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To avoid the inconvenience of reckoning { of a day with each year, every fourth year (called Leap year) is reckoned at 366 days and the others are reckoned at 365 days. A leap year may always be known by this, viz.:--Its number can be divided

Thus we know that 1852 is a leap year, because 1852 can be divided by 4 without a remainder.

The year in reality contains but 365 days, 5 h. 48 m. 48 sec. so that by reckoning 3654 days we make a slight error each year which in 100 years amounts to about 1 day. The Centennial years are not, therefore, reckoned as leap years unless the number of the year be divisible by 400. Thus the year 1900 will not be a leap year; but the year 2000 will be.

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A sheet folded into 2 leaves is called a folio.

4

" quarto. 8

" octavo. 12

o duodecimo or 12 mo. 18 * In Leap year February has 29 days.

18 mo.

Q. 1. What must be added to 16s. to give a sum equal to £1? What must be added to 13s. ? to 18s. ? to 7s. ? to 19s. ? to 11s. ? to 10s. ?

2. What must be added to 9d. to give a sum equal to 1 shilling? What must be added to 3d. ? to 11d. ? to 8d. ? to 4d.? to 7d.?

3. What must be added to 12 gr. to give a sum equal to 1 dwt. ? What must be added to 11 gr.? to 17 gr. ? to 23 gr. ? to 13

gr.
? to 15

gr.
? to 5

gr.

? to 19 gr. ? to 9 gr. ? 4. What must be added to 7 Avoirdupois ounces to give a sum equal to 1 lb. ? What must be added to 11 oz. ? to 9 oz. ? to 12 oz. ? to 2 oz. ?

5. What must be added to 17 lb. to give a sum equal to 1 qr.? What must be added to 19 lb. ? to 9 lb. ? to 11 lb. ? to 23 lb.? to 21 lb. ? to 17 lb. ? to 15 lb. ? to 5 lb. ? 25 lb. ? to 18 lb. ? to 3 lb. ?

6. What must be added to 121 sq. in. to give a sum equal to 1 sq. ft. ? What must be added to 134 sq. in. ? to 141 sq. in. ? to 107 sq. in. ? to 96 sq. in. ? to 87 sq. in. ? to 71 sq. in. ? to 115 sq. in. ? to 111 sq. in. ? to 47 sq. in. ? to 138 sq. in. ? to 104 sq. in. ? to 109 sq. in. ?

7. How many more than cwt. enough for 1 ton are there in 36 cwt. ? in 25 cwt. ? in 39 cwt. ? in 31 cwt. ? in 27 cwt. ? in 36 cwt. ?

Then how many tons and cwt. are equal in value to 37 cwt. ? to 25 cwt. ? to 39 cwt. ? to 31 cwt. ? to 27 cwt. ? to 36 cwt. ?

8. How many more than enough 3 for one lb are there in 16 į? Then how many lo and Z are there in 16 Z? in 18 Z? in 23 3? in 20 3? in 15 3? in 19 3? in 18 3?

9. What is the value of each of the following, expressed in as high denominations as possible ? 181 sq. in. ? 39 gr. Troy? 37 shillings? 15 3 ? 55 lb. Avoirdupois ? 21 in. ? 74 sq. rd. ? 16 sq. ft. ? 11 days?

10. What will be the value of 211 cu. ft. expressed in cords and feet? of 36 dwó. in oz. and dwt. ? of 107 sec. in minutes and seconds ?

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R. 1. What is the value of 33 lb. + 21 lb. expressed in the highest possible denominations ? Solution. 23 lb. +21 lb. 44 lb.

1 qr. 16 lb. 2. What is the value of each of the following, expressed in the highest possible denominations ?

3. Of 26 lb. + 25 lb. ? 16s. + 18s.? 13s. + 19s. ?

4. Of 17 hours + 21 h.? 22 h. + 23 h. ? 5. Of 22 gr. + 19 gr. Troy weight? 18 dwt. + 16 dwt. ? 6. Of 11 oz.+ 9 oz. Troy? 10d. + 8d.? 16s. + 18s. ? 7. Of 15 dr. + 13 dr. ? 9 oz. + 8 oz. Avoirdupois ? 8. Of 12 oz. + 15 oz. av. ? 26 lbs. + 8 lbs. ? 9. Of ils. + 12s. ? 5 qt. + 7 qt. Dry Measure ? 10. Of 135 sq. in. + 121 sq. in. ? 85 sq. in. + 79 sq. in. ? 11. Of 11d. + 8d. ?

