RECREATIVE SCIENCE. 



215 





65. A and B together can build a boat in 20 day* ; with the 

 assistance of C they can do it in 12 days. How long would it 

 take C to build the boat P 



66. There is a cistern with two aqueducts ; one will fill it in 

 30 minutes, the other will empty it in 40. How long will it take 

 to fill it if both run together .' 



67. Required to divide 1 shilling into pence and farthings in 

 such a proportion that there may be 39 pieces. 



68. A man divided a small sum of money among bis children 

 In the following manner: viz., to the first he gave of the whole 

 -f- 4 pence, to the second of the remainder -f- 8 pence, to the 

 third i of tho remainder +12 ponce, and so on, giving to all an 

 equal Bum till he had distributed the whole. Required the num- 

 ber of shares and the sum distributed. 



69. A hare has 50 leaps the start of a hound, and takes 4 

 leaps while the hound takes 3 ; but 2 leaps of the hound are 

 equal to 3 of the hare. How many leapa will the hound take in 

 catching the hare ? 



70. A and B start at the same time and place to go round on 

 island 600 miles in circumference. A goes 30 miles a day, and 

 B 20. How long before they will both bo at the starting-point 

 together, and how far will each have travelled P 



71. A has .100, B .48. A robber takos twice as much from 

 A as from B. A now has 3 times as much as B. What was 

 taken from each ? 



72. It is rcqmired to divide 1,200 between A, B, and C ; B 

 has .256 + i of A's share ; C has .270 + i of B's. What was 

 the share of each P 



73. There are three pieces of cloth of different value. The 

 average price of the first and second is 7s. per yard, that of the 

 second and third is 9s., and the average price of all is f of the 

 third. What are the several prices ? 



74. A pipe will fill a cistern in 11 hours. After running 5 

 hours another ia opened, and then the two fill it in 2 hours. 

 In what time would the last fill it P 



75. A man bought a cask of wine, and i of it leaking out, he 

 sold the rest at 25s. per gallon, and neither gained nor lost by 

 his bargain. What did he give per gallon for his wine ? 



76. A and B start at the same time and in the same direction, 

 but directly opposite each other, to go round a circular pond 

 536 yards in circumference; A goes 11 yards a minute, and B 

 34 in 3 minutes. In what time will B overtake A P 



77. A cask contains a certain number of gallons of rum, and 

 an mth part of that quantity of water : but if a gallons of rum 

 and b of water be added to the mixture, the water in the whole 

 compound will be an nth part of the rum. Required the quantity 

 of each contained in the cask at first. Examine also and explain 

 the case, in which m being equal to n, a is equal to n b, and the 

 one in which it is not equal to it ; and also tho case in which x 

 and y come out negative, x denoting tho original number of 

 gallons of tho rum, and y those of the water. 



78. Find a fraction, such that if its denominator be increased 

 by 1, the value becomes i ; while if the numerator bo increased 

 by 1, the value is $. 



79. Required a fraction, such that if tho numerator and 

 denominator be each increased by 1, the value is changed into 

 i ; but if they be each diminished by 1, tho value becomes J. 



80. One person says to another : " If you give me half your 

 money, I shall have a hundred pounds." The other replies : 

 " I shall have a hundred pounds if yon give me a third of your 

 money." How much had each ? 



81. At what time between 10 and 11 o'clock are tho hour 

 and minute hands of a common clock exactly together ? 



82. Find two numbers, such that | of the first exceeds J of the 

 second by 3, and that J of the first and J of tho second are 

 together equal to 10. 



83. Required two numbers, such that the sum of of the first 

 and I of the second may bo 29, and that J of the first and J of 

 the second may amount to 21. 



84. A number expressed by three digits, whose sum is 22, is 

 less by 297 than the number expressed by the same digits in a 

 reversed order, and its first digit is less by 1 than its second. 

 What is the number ? 



85. A bill of ,100 may be paid by 50 bank notes of one value 

 each, and by 38 of another ; or it may be paid by means of 75 

 of the former kind, and 17 of the latter. What are tho values 

 of the notes ? 



