SUGAR

The sugars of commerce may be conveniently classified into two
varieties, viz., sucrose (cane sugar or saccharose) and dextrose (grape
sugar or glucose). The former, which is the kind almost exclusively
employed for domestic uses, is chiefly obtained from the sugar cane of
the West Indies and American Southern States (_Saccharum officinarum_),
and, in continental Europe, from the sugar beet (_Beta vulgaris_).
A comparatively small quantity is manufactured in the United States
from the sugar maple (_Acer saccharinum_), and from sorghum (_Sorghum
saccharatus_).

_Cane Sugar_ (C_{12} H_{22} O_{11}).–Among the more important chemical
properties of cane sugar are the following:–It dissolves in about
one-third its weight of cold water–much more readily in hot water–and
is insoluble in cold absolute alcohol. From a concentrated aqueous
solution it is deposited in monoclinic prisms, which possess a specific
gravity of 1·580. Cane sugar is characterised by its property of
rotating the plane of a ray of polarised light to the right; the rotary
power is 66°·6. Upon heating its solution with dilute mineral acids, it
is converted into a mixture termed “invert sugar,” which consists of
equal parts of _dextrose_ and _levulose_. The former turns the plane of
polarised light to the right, the latter to the left; but owing to the
stronger rotation exerted by the levulose, the combined rotary effect
of invert sugar is to the left, _i. e._, opposite to that possessed by
cane sugar. Invert sugar exhibits the important property of reducing
solutions of the salts of copper, which is not possessed by pure cane
sugar. Cane sugar melts at 160°; at a higher temperature (210°) it
is converted into a reddish-brown substance termed _caramel_. When
subjected to the action of ferments, cane sugar is first transformed
into invert sugar, then into alcohol and carbonic acid, according to
the reactions:–

(_a_) C_{12} H_{22} O_{11} + H_{2}O = 2 C_{6} H_{12} O_{6}.
(_b_) C_{6} H_{12} O_{6} = 2 CO_{2} + 2 C_{2} H_{6}O.

The varieties of cane sugar usually met with in commerce are the
following:–

1. Loaf sugar, consisting either of irregular fragments, or (more
often) of cut cubes.

2. Granulated sugar.

3. Soft white sugar.

4. Brown sugar, varying in colour from cream-yellow to reddish-brown.

Molasses is a solution of sugar, containing invert sugar, gummy
matters, caramel, etc., which forms the mother-liquor remaining after
the crystallisation of raw cane sugar; the name “syrup” being commonly
applied to the residual liquor obtained in the manufacture of refined
sugar.

_Dextrose_ (C_{6} H_{12} O_{6}), occurs ready-formed in grape juice,
and in many sweet fruits, very frequently associated with levulose;
it is also contained in honey, together with a small amount of cane
sugar. As already mentioned, it constitutes an ingredient of the
product obtained by the action of acids and ferments upon cane sugar.
For commercial purposes, glucose is prepared by treating grains rich
in starch, with dilute acids. In France and Germany, potatoes are used
in its manufacture; in the United States, Indian corn or maize is
almost exclusively employed. The processes used consist substantially
in first separating the starch from the grain by soaking, grinding,
and straining, then boiling it, under pressure, with water containing
about 3 per cent. of sulphuric acid, neutralising the remaining acid
with chalk, decolorising the solution by means of animal charcoal,
and concentrating it in vacuum pans. In the United States thirty-two
factories are engaged in the manufacture of glucose, which consume
about 40,000 bushels of corn daily, their annual production having an
estimated value of 10 millions of dollars. In commerce, the term grape
sugar is applied to the solid product, the syrup or liquid form being
known as glucose. The chief uses of starch sugar and glucose are in
the manufacture of table syrups, and as a substitute for malt in the
brewing of beer and ale. Their other most important applications are as
a substitute for cane sugar in confectionery, and in the preparation
of fruit jellies; as an adulterant of cane sugar, as an admixture to
genuine honey, and as a source for the preparation of vinegar.

Dextrose is soluble in 1-1/5 part of cold water, and is much more
soluble in hot water. It has a dextro-rotary power of 56°. When
separated from its aqueous solution, it forms white and opaque granular
masses, but from an alcoholic solution, it is obtained in well-defined,
microscopic needles, which fuse at 146°. Two parts of glucose have
about the same sweetening effect as one part of cane sugar.[54] It does
not become coloured when mixed with cold concentrated sulphuric acid,
which distinguishes it from sucrose; on the other hand, its solution
is coloured dark-brown if boiled with potassium hydroxide, another
distinction from cane sugar. Dextrose is capable of directly undergoing
vinous fermentation, and, like invert sugar, it possesses the property
of reducing alkaline solutions of copper salts, especially upon the
application of heat.

