THE POPULAB EDUCATOR. 



processes you must go over again and again, until you are per- 

 fectly master of the whole, and can from memory write down 

 the alphabet, with all its forms and parts, as here given. I 

 advise you to take great pains in this matter, and not to pass 

 on until you have thoroughly accomplished this task. Your 

 Attention to this recommendation will save you a world of trouble. 



In the commencement, you will do well to confine yourself to 

 the small characters ; having acquired them, you will readily 

 make yourself familiar with the capitals. 



In the small characters, you will at once discover similarities 

 between the Greek and the English forms. The Greek o and 

 the English a are obviously the same. The English e and the 

 short e in Greek are very nearly alike. The two b's differ little. 

 The two i's are identical ; so are the two o's (o short) ; and the 

 Greek o long (a>) is nothing but two short o's (oo) put together. 



You will notice, in the Greek, two forms of the small letter s. 

 These two forms are or and s. Of these, the first occurs at the 

 beginning and in the body of a word ; the second stands at 

 the end of a word. This form of the sigma, namely, s, may also 

 be used in the middle of compound words, when the first of the 

 words of which the compound is formed ends in 3 : for example : 



Ordinary Sigma. 

 Sov\uff(i> 



Sigma at the end. 



tpafpot 



Sigma in Compounds. 



trposfpfpca 



Gamma, y, has the sound of n before 7, K, x t thus, 

 fayy-ris is pronounced gan'-ghees; (rvyKoirrj is pronounced sune- 

 ko-pe ; Ke7xpios, ken'-kri-os ; and Aapiryl, lar-unx. 



Chi, x, has a guttural sound, and so differs from kappa, K. 

 The letter x is never pronounced like our ch in church, but always 

 in a way resembling our k in kite, kitchen, kick. 



Over vowels, e in beta, i in epsilon, etc., this mark " will be 

 observed. It is used to denote a long vowel. The force of it 

 you may give by throwing the stress of the voice on the vowel 

 or syllable over which it is placed. Thus omicron is to be pro- 

 nounced o-mi'-kron. The opposite of is " , as in omega ; the 

 mark " denotes a short syllable ; accordingly, omega is pronounced 

 thus, o'-mcg-a, with the stress on the o. A vowel of doubtful 

 length is marked thus -, as d. When two vowels come together, 

 the former is generally short, as I\?ov, i'-li-on. Diphthongs, how- 

 ever, are long ; that is, on them you must throw the stress, as 

 Kva.vw, au'x-a-no. Syllables are short or long, as they contain a 

 short or long vowel. Syllables containing a diphthong are long. 



You may ascertain whether you have mastered the letters, by 

 practising yourself in the following 



EXERCISE FOR PRONUNCIATION. 



N.B. Every vowel in Greek, whether at the end of a word or 

 not, is pronounced as a separate syllable. 



Ka, /ce, Ktj, KI, KO, KV, KO>. Fe, 70, 77?, 701, 70, 71. XTJ, x>- 

 To, re, ro. As, 877. r), 61, Oea, OTJTO. Ill, TTW, TTOS. BaAAat. 

 1>(, (pfpu. 2a, ffov, ffiyt], $vyr), <j>vy<a. Marep, /utAos. Vi. 

 FaJJjo. Zrjra, VjTea>, ^ijTrjcrts ; savdos ; NuKres ; XOcav. 



AAe|acSpos, AuAjs. n\r;v, flicfavos. ClpcaTros. YOU/UJS, 

 Vufj.fHfTixs- Bias. FT;, T\avitos, Topyri. Xaplres, XapiAaos. 

 <r&>cei/s, QCOKIUV, *p76s. 'TSpo, "firo-vis, 'YAAos. AoAoif', 

 Aio(/0(Tos, AiosKovpoi. Epts. ZaicvvOos, Zeu^is. HAe/crpa, HXW, 

 Hois. Ki/n$poi. AuSta, Auinas, Ao/cpis, AaicsSaijucoj'. NIKTJ. 

 Vlivws. O\vfj.Tros. Ti\araia, HITTO.KOS. 2aAa/.us, 2a/cas, 2/cvflto. 

 Tirades. 'PoSos, "Paipy, 'Priyiov. s.av6os. 



You will find in the ensuing lessons these three marks or 



accents, namely, ' above the letter (or to the left of it in capitals), 



as in iVo , i under the letter, as in pSrj , and " above the letter, 



as in oOs. The first is called the spirituis asper, or rough breathing, 



being equivalent to our aspirated h ; pronounce, then, as with an 



h syllables before which this aspirate is placed, as 'ASijs, Hades. 



