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A new micro-balance and its use online

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Ur: Goteborgs Kungl. Vetenskaps- och Vitterhetssamhalles
Handlingar. Fjarde foljden. XVI.

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I. Introductory . . j 1

II. The new micro-balance.

1. Construction of the beam 9

2. The balance cases 11

3. Mounting and adjusting the balance 16

4. Weighing by pressure Theoretical 17

5. Practical 19

6. Accuracy of a weighing by pressure 22

7. The bulbs and the weights 23

8. Errors in the weighings 25

9. Theory of the balance with fibre suspension 26

10. Investigation of a micro-balance 35

1J. Conclusions 43

III. Experiments with the micro-balance.

1. The change in the weight of gold caused by heating it 47

2. The magnetic susceptibility of gases 51

3. The influence of temperature upon weight 65

4. The volatility of silica 77

5. Future experiments on the influence of temperature upon weight . 80

6. Suggested experiments with the micro-balance 81

IV. Summary 83

Curves and tables 85

Bibliography 89


I. Introductory.

Most weighing balances can be classed either as elastic balances
or as lever balances. On instruments of the first type the load is
suspended from an elastic structure of some kind, generally a spring
coil, which becomes deformed until the elastic forces caused by the
deformation counteract the downward pull of the load. The vertical
displacement of the latter is read on a scale, and the instrument is
standardized by producing different scale-deflections with a set of

On instruments of the second type the load is suspended from
one end of a rigid structure, the beam, which can rotate round a
horizontal axis, generally a knife-edge. The deflection of the beam
from its normal position is read on a scale. In order to keep that
deflection within certain limits the load is in most cases counterbal-
anced by suspending from the other end of the beam a counterpoise,
which is either made up from weights or is afterwards, in its turn,
counterbalanced by exchanging the load for an equivalent number
of weights.

On instruments of the first type an automatic compensation
is produced by the elastic forces, whereas the construction of most
lever balances aims at reducing all such compensatory effects to
a minimum.

The absolute sensibility, S, of a balance we define as the addi-
tional load, dW t which produces an observable deflection, da t of the
beam. S = dW. According to this definition a high sensibility corre-
sponds to a low numerical value of 8 and vice versa.

The sensibility may evidently be increased by reading the de-
flections more accurately on the scale used for that purpose. It is,
however, useless to carry this increase beyond a certain limit, the
instrumental limit , which is reached when da becomes of the same

M:' -"** * "sL j a

magnitude as the irregular and uncontrollable variations of the po-
sition of the beam that are due to constructional defects.

The absolute sensibility divided by the load is called the relative
sensibility; S r = = S : W

While the technique of most other physical measurements has been
brought to a high degree of perfection during the last decades, it is
only in the last few years that any considerable progress has been made
with regard to the absolute accuracy of weighings. Still, a considerable
number of attempts to that end were made by renowned men
of science. A short description of the more important balances which
have thus been constructed will be given in the following pages.

In 1886 Warburg and Ihmori [4] made a sensitive lever
balance, figure 1 a, which they used to study the formation of thin
films of condensed water-vapour on the surface of solids. The beam,
a thin- walled glass tube, slightly bent at the middle, was balanced
on a minute knife-edge made from a fragment of a razor. The scale
pans were suspended from similar knife-edges, one at each end of
the beam. The balance was mounted under the receiver of an or-
dinary air-pump and was worked in a vacuum. Read with mirror

and scale (at 272 cm) its sensibility was ^ mg. with a load of
600 mg.

Ihmori [5] afterwards improved the instrument in several re-
spects and brought its sensibility up to ^T^ mg. with a load of 500

mg. Balances of this type are difficult to construct and to work,
and they have therefore not been used by later experimenters.

K. Angstrom [6] made a balance in 1895 which gave quite good
results in spite of its simple construction. The very light beam,
figure 1 b, was made from wood, carefully varnished. Instead of
being balanced on a knife-edge it was suspended by two silk fibres
wound half round a central cylindrical axis, which rolled on the fibres
when the beam was swinging. The weight-pans were suspended in
the same way. With a load of 1 gr. the sensibility was of the

order TA^T. mg. Angstrom used the instrument for comparing and
standardizing light weights.