The chief commercial varieties of American glucose are the following:–

1. _Glucose_: Per cent. Glucose.
“Crystal H,” containing 40
“Crystal B” 45
“Crystal A” 50

2. _Grape Sugar_:
“Brewers’ grape” 70-75
“A” or “Solid grape” 75-80
“Grained” or “Granulated grape” 80-85

_Maltose_ and _levulose_ are isomers of dextrose. The former is
prepared by the action of malt or diastase upon starch. It has a
dextro-rotary power of 150° and its property of reducing copper salts
is only about 60 per cent. of that of dextrose. It is converted into
the latter compound upon boiling with dilute sulphuric acid. Levulose,
as previously stated, is formed, together with dextrose, from cane
sugar by treatment with dilute acids or with ferments. It turns the
plane of a ray of polarised light to the left, its rotary power varying
considerably at different temperatures.

_Lactose_, or milk sugar, has already been referred to under the head
of Milk. It is isomeric with cane sugar, possesses a dextro-rotary
power (58°·2), and undergoes fermentation when mixed with yeast, and
reduces alkaline copper solutions, but in a different degree from
glucose.

Many of the substances frequently enumerated as being used to
adulterate sugar are at present very seldom employed. The usual list
includes “glucose” (often meaning invert sugar), sand, flour, chalk,
terra alba, etc. Loaf sugar is almost invariably pure, although its
colour is sometimes improved by the addition of small proportions of
various blue pigments, such as ultramarine, indigo, and Prussian blue.
The presence of ultramarine was detected in about 73 per cent. of
the samples of granulated sugar tested in 1881 by the New York State
Board of Health. Tin salts[55] are also occasionally employed in the
bleaching of sugar and syrups. Granulated sugar is asserted to be
sometimes mixed with grape sugar, and powdered sugar has been found
adulterated with flour and terra alba; but the varieties which are most
exposed to admixture are the low grades of yellow and brown sugar, in
which, however, several per cent. of invert sugar are normally present.
Sand, gravel, and mites form a rather common contamination of raw
sugar. From the year 1876 to 1881, 310 samples of commercial sugar were
examined by the public health authorities of Canada, of which number
24 were reported as containing glucose, and 11 as of doubtful purity.
Of 38 samples of brown sugar recently analysed by Dr. Charles Smart,
of the National Board of Health, 9 were adulterated with glucose.
From the investigations of A. L. Colby, Analyst to the New York State
Board of Health, it was found that of the 116 samples examined, the
white sugars were practically pure; whereas, of 67 samples of brown
sugar, 4 contained glucose. Of 16 specimens of brown sugar, tested by
a commission appointed by the National Academy of Sciences in 1883,
4 contained about 30 per cent. of this body.[56] Many varieties of
sugar-house syrups, and the various forms of confectionery, are very
extensively adulterated with artificial glucose.

The average sugar-house syrup has the following composition:–

Per cent.
Water 16
Crystallisable sugar 36
Invert sugar 34
Gum, pectose, etc. 10
Ash 4

Dr. W. H. Pitt, in the Second Annual Report of the New York State
Board of Health, gives the following analysis of grocers’ mixed glucose
syrup, and of confectioners’ glucose:–

_American Grape Sugar Co.’s Syrup._

Per cent.
Ash 0·820
Water 18·857
Dextrine 34·667
Cane syrup 7·805
Glucose 37·851
——-
100·000
——-

_Confectioners’ Glucose._

Per cent.
Ash 0·431
Water 15·762
Dextrine 41·614
Glucose 42·193
——-
100·000
——-

It is stated that a large proportion of the American maple syrup and
maple sugar found on the market, consists of raw sugar, flavoured with
the essential oil of hickory-bark, for the manufacture of which letters
patent have been granted.

