102 



THE POPULAE EDUCATOR, 



number gives a compound quantity, and that a compound quan- 

 tity divided by a compound quantity of the same kind gives an 

 abstract number as a quotient. 



06s. The last remark is the same thing as saying that the 

 ratio (Art. 1, Lesson XXI., Vol. L, page 342) of two concrete 

 quantities of the same kind must be an abstract number. It is 

 of the nature of how many times. 



Furthermore, notice that if two concrete numbers are to be 

 compared that is, if one is to be divided by the other they 

 must be of the same kind. The ratio of one sum of money to 

 another sum can be found, or that of one weight to another 

 weight ; but money cannot be compared with weight or with 

 length. To talk, for instance, of the ratio of 25 shillings to 

 13 Ibs. would simply be an absurdity. 



12. EXAMPLE. Divide .87 10s. 7*d. by 47. 



Beginning with the pounds, we find that 87 divided by 

 47 gives 1, with a remainder 40. Reducing these .40 to 

 shillings, and adding in the 10 shillings of the dividend, we 

 get 810 shillings, which, divided by 47, gives 17 shillings, with 

 a remainder 11s. Reducing these 11 shillings to pence, and 

 adding in the 7 pence of the dividend, we get 139 pence, which, 

 divided by 47, gives 2 pence and a remainder 45 pence. 

 Reducing the 45 pence to farthings, and adding in the 2 far- 

 things of the dividend, we get 182 farthings, which, divided by 

 47, gives 3 farthings, and a remainder 41, which, divided by 47, 

 gives a fraction $ of a farthing. The answer, therefore, in 

 ,1 17s. 2d. 3|if. 



The operation may be thus arranged : 



47) 87 10 7.J (1 

 47 



40 

 20 



47) 800 + 10 = 810s. (17s. 



47 



340 

 329 



11 



12 



47) 132 + 7 = 139d. (2d. 

 94 



45 

 4 



47) 180 + 2 



Answer 1 17s. 2d. 



182f. (3f. 

 141 



41 Remainder. 



13. The principle upon the truth of which this process 

 depends is the same as that mentioned in Art. 3, Lesson V. 

 (Vol. I., page 69), namely, that when a quantity is to be 

 divided, if we separate it into a number of parts, and divide 

 each part individually, the sum of all the quotients so obtained 

 will be the required quotient. 



Here notice that we have, in reality, divided .87 10s. 7d. 

 into the following parts : 



47 + 799s. + 94d. + 182 farthings ; 



Or, 47 + (47 x 17s.) + (47 * 2d.) + (47 x 3Jf farthings). 

 The quotients of each of these separate sums, divided by 47, 

 are respectively 



1, 17s., 2d., and 3J4 farthings. 

 Hence the required quotient is 



1 17s. 2d. 3JK. 



14. From the above remarks we see the truth of the fol- 

 lowing 



Rule for Compound Division when the Divisor is an Abstract 

 Number. 



Beginning with the highest denomination, divide each sepa- 

 rately and in succession. When there is a remainder, reduce it 

 to the next lower denomination, adding the number of that 

 denomination contained in the dividend, and divide the sum as 

 before. Proceed in this manner through all the denominations. 



Obs. It is sometimes convenient, when the divisor is a com- 

 posite number, to separate it into factors, and divide succes- 



sively by them, instead of dividing at once by the whole divisor. 

 For instance, if it be required to divide 75 cwt. 2 qrs. 8 Ibs. by 

 35, which = 7 X 5, we can perform the operation thus : 



cwt. qrs. Ibs. 

 7 ) 75 2 8 



5) 10 3 5| 



2 171 + &. 



Notice that the ^ arises from the division of the by 5. 

 Adding i and ^, we get || ; so that the required answer would 

 be written 



cwt. 

 2 



qrs. 

 



Ibs. 

 17H 



And, if necessary, the || of a pound could be further reduced 

 to ounces, etc. 



15. When it is required to divide one compound quantity by 

 another of the same kind, we must reduce each to the same 

 denomination, and then divide as in ordinary simple division ; 

 for, clearly, the number of times which one compound quantity 

 contains another does not depend upon the particular denomina- 

 tion or denominations in which they happen to be expressed. 



Supposing one man to have 5 sovereigns in his pocket, and 

 another 1 sovereign, the former would still have 5 times as 

 much as the latter, if they had respectively 100 and 20 shillings 

 instead of the sovereigns. 



16. EXAMPLE. Divide .35 17s. 6d. by 2 11s. 3d. 



35 17s. 6d. = 8610 pence. 



2 11s. 3d. = 615 pence. 



615 ) 8610 ( 14 



615 



2460 

 2460 



Hence 14 is the answer. 



We shall, however, return to this part of the subject when 

 we treat of fractions in connection with compound quantities. 



EXERCISE 46. EXAMPLES IN COMPOUND DIVISION. 

 Divide 



1. 87 10s. 7d. by 18, 27, and 39. 



2. 33 by 96. 



3. 312 Ibs. 9 oz. 18 dwts. by 7, 43, 84, and 160. 



4. 410 Ibs. 4 oz. 5 dwts. 6 grs. by 8, 25, 39, 73, aud 210. 



5. 786 bshs. 18 qts. by 17, 19, 21, 25, 48, and 97. 



6. 216 yds. 3 qrs. by 20. 



7. 500 yds. 3 qrs. 2 nls. by 54, 63, and 108. 



8. 365 days 10 h. 40 min, by 15 and 48. 



9. Ill yrs. 20 d. 13 h. 25 min. 10 sec. by 11, 19, 83, and 100. 



10. 45 Q 17' 10" by 25, 35, and 45. 



11. How much a day is 200 a year ? 



How many times is 



12. 6s. 3.}d. contained in 5 ? 



13. 29 7s. 6d. contained in 523 15s. 3$d. ? 



14. 2 qrs. 13 Ibs. 5 oz. contained in 4 tons 3 cwt. 2 qrs. 6 Ibs. ? 



Divide 



15. 195 m. 7 fur. 30 ft. by 7 ft. 6 in. 



16. 531 m. 2 fur. 10 p. by 17 in. 5 fur. 27 p. 



17. 950 days 1 h. 11 min. 6 sec. by 4 days 8 h. 6 min. 54 sec. 

 ** Tlie Key to Exercises 44, 45 (Vol. II., page 78), will be found at 



end of Lesson XXVIII. 



LESSONS IN GEOGEAPHY. XVII. 



THE GEEAT CIRCLES OP THE EARTH THE MERIDIAN- 

 THE EQUATOR. 



ON the globe of the earth, or terrestrial globe, as it is called, the 

 first great circle of importance is the meridian ; this is a great 

 circle which passes through the two poles, P P (Fig. 6), of the axis 

 of the earth, and through any point, as M, on the earth's surface. 

 It is called meridian, because when the sun in our climate shines 

 on a gnomon or style (the pin of a sun-dial), and casts its shadow 

 in the direction of this line on the surface of the earth, it is 

 then (meridies) mid-day or noon; and whenever any heavenly 

 body appears in the plane of this circle, as determined by the 

 position of the style and its shadow at noon, it is said to be on 

 the meridian. 



The meridian of the point M in. Fig. 6 is, according to this 



