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turn towards the meridian, in order to compare the results with the table of Coulomb's observations, given by M. Biot (Traiti de Phy. Tome 3, p. 84). Now we have before proved that this force for any wire may be represented by

where, for abridgment, we have supposed

A-2/8(i-fir)It has also been shown that for any steel wire a/9=. 0548235,

the French inch being the unit of space, and as in the present case a —, there results /8 = .657882, It only remains therefore to determine K from one observation, the first for example, from which. we obtain 2T= 58'.5 very nearly; the forces being measured by their equivalent torsions. With this value of K we have calculated the last column of the following table:

[table]

The last three observations have been purposely omitted, because the approximate equation (a) does not hold good for very short wires.

The very small difference existing between the observed and calculated results will appear the more remarkable, if we reflect that the value of /9 was determined from an experiment of quite a different kind to any of the present series, and that only one of these has been employed for the determination of the constant

quantity K. which depends on f, the measure of the coercive force.

The table page 87 of the volume just cited, contains another set of observed torsions, for different lengths of a much finer

1 / 38

wire whose radius a ^\J ggg: hence we find the corresponding value of £ = 3,13880, and the first observation in the table gives Jk" = '.6448. With these values the last column of the following table has been calculated as before:

[table]

Here also the differences between the observed and calculated values are extremely small, and as the wire is a very fine one, our formula is applicable to much shorter pieces than in the former case. In general, when the length of the wire exceeds 10 or 15 times its diameter, we may employ it without hesitation.

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MATHEMATICAL INVESTIGATIONS
ooramaa m

LAWS OF THE EQUILIBRIUM QF FLUIDS

ANALOGOUS TO THE ELECTRIC FLUID,

WITH

OTHER SIMILAR RESEARCHES*.

From the Trantactions of the Cambridge Philosophical Society, 1833.
[Read Nov. H, 1831.]

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