Principles and practice of agricultural analysis. Volume 3 (of 3), Agricultural products

Thus, by gradually turning the analyzer, the field of vision passes slowly from maximum luminosity to complete obscurity. The expression crossed nicols refers to the latter condition of the field of vision.

62. Description of the Prism.—In a nicol made as described above, Fig. 31, suppose a ray of light parallel with the longer side of the prism be incident to the end a b at m. By the double refracting power of the spar the ray is divided into two, which traverse the first half of the prism. The two rays are polarized at right angles to one another. The less refracted ray when it strikes the film of Canada balsam passes through it without interference. The more refracted ray strikes the balsam at o at such an angle as to be totally reflected and made to pass out of the prism in the direction o r. If the prism be blackened at the surface the ray will be entirely absorbed. The other ray passes on through the other half of the prism and emerges in the direction of qs. It is evident that the emergent light from a nicol has only half the illuminating power possessed by the immergent rays.

The polarized plane of light from the nicol just described may be regarded as passing also into a second nicol of essentially the same construction as the first.

This second nicol, called the analyzer, is so constructed as to revolve freely about its longitudinal axis, and is attached to a graduated circle in such a way that the degree of rotation can be accurately read. If the planes of polarization of the two nicols are coincident when prolonged, the ray of light passing from the first nicol will pass through the second practically unchanged in character or intensity. If, however, the analyzing nicol be turned until the plane of polarization is at right angles to that of the polarizer the immergent ray will suffer refraction in such a manner as to be totally reflected when reaching the film of balsam and will be thus entirely lost. In making a complete revolution of the analyzer, therefore, two positions of maximum intensity of light and two of darkness will be observed. In intermediate positions the ray immergent to the analyzer will be separated as in the first instance into two rays g p varying intensities, one of which will be always totally reflected.

In Fig. 32 is given a more detailed illustration of the action of the rays of light. The film of balsam is represented as enlarged and of the thickness bb. Draw the perpendiculars represented by the dotted lines n₁ nʹ₁, n₂ nʹ₂, n₃ nʹ₃ and n₄ nʹ₄. In passing into the prism at m both refracted rays are bent towards the normal m nʹ₁. The degree of deflection depends on the refractive index of the two rays 1.52 and 1.66 respectively. The refractive index of the extraordinary ray in calcspar being 1.52, and in Canada balsam 1.54, it suffers but little disturbance in passing from one to the other. On the other hand the balsam, being considerably less refractive for the ordinary ray than the calcspar, causes that ray to diverge outwards from the normal o nʹ₂, and to such a degree as to suffer total reflection. The critical angle, that is the angle at which a ray issuing from a more refractive into a less refractive medium, emerges just parallel to the bounding surfaces, depends on the relative index of refraction. In the case under consideration the ratio for balsam and spar is 1.54/1.66 = 0.928 = sin 68°. Therefore the limiting value of m o n₃ so that m o may just emerge in the direction od is 68°. If now mo were parallel to o d the angle m o n, would be just 68°, being opposite b a d. which has been ground to 68° in the construction of the prism. But in passing into the prism, m o is refracted so that the angle m o n₃ is greater than b a d. It is therefore always certain that by grinding b a d to 68° the ordinary ray m o will be with certainty entirely thrown out in every case. In respect of the analyzing nicol the following additional observations will be found useful. In all uniaxial crystals there are two directions at right angles to each other, one of greatest and one of least resistance to the propagation of luminous vibrations. These planes are in the direction of the principal axis and at right angles thereto. Only light vibrating in these two directions can be transmitted through calcspar; and all incident light propagated by vibrations in a plane at any other angle to the principal section is resolved into two such component rays. But the velocities of transmission in the two directions are unequal, that is, the refractive index of the spar for the two rays is different. If the analyzing nicol be so adjusted as to receive the emergent light from the polarizer when the corresponding planes of the two prisms are coincident when extended, the emergent extraordinary ray falling into a plane of the same resistance as that it had just left is propagated through the second nicol with the same velocity that it passed the first one. It is therefore similarly refracted. If, however, the two prisms be so arranged that corresponding planes cross then the extraordinary ray falls into a plane which it traverses with greater velocity than it had before and is accordingly refracted and takes the course which ends in total reflection at the film of balsam. No light therefore can pass through the prism in that position. If any other substance, as for instance a solution of sugar, capable of rotating a plane of polarized light, be interposed between the two nicols the effect produced is the same as if the analyzer had been turned to a corresponding degree. When the analyzer is turned to that degree the corresponding planes again coincide and the light passes. This is the principle on which the construction of all polarizing instruments is based.[36]

63. The Polariscope.—A polariscope for the examination of solutions of sugar consists essentially of a prism for polarizing the light, called a nicol, a tube of definite length for holding the sugar solution, a second nicol made movable on its axis for adjustment to the degree of rotation and a graduated arc for measuring it. Instead of having the second nicol movable, many instruments have an adjusting wedge of quartz of opposite polarizing power to the sugar, by means of which the displacement produced on the polarized plane is corrected. A graduated scale and vernier serve to measure the movement of the wedges and give in certain conditions the desired reading of the percentage of sugar present. Among the multitude of instruments which have been devised for analytical purposes, only three will be found in common use, and the scope of this volume will not allow space for a description of a greater number. For a practical discussion of the principles of polarization and their application to optical saccharimetry, the reader may conveniently refer to the excellent manuals of Sidersky, Tucker, Landolt, and Wiechmann.[37]

64. Kinds of Polariscopes.—The simplest form of a polarizing apparatus consists of two nicol prisms, one of which, viz., the analyzer, is capable of rotation about its long axis. The prolongation of this axis is continuous with that of the other prism, viz., the polarizer. The two prisms are sufficiently removed from each other to allow of the interposition of the polarizing body whose rotatory power is to be measured.

For purposes of description three kinds of polarimeters may be mentioned.

1. Instruments in which the deviation of the plane of polarization is measured by turning the analyzer about its axis.

Instruments of this kind conform to the simple type first mentioned, and are coeteris paribus the best. The Laurent, Wild, Landolt-Lippich, etc., belong to this class.

2. Instruments in which both nicols are fixed and the direction of the plane of polarized light corrected by the interposition of a wedge of a solid polarizing body.

