114 



THE POPULAR EDTJCATOB. 



parts, of chords, secants, and polygons, on one side of each leg ; 

 and on the other side of each leg, two lines of sines, tangents, 

 etc., besides lines of the logarithms of the numbers expressing 

 these quantities along the whole length of the sector, when 

 etretched to an angle of 180, as well as the logarithms of the 

 natural numbers. 



As in the case of the plane scale, we can here only give one 

 or two examples of the use of the sector, by way of illustration. 

 Thus, in the figure, o is the joint of the sector, o A and o B 

 are its legs, the marks on the legs' represent the divisions of 

 the line into equal parts. Its use is to find straight lines 

 that shall be to one another in a given proportion. Suppose, 

 for example, that it is required to find a straight line whose 

 length shall be to the length of a given line as 3 to 10. Open 

 the sector until the distance of the two points marked 10 on its 

 legs is equal to the length of the given line, which may be 

 easily done by the help of a [pair of common compasses or 

 dividers ; then, the distance of the two points marked 3 on its 

 legs, will be the length of the straight line required. 



Again, suppose that two straight lines aro given, and it 

 is required to find their ratio to each other in numbers. Open 

 the sector until the distance of the two points marked 10 on its 

 legs, is equal to the length of the greater of the two given 

 straight lines ; then, taking the length of the smaller of the 

 two given lines in . a pair of compasses, apply this distance to 

 the two points of any number less than 10 marked on its legs, 

 until it be found that it coincides exactly with that of two 

 points having the same number, say 3 ; then the two given 

 straight lines are to one another in the ratio of 10 to 3 ; or, in 

 other words, the smaller is three-tenths of the greater. 



The Proportional Compasses, called by the French compos de 

 reduction the compasses of reduction are represented in Fig. 

 17, and consist of two legs A N, c M, intersecting (i.e., crossing) 

 each other at any point within certain limits, according to the 

 position of the button and screw, B, round which they are made 

 to turn. These legs are graduated in such a manner that, by 

 screwing the button at the proper place, the distance from A 

 to c may be at pleasure one-half, one-third, one-fourth, etc., 

 of the distance from M to N. By this instrument, a straight 

 line may be easily divided into any number of equal parts, or 

 into any other proportional parts required. 



The invention of this instrument is claimed, by a recent 

 writer, for James Besson, a French mechanician, who published 

 an account of it in his "Theatre des Machines," a work of 

 which the plates were engraved before 1569. He says it is 

 usually attributed to Justus Byrgius, who published his 

 description of it in 1603. John Eobertson, librarian to the 

 Royal Society, in his " Treatise on Mathematical Instruments," 

 London, 1775, ascribes the invention of a similar instrument to 

 Fabricius Mordente in 1554, according to a statement made by 

 his brother, Gaspar Mordente, in his book on the Compasses, 

 published at Antwerp in 1584. 



LESSONS IN FRENCH. VIII. 



SECTION I. FRENCH PRONUNCIATION (continued). 

 III. NAME AND SOUND OF THE VOWELS, 



46. Y, y. Name, EE, ee; sound, like the letters ee in the 

 English word bee. 



This letter is also a word; that is, it is one of the parts of 

 speech in the French language. It is usually an adverb, mean- 

 ing there. It is also used as a noun, and a pronoun. 



When y stands alone, and thus becomes a word, its pronun- 

 ciation is invariably like that of the letters ee in the English 

 word bee, viz. : II y a, pronounced eel ee a. This last a must 

 be sounded like a in the English word fat. 



Y is also pronounced like the letters ee in the English word 

 bee, when it begins or ends a word ; and also when it occurs in 

 the body of a word, after a consonant, namely : 



FRENCH. PRONUNCIATION. ENGLISH. 



Dey Day Dey. 



Style Steel Style. 



Systome Seess-taim System. 



Yole Ee-ol or E-ol A yawl. 



| Whenever y is found in the body of a word, between two vowels, 

 it has the sound of two French i's, that is, of two double e's, 

 namely : 



Moyen should be pronounced as if printed thus, namely, inoiien,; 

 divided thus, namely, moi-i-en, but pronounced in two syllabus, 

 namely, moi-ien. 



Joyeux should be pronounced as if printed thus, namely, joiieu; 

 divided thus, namely, joi-i-eu, but pronounced in two syllables, 

 namely, jo'l-ieu. 



Royaume should be pronounced as if printed thus, namely, 

 roiiaitme; divided thus, namely, roi-i-aume, but pronounced in two- 

 syllables, namely, roi-iaume. . 



The pupil need not attempt to pronounce these three French 

 words used as examples, because the combination of vowels and 

 other letters occurring in them has not yet been illustrated. 



The pronunciation of y with these and other combinations of 

 letters will be explained in future lessons. 



In the two following words the y, tlwugh not placed between 

 two voivels, is under the same rule, namely : 



Pays, meaning a country, should be pronounced as if printed 

 paiis ; divided thus, namely, pai-is, and pronounced pa-ee. 



Paysage, meaning a landscape, should be pronounced as if 

 printed paiisage; divided thus, namely, pai-i-saye, and pronounced 

 pa-ee-zazh. 



IV. NAME AND SOUND OF THE CONSONANTS. 



As a general rule, none of the consonants, when final, have a, 

 distinct and independent sound, unless immediately followed by 

 a word commencing with a vowel or h mute ; in which case the 

 consonant is joined with the following word in pronunciation. 



47. B, b. In any position within a word, this letter has the 

 sound of the English letter b. 



When doubled within a word, only one b is sounded, viz. : 



FRENCH. 

 Abbesse 

 Rabbi 

 Sabbat 



PRONUNCIATION. 

 Ab-ess 

 Rab-ee 

 Sab-ah 



ENGLISH. 

 Abbess. 

 Rabbi. 

 Sabbath. 



At the end of proper names, b is always sounded. 



In these two words, namely, a-plomb andplomb, the b is silent, 

 and the next two preceding letters in each word, namely, om, 

 take the nasal sound of on. 



48. C, C. This letter has two entirely distinct sound;;, 

 namely, hard and soft. Before the vowels a, o, u, and a?, and 

 also before the consonants c, I, n, and r, it has the hard sound 

 of the letter 7c in the English word kill, namely : 



When final, and not preceded by the letter n, c is generally 

 sounded like the letter fc in the English word book, namely : 



FRENCH. PRONUN. 

 Avec A-vek 



Bee Baik 



ENGLISH. 



With. 



Beak. 



i FRENCH. 



Caduc 

 1 fichec 



PRONUN. ENGLISH. 

 Kad-uko Declining. 

 Ay-shek Check. 



In a few words, however, c final is not sounded, and these 

 exceptions are best found out by consulting a French pronouncing 

 dictionary. In a few words, c has the sound of the letter g in 

 the English word go, namely, second, secondaire, secondairement y 

 seconde, secondement, seconder, secondine. 



In these words the c, which commences the second syllable,, 

 has the sound of the g, namelyj second, as if printed segond; pro- 

 nounced s'-gonh, etc. We do not illustrate all the sounds of 

 these French words here, because of the nasal sounds contained 

 in them. 



49. D, d. This letter generally has the sound of the letter 

 d in the English word deed. It is usually silent when final, 

 except in proper names. 



The principal exception to the above rule is, when d is final 

 just before a vowel or an h mute. In such a case, the d has the 

 sound of the letter t in the English word top; and in pronuncia- 



* See foot-note, page 19. 



