T A B L E I. Correc t ions for the W i l s o n - W e l l s m e t h o d . •

vl -- vz Ramsay This work &VlI2

4.0 18.5 30.6 4.2 17.5 29.2 4.4 16.6 28.0 4.6 15.8 26.8 4.8 15.1 25.8 5.0 14.4 24.8 5.2 13.8 23.9 5.4 13.2 23.1 5.6 12.7 22.0 5.8 12.2 21.5 6.0 11.8 20.8 6.2 11.3 20.2 6.4 10.9 19.6 6.6 10.6 19.0 6.8 10.3 18.5 7.0 9.9 17.9 7.2 9.6 17.5 7.4 9.4 17.0 7.6 9.1 16.6 7.8 8.8 16.1

¥I -- F2 Ramsay This work ~Vl/2

8.0 8.6 15.8 8.2 8.4 15.4 8.4 8.1 15.0 8.6 7.9 14.7 8.8 7.8 14.3 9.O 7.6 14.0 9.2 7.4 13.7 9.4 7.2 13.4 9.6 7.0 13.2 9.8 6.9 12.9

10.0 6.8 12.6 10.5 6.4 12.0 11.0 6.1 11.5 11.5 5.8 11.0 12.0 5.6 10.6 12.5 5.3 10.1 13.0 5.1 9.8 13.5 4.9 9.4 14.0 4.7 9.1 15.0 4.4 8.5

a All the corrections are given in percent of the measured area.

These corrections, however, require a perfect knowl- edge of the baseline. Generally, this information is hard to obtain, especially for intensity determinations in solution. In this view, it seems more practical to suppose the baseline through the end points of the interval and to include corrections for the surface area between the real and the supposed baselines. This leads to the following expression for the total correction:

% corr

[ ( ~2l--I _H _ arctg vl _-- v2 + Vl - - /22 1 + vi -- v2 2 AVl/2 /~/"1/2 " ~Vl/2 /] J =

. .i- ,i- =11 + "Vi- p2 2/--1\'1 a r c ~ g A~1/2 -t- ~/Yl/2 ~ k AYl/2 ] J

× 100 (2)

Table I shows the corrections, computed by Ramsay, 2 together with those obtained by using Eq. (2), for several integration intervals, expressed in terms of Av~. I t can be noticed tha t the corrections calculated with Eq. (2) are much larger. They prevent errors in standard intensity measurements due to imperfect baseline knowledge.

A C K N O W L E D G M E N T

The authors are grateful to Dr. H. O. Desseyn for fruitful discussions.

1. E. B. Wilson, Jr. and A. J. Wells, J. Chem. Phys. 14, 578 (1946).

2. D. A. Ramsay, J. Am. Chem. Soc. 74, 72 (1952).

Four-Function Calculator Used to Compute Wavelength Automatically*

Michiyuki Nakamura and George V. Shalimoff

Lawrence Berkeley Laboratory, University of Cali- fornia, Berkeley, California 94720 (Received 13 March 1974)

INDEX HEADINGS : Wavelength calculator; Four-function calcu- lator; Comparator.

An inexpensive four-function calculator is being used to calculate on-line the wavelengths of spectral lines on photographic plates measured with an optical com- parator. Although all precise wavelength calculations are made by fitting data to a polynomial equation in a computer program, it is often desirable to know quickly the wavelength of some spectral line or whether there is a line a t some known region. An on-line wavelength calculation while the spectrum plate is still on the optical comparator and the spectral line or region is still in view greatly assists the operator.

The four-function calculator has many features such as fixed or floating decimal point, abil i ty to do arith- metic operations following mathemat ical formulas in milliseconds, left-hand entry, suppression of leading zeros, eight or more digit display, and ability to present negative numbers, all of which are useful in the design of an on-line wavelength calculator. In the system described here computat ions are made repetit ively from the digitized screw position of the optical com- parator in 0.8 sec. The display duration is variable from 0.3 to 3 sec for the operator 's convenience.

