LESSONS IN GREEK.XXXVII.

PERMUTATION OF CONSONANTS.

THE variations in letters which have come under our notice are not arbitrary, but these, with others, depend chiefly on euphonic laws. Of such laws or observances we have already spoken, in giving the uncontracted and contracted vowel equivalents. The consonants, also, in coming together, undergo changes according to determinate rules.

The consonants are divided into liquids (namely, λ, μ, ν, ρ) and mutes (namely, π, κ, τ ; β, γ, δ; φ, χ, θ), and by the union of σ with these the double consonants 4, 5, and are produced; thus

The nine mutes are divided in three ways, namely-first, the organ chiefly employed in pronouncing them, as-(1) palatals (pronounced by the palate), κ, γ, χ; (2) linguals (pronounced by the tongue), τ, δ, θ-called, also, dentals ; and (3) labials (pronounced by the lips), π, β, φ. A second classification arises from considering what may be termed the predominant sound: thus, in κ, γ, χ, you have a k sound; in τ, δ, θ, a t sound; and in π, β, φ, a p sound. There is also a third division into tenues (or slender), κ, τ, π; media (or middle), γ, δ, β ; and aspirata (or aspirate), Χ, θ, Φ.

The following, then, are the facts which regard the use and interchange of the consonants :

A p sound (π, β, φ) or a k sound (κ, γ, χ) before a t sound (τ, δ, θ) must be of the same kind with the t sound that is, before a tenuis, as r, can only be placed a tenuis, as work ; before a media, as δ, only a media, as β or y; before an aspirata, as e, only an aspirata, as p or x. Thus you havе πт and кт, Bồ and γδ, φθ or χθ; thus

β before r becomes π, as τριβ-ω, I rub,

Τ

CORRECT FORM.

τετριβεται, τετριπται. π,,, γράφω, I write, γεγραφ-ται, γεγραπται. κ,,, λεγω, I speak, λελεγεται, λέλεκται. βρεχω, I wet, βεβρεχεται, βεβρεκται.

β, κυπτω, I bend, κυπ-δα,

β,,, γράφω, I write, γραφ-δην,

συγκαλέω, I call together.

εν πειρια εν-βαλλω

εν-φρων

ενόψυχος

συν-καλεω

συν-γιγνωσκω

συν-χρονος

συν-ξεω

εμβάλλω, I cast into.

συγγιγνωσκω, I know with. συγχρονος, being at the same time. συγξεω, I smooth.

Compare the Latin imbuo and imprimo. Nevertheless, we find συντείνω, I stretch; συνδεω, I bind with; and συνθεω, Ι run with.

The enclitics, or those words which receive a particle at the end, form an exception; as όνπερ (όν and περ), τοιγε (τον and γε). P sound (π, β, φ) unites with o to form ψ; (κ, γ, χ) ξ; (τ, δ, θ) disappears; as

κυβδα.

γραβδην.

τρίψω.

γραφω, I write,

γραψω.

βρεχ-δην,

πλεκω, I twist,

πλέξω.

βρεγδην.

λεγ-σω, βρεχ-σω,

λέγω, I say,

λεξω.

ετριβ-θην, τριφθην. πλεκω, I weave, επλεκ-θην, επλέχθην.

3. t sound. ανυτ-σω,

ελεγθην,

φ,,, πεμπω, I send, επεμπ-θην, επέμφθην.

The preposition ex remains unaltered before εκδοῦναι, εκθείναι, etc.-not εγδοῦναι and εχθειναι.

ελέχθην. and ; as

The tenues, namely, π, κ, τ, pass into the corresponding aspirata (aspirates), φ, χ, θ, not only in derivations and inflections, but also in compounds, before an aspirated vowel ; thus

Instead of επημερος, write εφήμερος (επι and ἡμερα, a day). εφυφαίνω (επι and ὑφαίνω, I weave). τετυφα (τυπτω, I strike).

επιφαίνω, τετυπτά,

ουκ όσιως,

ουχ όσιως (όσιος, holy).

δεχήμερος (δεκα, ten, and ἡμερα). τέτριφα (τριβω, I rub).

These changes take place also in crasis-that is, where two Towels are mixed into oneas θάτερα from τα ἑτέρα. If the tenues mr or ur precede, both must be converted into aspirates, as έφθημερος instead of ἑπτημερος from ἑπτα, seven, and ήμερα, day).

ελπίσω.

ερειδ-σω, πειθ-σω, ελπιδ-σω, Compare also, in the Latin, duxi, from duco; rexi, from rego; and coni, from coquo. As an exception, in the preposition the k before o remains ; as εκσώζω, I save.

