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The apparent dilatation of mercury for 1° F. in fractional parts of its bulk when contracted so as just to fill the bulb

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2 ab❜ Then will x = 3 c For the capacity of the bulb is evidently expressed by T a3 6

and the space occupied by 1° in the tube by

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From which we have, b2 =

The tube of which the thermometer is to be blown, is assumed, as will at once be understood from the construction of the instrument, to have a perfectly equable bore, so that equal lengths may indicate equal expansion. This may be proved by causing a column of an inch or two of mercury to pass through the tube, the length occupied by which ought to be the same in every part, and those rejected which are not nearly so; at the same time it were to be desired that instead of aiming at a mere approximation to this accuracy, instrument makers would more frequently proportion the degrees of standard instruments to the absolute capacities of different portions of the tube. As the least moisture retards the accuracy of the motion of mercury, And x = and prevents it from occupying the space with nicety, tubes as soon as formed should be sealed at the ends and not opened until they are to be made use of; the operation, too, of drawing the mercury into the tube for measurement, and of blowing the bulb, should by no means be performed with the mouth, but by an elastic caoutchouc bottle fixed to one extremity of the tube, and having a valve in its side. Tubes are sometimes made with a bore not circular but elliptical, or rather formed like the section of a double convex lens, by which means the height of the mercury becomes easily visible, whilst the area of the bore is no larger than that of a minute circular one, an advantage of no trifling degree, for the difficulty of inspecting the indications of a minute capillary thermometer causes an approach of the body, the heat of which affects surprisingly the accuracy of nice experiments. This we have constantly noticed in observing the sympiesometer, the capillary thermometer of which ought always to be first observed, as the approximation of the person of the observer, while making the adjustment of the column of oil, seldom fails, notwithstanding the nicest care, to raise the indications of the mercurial bulb, which is nearer the breath of the observer than that of gas, a considerable fraction of a degree.

The proportional adjustment of the diameter of the bulb to that of the bore of the instrument and the proposed size of the degrees, it is a matter of long practice to acquire; it may however be advis

able to show the nature of these relations as a matter of theoretical importance, and of occasional utility in abstract reasoning on the subject. Some complex formulæ have, we find, been long since proposed by M. Durand, but we venture to give the following, which we have lately contrived, as being, so far as we know, original, and by far the simplest yet suggested; it will be seen that their demonstration is perfectly elementary, yet mathematically accurate.

Put the diameter of the bulb

The ratio of the diam. of the bulb to that of the bore

Hence the internal diameter of the tube

The measure of 1° F. in length

The ratio of the circumference to the di

ameter

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Now, to find will be rendered very simple by the following considerations. Biot has shown,* that calling the apparent dilatation of mercury in glass, for any temperature t; ▲; the true dilatation of mercury, and the cubic expansion of glass for 1° F., K, we have ▲ St - Kt.

t

=

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The 9990 parts at 32°, would be 10000 at 42°, mercury we have only to diminish the denominahence as far as regards the true expansion of the tor of the fraction by as many unities as the first degree of the scale close to the bulb is below 32°; and the corrected number will express the dilatation for 1 F. in fractional parts of the capacity of the bulb. It must, however, be farther corrected for the increased size of the glass, the cubical expansion of which may be taken at 4th of that of necessary defects of experiment, and that arising mercury without an error nearly equalling the from different materials; we therefore arrive at this simple rule to find the expression for. The degrees at which the stem of the thermometer commences being denoted by h,

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Traité de Physique, i. 211.

1

Also having b

11387

= 25, x = =.009148 inches to 1° F.

2 x. 25 x 252 3 x 11387 312.5 The diameter 34161 of minute bores may be easily determined from the weight of mercury required to fill a certain length. For as tubes vary in capacity as the squares of their diameters, and as one inch in length of a tube an inch in diameter contains 2700 grains of mercury, we may use this proportion; as 2700: 12: the weight of one inch of mercury in the given tube: the square of its diameter in parts of an inch. The application of very minute bores to alcohol thermometers, especially when a thread of mercury is introduced as in the instrument proposed by the Chevalier Landriani,* we consider as inapplicable in practice.

