. | 7 | ... |Fine. ON EIGHT BALLOON ASCENTS IN 1862. 497 Meteorological Observations made at different Stations in connexion with the Balloon Ascent on July 17 (continued). HAWARDEN. a 3 Reading of | temp. Ten- |Degree Direc 3 Ss Time o' of the sion of | of 5 7|2 servation.| Barom.| Thermom. | Dew- Va. Humi-) #00 “ Be Bs Bremsxka. reduced | ———— -| point. | pour. | dity. Wind, £8/28 to 32°F.) Dry. | Wet. <0 /<0 | hm in. a - o in, fo ~oa.m.| 29°51 | 58°5 | 54°0 | 50°o |°361 | 73 |W-S.W.| 3 “4 opm.) 29°47 | 56°5 | 54°0 | 51°7 |°384 | 84 | S| we | 4 LIvERPOOL. J 45 a.m.| 29°81 | 59°8 | 54°8 | 5074 | °366 | About three-fourths of the | 71 eee aa cree g Oa.m,.| 29°81 | 61°2 | 55°0 | 49°7 |°357 | 66 oak cok hoa sky were covered with | I op.m.|29°80 | 64°8 | 62°r | 59°8 |*514 | 88 cee sen) ||bees cloud till noon; overcast | 3 op.m|29'8o | 59°5 | 65°6 | 52° |°389 | 77 = vce pes afterwards. Rain fell from | 9 Op.m.| 29°69 | 5670 | 53°7 | 515 | °38E | 87 | wee | wee | ore | 3 to 85 p.m. | WAKEFIELD. 51°7 | 384 . : 51°0 |°374 | 65 | S.We oO p.m,| 29°66 *5157°5 |51°7 |°384 | 63 | S.w. . *, 52°1 *389 i fi 29°93 |67°6 | sg-o | 522 |*391 | 58 | N-E. | 9 | «. |Cirrocumulus, cumulostratus, and cirrostratus. 410 ,, |29°93 |67°5 | 57°0 | 48°6 |°343 | 50 fee WO hax | cirrostratus in E.; 420 ,, |29°93 | 67°4 | 57°4 |49°4 |°353 | 53 act) ae) bright cirrocumulus and cumulostratus in S.W. 4 3° 5, |29°93 | 6771 157-7 | 50°71 | °362 | 54 n. | 10]... {A little clear sky in N.; else- where cirrocumulus and cu- i mulostratus. 440 » |29°93 | 66-9 | 5775 | 50°0 | "361 | 56 eee EO! | vee : 4 50 » |29°93 |66°5 | 57-4. | 50°12 |°362 | 56 ... | 10 |... | | Cirrocumulus, cumulostra- 5 © ,, | 29°93 | 66'9 | 57°0 | 4971 |°349 | 54 | NeW. | 10 | « tus, cirrostratus, and a 8 a » | 29°93 66's 57°5 503 385 56 a eee es little cirrus. [s. by E 29°93 | 67°71 *g | 50°6 | °3 55 2a =n 7 = + ad ee a Balloon last seen about 5% 25™ 5 32 » |29°93 | 66°5 | 57°0 | 49°3 |°352 | 55 | NeWe 8 | ... {Clear sky, principally in W. and : zenith; elsewhere cirrus, u cirrocumulus, and cumulo- stratus. § 40 ,, | 29°93 | 66°5 | 58-0 | 51°r |°375 | 59 eae 8 |... |Clear in S.S.E.; principally cirrus, cirrocumulus, and r cumulostratus. 5 5° » | 29°93 | 67:2 |57°3 |49°4 |°353 | 53 | oe 5 |... |Clear sky in W.S.W. and N.; dense cumulostratus in E. and S.E., cirrus, and cirro- Q cumulus. 6 0 ,, | 29°93 | 66-9 | 57°7 | 50°3 |"365 | 56 |N.N-w.| 5 | © [Half the sky covered with cir- $ rus, cirrocumulus, cirro- stratus, and cumulostratus. ° D>, | 29195 | 608 |... oon ods eee |W.S.We © » | 29°96 | 58-9 | 54:0 |49°6 |°356 | 72 |w.s.w.| 3] © Light cirrus, cirrocumulus, and cirrostratus. 498 3 REPORT—1862. Meteorological Observations made at different Stations in connexion with the Balloon Ascent on August 18. Royat OBseRvATORY, GREENWICH. _ Reading of Pepe Time of aaa ae ETT | Temp. Ten- Degree Direc- S a) & Observation. Barom.| Thermom. | ¢f the ee ee {on “3 Bo /8¢ Remarks. priced Dry. | Wet. point. | pour. | dity. rd Es Es h m- in = ° ° in. Noon | 29°79 | 59°7 | 56°5 | 53°7 |"413 | 82 | NW. | 10] 1 © Iop.m.| 29°80 | 60°o | 57°0 | 5474 | 424. | 82 wee 10 © 20 5, | 29°80 | 59°7 | 56°7 | 54°1 | 419 | 82 oes 10 © 30 5, | 29°80 | 60°3 | 56°8 | 5470 |-418 | 79 | N-W. | Io © 40 ,, | 29°81 | Gog | 56°8 | 53°3 | "407 | 76 eae 10 © 50 5, | 29°82 | 60°7 | 56°9 | 53°7 | "413 |. 77 set TO | os I © 5 \|29°81 | 60°4 | 57°5 | 5570 |°433 | 82 |N.N.wW.| 10 | os. I 10 5, |29°81 | 6r°0 | 57°8 | §5°0 |-433 | 81 ops QMEXO: {ket I 20 ,, | 29°81 | 60°6 | 57°3 | 54°4 |-424.| 81 «| To | ... | Overcast; cirrostratus. I 30 ,, |29°8r | 60°5 | 57°2 | 54°4 |*424.| 81 | N-W. | 10 I 40 5, |29°81 | 60°5 | 57°5 | 54°9 |°431 | 83 Py, LO omens I 50 4, | 29°81 | 6o'x | 56'9 | 54°1 | "419 | 81 ay TOr | avs 2 © y |29°8r | 60°4 | 57°1 | 54°3 |°422 | 81 |N.N.wW.] ro | «.. 210 ,, | 29°81 |60°5 | 57°2 | 54°4 | 424 | 81 ses TO Joass 2 20 5, |29°8r | 6074 | 57'2 | 54°3 |°422 | 81 «st TO! || kus 2 30 » | 29°81 | 60°3 | 57:2 | 54°5 | "425 | 82 | Nw. |] 10]... 2 40 5, |29°8r | 60°3 | 57°3 | 54°7 | 428 | 82 a IO || .08- 2 50 4, | 29°81 | 60°5 | 57°3 | 54°5 |°425 | 82 ». | 10]... [fhe clouds have just com menced to break. 3. © 5, | 29°80 | 61°5 | 58°3 | 55°6 |°443 | 82 N. Io | 1 3 10 ,, | 29°81 | 60'2 | 57°5 | 55°x |°434 | 84 eee TO | see 3 20 4 |29°8r | Gorr | 57°4 | 55°0 | °433.| 84 sop 1110 fiev 3 3° » | 29°80 | 59°9 |57°3 | 55°1 1434 | 85 | N. | 10] ... | > Overcast. 3 40 5, | 29°79 | 60°3 | 57°8 | 55°6 | °443 | 85 er TO |\ tes 3 59 » |29°79 | 59°7 | 57°4 | 55°4 |'439 | 86 | «. | 10] 4 © » |29°79 | 59°7 |57°3 | 552 |°436 | 86 | N | 10/ .., Wrortestey Hatt. I Op.m.| 29°47 | 61°7 | 57°1 | 53°r |°404 | 75 | NW. | oo | ... |Fine. 110 ,, | 2947 | 63:1 | 58°5 | 54°6 |°427 | 74 |W.N.w. 1 20 5, |29°47 | 63°0 | 57°9 | 53°6 |"412 | 71 | N.w. I 30 » | 29°47 | 62*1 | 56°9 | 52°4 "394 | 71 | New. : I 40 5, |29'47 | 62°9 | 57°r | 52°2 |°391 | 68 | N.w. | .., | oo» |Fine. I 50 5, | 29°47 | 64:0 | 58°5 | 53°9 |°416 | 69 |w.N.w. 2 © x |29°47 | 63°6 | 57°6 | 52°6 |°397 | 67 |N-byw. 210 5, | 29°46 | 6475 | 58°38 | 52°0 |°388 | 69 jN.N.w.| ... |... |Fine. 220 5, |29°46 | 64:4 | 58°4 | 53°4 |*409 | 67 |w.N.w. 2 30 5, |29°46 | 64°6 | 58°5 | 53°4 |*409 | 67 |W.N.w. 240 ,, | 29°46 | 654 | 59°0 | 53°8 [415 | 67 | Nw. | ... | oo |Fine. 2 50 5, (29°45 | 65:9 | 59°8 | 54°8 |*430 | 68 | w. \ 3 © 4» |29°45 | 66:0 | 59°7 | 54°6 |"427 | 67 |W.N.w. a 3 10 » | 29745 | 66:2 | 59°2 153°5 |"410 | 64 Weel] ag | coer RINE. 3.20 4, | 29°45 | 66°6 | 59°9 | 54°5 [425 | 65 | Ww. 3 30 » | 29°44 |66°8 | 59°9 | 54:1 |"419 | 64 | Ww. 3 40 1 | 29°44 | 66:0 | 59°0 | 53°3 |"407 | 64 | w. 3 50 5, |29°44 | 66:9 | Goro | 54°5 |-425 | 65 We, | ccs |) wos Ene, 4 © » |29°44 |67°0 | 59°9 | 54°2 |"421 | 63 |W.S.w. 410 4, | 29°44 | §7°0 59°4 |53°3 |°407 | 61 |S.s.w.] ... | « |Fine. ON EIGHT BALLOON ASCEN‘S IN 1862. 499 Meteorological Observations made at different Stations in connexion with the Balloon Ascent on August 18 (continued). Brtvorr CAstie. Reading of sly = Temp.| Ten- |Degree! p.... | 27 | 2 .. Barom.| _ Thermom. of ee sign of i. of | , ng E S = 3 Remarks, i reduced at ar. | dity, | Wind. | 22| 268 } to 32°F.) Dry. | Wet. | Pom" | pour. uty. <5/<0 m in. a a ms ne r "9 ©Oa.m.| 29°63 | 56°7 | 53°3 | 50°2 | 364] 79 N. 8 (Cloudy. 3° «Op.m.| 29°63 | 68°0 | s9°0 | 51°9 |°386 | 56 | s.w. o |Fair. Norrivenam. 9 ©a.m.| 29°83 | 64°0 | 58°0 | 53°0 | "403 67 w.n-E.| 8 | o |Dull till 88 a.m.; the clouds ! then broke. I 30 » | 29°84 | 65°4 | 58°9 | 53°6 |-412 | 66 |N.x.z.| 1 |... /From this time very fine and j warm. 3 «Op.m.| 29°83 | 75°7 | 63°5 | 54°8 |"430 | 49 |N.N.w.| 2 | ... |Very fine. 19 50 », | 29°83 | 57°2 |55°6 | qtr |-419 | 89 |w.n.w.| 1 . |Very fine. HAWARDEN. TO ©4.m.) 29°70 | 63°0 | 58°0 | 53°38 |°415 | 72 | Nw. Zr ex 4 oOp.m.| 29°67 | 63°0 | 57°0 | 51°9 |°386 | 67 | N.w. I 2 ’ LivERpPoot. i : : : 7 454.1.) 30°00 | 59°0 | $5°5 | 52°4 | 394 | 79 f9 0 4, | 30°00 | 60°8 | 560 | sr |-386 | 72 pe henley wat ih om ‘I Op.m.!} 30°00 | 63°7 | 58°0 | §3°3 |*407 | 70 Lisbon h ena Ys - - 5 Sate cirri till 1" p.m,; afters . Dp Maece?s) 044 157-8, | 52°3 | 393°) 64 wards quite clear. 9 © » | 29°99 | 59°4 | 56°5 | 53°9 |*416 | 85 i WAKEFIELD. 3 cam. 29°78 | 42°5 |42°0 | 40°8 |-255 | g2 | ENE. © » | 29°85 | 68°0 | 61'0 | 55°5 |-4qr | 64 | Nw. 3 Op.m.| 29°80 | 71°5 | 63°0 | 58°3 |-487 | 63 |w.N.w. 9 O w» | 29°82 | 54°0 | 53°C | 52°0 |°388 | 93 Ww. | 4 August 20, Royat Oxsservatory, GREENWICH. 6 op.m.) 29°82 | 64°3 | 62°3 | 60°6 |*529 | 88 |N.N.w.| 10 | 0 The sky is generally covered 10 ,, | 29°82 | 64°2 | 62°1 | 60°3 | +524 | 88 AH ee with light cirrus, cirro- 20 ,, | 29°82 | 64° | 61°6 | 59°5 | 509 | 85 10 stratus, and haze; a very H calm evening. i 30 » | 29°82 | 63°7 | 62*0 | 60°6 |*529 | 90 |N.N.wW.| 9 Very hazy all round the ho- 6 40 ,, | 29°81 | 62°5 | 618 | G12 | 541 | 96 9 rizon; cirrus clouds are 3 prevalent ; the Crystal Pa- 1s lace is scarcely discernible. 6 50 ,, | 29°81 | 63°r | 61°6 | 60°3 | *524 | ox 9 Cirrus clouds prevail generally; } the haze thickens; the sky ii is partially free from clouds ii in the zenith. 7 © » | 29°81 | 62°8 | 61'0 | s9°5 | *509 | 89 | N.N.E.| 10 . |The sky appears uniformly x covered with cirrus, cirro- ‘4 stratus, and haze. IO ,, | 29°81 | 62°6 | 60°0 | 57°9 |*480 | 84 10 20 ,, |29°81 | 62°5 | Go'2 | 58°3 1-487 | 86 one TOs. Cirrostratus and haze. 17 30 5, |29°8r | 62°7 | 60-3 | 58°3 |-487 | 86 | N.E. | to | 7 im 22 500 REPORT—1862. = Meteorological Observations made at different Stations in connexion with the Balloon Ascent on August 21. Roya OpservaTory, GREENWICH. Reading of wes | : ——_—_—__———_ Temp. | Ten- |D . Sess Time of De |enc egTee) Direc- | 24] 2 Observation. eile Thermom. hy pan of Humi- tion of Es a $ Remarks, to 32°F.| Dry. | Wet. point.| pour. | dity. Moore Es & B hm in. S ms ny eS eS August 20. é : ‘ ee Midnight | 29°82 | 59°7 | §9°7 59°7 |"512 | 100 |s.8.E. | 10 | o |Overcast; amount of cloud va- August 21. ' riable. TX TOAMA| GST | SOW discs || ede, [a see Netooe | Sek 2 0 3, | 29782") 59° S00 ae at, aia S.E. 3 80>, 9° )29°Sr el 588.) 3 ee at: 5 Ohya Bet BO. 55) N20 ai: ech ellivese || cc. | ~ te0 s. |... | se | | Generally cloudy during the Sito gy [2GTBO USSG I we. fice |] cee | SSeEe | oc. | cee night and early morning. 6 oO 5, | 29°80 |i5e-Sar are. | + se sot TeSeWhe y |) oes 7 GO 43 | 29780 |/Gg:OUF sor) ee |S ca I dee | BABE. | Seve | Mone 3 0 ,; |29°80 | 62708" we ee Ee 0) ws-x. Ye || Rey 9 © 5 |29°79 | 64°3 | 62°5 | 6org |° 8 E.S.E.| 10 | © | “de ely 9 September 1. Royat OnservaTory, GREENWICH. 4 oOp.m.) 29°79 | 61°8 | 564 | 51°7 | °384.| 70 ER. | x0 . \Sky is generally covered with cirrostratus. 4 10 ,, |29°79 | 61°5 | 56°3 | 51°8 |°385 | 71 He Ae iss 420 4, [29°79 | 60°9 | 55°9 | 51°6 |°383 | 71 A Mla: Overcast. 4 3° 5, |29°79 | 60°6 | 56°2 | 52°4 |°394| 74 | E.N.E.| 10 | ... 4 40 5, |29°79 | 60°3 | 56°0 | 52°3 |°393 | 75 hs 9 |... [Sky generally covered with cirrostratus; rain falling very gently. 4 5° ,, |29°78 | Gorx | 55°38 | 53°6 |*412 | 80 9 Rain still falling very gently ; cumulus clouds in the N.; light cirrostratus in the S. 5 © 4 |29°78 | 6orx | 55°8 | 53°6 |-412 | 80 | B.N.E.| 0 |... |Rain ceased; generally over- cast. 5 10 ,, |29°78 | 6orx | 56:2 | 52°8 | "400 | 76 ... | 10 | ... |Cirrostratus, cirrocumulus, cu- mulostratus, and a little cir- rus. § 20 4, |29°78 | 6orr | 56°3 | 53°0 |°403 | 77 ave to | ... |Ditto; clouds clearing away. 5 3° » |29°78 | 59°7 155°9 | 52°6 |°397 | 78 | E.N-E-| 9 | --- 5 42 4, |29°78 | 59°6 | 56°r | 53°0 | "403 | 80 pois g |... | | Cirrus, cirrostratus, cirro- 5 5° » |29°78 | 59°4 | 56°0 | 53°0 |°403 | 80 eT ED ll Gries cumulus, and cumulostra- 6 0 4, |29°78 | 59°0 | 55°7 | 52°7 |°399 | 80 | E.N.E.| 10 | ... tus. 6 10 ,, | 29°78 | 58°7 | 55°7 | 53°0 |°403 | 81 aeobaltero tlie: 6 20 ,, | 29°78 | 584 | 55°5 | 52°9 |‘4or | 82 soe g | .-. \Cirrocumulus, cirrostratus, and cumulostratus ; clouds cover the greater part of the sky. 6 30 ,, |29°98 |57°6 | 55x | 53°6 |*412 | 84 | NE. | 8 | ... |Light cirrus and clear sky in the S.; cirrocumulus and cirrostratus in the N. 6 40 ,, |29°78 | 57°2 | 5570 | 53°0 | "403 | 86 cee g | ... |Cirrus, cirrostratus, and cumu- lostratus in E. 6 50 ,, |29°78 | 57°0 | 54°8 | 52°8 | "400 | 85 fi g | ... {Cirrus, cirrostratus, and cumu- lostratus in W. and N.W. 7 © 5, |29°78 | 56°3 | 54°77 | 53:2 |*406 | 89 | NE. | 8 | ... |Clear sky and light clouds in zenith; dense cirrostratus round the horizon. ON EIGHT BALLOON ASCENTS IN 1862. 501 Meteorological Observations made at different Stations in connexion with the Balloon Ascent on September 5, Royat Oxsservarory, GREENWICH. Reading of bees? hae : ———_—__—_————|Temp. | Ten- |Degree} ;.... | °7 | 2 Time of = . Direc- | & 2 | . Th 7 f th f f : [eo leas Observation. arama sheen Dew. rae | Hum st 33 | a5 Remarks, to 32°F.| Dry. | Wet. | Pot. | pour. | dity. | 25/26 {hm in. * c a i, 7 ae | Noon. | 29°68 | 63°1 | 56’9 | siv7 |-384 | 66 | NE. | 7 | 0 | © top.m.| 29°68 | 64°3 | 57°6 | 52°0 |-388 | 64 se 7 |... | (Cirrus, cirrostratus, cirro- © 20 ,, | 29°68 | 65°2 | 58°5 | 53°0 | 403 | 64 Bad 7 41 cumulus. ] © 30 4, | 29°68 | 65°8 | 58°6 | 52°7 | +399 | 63 N.E. 7 . " 40 » ca ie te 53°9 ae oh oe 8 |---| | Cirrus, cirrostratus, cumulo- Be > 29729 | 85°85 | 58°7 | 53°9 | “41 I ee > A ae stratus, and cirrocumulus. HI © ,, | 29°69 | 64°5 | 57°83 | 52:2 |°391 | 64 | E.N-E.| 30 | ... | | } I 10 ,, | 29°69 | 63°9 | §7°8 | 52°8 |*400 | 67 Bb 10 . |Ditto; blue sky in N.W. 120 ,, | 29°69 | 63°5 | 58:0 | 53-4 |*409 | 70 en 9 Cirrus, cirrostratus, cirrocu- } t 30 ,, | 29°69 | 64°7 | 58°0 | 52°5 |*396 | 65 | S.w. 9 mulus and cumulostratus. I 40 ,, | 29°70 | 65"9 | §8°4 | 52°3 |°393 | 63 nea 10 Cirrus and dense cirrostratus ; rain has just commenced falling. I 50-4, | 29°70 | 57°I | 55°2 | 53°5 |*410 | 87 «» | ro | ,,. |Dense cirrostratus; rain fall- ing heavily ; strong negative : electricity. }2 © » | 29°70 | 56°4 | 55°8 | 55°3 1-437 | 96 | SE. | 10 } 2 10 » | 29°70 | 56°3 | 55°7 | 55°2 |"436 | 96 s+ | TO) «+ | | Overcast; cirrostratus; rain m2 20 » | 29°70 56°6 | 55°9 | 55°4 |°439 | 96 0a LO Were. still falling. } 2 30 4, | 29°70 | 57°2 | 56°5 | 55°8 |°446 | 95 | S.S.W.] I0 | ... 240 ,, | 29°70 | 57°9 | 57°9 | 57°9 |°480 | 100 =< DisEO } Rain has ceased. 2 5° 5, {29°70 | 57°9 | 57°9 | 57°9 | °480 | 100 wes TOS pe css } 3 © » |29°70 | 57°7 | 56°9 | 56:2 |'453 | 95 | S.S.wW.| 10 | 0 3 10 ,, | 29°70 | 58°0 oe 55°7 "444 | QI tee IO | see Beacons (29°70 | 57°7 |'56°6 | 5 459 | 93 ee | LON |) nc ee 13 30 » [29°70 | $7°9 | 568 | 568 |-462 | 93 | s.s-w.| 10 Overcast; cirrostratus. } 3 40 » |29°70 | 583 | 56°38 | 55°5 |*441 | go s+ | TO 3.50 » |29°70 | 584 | 56°38 | 55°4 |°439 | 89 ten 10 4 © 4, | 29°70 | 58°7 | 57°0 | 56°7 | "461 | 89 |"S.s.w.| 10 | ... 410 ,, | 29°70 | 58°4 | 56°38 | 55°3 |°437 | 90 .. | Io |... | | Overeast; cirrostratus and | 4 20 4, |29°70 | 58°5 | 569 | 55'4 |°439 | 89 wae TOR | cee stratus. | 4 30 55 | 29°70 | 58°2 | 57°0 | 55'9 |'447 | g1 | S.s.w.| 10 | ... |Overcast; cirrostratus in N.; | stratus. | 4 40 5, | 29°70 | 57°8 | 560 | 54°4 |°424 | 89 ... | 10 |... |Overcast; stratus and cirro- } Stratus. 4 50 5 |29°71 | 57°4 | 566 |55°9 |"447 | 94 | «-. | 10]... 4 15 © 5, [29°71 | 57°2 1564 15577 1444 | 95 | s.w. | 10 | ... | > Overcast; rain. }5 10 5, | 29°71 | 57°r | 56°2 | 55°4 |°439 | 94 | «- | IO]... ine § 20 ,, | 29°71 | 56°7 | 56°7 | 56°7 | 461 | 100 ae 1o | ... |Overcast; thin rain. 5 30 » |29°71 | 56°5 | 55°9 | 55°4 |°439 | 96 | N.-w. | 10 | ... |Overcast; rain ceased. 5 40 » |29°71 | 56°5 | 55°3 | 5572 |*436 | 96 | ... 9 5 50 = 29°71 | 56°4 | 56°4 | 56°4 |*456 | 1co eae Oiuiliees Clouds broken. 6 o ,, |29°71 | 564 | 564 | 564 |°456 | 100 | N.w. | 9g | ... |Cirrostratus; blue sky in ze- nith; fine. 502 REPORT—1862. Meteorological Observations made at different Stations in connexion with the Balloon Ascent on September 5 (continued). Wrottestey Hatt. Fee OF Temp.| Ten- |Degree] ,. wsl% . ae ilize Direc- | 97 | © Panik Ia Thermom. hai ae Honi- fibot BS 56 Remarks. reduced——————| point. | pour. | dity. Wind. 28 £8 to 32°F.) Dry. | Wet. 420 /|<0 h m in. a in. I. Op.M.| 29°37 | 57°6 52°9 48:6 343 | 72 N « {Dull 1 10 4, | 29°37 | 56-9 | 52°6 | 48°6 |°343 | 76 | N. 120 5, | 29°37 | 57°0 | 52°7 | 48°7 |°344 1 73 N. I 30 yy [29°38 | 56-1 | 52°1 | 483 |°339 | 75 | Ne |... | o [Dull. 140 yy |29°38-| 55-5 | 518 | 48°3 1°339 | 77 | ON. T 50 sy | 29°38 | 55-7 | 52°4 |49°3 |°352 | 80 | N. 2 © 4 129738 | 55°83 | 52:7 | 4g" |°349 | 8x N. soa ees | DUM. 2 10 y |29°38 | 56-1 | 52°6 |49°3 |°352 | 77 | N. 220 5, | 29°38 | 56:8 | 532 |49°9 |"360 | 84 |N.N.E. 2 39 5, |2939 | §7°0 | 53:2 |49°7 |°357 | 76 | N.N.E.| ... | ... |Dull. 2 40 wy 129°39 | 57°E | 53°I | 49°3 |°352 | 75 | N.NUE. 2 50 sy 129°39 1571 |53°4 | 50°0 |°361 | 77 | N.NVE. 3 © x |29°39 | 57°0 | 53°r | 49°3 |°352 | 75 | N.N.E.| woe | eee {Dull 3 10 5, | 29°39 | 57°2 |53°4.149°9 |°360 | 76 |N.N.E. 3.20 5, | 29°39 | 57°9 | 53°38 | Sor |°362 | 75 | N.NLE. 3 3° 5, | 29°39 | 58:1 | §4°0 | 50°3 |°365 | 76 |N.N.E.] ... | ... |Fine. 3 49 5, |29°39 | 580 | 53°3 | 4971 |°349 | 72 | NE. 3 5° + | 29°39 | 58°0 | §3°9 | 50°2 | 364 | 75 | N. 7 ; 4 © » | 29°39 | 58°3 |53°8 | 49°83 |-358 | 74 N. wed t Nene 4 10 5, |29°39 | 58:2 | 53°9 |49°1 |°349 | 75 |N-N.E. 4 20 5, | 29°39 | 58°0 | 54°0 | 50:4 |*366 | 76 |N.N.W. 4 30 5» | 29°39 | 58°0 | 54:2 | 50°7 |°370 | 77 |N.N.w.| ... | ... (Dull. 4 40 5, | 29°39 |57°8 | 54:0 | 50°6 |°369 | 77 |N.N.W. 4 5° » |29°40 |57°6 | 53°38 | 50°3 |°365 | 77 |N.N.W. HAwaRDEN. 10 0a.m.| 29°58 | 58°0 | 55-0 | 52°3 | 393 | 81 E. 4] 0 4 Op.m.) 29°62 | 59°0 | 55°5 407 | 84 | NE] 41] 0 LIveRpoot. a.m.| 29° : ; antl oe ie hare tHe BaE ) its ‘ 409 as “~ ye an “| "| «* || The sky was nearly free from 1 © p.m.| 29-93 | 60:8 | 53-9 | 47°9 |°334. | 72 velo. he cd tak cloud in the early morning. From 9g" to x4 overcast : 3 © 5 | 29°93 | 60°3 | 55°8 | 52°5 |*396 | 76 ao Ph wiiceaey |lzese ft 9 fi 9 © » | 29°98 | 567 cael | sry dmaka t Wd hekhecd et bees afternoon fine. September 8, Royat Onservatory, GREENWICH. Gore |\:522| 79 |S... | 50 |-a.. | 60°3 |*524.| 80 «| 10]... | + Generally overcast. 60°3 |°524.| 79 oa 1b) a 1 60°4 |*526 | 79 | s.w. | 10 | ... |Overcast; cirrostratus. ! 60°5 |*528 | 78 an To |: Generally overcast; cirrostratus. 60°6 |*527 | 83 mee 10 | ... |Balloon seen from top of Octa- | gon Room; overcast. ; ON THE THEORY NUMBRES. 508 Meteorological Observations made at different Stations in connexion with the Balloon Ascent on September 8 (continued). Rowat Opservatory, GREENWICH. Reading of Temp.| Ten- | Degree Sly 5 : | Direce- | 27 | 2 Sala Barom.| Thermom. ee ae Humi- tion of | BE | 8 ¢ oo reduced point.| pour.| dity, | Wind. Bale 8 to 32°F.) Dry, | Wet. <250|<0 h m in. 3 * O in. 5 Op.m.) 29°92 | 66:4 | 63°2 | 60°6 |*529 | 83 | sw. | ro | ... Overcast. Balloon disappeared behind clouds at 45 55™. Saw the balloon due S., mo- ving towards Eltham. 5 10 5, |29°92 | 66°7 | 63:0 | 6o'r |*520 | 80 9 Balloon seen for the last time. Overcast; cirrostratus. 5 20 5, | 29°92 | 65°7 | 63°0 | 60°9 |°631 | 84 9 Clouds broken in S. and W.; cirrocumulus. 5 3° », | 29°92 | 65°6 | 63°0 | 610 | "537 | 85 | s.w. 3 5 4° » |29°92 | 65:2 | 62°8 | G0°7 | °531 | 85 8 | 5 50 » |29°92 | 64°83 | 6274 | 60°4 | 526 | 86 oa 6 Cirrocumulus. 6 © 5, |29°92 | 64°7 | 62°2 | 60'2 |*522'| 86 | sw. | 6 6 10 5, | 29°92 | 64°2 | 62°0 |.60°2 | -522 | 87 5 6 20 5, |29°93 | 64°0 | 62°0 | 6073 | 524 | 88 8 | ... |Cirrocumulus ; sun shining on dome of Great Equatorial. 6 30 5, | 29°93 | 63°7 | 62°0 | 60°6 |*529 | 90 | s.w. | 10 | «. |Overcast. : 6 40 5, | 29°93 | 63°4 | 61°9 | 60°7 |°531 | gt 10 eee. cirrocumulus, cu- 6 50 5, | 29°93 | 63°3 | 61°7 | 60°4 | °526 | go se EO} [ler mulus, and cirrostratus. 62°7 | 61-5 | 60°5 |*528 | 94 | s.s.w.| 10 | ... |Overcast. | Report on the Theory of Numbers—Part IV. By H. J. Stepney Smita, M.A., F.R.S., Savilian Professor of Geometry in the Univer- sity of Oxford. 105. General Theorems relating to Composition.—The theory of the compo- sition of quadratic forms occupies an important place in the second part of the 5th section of the ‘ Disquisitiones Arithmetice,’ and is the foundation of nearly all the investigations which follow it in that section. In accordance with the plan which we have followed in this portion of our Report, we shall now briefly resume the theory as it appears in the ‘ Disquisitiones Arithmeticee,’ directing our special attention to the additions which it has received from subsequent mathematicians. We premise a few general remarks on the Problem of composition. If F, («,, v,,...,) be a form of order m, containing n indeterminates, which, by a bipartite linear transformation of the type U,=2 My, B,y Vp %y, 21,232,853 0, P=1,,2,3,...2, [7 -y=l1, 2, 3, bh te ~ 504 REPORT—1862. is changed into the product of two forms F.(y,, y,, .. yn) and F,(z,, z,,...z,) of the same order, and containing the same number of indletermitiates: Fr is said to be transformable into the product of F, and F,; and, in particular, if the determinants of the matrix | tasa.y |» which is of the type x n’, be relatively prime, F, is said to be compounded of F,andF,. Adopting this “definition, we may enunciate the theorem—*« If F, be transformable into F,x F,, and Ai F,, G,, G, be contained in G,, F,, F, respectively, G, is transformable into G, ibfce ss ‘and, in particular, if F be compounded of ', and F,, and the forms FE: Gg Ge be equivalent to the forms G,, F,, F, respectively, é, is compounded of G. and ee It is only i in certain cases that the multiplication of two forms gives rise to a third form, transformable into their product. Supposing that F, and F, are irreducible forms, 2. e. that neither of them is resoluble into rational factors, let I,, L,, I, be any corresponding invariants of F,, F,, F,, and let us represent by B and C the determinants dx, | = Troha fe dyg| B=1,2,3,...n,} and dx, o=1,'2, 3,75’. a dz, nam A, Wy ype Ms it The transformation of F, into F, x F, then gives rise to the relations I,xB* =I,xF,' I,xC*=1,x Fi, 7 denoting the order of the invariants I,, I,, I,. If one of the two numbers I, and I, be different from zero, we infer that. m isa divisor of n. For if “ be the fraction = reduced to its lowest terms, the equations v I’x BY =I’ x F." Tok Or oF oe BS imply that F, and F, (cleared of the greatest numerical divisors of all their terms) are perfect powers of the order pu; 7. ¢., w=1, or m divides n, since F, and F, are by hypothesis irreducible. We thus obtain the theorem (which however applies only to irreducible forms having at least one invariant different from zero)—‘‘ No form can be transformed into the product of two forms of the same sort, unless the number of its indeterminates is a multiple of its order.” For example, there is no theory of composition for any binary forms, except quadratic forms, nor for any quadratic forms of an uneven number of indeterminates. Again, when m is a divisor of n, let n=km, and let 4, ¢, d,, d, represent the greatest numerical divisors of B, a a respectively; we find r=( a) = r)= a), Ba (Fs), O_(F T=( b wy Vey 8 Ne. 6 o=(B) . The first two of these equations show that the invariants of the three forms F,, F,, F, are so related to one another, that we may imagine them to have . been all derived by transformation from one and the same form (see Art. 80) ; the last two (which, it is to be observed, present an ambiguity of sign ON THE THEORY OF NUMBERS. 505 when — is even) show that the forms B and F,*, C and F*, are respectively n identical, if we omit a numerical factor. Lastly, let ©,, ©,, @, be any corresponding covariants of F,, F,, F,. The relation of covariance gives rise to the equations np—q Sear, a, 3/0.) My, \, = O,(Y45. Yor 9,6 Ee > 2) mp—q (x, Vs, : .@,) Xx C : =6,(2,, 9 , -2,) xFPY,, aa )s where p and gq are the orders of the covariants in the coefficients and in the indeterminates respectively. Combining with these equations the values of q q B and C already given, we see that 6, x F,” and 6,xF,” are identical, ex- cepting a numerical factor ; 2. ¢. that ®, and ®, are either identically zero, or else numerical multiples of powers of F, and F,. If therefore two forms can be combined by multiplication so as to produce a third form transtormable into their product, their covariants are all either identically zero or else are powers of the forms themselves. There is, consequently, no general theory of composition for any forms other than quadratic forms, because all other sorts of forms have covariants which cannot be supposed equal to zero, or to a multiple of a power of the form itself, without particularizing the nature of the form. And even as regards quadratic forms, we may infer that com- position is possible only in cases of continually increasing particularity, as the number of indeterminates increases. 106. Composition of Quadratic Forms.—Preliminary Lemmas.—The follow- ing lemma is given by Gauss as a preliminary to the theory of the composition of binary quadratic forms (Disq. Arith., art. 234) :— (i.) “ If the two matrices ; fea Hey rele Bila By Bay ic-B, and a =| @, aves hy 0 Ra be connected by the equation [3 [415 es oe in which the sign of equality refers to corresponding determinants in the two matrices; and if the determinants of | 5 | admit of no common divisor beside A | [=| in which the sign of equality refers to corresponding constituents in the two matrices, is always satisfied by a matrix |k| of the type 2x2, of which the determinant is /, and the constituents integral numbers.”* The subsequent analysis of Gauss can be much abbreviated if to this lemma we add three others. * For a generalization of this theorem, see a paper by M. Bazin, in Tiiouville, vol. xix. p- 209; or Phil. Trans. vol. cli. p. 295. unity ; the equation ? a x5 506 REPORT—1862. In their enunciations we represent by X, Y, «, y, four functions, homo- geneous and linear in respect of each of the v binary sets, é, ,, &,n,,..-&, in by | ‘ | and | 4 | the matrices composed of the coefficients of X, Y and a, y, respectively; by (P, Q, R), (P’, Q’, R’) quadratic forms of which the coefii- cients are any quantities whatever ; and by & an integral number. (ii.) “If X, Y, x, y, satisfy the n equations included in the formula dX dY dXdY_, (dx dy dxdy dé, In, dy; dE, (aan dy; AS" the matrices | a | and | satisfy the equation 2? ee (iii.) “ The greatest numerical common divisor of the 7 resultants aX d¥_ aX ay dé, dy, dn; 4; is equal to the greatest common divisor of the determinants of ae (iv.) “If the n resultants of X and Y be not all identically equal to zero, the equation PX*+2QXY+4RY*=P’X*+2Q’XY+RY? implies the equa- tions P=P’, Q=Q’, roe ee ¥ 107. Gauss’s Six Conclusions.—Let F, f, f' represent the forms (A, B, C) (X, Y)*, (4,5,¢) (a, y)*, (a, 5', ¢) (a, yf, of which the determinants are D,d,d'; let also M, m, m' be the greatest common divisors of A, 2B, C, of a, 2b, c, and of a’, 2b',c’; $4, m, m’, the greatest common divisors of A, B, C, of a, 6, c, and of a’, b,c’, respectively. Supposing that F is transformed in f x f’ by the substitutionX=p, vw'+p,cy'+p,y+p,yy',Y=q,cx'+q,ry'+9q,vy +q,yy', let us represent the two resultants dX dY_dXdY = dX dY dX dY dxdy dy dx dx' dy dy’ dx' by Aand A’; the six determinants of the matrix ie aj = 3) (taken in 0 41 72 13 their natural order) by P,Q,R,S,T,U; the greatest common divisor of these six numbers by /, and the greatest numerical common divisors of A and A’ by 6 and @’, so that (Lemma 3) & is the greatest common divisor of é and é’. From the invariant property of the determinants of F, f and f’ we infer amet Fi ara f°, Di?=d'm’*, DP? =dm*. Hence the quotients ss and ¢ are squares. (Gauss’s Ist conclusion.) Also D divides d'm? and dm. (Gauss’s 2nd conclusion.) But & is the greatest common divisor of é and 6’; therefore Dk’ is the greatest common divisor of d'm? and dm?. (Gauss’s 4th conclusion.) Let oon ee and let the signs of x and n' be so taken that A’=n'f, A=nf"; these two equations are equivalent to the six following :— ae ars a a owes ee res em) (Gauss’s 3rd conclusion.) ON THE. THEORY OF NUMBERS. 507 Multiplying together the two resultants A and A’, we obtain an identity, which we shall write at full: (Po G1 —Pr Wo) @ + (Po Ya Pa Yo+P 2 1. Ps Va) PY + (Po Is —P 2) "| x (Po q2—P» Yo)? +( py Is —P 3 Lo +P, V2— Po %) vy ip, Y—Ps q)y") (U1 %— 0%) (Po te +p,xy'+p,v'y+p, yy'y + (9. Pst PoUs— U1 Pa— Yn Pr) (Po ee’ +p, vy +p, vyt+p,yy') --~ + () X (Gore +9, cy’ +9, cy +9, yy’) +(P,P.—Po Ps) (% awa! +4, xy’ +h w'y + qs yy’). Comparing this identity with the equation AA’=nn' ff’ =m F, we find by Lemma 4 % ae Gs —VoPs +P fees YoPi1_P\ P» oot nn' Gh (Q'.) The 5th and 6th conclusions relate to the order of the form compounded of two given forms. The equation AX?4 2BXY + CY? =(aa* + 2bay + cy’) x (av? + 2b'x'y' +c'y’?) shows that M divides mm’. But also mm’ divides Mk’. For operating on & ae P SM Capa ap Caeely, we find ody the equation just written with —, 2 2 aX on! 7 1G oe LT ey da? ‘dx dz dX dX dX dY ,dXd dY d¥ ) é 2[a dx dy ls (as at dy 7) +e dx a= ORs: ax dX? apex X16 dY* dy? dy dy dy* Whence AA’, 2BA’, CA’, and consequently Mo, are congruous to zero, mod mm’. Similarly Md*=0, mod mm’; i.e. mm’ divides Mk*?, If then k=1, i.e. of F be compounded of f and f', M=mm'. (Gauss’s 5th con- clusion.) Again, if in the congruences (j) we take m'm as modulus instead of mm’, we may omit the factor 2 in the second congruence, and may infer that AA?, BA’, CA* are all divisible by m'm, i.e. that mm’ divides #17", or fH, when F is compounded of f andj’. It is also readily seen that {#1 divides mm’ and mm’; whence observing that m=m or 3m, m'=m' or im’, f41=M or 1M, according as f, 7’, and F are derived from properly or improperly primitive forms, we conclude that if f and f' be both derived from properly primitive forms, the form compounded of them is also derived from a properly primitive form; but if either f or f be derived from an improperly primitive form, the form compounded of them is derived from a similar form. (Gauss’s 6th con- clusion.) In the transformation of F into fx/’, the form f is said to be taken directly or inversely, according as the fraction n is positive or negative. And similarly for f’ and n’. 108. Solution of the Problem of Ne Spans —It appears from the identity (I) that if A, B,C, p, p, P, Ps %o %, Ys Ys» _be integral numbers satisfying the nine equations (Q), the form (A 7 C) (X, Y)’ will be transformed into the product of the two forms (a, b, c) (w, y)° and (a', 5’, c’) (2’, yy by the sub- stitution X=p,we' +p, ry +p, ye' +P. Yy's Y=qve' +g, vy +9, ye +4,yy/. A = 0, mod mm’. 508 REPORT—1862. In order, therefore, to find a form, F, compounded directly or inversely of two given forms of which the determinants are to one another as two squares, we have to find eleven integral and two fractional numbers, satisfying the equa- tions (Q) and (Q’), in which a, 6, ¢, a’, 6', c', and the signs of n and x’, are alone given; the numbers p, P, P.Ps> %o 4%, V2 Yq» being further subject to the PoP. P2Ps| ave to admit of a f 0% Ws Ws ~ no common divisor. To determine n and n', we observe that the six deter- minants satisfy the identical relation PU—QT+RS=0; from which we infer, first, that P, Q, R—S, R+8, T, U must be relatively prime, if P, Q, R, 8, T, U are to be so; and secondly, substituting for the determi- nants their values given by the first six of the equations (Q), that dn? =d'n?. Denoting by a’ and 6 the greatest common divisors of P, R—S, U and of Q, R+58, T, so that 6 and 6’ are relatively prime, we have evidently condition that the determinants of the matrix Uy 6 — aes , ; n= +—, n=+-—; the positive or negative signs being taken according as v1) Mm f and f enter the composition directly or inversely ; and the absolute values of 6 and a’ being determined by the equation 6? d'm?=6" dm". The fractions n and w’ being thus ascertained, the values of P, Q, R, S, T, U are known from the equations (Q): these values are all integral: for P,Q, R—S, R+5S, T, U, this isevident from the equations (Q), and may be proved for R and § by means of the identity PU-QT+RS=0. We have next to assign such values to the constituents of the matrix | oP: P2 Ps , that its determinants may acquire the known values of P, Q, R, ST, U. To do so, it is sufficient * to obtain a fundamental set of solutions of the indeterminate system, v,U —xv, T+a, S=0 —«,U +a, R—v,Q=0 s , To Be” ae BAO 7 “Wer De ee) ee —w#, S+a,Q-—x, P =0, which is equivalent to only two independent equations. From the skew symmetrical form of the matrix of this system, it appears that if 6, 6, 6, 6, be any multipliers whatever, any four numbers (a, «, «, 7,) proportional to 6,P+6,Q+46,R —4,P 46,849. T = —§,Q—6,8 +6,U . . . . . . ( ) —),8 7 To will satisfy the system (S), and in addition the equation 6, +6, 4,46, 7,+4,7,=0. Assigning, then, to 6, 6, 4,4, any arbitrary values whatever, let ¢, 9, 9,9, be four numbers relatively prime, and proportional to the four numbers (2); let also 7, Qo +7, 9, +72 Go+7,9,=1; and employing x, 7, 7,7, in the place of §,9,4,4,, let us represent by p,p,p,p, the solution of (8) thus obtained. We have thus two solutions of (8), satisfying respectively the relations 2 * For a solution of the general problem, “ To find all the matrices of a given type, of which the determinants have given values,” see a paper by M. Bazin, in Liouville, vol. xvi. p. 145; or Phil. Trans. vol. cli. p. 302. For the definition of a fundamental set of solu- tions of an indeterminate system, see 2bid. p.297. It may be observed that the analysis ‘of Gauss, which is exhibited in the text, is applicable to any matrix of the type 2X (n+2). ; ee ON THE THEORY OF NUMBERS. 509 To Po +7,P, +7, p+ Ps = 0, and TQ +7, q +4, oF ™3%5 =1, which IREOVO that the two solutions form a fundamental set, 7. e. that the determinants PoP: PoPs| — (P,Q, R,8,T, Ul. Go i V2 It only remains to show that the values of A, B, C, which are now sup- plied by the equations (Q’), are integral. Operating on the identity (I) with ik BE iio and also with a a # we find, by reasoning dx’ da dy’ dy” da dx'dy"’ dy” es 2 similar to that which we have employed to establish the 5th conclusion, that 2Ann', 2Bnn', 2Cnn', which are certainly integral numbers, are divisible by 220’ if 34° ona 2S is uneven. In the former case A, B, C are evidently integral; in the latter, f 26 -- 2b'. ; : rae F either spel iar OS UB ONEN y te £- either m or m’ is even, and the quotients 2B” 20 : ——,.-——;, whence, again, mir mir are both eyen, and by é0' if either of these numbers of 2Ann', 2Bnn', 2Cnn' divided by 6d’ are ex mim A, B, C are integral*. 109. Composition of several Forms.—It will now be convenient to extend the definition of composition to the case in which more than two forms are compounded. If a quadratic form, F, be changed by a substitution, linear in respect of n binary sets, into the product of x quadratic forms, 7, f, . - «fu wn so that F(X, Y)= Il (a, 47+2ba; y,+¢,y°), we shall say that F is ‘= transformable into f,xf,x ..-f,; andif the determinants of the matrix of the transformation are relatively prime, we shall say that F is compounded of ff ---Jn . We shall retain, with an obvious extension, the notation of Art. 107. The invariant property of the determinant of F supplies the 2 equations A? fat [af}; from which we infer (1) that D, d,, d,,... are to one another as square numbers, (2) that Dx’ is the greatest common divisor of the 2 numbers a IIm?. According as the equation A; f; = A IIf is satisfied by a positive or negative value of the radical, we shall say that f, is taken directly or inversely. Adopting this definition, we can enunciate the theorem— “If F be compounded of f,,f,,.-f,, and F’ be transformable into f, xf, x .. Xf, the forms being similarly taken in each case, F" contains F.” For we infer from (2) that D'k?=D, whence A’;=k'A,, or by the Lemmas 2 and 1 of Art. 107, X'=aX+Y, Y’=yX+6Y, a, B, y, 6, denoting integral numbers which satisfy the equation ai—By=’. We thus obtain the equa- tion F’ (aX+,Y, yX+éY)=F(X, Y), whence, by Lemma 4, F’ is trans- formed into F by | fal | * Gauss shows that A, B, C are integral by substituting the values of p, »- +, Q+++5 IM G192—%oo»_$ (YoPs+Po%s— Ti P2—P 42)» PiP2—PoPs» and observing that the results, after division by nn’, are integral. The values of p,... are always obtained free from any common divisor by the process in the text; but Gauss has to determine four new multipliers 9, 4, 9, 4,, to obtain from the formule (2) the exact values of qo, .. - 5 and not equimultiples of those values. M. Schlafli (Crelle, vol. lvii. p. 170) has shown that Gauss’s demonstration is connected with a remarkable symbolical formula. 510 REPORT—1862. If F be compounded of f, f,...f,, and a single transformation of F into t,xf.x..f, be given, we may, by the same principles, find all the trans- formations of F into the product of f, f,, f,, taken asin the given transforma- tion. Forif F(X,, Y,)=lfrepresent the given transformation, and F(X, Y) =IIf be any other transformation, we find X=aX,+6Y,, Y=yX,+éY,, ao—Py=+1, and consequently F (4«X,+Y,, yX,+oy,)=F (X,, Y,); or a, 2 78 is, by Lemma 4, a proper automorphic of F. The formula X=aX, +fY,, Y=yX,+8Y,, in which oH represent all the transformations Zrteioe If F be transformable into f, xf, x..f,, and ® contain F, while f,, f,,..f,, contain 9,,%,,-+,, ® will be transformable into ¢,x@,.-¢,- This follows from a preceding general observation (Art. 105); but we must add here that if T, +; denote positive or negative units, according as the transformations of ® into F, and f, into ¢, are proper or improper, while v; denotes a positive or negative unit according as f,is taken directly or inversely, ¢,; will be taken directly or inversely according as T x7; x v; is positive or negative. This is is an automorphic of F, will therefore apparent if we observe that the sign of the quantity “- vee ‘is altered by an im- proper transformation of X, Y, or w;, y;, but is not pete by a transformation of any of the other sets. The theorem that “forms compounded of equivalent forms, similarly taken, are themselves equivalent” is included in the preceding. We may, there= fore, speak of the class compounded of any number of given classes. It is an important and not a self-evident proposition, that if F be com- pounded of ¢, f,, f,,--fn, and be compounded of f,, f,, F is compounded of Fis Fare -Fne Let p=at°+26n+yn’, let » be the greatest common divisor of a, 23, y, and vy the determinant of ¢; let also X, Y transform F into oxf,xf,x..xf,. Writing in X and Y for and » the bipartite expressions linear in w, y,, v, y,, by which ¢ is transformed into f, x f,, we obtain a trans- formation of F into f,xf,x..xjfn. Ifk be the greatest common divisor of the determinants of the matrix of this transformation, Dk* is the greatest common d; divisor of the n numbers — 3 me IIm?. But this common divisor is the same as 1=n the greatest common divisor of yx II m?;, and the n—2 numbers i=3 : s=n kad II m,? 4=3 CNG me 33 because v is the greatest common divisor of d, m,? and d, m,’ (4th condlu- sion), and because p =m, m, (5th conclusion) ; +. ¢., ‘Die= D, or k?= 1, and Fis compounded of f,, f,,..f,. Also, if 1 >2, f, is similarly taken in both coms Aifi Ai fi rT rt i “Oxh X.+Xf, _aXdY¥ en dX dY dé dn dé dn IS i= da, Ty, Uys da, —\ dé dn ~ dy x) (zr dy, dy, a) Wes ziy Q and w; be positive or negative units, according as g and f, are taken directly positions, for are identical; and if i=1, or ON THE THEORY OF NUMBERS. 511 or inversely in the composition of F and ¢ respectively, f, will be taken directly or inversely in the composition of F according as Ox w; is positive or nega- tive. By this theorem, the problem of finding a form compounded of any number of given forms is reduced to the problem of finding a form compounded of two given forms. For iff, f,..f, be the given forms, we may compound the first with the second, the resulting form with the third, and so on until we have gone through all the forms, when the form finally obtained will be compounded of the given forms, as will immediately appear from successive applications of the preceding theorem. We also see that we may compound the forms in any order that we please, or we may divide them into sets in any way we please, and compounding first the forms of each set, afterwards compound the resulting forms. If any of the given forms are to be taken inversely, we may substitute for them their opposites (Art. 92) taken directly. We may thus, without any loss of generality, and with some gain in point of simplicity, avoid the consideration of inverse composition altogether ; and, for the future, when we speak of the form compounded of given forms, or the class com= pounded of given classes, we shall understand the form or class compounded directly of the given forms or classes. 110. The solution of the problem of composition given in Art. 108 may be put into a form better suited to actual computation. The system (8) is evidently satisfied by (0, P, Q, R], and also by [P,0,—S,—T]; and these solutions are independent, because the determi- nants of their matrix cannot all be zero unless P=O, a supposition which may be rejected as it implies that a=0, 7. ethat dis a square. From this set of independent solutions a set of fundamental solutions is deduced, as fol- lows. Let « be the greatest common divisor of P,Q, R; and let & be deter- mined by the congruences & Q —S=0,k ae T=0, mod a which are simul- lt # rc Q taneously possible, because — and Me have no common divisorwith the modulus, Bb while the determinant 4 (RS—QT)=—UF is divisible by it. ‘The solutions H rf [us 1, Fa— ps ER p =|, [°. = QR are then a fundamental set, and may P P Hep be taken for [p, p, p, p,], [4 9, 995] respectively. We thus find Ann!= aS or A= ne ; 2Bnn'=R+S8—2k =. Multiplying this equation by A B I B B QR —, — in succession, and attending to the congruences satisfied by k, we obtain # # t Ul Ul t the congruences P p= wh, Q Bee ab,R B= bb +Dnn’ mod A; which deter- # a HOB mine B, for the modulus A, because £ a B are relatively prime, These Boe pw determinations [viz. of A, and of B, mod A] are sufficient for our purpose; 2 12 because if B’=B-+4NA, the forms (4 B, 2 <) anil (4 Bi, 3 x) ate equivalent. To obtain, therefore, the form compounded of two given forms (a, b,c), (a', b',c'), we first take the greatest common divisor of d’ m? and d m’” for D (giving to D the sign of @ or d’); we then determine n and n’ 512 REPORT—1862. by the equations n= / 2 [eo 2 and, representing by p the greatest common divisor of an’, a'n, bn'+b'n, we obtain A, B, C from the system Ante an __ ab’ bei vila Ghiptegs mod A. iP p bn'+b'n pee 66'+Dnn' B B j 2 —— I) ot A These formule, which are applicable to every case of composition, and are therefore more general than the analogous formule given by Gauss (Disq. Arith., art. 243), are due to M. Arndt*, who has also given an independent investigation of them, though our limits have compelled us here to deduce them from Gauss’s general solution of the problem of composition. That (A, B, C) is transformed into (a, b,c) x (a b' c!) by the substitution 3 ej beg A ee vy! + b6—Bn se Wada ee +6 hy. pe a a ad LYS an' vy’ +a'n a'y+(b'n+bn')yy', may be inferred from the vdfues of p,,...9,, .++3 or may be verified directly by observing that pl AX + (B+ VD)Y)=[ae+(b+4+n¥o D)y] x [a'a'+(0'+2' / D)y']. 111. Composition of Forms—Method of Dirichlet——Lejeune Dirichlet, in an academic dissertation (“ De formarum binariarum secundi gradus com- positione,” Crelle, vol. xlyii. p. 155), has deduced the theory of the composi- tion of forms from that of the representation of numbers. The principles of this method are applicable to any case of composition; but Dirichlet has restricted his investigation to properly primitive forms of the same deter- minant D. Let (a, 6, c), (a’, b,c’) be two such forms; let M and M’ be two numbers prime to 2D, and capable of the primitive representations M=am? +2bmn-+en*, M'=a'm? + 2b'm'n'+ cn", by the forms (a, b,c) and (a',b’, c’) respectively ; also let these representations appertain to the values w and w’ of 7D, so that w°=D, mod M, w?=D, mod M’, and so that the forms 2 (a, b,c), (a', b',c') are respectively equivalent to the forms (at o,— V ”) ; * Crelle’s Journal, vol. lvi. p. 64. In the new edition of the Disq. Arith. (Géttingen, 1863), a MS. note of Gauss is printed at p. 263, containing the congruences by which B is determined in the case of the direct composition of two forms of the same determinant. The account of the theory of composition in the preceding articles (106-109) differs from that in the Disq, Arith. (arts. 284-248) chiefly in the use which is here made of the invariant property of the determinant. , c) and (a’, b', c’)) whatever two numbers (subject to the conditions prescribed) are taken for M and M’. To prove this, a few preliminary remarks are necessary. (1.) Ifthe solu- tions w and w’ are concordant, there is but one solution Q (incongruous mod MM") comprehending them. (2.) The necessary and sufficient condition for the concordance of w and w’ is wa’, for every prime modulus dividing both M and M’. (3.) If Q, w, w’ satisfy the congruence x*==D for the modules MM’, M, and M' respectively ; and if, besides, Q=w, Q=w', for every prime divisor of M and M' respectively, w and w’ are concordant, and Q is the solution comprehending them. (4.) The value of /D to which any given primitive representation (such as M=am?>+2hmn-+en*) appertains, may be defined by congruences, without employing the numbers p and v which satisfy the equation my—nu=1 (see Art. 86); in fact, we find am+(b+w)n=0, mod M, (6—w)m+cen=0, mod M; whence also w==—8, mod d, w=-+6, mod d’, if d and d@’ are common LVIaDES of M and m and of M and n. We may suppose that the given forms (a, b, c) and (a’, b’, c’) are so prepared* that the representations of a and a’ by them appertain to concordant values of /D; 7.¢. that we can find a number B satisfying the congruences B?=D, mod aa’, B=), mod a, B=0', mod a’. Let state C; the forms a Mw’ ' wi? »W, will be a properly primitive form of determinant D, and (a, b,c), (a’, b',c’) are then equivalent to (a, B, a’ C), (a, B, a C) respectively ; and if X=wa' —Cyy', Y=aay'+a'a'y+2Byy', we find by actual multipli- cation aa'X?+2BXY + OY? = (aa? +2Bay+a'Cy’) x (av? + 2Ba'y' +aCw?). From this equation (which is included as a particular case in the formule of M. Arndt) it appears that MM’ is capable of representation by (aa’, B, C) ; it can also be shown (1) that this representation is primitive; (2) that it appertains to a value of /D, mod MM’, comprehending the values w and w’, to which the representations of M and M' by (a, 6, c) and (a’, 8’, c’) respectively appertain. (1.) If x, y, 2’, y', and X, Y are the values of the indeterminates in the representations of M, M’, and MM’ by (a, B, aC), (a', B, aC) and (aa’, B, C), the hypothesis that X and Y admit of a common prime divisor p is expressed by the simultaneous congruences wa’ — Cyy' = axy' +a'x'y+2Byy'=0, mod p. These congruences are linear in respect of the relatively prime numbers w’ and y's their coexistence implies, therefore, that p divides their determinant M; similarly it may be shown that p divides M’; so that w=w', mod p, because w and w’ are concordant. The congruences satisfied by w and w’ now give the relations av-+(B+w)y=0, * Tt is readily proved that a properly primitive form can represent numbers prime to any given number; thus a form can always be found equivalent to a given properly pri- mitive form, and having its first coefficient prime to a given number. ‘This transformation will be frequently employed in the sequel. ... In the present instance, we have only to substitute for the given forms any two forms respectively equivalent to them and haying their first coefficients relatively prime, 1 2M 514 REPORT—1862. a' v' +(B+w)y'=0, mod p; whence, eliminating # and w' from the congruence: Y=0, and observing that 2w is prime to M and therefore to p, we find yy'=0, mod p. If y is divisible by p, we infer, from the congruence X=0, that 2’ is also divisible by p; but the congruences satisfied by w and a’ give in this case the contradictory results o=+B, o=—B; i.e. y is not divisible by p, and similarly it may be shown that y' is not divisible by The congruence yy'==0, mod p, is therefore impossible ; or the represen- tation of MM' by (aa’, B, C) is primitive. (2.) Let Q' be the value of /D, to which this representation appertains ; and let p be any divisor of M; then Q/ satisfies the congruences aa’ X+(B+Q/)Y=0, (B—Q’')X+CY=0, mod p; and it will be found, on substituting the values of X and Y, that these congruences are also satisfied by w; whence it follows, since either X or Y is prime to p, that Q'==w,mod p. Similarly, if p be a prime divisor of M', Q'=.w', mod p; or ©’ is a solution of the congruence Q?