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When a portion of open country is occupied by trees not inclosed by any definite boundary, it should be sketched from its position in reference to one or more of the smaller secondary triangles. Hills and other inequalities should be sketched in a similar manner.

The acreage may be found from the plot, but if a more accurate method be insisted on, every triangle may be calculated from the field-book, which, by the by, may be kept as in the preceding survey.

In a large trigonometrical survey, the elevation of the different hills, lakes, &c. ought to be registered, with a view to ascertain their actual heights above the level of the sea, and also to serve as a guide to the engineer in the selection of the best trial lines for canals and roads of every description. A series of well arranged levels of a country must prove useful to land proprietors, as pointing out the lines of drainage and irrigation of any portion of their property.

There are three methods by which the solution of the primary spherical triangles may be effected :

Legendre's method effects the calculation by reducing each angle by one-third of what is called the spherical

excess.

They may be calculated as rectilinear triangles with the angles of the chords.

And lastly, they may be treated as spherical triangles with the corrected spherical angles.

During the entire of the survey of England, the spherical excess was computed for two purposes, namely, to correct the observations, and to diminish the observed angles by the amount of the excess. One of the large

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triangles formed in Dorsetshire had the sum of its three angles less than 180° by 0".5, while the spherical excess amounted to 1".29, indicating an error in the observation of 1".79. Now, each of the angles increased by onethird of this error is corrected as a spherical triangle. And again, one-third of the spherical excess deducted from each of these corrected spherical angles, reduces them to the angles of a plane triangle, the sum of whose angles amounts to 180°.

Topographical Scales.

Topographical maps are sometimes drawn upon a scale of 1000 of the extent of the country which it represents. Maps laid down to this scale show any considerable hill, stream, town, and village, the main roads, large lakes, and woods. A map laid down to a scale of, which is about 1 inch to 3 of a mile, exhibits every hill having an altitude of 100 feet, and a horizontal extent of 800 feet; of every stream having a length of course amounting to 800 feet; of every pond having a diameter of 100 feet; of all enclosures extending from 200 to 300 feet; of every town and village; and of large isolated buildings. When the country to be represented is very extensive, this last scale is very suitable. The scale upon which every map and plan are drawn, must vary according to the extent or minuteness of the objects which it is required to represent, and the particular purpose for which they are intended.

The Ordnance Survey of Ireland is plotted to a

scale of 6 inches to 1 mile, which is about 10.00 of the extent.

In large topographical surveys, requiring several survey sheets, it would be advisable, in order to carry on the work from one sheet to another, to have three or four drawing boards made to fit the same stand. Never leave less than an inch margin upon your board, upon which may be determined any conspicuous objects which properly belongs to the adjoining sheets. The distances of such objects, as well as of others within the marginal line of the survey sheet, from one another, should be accurately transferred to the adjoining sheet upon another board.

It very often happens that a part of the ground can be more easily seen from that which comes into the adjoining sheet, upon the margin of which, the situation of such objects may be marked, and afterwards transferred to their true places on the plan. Hence it appears, that the margin is almost indispensable when the survey requires several sheets; as it would be very difficult, without it, to carry on the work from one sheet to the other.

When two or more points are given upon each survey sheet, then instead of the work being carried over from one marginal line of one sheet to the corresponding one of another, as above, it must be commenced in each sheet from these points.

To Survey with the Circumferentor.

The circumferentor consists of a brass circle and

index, all of one piece; the diameter of the circle is generally about 7 inches; the index about 14 inches long, and an inch and a half broad. On the circle is a card or compass, divided into 360 degrees; the meridian line of which answers to the middle of the breadth of the index. A brass ring is soldered on the limb, or circumference of the circle, which, with another fitted with a glass, forms a kind of box for the needle, which is suspended on a pivot in the centre of the circle. It has also two sights, which are screwed on, and slide up and down the index; as also a spangle and socket, screwed on the underside of the circle, to receive the head of the three-legged staff.

This instrument is in very general use among surveyors. Its general adoption is owing perhaps to its low price, not certainly to any advantage it possesses as a surveying instrument. Angles and bearings are taken with this instrument, on the supposition that the magnetic needle preserves a parallel position throughout the entire survey-a supposition not founded on fact; for the state of the atmosphere, the hour of the day, the proximity of ferruginous matter, and various other causes, frequently produce a considerable variation in its direction.

The magnetic experiments which have been conducted for some years back, at the Observatory erected for that purpose in Trinity College, under the able superintendence of our illustrious countryman, Professor Lloyd, give results unfavourable to the use of the circumferentor. That indefatigable philosopher has found the maximum diurnal variation, which takes place in the summer months, to amount to 16 minutes,

and the minimum diurnal variation from 4 to 6 minutes. Hence the difficulty of ascertaining, with any degree of certainty, the mearings of old surveys from the bearings of their circumscribing right lines, as represented on old maps, when no instrument is used but the compass.

The date and variation of the needle should be registered on every map of an estate. The variation at present (1841) in Dublin, is 27° 16'.

Besides the annual change in the deviation of the needle, Colonel Beaufoy's experiments shew a daily variation somewhat similar to that observed by Professor Lloyd. Col. Beaufoy states that the variation is greatest in summer and least in winter, varying from 15 minutes to 7 minutes. The needle attains its maximum daily variation to the eastward about 7 A.M. From this time it continues to move towards the west, till between 2 and 3 P.M., when it begins again to travel towards the east.

As a further proof of the errors arising from the use of the circumferentor as a surveying instrument, I take the liberty of pointing out another instance of extraordinary disturbance of the magnetic needle, which took place at the Royal Observatory, at Greenwich, on the 25th of September last.

Professor Airy mentions that on the 25th of September of the present year, a most extraordinary disturbance of the magnetic instrument was observed at the magnetic observatory attached to the Royal Observatory at Greenwich. The disturbed state of all the instruments attracted the attention of Mr. Glaisher (chief assistant in the magnetic department,) at an

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