The form of the bulb of thermometers has varied according to their applications. Most frequently they are spherical, as at Plate DXXIV, Fig. 8., or elongated as Figs. 9 and 10, a form much to be commended as promoting an equilibrium of temperature through the mercury. So far indeed was this carried in former times, when from the size of the tubes the bulbs were necessarily so very large, that they were made extremely long and coiled up, as shown at Fig. 11, a form which we have often seen adopted both in France and Italy, as in the latter country, flattened bores seem quite unknown. To form the bulb, after the elastic bottle already mentioned has been attached, the other extremity of the tube is heated to fusion and then pressed flat by a piece of metal. The button thus formed is then raised to a white heat and kept constantly turning to prevent it from falling aside; by the action of the bottle the bulb is blown, but is repeatedly returned to the lamp till the requisite thinness is obtained, and the desired shape may then be given it, if it is to differ from the spherical; in addition to those already noticed, we may mention the lenticular, which is well fitted for exposing a large surface to the surrounding medium. It was proposed so long ago as by Drebbel, and is still imitated in Italy.

The next operation is to fill the tube, which is commenced by expelling a portion of the air by heat, and immersing the open end in clean mercury, which ought to be recently distilled; when a considerable quantity has thus entered the bulb, a paper cylinder should be formed by rolling a slip round the end of the tube, into which some mercury being placed, the contents of the half filled bulb are to be brought to a state of ebullition, and the vapour occupying the empty space, on condensing, the mercury will descend from the paper cylinder with rapidity and fill the instrument. Where considerable nicety is required, the mercury should be boiled carefully and repeatedly in the bulb and tube to expel all moisture and particles of air, during

which operation it will be prevented from escaping by the upper receptacle already mentioned. When completely filled, enough of mercury may be expelled from the top to render its height convenient, and the length of the tube must be proportioned to its entire range.

The tube must next be hermetically sealed, in doing which, if a vacuum above the mercury be desired, the termination of the tube being brought to a capillary orifice, the bulb must be heated till a few drops of mercury are in the act of escaping, when the flame of a lamp must be suddenly directed so as to close the communication with the atmosphere. With these precautions, and if the thermometer has throughout been well made, the mercury will run up from the bulb when reversed, even in very fine tubes, unless they have the last degree of capillarity. How far the accuracy of this vacuum is a matter of importance or even of benefit, has lately been questioned, and indeed vague notions seem to have prevailed regarding the resistance which the inclosed air offers to the motion of the mercury in expanding. It lately occurred to the author of this article, that considering the enormous effort of fluids to expand almost any degree of pressure which the glass of a thermometer can sustain, could have no effect in this way; but only perhaps a small one by dilating the glass of the bulb, which might have the effect of lowering the surface of the fluid. To ascertain this point, which seems not before to have been practically examined, the following experiment was made. Three thermometers without scales were procured, perfectly similar in size and structure, with flat tubes and small bulbs, two of which were sealed in vacuo, and the third was sealed, having the upper part of the tube filled with air at the temperature of 62°. All three were plunged in this state into ice cold water and afterwards into several warmer mixtures, and the most regular of the two vacuum thermometers was chosen for careful comparison. Several points were accurately marked with waxed thread, and being plunged into water, which by a suitable contrivance was kept very steady in temperature, it was compared with the instrument in which air was sealed, and on the tube of the latter minute file marks were made at the various points. The extremity of the tube of the latter was then broke off, and by a new comparison other marks were made, the results of which are shown in the following table:

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* Brande's Journal, vii. 183.

B 2

The first column shows the temperature indicated by the correct standard; the second the pressure in atmospheres computed from the reduction of space in which the air was confined, counting the upper limit of the tube = 145°, and hence the bulk of 83° (or 145-62) corresponding to one atmosphere. The third column marks the constant pressure to which the mercury was exposed after the end of the tube was broke; the fourth, the difference of pressure in the two cases; and the fifth, the errors of the thermometer corresponding to these. The last numbers, however, must be considered merely approximations, from the smallness of the degrees on the instruments employed; however, they sufficiently prove that the effect of any minute quantity of air left in the tubes must be wholly insensible.*