=D, mod MM’, comprehending the solutions w and w’. Hence Q'==Q, mod MM’, and 2 the form (ane, Q, a is equivalent to (aa’, B, C), because either of them is equivalent to (nr, QO; — . The equivalence of all the forms a? —D is therefore demonstrated. included in the expression ( MM’, Q, wr It will be seen that Dirichlet’s method may be applied to the composition of any number of forms, and that the theorems of Art. 109 present them- selves as immediate consequences of his definition of composition. 112. Composition of Classes of the same Determinant.—We shall now con- sider more particularly the composition of classes of the same determinant D. We represent these classes by the letters f, ¢, . . - , and we use the signs of equality and of multiplication to denote equivalence and composition respec- tively *, The following theorems are then immediately deducible from the six conclusions of Art. 107, and from the formule of Art. 110. (i.) “If f be a properly primitive class, fx ® is of the same order as ®.” (ii.) “A class is unchanged by composition with the principal class.” In consequence of this property, it is sometimes convenient to represent the principal class by 1. (iii.) “The composition of two opposite+ properly primitive classes pro- duces the principal class.” If, then, f denote any properly primitive class, we may denote its opposite by f-!, and we may write fx f-!=1. (iv.) “If f be a given properly primitive class, and ® any given class, the equation F x f=® is always satisfied by one class, F, and by one only ; viz, by the class F=® x f-!.” (v.) “If®,, ,,..be all different classes, and f be a properly primitive class, fx ©,, fx ®,, . . are all different classes,” (vi.) «A properly primitive ambiguous class produces by its duplication the principal class ;” for an ambiguous class is its own opposite, Conversely, if ¢°=1, i.e. if be a class which, by its duplication, produces the principal class, ¢ is a properly primitive ambiguous class; for we find ¢*x @-1=¢71, whence ¢=9~!, or @ and its opposite are properly equivalent. _ * Gauss uses the sign of addition instead of that of multiplication; thus /X¢ is /+¢ in the Disq. Arith., and f” is nf. The change appears to have been introduced by his French translator, and to have been acquiesced in by subsequent writers. ‘+ Two classes which are improperly equivalent are called opposite, because they con- tain opposite forms (see Art, 92). ; ; ON THE THEORY OF NUMBERS. 615 (vii.) “The class compounded of the opposites of two or more forms is the opposite of the class compounded of those forms.” It follows from this, or from vi., that a class compounded of ambiguous classes is itself ambiguous. (viii.) Let ®,, ©, ...,-1 represent all the classes of det. D, and of a given order ©; and let 1, f,, f,, . . . fr—1 represent the properly primitive classes of the same determinant; it may then be shown that w is a divisor _» *@ of n, and that, given two classes of the order Q, there always exist |, Pro perly primitive classes, which, compounded with one of them, produce the other, Assuming, for a moment, that a form ®, exists, such that the w equa- tions included in the formula ®,xf=®, can all be satisfied, we see that each of these equations is satisfied by the same number of properly primitive classes f; for if the equation ®, x f=, be satisfied by & primitive classes, 1, $5 do» + » $e-1, the equation ©, x f=,, which is, by hypothesis, satisfied by a single class, 7,,, 1s also satisfied by the /—1 classes f, x 9,,- +» fu X Gx—1> but by no other class. Since, then, the classes ®, x f, of which the number ‘is n, represent every class of the order Q k times, we have evidently n=kw. It is also readily seen that every equation of the type ®, x f=, admits of k solutions; and thus it only remains to justify the assumption on which the preceding proof depends. If the order Q be derived by the multiplier m from a properly primitive class of determinant Ay we may take for ®, the m class represented by the form (m, 0, —Am); if Q be derived from an im- properly primitive class, we take for ®, the class represented by the form (2m, m,— ma . Representing ©, in the first case by the form (ma, mb, me), and in the second by the form (2ma, mb, 2mc), and supposing (as we may do) that a in each case is prime to 2D, we see that the forms (a, mb, m*c) and (a, bm, 4cm”) are properly primitive ; and we find by the formule of compo- sition (Art. 110), (m, 0, —Am) x (a, bm, em*)=(ma, mb, me) (2, m, —™m ax ) x (a, bm, 4em?)=(2ma, mb, 2me) ; i.e. the equation ®, x f=, can be satisfied for every value of p. 113. Comparison of the numbers of Classes of different Orders—To deter- mine the quotient ” of the last article, Gauss investigates the properly pri- Ww mitive classes of det. D, which, compounded with the classes (m, 0, —Am) and (2m, m, —m , reproduce those classes themselves. He thus em- 2 ploys the theory of composition to compare the number of properly pri- mitive classes of a given determinant with the number of classes contained in any other order of the same determinant; or, which comes to the same thing, to compare the numbers of classes, of any given orders, of two de- terminants which are to one another as square numbers (Disq. Arith., art. 253-256). We have already seen (Art. 103) that the infinitesimal analysis of Dirichlet supplies a complete solution of this problem ; whereas, in the case of a positive determinant, the result in its simplest form was not obtained by Gauss. It has, however, been recently shown by M. Lipschitz (Crelle, yol. lili. p. 238) that the formule of Dirichlet may be deduced, in a very ele- mentary manner, from the theory of transformation, We propose in this 2u 2 516 REPORT—1862. place to give an account of this investigation, and to point out its relation to the method pursued by Gauss. We begin with the theorem « Every properly primitive class of determinant De? is contained in one, and only one, properly primitive class of determinant D.” Let (A,B,C) be a properly primitive form of det. De’, inwhich A is prime to ¢; let B! be determined by the congruence eB’=B, mod A, and C! by the equation 12 C' Bg ; then the forms (A, B, C) and (A, Ble, C'e*) are equivalent ; but (A, Ble, C'e?) is contained in (A, B’, C’), therefore also (A, B, C) is contained in (A, B’, C’), that is, in a properly primitive form of determinant D. Again, if (a, b, c), (a’, b,c) are two forms of det. D, each containing (A, B, C), these two forms are equivalent. For applying to (A, B, C) the system of transfor- m, mations of modulus e, included in the formula | 0 7 | (art. 88), we readily find that, of the resulting forms, one, and only one, will have its coefficients divisible by e?*; therefore the class represented by (A, B, C) contains one, and only one class of det. De‘, and of the type (ép, eg, @r). But, applying to (A, B, C) the transformations inverse to those by which (a, 6, c) and (a', b', c') are changed into (A, B, C), (A, B, C) is changed into (ea, €*b, e’c) and (¢éa', eb’, e’c’); these two forms are therefore equivalent ; 2. ¢. (a, 6, ¢) and (a’, 0’, c') are equivalent. We have next to ascertain how many different properly primitive classes of determinant De’ are contained in the class represented by (a, 6, c), a properly primitive form of det. D, in which a may be supposed prime toe. Applying to (a, 6, c) a complete system of transformations of modulus e, we inquire in the first place how many of the resulting forms are properly primitive. or this purpose we observe that if e=e, xe, xe, X ...(é,, @, ++. representing factors of which no two have any common divisor), a complete system of transforma- tions for the modulus ¢ is obtained by compounding, in any definite order, the systems of transformations for the modules ¢,, ¢,,...; te. if | e, |, | & |5-+- be symbols representing complete systems of transformations for the modules €,, &»++., every transformation of modulus ¢ is equivalent by post-multiplica- tion} to one and only one of the transformations | e, | x | e,| X | & | X-- It will, therefore, be sufficient to determine the number of properly primitive forms obtained by applying to a properly primitive form a complete system of transformations for a modulus which is the power of a prime. Let p be an uneven prime, and let (a, b, c) be changed into (A, B, C) by load “i >a formula which will represent a complete system of transformations for the modulus p”, if y receive every value from 0 to @ inclusive, and if & be the ge- neral term of a complete system of residues, mod p*~’ ; we find * em ‘i | transform (A, B, C) into (P, Q, R), we have P=Am?, Q=m(A‘+By), R= AX?+2Bhp+Cp2. Observing that A is prime to e, we infer from the congruence P=0, mod. e%, that m=e, p=1; the competes =0, mod. e”, then becomes A+++ B=0, mod. e, giving one, and only one, value of £ mod. e; and this value satisfies the remaining congruence R=0, mod. ¢, since AR=(Ak+B)?—De?. t If] A| and | B | are two transformations connected by the symbolic equation |B}=|A|x|V], in which | V | is a unit transformation, | A | and | B | are said to be equivalent by post- multiplication, or to belong to the same set. A complete system of transformations for any modulus contains one transformation belonging to each set. ON THE THEORY OF NUMBERS. 517 A=ap**-), B=(ak+ bp’) p*-%, C=ak? + 2bkpy + cp*” whence, if y=a, (A, B, C) is properly primitive ; and is so, or not, for every other value of y, according as C is not, or is, divisible by p. If y=0, we have C=0, for p*~ [2+(F)] values of /, incongruous mod. p*; if y have any ie value intermediate between 0 and a, we have C=0, for p*-’—' values of &, incongruous mod. p*~’, Hence the number of properly primitive forms is ae? Aishhde “MG ] se mipmcediee ) and similarly if p=2 it will be found that the number of properly primitive forms is 2%. Hence the number N of properly primitive forms, arising from the application of a complete system of transformations of modulus e¢ to the form (a, 6, c), is eII [2 —(5)}; p denoting any uneven prime dividing e, It remains to determine the number of non-equivalent classes in which these N forms are contained. For brevity, we consider the case of a positive determi- nant. Let [T,, U,] represent any solution of the equation T?—DU*=1, and let o be the index of the least solution of that equation which is also a solution of T?— eDU*=1, 2. e. let o be the index of the first number in the series U,, U,,...which is divisible by ¢; also let (A, B, C) represent any one of the N ‘properly primitive forms into which (a, b,c) is transformed. The trans- formations of modulus e by which (a, b, c) i is changed into (A, B, C) belong to o different sets, the transformations of ‘the same set being equivalent by post- multiplication, but those of different sets not being so equivalent. For if | a3 B| be a transformation of (a,b, c) into (A, B, C), any other transformation is represented (Art. 89) by the formula ie T,—bU,, —cU, a, and these two peak eieu will or will not belong to the same set, ac~ U, , satisfying the equation - : - r cording as a unit transformation | 7 lt i Rel ee eu: | ar, (3 y, 6 Vv, p au,, T,+06U, Y, 0 Y does or does not exist. Premultiplying each side of this equation by | 8, —B | , we find —Yy a ee ee eT..—BU,,, —CUs| v,p AU, ; iy et BUe whence, observing that A, B, C are relatively prime, we see that A, p, r, p are or are not integral according as U,, is, or is not, divisible bye; a conclu- — sion which implies that the transformations of (a, b,c) into (A, B, C) are con- tained in o different sets. It thus appears that, of the N transformations, which applied to (a, b,c) give properly primitive forms, there are « which give forms equivalent to (A, B,C); 7. ¢. the number of properly primitive classes ~ 518 REPORT—1862. of det. Dé, contained in (a,6,c), a properly primitive class of det. D, is Nive Pg jor 4 ; a result which is in accordance with the formula of o o Dirichlet ase 103). If D be negative, we have only to put o=1, as is suffi- ciently apparent from the preceding proof; if, however, D=—1, o—2. The properly primitive classes of det. De’, into which a given properly primitive class (a, b,c) of det. D is transformable, are always such that, com- pounded with the class (e, 0,—De), they produce the class (ea, eb, ec). For let (a, b,c) be transformable into (A, B, C) of det. De’, and let us take a form of the type (A, B’e, C’e*), equivalent to (A, B, C); then (a, 5, c) and (A, B’, C’) are equivalent. But (e,0,—De) x (A, Bre, Ce’) =(eA, eB’, eC’), therefore also (e, 0,—De) x (A, B, C)=(ea, eb, ec). And conversely the classes which, com- pounded with (e, 0,—De), produce (ea, eb, ec) are precisely the classes into which (a, b,c) is transformable. Thus the properly primitive classes of det. De*?, which compounded with (e, 0,—De) reproduce that class itself, are no other than the properly primitive classes of det. De* into which (1, 0,—D) is transformable. And it is by this substitution of a problem of transforma- tion for a problem of composition that M. Lipschitz has simplified and com- pleted the analysis of Gauss. A method similar in principle is applicable to the comparison of the num- bers of properly and improperly primitive classes. We can first show that if D=1, mod. 4, the double of every properly primitive class of det. D arises by a transformation of modulus 2 from one, and only one, improperly primi- tive class of the same determinant ; viz. if (a, b,c) is a given properly primitive form, in which a and 4 are uneven, (2 b, 7 is improperly primitive, and is changed into (2a, 2b, 2c) by : : ; and, again; if (2p, q, 2r), (2p’, q’, 2r') are two improperly primitive forms, each of which is transformable into (2a, 24, 2c), these two forms are equivalent, because («,),¢) is transformable into (4p, 2q, 4r) and also into (4p’, 2q', 47’), while it can be shown that (a, 6, c) is transform- able into the double of only one improperly primitive class. Also, applying the system of transformations, = ra - ie : | , to the improperly pri- > mitive form (2p, q,2r), we obtain, if D==1, mod. 8, the double of only one properly primitive form: in this case therefore the numbers of properly and improperly primitive classes are equal. If D=5, mod. 8, we obtain the doubles of three properly primitive forms; and we have to decide to how many different classes these three forms belong. It appears from Art. 89, that ie [28 y,€ : mitive form (a. 6,¢), all the transformations are included in the formula 2(T,—qU,), Sate | a, B PU A(T, +90)! ly 6 |T,, U,] denoting any solution of the equation T7—DU?=4. Taking the case of a positive determinant, and employing the same reasoning as before, we infer that if U, be the first of the numbers U,, U,,... which is even, these trans- formations are contained in ¢ different sets. But is either 1 or 3 according as U, is even or uneven (see Art. 96, vi.) ; the three forms will therefore re- present three classes or one, according as U, is even or uneven; and the number of properly primitive classes, in these two cases respectively, will be three times the number of improperly primitive classes, or equal to it. If D be a transformation of (2p, 7, 277) into the double of a properly pri- ’ i ON THE THEORY OF NUMBERS. 519 be negative, the three forms will belong to different classes; and there will be three times as many properly as improperly primitive classes. From this statement, however, we must except the determinant —3, which has one properly and one improperly primitive class. It will be found that the properly primitive class or classes, into the double of which a given improperly primitive class can be transformed, and which in turn can be transformed into the double of the given class, are also the class or classes which compounded with the class { 2, 0, a produce the given class. Thus every improperly primitive class is connected either with one or three properly primitive classes (see Art. 98, note, and Art. 118). 114. Composition of Genera.—Let f and f' be two properly primitive classes of det. D, m and m’ two numbers prime to one another and to 2D, and represented by f and f’ respectively; then mm’ is represented by fx’. Hence the generic character of fx /' is obtained by multiplying together the values of the particular characters of f and f’. For those generic characters which are expressed by quadratic symbols this is evident, since “) (=) (=) — j=—[ — ) Xi — };5 P P and it is equally true for the supplementary characters, since it will be found that mm!—1 m'—1 m2m!2—1 m*2—1 m/2—] m—1 eee ta (rt)? (1) 8 ti) ® x(—1) The genus I’, in which fx/’ is contained, is said to be compounded of the genera y and y’, in which f and f’ are contained; and this composition is expressed by the symbolic equation r=y xy’. It will be seen that the composition of any genus with itself gives the principal genus. The same considerations may be extended to improperly primitive classes. Thus, if f and f' be respectively properly and improperly primitive, m and m’ uneven numbers prime to one another and to D, represented by f and $7", the genus of the improperly primitive class, fx f', may be inferred from the number mm’, i.c. it is obtained bythe composition of the generic characters of fand f’. Or, again, if f and f’ be both improperly primitive, so that the class compounded of them is the double of an improperly primitive class, the generic character of this improperly primitive class is obtained by compound- ing those of the two given classes. It follows, from these principles, that the number of classes in any two genera [of the same order] is the same. For if ,, ,,..., be all the classes of any genus of properly or improperly primitive forms, F, a class belonging to any other genus of the same order, and @ a properly primitive class satisfying the equation ®,x@=F,, the classes’ ®,x¢,..-.- nx are all different, and all belong to the genus (F); consequently (F) has at least as many classes as (@), and vice versd (®) has at least as many as (F), i. e. they both contain the same number of classes. 115. Determination of the Number of Ambiguous Classes, and Demon- stration of the Law of Quadratic Reciprocity—The number of actually existing genera of properly primitive forms cannot exceed the number of properly primitive ambiguous classes. For let x be the number of classes in each genus, & the number of actually existing genera, so that kn is the number of properly primitive classes; let also 1, A,, A,, . . . A,-1 be the pro- perly primitive ambiguous classes. Every class produces, by its duplication, a class of the principal genus; and if K be a class of the principal genus 520 REPORT—1862. produced by the duplication of X, K is also produced by the duplication of XxA,, XxA,,.. Xx Aj, but by the duplication of no other class. If, therefore, there be »’ classes in the principal genus which can be produced by duplication, the whole number of properly primitive classes is hxm’, i.e. hn'=kn. But n'Sn, therefore k[C]. There are no properly primitive forms of the type (2B, B, C) unless D=3, mod. 4, or D=0, mod. 8; for one or other of these congruences is implied by the equation D=B (B—2C), because C is uneyen. Resolving D into any two factors relatively prime, if D=3, mod. 4, and haying 2 for their greatest common divisor, if D=0. mod. 8, we take one of them for B, the other for B—2C; and we obtain, in either case, 24+! pro- perly primitive forms of the type (2B, B, C). If BB'=—D,, it is easily seen that the forms (2B, B, C) and (2B’, B’, C')* are equivalent. We may thus diminish by one-half the number of forms of the type (2B, B, C), rejecting those in which [B]>[D]. We conclude, therefore, that if we now denote by p the number of wneven primes dividing D, we have in all 2++? ambiguous forms when D=0, mod. 8, 2 when D=1, or =5, mod. 8, and 24+! in every other case. These ambiguous forms we shall call Q, and we observe that their number is equal to the whole number of assignable generic characters Art. 98). To fn the number of non-equivalent classes in which these forms are contained, we consider separately the case of a positive and of a negative determinant. or a negative determinant, we diminish by one-half the number of the forms by rejecting the negative forms. The remaining forms, if of the type (A, 0, C), are evidently reduced, because AC, an inequality which implies that (C, C—B, C), to which (2B, B, C) is equivalent, is reduced (Art. 92). The number of [positive] ambiguous classes is, therefore, one-half the number of the ambiguous forms Q. For a positive determinant, we deduce from the forms © an equal number of reduced ambiguous forms. Thus (A, 0, C) is equivalent to (A, A, C’); and because [A] the character of which coincides with the character of 6, and therefore with that of the genus (I, I’), is capa- ble of representation by a form of det. D, or (I, I’) is an actually existing genus. If, then, « be the number of particular characters contained in (I, I’) and not in (I), the numbers of actually existing genera and assignable generic characters for the det. D are each 2« times the corresponding numbers for the det. A. It appears from this result that it will be sufficient for our present purpose to consider determinants not divisible by any square. If (a, b, c) be a form of the principal genus of sich a determinant (we suppose that a is prime to D), the equation ax*+ 2bay + cy?=w? is resoluble with values of w prime to ON THE THEORY OF NUMBERS. 523 D; for if a=a'o’, & representing the greatest square divisor of a, the equa- tion e te Dr? — al? is certainly resoluble in relatively prime integers, by virtue of a celebrated theorem of Legendre* ; and the values of £ which satisfy it are prime to D ; peg) ; whence, if «= pa »Y=pn, o=p *, p denoting a multiplier, which renders the values of x, Ys and w integral and relatively prime, the equation ax* + 2bay+cy’=w* will be atisied, and the values of w will be prime to D. The form (¢, 6, c) is therefore equivalent to a form of the type (w’, A; v); and this form 1s produced by the duplication of (w, A, vw) if w be uneven, and of (2w, \+, v') if w be even. 117. Arrangement of the Classes of the principal Genus.—If C be a class of the principal genus, the classes C, C*, C’,. . . will all belong to that genus. And it will be found, by reasoning similar to that employed in Kuler’s second proof of Fermat’s theorem (see Art. 10 of this Report), (1) that the classes 1, C, C?,... are all different until we arrive at a class Cr, equivalent to the principal class; (2) that p is either equal to, or a divisor of, the number » of classes in the principal genus; (3) that if C’=1, 7 is a mul- tiple of ». The p classes C, C*, C®,. . . C+—!, 1, are called the period ¢ of the class C; C is said to appertain to the exponent »; and the determinant is regular or irregular according as classes do or do not exist which appertain to the exponent n. With the former case we may compare the theory of the residues of powers for a prime modulus; with the latter the same theory for a modulus composed of different primes (see Art. 77). (i.) When the determinant is regular, we may take any class appertaining to the exponent n as a basis, and may represent all the classes of the principal genus (to which we at present confine ourselves) as its powers. It will then appear (1) that if d be a divisor of », the number of classes appertaining to the exponent d is ¥ (d); so that, for example, the number of classes that may be taken for a base is y (n): (2) that if ef=n, the equation X*=1 will be satisfied by ¢ classes of the principal genus; and if these classes be repre- sented by A,, A,,...A,, each of the equations X/=A will be satisfied by f different classes of ‘the same genus: (3) that the only classes of the prin- cipal genus which satisfy the equation X*=1 are those which satisfy the equation X7=1, where d is the greatest common divisor of & and n. It will be seen in particular that the equation X’=1 admits of only one, or only two solutions, according as n is uneven or even; 2. é. the principal genus of a regular determinant cannot contain more than two ambiguous classes. To obtain a class appertaining to the exponent n, Gauss employs the same method which serves to find a primitive root of a prime number (Art. 13; Disq. Arith., art. 73, 74), and which reposes on the observation, that if A and B be two classes appertaining to the exponents a and #, neither of which divides the other, and if M, the least common multiple of a and #, be re- solved into two factors p and q, relatively prime and such that p divides a % B and q divides 3, the class A? x B@ will appertain to the exponent M. (ii.) When the determinant is irregular, the classes of the principal genus * Théorie des Nombres, ed. 3, vol. i. p.41; Disq. Arith., art, 294. + These periods of non- equivalent classes are not to be confounded with the periods of equivalent reduced forms of Art. 93. 524 REPORT—1862. cannot be represented by the simple formula C’, and we must employ an expression of the form C,xC,?xC,?.... To obtain an expression thus representing all the classes of the principal genus, we take for C, a class ap- pertaining to the greatest exponent 6, to which any class can appertain; and in general for C, we take a class appertaining to the greatest exponent 6, to which any class can appertain when its period contains no class, except the principal class, capable of representation by the formula 0, x C, Sei C,_1'#-1, The number a=? x6,xX ... 18s called by Gauss the exponent of irregularity ; and similarly we might term &c., the second, n n 0, 6,” 0, 0, 6,” third, &c., exponents of irregularity. From the mode in which the formula C," x C,” x . . is obtained, it can be inferred that 0, is divisible by 6,, 0, by 6,, and so on; whence it appears that a determinant cannot be irregular un- less n be a divisible by a square; nor can it have r indices of irregularity unless ” be divisible by a power of order +1. Moreover, whenever the principal genus contains but one ambiguous class, the determinant is either regular or has an uneyen exponent of irregularity; if, on the contrary, the principal genus contain more than two ambiguous classes, the determinant is certainly irregular, and the index of irregularity even; if it contain 2 ambi- guous classes, the irregularity is at least of order x, and the « exponents of irregularity are all even. A few further observations are added by Gauss. Irregularity is of much less frequent occurrence for positive than for negative determinants; nor had Gauss found any instance of a positive determinant having an uneven index of irregularity (though it can hardly be doubted that such determinants exist). The negative determinants included in the formule, —D=216k+4 27, =1000k+4 75, =1000% 4 675, except —27 and —75, are irregular, and have an index of irregularity divisible by 3. In the first thousand there are five negative determinants (576, 580, 820, 884, 900) which have 2 for their exponent of irregularity, and eight (243, 307, 339, 459, 675, 755, 891, 974) which have 3 for that exponent; the numbers of determinants having these exponents of irregularity are 13 and 15 for the second thousand, 31 and 32 for the tenth. Up to 10,000 there are, possibly, no determinants having any other exponents of irregularity; but it would seem that beyond that limit the exponent of irregularity may have any value. 118. Arrangement of the other Genera.—In the preceding article we have attended to the classes of the principal genus only; to obtain a natural arrangement of all the properly primitive classes, we observe that, if the number of genera be 2, the terms of the product (1+T,)(1+T,)(1+T,)... _ (1+T,,),in which T; represents any genus not already included in the product of the i—1 factors preceding 1+4T;, will represent all the genera. If, then, A,, A,,... A, represent any classes of the genera I'|,T,,. . I’, respectively, and |C| be the formula representing all the classes of the principal genus, the expression |K|=|C| x (1+A,)(1+A,)...(1+A,) supplies a type for a simple arrangement of all the classes of the given determinant. When every genus contains an ambiguous class, it is natural to take for A,,A,,.. A,, the ambi- guous classes contained in the genera T,, l’,,.. I’, respectively. When the principal genus contains two ambiguous classes (and when, consequently, one-half of the genera contain no such classes), let C, be the class taken as base (or, if the determinant be irregular, as first of the bases) in the arrange- Oe a | ON THE THEORY OF NUMBERS. 525 ment of the classes of the principal genus, and let Q,7=C,; it may then be shown that Q, will belong to a genus containing no ambiguous class, and that the formula |K|=|C| x (1+Q,) (1+A,)...(1+A,),im which A,,.. A,, are ambiguous classes, represents all the classes*, In general, if the principal genus contain 2 ambiguous classes (a supposition which implies that the determinant is irregular, having « even exponents of irregularity, and that there are only 24—-« genera containing ambiguous classes)—let Q,’=C, ; 0,7=C,;...0,2=C,—it will be found that all the classes are represented by the formula |K!=|C| x (1+@,) (1+Q,) ..(1+Qc) (1+ Asi). . (1+A,), in which A,4;,...A, are ambiguous classes, and Q,, Q, . . . Qe classes belonging to genera containing no ambiguous class . A similar arrangement of the improperly primitive classes (when such classes exist) is easily obtained. Let 3% denote the principal class of im- : att D—1 properly primitive forms, 7. ¢. the class containing the form (2, jie "5*); we have seen (Art. 113) that the number of properly primitive classes which, compounded with 3, produce 3, is either one or three. When there is only one such class, the number of improperly primitive classes is equal to that of properly primitive classes; and if |K| be the general formula representing the properly primitive classes, the improperly primitive classes will be repre- sented by 3x|K|. When there are three properly primitive classes, which, compounded with ¥, produce 3, the principal class will be one of them, and if @ be another of them, ¢” will be the third; also ¢ and q* will belong to the principal genus, and will appertain to the exponent 38. When the deter- minant is regular, instead of the complete period of classes of the principal genus, 1, C, C?,.. C"-1, we take the same series as far as the class 0" exclusively ; when the determinant is irregular, we can always choose the bases C,, C,, . . in such a manner that the period of one of them shall con- tain @ and ¢’, and this period we similarly reduce to its third part by stop- ping just before we come to ¢ or 9’. Employing these truncated periods, instead of the complete ones, in the general expression for the properly pri- mitive classes, we obtain an expression, which we shall call |K’|, representing a third part of the properly primitive classes, and such that = x |K’| represents all the improperly primitive classes. 119. Tabulation of Quadratic Forms,—In Crelle’s Journal, vol. Lx. p. 357, Mr. Cayley has tabulated the classes of properly and improperly primitive forms for every positive and negative determinant (except positive squares) up to 100. The classes are represented by the simplest forms contained in them+; the generic character of each class, and, for positive determinants, the period of reduced forms (Art. 93) contained in it, are also given. The * Gauss employs a class Q, producing C, by its duplication, both when one and when two ambiguous classes are contained in the principal genus. The number of classes re- quisite for the construction of the complete system of classes is therefore in either case, since C, may be replaced by Q?,. + The principles employed by Gauss for the arrangement of the classes of a regular determinant are extended in the text to irregular determinants. If the determinant have x! uneven exponents of irregularity, the number of classes requisite for the construction of the complete system of classes is x+-x’. + The simplest form contained in a ciass is that form which has the least first coefli- cient of all forms contained in the class, and the least second coefficient of all forms con- tained in the class and having the least first coefficient. Ifa choice presents itself between two numbers differing only in sign, the positive number is preferred. In the case of an ambiguous class of a positive determinant, the simplest ambiguous form contained in the class is taken as its representative. 526 : REPORT—1862., arrangement of the genera and classes is in accordance with the construction of Gauss, explained in the preceding articles; and the position of each class in the arrangement is indicated by placing opposite to it, in a separate column, the term to which it corresponds in the symbolic formula (such as |K| or 3 x |K}) which forms the type of the arrangement, To the two Tables of positive and negative determinants Mr. Cayley has added a third, containing the thirteen irregular negative determinants of the first thousand. In a letter addressed to Schumacher, and dated May 17, 1841, Gauss expresses a decided opinion of the uselessness of an extended tabulation of quadratic forms. “If, without having seen M. Clausen’s Table, I have formed a right conjecture as to its object, I shall not be able to express an opinion in fayour of its being printed. If it is a canon of the classification of binary forms for some thousand determinants, that is to say, if it is a Table of the reduced forms contained in every class, I should not attach any importance to its publication. You will see, on reference to the Disq. Arith. p- 521 (note), that in the year 1800 I had made this computation for more than four thousand determinants ” [viz. for the first three and tenth thou- sands, for many hundreds here and there, and for many single determinants besides, chosen for special reasons]; ‘‘ I have since extended it to many others ; but I have never thought it was of any use to preserve these developments, and I have only kept the final result for each determinant. For example, for the determinant —11,921, 1 have not preserved the whole system, which would certainly fill several pages *, but only the statement that there are 8 genera, each containing 21 classes. Thus, all that I have kept is the simple state- ment viii. 21, which in my own papers is expressed even more briefly. I think it quite superfluous to preserve the system itself, and much more so to print it, because (1) any one, after a little practice, can easily, without much expenditure of time, compute for himself a Table of any particular determi- nant, if he should happen to want it, especially when he has a means of yerification in such a statement as vill. 21; (2) because the work has a cer- tain charm of its own, so that it is a real pleasure to spend a quarter of an hour in doing it for one’s self; and the more so, because (3) it is very seldom that there is any occasion to do it....... My own abbreviated Table of the number of genera and classes I have never published, principally because it does not proceed uninterruptedly.” + Probably the third of Gauss’s three reasons will commend itself most to mathematicians who do not possess his extraordinary powers of computation. An abbreviated Table of the kind he describes, extending from —10,000 to +10,000, would occupy only a very limited space, and might be computed from Dirichlet’s formule for the number of classes (see Art. 104), without constructing systems of repre- sentative forms. But it would, perhaps, be desirable (nor would it increase the bulk of the Table to any enormous extent) to give for each determinant not only the number of genera, and of classes in each genus, but also the elements necessary for the construction, by composition only, of a complete system of all the classes. For this purpose it would not be necessary to specify (by means of representative forms) more than 5 or 6 classes,’ in the case of any determinant within the limits mentioned. * Mr. Cayley’s Table of the first hundred negative determinants occupies about four pages of Crelle’s Journal; the determimant —11,921 would occupy about one page, + Briefwechsel zwischen C. F. Gauss und H. C. Schumacher, yol. iv. p. 30. A CATALOGUE OF OBSERVATIONS OF LUMINOUS METEORS. 527 Report on Observations of Luminous Meteors (ante, pp. 1-81). Apprennix I.—E#rrata. (1) p. 35, December 8, Dundee. Column Appearance, &c. For A spear- head-like crescent moon, &c. read A spearhead; like crescent moon, &c. (2) p. 41, December 24, London. Column Direction, &c. Insert the words Radiant point Aldebaran. (3) p. 43, December 27, 8° 57" p.m. Colwmn Appearance, &c. For Track ending, &c. read Track enduring, &c. (4) p. 57, April 29, 11" 55™ p.m. Column Appearance, &e. Read thus— Left no track. Brilliance vanished suddenly at b Lacertee. Remaining 12° of the course light red (Mars at maximum robbed of his rays), very intermittent and vacillating, died out, 2:3 seconds. (5) p. 64, August 12,11" 9" p.w. Column Position, &e. Omit the words short of the second. (6) From five accounts of the meteor 1862, September 19, the following is a calculation of its path :— At London, after explosion overhead, the meteor proceeded a considerable distance towards 69° W. of N. At Nottingham the meteor passed sixty-three miles over London, seeking an earth-point 42° W. from S$. At Hay (South Wales) the meteor passed fifty-seven miles over London, seeking an earth-point 70° E. from 8. At Torquay the meteor passed 573 miles over London, seeking an earth- point 9° K. from N. At Hawkhurst the meteor passed forty-seven miles over London, seeking an earth-point 66° W. from N. An earth-point seven miles S.W. from Hereford satisfies the observations in the following manner :— London, 70° W. from N. (observed 69° W. from N.). Nottingham, 46° W. from S. (observed 42° W. from 8.). Hay, 70° E. from §. (observed 70° E. from S.). ‘Torquay, 14° E. from N. (observed 9° FE. from N.). Hawkhurst, 62° W. from N. (observed 66° W. from N.). The errors of observation being in no case greater than 5°, from the calculated bearings. A ground-point so close to Hay sufficiently explains anomalies in the observation at that place ; but its distance is on the other hand 120 miles from London, where the meteor appears to have been fifty-six miles above the earth. The path of the meteor was therefore inclined downwards, from 25° above the horizon towards 70° W. of N. A visible flight of 115 miles, from eighty-three miles over Canterbury to thirty-three miles over Oxford, per- formed in three to four seconds of time, is the result obtained from the comparison of these observations. x = n~ tit capi walt o( 1B besa Ink) ean AE: 7 Wey kes ‘we nitete i yo te . in co > as sodam ak tp a BEA te ait i fos My £ + to “noiafre hts avis an fe ae P§re< - “28 MUA vi P pw = . F ayy - hl emer I t ‘) } 4 ] ae Pp, , wii mis i% 4th v; s . " raik uf Ra, e ~~ wid = Py - tf . i = | . ‘ ’ ,. - , d ’ x 7 : i jis , Lyre. 2 phe tlt ot rigwai eg tie ange ¥ : 7 es 4 7 — - Te.) \ ins 7 Wr Mate Ae + WN ee TPA ae ‘er : = tg at, " a 7 a ae ae — Ti te i ao - He ae Fy : aeiaey 5 < v aT NOTICES AND ABSTRACTS OF MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. BTOMTAGA GHA eTOITOM “i +10 “ih ‘ % es et aa PO: ee | ‘MMOS INT OT aKOITAITAUMUOD NOTICES AND ABSTRACTS OF MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. MATHEMATICS AND PHYSICS. MatTHEMATICS. Address by G. G. Stoxns, M.A., F.RS. Sc., Lucasian Professor of Mathematics in the University of Cambridge. {r has been customary for some years, in opening the business of the Section, for the President to say a few words respecting the object of our meetings. In this Sec- tion, more perhaps than in any other, we have frequently to deal with subjects of a very abstract character, which in many cases can be mastered only by patient study, at leisure, of what has been written. The question may not unnaturally be asked—If investigations of this kind can best be followed by quiet study in one’s own room, what is the use of bringing them forward in a sectional meeting at all? I believe that good may be done by public mention, in a meeting like the present, of even somewhat abstract investigations; but whether good is thus done, or the audience are merely wearied to no purpose, depends upon the judiciousness of the person by whom the investigation is brought forward. It must be remembered that minute details cannot be Slowed in an exposition vird voce; they must be studied at leisure ; and the aim of an author should be to present the broad leading ideas of his research, and the principal conclusions at which he has arrived, clearly and briefly before the Section. It is then possible to discuss the subject-matter; to offer suggestions of new lines of experiment, or new combinations of ideas; and such discussions and suggestions, it seems to me, are among the most import-— ant business of a meeting such as this, Any one who has worked in concert with another zealously engaged in the same research must have felt the benefit arising from the mutual interchange of ideas between two different minds. Sug- gestions struck out by one call up new trains of thought and fructify in the mind of another; whereas they might haye remained barren and unfruitful in the mind of the original suggester. The benefit of cooperation is by no means confined to the one bed out, according to a preconcerted plan, of a research involving labour rather than invention; it is felt in a most delightful form in the procecution of original investigations. In a meeting like the present, we have the benefit of the mutual suggestions, not of two, but of many persons, whose minds are directed to the same object. The number of papers already in the hands of your Secretaries shows that there will be no lack of matter in this Section: the difficulty will rather, I apprehend, be to get through the business before us in the time prescribed. On this account the Section will, I hope, bear with me if I should sometimes feel my- self compelled, in justice to the authors of papers which are placed later on our lists, to cut short reusetons which otherwise might have been further prolonged with some interest. 1862. 1: 2 REPORT—1862. On Capillary Attraction. By the Rey. F. Basnrortu, B.D. The theories of capillary action brought forward by Laplace, Young, and Poisson lead to the same form of differential equation to the free surface of a drop of fluid. During the last fifty years many attempts have been made to compare theory and experiment, but the results arrived at seem to be quite unsatisfactory. The expe- riments have generally been made by measuring the heights to which fluids rose in capillary tubes. The smaller the diameter of the tube, the greater is the elevation or depression of a fluid; but at the same time it becomes more difficult to secure a bore of a perfectly circular section and a surface perfectly clean. Laplace attempted to test his theory by comparing the measured thickness of large drops of mercury with their theoretical thickness obtained by an approximate solution of his differential equation. After duly considering all the circumstances of the case, it appeared to the author that the forms assumed by drops of fluid, of small or moderate size, afforded the best means for testing the theory of capillary action. The drops of fluid may rest on horizontal planes which they do not wet, or they may hang below horizontal surfaces which they do wet. Extensive tables have been calculated, which give the exact theoretical forms of all drops of fluid resting upon horizontal planes, as mercury on glass, within the limits of size to which it seems desirable to restrict experiments. n order to determine the exact forms of drops of fluid, a microscope has been mounted so that it can be moved horizontally or vertically by micrometer screws provided with divided heads. In th2 focus of the eyepiece are two parallel hori- zontal and two parallel vertical lines, .orming by their intersections a small square in the centre. The lines are purposely made rather thick in order that they may be seen without difficulty, and before reading off the screw-head divisions, care is taken to cause the image of the outline of the drop to pass through the middle point of the square caused by the intersection of the cross lines. Thus the co- ordinates are obtained of as many "a as may be thought necessary, and after- wards the form of a section of the drop, passing through the axis of its figure, may be drawn by a scale of equal parts. By trial, a theoretical form must be fitted to this experimental form, using the tables. When this is satisfactorily accomplished, the value of Laplace’s a is known, as well as the value of 6, the radius of curvature at the vertex: a determines the theoretical form of the drop, and 0 its size. Only one or two satisfactory measurements have been made at present, but suffi- cient has been done to show that such values may be assigned to the constants as to secure a most exact agreement of the theoretical with the experimental form of the free surface of a drop of fluid resting on a horizontal plane. It remains to he seen whether a is constant for drops of all sizes of the same fluid at the same tem- perature. If experiment be found to agree with theory, then the effect of a variation of temperature upon a must be determined. ' This method of proceeding affords the means of determining with great accuracy the angle of contact, because the tables calculated from theory give the coordi- nates for points, where the inclination of the tangent to the horizon is known, at intervals of one degree, and parts of a degree can be calculated for by proportional arts. If the experiments on mercury appear to confirm theory, it will be desirable to complete the tables for the forms of pendent drops of fluid, because it will be very difficult, if not impossible, to find supporting planes which such fluids as oils, water, spirit of wine, &c. do not wet or adhere to. In such case it appears to be possible to make use of pendent drops alone for the determination of a. When a has been determined for each of two fluids, as spirit of wine and oil, it will be desirable to examine the mutual action at their common surfaces, which may be done by measuring the forms of drops of one fluid immersed in a bath of the other fluid con- tained in a cell having parallel and transparent vertical sides and horizontal planes at the top and bottom. _ Since the differential equations of Laplace and Poisson are the same in form, it ‘is evident that the above measurements for a single fluid cannot decide the difference between them. It seems, however, manifest that the constitution of the surface is very different from the interior of a fluid, But the thiclmess of this surface of TRANSACTIONS OF THE SECTIONS. 3 supposed variable density is so small as to be insensible. Since there is a certain elastic force of vapour in contact with its fluid corresponding to every temperature, may we not assume that the density of this indefinitely thin envelope may vary from the density of the fluid inside to the density of the vapour outside ? On the Differential Equations of Dynamics. By Professor Boots, F.R.S. Referring to the reduction, by Hamilton and Jacobi, of the solution of the dyna- mical equations to that of a single non-linear partial differential equation of the first order, and to that, by Jacobi, of the latter to the solution of certain systems of linear partial differential equations of the first order,—the author showed, Ist, how, from an integral of one equation of any such system, a common integral of all the equations of the system could, when a certain condition dependent upon the pro- perties of symmetrical gauche determinants is satisfied, be deduced by the solution of a single ordinary differential equation of the first order susceptible of being made integrable by means of a factor; 2ndly, how the common integral could be found when this condition was not satisfied. On an Instrument for describing Geometrical Curves ; invented by H. Jounston, described and exhibited by the Rev. Dr. Boorn, F.R.S. This instrument supplies a want which has been felt by architects and sculptors. By its help, geometrical spirals of various orders may be described with as much manual facility as a circle may be drawn on paper by a common compass. On a Certain Curve of the Fourth Order. By A. Caxuny, F.R.S. The curve in question is the locus of the centres of the conics which pass through three given points and touch a given line; if the equations of the sides of the triangle formed by the three points are z=0, y=0, z=0, these coordinates being such that 2+-y+2=0 is the equation of the line infinity, and if ar+fy+yz=0be the equation of the given Jine, then (as is known) the equation of the curve is Vax (y+2—2) + V By GF2—y) + Veet y—)=0. The special object of the communication was to exhibit the form of the curve in the case where the line cuts the triangle, and to point out the correspondence of the positions of the centre upon the curve, and the point of contact on the given line. On the Representation of a Curve in Space by means of a Cone and Monoid Surface. By A. Carter, £.R.S,. The author gave a short account of his researches recently published in the ‘Comptes Rendus.’ The difficulty as to the representation of a curve in space is, that such a curve is not in general the complete intersection of two surfaces ; any two surfaces passing through the curve intersect not only in the curve itself, but in a certain companion curve, which cannot be got rid of; this companion curve is in the proposed mode of representation reduced to the simplest form, viz. that of a system of lines passing through one and the same point. The two surfaces employed for the representation of a curve of the mth order are, a cone of the nth order haying for its vertex an arbitrary point (say the point r=0, y=0, s=0), and a monoid surface with the same vertex, viz. a surface the equation whereof is of the form Qw—P=0, P and Q being homogeneous functions of (x, y, 2) of the degrees p and p—lrespectively (where p is at most=x—1). The monoid surface contains upon it p (p—1) lines given by the equations (P=0, Q=0); and the cone passing through n( p—1) of these lines (if, as above supposed, p >> n—1, this implies that some of these lines are multiple lines of the cone), the monoid surface will besides intersect the cone in a curve of the th order, On the Curvature of the Margins of Leaves with reference to thei Growth. By W. Esson, M.A. Leaves have a right and left margin on each side of their axis, These margins + A REPORT—1862. are of different lengths, but of the same shape. The length differs owing to circum- stances of growth, such as the left margin being next the stem or next a leaflet, forming with it a composite leaf. The curvature of the margin has been ascertained im many instances to be that of the reciprocal spiral r=5): In some leaves the pole of curvature lies on the axis, in others in the body of the leaf, and in others entirely outside the leaf. If the leaflets of a composite leaf have this curvature, their extreme points lie on a reciprocal spiral (e. g. the horse-chestnut leaf). It is probable that more irregular leaves have margins which are merely modifications of the reciprocal spiral or other spirals, such as the Lituus ro ‘ The growth of a margin may be represented by increments of an are of the spiral cut off by an increasing chord or radius vector. By this means may be accurately determined the growth of a leaf under given circumstances of soil, tem- perature, and moisture. It is only necessary to register the amount of angular rotation of the radius vector of the spiral. Quaternion Proof of a Theorem of Reciprocity of Curves in Space. By Sir Wit11am Rowan Hamitron, LL.D. sc. Let ¢ and y be any two vector functions of a scalar variable, and ¢',y', 6", p" their derived functions, of the first and second orders. Then each of the two systems of equations, in which c is a scalar constant, 4 (1).... Sép=e, Sp'p=0, Sp"y=0, (2) se ee Syo=c, Sy'o=0, Sy"o=0, or each of the two vector expressions, BY. rea bistaex ees AY) sa gis Nt eo | ORE tae (os SEE includes the other. If then, from any assumed origin, there be drawn lines to represent the recipro- cals of the perpendiculars from that point on the osculating planes to a first curve of double curvature, those lines will terminate on a second curve, from which we can return to the first by a precisely similar process of construction. And instead of thus taking the reciprocal of a curve with respect to a sphere, we may take it with respect to any surface of the second order, as is probably well lnown to geometers, although the author was lately led to perceive it for himself by the very simple analysis given above. On a certain Class of Linea\Differential Equations. By the Rev. Rosert Harrey, F.R.A.S. TuEorEM,—From any algebraic equation of the degree n, whereof the coefficients are functions of a variable, there may be derived a linear differential equation of the order n—1, which will be satisfied by any one of the roots of the given algebraic equa- tion. The differential equation so satisfied is called, with respect to the algebraic equation, its “ differential resolvent.”’ The connexion of this theorem, which is due to Mr. Cockle, with a certain general process for the solution of algebraic equations, led the author to consider its application to the two following trinomial forms, viz. Yany+(NH=DeHO. cee ween es eee GC) y"—ny"—14+(n—1)2=0, ...... leds OPA ee) to either of which any equation of the mth degree, when x is not greater than 5, can, by the aid of equations of inferior degrees, be reduced. The several differential resolyents for the successive cases n=2, 3, 4, 5 were calculated; and by induction the general differential resolvents were formed. © Following Professor Boole’s symbolical process and using the ordinary factorial notation, that is to say, repre- senting (n) (n—1) (2-2)... (w—7r+1) TRANSACTIONS OF THE SECTIONS. 5 by [n]", the differential resolvent of (I.) was found to take the form a ad n—-1,,_¢,—1)n-1[ _%_, @ _ 2n—1)*-F n-th, n Lez | 1 as ) a Ee aI xv y=[1] [m 1] Lees (A) In like manner, the differential resolvent of (II.) was found to be n—1 d2-1 d d AEA ig n-1 n [@ Dee | y—(n—1) (na —n—1) na —2 | gy=[n—1] aie,» (B) Every differential resolvent may be regarded under two distinct aspects. It may be considered either, first, as giving in its complete integration the solution of the algebraic equation from which it has been derived; or, secondly, as itself solvable by means of that equation. In the first aspect the author has considered the differential equation (A) in a paper entitled “ On the Theory of the Transcendental Solution of Algebraic Equations,” just published in the ‘Quarterly Journal of Pure and.Applied Mathematics,’ No. 20. In the second aspect every differential resol-- vent of an order: higher than the second gives us, at least when the dexter of its defining equation vanishes, a new primary form, that is to say, a form not recognized as primary in Professor Boole’s theory. And in certain cases in which the dexter does not vanish, a comparatively easy transformation will rid the equation of the dexter term, and the resulting differential equation will be of a new primary form. On the Volumes of Pedal Surfaces. By T, A. Hirst, F.2B.S, The pedal surface being the locus of the feet of perpendiculars let fall from any point in space, the pedal origin, upon all the tangent planes of a given fixed primi- tive surface, will, of course, vary in form as well as in magnitude with the position of its origin. If, however, the volume of the pedal be considered as identical with that of the space swept by the perpendicular, as the tangent plane assumes all pos- sible positions,—a definition which will apply to unclosed as well as to closed pedals,—the following two general theorems may be enunciated:—1l. Whatever may be the nature of the primitive surface, the origins of pedals of the same volume are, in general, situated on a surface of the third order. 2. The primitive surface being closed, but in other respects perfectly arbitrary, the origins of pedals of constant volume lie on a surface of the second order; and the entire series of - such surfaces constitutes a system of concentric, similar, and similarly-placed qua- drics, the common centre of all being the origin of the pedal of least volume. On the Exact Form and Motion of Waves at and near the Surface of Deep Water. By Wri11am Joun Macevorn Ranuine, C.L., LL.D., F.RASS. L. & E. §e. The following is a summary of the nature and results of a mathematical inyesti- gation, the details of which have been communicated to the Royal Society. The investigations of the Astronomer Royal and of Mr. Stokes on the question of straight-crested parallel waves in a liquid proceed by approximation, and are based on the supposition that the displacements of the particles are small compared with the length of a wave. Hence it has been legitimately inferred that the results of those investigations, when applied to waves in which the displacements are con- siderable as compared with the length of wave, are only approximate. In the present paper the author proves that one of those results—viz. that in very deep water the particles move with a uniform angular velocity in vertical circles whose radii diminish in geometrical progression with increased depth, and conse- quently that surfaces of equal pressure, including the upper surface, are trochoidal— is an exact solution for all possible displacements, how great soever. The trochoidal form of waves was first explicitly described by Mr. Scott Russell ; but no demonstration of its exactly fulfilling the cinematical and dynamical condi- tions of the question has yet been published, so far as the author knows. In ‘A Manual of Applied Mechanics’ (first published in 1858), the author stated that the theory of rolling waves might be deduced from that of the positions assumed by the surface of a mass of water revolving in a vertical plane about a 6 REPORT—1862. horizontal axis; but as the theory of such wayes was foreign to the subject of the book, he deferred until now the publication of the investigation on which that statement was founded. ae Having communicated some of the leading principles of that investigation to My. William Froude in April 1862, the author was informed by that gentleman that he had arrived independently at similar results by a similar pees although he had not published them. The introduction of Proposition I. between Propositions I. and III. is due to a suggestion by Mr. Froude. The following is a summary of the leading results demonstrated in the paper :— Proposition 1.—In a mass of gravitating liquid whose particles revolve uniformly in vertical circles, a wavy surface of trochoidal profile fulfils the conditions of uni- formity of pressure,—such trochoidal profile being generated by rolling, on the under side of a horizontal straight line, a circle whose radius is equal to the height of a conical pendulum that revolves in the same period with the eaters of liquid. ‘Proposition 11.—Let another surface of uniform pressure be conceived to exist indefinitely near to the first surface: then if the first surface is a surface of con- tinuity (that is, a surface always traversing identical particles), so also is the second surface. (Those surfaces contain between them a continuous layer of liquid.) Corollary—The surfaces of uniform pressure are identical with surfaces of con- tinuity throughout the whole mass of liquid. Proposition I1I.—The profile of the lower surface of the layer referred to in Pro- position II. is a trochoid generated by a rolling circle of the same radius with that which generates the upper surface ; and the tracing-arm of the second frochoid is shorter than that of the first trochoid by a quantity bearing the same proportion to the depth of the centre of the second rolling circle below the centre of the first rolling circle, which the tracing-arm of the first rolling circle bears to the radius of that circle. Corollaries.—The profiles of the surfaces of uniform pressure and of continuity form an indefinite series of trochoids, described by equal rolling circles, rolling with equal speed below an indefinite series of horizontal straight lines. The tracing-arms of those circles (each of which arms is the radius of the circular orbits of the particles contained in the trochoidal surface which it traces) diminish in geometrical progression with a uniform increase of the vertical depth at which .the centre of the rolling circle is situated. The preceding propositions agree with the existing theory, except that they are more comprehensive, being applicable to large as well as to small displacements. The following is new as an exact proposition, although partly anticipated by the approximative researches of Mr. Stokes :— PropositionTV.—The centres of the orbits of the particles in a given surface of equal pressure stand at a higher level than the same particles do when the liquid is still, by a height which is a third proportional to the diameter of the rolling circle and the length of the tracing-arm (or radius of the orbits of the particles), and which is equal to the height due to the velocity of revolution of the particles. Corollaries.—The mechanical energy of a wave is half actual and half potential— half being due to motion, and half to elevation. The crests of the waves rise higher above the level of still water than their hollows fall below it; and the difference between the elevation of the crest and the depression of the hollow is double of the quantity mentioned in Proposition II. The hydrostatic pressure at each’ individual particle during the waye-motion is the same as if the liquid were still.’ * In an Appendix to the paper is given’ the investigation of the problem, to find approximately the amount of the pressure required to overcome the friction between a trochoidal waye-surface and a wave-shaped solid in contact with it. The appli- cation of the result of this investigation to the resistance of ships was explained in a paper read to the British Association in 1861, and published in various engineering journals in October of that year. The following is the most conve- nient of the formule arrived at:—Let w be the heaviness of the liquid; f the coefficient of friction; gy gravity; v the velocity of advance of the solid; L its length, being that of a wave; 2 the breadth of the surface of contact of the solid and liquid; 8 the greatest angle of obliquity of that surface to the direction of advance a TRANSACTIONS OF THE SECTIONS, 7 of the solid; P the force required to overcome the friction; then 4 ase poly Lz (144sin? B-+sin4 8). In ordinary cases, the value of f for water sliding over painted iron is 0036. The quantity Is z (144 sin? 6+ sin‘ 8) is what has been called the “ augmented surface,” In practice, sin‘ 6 may in general be neglected, being so small as to be unimportant. Some Account of Recent Discoveries made in the Calculus of Symbols. By W. H. L. Rosser, A.B. Before the publication of Professor Boole’s memoir on a “General Method in Analysis,” which appeared in the ‘Philosophical Transactions’ for 1844, those mathematicians who adopted the symbolical methods suggested by the researches of Lagrange and Laplace, confined themselves to the use of commutative symbols, and the science was consequently very limited in its applications. It received a fresh impulse from the very remarkable memoir of Professor Boole mentioned above, in which an algebra of non-commutative symbols was invented and applied to the integration of a large class of linear differential equations. It occurred to the author that the proper method of extending the calculus was to construct systems of multiplication and division for functions of non-commutative symbols. This he Pitingly effected in his memoir published in the ‘Philosophical Transactions’ for 1861. “As the symbols are non-commutative, two distinct systems of multi- — and division, internal and external, arise for each class of symbols em- oyed. q Let p and r be two symbols combining according to the law F (n). pm=pmf (x-+m), where f (7) is any function of (m), then he gave, in the memoir alluded to, equa- tions to determine the conditions that a symbolical function such as pr dy (m) +p" bya (m) +P” bn—a (a) + &e. +h (m7) may be divisible internally and externally without a remainder by the symbolical function py, (7)+, (7), where Pn (7) Pr—r (7); Pn—a (F) +++ Po (m7), Pr (w) and y, (7) are all rational functions of (z), or, in other words, that py, (+) +, (7) may be an internal or external factor of p* (m)+p"—' hy _1(7)+ &e., and also an equa- tion to determine the condition that y, (p) «7+ (p) may be an internal factor of h: (p) +m +h. (p) m+, (p) «m+ (p): He then gave some theorems for the transformation of certain functions of these symbols, which lead to some very curious theorems in successive differentiation : he has treated this part of the subject more fully in the ‘ Philosophical Magazine’ for April 1862. In a subsequent part of his paper in the ‘Philosophical Transac- tions,’ he established binomial and multinomial theorems for these symbols, by showing how to expand (p?+ pO ())” and (p%+p*—? 8, (7)+p*? 6, (7) + ....)” in terms of (p) and (7). At the end of the paper he gave some methods for solving differential equations by a process analogous to the “Method of Divisors” in the theory of algebraical equations. In his second memoir “On the Calculus of Symbols,” published in the ‘ Philosophical Transactions’ for 1862, he has shown how we may find the highest common internal divisor of functions of non-commutative symbols, and also how we may resolve them in all possible cases into two equal factors, a process analogous to that for extracting the square root in common algebra. He then in- vestigated the theory of multiplication in this calculus more generally. He gave a rule to find the symbolical coefficient of p™ in a continued product of the form (p+, ()) (p45 (m)) (p+4, (7) vvsseees (P4On (H)): After this he resumed the consideration of the binomial and multinomial theorems explained in the former memoir, He gave the numerical calculation of the coefti-~ 8 REPORT—1862. cients of the general term of the binomial theorem, as explained in the first memoir. In this the expansion was effected in terms of p and 7, but we may suppose the expansion effected in terms of (p) alone. In that case the coefficient of the general term would be symbolical, and a function of (7). He had calculated its value in the memoir, and also the value of the corresponding general symbolical coefficient in the multinomial theorem supposed expanded in powers of p alone. He concluded the paper by giving a method to expand the reciprocal binomial (7?+ 6 (p) dz)” in terms of (7). The general cases of division yet remained to be worked. This has been effected by Mr. Spottiswoode in a very able and beautiful paper published in the ‘Philosophical Transactions’ for 1862. He has there given in full the division of gn (p) a" + pn—1 (p) 7"! +hn—2(p) 7” 7 +.&C, «+ +, (p) internally and externally by W, (p) 7+, (p); secondly, the division of Pn (P)™ +Pn—1(p) + Pn—a (p) "bese + tho (P) internally and externally by Ym (p) + m_1 (p) + Yn—o (p): 7-3-4. os Wo (p) 5 thirdly, the division of p” Pn (7) +p"—" Pay (m)+p"~" bn» (m)+. 3" +, (7) internally and externally by OPV (+P n—1 (7) +p” Wma (4) ++ +++ Yo (m7) He has fully investigated the conditions that the divisor in each case may be an internal or external factor of the dividend, and his results, which are expressed by means of determinants, will be found extremely interesting. The author in conclu- sion states that he believes the form in which the calculus now stands will be per- manent, and that subsequent improvements will be very much based on extending sees of multiplication and division to other symbolical expressions, in which the laws of symbolical combination are different from those here assumed, On some Models of Sections of Cubes. By C. M. Wrtttcn. These were carefully-executed models, designed to illustrate certain simple pro- positions in solid geometry relative to the volumes, &c. of solids formed by the section of a cube by planes. The author wishes, at the same time, to place on record the simple fraction 444, which gives an extremely close approximation to the side of a square equal in area to a circle of which the diameter is unity. ASTRONOMY. Some Cosmogonical Speculations. By Isaac Asun, VB. The author considered that the present planiform condition of the system dis- proved the common view that it had formerly been a gaseous sphere, and proved that it had originally been a liquid plane, as Batarnts rings are at present; nor yet in a heated condition, since he thought that, though capable of transformation, heat could no more be absolutely Jost than its equivalent, motion. The planets had, doubtless, been originally molten; but this heat the author ascribed to the collision of particles, during their formation, from the liquid plane described. This formation he ascribed to the development of a centre of attraction in the liquid plane, and showed how, in a revolving plane, a diurnal rotation from west to east might hence be originated, the particles so attracted acting as a mechanical “couple” of forces on the planet during its formation. From the distance between the interior and exterior planets, he inferred the former existence of two rings, as in the system of Saturn, the asteroids being probably formed from small independent portions of matter between these rings. He considered that the planets also first existed in- dividually as planes, basing this view on the uniformity of plane observed in the — — TRANSACTIONS OF THE SECTIONS. 9 orbits of the satellites, The satellites themselves he considered to have been formed from portions of matter left behind during the contraction into a globe of such a plane, which had at first occupied the whole space included within the pre- sent orbits of the satellites. This view of the formation of the satellites he based on the fact that the period of diurnal rotation in each of them corresponded with the period of its revolution round its primary, which he showed would be the case with any body whatever, if so left behind or lifted off a planet. The author then discussed the chemical changes that would ensue on the surface of the earth after it had assumed the globular form. Oxidization of its metallic constituents would absorb a vast proportion of its gaseous matter, and the forma- tion of water would remove a great deal in addition. Hence the absence of atmo- sphere or water on the moon’s surface might be accounted for, as she would carry oif with her only j;th portion of the gaseous elements of the planet, and her sur- face exposed to the chemical action of those elements would be much more than sth that of the earth. Water also might be quite absorbed on her surface in the formation of hydrates of the alkaline and earthy bases. On the earth, sodium would unite with chlorine, and common salt would result; and to the large amount of salt so formed the author ascribed the saltness of the ocean; rivers could only carry to the sea salt obtained from soil originally deposited by the ocean, and which must therefore have derived its salt from the sea. This rocess must be still going on, and hence Dr. Ashe inferred that the sea could never ave become salt, or be now increasing in saltness, from that cause; hence he dis- sented from that view, which was the one universally put forward by geologists, On a Group of Lunar Craters imperfectly represented in Lunar Maps. By W. R. Bret, FLAS. One of the objects of lunar maps should undoubtedly be such a representation of the forms of the irregularities of the moon’s surface, that a student may readily, at the switable epochs, ascertain the general outlines and configurations of the parts as hs he is studying, so as to be certain that he has not misapprehended either the position or form of any particular portion of the lunar surface. A map constructed for a given epoch, at the full for instance, that shall give those features by which every crater, mountain-chain, and plain may be instantly recog- nized, is at the present moment a desideratum. Indeed, on such a map some craters would not find place, A certain angle of illumination is necessary to bring out saliently the distinguishing features of a crater or mountain-chain; and a series of maps that would exhibit each to the best advantage, must include as many distinct epochs of illumination in their construction as there are meridians encircling the lunar globe. One of the greatest monuments of the skill and industry characterizing astrono- mical science is undoubtedly Beer and Méidler’s large map of the Moon. To the student of selenography it is invaluable; his progress would be slow without it. The writer of this paper cannot, however, agree with Crampton “that every mountain and every valley, every promontory and every defile on the moon’s surface, finds its representative on that map.” On the contrary, in his examination of the lunar surface, he has met with several instances of features not recorded thereon, a recent instance of which forms the subject of the present paper. In the neighbourhood of a fine chain of craters that come into sunlight from ten to thirteen days of the moon’s age, and are well seen under the evening illumination from twenty-one to twenty-four days of the moon’s age, lying in the northern regions of the moon from 57° to 74° N. Lat., and from 25° to 50° J E Long., and designated Philolaus, Anaximenes, and Anaximander, with an unnamed crater between Anaxi- menes and Anaximander, are three crater-form depressions, of which there are nume- rous examples on the moon’s surface,—the usual characteristics being, Ist, an extensive floor, exhibiting a variety of surface in different specimens, often pierced with small craters and diversified with hills; 2nd, a more or less perfect rampart, here and there pierced with craters, and rising into elevated peaks, so that the entire depression is readily recognized as a distinct formation, completely separated from its surrounding neighbours. Two such depressions, lying nearly in the same meridian, and connected by a table-land or plateau, are very imperfectly, if at all, 10 REPORT—1862. represented by the German selenographers. The sketch accompanying this com- munication, taken at Hartwell, on Sept. 18, 1862, under the evening illumination, exhibits the general characters of the northern depression, viz. a floor pierced by a line of eruption (a common feature in several lunar forms), a nearly continuous rampart on the east and west sides, rising into a considerable mountain mass at the north angle marked B by Beer and Midler, pierced by the crater Horrebow, and connected by the steep rocks that form the north boundary of the plateau. It is proposed, in accordance with a suggestion by Dr. Lee, to designate this depression “ Herschel II.” Beer and Midler thus describe the table-land :— “ South-easterly of Horrebow is a large plateau, fourteen German miles broad, and from twenty to twenty-five German miles long, appearing less from foreshort- ening. The western border stretches from the western corner of Horrebow to that of Pythagoras, and is rather steep. An offshoot from the same stretches to Anaxi- mander. The southern boundary is denoted by the crater Horrebow B (+58° 9’ Lat., and —42° 0’ Long.), the northern boundary by two craters e and f Pythagoras. It rises on the east, in three great steep mountains of a very dark colour, straight up to the plateau, and only faint traces extend from thence still further towards the east. The most southerly of these three mountains is 919 toises high, while all three of the mountains appear to be exactly similar to each other in height, form, and colour. “The surface of the plateau itself has, besides several craters,—among which Horrebow A (+58°40' Lat., and —45° 30’ Long.), 2°67 German miles in diameter, is the largest, deepest, and brightest,—only a few scarcely perceptible ridges, and may accordingly be considered as an actual level. But whether this landscape, containing nearly 200 square German miles, is to be distinctly recognized as one connected whole, depends very much upon illumination and libration.” It is proposed to designate this table-land “ Robinson,” in honour of the Astronomer of Armagh. The following description of the same table-land is taken from the author's observations, dated London, 1862, March 12, 6" to 10" 30" G. M. T., moon’s age 12413, morning illumination. Instrument employed, the Royal Astronomical Society's Sheepshanks telescope No. 5, aperture 2°75 inch. “ South of the crater or depression Herschel II. is another, well defined, but not so large. Between the two is a table-land, in which at least five craters have been opened up. Two are ina line with Horrebow ; both are given by Beer and Midler ; the northern one is marked B [Horrebow B], the southern is undesignated. The principal crater in this table-Iand is marked A by Beer and Midler [Horrebow Ali the three form a triangle: the two remaining craters are near together, and nearly east of A; the largest is marked d by Beer and Midler, the othere. All the craters are shown on the map. _[ Note.—The crater d is referred to in the foregoing trans- lation as f Pythagoras; Beer and Midler thus speak of it :—“ Through an oversight, the lettering Pythagoras d occurs twice on our map; once for a slightly depressed crater on the edge of the previously-described plateau.” ] “The table-land lies nearly in the direction of the meridian: the mountains on the north slope, or rather their rugged and precipitous slopes, dip towards the large crater Herschel II.; while those on the south Fthe three dark mountains before mentioned] dip towards the other and smaller crater, which it is proposed to designate ‘South.’ On the west the table-land abuts on the border of the Mare Frigoris, while on the east it extends to some mountain-ranges beyond Anaxi- mander.” [The reader will notice a discrepancy in the descriptions as regards the points of the lunar horizon. It was thought better to leave each description as given by the writers, rather than attempt a conversion of them; especially as future observers can decide upon which they will adopt, consistent with the principles of lunar topography. The form of fis table-land before described is irregular. In the sketch it appears to be confined to the area between Herschel II. and “ South,” and this is the most conspicuous portion of it; but on the night of the 31st of January, 1863, under the morning illumination, it was seen to extend to the north of a crater then coming into sunlight eastward of “South,” which it is proposed to designate “ Babbage.” A ue = ea oe a Cas TRANSACTIONS OF THE SECTIONS. ll chain of mountains, connecting “ Babbage ” with Anaximander, forms the eastern boundary of the table-land. Beer and Midler have leftits boundaries undetermined, and further observations are necessary to mark them out with precision. Eye-sketch of a chain of Lunar craters, with three large unnamed and unrepresented craters, taken at Hartwell on the morning of Sept. 18, 1862. I. Philolaus (Riccioli). A ringed mountain. If. Anaximenes (Riccioli). A ringed mountain. Til. An unnamed crater on Beer and Midler’s map. It is marked “ Sommering”’ by Le Couturier. Beer and Midler have another “Sommering” near the centre of the disk. IV. Anaximander (Riccioli). The ring of this crater is imperfect, and requires further observation to define its outline accurately. Between it and V there is a well-marked mountain, besides other interesting features. V. Herschel I. (Birt). An extensive depression of the character of a walled plain, with a nearly perfect ring not shown by Beer and Madler, who describe the region between Horrebow, Anaximander, and Fontenelle as an exceedingly rich crater country ; the principal part consisting of the region of Herschel II. The following features are common to the eye-sketch and Map :— B. A high mountain mass marked Anaximander B by Beer and Madler. It really forms the north angle of the wall of the large depression Herschel I. e. A mountain mass forming the N.W. angle of the ring of Herschel I. f. A crater exterior to Herschel IT. c,d. Two craters in the line of eruption that crosses Herschel II. in a curvi- linear direction. The eye-sketch shows the general direction of this eruptive line from the portion of the ring that is absent to a crater east of Horrebow(X). It is not shown on the German map. VI. The table-land “ Robinson ” (Birt). A, B, and C. Craters on the table-land. E. A steep mountain “steppe” on the south, not shown in the sketch, dipping to the depression “South.” It contains the three dark mountains of Beer and Midler. F. A steep mountain “steppe” on the north, dipping to Herschel I. E and F were observed and figured by Schroter in his ‘Selenotopographische Fragmente,’ T. xxvi. fig. 1. VII. A depression south of the table-land “ Robinson.” Proposed name “ South ” irt). The central crater D is shown by Beer and Madler. VII. Another depression eastward of “South,” and between it and Pythagoras. The crater A on Beer and Médler’s map is really nearer the west border than shown in the eye-sketch. Proposed name “ Babbage” (Birt). Schroter observed this walled plain. Figures of it, with the interior crater A close to the western edge, are given in T, xxvi. (figs. 1 and 2) of his ‘Selenotopo- graphische Fragmente.’ It would appear that he designated it “ Pythagoras,” the crater now bearing that name being termed Pythagoras borealis, By far the most suitable name for the large crater with the central mountain is that on the large 12 REPORT—1862, German map, “Pythagoras ;” while to prevent misapprehension as to the western walled plain with the included crater, and to distinguish it from the eastern crater, it is proposed to call it “ Babbage.” Ix. Pythagoras (Riccioli), The largest and most magnificent crater in this part of the moon, showing itself as a conspicuous object with its central mountain, when nearly the whole of the previously-described craters and walled plains are lost to view. X. Horrebow (Schroter). This crater, which pierces the S.W. angle of the rim of Herschel, has hitherto been treated as being independent of any other formation. Schroter, who named it, figured it in its proper position at the west of the mountains F, and he gives (see T. xxvi. fig. 1, above referred to) the chain of mountains, omitted by Beer and Madler, forming the continuation of the rim from the steep mountains F to the rim of Anaximander, where he gives a small crater shown in the eye-sketch. On the other hand, Schroter has omitted the western rim extending northwards from Horrebow, which is given by Beer and Midler. Horrebow is clearly a part of Herschel II. Schroter does not appear to have recognized or figured “ South.” On the Augmentation of the Apparent Diameter of a Body by its Atmospheric Refraction. By the Rev. Professor Cuatuis, M.A., F.RS., F.RAS. For reasons given in another communication, it was assumed that atmospheres generally have definite boundaries at which their densities have small but finite values. Two cases of refraction were considered: in the one, the curvature of the course of a ray through the atmosphere was assumed to be always less than that of the globe it surrounds; and in the other, the curvature of the globe might be the greater. The former is known to be the case with the earth’s atmosphere ; and it was supposed that, a fortiori, this must be the case with respect to any atmo- pape the moon may be supposed to have. On this supposition it was shown that the apparent diameter of the moon, as ascertained by measurement, would be greater than that inferred from the observation of an occultation of a star, because, by reason of the refraction of its atmosphere, the star would disappear and reappear when the line of vision was within the moon’s apparent boundary. The same result would be obtained from a solar eclipse. It was stated that, by actual comparisons of the two kinds of determinations, such an excess to the amount of from 6” to 8” was found. This difference may reasonably be attributed to the existence of a lunar atmosphere of very small magnitude and density. The author also stated that from this result there would be reason to expect, in a solar eclipse, that a slender band of the sun’s disk immediately contiguous to the moon’s border would be some- what brighter than the other parts, and advised that especial attention should be directed to this point on the next occurrence of a solar eclipse. The case in which the curvature of the path of the ray is greater than that of the globe was assumed to be that of the sun’s atmosphere; and it was shown, on this supposition, that all objects seen by rays which come from the sun’s periphery are brought by the re- fraction to the level of the boundary of the atmos fs from objects on the surface of the interior globe, or from clouds supposed to be sus- pended in the atmosphere. Accordingly, the contour of the sun should appear quite continuous, and the augmentation of ba ik semidiameter will be equal to the angle subtended at the earth by the whole height of the atmosphere. The apparent diameters of the planets will, for like reasons, be augmented to a certain amount by their atmospheric refractions; and on account of the great distances of these bodies from the earth, the eclipse of a satellite will take place as soon as the visual ray is bent by the interposition of the atmosphere. On the Zodiacal Light, and on Shooting-Stars. By the Rev. Professor Cuatuis, M.A., F.RS., F.RAS. _ The phenomena of the zodiacal light, as gathered from observations made both in northern and in southern latitudes, were stated to be as follows. As seen in north latitudes, it appears in the West after the departure of twilight, as a very faint light, ere, whether they proceeded ~ | } : 7a TRANSACTIONS OF THE SECTIONS. 18 stretching along the ecliptic, about 10° broad at its base in the horizon, and coming to an apex at an altitude of from 40° to 50°. It is most perceptible in the West in the months of February and March, at which time its apex is near the Pleiades. Similar appearances are presented in the morning before sunrise in the East in the months of August and September. The light seen in the autumn lies in the same direction from the sun as that seen in the spring. In the southern hemisphere the appearances are strictly analogous, but the times and positions of maximum visi- bility are, the evenings in autumn in the West, and the mornings in spring in the East. The portion best seen in the southern hemisphere lies in the opposite direction from the sun to that which is best seen in the northern hemisphere. The portion seen, and the degree of visibility, depend on the inclination to the horizon of the part of the ecliptic along which the light*stretches. The greater the inclination the better it is seen. At the December solstice opposite portions haye been seen in the northern hemisphere, one in the morning and the other in the evening; and in the southern hemisphere opposite portions have been similarly seen at the June solstice. At these seasons the ecliptic is inclined at large and equal angles to the horizon at equal intervals before sunrise and after sunset. The southern observa- tions, from which these inferences are drawn, are those made by Professor Piazzi Smyth at the Cape of Good Hope in the years 1843, 1844, and 1845, and published in vol. xx. of the ‘ Edinburgh Transactions,’ and evening observations in the autumn of 1848, communicated by a friend of the author resident in the interior of Brazil. More recently, in vol. iv. of the ‘American Astronomical Journal’ were published observations by Mr. Jones, a chaplain of the United States Navy, who makes the following statement :—“ When in latitude 23° 28’ N., the sun being in the opposite solstice, I saw the zodiacal light at both east and west horizon simultaneously from eleven to one o’clock for several nights in succession.” The ecliptic must at the time have nearly passed through the zenith of the observer at midnight. It is clear, therefore, that to be seen an hour before and after midnight, the zodiacal light must have extended beyond the earth’s orbit. Taking this as a necessary inference from the observations, it follows that the earth is either always enveloped by the zodiacal light, or at least when passing through the line of its nodes. Protecads Challis considers this to be the explanation in part of the luminosity of the sky which is generally perceptible on clear nights, and at some seasons in greater degree than at others. The American observer also states that he saw when at Quito, “every night, and all through the night, a luminous arch from east to west quite across the sky, 20° wide, and most apparent when the ecliptic is vertical.” This light is distinguished from the zodiacal light by its being of uniform width. From the ensemble of the observations, the zodiacal light is of the form of a double convex lens, with the sun in the centre, and the principal plane coinciding nearly with that of the sun’s equator. As it may be inferred from the foregoing statements that it envelopes the earth, we 9 conclude that it is simply dwminosity, without accompanying bodies. Professor Challis proposes, therefore, to account for it by the effect which the rotation of the vast body of the sun produces on the lumini- ferous medium, this effect being rendered visible by the disturbance of the gyratory motion by the motion of translation of the sun in space. In a similar manner, magnetic currents are rendered visible in the form of the aurora by the effect of transverse currents. This explanation he stated to be in accordance with the prin- ciples of the undulatory theory of light. he appearance of shooting-stars in the August and November periods was accounted for on like principles, by the disturbance given to the luminiferous medium by the curvilinear motion of the earth resulting from its proper motion and the motion of the solar system through space. At two epochs depending on the vari- ations of the rate of motion, and of the rate of deviation from rectilinear motion, the disturbances would be at a maximum, and these two epochs were assumed to correspond to Aug. 10 and Noy. 12. The kind of disturbance which the earth impresses by its curvilinear motion was supposed to be such as would produce eddies or whirls. Besides this, there might be a disturbance of terrestrial origin, analogous to that which produces the zodiacal light, which might account for the luminous arch noticed by the American observer. 14. ; REPORT—1862. On some of the Characteristic Differences between the Configuration of the Surfaces of the Earth and Moon. By Professor Hunnissy, F.R.S, The author pointed out that the peculiarities observed on the surface of our gatellite should be ascribed to the sole action of volcanic forces, whereas those which we find on the earth result from a combination of volcanic and atmospherical agencies. In order more perfectly to study these contrasts, he called attention to the most characteristic feature of all lunar volcanos, namely the ring- or hoop-shaped crater, surrounded by circular, nearly concentric ridges. On the earth’s surface, volcanos deviated more or less from this type; and if the deviations are due to the differences between terrestrial and lunar superficial forces, it must follow that such differences will be most distinctly manifested in those cases where such terrestrial forces possess the highest degree of energy. He illustrated this proposition by re- ferring to the peculiar structure of the volcanos in the island of Java, where the action of tropical rains and hurricanes has been effective in producing the widest differences between the terrestrial volcanic summits and those observed on the moon’s surface. While the hooped structure of the latter cannot be traced among the views of Javanese volcanos which are presented in the comprehensive work published by Dr. J unghuhn, we frequently find diagrams of volcanic cones show- ing radiating ribs like those of a folded lamp-shade or an umbrella half closed, an appearance due to the very recular manner in which the tropical torrents scoop out the friable and scoriaceous summits of the craters. The contrast which arises by comparing some of these drawings with the best lunar diagrams and photographs may prove highly interesting to geologists as well as to selenographers. On aBrilliant Elliptic Ring in the Planetary Nebula, AR 20° 56',N.P.D.101° 56’. By Wurm Lassett, .RS.; in a Letter to Dr. Len, RS, 9 Piazza Sliema, Malta, 26th Sept. 1862. My prar Sir,—In directing my large equatorial upon the well-known plane- tary nebula situated in AR 20" 56", N.P.D. 101° 56’ (1862), it has revealed so marvellous a conformation that I cannot forbear to send you a drawing of it, with some description of its appearance. With comparatively low powers, e. g. 231 and 285, it appears at first sight as a vividly light-blue elliptic nebula, with a slight prolongation of the nebula, or a very faint star at or near the ends of the transverse axis. In this aspect the nebula resembles in form the planet Saturn when the ring is seen nearly edgewise. Attentively viewing it with higher powers, magnifying respectively 760, 1060 and 1480 times, and under the most favourable circumstances which have presented themselves, I have discovered within the nebula a brilliant elliptic ring, extremely well defined, and apparently having no connexion with the surrounding nebula; which indeed has the appearance of a gaseous or gauze-like envelope, scarcely interfering with the sharpness of the ring, and only diminishing somewhat its brightness. This nebulous envelope extends a little further from the ends of the conjugate than from the ends of the transverse axis; indeed it is but yery faintly prolonged, and only just traceable towards the preceding and fol- lowing stars. There is a star near its border northwards, in the projection of the conjugate axis. The breadth or thickness of the ring is, unlike that of Saturn, nearly uniform or equal in every part, so that its form most probably is either really elliptic, and seen by us in aline nearly perpendicular to its plane ; or if really circular and seen foreshortened, a section through any part of it limited by the internal and external diameters must be acircle. In other words;it will be like a circular cylinder bent round. It could scarcely fail to bring to my mind the annular nebula in Lyra, especially as there is a conspicuous central star (proportionally, however, much brighter than that which is in the centre of that nebula) ; and yet the resemblance is only rudely in form ; for this ring is much more symmetrical and more sharply defined, suggesting the idea of a solid galaxy of brilliant stars. The ring is not perfectly uniform in brightness, the south-preceding part being slightly the most vivid. ‘The transverse axis is inclined to the parallel of declina~ tion about 13°, A, series of micrometrical measures of the length and breadth of TRANSACTIONS OF THE SECTIONS. 