Mathematical Questions and Solutions, from the "Educational Times": With ...

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LIST OF CONTRIBUTORS.

ALDIS, J. S., M.A.; H.M. Inspector of Schools.
ALLEN, Rev. A.J.C., M.A.; St. Peter's Coll., Camb.
ALLMAN, Professor GEO. J., LL.D.; Galway.
ANDERSON, ALEX., B.A.; Queen's Coll., Galway.
ANTHONY, EDWYN, M.A.; The Elms, Hereford.
ARMENANTE, Professor; Pesaro.
BALL, ROBT. STAWELL, LL.D., F.R.S.; Professor
of Astronomy in the University of Dublin.
BASU, SATISH CHANDRA; Presid. Coll.,Calcutta.
BATTAGLINI, GIUSEPPE; Professore di Mate-
matiche nell' Università di Roma.
BAYLISS, GEORGE, M.A.; Kenilworth.
BELTRAMI, Professor; University of Pisa.
BERG, F. J. VAN DEN; Professor of Mathematics
in the Polytechnic School, Delft.
BESANT, W. H., D.Sc., F.R.S.; Cambridge.
BHUT, ATH BIGAH, M.A.; Delhi.
BICKERDIKE, C.; Allerton Bywater.

BIDDLE, D.; Gough H., Kingston-on-Thames.
BIRCH, Rev. J. G., M.A.; London.
BLACKWOOD, ELIZABETH; Boulogne.
BLYTHE, W. H., B.A.; Egham.
BORCHARDT, Dr. C. W.; Victoria Strasse, Berlin.
BOSANQUET, R. H. M., M.A.; Fellow of St.
John's College, Oxford.

BOURNE, C. W., M.A.; Bedford County School.
BROOKS, Professor E.; Millersville, Pennsylvania.
BROWN, A. CRUM, D.Sc.; Edinburgh.
BROWN, Prof.COLIN; Andersonian Univ. Glasgow.
BUCHHEIM, A.,M.A., Ph.D.; Schol. New Coll.,Oxf.
BUCK, EDWARD, M.A.; Univ. Coll., Bristol.
BURNSIDE, W. S., M.A.; Professor of Mathe-
matics in the University of Dublin.
CAPEL, H. N., LL.B.; Bedford Square, London.
CARMODY, W. P., B.A.; Clonmel Gram. School.
CARR, G. S., B.A.; Endsleigh Gardens, London.
CASEY, JOHN, LL.D., F.R.S.; Prof. of Higher
Mathematics in the Catholic Univ. of Ireland.
CAVALLIN, Prof., M.A.; University of Upsala.
CAVE, A. W., B.A.; Magdalen College, Oxford.
CAYLEY, A., F.R.S.; Sadlerian Professor of Ma-
thematics in the University of Cambridge,
Member of the Institute of France, &c.
CHAKRAVARTI, BYOMAKESA, M.A.; Professor
of Mathematics, Calcutta.

CHASE, PLINY EARLE, LL.D.; Professor of Phi-
losophy in Haverford College.
CLARKE, Colonel A. R., C.B., F.R.S.; Hastings.
COATES, W. M., B.A.: Trinity College, Dublin.
COCHEZ, Professor; Paris.

COCKLE, Sir JAMES, M.A., F.R.S.; Bayswater.
COHEN, ARTHUR, M.A., Q.C., M.P.; Holland Pk.
COLSON, C. G., M.A.; University of St. Andrew's.
CONSTABLE, S.; Swinford Rectory, Mayo.
COTTERILL, J. H., M.A.; Royal School of Naval
Architecture, South Kensington.
CREMONA, LUIGI; Direttore della Scuola degli
Ingegneri, S. Pietro in Vincoli, Rome.
CROFTON, M. W., B.A., F.R.S.; Prof. of Math.
and Mech, in the R. M. Acad., Woolwich.
CULVERWELL, E.P.,B.A.; Sch. of Trin. Coll..Dubl.
CURTIS, ARTHUR HILL, LL.D., D.Sc.; Dublin.
DARBOUX, Professor; Paris.
DAVIS, J. G., M.A.; Abingdon

