Barometrical Measurements It

Newton has given a sort of geometrical solution of the problem. But a more precise, and, in this case, a clearer investigation, is obtained by help of the symbols of the integral calculus. Let x and x' ex press the altitudes of two strata olatmosphere, and y and y' the corresponding densities, the radius of the earth ; suppose farther, that e represents the al titude of the equiponderant column which measures the elasticity of the air. Since the density of the air depends on the incumbent pressure, its decre ment must evidently be proportional to the weight of each auperadded minute stratum, or to the density of this stratum multiplied into its thickness and power specting the reality or accuracy of' the law of geo metrical progression in the atmosphere. Daniel Ber noulli, a man of candour on the whole as well as in. genuity, but who, with some proneness to specula tive reasoning, had imbibed unfortunately many of the prejudices of the Cartesian and Leibnitzian schools, proposed in his capital work, the Hydrodynasnica, which came out in 1736, certain vague hypotheses regarding the constitution of the atmosphere, as de duced from certain internal motions attributed to its component strata. The specious results of those cal culations led him hastily to deviate from the princi ple of the geometrical progression of density in the upper regions. In this departure he was followed by Cassini mid Horrebow, who concluded from some partial observations they had made, that the barome ter, in its indications of atmospheric pressure, is sub ject to irregularity ; and that, near the surface of the earth, it obeys a different law from what it ob tains at great elevations. A strong light, however, was thrown upon the subject in 1753 by Bouguer, an able mathematician, and a very skilful and inge. nious observer, who, with other academicians, had been employed for several years in measuring a •de gree of the meridian along the stupepdous ridge of the Andes. From the comparison of more than thir ty distinct observations, he deduced a simple and ele gant rule for computing heights by means of the ba rometer. It is, that the difference between the lo garithms of the mercurial columns at the two star dons being diminished by one-thirtieth part, and the decimal point shifted four places to the right, will express the required elevation in Mises. Since the English was to the • French foot nearly as fifteen to sixteen, the rule would be accommodated to our measures, and the result expressed in feet, if the lo garithmic difference were augmented by the thirtieth part, then multiplied by six, and the-decimal point thrown back four places ; or, what is the same thing, if that logarithmic difference were multiplied at once by 62,000. But Bouguer imagined, that this rule would not hold exactly in Europe, or in the lower regions of the torrid zone ; and to explain the devia tion, he had recourse to the forced supposition that the particles of air possess different degrees of elasti city. Lambert, a philosopher of great originality and penetration, afterwards published some excellent remarks on the comparison of barometrical measure ments. But no material progress was made till 1755, when M. de Luc of Geneva resumed the subject, and carefully combined experiment with observation. For the space of upwards of fifteen years, he prose cuted his inquiries with diligence and perseverance, aided by the peculiar advantages of local situation, in a city abounding with skilful artists, and seated in the neighbourhood of lofty mountains. The discre pancies which had hitherto created so much embar rassment, proceeded mostly from the inattention of observers to the disturbing influence of heat, and particularly its effect in expanding the air, and con sequently augmenting the elevation due to a given difference of atmospheric pressure. De Luc's first object was to improve the thermometer of Reaumur, which, though greatly inferior to that of Fahrenheit, had been adopted in France and the adjacent parts of the continent. klaving ascertained that mercury Mb the valuable property of expanding equably with equal additions of heat, he substituted that metallic fluid for spirit of wine, but retained its arbitrary and in convenient scale of 80 degrees between the points freezing and boiling water. He next examined the dilatation of air at different temperatures, and cor rected those results by numerous observations made on the mountains of Savoy, and the mines of the Hartz, in which the barometer was combined with the thermometer. formula which he thence de duced for the computation of barometrical measure , ments was, in 1772, published in his Recherches sur ks Modi/ications de CAtmosphere, and seemed to draw, especially in England, a very considerable de