15 the ellipse, gives a mean of 26"-2 for the transverse, and 166 for the conjugate axis. The accompanying drawing has not been at all corrected by these measures, ———~_ but is the result of several sketches made * during different observations, and is a oa faithful transcript of the appearance of the nebula to my eye, when most favour- ably seen. The object is, as may be supposed, one of extreme difficulty, requiring in the highest degree the combination of light and definition in the telescope, and a fa- yourable state of atmosphere,—which will further appear when I state that it was not until I was favoured with an unusually fine night, and had applied a power of 1480, that the whole of the details were brought out. I confess I have been greatly impressed by the revelation of this most wonderful object, situated on what perhaps we may consider as the very confines of the acces- sible or recognizable part of the universe, affording ground for the inference that more gorgeous systems exist beyond our view than any we have become acquainted with. Tam, &c., W. LasseLt, Observed R.A. and N.P.D. of Comet II. 1862. By the Rey. R. Mary, M.A., FBS. This paper gave the results of observations of the comet from August 5 to August 29, on ten nights. It was observed on the meridian with the Carrington transit- circle on August 7 and 9, and off the meridian with the heliometer, used as an or- dinary equatorial, on August 5, 7, 9, 14, 18, 19, 22, 23, 25, and 29. The observations have bccn rigorously reduced, and all necessary corrections for refraction, parallax, &e. have been applied. The assumed mean places of the companion stars for 1862, January 1, taken mainly from the ‘ Radcliffe Catalogue of Circumpolar Stars,’ were also given. On the Dimensions and Ellipticity of Mars. By the Rev. R. Mary, M.A., PRS, This paper gave the results of seven sets of measures of the disk of Mars, made for the determination of his ellipticity with the heliometer, by the method of contact of limbs of the two images formed by the half-object-glasses. The power used was 300, which is found by experience to be very suitable for such measures. The direction of the polar diameter was determined by a well-defined circular white cap near the southern limb, the centre of which was assumed to be coincident with the South Pole. The directions, separately estimated, of the polar and equatorial diameters agreed well on separate evenings, their difference never deviating much from 90°, thus proving the precision of the estimations. The measured diameters haye been corrected for defect of illumination. The following are the results of the measures :— Polar diam. Equat. diam. Ellipticity. uu “ 1862, Sept. 18 21-844 22386 ar pe MIS” yy eRadb 22-986 = * 22 22-704. 22-974 a ae 22-138 22-911 as F aiktelh 22-551 23-106 s eo aan 22-519 23-125 He pb 80 22-896 23-012 eS 198°4 Mr. Main drew particular attention to the difference in the degrees of consistency in the results for the polar and for the equatorial diameter, the latter agreeing sur- 16 REPORT—1862., prisingly well from night to night, while the former exhibit discordances of consider- able amount. This it is difficult to account for, except on the supposition that the snowy cap before referred to may have had some influence in distracting the eye from the real borders of the images in making the contacts. Still, on the whole, the measures all agree in establishing a measurable ellipticity, and Mr. Main intended to continue them at every opportunity during the present opposition, with the utmost care and caution. On some Peculiar Features in the Structure of the Sun’s Surface. By J. Nasmyru. The author gave a short sketch of the character of the sun’s surface as at pre- sent known. lie described the spots as gaps or holes, more or less extensive, in the luminous surface or photosphere of the sun. These exposed the totally dark nucleus of the sun; over this appears the mist surface—a thin, gauze-like veil spread over it. Then came the penumbral stratum, and, over all, the luminous stratum, which he had discovered was composed of a multitude of very elongated, lenticular-shaped, or, to use a familiar illustration, willow-leaf-shaped masses, crowded over the pho- tosphere, and crossing one another in every possible direction. The author had pre- ared and exhibited a diagram, pasting such elongated slips of white paper over a sheet of black card, crossing one another in eyery possible direction in such multi- tudes as to hide the dark nucleus everywhere, except at the spots. These elongated lens-shaped objects he found to be in constant motion relatively to one another; they sometimes approached, sometimes receded ; and sometimes they assumed a new an- gular position, by one end either maintaining a fixed distance or approaching its neighbour, while at the other end they retired from each other. These objects, some of which were as large in superficial area as all Europe, and some even as the surface of the whole earth, were found to shoot in thin streams across the spots, bridging them over in well-defined streams or comparative lines, as exhibited on the diagram; sometimes by crowding in on the edges of the spot they closed it in, and frequently, at length, thus obliterated it. These objects were of various di- mensions, but in leng th they generally were from 90 to 100 times as long as their breadth at the middle or widest part. Observations on Three of the Minor Planets in 1860. By Norman Poeson. Communicated by Dr. Ler, F.2.S. Observations of Minor Planets made at Hartwell in 1860, Eunomia (15) R.A. | P.D. s / af 1860, Sept. 1. 12 14 46 21 35 50:07] 90 51 31-6 | +9-089 | —0°832| 6 withg » 9» 1. 1257 59 | 21 35 48:34] 90 51 41-0 | +9-262) —0-831] 12 ,, g » oy» 4 1057 59 | 21 33 16-34] 90 54 41°5 | 48-454 | —0-832| 7 ,, p » » 7 1135 5|21 30 4818| 90 58 17-4 | 4+9-027| —0:832] 5 ,, 0 Olympia (59). 4 | —8:195| —0-832| 12 with n 0 | +9:190 | —0-837| 10 ,, m 3 | —9-426| —0-805| 6 ,, m 3 | —8-990| —0-835] 6 ,, m 1860, Sept.25. 12 413] 0 31 0°68) 90 49 2 » Oct. 2. 13 24 59} .@ 25 52°73) 91 53 5 ” Oo” 3. 938 14] O 25 16°45; 92 12 » y» 3 1055 11}, 0 25 14:09) 92 15 Thalia (28). 1860,Sept.25. 13 4 37] 0 11 55°55 104 34 25:3 | +9-039 | —0°891] 8 with 7 » Oct. 3. 12 28 38; O 4 38°05 /105 3 11-1 +9°056 | —0892| 10 , & 3: 6° 9: 7 TRANSACTIONS OF THE SECTIONS. 17 The first observation of Eunomia was made with the parallel wire micrometer, and power 110; all others with the ring micrometer, and power 84 of the Hartwell Equatorial. The comparison stars employed were as in the annexed list :— Mean R. A. | Mean P. D. Authority. Mag. 1860. 1860. hm s ow Oeltzen Arg. 33 & 34=9 Lalande (weight 3). | 89 | 0 3 16°86) 105 13 43:0 Weisse 0°227. 9 | 013 40°42 | 104 24 31°4 11 Ceti; Madler’s Bradley 36 ; 78 Robinson. 78 | 0 22 44:01} 91 53 209 Weisse 0°592. 9} 0 34 46°05} 90 47 32°5 4704 Robinson. 7 | 21 30 22:25] 91 0 563 24 Aquarii; Miadler’s Bradley 2°816. 7 | 21 32 1844/9041 13 Weisse xxi. 916=42598 Lalande (weight 4). 9 | 21 38 11°65] 90 51 2-9 The following magnitudes have been carefully estimated; generally, by com- parison with apparently similar objects in the nearest variable star-map then in course of construction :— Victoria, 1860, April 3...... 10°5 mag. | Eunomia, Sept. 1, 8-2 ; Sept. 4,8°6 ; Sept. 7, 8°3. Thetis By PS il Peace 10°5 ,, | Olympia, Sept. 25, 9°6; Oct. 3, 10°2. Metis ps Sept. Bes sees 9:0 ,, | Amphitrite, Oct. 3, 9-0. Thalia, Sept. 7, 11:0; Sept. 10, 11:2; Sept. 13, 11:0; Sept. 25,11°0; Oct. 3, 11:5. The preceding observations of minor planets were the last made by Mr. Pogson before leaving England for Madras in January 1861; it was his intention to reduce them speedily, and to send them to me from Malta or Alexandria; but, as antici- pated, the inconveniences of a sea-yoyage prevented him from fulfilling his design, and the pressure of official duties in his new position has not permitted him to attend to his former unfinished pursuits until recently. On the Excentricity of the Earth, and the Method of finding the Coordinates of its Centre of Gravity. By W. Oattsy, F.GS. On the probable Origin of the Heliocentric Theory. By J. Scuvarcz. The author traced the origin of the Copernican system to Pythagoras, through Aristarchus the Samian and Archimedes of Syracuse. On Autographs of the Sun, By the Rey. Professor Setwyn, The author showed several “ autographs of the sun,” taken with his “heliauto« graph” by Mr. Titterton, photographer, Ely, which consists of a camera and in- stantaneous slide by Dallmeyer, attached to a refractor of 2$ inches aperture by Dollond; the principle being the same as that of the instrument made, at the suggestion of Sir J. Herschel, for the Kew Observatory. The autographs are of July 25,°26, 28, 29, 31; August 1, 2, and August 4, 10.15 a.m. and 11.30 a.m. (a series of bright days coincident with a large group of spots); August 19, 20, 23 and 25, where the same group reappears, much diminished; September 19, 23, 26, 30, Oct. 1, in which is seen a group of 118,000 miles in length. On the 23rd three autographs were taken, two of them with the edge of the sun in the centre of the Aap goes plate, showing that the diminution of light towards the edges of the disk is a real phenomenon, and not wholly due to the camera. In the two of the 4th of August, where the great spot (20,000 miles in diameter) appears on the edge, a very distinct notch is seen, and the sun appears to give strong evidence that the spots are cavities ; but eye observations and measurements by the Rey. F. How- lett, and others, tend to show that this evidence is not conclusive, for there was still a remaining portion of photosphere between the spot and the edge. The phe- nomena shown in these autographs appear to confirm the views of Sir J. Herschel, eT tes two parallel regions of the sun where the spots appear, are like the tro- 18 REPORT—1862. ical regions of the earth where tornadoes and cyclones occur, and those of Wilson in the last century. The facule are clearly shown, and seem to prove that the tro- pical regions of the sun are highly agitated, and that immense waves of luminous matter are thrown up, between which appear the dark cavities of the spots, whose sloping sides form the penumbrz, as explained by Wilson and others. Other ana- logies between solar spots and earthly storms were pointed out, and reference was made to the glimpses of the structure of the sun exhibited by Mr. Nasmyth as confirming the above views. On the Hindu Method of Calculating Eclipses. By W. Svotrtswoonn, F.R.S. The astronomy of the Hindus is contained in a series of works known by the general name of “ Siddhanta.”’ These have been composed at different times over a period of 2000 years. In them are some incidental allusions to the configurations of the heavenly bodies, by means of which Baily, Davis, and others have attempted to calculate the dates of some of the works. ‘There were two points to which the author drew particular attention, viz. the process of correction whereby the true longitudes were deduced from the mean, and the precession of the equinoxes. It had been noticed that the apsides, or points of slowest movement, and the positions of conjunction with the sun had proper motions. These were attributed to influences residing in the apsides and conjunctio:s respectively, and corrections due to each were accordingly devised. The undisturbed orbit was considered a circle, with the earth (E) in the centre, and upon it the centre of a smaller circle or epicycle moved with a uniform angular velocity equal, but opposice in direction, to that of the urdisturbed planet; so that M being the centre, ard m any given point on the epicycle, Mm always remained parallel to itself. If, then, at the apse or conjunction (according as the correction of one or the other was being calcu- lated) Mm was in a straight line with EM, the true position of the planet was conceived to be at the point where Em cut the undisturbed orbit. The radius, moreover, of the epicycle was variable, and its magnitudes at the odd and even quadrants being determined so as to satisfy observation, its intermediate variation was considered proportional to the sine of the mean anomaly. The precession of the equinoxes is an important element in Hindt astronomy, not only as a question of scientific accuracy, but also as marking an epoch in the history of discovery. It is an ascertained fact that their earlier writers, among the foremost of whom Brahmagupta may be mentioned, took no account of it whatever. The statement in the Surya Siddhanta, when divested of its obscure terminology, seems to amount to this, that the sidereal circle shifts on the zodiac with an oscillating motion, whose period is 7200 years, and whose maximum range is 27°. This gives an annual rate of 54”. On some Improved Celestial Planispheres. By C. J. Vita. Licut anp Heat. - On the Means of following the Small Divisions of the Scale regulating the Distances and Enlargement in the Solar Camera. By A. Cuavvet, F.R.S. The author, in a former paper, had proposed a new method for measuring both the distances of the negative and screen for any degree of enlargement of the image, by means of a scale or unity divided into 100 parts, and smaller fractions if possible. This scale being fixed on the table of the optical apparatus, an index connected with the frame holding the negative was brought exactly on any division of the scale which was indicating the proportion and distance of the image. This arrangement would be very complete and satisfactory if the scale were always long enough to be marked with divisions sufficiently conspicuous; but the shorter the focus of the object-glass, the smaller the divisions of the scale must be. In order to meet this difficulty, he has adopted the following plan :—He traces on the table an equilateral TRANSACTIONS OF THE SECTIONS. 19 triangle, the base of which is the exact length of the scale. Taking 8 inches, for example, as that length, the three sides of the triangle will be 8 inches. Now, it is possible to enlarge the base three, four, five, or any number of times, by extending the sides of the triangle in the same ratio; so that if it be desirable to enlarge the scale four times, a triangle is formed haying its base four times longer, viz. equal to 52 inches; and dividing this new base into 100 parts, it is evident that each divi- sion will be four times larger than it could have been on the original base. Now, describing an arc, the chord of which is the base of the triangle, and attaching to the summit a thin metallic wire, the other end of which can slide on the are, it is evident that each division of the magnified scale which may be covered by the wire will correspond exactly with an equal division of the original scale, so that, after having brought the metallic wire on the division of the increased scale indicating the size of the required image, and the wire being fixed on the index, it will be brought exactly on any division of the unity of measure, however small it may be. The author has described another plan to obtain the same result, and, perhaps, more effectively : it consists in fixing the negative on a rack exactly the leneth of the scale, which, acting on a pinion adapted to a sufficiently large wheel containing the requisite divisions, will produce an entire revolution of the wheel; and an index being fixed on the table, will indicate on the wheel the exact amount of the course effected by the negative on the scale; and by turning the wheel to the division required, this will bring the negative with the greatest accuracy to the distance corresponding with the division. This system of focusing all camera-lenses might be very advantageous in photographic operations, and would be less subject to errors than the usual way of focusing on the ground glass. Relation entre les Phénoménes de la Polarisation Rotatoire, et les Formes Heémitdres ou Hémimorphes des Cristaux d un ou ad deux Axes Optiques, Par A. Drs Crorzeavx. Tout le monde sait que la découverte de la polarisation de la lumiére a rendu possible l’institution de nombreuses recherches, inabordables 4 tout autre mode d’observation, sur la constitution moléculaire des corps solides et liquides. Je n’entreprendrai pas ici de passer en revue les faits intéressants et les lois remarqua- bles dont on doit la connaissance aux travaux des Malus, des Fresnel, des Herschel, des Arago, des Brewster, des Biot, &c. Je m’occuperai seulement de la polarisation rotatoire et des relations que ce phénoméne peut avoir avec la structure physique des corps cristallisés. Depuis que la science a été dotée des microscopes polarisants d’Amici et de Noérrenberg, on a pu étendre les observations optiques & un grand nombre de substances trop peu transparentes ou de trop petites dimensions pour se préter 4 l'emploi des instruments généralement usités Jusque dans ces derniéres années. Le quartz est resté pendant tré8 longtemps le seul corps solide dans lequel on eut constaté l’existence du pouvoir rotatoire, et Sir John Herschel a le premier fait remarquer qu’il paraissait y avoir une relation constante entre le sens de la rotation des cristaux et le sens suivant lequel s’enroule la spirale formée par plusieurs des faces connues sous les noms de faces plagiédres et par la face rhombe, lorsque l’axe principal des cristaux est placé verticalement devant l’observateur. Ce rapproche- ment a conduit a regarder le phénoméne de la polarisation rotatoire comme di a un arrangement particulier des molécules physiques qui se manifesterait quelquefois par des formes cristallines présentant l’hémiédrie dite plagiédre ou tournante. On sait que le caractére de cette hémiédrie est la non-superposition des solides symé- triques résultant de la réunion des faces plagiédres situées 4 droite et 4 gauche d’une méme face prismatique du quartz. L’observation prouve d’ailleurs qu’elle peut s’allier avec ’hémiédrie qui fournit pour la face rhombe deux solides inverses mais superposables. I est en effet probable que c’est une structure de ce genre qui donne aux cristaux dextrogyres et aux cristaux lévogyres la propriété d’imprimer a la lumiére polarisée des modifications de sens contraire; car on n’a jamais observé de phé- noménes rotatoires dans les cristaux d’apatite, de Schéelite, d’érythroglucine, &c., sur lesquels on ne connait jusqu’a présent que des formes hémiédres superposables. Malheureusement la dissymétrie intérieure n’est pas toujours accusée par des signes extérieurs, et l’observation seule indique si un corps cristallisé posséde ou ne posséde Q% 20 REPORT—1862. pas la polarisation rotatoire. Ainsi, un grand nombre de cristaux de quartz ne por-» tent aucune face plagiédre; le chlorate de soude, dans les cristaux duquel M. Mar- bach a découvert le pouvoir rotatoire, s’obtient tantdt en cubes parfaits, tantot en tétraédres simples ou en tétraédres modifiés par les faces d’un dodécaédre pentagonal qui occupent relativement 4 celles du tétraédre deux positions inverses l’une de l’autre en rapport avec le sens de la rotation; le cinabre rhomboédrique et le sulfate de strychnine quadratique, qui, d’aprés mes observations, impriment aussi au plan de polarisation une déviation égale, pour le premier 4 16 fois et pour le second 4 la moitié de celle que produit le quartz, n’ont offert jusqu’ici aucune trace d’hémiédrie ; cependant j’ai trouvé dans le cinabre des cristaux dextrogyres, des cristaux lévogyres, et des cristaux complexes ou l’emploi de la lumiére polarisée convergente manifeste les spirales d’Airy absolument comme dans le quartz. La cause qui donne naissance la polarisation rotatoire dans les cristaux parait donc indépendante de celle qui produit les formes hémiédriques ; seulement, comme l’a fait voir M. Marbach, la production de ces formes peut étre favorisée artificiellement en faisant varier les conditions dans lesquelles s’opére la cristallisation. I] est done probable que les cristaux de quartz 4 faces plagiédres n’ont pas pris naissance dans les mémes cir- constances que ceux ou les faces plagiédres manquent; tous les cristaux de cinabre connus jusqu’a ce jour ont di au contraire se former sous l’influence de phénoménes géologiques semblables. Depuis que M. Biot a découyert la déviation imprimée au plan de polarisation par certains liquides et certaines dissolutions, on s’est souvent demandeé si les dissolu- tions actives susceptibles de cristalliser produisaient nécessairement des cristaux doués du pouvoir rotatoire. La plus grande partie des substances actives en disso- lution cristallisant sous des formes qui possédent deux axes optiques, la question est longtemps restée sans réponse expérimentale. Mais les travaux de M. Marbach et les miens, en révélant l’existence des trois seuls cas réalisables dans les cristaux dépourvus de la double réfraction ou dans les cristaux & un seul axe optique, sem- blent prouver que les deux genres de phénoménes sont indépendants l’un de l'autre. En effet, 1°, le chlorate de soude, inactif en dissolution dans ]’eau, jouit du pou- voir rotatoire lorsqu’il est en cristaux ; le quartz fondu ou a l’état de silice soluble et le quartz cristallisé présentent les mémes différences. 2°, Le sulfate de strychnine quadratique 4 13 équivalents d’eau, en dissolution. comme en cristaux, dévie 4 gauche le plan de polarisation, seulement le pouyoir ro- tatoire des cristaux est environ 30 fois plus grand que celui de la dissolution. 3°. Le camphre ordinaire des laurinées, actif en dissolution et a l'état fondu, donne par sublimation des cristaux appartenant au systéme hexagonal, dans lesquels on ne peut constater aucune déviation du plan de polarisation, méme sous une épaisseur de plusieurs millimétres. Les cristaux 4 deux axes optiques, dont la dissolution posséde le pouvoir rota- toire, sont assez nombreux; on a donc pweles soumettre a des expériences variées. D’aprés les recherches de M. Pasteur, l’existence du pouvoir rotatoire dans une dis- solution serait le plus souvent (a l’exception des sulfamylates) accompagnée par Vhémiédrie non superposable ou l’hémimorphie d’une ou de deux des formes sim- ples que présentent les cristaux dissous. Cette hémiédrie se montre d’ailleurs quelquefois sur les cristaux formés naturellement au sein d’une dissolution dans Veau pure, d’autres fois elle doit étre provoquée, soit en faisant varier la nature du dissolvant, soit en blessant les cristaux et les replagant dans leur eau-mére*. Svil existe, comme pour l’acide tartrique, les tartrates et quelques autres substances Worigine organique, deux dissolutions, l’une lévogyre et l'autre dextrogyre, les formes hémiédres ou hémimorphes correspondantes produisent ordinairement (le sel de seignette potassique parait seul faire exception) deux solides symétriques mais non superposables. La réciproque n’est pas yraie dans tous les cas, puisque le sulfate de magnésie et le formiate de strontiane, dont les cristaux offrent l’hémiédrie non superposable, fournissent des dissolutions inactives. Les causes qui produisent les formes cristallines hémiédres paraissent donc agir d’une maniére plus générale que celle & laquelle est du le pouvoir rotatoire moléculaire. * Ann, de Chimie et de Physique, tom, xxxviii. et xlix, TRANSACTIONS OF THE SECTIONS. 21 On the Cohesion of Gases, and its relations to Carnot’s Function and to recent Experiments on the Thermal effects of Elastic Fluids in Motion, By James Crott, Glasgow. From the fact that those gases which are most easily liquefied by compression are those which are found to deviate most from the law of Mariotte, we are led to the conclusion that their deviations from this law are due to the mutual attraction of their particles. Deviations from Mariotte’s law after the manner of carbonic acid follow as necessary consequences from cohesion. Other phenomena are also ex- plainable on the same principle; such, for instance, as why the coefficient of expan- sion is greatest for the gases which deviate most from Mariotte’s law—why the coefficient of expansion increases with the density in gases which deviate from this law—why, when equal weights are employed to compress different gases under the same conditions, the greatest amount of work is performed on the gas which deviates most—why, in the expansion of gases by heat, least work is performed by heating the gases which present the greatest deviation. The influence of Cohesion in relation to the Experiments of Prof. W. Thomson and Dr. Joule on the Thermal effects of Elastic Fluids in Motion. In these experiments, air, carbonic acid, or hydrogen, under very high pressure, was made to expand by forcing itself through a porous plug, and it was found that the temperature of the gas after expansion was somewhat less than before it; in other terms, the heat of friction was found to fall short of compensating the cold of expansion. The expenditure of elastic force experienced by the gas, in forcing itself through the porous plug, tends in the first instance to lower its temperature ; but as this force is spent in friction, the heat produced from friction ought exactly to compensate the cold of expansion. This is only the case, however, when all the force of expansion has been spent in friction; ifa portion of this force be consumed in producing some other effect than heat, then the heat of friction will not com- pensate the cold produced by the waste of force in expansion, and a cooling effect will be the result. Now it is perfectly evident that if the atoms of a gas when compressed attract each other, the force of expansion cannot be all converted into heat, a portion of it must be consumed in overcoming attraction, hence the heat of friction will fall short of compensating the cold of expansion by an amount equal to the equivalent of the work against attraction. It is generally understood that in certain cases a heating instead of a cooling effect may take place. How this may occur is not so apparent. Prof. W. Thomson states, that when the temperature of air rises above a certain height, the heat of friction will exceed the cold of expansion, because P'V', the work which a pound of air must do in expanding through the plug, is rather less than P V, which is the work done on it in pushing it through the spiral up to the plug. It is by no means obyious how this can result in a heating effect. That which produces the cold of expansion is the expenditure of the elastic force in expanding through the plug; but as this force is not consumed on external work, but entirely spent in friction on the particles of the air itself, the force which it loses on the one hand is entirely restored to it on the other. But more force cannot be restored than was lost; for the force restored is just what was lost. : The only way whereby it is possible to account for a heating effect, is by supposing that a gas which exhibits the heating effect possesses a certain amount of elastici independent of heat, and that the expenditure of this force in the production of heat by friction, is an expenditure of elastic force, but not an expenditure of heat—a conclusion which is very improbable. The Influence of Cohesion in relation to Carnot’s Function, The following was suggested by Dr. Joule, in a letter to Prof. W. Thomson in 1848, as the true expression of Carnot’s function, mG eT) ie a) Renee J denoting Joule’s equivalent, E the coefficient of expansion*, and ¢ the tempera- * In this formula Carnot’s function is equal to the mechanical equivalent of the thermal 22 : REPORT—1862. ture in Centigrade degrees, measured from the temperature of melting ice. Prof. W. Thomson has been led, from calculations based upon Regnault’s observa- tions on the pressure and latent heat of steam, to the conclusion that p cannot in all cases be expressed by the above formula. May not the deviations, however, be entirely due to the influence of cohesion ? It is evident that cohesion must affect the value of this function in the following manner: if a mutual attraction exist between the particles of a gas at a given temperature, then that gas in cooling itself down one degree below that tempera- ture, by performing mechanical work in expanding, will execute less work than it would otherwise do did no cohesion between the particles exist; for a portion of the heat must be consumed in work against the cohesion. The quantity consumed by cohesion will continually increase as the temperature diminishes; for as the tem- perature diminishes the cohesion increases. But in regard to steam and all other saturated vapours, the reverse holds true, for the cohesion of the particles of vapours increases as their temperature rises, because their density increases with rise of tem- perature. In the case of a perfect gas, the function will agree with the formula at all temperatures ; but in imperfect gases and vapours the function will deviate from the formula, but in opposite directions. In both cases the actual function will fall short of the ges On the Supernumerary Bows in the Rainbow. By the Rev. J. Duxexz. The author gave a method of approximating to the size of the drops of rain corresponding to any given position of the supernumerary bows produced by the in- terference of the two luminiferous surfaces proceeding from each drop. It appeared from his tables appended to the paper that the size which Dr. Young (without giving his method of calculation) had assigned to the drops under certain conditions was within 5;/;;th of an inch of the truth, and was more accurate than that assigned subsequently by Mr. Potter. On the Duration of Fluorescence. By Dr, Essripacu. The author described the apparatus by which he succeeded in 1856 in proving the duration of fluorescence (z;1;5 second with uranium glass), thereby establishing a year before M. Becquerel the experimental link between this interesting pheno- menon and phosphorescence. Description of an Optical Instrument which indicates the Relative Change of Position of Two Objects (such as Ships at Sea during Night) which are maintaining Independent Courses. By J. M. Menzies. This instrument consisted of a lantern-shaped case, containing a lens in front and a coacentric sheet of bent glass behind, at the focal distance of the lens, ruled with parallel vertical lines. This was hung up on gimbals so as to have its axis parallel to the course of the vessel, and the biight spot (the image of the light of the approaching vessel) showed by its position ‘cal shifting the relative place and course of the approaching vessel. Experiments on Photography with Colour. By the Rev. J. B. Reapr, F.2.S. A recent examination of the phenomena of polarized light in their immediate connexion with the undulatory theory led the author to inquire into the causes of natural colours, and thence to the possibility of coloured objects setting up, in sen- sitive films on which their image is thrown, the very same causes which regulate and determine their own respective colours. This being effected, the image of an object would communicate to the eye the identical colour of the object itself. The propositions, in general terms, are—that radiant-coloured light consists in un- dulations of the luminiferous ether—that all material bodies have an attraction for the ethereal medium, by means of which it is accumulated within their substance unit, divided by the absolute temperature. The reciprocal of E must be the absolute tem- perature of melting ice, or the formula is erroneous: 2 TRANSACTIONS OF THE SECTIONS. 23 and exerts its influence beyond them—and that the luminous phenomena are exhi- bited under two modifications, the vibratory or permanent, and the undulatory or transient state. This theory leads to the conclusion that the undulations within the substance of material bodies communicate their vibrations to the ethereal medium without them, and thence to the same medium within the eye. If the undulations be such as to produce red, red is seen by the eye, and so for other colours. Now, as we have films eminently sensitive to the action of reflected light, and capable occasionally of being coloured by such light, it is clearly within the laws of physical science to suppose that the several portions of the excited film may retain within themselves, in the vibratory and permanent state, the varying undulations of the coloured objects whose images they receive. A picture with the colours as in nature would be the result, instead of the mere black and white mezzotint at present obtained. The desiderata are—a sensitive silver compound capable ot yeceiving and transmitting the undulations, and energetic reflexions from the objects themselves. hortly before the meeting he happened to obtain unusual traces of colour in photographie portraits. The chief difference in manipulation was a slight excess of the iodizer in the collodion, and the addition of acetic acid and acetate of soda to the bath, And in order more fully to test the effect of the cadmium and bromo- iodizers, he increased the quantity until natural colours ceased to be strengthened. The final proportion of iodizing solutions gave the portrait which was exhibited. The general warm colours of the forehead and face, and the tone of the coat were fairly represented in the portrait. Remarks on the Complementary Spectrum, By J, Surtu. The author endeavoured to explain, on the principle adopted by him in his chro- matrope experiments, the well-known fact that the spectrum of a hole in the win- dow-shutter, when received on a screen, has the violet end above and the red below, but when looked at through the prism, the red appears above and the violet below. On the Motion of Camphor, &c. towards the Light. By Cuantxs Tomtinson, King’s College, London. Books on chemistry from the time of Chaptal (1788) to the present, recognize the fact that salts in crystallizing move towards the light; that camphor, water, alcohol, &c. form deposits on the most illuminated side of the bottles that contain them. The history of the subject includes the names of Petit, Chaptal, Dorthes, Draper, &c. Chaptal’s experiments were made with saline solutions, and he found that crystalline deposits could be determined to any point by admitting the light to that point, or prevented by shutting out the light. Dr. Draper, who named these phenomena perihelion motions, found that in the case of camphor deposits were sometimes made nearest the sun, and at other times furthest from him, the latter being termed aphelion motions; that reflected light and coloured light produced aphelion movements ; that the deposits are not produced in the dark, or by artificial light, and that rings and disks of tinfoil prevent the formation of deposits. He supposed electricity to be concerned in the production of these phenomena. Mir Tomlinson shows that neither light nor electricity has anything to do with these effects, but that they are the simple results of cooling. By treating the vapour of camphor, &c. as dew, all the effects follow; and Chaptal’s results are obtained in full sunshine without any shutting out of the light, but simply by preventing radiation by means of transparent screens. When a bottle containing camphor, &e. is exposed to light, the illuminated side is generally the colder, and hence the deposit on this side; but when the sun is shining on the bottle, the furthest side is the colder, and there the deposit takes place. Bottles of camphor kept in the dark, 7. e. in a cupboard or drawer, are equally warm all round, and hence no deposit is formed; but if such a bottle be cooled on one side by means of a piece of filtering-paper dipped in ether, a deposit is instantly formed. If a bottle of camphor be plunged into water at 100° no deposit is formed, because it is equally hot all round. If a number of bottles be covered with opake substances and exposed to the sun, or to a heated cannon-ball, deposits are formed or not according - DA REPORT—1862. as the screens absorb or reflect heat: a screen of tinfoil will not allow a deposit to be formed ; but if the screen be of brown age there will be an abundant furthest deposit. So also if a bottle have attached to it disks and rings of tinfoil, paper of various colours, &c., no deposit will be formed in and about such disks, because they keep the bottle warm by preventing radiation, and even by absorbing heat. A disk of black paper put on a deposit already formed will clear away a much larger space than tinfoil will do. The author found that crude camphor was more sensitive in its action than refined; but that the experiments succeed with ordinary camphor, Borneo cam- phor, artificial turpentine camphor, camphoric acid, iodine, naphthaline, chloral, water, alcohol, ether, &c. Exrcrricity, Magnetism. On the Mechanical Power of Electro-Magnetism, with special reference to the Theory of Dr. Joule and Dr. Scoresby. By James Croxt, Glasgow. In an article by Dr. Joule and Dr. Scoresby on the mechanical power of Electro- magnetism*, it is stated that when the electro-magnetic engine is set in motion and the current in consequence reduced from a to 6, the heat manifested in the circuit is reduced from a? to 67, but the heat which is produced by the oxidation of the zine is only reduced from a to b; hence they conclude that the quantity of heat equal a—b produced by the zine plates, but which does not appear in the circuit, is con- sumed in the production of mechanical effects. That this conclusion is not satis- factory will appear, the author thinks, from the following considerations, viz. if we reduce the current from a to 6 by merely reducing the consumption of the zinc from a to b, the heat evolved in the circuit will in this case also be reduced from a? to 6%, The question now arises, what becomes of the amount of force a—6 which disap- pears in the circuit here also? It is not consumed in work, for no mechanical effect takes place. Hence, from the disappearance of heat when the electro-magnetic machine is set in motion, we are not warranted to conclude that it went to produce mechanical effects ; for it equally disappears in the other case when no meine] effect is produced. The true explanation of the matter, he thinks, is this : when we reduce the current from a to b, we reduce the heat evolved in the conducting wire from a? to b’, but we only reduce the heat evolved in the entire circuit from a to b; hence there is no disappearance of heat whatever. The simple fact is, the heat which is missing in the conductor will be found in the battery; however, when the engine is in motion there will be a deficiency in the total heat evolved equal to the thermal equivalent of the mechanical work performed. When the engine being at rest the current is equal 6, the total heat evolved is also equal 6; but when the current is reduced to b by the motion of the machine, the total heat evolved will then be equal 6—x; x being the equivalent of the mechanical work performed. The value of zx, therefore, is not determined by the theory of Dr. J oa and Dr. Scoresby. Let us consider the theory in relation to the origin of the mechanical work. When the current is equal 6, without mechanical work being performed, the heat evolved in the conductor is 6?; when the current is 6, and mechanical work per- formed, according to the theory the heat evolved in the conductor is also equal 6, In this case there is no reduction of heat in the conductor corresponding to the me~ chanical effect produced; for the heat is as great when the mechanical effect takes place as when it does not, being in both cases equal 67. This would lead to the conclusion that the mechanical effect is not derived from the current 6, for it could not possibly produce its full equivalent of work, in the shape of heat 6? and x amount of work in addition. The work xz must, therefore, according to this theory, be derived directly either from the chemical action in the battery or from the heat evolved. That it is not directly dependent upon chemical action is evident from * Philosophical Magazine, June 1846, TRANSACTIONS OF THE SECTIONS. 25 the fact that, if the current exist, 2 will arise the same as before, whether there be chemical action or not, as, for example, when the current has a thermal origin; and that it is not derived from the heat evolved is evident also from the fact that it has no existence when the heat is present in the circuit without the current. The mechanical work is therefore, contrary to the above theory, derived directly from the electric current; and it follows from hence that when we have two cur- rents equal in every respect, the one performing mechanical work and the other roducing nothing bot heat, less heat must be evolved by the former current than y the latter; consequently the law involved in the theory, viz. that the heat evolved in similar conductors is proportional to the square of the currents, does not hold true when one of the currents produces magnetical effects. Facts seem to lead to the following theory asa true explanation of the mechanical power of electro-magnetism. Whatever our views may be regarding the nature of the electric current, we must allow that the molecules of bodies offer a certain amount of resistance to the passage of the current, which amount differs according to the nature of the body through which the electricity is propagated. It must also be admitted that the molecules of the body, in consequence of the resistance which they offer, become heated. Let us take now the case of the conducting wire con- necting the pole of a battery. Suppose it to be composed of a succession of mole- cules A, B, C, D, &c. The chemical action in the battery communicates a certain amount of motion to the atom A, in consequence of which its equilibrium is de- stroyed, and to regain this state it transmits motion to the next adjoining atom B; but B offers resistance to A, and the consequence is that A is unable to communi- cate to it the full amount of motion necessary to restore its own equilibrium, so that A must still retain a portion of the disturbing force or motion received from the battery; but on account of its position in space being limited by its relations to surrounding molecules, it can only retain motion or force in itself by vibrating, and in virtue of these vibrations we affirm it to be hot. Bin like manner, to regain its equilibrium, transmits motion to C, but C likewise offers resistance to B, and, of course, B must also retain a portion of the disturbing force in the form of heat, and what holds true of A, B, and C, holds equally true in regard to all the other mole- cules of the conductor. Let us now observe what takes place when work is being performed by an elec- tro-magnetic engine. We have, in the first place, a continual evolution of force arising from chemical action in the battery. This chemical force becomes imme- diately transformed into electric current, and the electric force must in turn be constantly transformed into some other form of force, or else we should instantly have an accumulation of current. When the current is allowed simply to circulate in the conductor without producing any work, either chemical or magnetical, its entire force is transformed into heat, and the heat in turn is transmitted to sur- rounding objects and radiated into space. This, as we have shown, is the effect of forces tending to a state of equilibrium. When the soft iron of the electro-mag- netic engine is brought into the presence of the conductor, another channel or out- let is then offered to the molecules of the conductor, whereby they may get rid of the disturbing force, the electric current; a portion of this force will be transferred to the molecules of the iron, causing them to assume the magnetic state, and, of course, whatever is consumed in work upon the molecules of the iron cannot appear in the molecules of the conductor in the shape of heat. The moment the mole- cules of the iron assume the magnetic state, no further transference of force in this direction can take place; but if they are allowed to perform mechanical work while they are assuming this state, as is the case when the electro-magnetic engine is in motion, then a constant outlet is afforded in this direction to the disturbed mole- cules of the conductor to regain their equilibrium. But it must be observed that the relative proportions of the force which pass through each of the two channels or outlets, heat and magnetical work, do not remain the same, as Dr. Joule and Dr. Scoresby’s theory implies; for as the force will always tend to the path of least resistance, the relative proportion passing through each outlet will be determined by the relative resistance offered—the quantity passing through each being in- versely as the resistance to be overcome. Now the quantity « of mechanical work that can be produced by an electro-magnetic engine from a given quantity of elec- 26 REPORT—1862. tric current, well depend entirely upon the amount of resistance offered by the magnetic element as an outlet to the electric force. If the iron is hard, and the resistance con- sequently great, the amount of work will be but small; but if the iron is soft and the resistance offered small, then the amount of force transformed into magnetism and available for mechanical purposes will be greater. In a paper read before the Chemical Society in March last, the author showed that the same principle holds true also in regard to heat. When heat is applied to a solid or a liquid body, a portion of the heat goes to raise its temperature, and another portion is consumed in internal molecular work against cohesion. The rising of the temperature and the separation of the molecules are the two paths or outlets for the force, and the relative proportion which passes through each is determined here in like manner by the resistance offered by each to the passage of the force. Hence the reason why the specific heat of bodies increases as their temperature rises; for the resistance offered by cohesion decreases with rise of tem- erature, thus allowing a greater proportion of the heat applied to become latent in mternal molecular work. It was stated as a general principle that, other thinys being equal, the more easily fused a body is the greater is its specific heat. This was shown also experimentally to be the case. In conclusion, in the production of molecular work by heat or mechanical work by means of electro-magnetism, there exists no fixed relation between the amount of heat applied and the work performed, for in both cases the quantity of work varies with the molecular resistance offered. On Electric Cables, with reference to Observations on the Malta-Alewandria Telegraph. By Dr. Ernest Esse.Bacu. The three sections of this cable touching the shore at Tripoli and Benghazi represent three condensers of 75,000 to 150,000 feet square, which, on account of their size, disclosed several important facts in regard to the nature of the dielectric, They allowed, in the first instance, a clear separation of the residual charge from the resistance test. Dr. Esselbach arrived thereby not only at the true resistance of gutta percha, but attained a new and entirely different test for insulation (electri- fication test), by which the absence of electrolytic action in the covering could be distinctly ascertained. These observations further afforded proof that the residual charge on Leyden jars was not a penetration of electricity like that of heat in a metal, but an increase of the specific inductive capacity of the material, and merely a function of time, analogous to certain corresponding phenomena of torsion and magnetism. The absolute quantity of charge, as ascertained in Dr. Esselbach’s pre- vious paper, showed that an increase in inductive capacity of one per cent., under the influence of electric tension, was sufficient to account for what appeared to the galvanometer as a change in resistance amounting sometimes to as much as 50 per cent. Dr. Esselbach further showed his diagrams on earth-currents, extending over one month’s observation, indicating the great advantage which two lines of 500 and 600 miles from east to west, and one from north to south, in one continuation, sh and the facility and precision with which they are observed by Wheatstone’s ridge. The cable is taken roughly as being 2000 times better than the old Atlantic cable ; and whereas in this latter at least 80 per cent. of the strength of current was lost in the transit, more than 99 per cent. actually arrives in the present case at the other end. The speed of a signal through this cable has been ascertained in different ways, and in the most perfect way by Captain Spratt, C.B., incidentally, upon a comparison between the longitude of Malta and Alexandria. The time for one signal through the whole length of 1300 miles approaches one second nearly. The author drew attention to the fact that the question of practical speed, after having first been brought into prominence by Mr. Latimer Clark’s experiments, had re- mained in abeyance since Professor Thomson’s researches at the time of the laying of the Atlantic cable, after which all interest had been absorbed by the insulation question, and very rightly, since it was first necessary to establish communication, and with certainty, before trying to precipitate it. This appearing now assured by TRANSACTIONS OF THE SECTIONS. 