The vacuum which has generally been left above mercury is supposed to be the cause of an irregularity observed in old thermometers, their indications being somewhat too high. This inquiry, a few years ago, produced several series of experiments by different observers, the discordance of whose results seems to have prevented the final settlement of the question. M. Flaugerguest at tributed the rise of nine-tenths of a degree which he observed in the freezing point of thermometers, to the atmospheric pressure on the exterior of the bulb, as did MM. De la Rive and Marcet of Geneva, who recommended, that the upper end of thermometers should be left open. Bellani of Milan, however, denies that this precaution has the desired effect, and imputes the alteration to molecular action in the parts of the glass, and to the time which that rigid material takes to assume its final form after the operation of blowing. M. Arago, attributes the alteration to the escape of particles of air from between the mercury and the glass. Professor Moll doubts the existence of the alleged rise at all; we think, however, it has been satisfactorily proved by a great number of comparisons, though we know not if it has been suggested that some of these errors might be explained by the use of freezing water instead of melting ice in graduation, which was common in the last century, and which usually gives a temperature somewhat lower than the melting ice. Perhaps the most unequivocal proofs of the fact are those given by Mr. Daniell, in his excellent Meteorological Essays, who examined two thermometers made in the last century by Mr. Cavendish, who had graduated them only a little above and below the freezing point, and made the degrees very large; in one of these the freezing point had risen 0.04, and in the other 0.035.** Should the pressure of the air be proved to be the final cause, we should

prefer inclosing a little air in the tube to act as a counterpoise, to leaving the extremity open which would admit moisture and injure the delicacy of the instrument.

When the thermometer is sealed it must next be graduated; the materials used for scales are various, and of these, perhaps, ivory is the best: metal scales injure the delicacy of the instrument by their high conducting power. Perhaps the best of all is that engraved on the tube, which is sometimes done in chemical thermometers. We have already discussed the fixed points of thermometers, but we must here say a few words upon the precautions in using that of boiling water, requiring an equation, to which we have alluded in a former part of this article.

From various causes, the precise temperature of boiling water may be subject to considerable variation, for instance, from the nature of the vessel employed, Gay Lussac having found†† that while water in a metallic vessel vaporizes at 212°, it will sustain a heat of 214o or even 216° in one of glass. It was with great judgment, therefore, that the Royal Society of London, about the middle of the last century, appointed a committee, at the head of which was Mr. Cavendish, to investigate the fixed points of thermometers, and their elaborate report published in the Philosophical Transactions‡‡ seems calculated to put to rest all further doubts on the subject. They recommend a tall vessel of tin plate, with a tight cover, having two apertures, one through which the thermometer is introduced, and fitted by a pierced cork; the other to which a chimney is affixed, two or three inches long, for the escape of steam, and over which a thin piece of metal is laid to act as a valve to prevent its too rapid escape. The thermometer is recommended to be suspended in steam a little above the surface of the water, it is therefore necessary that the steam should be kept of uniform tension. Fahrenheit first observed about 1724 the effect of atmospheric pres sure on the boiling points of liquids, which rendered it necessary to graduate thermometers at a fixed state of the barometer, which ought to be 29.50, when the temperature of the water is taken and 29.80 when that of the steam. Deluc afterwards investigated the laws of this variation, and his formula for the equation of it, reduced to English measures, is the following:

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As it was only the general fact which was desired to be ascertained, we have not thought it necessary here to inquire more particularly into the causes or precise magnitudes of the differences observed; indeed it would have been superfluous with the means employed to have attempted greater accuracy, since a tenth of a degree was hardly perceptible. We are convinced, however, that the difference under the two cases of observation did not exceed that quantity either at 329 or at 63°, the latter observation being twice repeated with the nicest accuracy. It is, however, rather remarkable that the defect at higher temperatures appears in no respect proportional to the pressure sustained.

+ Bibliotheque Universelle, xx. 117: xxi. 252.

§ Giornale di Fisica, tom. 5.

Edinburgh Philosophical Journal, ix. 196.

tt Ann. de Chimie, vii. 308, and Brande's Journ. v. 361.

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The numbers refer to the temperature of the water, that of steam is about 0°.4 lower.