86. Two persons set out from a certain place on tho same 



day, and proceed in the same direction, the one travelling 80 

 mile* the first day, and going each day a mile leas than he did 

 on the preceding ; while the other travel* at the constant rate of 

 20 mile* a day. When will they next be together? 



87. How many lines are contained in a page of a book, and 

 how many letters at an average in each line of that page, if it bo 

 found that by adding one line to each page, and making each 

 line contain an additional letter, the page will be increased by 

 96 letters ; while, by adding two line* to the original page, and 

 making each line contain four additional letters, the number of 

 letters will be increased by 286 P 



88. Two persona get each a legacy of .300, and one of them 

 is then found to be worth three time* M much M the other ; but 

 had the legacy to each been .800, the one would hare been 

 worth only twice as much as the other. How much had each 

 originally '< 



89. A cistern can be filled by three pipes ; by the first in 80 

 minutes, by the second in 200 minutes, and by the third in 300 

 minutes. In what time will the cistern be filled when all three 

 pipes are open at once ? 



90. Two gentlemen play at billiards ; A, before he began to 

 play, had .42, and B 24. Each lost and won in torn, when 

 A found he had five times as much as B had remaining. How 

 much did A win ? 



91. What capital is that which, with five years' interest at 4 

 per cent., will amount to .8,208 P 



92. A capital was put out for one year at 4} per cent, pe" 

 annum ; at the expiration of the year there was received back, 

 as capital and interest, 13,167. What was the amount of the 

 capital P 



93. A fortress has a garrison of 2,600 men, among whom are 



9 times as many foot soldiers and 3 times as many artillery 

 as cavalry. How many are there in each corps ? 



94. Divide the number 46 into two parts, so that when the 

 one is divided by 7, and the other by 3, the quotients together 

 may amount to 10. What are the parts ? 



95. From the first of two mortars in a battery 36 shells are 

 thrown before the second is ready for firing. Sheila are then 

 thrown from both in tho proportion of 8 from the first to 7 of 

 the second ; tho second mortar requiring as much powder for 3 

 charges as the first does for 4. It is required to determine after 

 how many discharges of the second mortar the quantity of powder 

 consumed by it is equal to the quantity consumed by the first. 



96. Suppose the crown of Hiero of Syracuse weighed 100 

 ounces ; suppose the two crowns, one gold and the other silver, 

 weighed the same, 100 ounces each; and supposing, what would 

 be very nearly the case, that tho gold crown, weighed in water, 

 lost 5 ounces, the silver one lost 9 ounces ; and supposing the 

 compound or mixed crown lost 6 ounces, it is required to find 

 the proportion of gold and silver in the crown of Hiero, 



97. A footman agreed to serve his master for 8 a year and 

 a livery, but was turned away at the end of 7 months, and 

 received only 2 13s. 4d. and his livery. What was its value ? 



98. A fish was caught whoso tail weighed 91bs. ; his head 

 weighed as much as his tail and half his body ; and his body 

 weighed as much as his head and tail. What is the weight of 

 the whole fish P 



99. If A and B together can perform a piece of work in 8 

 days, A and C together in 9 days, and B and C together in 



10 days, how long will each person take to perform it alone ? 



100. The fore- wheel of a carriage makes 6 revolutions more 

 than the hind- wheel in going 120 yards; but if the circumference 

 of each wheel be increased by 3 feet, the fore-wheel makes only 4 

 revolutions more than the hind-wheel. What is the circumference 

 of each wheel? 



RECREATIVE SCIENCE. 1 1 T. 



THE NATURE AMD MEASUREMENT OF LIGHT- 

 PHOTOMETRY. 



THE sources of light and the principles which regulate the pro- 

 duction of artificial light having been discussed in the previous 

 papers, it seems quite in the natural order of things to go 

 further and attempt to solve the nature of light in fact, to 

 try to understand its relation to non-luminous bodies, and the 

 uses of various optical instruments. In determining the nature 

 of light, it may be asked why it can travel so fast from the 

 sun, and although the distance of that luminary from the earth 



