CHAPTER V.

_GRADUATING AND CALIBRATING GLASS APPARATUS._

Although the subjects to which this concluding chapter is devoted do not, properly speaking, consist of operations in glass-blowing, they are so allied to the subject, and of such great importance, that I think a brief account of them may advantageously be included.

=Graduating Tubes, etc.=--It was formerly the custom to graduate the apparatus intended for use in quantitative work into parts of equal capacity; for example, into cubic centimetres and fractions of cubic centimetres. For the operations of volumetric analysis by liquids this is still done. But for most purposes it is better to employ a scale of equal divisions by length, usually of millimetres, and to determine the relative values of the divisions afterwards, as described under calibration. It rarely happens that the tube of which a burette or eudiometer is made has equal divisions of its length of exactly equal capacities throughout its entire length, and indeed, even for ordinary volumetric work, no burette should be employed before its accuracy has been verified. An excellent method for graduating glass tubes by hand[17] has been described in Watts's _Dictionary of Chemistry_, and elsewhere. Another excellent plan, which I have permission to describe, has been employed by Professor W. Ramsay. It will be sufficient if I explain its application to the operation of graduating a tube or strip of glass in millimetre divisions.

[17] Originally suggested by Bunsen.

The apparatus required consists of a standard metre measure,[18] divided into millimetres along each of its edges, with centimetre divisions between them, a ruler adapted to the standard metre, as subsequently explained, and a style with a fine point for marking waxed surfaces.

[18] Such measures can be obtained of steel for about _fifteen shillings_ each. They are made by Mr. Chesterman of Sheffield. They can be obtained also from other makers of philosophical instruments, at prices depending upon their delicacy. Those of the greatest accuracy are somewhat costly.

Fig. 38 represents the standard measure, and the ruler.

At _AA_ are the millimetre divisions on the edges of the measure, the longer transverse lines at _BB_ are placed at intervals of five millimetres and of centimetres. The ruler is in the form of a right-angled triangle; it is shown, by the dotted lines, in position on the standard metre measure at _I_; and again, with its under surface upwards, in the smaller figure at 2. It consists of a perfectly flat sheet of metal, about ten centimetres in length from _C_ to _C_, sufficiently thick to be rigid, and has a ledge, _DD_ in each figure, which is pressed against the side of the measure when using it, to ensure that the successive positions of the edge (_LL_) shall be parallel to each other. At _GG_ are two small holes, into which fit small screws with fine points. These must be in a line parallel to the edge (_LL_), so that when the ruler is in position on the scale, the points of the two screws, which project slightly, shall fall into corresponding cuts on the divided scales (_AA_).

To graduate a strip of glass, or a glass tube (_HH_), the surface to be marked must first be coated with wax, which should be mixed with a little turpentine, and be applied to the surface of the glass, previously made _warm_ and _dry_, by means of a fine brush, so as to completely cover it with a thin, closely-adherent, and evenly-distributed coat of wax, which must be allowed to cool.

Fix _HH_ firmly on a table, and fix the standard measure by the side of _HH_. If the thickness of _HH_ be about equal to, but not greater than that of the standard measure, this may be done by large drawing-pins. If, however, a large tube or thick sheet of glass is to be graduated, fix it in position by two strips of wood screwed to the table on each side of it. One of these wooden strips, on which the measure may be placed, may be about as broad as the standard measure, and of such thickness that when the measure lies upon it beside the tube to be graduated, the ruler, when moved along the measure, will move freely above the tube, but will not be elevated more than is necessary to secure free movement. The second strip of wood may be narrower, and of the same thickness as the broader piece on which the standard measure rests. In any case, let the standard measure and the object to be graduated be very firmly secured in their places. Bring the ruler into position at any desired part of the tube by placing the points of the screws (_GG_) in corresponding divisions of the scales (_AA_). With the style, which may be a needle mounted in a handle, make a scratch in the wax along the edge of the ruler at _F_, move the ruler so that the screws rest in the next divisions, and repeat the operation till the required number of lines has been ruled. Longer marks may be made at intervals of five and ten millimetres. Great care must be taken to hold the needle perpendicularly, and to press it steadily against the edge (_LL_) of the ruler in scratching the divisions.[19] The length of the lines marking the millimetre divisions should not be too long; about 1 mm. is a good length. If they are longer than this, the _apparent_ distance between them is diminished, and it is less easy to read fractions of millimetres. Before removing the scale to etch the glass, carefully examine it to see that no mistakes have been made. If it is found that any lines have been omitted, or that long lines have been scratched in the place of short ones, remelt the wax by means of a heated wire, and make new marks. Finally, mark the numbers on the scale with a needle-point, or better, with a fine steel pen.

