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transit, seems to be amongst the most insatiable longings and necessities of the present age. Why else is the world becoming a gigantic gridiron of railroads! And why does the electric telegraph "put a girdle round about the earth," faster than Robin Goodfellow? In furtherance of this law the mighty tide of human intercourse between the old and new worlds, must sooner or later (with the certainty of the tides in her ocean boundary) flow across Ireland, bringing wealth and influence to those who undertake the operation. If it be conducted under the flag

"Which spread its cross o'er Juda's sea,
And waved in gales of Galilee;"

if the proud old banner "which braved a thousand years the battle and the breeze," shall be seen upon the stern of the Atlantic steamers, it is all as it should be. But if our government will not effect this object and that the government of America will, then will it assuredly be said by the Irish "very pleasant art thou unto us our Brother Jonathan," open shall our arms be to receive thee.

Rosmead, Castle Town, Delvin,
April, 1851.

HERCULES ROBINSON.

* I had actually inserted charts of parts of Labrador and a map of the routes between New York and London, but I find the expense of lithographing would be more than this work would justify. I must therefore omit their publication here, and would refer the enquirer for the former to the surveys made by the Favorile, in the Hydrographical Office, at the Admiralty, and for the latter to the map which is affixed to Mr. Hemans valuable report, and I will merely subjoin the figures as given in such map.

1.

New York to Whitehaven

2.

New York to Whitehaven

3.

-Galway and London, S

860 miles.

4. New York to Liverpool

5. Whitehaven to Galway..

6.

3410 99

3100 2090

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Boston to Galway via Whitehaven......... 2600

In all cases from Whitehaven or Halifax, Cape Race first, and then Canso would be the land made, the course to New York would lie some 30 or 40 leagues to the southward of Cape Race.

From Galway to the Straits of Belleisle, the distance appears to be about 1550 miles. This line would shorten the distance to Quebec, but prolong it something to Whitehaven or Halifax.

Sketches of the land and various views as well as a map of the supposed ancient colony in Conception Bay, and also a return of the fisheries; a vocabulary of the native language; meteorological remarks during the summer, and a mineralogical report of the parts we visited; and sailing directions for the different harbours are also omitted here. If the anticipated interest in those countries shall be realized these particulars may appear in a second edition. As yet their appearance would be premature and unnecessarily expensive.

ON TRANSFORMING PLANE TO MERCATOR'S CHARTS.

The surface of the earth cannot be developed on a plane, viz. cannot be peeled off and laid out on a plane, some of the consequences of which force themselves on the notice of a practical surveyor, whenever operations are conducted on an extended scale. For instance he will observe the bearings of different places from each other, and will find that the line joining two stations does not cut the meridians at a constant angle, or in any other words, the sum of the two bearings observed, back and forward, referred to the elevated pole will always be less than two right angles, and the difference between this sum and two right angles will in the same latitude vary with the departure between the two places.

To do away with this change of bearing, in passing from one point to another, in the line joining two stations on the chart, Mercator's projection was introduced, and has the property that the straight line joining any two points on it, cuts the meridians at a constant angle. It must however be recollected that Mercator's projection is a distortion, no bearing on it corresponding to that which would be observed at the place, and differing therefrom by a quantity depending on the departure between the two places; and that places in different latitudes do not preserve their relative proportions, those towards the elevated pole appearing in larger proportions than those towards the equator,

This being premised, we will endeavour to determine

1. The amount of inclination of the meridian at two points on the earth's surface, supposed spherical, and apply it to reduce all the bearings observed to one point, in order to take the mean of all the bearings observed within the limits of the sheet.

2. The Mercatorial bearing of points from the observed bearings. 3. Apply the above results to reduce a plane chart to a Mercatorial

one.

First Let A, B be two points near each other on the earth's surface supposed spherical, P the elevated pole, P C the meridian bisecting the angle APB cutting A B in C, through which let E C F pass at right angles to P C cutting P A and PB in E and F respectively.

Let i inclination of P EA to PC

.. 2 i

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PC the complement of the middle latitude l =c
E F the departure between A and B = 2 d

.. FC d

=

From the spherical triangle PE C right angled at C we have

i

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sin d .. tan i

i

cot E tan c = sin d tan l

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B

since i and d are both very small unless I near a right angle or at places in high latitudes.

Hence the Rule.-To log distance expressed in miles add the log sine of the mean* bearing, and the log tangent of the middle latitude the sum will be the logarithm of the inclination of the two meridians expressed in minutes of a degree.

* In practice either observed bearing will suffice.

To make this clear to those who have only an acquaintance with plane Trigonometry.

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Example.-At Cape Sable station, Cat station bore N. 55° 37' 32" E., mean of 5 observations, distant 42,854 feet; at Cat station, Cape Sable station bore N. 124° 16′ 45′′ W., one observation. Lat Cape Sable 43° 23′ 40′′ N., and 6,075 feet to a mile of latitude determine the inclination of the Meridians through Cape Sable station and Cat station to each other and take the mean of the bearings.

