INSTRUMENTATION BY RALPH H. MÜLLER
Desk Calculator Offers Computer Capabilities Qments produce data faster than they
UITE a few of our analytical instru-
can be assimilated and, for some time, suitable computer programs have been written to close t h e gap. I n many cases, t h e computer solution actually permits one to use the full capabilities of the analytical method. One excellent example is afforded by the paper of J. W . Criss a n d L. S. Birks on Calculation Methods for Fluorescent X - r a y Spectrometry: Empirical Coefficients vs. Fundamental Parameters, A N A L . C H E M , 40, 1080 (1968). I t is well
known that matrix effects complicate the procedure in this precise and important method. Two calculation p r o cedures are compared. One method uses primary spectral distributions rather than a theoretical expression, and accounts for matrix effects b y means of measured mass absorption coefficients μ. and fluorescent yields ω a n d a method of interaction is proposed to facilitate rapid computer analysis. T h e fundamental parameter method is more general than t h e empirical techniques but, a t present, is limited by uncertain ties in μ and ω. To quote the authors, "The purpose of all calculation methods is to reduce the need for comparison standards in quantitative analysis and thus to save time (ergo, money). Both of the methods satisfy t h e criterion but only a variety of industrial applica tions will determine which is better suited for a specific problem." While large computers are becoming more sophisticated, faster, a n d with greater storage capacities, a n interest ing development has been the improve ment of desk calculators t o achieve computer capabilities. Details of one of the more recent ones have been brought to our attention. The Hewlett-Packard Model 9100A electronic calculator, a general view of which is shown in Figure 1, is said t o be capable of outperforming some com puters. T h e 40-pound calculator is Circle No. 36 on Readers' Service Card
entirely self-contained. Single-key functions never before found in cal culators include hyperbolic and trigon ometric functions and coordinate trans formations. The pushbutton program ming needs n o special language. Conditional qualifier keys produce loop ing a n d branching programs. These make decisions while calculating, much as computers do. The keyboard of the 9100A is illus trated in Figure 2. T h e capabilities of the calculator are such t h a t one would have little or no need to look u p func tions in tables. I t can find sinh, cosh, tanh, arcsinh, arcosh and arctanh, each in less than 150 milliseconds. Hereto fore, no desk-top machines could solve problems involving hyperbolic func tions without requiring lengthy pro
gram sequences. Display is on a cathode-ray tube, chosen for its compactness, simple drive circuit requirements and low cost per displayed character. As shown in Fig ure 3, the cathode-ray tube permits the contents of three registers to be dis played simultaneously. Numbers en tered into the keyboard are displayed on the lowermost (x) line a n d keyboard positioning controls enable the number to be moved to the other lines ( Y a n d Z) after it has been entered. T h e use of three registers enables retention of a number for later reference, while op erations a r e being performed on t h e other two. The illustration also em phasizes the extreme range of the cal culator—i.e., from 1 0 - 9 8 to 1 0 " with 10 significant digits.
Figure 1. Hewlett-Packard Model 9100A electronic calcu lator
DEGREES
RADIANS
FLOATING
FIXED POINT
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Figure 2 . Keyboard of Model 9100A calculator VOL 40, NO. 8, JULY 1968 ·
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INSTRUMENTATION
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CHROMATOGRAPHIC ELUTION OR FILLING ZONAL ROTORS.
The ISCO Model 190 DIALAGRAD Programmed Gradient Pump will form almost any two component concentration, pH, or other gradient by simply setting a series of dials. A completely mixed, essentially non-pulsating flow at a uniform rate is produced with no cams to cut or multiple solutions to mix at estimated con centrations. The shape of the curve is determined by setting eleven 0 to 100% dials which rep resent the i n i t i a l , f i n a l , and nine evenly spaced intermediate ratios. This gives 10 program in tervals, each of which are auto matically subdivided into five linear interpolations to produce a smooth gradient. Calibrated flow rates from 0.5 to 500 milliliters per hour and program durations from 10 minutes to 12 days are set with positive stop switches. The DIALAGRAD will produce linear or curved gradients with equal ac curacy and the program will be perfectly reproducible run after run. The instrument takes but a few seconds to program and re quires no attention during a program run. For more information, ask for brochure DP31G.
INSTRUMENTATION SPECIALTIES CO., INC.
ISCO
5 6 2 4 SEWARD AVE. LINCOLN. NEBR. 6 8 5 0 7 See ACS Laboratory Guide for All Products/Sales Office Circle No. 50 on Readers' Service Card
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ANALYTICAL CHEMISTRY
Figure 3. Cathode-ray tube permits the display of three registers simultaneously Some features exhibit unusual con sideration for the operator. In addi tion to the usual operating manual and for the benefit of the occasional user, a plastic instruction sheet, which briefly describes the function of all keys and includes appropriate examples, is per manently attached to the calculator in a slide-out tray. Programs may be stored on and re-entered from creditcard size magnetic cards. These are erasable and reusable. Each card will carry two 196-step programs and cards may be put in successively to link pro grams. Any recorded program can be protected permanently against acci dental erasure simply by cutting off the corner of the card. A cut corner inhibits the machine from recording new information on the card. A special card carries a protected diagnostic pro gram for quick reassurance of proper calculator performance. When will we build things like this into our analytical instruments? Service will be by ex change replacement of sub-modules to minimize downtime. A loose-leaf program library note book is also included. I t contains more than 100 sample programs. It pro vides directly usable solutions to many common scientific and engineering problems and presents examples of pro gram techniques useful to solve many more. Pads of program sheets, sup plied with the calculator, simplify the preparation and debugging of programs. The program library, among other things, includes roots of a fifth degree polynomial, solution to three simultane ous equations, Bessel functions, Fourier analyses, solution of incomplete elliptic integrals of the first and second kinds,
Fresnel integrals, real and complex polynomial evaluation. Of the hundreds of tasks which can be performed we select but two which are of constant use to analytical chem ists, as the common one of treating data to fit a straight line: y — mx + b. The method of least squares is usu ally used, squaring the deviations, then minimizing this sum of squares. The method of least squares also yields the coefficient r in the regression analysis. For perfect correlation r = ± 1 . If r yields a value near zero, there is almost no linear correlation between the vari ables. When set up for this task after the entry of an arbitrary number of data points, the 9100A gives a display on the monitor in milliseconds. The correlation coefficient appears in the Ζ register, the intercept in the Y register and slope in the X register. The problem of getting the area un der a curve for which there is no mathematical equation can be solved accurately by numerical integration. With the speed of the 9100A, integra tion becomes a routine solution with answers available as fast as the data can be entered. The program can be based on Simpson's one-third rule, or can use the Euler-Maclaurin series. This calculator should be very valu able to the analyst. One might hope that more people will become interested in giving their data more thorough treatment. While the price of $4900 is modest, we cannot afford it or justify its purchase; were that not the case we might even stop grumbling about data copied directly from recorder charts and published as such, leaving it to others to unravel its implications.