A balance suspended in the same way was described by G. E.
Weber in 1841 [1], a fact of which Angstrom w r as not aware until
after his own balance had been completed.

Fig. /.

a (1:2)
Warburg & Ihmori.

b (1:3)

d (2:9)

e (2:5)
Stsele & Grant.


Different types of micro-balances.

(a d reproduced from papers previously cited.)

Guglielmo [7] in 1901 adopted an ingenious device for reducing
the weight of the balance beam by immersing it completely in water.
It was made from glass tubes filled with air and was balanced on
two fine metal points.

The sensibility varied from ^ mg. to ^ mg. with loads weigh-
ing 236 to 2.5 mg.

The instrument was used chiefly for measuring the density of mi-
nute quantities of solid substances.

In 1901 Salvioni [8] published the description of an elastic ba-
lance, figure 1 c, the first instrument which was called a micro-balance.
A thin rod of glass was fixed at one end in a position slightly in-
clined to the horizontal. The load was suspended from the free end of
the rod, the downward displacement of which was observed with a
reading microscope, a piece of cob- web attached to the red serving as
index. According to the laws of elasticity the displacement should be in
direct proportion to the weight of the load, which was varied from 1 mg.

to 200 mg. The highest absolute sensibility was of the order rr^ mg.
With the aid of this instrument Salvioni [9] found it possible to measure
the continual decrease in the weight of a strongly odorous substance
like musk. A balance of the same type, but with an elastic strip cf silver
plate instead of the glass rod, has been described (in 1886) by Lord
Kelvin (then Sir W. Thomson) [3].

Giesen [10], in 1903, used a slightty modified Salvioni balance to
measure the density of gases and their absorption by charcoal, and
also for a repetition of Warburg's and Ihmori's experiments on
surface sheets of moisture.

The well-known Nernst balance, figure 1 d, was described by
its inventor in 1903 [11]. A thin glass rod, serving as beam, was
cemented to a very fine quartz fibre stretched horizontally between
two supports. A tiny metal capsule at one end of the beam held
the load, and was counterbalanced by a rider attached to the other
arm of the beam. The end of that arm had been bent twice and
drawn out to a fine pointer moving over a scale. In order to have
a very small restoring torque of the quartz fibre it must be ex-
tremely thin. For that reason the balance could not be charged with
loads heavier than a couple of mg., the sensibility being then about

|jQ mg. The simple construction of the Nernst balance has caused

it to be widely used in spite of its very limited range. Nernst him-
self has employed it for a determination of the atomic weights of several
rare earths. Later O. Brill [15] has carried out a similar research
and has also investigated the dissociation of carbonates at high tem-
peratures with the Nernst balance, after having improved it in cer-
tain respects. 1 ),

It is an interesting fact that an instrument almost identical in
construction to the Nernst balance was used for a hygrometer by
Hertz [2] in 1882.

So far, the results attained in the course of twenty years had not
been very brilliant. It must be admitted, however, that there were
considerable technical difficulties to overcome before any further pro-
gress could be made.

To find a suitable material for the beam and the weights was the first
problem to be solved. As the dimensions of the instrument are re-
duced, the relative influence of all surface effects, such as the condens-
ation and adsorption of vapours and gases, and the corrosion by the
oxygen and the moisture of the air, increases. An ideal substance should
therefore be non-hygroscopic and non-corrosive, and must in addition
to that have a low density and a high tensile strength.

How to make sufficiently light weights was another most diffi-
cult problem. The balances described above were all read by deflec-
tion, that is, the exact value of the weight of the load was calculated
from the observed scale-reading by interpolation according to a pre-
vious standardization of the scale with very light weights. Such an
interpolation cannot be made much more accurate than to 0,i % of
the lightest weight employed. Now a weight of less than 0,i mg. is
most troublesome to handle, which gives 0,oooi mg. as the practical li-
mit of accuracy. Again, if such a weight is used as a rider, its position
cannot very well be more accurately defined than to a thousandth part
of the length of the beam, which gives the same limit as the other me-
thod. It would therefore seem to be useless to try to construct balan-
ces of a still higher sensibility. This view has been expressed as re-
cently as in 1904 by Scheel [12] in his criticism of Giesen's work with
the Salvioni balance. It appears indeed most likely that, but for

l ) I have recently found, that Brill has since found it possible to increase
nsibility of the balance t<
soc. London 93 p. 1442; 1908.]

the sensibility of the balance to mg. [O. Brill and Miss Evans. Journ,. chem.

the inventive genius of two Australian men of science, the aforesaid li-
mit must have remained unsurpassed for many years.