[19] To avoid variations of the position in which the needle is held when marking the divisions, the edge (_LL_) should not be bevelled; and an upright support may be placed upon the ruler, with a ring through which the handle of the needle passes, thereby securing that the angle formed by the needle and surface of the ruler is constant, and that equal divisions are marked.

The marks on the wax should cut through it. When they are satisfactory, they may be etched by one of the following processes:--

(1.) By moistening some cotton wool, tied to a stick, with solution of hydrofluoric acid, and gently rubbing this over the scratched surface for a minute or so; then washing away the acid with water, and cleaning off the wax. This is the simplest method, but the marks made are generally transparent, and therefore not very easy to read. The simplicity of this method is a great recommendation, however.

(2.) Expose the tube to the fumes of hydrofluoric acid generated from a mixture of powdered fluor-spar and strong sulphuric acid, in a leaden trough. The marks produced in this way are usually opaque, and are therefore very visible, and easily read.

After the above detailed account it will only be necessary to give an outline of the other process of graduating tubes.

The standard scale to be copied, _A_, which may in this case be another graduated tube, or even a paper scale, and the object to be ruled, _B_, are securely fixed, end to end, a little distance apart, in a groove made in a board or in the top of a table. A stiff bar of wood, _C_, has a point fixed at _D_, and a knife edge at _E_, _D_ is placed in any division of _A_, _C_ is held firmly at _E_ and _D_, and a cut is made by the knife through the wax on _B_, the point _D_ is then moved into the next division, and the operation is repeated. To regulate the length and position of the cuts, _B_ is usually held in position by two sheets of brass projecting over the edges of the groove in which it lies; the metal sheets have notches cut into them at the intervals at which longer marks are to be made.

When the scale is completed, the equality of the divisions in various parts of it may be, to some extent, verified as follows:--Adjust a compass so that its points fall into two divisions 5, 10, or 20 mm. apart. Then apply the points of the compass to various parts of the scale. In every part the length of a given number of divisions should be exactly the same. The individual divisions should also be carefully inspected by the eye; they should be sensibly equal. If badly ruled, long and short divisions will be found on the scale. Very often a long and a short division will be adjacent, and will be the more easily observed in consequence.

=To Divide a Given Line into Equal Parts.=--Occasionally it is necessary to divide a line of given length into _x_ equal parts. For instance, to divide the stem of a thermometer from the freezing-point to the boiling-point into one hundred degrees.

The following outline will explain how a line may be so divided. Suppose the line _AB_ (Fig. 40) is to be divided into nine equal parts. Adjust a hinged rule so that the points _A_ and _B_ coincide with the inside edges of the limbs, one of them, _A_, being at the ninth division (_e.g._ the ninth inch) of _CE_. Then if lines parallel to _ED_ be drawn from each division of the scale to meet _AB_, _AB_ will be divided into nine equal parts.