Belonging to this class are the apparatus of Soleil, Duboscq, Scheibler, and the compensating apparatus of Schmidt and Haensch.

3. Apparatus in which the analyzer is set at a constant angle with the polarizer, and the compensation secured by varying the length or concentration of the interposed polarizing liquid.

The apparatus of Trannin belongs to this class.

65. Appearance of Field of Vision.—Polarimeters are also classified in respect of the appearance of the field of vision.

1. Tint Instruments.—The field of vision in these instruments in every position of the nicols, except that on which the plane of vibration of the polarized light is coincident with the three principal sections, is composed of two semi-disks of different colors.

2. Shadow Instruments.—The field of vision in this class of polarimeters in all except neutral positions, is composed of two semi-disks, one dark and one yellow. As the neutral position is approximated the two disks gradually assume a light yellow color, and when neutrality is reached they appear to be equally colored.

The Laurent, Schmidt and Haensch shadow and Landolt-Lippich instruments, are of this class.

3. Striated Instruments.—In this class the field of vision is striated. The lines may be tinted as in Wild’s polaristrobometer or black, as in the Duboscq and Trannin instruments. The neutral position is indicated either by the disappearance of the striae (Wild) or by the phenomenon of their becoming continuous. (Duboscq, Trannin.)

66. Character of Light Used.—Polariscopes may be further divided into two classes, based on the kind of light employed.

1. Instruments which Use Ordinary White Light.—(Oil lamp, etc.) Scheibler, Schmidt and Haensch.

2. Instruments Employing Monochromatic Light.—(Sodium flame, etc.) Laurent, Landolt-Lippich, etc.

67. Interchangeable Instruments.—Some of the instruments in common use are arranged to be used either with ordinary lamp or gas light, or with a monochromatic flame. Laurent’s polarimeter is one of this kind. The compensating instruments also may have the field of vision arranged for tints or shadows. Theoretically the best instrument would be one in which the light is purely monochromatic, the field of vision a shadow, and the compensation secured by the rotation of the second nicol.

The accuracy of an instrument depends, however, on the skill and care with which it is constructed and used. With quartz wedges properly ground and mounted, and with ordinary white light, polariscopes may be obtained which give readings as accurate as can be desired.

Since many persons are more or less affected with color-blindness, the shadow are to be preferred to the tint fields of vision.

For practical use in sugar analysis the white light is much more convenient than the monochromatic light.

For purposes of general investigation the polarimeters built on the model of the laurent are to be preferred to all others. Such instruments are not only provided with a scale which shows the percentage of sucrose in a solution, but also with a scale and vernier by means of which the angular rotation which the plane of vibration has suffered, can be accurately measured in more than one-quarter of the circle.

DESCRIPTION OF POLARIZING INSTRUMENTS.

68. Rotation Instruments.—This instrument has already been described as one in which the extent of deviation in the plane of polarized light caused by the intervention of an optically active substance is measured by rotating one of the nicols about its axis and measuring the degree of this rotation by a vernier on a graduated arc.

In Germany these instruments are called polaristrobometers, and in France polarimètrés. In England and this country the term polariscope or polarimeter is applied without discrimination to all kinds of optical saccharimeters.

The polariscope of Mitscherlich was one of the earliest in use. It has now been entirely superseded by more modern and accurate instruments.

69. The Laurent Instrument.—A polariscope adapted by Laurent to the use of monochromatic yellow light is almost exclusively used in France and to a considerable extent in this country. In case a worker is confined to the use of a single instrument, the one just mentioned is to be recommended as the best suited to general work. It has the second nicol, called the analyzer, movable and the degree of rotation produced is secured in angular terms directly on a divided circle. The scale is graduated both in angular measurements and in per cents of sugar for a definite degree of concentration of the solution and length of observation tube. The normal solution in the laurent instrument contains 16.19 grams of pure sugar in 100 true cubic centimeters, and the length of the observation tube is 200 millimeters. Both the angular rotation and the direct percentage of sugar can be read at the same time. Great accuracy can be secured by making the readings in each of the four quadrants. The light is rendered yellow monochromatic by bringing into the flames of a double bunsen, spoons made of platinum wire, which carry fragments of fused sodium chlorid.

70. The Laurent Burner.—The theory of the illumination of the laurent burner is illustrated by the accompanying Fig. 33. The lamp consists essentially of two bunsens, surmounted by a chimney.[38] A curved spoon made of platinum gauze serves to hold the fused particles of sodium chlorid which are used to produce the yellow light. The spoon is shown at G, held by the arm F, fastened by the key P. The interior intense flame B B is surrounded by an exterior less highly colored flame A A. It is important that the optical axis of the polariscope be directed accurately upon the disk B, which is the most intense part of the illumination. The point of the spoon carrying the salt should be coincident with the prolongation of the lamp TT, so that it just strikes the edge of the blue flame. Care should be taken not to press the spoons into the interior of the flame as by so doing the intensity of the illumination is very much diminished. Great care must be observed in the position of the spoon G, and the platinum arm F being flexible, the operator with a little patience, will be enabled to properly place the spoon by bending it. Moreover, if the spoon be pressed too far into the flame, the melted particles of salt collecting in the bottom of G may drop into the lamp and occlude the orifices through which the gas enters. The light of the yellow flame produced by the lamp may be further purified by passing through a prism filled with a solution of potassium dichromate, or better, a homogeneous disk cut from a crystal of that salt.

Since the flame produced by the above device is not perfectly constant, being more intense at the moment of introducing a fresh portion of the fused salt, the author has used a lamp designed to furnish an absolutely constant flame.[39] This device which is shown in Fig. 34, is based on the principle of adding constantly a fresh portion of the salt to the flame. The flame is thus kept perfectly uniform in its intensity.