In the Proceedings of the Royal Society of London for 1909 Steele
and Grant [16] published a paper on "Sensitive micro-balances and a
new method of weighing minute quantities", which opened a new era
in the history of weighing instruments.

They found the best possible solution for the problem of the ma-
terial by making the whole of their balance from fused silica. This
substance possesses in a high degree all the desired qualities before
mentioned, and in addition to this it presents the advantage of be-
coming fusible and even slightly volatile at the temperature of the
oxy-coalgas flame.

Thin cylindrical silica rods were fused together by means of the
blowpipe to a plane structure of considerable rigidity. This beam was
balanced on a knife-edge, ground at the end of a short silica rod. A fibre
provided with a hook for the load was drawn out from one end of the
beam, a lump of silica at the other end serving as counterpoise. A
quartz mirror and another counterpoise were fused to opposite sides
of the beam near its central axis. The centre of gravity of the beam
was adjusted so as to give the balance the desired sensibility simply
by drawing off or volatilizing away minute quantities of silica from
the lower end of the mirror-counterpoise.

Still more ingenious is the way in which the authors have overcome
the difficulty of making sufficiently light weights. The balance was
mounted inside a vacuum-tight case and the weighing done by varying
the pressure of the enclosed air. This would of course have no effect on the
equilibrium of the system if its density were uniform, that is, if the load
consisted only of solid silica. There was, however, also a sealed silica
bulb of known capacity, v, suspended from the beam. Therefore, when
the pressure in the case was reduced from p 1 to p 2 , there would be an
uncompensated decrease in the buoyancy of the air acting on the bulb,
equivalent to an apparent increase, dW, in its weight. It is easy to see

that approximately dW v l t 2 . & , where ( ), is the density


of the air at normal pressure and at the temperature of the experi-
ment. One might also say that dW is the weight of the air which
would have escaped from the bulb, if it had been open when the pres-
sure was reduced.

If the capacity of the bulb is very small, its effective weight can
evidently be varied by extremely small amounts, the exact values
of which are found by reading the change in pressure on a manometer
in communication with the case.

The most delicate balance made in this may, fig. 1 e, was sensi-
tive to 2 - oouo m ' w ith a load which was probably about 20 nig. The
total weight of the balance with mirror, counterpoise, and a bulb of
8,65 mm 3 ., was 177 mg.

With the aid of such balances the authors [17] afterwards made
attempts to weigh the active deposit from a small quantity of niton
(radium emanation).

The reliability of instruments of this type and their usefulness
both for chemical and physical work has received a striking illustration
through two investigations by Sir William Ramsay and Dr. Whytlaw-
Gray. Operating on aquaritity of only 0,i mm 3 , of niton they succeeded
in measuring its density [18] with a mean error of about one per cent,
the result giving a conclusive proof in favour of Rutherford's Disin-
tegration theory. Afterwards they redetermined the atomic weight
of radium [20] on a minute quantity (less than 3 mg) of pure Ra Br,,.

The balances used in these investigations were made according
to instructions from Steele and Grant, but the technique of their con-
struction and of the weighings was modified in certain respects.

On the plane surface of a block of gas-coal fine grooves were ruled
to a figure representing the shape of the beam. Thin silica rods were
put into these and their ends fused together with the blowpipe. In
this way a perfectly plane structure was secured, free from all after
effects due to inner strain, which had sometimes troubled Steele and

It was also found more convenient to seal a piece cut off from a
previously made silica fibre to the end of the beam rather than to draw
out the fibre from a T -piece of silica fused to the tip of the beam.