_Analysis of Sugar._–The examination of sugar is ordinarily confined
to the estimation of the water, ash, and determination of the nature
of the organic matters present. The proportion of water contained in
a sample is found by drying it for about two hours in an air-bath, at
a temperature of 110°. Moist and syrupy sugars, such as muscovadoes,
are advantageously mixed with a known weight of ignited sand before
drying. The ash is determined either by directly incinerating a few
grammes of the sugar in a tared platinum capsule, or by accelerating
the process of combustion by first moistening the sample with a little
sulphuric acid. In this case the bases will naturally be converted
into sulphates, and a deduction of one-tenth is usually made from
the results so obtained, in order to reduce it to terms of the
corresponding carbonates. The proportion of ash in raw cane sugar
varies somewhat, but it should not much exceed 1·5 per cent. Its
average composition, as given by Monier, is as follows:–

Calcic carbonate 49·00
Potassium carbonate 16·50
Sodium and potassium sulphates 16·00
Sodium chloride 9·00
Alumina and silica 9·50
——
100·00
——

Insoluble mineral adulterants are readily separated by dissolving a
rather considerable amount of the sample in water and filtering. In
this manner the presence of sand, terra alba, and foreign pigments may
be recognised.

The determination of the character of the organic constituents of
commercial sugars is effected, either by chemical or by physical tests,
and, in some instances, by a combination of these methods. The presence
of such adulterants, as flour or starch, is very easily detected upon a
microscopic examination of the suspected sample.

If cane sugar, containing grape sugar, is boiled with water, to which
about 2 per cent. of potassium hydroxide has been added, the solution
acquires a brown colour.

Upon mixing a solution of pure cane sugar with a solution of cupric
sulphate, adding an excess of potassium hydroxide, and boiling, only a
slight precipitation of red cupric oxide takes place. Under the same
conditions, grape sugar at once produces a copious green precipitate,
which ultimately changes to red, the supernatant fluid becoming nearly
or quite colourless. A very good method for the quantitative estimation
of grape sugar when mechanically mixed with cane sugar, is that of P.
Casamajor. It is executed by first preparing a saturated solution of
grape sugar in methylic alcohol. The sample to be tested is thoroughly
dried, and then well agitated with the methylic alcohol solution, in
which all cane sugar will dissolve; any grape sugar present remains
behind, and upon allowing the mixture to remain at rest for a short
time, forms a deposit which is again treated with the grape sugar
solution, and then collected upon a tared filter, washed with absolute
methylic alcohol, and weighed. Glucose and invert sugar are usually
quantitatively determined by means of Fehling’s solution.

As this preparation is liable to decompose upon keeping, it is
advisable to first prepare cupric sulphate solution by dissolving
exactly 34,640 grammes of the salt in 500 c.c. of distilled water,
and then make up the Rochelle salt solution by dissolving 68 grammes
of sodium hydroxide, and 173 grammes of Rochelle salt in 500 c.c. of
water, the solutions being kept separate. When required for use, 5
c.c. each of the copper and Rochelle solutions (corresponding to 10
c.c. of Fehling’s solution) are introduced into a narrow beaker, or a
porcelain evaporating dish, a little water is added, and the liquid
brought to the boiling point. The sugar solution under examination
should not contain over 0·5 per cent. of glucose. It is cautiously
added to the hot Fehling’s solution from a burette until the fluid
loses its blue colour (see p. 37). The number of c.c. required to
completely reduce 10 c.c. of Fehling’s solution, represents 0·05 gramme
of grape sugar. The foregoing volumetric method is sometimes applied
gravimetrically by adding a slight excess of Fehling’s solution to the
sugar solution, collecting the precipitated cupric oxide upon a filter
and weighing, after oxidation with a few drops of nitric acid; or, it
may be dissolved, and the copper contained deposited by electrolysis,
in which case the weight of copper obtained, multiplied by 0·538, gives
the equivalent amount of glucose. The proportion of cane sugar in a
sample of raw sugar can be determined by first directly estimating the
proportion of invert sugar contained by means of Fehling’s solution, as
just described. The cane sugar present is then inverted by dissolving
one gramme of the sample in about 100 c.c. of water, adding 1 c.c.
of strong sulphuric acid, and heating the solution in the water-bath
for 30 minutes, the water lost by evaporation being from time to
time replaced. The free acid is next neutralised by a little sodium
carbonate, its volume made up to 200 c.c., and the invert sugar now
contained estimated by Fehling’s solution. The difference in the two
determinations represents the glucose formed by the conversion of the
cane sugar; 100 parts of the glucose so produced is equivalent to 95
parts of cane sugar.

Commercial cane sugar is, however, generally estimated by the
instrument known as the saccharimeter or polariscope.

