The NEW SARTORIUS-RAMBERG
MICRO-BALANCE' JULIUS KUCK
AND
ERICH LOEWENSTEIN2
The City College of the College of the City of New York, New York City
A
LTHOUGH the first microchemical balance was built in 1886 by E. Warburg and T. Ihmori ( I ) , and other types appeared in the decades following (2, 3, 4, 5), it was not until 1910 that F. Emich of Graz adapted the refined assay balance to microchemical work (6). This short-beam type of balance possesses many advantages peculiar to this kind of construction, the most important being a lighter beam mass, a greater freedom from deviations caused by unequal expansion of the lever arms, less flection of the beam, and a shorter period of oscillation. F. Pregl quickly recognized these advantages of the assay balance, but be realized that certain improvements would have to be made in order to make i t a useful instrument for ordinary laboratory work. Therefore, he commissioned W. H. F. Kuhlmann of Hamburg to construct an improved microchemical balance with the special rider, the reading lens, the screw for the adjustment of the center of gravity, and the hooks for the absorption of filter tubes. This was the famous model Number 19-b (7). In recent years several other firms have put on the market micro-balances embodying the same principles of construction as those of the Kuhlmann balance, but differing slightly in a few features. Kuhlmann has added a few innovations to his balance, the telescopic reading device and the detachable housing, but be has not changed the fundamental principles of his instrument, particularly the form of the rider and the style of the rider-carrying mech%nism. In 1933 Professor Ramberg of the University of Upsala reported his careful study of different riders and the causes of rider error (8). At his suggestion the Sartorius Company of Gottingen, Germany, undertook the construction of a special micro-balance equipped with a small two-milligram quartz-stick rider, because Ramberg had proved mathematically that such a rider has the optimum form. Unfortunately, the original report of this balance was in Swedish and did not readily come to the attention of microchemists in the English-speaking countries. Moreover, in spite -
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'Since this article was submitted for publication the experimental model in question was returned to the Sartorius factory for a few minor changes in design, including the addition of a magnifying lens for the rider-carrying device. Before the outbreak of the war onlv three of these balances had been received in this country. Recently an American manufacturer has agreed to attempt the production of a microchemical balance embodying the features described in this article. Technical Adviser, Pfaltz & Bauer, Inc., 350 Fifth Avenue. New York City.
of the fact that both the theory and design of this balance were sound, the actual workmanship of the first of these micro-balances which appeared in this country was inferior to the artistic craftsmanship of Kuhlmann. The chief trouble with the tiny quartzstick rider was its tendency to fall from the notch in the balance beam unless i t was deposited exactly balanced in its middle by the rider carrier. Since the balance
.. case was of woo'd and the rider-carrying device was attached to it by means of screws, only a slight warping of the wood sufficed to throw the rods of the rider carrier out of line with the beam and attempts to correct this made matters worse., The thin quartz stick was easily lost and hard to pick up with the forceps when found. Its constant replacement to the balance beam was a source of annoyance to the analyst. To meet this objection the Sartorius Company withdrew its original Ramberg micro-balance from sale on the market and after considerable research hy its technical staff is now introducing a new micro-balance with a metal case by which the rider carrier is kept in a more perfect alignment. The new balance is shown in the accompanying illustration and is subsequently described. THEORYOPTHERAMBERGEALANCE
Because of the theoretical importance of Ramberg's article it has been thought advisable to give a dsume of i t in English. The starting point of his consideration is the mathematical statement that for an accuracy of one microgram in a weighing on a microchemical balance, the moment of the rider (force X distance or r X 1) must be so reproducibly defined that its error does not exceed the moment of a mass of 0.001 mg. on the right pan; (r X I ) must be equal to or
p = (Z * d.sin .#.).PC less than 0.001 L/2 where r is the mass of the rider, (1) I its distance from the central knife, and L the total where p = moment in dynes, I = distance in millilength of the beam between the end knives. He meters of the carrying line from the vertical plane of pointed out the concept of an ideal rider which is asthe central knife edge, d = distance in millimeters sumed to be perfect in form and frictionless, the ideal between the carrying line and the center of gravity notch which is smooth and symmetrical, and the real of the rider, 6 = the acute angle between the plane rider and notch which are actually met in practice. of the rider and the vertical plane of symmetry of the A rider may be considered to liave four contacts which notch, r = the mass of the rider in milligrams, and g = lie in one plane. The intersection of this plane with the gravitational force on a mass of one milligram the rider plane is called the "carrying line." In (0.980 dynes). (Figure 1) the ideal case the carrying line should lie in Dislocation and angle errors are known as "nonthe plane 'of symmetry of the notch, but in the real inreproducible errors" since the moment of the rider in stance it is not sharply defined, since the same rider may a given notch cannot be reproduced with certainty if have different carrying lines in the same notch dependthe rider is raised from the notch and replaced. ing upon its position in that notch. All of the sources of error may be grouped as follows: Certain errors in miaochemical weiahina - may be grouped into two types: (A) those due to errors in errors (61) Length errors ( A l ) { Division Dislocation errors ( 6 1 ) the instrument, and (B) those due to the faulty rider (Non-reproducibleerrors) Angle position, which are termed "dislocation errors." In the former group (A) we find: (a) The mass of the Ramberg deduced the following for the . expression . length tolerance for an accuracy of *l miaogram (T,) which may be defined as the greatest allowable error in the position of the carrying line.
VERTICIL COMPONENT
TRANSVERSE COMPONWT
where L = distance between the end knives and when = 0 or remains constant. From equations (1) and
+
OO1.L where AJ = 61 (AJ) = O' 2r (algebraic sum). : , .L = ' (&) = 0.001 ----
(2) we get: rider deviates from its earmarked value (for example, a Kuhlmann rider may not exactly equal 5 mg.). (b) There may be divisional errors symbolized by (61) where the distance of the notch from the vertical plane of the central knife edge is in error. In the fabrication of the instrument the divisions on the rider scale may not be exactly a proportionate distance from the vertical plane of the fulcnim. However this error is not serious because 61 is a cmstant. (c) The middle of the notch may not lie in a plane perpendicular to the rider scale and parallel to the central knife edge. Dislocation errors (B) depend upon the form of the rider, the condition of the notch, and various uncontrollable factors. In this category may be included: (a) the case where the rider sticks to the side of the notch and does not reach its lowest point-(6'1). Here the carrying line obviously cannot coincide with the plane of symmetry of the notch. (b) "Angle errorsw-(A+): the rider is not frictionless, and its plane is inclined to a horizontal plane which is perpendicular to the rider scale and which passes through the central knife edge. Its position has two components, since the rider plane may make either a horizontal or a vertical angle with the vertical plane perpendicular to the longitudinal axis of the rider scale (Figure 2). By the geometry of the adjacent diagram, an equation for the moment of the rider (beam horizontal) can be easily deduced (Figure 3).
2
+
(Tdr
6'1
(3)
For a Kuhlmann balance where r = 5 mg. and L = 70 mm., (T,) = 0.007 mm. This means that the position of the carrying line must be exactly reproducible owthe Kuhlmann microbalance to within 0.007 mm. Although the dislocation error may be just within this tolerance limit, there is no latitude for a divisional error in the same direction. Table 1 gives the length tolerance for some other micro-balances which are in common use. TABLE 1 Rid., wrish1
M