27 a great and deserved success of manufacturers, attention could freely be turned to experiments on speed, as entered upon by Messrs. Jenkin and Varley; and he men- tioned that applications had been made to Government from the first authorities to take advantage of the Malta-Alexandria Telegraph for the purpose. On an Experimental Determination of the Absolute Quantity of Electric Charge on Condensers. By Dr. EssrnBacu, This quantity having first been approximately ascertained by Faraday, had been afterwards established by the researches of Weber, Thomson, and Joule; but the application of these results to submarine cables requiring intermediate reductions, the author undertook a direct determination, for which the means had since become available. A cable of certain description was charged (and discharged) by 100 Daniell’s 400,000 times in 14" 30’; this quantity of electricity deposited in four several yoltameters 12-9 mer. of silver. ‘The determination was repeated under different conditions, The absolute quantity can hence be calculated for any other cable by means of the well-known formula for determining their relative capacities. The quantity of charge on the whole Malta-Alexandria cable by 20 cells (the ordinary speaking power) is accordingly equivalent to 0-013 mgr. of silver, a quantity which is furnished in 0-964 second by the battery in a closed circuit of 2500 units (one Daniell by 1000 mercury units depositing 4:01 mgr. of silver per hour), This would therefore be the maximum speed with this battery, as far as merely the quantity of electricity is concerned. During the investigation of the method which receded the experiment, Dr. Esselbach found the charge and discharge influenced fy the resistance to sufficient extent to admit of verifying experimentally the second case of Professor Thomson’s theory of discharge, which is of practical import ance for the question of velocity. Account of an Electromotive Engine. By G. M. Guy. The author explained the difficulty of obtaining, by any of the methods hereto- fore suggested, a sufficiently rapid motion within the small spaces through which magnets or electro-magnets acted with sufficient energy, and chiefly in consequence of the rapid diminution of that energy as the distance of the poles increased, even by very minute quantities, He exhibited and explained to the Section a working model of the engine. METEOROLOGY. Suggestions on Balloon Navigation. By Isaac Asun, M.B. The author ae a a simple contrivance by means of which the opening of the escape-valve should depend, when desirable, on the relaxation of voluntary exertion on the part of the aéronaut, so that in the event of insensibility supervening at great altitudes, the valve should open spontaneously by means of a weight attached to its rope, thus causing a descent of the balloon to safer altitudes, and obviating the danger to life incurred by Messrs. Glaisher and Coxwell during their recent scien- tific ascent from Wolverhampton in consequence of their becoming insensible. Dr. Ashe also proposed the adaptation of screw propulsion to balloons, suggesting a very light screw, capable of being elevated and depressed through an angle of about 150°, so as to be capable of being hoisted while the balloon should be on the ground, of being used horizontally as a propeller, or vertically underneath the car to cause a temporary ascent, as for the purpose of crossing a mountain-range without loss of ballast, which would involve remaining at the elevation so gained, or, on the other hand, by reversing the action of the screw, to effect a descent without loss of gas. Such a screw he considered could be worked at small elevations (2000 feet) by the exertions of the aéronaut ; and its advantages would consist in the conferring, to 28 REPORT—1862. a certain degree, of definite direction, and also of steering-power, and in obviating the objection to hydrogen balloons, which consisted in the expense of this gas, as a descent could be effected without loss of gas; hence smaller and much more ma-~ nageable balloons might be constructed than those now in use, and propulsion by means of a screw would be so much easier. Steering-power being obtained,Dr. Ashe hoped that a modification of shape might be found practicable, so as to present a minimum of resistance to propulsion by the screw. He proposed to steer by means of two small screws connected by a cranked axle placed at right angles to the action of the propeller, and situated in front of the car, so as not to interfere’with the hoisting of the propeller; these steering= screws should have their spirals turned in the same direction, and by revolving them in one direction, or the reverse, the balloon might be made to rotate on its vertical axis as might be desirable. The disagreeable rotation incident to balloons might also thus be obviated. Dr. Ashe suggested the employment of balloons in the in- vestigation of aérial currents and circular storms, and for the exploration of unknown continents: water, that great desideratum in such explorations, could be observed from an elevation when it would otherwise be passed by unobserved, and a descent being effected by the screw, its position might then be taken by observation, and marked for the guidance of foot explorers. Similar remarks would apply to the discovery of the easiest routes by means of balloon observations, On some Improvements in the Barometer, By Isaac Asue, MB. The author suggested a contrivance by which a water-barometer might be con- structed, having a tube of not more than 3} feet in length, with a range in the height of the column of liquid equal to about 39 inches. Though correct in theory, this contrivance seemed to have some defects which would practically interfere with its accuracy. On the Determination of Heights by means of the Barometer, By Joun Bax. The object of this paper was to direct attention to the serious errors which are in- volved in the ordinary process of reducing barometric observations taken for hypso- metrical purposes. This process involves two assumptions: Ist, that the volume of a column of air unequally heated is nearly the same as that of an equal weight of air of the same mean temperature ; 2ndly, that the mean temperature of the column or stratum of air between the stations of observation corresponds to the mean of the readings of thermometers standing in the shade at each station. The error involved in the first assumption is not very considerable ; that arising from the second is, on the contrary, highly important. M. Brayais, who along with M. Charles Martins has contributed largely to our knowledge of the meteorology of the Alps, was the first to propose a practical plan for applying a correction to the assumed mean temperature of the air depending upon the hour of the day and the season of the year at which observations are made, but it is to M. Plantamour, the distinguished astronomer of Geneva, that we owe the fullest investigation of this important subject. Having ascertained by careful levelling the true height of the Great St. Bernard above Geneva, M. Plantamour finds that the mean of all the barometric observa- tions, made during eighteen years, deviates by fourteen English feet from the true height, and he attributes this deviation, with great apparent probability, to an ab- normal depression of the mean temperature of Geneva, owing to the neighbourhood of the lake. The readings of the barometer and thermometer at the observatories of Geneva and the St. Bernard are taken daily at nine hours or epochs. M. Plantamour assumes that, on an average of a long period of years, the mean of the observations taken at any one epoch in the twenty-four hours should give the true difference of height between the two stations, with an error due to the difference between the mean of the readings of the thermometers at both stations at the same epoch, and the true mean temperature of the air in the intervening stratum. Calcula- ting then the height of the St. Bernard by the elements corresponding to each epoch of the day during the four summer months, from June to September, TRANSACTIONS OF THE SECTIONS. : 29 he obtains a series of measures differing from the true height—those corre- sponding to the hottest hours being in excess, and those appertaining to the coldest hours in defect of the true height. He then ascertains the amount of cor- rection which, being applied to the mean sum of the readings of the thermometer at each epoch in each of those months, would bring out the true height. In this manner he obtains a table, showing what he calls the normal correction for each of the nine epochs of the day during the four summer months. There is good reason to believe that, in reducing barometric observations which are to be com- pared with Geneva and the St. Bernard, the application of the normal correction ascertained in the manner above stated will in general give truer results than those where this is not applied; but as it is obvious that the conditions of temperature at the moment when a given observation is made are constantly yarying from the mean of the corresponding day and hour, it follows that a further supplemental correction should be made on this account. To apply this further correction is a matter of no slight difficulty. The method employed by M. Plantamour is as follows. He obtains from the observations at Geneva and the St. Bernard (by interpolation when necessary) the elements corre- sponding to the day and hour of the observation which is sought to be reduced, and from these he calculates the height of the St. Bernard. The height so obtained, when compared with the measure which is derived from the mean of the readings for the same day and hour, as shown in his Table of normal corrections, furnishes a criterion by which to judge of the conditions with respect to temperature of the moment when the observations to be reduced were made. M. Plantamour thinks it not difficult to infer from the observations themselves, and from the general state of the weather at the time, whether the moment was one of atmospheric equilibrium or the reverse. In the latter case the observation is treated as one of inferior utility, to which a lower value should be assigned in the final calculation. Supposing, on the contrary, the observations not to betray a disturbance of equilibrium between the two stations, the deviation of the height, as calculated for that particular mo- ment from the height derived from the corresponding means, is the measure of the amount and sign of the supplemental correction corresponding to the moment of observation. Without entering at present into sundry points of secondary importance, the writer believes that, while it is at present impossible to clear the mode of dealing with this correction of some arbitrary elements, it is easy to adopt a system less cumbrous and less inconvenient, and at least equally accurate with that proposed by M. Plantamour. He finds that many of the observations which appear to ML Plan- tamour to be clear of anomalies arising from the disturbance of atmospheric equi- librium, show unequivocal traces of such disturbance. These anomalies can be eliminated only by comparing the observations in hand with many ditierent stan- dard stations, such as Milan, Turin, &c.; but, in the absence of direct evidence, the introduction of an empirical correction in the manner proposed is likely to lead to error. The writer proposes to deal directly with the correction for temperature upon the best information that is available in regard to each of the stations where observa- tions are recorded. He considers that the deviation of the thermometer at the time of observation from its mean height at the corresponding day and hour, is a tolerably accurate measure of its greater or less deviation at that time from the true temperature of the air freed from surface-radiation, and may therefore be taken with its proper sign for the supplemental correction. It is important that the comparison between Geneva and St. Bernard, made by M. Plantamour, should be extended to other stations near the base of the Alps, and for this, as well as other reasons, it is highly desirable that the observations at Milan and Turin should be made at hours which correspond with the Swiss observations. On the Extent of the Earth’s Atmosphere. By the Rey. Professor Cuarus, M.A., F.RS., F.R.A.S, The object of this paper was to show that the earth’s atmosphere is of limited 80 F REPORT—1862. extent, and reasons were adduced, in the absence of data for calculating the exact height, for concluding that it does not extend to the moon. It was argued on the hypothesis of the atomic constitution of bodies, that the upward resultant of the molecular forces on any atom, since it decreases as the height increases, must eventually become just equal to the force of gravity, and that beyond the height at which this equality is satisfied, there can be no more atoms, the atmosphere termi- nating with a small finite density. It has been generally supposed that the earth’s atmosphere is about 70 miles high, but on no definite grounds, and the estimates of the height have been very various. Against the opinion that it extends as far as the moon, it was argued that, as the moon would in that case attach to itself a con- siderable portion by its gravitation, which would necessarily have some connexion with the rest, there would be a continual drag on the portion more immediately surrounding the earth, and intermediately on the earth itself, which would in some degree retard the rotation on its axis. Hence if, as there is reason to suppose, the rotation be strictly uniform, the earth’s atmosphere cannot extend to the moon. The author also stated that if by balloon ascents the barometer and thermometer were observed at two heights ascertained by observation, one considerably above the other, and both above the region in which the currents from the equator influence the temperature, data would be furnished by which an approximate determination of the height of the atmosphere might be attempted. On the “ Boussole Burnier,”’ a new French Pocket Instrument for measuring Vertical and Horizontal Angles. By F. Gatton, F.R.S., F.R.G.S. This instrument is about 3 inches long and ¢ inch deep. Its outside is composed of two faces of brass with pear-shaped outlines, separated by vertical sides. In the body of the instrument are two delicate circles placed in parallel planes; at its smaller end is a cylindrical lens, which views the nearer graduations on the rims of the two circles; on the upper face of the instrument are sight-vanes like those of an azimuth compass; on the lower face is a light universal joint, which is used when the instrument is attached to a support, and not held, as it may be, in the hand. One of the circles is of aluminium, and is borne by a compass-needle; it gives horizontal angles when the instrument is held horizontally. The other is of silvered copper, unequally weighted, and is supported by a delicate axis playing in jewelled holes: it gives vertical circles through the action of gravity when the instrument is held vertically, just as the compass-circle gives azimuthal angles through the action of the magnetic force when the instrument is held horizontally. The remarkable simplicity and compactness of the Boussole Burnier would make it useful to the traveller, the geologist, and the military engineer. It is the inven- tion of Lieut.-Col. Burnier of the French Engineers, and has been perfected in its details by M. Balbreck, No. 81 Boulevard Mt. Parnasse, Paris. European Weather-Charts for December 1861. By F, Gatton, 7.B.S., F.R.GS. The author submitted for examination a series of printed and stereotyped charts, compiled by himself, that contained the usual meteorological observations made at eighty stations in Europe, on the morning, afternoon, and evening of each day of December 1861. They were printed partly in symbols and partly in figures, in such a form that each separate group of observations occupies a small label, whose centre coincides with the geographical position of the station where the observations were made. The amount of cloud is expressed by shaded types, the direction of the wind by an equivalent to an arrow, and its force by a symbolical mark. The tempera- ture of the wet and dry thermometers, and the barometric readings (reduced to zero and sea-level) are given in figures. As the charts had been too recently printed to admit of a thorough examination, and as they were ultimately to appear as a sepa- rate publication, the author abstained from other deductions than those that were obvious on inspection. Among these, the enormous range and the simultaneity of the wind-changes, testifying to the remarkable mobility of the air, were exceedingly conspicuous. TRANSACTIONS OF THE SECTIONS. 381 On the Distribution of Fog round the Coasts of the British Islands. By Dr. Guavstonz, F.RS. Certain conclusions on this subject formerly arrived at by the author had been re-examined by means of additional returns from the meteorological journals kept at all the stations belonging to the three general lighthouse authorities in England, Scotland, and Ireland, and some returns lent him by Mr. James Glaisher. These afforded confirmation of the greater uniformity of distribution of fogs over the surface of the sea than on land, of their great prevalency where the south-west wind from the ocean strikes upon high ground, of the comparative infrequency of foe on the coasts of straits or portions of sea nearly surrounded by land, and other oints previously noted. The returns also indicated that some years are much more oggy than others in nearly all localities; that the same fog sometimes prevails over a large extent of country; and that the frequency of fog differs very greatly in different months of the year, January, February, or March being on some coasts almost free. A generally accepted means of distinguishing between “fog” and “mist” is a great desideratum. On a New Barometer used in the last Balloon Ascents. By J. Guatsumr, F.R.S, Mr. Glaisher exhibited a mercurial barometer which had been designed and con- structed by Messrs. Negretti and Zambra for the purpose of checking the readings of the Gay-Lussac’s barometer which had been used in the several late balloon ascents. ‘The correctness of the readings of a Gay-Lussac’s barometer at low pressure depended upon the evenness of the tube, and it is difficult to calibrate so large a tube. Messrs. Negretti and Zambra selected a good tube, 6 feet in length, attaching a cistern to its lower end. Mercury was boiled throughout the length of the tube; at the entrance of the cistern was placed a stopcock, by which means any definite quantity of mercury could be allowed to pass from the upper half of the tube into the cistern, and its height in the cistern noted and engraved; then a second portion, and so on. This process could be repeated. When the cistern was thus satisfactorily divided, the tube was cut in two, and to the upper half the cistern was joined ; a scale was attached to this portion, and the reverse operation was performed, viz., allowing portions of the mercury to pass from the cistern into the tube, which could be regulated by means of the stopcock, and thus the scale was divided. The process, in fact, is using the tube to graduate itself. In carriage, the stopcock locks the mercury in the tube. This instrument was used, and acted well on the extreme high ascent. On the Additional Evidence of the Indirect Influence of the Moon over the Temperature of the Air, resulting from the Tabulation of Observations taken at Greenwich rn 1861-62. By J. Park Harrison, M.A. The author stated that the additional evidence derived from the observations of mean temperature at Greenwich for the years 1861-62 confirmed the conclusions arrived at from a tabulation of the observations for the forty-seven years previous, viz., that the temperature of the air at the moon’s first quarter is higher than it is at full moon and last quarter, and that this is due to the amount of cloud at first quarter being greater on the average than it is at the periods of full moon and last quarter. The difference in the amount of rain also at first quarter in 1861-62 was 2-27 inches more than at full moon, on a mean of eighty-four observations on seven days at each period. On the Relative Amount of Sunshine falling on the Torrid Zone of the Earth. By Professor Hunnussy, F.R.S. By the aid of the author's transformations of formule given by Poisson, the area of that portion of the equatorial regions of the earth which receives as much sun- shine as the rest of the earth’s surface is ascertained. This area, at the outer limits of the earth’s atmosphere, is thus found to be bounded by parallels situate at distances of 23° 44’ 40” at each side of the equator; hence the amount of sunshine falling on oe REPORT—1862. the outer limits of the earth’s atmosphere between the tropics is very nearly equal to that which falls on the remaining portions of the earth’s surface. If we reflect that, according to Principal Forbes’s researches, the amount of heat extinguished by the atmosphere before a given solar ray reaches the earth is more than one-half for in- clinations less than 25°, and that for inclinations of 5° only the twentieth part of the heat reaches the ground, we immediately see that the torrid zone of the earth must be far more effective than all the rest of the earth’s surface as a recipient of solar heat. It follows, therefore, that the distribution of the absorbing and radiating surfaces within the torrid zone must, upon the whole, exercise a predominating in- fluence in modifying general terrestrial climate. On the Hurricane near Newark of May 7th, 1862, showing the force of the Hailstones and the violence of the Gale. By KE. J. Lown, F.R.AS. §e. The hurricane about to be described was accompanied by a thunder-storm, which was more or less spread over the centre of England. On the previous evening there were violent thunder-storms, accompanied in various places with large hailstones and with rose-coloured lightning. The hurricane of the 7th of May was remarkable for its violence near Newark, and for the violence of the thunder-storm which oc- curred at the same time ; it will long be remembered in the neighbourhood on account of the devastation that was caused, for the particularly striking night-like darkness, for the great size and curious forms of the hailstones, and on account of the mag= nificence of the colour of the lightning. At Highfield House the morning was sultry, with thunder about noon, and again continuously in 8. and 8.E. at three o'clock. At half-past two the temperature in shade had risen to 73°°6 with a west wind, but the clouds whirling round in all directions, a low current carried broken nimbi rapidly from west, whilst the storm-cloud was approaching in a 8.S.E. cur- rent, At half-past four o’clock the temperature had fallen to 60° (a descent of 13°-6 in two hours), whilst the wind had risen to half a gale. The thunder, though distant, was frequent. The sky gradually became blacker and blacker, until at five o’clock it was darker than I had ever before seen it except during a total eclipse of the sun. A book with bold type could scarcely be read at a window, nor away from it could the hands of a watch be seen. This storm put on very much the appearance of a total eclipse; near objects had a yellow glare cast upon them, and the landscape was closed in on all sides at the distance of half a mile by a storm-cloud wall. Rain fell in torrents, but not in an ordinary manner; it was swept along the ground in clouds like smoke. Flashes of lightning also came in impulses, four or five following each other in rapid succession, succeeded by a brief pause, and then four or five more. The colour of the lightning was lovely beyond description, being an intense bluish red—almost rose, The wind now veered to the 8.S.E., taking the storm’s di- rection. The temperature had descended to 51° (a fall of more than 223°), and the anemometer showed 9 lbs. pressure on the square foot. Severe as this storm was at Highfield House, it dwindled into insignificance when compared with its violence near Newark. It is scarcely possible to imagine any destruction more complete than that effected by this fearful storm. Fortunately its ravages were confined within narrow limits, being restricted to three miles in length and 150 yards in width, commencing at the village of Barnby; after proceeding a mile its violence considerably increased ; before reaching Coddington it tore up the hedges that sur- rounded the fields and unroofed the farm buildings. At Balderton Lane it threw down farm buildings and uprooted enormous oak-trees ; a quarter of a mile further it unroofed the house of Mr. James Thorp’s head keeper, the hailstones breaking nearly all the windows, having in many instances been driven through the glass, cutting out smooth holes. The spout of this house, too heavy for one man to lift, was carried 100 yards, and a perfectly sound elm-tree, about 60 feet in height and 5 feet 10 inches in circumference (where broken off), was snapped asunder four feet from the ground, and the tree carried twenty-nine yards through the air. The wood of this tree was twisted to the very heart. Here a man was lifted off the ground and then carried twenty yards, being unable to save himself, finally lodging inahedge. Thirty or forty yards from Mr. Thorp’s house at Beaconfield the hur- ricane divided, leaving the house itself intact, and also the trees in its immediate TRANSACTIONS OF THE SECTIONS. 33 neighbourhood, from 8. round by E. to N., while on the W. side outbuildings were unroofed or destroyed, the large garden wall thrown down, and the fencing around the plantations broken off and carried into the fallen timber. A few yards beyond the Fonds the gale reunited, and passing through a wood destroyed all the trees; it then proceeded across fields as far as Winthorpe, and here its fury became exhausted. The gale rotated in the direction of W. to 8., which was apparent from the twist of the wood of the snapped-off trees, and also from an avenue of chestnuts situated on the extreme eastern edge of the hurricane having all the torn-off boughs lying on the S. or storm-side, and being carried back beyond the level of the trees. Proposed Measurement of the Temperatures of Active Volcanic Foci to the greatest attainable Depth, and of the Temperature, state of Saturation, and Velocity of Issue of the Steam and Vapours evolved. By Rozurt Mater, C.E., M.A., FBS. The author having circulated the following document amongst various Members of the British Association a short time prior to the Meeting and during same, en- larged upon the objects of his proposed experimental inquiry ; and explained to Section A, in part, the methods he intended to employ. Determination of Voleanie Temperatures.—It is a singular fact, and one scareely creditable to the past investigation of volcanic phenomena, that up to this time no careful attempt has been made to determine, even approximately, the temperature of the heated or incandescent focus of any active volcano, even at the mouth of the crater, still less to depths lower down. Much labour and time have been lavished upon analysation of the gases and solid products evolved, and upon other still more minute inquiries—more than was ne- cessary, indeed, to obtain all the leading information as to the nature of yulcanicity (using that general term to express the train of forces and of events whence the supply of voleanic heat and energy is kept up) which such results are capable of yielding ; but the most obvious of all physical data, viz. those referring to the actual temperature of volcanic foci at the greatest attainable depths, have been completely neglected by vulcanologists, either because they too hastily concluded that experimental measurements of such were impossible, or, more probably, be- cause, as often happens in the investigation of nature, the most obvious question is that which is longest neglected being put to nature. The experiments that have been made on the heat of lava-fisswes, and upon the temperatures of geysers, hot-springs, mines, &c., do not of course bear upon those here in point. _ It seems almost unnecessary to dilate upon the importance to vulcanology, and to all cosmical physics, of some precise information as to these focal temperatures, the knowledge of which would assign limits at once to many speculations at pre- sent vague and perhaps valueless, give measure to the estimation of the forces con= ai and direct further investigation as to the sources whence these may be erived. For brevity, the writer may venturé to quote on this subject the following passiee from his Report to the Royal Society on the great Neapolitan earthquake of 1857 :— “T cannot find that any professed investigator of volcanos has ever thought of making the very obvious on important experiment of lowering, with an iron wire, a pyrometer as far as possible into a crater, in order to get some idea of its actual temperature, even within a few score yards of its mouth. “ When on Vesuvius, on the occasion of this Report, I feel satisfied that I could have so measured the temperature of the minor mouth—then in powerful action— to the depth of several hundred feet, had I possessed the instrumental means at” hand. To this smaller mouth it was then possible, b Minne the face in a wet cloth, to approach so near upon the hard and ahienly -defined (though thin and dangerous) crust of lava through which it had broken, as to see its walls for quite 150 feet down, by estimation. They were glowing hot to the very lips, although constantly evolving a torrent of rushing steam with varying velocity. Accustomed as I have been by profession for years to judge of temperature in large furnaces by the eye, I estimated the temperature of this mouth, by the appearance of its heated Ss] 1862, | $4 REPORT—1862. walls, at the lowest visible depth ; they were there of a pretty bright red, visible in bright winter sunlight overhead. Ihave no doubt then that the temperature of the shaft at from 300 to 500 feet down was sufficient to melt copper, or ata 1900° to 2000° Fahy. “From the extremely bad conducting power of the walls of a volcanic shaft, there is scarcely any loss of heat from any cause, except its enormous absorption in the latent heat, of the prodigious volume of dry steam, which is constantly being evolved. It is perfectly transparent for several yards above the orifice of the shaft, and is not only perfectly dry steam but also superheated; and although this steam may be at the mouth very much below the highest temperature of the hottest point, the temperature of the shaft or duct that carries it off will be very nearly at all depths the same, to probably within a very short distance of the point of greatest incandescence.”—Rep. Roy. Soc., &c., Pt. 1. chap. xii. vol. i. pp. 313, 314. The writer respectfully urges that the organization of experiments to determine such data is a subject worthy the immediate attention of the British Association, the Royal Society, and other similar scientific bodies. From recent information he has reason to believe that the existing state of Vesuvius is favourable to such experiments, which the writer is himself prepared to attempt, provided the necessary apparatus and other means be placed at his dis- posal. The experiments that he would in the first instance propose are— (1) The temperature at the mouth or mouths, to the lowest reachable depths within the Vesuvian craters. (2) The temperature of the issuing steam vapours or gases at the mouths, and the degree to which the former are superheated. (8) Approximate determination of the velocity (extreme and mean) of the issuing discharge of steam, &c., with a view to estimation of the volume, in given time, and of the total heat carried off, in same. For the 1st and 2nd, three or more mutually controlling methods may be employed. a, The air pyrometer, or that of Daniell, maximum self-registering. b. The differential bar pyrometer (of two metals), with constant galyanic con- nexion to the surface. c. The resistance coil thermoscope, also in constant con- nexion with the surface. The writer, as a practical engineer, has well-founded hope of inserting either or all of these to a considerable and known depth within the crater or craters. For the 3rd, analogous methods should be employed. For the 4th, there is no doubt that Dr. Robinson’s anemometer may be so modified as to be made avyail- able to determine the issuing velocity in various parts of the column. Into the mechanical arrangements for placing, lowering, and observing, &c. these instru- ments, it is not necessary here to enter. Vesuvius presents many advantages as a first experimental station; but the inquiry would afterwards be advantageously extended to other volcanic vents. Whatever presumable difficulties may exist, if successfully overcome in the first case, will nearly vanish as regards subsequent repetitions elsewhere. On Meteorology, with a Description of Meteorological Instruments. By T. L, Pranrt. Meteorological Observations registered at Huggate, Yorkshire, By the Rey. T. Ranxrn, This notice was in continuation of those annually made for many years by the author on the Wolds of Yorkshire, at an elevation of 650 feet above the level of the sea. They contained the annual tables of means, with notes of the days on which eis most remarkable events connected with the weather and meteors occurred during the year. On Objections to the Cyclone Theory of Storms. By 8. A, Rowett. Admitting that the winds in storms do at times take a more or less circular eourse, and that whirlwinds may sometimes occur during storms, the author believed TRANSACTIONS OF THE SECTIONS. 35 that these are only occasional and minor phenomena in storms, and not the storm itself, as represented in the cyclone theory. He objected to the cyclone theory on the grounds that it is opposed to all the known natural laws which affect the con- dition of the atmosphere, as he believed it to be impossible that a disk of some hundreds of miles in diameter, but of a mere mile or so in thickness, of air lighter than the general atmosphere, could make its way for days and days in succession through the densest part of the atmosphere,—that the evidence in support of the theory is insufficient (this he attempted to show by the aid of diagrams from Reid’s ‘Law of Storms,’ and a general reference to works of the kind), and that the phe- nomena of the (so-called) cyclone storms may be otherwise accounted for, On the Performance, under trying circumstances, of a very small Aneroid Barometer. By G. J. Symons, This instrument, which the author exhibited, had been worn constantly by him recently while at sea in rough weather, while riding and driving over roadless districts in the Orkneys, and also on several occasions when rough climbing and severe jumps had been necessary: he therefore presumed he might reasonably con- clude that it had been fully tried. It had been tested before, during, and after the voyage, and had in each case given the same result when compared with mercurial standards. He therefore inferred that it might be considered even less liable to derangement from travel than an ordinary watch. The instrument was very small, being only two inches in diameter and three-quarters of an inch thick, On the Disintegration of Stones exposed in Buildings and otherwise to Atmo- spheric Influence. By Professor James Toomson, M.A., C.E. The author haying first guarded against being understood as meaning to assign any one single cause for the disintegration of stones in general, gave reasons to show—lst. That there may frequently be observed cases of disintegration which are not referable to a softening or weakening of the stone by the dissolving away or the chemical alteration of portions of itself, but in which the crumbling is to be attributed to a disruptive force possessed by crystalline matter in solidifying itself in pores or cavities from liquid permeating the stone. 2nd. That in the cases in question the crumbling away of the stones, when not such as is caused by the freez- ing of water in pores, usually occurs in the greatest degree at places to which, by the joint agency of moisture and evaporation, saline substances existing in the stones are brought and left to crystallize. 3rd, That the solidification of crystal- line matter in porous stones, whether that be ice formed by freezing from water, or crystals of salts formed from their solutions, usually produces disintegration— not, as is implied in the views commonly accepted on this subject, by expansion of the total volume of the liquid and crystals jointly, producing a fluid pressure in the pores—but, on the contrary, by a tendency of crystals to increase in size when in contact with a liquid tending to deposit the same crystalline substance in the solid state, even where, to do so, they must push out of their way the porous walls of the cavities in which they are contained, and even though it be from liquid permeating these walls that they receive the materials for their increase, CHEMISTRY. | Address by Professor W. H. Mitime, 1.4., F.B.S., President of the Section. Once in about a quarter of a century a mineralogist is placed in the chair of the Chemical Section of the British Association. This procedure is not without its inconvenience: many important questions are likely to present themselves during the meetings of the Section which a mineralogical president can rarely be competent todecide, In another point of view, however, this arrangement is more satisfactory ; * 36 REPORT—1862. it is symbolical of the removal of a barrier which once threatened to separate mineralogy from chemistry, to the serious detriment of both. While some minera- logists sought to exclude chemistry from their systems, chemists intent upon dis- covery in the newly opened field of organic chemistry neglected mineral analysis. But of late these mutually estranged sciences have exhibited a growing tendency to reunite, and to aid one another. The chemists now freely admit the mineralogists as their associates, not unfrequently sharing their labours, and include geometrical and optical characters in the descriptions of the new combinations they discover. Of this we have instances in the memoirs of Kopp, Rammelsberg, Hofmann, Sella, Marignac, Des Cloizeaux, and in those of Haidinger, Leydolt, Grailich, Dauber, Schabus, v. Lang, Schrauf, v. Zepharovich, Rotter, A. and E. Weiss, Murmann, and Handl. The experiments on the formation of minerals, commenced by Berthier and Mitscherlich, have since been varied in almost every possible way. Ebelmen, de Sénarmont (whose recent death is a grievous loss to the sciences we cultivate), Daubrée, Wohler, Manross, and H. Deville have successfully imitated the processes of nature in producing a large number of crystallized minerals in the laboratory, and thus have helped to obliterate the boundary arbitrarily drawn between the studies of the chemist and those of the mineralogist. The memoirs I have cited in proof of the intimate connexion of chemistry and mineralogy deserve our especial attention for another and more important reason. The observations they record, being made on crystals of accurately known compo- sition, far exceeding the crystallized minerals in number, and differing from minerals in being quite free from any admixture of foreign matter, furnish the only data from which we may hope that some future Newton of the science will be enabled to discover a simple law of the dependence of the form, optical and physical pro- perties of crystallized bodies on the substance of which they are composed. On the Formation of Organo-Metallic Radicals by Substitution. By Gzorce Bowprer Bucxton, F.R.S. The object of this inquiry was to investigate the order in which the metals of the organo-metallic radicals were capable of substitution, through the agency, in the first place, of simple metals, in the second place, of salts of simple metals, and in the third place, of salts of other organo-metallic bodies. It was found that when metals acted upon these radicals, substitutions were affected, in the greater number of cases, in the order indicated by the ordinary electro-positive or electro-negative position of the contained metals. Exceptional cases, however, occurred. By the action of sodium on mercuric ethyl, the mercury is partly extruded, and a double compound of mercuric and sodium-ethyl is obtained. By the action of chloride of cadmium on zinc-ethyl, appreciable quantities of cad- ‘mium-ethyl were formed, which, however, could not 3 satisfactorily separated, either by distillation or the action of anhydrous solvents, from the unctuous mass of chloride of zinc which is one product observed. Mercurie ethyl and bichloride of tin react powerfully with the evolution of much heat, and result in the separation of chloride of mercuric ethyl and chloride of stannic sesquiethyl, according to the equation Et \S" 61 Et 5) HeR + 6.0 =3 | Hg Bl 4 Terchloride of antimony, on the other hand, is converted by mercuric ethyl into triethylstibene, the whole of the chlorine passing over to the mercuric radical. Ey Cl Et Et (osB)o() (08) (8) From the circumstance that titanium, in many respects, imitates the behaviour of the metal tin in its combinations, experiments were made with the bichloride, Zinc-ethyl strongly reacts upon this body, if assisted by gentle heat. Chloride of Sn = TRANSACTIONS OF THE SECTIONS. 37 zine is formed, but gases are immediately disengaged if distillation is attempted. Bichloride of titanium and stannic diethyl result in the reduction of the bichloride to the condition of sesquichloride, whilst the oily chloride of stannic sesquiethyl separates according to the equation Et Cl Et Sn Ti 7 Cl Sn Et Cr=2 40 Cle Ht 1.0, H, CL ssp (Ta (MO sng The paper concluded with considerations upon the possibility of substituting ethyl for oxygen in the organo-metals, and also remarked upon the question, pos~ sessed of considerable interest, how far, and in what manner, the introduction of different metals can be effected in the organo-metallic radicals, represented by the type X+ File X+ R/xt Can RR be represented by different metals, in the same manner as X may re~ present different alcohol radicals? The author hoped shortly to be in a position to answer this inquiry. On the Action of Nitric Acid upon Pyrophosphate of Magnesia. By Dueatp Campsett, Analytical Chemist to the Brompton Hospital, London. When pyrophosphate of magnesia was dissolved in ordinary nitric acid, and ex- posed in an open capsule to temperatures ranging from 320° F. to 550° F, till the weight became constant for each temperature, it was invariably found to have in- ee very much in weight; although not always to the same extent, as shown elow :— Temperature. Percentage increase of weight. - Difference. 320° F. 22 to 30 8 per cent. 420 19 - to 21 a ea, 550 135 to 14:5 ilar When the pyrophosphate of magnesia, still retaining nitric acid, but constant in weight at 320° F., was heated sufficiently to drive off all the nitric acid, it was found to have decreased in weight, not to a uniform amount, but varying from 9 to 16 he cent., according to the greater or less rapid application of heat; on heating in he same manner the pyrophosphates of magnesia retaining nitric acid, and constant in weight at 430° F. and 550° F., they were found likewise to have decreased much in weight, although not to so great an extent, by pyrophosphate of magnesia being volatilized along with the nitric acid. It is inferred from these experiments that nitric acid has a stronger affinity for magnesia than pyrophosphoric acid has, and that on adding nitric acid to pyrophos- phate of magnesia, nitrate of magnesia is formed, pyrophosphoric acid being libe-~ rated; and this was proved to be the case by dissolving pyrophosphate of magnesia in nitric acid, evaporating the solution till syrupy, and then placing it under a bell-jar over sulphuric acid; after a time nitrate of magnesia crystallized, and pyrophosphoric acid could be drained off. But although nitrate of magnesia is formed and pyrophosphoric acid set free on the addition of nitric acid to pyrophosphate, it is probable that, when this mixture is evaporated and heated, the products are not always mere mixtures of nitrate of magnesia and pyrophosphoric acid, but that they are sometimes compounds; and the reasons for this opinion are, that these products are but slightly deliquescent, that ‘nitric acid is less readily expelled from them than from nitrate of magnesia, and that on heating these products suddenly, pyrophosphate of magnesia is yolati- lized, though it is not under ordinary circumstances a volatilizable salt. From the above results, the author recommends the discontinuance of moistening the pyrophosphate with nitric acid when calcining it, when estimating phosphoric acid or magnesia, as it may be apt to lead to a source of error. 358 REPORT—1862. Mémoire sur les modifications temporaires et permanentes que la chaleur apporte ad quelques propriétés optiques de certains corps cristallisés. Par A. Dus CLOIZEAUX. On sait, d’aprés d’anciennes recherches de MM. Brewster et Mitscherlich, que dans certains cristaux l’écartement des axes optiques et l’orientation de leur plan varient avec la température. Pendant longtemps on n’a guére connu que les phéno- ménes si tranchés qui se manifestent dans la Glaubérite et le gypse. d’ai constaté récemment qu’un assez grand nombre de substances anhydres ou hydratées, telles que le feldspath orthose, la Heulandite, la Prehnite, le clinochlore, la eymophane, la Brookite, &c., subissaient aussi l'influence de la chaleur d’une maniére plus ou moins marquée ; mais de plus j’ai découvert que si l’on élevait suffisamment la température, ce qu’il est facile de faire pour Vorthose, la cymophane et la Brookite, par exemple, les modifications optiques, de temporaires qu elles sont lorsqu’on ne dépasse pas 300 4 400 degrés Centigrades, deviennent enti¢rement permanentes. Le minéral qui, par sa transparence et son homogénéité, se préte le mieux aux expéri- ences les plus variées et les plus exactes, est un orthose vitreux de Wehr dans l’Lifel, et c’est sur une plaque de cette nature que j’ai obtenu les résultats suivants, Modifications temporaires. Ecartement des tem pe Riek cleeenag a Température axes optiques. Centigrades. plan paralléle au en degrés plan de symétrie. Centigrades. 16° axes rouges; eae ; 4 paralléle & la diagonale Ciao eegeen eee ter pe pala Horizontal 6 yes <.+;s60e cueyeiers { & 39 cy pee eee ee 145 12° a 13° axes bleus; 18-7 Ale Nein: sci eee 150 plan paralléle au plan de All sahes!is tot ldco: Maen . 155 symétrie, .......... bees BA ci ie eae cee « 1625 AD ot acral » GREENE esl) eerie des fe MATL Sa dear te fas ‘plan paralitle au ‘ SO ere ad i ee plan de symétrie. AG: 9.;, atiartiintatceee . 