

the purchase- mom-y to put into repair. It then stood empty 

 for a year, duriutr which time he reckoned he was losing 5 per 

 cent, upon his total outlay. He then Bold it for .1192, by 

 which means he gained 10 per cent, upon the original purohase- 

 money. Wliat did ho give fur the hooM ? 



The expeuto of repair wan l { of the cost price ; therefore the total 

 was It of the ooct price. 



By the house standing empty he lost A x f ! of the ooet prico. 

 Therefore, before he sold the home, hi* expenses bad been fi x |{ of 

 the oost price, and by selling it (or 1192 be gamed f s of the ooet price. 



Henoo, ?i x J of the cost price + & of the ooet price is Jt: 

 Jtf of the cost price is jBl 192; or T}J of tbe cost price is 8. Therefore 

 the ooet price was 1000. 



9. A person buys an article, and soils it BO as to gain 5 per 

 cent. If he had bought it at 5 per cent, less, and sold it for 

 IB. leas, he would have gained 10 per cent. Find the co-- 



181 of the cost price is tbe selling price. If he bad bought it for 

 he cost price, and sold it for {"I of tbe cost price Is., he 

 would bare gained 10 per cent. 



Therefore }J of iVo of the cost price is JgJ of the cost price - Is. ; 

 or HI (IJ x iJ) of the cost price is Is.; or T J 3 of tbe cost price is Is. 

 Tbe cost price was therefore .10. 



10. A man allows his agent 5 per cent, on his gross income 

 for collecting his rents. He spends } of his net income in in- 

 suring his own life, and this part of hifl income is in consequence 

 exempt from income tax. The income tax being lOd. in the 

 pound, and his income tax amounting to .38 19s. ; find his 

 gross income. 



After paying 5 per cent, to his agent, i of his gross income is left, 

 which is bis net income ; but since } of this is exempt from income 

 tax. be pays tax on f x ' J of bis gross income. 



Now since .38 19s. = Vo*, if he paid tax upon his gross income, it 

 would amount to 



Hence, as 



6x19 

 : 1 : : 



Hence gross income 



7x 41 

 : g : gross income. 



_ 7 x 41 x 24 



6 



1148. Amvtrr. 



11. Suppose the cost of working a train to be directly pro- 

 portional to the speed, and the number of passengers. Then, 

 if the ca-st be .37 for conveying 18- c passengers 53-J miles in If 

 hours, how far can 1070 be conveyed in 2J hours for .161 ? 



Suppose tbe speed be reckoned by tbe number of miles travelled in 



rol 21 -t 



one hour. This, in the first case, is *, or - miles per hour ; and, 

 in tbe second case, if z represent tbe required distance, tbe speed will 

 be represented by -, 



Hence [see Lesson XXXIII., Art. 10, Vol. II., page 326] we have 

 161 



1070 x- 



2J, from which x is found to be 51| miles. 



185 x *f 



12. A cistern has two pipes, A and B, which singly could fill 

 it in 9 and 10 hours respectively. It has also two taps, C and 

 D, which could empty it in 12 and 8 hours respectively. When 

 the cistern is half full, A and D are turned on for 3 hours ; then 

 B is also turned on for 2 hours ; next A and D are turned off, 

 and C is turned on for 8 hours. Then, all being shut, it is found 

 that the cistern contains 95 gallons more than the half content. 

 Find the capacity of the cistern, and how much the cistern 

 could lose or gain in an hour if all four pipes were set open 

 together. 



A can fill i of the cistern in 1 hour ; B can fill & hi 1 hour ; C can 

 empty -ft in 1 hour ; D can empty ^ in 1 hour. 



A is open altogether 5 hours ; B is open altogether 10 hours ; C is 

 open altogether 8 hours ; D is open altogether 5 hours. 



Hence the effect will be to add | + {-&- |, or f I of the whole 

 cistern, and this by the question is 95 gallons. 



Hence the cistern holds }J x 95, or 360 gallons. 



If all the pipes were set open at once, in one hour the cistern would 

 gain I * A ^, J, or *}; of its contents, that is, 1 gallon. 



13. The time between the firing of two guns at a railway 

 station is 6 minutes, and a passenger in a train which i? 

 approaching the station at a uniform rate hears the second 5m. 



after the first. Now, supposing that the sound of the 

 train when it is two miles off will reach the station, how long 

 after it is heard approacuing will it pass the station, the velocity 

 of sound being 1125 feet per second 



If the passenger had remained stationary at the place where be heard 



the first m. he would have beard the second minutes afterwards. 

