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Of this series there have now been published forty-two Volumes, each of which coutains, in addition to the papers and solutions that have appeared in the Educational Times, about the same quantity of new articles, and comprises contributions, in all branches of Mathematics, from most of the leading Mathematicians in this and

other countries. New Subscribers may have any of these Volumes at Subscription prices.

LIST OF CONTRIBUTORS.

ALDIS, J. S., M.A.; H.M. Inspector of Schools. | EVANS, Professor, M.A.; Lockport, New York.
ALLEN, Rev. A.J.C., M.A.; St. Peter's Coll., Camb. FICKLIN, JOSEPH ; Prof. in Univ. of Missouri.
ALLMAN, Professor Geo. J., LL.D.; Galway. FINCA, T. H., B.A.; Trinity College, Dublin,
ANDERSON, ALEX., B.A.; Queen's Coll., Galway. FORTEY, H., M.A.; Bellary, Madras Presidency.
ANTHONY, EDWYN, M.A.; The Elms, Hereford. FOSTER, F. W., B.A.; Chelsea.
ARMENANTE, Professor; Pesaro.

FOSTER, Prof.G.CAREY, F.R.S.; Univ.Coll.,Lond. BALL, ROBT. ŚTAWELL, LL.D., F.R.S.; Professor / FRANKLIN, CHRISTINE LADD,M.A.; Prof.of Nat.

of Astronomy in the University of Dublin. Sci. and Math., Union Springs, New York. BABU, SATISH CHANDRA ; Presid. Coll.,Calcutta. FUORTES, E.; University of Naples. BATTAGLINI, GIUSEPPE; Professore di Mate- GALBRAITII,Rev.J.,M.A., Fell.Trin.Coll., Dublin. matiche nell'Università di Roma.

GALE, KATE K.; Worcester Park, Surrey. BAYLISS, GEORGE, M.A.; Kenilworth.

GALLÁTLY, W., B.A.; Earl's Court, London. BELTRAMI, Professor ; University of Pisa. GALLIERS, Rev. I., M.A.; Kirkstead Rectory, BERG, F.J. VAN DEN; Professor of Mathematics Norwich. in the Polytechnic School, Delft.

GALTON, FRANCIS, M.A., F.R.G.S.; London. BESANT, W. H., D.Sc., F.R.S. ; Cambridge. GENESE, Prof., M.A.; Univ. Coll., Aberystwith. BHUT, ÁTA BIGAH, M.A.; Delhi.

GERRANS, H. T., B.A.; Stud. of Ch. Ch., Oxford. BICKERDIKE, C.; Allerton Bywater.

GLAISHER, J. W. L., M.A., F.R.S.; Fellow of BIDDLE, D.; Gough H., Kingston-on-Thames. 'Trinity College, Cambridge. BIRCH, Rev. J. G., M.A.; London.

GOLDENBERG, Professor, M.A.; Moscow, BLACKWOOD, ELIZABETH; Boulogne.

GRAHAM, R. A., M.A.; Trinity College, Dublin. BLYTHE, W. H., B.A.; Egham.

GREENFIELD, Rev. W.J., M.A.; Dulwich College. BORCHARDT, Dr. C. W.; Victoria Strasse, Berlin. GREENSTREET, W. J., B.A.; Framlingham. BOSANQUET, R. H. M., M.A.; Fellow of St. GREENWOOD, JAMES M.; Kirksville, Missouri. John's College, Oxford.

GRIFFITH, W.; Superintendent of Public Schools, BOURNE, C, W., M.A., Bedford County School. New London, Ohio, United States. BROOKS, Professor E., Millersville, Pennsylvania. GRIFFITHS, G. J., M.A.; Fell. Ch. Coll., Camh. BROWN, A. CRUM, D.Sc.; Edinburgh.

GRIFFITHS, J., M.A. ; Fellow of Jesus Coll., Oxon. BROWN,Prof.COLIN; Andersonian Üniv.Glasgow. GROVE, W. B., B.A.; Perry Bar, Birmingham. BUCHHEIM, A.,M.A., Ph.D.; Schol. NewColl.,Oxf. HADAMARD, Professor, M.A.; Paris. BUCK, EDWARD, M.A.; Univ. Cull., Bristol. HAIGH, E., B.A., B.Sc.; King's Sch., Warwick. BURNSIDE, W. S., M.A.; Professor of Mathe- HALL, Professor ASAPH, M.A.; Washington. matics in the University of Dublin.

