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It will be perceived from above that the mantissa remains unaltered so long as the numbers consist of the same significant figures : change the numbers and the mantissa must also change. Examples, No.

Log. 2516

3.400711 303.3

2:481872 6.561

0.816970

1.924641 •8407

9.924641 The reverse of the foregoing rule holds good in every particular, i. e. having sought in the the tables of logarithms for the number corresponding to the given mantissa, the index will determine the number of digits in the integral part. Examples, Log.

No. 3.892873

7814 2.954435

900.4 0.620968

4.178 1.817631

.6571 or 9.817631

e.

3

or 9:176091}

0015

3

Examples for Practice. 1. Required the logarithm of the following numbers,

6754 7200 43710 39906 400000

•1463 .00647 3.874 18.006 .0046 2. Find the number corresponding to the following

logarithms - 0.768432 0.821567 2.374900 1.610432 4.000710

1.874216 1.914000 3.100300 3.214797 5:001476 3. Find the log. sine of 47° 30' 52" 170° 30' 39"

1° 49' 47"
72 4 25
110 11 18

1 0 40
Find the log co-sine of
36 7 21
88 40 56

88 59 19
20 8 40
30 0 50

108 40 6
Find the log tangent of
22 20 11

1 8 7

52 10 46 37 941

1 2 18

114 9 30 4 Find the log co-tangent of 38 50 19

58 43 37

71 43 6
64 10 40
9 8 39

7
Find the log secant of
20 30 15

45 10 19

71 43 6
29 11 40
101 8 7

38 7 4
Find the log co-secant of
45 8 29

70 30 24

141 16 51 127 30 40

60 11 9

16 0 20 5 Find the arc to the log, sine of 9.180641 9.990640 8.462167

8.846217 co-sine of 9.344178 9.983862 9.876419

8.967391 tangent of 9.642876 10.846215

9.846175 10.060431

co-tangent of
9.742691
10.876432
9.374611

8.460000
secant of
10.034687 10.090188 11:546718 11 .200000

CO-secant of 10.109761 10.061462 11.467931 11:000873 6. Multiply 4 by 75 by logs. 7. Multiply 75 by 60 by logs. 8. Multiply 701 by 9 by logs. 9. Multiply 1074 by 2 by logs.

10. Multiply 7000 by 1 by logs.
11. Multiply 476 by 682 by logs.
12. Multiply -3746 by .6168 by logs and decimals.
13. Find the product of 38, 1•74, 96, and •0756, by logs
14. Find the product of 376, 0069, and 1:476 by logs.
15. Find the product of 2:4, '008, .62 and 3.1.
16. Divide 66 by 3 by logs.
17. Divide 777 by 11 by logs.
18. Divide 1728 by 144 by logs.
19. Divide 1000 by 1000 by logs.
20. Divide 1010 by 101 by logs.
21. Divide 87469 by 364 by logs.

Divide 37 by .02 by logs. and decimals.
23. Divide 76 by 874 by logs.
24. Divide 10 by 5.86 by logs. and decimals.
25. Divide 6748 by .00763 by logs.
26. Divide •34761 by 2674 by logs and decimals.

27. Required the square of 46, of 94, of •163 and of ·0075 by logs.

28. Required the cube of 47, of 63, of 109 and of 00861 by logs.

29. Required the square root of 4796, of 746937 and of •6470, by logs.

30. Required the cube root of 36472, of 62154 and of -7564 by logs.

31. What is the cost of 243 yards at 9s. 3 d. per yard, by logs and decimals.

32. What is the cost of 3 tons 2 cwt. 3 qrs. at 4s. 6d. for 7lbs. by logs.

33. If 100 yards cost £ 70. 158. what does 1 foot cost at the same rate ?

34. If j of a lb. cost 4s. 8}d. what will 27 Polbs. cost ?

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P.M. I take my departure from a point of

land, in Lat. 40° 29'N. Long. 124° 32'W bearing by compass E. S. distant 17 miles.

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8

DAYS WORKS.

H.K.

1
Courses.

Lee 10

Winds.

way. 1 2 4 4 W.by S: S. by W. 0 3 5 6 4 5 6 S.E. by S. S.W. by S. I 5 6 6 6 76 7 8 7 6 S.S.E. S.W. 1 9 7 4 10 6 | 4 11 12 7

7 S.W. by W. S.E. 各 2 7 3 70 4 | 7 4 5 66 6 6 0S.S.W.W. E. by N. 0 7 6 8 5 9 65 10 6 N.W.W.

0 11 6 12 7

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Remarks.

P.M. I take my departure from a point of land in Lat. 25° 39's. Long 45° 2' E. bearing by compass N.W. by N.IN. distant 21 miles.

A.M.

A current set the ship S W.bys. by com

pass, at the rate of 4 miles an hour, during the last 8 hours.

Variation 2 pts. W.

Remarks.

P.M. I take my departure from a point

of land, bearing by compass S.W. distance 18 miles, in Lat 37°35'S. Long. 150° 5'E.

A.M.

A current set the ship 18 miles S. by W. by compass

Variation & pts E.

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