Charles Davies.

School arithmetic. Analytical and practical online

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=3

= 16
= 66



yd.
=1



= 220



the equator
a circum'nce of the earth.
rd.



63360 = 5280 = 1760



= 1

= 40
= 320



fur.



_ i _ t

= 8



mi.



NOTES. 1. A fathom is a length of six feet, and is generally
Bed to measure the depth of water.

2. A hand is 4 inches, used to measure the height of horses.

3. The units of the scale, in passing from inches to feet, are 12 ;
in passing from feet to yards, 3 ; from yards to rods, 5 ; from
rods to furlongs, 40 ; and from furlongs to miles, 8.

1. How many inches in 5 feet ? In 10 feet ? In 16 feet ?

2. How many yards in 36 feet ? In 54 feet ? In 96 ?

3. How many feet in 144 inches ? In 96 inches ? In 48 ?

4. How many furlongs in 3 miles ? In 6 miles ? In 8 ?



EXAMPLES.



1. How many inches in
&rd. 4yd. 2ft. 9in.

OPERATION.

6rdL 4yd. 2ft. 9in.

_M

3

34



37 yards.
3

113 feet.
12
1365 inches.



2. In 1365 inches, how

many rods ?



OPERATION.

12)1365

3)113 feet 9m.
5|)37 yards 2ft
11)74
6rd.



Ans. Qrd. 4yd. 2ft. 9m.



DENOMINATE NUMBERS.



101



NOTE. When we reduce rods to yards, we multiply by the
scale 5i ; that is, we take 6 rods 5 and one-half times. When we
reduce yards to rods, we divide by 5i, which is done by reducing
the dividend and divisor to halves : the remainder is 8 half-yards,
equal to 4 yards.

3. In 59wi. *lfur. 38rY?., how many feet ?

4. In 115188 rods, how many miles?

5. In 719??u'. I6rd. 6yd., how many feet?
(6. In 118, how many miles?

7. In 54 45mi. 7/ur. 20rd. yd. 2ft. Win., how many
Inches ?

8. In 481401716 inches, how many degrees, &c. ?

CLOTH MEASURE.

107. Cloth measure is used for measuring all kinds of
cloth, ribbont;, and other things sold by the yard.

TABLE.

nail, marked na.
quarter of a yard, qr.
Ell Flemish, E. Fl.

yard, - yd.

Ell English, , E. E.



2J inches, in.
4 nails


make 1
1


3 quarters -
4 quarters -
5 quarters -


1
1

1


in. na.
2J 1


qr.


9 =4


= 1


27 = 12


= 3


36 = 16


= 4


45 = 20


= 5



E.Fl



= 1



yd.



- l



E. E.



= 1



NOTE. The units in this measure are, inches, nails, quarters, Klls
Flemish, yards, and Ells English.

1. In 9 inches, how many nails ? How many nails in 1
yard ? In 2 yards ? In 6 ? In 8 ?

2. In 4 yards, how many quarters ? How many quarters
in 8 yards ? In 7 how many ?

3. How many quarters in 12 nails? In 16 nails? In 20
nails? In 36? In 40 ?



107. For what is cloth measure used ? What are its denominations ?
Repeat the table. What are the units of this measure ?



102



REDUCTION OF



1.



How many nails are
there in 35yd. 3^r. 3na. ?

OPEKATION.

35t/d. 3(?
4



EXAMPLES.



143 quarters.
4



575 nails.



2. In 575 nails, how
many yards ?

OPERATION.

4)575



4)143 3na.
35 3 jr.



Ans.



. 3gr.



3. In 49 E. E., how many nails ?

4. In 51 i?. FL, 2qr. 8na., how many nails ?

5. In 3278 nails, how many yards ?

6. In 340 nails, how many Ells Flemish ?

7. In 4311 inches, how many E. E. ?

SQUARE MEASURE.

108. Square measure is used in measuring land, or anything
in which length and breadth are both considered.

1 Foot.

A square is a figure bounded by four equal
lines at right angles to each other. Each
line is called a side of the square. If each
side be one foot, the figure is called a
square foot.