The lamp consists essentially of two wheels with platinum gauze perimeters and platinum wire spokes, driven by a clock-work D, and mounted by the supports AAʹ as shown in the figure. The sodium salt, chlorid or bromid, in dilute solution, is placed in the porcelain crucibles F, supported by BBʹ as indicated in the figure, to such a depth that the rims of the platinum wheels dip beneath the surface as they revolve. The salt is volatilized by the lamp E. By means of the crossed bands the wheels are made to revolve in opposite directions as indicated by the arrows. The solution of the salt which is taken up by the platinum net-work of the rim of the wheel, thus has time to become perfectly dry before it enters the flame and the sputtering which a moist salt would produce is avoided. At every instant, by this arrangement, a minute fresh portion of salt is introduced into the flame with the result of making a perfectly uniform light which can be used for hours without any perceptible variation. The mechanism of the apparatus is so simple that no further description is necessary. The polariscope should be so directed toward the flame as to bring into the field of vision its most luminous part. The platinum wheels are adjustable and should be so arranged as to produce between them an unbroken yellow flame. The wheels are eight centimeters in diameter and are driven at a rate to make one revolution in from six to ten minutes.

71. Construction of Laurent’s Apparatus.—The shadow polariscope invented by Laurent is constructed as follows: The polarizer is a special nicol which is not fixed in its position, but is so arranged as to be turned through a small arc about its axis. By this device, the quantity of light passing through it can be regulated, and the apparatus is thus useful with colored solutions which are not easily cleared by any of the common bleaching agents. The greater the quantity of light admitted, however, the less delicate is the reading of the shadow produced. The plane of polarized light emergent from this prism, falls on a disk of glass half covered by a thin lamina of quartz which thus divides the field of vision into halves. It is this semi-disk of quartz which is the distinguishing feature of the apparatus.[40] The polarized light thus passes without hindrance the half field of vision which is covered by the glass only, but can not pass the quartz plate unless its axis is set in a certain way. The field of vision may be thus half dark, or both halves may be equally illuminated or equally dark according to the position of the nicol analyzer which is freely movable about its axis and carries a vernier and reading glass over a graduated circle. The field of vision in the laurent may have any of the following forms.[41] Let the polarizer be first so adjusted that the plane of polarization of the transmitted pencil of light is parallel to the axis of the plate lying in the direction A B. The two halves of the field of vision will then appear equally illuminated in every position of the analyzer. But if the polarizing nicol be inclined to AB at an angle a, the plane of polarization of the rays passing through the quartz plate will undergo deviation through an equal angle in the opposite direction.

It happens from this, that when in the uncovered half of the field, the plane of polarization has the direction AC, in the other half it will have the direction ACʹ. When the analyzer is rotated, if its plane of polarization lie in the direction cc, the rays polarized parallel to AC will be completely extinguished and the corresponding half of the field will be dark. The opposite happens when the plane of polarization lies in the direction of cʹcʹ. When one-half of the field is thus obscured, the other suffers only a partial diminution in the intensity of its illumination. When the middle position bb is reached in the rotation of the analyzer, the illumination of the two halves is uniform, and this is the point at which the zero of the scale is reached. The slightest rotation of the analyzer to the right or left of this neutral point will cause a shadow to appear on one of the halves of the field, which by an oscillatory movement of the analyzer, seems to leap from side to side. The smaller the angle a or BAC, the more delicate will be the shading and the more accurate the observation. This angle being adjustable by the mechanism already described, should be made as small as will permit the admission of the quantity of light requisite for accurate observation.

The various pieces composing the polariscope are arranged in the following positions, beginning on the right of Fig. 36, and passing to the left, where the observer is seated.[42]

1. The lamp VV, TT, AA, or the wheel burner:

2. The lens B for condensing the rays and rendering them parallel:

3. The tube I, blackened inside to carry the lens:

4. A thin lamina E, cut from a crystal of potassium bichromate, serving to render the sodium light more monochromatic: When the saccharine liquids under examination are colored the crystal of bichromate is removed before the observation is made.

5. The polarizer R, which is rotatable through a small angle by the lever K:

6. The lever JK for rotating the tube containing the polarizer: This is operated by the rod X extending to the left.

7. Diaphragm D, half covered with a lamina of quartz.

8. Trough L for holding the observation tube: In the large instrument shown in the figure, it is more than half a meter in length and arranged to hold an observation tube 500 millimeters long.

9. Disk C, carrying divided circle and arbitrary sugar scale:

10. Mirror M, to throw the light of the lamp on the vernier of the scale:

11. Reading glass N, carried on the same radius as the mirror and used to magnify and read the scale:

12. Device F, to regulate the zero of the instrument:

13. Tube H, carrying a nicol analyzer and ocular O for defining the field of vision: This tube is rotated by the radial arm G, carrying the mirror and reading glass.

72 Manipulation.—The lamp having been adjusted, the instrument, in a dark room, is so directed that the most luminous spot of the flame is in the line of vision. An observation tube filled with water is placed in the trough and the zero of the vernier is placed accurately on the zero of the scale. The even tint of the field of vision is then secured by adjusting the apparatus by the device number 12.

73 The Soleil-Ventzke Polariscope.—A form of polariscope giving a colored field of vision was in use in this country almost exclusively until within ten years, and is still largely employed. There are many forms of tint instruments, but the one almost exclusively used here is that mentioned. A full description of their construction and manipulation is given by Tucker.[43] By the introduction of a third rotating nicol in front of the lens next to the lamp, the sensitive tint at which the reading is made can be kept at a maximum delicacy. These instruments are capable of rendering very reliable service, especially in the hands of those who have a delicate perception of color. They are inferior, however, to the shadow instruments in delicacy, and are more trying to the eye of the observer. The shadow instruments therefore, especially those making use of an ordinary kerosene lamp, have practically driven the tint polariscopes out of use.

The general arrangement of a tint instrument as modified by Scheibler is shown in Fig. 37.

Beginning on the right of the figures, its optical parts are as follows: A is a nicol which, with the quartz plate B, forms the apparatus for producing the light rose neutral tint. The proper degree of rotation of these two parts is secured by means of the button L attached to the rod carrying the ratchet wheel as shown. The polarizing nicol is at C, and D is a quartz disk, one-half of which is right-handed and the other left-handed. At G is another quartz plate belonging to the analyzing part of the apparatus. This, together with the fixed quartz wedge F, and the movable quartz wedge E, constitute the compensating apparatus of the instrument whereby the deviation produced in the plane of polarized light by the solution in the tube is restored.

