Quid sum miser tunc dicturus, Rex tremendæ majestatis, Recordare, Jesu pie, Quærens me, sedisti lassus, Juste Judex ultionis, Ingemisco tanquam reus, Præces meæ non sunt dignæ, Inter oves locum præsta, Confutatis maledictis Oro supplex et acclinis, Lachrymosa dies illa! Oh, what then shall I be saying; King of majesty and splendor, Blessed Jesus, my salvation Toiling, weary, thou hast sought me, Holy Judge of retribution, As in guilt I groan repenting, Sin in shame's red blush lamenting; Mary's sin thou saw'st condoning; With the sheep from goats divided, When the wicked, headlong flying, Low in prayer before thee bending, Day of tears and lamentation, This hymn is sometimes called Prosa de mortuis, also De die judicii. The Germans call it Gigantenhymnus, (" the hymn of the giants.") It is used in the Latin Church on the day of All-Souls (November 2). It is based upon Zeph. 1, 15: Dies ira, dies illa, etc, as given in the Vulgate; also other texts of Scripture the author had in view, Psalms XCVI, 13; XCVII, 3; CII, 26; whence David is introduced in the first stanza. II Peter III, 7-11 ; in soms versions of the hymn the name of Peter is used instead of David. The Sibyl referred to is supposed to be the Erythræan, the author of the VIIIth of the Sibylline Books, containing the famous acrostical lines on the judgment (N. AND Q. Vol. III, p. 137), IESOUS CHREISTOS THEOU UIOS Soter. Virgil founds one of his Pastorals (Pollio vi) on these lines. Pope also reverts to it. A bibliography of the translations of Dies Ira is published in the "Bulletin " of Mercantile Library, Philadelphia, Vol. I, Nos. 9 and 10. I. QUESTIONS. Who was "King Ramirez," and what was the legend concerning him? "King Ramirez" is the subjeet of a striking painting, by one of the best known modern Spanish artists. W. E. MOORE, Manchester, N. H. 2. Who was "Marechal Neil"? and why was the celebrated rose named for him? W. E. MOORE. 3. Many persons whose ancestors came to America 150 to 200 years ago, speak of large inheritances due them in the land of their ancestors' nativity. As such instances, take the Jennings heirs of England, and the Graf heirs of Holland. Are these claims due to self deceptive vanity in general, or, is there any basis for the claims. What is the law of limitation as to time regarding these claims. I. B. 4. What is the origin of the expression, "Sound on the goose question"? A. HAMILTON, Toronto, Can. Whose last dying words are the following quotations. (a)" Adieu, my dear Morand. I am dying. (b)"He is the kindest, best man in the world." (Referring to her husband). (c) "The South! The Poor South! God knows what will become of her !" (d) "Jesus." (Tracing a cross with his blood, and kissing it). (e) "Oh Lord God Almighty, as thou wilt." (f) "Dei me nun katheudin." (The dying man was not a Greek, but deceased in the present century). R., JUNIOR, Boston, Mass. 6. When was Fort Ticonderoga built, and by whom? S. F. C., JUNIOR. 7. In Mansfield Merriman's bibliography of writings relating to "The Method of Least Squares," p. 224, quoting from Galton" on "Statistics by Intercomparison," he says the equation: "y=ce ̄hQxQ” is called an ogive, and the curve is regarded as more likely to be approximately true of a statistical series than any other that can be specified ápriori." What is the shape of the "ogive"? TYRO. 7. "Or those eighteen upon whom the tower in Siloam fell, and slew them."-Luke XIII, 4. Where can be found an account of the catastrophe referred to and the names of the " eighteen slain" "? STUDENT. What gave the name ampersand (&) to the body of water in the Adirondacks called "Lake Ampersand "? JONATHAN. 1. What is the shape of the solid called "a circular groin," mentioned by Docharty, page 291, " Analytical Geometry and Calculus"? TYRO. 2. Please explain the word Deucalion as applied to a flood, i. e. "Deucalion's Flood." Does it mean the "second deluge"? as Deuteronomy, "the second law;" deuterogamy, "the second marriage"? LEWIS G. HOLDEN. 3. Where can be found an account of "The Wandering Jew"? Some writers refer to John the Apostle as being the man, from the text of John XXI, 22. Others say it is Ahasuerus, before whose door Jesus halted to rest when bearing his cross to Golgotha, Jesus saying, "I shall stand and rest, but thou shall go till the last day," this being a reply to the Jew's request to Jesus to move on." WELLINGTON HOWARD. 4 Where can be found the legend of the Ass's broken leg, referring to the miracle performed by Jesus making whole the leg when he rode into Jerusalem. WELLINGTON HOWARD. 