If the sides of the square be each one
yard, the square is called a square yard.
In the large square there are nine small
squares, the sides of which are each one
foot. Therefore, the square yard contains
9 square feet.

The number of small squares that is contained in any large
square is always equal to the product of two of the sides of the
large square. As in the figure, 3 x3~9 square feet. The number
of square inches contained in a square foot is equal to 12 x 12=144.

108. For what is Square Measure used? What is a square? If
each side be one foot, what is it called ? If each side be a yard, whnt
is it called ? How many square feet docs the square yard contain ?
How is the number of small squares contained in a large square found ?
Repeat the table. What are the units of the scale ?




DENOMINATE NUMBERS.



103



TABLE.

144 square inches, sq. in., make 1 square foot,

9 square feet

30 J square yards -

40 square rods or perches -

4 roods -

640 acres -



Sq.ft.

I square yard, Sq. yd.

1 square rod or perch, P.
1 rood, - E.

1 acre, - A.

1 square mile, M.



Sq. in.

144

1296

39204

1568160

6272640



_Sq.ft.

= 9
= 272J
= 10890
= 43560



Sq. yd.

1

301

1210

4840



P.



1

40
160



E.



= 1

= 4 =1.



NOTE. The uDits of the scale are 144, 9, 30L 40, 4 and 640.

1. How many square inches in 2 square feet? How many
square feet in 3 square yards ? How many in 6 ? In 8 ?

2. How many perches in 1 rood ? In 3 roods ? How many
roods in 4 acres ? In 8 ? In 12 ?

3. How many perches in an acre ? How many in 2 acres ?
How many square yards in 81 square feet?

SURVEYORS' MEASURE.

109. The Surveyor's or Gunter's chain is generally used in
surveying land. It is 4 poles or 66 feet in length, and is
divided into 100 links.



inches make

4 .rods or 66/X
80 chains -

1 square chain
10 square chains



TABLE.

1 link, marked - I.

1 chain, - c.

I mile, - mi.

16 square rods or perches, P.

1 acre, - A.



NOTE. 1. Land is generally estimated in square miles, acres>
roods, and square rods or perches.
2. The units of the scale are 7 f 9 o 2 -, 4, 80.



109. What chain is used in land surveying ? What is its length ?
How is it divided? Repeat the table. In what is land generally esti-
mated ? What are the units of the scale ?



104 REDUCTION OF

1. How many rods in 1 chain ? How many in 4 ? In 5 ?

2. How many chains in 1 mile ? In 2 miles ? In 3 ?

3. How many perches in 1 square chain ? In 4 ? In 6 ?

4. How many square chains in 2 acres ? How many
perches in 3 acres ? In5? In 6?



EXAMPLES.



1. How many perches in
32Jf. 25A 35. 19P.?



OPERATION.



323f. 25A 3P. 19P.
640



20505 acres.
4



82023 roods.
40



2. How many square



miles, &c., in 3280989P.1



OPERATION.



40)3280939 19P.

4)82023 37?.
640)20505 25A
32

, Ans. 321T. 25 A ZR 19P.

3280939 perches.

3. In 19A 272. 37P., how many square rods ?

4. In 175 square chains, how many square feet ?

5. In 37456 square inches, how many square feet ?

6. In 14972 perches, how many acres ?

7. In 3674139 perches, how many square miles?

8. Mr. Wilson's farm contains 104A 3P. and 19P. ; he
paid for it at the rate of 75 cents a perch : what did it cost?

9. The four walls of a room are each 25 feet in length and
9 feet in height and the ceiling is 25 feet square : how much
will it cost to plaster it at 9 cents a square yard ?

CUBIC MEASURE.

110. Cubic measure is used for measuring stone, timber,
earth, and such other things as have the three dimensions,
length, breadth, and thickness.

TABLE.

1728 cubic inches, Cu. in., make 1 cubic foot, Cu. ft.
27 cubic feet, - 1 cubic yard, Cu. yd.

40 feet of round or ) -, . n,

50 feet of hewn timber, J

42 cubic feet, - 1 ton of shipping, T.

16 cubic feet, - - 1 cord foot, C.ft.