Next to the compensating apparatus is the analyzing nicol which in this instrument is fixed in a certain place, viz., the zero of the scale. The analyzer and the telescope for observing the field of vision are carried in the tube HJ. The movable quartz wedge has a scale which is read with a telescope K, provided with a mirror inclined at an angle of 45°, just over the scale and serving to illuminate it. The quartz wedges are also provided with a movement by which the zero point of the scale can be adjusted. A kerosene lamp with two flat wicks is the best source of illumination and the instrument should be used in a dark room and the light of the lamp, save that which passes through the polariscope, be suppressed by a shade. The sensitive or transition tint is produced by that position of the regulating apparatus which gives a field of view of such a nature that a given small movement of the quartz compensating wedge gives the greatest contrast in color between the halves of the field of vision. For most eyes a faint rose-purple tint, as nearly colorless as possible, possesses this quality. A slight movement of the quartz wedge by means of the screw head M will, with this tint, produce on one side a faint green and on the other a pink color, which are in strong contrast. The neutral point is reached by so adjusting the quartz wedge as to give to both halves of the field the same faint rose-purple tint.

74. The Shadow Polariscope for Lamp Light.—This form of instrument is now in general use for saccharimetric purposes. It possesses on the one hand, the advantages of those instruments using monochromatic light, and on the other, the ease of manipulation possessed by the tint polariscopes. It differs from the tint instrument in dispensing with the nicol and quartz plate used to regulate the sensitive tint, and in having its polarizing nicol peculiarly constructed in harmony with the optical principles of the jellet-corny prism. The more improved forms of the apparatus have a double quartz wedge compensation. The two wedges are of opposite optical properties, and serve to make the observations more accurate by mutual correction. The optical arrangement of the different parts of such a polariscope is shown in the following figure.

The lenses for concentrating the rays of light and rendering them parallel are contained in the tube N. At O is placed the modified polarizing nicol. The two compensating quartz wedges are moved by the milled screw-heads EG. The rest of the optical apparatus is arranged as described under the tint polariscope. For practical purposes, only one of the wedges is employed, but for all accurate work the readings should be made with both wedges and thus every possible source of error eliminated.

75. The Triple Shadow Instrument.—When properly made, all the instruments which have been mentioned, are capable of giving accurate results if used in harmony with the directions given. In the use of polariscopes having colored fields of vision a delicate sense of distinguishing between related tints is necessary to good work. Color-blind observers could not successfully use such apparatus. In the shadow instruments it is only necessary to distinguish between the halves of a field of vision unequally illuminated and to reduce this inequality to zero. A neutral field is thus secured of one intensity of illumination and of only one color, usually yellow. Such a field of vision permits of the easy discrimination between the intensity of the coloration of its two halves, and is consequently not trying to the eye of the observer, and allows of great accuracy of discrimination. This field of vision has lately been still further improved by dividing it into three parts instead of two. An instrument of this kind, Fig. 39, in use in this laboratory, permits a delicacy of reading not possessed by any other instrument used for sugar analysis, and approaching that of the standard Landolt-Lippich apparatus, used by us for research work and for determining the rotation of quartz plates and testing the accuracy of other polariscopes.

The triple shadow is secured by interposing in front of the polarizing nicol two small nicols as indicated in Fig. 40. The end views in different positions of the polarizer are shown in the lower part of the diagrams.

Instead of the comparison of the intensity of the illumination being made on the halves of the field of vision it is made by comparing the segments of the halves with a central band, which also changes in intensity synchronously with the two segments, but in an opposite direction.

THE ANALYTICAL PROCESS.

76. General Principles.—Having described the instruments chiefly employed in the optical examination of sugar solutions, the next step is to apply them to the analytical work. A common set of directions for use will be found applicable to all instruments with such modifications only as are required by peculiarities of construction. With the best made instruments it is always advisable to have some method of controlling the accuracy of the observation. The simplest way of doing this is to test the apparatus by standard quartz plates. These plates are made from right-handed polarizing quartz crystal ground into plates of definite thickness and accurately tested by standard instruments. Theoretically such quartz plates deflect the plane of polarized light in a degree proportionate to their thickness, but practically some small deviations from the rule are found. With a source of light of the same tint, and at a constant temperature, such plates become a safe test for the accuracy of the graduation of polariscopes. They are more convenient for use than pure sugar solutions of known strength which are the final standards in all disputed cases. These quartz plates are conveniently mounted in tubes of the same size as those holding the sugar solution, and thus fit accurately into the trough of the polariscope, the optical axis of which passes through their center. The quartz plate when used for setting the scale of a polariscope should be placed always in the same position. In some plates slight differences of reading may be noticed on rotating the tubes holding them. Theoretically, such differences should not exist, but in practice they are sometimes found. The temperature of observation should also be noted, and if not that at which the value of the plate was fixed a proper correction should be made.

77. Setting the Polariscope.—While mention has been made of several forms of apparatus in the preceding paragraphs, those in common use are limited to a very small number. In this country quite a number of color instruments may still be found, together with a few laurents, and a constantly increasing number of shadow instruments for use with lamp light. The following description of setting the polariscope is especially adapted to the last named instrument, but the principles of adjustment are equally applicable to all.

The scale of the instrument is first so adjusted by means of the adjusting screws provided with each instrument, as to bring the zero of the vernier and that of the scale exactly together. The telescope or ocular is then adjusted until the sharp line separating the halves of the field of vision is brought into focus. This being accomplished an observation tube filled with pure water is placed in the apparatus and the telescope again adjusted to bring the dividing line of the field into focus. The beginner especially, should repeatedly study this adjustment and be impressed with the fact that only in a sharply defined field are practical observations of any worth. The importance of having all the lenses perfect and all the cover glasses without a flaw may be fully appreciated when it is remembered that the polarized ray, already deprived of half its original luminous power, must pass through several centimeters of crystallized calcium carbonate, and half a dozen disks of glass and quartz, and as many lenses before reaching the eye of the observer. Only with the greatest care and neatness is it possible to secure the required degree of illumination. The zero point having been well studied and accurately adjusted, the scale of the instrument may be tried with a series of quartz plates of known polarizing power at the temperature of the observation. In the apparatus with double quartz wedge compensation, it will be noticed that the marks on one scale are black and on the other red. The black is the working and the red the control scale. To operate this instrument, the red scale is placed exactly at the zero point. The black scale is also placed at zero, and if the field of vision is not neutral, it is made so by the micrometer screw with which the black scale is provided. In a right-handed solution, the red scale is left at zero and the black one moved to the right until neutrality in the field of vision is reached and the reading is taken. The observation tube containing the sugar solution is taken out and the red scale moved until the field of vision is again neutral and the reading of the red scale taken. The two readings should agree. Any failure in the agreement shows some fault either in adjusting the apparatus or in its construction, or some error in manipulation.