The second mark is called iota subscript (i underwritten), so 



' termed because the letter i, instead of appearing at the end, as 



in Ao70M, is written or placed under the co as in \oyca : this 



' mark is commonly disregarded in pronunciation. The third is 



, called the circumflex, being made up of the acute accent ' and 



the grave accent x , from the union of which A the circumflex " is 



produced. The circumflex denotes a contraction, as in the 



diphthong oOj, an ear. 



In printed Greek books you will see several marks of accen- 

 tuation over the letters. These I shall for the most part omit, 

 as the study of them would embarrass the beginner, and as a 

 knowledge of them is not necessary to either the understanding 

 or the pronunciation of Greek. When you have mastered the 

 real and inevitable difficulties of the language, you will readily 

 acquire an acquaintance with these now almost useless signs. 



LESSONS IN GEOGRAPHY. XIV. 



ASTRONOMICAL PRINCIPLES OF GEOGRAPHY. 



SUPPOSE that you were elevated in the heavens, or in the vast 

 space in which roll all the stars, to a point millions of miles above 

 the sun ; and that you were furnished with a telescopic eye so 

 powerful, that from that point you could observe the magni- 

 tudes, motions, and distances of all the bodies in the Solar 

 System that is, the bodies or planets which revolve round the 

 sun in consequence of the laws of attraction and tangential 

 impulse you would perceive among them a highly-favoured 

 planet called the Earth, accompanied by a satellite (an attend- 

 ant) in its course, called the Moon. 



This earth and her satellite, like all the other planets and 

 their satellites which you would behold in this bird's-eye view, 

 receive both their light and their heat from the sun ; the in- 

 fluences of light and heat being invariably distributed to all 

 the planets in the same ratio as the power of attraction which 

 keeps them revolving in their orbits (tracks or paths) ; that is, 

 in the inverse ratio of the squares of their distances ; or, to 

 express it more clearly, the power of the attraction, the light 

 and heat of the sun on one planet, is to that on another planet, 

 as the square of the distance of the latter is to the square of 

 the distance of the former. 



In your elevated position you would next perceive that the 

 planets, in their various revolutions, would at some times be 

 nearer to the sun than at other times ; and that if the orbit of 

 each were traced by a white line in space, it would appear to your 

 eye, if rightly placed, to have the form of an oval nearly, being 

 in fact, what is called in mathematics, an ellipse. 



In order that you may understand the nature of this curve, we 

 shall explain it by means of a diagram. Thus, in Fig. 1, if you 

 fix two pins on a board, at the points F and 

 F', and fasten a string F M F, of any con- 

 venient length, but greater than the dis- 

 tance between the two points, by its extre- 

 mities, at these points ; and if you take a 

 crayon or chalk pencil, and press it on the 

 string horizontally at M, so as to keep it 

 always tense (i.e. stretched), and parallel to 

 the board, moving the pencil round and 

 round at the same time, from one side to the other, you will 

 describe the curve A c B D, which is called an ellipse. It is 

 evident that the limits of the form of this curve are the circle 

 and the straight line. If the two points F and F' are brought close 

 together, the curve will be a circle ; if they be separated as much 

 as the string will allow, the curve will become a straight line. The 

 two points F and F' are called the/oei (the plural of the Latin 

 word focus) of the curve ; the straight line A B drawn through 

 them, and terminated both ways by tho curve, is called the 

 major axis; and the straight line c r> drawn at right angles to 

 this axis from its middle point o, and terminated both ways by 

 the curve, is called its minor axis. If a straight line be drawn 

 from F' to c, it will be equal to the straight line A o, or half the 

 major axis. The point o is called the centre of the ellipse, and 

 the ratio of F o to A o that is, of the distance between the 

 centre and the focus to half the major axis is called the eccen- 

 tricity of the ellipse. The distance from the focus F to any point 

 M in the curve is called the radius vector of the ellipse ; it is 

 least at A, and greatest at B. With these explanations, while 

 you are supposed to be looking at the orbit of a planet from 

 your elevated position; in space, you will now be able to com- 

 prehend the fundamental principles of Astronomy, namely, 

 Kepler's Laws. 



The eminent Germa.n astronomer just mentioned, who flou- 

 rished at the close of the sixteenth century and the beginning of 

 bhe seventeenth, discovered by laborious observations and calcu- 

 lations, the following remarkable laws, which were afterwards 

 mathematically demonstrated by Sir Isaac Newton : 



1. That the planets all revolve in elliptic orbits, situated in 