A very convenient and simple arrangement on this principle for dividing a line into any number of equal parts with considerable accuracy, is described by Miss S. Marks in the _Proceedings of the Physical Society_, July 1885.[20] One limb of a hinged rule _D_ is made to slide upon a plain rule fixed to it; the plain rule carries needles on its under surface which hold the paper in position. The position of the divided rule and line to be divided being adjusted, the hinged rule is gently pushed forwards, as indicated by the arrow in Fig. 40, till division eight coincides with the line _AB_. A mark is made at the point of coincidence, and division seven on the scale is similarly brought to the line _AB_, and so on. The inner edge of _EC_ should have the divisions marked upon it, that their coincidence with _AB_ maybe more accurately noted. The joint _E_ must be a very stiff one.

[20] Since this was printed I have observed that the above method is not identical with that described by Miss Marks, but for ordinary purposes I do not think it will be found to be inferior.

A line drawn of given length or a piece of paper may be divided into any given number of equal parts, and will then serve as the scale _A_ of Fig. 39, p. 74, the thermometer or other object to be graduated taking the place of _B_.

Scales carefully divided according to any of the methods described will be fairly accurate _if trustworthy instruments have been employed as standards_.

It will be found possible when observing the volume of a gas over mercury, or the height of a column of mercury in a tube, to measure differences of one-sixth to one-eighth of a millimetre with a considerable degree of accuracy. To obtain more delicate measurements a vernier[21] must be employed.

[21] For the nature and use of the vernier, a treatise on Physics or Physical Measurements may be consulted.

=To Calibrate Apparatus.=--The glass tubes of which graduated apparatus is made are, as already stated, very rarely truly cylindrical throughout their entire lengths. It follows that the capacities of equal lengths of a tube will usually be unequal, and therefore it is necessary to ascertain by experiment the true values of equal linear divisions of a tube at various parts of it.

A burette may be calibrated by filling it with distilled water, drawing off portions, say of 5 c.c. in succession, into a weighing bottle of known weight, and weighing them.

Great care must be taken in reading the level of the liquid at each observation. The best plan is to hold a piece of white paper behind the burette, and to read from the lower edge of the black line that will be seen. Each operation should be repeated two or three times, and the mean of the results, which should differ but slightly, may be taken as the value of the portion of the tube under examination.

If the weights of water delivered from equal divisions of the tube are found to be equal, the burette is an accurate one, but if, as is more likely, different values are obtained, a table of results should be drawn up in the laboratory book showing the volume of liquid delivered from each portion of the tube examined. And subsequently when the burette is used, the volumes read from the scale on the burette must be corrected. Suppose, for example, that a burette delivered the following weights of water from each division of 5 c.c. respectively:--

C.C. Grams.

0 to 5 gave 4.90 5 " 10 " 4.91 10 " 15 " 4.92 15 " 20 " 4.93 20 " 25 " 4.94 25 " 30 " 4.95 30 " 35 " 4.96 35 " 40 " 4.97 40 " 45 " 4.98 45 " 50 " 4.99

and that in two experiments 20 c.c. and 45 c.c. respectively of a liquid re-agent were employed. The true volumes calculated from the table would be as 19.66 to 44.46.

If the temperature remained constant throughout the above series of experiments, and if the temperature selected were 4 deg. C., the weights of water found, taken in grams, give the volumes in cubic centimetres, for one gram of water at 4 deg. C. has a volume of one cubic centimetre. If the temperature at which the experiments were made was other than 4 deg. C., and if great accuracy be desired, a table of densities must be consulted, with the help of which the volume of any weight of water at a known temperature can be readily calculated.

Pipettes which are to be used as measuring instruments should also have the relation one to another of the volumes of liquid which they deliver determined, and also the proportions these bear to the values found for the divisions of the burettes in conjunction with which they will be employed.