The double compensating shadow instruments are more readily tested for accuracy in all parts of the scale than those of any other construction. The two compensating wedges are cut with the greatest care, one from a left-handed and the other from a right-handed perfectly homogeneous quartz crystal. Since faults in these wedges are due either to lack of parallelism of surface, or of perpendicularity to the optical axis of the crystal, and since these faults of crystallization or construction must be in a very limited degree common they would not coincide once in many thousand times in the two wedges. This is easily shown by the theory of probabilities. If, therefore, the two readings made at any point, should not agree, it must be due either to a fault in one of the wedges, or to a fault in reading or a lack of adjustment, as has been mentioned. In such cases the readings should be retaken and the errors are usually easily discovered.

78. Control Observation Tube.—Instead of using quartz plates of known values for testing the accuracy of the scale, an observation tube may be used, the length of which can be varied at the pleasure of the observer.

The construction of a tube of this kind is shown in Fig. 40. The tube B is movable telescopically in A by means of the ratchet wheel shown. It is closed at D water-tight by a glass disk. The tube B fits as accurately into A as is possible to permit of free movement, and any liquid which may infilter between its outer surface and the inner surface of A is prevented from gaining exit by the washer C, which fits both tubes water-tight. The ratchet which moves B in A carries a millimeter scale and vernier N whereby the exact thickness of the liquid solution between the surfaces of the glass disks D and E can be always determined.

By this device the length of liquid under observation can be accurately read to a tenth of a millimeter. The cover glass E is held in position by any one of the devices in common use for this purpose in the case in question, by a bayonet fastening. The funnel T, communicating directly with the interior of A, serves to hold the solution, there being always enough of it to fill the tube when D is removed to the maximum distance from C, which is usually a little more than 200 millimeters.

Let the control tube be adjusted to 200 millimeters and filled with a solution of pure sugar, which reads 100 per cent or degrees in a 200 millimeter tube. Since the degree of rotation is, other things being equal, proportional to the length of the column of polarizing solution, it follows that if the tube B be moved inward until the distance between D and C is 100 millimeters, the scale should read 50° or per cent. By adjusting the length of the distance between B and C it is easily seen that every part of the scale can be accurately tested.

The tube should be filled by removing the funnel and closing the orifice with a screw cap which comes with the apparatus. The cap E is then removed and the tube filled in the ordinary manner. This precaution is practiced to avoid carrying air bubbles into the tube when filled directly through the funnel. With a little care, however, this danger may be avoided, or should air bubbles enter they can be easily removed by inclining the tube.

In case the solution used be not strictly pure it may still be employed for testing the scale. Suppose, for instance, that a solution made up in the usual way, has been made from a sample containing only 99.4 per cent of sugar. Then in order to have this solution read 100° on the scale the tube should be set at 201.2 millimeters, according to the formula

By a similar calculation the position of the tube for reading any desired degree on the scale can be determined. The importance of controlling all parts of the scale in compensating instruments is emphasized by the fact that a variation of only 0.016 millimeter in the thickness of the compensating wedge will cause a change of one degree in the reading of the instrument.

79. Setting the Polariscope with Quartz Plates.—Pure sugar is not always at the command of the analyst, and it is more convenient practically to adjust the instrument by means of quartz plates, the sugar values of which have been previously tested for the character of the light used. Assuming the homogeneity of a plate of quartz, the degree of deflection which it imparts to a plane of polarized light depends on the quality of the light, the thickness of the plate, and the temperature.

In respect of the quality of light, red polarized rays are least, and violet most deflected. The degree of rotation produced with any ray, at a given temperature, is directly proportional to the thickness of the plate. Temperature affects the rotating power of a quartz plate in a degree highly significant from a scientific point of view and not wholly negligible for practical purposes. The rotating power of a quartz plate increases with the temperature and the variation may be determined by the formula given below:[44]

The formula is applicable for temperatures between 0° and 100°. Its values are expressed in degrees of angular measure which can be converted into degrees of the sugar scale by appropriate factors:

Formula.— aᵗ = a°(1 + 0.000146t);

in which a° = polarization in angular degrees at 0°, t the temperature of observation and aᵗ the rotation desired.

Example.—A quartz plate which has an angular rotation of 33° at 0° will have a rotation at 20° of 33°.09834.

aᵗ = 33(1 + 0.000146 × 20) = 33.09834.

Since in instruments using the ventzke scale one degree of the sugar scale is equal to 0.3467 degree angular measure, the sugar value of the quartz plate mentioned is equal to 95.47 percent; 33.09834 ÷ 0.3467 = 95.47.

The sugar value of this plate at 0° is 95.18 per cent; 33 ÷ 0.3467 = 95.18.

80. Tables for Correcting Quartz Plates.—Instead of calculating the variation in quartz plates for each temperature of observation, it is recommended by the Bureau of Internal Revenue of the Treasury, to use control quartz plates the values of which at any given temperature, are found on a card which accompanies each one.[45] The variations given, are from temperatures between 10° and 35°. Three control plates are provided with each instrument used by the Bureau, for polarimetric work in the custom houses, or in ascertaining bounties to be paid on the production of domestic sugars. For example, the case of a sugar which polarizes 80°.5 may be cited. One of the control plates nearest to this number, is found to have at the temperature of observation, a polarization of 91°.4, the reading being made in each case at 25°. On consulting the card which accompanies the control plate, it is seen that its value at the temperature mentioned, is 91°.7. The reading of the instrument is therefore too low by three-tenths of a degree, and this quantity should be added to the observed polarization, making it 80°.8. In this method of correcting the reading for temperature, it is assumed that the compensating wedges of the instrument, are free of error at the points of observation. The plates used for the purpose above, are all standardized in the office of weights and measures of the Coast and Geodetic Survey, before delivery to the analysts.