N vanishes before σ, and if is connected with a t sound both sounds vanish before σ; but the short vowel before the is lengthened that is to say, e into e, o into ou, and ă, i, u into a, i, ϋ ; a8

:εν, as ενσπειρω, I sou in; παλιν, as παλινσκιος, thickly shaded, some infections and derivations in σαι and σις, as πεφανσαι, from φαίνω, I show; and a few substantives in urs and uys. The v in ovv in compounds before r and a following vowel passes into σ, as συσσω ω; but if after να σwith a consonant or a ( follows, then the y disappears, as συν-στημα, συστημα; συν-ζύγια, συζυγία.

An exception to the extension of into e before v and at sound appears in the adjectives which end in εις, εσσα, εν, the dative plural masculine and neuter of which is eo instead of 101. Two immediately following syllables of a word cannot in certain cases begin with aspirates, but the first aspirate passes into the kindred tenuis. This fact is exemplified in

1. The verbal reduplication; asInstead of φε-φιληκα, from φιλεω, I love,

we have πε-φιληκα.

becomes συλλογίζω.

The same is seen in the Latin illino (in and lino), immineo (in and maneo).

εμμένω. συρρίπτω.

translations from English into Latin, and questions on Grammar, History, and Antiquities. Moderate proficiency in Latin prose composition is required. Greek.-Homer, "Iliad," Books xv., xvi.; Herodotus, Book v.; Euripides, "Hecuba;" with questions upon Grammar and History.

Logic. The Professor's lectures, and Whateley's "Logic, Books ii. and iii.; Reid's "Intellectual Powers," Essay ii, for students who have not attended the Professor's lectures. Moral Philosophy.-The Professor's lectures, or Fleming's "Manual of Moral Philosophy."

English Literature.-Lectures of the Professor. Natural Philosophy.-Examination on the subjects explained in the class. On the Elements of Statics and Dynamics, with the solution of problems not requiring the Differential or Integral Calculus; Experimental Science, including heat, electricity, and magnetism; Herschel's "Astronomy; "Thomson's "Elements of Dynamics," Part I.; Thomson and Tait's "Outlines of Dynamics."

Mathematics.-Euclid, first six books; Algebra, including Quadratic Equations; Plane Trigonometry as far as the solution of triangles by the aid of logarithmic tables.

The examinations for the degree of M.A. are held in April and November, and the graduation takes place in the beginning of May.

In Medicine three degrees are granted by this University, viz., Bachelor of Medicine (M.B.); Master in Surgery, (C.M.); and Doctor of Medicine (M.D.). Candidates for these degrees are required to undergo a preliminary examination in English, Latin, Arithmetic, Mathematics, and Mechanics. The professional examinations embrace all the departments of medical study required in the curriculum. They are in three divisions, as follows:-First, on Chemistry, Botany, and Elementary Anatomy; Second, on Advanced Anatomy, Zoology with Comparative Anatomy, and Physiology; and Third, on Materia Medica, General Pathology, Surgery, Practice of Medicine, Midwifery, Medical Jurisprudence, Clinical Surgery, and Clinical Medicine. On these subjects the examinations are conducted partly in writing and partly viva voce.

An ordinance of the Universities Commissioners regulates the conditions on which the degree of Bachelor of Laws is conferred. It is necessary that the candidate for this degree shall be a graduate in arts. His course of study in law must extend over three academical years, and include attendance on lectures in each of the following departments:-(1), Civil Law; (2), Law of Scotland; (3), Conveyancing; (4), Public Law; (5), Constitutional Law and History; (6), Medical Jurisprudence.

In the Faculty of Theology the degree of Bachelor of Divinity has been revived by the University Court and Senatus Academicus. Proficiency in Theology, Church History, Hebrew, and Biblical Criticism is required of candidates.

With reference to the degree of D.D. some new regulations have been quite recently adopted by the Senate of the University. By these regulations a Bachelor of Divinity of fifteen years' standing may proceed to the degree of Doctor of Divinity when he composes a thesis on a theological subject approved by the Professor of Divinity, and preaches a University sermon by appointment of the Vice-Chancellor and the Professor of Divinity.

ENDOWMENTS.

of Forfar in 1737. They are open for competition to all students in the Faculty of Arts, and are tenable for four years. In 1860 two bursaries were founded by William Patrick, Esq., of Roughwood, "the one consisting of the free annual proceeds of a sum of £2,000 of consolidated stock of the Glasgow and South-Western Railway, the other of the free annual proceeds of £1,000 of the same stock." The remaining bursaries in the Faculty of Arts range in annual value from £5 to £15.