8 cord feet, or ) . , r

128 cubic feet, \ ' l cord '




DENOMINATE NUMBERS. 105

NOTE. 1. A cord of wood is a pile 4 feet wide, 4 feet high,
and 8 feet long.

2. A cord foot is 1 foot in length of the pile which makes a
cord.

3. A CUBE is a figure bounded by six equal squares, called
faces; the sides of the squares are called edges.

4. A cubic foot is a cube, each of whose faces is a square foot,
its edges are each 1 foot.

5. A cubic yard is a cube, each of
whose edges is 1 yard.

6. The base of a cube is the face
on which it stands If the edge of
the cube is one yard, it will contain

3x3=9 square feet ; therefore, 9 ^ __

cubic feet can be placed on the base, j

and hence, if the figure were 1 foot

thick, it would contain 9 cubic feet ; d feet - 1

if it were 2 feet thick it would contain 2 tiers of cubes, or 18 cubic

feet ; if it were 3 feet thick, it would contain 27 cubic feet ; hence,

The contents of a figure of this form are found by multi-
plying the length, breadth, and thickness together.

7. A ton of round timber, when square, is supposed to produce
40 cubic feet ; hence, one-fifth is lost by squaring.

1. In 1 cubic foot, how many cubic inches? How many
in 2 ? In 3 ?

2. In 1 cubic yard, how many cubic feet ? How many in
2 ? In 4 ? In 6 ?

3. How many cord feet in 3 cords of wood ? In 5 ? In 6 ?

4. How many cubic feet in 2 cords ? In half a cord, how
many ? How many in a quarter of a cord ?

5. How many cubic yards in 54 cubic feet ? In 81 ?

6. In 120 feet of round^ timber, how many tons ?

7. How many tons of shipping in 84 cubic feet ? In 168 ?

8. How many cords of wood in 64 cord feet ? In 96 ? In
128?

9. How many cubic feet in a stone 8 feet long, 3 feet
wide and 2 feet thick ?

110. For what is cubic measure used ? What are its denominations ?
What is a cord of wood ? What is a cord foot ? What is a cube ?
What is a cubic foot ? What is a cubic yard ? How many cubic feet
in a cubic yard? What are the contents of a solid equal to? Repeat
the table. What are the units of the scale ?



106 REDUCTION OF



EXAMPLES.



1. In 15cw. yd. IScu. ft.
16cw. in., how many cubic
inches ?



OPERATION.



cu. yd. cu. ft. cu. in.
15 18 16



113

31

423x1728 + 16=730960.



2. In 730960 cubic inch-
es, how many cubic yards,
&c.?

OPERATION.

1728)730960 cu. in.



27^423 cu. ft. 16
15ctt.yd.18



cu. yd. cu.ft. cu. in.
Ans. 15 18 16



3. How many small blocks 1 inch on each edge can be
sawed out of a cube 7 feet on each edge, allowing no waste
for sawing ?

4. In 25 cords of wood, how many cord feet ? How many
cubic feet ?

5. How many cords of wood in a pile 28 feet long, 4 feet
wide, and 6 feet in height ?

6. In 174964 cord feet, how many cords?

7. In 7645900 cubic inches, how many tons of hewn
timber ?

WINE OR LIQUID MEASURE.
111. Wine measure is used for measuring all liquids.

TABLE.



4 gills, gi. make


1 pint, marked


pt.


2 pints


1 quart, -


qt.


4 quarts


1 gallon, -


gal.


31 1 gallons -


1 barrel, - bar.


or bbl.


42 gallons -


1 tierce


tier,


63 gallons -


1 hogshead,


hhd.


2 hogsheads


1 pipe


pi.


2 pipes or 4 hogsheads


1 tun,


tun.



111. What is measured by wine or liquid measure ? What are its
denominations ? Repeat the table. What are the units of the scale ?
What is the standard wine gallon?



DENOMINATE NUMBERS. 107

gi. pt. qt. gal. bar. tier. hhd. pi. tun.
4 = 1

8 =2 =1

32 =8 =4 =1

1008 =252 =126 =311 -i

1344 =336 =168 =42 =1

2016 =504 =252 =63 =1$ =1

4032 =1008 =504 =126 =3 =2 = 1

8064 =2016 =1008 =252 =6 =4 = 2 =1

NOTE. The standard unit, or gallon of liquid measure, in the
United States, contains 231 cubic inches.