=To Calibrate Tubes for Measuring Gases.=--Prepare a small glass tube sealed at one end and ground at the other to a plate of glass. The tube should hold about as much mercury as will fill 10 mm. divisions of the graduated tube. Fill this tube with mercury, removing all bubbles of air that adhere to the sides by closing the open end of the tube with the thumb, and washing them away with a large air-bubble left for the purpose. If any persistently remain, remove them by means of a fine piece of bone or wood. Then completely fill the tube with mercury, removing any bubbles that may be introduced in the operation, and remove the excess of mercury by placing the ground-glass plate on the mouth of the tube, and pressing it so as to force out all excess of mercury between the two surfaces. Clean the outside of the tube, and place it on a small stand (this may be a small wide-mouthed glass bottle), with which it has been previously weighed when empty, and re-weigh. Repeat this operation several times. From the mean of the results, which should differ one from another but very slightly, the capacity of the tube can be calculated.

The purest mercury obtainable should be used. Since the density of pure mercury at 0 deg. C. is 13.596, the weight of mercury required to fill the tube at 0 deg. C., taken in grams, when divided by 13.596, will give the capacity of the tube at 0 deg. C. in cubic centimetres. If the experiment be not made at 0 deg. C., and if a very exact determination of the capacity of the tube be required, the density of mercury must be corrected for expansion or contraction.

Having now a vessel of known capacity, it can be employed for ascertaining the capacities of the divisions of a graduated tube in the following manner:--The graduated tube is fixed perpendicularly, mouth upwards, in a secure position. The small tube of known capacity is filled with mercury as previously described, and its contents are transferred to the divided tube. The number of divisions which the known volume of mercury occupies is noted after all air-bubbles have been removed. This process is repeated until the divided tube is filled. A table of results is prepared, showing the number of divisions occupied by each known volume of mercury introduced.

In subsequently using the tube the volumes of the gases measured in it must be ascertained from the table of values thus prepared.

In observing the level of the mercury, unless a cathetometer is available, a slip of mirror should be held behind the mercury close to the tube, in such a position that the pupil which is visible on the looking-glass is divided into two parts by the surface of the mercury.

A correction must be introduced for the error caused by the meniscus of the mercury. As the closed end of the tube was downwards when each measured volume of mercury was introduced, and as the surface of mercury is convex, the volume of mercury in the tube when it is filled to any division _l_ (Fig. 41) is represented by _A_ of 1. But in subsequently measuring a gas over mercury in the same tube, when the mercury stands at the same division _l_, the volume of the gas will be as represented by _B_ of 2, which is evidently somewhat greater than _A_. This will be seen still more clearly in 3, where _a_ represents the boundary of the mercury, and _b_ the boundary of the air, when the tube is filled to the mark _l_ with mercury or a gas over mercury respectively.

It is plain that when the level of the mercury in measuring a gas is read at _l_, the volume of the gas is greater than the volume of the mercury recorded, by twice the difference between the volume _A_ of mercury measured, and that which would fill the tube to the level _l_, if its surface were plane.

The usual mode of finding the true volume of a gas collected over mercury is as follows:--

Place the graduated tube mouth upwards, introduce some mercury, and, after removing all bubbles, note the division at which it stands. Then add a few drops of solution of mercuric chloride; the surface of the mercury will become level, read and record its new position. Then, in any measurement, having observed that the mercury stands at _n_ divisions of the tube, add twice the difference between the two positions of the mercury to _n_, and ascertain the volume which corresponds to this reading from the table of capacities.

=To Calibrate the Tube of a Thermometer.=--Detach a thread of mercury from half an inch to one inch in length from the body of the mercury. Move it from point to point throughout the length of the tube, and note its length in each position. If in one part it occupies a length of tube corresponding to eight degrees, and at another only seven degrees, then at the former point the value of each division is only seven-eighths of those at the latter position.

From the results obtained, a table of corrections for the thermometer should be prepared.

It is sometimes necessary to join soda glass to lead glass. In this case the edge of the lead glass tube may be bordered with white enamel before making the joint. Enough enamel must be used to prevent the lead and soda glasses from mingling at any point. The enamel is easily reduced, and must be heated in the oxidising flame. Dr. Ebert recommends _Verre d'urane_ for this purpose. It is supplied by Herr Goetze of Leipzig (Liebigstrasse).