166 



THE POPULAR EDUCATOR. 



45. The preceding tables and remarks clearly show the ad- 

 vantages which the common system of logarithms possesses 

 over every other, in consequence of its base being the same as 

 the root of the decimal scale of notation. By merely increasing 

 or diminishing by unity the index of the logarithm of a number, 

 the logarithm of a decimal multiple or sub-multiple of that 

 number is immediately obtained. Hence, the calculation of the 

 logarithm of one number is sufficient for the determination of 

 innumerable others ; for, by tabulating the decimal parts of the 

 logarithms of all integers from 1 to 10,000, or from 1 to 100,000, 

 etc., the complete logarithms of such numbers can easily be 

 found, whether they be considered as integers, decimals, or 

 mixed numbers ; the proper indices being supplied according to 

 the foregoing rules. 



46. A system of logarithms founded on any other base but 

 10 would want all the advantages above-mentioned. The loga- 

 rithms of all such numbers as are determined by the mere 

 change of the index in the common system, would require to be 

 separately calculated and tabulated with their indices. The 

 logarithms of all fractions, as well as integers, and the loga- 

 rithms of all numbers of which the factors were powers of the 

 base, would require the same operation to be performed. For 

 though, in the latter case, the calculation of the logarithms 

 would be as easy as before, yet their tabulation with indices 

 would still be necessary, as the bare inspection of the numbers 

 themselves would not be sufficient to suggest the proper index 

 as in the common system. The disadvantages would be even 

 more strongly felt in the reverse operation of finding from tha 

 tables the number corresponding to any given logarithm. 



47. In addition to the decimal parts of the logarithms of the 

 common system, which are given in tables of logarithms, the 

 average differences of every five logarithms are usually given i:i 

 an adjoining column, for the purpose of rendering it easy to 

 obtain the approximate logarithms of numbers greater than 

 those contained in the table. The approximate logarithms of 

 such .numbers are obtained on the principle, that the differences 

 of numbers which differ little from each other are nearly pro- 

 portional to the differences of their logarithms. Thus in Part I. of 

 the Third Skeleton Table, Art. 32, the successive difference of the 

 numbers 1-00056, 1-00028, and 1-00014, are '00028 and -00014; 

 and the differences of their logarithms are '000122 and '000061 ; 

 now, the following proportion is correct, as far as the decimals 

 extend ; 



00028 : -00014 : : '000122 : '000061. 



But were the decimals further extended, this proportion would 

 be found to be only nearly correct. The application of the 

 principle thus established, however, is sufficiently correct for all 

 practical purposes. 



LESSONS IN FRENCH. LXXX VII. 



144. ANALOGY BETWEEN MANY ENGLISH AND FRENCH 

 WOKDS. 



(1.) MOST words ending in al, ce, de, ge, le, ne, ant, ent, ion, 



are the same in both languages : 



al Mineral, general, animal, principal, fatal. 



ce Eace, prudence, notice, sacrifice, edifice. 



de Parade, grade, ambuscade, parricide, prelude. 



ge Courage, page, vestige, orange, deluge. 



le Docile, capable, table, possible, fertile, ridicule. 



ne Doctrine, mine, scene, famine, machine, Ix-roine. 



ant Dormant, vigilant, constant, instant, arrogant. 



ent Present, content, accident, president, resident. 



ion Question, fraction, legion, pension, religion. 



(2.) Most words ending in ary, ory, gy, ncy, ty, ous, or, our, 

 ine, ive, become French by changing 



NOTE. Students should "not assume that because some 

 French words are more or less similar in spelling to some 

 English words, they are also similar in signification. It is far 

 from being* always so. See 147, table of homonyms and 

 paronyms. 



145. GALLICISMS OR IDIOMATIC PHRASES. 



Gallicisms, or idioms peculiar to the language, are very nu- 

 merous in French. We have already in the first part of these 

 lessons presented a considerable number of such expressions, 

 and will here give a somewhat extended list of those not placed 

 in the examples and exercises. In proverbial sayings, we have 

 endeavoured to give the equivalent English phrase. We would 

 advise the student to analyse carefully the following idiomatic 

 sentences, and particularly those which do not admit of a literal 

 or near translation. Idioms and proverbial phrases give a 

 great insight into the character and customs of a nation, and 

 their analysis is often of great assistance in the acquisition of a 

 language : 



Ce piano n'est pas d'accord. 

 Arrangez cette affaire a 1'amiable. 

 Nous sommes d'accord sur ce 



point. 

 Quel age donneriez-vous a cet 



houime? 



Cela fera bien mon affaire. 

 Allous au fait. 



Vous mettez ma patience a bout. 

 Ce sont deux tetes dans un bonnet. 

 Vous avez toujours ces propos a la 



bouche. 

 Entre nous soit dit, ce n'est pas 



la mor a boire. 

 Vous ne savez plus de quel bois 



faire fleche. 

 J'avais ce mot sur le bout des 



Icvres. 



C'est son bras droit. 

 II nous a forme 1 la porte au nez. 

 Vous allez toujours droit au but. 

 En tout cas, je leur remettrai 



votre lettre. 

 Ne voyez-vous pas qu'il rit sous 



cape ? 



Nous avous pique 1 des deux. 

 Nous en sommes sur ce chapitre. 

 Oli ! pour le coup, vous avez 



raison. 

 Cet orateur bat la campagne. 



Parlez-moi a coeur ouvert. 



Nous avous couche 1 a la belle 

 dtoile. 



Je n'ai que faire de son argent. 



J'oi fait si bien mon compte, que 

 j'ai obtenu cet argent. 



Cela ne me fait rien du tout. 



Faites-ruoi grace de tous ces dd- 

 tails. 



C'en est fait. 



Comme vous voila fait ! 



II in'a prid de vous faire ses aim- 

 tie's. 



En attendant, faites-lui mes com- 

 pliments. 



Chemin faisant, nous le rencon- 

 trames. 



Le plus fort est fait. 



Ce soldat u'a jamais vu le feu. 



II s'est bieu tire 1 d'affaire. 



This piano is out of tune. 

 Settle that business amicably. 

 We agree upon tliat point. 



Sow old would you take that man 



to le ? 



That mil suit me exactly. 

 Let us come to the point. 

 You exhaust my patience. 

 They are both of the same mind. 

 You always use those expressions. 



Between ourselves, the thing i not so 



very difficult. 

 You are put to your last shift. You 



ai<! at your wit's end. 

 I had that word at my tongue's end. 



He is his right hand. 



He shut the door in our face. 



You come always to the main point. 



At all events, I will give them your 



letter. 

 Do you not see that he lauglis in his 



sleeve ? 



We put spurs to our horses. 

 We are speaking about this matter. 

 Oh / for this time you are right. 



That speaker wanders from his 



subject. 



Speak to me without reserve, openly. 

 We slept in the open air. 



I do not want his money. 



I managed matters so icell, that I 



obtained that -money. 

 That is nothing at all to me. 

 Spare me all those particulars. 



It is all over. All is gone. 



What a condition you are in ! 



He wished me to give his love to you. 



In the mean while, present iny com- 

 pliments to him. 

 Going along, we met him. 



The most difficult part is done. 

 That soldier has never smelt gun- 

 powder. 

 He came off very well. 