DAVIS, R. F., B.A.; Wandsworth Common.
DAWS N, H. G., B.A.; Baymount, Dublin.
DAY, Rev. H. G.,M.A.; RichmondTerr,, Brighton.
DEY, Prof. NARENDRA LAL, M.A.; Calcutta.
DICK, G. R., M.A.; Fellow of Caius Coll., Camb.
DOBSON, T., B.A.; Hexham Grammar School.
DROZ, Prof. ARNOLD, M.A.; Porrentruy, Berne.
DUPAIN, J.C.; Professeur au Lycée d'Angoulême.
EASTERBY, W., B.A.; Grammar School, St. Asaph.
EASTWOOD, G., M.A.; Saxonville, Massachusetts.
EASTON, BELLE; Lockport, New York.
EDWARD, J., M.A.; Head Mast., Aberdeen Coll.
EDWARDES, DAVID; Erith Villas, Erith, Kent.
ELLIOTT, E. B., M.A.; Fell. Queen's Coll., Oxon.
ELLIS, ALEXANDER J., F.R.S.; Kensington.
EMTAGE, W. T. A.; Pembroke Coll., Oxford.
ESCOTT, ALBERT, M.A.; Head Master of the
Royal Hospital School, Greenwich.
ESSENNELL, EMMA; Coventry.

EVANS, Professor, M.A.; Lockport, New York.
FICKLIN, JOSEPH; Prof. in Univ. of Missouri.
FINCH, T. H., B.A.; Trinity College, Dublin.
FORTEY, H., M.A.; Bellary, Madras Presidency.
FOSTER, F. W., B.A.; Chelsea.
FOSTER, Prof.G.CAREY, F.R.S.; Univ.Coll., Lond.
FRANKLIN, CHRISTINE LADD, M.A.; Prof.of Nat.

Sci. and Math., Union Springs, New York.
FUORTES, E.; University of Naples.
GALBRAITH,Rev.J.,M.A., Fell.Trin.Coll., Dublin.
GALE, KATE K.; Worcester Park, Surrey.
GALLATLY, W., B.A.; Earl's Court, London.
GALLIERS, Rev. I., M.A.; Kirkstead Rectory,
Norwich.

GALTON, FRANCIS, M.A., F.R.G.S.; London.
GENESE, Prof., M.A.; Univ. Coll., Aberystwith.
GERRANS, H. T., B.A.; Stud. of Ch. Ch., Oxford.
GLAISHER, J. W. L., M.A., F.R.S.; Fellow of
Trinity College, Cambridge.

GOLDENBERG, Professor, M.A.; Moscow.
GRAHAM, R. A., M.A.; Trinity College, Dublin.
GREENFIELD, Rev. W. J., M.A.; Dulwich College.
GREENSTREET, W. J., B.A.; Framlingham.
GREENWOOD, JAMES M.; Kirksville, Missouri.
GRIFFITH, W.; Superintendent of Public Schools,
New London, Ohio, United States.
GRIFFITHS, G. J., M.A.; Fell. Ch. Coll., Camb.
GRIFFITHS, J., M.A.; Fellow of Jesus Coll., Oxon.
GROVE, W. B., B.A.; Perry Bar, Birmingham.
HADAMARD, Professor, M.A.; Paris.
HAIGH, E., B.A., B.Sc.; King's Sch., Warwick.
HALL, Professor ASAPH, M.A.; Washington.
HAMMOND, J., M.A.; Buckhurst Hill, Essex.
HARKEMA, C.; University of St. Petersburg.
HARLEY, Harold, B.A.; King's Coll., Cambridge.
HARLEY, Rev. R., F.R.S.; Huddersfield College.
HARRIS, H. W., B.A.; Trinity College, Dublin.
HARRIS, J. R., M.A.; Clare College, Cambridge.
HART, Dr. DAVID S.; Stonington, Connecticut.
HART, H.; R.M. Academy, Woolwich.
HAUGHTON, Rev. Dr., F.R.S.; Trin. Coll., Dubl.
HENDRICKS, J. E., M.A.; Des Moines, Iowa.
HEPPEL, G., M.A.; The Grove, Hammersmith.
HERBERT, A.,M.A.; King Alfred's Sch., Wantage.
HERMAN, R. A., M.A.; Trin. Coll., Cambridge.
HERMITE, CH.; Membre de l'Institut, Paris.
HILL, Rev. E., M.A.; St. John's College, Camb.
HINTON, C. H., M.A.; Cheltenham College.
HIRST, Dr. T. A., F.R.S.; Director of Studies in
the Royal Naval College, Greenwich.
HOLT, J. R., M.A.; Trinity College, Dublin.
HOPKINS, Rev. G. H., M.A.; Stratton, Cornwall.
HOPKINSON, J., D.Sc., B.A.; Kensington.
HUDSON, C. T., LL.D.; Manilla Hall, Clifton.
HUDSON, W.H.H.,M.A.;Prof.in King'sColl., Lond.
INGLEBY, C. M., M.A., LL.D.; London.
JENKINS, MORGAN, M.A.; London.
JOHNSON, W. E., B.A.; King's Coll., Cambridge.
JOHNSON, Prof., M.A.; Annapolis, Maryland.
JOHNSTON, SWIFT; Trin. Coll., Dublin.
JONES, H. S., M.A.; Llanelly.
JONES, L. W., B.A.; Merton College, Oxford.
KEALY, J. A., M.A.; Wilmington, Delaware.
KENNEDY, D., M.A.; Catholic Univ., Dublin.
KIRKMAN, Rev. T. P., M.A., F.R.S.; Croft Rect.
KITCHIN, Rev. J. L., M.A.; Heavitree, Exeter.
KITTUDGE, LIZZIE A.; Boston, United States.
KNISELY, Rev. U.J.; Newcomerstown, Ohio.
KNOWLES, R., B.A., L.C.P.; Tottenham.
KOEHLER, J.; Rue St. Jacques, Paris.
LACHLAN, R., B.A.; Lewisham.
LARMOR, J., M.A.; Queen's College, Galway.
LAVERTY, W. H., M.A.; Public Examiner in the
University of Oxford.

