observation, and see to what point the seconds-hand has reached; when, of course, the time of that altitude will be the number of minutes, plus the seconds travelled over by the seconds-hand. Should this last have made more than one entire revolution while the observer was occupied in the observation, he will easily be conscious of it, and take it into the account.

Or, if convenient, you can employ another person to read the chronometer while you take the altitudes; you prepare,—he at the chronometer and you at the side of the vessel to observe; when ready, you say "look out," as a caution; immediately that you have taken the altitude you say "stop"; at that moment the chronometer is read, and then noted down on paper by the side of the altitude which you also give; and so on through 3, 5, or 7 observations; but both observer and chronometer-reader must be sharp and instantaneous in what they do.

To correct the Sun's Declination.—For the chronometer time, take the declination from p. II. of the Naut. Alm., entering for the given month and day; also take "Var. in 1 h." from p. I. for same date; multiply the "Var. in 1 h." by the Green. time (i.e. by the hours, with the minutes converted into tenths of an hour); mark off from the right of the product as many decimal places as there are decimals in the "Var." and Green. time together. The number to the left of the decimal point will be seconds, which must be divided by 60 (if more than 60) to convert into minutes and seconds; this is the correction of Declination.

Rule to apply the correction :

Declination increasing, add correction to Declination.
Declination decreasing, subtract correction from
Declination.

But note, the correction is subtractive on the day in March when Declination changes from S. to N., also on the day in September when Declination changes from N. to S.; at either date, if correction is greater than Declination, subtract the Declination from the correction; then, in March the remainder will be the Dec. N., but in September the remainder will be the Dec. S.

But the Declination will always be more accurate when corrected from the noon nearest to the Green. time. In this case, when the hours of Green. date are less than 12, the Method already given on p. 79 applies in every respect.

But when the hours of Green. date exceed 12, subtract the time from 24 hours; take out the Dec. as well as the Var. in 1 h. for the noon in advance of the Green. date; multiply this "Var. in 1 h." by the time short of 24 hours, and the product will be the correction; thus, if the time is 8d. 18h. 42m., this is 5h. 18m. from the next noon, or noon of the 9th; hence take the Dec. and "Var. in 1 h." for the 9th; and multiply the Var. by 5-3 for the correction of the Dec. of the 9th: then—

If Dec. is increasing, subtract correction.
If Dec. is decreasing, add correction.

To correct the Equation of Time.—For the given day take the Equation from Naut. Alm. p. II. of month; also, take "Var. in 1 h." for same day from p. I. of month; multiply the "Var. in 1 h." by the houra and tenths of Green. time, mark off as many decimal places in the product as there are decimal places in the "Var." and time together. This is the correction of Equation— To be added if Equation is increasing ;

To be subtracted if Equation is decreasing.

Also, take special notice, on p. I. of Naut. Alm. of

the day, when the Equation changes; in the column it is marked by a strong dash and at top thus

add. sub.

or

sub. add.

For the Apparent Time at Ship.—Add together the true Altitude, the Latitude of the place, and the Polar Distance of the object; divide the sum by 2, for the Half-sum; and subtract the Altitude from the Halfsum, which call Remainder.

Then, add together the Log. Secant of the Latitude, the Log. Cosecant of the Polar Distance (take Secant of Declination if Pol. Dist. is greater than 90°), the Log. Cosine of the Half-sum, and the Log. Sine of the Remainder. The sum of these four Logs. (rejecting index 30) will be the Log. of the Hour-angle, that is, the time from the nearest noon, which take out in hours, minutes, and seconds.

N.B.—All Logs, should be taken out to seconds of arc, when the sum of the three arcs exceeds 165°, otherwise the seconds may be rejected. The Logs, used are— first Table V., and then Table XVIII. for the Horary Angle.

Proceed as follows when using the seconds of arc :—

Hour-angle 2h. 38m. 8.5s. Log. 9.058363

This, computed to the nearest minute of arc only, gives 2h. 38m. 16s., which would cause an error of 2' in the longitude.

I wish you to look at these Hour-angles very carefully, and to remember that the resolution of the spherical triangle determines merely the meridian distance (in time) of the sun from the nearest noon. Hence, with regard to the first, if we suppose the Ship Date to be July 23rd, P.m., we get for the Apparent Time at Ship, July 23d. 5h. 0m. 26s.: but if the Ship Date be July 23rd A.m., then the Hour-angle must be subtracted from 24 hours, and the date put 1 day back, as in the following example,—the reckoning being in astronomical time.

Apparent time, July 22d. 18 59 34

Similarly with the second Hour-angle, if we suppose the Ship Date to be October 17th, P.m., our Apparent Time at Ship is October 17d. 2h. 38m. 8s.; but for October 17th, A.m., our Apparent Time at Ship is October 16d. 21h. 21m. 52s.

It will be observed that in the calculation for finding longitude, our latitude is used, so that if our lati

tude is erroneous, so will our longitude be. The best time for making the observation is when the sun is on the prime vertical, i.e. true East or West, because an error in the latitude then produces the least effect on the hour-angle; but you can only take an altitude in this position when the latitude and declination have the same name. When these are of different names, the sun never comes to the prime vertical, and in that case you should take the altitude as early as convenient and as far from the meridian as possible; an object observed near the meridian never gives a good hour-angle.

It is far more general to make the observation in the forenoon in preference to the afternoon, for in the latter case the sea, being more or less affected by the day's sun, the refraction of the atmosphere is more precarious than it is in the forenoon.

Should you be doubtful about your latitude, having taken the altitudes and their corresponding times, you can wait until you have found your latitude at noon, carefully keeping the Dead Reckoning during the interval; so that working it back you arrive at the true latitude you were in when you took your altitudes for the time. Work these out for your longitude at that moment, and, allowing for the difference of longitude since made, prick the ship's place at noon.

Should the forenoon be too cloudy for an observation, it is customary to make it in the afternoon, but with favourable weather it would be advisable to work out the longitude at both forenoon and afternoon. Remember that when an afternoon observation is made, there is to be no subtracting from 24 hours; for we only learn the time elapsed since the preceding noon.

Latitude and Longitude by Observation is preferable to Dead Reckoning; but you should lose no opportunity of checking the chronometer while in harbour, or when