In order to convey an intelligent idea of the physical laws which
govern the practical working of the polariscope, it will first be
necessary to refer to the subject of the polarisation of light. The
transformation of ordinary into polarised light is best effected either
by reflection from a glass plate at an angle of about 56°, or by what
is known as double refraction. The former method can be illustrated by
Fig. 1, Plate X., which represents two tubes, B and C, arranged so as
to allow the one to be turned round within the other. Two flat plates
of glass, A and P, blackened at the backs, are attached obliquely to
the end of each tube at an angle of about 56°, as represented in the
figure. The tube B, with its attached plate, A, can be turned round
in the tube C without changing the inclination of the plate to a ray
passing along the axis of the tube. If a candle be now placed at I,
the light will be reflected from the plate P through the tube, and,
owing to the particular angle of this plate, will undergo a certain
transformation in its nature, or, in other words, become “polarised.”
So long as the plate A retains the position represented in the figure,
the reflected ray would fall in the same plane as that in which the
polarisation of the ray took place, and an image of the candle would
be seen by an observer stationed at O. But, suppose the tube B to be
turned a quarter round; the plane of reflection is now at right
angles to that of polarisation, and the image will become invisible.
When the tube B is turned half-way round, the candle is seen as
brightly at first; at the third quadrant it disappears, until, on
completing the revolution of the tube, it again becomes perfectly
visible. It is evident that the ray reflected from the glass plate P
has acquired properties different from those possessed by ordinary
light, which would have been reflected by the plate A in whatever
direction it might have been turned.

PLATE X.

[Illustration:

Fig. 1.

Fig. 2.

Fig. 3.

Fig. 4.

Polariscope.]

ARTOTYPE. E. BIERSTADT N. Y.

If a ray of common light be made to pass through certain crystals,
such as calc spar, it undergoes double refraction, and the light
transmitted becomes polarised. The arrangement known as Nicol’s prism,
which consists of two prisms of calc spar, cut at a certain angle and
united together by means of Canada balsam, is a very convenient means
of obtaining polarised light. If two Nicol’s prisms are placed in a
similar position, one behind the other, the light polarised by the
first (or polarising) prism passes through the second (or analysing)
prism unchanged; but if the second prism be turned until it crosses
the first at a right angle, perfect darkness ensues. While it would
exceed the limits of this work to enter fully upon the theoretical
explanations which are commonly advanced concerning the cause and
nature of this polarised, or transformed light, it may be well to state
here that common light is assumed to be composed of two systems of
beams which vibrate in planes at right angles to each other, whereas
polarised light is regarded as consisting of beams vibrating in a
single plane only. If, now, we imagine the second Nicol’s prism to be
made up of a series of fibres or lines, running only in one direction,
these fibres would act like a grating and give free passage to a
surface like a knife blade only when this is parallel to the bars,
but would obstruct it if presented transversely. This somewhat crude
illustration will, perhaps, serve to explain why the rays of light
which have been polarised by the first Nicol’s prism are allowed to
pass through the second prism when the two are placed in a similar
position, and why they are obstructed when the prisms are crossed
at right angles, it being remembered that in a polarised ray the
vibrations of the beams of light take place in a single plane.

Suppose we place between the two Nicol’s prisms, while they are at
right angles, a plate cut in a peculiar manner from a crystal of
quartz, we will discover that rays of light now pass through the
second prism, and that the field of vision has become illuminated
with beautiful colours–red, yellow, green, blue, etc., according
to the thickness of the quartz plate used. On _turning_ the second
Nicol’s prism on its axis, these colours will change and pass through
the regular prismatic series, from red to violet, or the contrary,
according to the direction of the rotation produced by the intervening
plate. Quartz, therefore, possesses the remarkable property of rotating
the plane of polarisation of the coloured rays of which light is
composed; and it has been discovered that some plates of this mineral
exert this power to the right, others to the left; that is, they
possess a right or left-handed circular polarisation. Numerous other
substances, including many organic compounds, possess this quality
of causing a rotation–either to the right or left–of a plane of
polarised light. For example, solutions of cane sugar and ordinary
glucose cause a right-handed rotation, whilst levulose and invert sugar
exert a left-handed rotation. The extent of this power is directly
proportional to the concentration of the solutions used, the length
of the column through which the ray of polarised light passes being
the same. It follows that on passing polarised light through tubes of
the same length which are filled with solutions containing different
quantities of impure cane sugar, an estimation of the amount of pure
cane sugar contained in the tubes can be made by determining the degree
of right-handed rotation produced; and it is upon this fact that the
application of the polariscope in sugar analysis is based. The optical
portions of the most improved form of the polariscope–that known as
the Ventzke-Scheibler–are represented by Fig. 2.