195 one ; AB SD, ssi Lise aaa 204 OM as cietaisas nant ts 42-5 LW is (ys adn tasgeterste etn 207 CO ets tina es Wa artis 45 Zl ‘el Octo n. coetias itt 545i ee © G cieituaye's Sid Sh aauleve 45 ASI AD. 1, corre siete ee ae 212 DOS steht sick cee eis 46 AQ dbase herp et eM 215 DN oe oc eyed We, 2 48 50 HASH Se see uf 225 1x Mai eitstew swlelee ne eis 50 51 alse vistoaieraeOe ee 228 ieee d,s Sis sarees 5 . 53 ED tess ate oasncinteeieast eae 237 1D Fy eee Ble akawhe.s & ortteks 56 ES OD vids ticsneeine ree aoe 240 UC, eRe i ooh ie teg ad sooo, ot 58 De ine Wisechenetee Ec 250 18 Sass sTieiei ss ire S 60 A at orth arch eee 260 21 Ween thas sceel ie Cars pols 35, Bi, SOM i yaar erat » ofclb, EO D2. Metaetns tae tais ace Saok oe 7 ACAD: eke cis Sais helenae 4% 275 DS! sehen ere eae CRS 725 DSi teats cunt tiieecites hale 275 ps Pe eee eee 75 ‘oh HW ree mae Bip pe a oe hr 279°5 QD.” ei oia «Miele errant bats 80 BE SO esis tésnp ita eter 290 DG oe. as ico eee 82 FI AN 2s sFayenciy ke Soe ae 28 yl PEI ES st IER a $0 21S Bt I ane nee ee Cece » 295 yo am IR Raba iy GE Yigal 93 EO rat ales oun tire ee 302 SU al. Seueen ee Ate 100 GO AO Less. co .crcteen area 306 BP oe rel veneered oe tee 105°5 2B a 8 RR ON 312 5s Se LSE i 12 GL AD 2 oe ae rset a 3155 SA.» hs chance eee 125 A Ce. Fee ae 319 als PMR NS TSR eee 128 G5).49 aware stare sete wine ee 5 1A ic Ses HR ma os MO 152-5 64 ofvanaiie i vin 1h legen ee ee 8 Be ee ~ oe TRANSACTIONS OF THE SECTIONS, 39 On voit que l’écartement des axes Poe va toujours en augmentant avec la tem- pérature, et que Vaugmentation est beaucoup plus rapide de 42° 4 142° que de 142° a 342°. Les observations, répétées un grand nombre de fois, ont été faites au moyen d’un goniométre particulier installé sur un microscope polarisant, dont j’ai donné une de- scription abrégée en 1859 dans le tom. xvi. des ‘ Annales des Mines,’ et que j’ail’hon- neur de mettre sous les yeux de la Section. La plaque estsoumise 4 un courant d’air chaud fourni par une lampe a alcool, et circulant dans une cheminée horizontale en cuivre placée sur le microscope; l’écartement des axes optiques peut étre mesuré & chaque instant a travers deux ouvertures pratiquées au centre des parois horizontales de la cheminée et munies d’une glace mince; la température de l’air est indiquée en méme temps par deux thermométres placés 4 droite et 4 gauche de ces ouvertures. LO Mais en employant ce procédé, je ne pouvais pas dépasser une température d’environ 350°. Pour m’assurer si les phénoménes suivaient la méme marche au-dela de cette température, j’ai placé mon microscope dans une position horizontale, et sur le pror longement de son axe derriére ]’éclaireu= j/ai disposé un prisme de Nicol servant de polariseur. Entre l’éclaireur et l’obj ectif, distants d’enyiron deux centimétres, j’al pee / || |\ 1 Some | aA suspendu, a l’aide d’une pince en rlnieiel une trés petite lame parfaitement limpide et homogéne d’orthose de Wehr sur laquelle pouvait étre dirigé le dard d’un chalumeau @ gaz; un cercle horizontal gradué, au centre duquel passe la tige qui soutient la pince de platine, permet de mesurer l’écartement des axes optiques; pour plus de facilité j’ai opéré avec un verre rouge monochromatique. Une plaque, qui a 14° Cent. avait ses axes rouges ¢cartés de 18° 30’ dans un plan aralléle au plan de symétrie, a montré, dés la premiére application de la chaleur, eux systémes d’anneaux dont le nombre augmentait rapidement tandis que leur diamétre diminuait ; leur forme ainsi que celle des hyperboles qui les traversent a conservé toute sa symétrie jusque vers la naissance du rouge ou ]’écartement des axes a été trouvé de 70°. Aussitét que le rouge est deyenu apparent, les anneaux et les hyperboles se sont déformés en se brisant, la mesure de l’écartement ne s’est pe faite qu’avec difficulté, et vers 700° elle a donné successivement 2E = 118°, 122°, 24°, L’expérience ayant été arrétée pour ne pas faire éclater les lentilles du mi- croscope, la plaque s’est refroidie rapidement, les phénoménes optiques ont repassé Ee toutes les phases qu’ils avaient déja parcourues, et A 15° Cent. j’ai retrouvé ‘angle des axes égal 4 19°; il ne s’était donc produit aucune modification perma- nente. Cette plaque soumise plusieurs fois aux mémes épreuves a toujours offert des - apparences semblables; Vaccroissement de température semblait augmenter son €paisseur, et sa structure au rouge se rapprochait de celle que présentent a la tem- on ordinaire certains cristaux de Prehnite, de Heulandite, &c., composés de ames irréguliérement encheyétrées. Une seconde plaque carrée, ayant 4 15° Cent. ses axes rouges écartés de 13° dans un plan paralléle a la diagonale horizontale de la base et ses axes bleus écartés de 16° 30’ dans un plan paralléle au plan de symétrie, s’est comportée d’une maniére analogue. A partir du rouge naissant le plus foible, les anneaux se déformaient fortement, les hyperboles disparaissaient, et l’angle apparent des axes, qui était con- sidérable, ne pouvait plus se mesurer exactement, 40. REPORT—1862. Des résultats précédents il semble permis de conclure que jusqu’é 350° environ la conductibilité calorifique n’éprouve pas de changement notable dans l’intérieur du feldspath orthose, mais qu’a partir de 400° ou 500° la propagation de la chaleur s’y fait d’une maniére assez inégale pour provoquer temporairement une perturbation plus ou moins profonde dans l’équilibre de ses arrangements moléculaires. Cet équilibre peut reprendre son état primitif aprés le refroidissement, si la perturba- tion n’a duré que 2 ou 3 minutes 4 une température qui ne dépasse pas 700°. Nous allons yoir maintenant qu’en prolongeant l’action de la chaleur pendant un temps suffisant, au rouge sombre ou au rouge blanc, il en résulte une nouyelle disposition physique qui se manifeste par des modifications permanentes dans lorientation et l’écartement des axes optiques. Modifications permanentes. lére plaque d’orthose de Wehr donnant a 13° Centig. avant calcination : 2H*=13° axes rouges, plan paralléle a la diagonale horizontale ; 17° axes bleus, plan paralléle au plan de symétrie._ Aprés calcination de 1 heure sur une lampe 4 alcool ordinaire : 2H =10° axes rouges, plan paralléle a la diagonale horizontale ; 21° axes bleus, plan paralléle au plan de symétrie, a 13° Centig. Aprés calcination de 4 heures sur une lampe & gaz vers 600° 4 700° et refroidisse- ment lent de 4 heures: pone patel ia plan paralléle au plan de symétrie, 4 13° Centig. : Aprés une nouvelle calcination de 7 heures sur la lampe & gaz et refroidissement rusque : : Baan a mies Wea, plan paralléle au plan de symétrie, 4 15°-5 Centig. Qieme plaque de Wehr donnant avant calcination 4 13° Centig. : chins & 30! ae pa vtene plan paralléle 4 la diagonale horizontale. Aprés une calcination de 8 heures sur la lampe 4 gaz et refroidissement brusque : re ted 30) ar tees” plan paralléle au plan de symétrie, 4 15°-5 Centig. Aprés une exposition de 8 jours, dont 36 heures de calcination vers 800° et 6 jours de refroidissement gradué, dans un four de Sévres cuisant au dégourdi ; 2H=37° axes rouges, 49° axes bleus, 8itme plaque de Wehr trés epaisse donnant avant calcination a 12° Centig. : 2H=25° axes rouges, 17° axes bleus, Aprés 1 heure de calcination sur la lampe & gaz, pas de changement. Aprés 5 minutes de calcination sur un chalumeau 4 gaz vers 900° et refroidisse- ment brusque : 2E=33° 30’ axes rouges, 38° axes bleus, plan paralléle au plan de symétrie, 4 19°-5 Centig. plan paralléle a la diagonale horizontale. plan paralléle au plan de symétrie, A 18° Centig. Aprés 8 jours d’exposition dans un four de Sévres cuisant au dégourdi: 2K =45° axes rouges, 48° axes bleus, 4 4ieme échantillon de Wehr débité en 3 plaques donnant ayant calcination 4 13° entig. : 2K=17° 30! axes rouges, 27° axes bleus, plan paralléle au plan de symétrie, 4 19°-5 Centig. plan paralléle au plan de symétrie. * 2E désigne l’angle apparent des axes optiques dans l’air. EE TRANSACTIONS OF THE SECTIONS. 4] La lee plaque, chauffée pendant 7 heures au rouge foible sur une lampe’a gaz et refroidie brusquement, a donné : =21° o 2H - zee oateg plan paralléle au plan de symétrie, 4 13° Centig. ? > Aprés une calcination de ¢ heure sur un chalumeau 4 gaz au rouge vif (fusion du cuivre) et refroidissement brusque, l’écartement est devenu: 2H=45° 30' axes rouges : aon es : sa 49° 30 axes bleus, g plan paralléle au plan de symétrie, 4 15° Centig. La 2ieme plaque exposée 4 Sévres pendant 8 jours dans un four chauffant au dé~ gourd: et relroidie trés lentement, a donné : _ ‘e] , raed ae ices, plan paralléle au plan de symétrie, 4 19°-5 Centig. Aprés une nouvelle exposition de 8 jours dans un four cuisant au grand feu et un refroidissement trés lent, on a obtenu: ‘ = Oo U ‘giuae ay eae ica” plan paralléle au plan de symétrie, 4 18° Centig. La 3itme plaque, mise & Séyres au grand few en méme temps que la précédente, a donné : 7 Oo —. — vet plan paralléle au plan de symétrie, 4 20° Centig. ? Plusieurs plaques d’adulaire du Saint-Gothard, calcinées au rouge foible sur une lampe & gaz, n’ont éprouvé aucun changement dans l’écartement de leurs axes op- tiques. ne plaque d’adulaire donnant avant calcination, 4 16°-5 Centig., 2E=108° axes rouges, a été calcinée pendant } d’heure au rouge vif (fusion de l’argent) sur un chalumeau a gaz; elle est devenue laiteuse et translucide par places, et 4 18° Centig. l’écartement de ses axes rouges n’est plus que de 102° 95’. Une autre plaque d’adulaire dans laquelle 2K =111° 23’ pour les axes rouges, & 20° Centig. avant calcination, a donné aprés une 3-heure de calcination au rouge vif sur le chalumeau a gaz, 2E=90° 27’, 4 16° Centig. Dans les fours de Sévres, la teinte laiteuse augmente, la translucidité diminue, et l’angle des axes ne peut plus étre apprécié bien exactement. ne plaque de pierre de lune (moonstone) de Ceylan, dans laquelle l’écartement des axes était de 121° 15’ avant calcination, & 15°-5 Centig. a perdu son réflet cha- toyant et pris une teinte laiteuse aprés une exposition de } d’heure sur le chalu- meau 4 gaz (fusion de l’argent), et 4 18° Centig. cet écartement est devenu 117° 31’. En répétant ces expériences sur les variétés d’orthose connues sous les noms de eisspath de la Somma, sanidine des trachytes des bords du Rhin et de l’Auvergne, loxoclase de New York, microcline de Fredrikswiirn (variété chatoyante) ou de Bodenmais (variété verte non chatoyante), Murchisonite du Devonshire, hyalophane de Binnen, j’ai trouvé que toutes éprouvent sous l’influence de la chaleur des modi- fications permanentes et temporaires analogues a celles du feldspath vitreux de Wehr. Gilets au rouge sombre ou au rouge vif, les échantillons les plus trans- arents et les plus homogénes, comme ceux de Wehr et de la Somma, conservent eur aspect primitif sans autre changement apparent que celui des fissures, paralléles a leurs deux clivages rectangulaires, qui deviennent plus prononcées ; d’autres pren- nent une teinte laiteuse plus ou moins marquée; d’autres enfin, comme ceux des trachytes, deviennent presque complétement opaques. Dans tous les cas, la perte en poids ne dépasse pas 1 milligramme par gramme, quant aux axes cristallogra- phiques leur orientation ne parait pas changer d’une maniére appréciable, car j’ai trouvé sur plusieurs plaques qu'une base produite par clivage faisait avant et aprés calcination, avec la face artificielle normale a la bissectrice aigué, un angle identique & une ou deux minutes prés. Les feldspaths du sixiéme systéme cristallin n’éprouvent par la chaleur aucun changement temporaire ou permanent dans leurs propriétés optiques biréfringentes. Les axes optiques y sont toujours orientés 4 trés peu-prés comme dans I’albite, et leur bissectrice aigué est positive; leur écartement dans lair dépasse 135°. IL parait donc bien probable que, quelque ait été le mode de formation des feldspaths 42 REPORT—1862. tels que l’albite, V’oligoclase, le labradorite et Vanorthite, ils n’ont pas été soumis dans la nature aux mémes influences que ceux dont l’orthose est le type. Les cristaux de cymophane (H1 O, Al? O°) du Brésil, et ceux de Brookite (Ti O7) de la Téte noire en Valais et du Dauphiné, otfrent souvent des plages dans lesquelles les axes optiques présentent 4 la température ordinaire des écartements trés differents et une orientation qui peut avoir lieu dans deux plans rectangulaires entre eux, avec une dispersion d’autant plus considérable que l’écartement est plus petit. I] existe done une grande analogie entre la constitution physique de ces deux minéraux et celle des feldspaths du cinquiéme systéme cristallin. Aussi la calcination détermine- t-elle dans leurs propriétés optiques des modifications permanentes et temporaires entiérement semblables 4 celles que j’ai découvertes dans l’orthose. Si l’on rapporte les formes de la cymophane a un prisme rhomboidal droit de 119° 46’, on voit que dans les cristaux du Brésil les plus transparents et les plus homogénes, le plan des axes optiques est normal a la base et la bissectrice aigué positive, paralléle a la petite diagonale de cette face. L’angle des axes correspondant au rouge peut s’élever jusqu’é 120°, et celui des axes correspondant au bleu jusqu’a 118°. Certaines plages a réflets opalins montrent des axes rouges réunis et des axes bleus séparés dans un plan paralléle ala base; d’autres plages font voir les axes correspondant a toutes les couleurs séparés dans ce méme plan. Une élévation de température a pour effet de Rod art les axes orientés parallélement i la base et d’écarter ceux dont l’orien- tation lui est perpendiculaire. Jusqu’au rouge naissant les changements ne sont sae temporaires, mais une calcination de 15 minutes 4 la température de la fusion e l’argent suffit pour les rendre permanents et déja considérables. La perte en poids est, comme pour lorthose, de 1 milligramme par gramme, et l’aspect extérieur de la substance n’est nullement modifié. Pour la Brookite dont on peut faire dériver les formes d’un prisme rhombique de 99° 50’, le plan des axes optiques est tantot paralléle, tantot perpendiculaire a la base; la bissectrice est positive et reste toujours paralléle 4 la petite diagonale de cette face. La dispersion est trés considérable, et lorsque les axes sont situés dans le plan de la base, les rouges sont plus écartés que les violets ; leur écartement aug- mente d’une maniére temporaire par une calcination foible, et d’une maniére perma- nente par une calcination plus énergique. Dans un échantillon du Dauphiné ou Vangle des axes était de 52° a 20° Centig. j’ai observé temporairement un écarte- ment de 65° 4 220° Centig. Une autre plaque, chauffée avec précaution dans une moufle, a éprouvé une modification permanente qui a porté l’angle de ses axes rouges de 42° a 47°. Les perturbations permanentes que le changement de température apporte dans Véqui sbte moléculaire du feldspath orthose ayant également lieu dans la cymophane et la Brookite, sont évidemment indépendantes de la composition chimique des corps cristallisés. Les expériences faites dans les fours de Sévres, ot le refroidissement est trés lent, ne permettent pas d’ailleurs d’attribuer ces perturbations a des effets de trempe, comme on pourrait étre tenté de le faire au premier abord; on peut done les regarder réellement comme en rapport avec la constitution physique de certains cristaux, et l’on doit admettre que la position dés axes optiques ainsi que leur dis- persion est susceptible de varier dans une méme espéce minérale avec la température a laquelle les cristaux sont ou ont éé soumis. On the Mode of preparing Carbonic Acid Vacua in large Glass Vessels. By J. P. Gasstor, F.BRS. During the process of preparing carbonic acid vacuum-tubes for his experimental researches on the Stratified Electrical Discharge (Philosophical Transactions, 1859 ; Proceedings, 1860-1861), the author ascertained that when the stopper of a glass vessel is very carefully ground, the vacuum will remain without the slightest alter- ation for many months: among a variety of tubes thus prepared, he has one with four glass stoppers, three of which are nearly one inch in diameter. It is upwards of twelve months since this vacuum was prepared, and to the present time, when- ever the discharge from an induction coil is passed through it, there is not the slightest alteration in the appearance of the striz. If a larger aperture is requisite instead of the stopper, all that is requisite is to TRANSACTIONS OF THE SECTIONS. 43 have the two surfaces of the glass very carefully ground, in the same manner as the bell-glasses for an air-pump are prepared; by these means glass vessels of almost any required dimensions can be used, provided care is taken that the form is such as will resist the pressure of the atmosphere. The potash necessary to absorb the residue of the carbonic acid after the exhaus- tion by the air-pump, may be placed at the bottom of the vessel, and gently heated on a sand-bath or by a spirit-lamp, or it may be placed in a tube, and subsequently sealed off by the blowpipe. On the Essential Oil of Bay, and other Aromatic Oils. By J. H. Guapsrone, Ph.D., FBS. This paper consisted of—1st. A description of the essential oils of Bay, Bergamot, Carraway, Cassia, Cedar-wood, Cedrat, Citronella, Cloves, Indian Geranium, Layender, Lemon Grass, Mint, Neroli, Nutmeg, Patchouli, Petit-grain, Portugal, Rose, Santal-wood, Turpentine, and Winter-green, with the specific gravities and powers of refraction, dispersion, and circular polarization. 2nd. Some remarks on the isomeric hydrocarbons, which may be derived from the majority of the essen- tial oils, and which generally resemble each other very closely, though they are rarely identical: 3rd. Notices of some of the oxidized bodies present in these oils, which are generally more refractive and more aromatic than the hydrocarbons of which they are oxygen substitution products. Among the observations were the following :—Oil of Bay consists of a hydrocarbon of the bet hary type, C,, H,,, and eugenic acid. Oil of Neroli contains two hydro- carbons, one of which is a fluorescent body. The essential oil of Petit-grain, which is derived from the leaves of the orange-tree, contains a hydrocarbon resembling the more volatile one from oil of Neroli, which is prepared from the orange flower; and so does the oil of Portugal, from the orange peel. Otto of roses is an oxidized oil; the crystallizable portion of it has a great attraction for ether vapour. The oils of Citronella and of Lemon-grass, from different species of Andropogon, cultivated in Ceylon, consist mainly of oxidized oils which are nearly if not quite identical. There is a very wide difference in the action on the polarized ray exerted by dif- ferent essential oils, both in regard to amount and direction. On the Means of observing the Lines of the Solar Spectrum due to the Terres- trial Atmosphere. By J. H. Guapstone, Ph.D., PRS. The object of this communication was to incite observers in various parts to notice those lines and bands which appear in the spectrum when the sun is near the horizon. They vary under different atmospheric conditions, and probably in different parts of this and other countries. The author had found one of Crookes’s pocket spectroscopes sufficiently powerful to exhibit all the most important of them, and very convenient for taking up mountains, &c. All observations should be referred to the map published in the Philosophical Transactions for 1860, On a particular Case of induced Chemical Action. By A. Vernon Harcourt, M.A. It has been observed by Mohr, Scheurer-Kestner, and other chemists, that when a protosalt of tin is determined by means of a standard permanganate solution, the results obtained vary according to the degree in which the solution of tin-salt is diluted. The greater the dilution, the less is the amount of permanganate required. This variation is justly ascribed by the two chemists above named to the influence of the oxygen which the water used in diluting holds dissolved. With recently boiled water, the effect is less; with water which has been absolutely freed from air, it disappears. If these facts stood alone, their explanation would seem simple, viz. that chloride of tin is speedily oxidized when mixed with water containing oxygen. But this is not the case, especially when much free acid has been added. If iodine, or per- chloride of iron, or sulphate of copper is used as the oxidizing agent, the result of the determination is the same, whether the tin solution be little or much diluted. 44, REPORT—1862. Hence it appears that in the former case the action of the dissolved oxygen is de- termined by the action of the permanganate*. In order to investigate quantitatively the relation of these two actions, several series of determinations were made in the following manner :—A measured quantity of a solution of protochloride of tin of convenient strength was determined, first without dilution, and then, in successive experiments, after dilution with regularly increasing quantities of water. Immediately before and during each determina- tion, a stream of carbonic acid was poured into the flask containing the liquid to be determined, in order to guard it from contact of air. The conclusions to which these experiments have led are as follows :—(1) When the diluting water contains only so much oxygen asis sufficient to oxidize about one-third of the protochloride of tin present, the whole of this oxygen is appropriated in the reaction; (2) after this point, the amount of induced oxidation is still increased by further dilution, but in a continually diminishing degree, until it bears to the primary oxidation (that by the permanganate) about the ratio of 2:3; (3) still greater dilution produces no farther change. It has not yet been found possible to determine the exact ratios of the primary and of the induced oxidation one to another at that point at which the absorption of dissolved oxygen ceases to be complete, and at the final limit, where the induced oxidation has reached a maximum. With what other chemical actions are we acquainted which belong to the same class as this action ? Four examples may be adduced of actions more or less analogous. 1. The action of platinum-black, and other similar substances, in causing oxidation. These sub- stances, however, do not, so far as we know, themselves undergo any change; whereas the permanganate can act inductively only during the moment of its own direct action. 2. The action of nitric oxide upon sulphurous anhydride and oxygen. 8. The action of pentachloride of antimony in presence of free chlorine in causing the formation of chlorine compounds. But in these two cases also an important distinction is to be noted. The products of the initial action, nitrous oxide and terchloride of antimony, are capable of combining directly with free oxygen and free chlorine respectively ; whereas the final product at least of the reduction of an acid solution of permanganate is not liable to reoxidation, and such a solution can accordingly be reduced ‘by many substances in the presence of dissolved oxygen without appropriating or conveying it. 4. The acetous fermentation. The fact that the oxidation of alcohol by free oxygen may be induced by the presence of other substances undergoing chemical change bears some resemblance to the fact here brought forward. It is not improbable that the two may depend upon a common cause. But no case that has been yet examined is directly and unmistakeably parallel to this action. At the same time, it is doubtless but one of a class. The action of other similar oxidizing bodies, such as chromic acid, and of other substances readily susceptible of oxidation, such as sulphurous acid, hydriodice acid, &e., in presence of dissolved oxygen, may probably present similar phenomena. With the action, in dilute solutions, of chromic acid on sulphurous acid, and permanganic acid on sulphurous acid, this has been ascertained to be the case. On Schénbein’s Antozone. By G. Hartzy, M.D., Professor in University College, London. In 1842 Schafhaiitl called attention to a fluor-spar, the peculiar smell of which he imagined to be due to the presence of hypochlorite of lime. Schénbein shortly afterwards found that it contained an oxidizing agent which Schrétter subsequently described as ozone. Schénbein has now repeated his experiments on a better quality of the mineral, and finds that the oxygen contained in it resembles that — yielded by BaO,; and that distilled water in which the mineral has been pounded — * Since reading the paper of which the above is an abstract, the author has become aware that this fact had already engaged the attention of the German chemist Liwenthal, who, in conjunction with E. Lennsen, has recently shown that dissolved oxygen is similar] rendered active in some other cases (Journ. fiir Prakt. Chem, 1859, part i. p. 484, an vol, Ixi. (1862) p. 193), —— _ TRANSACTIONS OF THE SECTIONS. 45 acquires peculiar properties. At the request of Professor Liebig, who had given Dr. Harley some fine specimens of the mineral, the latter gentleman showed some of the more striking properties of the mineral to the members of the Association. For example, the distilled water in which the mineral has been pulverized, when filtered gives no precipitate with nitrate of silver, and only the very slightest tur- bidity with oxalate of ammonia and with weak sulphuric acid. From this it is seen that no chlorine is present, and only a trace of an earthy base. The liquid blues iodized starch, decolorizes a solution of permanganate of potash acidified with sulphuric acid, at the same time liberating oxygen gas. The liquid gives a blue with the brownish mixture of dilute ferridcyanide and perchloride of iron, and _gradually precipitates prussian blue. When mixed a short time with the peroxide of lead and finely reduced platinum-powder, it loses some of the above-named pro erties. Heating the mineral entirely destroys its properties. Schinbein concludes om these and other facts that the mineral contains antozone. On the Adulteration of Linseed Cake with Nut-cake. By W. H. Harris, F.C.S. The frequent adulteration of linseed cake, used for cattle-feeding purposes, has drawn considerable attention on the part of the agricultural chemist to the ditfer- ent adulterative substances employed by the trade. Many of these have been from time to time exposed. But there is one substance largely used for adulterating lin- seed cake, which has not, that I am aware of, received the notice which it deserves. The substance I refer to is the market nut-cake, obtained from the fruit of the Arachis hypogea, or Ground-nut of America, indigenous to Mexico, but cultivated in the West Indies. As botanists are aware, it derives its name from the singular manner in which its fruit is perfected; for as its yellow papilionaceous flowers fall from their stalks, the pods which follow are forced by a natural motion of the plant into the ground, where the seeds ripen and come to perfection—hence the name of Ground-nut. | As the cake composed of the marc of these seeds can be purchased at about half the price of linseed cake, it is often used for the purpose of adulteration—a fact patent to most agricultural chemists. But this substance seems to have been gene- rally condemned as a worthless article ; for we have seen this verdict given against it in several instances by eminent agricultural chemists; at any rate, if I am mis- taken in the article of commerce which has been classed with bran, rice dust, and treated as rubbish, the mistake is attributable to an unfortunate looseness of lan- guage adopted by the authorities in question. My attention being directed to the true feeding qualities of this substance was accidental; for having to analyse a sample of linseed cake which contained a con- siderable quantity of bran, I was surprised to find the analytical result, in reference to the percentage of flesh-formers, was considerably superior to the result I had aiiained from many genuine samples I had analysed. This led me to resubmit the cake to a careful microscopic examination, which enabled me to detect what afterwards proved to be the decorticated nut-cake of commerce. My next step was to get a sample of this nut-cake in its simplicity; this, through the kindness of a gentleman connected with the trade, I succeeded in doing, On submitting this sample to analysis, the result exceeded my highest expectations, as the following results of the examination will show :— Per cent Moisture... eee aeeenne eeeeebovueod eoee 6, OD 6.9 SIAR Ob 8:50 REE SCRERG Dis 2a hale aia's oie VRS FEELS TAS OP 3 4:94 Cellulose, insoluble in warm solution of potash, sp. gr. 1045 3°51 Albuminots compounds”. sve secs b gases ev nces 43°31 Amylaceous constituents......., i PONE D Me rabies oe B74 Onl Shae Mee eWN Ea ad Oat dees Khang ag ED pedsaas ag 12:40 100-00 To be able to introduce to the cattle-feeder a highly nutritious substance, capa- * Containing nitrogen 6-93 per cent, 46 REPORT—1862. ble of sustaining a successful competition with linseed cake itself, and not more than two-thirds the market value of the latter, it now only remained to prove that its practical answered to its theoretic value. Of this there did not appear to me to be any serious doubt; nevertheless I thought it better to the matter to the test of practical experiment. A friend to whom I named the subject readily entered into the plan of trying the effect of this cake upon a portion of his stock; the result roved his cattle would eat it with eagerness, and, as far as the experiment has gone, it has answered our highest expectations. On a Simple Method of taking Stereomicro-photographs. By Cuarius Haerscu, F.C.8., Lecturer on Chemistry at the Middlesex Hospital. After trying various plans, the author devised the following, which answered perfectly. A microscope with its eyepiece removed is placed in a horizontal posi- tion, and fitted to an ordinary sliding back, single lens, stereoscopic camera, Be- hind the object-glass is screwed an adapter, in the inside of which is a tube, which can be turned half round by means of a lever from the outside. Sliding in this tube is a second, furnished with a stop which cuts off half the pencil of light coming from the object-glass, in fact occupies the same place as the prism of a binocular microscope. The distance of this stop from each object-glass is adjusted experi- mentally by sliding the tube backwards and forwards till the best effect is obtained. The prepared plate being put in its place after carefully focusing the object, the first picture is taken. The plate is then shifted, the stop turned half round, and the second picture taken on the other half of the plate. If the object be of any thickness, its upper surface should be focused for one picture, and its under surface for the other. The adapter with its stop was exhibited to the meeting. Lowe’s Ozone Bow. By KE. J. Lown, F.R.AS. Se. This box has been constructed so as to ensure perfect darkness to the test-paper without interfering with the passage of a current of air. There are two openings into this cylindrical box, the one above and the other below. These openings are not direct into the box itself, but into narrow winding passages in the first instance ; they are also opposite each other. If the wind is blowing in an easterly current, and the upper opening is on the east side, then the air will enter the box on the Fig. 1. Fig. 2. upper half (fig. 1), will move round the circular passage until it enters the central cavity (A) where the test-paper is hung, afterwards passing round the lower pas- sage (fig. 2) in a contrary irection, and out again at the west aperture. Or if the wind happens to be in the opposite direction, it will enter from below and leave the box from above. The advantage is obvious—a current of air passes through a dark chamber. The box is small, and its price almost nominal, Observations on Ozone. By E. J. Lown, F.R.AS. $e. The following are results of observations made at the Beeston Observatory during the past four years :— 7 Ist. If the temperature is raised, the amount of ozone will increase. 2nd. If the current of air through the box increases in rapidity, the amount of ozone will increase, TRANSACTIONS OF THE SECTIONS. A7 3rd. As the barometer becomes lower, the amount of ozone becomes greater. Ist. If the temperature be ranged in 10° series, a temperature between 30° and 40° will give less ozone than one between 40° and 50°, and this less than one between 50° and 60°. Artificially, if a night-light be made to bum in a cell below the box so as to warm it, there will be an increase in the amount of ozone over another box that is without a night-licht. 2nd. With respect to an increase in ozone resulting from an increase in the speed of the air, it is shown from this series of observations that the most ozone has been present when there has been a gale blowing. It does not necessarily prove that under these circumstances there is actually more ozone in the air; for it must be borne in mind that if the amount of ozone in a cubic foot of air were always the same, still if today 300 cubic feet of air only occupies the same space of time in passing through the box as 100 cubic feet occupied yesterday, we shall have more ozone apparently shown today than yesterday. Then again, as chemical action increases with an increase of heat, it is also manifest that the same amount of ozone passing through the box at a temperature of 60° would necessarily darken the paper more than the same amount at a temperature of 40°. It is quite clear that certain corrections are requisite in order to find the actual amount of ozone. 3rd. With regard to the pressure of the air, there is a striking difference be- tween the readings of the ozonometer with a high or low barometer. Taking the four days in each month during the past year on which the mean pressure was greatest, the average amount of ozone was 1-2, whilst on taking the same number of days when the barometer was lowest, the mean was 4-1, or nearly four times as much ; four years’ observations give very similar results. The mean maximum pressure for the whole twelve months of the four years is 30°22 inches, the mean ozone being 1:0; the mean minimum pressure for the like period is 29-18 inches, the mean ozone heing 3:2, With the barometer at 283 inches the mean ozone is 5:7 ” 283 ” ” 4] ” 29 ” ” 35 ” 294 ” ” 2°8 ” 293 ” 2:0 ” 293 ” ” 16 ” 30 ” ” 13 ” 30} ” ” 0-5 ” 303 ” ” 0-4 There is a difference between the amount of ozone during the night and day at different seasons. In December and January an excess at night over the day of 0:8 0: In February and March “ x In April and May i + 0:7 In June and July ip 0-1 In August and September a fe 0-4 In October and November “ “ 05 The average of the summer months being in excess only one-half of that which occurs in the winter. On the Luminosity of Phosphorus. By Dr. Morrar. If a piece of phosphorus be put under a bell-glass and observed from time to time, it will be found at times luminous, and at others non-luminous. When it is luminous, a stream of vapour rises from it, which sometimes terminates in an in- yerted cone of rings similar to those given off by phosphuretted hydrogen ; and at others it forms a beautiful curve, with a descending limb equal in length to the ascending one. Results deduced from daily observations of the phosphorus in con- nexion with the readings of the barometer, the temperature and degree of humidity of the air, with directions of the wind, for a period of eighteen months, show that periods of luminosity or phosphorus and non-luminosity occur under opposite con- 48 REPORT—1862. ditions of the atmo&phere. By the catalytic action of pale on atmospheric air, a gaseous body (superoxide of hydrogen) is formed, which is analogous to, if not the same as, atmospheric ozone, and it can be detected by the same tests. The author has found, by his usual tests, that phosphoric ozone is developed only when the phosphorus is luminous, On Ferrous Acid. By W. Ovirne, M.B., F.R.S. The author found that when ferric oxide was ignited with the carbonates of potassium, sodium, and calcium, each atom of fe, Q, drove out one of COQ,, to form two atoms of an alkaline ferrite, having the general formula M fe O,, which salts were decomposed by water into caustic alkali and ferric monohydrate or brown hematite ; thus, M fe 0,+H, 0=H fe 0,4 MHO, On the Synthesis of some Hydrocarbons. By W. Ovutne, V.B., PRS. The author found, in particular, that when a mixture of carbonic oxide and marsh- gas was passed through a red-hot tube, acetylene was abundantly formed according to the equation CO+CH,=C,H,+H,0. On the Nomenclature of Organic Compounds. By W. Ovuine, M.B., FBS. Admitting the impossibility of establishing a thoroughly systematic nomencla- ture in organic chemistry, the author advocated a gradual improvement of that now in more or less general use, by removing its chief incongruities, and remedying its more striking inconveniences. He showed, by many examples, how great an improvement might be effected by an introduction of very few and trivial changes. On the Essential Oils and Resins from the Indigenous Vegetation of Victoria. By J. W. Ospornu. The indigenous trees and shrubs of the colony of Victoria belong for the most part to the genera Eucalyptus and Melaleuca, which grow in great luxuriance over the greater part of the Australian continent. In no other localities are oil-bearing plants to be found in the same abundance, especially such as attain to arborescent growth, nor is the yield of oil as great elsewhere. The thirty-five samples sub- mitted to the Section are identical with these exhibited in the Victorian Depart- ment of the International Exhibition. They were distilled by the Exhibitors, at the request and under the auspices of Dr. Ferdinand Miiller, the Government Botanist of Victoria, to whose great talents and untiring energy the colony is largely indebted. In the present case the rigorous accuracy of the specific name of each specimen may be accepted on his authority. The author, as Juror, examined the essential oils and resins with respect to their technological value, for the Victorian Commissioners. Those from the genera Eucalyptus and Melaleuca (nineteen different oils) resem- ble the Cajuput of India, Melaleuca leucadendron. In smell and taste they are generally more camphoraceous, partaking sometimes of the odour of oil of lemon. Their colour is for the most part a pale yellow, sometimes colourless, and occasion- ally green. Their specific gravity, in the samples submitted to the Section, varies from 0-881 to 0-940, the average being about 0-910. These oils have all two boil- ing-points, the lower being, generally speaking, about 325°, and the other about 40° higher. They burn well in suitable lamps, and are not dangerous, as they are ignited with difficulty. As solyents for resinous bodies, they surpass most liquids of the kind, and form varnishes, attacking with readiness the intractable Kauric gum of New Zealand. The yield from individuals of the series is sometimes exceedingly large, E. amygdalina giving by distillation of 100 lbs. of its green leaves and branchlets, three pints of oil; £. oleosa, 20 ounces; L. sideroxylon, 16 ounces; MM. linarifolia, 28 ounces, &c. It is estimated that 12,000,000 acres of the colony of Victoria are covered with myrtaceous vegetation of this description, some of it of a shrubby character, densely covering vast tracts (L. oleosa, F. M.; £. dumosa, Cunn.; 2, TRANSACTIONS OF THE SECTIONS. 49 soctalis, F. M., all known as Mallee Scrub). The other oils were chiefly endowed with medicinal characteristics, including several true mints, Mentha Australis, M. gracilis, and M. grandiflora ; also some related to plants of the Rue species, and one fragrant perfume distilled from the blossoms of the Pittosporum undulatum. Also a heavy oil from the bark of the Atherosperma moschatum, possessed of powerful medicinal properties. The resins and gum-resins include several obtained from the genus Eucalyptus, which are powerfully astringent, and more or less soluble in water. Also one from the Calhtris verrucosa and cupressiformis of Northern Victoria, the sandarac of commerce; one from the Xanthorrhea australis, a balsamic resin containing ben- zoic acid, and resembling dragon’s-blood; together with some true gums from the genus Acacia, which is well represented in the Australian colonies. The following is a list of the oils submitted to investigation, with their verna- cular names as far as known, Eucalyptus amygdalina (DaudenongPep- Melaleuca ericifolia (Common Tea-tree)* permint), M. Wilsoni. E. oleosa (Mallee Scrub). M. uncinata. E. sideroxylon (Iron-bark). M. genistifolia. E. zonicalyx (White Gum). IM. squarrosa. E. globulus (Blue Gum). Atherosperma moschatum (Sassafras). E. corymbosa (Blood-wood). Prostanthera lasianthos. E. fabrorum (Stringy-bark). P. rotundifolia. E. fissilis (Messmate). Mentha australis, E.. odorata LEeppenuant)- . M. grandiflora. E. Woollsit (W oolly-butt). M. gracilis. E. rostrata (Red Gum). Zieria lanceolata. E. viminalis (Manna Gum). Eristemon squameus. Melaleuca linariifolia. Pittosporum undulatum. M. curvifolia. Details of a Photolithographic Process, as adopted by the Government of Victoria, for the publication of Maps. By J. W. Osporne. The author referred to his having read a paper ae this subject before the Royal Society of Victoria, in November 1859, his process having been previously patented in the Colony on the 1st of September, 1859. The process had then been adopted by the Government, and had come info active use in the Department of Lands and Survey at Melbourne. By its means many hundreds of maps had been published, of a quality and for a price which left nothing to be desired. The Victorian Government had recently erected an office, the design and arrangements of which were admirably adapted for the prosecution of this description of work. To pro- duce a photolithographic copy with or without reduction, the original map or en- graving was extended upon an upright board, and by the help of a camera placed opposite, a negative of it was taken. A sheet of paper was now prepared by coat- ing one of its surfaces with a solution of gelatine in water, to which a certain pro- portion of bichromate of potash and liquid albumen had been added. The surface thus prepared, after it had dried in a dark and warm room, was sensitive to the chemical action of light, and the next operation was to expose to the sun’s rays a suitable piece of it, in an ordinary pressure frame, under the negative already obtained. The positive ee print thus produced was inked all over with lithographic re-transfer ink, and was then placed floating upon boiling water, with its inky side upwards and unwetted. After a short time the gelatine would be found to have softened and swelled under the ink, save where the light had acted, the ‘organic matter upon such places haying suffered a peculiar change. Another effect of the boiling water was to coagulate the albumen in the film. When sufficiently soaked, the ees ink was removed by means of a sponge, and the result was a pho- tographic print in greasy ink; inasmuch as the latter substance adhered firmly to all the unsoftened, or, in other words, the altered parts of the gelatinous coating. It would also be found that the delineation thus obtained was upon a smooth sur- 4 1862. 50 REPORT—1862. face of coagulated albumen. Boiling water in abundance was now poured over the paper, after which it was carefully dried. The photographic print thus produced, in consequence of the greasy ink upon the positive portions of the work, was capable of being transferred to stone by the printer, by the well-known mechanical process ; and from stones thus prepared, impressions could be pulled in the lithographic press. Numerous specimens were exhibited to the Section. On the Manufacture of Hydrocarbon Oils, Paraffin, Sc., from Peat. By B. H. Pav, Ph.D, The author described the results that had been obtained at some works lately erected under his direction in the island of Lewis, N.B. The peat of that locality was described as a peculiarly rich bituminous variety of mountain peat, yielding from five to ten gallons of refined oils and paraffin from the ton, The results ob- tained at these works were contrasted with those obtained at the works of the Irish Peat Company some years ago, where the produce of oil was not more than two gallons from the ton of peat. This difference in the produce was ascribed, in a great degree, to the improper mode of working adopted at the Irish works. One of the most important points dwelt upon was the necessity of regarding the hydrocarbon oils and paraffin as the only products that would afford a profit in working peat; and the failure of the Irish works was attributed to the attempt to obtain other pro- ducts which could only be regarded as waste, and not worth working, unless the oils and paraffin were obtainable in a remunerative amount from the peat. On the Decay and Preservation of Stone employed in Building. By B. H, Pavz, Ph.D. The causes and nature of the decay of building-stone were described as being both chemical and mechanical, and varying according to the nature of the stone an the conditions to which it was exposed. The various methods which have been proposed for the preservation of stone from decay were described in detail; the author considering, from a chemical point of view, that none of them presented any probability of success in effecting the desired result, and that the discovery of an efficient and practicable means of preventing the decay of stone, especially in towns, still remains to be made, On the Artificial Formation of Populine, and on a new Class of Organie Compounds. By T. L. Pureson, M.B., Ph.D., F.CS. Fe. The interesting substance populine was extracted in 1830 by Braconnot from the mother-liquors which had deposited salicine when the latter was obtained from the leaves and the bark of the pop'ar tree (Populus tremula). It was submitted to an important series of experiments by Piria in 1852, who found, among other interesting facts, that, in a variety of circumstances, populine split up into benzoic acid and salicine :— Co H22 ore + 9 HO = Cu He 0’, HO + O26 H}8 O4, Populine. Benzoic acid, Salicine. It occurred to me that salicine and benzoic acid might be combined so as to reproduce pee And this I find to be the case: when equal equivalents of salicine and benzoic acid are dissolved in alcohol and the liquid evaporated tc about half its bulk, magnificent acicular crystals of populine are obtained, some of which in my experiments measured nearly an inch in length. For every 100 parts of salicine must be taken 43 parts of benzoic acid. Or fo: 100 parts of salicine, 53-5 parts of benzoate of soda and a sufficient quantity of diluted sulphuric acid to satu- rate the soda of the benzoate ; alcohol is then added, and the sulphate of soda sepa- ee i filtration. By evaporating the solution long needles of populine are obtained :— Cu Hé Ot + O76 Hs Ou = (Ox H owe + 2 HO). Benzoic acid. Salicine. Crystallized populine. The properties of the populine thus formed are precisely those of the natural TRANSACTIONS OF THE SECTIONS. 