HAMMOND, J., M.A.; Buckhurst Hill, Essex. CAPEL, H. N., LL.B.; Bediord Square, London. HARKEMA, C.; University of St. Petersburg. CARMODY, W. P., B.$. ; Clonmel Gram. School. HARLEY, Harold, B.A.; King's Coll., Cambridge. CARR, G. S., B.A.; Endsleigh Gardens, London. HARLEY, Rev. R., F.R.S.; Huddersfield College. CASEY, John, LL.D., F.R.S.; Prof. of Higher HARRIS, H. W., B.A.; Trinity College, Dublin.

Mathematics in the Catholic Univ. of Ireland. HARRIS, J. R., M.A.; Clare College, Cambridge. CAVALLIN, Prof., M.A.; University of Upsala. HART, Dr. David S. ; Stonington, Connecticut. CAVE, A. W., B.A.; Magdalen College, Oxford. HART, H.; R.M. Academy, Woolwich. CAYLEY, A., F.R.S.; Sadlerian Professor of Ma- HAUGHTON, Rev. Dr., F.R.S.; Trin.Coll., Dubl.

thematics in the University of Cambridge, HENDRICKS, J. E., M.A.; Des Moines, Iowa.

Member of the Institute of France, &c. HEPPEL, G., M.A.; The Grove, Hammersmith. CHAKRAVARTI, BYOMAKESA, M.A.; Professor HERBERT, A.,M.A.; King Alfred's Sch., Wantage. of Mathematics, Calcutta.

HERMAN, R. A., M.A.; Trin. Coll., Cambridge. CHASE, PLINY EARLE, LL.D.; Professor of Phi- HERMITE, CH.; Membre de l'Institut, Paris. losophy in Haverford College.

HILL, Rev. E., M.A.; St. John's College, Camb. CLARKE, Colonel A. R., C.B., F.R.S.; Hastings. Hinton, C. H., M.A.; Cheltenham College. COATES, W. M., B.A.; Trinity College, Dublin. HIRST, Þr. T. A., F.R.S.; Director of Studies in COCHEZ, Professor; Paris.

the Royal Naval College, Greenwich. COCKLE, Sir JAMES, M.A., F.R.S.; Bayswater. HOLT, J. R., M.A. ; Trinity College, Dublin. CODEN, ARTHUR, M.A., Q.C., M.P.; Holland Pk. HOPKINS, Rev. G. H., M.A.; Stratton, Cornwall. Colson, C. G., M.A., University of St. Andrew's. HOPKINSON, J., D.Sc., B.A.; Kensington. CONSTABLE, S.; Swinford Rectory, Mayo. Hudson, C. T., LL.D.; Manilla Hall, Clifton. COTTERILL, J. H., M.A.; Royal School of Naval HUDSON, W.H.H.,M.A.;Prof.in King's Coll.,Lond. Architecture, South Kensington.

INGLEBY, C. M., M.A., LL.D.; London. CREMONA, LUIGI; Direttore della Scuola degli JENKINS, MORGAN, M.A.; London.

Ingegneri, S. Pietro in Vincoli, Rome. JOHNSON, W.E., B.A.; King's Coll., Cambridge. CROFTON, M.'W., B.A., F.R.S.; Prof. of Math. JOHNSON, Prof., M.A.; Annapolis, Maryland.

and Mech. in the R. M. Acad., Woolwich. JOHNSTON, SWIFT; Trin. Coll., Dublin. CULVERWELL,E.P.,B.A.; Sch.of Trin. Coll.. Dubl. JONES, H. S., M.A.; Llanelly. CURTIS, ARTHUR HILL, LL.D., D.Sc.; Dublin. JONES, L. W., B.A.; Merton College, Oxford. DARBOUX, Professor; Paris.