1. How many gills in 4 pints ? How many pints in 3
quarts ? In 6 quarts ? In 9 ? In 10 ?

2. How many quarts in 2 gallons ? In 4 gallons ? In 6
gallons ? How many pints in 2 gallons ? In 5 ?

3. How many barrels in a hogshead ? How many in 4
hogsheads ? In 6 ?

4. How many quarts in 3 gallons? In 5 gallons? In 20?
In a barrel how many ? In a hogshead how many ?



EXAMPLES.



1. In 5 tuns 3 hogsheads
17 gallons of wine, how
many gallons?



OPERATION.



btuns 3hhd. 17 gal.
4



23
63

76



139



2. In 1466 gallons, how-
many tuns, &c. ?



OPERATION.

63)1466

4)23 17 gal.
5 3 hhd.



Ans. Stuns Bhhd. llgal.
14 66 gallons.

3. In 12 pipes 1 hogshead and 1 quart of wine, how many
pints ?

4. In 10584 quarts of wine, how many tuns ?

5. In 201632 gills, how many tuns?

6 What will be the cost of 3 hogsheads, 1 barrel, 8 gal-
lons, and 2 quarts of vinegar, at 4 cents a quart ?



108



REDUCTION OF



ALE OR BEER MEASURE.

112. Ale or Beer Measure was formerly used for mea-
suring ale, beer, and milk.

TABLE,
make 1 quart, marked qt.

- 1 gallon, -

- 1 barrel, -

- 1 hogshead,



2 pints, pt.

4 quarts
36 gallons
54 gallons
pt.



2
8

288
432



4
144

216



gal.



bar.



gal.
bar.
hhd.
hhd.



= 1

= 36 =1
= 54 =11 =1
NOTE. 1 gallon, ale measure, contains 282 cubic inches.

1. How many pints in 3 quarts ? How many in 5?

2. How many quarts in 3 gallons ? In 4 gallons ? In 9 ?

EXAMPLES.



1 . How many quarts are
there in hhd. 26ar.



OPERATION.

4hhd. 26ar. Wgal. 8qt.

li

4

4

86ar.
36

57
26

317 gal.



2. In 1271 quarts, how
many hogsheads, &c. ?

OPERATION.

4)1271
36)317 Zqt.



Ans. hhd. 26ar. ZSgal. Zqt.



3. In^476ar. Ifigal. &qt., how many pints ?

4. In 27Md. 36ar. 25</a/. 3(?., how many pints ?

5. In 55832 pints, how many hogsheads ?

6. In 64972 quarts, how many barrels ?



112. For what is ale or beer measure used?
iuatious ? Repeat tho table.



What are its denotn-



DENOMINATE NUMBERS.



109



DRY MEASURE.

113. Dry Measure is used in measuring all dry articles,
such as grain, fruit, salt, coal, &c.



TABLE.



2 pints, pt.

8 quarts -

4 pecks -

36 bushels -



make 1 quart, marked



1 peck, -



bushel,
chaldron,



bu.



pk.
bu.
ch.

ch.



_



16 =8 =1

64 =32 =4

2304 = 1152 = 144

1. How maty quarts in 2 pecks ?

2. How many pecks in 24 quarts ?

3. How many pecks in 6 bushels ?
many bushels in 16 pecks ? In 32 ?



= 1

= 36 = 1.

In 5 ? In 8 ?
In 32 ? In 64 ?
In 8? In 12? How
In 40?



4. How many bushels in 2 chaldrons ? In 3 ? In 4 ?

NOTE. The standard bushel of the United States is the Win-
chester bushel of England. It is a circular measure, 18 inches in
diameter and 8 inches deep, and contains 2150s cubic inches, nearly.

2. A gallon, dry measure, contains 268 cubic inches.



EXAMPLES.



1. How many quarts are
there in 65c7i. 206w. 3pk.

Iqt. ? OPERATION.

5c/i. 206w. Bpk. *lqt.
36


2. How many chaldrons,
&c., in 75551 quarts?

OPERATION.

