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the glass or other transparent measuring plate be made of an inch, it would represent on that scale about 18 of an acre, and it may therefore be readily understood how accurately the acreage of the subdivisions may be determined; the acreage of the whole having been previously given, as a quantity practically free from error.

When the Irish survey was first projected, a valuation of the land, with a view to the more just allocation of taxation, was the main or rather its sole object, and for this purpose alone an engraved and published map would not have been necessary, as a few copies of the plots of the survey might have sufficed for the wants of the valuations. General Colby however, not only foresaw the inconvenience of such a narrow system, as it would then have been impossible that every farmer should check, if he thought fit, the accuracy of assessments made upon him, but he also anticipated the great advantages which would result from the use of such a map for agricultural, engineering, and many other purposes, and he therefore, though still looking forward to the extension to Ireland of the one inch map, successfully urged the publication of the 6 inch map, so that he must always be remembered as the author of the first great practical national map in this country.

ALTITUDES.-The 13th article of Sir W. Petty's instructions refers to this important subject, in these words: "You shall measure the height of all notoriouse high hills and mountains, describing their feet and manner of rising, together with their names

and true places." This was as much as could have been expected, at the time of the Down survey, and little more had been done in the British survey than the determination of the heights of the principal mountain or hill stations; but in the Irish survey, General Colby introduced a new system, by spreading altitudes over the whole face of the map, as well on low as on high ground. For this purpose, the principal stations were fixed in altitude with great precision, partly by direct observation to referring objects at once close to them and the sea, and partly by levelling from the sea line to the referring objects. From the principal stations the heights of secondary points, either hill stations, church towers, or other easily recognizable objects were then deduced; and these, in turn, became initial points for the districts and divisions. Finally, the measurement of the chain lines between stations, the altitudes of which had been determined by triangulation, afforded the means of fixing the levels of a vast number of intermediate points, and thus of placing, at every step, a known altitude mark within a convenient distance for reference. The "Field Levelling Book," and the corresponding calculation books provided for the calculation and record of these subsidiary altitudes in a systematic form, and a comparison of the results from the two trigonometrical altitudes, on which they were based, afforded a check upon their accuracy. Perhaps no published maps have ever been supplied so copiously with altitudes, determined in such a manner as to be practically useful for farming and

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engineering purposes, and many able judges have acknowledged the assistance they have derived from them. In considering this subject, however, it is right to remember that the success of the system depends on the accuracy of the primary initial altitudes, and on the mode of deducing the secondary and other altitudes from them; so that it becomes interesting to trace out the steps by which the altitudes of the Irish survey have been brought to their present high degree of accuracy.

In Great Britain, as before observed, the height of certain hills, or other stations near the sea, were determined partly by angles of elevation and depression, and partly by levelling from the low water mark of spring tides. These altitudes were then used for obtaining others, either by reciprocal observations, using two stations, or simply by elevation or depressions from one station only. Such observations required, of course, two corrections, namely, that for curvature and that for refraction, the one constant and certain, the other variable and uncertain. From several reciprocal observations in England, it had been concluded that the refraction was about of the arcal distance between the objects, and this amount of refraction therefore was adopted and constantly used in correcting observations for elevation or depression. In the first instance, the same correction was applied to the observations of the Divis mountain, near Belfast, which was the first great observing station of the Irish survey, and the first primary initial altitude, and many secondary

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altitudes, such as the bands or other distinguishing marks of Antrim and other church towers. posing the instrument supplied with adequate means for taking the angles of elevation and depression, the value of the resulting altitudes would necessarily depend on the unchangeableness of the proportional correction for refraction, and on the accuracy of the horizontal distances to be used in calculation. In respect to the distances, their accuracy was certain to be far within the limits of required accuracy; but as regards the correction for refraction, the same certainty could not be expected, and in proportion as it deviated from the assumed ratio of of the arcal distance, so would the calculated diverge from the true altitudes, the difference increasing as the distance increased from the observing station. Hence, as a natural result, there was often a difference of 5 or 6 feet in the amount of error of secondary stations, and in consequence the common points of adjoining districts were found to differ widely in altitude from each other, when determined from independent secondary stations, the altitudes of which had been supplied from the great triangulation. This inadequacy of the system of the British survey for determining altitudes with the precision required in a practical work, was almost immediately discovered, in consequence of a comparison of the reciprocal observations of Divis, taken by General Colby, and of Knocklayd, also in Antrim, taken by the author, when it was found that a refraction not ofth, but of was required to harmonize the results of the

two sets of observations when used seperately; and as this amount was subject to very great variation, sometimes approximating to and sometimes approaching a system of standard heights was introduced so as to get rid of the errors due to uncertain refraction.

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In this system, the altitudes of points near the sea in various directions were determined with precision, and these were used as points of reference; the refraction at the observing station being deduced from the known heights of the observing and observed stations, as it was necessarily equal to the difference between the observed angle of depression or elevation, and the angle which would actually give the known difference of altitude between the two stations. The refraction thus obtained was used in determining the altitudes of any other stations nearly in the same direction; and so on with other standard heights, as it was found that the amount of refraction was not constant in all directions at the same time, being much affected by local circumstances. It was not, however, always possible to have a standard point of altitude in the required direction, and hence, notwithstanding the improvement in the altitudes effected by this simple arrangement, it became necessary to abandon the determination of altitudes by observations from distant stations, and to restrain the limits of observation, even by the great theodolite, to distances of about 10 miles as the maximum; and the necessity of such limitations in respect to distance, may be judged