Much labor can be saved in performing examples like those under this letter, by applying the principles illustrated in the following example:

What is the value of 23 lb. + 21 lb. ?

Observing that 23 lb. lack but 5 lb. of being 1 qr., we take 5 lb. from 21 lb. and add it to 23 lb., which gives the following solution: 23 lb. + 21 lb 28 lb. + 16 lb. 1 qr., 16 lb. Ans.

Perform all the examples under this letter by the method last explained.

49 lb.

or 1

s. 1. What is the value of 23 lb. + 26 lb. + 27 lb. ? Solution. 23 lb. + 26 lb.

qr. 21 lb., and 1 qr. 21 lb. +27 lb.=1 qr. 48 lb.=1 qr. +1qr. 20 lb.=2qr. 20 lb., Ans. Or, adding and reducing by naming only results, we say, 23 lb.; 49 lb., or 1 qr. 21 lb.; 1 qr. 48 lb., or 2 qr. 20 lb., Ans.

2. What is the value of 24 lb. + 19 lb. + 25 lb. ? 3. 23 lb. + 21 lb. + 24 lb.? 17cwt.+ 18 cwt.+ 19 cwt. ? 4. 13 oz. + 15 oz. + 11 oz. Avoirdupois ? 5. 15 dr. + 10 dr. + 13 dr. Av. ? 83 +11 3+ 93? 6. 18 gr. + 15 gr. + 17 gr. Apothecaries? 7.73 +63 +53 +7 3? 8. 8 in. + 11 in. + 7 in. + 4 in. ? 9. 36 rd. + 29 rd. + 38 rd. ? 17s. + 11s. + 16s. + 18s.? 10. 8d. + 6d. + 5d. + 9d. ? 47 sec. + 52 sec. +39 sec. ? 11. 13 h. + 21 h. + 17 h. + 22 h. ? 12. 132 sq. in. + 100 sq. in. + 140 sq. in. ? 13. 126 sq. in. + 134 sq. in. + 127 sq. in. ? 14. What is the value of 23 lb. + 26 lb. + 27 lb. ? Solution. Since 26 lb. lack but 2 lb. of being 28 lb., or

=l

1 qr., we have 23 lb. + 26 lb.

qr. 21 lb.; and, since 27 lb. lack but 1 lb. of being 1 qr., we have 1 qr. 21 lb. + 27 lb. = 2 qr. 20 lb. Therefore, 23 lb. + 26 lb. + 27 lb. = 2 qr. 20 lb. Or, adding and reducing by naming only results, we say 23 lb. ; 1 qr. 21 lb.; 2 qr. 20 lb., Ans.

15. Apply the principles illustrated in the last solution to each of the examples under this letter.

Note. The pupil should master all the forms of solution given above, so that in practice he may use one or the other, as may seem best adapted to the numbers he has to add.

16. What is the value of 7 oz., 11 dr. + 3 oz., 14 dr. ?

Solution. 7 oz. 11 dr. + 3 oz. 14 dr. 7 oz. 11 dr. + 3 oz. + 14 dr. = 10 oz. 11 dr. + 14 dr. 11 oz. 9 dr.

Solution, naming only results, 7 oz. 11. dr.; 10 oz. 11 dr.; 11 oz. 9 dr., Ans.

17. What is the value of 5 oz. 13 dr. + 4 oz. 5 dr. ? 18. 1 qr. 25 lb. + 1 qr. 23 lb. ? 12 lb. 13 oz. + 8 lb. 14 oz. ? 19. 15 dwt. 21 gr. + 2 dwt. 19 gr.

? 20. 8 dwt. 14 gr. + 3 dwt. 13 gr.

