Some of the sources of error in measuring altitudes, which are not to be eliminated by any adjustment or correction of instruments, are clearly stated by Prof. Elias Loomis, in a paper read before the National Academy of Sciences, April 19, 1881.

“The Laplace formula assumed that the atmosphere has attained a condition of equilibrium, and in such a case it gives the reduction to sea level with tolerable accuracy. The average of a long series of observations represents approximately such a condition of equilibrium; but in the daily observations this equilibrium is very much disturbed. The mean between the temperatures at the upper and lower stations does not represent the average temperature of the intermediate column of air; and when the atmosphere is in rapid motion the downward pressure is modified by the earth’s rotation, in a manner not represented by the Laplace formula. There is no doubt that the formulæ of reduction now employed may be considerably improved; but it does not seem possible that any single formula, with constant coefficients, should provide for the immense variety of conditions which prevail in the neighborhood of mountain stations; and we may be compelled for each mountain region to adopt tables founded upon a direct comparison of observations made at stations of different elevations and not very remote from each other.”

The following remarks bearing upon the same subject are from an article by J. Allan Brown, F. R. S., on “Periodic Oscillations of Barometric Pressure,” published in Nature in April, 1881:

Sedgwick has said: [“To explain difficulties in these questions” (relating to pressure and temperature) “the atmospheric strata have been shuffled in accordance with laboratory experience.”]

“If we suppose that the attraction of gravity is not the only attraction which affects the pressure of the atmosphere, but that this pressure varies through some other attracting force—such as an electric attraction of the sun depending upon the varying humidity of the air, and this again depending on its temperature, we should find another method of relating the two variations which does not exist if gravitation alone is employed. It is quite certain that many physicists will not admit the idea of an electric attraction on our atmosphere in the present state of our knowledge, hence the efforts to make expansion, and a shuffling of the atmospheric strata suffice. We must not, however, in our ignorance, attempt to force conclusions in opposition to facts, and if these can be satisfied more easily and with greater probabilities in its favor by the aid of the hypothesis of an electric attraction of the sun, that hypothesis will have a better claim to acceptance than the other. I shall here note a few facts which cannot be explained by thermic actions.

“1. I have shown that, on the average of many years’ observation in our latitudes, the mean pressure diminishes at the rate of 0″.038 of mercury for every one hundred miles we proceed toward the north. This has been called a gradient from the similar term used in railway slopes: but it is no slope, it is a level of a surface of equilibrium like that of the sea. It is the mean heights of the barometer at the sea level which indicate the form, if we may so say, of the equilibrating atmosphere.

“2. In India we have seen that the atmospheric pressure oscillates at each station even when these are quite near to each other, independently of the known laws of equilibrium of gases. When we turn to the semi-diurnal oscillation of the barometer we are only amused at the attempts made to explain it by shuffling the atmospheric strata. Nothing can be more certain than that the theories of expansion, or resistance to expansion and overflow, are the vain efforts to make the laws of nature agree with a theory. Over the great ocean within the tropics, where the diurnal variations of temperature are small and the air is absolutely without perceptible currents for days together, the barometer rises and falls a tenth of an inch twice in twenty-four hours with the regularity of the solar clock. The action of the sun on the whole atmosphere which produces this movement varies chiefly during the day hours at inland stations with the temperature oscillation, so that, as in the case of the annual variation, the fall of the barometer at 4 p.m. is greater in the same latitude as the temperature is higher. This variation occurs during the most complete calms; the smoke rises vertically from the plain of Tinnevelly; no current is visible in the motion of the clouds; yet the barometer falls at four in the morning as it did at four in the afternoon, only it falls less.”

It seems probable that the use of the Aneroid will soon become more widely extended, and that engineers, when made familiar with the qualities of well-made instruments, will welcome so valuable an aid in preliminary surveys. The conditions of satisfactory work with barometers are certainly peculiar, and to field workers familiar only with the level and transit, may seem unique. But when the conditions are fully understood, the engineer may easily take precautions which will avoid too large errors, and conduct surveys in hilly regions with a celerity not heretofore attained.

TABLE I.
FOR ESTIMATING HEIGHTS
BY THE ANEROID.

Take readings of the barometer and thermometer at both stations; find in the the heights corresponding to the barometric readings, and subtract them. Multiply the remainder by