The weighings were carried out according to the zero principle,
that is, the pressure was adjusted so as to bring the beam back
to almost identically the same position.

The most delicate instrument made by Ramsay and Gray had a


sensibility of 2 (nmg. (= 2 10' 6 mg) with a load of about 50 mg. The
atomic weight of radium was determined on a rougher instrument,
symmetrical in shape, on which loads of some 70 mg. could be weighed

to 25000 m %'

Though balances of this type work perfectly under normal condi-
tions, they have certain drawbacks. The end-fibres, which have to be
very thin in order not to offer too great resistance when the beam swings,
seem to get very brittle at the points where they are sealed to the beam.
For this reason these balances cannot safely be worked with loads
heavier than about 0,i gr.

Fine dust particles will now and then get under the knife-edge
and put the balance out of working order untrl the case is opened
and the particle removed.

When I started working at the University College of London in
November 1911, Sir William Ramsay suggested to me that I should
try to make a new kind of micro-balance, suspended by fine platinum
wires instead of the knife-edge, and with the same suspension for the
loads. By this arrangement the carrying strength of the instrument
would probably be much increased.

In the course of their work with niton [ 1 8 ; 1 9] Ramsay and Gray had
observed that when a tiny gold capsule was heated and suspended from
the balance, its weight on cooling continually increased for several
hours and even for days. Sir William therefore advised me to use the
balance which I was to construct for a closer study of this phenomenon.

It will be seen from the following that the first of the two pro-
blems set before me has been solved. A new type of micro-balance
suspended by fibres, though not of platinum, has been constructed,
which is superior to the knife-edge balances in several respects. The
technique of the new instrument has been developed and studied, and
its usefulness for certain physical measurements has been demon-

As regards the second problem only preliminary experiments have
hitherto been made. This is largely due to the fact that the pheno-
menon proved to be of too complicated a nature to be studied by the
simple methods originally devised.


I wish to express here my siiicerest gratidude to Sir William
Ramsay for having suggested this research, and for the kind and en-
couraging interest which he has constantly taken in it.

After working for about ten months at University College, it became
necessary for me to go back to Sweden, where I resumed my work at
Fysiska Institutct, Stockholms Hogskola. I have much pleasure in
acknowledging my indebtedness to its director, Professor Carl Bene-
dicks, for having placed the necessary instruments at my disposal, and
for much help and advice.

II. The new micro-balance.

i. Construction of the beam.

The shape chosen for the beam (see fig. 1 f) is that of a rhombus
with its two intersecting diagonals, a structure which is at the same
time light and fairly rigid. The longer, horizontal, diagonal is about
9 cm. in length, the shorter, vertical, diagonal is 4cm. The diagonals
are made to protrude by half a cm. outside the corners of the figure
so that each arm of the beam is about 5 cm. long.

The beam was made flat on a piece of gas-coal from silica rods,
0.5 to 1 mm. thick, according to the method of Dr. Whytlaw-Gray, to
whom I am much indebted for valuable advice on the technique of the
silica work and of the weighings. Short pieces of silica rod were fused
to the centre of the beam at right angles to its plane. To these cross-
pieces the central fibres of suspension were attached.

I first attempted to suspend the beam and its loads by platinum wires
of which three different dimensions were tried, viz. wire 0,025 mm. thick,
drawn in the ordinary way, and Wollaston wires of 0,012 mm. and
of 0,008 mm. The ends of the wires were soldered to the tips of the
central crosspieces and of the horizontal diagonal, where the silica had
previousfy been platinized with colloid platinum. The soldering was


carried out under the microscope with the aid of a minute electric
soldering apparatus.

Unfortunately the wires got very brittle at the junction, so that
they almost invariably snapped when any strain was put on. A con-
siderable number of unsuccessful attempts were made before a beam
could be suspended and loaded with all four fibres (0,008 mm) intact.

It was, however, not possible to make it more sensitive than to TTT mg.

(scale-distance 0,8 m, loads about 1 gr.), and even at that low sen-
sibility the zero of the instrument was not constant.