In the Faculty of Theology the Brown bursaries, which consist of the annual interest and proceeds of a sum of £1,000, are open to divinity students of the first year, with a preference to such as can speak Gaelic-not an uncommon accomplishment among the students who attend Glasgow University. To English students a special interest attaches to the Williams bursaries. In 1711 the Rev. Dr. Williams, London, bequeathed to some persons in the metropolis, in trust, an estate to found bursaries for educating natives of England at this university. It is necessary, however, that the bursars on this foundation shall promise in writing to become preachers among Dissenting bodies in England. The annual value of each bursary is £40. The other bursaries connected with this faculty yield annual salaries of from about £5 to £25.

In the Faculty of Medicine the most important is the Brisbane bursary. The annual value is £50, and it is tenable for four years. Of the "bursaries in any faculty," a noticeable one is that which was founded in 1867 by the Highland Society of London. The value is £50, and it is tenable for four years. The competition is open to natives of the fourteen Highland counties, and the subjects of examination are Gaelic, Latin, Greek, Mathematics, and Scottish History.

Within recent years scholarships and fellowships of some value have been added to the endowments of the University. There are two Breadalbane scholarships, of £50 each, devoted to the encouragement of pure and applied science. The Sandford Greek scholarship, founded in memory of Sir Daniel K. Sandford, yields a salary of £19 per annum. The Eglinton fellowships (of about £90 each) are open only to students who have taken the degree of M.A. in Glasgow University. The Luke fellowship (value £120 per annum) is awarded on examination in Classics and Ancient History, Moral Philosophy, Logic and Metaphysics, and English Literature. The Clark scholarship (£50 annual value) is open for competition to "Protestant students, sons of Protestant parents," who have completed their curriculum in Arts in Glasgow University. The Fer guson scholarships, six in number (each of the annual value of £80), have been instituted by the trustees of the late Mr. Ferguson, of Cairnbrock, out of his legacy of £50,000 for educational and other purposes.

In this connection may also be noticed the Snell exhibitions, which were founded in 1677 by John Snell, Esq., of Uffeton, Warwickshire, for the purpose of educating Scottish students at Oxford. Two of the exhibitioners are nominated annually, after competition, by Glasgow University. Owing to an increase in the value of the estate from which the exhibitions are derived, the fund now affords about £108 annually to each of the exhibitioners.

We may notice some of the more important. The Dundonald bursaries, now twelve in number, were founded in 1672, by William Earl of Dundonald. The Dundonald bursars in Philosophy receive £40 each per annum, and those in Divinity a little above £41. The former hold their bursaries for four years, and the latter for two. Owing to the great accumulation of the surplus funds of this foundation, an Act of Parliament was obtained in 1858 authorising an increase in the number of bursars. There are four foundation bursaries for students in Languages and Philosophy. They were founded by James VI. in 1577, and the annual value of each is £10. The Forfar bursaries (£20), four in number, were founded by the Countess

LIBRARY, HUNTERIAN MUSEUM, AND BOTANIC GARDEN. The Library connected with the University was founded in the fifteenth century, and it contains a valuable collection of books. Another interesting possession of the College is the Hunterian Museum, which was founded by the eminent William Hunter, M.D., who bequeathed to the University his extensive collection of books, manuscripts, paintings, scientific specimens, and antiquarian relics, and appropriated £8,000 for the erection of a building to contain his munificent bequest. A large hall on the basement floor is set apart for Hunter's extensive series of ana

tomical and pathological preparations. There is also a Botanic Garden in connection with the University, but it lies so far remote, owing to the great extension of the city, that the Professor of Botany is under the necessity of delivering most of his lectures at the College.

LESSONS IN GEOGRAPHY.-XLIII.

MAP MAKING MERCATOR'S PROJECTION.

WE shall now bring our Lessons on Geography to a close, in this and another paper, with a few practical remarks on map-making in addition to the instructions that have been already given in previous lessons for delineating the continents of Europe, Asia, Africa, North and South America, or any large portion of the world's surface, the form of projection known as the conical projection being chiefly used. In the present lesson we shall consider the method of drawing a map of the world, by means of the rectangular form of projection, called, after its inventor, Mercator's Projection, after making a few remarks on the mode of procedure to be adopted in delineating and colouring maps of all kinds.

