2. Since the work of 5 men is equivalent to that of 7 women, the work of 1 woman is denoted by that of a man; and the work of 7 men and 5 women will be lenoted by The number of days is 34. work of a man. 3. The work of two men is equivalent to that of 3 boys, and the work of 9 boys will be equal to that of 6 men, and therefore the work of 12 men and 9 boys will be the same as that of 18 men. 1 man can perform of the work in 1 day, and the work of a boy as of that of a man, or in 1 day. Hence the work of 1 man and 1 boy in 1 day is denoted by. The number of days is 30. 4. 30 boy in 38 9. 4 days. days. 5. 28 days. 6. A man in 11 days, a woman in 33 days, and a days. 7. A man in 31 days, and a boy in 252 days. 8. 360 days. 1. If the work be denoted by 1. XXX. Then A and B do 1 in 20 days, or in 1 day. Hence A does 2-18 in one day, and 1-180-190=33 days in which A could finish the work by himself. B does 1 in 50 days, or in 1 day. 2. A does 1 in 11 days, therefore in 1 day. B does 1 in 17 days, therefore in 1 day. 3. A and B do day. And ▲ does 1 in 6 days, and in 1 day. B does in 15 days, and in 1 -=: and 1÷=30 days, 1÷2=4=7!. That is, A does the work in 30 days, and B in 7 days. 4. A and B do 1 in 12 days, and in 1 day; similarly A and C do 3 in 1 day, and B and C in 1 day. And A, B, C, separately, do the work in 20, 30, and 60 days respectively. 5. A does 1 in 15 days, and in 1 day. B does 1 in 18 days and in 1 day. Here B leaves, A continues, and is joined by C, who together finish the part That is, C could do the work by himself in 1012 days. 6. 1019 days. 7. 13 hrs. 8. 414 days, 413 days, 5 days. 9. 2 days. 10. 23 hrs. or B will require 67 days to complete what A can perform in 6 weeks. 12. 3 days. 13. 3 days. 14. 5 days. XXXI. 1. 1728 cubic inches = 1000 ounces Avoirdupois. 1oz. water lb. = 7000 grains. Hence 1 cubic inch of water=1900×7000=252104 grains Troy. 2. 47 cubic yards. 3. Content of the cistern= X 16 56 31 27 3 3 4 1 cubic foot of water = 1000oz. =14x31x3 cubic feet. 14x31x3x1000 31x3×25 2325 = 64 the pressure on the bottom of the cistern, which is at the rate 539 tons on the square foot. 4. 3402 hogsheads. 5. 120 gallons. 6. Glass A contains 3 parts water + 1 part spirits=4 parts. Glass B contains 4 parts water + 3 parts spirit=7 parts. of water of spirit=1, and of water + of spirit=1, therefore 1 of water+ of spirit=2. Or the mixture consists of 1 of water, and 1 of spirit. 7. The first vessel contains 1323 gallons, the second 23 ounces. yard. 1. gallons. 8. 79459 9. 2115lbs. on the square foot, and nine times this pressure on the square 10. 3266lbs. 11. 17 feet. XXXII. hour. 2. 84 minutes. 3. 60 minutes. 4. z full. 5. The capacity of the cistern may be represented by 1. Pipe A fills the cistern in 3 hours, and pours in } in 1 hour. Pipe B fills it in 4 hours, and pours in 4 in 1 hour. The pipes A and B pour in + or in 1 hour; but pipe C empties the cistern or pours out 1 in 1 hour. Hence the quantity poured out being greater than the quantity poured in during the same time, the cistern will become empty in a certain time. At 3 o'clock, when pipe C is opened, the cistern contains 3+1, or 11. And in 1 hour, 1- is excess of quantity poured out above that poured in. The vessel will be empty 24 hours after 3 o'clock, or Hence÷=23 hours. at 12 minutes past 5 o'clock. 6. of a day. 7. I am a brazen lion, with fountains in my two eyes, my mouth, and in my right foot. The water flowing from my right eye fills a reservoir in two days, and from the left in three, and from the foot in four. But when the water flows from my mouth, it fills the reservoir in six hours. In what time will the reservoir be filled by the water from the mouth, the eyes, and the foot, if all be opened together? In 3 hours the reservoir will be filled. XXXIII. 1. The difference is. 1760×3×12 × 60 minutes, or more than 14, but less than 1 of a minute. 