81. Applicability of Quartz Plates.—Quartz plates which are correctly set for one instrument or kind of light, should be equally accurate for the sugar scales of all instruments, using the same sugar factor. In other words a quartz plate which reads 99° on a scheibler color polariscope, should give the same reading on the sugar scale of a shadow compensating or a monochromatic direct reading apparatus using 26.048 grams of sugar.

The most useful quartz plates for sugar analysis, are those which give the readings at points between 80° and 96°, which cover the limits of ordinary commercial sugars. For molasses the plates should read from 45° to 55°. For sugar juices of the cane and beet, the most convenient graduation would be from 10° to 20°, but plates of this value would be too thin for practical work and are not in use. When quartz plates are to be used for control purposes, they should be purchased from reliable manufacturers, or better, tested directly against pure sugar solutions by the observer.

In practice we have found quartz plates as a rule, true to their markings.

82. The Sugar Flask.—Sugar solutions are prepared for polarization in flasks graduated to hold fifty or one hundred cubic centimeters. For scientific work a flask is marked to hold 100 grams of distilled water at 4°. The weights are all to be reduced to a vacuum standard. One flask having been marked in this way, others may be compared directly therewith by means of pure mercury. For this purpose the flasks must be perfectly dry and the mercury pure, leaving no stain on the sides of the flask. The glass must also be strong enough to undergo no change in shape from the weight of mercury used.

For sugar work the true 100 gram flask is not usually employed, but one graduated by weighing at 17°.5. These flasks are graduated by first weighing them perfectly dry, filling with distilled water and again weighing fifty and fifty-five, or 100 and 110 grams of water at the temperature named. Since the volume of water at 17°.5 is greater than at 4° the sugar flask in ordinary use has a greater volume by about 0.25 cubic centimeter than the true flask. The observer should always secure a statement from the dealer in respect of the volume of the flask used in testing the scale of the polariscope purchased. In the graduation of a flask in true cubic centimeters, when brass weights are used it will be necessary to correct the weight of each gram of water by adding to it one milligram, which is almost exactly the weight of the volume of air displaced by one gram of water in the circumstances named. If the flask be first counterbalanced and it be desired to mark it at 100 cubic centimeters the sum of the weights placed in the opposite pan should be 100 - 0.100 = 99.900 grams. While this is not a rigidly exact correction it will be sufficient for all practical purposes. A liter of dry air weighs 1.29366 grams; and 100 cubic centimeters of water would therefore displace 0.129 gram of air. But the brass weights also displace a volume of air which when deducted reduces the correction to be made for the water to nearly the one named. For convenience in inverting sugar solutions the flasks used in practical work are graduated at fifty and fifty-five and 100 and 110 cubic centimeters respectively.

83. Preparing Sugar Solutions for Polarization.—If sugar samples were always pure the percentage of sugar in a given solution could be directly determined by immediate polarization. Such cases, however, are rarely met in practice. In the majority of cases the sample is not only to be brought into solution but is also to be decolorized and rendered limpid by some one of the methods to be described. A perfectly limpid liquid is of the highest importance to secure correct observations. With a cloudy solution the field of vision is obscured, the dividing line of the two halves, or the double line in the triple field, becomes blurred or invisible and the intensity of illumination is diminished. A colored liquid which is bright is far more easy to polarize than a colorless liquid which is turbid. In fact, it is only rarely in sugar work that samples will be found which require any special decolorizing treatment other than that which is received in applying the reagents which serve to make the solutions limpid. In the following paragraphs the approved methods of clarifying sugar solutions preparatory to observation in the polariscope will be described.

84. Alumina Cream.—The hydrate of alumina, commonly known as alumina cream, is always to be preferred as a clarifying agent in all cases where it can be successfully applied.[46] It is a substance that acts wholly in a mechanical way and therefore leaves the sugars in solution unchanged, carrying out only suspended matters. In the preparation of this reagent a solution of alum is treated with ammonia in slight excess, the aluminum hydroxid produced washed on a filter or by decantation until neutral in reaction. The hydroxid is suspended in pure water in proportions to produce a creamy liquid. Although apparently very bulky, the actual space occupied by the amount of dry hydroxid added in a few cubic centimeters is so small as to produce no disturbing effect of importance on the volume of the sugar solution. The cream thus prepared is shaken just before using and from one to five cubic centimeters of it, according to the degree of turbidity of the saccharine solution, are added before the volume in the flask is completed to the mark. After filling the flask to the mark the ball of the thumb is placed over the mouth and the contents well shaken and allowed to stand for a few moments before filtering.

The alumina cream is well suited to use with solutions of commercial sugars of not too low a grade and of most honeys and high grade sirups. It is usually not powerful enough to clarify beet and cane juices, molasses and massecuites.

85. Basic Lead Acetate.—A solution of basic lead acetate is an invaluable aid to the sugar analyst in the preparation of samples for polarimetric observation. It acts as a clarifying agent by throwing out of solution certain organic compounds and by uniting with the organic acids in solution forms an additional quantity of precipitate, and these precipitates act also mechanically in removing suspended matters from solution. The action of this reagent is therefore much more vigorous than that of alumina cream. Coloring matters are often precipitated and removed by treatment with lead acetate. It happens therefore that there are few samples of saccharine bodies whose solutions cannot be sufficiently clarified by lead acetate to permit of polarimetric observation.

The reagent is most frequently employed of the following strength:[47] Boil for half an hour in one and a half liters of water 464 grams of lead acetate and 264 grams of litharge with frequent stirring. When cool, dilute with water to two liters, allow to stand until clear, and decant the solution. The specific gravity of this solution is about 1.267.

In a solution of basic lead acetate of unknown strength the percentage of lead acetate may be determined from its specific gravity by the following table:[48]

Percentage of Lead Acetate Corresponding
to Different Specific Gravities at 15°.

86. Errors Due to use of Lead Solutions.—In the use of lead solutions there is danger of errors intruding into the results of the work. These errors are due to various sources. Lead subacetate solution, when used with low grade products, or sugar juices, or sirups from beets and canes, precipitates albuminous matters and also the organic acids present. The bulk occupied by these combined precipitates is often of considerable magnitude, so that on completing the volume in the flask the actual sugar solution present is less than indicated. The resulting condensation tends to give too high a polarimetric reading. With purer samples this error is of no consequence, but especially with low grade sirups and molasses it is a disturbing factor, which must be considered.

