Barometrical Measurement. By the perfection now attained in the construction of barometers, and the skill applied to their use by the best observers, differences of elevation may be ascertained by them with greater accu racy than by the most carefully conducted . angulation - at least, in places where the eleva tions are great and difficult of access. Hig summits, covered with shifting clouds, involv uncertain errors, arising from constantly var -ying refraction; and inaccessible mountains can only be observed under very small angles from a the termini of a carefully constructed base line, in some smooth district, at a considerable distance from them. A comparison of results obtained by both methods is generally in fa- of the barometer. Humboldt noticed this, par-ticularly in the numerous measurements had been made of the peak of Teneriffe, and determining this elevation by the mean results of the various observations, he rejected eight out of nine geometrical measurements, and one out of four barometrical measurements.

Both modes, however, are capable in many localities of a great degree of accuracy, as shown in the two measurements of Mt. Wash-ington, the first by Prof. Guyot with the barometer, and the second by the officers of the coast survey, in which the difference was only 3 ft. in the height of 6,285 ft. determined by Prof. Guyot. To insure the greatest degree of accuracy, it is essential to use two good barometers, one at the lower and the other at the upper point. If only one be employed, there is a liability of error from a change of atmospheric pressure taking place during the time spent in passing from one station to the other, these barometers should have been carefully compared by many observations, and the mean of their variation noted, to be always allowed in the calculation. They should also have been compared with other barometers of known character, and their differences with these noted, and this comparison should be repeated after their use, in the same way as chronometers are compared, and their rates noted, before and after a voyage. Repeated observations should also be made at both stations at the same times, and the mean of all be taken unless some show good reasons for their rejection. It is also important that the two stations be not very far apart.

In a distance of 40 or 50 m. there may well be varying conditions of the atmosphere that cause a difference of pressure not due altogether to the difference of elevation. This cause of error may be avoided by using intermediate stations, and advancing step by step - One point determined serves as the established base for determining the next beyond. In measuring the heights of the principal summits of the Black mountains of North Carolina Prof. Guyot used as his starting point the level determined by a railroad survey, 7 m. distant from the nearest hill. The next sta-tion was taken half way to the summit, and by repeated observations at both, continued during two days, the liability to error resulting from too great distance was avoided; so also was that from a faulty correction for temperature. This correction, as applied by the tables, counts sometimes to 300 ft. But it supposes actual temperature of the stratum of air between the two points to be represented by the mean of the temperature at the two places, and a moderate variation from this may well involve an error of 1/10 or 1/12 of the whole correction. Such a variation is not at all improb-able where the difference of elevation is very great, as in the higher regions the decrease of temperature takes place more and more rapidly.

The next station was the summit of the first the height of which was ascertained by parative observations made upon it and at same time at the second station. The dif-ferent peaks were then compared one with another by observations made upon them in pairs. So exactly were these measurements conducted by Prof. Guyot, that, as he states, his single observations differed only two or three metres from the means, and the mean of one day cely differed one metre (39 inches) from the mean of another. But for these precautions an error might have resulted in the determination of the first summit of 50 ft. or more, such as Prof. Guyot found he was liable to in the course of his observations at the White mountains when the two stations were from 10 to 20 m. apart. As the distance between stations increases, the number of observations should also be multiplied, in order to obtain a correct mean. The barometers are to be carefully suspended, so that the column shall be perfectly vertical, and they should be placed in a situation not subject to sudden change of temperature. The reading of the height of the mercurial column is to be taken at the same time as that of the thermometer attached to the barometer, and also of the detached thermometer.

If the instrument has been suspended for some moments, the two temperatures may not differ. When these observations are compared with those made at the same time at the other station, the calculations for the difference of elevation are usually made by the aid of the tables prepared by M. Oltmanns. This is a much more simple process than calculating the difference by the theorem of Laplace, which gives the same result. If the instruments are graduated in inches, these must be turned into metres, and the temperatures must also be expressed in degrees of the centigrade thermometer. With the tables for these conversions and calculations are given very simple directions for their use, and applying the necessary corrections. - Some singular barometric anomalies are reported by Lieut. Herndon to have been observed by him in the vicinity of the Andes. At the eastern base he found the pressure, as measured by the boiling point of water, to be nearly as great as at the level of the sea. Having descended nearly 1,000 m. on the Amazon, the boiling point indicated an ascent of nearly 1,500 ft.

Maury explains this by referring it to the effect of the trade winds, which strike upon the flanks of the mountains and are banked up against them, as a current of water interrupted by impediments in the channel is piled against these. By the banking of the current of air an increased pressure is supposed to be exerted upon the surface at their base. - In the earlier measurements made with the barometer the air was considered as a uniform fluid, no regard being paid to the gradual diminution of density in ascending into the higher regions; but when this gradation was taken into the calculations, it became necessary to determine the relation between the density of the air and its elastic force. Mari-otte, who published his "Discourse on the Nature of Air" in 1676, and who was the first to demonstrate the law which bears his name, that the volume of a gas is in the inverse proportion to the pressure upon it, opened the culture of a new field from which rich harvests were subsequently reaped. From the suggestions afforded by this simple law he proposed to compute heights from barometrical observations by the rule usually employed in constructing tables of logarithms, seeming to have obtained some idea of the remarkable fact that the density of the atmosphere decreases in a geometrical progression corresponding to the elevations taken after an arithmetical one.

But for some reason he seemed not to be aware of the importance of the great principle, and abandoned the method for another in which he repeated the bisection of a column of air between two stations into successive horizontal strata, calculating the densities according to a harmonic division.