PAPER II.

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

Seventy-four thousands six hundred and nine.

2. Add the following quantities together :

1. Write in figures :-Twenty thousands and six.

2.

Seventeen thousands four hundred and one

Add the following quantities together :

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

4. Multiply the following quantities together :

Multiply 79865073 by 12

Multiply 240076 by 8907

5. Divide as follows:

9807645 by 90

Divide 7649874272 by 3296.

RULES AND EXAMPLES FOR WORKING THE

PAPERS.

Multiplication of Numbers by common Logarithms.

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.

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.

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

1.799272 gives 62.99

2-799272 gives 629.9

3.799272 gives 6299.

and so on.

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 course. 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.

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. is the true altitude of the Sun's centre.

The result

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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