LAWRENCE, E. J.; Ex-Fell. Trin. Coll., Camh.
LAX, W. G., B.A.; Trinity College, Cambridge.
LEIDHOLD, R., M.A.; Finsbury Park.
LEUDESDORF, C., M.A.; Fel. PembrokeColl., Oxon.
LEVETT, R., M.A.; King Edw. Sch., Birmingham.
LOWRY, W. H., M.A.; Blackrock, Dublin.
MACDONALD, W. J., M.A.; Edinburgh.
MACFARLANE, A., D.Sc., F.R.S.E.; Ontario.
MACKENZIE, J. L., B.A.; Gymnasium, Aberdeen,

EVERETT, J.D., D.C.L.; Professor of Natural Phi- MACMAHON, Capt. P. A.; R. M. Academy.

losophy in Queen's College, Belfast.

MACMURCHY, A., B.A.; Univ. Coll., Toronto.

MCALISTER, DONALD, M.A., D.Sc.; Cambridge.
MCCAY, W. S., M.A.; Fellow and Tutor of
Trinity College, Dublin.
MCCLELLAND, W. J.,B.A.; Prin.of SantrySchool.
MCCOLL, H., B.A.; 73, Rue Sibliquin, Boulogne.
MCDOWELL, J., M.A.; Pembroke Coll., Camb.
MCINTOSH, ALEX., B.A.; Bedford Row, London.
MCLEOD, J., M.A.; R.M. Academy, Woolwich.
MCVICKER, C. E., B.A.; Trinity Coll., Dublin.
MALET, Prof., M.A.; Queen's Coll., Cork.
MANNHEIM, M.; Prof. à l'Ecole Polytech., Paris.
MARKS, SARAH; Cambridge Street, Hyde Park.
MARTIN, ARTEMAS, M.A., Ph. D.; Editor & Prin-
ter of Math. Visitor & Math. Mag., Erie, Pa.
MARTIN, Rev. H., D.D., M.A.; Edinburgh.
MATHEWS, G. B., B.A.; Univ. Coll., N. Wales.
MATZ, Prof., M.A.; King's Mountain, Carolina.
MEE, W. M., B.A.; Belturbet.

MERRIFIELD, J., LL.D., F.R.A.S.; Plymouth.
MERRIMAN, MANSFIELD, M.A.; Yale College.
MEYER, MARY S.; Girton College, Cambridge.
MILLER, W. J. C., B.A., (EDITOR);
The Paragon, Richmond-on-Thames.
MINCHIN, G.M.,M.A.; Prof. in Cooper's Hill Coll.
MITCHESON, T.,B.A.,L.C.P.; City of London Sch.
MONCK, HENRY STANLEY, M.A.; Prof. of Moral
Philosophy in the University of Dublin.
MONCOURT, Professor; Paris.
MOON, ROBERT, M.A.; Ex-Fell. Qu. Coll., Camb.
MOORE, H. K., B.A.; Trin. Coll., Dublin.
MOREL, Professor; Paris.