8)75551


390
19T


4)9443 Iqt.
36)2360 Zplc.


2360
4


65 206w.


9443

8


Ans 65cA 20ta 3 Ic 7 t


75551 quarts.





113. What articles are measured by dry measure? What are its
denominations? Repeat the table. What J3 the standard bushel?
What arc the contents of a gallon?



110 REDUCTION OF

3. In 312 bushels, how many pints ?

4. In 5 chaldrons 31 bushels, how many pecks ?

5. In 17408 pints, how many bushels?

6. In 4220 pints, how many chaldrons ?

AVOIRDUPOIS WEIGHT.

114. By this weight all coarse articles are weighed, such
as hay, grain, chandlers' wares, and all metals except gold
and silver.

TABLE.

16 drams, dr. make 1 ounce, marked oz.

16 ounces 1 pound, lb.

25 pounds 1 quarter, - qr.

4 quarters - - 1 hundred weight, cwt.

20 hundred weight 1 ton, - T.

qr. cwt. T.



dr.


oz.


lb.


16


= 1




256


= 16


= 1


6400


= 400


= 25


25600


= 1600


= 100



= 4 =1

512000 = 32000 = 2000 = 80 = 20 = 1

NOTES. 1. The standard avoirdupois pound is the weight of
27.7015 cubic inches of distilled water.

2. By the old method of weighing, adopted from the English
system, 112 pounds were reckoned for a hundred weight. But now,
the laws of most of the States, as well as general usage, fix the
hundred weight at 100 pounds.

3. The units of the scale, in passing from drams to ounces, are
16 ; from ounces to pounds, 16 ; from pounds to quarters, 25 ;
from quarters to hundreds, 4 ; and from hundreds to tons, 20.

1. In 2oz., how many drams ? In 3 ? In 4 ? In 5.

2. In 4/6., how many ounces ? In 3 how many ? In 2 ?

3. In Qqr., how many hundred weight ? In bqr. ?

4. In Scwt., how many quarters ? How many in cwt. ?

5. In 60 hundred weight, how many tons ? In 80 ?



114. For what is avoirdupois weight used ? How is the table to be
read ? How can you determine, from the second table, the value of
any unit in units of the lower denominations ?



DENOMINATE NUMBERS.



Ill



EXAMPLES.



1. How many pounds are
there in 15T. Scurf. 3qr. '
15/6. ?

OPERATION.

15 T. Scwt. Sqr. 15/6.
20



308 cwtt
4



1235 qr.

25

~6l80 5 /6. added.
2471 1 ten added.
30890 Ib.



2. In 30890 pounds, how
many tons ?

OPERATION.

25)30890
4)1235gr. 15/6.
. Zqr.
Scwt.



Ans. 15 T. 8cut. 3qr. 15/6.



3. In 5T. Scurf. 3#r. 24/6. 13oz. 14dr., how many drams ?

4. In 28 T. 4curf. Iqr. 21/6., how many ounces?

5. In 2790366 drams, how many tons?

6. In 903136 ounces, how many tons?

7. In 3124446 drams, how many tons?

8. In 93 T. 13cwrf. 3qr. 8/6., how many ounces?

9. In 108910592 drams, how many tons ?

10. What will be the cost of 11 T. 17curf. Sqr. 24/6. of hay
at half a cent a pound ? How much would that be a ton ?

11. What is the cost of 2T. 13cw;/. 3?r. 21/6. of beef at
8 cents a pound ? How much would that be a ton ?

TROT WEIGHT.

115. Gold, silver, jewels, and liquors, are weighed by
Troy weight.

TABLE.

24 grains, gr. make 1 pennyweight, marked pwt.
20 pennyweights - 1 ounce - - - oz.
12 ounces - 1 pound - - Ib.



gr.
24

480
5760



pwt.
= 1
= 20
= 240



oz.

i

= 12



Ib.



1.



112 REDUCTION OF

NOTES. 1. The standard Troy pound is the weight of 22.794377
cubic inches of distilled water. It is less than the pound avoirdupois.

2. The units of the scale, in passing from grains to penny-
weights, are 24 ; from pennyweights to ounces, 20 ; and from
ounces to pounds, 12.