This poor result was undoubtedly due to the considerable elastic
after-effects which metal wires are known to show.

Nearly three months had been spent on these attempts, and it
appeared that I would have to fall back on knife-edge balances of the
older type for my investigation. However, before definitely giving
up suspension by fibres I decided to try to suspend a beam by fibres
of silica instead of platinum.

The general shape of the beam, figure 1 /, was the same as before.
The fibres were drawn out from four short silica rods bent to a hook
at one end and fused by the other end to the central crosspiece and to
the ends of the beam. These had been bent to the shape shown by the
figure in order to make the starting points of all the four fibres fall
nearly at the same level as the centre of the beam. Only the first mm's
of the fibres next to these points were drawn very thin, some ja in
diameter. The theory of the balance, which will be given further on,
proves that the thickness of the rest of the fibre is of no importance.

Finally a ground and polished silica mirror, covered with a re-
flecting layer of palladium by the spray method, was sealed to one
of the central crosspieces, and a counterpoise of the same weight
to the other crosspiece. The balance was then ready to be mounted
in its case, loaded, and adjusted to the desired sensibility.

The first instrument of this type which I made possessed a sensi-
bility of rr-rr mg. when charged with loads of about 2 grammes each.

The period of a complete swing was then some 40 seconds, and the scale,
which was at a distance of 1 m., was read to millimetres. After that, a highty
sensitive balance was made of the same construction but with thinner
fibres. A detailed account of the properties of this instrument will


be given in a succeeding paragraph. After my first two balances had been
completed, I was made aware of the fact that an instrument of similar
construction, but with elastic strips of metal instead of the fibres, has
been described in 1841 by W. Weber in his "De tribus novis librarum
construendarum methodis" [1]. Quite recently a balance of the Weber
type, hanging by two strips of steel, has been used by Piccard [22] for
magnetic investigations.

2. The balance cases. 1 )

The first case used with the new micro-balance is drawn in figure 2.
The floor of the case is a brass plate, 10 mm. thick, which has been care-
fully tinned over its lower surface. It is carried by three screw legs
of brass, of which only one is seen in the figure. The cover is a
pneumatic glass trough (9 by 10 by 15 cm.), the edges of which have
been ground on the brass plate. When readings are taken the light
from a Nernst lamp is sent through a positive lens and then through a
kind of window, PF, made by cementing two pieces of plate-glass with
Canada balsam to the wall of the cover. After a reflection against the
balance mirror an image of the incandescent filament is formed
across a vertical scale, 4 metres away, which is read to millimetres.

The released balance hangs by its central fibres from two brass
hooks carried by adjustable supports (not visible in the figure). It
is arrested when the U-piece of brass, B, is raised by turning the screw
S, which is ground into a conical jacket. The balance is then lifted
at a 1 and a 2 by two horizontal silica rods, while two vertical silica
hooks, b 1 and 6 2 , complete the arrestment.

One of the loads is made accessible without removing the cover,
by the same arrangement as with the case used by Steele and Grant
[16 p. 582]. One of the end-fibres from the beam comes down into a
detachable glass tube, G, under the floor of the case, which is ground
to fit over a glass' ring cemented into a hole through the brass plate.
The other end-fibre is quite short and carries a counterpoise of silica.
All joints are made air-tight with rubber-grease.

This case was used chiefly for investigating the properties of the
micro-balance and also for making weights. It can be made perfectly

x ) The description of the technique of the balance and of the weighings given
in the following paragraphs is in part to be found in the papers of Steele & Grant and
of Ramsay & Gray.





air-tight, it is comparatively light, and also presents the advantage
that the movements of the released balance may be closely observed
through the transparent walls of the cover. On the other hand the
low thermal conductivity of the cover is a disadvantage, as it
is important for the accuracy of the weighings that the air in the case
shall be surrounded by an isothermal surface. The case also appears
to be rather sensitive to tremors, probably in consequence of its light
weight and of the unelastic properties of its supports.

Certain experiments, Avhich will be related further on, had indi-
cated to me, that a considerable number of investigations can only be
made with a balance case where it is possible:

1. to heat one of the weight-tubes suddenly to high tempera-

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