KEALÝ, J. A., M.A.; Wilmington, Delaware. Davis, J. G., M.A.; Abingdon

KENNEDY, D., M.A.; Catholic Univ., Dublin. DAVIS, R. F., B.A.; Wandsworth Common. KIRKMAN, Rev. T. P., M.A., F.R.S.; Croft Rect. Daws N, H. G., B.A.; Baymount, Dublin. KITCHIN, Rev. J. L., M.A.; Heavitree, Exeter. Day, Rev.H.G.,M.A.; Richmond Terr,,Brighton. KITTUDGE, LIZZIE A.; Boston, United States. DEY, Prof. NARENDRA LAL, M.A.; Calcutta. KNISELY, Rev. U.J.; Newcomerstown, Ohio. DICK,G. R., M.A.; Fellow of Caius Coll., Camb. KNOWLES, R., B.A., L.C.P.; Tottenham. Dobson, T., B.A.; Hexham Grammar School. KOEHLER, J.; Rue St. Jacques, Paris. DROZ, Prof. ARNOLD, M.A.; Porrentruy, Berne. LACALAN, R., B.A.; Lewisham. Dupain,J.C.; Professeurau Lycée d'Angoulême. LARMOR, J., M.A.; Queen's College, Galway. EASTERBY, W., B.A.; Grammar School, St. Asaph: LAVERTY, W. H., M.A.; Public Examiner in the Eastwood, G., M.A.; Saxonville, Massachusetts. University of Oxford. Eastox, BELLE; Lockport, New York.

LAWRENCE, E. J.; Ex-Fell. Trin. Coll., Camh. EDWARD, J., M.A.; Head Mas., Aberdeen Coll. Lax, W. G., B.A.; Trinity College, Cambride. EDWARDES, DAVID; Erith Villas, Erith, Kent. LEIDHOLD, R., M.A.; Finsbury Park. ELLIOTT, E. B., M.A.; Fell. Queen's Coll., Oxon. LEUDESDORP, C., M.A.; Fel.PembrokeColl.,Oxon. ELLIS, ALEXANDER J., F.R.S.; Kensington. LEVETT, R., M.A.; King Edw. Sch., Birmingham. EMTAGE, W. T. A.; Pembroke Coll., Oxford. LOWRY, W, H., M.A.; Blackrock, Dublin. Escort, ALBERT, M.A.; Head Master of the MACDONALD, W.J., M.A. ; Edinburgh. Royal Hospital School, Greenwich.

MACFARLANE, A., D.Sc., F.R.S.E.; Ontario. ESSENNELL, EMMA; Coventry.

MACKENZIE, J. L., B.A.; Gymasium, Aberdeen. EVERETT,J.D., D.C.L.; Professor of Natural Phi. MACMAHON, Capt. P. A.; R. M. Academy.

losophy in Queen's College, Belfast. MACMICRCUY, A., B.A.; Univ. Coll., Torouto.

:

iv

W.

3

MCALISTER, DONALD, M.A., D.Sc.; Cambridge. SALMON, Rev. G., D.D., F.R.S.; Regius Professor MCCAY, W. S., M.A.; Fellow and Tutor of of Divinity in the University of Dublin. Trinity College, Dublin.

SAMPSON, C. H., M.A.; Balliol College, Oxford. MCCLELLAND, W.J.,B.A.; Prin.of SantrySchool. SANDERS, J. B.; Bloomington, Indiana. MCCOLL, H., B.A.; 73, Rue Sibliquin, Boulogne. SANDERSON, Rev. T. J., M.A.; Royston, Cambs. McDOWELL, J., M.A.; Pembroke Coll., Camb. SARKAR, NILKANTHA, M.A.; Calcutta. MCINTOSH, ALEX., B.A.; Bedford Row, London. SAVAGE, THOMAS, M.A.; Fell. Pemb.Coll.,Camb. MCLEOD, J., M.A.; R.M. Academy, Woolwich. SCHEFFER, Professor; Mercersbury Coll., Pa. MOVICKER, C. E., B.A.; Trinity Coll., Dublin. SCOTT, A. W., M.A.; St. David's Coll., Lampeter. MALET, Prof., M.A.; Queen's Coll., Cork. Scott, CHARLOTTE A., B.Sc.; Manchester. MANNHEIM, M.; Prof. à l'Ecole Polytech., Paris. SCOTT, R. F., M.A.; Fell. St. John's Coll., Camb. MARKS, SARAN; Cambridge Street, Hyde Park. SERRET, Professor ; Paris. MARTIN, ARTEMAS, M.A., Ph.D.; Editor & Prin- SHARP, W.J. C., M.A.; Hill Street, London.

ter of Math. Visitor & Math. Mag., Erie, Pa. SIARPE, J. W., M.A.; The Charterhoutse. MARTIN, Rev. H., D.D., M.A.; Edinburgh. SHARPE, Rev. H. T., M.A.; Cherry Marham. MATHEWS, G. B., B.A.; Univ. Coll., N. Wales. SHEPHERD, Rev. A. J. P., B.A.; Fellow of MATZ, Prot., M.A.; King's Mountain, Carolina. Queen's College, Oxford. MEE, W. M., B.A., Belturbet.