The light from a gas burner enters at the extremity of the instrument
and first passes through the “regulator A,” which consists of the
double refracting Nicol’s prism _a_ and the quartz plate _b_, it being
so arranged that it can be turned round its own plane, thus varying
the tint of the light used, so as to best neutralise that possessed
by the sugar solution to be examined. The incident ray now penetrates
the polarising Nicol’s prism B, and next meets a double quartz plate
C (3·75 millimetres in thickness). This quartz plate, a front view of
which is also shown in the figure, is divided in the field of vision,
one half consisting of quartz rotating to the right hand, the other
half of the variety which rotates to the left hand. It is made of the
thickness referred to owing to the fact that it then imparts a very
sensitive tint (purple) to polarised light, and one that passes very
suddenly into red or blue when the rotation of the ray is changed.
Since the plate C is composed of halves which exert opposite rotary
powers, these will assume different colours upon altering the rotation
of the ray. After leaving the double quartz plate the light, which,
owing to its passage through the Nicol’s prism B is now polarised,
enters the tube D containing the solution of cane sugar under
examination; this causes it to undergo a right-handed rotation. It next
meets the “compensator” E, consisting of a quartz plate _c_, which has
a right-handed rotary power, and the two quartz prisms _d_, both of
which are cut in a wedge shape and exert a left-handed rotation. They
are so arranged that one is movable and can be made to slide along the
other, which is fixed, thus causing an increase or decrease in their
combined thickness and rotary effect. The ray of light then passes
through the analysing Nicol’s prism F, and is finally examined by
means of the telescope G, with the objective _e_ and ocular _f_. Fig.
3 gives a perspective view of the Ventzke-Scheibler polariscope. The
Nicol’s prism and quartz plate which constitute the “regulator” are
situated at A and B, and can be rotated by means of a pinion connecting
with the button L. The polarising Nicol’s prism is placed at C, and
the double quartz plate at D. The receptacle _h_ contains the tube
P filled with sugar solution, and is provided with the hinged cover
_h´_, which serves to keep out the external light while an observation
is being taken. The right-handed quartz plate and the wedge-shaped
quartz prisms (corresponding to _c_ and _d_, Fig. 2) are situated at G,
and at E and F, and the analysing Nicol’s prism is placed at H. When
the wedge-shaped prisms have an equal thickness coinciding with that
of the quartz plate _c_ (Fig. 2) the left-handed rotary power of the
former is exactly neutralised by the right-handed rotary power of the
latter, and the field of vision seen at I is uniform in colour, the
opposing rotary powers of the two halves of the double quartz plates
C (Fig. 2) being also equalised. But if the tube, filled with a sugar
solution, is placed in the instrument, the right-handed rotary power
of this substance is added to that half of the double quartz plate
which exerts the same rotary effect (the other half being diminished
in a like degree), and the two divisions of the plate will now appear
of different colours. In order to restore an equilibrium of colour
the movable wedge-shaped quartz plate E is slid along its fellow F by
means of the ratchet M, until the right-handed rotary power of the
sugar solution is compensated for by the increased thickness of the
left-handed plate, when the sections of the plate C will again appear
uniform in colour. For the purpose of measuring the extent to which the
unfixed plate has been moved, a small ivory scale is attached to this
plate, and passes along an index scale connected with the fixed plate.
The degrees marked on the scale, which are divided into tenths, are
read by aid of a mirror _s_ attached to a magnifying glass K. When the
polariscope is in what may be termed a state of equilibrium, _i. e._
before the tube containing the sugar solution has been placed in it,
the index of the fixed scale points to the zero of the movable scale.

