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and loss are nearly neutralized, and we obtain nearly the same proportions of the constituents in relation to one another, as is afforded by either of the actual results. The mean of the two analyses is as follows:- .
Silica, , ... , . 53.666
When we endeavour to ascertain in what atomic proportions these constituents are combined, we find that the formula of Berzelius, in so far as respects the solid contents of the mineral, comes near its constitution, if we substitute strontia and baryta for lime and soda. The relative proportions of water, however, afford a considerable obstacle to their accommodation. In the above analysis, it will be observed that the proportions of the baryta and strontia to one another, approach the ratio of 1 atom of the former to 2 of the latter. For,
9.75 [atom baryta] : 13 [2 atoms strontia] :: 6:5 : 8.666. -In one of my analyses, the proportions obtained bore almost exactly that ratio to one another.
If we substitute strontia and baryta for lime and soda in Berzelius' formula, we get
S3 + 4 A S3 + 8 AQ;,
and if we multiply the whole by 3, we get
2 Sr S3 + B S3 + 12 A S3 + 24 A q. If we calculate this latter formula, or the preceding one, taking Sr 2 at. Stron. + at. Bar.
-, we get
Silica, . . . . . . 53.973 Alumina, . . . . . 16.192 Strontia, . 7.7967
ļ 13.642 Baryta, . 5o846 Water, . . . . .
Which comes near the preceding analysis, with the exception of the water. With respect to this constituent, I may observe, that, on igniting a portion of the mineral containing a larger proportion of crystals than the specimen analysed, I got 13.859 per cent.; so that, if nothing but crystals were analyzed, the proportion might be still greater, although it is not likely that it would be so great as shewn by Berzelius' formula. If we could suppose that the mineral analyzed by Retzius really differed from the Brewsterite from Strontian, only in lime and soda being replaced by strontia and baryta, this mineral would afford a good illustration of the doctrine of replacement.
According to the results of my own researches, however, the formula which best expresses the constitution of Brewsterite from Strontian, is
SS2 + 4 A S3 + 6 A q; which gives,
Silica, . ..... 54-58
100 Or, if we suppose the proportion of the strontia and baryta to be 2 atoms of the former to 1 of the latter, the constitution will then be, 2 atoms bisilicate of strontia + 1 atom bisilicate of baryta + 12 atoms tersilicate of alumina + 6 atoms of water.
The title of this mineral to be viewed as the first instance of strontia occurring as a silicate, seems to be established.
À Series of Barometric Observations. By W. GALBRAITH,
Esq., A. M. Communicated by the Author.
I BEG leave to communicate to you a few more barometric observations, to which I alluded in a former paper about two years ago. In that I calculated the height of Benlomond by a process depending on several tables which I had computed for the purpose, involving the dew-points at the two places of observation, and some other minor considerations, for purposes of extreme accuracy, as far as could by that method be obtained. Indeed there is no method, where great precision is required, that does not involve difficulties and sources of error in a greater or less degree. The variable nature of terrestrial refraction, the distance of the objects observed from the situation of the instruments in trigonometrical surveying on a grand scale, as that of the British Islands by the Board of Ordnance, all tend to involve circumstances that produce error. The barometric method is not, therefo. more liable to error than the geometrical when performed trigonometrically, even with the best instruments, which are much more expensive, while the method of levelling, in the usual acceptation of the term, is seldom practicable for considerable heights. In the barometric method, the instruments are of moderate expense, especially the sympiesometer; and it will be seen, that, so far as my experience extends, the results derived from it are nearly of equal accuracy with those of the best mountain barometers, while its cheapness and portability are additional recommendations. It appears to me, however, that the sympiesometer requires rather more care in its use than the mountain barometer, on account of its being more rapidly suceptible of receiving impressions from a change of pressure from currents of air, from changes of temperature, and even. I am not sure that it does not occasionally suffer changes difficult to be accounted for from photometrical influence. All these circumstances require the observer to bestow great care in the use of it, so as to prevent any irregular influence to affect it unequally during the time of observation, on account of its extreme susceptibility. Though the mercurial barometer is a less suddenly susceptible instrument, yet the same care, nearly, must be employed when it is used, otherwise accurate results will not be obtained. Hasty observations should never be made, except from necessity, or where great precision is not required. I have repeatedly found, that when the observations are made too hurriedly, little confidence can be placed in them. To procure the utmost accuracy, good weather should be chosen, when the barometer is steady; two barometers should be used, one at the top of the height to be measured, and the other at the bottom, and the observations
should be made at the same time, either by signal, or by watches set together at times previously agreed upon. The instruments should be protected from the sun, wind, and rain, or snow, in a tent, if circumstances and convenience permit, and they should be properly adjusted before making any observations.