5' 512 =

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5′ 30.7" inclination of two meridians.

Observed bearing at Cat Station N. 124° 16′ 45′′ W.

Corrections for inclin. of meridians Į

to reduce to Cape station

Cape Sable, bearing

or

(1) observation Observed bearing at Cape (5) obs.

Difference

.. Correction due to Cape, bearing

or mean of sin, bearings

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+5 30.7

N. 124° 22

15.7 W.

N.

55 37

44 E.

N. 55 37 32 E.

+12 + 2

N. 55° 37' 34" E.

Note.-The traverse table may be used to determine the departure, and then to the log departure in miles add the log tan of the middle latitude, the log inclination of meridians in minutes will result.

To determine the Mercatorial bearings from the observed true bearing.

To the observed bearing reckoning from the elevated pole, add half the inclination of the meridians at the two places, and the results will be the Mercatorial bearing.

No. 8.-VOL. XX.

3 I

Example.-Cat Station observed bearings from Cape Sable station
N. 55° 37' 34" E.

+2 45 half the inclination of the meridian.

N. 55 40 19 E. the Mercatorial bearing of the two stations.

To reduce a plane chart to one of Mercator's construction.

First prepare a sheet with a Mercator's scale, viz. with parallels of lat. and longitude comprising, the limits of the latitude and longitude of the portion of the chart to be reduced, according to the usual mode, the parallels being drawn at convenient distances and dividing the sheet into a series of oblongs.

D

E

B

b

Select some of the main stations as A, B, C, D, E, &c., in the figure, A, being some where in the middle of the plane chart, determine the differences of latitude and longitude between A, and each of these points by means of the triangulation, and reducing all the astronomical observations to A, mean the results, and thus determine its latitude and longitude.

Through A draw the meridian NA S; N being the north supposed elevated pole, and draw the straight line F A G perpendicular thereto and through B and C the extreme east and west stations on the sheet draw the meridians Bb G, c FC inclined to NAS with their respective inclinations, and cutting F A G in G and F respectively. From A draw A b inclined to A G towards the elevated pole, at an angle G Ab equal to half the inclination of Bb G to NAS and in like manner draw A c inclined to A F towards the elevated pole at an angle c A F equal to half the inclination of C F c to NA S. Divide Ab, into any convenient number of equal parts

such that each part be equal to two or three miles; suppose this to be four equal parts; through each of the points of division draw meridians duly inclined to NAS and divide each of the parts 1, 2, 3, of these meridians intercepted between Ab and A G into four equal parts respectively, and reckoning from A, and on A G let 1 be the first division on the first intercepted meridian, 2 the second division on the second, and 3 the third on the third, join A 1, 12, 23, 3b, the polygon thus described will differ very slightly from the curve of equal latitude through A; the nearer the meridians 1, 2, 3, are taken, the nearer will be the agreement. In like manner the polygon of equal latitude through A and c may be drawn, and we shall obtain a line through the chart differing from the curve of equal latitude through A as slightly as we please; by referring to the longitudes of A, B, and C, sub-divide this line so that the meridians drawn through the points of division correspond to the parallels drawn on the Mercator's chart, and through them draw the meridians with their respective inclinations to NAS. Take two stations on the extreme north and south of the sheet respectively and by means of lines of equal latitude through them refer them to a common meridian, sub-divide the distance between the points in which these lines intersect the meridian, and thus obtain a scale of latitude for the plane chart, from the points in which each merridian is intersected by the line of equal latitude through A, set off on the meridians respectively, the distances corresponding to the difference of latitude of A, and each parallel of latitude already drawn on the Mercator's sheet, and by joining the points we shall obtain curves at polygons of equal latitude corresponding to the parallels on the Mercator's sheet, and shall thus obtain a trapezium corresponding to each oblong on the Mercator's sheet, and which trapezium will differ less and less from an oblong the smaller they are taken.

The portion of the plane chart included in each trapezium must by means of proportional compasses be reduced into the corresponding oblong on the Mercator's sheet, and thus from the plane chart one constructed on Mercator's principle will be reduced.

P. F. SHORTLAND, Commander.
H.M.S. Columbia, Halifax.

DISCIPLINE IN MERCHANT SHIPS.

SIR.-Perhaps the following statement relative to the inefficiency of the laws to enforce discipline in the Merchant Service, may not be unworthy a page in your valuable publication.

Being on a passage from London to Shanghai, I was obliged from stress of weather, to put into the port of Singapore for repairs. It was my misfortune to have on board two very refractory characters, the cook and one of the seamen. On engaging the crew in London, I particularly told the cook that he would be expected to assist when all hands were called to shorten sail, and also to attend the fore-sheet in working ship, to which he very

This curve is a circle.

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