1. How many grains in 2 pennyweights ? In 3 ? In 4 ?

2. How many pennyweights in 48 grains ? In 72 ?

3. How many ounces in 40 pennyweights ? In 60 ?

4. How many ounces in 4 pounds ? In 12 ? In 9? In 7 ?

5. How many pounds in 24 ounces ? In 36 ?" In 96 ?



EXAMPLES.



1. How many grains are
there in 16/6. lloz. Ibpwt.



OPERATION.

16/6. lloz. 15pwt. 17or.
12

203 ounces.
20

4075 pennyweights
24



97817 grains.



2. In 97817 grains, how
many pounds ?



OPERATION.



24)97817

20)4075 pwt. 17or.

12) 203 oz. 15pwt.

16/6. lloz.



Ans. 16/6. lloz. I5pwt. 11 gr.



3. In 25/6. 9oz. 20or., how many grains ?

4. In 6490 grains, how many pounds ?

5. In 148340 grains, how many pounds ?

6. In 117/6. 9oz. Ibpwt. ISgr., how many grains ?

7. In 8794pio/., how many pounds ?

8. In 6/6. 9oz. 21grr., how many grains ?

9. In 1/6. loz. Wpivt. 16#?\, how many grains t

10. A jewel weighing 2oz. \pwt. 18</r., is sold for half a
dollar a grain : what is its value ?

Notes. 1. What is the standard avoirdupois pound ?

2. What is a hundred weight by the English method? What is a
hundred weight by the United States method ?

'.>. Name the units of the scale in passing from one denomination to
another.

115. What articles are weighed bv Troy weight ? What arc its de-
nominations? Repeat the table? What is the standard Troy pound ?
What arc the units of the scale, in passing from one unit to another ?



DENOMINATE NUMBERS.



113



APOTHECARIES' WEIGHT.

110. This weight is used by apothecaries and physicians
in mixing their medicines. But medicines are generally sold,
in the quantity, by avoirdupois weight

TABLE.

20 grains, gr. make 1 scruple, marked 3.

3 scruples - - 1 dram, - - - 3

8 drams - - - 1 ounce, - - - | .

12 ounces- - - 1 pound, - - - fi>.



gr.

20
60

480
5760



3
1

3
24

288



.1
8
96



I



__

= 12



= 1



NOTES. 1. The pound and ounces are the same as the pound
and ounce in Troy weight.

2. The units of the scale, in passing from grains to scruples,
are 20 ; in passing from scruples to drams, 3 ; from drams to
ounces, 8 ; and from ounces to pounds, 12.

1. How many grains in 2 scruples ? In 3 ? In 4 ? In 6 ?

2. How many scruples in 4 drams ? In 7 drams ? In 5 ?

3. How many drams hi 5 ounces ? How many ounces in
32 drams ?



EXAMPLES.



1. How many grains in
> 8 63 23



OPERATION.

9fi> 8 3 63
12



23



116 ounces.
8

9d4 scruples.
_3

2804 drams.
20

56092 grains.



2. In 56092 grains, how
many pounds ?



OPERATION.

20)56092

3)28043
~8)9343



23

63

81



Am. 9fi> 8 | 63 23



REDUCTION OF



3. In 27 ft> 9 63 13, bow many scruples ?

4. In 94ft) 11 | 13, how many drams ?

5. 8011 scruples, how many pounds?

6. In 9113 drams, how many pounds ?

7. How many grains in 12ft> 9 73 23

8. In 73918 grains, how many pounds?



MEASURE OF TIME.

117. TIME is a part of duration. The time in which the
earth revolves on its axis is called a day. The time in which
it goes round the sun is 365 days and 6 hours, and is called a
year. Time is divided into parts according to the following



TABLE.



60 seconds, sec.
60 minutes -
24 hours -

7 days

4 weeks -
13 wo. Ida. and 6/irs. ;

or 365 da. Qhr.
12 calendar months -



sec.
60

3600
86400
604800



m.
= 1

= 60
1440

= 10080



nak


e 1 minute, marked
1 hour,
1 day,
1 week,
1 month,


m.
hr.
da.
wk.
mo.


j-


1 Julian year,


yr.