The various mathematical instruments required have been already enumerated at the commencement of our "Lessons in Geometry," and it will suffice to repeat here that the draughtsman must-in addition to compasses, rulers of various kinds, ruling pens suitable for drawing fine and thick lines, and a T square also provide himself with a beam compass, for describing arcs of circles having a radius too long to admit of their being drawn by an ordinary compass, and a flexible steel bow, for drawing a curved line through any number of given points not less than three in number.

It is best, if possible, to pin the drawing paper on which a map is to be drawn on a drawing board of considerable size, or, what is still better, on the well-planed top of a deal table, the edges of which have been truly squared. The beam compass can be used with ease on the flat top of a table, while the management of this instrument on a board too small to include the centres from which it is required to strike aros of small curvature is attended with difficulty, owing to the necessity of taking the centres on a plane that is lower than the plane of the board on which the paper is pinned-as, for example, when the board is laid on a table in which we are obliged to fix the leg of the beam compass round which the beam must revolve in striking

the arcs.

The outline of a map consists of the delineation of the coastline, rivers, canals, railroads, etc. The coast-line should be a carefully-drawn line of uniform thickness throughout, more or less broken by salient and retiring curves and angles, according to the character of the coast. The head-streams of rivers should be finely traced, the main-stream being a line that gets thicker and thicker as it approaches the coast-line. All angles should be sedulously avoided in drawing a river's course. Canals and railroads must be indicated by lines of equal thickness throughout. All work of this kind should be done with etching pens or good steel pens, as well as the names of towns, rivers, etc., in smaller type or writing. The large names should be outlined with a pen and filled in with a brush, as the scraping of the pen in colouring over a wide space makes the work look scratchy when done. Swamps and woods may be drawn in with the pen, and mountain ranges shaded with either pen or brush, the latter being preferable for fine as well as coarser work. Degree lines should be ruled with the finest of ruling pens, a larger and heavier pen being used for the thick lines that form the outer border.

Be careful always to use Indian ink, as this will not run, like ordinary writing ink, when the map is coloured. For colouring, we should use colours derived from animal and vegetable substances rather than those obtained from mineral substances. For instance, Prussian blue and indigo furnish far more even tints than cobalt, and crimson lake a smoother, less cloudy wash than vermilion or red ochre. Mineral colours may, however, be used where variety is required in indicating boundary lines.

To give our

straight lines at right angles to one another. readers a clearer idea of what is meant, suppose that a sphere having an extremely elastic surface were placed inside a circumscribing cylinder touching the sphere at the equator. If the sphere were then subjected to a uniform expansion in every direction until its elastic surface was extended far enough to come into contact with the inside of the circumscribing cylinder, the meridians would be extended into straight perpendicular lines, and the parallels into equal circles, the whole being inscribed within the cylinder. If the cylinder were then cut open down one of the meridians and flattened out, the interior would represent the form of projection known as Mercator's Projection, in which all the meridians and parallels assume the aspect of straight lines at right angles to one another

C B.

To draw the parallels and meridians for a map of the world on Mercator's Projection, first draw a straight line, A B, as in Fig. 19, in a horizontal position, and through a point c in it, taken as near the centre as possible, draw the straight line DE at right angles to it. Then assume a space for 5°, 10°, 15°, or 20°, on the equator, which is represented by the line AB, and set off 36, 18, 12, or 9 of these spaces accordingly from the point of intersection c of the two straight lines, along CA and In Fig. 19, we have assumed 15° as the space between the meridians to be laid down on the map, and from c twelve spaces have been set off on either side along C A and C B, numbered 15, 30, etc., and terminating at the points F and G, also marked 180 west and 180 east. Through F and G, two straight lines HK, LM must be drawn, cutting A B at right angles and parallel to D E. They will determine the limits of the map on the west and east, but it is sometimes thought necessary to repeat the last meridional division on one side of the map upon the other in order to show the connection more clearly, but this is not absolutely necessary. Now in the sphere, as the meridians approach the poles, the arcs of latitude included between any pair of these diminish; but in Mercator's Projection, as the meridians are represented by parallel straight lines, the distance included between them remains the same throughout; the parallels, therefore, must be represented by horizontal straight lines parallel to the equator, but placed at distances from it, which increase in proportion, the more distant the parallels are from the equator instead of being at equal distances, as when they are represented by circles as in the sphere, arcs of circles as in the conical form of projection, and by right lines as in the method adopted for drawing the maps of Africa and South America.