 But since he bears it S51 seconds afterwards, be has fa Uus 

 travelled over a space which send womld BMTMI to 9 

 Therefore tbe velocities of tbe train sad of sound sse to fee ratio of 

 9:351. Hence tbe speed at tbe train is rf f x ll feet per ssnnsjil. 

 that is, ,V feet per second. 



Tbe noise which tbe train makes at a distance of 2 miles win take 



f> seconds to reach tbe station. During this time tbe train will 



travr 1760 X 

 1125 



Hence, when tbe truiu is first heard it will be actually at a 

 of 1760 x 6 - A * 1760 feet, or **Jl* feet from the station. 

 therefore, pass tbe station L& H** * M seconds after that, 

 56-7 seconds afterwards. 



KEY TO EXERCISES IN LESSONS IN AmiTHJCETIC.-XLIV. 



It will. 



1. 41745(6,206630142. 



2. Mfc 



3. 117261. 



4. 335553. 



5. 7335344. 



6. 227950. 



7. 28 sq. ft. 82 sq. 



in. 



8. 268 cub. ft. 996 cub. 

 in. 



EXERCISE 63. 

 9. 105 sq. ft. 5' 4" 5~ 



5,4. 

 10. 85 sq. ft. 1' 11" 0" 



5, - 



-. *id. 

 12. 33750. 

 i;.. (a) 5 Os. lOd. 



(I) 8 14 9|. 



(e) 7 12 21'}. 

 14. 1 15s. 5;d. 



15. 48 feet. 



16. 8Ce. 4,*,d. 



17. lOBffeet. 



18. 195 square yard.. 



19. 12) feet. 



2l! 1406 sqsmn feet 



36 in. 

 22. 

 23. 



Erratum. Lesson XLII., Example 6. Answer should be 100 Is*. 



HISTORIC SKETCHES. XXXVL 



THE JEWS. IL 



FOB a while the Jews bore with the theocracy, especially when, 

 as under Joshua, it was associated with the warrior element in 

 their leader ; for a term, after their advent into the promised 

 land, they consented to remain under the guidance of judges, 

 who were the avowed lieutenants of the heavenly King himself, 

 the self-denying " servants of the servants of God." But the 

 temptations to which the people subjected themselves, and before 

 which they fell, were too strong to be counteracted by the severe 

 law of unswerving right ; the sins and follies of the people in- 

 fected the judicial office also, till at length it became question- 

 able whether aught was gained, whether something was not 

 rather lost, by the continuance of the regime which had been 

 tried and found wanting. The scandal presented by some 

 bearers of the judicial office, both as regards their life and 

 doctrine, was such that no good, humanly speaking, could 

 possibly accrue from the continuance of the office ; experience 

 had proved that the pure priestly government, even the visible 

 presence of God between the cherubim, would not suffice to keep 

 the people in the straight but narrow path ; it was better, there- 

 fore, to withdraw the presence which overbore the people, and 

 which could not adequately be represented by ordinary men, and 

 to substitute for it a system of government, lower in kind and 

 { degree, which yet might be under guidance, and confess the 

 Lord Jehovah as supreme. Thus it happened that Saul wms 

 made king over Israel, and thus it happened that Samuel, pre- 

 serving the character but not the local power of his predeces- 

 sors, exercised a sort of irresponsible control over him, even an- 

 nouncing to him at the end how that the Lord repented he had 

 made him king. Successors of Samuel there were in the long 

 line of illustrious prophets, of some of whom mention is made 

 so frequently in the Old Testament, men who fully accepted 

 the new position which spiritual influences were to occupy in 

 relation to man, who ceased to terrify by govennental acts, and 

 looked to uncarnal weapons as best befitting the servants of 

 Him, who not being of this world was yet to come into it Suc- 

 cessors they had and ever have had, both before and after the 

 advent of the Redeemer whose witnesses they were, and who 

 came to restore once again in his own person the functions of 

 the priest and king. To preserve pare and nndefiled the word 

 of God to man, to warn, to exhort, to threaten, as fathers oaring 

 for their own children this became the function of the prophets 

 as representatives of the Lord Almighty. The duty of the kings 

 whom God gave the people was to lead them by means which 

 they could understand to that goal to which prophets and 

 judges, acting directly, had pointed in vain, and to show them, 

 by precept and example, the sort of life which the chosen people 



