1874.-September 23rd, at 6h. Om. P.M., App. T. Ship; in lat. 22° 30'; long. 156° 45′ E. Sun's amp. by compass W. 2° N. Find the error of compass; and supposing the Variation to be 11° E.: find the Deviation.

1. 1874. January 19th, at 5h. 4m P.M., Apparent time at ship: in lat. 30° 30': long. 50° W. Sun's amplitude by compass W. 5° 38' S. Find the error of compass.

2. 1874. June 8th, at 7h. 45m. A.M., Apparent time at ship: in lat. 47°: long. 50° E. The sun's amplitude by compass

E. 45° N. Find the error of compass.

3. 1874. March 17th, at 6h A.M., App. T. ship: in lat. 13° 25': long. 129° W. Sun's amp. by compass E. 11° 15′ N. Find the error of compass; and supposing the Variation to be 5° 16' E: find the Deviation.

4. 1874. July 23rd, at 7h 39m P.M., App. T. ship: in lat. 49° 39' long. 179° 30′ E. Sun's amp. by compass W. 22° 30' N. Find the error of compass; and supposing the Variation to be 12° E: find the Deviation.

LONGITUDE BY CHRONOMETER.

When two errors are given take a look at the dates of them, and note which is the earlier of the two. Thus, if the chronometer is 3m 108 fast on 1st May, and 4m 10s. fast on 4th April; the earlier error and date will be 4m 10. fast on 4th April. Call the earlier error and date the 1st error and the 1st and the other error and date, the 2nd error and 2nd date.

date;

TO FIND THE GREENWICH DATE.-Write down the time by chronometer and under it place the 2nd error; add if slow; but subtract if fast. Under this time place the accumulated rate, add if losing, subtract if gaining.

To find the rate.-Write down the 1st error, and under it put the 2nd error :

Add the errors if one is Fast and the other slow; but

Subtract the less from the greater if both are Fast or both slow.

Reduce the result to seconds by multiplying the minutes by 60 and adding in the seconds.

Divide this sum or difference of the errors by the number of days between the 1st and 2nd dates and we have the daily rate.

To find the accumulated rate.-Multiply the daily rate by the number of days between the 2nd date and the day at ship.

To tell if the chronometer is losing or gaining:

When one error is Fast and the other Slow,

If the 1st error is Fast, and the 2nd Slow, losing, If the 1st error is Slow, and the 2nd Fast, gaining. When both errors are Slow,

If the 1st error is less than the 2nd, losing,

If the 1st error is greater than the 2nd, gaining.

When both errors are Fast,

If the 1st error is greater than the 2nd, losing,
If the 1st error is less than the 2nd, gaining.

TO CORRECT THE DECLINATION.-Take out the Declination from page 2 of the month, for the Greenwich day, and put the Declination for the following day under it.

If these Declinations are both North or both South, subtract the less from the greater; but, if one is North and the other South, add them together, and name the result the Daily Variation.

Under the Daily Variation put the hours and minutes of the Greenwich time, and take the log. of each from Table 33, Norie; these two logs added together will be the log. of the correction for Declination found in the same Table 33.

Declination increasing, add;
Decreasing, subtract.

TO FIND THE POLAR DISTANCE.-If the Latitude and corrected declination are both North, or both South, subtract the corrected declination from 90°; but, if one is North and the other South, add 90° to the corrected declination.

TO CORRECT THE EQUATION OF TIME.-Take out the Eq. of time for the Greenwich date and day following from page 2 of the month, using only minutes and seconds, and subtract the less from the greater (unless there is a line between them, if so add them together); name the result Daily Variation.

Under the Daily Variation write the hours and minutes of the Greenwich date, and take the log. of each from Table 33, Norie. The sum of these logs. is the log. of the correction found in the same table.

Equation of time increasing, add.

Equation of time decreasing, subtract the correction from the Equation for the Greenwich date.

Note.-The Decl. and Equation of time can also be corrected by the Diff. for 1 hour.

FIND THE TRUE ALTITUDE, by applying to the observed;— INDEX ERROR (+ add); (— subtract);

DIP for height of eye, Table 5, subtract;

SUN'S CORRECTION for altitude, Table 18, subtract; SEMIDIAMETER, page 2 of month, for the date, lower limb add, upper limb subtract.

Divide the sum by 2; name this Half Sum;

From the Half Sum subtract the True Altitude, and name the result Remainder.

FIND THE HOUR ANGLE.-Add together the logs. from Table 25;

Secant Latitude

Cosecant Polar distance

Cosine Half Sum.

Sine Remainder.

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10 subtracted from index of each.

The sum of these four logs., subtracting 10 from the index. is the log. of the Hour angle found in Table 31, Norie.

Polar distance greater than 90°. To find the log. Cosecant when the Polar distance exceeds 90°, take the Secant of the corrected Declination.

FIND THE APPARENT SHIP TIME.

If P.M. at ship, place the date at the head of the question before the hour angle.

If A.M. at ship, subtract the hour angle from 24h. 0m. Os, and place a day less than the date at the head of the question before the remainder.

FIND THE MEAN SHIP TIME.-To the Apparent ship time apply the corrected Equation of time as directed at the top of page 1 of the month.

FIND THE LONGITUDE.-Bring down the Greenwich date, or Greenwich mean time as it is called, under the mean ship time, and subtract the less from the greater. Turn the time into Longitude or arc by multiplying by 15, or by Table 19, Norie.

TO NAME THE LONGITUDE.-If the Greenwich time is greater than the ship time name the Long. West; but if the Greenwich time is less than the Ship time name it East; or

Greenwich time best, Longitude West.

Greenwich time least, Longitude East.

Latitude nothing.-When the Lat. is nothing, either add the corrected decl. to 90°, or subtract it from 90° to find the polar distance.

When the declination is nothing, the polar distance is 90°.

When the Lat. and corrected Decl. are both nothing, subtract the true altitude from 90°, and turn the remainder into time by Table 19, or by multiplying by 4 and dividing by 60, and the result is the hour angle.

When the polar distance exceeds 90°, to find its Cosecant, take the Secant of the corrected declination.

To find the Greenwich date when the rate is given.-To the time by chronometer apply the error, add if slow, subtract if fast; and to this time apply the accumulated rate, add if loss, subtract if gain.

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