51 product. Its peculiat taste, acrid and sweet at the same time, reminding us of the taste of liquorice, is characteristic. With sulphuric acid it takes a red colour; distilled with bichromate of potash and sulphuric acid it yields salicylous acid. It is more soluble in water and alcohol than salicine. It is curious also to note that in this combination the salicine has lost its bitter taste, which renders it probable that populine is in reality a compound of benzoic acid, sugar, and saligenine; for, when boiled with dilute sulphuric acid, it breaks up into benzoic acid, sugar, and saliretine (saligenine minus 2 equivs. of water) :— C“H® O+ Saligenine. CY HY O Sugar. C™“H® O* Benzoic acid. C*° H* 01 Populine. As soon as the sugar is set free, it takes up 4 equivs. of water and passes into grape- ugar (C!? HO), he molecule of populine is therefore a very complex one. And these kinds of compounds may, perhaps, be compared to the combinations of two or more salts in mineral chemistry, for instance to alwm, if we compare the sulphate of alumina to the benzoic acid, the sulphate of potash to the saligenine, and the 24 equivalents of water to the sugar. But I have also found that citric acid and tartaric acid, when taken in equivalent proportions, dissolved in water, and the solution evaporated, enter into cheinical combination. It is well known that these acids crystallize in two different systems, the forms of which are incompatible, and by evaporating a mixture of them we should obtain two kinds of crystals if no combination took place. But I find that they combine and produce one kind of crystal only, namely, long prismatic needles, and when one of these crystals is taken and analysed, it is found to be composed of eitric and tartaric acids. ; This combination of citric and tartaric acids is probably only one example of a new class of organic compounds, similar in some respects to populine, which remains to be studied. Already Prof. Williamson has shown that the different acetones may he made to combine so as to produce complex acetones. Thus when valerate and acetate of lime are distilled together in equivalent proportions, we obtain acetovalerone, a compound of acetone and valerone, and so on for the others. It is highly probable from what precedes that other organic acids besides benzoic acid may be made to combine with salicine; likewise that other bitter principles analogous to salicine may be combined with organic acids to produce substances similar to populine, On the Existence of Aniline in certain Fungi which become Blue in contact with the Air, Fc. By T. L. Pureson, WB., Ph.D., F.OS. Se. Two years ago I published in Brussels a memoir upon the Boleti which become blue when cut with a knife, and upon the formation of colouring matters in fungi*. In this paper I called attention to a remarkable set of reactions occurring in nature when one substance causes atmospheric oxygen to assume the state of ozone and to act upon another substance in contact with the first, a fact originally pointed out by Prof. Scheenbein. In this paper also I endeavoured to show that the production of the blue colour observed when Boletus cyanescens, Boletus luridus, &c. are cut with a knife and exposed to the air, is owing to the existence of aniline in the sap of these fungi. Nothing is easier than to extract the principle to which these Boleti owe their remarkable property of taking a deep, though fugitive, blue colour when their in- ternal tissue is put in contact with the air. But it is not easy to obtain it perfectly * Sur les Bolets bleuissants : étude sur la formation de principes colorants chez plusieurs Champignons (Journal de Médecine et de Pharmacologie, Bruxelles, Mars et Avril 1860). See also ‘Comptes Rendus de l’ Acad. des Sciences,’ Paris, 1860, 2i#me semestre. Also my prize memoir, ‘‘ La Force Catalytique : études sur les phénoménes de contact,” to which the atch Society of Science awarded their Gold Medal, Haarlem, 1858. 4* 52 REPORT—1862. ure, and very difficult to obtain it in any quantity, as its power of producing the iiate colour is so great that a very minute proportion suffices to colour the entire tissue of a large Boletus, When one of these fungi is treated with ordinary alcohol, the aniline it contains is dissolved with several other matters, which, however, do not prevent the ordinary characteristic reactions of aniline. This principle appears to be present in the fungus as acetate of aniline. I have not extracted it in suffi- cient quantity or of sufficient purity to submit it to more than a qualitative exami- nation ; but the data which follow will, I think, sufficiently establish the point in question. case the result is identical for both :— Characters of the colouring principle of the Boletus. 1. Colourless. 2. Very slightly soluble in water. 3. Soluble in alcohol. 4. The alcoholic solution resinifies sooner or later in the air, becoming yellowish. 5. Does not become blue by ordinary atmospheric oxygen unless this oxygen is in the state of ozone, 6. Gives a deep blue colour with ozone, or nascent oxygen; this colour is ephemeral, and is sometimes greenish, passing to wine-colour or rose tint. 7. Chloride of lime or bleaching powder developes the characteristic blue or greenish blue given by aniline salts. This coloration is ephemeral, assing to a port-wine tint, and finally isappearing. 8. Turns deep yellow with hydro- chloric acid. I give here, in the form of a Table, the characters observed, of the prin- ciple extracted from these Bolett, together with the characters of aniline. In every Characters of Aniline. 1. Colourless, 2. Very slightly soluble in water. 3. Soluble in alcohol. 4. Its solution resinifies in the air and takes a yellow colour. 5. Does not become blue by ordinary atmospheric oxygen unless the latter be in the state of ozone. 6. Gives a deep blue with ozone; the colour is ephemeral, and passes to wine- coiour ; with some salts of aniline a green- ish blue is produced; others give a rose tint when exposed to the air. 7. Bleaching powder developes the cha- racteristic blue tint (with some salts of aniline, greenish blue). The colour is ephe- meral, soon passing to wine-colour, disap- pearing with an excess of chlorine. 8. Turns deep yellow with hydrochlo- ric acid, These characters suffice, I think, to establish the identity of the principle con- tained in Boletus luridus and B. cyanescens with the artificial alkaloid aniline ex- tracted from coal-tar. nature. It is the first time that aniline has been shown to exist in The manner in which the blue colour is produced when the tissue of these Boleti is broken and exposed to the air is easily accounted for: I have shown in several of my former papers (/oc. cit. p. 1) that when oxygen reacts upon organic matters in nature, it is generally in the state of ozone. The presence of some ferment in the tissue of plants, and in contact with the substance which combines with the oxygen, appears to be the cause of this remarkable modification of oxygen. Thus, when an apple is cut in two halves, the brown colour which ensues is owing to the action of ozone (as may be proved by directly applying the tests for ozone), and the ozone is produced by the influence of the ferment: for ordinary oxygen will not produce the coloration ; and when the ferment is destroyed by boiling, the colour is not produced either. In the case of the Boleti, the aniline which exists in their tissue as a colourless salt, turns blue under the influence of ozone produced in con- tact with the ferment present in the fungus; for when this ferment is destroyed by Wire no coloration ensues when the tissue of the fungus is broken and exposed to the air. It is well known that some salts of aniline, when exposed for some time to the ~ TRANSACTIONS OF THE SECTIONS.. 53 air, take a delicate rose-colour. This accounts for the beautiful rose tint not un- frequently remarked upon the stalks of those Boleti which contain aniline. Analysis of the Diluvial Soil of Brabant, Fe., known as the Limon de la Hesbaye. By T. L. Pureson, M.B., Ph.D., P.CS. Se. The curious geological formation known as the Limon de la Hesbaye, which ex- tends from the Seine to the Rhine, traversing Belgium from east to west, where it covers the whole of the district of Hesbaye, a great part of Brabant, Hainault, and Flanders, is exceedingly remarkable for its fertility. “J¢ ts to this deposit,” says D’Omalius d’Halloy, “that we may attribute the richness of the most fertile countries of Belgium.” It extends also over Picardy, stretching from the Seine to the other side of the Rhine, and is everywhere characterized ‘by its great fertility and the excellence of the vegetable mould to which it gives birth by culture. No fossils have as yet been discovered in this deposit; it ranks among the “modern,” “ post- tertiary,” or “ diluyial ” formations of geologists; and there exist, on different por- tions of the globe, similar modern deposits equally interesting in an agricultural point of view. I have submitted this remarkable deposit to analysis, and its composition shows that though the Limon de la Hesbaye contains upwards of 90 per cent. of pure sand, yet the chemical ingredients necessary to form a fertile soil are present in it in notable quantity ; besides which, its porosity, which allows water to pass slowly through it and admits the ingress of atmospheric oxygen, is an important condi- tion of fertility. When pulverized and exposed to the air, the Limon de la Hesbaye dries com- pletely, but when in mass it retains its moisture for some time. When seen in mass it is brownish yellow, becoming of a lighter colour when dry, and giving a whitish-yellow powder when pulverized. Its density is about 2:00 (water=1-00) ; it has a straight fracture, possessing a certain compactness, though it can be pul- verized in the hands without much difficulty. The sample analysed by me was taken in the neighbourhood of Brussels: I was careful in selecting it from the centre of a stratification about 2 yards thick, and where it had never been submitted to cultivation. The result obtained is as follows :— NGAUS a otios Sc pagdseegetancacseies traces Organic matter and combined water........ 3°00 PACTIMIOTIA Ts ale ofs.siolae raze leveteiarelale igs eieCeadle chaisle 0:10 Potash, with a little soda ................ 0:23 Ibe, Boconrecncqpancocgqdoneoagnognde .. 0-40 DPN oy a wetness, cp). Some, Kabeia tears sata viele 0:07 Alumina, with a little oxide of manganese .. 1:20 Oxidecof irons sacri nee reeled iia derstelsrtets 2:56 PHOnphOMe HIG) ois hie GGEen sweaivages § OZO Sulphuric acid OHTOMNE spose ag htaeigtere Rs Reneuates arom +eeee traces Carbonic acid Qua rbZGsO: SACs eyfarte, oat eyeher dale esehinre atid alent oats 1 A. 100-00 This composition resembles that of another deposit of Limon, equally remarkable for its fertility and the readiness with which it is converted into excellent arable land,—I allude to the celebrated tchornoizen, or black diluvial soil of the Ukraine, which has been analysed by several chemists; it extends from the Carpathian Mountains to the Urals, giving to the whole district included between these two ranges a characteristic fertility. It is not my intention to discuss the geological origin of these deposits which are so important to agriculture, but I may state here that they are all post-tertiary formations, that they exist in seyeral parts of the globe, and that the regions where they are present appear to be, in an agricultural sense, highly favoured by nature. 54 REPORT—1862. On Hypobromous Acid. By Prof. H. E. Roscoz. Professor Roscoe communicated to the Section the results of an investigation upon the lowest oxide of bromine, hypobromous acid, which had been made in the iabarsbeee of Owens College, Manchester, by Mr. William Dancer. Balard in 1826 mentions the formation of a colourless bleaching salt formed by the action of bromine upon the alkalies, and since that date many chemists have indicated the resence of such a body, but it has not been prepared in a pure state or analysed. Mir. Dancer has succeeded in preparing the aqueous acid in a pure state, and has examined its chief properties and determined its composition. If bromine-water and nitrate-of-silyer solution be brought together, one-half the bromine is precipi- tated as bromide of silver, whilst the other half remains in solution as hypobromous acid (BrOHO). The aqueous acid may be obtained by distillation at 30° C. in vacuo, but decomposes into bromine and oxygen at 100° C. The aqueous acid may likewise be prepared by shaking bromine-water together with oxide of mercury, and distilling 7m vacuo; in this case half the bromine hte the bleaching compound. Hypobromous acid unites with the alkalies, and forms salts analogous in smell and bleaching properties to the corresponding hypochlorites. Owing to the ease with which this compound splits up into bromine and oxygen, it was found impossible to prepare the hypobromous anhydride by any of the methods used for the isolation of the corresponding chlorine compound. Description of a rapid Dry-Collodion Process. By T. Surton, A rapid dry-collodion process, by which dry plates can be prepared as sensitive as with wet collodion, has more than any other problem interested photographers. By the wet process, the negative has to be finished on the spot, The rapidity of this dry process depends upon the effect of bromine in dry collodion. In the Daguerreotype process a silver plate iodized is extremely insensitive, but when sub- mitted to the fumes of bromine it is increased a hundredfold. In the wet, but not in this process, nitrate of silyer is required, which is the element of instability. In preparing, therefore, rapid dry-collodion plates, bromo-iodized collodion must be used, But the image produced thus is extremely thin and superficial ; it is there- fore necessary to apply to the film a coating of some organic substance, in order to darken parts of the negative. Many substances have been tried for this purpose, but none produce so good an effect as gum-arabic, The paper concluded with the operations required for this process. GEOLOGY. Address to the Geological Section by J. Brrte Juxus, M.A., F.R.S. It is now thirty-two years ago since I first, when a “freshman” of this Univer- sity, attended the geological lectures of Professor Sedgwick. I had previously had access to a cabinet of fossils, and had been accustomed to seek for specimens in my schoolboy rambles on the hills near Dudley. It may be imagined, therefore, with what interest I listened to the “winged words” of the Woodwardian Pro- fessor, which used day after day to delight an audience composed of all ranks of the University. Geology and its kindred sciences did not then, indeed, form any part of our re- gular course of university studies, and many of the college tutors were so far from encouraging our attention to them, that they rather discountenanced it, considering them as at best useless and probably even dangerous pursuits. With such a man as Professor Sedgwick, however, in the Woodwardian chair, whose wit and humour delighted, while his eloquence aroused and informed his hearers, the love of the science and the knowledge of it could not fail to extend from one year to another. The natural sciences are now considered as worthy of study, by those who haye a taste for them, both in themselves and as a means of mental training and disci- TRANSACTIONS OF THE SECTIONS. 55 pline. In my time, however, no other branches of learning were recognized than classics and mathematics, and I have with some shame to confess that I displayed but a “truant disposition” with respect to them, and too often hurried from the tutor’s lecture-room to the river or the field, to enable me to add much to the scanty stores of knowledge I had brought up with me. Had it not been, then, for the teaching of Professor Sedgwick in Geology, my time might have been altogether wasted, But it was not only in the lecture-room that I learnt from him. With that kind- ness of heart and geniality of disposition which make him as much loyed as his powers cause him to be admired, he was good enough to step down from his high place as a Professor of the University, and to take some notice of the young under- graduate whom he saw lingering over the trays of specimens when the lecture was over, to inquire his name, and to inyite him to his table. He subsequently allowed me to accompany him on some excursions in different parts of England, and gave me some of those practical lessons in the field, which, as you know, teach more in three days than can be learnt in months or yearsin the museum or the lecture- room. I look back upon these circumstances as those which gave direction to the whole course of my life, and as the origin of a paternal friendship with which Pro- fessor Sedgwick has honoured me for so many years, and which it has been my chief pride to endeavour to deserve. I hope, Ladies and Gentlemen, I may be pardoned for these few personal allusions; but amid all the gratification which I must ne- cessarily feel at the honour which has now fallen upon me, that, namely, of being called upon to preside, within the walls of my own Alma Mater, over the Geolo- gical Section of the British Association, it was impossible for me to neglect the opportunity of acknowledging the debt of gratitude I owe to one of the ruling spirits of both bodies, and of ayowing that my chief claim to occupy this chair is that Iam an old pak of Professor Sedgwick. One of the most obvious difficulties in the way of any person who now under- takes to preside over this Section is the thought of the contrast that will neces- sarily arise in the minds of many of you between him and his predecessors, That I am now occupying the seat that has been filled by Sedgwick, Buckland, Lyell, Murchison, Hopkins, De la Beche, Forbes, and so many other illustrious men, may well cause me to doubt my own capability of fulfilling its duties. One lesson I must certainly learn, and that is, to endeavour to make up for other deficiencies by atten- tion and assiduity, and, above all, not to take such an advantage of the postions as to bring anything of my own before your notice, to the hindrance of others who may have something to produce that may be more worthy of it. At the end, then, of this Address, which I will endeavour to make as brief as possible, I shall consider my own mouth as almost closed for the remainder of the meeting, and shall endeavour so far to imitate the Speaker of the House of Commons as to say as little as possible. I propose to take for my subject the external features of the earth’s surface. The principal business of Geology is to acquire as accurate a knowledge as we can of the internal structure of the crust of the earth, and to learn as much as possible of all the operations by which that structure was originally formed, or by which it has been subsequently modified. The crust of the earth has always been receiving accessions to its composition, both from within and from without. In like manner it has always been subject to modifying influences proceeding both from within and from without. It is obvious that the external influences act directly upon the actual surface of the time being. It is equally obvious that the internal influences can only reach that surface by penetrating through the thickness of the crust. If, therefore, we ask by what means the present surface of the earth, or, to bring the problem within more narrow limits, by what means the present surface of any of our dry lands, has been produced, we should naturally conclude that it owes its form to the external influences that have been brought to bear directly upon it, rather than to the indirect action of those deep-seated agencies, which can only reach it through an unknown thickness of solid rock. I believe this conclusion to be a true one. It is, however, by no means the idea which is commonly entertained, even by many geologists, while those who are not geologists are always inclined to refer all the more striking features of the surface 56 REPORT—1862. of the earth to the direct action of convulsive force proceeding from the interior, rather than to their true source in the gentle, gradual, silent influence of the “‘ weather,” continued through an indefinite period of past time. I have heard even educated men speak of the correspondence in the chalk cliffs of the opposite sides of the Straits of lever: as evidence in favour of the notion that Fugiede fad been separated from France by the tearing open of those straits by what they called some “ great convulsion of nature.” There is hardly a description to be found in any book, of any deep and narrow valley or mountain gorge—especially if the precipices on each side of it show entering and re-entering angles, and rocks that were obviously once continuous across the gap,—but what its formation is un- hesitatingly attributed to this vague imaginary force, a “convulsion of nature.” Nay, I have even heard the existence of broad valleys over an anticlinal arch, such, for instance, as the valley of the Weald, attributed to the effect of the gaping of the rocks at the surface, consequent on the upward flexure of the beds. Mythical powers of disturbance are called into existence with as bold a personification as the Bia and Kpartos of the poet, and with even less warrant for their existence. It seems to me, therefore, that the time is come when geologists should study a little more closely this problem of the mode of production of the surface of the land, and determine exactly the method of the formation of those variations in its outline which we call mountains, hills, table-lands, cliffs, precipices, ravines, glens, valleys, and plains. Few men, perhaps, ever pause to inquire into the origin of a great plain; never- theless the question may well be put, and it is one which deserves an answer. Some plains are doubtless the result of original formation. They are level and flat, because the beds beneath the surface are horizontal. Even these, however, have very rarely a surface formed simply by the last-deposited beds. The actual surface is one that has been formed by the erosion and removal of more or less of the uppermost beds, and the production of undulations formed by the act of cutting down into the beds below. This erosion or denudation has even in many such cases gone to the length of entirely removing a much greater thickness than we sucky at first suspect, the present surface being one that has been laid bare by that remoyal. In all cases where the beds below the surface are not strictly horizontal, or do not accurately coincide as to their “lie ” with the form of the surface, it is obvious that the plain must be one of denudation. Suppose we take the great plain on which we now are, and which stretches from Cambridge far into Lincolnshire. The hills which rise from it towards the east are formed by the escarpment of the Chalk, the beds of which terminate abruptly at that escarpment, and allow the clays which lie beneath the Chalk to come up to the surface and spread beneath the plain. The hills rising to the west of the plain, on the other hand, are formed of the Oolites, the beds of which lie below these clays and rise gently from beneath the plain, and themselves terminate in an escarpment still further west. There can be no reasonable doubt that the whole thickness of the Chalk and the beds below it once spread many miles to the westward of their present boundaries. The little chalk-capped monticule of the Castle Hill, at the western end of the town of Cambridge, and the hills near Madingley show that the Chalk was once continuous that far, at all events, from the Gogmagogs; and, had still higher ground been left by the denudation still further west, that would in like manner have been capped by the bottom beds of the Chalk. The hal on which Ely stands is, I believe, an outlier of the Lower Greensand, the general mass of which crops out some miles to the eastward; and other hills rising from the plain will in like manner be found to have their summits capped by beds, apparently horizontal, but in reality dipping at a very gentle angle to the eastward, so as to ultimately cut the surface of the plain in that direction and then sink beneath it. All such outliers are clear proof that the beds formerly extended over the intervening spaces, and show us that the rocks now left in the ground are only a portion of those that were originally deposited. The great plain of the Fens, then, is one of denudation, its surface being one that TRANSACTIONS OF THE SECTIONS. 57 is now bare in consequence of the removal from above it* of a thickness of many hundred feet of Chalk, and of other beds below the Chalk. But this reason- ing may be carried out with respect to the whole of the flat lands of England and the British Islands. The great central plain of Ireland, for instance, stretching from Dublin Bay to Galway Bay, with an average elevation of less than 300 feet above the sea, has immediately beneath it abruptly undulating beds of Carboniferous limestone, rising up at all angles, and dipping in all directions. The most level arts of the surface sometimes cut horizontally across the most contorted and highly inclined beds. The small isolated hills scattered here and there about the plain are formed sometimes of beds of Old Red Sandstone that rise up from honest the bottom of the Limestone, and sometimes of beds of Coal-measures which rest upon the top of it. It is here abundantly evident, then, that the internal forces of dis- turbance which have bent the beds from their original horizontality into so many euryes, and broken them by so many dislocations, had nothing at all to do with the production of the present surface, which has been formed across all these bent and ftoken beds after the disturbances had ceased. But, in fact, the very first glance at a geological map of a flat country, if there be two or more colours on it representing conformable groups of stratified rocks, is = as good a proof of this vast denudation as the most elaborate reasoning. The ast-deposited group of beds would of course conceal all those beneath it; itwould be represented by one uniform colour. Let the internal forces bend, or tilt, or break it in any fashion you like, they cannot of themselves remove a particle of it. It will still lie over all those on which it was originally deposited, and the map would show the one colour only, unless we go the length of supposing that a piece of the crust of the earth could be tossed over like a pancake, and laid down again with its bot- tom upwards. Ihave taken the case of a plain in the first instance, because it is obvious that if we arrive at the conclusion that many plains are low and level because moun- tainous masses of rock have been removed from above their present surface, it will be easy for us to recognize the proofs of denudation in the hills and mountains, on whose flanks the obvious marks of it are still left. A little reflection will show us that the outcrop of a bed is always a proof of denudation, for the present surface cannot possibly tie the original termination, not only of that particular bed, but of all the beds above it. When then a succession of beds crop out rapidly one after another, as they always do in all hill-ranges and mountain-chains, we cannot escape from the conclusion that the existing surface has been formed by the removal of the former extension of the beds. This is the inevitable conclusion, whether the surface be horizontal and the beds below it in- clined, or the beds be horizontal and the surface inclined, or the surface slope one way and the beds dip another, or there be any kind of discordance between the “lie” of the beds and the form of the surface of the ground. The only possible escape from this conclusion would be in the case where a succession of beds had been deposited on a slope, and had never been covered by any other deposit. This, however, is a case that could only occur in very recently formed rocks, and cannot apply to the outcrop of beds on the flanks of hills or mountains, where the surface of the ground itself has a high inclination. In such situations the only escape from the conclusion that the surface was formed by denudation would be, proof that the undulations of the surface were exactly fol- lowed by the undulation of the beds below it, and, in fact, that the very same bed was everywhere found to be the one immediately below the surface. If we except Volcanos or “ Mountains of Ejection,” all other hills and mountains are either caused by the removal of the rocks which once surrounded them, or haye suffered from the removal of those that once spread over them. The first kind of hills have simply been left high, while the surrounding ground has been worn down to a low level about them. In the second kind, the rocks composing them haye, indeed, been thrust up from beneath by internal force to a much greater elevation than those same rocks have in the surrounding area, and their height is due entirely * In this general statement the few feet of peat, or the little banks of drift gravel and sand which have been subsequently deposited on or grown over the plain, are, of course, disregarded. 58 REPORT—1862. to that upward tilting, vast masses of once superincumbent beds having been removed from aboye them. ‘Ihese hills are high, not in consequence of, but in spite of de- nudation. I haye elsewhere proposed to call the first kind “ hells of curcumdenu- dation,” and the second “hills of uptilting.” To the latter class belong all the great mountain-chains of the world, and most of the smaller ones. It may be taken as an inyariable rule, that, as we approach all mountain-chains formed by uptilting, the beds rise towards them, and end successively at the sur- face; lower and lower beds still rising up, until the lowest of all appear in the heart of the mountains, where they are often reared up into the loftiest peaks. True as is this general statement, it is only generally true. The great groups of rocks thus rise successively one from beneath another; but this general rise is often complicated by numerous folds and reduplications, by great longitudinal fractures, or by complex flexures. The geological axis of a mountain-chain runs along the line where the lowest group of beds rises to the surface. The geogra, hical axis may be said to run along that dominant crest which forms the watershed of the chain. But it by no means follows that these two axes are coincident, that the lowest group of beds is always confined to the line of watershed, or eyen that the loftiest peaks and summits rise from that crest. The geological axes are dependent solely on the internal forces of elevation; if, therefore, the geographical axes do not coincide with them, it shows at once that they are independent of those forces; in other words, that the great external features have not been caused by the direct action of internal movement. The position of the geological axes of mountain-chains has, however, been often erroneously placed, from the tendency to refer them to any great masses of granite or other plutonic rocks that may show themselyes,—a reference which is more often erroneous than correct. All mountain-chains of uptilting tell the same story, that if the internal forces of disturbance and elevation had acted alone, without any external action of denu- dation, and if they had acted without it to the same extent which they haye with it (supposing that possible), the mountain-chains would haye been many times more lofty than they are. I say “supposing that possible,” because it appears to me that the elevation of the lowest rocks might never have proceeded to the same extent, if the internal force had not been gradually relieved of some of the external weight which it had to lift. However that may be, we see now that the lowest beds which appear at the surface, about the geological axis of a mountain-chain, dip on either hand beneath an ever-increasing thickness of superincumbent rock, as we recede from the axis. All the rocks which have been affected by the same action of disturbing force must have stretched unbroken across the disturbed district, before the disturbance commenced; for the lowest rocks appear at the surface now, not in consequence of the flexure or fracture of those that were aboye them, but in consequence of their removal, That remoyal could not haye taken place prior to the internal disturbance, unless we assume the existence of a deep hole or trough of erosion along the space where the mountain-chain was subsequently thrust upwards. The remoyal of the hent or broken beds, then, must have taken place either during the action of disturbance or subsequently to its termination. In either case it was an external action, the result, in fact, of moving water, which slowly wore away and carried off so many square miles or, as in some cases, so many hundreds or thousands of square miles of rock, so many thousands of feet in thickness. The internal forces operated simply by lifting up the rocks to within the region of the denuding influence, and they have only produced that indirect effect upon the features of the surface which results from their haying brought up to different levels, and placed in yarious positions, masses of rock of yarions hardness and constitution, on which the forces of erosion and transport have had a corresponding yariety of effect, when they reached them. I believe that all our uptilted mountain-chains haye thus grown by a very slow and gradual growth, the internal force thrusting upwards what the external agen- cies always tended to wear down. The investigation of the nature and effects of the mechanical forces that have acted on the crust of the earth from the interior has been undertaken by many eminent philosophers, by none with more acuteness and profundity than by our pre- TRANSACTIONS OF THE SECTIONS. 59 sent General Secretary, Mr. W. Hopkins, who is so distinguished an ornament of this University. To the correctness of the mathematical reasonings employed in these researches no exception is of course to be taken, even by those who may withhold their assent from some of the conclusions arrived at. I profess my in- capacity to engage in the discussion of mathematical problems. Nevertheless, it es sometimes occurred to me to suppose that, however sound and legitimate may be the conclusions thus drawn from the premises assumed, they may still be imperfect or inadequate as conceptions of the truth, in consequence of the incom- leteness of the assumptions on which they are based. I shall not venture, even by a guess, to attempt to supply this defect. I only wish to regard the question as still an open one, thinking it possible that some condition or some agency may have been hitherto omitted from the speculation, of which no one has as yet, per- haps, formed even a conception. The researches already made may be admirable euides in all future investigations, and most useful in clearing the way for them; but it may nevertheless be dangerous to take the conclusion as so far established as to render future inyestigation unnecessary. There is one line of research, however, in pursuing which we may feel sure of the ground on which we tread, and that is the observation of occurrences which take place before our eyes, and of structures which each one may see and examine for himself. We have, in Earthquakes and Volcanos, the external symptoms of the action of the earth’s internal forces. What they do now, we may feel sure they were able to do formerly ; and we have no right to assume that they ever did either more or less within a given period than they have done during historic times. Volcanos drill holes through the crust of the earth, and eject lava and ashes through these holes. ‘These holes are often arranged in lines, as if they were con- nected with linear cracks in the earth’s crust. Earthquakes jar and shake the earth’s crust, throw its surface into transient wayes, and cause sometimes cracks and open fissures to appear at that surface, The largest of these fissures, however, are rarely more than a few miles in length and a few yards in width, and they appear rarely to leave any permanent traces on the surface, or to give rise to any of its more striking features. No one has ever yet pointed to any yalley or any glen, still less to any river-course, as haying been entirely caused by the gaping of the surface during any known earthquake, and in- dependently of subsequent erosion by running water. Mx. Mallet’s researches have given us the means of calculating the depth at which the impulse of an earthquake may originate. This Benth seems to be always proportional to the extent of the surface affected, from which it is obvious that in many cases a yery considerable thickness of the external envelope of the earth must have been traversed by these moyements. Supposing them to have a local origin, and to be caused by, or to he accompanied by, any considerable disturhance, either of flexure or fracture, in the solid or quasi-solid rocks at or about the centre of origin, it seems necessarily to follow that the amount of disturbance must lessen as we recede from that centre, in proportion to the thickness and extent of the matter oyer which it is diffused. ‘The tremblings and undulations, then, and the surface-cracks and fissures produced hy earthquakes are probably only the slight external indications of more intense but more local disturbance below. Great open fissures and gapings of the surface could only, as it appears to me, be caused by disturbances originating at a comparatively slight depth, where it is difficult to imagine any cause for them, and where, as a matter of fact, great disturbances never do seem to originate, In addition to the more conyulsive movements of the shocks, permanent eleya- tion and depression of the surface take place during earthquakes, and also to an equal if not greater extent by a slow gradual movement, unaccompanied by earth- quakes, and therefore not perceptible to our senses. These risings and sinkings of the surface are evidently the result of the upward or downward moyement of the whole thickness of the earth’s crust, whatever that thickness may be. _ Resting on considerations such as these, thus hastily sketched out, I am inclined to be bold enough to dispute the physical possibility, or at all events to deny the actual occurrence, at any time, of such surface manifestations of internal force as; 60 REPORT—1862. could give rise to what have been called “craters of elevation,” “valleys of eleva- tion,” or any other large openings of the surface of the ground. I would go even further than this, and hesitate to believe that any high inclination or great con- tortion had ever been imparted to any beds at, or close to, the surface*. I believe all such disturbed positions to have been acquired by a slow creeping movement, the result of the combination of great force acting against almost, but not quite, equally great superincumbent pressure, and therefore at a correspondingly great depth, and that, by the very constitution of the interior of the earth, such great force could not be brought to bear upon any mere point or line of the surface. The rocks thus disturbed ultimately arrive at the surface, because they have been laid bare by the stripping off of veil after veil of covering, by the external erosive forces acting over the upraised area—upraised either during the disturbance, or by a subsequent action of elevation of a broader and more equable character. These same combined actions, still further carried out, ultimately bring to the sur- face the Metamorphosed Schists, which had heen deeply buried by the converse actions of depression and deposition, as well as the granitic masses, which, pro- ceeding from the interior, slowly worked their way upwards to a certain height, but cooled and consolidated before they were able to approach the surface as it existed at the time of their intrusion. No one can study a mountainous district, in which the rocks have been greatly bent and broken, with the same care and attention that has been bestowed by the Geological Survey on the mountains of the British Islands, without perceiving that the external features, whether of hill or valley, do not depend on the frangibility of the rocks, but on their relative power of resistance to erosive action. The hard siliceous rocks, or those best adapted to resist the chemical and mechanical action of water, form the prominences ; the softer or more soluble rocks form the valleys and low grounds, ‘The upward or anticlinal curves in the beds, over which, if any- where, external gaping fissures would be formed, are at least as often marked by the occurrence of hills and ridges over them as of valleys, the external feature depending altogether on the ‘ weatherable”’ nature of the rock. The same reasoning is applicable to great faults and dislocations. We are all familiar with the fact that, of faults that have a dislocation of hundreds or even thousands of feet, there is often not the least indication at the surface of the ground, which may be a perfect plain, or may undulate, without any regard to the subter- ranean structure of the rocks. This seems to me to be strong evidence in favour of the supposition that these dislocations never did make any great feature at the surface. The amount of dislocation has been gained foot by foot and inch by inch below, the movement being so slow as to allow of the surface-irregularity being always diminished or obliterated as fast as it was formed. If a great disloca- tion had taken place at once, and an equally great cliff had been formed by it, surely the traces of such a feature would have been more often preserved than they are. Small cliffs do occur sometimes along the line of a fault, but only when it so hap- pens that at the present surface of the ground a hard unyielding rock is brought against a soft and more perishing one ; and the cliff or bank is always in proportion to the “weatherable ” natures of the two rocks, and not to the amount of the dislo- cation. In like manner, valleys sometimes run along the line of faults, and especially of large faults, and there is sometimes a sort of proportion between the magnitude of the dislocation and that of the external feature ; but even in these cases the mag- nitudes are not of the same kind, the width of the fault being very slight indeed as compared with the width of the valley. The coincidence is one of direction only, the original fracture having determined the direction of the subsequent * The contortions in the Chalk and the glacial Drift described by Sir C. Lyell, from Messrs. Forchhammer and Pugaard, as occurring in the Island of Méen in Denmark, show that this belief must be somewhat modified, and that local flexures and fractures do sometimes take place even at the surface. If so, then some of those apparent in the Alps and other recently formed mountain-chains may have also taken place at or near the surface. It is, however, demonstrable in all these cases that subsequent denudation has acted upon these areas, though the amount of matter removed may not be so great as the expressions in the text would imply. : 4 TRANSACTIONS OF THE SECTIONS. 61 eras. forces, so as to cause them to excavate the valley along that line rather than any other. ‘When, moreover, we examine faults below ground, we find no trace of any wide- gaping fissures; the walls of the fault, on the contrary, are jammed tightly against each other, and show frequent evidence of immense grinding force, proving the friction of the sides to have been enormous. In hard massive rocks there doubtless occur open spaces here and there between the walls, “pockets”’ or “bellies” between their projecting protuberances, or where they have been partly kept asunder by fragments detached from the sides. These are often full of crystalline minerals, and form “mineral veins” below, but seldom, if ever, form valleys or ravines at the surface. If these ideas as to the relative action of the internal and external forces at work upon the crust of the globe be well founded, it follows that none of the present features of the surface of the globe have been produced by the direct action of the internal forces, except volcanic orifices and cones, and that all others have been produced by the process of external erosion, except such as have been formed by external deposition, like hills of blown sand or alluvial flats and deltas. The surfaces of our present lands are as much carved and sculptured surfaces as the medallion carved from the slab, or the statue sculptured from the block. They have been gradually reached by the removal of the rock that once covered them, and are themselves but of transient duration, always slowly wasting from decay. Eyen, then, if the internal forces could produce such external features, it can always be shown that the surface which existed when they operated has long since dis- appeared, together with, in many cases, vast thicknesses of rock that intervened between it and the present one. It remains to say a few words on the nature of the erosive agencies which form these surfaces. The ocean is the grandest of these. The ceaseless breaking of its waves against the margin of the land constantly gnaws into and undermines it, and the tides and currents carry off the eroded materials and deposit them on some part or other of the ocean-bed. This action is that of a great horizontal planing-machine, always tending to the production of level surfaces, the cutting power being confined to the sea-level, while the matter carried off tends to fill up the hollows of the in- equalities that lie below it. The denuding action of the sea, therefore, produces “plains of denudation” on the parts it has passed over, and long lines of cliffs or steep banks along the margin where its influence ceased. It is essential for the energetic action of the sea that it should be the open sea, where a heavy swell can roll in upon the land, and where gales of wind can hurl furious waves against it. In sheltered bays and narrow inlets and fiords its erosive agency becomes compara- tively small, and in very protected places sinks to nothing. While, then, we look to marine denudation as the cause of wide plains, of long escarpments, of bold headlands and isolated hills, and of the general outline of mountain-chains, and as the remover of the great groups of rock that were con- tinuous over the area of the mountains before their elevation was commenced, I believe we err when we attribute to that cause the lesser features by which these greater ones are themselves modified. The river valleys that traverse the great plains, the gullies that run down the sides of the hills, the valleys, glens, ravines, and gorges that furrow the flanks of the mountain-chains, have, I believe, all been caused by atmospheric agency on the land, while standing above the level of the sea. The only case in which the sea tends to produce anything like a valley is that in which it forms open sounds or straits between islands, where the set of the tides and currents imparts to it a river-like action. Those depressions in the crest of a mountain-chain which are called “passes” or “ gaps” have doubtless been often eaused by this action, but it is obvious that this ceases as soon as the summit of the pass once rises above the sea-level and prevents the currents from sweeping through it. While the ordinary erosive action of the sea is a horizontal one, tending to the production of plains bordered by cliffs, that of the atmospheric agencies is a ver- tical one, always tending to the production of furrows, or more or less steep-sided channels, on all the land eet to their influence. 