MORGAN, C., B.A.; Salisbury School.
MORLEY, FRANK, B.A.; Bath Coll., Bath.
MORLEY, T., L.C.P.; Bromley, Kent.
MORRICE, G. G., B.A.; The Hall, Salisbury.
MOULTON, J. F., M.A.; Fell. of Ch. Coll., Camb.
MUIR, THOMAS, M.A., F.R.S. E.; Bishopton.
MUKHOPADHYAY,ASUTOSH, M.A.; Bhowanipore.
NASH, A. M., M.A.; Prof. in Pres. Coll., Calcutta.
NELSON, R. J., M.Á.; Naval School, London.
NEWCOMB, Prof. SIMON, M.A.; Washington.
NICOLLS, W., B.A.; St. Peter's Coll., Camb.
OPENSHAW, Rev. T. W., M.A.; Clifton.
O'REGAN, JOHN; New Street, Limerick.
ORCHARD, H. L., M.A., L.C.P.; Burnham.
OWEN, J. A., B.Sc.; Tennyson St., Liverpool.
PANTON, A. W., M.A.; Fell. of Trin. Coll., Dublin.
PENDLEBURY, Rev. C., M.A.; London.
PERRYMAN, W.; Carbrook, Sheffield.
PHILLIPS, F. B. W.; Balliol College, Oxford.
PILLAI, C. K., M.A.; Trichy, Madras.
PIRIE, A., M.A.; University of St. Andrew's.
POLIGNAC, Prince CAMILLE DE; Paris.
POLLEXFEN, H., B.A.; Windermere College.
POTTER, J., B.A.; Richmond-on-Thames.
PRUDDEN, FRANCES E.; Lockport, New York.
PURSER, Prof. F., M.A.; Queen's College, Belfast.
PUTNAM, K. S., M.A.; Rome, New York.
RAU, B. HANUMANTA, B.A.; Head Master of
the Normal School, Madras.
RAWSON, ROBERT; Havant, Hants.
RAYMOND, E. LANCELOT, B.A., Surbiton.
RAY, Prof. SARADARANJAN, M.A.; Dacca Coll.,
Bengal.

READ, H. T., M.A.; Brasenose Coll., Oxford.
REEVES, G. M., M.A.; Lee, Kent.
RENSHAW, S. A.; Nottingham.
REYNOLDS, B., M.A.; Notting Hill, London.
RICHARDSON, Rev. G., M.A.; Winchester.
RIPPIN, CHARLES R., M.A.; Woolwich Common.
ROBERTS, R. A., M.A.; Schol.of Trin.Coll., Dublin.
ROBERTS, S.,M.A., F.R.S.; Tufnell Park, London.
ROBERTS, Rev. W., M.A.; Senior Fellow of
Trinity College, Dublin.

ROBERTS, W. R.,M.Á.; Ex-Sch. of Trin. Coll.,Dub.
ROBSON, H. C., B.A.; Sidney Sussex Coll., Cam.
ROSENTHAL, L. H.; Scholar of Trin. Coll., Dublin.
ROY, Prof. KALIPRASANNA, M.A.; St. John's
Coll., Agra.

RÜCKER, A. W., B.A.; Professor of Mathematics

in the Yorkshire College of Science, Leeds. RUGGERO, SIMONELLI; Università di Roma. RUSSELL, J. W., M.A.; Merton Coll., Oxford. RUSSELL, R., B.A.; Trinity College, Dublin. RUTTER, EDWARD; Sunderland.

SALMON, Rev. G., D.D., F.R.S.; Regius Professor
of Divinity in the University of Dublin.
SAMPSON, C. H., M.A.; Balliol College, Oxford.
SANDERS, J. B.; Bloomington, Indiana.
SANDERSON, Rev. T. J., M.A.; Royston, Cambs.
SARKAR, NILKANTHA, M.A.; Calcutta.
SAVAGE, THOMAS, M.A.; Fell. Pemb.Coll.,Camb.
SCHEFFER, Professor; Mercersbury Coll., Pa.
SCOTT, A. W., M.A.; St. David's Coll., Lampeter.
SCOTT, CHARLOTTE A., B.Sc.; Manchester.
SCOTT, R. F., M.A.; Fell. St. John's Coll., Camb.
SERRET, Professor; Paris.
SHARP, W. J. C., M.A.; Hill Street, London.
SHARPE, J. W., M.A.; The Charterhouse.
SHARPE, Rev. H. T., M.A.; Cherry Marham.
SHEPHERD, Rev. A. J. P., B.A.; Fellow of
Queen's College, Oxford.