Upon the principle suggested by this table of measuring the pressure of atmosphere by the thermometer, Cavallo (though Fahrenheit had before hinted at it) proposed his thermometrical barometer, in the execution of which, several practical difficulties occurred till they were overcome by the Rev. Mr. Wollaston, who has more lately constructed a very elegant instrument on this principle.* It consists of a bulb a, Plate DXXIV. Fig. 12, one inch in diameter, the tube of which d e contains a few degrees near the boiling point, of such a length, that in the most delicate instruments, each of them admits of a division into 1000 parts by means of a scale ef with a vernier; one of these parts corresponds to a difference of level of six inches. When in use, the thermometer is placed as shown in the figure in the cistern A containing water, which is made to boil by means of the spirit lamp B. When the observation is finished, the mercury contracts into the dilated part of the tube b, and being then inverted into the cistern and fixed by the screwing plate g g into which the stem of the thermometer is secured, a cap being screwed over the bulb which is then exposed, the instrument becomes extremely portable, the boiler being only 5.5 inches deep, and 1.2 in diameter. In order to shorten the tube without diminishing the range or the sensibility, a cap c is added by which some of the mercury may be expelled from the tube, or united to the column if the heights are great, and the depression likely to be considerable. A steam-pipe is employed similarly to the instrument of the Royal Society's Committee above described. The principal defect of Mr. Wollaston's thermometer is its liability to breakage in carriage, on account of the great weight of the large mercurial bulb. We Phil. Trans. 1817, p. 184.

are disposed to think that some fluid, such as sulphuric acid, which has a moderate specific gravity, and boils at a very high temperature, might, by being substituted for mercury, obviate this defect; any small inequalities of expansion (if such exist) would be quite insensible in so small a range.

We shall now describe as concisely as possible the principal modifications of the simple thermometer; the most interesting of these are termed selfregistering, which by inspection denote the greatest heat or cold which has occurred since the last observation, or else are employed to note the temperature at any moment in the absence of the observer. Of the former kind, the first which deserves notice, though Bernouilli seems to have the merit of originating the idea, is the thermometer of Lord Charles Cavendish. For the maximum, he employed a mercurial thermometer, A b, Fig. 13, in which the temperature at the time of observation was indicated by the height of the mercury at C, while resting upon it was a column of alcohol which filled the tube. The termination of the bore was capillary, and covered by a glass receptable b, into which the capillary termination projected about two-thirds of the depth of the cap. By a rise of temperature, the mercury forces a portion of the spirits over the extremity of the tube, and as it cools, sinks without the possibility of the column of spirit carrying back what was expelled; the empty space of the tube, therefore, indicates the excess of the highest temperature since the last observation, above that indicated by the actual height of the mercury. It is adjusted by reversing the instrument and heating the bulb with the hand till the column unites with the spirit in the cap b, when the termination of the tube being covered, in this position it is allowed to cool, and the column is again made continuous. There are two defects in this instrument, the time required to assume the temperature of the air in the adjustment, which is obviously necessary, and that when in a reversed position and contracting, the mercury allows some of the spirit to pass it. We have found it useful in employing this thermometer to cool the bulb by means of ether, more speedily than it would otherwise have done to the temperature of the air. The minimum thermometer of the same philosopher was far more complex, and we suspect nearly impracticable. Its principle is represented at Plate DXXIV. Fig. 14, where the bulb A is filled with spirit, and also the bulb B, except a small portion of the mercury in the bottom, a column of mercury commences in the leg of the syphon a b, and indicates the temperature by its height at C. As the temperature declines, the mercury at b is drawn up into the bulb B into which it is intended to trickle by minute drops, the neck of communication a having a fine glass thread within it; a plan ingenious in theory, but we fear almost unattainable for practical purposes of adjustment, more especially as when it was to be prepared for a new observation, it was expected that on being inclined, the mercury would trickle back through a, and pass

† Phil. Trans. 1757.

ing the spirits which had occupied it, reunite with its own column, a supposition rather startling to those who are acquainted with the motions of mercury and spirit.

*

A modification of Lord Charles Cavendish's thermometers, combining both a maximum and minimum register, in which the contrivance for the latter is greatly simplified, has recently been proposed by Mr. Forbes, and a figure of it is given at Fig. 15, where a is the bulb filled with spirits, and having a little mercury in the bottom, being of the peculiar form there represented. The tube which terminates with it in a capillary orifice c is filled with mercury as far as h, which marks upon a scale the true temperature of the moment: above the mercury is a column of spirit, which by means of a capillary orifice, and cover d, indicates the maximum as in the thermometer just described. The portion of the tube ef, which is filled with spirit at any observation, of course indicates the quantity of mercury expelled into the bulb, and consequently by the application of a scale, the greatest depression of temperature. The instrument is adjusted by reversing it, when the spirit will cover the upper orifice, and the mercury the lower one; the hand is applied to the bulb till the spirit column is joined, and ether is then poured upon it till the mercurial column is brought in contact with the magazine in the bulb, the hand may be again employed to raise the temperature to that of the air as previously observed by the height h. By this means the instrument will be much quicker adjusted than even in Lord C. Cavendish's maximum, for which also we have found it advisable to use ether to reduce it quickly by the actual temperature. Notwithstanding the immense superiority in the simplicity of this instrument to the minimum one above described, we suspect from some attempts we have made on the subject, that there are almost insupportable practical obstacles to the satisfactory or general use of this thermometer, however accurate it may be in theory.