5. In Abraham Cole's "Latin Hymns, with original translations," the second stanza of Stabat Mater, has these two lines: "O how mournful and distressèd The grave accent (è) is used in the terminal of the first two lines. Other writers in these and similar words use the acute accent (é). Which is the correct accent? X. Y. Z. 6. What is the origin of, or legend, connected with the words "Kyrie eleeson," (Lord, have mercy upon us)? X. Y. Z. Some philosopher a few years ago published his theory that the earth is "lopsided," with other claimed novel discoveries. Where can the account be found, or who can explain his theory? ANDREW SMITH. 8. What is the history and religious veneration connected with the well Zem Zem often mentioned by Mohammedan writers. J. PAYSON SHIELDS. 9. In the Apocrypha, Book of II Esdras VI, 49, we read this : "Then didst thou ordain two living creatures, the one thou calledst Enoch and the other Leviathan." What animal is meant by the Enoch? Does it mean the Behemoth, mentioned in Job XL, 15; with Leviathan, Job XLI, I; PS. CIV, 126 ? Why did Thomas Hobbes of Malmesbury call some of his books Volume VI, Leviathan; Volume XIII, Behemoth ? 'OMERUS. Expressions for the Area of a Plane Triangle. By B. F. Burleson, Oneida Castle, N. Y. In April, 1883, Mr. James Main, formerly of the U. S. Coast and Geodetic Survey, published in the Mathematical Magazine* forty-six formulæ expressing the area of a plane triangle. This collection was classified and reprinted with one additional formula by M. Ed. Lucas in Mathesis. It was also copied into the Danish mathematical journal, Tidsskrift for Mathematik.‡ In 1885, Mr. Marcus Baker, of the U. S. Coast and Geodetic Survey, published in the Annals of Mathematics,§ after its reading before the mathematical section of the Philosophical Society of Washington, D. C., a still larger collection of such expressions. He gave 288 formulæ classified under 6 groups, as follows: Group I contained formula which Mr. Lucas styled unique, that is, those in which all similar elements of the triangle entered. Hence, they do not admit of similar formulæ by permutating the letters. Group II contained formula which admit of two similar expressions, giving three of a kind by permutation. Group III contained formula which admit of three similar expressions, giving four of a kind by permutation. Group IV contained formula which admit of five similar expressions, giving six of a kind by permutation. Group V contained one formula which admits of eleven similar expressions, giving twelve of a kind by permutation. Each group was subdivided into two parts, the first not containing, and the second containing trigonometric functions of the angles. In 1886, the Parisian Journal de Mathematiques,|| published, in con * The Mathematical Magazine, edited and published by Artemas Martin, Erie, Pa. 1883, April, Vol. I, No. 6, pp. 94-95. ↑ Mathesis. Publié par P. Mansion et J. Neuberg, Gand, 1883, Juin, Vol. III, pp. 136-138, 167-170. Tidsskrift for Mathematik Udgivet af J. P. Gramog H. G. Zeathen, Kjobenhavn, 1883, Vol. 5th, series first year, No. 3, pp. 82-84; No. 4, p. 136. § Annals of Mathematics, edited by O. Stone and W. H. Thornton, Charlotteville, Va., 1885. January, Vol. I, No. 6, pp. 134-138; Vol. II, No. 1, pp. 11-18. Journal De Mathematiques, published by M. Henry Vuibert, Paris, 1886. pp. 76-80. Fevrier, No. 10, nection with a large collection of formulæ appertaining to the triangle, 50 unclassified expressions for the area of the triangle, many of which were different from any previously given. The number of such possible expressions for the area of the trian gle is obviously very great. Were it of practical moment the possible number might be determined in accordance with the elements assumed of the triangle. We think that the various trigonometrical functions of the angles constitute not one, but many elements of the triangle. The formulæ in NOTES AND QUERIES, Vol. V, pp. 17-19, will be found useful in finding various expressions for the area of a triangle as well as for other purposes. A few of these formulæ the writer has discovered, since their publication, are erroneous. Those that were found to be wrong we here append in accurate terms. 32. 33. 34. 35. 36, 42. 48. 50. m2 2+m2 +m1 :=(9s1—36s2m+36sn+18m2)÷16. Cos A CosB Cos C—(s1t2—8snt2—ta—16s2n2)÷16s2n2. Cos2A+ Cos2B+Cos2C (24s2n2+8snt2+ta—s1t2)÷8s2n2. By the aid of these formulæ we have found over 30 new expressions for the area of a triangle not found in any of the collections referred to. We append them without classification. We think they may all properly be placed under Mr. Baker's Group I. Had we the time at our disposal, and space were permitted, we are confident we could extend the list to several hundred. We leave to the reader the pleasant task of lengthening the roll of the expressions, for himself. A = 1. {√[4(a+b+c)(a2b+b2c+a2c+ab2+bc2+ac2+abc)—(a+b+c)4] |