This salt suffered no change by exposure to the air: the aqueous solution reddened turmeric paper strongly. One hundred grains, cautiously decomposed by an acid, gave out 40 grains of carbonic acid gas.

One hundred grains were dissolved in water, and added to a neutral solution of muriate of lime; with the assistance of heat, 64 grains of carbonate of lime were precipitated, equivalent to 39.72 of soda.

It appears, therefore, that 100 parts of this salt consist of nearly,

Adopting the numbers on the Synoptic Scale, it will be seen

that this salt is constituted as follows:

3 atoms of carbonic acid

....

82.62

40.08

....

In the second volume of the Mémoires d'Arcueil, p. 474, M. Berthollet has remarked the existence of carbonates of potash, and of soda, containing more carbonic acid than the carbonate, and less than the bicarbonate: he also notices Klaproth's examination of the African carbonate of soda, detailed in p. 65, Vol. II. of his Analytical Essays. This substance gave out 38 per cent. of carbonic acid, and lost 31 per cent. by exposure to a red heat. It is stated to consist of,

Allowing 1.5 of the water to be combined with the sulphate of soda, 100 parts of the pure salt consist very nearly of,

It will be observed that this analysis coincides very nearly with that which I have deduced from Dr. Wollaston's scale, and it does not differ very materially from my analysis of the artificial compound.

Alluding to this native carbonate, and stating that it consists of 39 carbonic acid, +38 soda +23 water Dr. Thomson observes, (Chemistry, Vol. II. p. 480,) " it is evident that the African bicarbonate had lost a portion of its acid, or had never been fully saturated with carbonic acid. If we suppose this salt to be a compound of one atom of anhydrous salt, and two atoms of water, the water would amount to 19 per cent., instead of 23. If we add the four which Klaproth places to the account of the water to the acid, it would raise it to 43, which would make Klaproth's analysis approach somewhat nearer to the truth."

It appears to me, however, that, if the transfer proposed by this able chemist were made, the error would still be very considerable; the salt would then be a compound of 43 carbonic acid, and of 38 soda, whereas bicarbonate of soda consists of 43 acid, and 30.5 soda; indeed, supposing the salt ever to have been a bicarbonate, it must have lost one-fourth of its carbonic acid; but it is evident, from Klaproth's statement, that the salt which he analyzed had not suffered any change, for he remarks that the excess of carbonic acid had probably prevented efflorescence.

Mr. Faraday having obligingly supplied me with a specimen of the African salt, I found that it was distinctly crystalline in appearance, when recently broken; but the surface was not transparent, evidently from the attrition which it had undergone. The transparent salt suffered no change by exposure to the air; when moistened, it reddened turmeric paper strongly; and I found that 100 parts of it lost nearly 36.5 of carbonicacid, during solution in sulphuric acid, and it lost 30 per cent. by exposure to a red heat. It contained nearly 7 per cent. of saline and earthy impurity, which is

almost five more than the salt analyzed by Klaproth, and which will in some degree account for the smaller quantity of carbonic acid which it yielded.

The experiments which I have now detailed are, I think, sufficient to shew that the salts in question are definite compounds of 3 atoms of acid, and 2 of base; or they may be regarded as compounds of the carbonate and bicarbonate; but, whatever may be the theoretical view of their composition, they will be accurately described by prefixing sesqui to carbonate, as has been already done by Dr. Thomson, with respect to the sesquiphosphate of barytes; it will, however, be proper to remark that Dr. Thomson has accidentally stated the sesquiphosphate* to be a compound of three atoms of base, and two of acid, instead of the reverse; and I notice this, because it might otherwise be supposed that I had employed the term in a sense different from that in which he evidently intended to use it.

ART. XI. On the Figure of the Earth, as deduced from the Measurements of Arcs of the Meridian, and Observations on Pendulums. By George Fisher, Esq.

THE figure of the earth has always been an object of interesting and important inquiry. The conclusions, however, which have hitherto been drawn from such observations as have been made for determining it, are far from affording such a satisfactory agreement in the general result, as the accuracy of the instruments and skill of the observers would have led us to expect.

The observations which I allude to are the measurements of arcs of the meridian in different parts of the world; they have hitherto (with the exception of those made in middle latitudes) been found inconsistent with an elliptical meridian; and the ratio of the earth's axes as assigned by Newton on the simple supposition of homogeneity, has been discarded to make way for other suppositions of density, which, although perhaps specimens of analytic dexterity, have been as little capable of affording us any real satisfaction as the other.

In determining the ratio of the earth's axes by comparing two measured arcs of the meridian in different latitudes, it has hitherto been taken for granted in the solution of the problem, that the measured lengths of arcs of the meridian, may, without any sensible error, be taken proportional to the radii of curvature at the middle points of those arcs.

The following table, however, shews the amount of error in the amplitude of the celestial arc subtending each degree of latitude, arising from this supposition:

This table has been computed by estimating the efficacy of that part of the centrifugal force in every degree of latitude, by which a plumb line will deviate towards the southwards, from a line drawn to the earth's centre from a point on the surface, supposing

the earth a perfect sphere; and the difference of these deflections at each extremity of the measured arc, will be the error in the ce lestial angle subtending that arc. Thus, for instance, there will be an error in the celestial are subtending a measured degree from 66° to 67° of no less than 8",5; from 50° to 53° of 8",5; from lat. 45° to 46° of 0",2 only, and at the equator and poles of 12",5.

This accounts for Mr. Dalby's remark in the Phil. Trans. 1793, where he has given some calculations on measured degrees of the meridian, whence he infers that those degrees measured in middle latitudes, will answer nearly to an ellipsoid whose axes are in the ratio assigned by Newton of 229: 230. And as to the deviation of some others, viz., towards the poles and equator, he thinks they are caused by the errors in the observed celestial arcs.

If the earth be an ellipsoid of revolution, it may be conceived that since the effect of this part of the centrifugal force in urging a body towards the equator, has been duly estimated in the constitution of this solid, that a correction for this deflection will not obtain; since, from the nature of fluids, a plumb line must always be perpendicular to its surface, in order that the whole may be in equilibrio. This is true; but as the earth becomes elliptical by virtue of this centrifugal force, so will measured arcs of the meridian no longer be legitimate measures of the radii of curvature. And so long as these measured arcs are considered arcs of circles this correction for deflection will obtain. This is an instance of the fallacia suppositio" of Bishop Berkeley, or shifting the hypothesis, for the meridians are supposed elliptical in the general solution of the problem, and afterwards, that the radius of curvature due to the middle point of a measured arc (considered as an arc of a circle) is a mean nearly between the true radii of curvature at each extremity of that arc.

66

Dr. Hutton, after giving a formula expressing the relation between the earth's axes, observes-" This expression which is sim

ple and symmetrical, has been obtained without any omission " of terms on the supposition that they are indefinitely small, or

any possible deviation from correctness, except what may arise " from want of coincidence of the circles of curvature at the mid

"dle points of the arcs with the arcs themselves; and this source VOL. VII.

X

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