The thermometer which succeeded those of Cavendish was that of Mr. Six, described in the Philosophical Transactions for 1782.† It is represented in Fig. 16, where a represents an elongated bulb filled with spirit, which is continued through the curve b down to h, where mercury begins, and occupying the lower bend of the tube, reaches up to i, where the spirit recommences, and partly fills the expansion of the tube c, so as to give it space for its enlarged bulk when the temperature of the bulb a is raised. Placed within the spirit above its contact with the mercury are the two indices e, f,

which are composed of steel coated with glass, and terminated with a dot of enamel on each end; to prevent them moving through the spirit by their own weight, a spring of glass was attached to them, for which now a bristle is more generally employed. It is obvious that, by the motion of the mercurial column as the spirit in the bulb contracts and expands, the indices will be left in the tube at different heights e and f, the indications of which are ascertained by two scales shown in the figure, the one of which is of course numbered downwards, the other upwards. The adjustment is made by means of a magnet, which brings down the indices into contact with the mercurial column.

This instrument, it will be observed, is not a little complex in its parts, having two contacts of spirit and mercury, and two indices, all which are detrimental to the practical accuracy of the thermometer. On this account the instrument has usually been made on a large scale, to prevent derangement in working; Mr. Six made the bulb no less than sixteen inches long, and half an inch diameter, while the tube had a bore of inch. But this enormously clumsy instrument had from its size still greater defects for any delicate purposes, and has since been much reduced; an instrument of this description, which we used almost constantly for nearly two years, made by one of the best London makers, had a bulb of only six inches in length. Yet we cannot help noticing the extremely slovenly manner in which all register thermometers are still made. The very instrument just mentioned had a tube of large bore, and two indices more than three quarters of an inch long, where half that size would certainly have been much better, and was farther mounted on a clumsy scale of boxwood, so that we confess it always surprised us that the instrument should act so well as it did. We observed sometimes a liability in the mercury to change its position in the column of spirits, which made the two ends not always point to the same degree on the opposite scales, a defect to which the varying length of the column of mercury itself, by great extremes of temperature, may also contribute. The indices are likewise liable to go wrong, and one of them constantly required the use of a very powerful horse shoe magnet after it had been for a short time in use. Were Six's thermometer, however, made with all the care and delicacy of which it is susceptible, it might, we have no doubt, be rendered an excellent instrument. It is perhaps better fitted than any yet contrived to measure the temperature of considerable depths

† Vol. Ixxii. p. 72.

Dr. Brewster's Journal of Science, No. XIX. Jan. 1829, p. 159. Six's self-registering thermometer is a spirit of wine thermometer, the mercury serving only to float the indices. This instrument, as now made by Carey, Jones, and other meteorological instrument makers, is of more convenient dimensions than that mentioned by Dr. Brewster. By information derived from gentlemen well acquainted with this instrument, and who have had ample opportunities of comparing with others of similar design, it is believed to be the best and most correct of any of the self-registering thermometers now in use. It is, however, liable to the general objection against all spirit thermometers for high temperatures. The irregularity remarked by Dr. Brewster as respects pointing to the same degree of heat on the opposite scales, often arises from the position of the observer, who, in place of looking horizontally on both lines of mercury, looks down upon one and up to the other; this will make with each in appearance the difference of half a degree or more from the real height, occasioning an apparent difference of more than a degree between the two lines. As in all other thermometers, it must be made with a careful regard to the uniformity of the bore of the several bendings of the instrument. Six's son published in 1794 an excellent posthumous work of his father's on the construction and use of a thermometer for showing extreines of temperature in the atmosphere during the observer's absence, with experiments on the variations of local heats, &c. &c.-Editor Am. Ed.

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