SIMMONS, Rev. T.C., M.A.; Christ's Coll., Brecon. MERRIFIELD, J., LL.D., F.R.A.S.; Plymouth. SIVERLY, WALTER; Oil City, Pennsylvania. MERRIMAN, MANSFIELD, M.A.; Yale College. SMITH, C., M.A. ; Sidney Sussex Coll., Camb. MEYER, MARY S.; Girton College, Cambridge. STABENOW, H., M.A.; New York. MILLER,

J. C.,

B.A.,

(EDITOR); STEGGALL, Prof. J. E. A., M.A. ; Clifton. The Paragon, Richmond-on-Thames.

STEIN, A.; Venice. MINCIIIN, G.M.,M.A.; Prof.in Cooper's Hill Coll. STEPHEN, ST.JOHN, B.A.; Caius Coll., Cambridge. MITCHESON, T.,B.A.,L.C.P.; City of London Sch. STEWART, H., M.A.; Framlingham, Suffolk. MONCK, HENRY STANLEY, M.A.; Prof. of Moral STORR, G. G., B.A.; Blackburn.

Philosophy in the University of Dublin. SWIFT, C. A., B.A.; Grammar Sch., Weybridge. MONCOURT, Professor; Paris.

SYLVESTER, J.J., D.C.L., F.R.S.; Professor of Moon, ROBERT, M.A.; Ex-Fell. Qu. Coll., Camb. Mathematics in the University of Oxford, MOORE, H, K., B.A.; Trin. Coll., Dublin.

Member of the Institute of France, &c. MOREL, Professor ; Paris.

SYMONS, E. W., M.A.; Fell. St. John's Coll.,Oxon. MORGAN, C., B.A.; Salisbury School.

TAIT, P. G., M.A.; Professor of Natural PhiloMORLEY, FRANK, B.A.; Bath Coll., Bath.

sophy in the University of Edinburgh. MORLEY, T., L.C.P.; Bromley, Kent.

TANNER, Prof. H.W.L.,M.A.;S. Wales Univ. Coll. MORRICE, G. G., B.A.; The Hall, Salisbury. TARLETON, F.A., M.A.; Fell. Trin. Coll., Dub. MOULTON, J. F., M.A.; Fell. of Ch. Coll., Camb. TAYLOR, Rev. C., D.D.; Master of St. John's MUIR, THOMAS, M.A., F.R.S.E.; Bishopton. College, Cambridge. MUKHOPADHYAY,ASUTOSH, M.A.; Bhowanipore. TAYLOR, H.M., M.A.; Fell. Trin. Coll., Camb. NASH, A. M., M.A.; Prof. in Pres. Coll., Calcutta. TAYLOR, W. W., M.A. ; Ripon Grammar School. NELSON, R. J., M.A.; Naval School, London. TEBAY, SEPTIMUS, B.A.; Farnworth, Bolton. NEWCOMB, Prof. SIMON, M.A.; Washington. TERRY, Rev. T. R., M.A., Fell. Magd. Coll.,Oxon. NICOLLS, W., B.A.; St. Peter's Coll., Camb. THOMAS, Rev.D., M.A.; Garsington Rect.,Oxford. OPENSHAW, Rev. T. W., M.A.; Clifton.

Thomson, Rev.F.D.,M.A. ; Ex-Fellowof St.John's OʻREGAN, JOHN; New Street, Limerick.

Coll., Camb.; Brinkley Rectory, Newmarket. ORCHARD, H. L., M.A., L.C.P.; Burnham. TIRELLI, Dr. FRANCESCO; Univ. di Roma. OWEN, J. A., B.Sc.; Tennyson St., Liverpool. TODHUNTER, ISAAC, F.R.Ś.; Cambridge. PANTON, A. W., M.A. ; Fell. of Trin. Coll., Dublin. TORELLI, GABRIEL; University of Naples. PENDLEBURY, Rev. C., M.A.; London.

TORRY, Rev. A. F., M.A.; St. John's Coll., Camb. PERRYMAN, W.; Carbrook, Sheffield.

TRAILL, ANTHONY, M.A., M.D.; Fellow and PHILLIPS, F. B. W.; Balliol College, Oxford. Tutor of Trinity College, Dublin. PILLAI, C. K., M.A.; Trichy, Madras.