SIMMONS, Rev. T.C., M.A.; Christ's Coll., Brecon.
SIVERLY, WALTER; Oil City, Pennsylvania.
SMITH, C., M.A.; Sidney Sussex Coll., Camb.
STABENOW, H., M.A.; New York.
STEGGALL, Prof. J. E. A., M.A.; Clifton.
STEIN, A.; Venice.
STEPHEN, ST. JOHN, B.A.; Caius Coll., Cambridge.
STEWART, H., M.A.; Framlingham, Suffolk.
STORR. G. G., B.A.; Blackburn.
SWIFT, C. A., B.A.; Grammar Sch., Weybridge.
SYLVESTER, J. J., D.C.L., F.R.S.; Professor of

Mathematics in the University of Oxford, Member of the Institute of France, &c. SYMONS, E. W., M.A.; Fell. St. John's Coll., Oxon. TAIT, P. G., M.A.; Professor of Natural Philosophy in the University of Edinburgh. TANNER, Prof. H.W.L.,M.A.; S. Wales Univ. Coll. TARLETON, F. A., M.A.; Fell. Trin. Coll., Dub. TAYLOR, Rev. C., D.D.; Master of St. John's College, Cambridge.

TAYLOR, H. M., M.A.; Fell. Trin. Coll., Camb. TAYLOR, W. W., M.A.; Ripon Grammar School. TEBAY, SEPTIMUS, B.A.; Farnworth, Bolton. TERRY, Rev. T. R., M.A., Fell. Magd. Coll.,Oxon. THOMAS, Rev.D., M.A.; Garsington Rect., Oxford. THOMSON, Rev. F.D., M.A.; Ex-Fellowof St.John's

Coll., Camb.; Brinkley Rectory, Newmarket. TIRELLI, Dr. FRANCESCO; Univ. di Roma. TODHUNTER, ISAAC, F.R.S.; Cambridge. TORELLI, GABRIEL; University of Naples. TORRY, Rev. A. F., M.A.; St. John's Coll., Camb. TRAILL, ANTHONY, M.A., M.D.; Fellow and Tutor of Trinity College, Dublin.

TROWBRIDGE, DAVID; Waterburgh, New York.
TUCKER, R., M.A.; Mathematical Master in Uni-
versity College School, London.
TURRELL, I. H.; Cumminsville, Ohio.
TURRIFF, GEORGE, M.A.; Aberdeen.
VINCENZO, JACOBINI; Università di Roma.
VOSE, G. B.; Professor of Mechanics and Civil
Engineering, Washington, United States.
WALENN, W. H.; Mem. Phys. Society, London.
WALKER, J. J., M.A., F.R.S.; Hampstead.
WALMSLEY, J., B.A.; Eccles, Manchester.
WARBURTON-WHITE, R., B.A., Salisbury.
WARREN, R., M.A.; Trinity College, Dublin.
WATHERSTON, Rev. A. L., M.A.; Bowdon.
WATSON, Rev. H. W.; Ex-Fell. Trin. Coll., Camb.
WERTSCH, Fr.; Weimar.

WHITE, J. R., B.A.; Worcester Coll., Oxford.
WHITE, Rev. J., M.A.; Cowley College, Oxford.
WHITESIDE, G., M.A.; Eccleston, Lancashire.
WHITWORTH, Rev. W. A., M.A.; Fellow of St.

John's Coll., Camb.; Hammersmith. WICKERSHAM, D.; Clinton Co., Ohio. WILKINS, W.; Scholar of Trin. Coll., Dublin. WILLIAMSON, B., M.A.; Fellow and Tutor of Trinity College, Dublin. WILSON, J. M., M.A.; Head-master, Clifton Coll. WILSON, Rev. J., M.A.; Rect. Bannockburn Acad. WILSON, Rev. J. R., M.A.; Royston, Cambs. WOODCOCK, T., B.A.; Wellington, Salop. WOLSTENHOLME, Rev. J., M.A., Sc.D.; Professor of Mathematics in Cooper's Hill College. WOOLHOUSE, W. S. B., F.R.A.S., &c.; London WRIGHT, Dr. S. H., M.A.; Penn Yan, New York. WRIGHT, W. E., B.A.; Herne Hill.

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

CONTENTS.

Mathematical Papers, &c.

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

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

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

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

A New Method of deriving Legendre's Formula

(Professor Cavallin, M.A.)

Questions Solved.

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115