One of the best methods of correcting it has been proposed by Scheibler.[49] To 100 cubic centimeters of a solution of the sample, ten of lead solution are added, and after shaking and filtering the polarimetric reading is taken. Another quantity of 100 cubic centimeters of the solution with ten of lead is diluted to 220 cubic centimeters, shaken, filtered, and polarized. Double the second reading, subtract it from the first, multiply the difference by 2.2, and deduct the product from the first reading. The remainder is the correct polarization.

The process just described is for the usual work with beet juices and sirups. For cane juices measured by the graduated pipette, hereafter to be described, and for weighed samples of molasses and massecuites, the following method of calculation is pursued.[50] To the sample dissolved in water, add a measured portion of the lead subacetate solution, make its volume 100 cubic centimeters and observe the polarimetric reading. Prepare a second solution in the same way and make the volume double that of the first and again take the polarimetric reading. Multiply the second reading by two, subtract the product from the first reading and multiply the remainder by two, and subtract the product from the first reading.

The corrected reading therefore shows that the sample contained 29.6 per cent of sugar.

87. Error Due to Action of Lead Subacetate on Levulose.—In the use of lead subacetate solution not only is there danger of error due to the causes just described, but also to a more serious one, arising from the chemical interaction of the clarifying agent and levulose.[51]

Lead subacetate forms a chemical union with levulose and the resulting compound has a different rotatory power from the left-handed sugar in an uncombined state. By adding a sufficient quantity of subacetate solution, the left-handed rotation of levulose may be greatly diminished if not entirely destroyed. In this case the dextrose, which with levulose forms inverted sugar, serves to increase the apparent right rotation due to the sucrose in solution. The reading of the scale is therefore higher than would be given by the sucrose alone. If the lead subacetate could be added in just the proportion to make the invert sugar neutral to polarized light, its use would render the analysis more accurate; but such a case could only arise accidentally. To correct the error, after clarification, the compound of levulose and lead may be decomposed by the addition of acetic acid according to the method of Spencer. In this case the true content of sucrose can only be obtained by the method of inversion proposed by Clerget, which will be described in another paragraph.

88. Clarification with Mercuric Compounds.—Where the disturbing bodies in a solution are chiefly of an albuminoid nature, one of the best methods of securing clarification is by the use of a solution containing an acid mercuric compound.[52] In the case of milk this method is to be preferred to all others. Albuminoid bodies themselves, have the property of deflecting the plane of polarization, as a rule, to the left, and therefore, should be completely removed from solutions containing right-handed sugars such as lactose. For this purpose the mercuric compound is more efficient than any other. It is prepared and used as follows.[53] Dissolve mercury in double its weight of strong nitric acid and dilute the solution with an equal volume of water. One cubic centimeter of this solution is sufficient to clarify fifty times its volume of milk.

89. Decolorization by Means of Bone-Black.—Where the means already described fail to make a solution sufficiently colorless to permit of the passage of a ray of polarized light, recourse should be had to a decolorizing agent. The most efficient of these is bone-black. For laboratory work it is finely ground and should be dry if added to an already measured solution. When moist it should be added to the flask before the volume is completed, and a correction made for the volume of the dry char employed. Bone-black has the power of absorbing a certain quantity of sugar, and for this reason as little of it should be employed as is sufficient to secure the end in view. If not more than one gram of the char be used for 100 cubic centimeters of solution, the error is not important commercially. The error may be avoided by placing the char on the filter and rejecting the first half of the filtered solution. The char becomes saturated with the first portion of the solution, and does not absorb any sugar from the second. This method, however, does not secure so complete a decolorization as is effected by adding the black directly to the solution and allowing to stand for some time with frequent shaking.

90. Remarks on Analytical Process.—Since large weights of sugar are taken for polarization, a balance which will weigh accurately to one milligram may be used. In commercial work the weighing is made in a counterpoised dish with a prominent lip, by means of which the sample can be directed into the mouth of the flask after partial solution. Where the air in the working room is still, an uncovered balance is most convenient. With a little practice the analyst will be able to dissolve and transfer the sample from the dish to the flask without danger of loss. The source of light used in polarizing should be in another room, and admitted by a circular opening in the partition. In a close polarizing room, which results from the darkening of the windows, the temperature will rapidly rise if a lamp be present, endangering notably the accuracy of the work, and also interfering with the comfort of the observer. The greatest neatness must be practiced in all stages of the work, and especially the trough of the polariscope must be kept from injury which may arise from the leaking of the observation tubes. Dust and dirt of all kinds must be carefully excluded from the lenses, prisms, wedges and plates of the instrument.

91. Determination of Sucrose by Inversion.—In the foregoing paragraphs directions have been given for the estimation of sugar (sucrose) by its optical properties. It has been assumed so far, that no other disturbing bodies have been present, save those which could be removed by the clarifying agents described. The case is different when two or more sugars are present, each of which has a specific relation to polarized light. In such cases some method must be used for the optical determination of sucrose, which is independent of the influence of the other polarizing bodies, or else recourse must be had to other methods of analysis. The conversion of the sucrose present into invert sugar by the action of an acid or a ferment, affords an opportunity for the estimation of sucrose in mixed sugars, by purely optical methods. This process rests upon the principle that by the action of a dilute acid for a short time, or of a ferment for a long time, the sucrose is completely changed, while other sugars present are not sensibly affected. Neither of these assumptions is rigidly correct but each is practically applicable.

The sucrose by this process of hydrolysis is converted into an equal mixture of levulose and dextrose. The former, at room temperatures, has the higher specific rotating power, and the deflection of the plane of polarization in a solution of inverted sugar is therefore to the left. The levorotatory power of invert sugar varies with the temperature, and this arises from the optical properties of the levulose. The influence of temperature on the rotating power of other sugars, is not imperceptible in all cases, but in practice is negligible.