In the practical use of the Ventzke-Scheibler saccharimeter the
method to be followed is essentially as follows: 26·048 grammes of
the sugar to be tested are carefully weighed out and introduced into
a flask 100 cubic centimetres in capacity; water is added, and the
flask shaken until all crystals are dissolved. The solution is next
decolorised by means of basic plumbic acetate, its volume made up to
100 cubic centimetres, and a little bone-black having been added if
necessary, a glass tube, corresponding to P (Fig. 3) which is exactly
200 millimetres in length, and is provided with suitable caps, is
completely filled with the clear filtered liquid. This is then placed
in the polariscope, and protected from external light by closing the
cover shown at _h´_. On now observing the field of vision by means of
the telescope, it will be seen that the halves into which it is divided
exhibit different colours. The screw M is then turned to the right
until this is no longer the case, and absolute uniformity of colour is
restored to the divisions of the double quartz plate C (Fig. 2). The
extent to which the screw has been turned, which corresponds to the
right-handed rotation caused by the sugar solution, is now ascertained
on reading the scale by the aid of the glass K. The instrument under
consideration is so constructed that, when solutions and tubes of the
concentration and length referred to above are used, the reading on the
scale gives directly the percentage of pure crystallisable cane sugar
contained in the sample examined. For instance, if the zero index of
the fixed scale points to 96°·5 on the movable scale, after uniformity
of colour has been obtained, the sample of sugar taken contains 96·5
per cent. of pure cane sugar. The results given by the polariscope
possess an accuracy rarely, if ever, attained by any other apparatus
employed in the determination of practical commercial values.[57]

The proportion of grape sugar intentionally added to cane sugar can
also be determined by the use of the polariscope, certain modifications
being observed in its application. As previously stated, cane sugar
is converted into a mixture of dextrose and levulose, termed invert
sugar, by the action of dilute acids. While the rotary effect of
dextrose upon the plane of a ray of polarised light is constant at
temperatures under 100°, that exerted by levulose varies, it being
reduced as the temperature is increased; hence it follows that at a
certain temperature the diminished levo-rotary power of the levulose
will become neutralised by the dextro-rotary effect of the dextrose,
_i.e._ the invert sugar will be optically inactive. This temperature
has been found to approximate 90°. Since dextrose is not perceptibly
affected by the action of weak acids, it is evident that by converting
cane sugar into invert sugar and examining the product by the
polariscope at a temperature of about 90°, the presence of any added
dextrose (glucose) will be directly revealed by its dextro-rotary
action. This is accomplished by a method suggested by Messrs. Chandler
and Ricketts,[58] which consists in substituting for the ordinary
observation tube of the polariscope a platinum tube, provided with
a thermometer, and surrounded by a water-bath, which is heated to
the desired temperature by a gas burner (Plate X. Fig. 4). The sugar
solution to be examined is first treated with a little dilute sulphuric
acid, then neutralised with sodium carbonate, clarified by means of
basic plumbic acetate, filtered, and the polariscopic reading taken at
a temperature of 86° to 90°.

Since the results given by the foregoing method represent pure
dextrose, it is necessary to first ascertain the dextro-rotary
power of the particular variety of glucose probably employed for
the adulteration of the sugar under examination, and then make the
requisite correction. This process for the estimation of glucose is
especially advantageous, in that the optical effect of the invert sugar
normally present in raw cane sugars is rendered inactive.

It is sometimes desirable to determine the relative proportions of
the organic constituents which are present in commercial glucose.
These usually consist of dextrose, maltose, and dextrine, all of which
possess dextro-rotary power, but not in the same degree; that of
dextrose being 52, that of maltose 139, and that of dextrine 193. An
estimation of the amount of each can be made by first ascertaining the
total rotary effect of the sample by means of the polariscope.[59] This
is expressed by the equation

P = 52 _d_ + 139 _m_ + 193 _d´_, (1)

in which P is the total rotation observed. Upon now treating the
solution of glucose with an excess of an alkaline solution of mercuric
cyanide (prepared by dissolving 120 grammes of mercuric cyanide and 25
grammes of potassium hydroxide in 1 litre of water), the dextrose and
maltose contained in the sample are decomposed, leaving the dextrine
unaffected. A second polariscopic reading is then made, which gives the
amount of dextrine present, that is

P´ = 193 _d´_, (2)

from which the proportion of dextrine is calculated.

Subtracting the second equation from the first, we have

P – P´ = 52 _d_ + 139 _m_. (3)

Both dextrose and maltose reduce Fehling’s solution, the total
reduction (R) being the reducing per cent. of the former (_d_) added to
that of the latter (_m_). The reducing power of maltose is, however,
only 0·62 as compared with dextrine, therefore

R = _d_ + 0·62 _m_. (4)

Multiplying by 52, we have

52 R = 52 _d_ + 32·24 _m_,

and subtract from (3), which gives

P – P´ – 52 R = 106·76 _m_, (5)

whence

_m_ = (P – P´ – 52 R) / 106·76 (6)

_d_ = R – 0·62 _m_ (7)

and

_d´_ = P´/193.