The proper distance of every parallel of latitude from the equator in Mercator's Projection has been calculated by a process, to understand which requires a knowledge of trigonometry, and the results embodied in the table given below, in which the distance of each parallel of latitude, the tropics and the arctic and antarctic circles, has been shown in terms of minutes of the equator. TABLE FOR THE CONSTRUCTION OF MAPS ON MERCATOR'S

Degs.

PROJECTION, SHOWING THE DISTANCE OF EVERY PARALLEL OF LATITUDE FROM THE EQUATOR IN TERMS OF MINUTES OF THE EQUATOR.

We shall find this table of the utmost importance in constructing maps and charts on Mercator's projection: indeed, it would be impossible to work with accuracy without it.

On referring to the table, in the present case, we find that the distance of the 15th parallel of latitude north or south of the equator is 910 minutes (neglecting the decimals, which are unimportant in small maps), or 10 minutes more than the space assumed for 15°, in which, of course, there is 15 x 60, or 900 minutes. In other words the distance between the equator and the 15th parallel of north or south latitude is more than the space assumed for 15° at the equator by its 90th part. To measure these fractional parts a diagonal scale must be constructed on the principle shown in Fig. 16 (Vol. II., p. 356), a square being constructed on the space assumed for 15°, and the sides being divided into six parts, each representing 150 minutes, and the top and bottom into ten parts; diagonal lines being drawn from side to side, as shown in the figure to which reference has been made, and perpendiculars from top to bottom-the

H

D

the parallels of latitude. It is generally considered sufficient to carry the map of the world on Mercator's Projection as far as the 80th parallel of north latitude and the 60th parallel of south latitude, as all the land on the earth's surface of which we have any certain knowledge is included within these limits.

The meridians of longitude must now be drawn on either side of, and parallel to, the straight line D E, through the points numbered 15, 30, 45, 60, etc., and carried as far as the lines HL, KM, which form the limits of the map at the top and bottom. The central line, D C E, is the meridian of Greenwich. The projection must be completed by drawing the border, and marking or numbering the meridians and parallels at the sides and top and bottom of the map. If it be desired to divide the spaces between each ruled parallel in the inner part of the border into degrees, the distance of each degree must be separately set off from the equator, in terms of minutes of the equator, by aid of the table and diagonal scale. It should be said that in Mercator's Projection the relative

perpendiculars will divide the diagonals into fifteens, from which the fractional parts may be taken with tolerable accuracy. The proportionate length of a line of 910 minutes being thus determined, it must be marked off on either side of F and G, along the lines FH, FK, GL, G M. In the diagram this is shown by the points numbered 15, above and below F and G. Straight lines drawn through these opposite pairs of points, above and below the equator, will determine the 15th parallel of latitude north and south of the equator.

In the same way the parallel of 30° north and south latitude will be found to be 1,888 minutes in distance from the equator, which is equal to twice the space assumed for 15° x 88 minutes. It will therefore be necessary to take the length of 88 parts from the diagonal scale and add it to twice the space assumed as 15° at the equator, and again set off the whole of the distance thus obtained on the lines F H, F K, GL, GM, from the points F and G. This distance is shown by the points marked 30 above and below F and G. The parallels of 30° north and south of the equator must be drawn through the opposite pairs of these points, as in the case of the parallels of 15°. A similar course must be adopted for the remaining parallels, and the tropics of Cancer and Capricorn, which are not shown in the diagram. The parallels may be carried as far north and south of the equator as may be considered desirable, and the limits of the map fixed by drawing straight lines, HL, K M, parallel to the equator or

proportions of the land and water between every successive pair of parallels, and even of the meridians and parallels themselves, are carefully preserved; but the necessity that exists of increasing the size of the meridians and parallels towards the north and south of the map, renders a far greater space to be given to the land and water in these regions than they actually occupy, and unless this is fully understood a false notion is apt to be conceived of the relative proportions of different parts of the world at the equator, and in high northern and southern latitudes, in length, breadth, and superficial area. For this reason it is impossible to effect measurements on a map of this kind by a scale of miles, as no scale can be constructed that would suit every part of the map.

Mercator's Projection is especially used for drawing charts for the use of sailors, because on a map of this kind a ship's course may be laid down in a straight line, since a straight line drawn in any part of it, and in any direction, would intersect all the meridians at the same angle, and this would also be the case with the parallels. This part of the subject, however, belongs properly to navigation, and we need not enter on it here further than to point out the advantage which this kind of construction offers to the mariner who, in an ordinary map, or on a planisphere or projection of a hemisphere on a flat surface, would have to mark his course by a curved line, which would be attended with considerable difficulty.