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III. On the Causes which affect the Accuracy of Barometrical Measurements

Published online by Cambridge University Press:  17 January 2013

John Playfair
John Playfair
Affiliation:
Professor of Mathematics in theUniversity of Edinburgh.
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Extract

Though the labours of M. De Luc, and of the excellent observers who followed him, have brought the barometrical measurement of heights to very great exactness, they have not yet given to it the utmost perfection it can attain. Some causes of inaccuracy are still involved in it; of which we ought, at least, to estimate the effects, if we cannot correct them altogether. The allowance made on account of the temperature of the air, implies in it a hypothesis that has not been examined, nor even expressed, and many other circumstances that affect the denfity of the atmosphere, have either been wholly omitted, or improperly introduced. The object of the present paper is to correct, the errors that arise from these causes, or, where that cannot be done, to assign the limits within which those errors are contained.

Type
Papers Read Before the Society
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 1 , Issue 2 , 1788 , pp. 87 - 130
Copyright
Copyright © Royal Society of Edinburgh 1788

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References

page 88 note * General Roy makes the fixed temperature 32° and the expansion for 1°, = .00245, at a medium. Sir G. Shuckburgh makes the fixed temperature 31°¼, and the expansion, as here assigned, viz. .00243. Phil. Trans. 1777. It is sufficient for us at present to know these numbers nearly. According to the formula laid down hereafter, they will all require to be corrected.

page 88 note † Phil. Trans. 1777.

page 93 note * Tab. 2. and 3. p. 701. 703. Trans. 1777. part 2.

page 101 note * If we take M. De Luc's rule, as improved by the later observations of General Roy and Sir George Shuckburgh, p = 4342.9448 = the modulus of the tabular logarithms multiplied by 10000: r = 32° and m = .00245 nearly. It is unnecessary to remark, that the logarithms understood in all these formulas are hyperbolic logarithms, and that the multiplication of them by p is saved, by using the tabular logarithms, and making the first four places of them, excluding the index, integers.

page 101 note † Phil. Trans. vol. 64. part 1.

page 104 note * According to the experiments of General Roy, above quoted, the expansion of air, for 1° of heat, at the temperature 32°, is .00245 nearly, that air being compressed at the same time by the weight of a column of mercury 29.5 inches high. As we have supposed m in the preceding computations, to be .00245, we must suppose γ = 29.5. The formula supposed here to give the space occupied by the air, so far as heat is concerned, viz. is changed from the exponential expression of § 8. in consequence of what has been just observed about the effect of neglecting one inequality in the computation of another.

page 108 note * The mercury in the barometers is supposed to be reduced to a fixed temperature, by the application of a correction on account of the thermometers attached to them, after the manner of M. De Luc, or of General Roy; the latter reduces the mercury always to the temperature of 32 °. When the difference of temperature is not very great in the two barometers, the correction of their heights may be made according to the very ingenious remark of the astronomer royal. Phil. Trans. vol. 64. part 1. p. 164.

page 128 note * See General Roy's experiments, reaction 2. Phil. Trans. vol. 67. part 2.