FINDING that engineers use the barometer as an approximative method of measuring the altitudes of the interior parts of the country, I cannot probably do a greater service at this time, when surveys are actively going on, than give a simple rule or two for that purpose. I do this the more willingly, as barometric altimetry is a subject on which a few years since I bestowed great attention, and succeeded in constructing tables and inventing rules which are far simpler and, I apprehend, more accurate for great altitudes than any heretofore given. The theorem in p. 261 is that whichcontains the rules alluded to; but here such lofty altitudes are not wanting.

The object of engineers in using the barometer is merely for the sake of expedition in getting such approximative heights as may guide them in the most probable course for conducting their survey. As to levelling for the purpose of laying down rails the barometer is totally unfit. We may easily satisfy ourselves on this point by considering-1, that the barometer will occasionally stand at one, two, or more tenths of an inch different the same moment at places only two or three miles apart, though the actual levels of the places be the same;-2, that a single hour will sometimes occasion a difference of a quarter of an inch in its height at the same place;-3, that the places of simultaneous observation will in general be far distant;-4, that every tenth of an inch in the height of the barometer corresponds to near 91 feet of altitude in the average. There is indeed no way that we know of, for accurate levelling, equal to that of the ordinary mode when the instruments are good, and the observers competent and careful.

Notwithstanding all these disadvantages the barometer may, nevertheless, be very usefully employed both in laying out lines and in checking summit heights as taken by levelling.

For this purpose I should recommend the simultaneous use of three barometers, one at each terminus, if not too far apart, and the other at the points whose altitudes are wanted. If the termini are too widely distant, then it will be advisable to select two points whose heights, comparatively with the termini, can be readily obtained, one on one side of the summit to be observed, and the other on the contrary side. My reason for choosing two such points is, that we should be able more correctly to conclude what would be the height of a barometer under the point of observation, and hence the height of the hill, than we could from an observation at one distant place only. As it would be difficult to fix on the precise times for simultaneous observations, I should also recommend recording the heights of the barometers at each of the termini every half hour, or, at furthest, every hour during the day-time, with the corresponding temperatures of the external atmosphere, if great nicety is intended. By this means latitude would be given to the distant observer, and if he noted the time of his observation with the temperature of the atmosphere, if this be thought needful, any fluctuations in the atmospheric pressure might easily be allowed for.

In noting the height of the mercury in the barometer tube some care is necessary; for, if the mercury is rising, its surface is convex, and the line marking the close contact of the mercury with the glass is below the upper surface of the mercury, which not being so well defined, its true height is not so easily taken. On the contrary, as the mercury descends, its surface in the tube is either concave or flat, generally, I believe, the latter. Now, by leaning the barometer out of the perpendicular, and then slowly restoring it, we can always produce this concavity or flatness of surface, though we cannot so easily the convexity. If, therefore, this was done by all the observers at every observation, the line of contact with the tubes would be well defined, and could be accurately taken; and, if there be any concavity, it would be nearly the same in each, and no sensible error could arise from not exactly knowing how much it is.

This precaution some perhaps will think too refined; but one may as well use a little care, when the trouble is so trifling, as not; and, if the error to be avoided should be

only the one-thirtieth of an inch, which in my barometer it sometimes is, it will save an error of no less than 30 feet in the altitude.

If the mercurial columns in the barometers differ much in temperature, which is ascertained by the attached thermometers, in strictness they should be reduced to a common temperature; but, in such cases as those we have in hand, it will, I apprehend, seldom be necessary. I am even doubtful whether the difference of temperature of the atmosphere will produce effects equal to the probable amount of the errors of observation in such cases as we should have to deal with. This, however, I leave to the judgment of the parties; but, if it should be deemed adviseable to notice it, recourse must be had to the theorem I have given, p. 261, or to the one below.

For the purpose of getting the altitude of the hill tolerably near it, it will be needful to get the height of an imaginary barometer directly under the one observed, and in the plane of the termini. For this purpose, take the distance of the place of observation from each terminus nearly, for great accuracy is not required. Then multiply the difference in the heights of the barometers at the termini by the distance of the place of observation from the lower barometer, and divide the product by the sum of the two distances before found. The quotient will be to be added to the height of the lower barometer to have the height of the imaginary barometer under the hill.

Then, to find the height of the hill, multiply the difference in inches between the height of the imaginary and real barometers by 907.5. To this sum add four-fifths multiplied by the said difference and then by ten times the difference less one, and the result will be the height in feet very nearly.

Example.-Suppose the barometer on a hill, 50 miles from one of the termini and 60 from the other, stands at 29.25 inches, while that at the former terminus stands at 30-15, and at the latter 30.55, required the height of the hill above the plane joining the termini.

To find the height of the imaginary barometer :