Circular Slide Rule for Microanalysts. Ralph E. Schachat' and Walter 1,. Savell, Laboratory of Advanced Research, Remington Rand, Inc.. South NorLYalk, Conn. r
THOMPSON
[Thompson, R. C., ASAL. CHE\I.,25,535 (1953)l re-
1cently discussed the advantages of choosing a definite weight
of sample for a carbon-hydrogen determination rather than a random quantity. She described the construction of a linear instrument that permitted the analyst to compute quickly the optimum weight of sample for the probable carbon and hydrogen content. The instrument described here is simple in construction and operation. I n addition, by means of extra scales, the computation of optimum weight of sample for a Dumas nitrogen analysis is made possible. The instrument can also be used as a conventional circular slide rule, enabling the operator to multiply, divide, and determine reciprocals. Other scales, such as square root, cube root, log log, eta., may be added if desired.
ing figures. Figures 1 and 2 represent the arrangement of the two sides of the slide rule, where the inner scale refers to the theoretical per cent of the element sought and the outer scale refers to the optimum sample weight in milligrams. All the scales are based on the formula @ = 180 loglo X so that each 360" scale is actually composed of a regular linear slide rule scale arranged so that the numbers 1t o 10 extend from 0' to 180' and numbers 10 to 100 extend from 180" to 360". The reason for choosing the numerical range of 1 to 100 for the inner scale is that 1 to 100 indudes all possible percentages of carbon, hydrogen, and nitrogen found in organic compounds (except for a very few isolated cases).
THEORY Dumas Nitrogen Scales
The symbols used in calculating the layout of the scales and slidrrs are as follows: angle in degrees from the starting point or "index" for any value of X ec = angle between the dotted line of the carbon slider and the carbon content-indicating arrow eH = angle between the dotted line of the hydrogen slider and the hydrogen cont,ent-indicating arroR = open area angle on the carbon slider between the broken BR and solid line. The solid line is refrrred to as the "indicator line" for multiplying and dividing operations. 0 9 = open area angle on the hydrogen slider between the broken and solid line e: = angle between the nitrogen-indicating arrow and the 1-ml. selector eo,5 = angle between the nitrogcn-indicating R ~ T O Vand the 0 5ml. selector X = any number between 0 and 100 B
=
The instrument consists of five parts, shonm in the accompany-
Figure 2. Dumas-Nitrogen Scales
1 Present address, Central Laboratories, General r o o d s Corp. 1125 Hudson S t Hoboken, h-. J.
Figure 3.
Carbon Slider
Scale up to same size as Figure 1
Figure 1. Carbon-Hydrogen Scales
The range 1 to 100 was chosen for the outer scale because this range in milligram includes all likely sample weights. As an additional advantage, keeping the same range for both scales allows reciprocals to be conveniently determined (see Use of Rule). The two scales on one side start a t the same point, but run in opposite directions.
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1780
ANALYTICAL CHEMISTRY
The "open area" angle on the C slider (Figure 3) and H slider (Figure 4) is obtained as follows: The optimum weight of carbon dioxide obtained may be considered to be 5 to 20 mg. (1 to 4 ratio), while o timum of weight of water is 2.5 to 10 mg. (also 1 to 4ratio). ?%erefore, the angle will be = es = 180 loglo(4/1) = 108.4' for both the C and H sliders. The positions of the indicator arrows are computed as follows: Each milligram of hydrogen in the compound produces about ,9 mg. of water. Therefore, OH = 180 log,, (2.5/9) = -100.2 , the angle between the broken line of the H interval indica:or and the H arrow. Similarly, ec = 180 loglo5/(44/12) = 24.0 . The form of the nitrogen indicator (Figure 5) is calculated as follows: At 25" C. (approximately room temperature) and 1atmosphere pressure, 1 ml. of nitrog:n weighs 1.1457 mg. Therefore, Ob = 180 log,, (1.1457) = 10.6 . A 0.5-ml. selector (dotted line) is also included; its angle (@) is calculated in the same manner. Since 0.5 ml. of nitrogen a t 1-atmosphere pressure and 25" weighs 0.5729 mg., PV5= 180 loglo (0.5729) = -43.8".
indicate the optimum range of Sam le weight in milligrams. For the few cases in which there is no cLar area, the optimum sample range is indicated by the doubly covered (green) part of the scale. As there will be two green areas, choose the one most distant from the index position of the scale, For Dumas Nitrogen Determinations. If 1 ml. of nitrogen is desired, set the arrow to the theoretical per cent nitrogen on the inner scale and read the sample weight indicated by the A' ( 1 ml.) line on the outer scale. If 0.5 ml. of nitrogen is preferred, use theN(0.5ml.)Iine.
