the subsequent triangles, is an excellent one.

Let AB

be the base line; at A and B measure the angles CAB,

DAB, CBA, DBA; hence CD may be found. Next, the angles ECD, FCD, EDC, FDC are measured, from which, with the computed line CD, the length of the line EF may be computed. In like manner, by measuring the angles at the points E and F, the line GH may be computed. By such a process the triangles must soon arrive at the greatest limit at which the station point can be rendered visible. Colonel Colby and Captain Kater employed a plane mirror to render distant objects visible. It was by this means they verified General Roy's triangulation for connecting the meridian of Greenwich and Paris.

Captain Drummond, R.E., our late under Secretary of State for Ireland, having been aware of the utility of thus employing the reflected rays of the sun, invented an instrument, by means of which the solar rays were directed towards the station to be rendered visible.

A description of this instrument may be seen in a paper written by himself, and published in the Philosophical Transactions for the year 1826.

This Heliostat being useful only when the sun shone, another contrivance was still wanting to produce a light sufficiently strong to render distant stations visible at night. General Roy employed Bengal lights for this purpose, which were superceded by argand lamps and parabolic reflectors, which rendered objects visible at the distance of forty-eight miles. But the light invented by the late Captain Drummond, above alluded to, surpasses them all in intensity of brilliancy. This invention consists in a stream of oxygen gas directed through a flame of alcohol to a ball of lime, about a quarter of an inch in diameter, placed in the focus of a parabolic reflector. This produced light eighty times as intense as that produced by Argand's lamp. Any one having seen this light must be at once convinced of its fitness for light-houses where the strongest illumination is required.

The superior power of the Drummond light was proved in a special manner in the neighbourhood of Belfast, where, in hazy weather, it was brilliantly visible at the distance of sixty-seven miles.

The author has had opportunities of seeing all the instruments used by Colonel Colby in the Ordnance Survey of Ireland, and has been particularly struck with the beautiful contrivance resorted to for preventing any expansion or contraction between the points marked at the extremities of the metal rods used to measure the base line.

Two parallel bars, the one of iron and the other of

brass, each ten feet long, are rivetted together at their centres. The brass bar is coated with some non-conducting substance, to equalize the susceptibility of the metals to change of temperature.

The extremity of each bar is furnished with a tongue of iron, having a minute dot of platinum, and so placed on this tongue, that under every degree of expansion or contraction of the rods, the dots at each end remained at the constant distance of ten feet. There are accompanying microscopes attached to the end of similar compound bars, six inches long. The microscopes in these short bars occupy the position of the dots in the longer bars. After repeated experiments, to ascertain the relative expansion and contraction of these bars, in their transitions from cold to heat, and from heat to cold, they were found to be in the proportion of three to five.

This invention of Colonel Colby's is more expeditious in its practical application than any other method employed before for the measurement of a base line. In the methods usually employed for this purpose, the temperature is noted as every chain or rod is laid, and an allowance made for the contraction or expansion occasioned by every change in the thermometor.

What has been given here is but a faint outline of Colonel Colby's invention, a full account of which, it is hoped, will soon be published by himself, with the other details of the Ordnance Survey of Ireland.

When a base line is measured on an elevated plain, it must be reduced to its proper measure at the level of the sea; and though this correction is in general but very small, yet in the measurement of a base line, upon

which so much of the correctness of the entire work depends, it should by no means be neglected.

Let the measured base AB be put

A

B

=B

ab, its value at the level of the sea-b

Ca, the rad. of the earth

=R

こん

Now if we consider the radius of the earth to be =21008000 feet, the above equation may be solved by the following logarithmic rule :

From the sum of the logs. of the radius and measured base, deduct the log. of the sum of the radius and altitude, and the remainder will give the true measurement of the base at the level of the sea. If we desire to know the correction to be applied to AB, in order to reduce it to ab, we have

From the sum of the logs. of the base and altitude, in feet, deduct the log. of the sum of the radius and altitude, and the remainder will give the log. of the correction, which must be deducted from the measured base, to reduce it to its corresponding measurement at the level of the sea.

Mr. Airy gives the following formula :-Call the radius of the earth at the level of the sea r, the elevation of the measured base h; then the measured length must be multiplied by or 1-2; or it must be diminished by the part of the whole. When the surface

r+h

h

slopes uniformly, take the mean height for h. When the surface is very irregular, it may be divided into several parts.

Interior Filling-in of the primary Triangles.

The preceding part of the work furnishes ample instructions for filling-in the large triangles, so that very little more is left to be done here.

Form small triangles, by actual measurement, between the nearest trigonometrical points, taking care that the direction of each side be so selected as to answer some ulterior object in the delineation of such objects or lines as are to be represented on the map, such as castles, churches, the boundaries of woods, parishes, townlands, estates, &c. From the extremities of these measured lines, whose positions are ascertained from the primary trigonometrical points, take angles to all the surrounding objects, as before directed. In doing this it may be necessary to observe, that the lines joining the distant object with the extremities of the base, should not form an angle less than 30 degrees. When the angle at the distant object, subtended by the base line, is very small, the most trifling error in the angles at the extremities of the base line will remove the distant object far from its true position on the plan. In the progressive execution of the work, the lines employed should be checked as often as favourable opportunities presented themselves of doing so, as taught in the preceding methods of surveying by the chain only, and by the chain and theodolite.