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PAPER II.

1. Write in figures :-Nine thousands and four.

Seventy-four thousands six hundred

and nine.
Add the following quantities together :-
47625

3645604
52476

764 23651

17045 69843

3987 12345

476249

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4. Multiply the following quantities together :

Multiply 4679842 by 7 4769876 by 80

Multiply 769876 by 2697 5. Divide as follows:

Divide 62476243 by 4762

PAPER III.
Write in figures :--Twenty thousands and six.

Seventeen thousands four hundred

1.

and one

2. Add the following quantities together :327698

987624 987246

12476 213762

764 594769

3986 123456

476041

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4. Multiply the following quantities together :

Multiply 987654 by 12 2798643 by 240

Multiply 7500032 by 9007 5. Divide as follows:

Divide 1276498 by 736

PAPER IV.

1. Write in figures:-One thousand eight hundred and sixty-six.

Three millions two hundred and five

thousands and ten. 2. Add the following quantities together :27698762

9876543 714987

729865 6329846

3145796 7698

237954 32469379

6398679

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4. Multiply the following quantities together :

Multiply 79865073 by 12 9807645 by 90

Multiply 240076 by 8907 5. Divide as follows:

Divide 7649874272 by 3296.

RULES AND EXAMPLES FOR WORKING THE

PAPERS.

Multiplication of Numbers by common Logarithme.

Take out the log. opposite to each of the given numbers, add them together, and seek the corresponding one in your table of logs., opposite to this you have the required number. EXAMPLE.--Multiply 36 by 105, by common logs. 36..

1.556302 .2.021189

105.

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Division of Numbers by common Logarithms. Take out the logs. the same as in Multiplication, but subtract and find the number as before. EXAMPLE.—Divide 1860 by 25, by common logs. 1860...

3.269513 .1.397940

25.

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The index to be placed before your log. is always one figure less than the number of given figures; for example, The index of 8 (or one figure) is 0

56 (or two figures) is 1 329 (or three figures) is 2 8654 (or four figures) is 3

and so on. In taking out the number corresponding to a given log., the opposite rule is used; for example,

0.799272 gives 6.299
1799272 gives 62.99
2:799272 gives 629.9
3.799272 gives 6299.

and so on.

course.

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DAYS' WORKS. Each course must be corrected for variation and lee-way; Easterly variation allowed to the right, and Westerly, to the left

. The opposite point must always be taken in the departure

After finding the d.lat. and dep. made good, find the latitude and longitude of the ship thus: to the given latitude apply the d.lat., adding if the same names, subtracting if different names; the result will be the latitude of the ship.

With the nearest degree of latitude as course in Table II.) and dep. in lat. column, get d.long, in the distance column opposite, which applied to the longitude left, adding if the same names, and subtracting if different names, will give the longitude of the ship. Then in the same table seek where the d.lat. and dep. are opposite to each other; when found, the degrees from the top when d.lat. is greatest will give the course ; and from the bottom when dep. is greatest, the distance will be opposite to the d.lat. and dep. The course in degrees must be named the same as the d.lat. and dep.

EXAMPLE

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1. Convert the longitude into time.

2. Apply it to the apparent time at ship; adding if the longitude is W., and subtracting if E. for the Greenwich time.

3. Take the declination out of the Nautical Almanac from the first page of the month given and for the Greenwich day, and at the same time take out the “ diff. for 1 hour."

4. Multiply this “diff. for 1 hour" by the hours in the Greenwich time and as many 6's as there are in the minutes for tenths of an hour, cut off as many figures from the right to left of the product as there are decimals.

The figures remaining are the seconds of the correction. Divide by 60 to bring them to minutes.

5. If the declination is greater next day, add the correction ; but if less, subtract it. The result is the corrected declination.

6. Correct the observed altitude for index error, if any, and add the correction for altitude from Table IX. The result is the true altitude of the Sun's centre.

7. Subtract the true alt. from 90° 00'00”, for the Zenith distance, naming it always the opposite to the bearing.

8. To the Zenith distance apply the corrected declination; adding if the Z. dist. and dec. are the same names, and subtracting if different names. The result is the latitude, and is of the same name as the greater.

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