From my experience, I am of opinion, that the attached and 'detached thermometers, in circumstances that permit, should be allowed to come to the same temperature before any observations from which computations are to be made, should be registered, though it would be right to note them, to know whether the barometer attained a state tolerably stationary. This appears to me necessary, for circumstances have occurred which I could not explain on any other principle than that, though the attached thermometer was nearly the same as the detached, yet I was persuaded that the comparatively large mass of mercury in the barometer tube and basin which communicated with it, had not attained the same temperature, which, of course, caused small variations in the height of the column, difficult to be accounted for on any other principle. : . .
I may also remark, that when different barometers are employed, they should be carefully compared, to obtain their index errors, both at the commencement and termination of the operations, to detect any alterations, which might possibly have taken place. . On repeating the operations on different days, it would be useful for the observers to change their stations alternately from the top to the bottom. Indeed other precautions will occur to the experienced observer which the circumstances of the case and the nature of the situation seem to demand. · It sometimes happens, that the observer would think it convenient to obtain the height of objects when he has not access to tables or books, and in this case the sympiesometer would be most convenient, since the instrument performs the whole operation itself, with the exception of a simple multiplication. On the instruments now made, a small table is engraved, from which the factor answering to the sum of the temperatures at the top and bottom is immediately taken, by which the approximate height from the sliding scale is to be multiplied to produce the true height.
I shall endeavour here to investigate an easy formula, which
will be readily recollected, to procure the same advantage nearly from the mercurial barometer, and then make a comparison of the results derived from these two instruments, from heights, where I have had an opportunity of employing them ;-the first example, where they were used at different times, the other, where they were used conjointly, and read simultaneous
· Since heights determined geometrically, are proportional to the differences of the logarithms of the altitudes of the mercurial columns, a formula may be derived from the usual series, for the computation of logarithms, thus :
Let B be the altitude of the mercury at the lower station, and b that at the upper; then,
M B -6, 1/B-013 Log. B — log. b = 2M
*3B+) To apply this to the purpose required here, it will be necessary to obtain a constant factor, by which the difference of the logarithms must be multiplied, to give the heights in some known measure, such as English fathoms, or rather feet, which are now generally preferred. This number, from the observations of Ramond and the experiments of Biot, is 60155 English feet at the freezing point, or 32° of Fahrenheit's scale, and 2 M is 0.86858896, or twice the logarithmetic modulus; consequently 60,155 x 0.86858896 = 52,250, the constant co-efficient at the freezing point.
In this country, as Fahrenheit's thermometer is very generally used, it would therefore be more simple, if reduced to zero of its scale. Now, the expansion or contraction of air in its ordinary state, for 1° of Fahrenheit, is about 0·0024, whence 52250 0.0024 x 32 = 4013. Hence 52250 — 4013 = 48237, the co-efficient at zero of Fahrenheit's scale.
In practice, the mean of the temperatures of the air at the top and bottom is employed, wherefore, the result derived from the logarithmic series must be multiplied by the factor depending upon the product of the mean temperature, and the variation of the bulk of air for lo increased by unity; or it must be
multiplied by 1 +0-0024 (
) = +0-0012 (+ ++), t being