41 +3=1, and the unit is 100 miles. Hence A walks of 100, or 40 miles, when they meet. 2. Here 6+4=10, and of 100, or 60 miles, and B Again of 5036 miles, and 3 of 50-20 miles. When A had travelled 30, and B 20 miles, they were 50 miles apart. They will a second time be 50 miles apart after having passed each other, when A is 30 and B 20 miles distant from the places from which B and A respectively started. 3. 3 hrs. 233 min. 4. of 1 minute, and of 1 minute. 5. 7 of 1 minute. 6. 28 seconds through air, 6134 seconds through water, and 4,9,25 seconds through land. 7. 1344 yards. 8. The shooter notes the times of the flight of ball over 500 yards, and of sound over the same distance in 4 seconds. The spectator observes the difference of these to be 2 seconds. Hence it appears sound moves over 500 yards in second, which gives 1125 the velocity of sound in 1 second. 9. The time required will be the same part of one second as 24900 miles is of 288000; that is, the time is 24906 or of 1 second, which is between and of a second. 2880009 10. 192697 miles. 11. 24 revolutions. 12. In 11 hours. 13. 3960 revolutions. 1. 3hrs. 54 min. p.m. XXXIV. 2. The hour and minute hands of a clock are coincident or in conjunction at 12 o'clock. They are also in conjunction at some point of time in each successive hour (except from 11 to 12 o'clock) until they are again in conjunction at 12 o'clock. The motions of the hour and minute hands are uniform, and the minute hand moves 12 times as fast as the hour hand. Now, after the conjunction at 12 o'clock, the minute hand reaches XII. again when the hour hand points to I. And when the minute hand reaches I. the hour hand will have moved over of the distance between I. and II., and when the minute hand actually overtakes the hour hand, the hour hand will have gone over of the distance between I. and II.; and in the same time the minute hand will have moved over . And therefore, or 1, is the space moved over by the minute hand from XII. while the hour hand has moved of the equal space I. to II. And the exact time of the first coincidence of the hands after 12 o'clock, is 1 hours or 5 minutes past 1 o'clock. In the same way it may be shewn that the next coincidence will take place at 2 hours, or at 10 minutes after 2 o'clock. The successive times of conjunction will be found by adding 1 hour to the time of each preceding conjunction, reckoning from 12 o'clock Chr. They are at 1, 2, 3, 4, 5, 6, 7, 8ft, 9ft, 101, 11 spectively. hours re The hour and minute hands will be exactly opposite, or in opposition, at 6 o'clock, and also once in every hour until they are again in opposition at 6 o'clock. The hour and minute hands will be at right angles to each other when the minute hand points to XII., and when the hour hand points to III. and to IX., or at 3 and at 9 o'clock; and in every hour there will be two points of time when the two hands are at right angles to one another. The preceding remarks on the solution of the first question will suggest the mode of proceeding for the exact solution of the second and third questions. 3. See the preceding solution. 4. 4min. 58sec. too slow. 5. At 10hrs. 15min. am. on Saturday, the watch is 5min. 367 sec. too slow. 6. The angle is 109 degrees. 7. The angles at which the hour and minute hand are inclined to the vertical is 60°, when both are equally inclined between the hours of 2 and 3 o'clock. 8. 10 minutes too slow, and 10 minutes too fast. 9. 8hrs. 15 min. a.m. 10. There are 11 intervals between 1 and 12 strikes. The interval of two strikes of the first clock is sec., and of the second sec., and the seventh strikes take place on the completion of the sixth interval. The times are 410 and 150 seconds, their difference is ff of 3 seconds, or of 1 minute. EDITED BY ROBERT POTTS, M.A., TRINITY COLLEGE, CAMBRIDGE. HON. LL.D. WILLIAM AND MARY COLLEGE, VA., U.S. PALEY'S EVIDENCES OF CHRISTIANITY and the Hora Paulinæ, edited with Notes; with an Analysis and a selection of Examination Questions from the Cambridge Papers 8vo., pp. 588, 10s. 6d., cloth. "Mr. Potts' is the most complete and useful edition yet published."-Eclectic Review. 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