For the analyst who prefers other volumes of nitrogen, other indicating lines can be constructed in an analogous manner. Alternatively, the slider can be divided into segments that will show the sample weight range for any desired volume range. CONSTRUCTION OF RULE
The scales and sliders were computed by use of the e values as described under Theory. A small arrow or "index position" indicated the starting point of the outer scale. Actual construetion of a workable rule consisted of pasting the carbon-hydrogen scale (Figure 1 ) on one side of a piece of stiff cardboard and the nitrogen scale (Figure 2) on the other. The three sliders were traced onto stiff plastic and scaled up to the same size as the scalesofFigures l a n d 2 Thus, the length of the arrows was made equal to the radius of the inner circle of the scales. The length
. Figure 5. Kitrogen Slider Scale up to same size as Figure 1
For Multiplying any two numbers (outer C and H scale and solid lines extending to indicator tabs are used). To multiply ;M X N , set the solid line of the C indicator on M and the solid H indicator line on the index point of the scale. The indicator lines thus form an angle. Without disturbing the angle, move both sliders together so that the H indicator line falls on :V. Read the answer under the C indicator line. The decimal point is set as usual in slide rule calculations. For Dividing (use outer scale and solid C and H indicator lipes). To divide M by N , set the C indicator line on iM and the H indicator line on N . Move both sliders together until the H indicator line rests on the index position. The answer is indicated under the C indicator; fix the decimal point by an approximate calculation. Multiple Operations. The slide rule can be used to perform operations of the type
M XN X 0X P Q X R X S
Figure 4.
Hydrogen Slider
Soale up to same size as Figure 1
of the solid and broken lines and, hence, the radius of the outer circle of the slider was made equal to the radius of the outermost circle of the scales. The indicated area on the carbon slider was colored yellow by masking the uncolored area and then spraying the exposed portion with transparent waterproof ink from an air brush. Similarly, the indicated portion of the hydrogen slider was colored blue. The width of the colored band was sufficient to cover the outermost series of numbers, No coloring was used on the nitrogen slider. Holes were punched with a cork borer in the exact center of the scales and sliders. The apparatus was assembled with a loose-fitting rivet with the sliders face up on the appropriate side of the scales; the carbon indicator placed under the hydrogen indicator. USE OF RULE
For Carbon and H drogen Determinations. Point the C arrow a t the theoreticayper cent carbon and the H arrow a t the theoretical per cent hydrogen (inner scale). The clear area between the yellow and the blue fields on the outer scale will then
by combining the multiplying and dividing steps described above. Reciprocals. The reciprocal of any number may be conveniently obtained by using the Dumas nitrogen scales and the solid line of the indicator. To perform the operation 1/-41, set the indicator to M on the inner scale and read the answer under the same hairline on the outer scale. Fix the decimal point by an approximate calculation. ACBNOWLEDGMENT
The authors wish to extend their appreciation to William L. Braun, Jr., and Alexander J. Tatun for assisting in the construction of the working models. Grinders for Mulling Infrared Microsamples. Jesse S. .4rd, Eastern Regional Research Laboratory, Philadelphia 18, Pa. VIBRATION
grinder of exceptional simplicity was developed ( 1 )
A for mulling a series of irreplaceable microsamples, and has proved satisfactory over several years of service. Mulling on a
micro basis with this apparatus has been so convenient that the method has replaced all others for crystalline substances in the author's work, even when an abundant sample is available. Microsamples may also be ground with a reversed drill. Mulls may be prepared with a mortar and pestle ( 5 ) , by mashing between the cell WindOWE (S),and by rotating cones (6); and methods developed for tissue mincing (IO)are readily adaptable