62 : REPORT—1862. Rain falls vertically, and tends to sink vertically into rocks, producing decompo- sition in them, both by mechanical and chemical action. A superficial coating of greater or less thickness is always thus kept in a state of decay. In almost all granite districts, the rock beneath the hollows and flatter parts of the ground will often be found to be decomposed in situ to a mere sand, so that it could be dug out with a spade to a depth of several feet. Roundish lumps are found here and there in this sand, which were the centres of the original blocks; these, as well as the solid rock below, showing every gradation of firmness, from hard crystalline rock to a mere incoherent sand. I have observed this in granite districts in all parts of the world, and was much struck with it during the past summer in the southern part of Brittany, where the deep narrow lanes often showed both granite and gneiss thus rotten and soft, to a depth sometimes of fifteen or twenty feet. On the steeper slopes the exposed rock was much less decomposed, obviously because the particles had been washed down and carried off as fast as they became completely disintegrated. Hard limestones, again, exhibit the effects of the action of the rain in the numerous open fissures and caverns that are always found in them, the water here having dissolved the rock and carried it off in solution, as if it were so much salt or sugar. The fantastic forms and honeycombed surfaces of all limestone crags attest the same action. In baring the surface of a limestone quarry where the beds are in= clined at anty donsiderable angle, they are often found to be furrowed by rain-channels one or two feet in depth and several inches in width, the hollows being filled with the finest earth. A deep covering of mould and turf is no protection against this action, and perhaps even aids it by contributing an additional dose of acid to the rain-water. Even where hard siliceous rocks exhibit a weathered coat of a very slight depth, a mere skin perhaps of a quarter of an inch thick, as is the case in some Felstones, still it merely proves that the atmospheric influences cannot affect a great thickness at any one time, and does not render it impossible that many such weathered coats may have been formed outside the present surface, and successively removed altogether by the completion of the process. The joints of rocks when first formed are doubtless mere planes of separation, without any interstice that would allow the insertion of even the thinnest edge of a knife ; they would be quite insensible to the sight, and would perhaps scarcely of themselves be sufficient to cause the separation of the rock into distinct blocks. In working deep mines it is sometimes said that the rocks cease to show any joints at all. The joints, however, doubtless exist, although they are invisible, while the open joints, such as we see in all rocks near the srirfabe, have been opened by the “ weather” acting along these concealed planes of separation. The action of the atmosphere, then (7. e. the chemical action of air and water and the various gases mingled with them, and their mechanical action, owing both to their movements of gravity and their expansion and contraction from changes of temperature), is operative in the gradual destruction of rock, to a much greater vertical depth beneath the surface than is commonly recognized. Its superficial action is still greater, and has also, as I believe, generally failed, as yet, in receiving due appreciation. The rain that falls upon the surface and does not sink beneath it runs, of course, down the shortest and steepest slopes it can find, and is collected first into rills, then into brooks and rivulets, and finally passes by rivers to the sea. This superficial drainage of a country is often augmented and kept up by springs, which are caused by that part of the water that had sunk beneath the surface finding its way back to it. The natural tendency of running water is to cut its channel deeper, and that at a rate compounded of the rapidity of the current and the nature of the rock below. Let any one take the basin of drainage of any great river, and trace it up to its source, following all its tributaries to their sources, and he will not fail to perceive that all the varied features of the different channels of this system of running waters are the result of these two circumstances only. In the mountain glens he will see those that traverse granite commonly with rounded open forms; those that cut through hard slates, or thick horizontal sandstones, are commonly narrow and precipitous, with jagged cliffs and overhanging ledges, perhaps, jutting from TRANSACTIONS OF THE SECTIONS. 63 the sides of the ravines. He will see the marks of the old cataracts that once fell over these ledges, but which now are removed to other places, or converted into mere rapids, or perhaps altogether obliterated by the cutting down and cutting back of the streams. Torrs and pinnacles will be left here and there, perhaps, rising up from the bed of the stream, showing the former islets and rocks which resisted the erosive action better than the parts on each side of them. Where a softer and more yielding mass of rock occurred, there the glen widens into an open valley ; the narrowest and most jagged and steep-sided glens are just where the rocks are most hard and intractable, and best calculated for resisting the chemical and mechanical action of running water. The scale upon which these operations have been carried out does not affect the nature of the argument. The action has been the same in the miniature glens of our own mountains and in the grander and more awful abysses that gash the sides of the Alps, the Andes, and the Himalayas. In all cases when the river comes down now, or has formerly come down, in the form of a glacier, before springing into running water, the ice-mass has of course scooped out and deepened and widened the valley in its own peculiar fashion. When we leave the mountains and come down into the lower lands, where the rivers wind with a more gentle stream from side to side of broad open valleys, through wide alluvial flats, still it is to the river that the present form and depth of the valley are due. Whatever may have been the undulation of the original surface of marine denudation which determined the course of the primary stream, the river has long since cut down beneath that surface, and is still occupied in cutting deeper, so long as it retains any sensible current at all. It effects this by undermining the bank now on one side and now on the other side of the valley, shaving off a little corner here and another there, so that a river not a hundred ards broad, perhaps, may eventually form a valley of several miles in width. The obstructions it accumulates from time to time in its own bed constantly deflect its channel, so that ultimately it visits every part of the valley. In many cases the mere deepening of the valley may necessarily widen it also, since the rocks may be of such a composition, or may lie in such a way, as not to be able to form a bank of any steepness; and the materials, therefore, always slip down towards the bottom of the valley as fast as their bases are cut into. It is true that all these processes are infinitesimally slow; but if carried on through a period of time indefinitely great, it is obvious that it is impossible to assign a limit to the amount of their results. I have for several years been studying the origin of the river-valleys of the South of Ireland, and have, since the last meeting of this Association, been com= elled to arrive at the conclusion that the great limestone plain of the centre of ‘ieee has lost a thickness of 300 or 400 feet at least, by the mere action of the rain that has fallen upon it. As a corollary of this conclusion, I have also been led to perceive that the longitudinal and lateral valleys of the Irish mountains—and if of them, then those of all other mountain-chains of the world—are the result of the action of the water or the ice that has been thrown down on them from the atmosphere. Tf we take any mountain-chain and its adjacent lowlands, and suppose no rain to fall upon them for a time, and that all the valleys of whatever description were filled up, and the sides of the mountains smoothed over from their peaks to their bases, 1 believe the surface thus produced would be one representing the limits of marine denudation ; then let rain begin to fall on such a country, and all the ela- borate structure of valleys, gorges, glens, and ravines would be produced by it. I believe that the lateral valleys are those which were first formed by the drain- age running directly from the crests of the chains, the longitudinal ones being sub- sequently elaborated along the strike of the softer or more erodable beds exposed on the flanks of those chains. Ido not, of course, intend to say that any country ever existed without valleys, since valleys of some kind must commence as soon as the first peaks of the mountains show themselves above the sea, and must be continued and extended in proportion to the extent of the land which gradually rises into the atmosphere. Atmospheric denudation and marine denudation have always been at work simultaneously upon the different parts of every land in the globe, and their 64 REPORT—1862. action may be very complex, so that it is often difficult or impossible to separate the results of one from those of the other at any particular place. Still I believe we may generally regard the external form of a mountain-chain as due to marine, and the valleys within it as the result of atmospheric erosion. Most of you will be aware that the views I have thus endeavoured to place be- fore you are not altogether original ; other persons have before now proposed the same method of explanation of the form ofground. M. Charpentier long ago referred the origin of the valleys of the Pyrenees to the action of the rivers which traverse them. Mr. Dana had pointed to the same action as the cause of the wonderful system of ravines that furrows the sides of the Blue Mountain range in New South Wales, and of the deep ravines separated by knife-edged ridges which radiate from the centres of the high islands of the Pacific. I confess, however, that I had, up to the present year, hesitated to accept this explanation without reserve ; and there- fore, since I am now convinced of its truth, I am anxious to take the earliest oppor- tunity of recording that conviction*. Mr. Prestwich, in his recent papers read before the Royal Society, has adopted the hypothesis of the subaérial deepening of the valleys of the Somme and the Seine, and other river-valleys both in France and England, to account for the for- mation of the freshwater gravels which he finds on the flanks of those valleys, so- high above the present levels of the rivers or of any possible floods. Professor Ramsay has in like manner attributed the formation of the hollows in which the lakes of Switzerland lie, to the ploughing action exercised on the sub- jacent rocks by the action of the glaciers, when far more extensive than now. The formation of lakes lying in “ rock-basins,” and not formed by the mere stoppage or damming up of a river, had always been a complete puzzle to me until I read ‘a fessor Ramsay’s paper in the last Number of the Geological Journal (May 1862), I believe his explanation of their origin to be the true one. That he and Mr. Prestwich and myself should all, within the space of the same twelvemonth, have been compelled to appeal to external atmospheric action as the only method of explaining the origin of the different surface-phenomena we were studying, is of itself, I think, good evidence that we are all three pursuing the right track in our search after truth. At the instant of penning this sentence, I see by a newspaper paragraph that Dr. Tyndall follows us in his speculations as to the origin of the valleys of the Alpst. * Had I not become previously convinced of the extent and power of atmospheric and river action in consequence of my own observations, all scepticism must have yielded to the proof of it detailed in the admirable Report by Dr. Newberry on the Geology of the Colorado River of the West, published by the United States Government at Washington in 1861. It was only in February 1863 that I saw this work through the kindness of Dr. Newberry, who himself transmitted to me a copy of it. The beautiful maps and plates and the numerous woodcuts illustrate the text in a way that puts to shame the miserable niggardliness of our own Government in such matters; for here they are either committed to the red-tape ignorance of mere clerks whose duty it is simply to curtail expenditure, or to the equally uninstructed indifference of higher officials in dread of the well-meant but blundering questioning of some man of figures in the House of Commons, or still oftener left to the enterprise of some publisher, who has of course his profit to make out of the work. An advertisement at the beginning of the American Report shows that the Senate of the United States ordered ten thousand extra copies of it to be printed, five hundred of which were given to the officer commanding the expedition. Dr. Newberry shows in his Report that the wonderful cazons which traverse much of the country of California, and some of which are from 5000 to 6000 feet deep, and only wide enough for the waters of the rivers to flow through them, have been cut down by those rivers through horizontal and quite undisturbed beds belonging to the Carboniferous, Devonian, and Silurian periods into the Granite below, and moreover that wide valleys in other parts have also been excavated by the gradual action of atmospheric erosion, leaving numerous perpendicular torrs, crags, or pinnacles of rock here and there, all showing the same horizontal beds. + A subsequent reading of Dr. Tyndall’s paper, and of a notice of it afterwards by Pro- fessor Ramsay, showed me that Dr. Tyndall was inclined, at the time of writing it, to attribute the Alpine valleys too exclusively to the action of glaciers. The valleys must have been commenced and many of them almost completed before the glaciers, although the TRANSACTIONS OF THE SECTIONS. 65 As a concluding observation, allow me to remark how curiously the threefold physical agencies that are in simultaneous operation on the crust of the globe were typified in the old heathen mythology. The atmosphere which envelopes the land and rests upon the sea, the ocean which fills up the deeper hollows of the earth’s surface, and the nether-seated source of heat and force that lies beneath the crust of the earth are each personified in it as a great divinity. If one of the old Greek poets were to revisit the earth, and clothe these ideas in his own imagery, he would tell us in sonorous verse of Zeus (or Jupiter), the God of the Air, ruling all things upon the land with his own absolute and pre-eminent power; of Poseidon (or eptune) governing the depths of the ocean, but shaking the shores which en- circle it; and of Hades (or Pluto), confined to his own dark regions below, tyran- nizing with all the sternness of a force irresistible by anything which can there oppose it, but rarely manifesting itself by any open action within the realms of the other divinities. On an Early Stage in the Development of Comatula, and its Paleontological Relations. By Professor Atuman, M.D., IRS. The subject of this communication was a small Echinodermatous animal, a single specimen of which was obtained by the author on the south coast of Devon, where it was found attached to one of the larger Sertularidé, dredged from about four fathoms’ depth. The author regarded it as one of the early stages in the de- velopment of Comatula, and though quite distinct from the well-known Pentacrinus stage of this crinoid, believed that it had been witnessed both by Thompson and Dujardin, but not correctly described or figured by either of them. It consisted of a body borne upon the summit of a long jointed stem. The body had the form of two pyramids placed base to base. The upper pyramid is formed of five triangular valve-like plates, moveably articulated upon the upper side of the lower pyramid, and capable of being separated from one another at the will of the animal, so as to present the appearance of an expanding flower-bud, and again approximated till their edges are in contact and the original pyramidal form restored. From between the edges of these plates, long flexile tentaculoid appendages, which must not be confounded with the permanent arms of Comatula, are protruded in the expanded state of the animal, and within these is a circle of shorter, more rigid, rod-like ap- endages which seem to be moveably articulated to the upper side of the calyx, immediately round the centre, where it is almost certain that the mouth is placed. The lower pyramid or proper calyx is mainly formed of five large hexagonal plates, separated from the summit of the stem by a zone, whose composition out of distinct lates could not be demonstrated, and haying five small tetragonal plates interca- ated between their upper angles. In assigning their proper value to the several plates thus entering into the body, the author regarded the lower zone, which rests immediately on the stem, as simply a metamorphosed joint of the stem itself, while the verticil of plates, situated immediately above this, is the true basilar portion of the calyx. The five sma'l intercalated plates are the equivalents of the radialia, and destined to carry afterwards the true arms of the crinoid ; while the five tri- angular plates which constitute the sides of the upper pyramid are cnterradialia. Professor Allman considered the little animal described in this communication as of special interest, in the light which it seemed capable of throwing on the real nature of certain aberrant groups of Crinotdea, such as Haplocrinus, Coccocrinus, &c., in which the calyx supports a more or less elevated pyramidal roof, composed en- tirely or in great part of five triangular plates, which find their homologues in the five sides of the pyramidal roof of the little crinoid which formed the subject of his paper. fig On Bituminous Schists and their Relation to Coal. By Professor Anstep, /.R.S. The occurrence of rocks of all geological periods, and in most parts of the world, containing a sufficient quantity of the mineral hydrocarbon to be worth distilling present depth, width, and regularity of many of them are doubtless ascribable to glacier action. i 1862, i) 66 - REPORT—1862. for various economic purposes is well known; and there are certain cases in which there is an apparent passage from the shale or schist containing so large a quantity of these mineral oils as to burn like fuel, into true coal, which also sometimes con- tains a large quantity of hydrogen, and can he distilled for some purposes with ad- vantage. The chief object of this paper was to direct attention to some of the rocks known among geologists as bituminous schists, Two deposits of this kind have long been known in France, and have recently been visited by the author,—one between Nantes and Rochelle, in the Bourbon- Vendée, the other near the town of Autun, The former are called the Feymoreau schists, and they were distilled with success in 1830 for paraffine oil, other light burning oils, and lubricating oils, by the method since patented by Mr. Young, Owing to the absence of means of communication, the works were suspended ; and afterwards M, Selligué, the inventor of the process, carried on similar operations with greater success near Autun, where there is now a very large manufacture of light oils and paraftine. The Feymoreau schists resemble in appearance the rich Torbane Hill mineral of Scotland, and resemble both that and Boghead coal very closely, but they cannot be used as fuel; they only yield about 15 per cent. of light oils. They are very thick, but do not extend far in a horizontal direction. They underlie the coal- measures, or rather the productive part of the measures, and almost represent the underclay of a poor coal-seam. In this respect also they resemble the Scotch bitu- minous shale, The Autun schists occur considerably above the highest seam of coal in the coal- measures, They are quarried or obtained from drifts, They are thick shales, bearing no resemblance whatever to coal, and not in any way capable of being used as fuel. The best varieties yield 50 per cent. of oils of all kinds, but others are very poor. They are caieratele rich in paraffine. The shales of the paper-coal, near Bonn, on the Rhine, are also used for distilling, and paraffine is made from them; they have no resemblance whatever to coal, and could not be mistaken for it. The lias-shales (Posidonia-schists) in many parts of Germany are also distilled for the light oils and paraffine, with some success. Bituminous schists of all geological dates, some passing into coal and others hardl distinguishable from common clay, thus exist in many parts of the world, and all ee in the one important point, that they may be used for obtaining certain valu- able products by special treatment. “It is important,” the author concluded, “ that such substances should be recognized as a class, and not mixed up with or mistaken for coals, and that there should be some understanding among scientific and practical men what coal is, and in what it differs from certain minerals containing hydro- carbons sometimes associated with it.” On a Tertiary Bituminous Coal in Transylvania, with some remarks on the Brown Coals of the Danube. By Professor Anstep, F.2,S, The deposits of mineral fuel on and near the Danube are, for the most part, lignites or brown coal. These are extensive, and have been much used. The fuel burns freely, and can be employed for all purposes; but it has two faults. Tt contains a large percentage (averaging 15 per cent.) of hygroscopic water, and it falls to powder on exposure to air, especially in changeable weather. Itis uneconomical, and cannot be stored. These deposits are newer Miocene ; they occur in and with sands not con- verted into sandstone, and marly clays not shales. They are generally in lenticular masses, unconnected one with another. : These lignites do not occur in the smaller mountain-valleys of the Carpathians, In their place, in the Zsil valley, is a disturbed deposit, also tertiary, and also con- taining mineral fuel; but the fuel is here an accent bituminous coal, and not a brown coal. There are twelve well-defined workable beds, one of them varying from 30 feet to 50 feet thick, four others 5 feet to 10 feet, and the rest smaller. They are associated with good hard coal-grits, shales, and ironstone bands. Two e ee serra are well marked by an overlying bed of fossil shells (a species of erithium). All these coals are nearly free from hygroscopic water, and stand exposure for TRANSACTIONS OF THE SECTIONS, 67 years without injury. They have been examined by the authorities at the Geo- logical Institute at Vienna, and found to consist of carbon 57°8, ash 6:5, water 2-1, and the carbonic unit is stated at 5582. This is equal to the average of Austrian bituminous coal, and yery much superior to the average of brown coal, There is no doubt of the tertiary origin of the Zsil coal. The beds containing it have, however, been much altered and broken, and since covered by unconformable tertiary rocks of newer date. Above these again is a thick gold-alluvium. In conclusion, the author drew attention to the fact that coal, like salt, is limited to no geological period, and required no high temperature either to elaborate the lants of which it was made, or to complete the conversion of the vegetable matter into coal. There is no volcanic district at all near the locality in which the Zsil coal occurs. There is no underclay beneath the Zsil coal, nor is there beneath the Liassic and Cretaceous coals, somewhat extensively worked on and near the Danube or in the Carpathians. These coals have therefore, in all probability, been formed of transported vegetable matier. The presence of a true bituminous coal of economic importance in a geological position h*therto limited to lignite, the author submits as a fact too important to pass without being placed on record, On the Glacier Phenomena of the Valley of the Upper Indus. By Capt. Gopwiy-Avsten, 24th Regiment. The glaciers noticed in this paper are supposed to be of greater extent than any yet known; they occur in that part of the great Himalayan chain which separates Thibet from Yarkund, in E. long. 76°, and N. lat. 35-36°, and extend over an area about 100 miles from east to west, from Karakorum Peak, No, 2 (28,265 ft.), to the Mountain of Haramosh. The glaciers which supply the Hushé River, which joins the Indus opposite Ka- peloo, were first described. Those of the upper portion of the yalley take their rise on the southern side of the Peak of Masherbrum, and are about 10 miles in length. The Great Baltoro Glacier takes its rise on the west of Gusherbrum Peak; on the north it is joined by a great ice-feeder which comes down from Peak No. 2; op osite to it, from the south, is another; both of these extend 9 or 10 miles on either side of the main glacier. This, from its rise to its further end, measures 30 miles; its course is from E. to W.; the breadth of the valley along which it flows is 12 miles. It receives numerous tributaries along its course, some of which are 10 miles and more in length ; two of them, on the N., lead up to the Mastakh Pass into Yarkund (18,000 ft.), whence a glacier descends to the N.E., about 20 miles in length. tthe Nobundi Sobundi glacier takes its rise from a broad ice-field which lies to the N. of lat. 36°, and has a S.E. course for 14 miles, with numerous laterals; it then turns S., when it bears the name of the Punmah Glacier; about 5 miles from the termination it is joined by a glacier from the N.W., 15 miles in length, The Biafo Glacier is pernape the most remarkable of any of this part of the Hima- layan range; it has a linear course of upwards of 40 miles; the opposite sides of the valley are very parallel along its who'e length, and the breadth of ice seldom exceeds a mile, except where the great feeders join it from the N.E. From the summit-level of the Biafo Gause a glacier is continued westward to Hisper in Nagayr, 28 to 30 miles in length. The Chogo, which terminates at Arundoo, takes its rise between the Mountain of Haramosh and the Nishik Pass; it is about 24 miles in length, with numerous branches from Haramosh, 8 miles in length. The waters from all the glaciers, from that of Baltoro in the E. to Chogo in the W.., are collected into the Shigar River, which joins the Indus at Skardo. All these glaciers carry great quantities of rock-detritus, The blocks on the Punmah Glacier are of great size. The author next described the groovings and old moraines of a former extension of the glaciers in this region, showing that they reached many miles beyond their present terminations, and rose upwards of 400 feet above their present levels. The paper also described the thick alluvial accumulations of the yalley of the Indus, particularly those of the neighbourhood of Skardo, 5* 68 REPORT—1862. On a New Species of Plesiosaurus from the Lias near Whitby, Yorkshire. By Dr, A. Carts, F.L.S., and W. H. Batty, F.G.S. The very large and perfect Plestosawus, the description of which formed the subject of this communication, was discovered in the Lias at the Kettleness Alum- its, near Whitby, on the 27th of July, 1848, and presented by the Marquis of Nstuinkby to the late eminent Surgeon, Sir Philip Crampton, as a mark of regard for his scientific attainments, who, in accordance with the anxious desire he always felt for the advancement of science, bequeathed it to the Royal Zoological Society of Dublin, in whose Gardens it was first exhibited to the public in May 1853; that Society, with the same object in view, has now deposited it in the Museum of the Royal Dublin Society, where every facility is offered for the study of this magni- ficent and largest example of-the genus known. The total leneth of this skeleton (of which a drawing of the natural size was exhibited), measured in the line of its vertebree, is 22 ft. 5 in. It lies in very nearly a natural position, resting upon the ventral surface, with the head and neck slightly inclined towards the right side ; the head, with the under jaw, is in a good state of preservation, and, being freed from the surrounding matrix, the principal bones composing it may be easily re- cognized ; the vertebral column has throughout its entire length fallen over towards the right side, presenting a slight irregular curve ; it exposes in the cervical series a side view of the centra or bodies of the vertebree, with their large neural spines (neurapophyses), and in some instances remains of the cervical ribs or hatchet- shaped bones (plewapophyses), the bodies of the dorsal vertebrae being almost entirely concealed, the massive ends of the neural spines and transverse processes projecting prominently above the general surface. ‘lhe caudal portion of the ver- tebral column is somewhat dislocated and thrown out of position, especially near its junction with the sacrum; the bodies are, however, in some cases well exposed, with their spines and processes. The ribs, thirty in number, are spread out on either side of the dorsal vertebrze, those of the left side being almost in their natural position. The anterior paddles are extended from both sides, on a plane nearly at right angles with the head and neck, the right posterior paddle stretching out in a direction parallel to the anterior, that on the left side inclining more to- wards the tail; in this paddle the tarsal bones, with their phalanges, are deficient, that portion haying been unfortunately carried to the calcining-heap before it was observed. The following are some of the principal measurements of this species, which it was proposed to call Plesiosawus Cramptont. ft. in. Total length of skeleton. ............04. COOLER: Thc i acgld Length of the skull from the point of the premaxillaries to 211 thie pariotalierestiyy 34. FFL tals PF Lae NS Oe ae Leap Length of the lower jaw, from the symphyses to the extremity 3 10 of the angular piece. ............... Sees Aa goo aye che Breadth of lower jaw across the tympanic condyles. ......... 2, oes Breadth of skull across the orbits ..............eceeceeees of ee ee Breadth of skull across the snout ..............cccceeeueee ORG Height of skull at posterior end, from angular piece of lower bat jaw to‘parietaltcrest 2. 22.52 eens On elon eel ets Height at extreme point of snout ............. ccs cec esse eee 0 6 Length of cervical portion of vertebree, twenty-seven in number 6 0 Length of dorsal and lumbar, thirty in number ........... ele Length of caudal, about thirty-four (some of the terminal ver- 5 6 tebree being deficient) "40. SPATE RS, ypottaaieet (Total number of vertebree which can be counted ninety-one, Length of huieriy 200 SU ae ae eee Eien sabia! Snes’. Breadth of humerus at radial extremity ..................+. 010 Leng th ‘oferatlins ay Hainer ule Ped Buy Pee Bry peice oe, Breadth of radius at proximal extremity .........cceeceeeeee 0 6 Hiengthiofelnar eee, av Heyes 4 ey. Pad ea Ba ik Deed cones ieee Breadth of ulna at proximal extremity. ..,..escsceseeerreeee O 42 _— TRANSACTIONS OF THE SECTIONS. 69 ft. in. Length of femur ..scc.csceseterecccsccasesesesservaccean, 110 Breadth of femur at distal extremity ...sceceeeeesseeeeeeee 0 105 Length of tibia... .. ccc ee eee RC: COC Omm nit sjererees ba OraRO Breadth of tibia........ eR Galshelatatsls fame ZR arya LA td * ypuigy ‘mqroyg L seeeeeee snueseyra —— ae (RP a (PS ent ier oe veer eveees gnuToTpayy Se ELL Bid « nah ee aie fenquioszod 2" F lane “SNIIBIOUIN SNTIOLY, — | — | — [egg te reer c terete ene tees eenuelene el asieyecais stqzoueyd —— | SP aa af “oumissTpryTU wasopenIQ reete tes) SUnISEIpTy tt aay eS apeQfretcerrensrccvanrerserys Mit aabeiies * BStATp —— eRe! — | 0 "x \yovony‘eyenysoo vuretjso0poXo|" * * HUH “eyeqnqsoo Bomex ae Sa See Aiged towns ne aire seins 6 Ba tose wines) w ateatae whe ve eyerrygs —— — f— faa nBopuopy ‘sngdni1equt oqmy|*** “Tea ‘eared BOSSTIT Oe ha ee | oy [teeter eter eee rere ene ee - ‘snyder eindin ar — |} — | — Joa)" * waynpy ‘epomssty vyjeyeg|"*** vUurqovoyy vTemnyoung ae ee TPR she ED ecelcn wiv wretore ore ae shes ae ags tutte eye Sma Upper — | — | — | aa lyouorg (qauey ) ‘vorpueysy “N] ttt SOPlooljayy —— ot] — | — | "9 a) youonr (umpours) ) Srays "N'A eins ‘eSne[O BOIL NT ee He Sts oan eeteler ete ots Weve ae oa trees” emortamy — male eda eer ehe rain eieveterane rereereserss uouy ‘stpeprorerkd erpesue yy ree} } — | oo [er yg ‘snsuedxe oqmy|mog 2 ‘poug “eprpenbs —— ——_ aa —- S, o9 ha . . eee eee . eevee eeere aS 6 0) “IVA puv sIpNI —— ae ee ea moe oa | ais Beatin en A 0 31}213 +++ -BazOqT] BULIO}IIT] — | — | — | 8 [ote rer serrereseresevess| gaugRnore ‘Ted 2 GYULA —— oa ees Ce ae a Sie ie ee en snjooynd cai 8 are Ace es) a8! 2c OBS ig 0) OH pate” * emprred vunowy , eee — [Ori er etter erereseesrerens "| Yom “MMOGIOH *Trequmyop ee | oe spiuieia #038 6.sssceipiaielogeie. sini szeianell int aiken ice tania roqnt — T&x 6Gx SGx OO 8L | gs | 06 G9 | ZG | 9G "els" * wogsuyor “eye[ao vuoI[D] Bg ‘SHDNOdG I a aa oY oad ee ICI a hy 4d CTOAVqoOT VUTTNZWOUNAy, 3¢ Gnas /eanelipee el aca fa | — (190) Mth [feels olniiay ens ne ee a0. e nee (araogn 1g PUNT ROTO sew ele wel wee Gs-0z| — ee OO ry cy fl “WA TUN MNUMUAS VUTTOITEY 99 ‘VUTAININV UOT ‘ysngy 0} Surproooe ‘sardeds Suro OUTT[VIOD Wl. + +e |e eee leeee Ql-0F| — | — force] ct frettee testes eres esse ssl msemar “esoorjiea wrpeadery] gg ‘VOZX'IOg ‘Ajao ourdg). . ‘saurds pu sozvyd yo suorsog}. . . . . . GO-GL] — | — ree] acalrc tre rtceeeeeeeeeeeeeesleces sane Gnorseaton ——| HQ O9-GT] — | — [rtf tot pst saga ‘snqoopseu “Tyan py‘stsuodeqeorqy snuryony| eg ‘VLVNUECONTLOST Say ee CY | retceceessererecesestensl guuyr EIiBinormtied Bdzeg ze 8L | FE | 04 FP | GP | 9G ‘VCITANNY . H . . . "enn “ermgyg wont A| Tg veeef fee elgg | ‘| * “ngsog gr ‘snzvocod reef foes dang ig | | [awe] ag [ree tude ecensceeseeess a” tthe eo tilereld o CZ—"T als — feet elegy reeresseeeessrersceesss «| gudmbnug ‘snqvuorto snUvpeg 6P ‘VICHATUUI() me | 3 pls.) pe lee FE L| &|wiol 2 (EE) 2 Be | “SyIVULOY 4. SG]. Jo-.| Es E @ |. Bg ‘surftoudg .. ‘sorodg jo ome yy ‘ON : | & & oSURIyT ® & ; TRANSACTIONS OF THE SECTIONS. a's On the Geology of the Gold-fields of Otago, New Zealand. By W. Lavvrr Linpsay, M.D. & F.RS. Edinburgh, F.LS. §& F.R.GS. London, $e. The author had made a personal geological survey of the Tuapeka and other gold- fields of Otago between October 1861 and January 1862, some of the general results whereof were published, under the section on the “ Geology of Otago,” in a Lecture by him, printed in Dunedin in January 1862, entitled “ The Place and Power of Natural History in Colonization, with special reference to Otago ; being portions of a Lecture prepared for, and at the request of, the Young Men’s Christian Association of Dunedin,” and issued as a pamphlet by and under the auspices of the said Asso- ciation. He had also formed and brought home a considerable collection of the rocks and minerals of the Otago gold-fields, with relative field-memoranda, maps, and drawings. F The general results of his observations and deductions may be tabulated as fol- ows :— 1. The gold and gold-bearing rocks of Otago do not differ essentially, guoad mineralogical or geological characters, from those of every other part of the world hitherto known to be auriferous. 2. The original matrix of the gold is quartz; and the latter occurs interbedded in, or associated with, metamorphic slates, especially of the gneiss, mica, tale, chlorite- and clay-slate families. 3. These slates vary greatly in mineralogical character; but they bear a closer resemblance to those of central and southern Scotland (Grampians, &c.) than to the more altered Silurian auriferous slates of Victoria (Australia). 4, The slates in question are probably of Silurian age; but this has yet to be proved, for they are themselves non-fossiliferous ; and as yet the subjacent rocks are unknown. 5. At various points there are evidences of considerable disturbance in the schistose strata by the intrusions and eruptions of trappean rocks, apparently refer- able to the Tertiary era. 6. The valleys among the schistose hill-ranges are generally occupied by alluvial drifts, apparently of Tertiary age, naturally divisible perhaps into a lower or older group, characterized by its abundant lignites, and a superficial or newer series, which is chiefly the seat of the operations of the gold-miner. 7. The lignitiferous or older drift consists chiefly of quartz gravels—in certain deposits cemented by means of peroxide of iron and other materials into a hard red conglomerate—associated with thinner strata of clays, sands, and gravels. This series of beds sometimes occurs at a height of from 500 to 1000 feet above the sea- level, on the flanks of trappean and other hills. 8. The upper or newer drift bottoms—the valleys and “ flats,” so common in the hilly parts of the country (where the hills are schistose)—consist essentially of (a) clays, blue, yellow, or red; () boulder-clays ; and (c) gravels, so called, which are really the little-worn or abraded débris of the subjacent and circumjacent slates, and which are more correctly denominated by the miner’s phrase, “ chopped slate.” These beds are immediately superjacent (in the order in which they are above enumerated) on the generally upturned and very irregular edges of the slates ; and the latter, according to their mineralogical character, give a dominant colourt o the former,—the clays aud gravels of the gneiss being bluish or greyish, of the chlorite-slates greenish, of the mica-slates, in proportion as they are less or more ferruginous, yellow or red. 9. Gold occurs chiefly in the gravel or “chopped slate” above described,—this constituting the “ wash-dirt” of the miner. It is frequently found most abundantly in “pockets” (hollows or crevices) of the irregular upturned edges of the subja- cent slates, whereon the gravel immediately reposes. It is disseminated through the clays in some localities; while in others it is sometimes collected in quantity in cavicies, or “ pockets,” under the boulders of the boulder-clay beds. 10. The gold is partly granular or gunpowder-like, partly scaly, nuggety, or erystallized ; and it exhibits every gradation, intermixture, and variety of each of these forms or kinds in different localities. 11, It is associated, in different localities, with iserine (titaniferous iron-sand) ; 78 : REPORT—1862. iron-pyrites, common and arsenical (mispickel) ; cassiterite (tin-sand or oxide of tin) ; topaz (of the gowttes-d'eau character, blue or colourless) ; garnets, and other minerals. Much of Otago remains yet to be explored, especially the mountainous western portion of the province; but, from the geological structure of those portions of the province he personally examined, the author draws or makes the following in- ferences, deductions, or predictions :— 1, That the geological basis of the greater part of Otago consists of auriferous metamorphic slates. This refers especially to the great central and western moun- tain-ranges; for instance, those which encircle the large interior lakes (Hawea, Wanaka, and Wakatip). 2. That these great mountain-systems are probably the source of the tertiary drift so abundantly distributed over the lower parts of the province, which drift consists mainly of quartzose and schistose débris. 3. That this tertiary drift, in both its lignitiferous and more strictly auriferous series of beds, will be found much more extensively and largely distributed over the province than at present. 4, That gold is very extensively and largely distributed over the province; and that many gold-fields remain to be discovered, especially in the interior; though nothing short of actual mining, or “digging,” can determine the localities of “ payable gold-fields.” 5. That the supply of gold is at present practically unlimited; and that the auri- ferous resources of Otago are only beginning to be developed, and will only be fully developed in the course of many years, by—a. The addition of quartz-mining, and others of the skilled branches of gold-mining, to the shallow or “ alluvial digging,” to which the miner’s operations are at present mainly confined. This implies a greater concentration of attention than at present on the auriferous quartzites, from which the drift or alluvial gold has originally been derived, the working whereof, should they exist to any extent, is much more likely to yield a permanently remu~ nerative employment, and a nein and valuable source of, revenue, than the said “ alluvial digging.” 6, The systematic application of improved chemical and mechanical, or chemico-mechanical, processes to gold-mining, and the expenditure thereon, or application thereto, of suitable capital. ec. The establishment of gold- mining as one of the speapstal industrial resources of the province. d. The systematic i peal y exploring and experimental parties suitably equipped, partly geological and renin partly mining and “digging.” e. The liberal and enlightened encouragement of mining and of the miners by the construction of rail- and tramways, the opening-up of roads, the building of bridges, the establish- ment of townships, the sale of waste lands at suitable prices, the adequate supply of fuel by the working of lignite-heds or otherwise, the institution of proper mining laws and mining boards, and other measures pertaining strictly to the legislative function of the State. The following Tables illustrate the comparative prolificness of the Otago gold- fields, from their discovery in June 1861 to the end of March 1862 :— I, Showing the amount of gold brought to Dunedin by each Government escort from the chief gold-fields of Otago (compiled from the Receiving Officer’s returns), Date of arrival of escort. Tuapeka. | Waitahuna.| Waipori. Total by each escort. 1861 ZS. ozs ozs ozs “Vi gel be RAR RA sisiais'? ES hacen | a pet ah Rear aise 480 99, TOL nm stale duldan oe alates RGEC BN > cstetat’ af vcvekins ¢o 1,462 PAUP USUI gcse g aticlbahis AUS cme Al hg RR sal eae re 5,056 September 4 ..,..,..,... TAC) de na ae te gag IRE yes 7,759 “ wD oe ein eins tas ib 5.43 | ums Ii PrP a SEPT ee SP 11,280 October 47; or. neremjer atone dy oping bP ag Soe er, A 12,126 | TRANSACTIONS OF THE SECTIONS. Tas eE I. (continued), Oetober 18 Seis oi wegen sities 14,438 soo. aE I ao iargroreoste ore LO TE a ame JIE gia.ejate November 15............ 30,584 AGED te vga cis Ne 15,402 at On ae Ke epee | tae 4 13,520 Ato) Nn eee December 5 ............ 10,198 4BBB [hl cisiaieis He WIT Sa ly opih.s 98 10,953 tt re BO MD bhoilecige t 9,594. AOLbinN aap, is ay EG Kart aah ee 10,080 BOBS! hr Jerriyle 1862. January 2....,..,.0500- 8,447 hat: We blips Pabe oo EE aia 7,435 PAT an ea PO svesté veecaane 8,867 Nil aN oss PEs. ta waen cave tt 9,488 DOGT Oe tresses SMM a roc ede ease mee 8,722 1,588 969 MebrIAry 0 ca vsherea sas 9,749 OBB rags, . he eeeae 8,027 Ae Bd epee MO an, 7856 ie Jpeg eerie OO ee 7,308 1,833 1617 PE ceca cnseavins 5,901 1,144 195 BLOM eicisicclogple sees: 7,201 1,695 604 NNR 6,054 ty] song ge SMT Ts ies ae sacs «ace 5,447 1,399 1293 Metlc ss tas cincac 272,558 | 58821 | 4678 Average by each escort .. 9,734 2,916 936 79 835,552 11,984 II. Showing the quantity and value of, and duty on, gold exported from Otago between 3rd August, 1861, and 31st March, 1862. Quantity. Value. 1861, ozs. dwts. Ang.3 to Dec. 31......+,.55°- 187,695 9 1862, dem.1 to March 3]. ,..,s20+4: 170,770 13 PUM ts ei falsact senate: 358,466 2 | 1,889,056 2 9 Duty. £ a @. Li eal ed 727,319 17 5) 23,461 19 10 661,736 5 4| 21,346 8 6 44,808 8 4 III. Showing the quantity and value of all the gold exported from the whole of New Zealand up to 31st March, 1862. Produce of Port of export. gold-fields in Quantity. province of “we a ozs. leton., Hehe San ree pistes cee Otago 359,639 Wellington Nelson Wellington ererepeeer eee eae Nelson 46,591 PANIC ANG st acee hie aicters als ‘cis rs Auckland 354 Totals. ieee ach RABE OPO sae 406,584 ———— Value. £ 8. d. 1,393,600 0 0 180,541 0 0 1,372 0 0 ——_— 1,575,513 0 0 80 REPORT—1862, Tables I. and II. are compiled from statistics given in the ‘Otago Daily Times’ of April 6, 1862, and Table ILI. from those given in the ‘Otago Colonist’ of July 15, 1862. On the Geology of the Gold-fields of Auckland, New Zealand. By W. Lavprr Linpsay, ID. & F.RS. Edinburgh, F.LS. §& F.R.GS. London, §e. The author had. personally made a geological examination of the Coromandel gold-field, in the province of Auckland, in February 1862, having previously spent several months on a similar survey of the Otago gold-fields. He described Coromandel as a different type of gold-tield from Tuapeka (Otago), and, as such, of interest as illustrative of the general geology of the New Zealand gold-fields. The main results of his observations and deductions may be concisely stated thus :— 1. The geology of the northern gold-fields of New Zealand, including those of Nelson as well as of Auckland, does not differ essentially from that of the southern or Otago gold-fields (as the geology of the latter is described in his paper “On the Geology of the Otago Gold-tields,” save in so far as regards certain minor details. The parent slates, for instance, are in the north more frequently of a clay-slate or argillaceous character than in the south; the auriferous quartzites are frequently developed to an extent as yet unknown in Otago; the evidences of trappean dis- turbance are more numefous, and the metamorphism of the slates by the contiguity of the erupted or intruded traps better marked. Nor does the character of the gold differ materially, save in so far as, in certain localities, it is more generally associated with its quartz matrix. 2. The Coromandel Peninsula consists mainly of a mountain ridge, running nearly north and south; the mountains haying a bold serrated outline, and varying in height from 1000 to 2000 feet. The valleys between the spurs given off laterally by this main or dividing range are of the character generally of ravines or gorges, occupied by mere mountain streams ; the “flats” or alluvial tracts at their mouths, and on the coast, are inconsiderable. 3. This mountain-range consists apparently of slates of Silurian age, generally of argillaceous character, but greatly altered by contact with, or proximity to, numerous outbursts or intrusions of trappean and other rocks. ‘The mountains are so densely wooded, and so difficult of access, that it is only here and there in the gorges of the streams that sections of these slates may be examined. In these sections the slates are frequently found to resemble Lydian stone or the slaty varieties of basalt (such as clinkstone); while they are disposed more or less vertically, their irregular upturned edges affording the most convenient and abundant “pockets” for the detention and storage of the alluvial gold washed from the higher grounds. 4, [Local geologists describe the fundamental rock of the Coromandel mountain- system as granitic, and the granite as forming here and there the “aiguilles” of the dividing ridge. The author met with no granite zz situ; nor did he discover granitic boulders or pebbles in the boulder-clays of the auriferous drift, or in the shinely beds of the mountain streams about Coromandel Harbour. | 5. The Coromandel slates are characterized by their prominent and numerous quartz “reefs,” consisting of auriferous quartzites. Here and there, where the dense vegetation admits, these reefs are met with in situ, frequently as “dykes,” standing prominently above the general level of the slates ; sometimes forming the top of the dividing ridge itself. The proximity and abundance of such quartzites are sufficiently indicated by the immense numbers of huge quartz-boulders or blocks which bestrew the low ground and occupy the ravines and gorges, which blocks are characterized by comparative angularity. The quartz is frequently of the porous, light, spongy character so prevalent in the gold-fields of Australia, Nova Scotia, California, and other auriferous countries ; and its colour is frequently buff, brown, ochrey, or vermilion, the result, anparently, of different degrees of ferruginous impregnation. 6. The auriferous drift is mostly of the charac.er of the newer or upper Tertiary drifts of the Otago gold-fields, consisting essentially of—u. variously coloured clays ; b. houlder-clays, also variously coloured; and ¢. gravels, of the “chopped slate”