NOTE. This correction will not be the same, when we correct backwards in this case, as it was in VIII. Because the error back

As the Corrections are proportional to t2 and (t1), it is evident that if the time t is less than 12h., t1 will be greater; and vice versa when t is greater than 12h., t1 will be less. Therefore it will be preferable to correct declination from the nearest noon, as the error will be the less: whereas this was indifferent in the case of the Old Diffs. for 1h. (seo V. Note).

XI.-COMPARISON BETWEEN THE ERRORS IN THE OLD AND NEW.

3 to da
24

In the Old method, the calculation was all but universally instructed to be made for t that is onwards; consequently the errors being for Old and for New, it is evident that the New is more correct when t is less than 12h., but the Old has the preference when t is greater than 12h.

t t1 d2
24

If, however, we adopt the method of always correcting from the nearest noon, it is evident that the New is always preferable: because 1 tt1 da

if t is less than 12h., the New error

1 t 28 2
24

is less than Old

24

SECOND COROLLARY.

By IX. Corol., it was proved that the max. error of the Old method was 3 de.

And it is evident that the New

1 t2 d
24

will increase as t increases;

which at its max. has been fixed at 12h.; because, if above 12h. we

would calculate with t1. Hence max. error of New

32 viz., the same as the Old.

REMARK.

=

× 144 da

==

24

Hence (when the approximate method is used), it follows that the utmost advantage gained by using the new instead of the old 'diffs. for 1 h." being less than 2" (in 1870, d, is at its maximum in December and 1.18", therefore, 1.77). To prevent confusion to practical navigators, would it not have been preferable to have retained the old " diffs. for 1 h." especially as the calculation for 2nd diffs. is equally easy in both methods (see III. and IV.).

XII.-ON FINDING THE LATITUDE FROM A MERIDIAN ALTITUDE.

This Problem (to use a strong and rough phrase) may be truly said to have been more shockingly murdered than any other Problem in all navigation.

1st. In the extensively used " "Epitome on Navigation" by Norie, as well as in others, the following Rule is given :If Long. W., add correction if Declination be increasing.

This Rule, however, is erroneous twice a year, viz., at the Solstices, when the Declination decreases from the greatest declination, whether we reckon forwards or backwards. Whereas the Rule assumes that a declination if increasing forwards, must decrease backwards; and vice versa.

2nd. When the old "diffs. for 1 h." were used, a candidate at the Marine Board Examination would have been plucked and fined, if he corrected the Declination for Longitude by taking the declination for ship's date, and correcting by means of the "diff. for 1 h." as found opposite to that day. Whereas now he would be liable to the same penalties if he did not use that "diff." (which is un

2

1

doubtedly the correct way). Because if we used ▲ instead of A (which we ought not to do) just the same as in the case of the old "diffs." we used d, and not d2, we would incur a much larger error. For in this case we are correcting backwards for t1as the } (t1)2 de and

long. is E., and therefore D

24

(because A21

we are reckoning backwards and and- de, instead of t1, A, and d2 in

1

24.

Consequently D = D2 - t1 A1 +ť1 d2

But DDA, approximately; therefore the correction

of the approximate method is t1 d2

value of (¿1) h is 12 h (or 180°), the maximum is (12 — 122

de 9 d. This on 22nd December, 1870, is 10" 6 S, because da 1.18 S, reckoning backwards.

3rd, Therefore the correct Rule for finding the nearest approximation is as follows:

RULE. Tako the declination also "diff. for 1h" for given ship's date; then in W. Long. correct as for t (IV.); but in E. Long. correct as for t1(V.). This will prevent an error of 1⁄2 d, (XI.).

XIII.-CORRECTING LOG. SINES, ETC., FOR SECOND DIFFERENCES.

The differences are given in Mathematical Tables for 100", as between the Sine for the given deg. and min. (call this D1), and for (D2 — D,) × 100 1' more (call this D2); and the diff. is=

2

Let the Sine of D° M' S be required.
Then it is easily deduced from III. that :

Sine D° M′ S = Sine D° M2 + 15 (d, — (30—15). d:)

One practical conclusion from the preceding is, that if we correct Declinations from the nearest noon, the greatest error by the approximate method will be 382; and this method should therefore bo always adopted,

It may be observed that after correcting approximately, if we wish to correct for 2nd differences, we must apply to the approximate Declination the correction of ▲, for 2nd diff. as found in III. Rule 3 after this is multiplied by t.

1

STORM SIGNALS.

Meteorological Office, 116, Victoria Street,
London, S.W., December 12th, 1871.

To the Editors of the Nautical Magazine.

Dear Sirs,—I send for your information extracts from two notices which have lately been received at this office, relating to telegraphic intelligence of storms.

The signals exhibited at the Scaw are in connection with the Meteorological Institute at Christiania, and only came into operation this month, but those issued by the Sydney Observator y, as probably you are aware, have been in operation for several years, on the coast of New South Wales.

I am, yours faithfully,

ROBERT H. SCOTT, Director.

STORM SIGNALS AT THE SCAW.

In connection with storm warnings, communicated by the Meteorological Institute at Christiania, storm signals will be shown from the signal station on the Scaw from the 1st of December, 1871, and until further notice, whenever a gale is or may be expected in the course of one, or, at the most, of two days, in the North Sea or Skagerrack.

Most gales begin, in the waters referred to, with the wind at S.; but when a gale blows from the S. we may always be prepared for its veering to W. Some gales, including very heavy ones, set in when the wind has veered from N.W. to N.

For signals there will be employed a drum and a cone, which will be hoisted to the gaff at the signal staff, and will, as a rule, bo kept up thirty-six hours. The drum above and the cone below, with its point downwards, indicates a S. gale; the drum below and

doubtedly the correct way). Because if we used ▲ instead of A (which we ought not to do) just the same as in the case of the old "diffs." we used d, and not de, we would incur a much larger error. For in this case we are correcting backwards for t'as the } (t1) 2 E z

long. is E., and therefore D

D. - A

2

24

and

formulas V. and I. 7).

Consequently D = D2 — t1 A1+ t1 d2 24.

1

in

(12 - 3 x 12°)

value of (t1) h is 12 h (or 180°), the maximum is (12

24

9 d. This on 22nd December, 1870, is 10" 6 S, because 21.18 S, reckoning backwards.

3rd, Therefore the correct Rule for finding the nearest approximation is as follows:

RULE. Take the declination also "diff. for 1h" for given ship's date; then in W. Long. correct as for t (IV.); but in E. Long. correct as for t1(V.). This will prevent an error of 1⁄2 d, (XI.).

XIII.-CORRECTING LOG. SINES, ETC., FOR SECOND DIFFERENCES.

The differences are given in Mathematical Tables for 100", as between the Sine for the given deg. and min. (call this D,), and for (D2 - D) × 100 1' more (call this D2); and the diff. is =

Similarly for d., then d. d1 = d2.

60

(30"-S). d2

1

60

One practical conclusion from the preceding is, that if we correct Declinations from the nearest noon, the greatest error by the approximate method will be 3d2; and this method should therefore be always adopted,