166 



THE POPULAE EDUCATOE. 



EXERCISE 120 (Vol. H, page 74). 



1. Ne liriez-vous pas si vous aviez le temps ? 2. Je lirais deux 

 heures, tous les jours, si j'avais le temps. 3. Quel habit mettrait M. 

 votre frore, s'il allait a I'tJglise? 4. II mettrait un habit noir. 5. 

 Mettriez-vous un chapeau noir ? 6. Je mettrais un chapeau de paille, 

 s'il faisait chaud. 7. Ne vous approcheriez vous pas du feu, si vous 

 aviee froid? 8. Nous nous en approcherions. 9. N'oteriez-vous pas 

 votre habit ? 10. Je I'oterais, s'il e'tait mouilW. 11. Iriez-vous chez 

 mon pore, e'il vous invitait ? 12. J'irais chez lui et chez M. votre 

 frere, s'ils m'invitaient. 13. Mettriez-vous vos bottes, si elles etaient 

 niouilldes ? 14. Si ellea etaient mouille'es, je ne les mettrais pas. 15. 

 Combien d'argent vous faudrait-il, si vous alliez en Angleterre ? 16. II 

 nous faudrait trois mille francs. 17. Ne vous porteriez-vous pas 

 mieux, si vous demeuriez a la campagne ? 18. Je ne me porterais pas 

 juieux. 19. Ne vaudrait-il pas mieux e'crire a votre frere ? 20. II 

 vaudrait mieux lui e'crire. 21. Liriez-vous le livre, si je vous le pretais ? 

 22. Je le lirais ccrtainement. 23. Si vous e'tiez a sa place, iriez-vous a 

 1'^cole ? 24. Si j'etais a sa place j'irais. 25. Si vous e'tiez a ma place, 

 lui e'cririez-vous ? 26. Je lui e'crirais tous les jours. 27. Ml'"-' votre sceur 

 se tromperait-elle ? 28. Elle ne se tromperait pas, elle est tres atten- 

 tive. 29. Si vous voua leviez tous les matins a cinq heures, vous por- 

 teriez-vous mieux ? 30. Je ne me porterais pas mieux. 31. Aimeriez- 

 vous mieux aller a pied ? 32. J'aimerais mieux aller a cheval. 33. Ne 

 vous assieriez vous pas ? 34. Je m'assierais, si j'dtais fatigud. 



LESSONS IN ARITHMETIC. XLI. 



EXCHANGE. 



1. THE value of a fixed sum of the money of one country expressed 

 in that of another, when this value is calculated by a comparison 

 of the weight and fineness of the coins of the two countries, is 

 called the Par of Exchange. When for this fixed sum the 

 correct equivalent in money of the other country, calculated on 

 this supposition, can be obtained, the exchange is said to be at 

 par. The exchange, however, between any two countries fluc- 

 tuates from various causes. 



The Course of Exchange is the variable sum of the money of 

 one country which happens at a particular time to be equivalent 

 to a fixed sum of the money of another country. Thus, for 1 

 sterling at one time, 25'15 francs, at another 25*20 francs, may be 

 obtained, according to the course of exchange between England 

 and France. 



2. If A owes a correspondent in Berlin, for instance, .500, 

 he might pay his debt by transmitting the value in coin or 

 bullion. But this would bo both cumbersome and expensive. 

 If, then, he can find a person, B, who has money owing to him 

 in Berlin, B can draw a bill upon his debtor in Berlin, and sell 

 it to A, who then transmits it to his own correspondent in 

 Berlin. Such bills of exchange are the means by which money 

 transactions between different countries are conducted. The 

 price of such bills will fluctuate according to the demand there 

 may be for them at the time. .The flxcess of their price over the 

 sum they represent can clearly never exceed the amount of the 

 cost of carriage and money value of the risk incurred in for- 

 warding the same sum in specie or bullion. 