-


1 year,


yr.




hr. da. wk.




__


1







24 = 1







168 =7 =1





yr.



31557600 = 525960 = 8766 = 365J =52 =1

NOTES. 1. The years are numbered from the beginning of the
Christian Era. The year is divided into 12 calendar months,
numbered from January : the dtays are numbered from the begin-
ning of the month : hours from 12 at night and 12 at noon.



. 31

- 31
. 30

- 31

. 30

. 31



Names.
January,- -
February, -
March, - -
April, - - -
May, - . .
June - - -


No.
- 1st.
- 2d.
- 3d.
- 4th.
- 5th.
. 6th.


No. i


lays.
31
28
31
30
01
30


Names.
July, - - -
August, - -
September, -
October, - -
November, -
December, -


No.
. 7th.
- 8th.
- 9th.
- 10th.
- llth.
- 12th.



DENOMINATE NUMBERS. 115

2. The leogth of the tropical year is 365<J. 57ir. 48m. 4Ssec.
nearly ; but in the examples we shall regard it as 365d. 6/w.

3. Since the length of the year is 365 days and 6 hours, the odd
G hours, by accumulating for 4 years, make 1 day, so that every
fourth year contains 366 days. This is called Bissextile or Leap
Year. The leap years are exactly divisible by 4: 1872, 1876, 1880,
are leap years.

4. The additional day, when it occurs, is added to the month of
February, BO that this month has 29 days in the leap year.

Thirty days hath September,
April, June, and November ;
All the rest have thirty-one,
Excepting February, twenty-eight alone.

1. How many seconds in 4 minutes ? How many in 6 ?

2. How many hours in 3 days ? How many in 5 ? In 8 ?

3. How many days in 6 weeks ? In 8, how many ?

4. How many hours in 1 week ? How many weeks in 42da. ?



EXAMPLES.



1. How many seconds in
Qhr. ?



OPERATION.



365da. 6/ir.
24

1466
730



2. How many days, &c.
in 31557600 seconds?

OPERATION.

60)31557600
60)525960



24)8766



365 6/ir.
Ans. 365tfa. Qhr.



8766
60

525960x60 = 31557600 sec.

3. If the length of the year were 365da. 23/ir. 57m. 39sec.,
how many seconds would there be in 12 years?

4. In 126230400 seconds, how many years of 365 days?

5. In 756952018 seconds, how many years of 365 days ?

117. What are the denominations of time? How long is a year?
How many days in a common year? How many days in a Leap year?
How many calendar months in a year ? Name them, and the number
of days in each. How many days has Februarv in the leap year ? How
do you remember which of the months have 30 days, and which 31 ?



116 REDUCTION OF

6. In 285290205 seconds, how many years of 365da. 6Ar.
each?

7. How many hours in any year from the 31st day of March
to the 1st day of January following, neither day named being
counted ?

CIRCULAE MEASURE.

118. Circular measure is used in estimating latitude and
longitude, and also in measuring the motions of the heavenly
bodies.

The circumference of every circle is supposed to be divided
into 360 equal parts, called degrees. Each degree is divided
into 60 minutes, and each minute into 60 seconds.

TABLE.

60 seconds' make 1 minute, marked '.

60 minutes 1 degree, - - .

30 degrees - 1 sign s.

12 signs or 360 - 1 circle c.



60 = 1

3600 =60 =1

108000 = 1800 =30 =1

1296000 = 21600 =360 =12 =1

1. How many seconds in 3 minutes ? In 4 ? In 5 ?

2. How many minutes in 6 degrees ? In 4 ? In 5 ?

3. How many degrees in 4 signs ? In 6 ? In 7 ? In 8 ?

4. How many degrees in 240 minutes ? In 720 ? How
many signs in 90 ? In 150 ? In 180 ?

EXAMPLES.

1. In 5s. 29 25', how many minutes ?

2. In 2 circles, how many seconds ?

3. In 27894 seconds, how many degrees, &c. ?

4. In 32295 minutes, how many circles, &c. ?

5. In 3 circles 16 20', how many seconds :

6. In 8s. 16 25", how many seconds ?

7. In 8589 seconds, how many degrees, &c. ?



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