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gree of notice. Dr Maskelyne, the astronomer

royal, adapted it to our system of measures, and Dr Horsley made annotations and comments on it. But, what was of more importance, other accurate observers, incited by De Luc's example, enterod the same field of inquiry, provided with instruments of greater delicacy and much better construction. In 1475, Sir George Shuckburgh 'Evelyn visited the Alps, and combined trigonome trical operations with corresponding observations by barometers and thermometers from the hands of Rainsden ; and about this time likewise, General Rey not only measured, with instruments made by that excellent artist, some of the principal moun tains in Scotland and Wales, but instituted a series of manemetrical experiments. It resulted from all these researches that, for each degree on Fahren heit's scale, mercury expands the 9700th part, and air the 435th part of their respective bulks. It fur ther appeared that the atmosphere has its tempera ture almost uniformly diminished at equal ascents ; and that the logarithmic difference, reckoning as integers the first four digits, expresses in Eng lish fathoms the height of an aerial column as cold as the point of congelation. General Roy proposed likewise another correction depending on the enfeebled gravity, and consequently the aug mented altitude of the equiponderant column of at mosphere in the lower latitudes, occasioned by the influence of centrifugal force arising from the earth's rotation. Several years afterwards, Professor Play fair, in a learned paper, printed in the first volume of • the Transactions of the Royal Society of Edinburgh, examined all the circumstances which can affect ba rometrical measurements, and discussed each ques tion with the correctness and perspicuity that we might expect from his distinguished abilities. At nearly an equal interval of time, the celebrated La " place resumed the subject in his Mecanique Celeste, and brought all the conditions together in a very complicated formula. Such an appearance of ex treme accuracy, however, is perhaps to be regarded merely as a theoretical illusion, unsuited and inappli cable to any real state of practice. Blot has since attempted to arrive at a similar conclusion, by setting out a priori from some careful experiments on tbe relative density of air and mercury, performed by him in conjunction with Arago. He thence infers, that, in the latitude of Paris, and at the point of con gelation, air, under a mercurial pressure of 76 metres, or 29.922 English inches, is 10.463 times lighter than mercury at the temperature of water at its lowest contraction. This would give 26,090 feet for the height of a column of homogeneous fluid, whose pres sure is equivalent to the elasticity of the atmosphere. The coefficient adapted to common logarithms, and ad justed to the torte of attraction at the level of the sea, would therefore be 60,148 feet, or 18,234 metres; scarcely differing sensibly from the quantity which Ramond had deduced from a very numerous set of experiments made by him on the Pyrenees. But Blot prefers, as the coefficient, the number answering for an elevation of 1200 metres, or about 4.000 feet above the sea, which is not far from the general level of such observations. The formula is hence, in English feet, 60,346 (1 +.002837 cos. 24) ( 1 -I- -Ft)) log. ; where 4, denotes the lati tude of the place, T and t the temperatures of the air at the two stations, as indicated by the centesimal thermometer, and H and h the heights of mercurial columns corrected for the effects of heat.

'Ibis active writer has likewise given tables for ex pediting the calculation of barometrical measure ments ; in which he was anticipated, however, by Olt mans of Berlin, who published, in 1809. large Hypso metrical Tables, as they are called, accommodated to the complex formula of Laplace. Such tables might, no doubt, prove useful where very frequent compute. tions are wanted, as in the case of the reduction of the numerous observations brought home by Baron Humboldt, for which, indeed, they were first design ed. But still they contain a needless profusion of figures, and hold forth a show of extreme accuracy which the nature of the observations themselves can never justify. The mere calculation of barometrical measurements is a secondary object ; the great diffi culty is to procure good observations, and to combine tolerable accuracy with expedition. For this purpose, a very portable barometer is still wanted ;—an instru ment light and commodious, exempt from injury or derangement, and yet sensible to minute changes of atmospheric pressure. These properties, indeed, are seldom conjoined, and one advantage must generally be sacrificed to obtain another.