This method of analysis is invaluable in control work in factories, in the customs and in agricultural laboratories. Since the rotating power of levulose diminishes as the temperature rises, an accurate thermometric observation must accompany each polarimetric reading. At about 88° the rotatory powers of dextrose and levulose are equal, and a solution of pure invert sugar examined at that degree, is found to be neutral to polarized light.

92. Clerget’s Method of Inversion.—The classical method of Clerget for the determination of cane sugar by double polarization before and after inversion, was first described in a memoir presented to the Society of Encouragement for National Industry on the 14th of October, 1846. The following description of the original method is taken from a reprint of the proceedings of that Society, dated Nov. 1846:

Clerget points out first the observation of Mitscherlich regarding the influence of temperature on the rotatory power of invert sugar, and calls attention to the detailed experiments he has made which resulted in the determination of the laws of the variation. From these studies he was able to construct a table of corrections, applicable in the analysis of all saccharine substances in which the cane sugar is polarized before and after inversion. The basis of the law rests upon the observation that a solution of pure sugar, polarizing 100° on the sugar scale, before inversion, will polarize 44° to the left after inversion at a temperature of zero. The quantity of sugar operated upon by Clerget amounted to 16.471 grams in 100 cubic centimeters of liquid. On the instrument employed by him this quantity of sugar in 100 cubic centimeters gave a reading of 100° to the right on the sugar scale when contained in a tube twenty centimeters in length. The process of inversion carried on by Clerget is as follows:

The sugar solution is placed in a flask, marked on the neck at 100 and 110 cubic centimeters; or if smaller quantities are used, in a flask marked on the neck at fifty and fifty-five cubic centimeters. The flask is filled with the sugar solution to the first mark and then a sufficient quantity of strong hydrochloric acid added to bring the volume of the liquid to the second mark. The mouth of the flask is then closed with the thumb and its contents thoroughly mixed by shaking. A thermometer is placed in the flask which is set in a water-bath in such a way that the water comes just above the level of the liquid in the neck of the flask. The water is heated in such a manner as to bring the temperature of the contents of the flask, as determined by the thermometer, exactly to 68° and at such a rate as to require fifteen minutes to reach this result. At the end of fifteen minutes the temperature having reached 68° the flask is removed and placed at once in another water-bath at the temperature of the room, to which temperature the contents of the flask are cooled as rapidly as possible. To make the polarimetric observation a tube twenty-two centimeters in length is filled with the inverted sugar solution by means of a tubulure in its center, which serves not only the purpose of filling the tube but also afterwards to carry the thermometer, by means of which the temperature of observation can be taken. If the sugar solution be turbid, or contain any lead chlorid due to the previous use of basic lead acetate in clarification, it should be filtered before being introduced into the observation tube. This tube being one-tenth longer than the original compensates for the dilution caused by the addition of the hydrochloric acid in inversion.

When reading, the bulb of the thermometer should be withdrawn far enough to permit the free passage of the ray of light and the exact temperature of the solution noted.

The above outline of Clerget’s method of inversion is given in order that the analyst may compare it with any of the variations which he may find in other works. The chief points to which attention is called, are, first, the fact that only a little over sixteen grams of sugar are used for ten cubic centimeters of strong hydrochloric acid, and second, that the time of heating is exactly fifteen minutes, during which time the contents of the flask should be raised from room temperature to exactly 68°.

From the above it is seen that the process of Clerget, as originally described, can be applied directly to all instruments, using approximately sixteen grams of sugar in 100 cubic centimeters. Experience has also shown that even when larger quantities of sugar are employed, as for instance, approximately twenty-six grams, the inversion is effected with practical completeness in the same circumstances. It is advised, therefore, that in all analytical processes, in which cane sugar is to be determined by the process of inversion with an acid, the original directions of Clerget be followed as strictly as possible. Experience has shown that no one of the variations proposed for Clerget’s original method has any practical advantage and the analyst is especially cautioned against those methods of inversion in which the temperature is continued at 68° for fifteen minutes or in which it is allowed to go above that degree.

93. Influence of Strength of Solution and Time of Heating on the Inversion of Sucrose.—As has been intimated, the strength of a sugar solution and the time of heating with hydrochloric acid are factors that must be considered in determining a formula for the calculation of sucrose by inversion. The Clerget formula holds good only for the conditions specified and these conditions must be rigidly adhered to in order to secure the proper results. This matter has been thoroughly studied by Bornträger, who also gives a nearly complete bibliography of the subject.[54] As a result of his investigations it seems well established that the original Clerget formula is practically correct for the conditions indicated, Bornträger modifying it only by substituting in the formula 143.66 for 144. This is so nearly the same as the Clerget factor that it is not advisable to substitute it therefor. If, however, the inverted sugar solution be diluted to double its volume before polarization the factor proposed by Landolt, viz., 142.4, gives more nearly accurate results. If the hydrochloric acid be neutralized before polarization by an alkaline body, the character of the salt which is formed also influences, to a greater or less extent, the specific rotatory power of the solution. Hydrochloric acid itself also influences the rotation to a certain degree.[55]

94. Calculation of Results.—The percentage of sucrose in a solution which has been polarized before and after inversion is calculated by an appropriate formula from the data obtained or is taken directly from tables. These tables are too long to insert here, and in point of fact the calculation can be made from the formula almost as quickly as the result can be taken from a table.

Two factors are commonly used in the calculations, one based on the supposition that a sugar solution polarizing 100° to the right will, after inversion, give a reading of 44° to the left, at zero temperature. In the second formula in common use the polarization to the left in the circumstances mentioned above is assumed to be 42.4, a number reached by Landolt after a long series of experiments.[56] The principle of the calculation of the percentage of sucrose is based upon the original observation of Clerget to the effect that the algebraic difference of the two readings, divided by 144, less half of the temperature, will give the percentage of sucrose desired. The formula by which this is obtained is

In this formula a is the polarization on the sugar scale before inversion, b the polarization after inversion, K the constant representing the algebraic difference of the two polarizations of pure sugar at 0° and t the temperature of the observation. To K may be assigned the values 144 or 142.4, the one in more common use. In case the polarization, after inversion, is to the left, which is more commonly the case, the sum of the two readings is taken for a - (-b) = a + b; when both polarizations are to the right or left the difference is taken. S is the percentage of sucrose desired.