TROWBRIDGE, DAVID; Waterburgh, New York. PIRIE, A., M.A.; University of St. Andrew's. TUCKER, R., M.A.; Mathematical Master in Uni. POLIGNAC, Prince CAMILLE DE; Paris.

versity College School, London. POLLEXFEN, H., B.A.; Windermere College. TURRELL, I. H.; Cumminsville, Ohio. POTTER, J., B.A.; Richmond-on-Thames. TURRIFF, GEORGE, M.A.; Aberdeen. PRUDDEN, FRANCES E.; Luckport, New York. VINCENZO, JACOBINI; Università di Roma. PURSER, Prof. F., M.A.; Queen's College, Belfast. VOSE, G. B.; Professor of Mechanics and Civil PUTNAM, K. S., M.A.; Rome, New York.

Engineering, Washington, United States. Rau, B.'HANUMANTA, B.A.; Head Master of WALENN, W. H.; Mem. Phys. Society, London. the Normal School, Madras.

WALKER, J.J., M.A., F.R.S. ; Hampstead. RAWSON, ROBERT; Havant, Hants.

WALMSLEY, J., B.A.; Eccles, Manchester. RAYMOND, E. LANCELOT, B.A., Surbiton. WARBURTON-WHITE, R., B.A., Salisbury. RAY, Prof. SARADARANJAN, M.A.; Dacca Coll., WARREN, R., M.A.; Trinity College, Dublin. Bengal.

WATHERSTON, Rev. A. L., M.A.; Bowdon. READ, Ü. T., M.A.; Brasenese Coll., Oxford. Watson, Rev. H. W.; Ex-Fell. Trin. Coll., Camb. REEVES, G, M., M.A.; Lee, Kent.

WERTSCH, Fr.; Weimar. RENSHAW, S. A.; Nottingham.

WHITE, J. R., B.A.; Worcester Coll., Oxford. REYNOLDS, B., M.A.; Notting Hill, London. WHITE, Rev. J., M.A. ; Cowley College, Oxford. RICHARDSON, Rev. G., M.A.; Winchester. WHITESIDE, G., M.A. ; Eccleston, Lancashire. RIPPIN, CHARLES R., M.A.; Woolwich Common. WHITWORTH, Rev. W. A., M.A.; Fellow of St. ROBERTS, R. A., M.A., Schol.of Trin.Coll., Dublin. John's Coll., Camb.; Hammersmith. ROBERTS, S.,M.A.,F.R.S.; Tufnell Park, London. WICKERSIAM, D. ; Clinton Co., Ohio. ROBERTS, Rev. W., M.A.; Senior Fellow of WILKINS, W. Scholar of Trin. Coll., Dublin. Trinity College, Dublin.'

WILLIAMSON, B., M.A.; Fellow and Tutor of ROBERTS, W. R.,M.A.; Ex-Sch.of Trin. Coll.,Dub. Trinity College, Dublin. ROBSON, H. C., B.A.; Sidney Sussex Coll., Cam. WILSON, J.M., M.A.; Head-master, Clifton Coll. ROSENTIAL, L. H.; Scholar of Trin. Coll., Dublin. Wilson, Rev.J., M.A.; Rect. Bannockburn Acad. ROY, Prof. KALIPRASANNA, M.A.; St. John's WILSON, Rev. J. R., M.A.; Royston, Cambs. Coll., Agra.

WOODCOCK, T., B.A.; Wellington, Salop. RÜCKER, A. W., B.A.; Professor of Mathematics WOLSTEN HOLME, Rev.J., M.A., Sc.D.; Professor

in the Yorkshire College of Science, Leeds. of Mathematics in Cooper's Hill College. RUGGERO, SIMONELLI; Università di Roma. WOOLHOUSE, W. S. B., F.R.A.S., &c.; London RUSSELL, J. W., M.A.; Merton Coll., Oxford, WRIGUT, Dr. S. H., M.A.; Penn Yan, New York. RUSSELL, R., B.A.; Trinity College, Dublin. WRIGIT, W. E., B.A.; Herne Hill. RUTTER, EDWARD; Sunderland.

YOUNG, JOHN, B.A.; Academy, Londonderry.

CONTENTS.

Mathematical Papers, &c.

Page
Note on the Symmedian-Point Axis of a System of Triangles.

(R. Tucker, M.A.)...

25

Note on Biot's Formula. (Âsûtosh Mukhopadhyây.)

80

Note on the Solutions of Question 5672..........

115

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