3. The Arbitration of Exchange is the process of fixing the rate 

 or course of exchange between two places, by means of a com- 

 parison of the exchange between them and one or more inter- 

 vening places. Thus a debt in Paris may be paid by means of 

 a bill on Berlin, which is to be again replaced by one on Ham- 

 burg, and that, finally, by one from thence upon Paris. The 

 arbitration is said to be simple when there is only one inter- 

 mediate place, compound when there are more. 



The subject of exchange, however, is too complicated for us to 

 go into more than very superficially. 



For information we refer our readers to Kelly's '" Universal 

 Cambist." 



A large number of questions in exchange can be worked out by 

 the aid of the principles already laid down. Before proceeding 

 to treat of them, we shall explain a method called the Chain 

 Rule. 



THE CHAIN RULE. 



4. If the equivalent of any amount of one quantity is given 

 in terms of another, that in terms of a third, and so on, it is 

 required to find the equivalent of a certain amount of the first 

 quantity in terms of the last. 



EXAMPLE 1. 40 Ibs. Troy of standard gold are coined into 

 1869 sovereigns, and standard gold contains 11 parts in 12 fine 



gold. Calculate the value of the money which can be coined 

 out of 1 oz. of fine gold. 



no's x 12 = weight of one sovereign in ounces. 



This contains H x T *fa x 12 ounces of fine gold, which (neglecting 

 the value of the alloy) are worth JE1. 



11 x 40 

 Therefore, as oz. : 1 : : 1 oz. : value of 1 oz. 



440) 1869 (4 4s. ll^d.-Answer. 

 1760 



109 

 20 



2180 

 1760 



420 

 12 



5040 

 4840 



200 



5. A convenient way of arranging the operation in questions of 

 this kind is called the Chain Rule. It is especially useful in all 

 questions connected with Exchange, and is the method generally 

 used by merchants. 



Write down the quantity of which the equivalent is required 

 at the head of a column, as in the working given below. This 

 quantity is generally called the Term of Demand. 



Draw a sloping line from it to the left, at the extremity of 

 which write down in a second column a quantity of the same 

 kind as the first. Opposite to this place in the first column its 

 equivalent in value of another quantity, and so on. 



1 oz. fine gold 



12 oz. standard gold 



li! oz. 1 pound Troy 



1869 sovereigns 



11 x 12 x 40 12 x 1869. 

 12 x 1869 



The answer is 



11 x 12 x 40 



= 4 4s. 



Thus, in the example already given, 1 oz. of fine gold is 

 the term of demand. 11 oz. fine gold are equivalent to 12 oz. 

 standard gold, 12 oz. standard gold are equivalent to 1 pound 

 Troy standard gold, and 40 pounds Troy standard gold are 

 equivalent to 1869 sovereigns ; the last term in the right hand 

 column being arranged to be sovereigns, because the answer is 

 required in sovereigns. 



Multiply together all the numbers in the longer column, and 

 divide by the product of the numbers in the other column. This 

 will give the equivalent of the term of demand in terms of the 

 quantity standing lowest in the longer column (in the above 

 example, sovereigns). 



N.B. The sloping lines connect quantities of the same kind ; 

 the horizontal lines, quantities of equivalent value. 



6. The reason of the truth of this rule may be gathered from 

 observing that in reality we multiply the term of demand by a 

 succession of fractions which respectively express the value of 

 one unit of a quantity in terms of the succeeding quantity. 

 Thus we multiply the term of demand, which is 1 oz. fine gold, 

 by if, the number of ounces of standard gold equivalent to 1 oz. 

 of fine gold. This gives us the amount of standard gold equi- 

 valent to 1 oz. of fine gold. We next multiply by A, which 

 expresses the same quantity in pounds Troy, and next by i ^~, 

 which is the equivalent of 1 pound Troy of standard gold in 

 sovereigns. 



For a more detailed explanation of the rule we refer our 

 readers to Peacock's " Algebra, Vol. I., Arts. 346 353. 



We give some additional examples worked out. The reader 

 should carefully in each case examine the reason for the process 

 in the way indicated above. 



EXAMPLE 2. If 7 Ibs. of rice be worth 2 Ibs. of currants, 