? 21. 3 oz. 17 dwt. + 2 oz. 8 dwt. ? 4 ft. 11 in. + 2 ft. 8 in. ? 22. 3 fur. 28 rd. + 2 fur. 27 rd ? 7£ 15s. + 8£ 14s. ? 23. 9£ 17s. + 6£ 18s. ? 9s. 11d. + 8s. 8d.? 24. 3 da. 19 h. + 2 da. 21 h. ? 25. 2 sq. ft. 107 sq. in. + 4 sq. ft. 124 sq. in. ? 26. 3 sq. ft. 87 sq. in. + 3 sq. ft. 78 sq. in. ?

3 3?

T. 1. What is the value of 4£ 16s. 3s. ?

Ans. 4£ 13s. 2. What is the value of 28£ 19s. - 6s. ? 17s. 9d. - 7d.? 3. 9£ 18s. 15s.? 2 qr. 23 lb. – 14 lb. ? 4. 6 da. 13 h. 7 h.? 3 3 7 3 5. 2 14 gr. - 12 gr.? 5 sq. ft. 127 sq. in. - 54 sq. in. ? 6. What is the value of 28£ 5s.? Solution. 28£ 5s. = 27£ 20s. 5s. = 27£ 15s. 7. What is the value of 19£ 16s.? 16s. 7d.? 8. 3 R. 15 sq. rd. ? 2 qr.

14 lb.? 3 qr.

- 23 lb. ?

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9. 24 lbs. 11 oz. (Avoirdupois)? 8 oz. - 8 dr. ? 10. 3 dwt. 3 gr. ? 17 dwt.

8 gr. ? 48 m. 17 sec. ? 11. What is the value of 1 dwt. 14 gr.

21
gr.

? 1st Solution.

1 dwt. 14 gr.

21 gr.

38 gr.

21 gr.

17 gr.

17 gr.

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2d Solution. Since we cannot subtract 21 gr. from 14 gr., we will subtract it from 1 dwt., or 24 gr., leaving 3 gr., which added to 14 gr.

3d Solution. Subtracting 14 of the 21 grains from the 14 grains, we leave 7 gr. to subtract, which taken from the 24 gr. leaves 17 gr.

Note. The second or third forms will usually be more convenient than the first. 12. What is the value of 1 dwt. 21 gr.

23 gr. ? 13. 1 dwt. 7 gr.

15 gr. ? 1 qr. 17 lbs. 19 lbs. ? 14. 1 qr. 15 lb. 27 lb. ? 1£ 4s. 17s. ? 15. ls. ld. 11d.? 1 m. 27 sec. - 54 sec. ? 16. 1 m. 4 sec.

37 sec. ? 17. 1 sq. ft. 123 sq. in. 138 sq. in. ? 18. 1 sq. ft. 14 sq. in. 103 sq. in. ? 19. 1 R. 13 sq. rd. 29 sq. rd. ? 20. What is the value of 4 fur. 21 rd. 27 rd. ? Solution. 4 fur. 21 rd. - 27 rd. 4 fur.

3 fur. 34 rd.

21. What is the value of 7 fur. 18 rd. 23 rd.?
22. 5 fur. 1 rd. - 37 rd. ? 7. 3d. 11d.?
23. 9 lb. 43-93? 24 gr. - 16 gr.?
24. 4 da. 15 h. 19 h.? 28 m.

53 sec. ? 25. 17 T. 17 cwt. 13 cwt.

16 dwt. 4 18 gr. ? 26. 8 cu. yd. 3 cu. ft. 23 cu. ft. ? 2 m. 1 fur. 7 fur. ? 27. What is the value of 18 gal. 2 qt. 3 gal. 3 qt. ? 28. 17 bu. 1 pk. - 4 bu. 3 pk.? 3 pk. 4 qt. - 2 pk. 7 qt. ? 29. 24£ 4s. 13£ 16s. ? 3 qr. 8 lbs. 1

qr.

25 lbs. ? 30. 3 qr. 16 lb. 1 qr. 18 lb. ? 6 da. 20 h. 3 da. 22 h.? 31. 4 da. 12 h. 1 da. 19 h. ? 18s. 4d. 15s. 6d. ? 32. 12s. 2d. - 5s, 6d. ?

6 rd. =

28 sec.

gr.

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