There is a small variat ion with wavelength of the reciprocal linear dispersion (plate factor in angstroms per millimeter) of diffraction grating spectrographs. This relation is used by all spectroscopists to hand calculate wavelengths and is the basis of the calcula- tion with this device.

When measuring wavelengths of a spectrum plate positioned on the comparator which increase with distance from left to right, which we call the normal mode, the wavelength (X) is given by the equation:

= (d - dl) P F + Xl (1)

where

P F = plate factor - ~2 - h i

d2 - d l (2)

Xl = wavelength of first known spectral line; •2 = wavelength of second known spectral line; dl = digitized screw position of first known spectral line; d2 = digitized screw position of second known spectral line; and d = digitized screw position of unknown spectral line.

* Work performed under the auspices of the United States Atomic Energy Commission.

V o l u m e 28, N u m b e r 6, 1974 A P P L I E D S P E C T R O S C O P Y 5 8 1

Occasionally we must measure plates where the wavelengths decrease with the distance from left to right. We call this the reverse mode, and when this oc- curs we use the following equation:

- ~ = (d - dl) l°F - hi (3) where the answer in the calculator is given as a nega- tive number. This takes advantage of one of the fea- tures built into the calculator and simplifies the design of a controller to effect the calculation. The negative sign of the result is ignored by the user.

The optical comparator in use at this laboratory has a precisely machined screw which can position a spec- t rum line of a photographic plate to a precision of 1 #m (10 -6 m). The screw position is digitized via an optical encoder which can be readily mounted on most com- parators.

A controller has been built to enter into the calcu- lator the arithmetic functions, the fixed digital infor- mation, and the variable digitized screw position at the proper time and sequence. Thumbwheel switches on the controller are used to enter the constants dl , PF, and ~1. The modifications to the calculator itself do not impair the normal operation of the calculator. More detailed information about the controller cir- cuitry and the calculator modifications are available in Report LBL-2331 from this laboratory.

To measure wavelengths of a spectrum, reference lines of known wavelength are first marked on the plate, which is then carefully aligned on the comparator. The reciprocal linear dispersion or plate factor is deter- mined with a pair of known lines and their positions on the comparator in the region of interest. The calculator can be used in its ordinary mode of operation for this calculation. The reference wavelength position and plate factor are entered into the controller with the thumbwheels. A normal or reverse plate switch on the controller is positioned depending on whether the wave- lengths on the plate being measured increase or de- crease with distance. The decimal point is located on the calculator, generally three places after the decimal. A s tar t /s top switch on the controller is thrown to start, and immediately the wavelength which cor- responds to the comparator screw position auto- matically appears on the display. The result will be repetitively displayed at a rate variable from 0.3 to 3 sec until a new screw position is chosen. Measurements can now be made in the region for which the plate factor is applicable.

Although the reciprocal linear dispersion of spectra taken on diffraction grating spectrographs is fairly constant, there can be a gradual change from one end of a plate to the other. For example, a 10-in. spectrum in the first order taken on a 3-m spectrograph with a grating haying 1200 grooves/mm shows a plate factor of 2.769 A/ram at one end and 2.757 A/ram at the other end. If an average plate factor for the entire 10- in. plate is used, the calculated wavelengths will diverge away from the correct values by as much as 0.43 A at the positions farthest from the reference positions. Even this kind of accuracy can be useful in initial surveys of plates.

However, of greater interest is this quick calculation of wavelengths within the given areas where the plate factor is more accurate for tha t region. On the same plate described above, over a 30-ram range, the calcu- lated wavelengths are never more than 0.03 ~ from their true values, and lines nearest the reference posi- tions were calculated to bet ter than 0.01 A. From this instant calculation of wavelengths or from the differ- ence of two wavelength calculations, immediate identi- fication of many spectral lines is possible.

The instant wavelength calculation is especially useful when one must bootstrap the reference lines in spectra taken in regions where it is not easy to photo- graph common reference spectra, such as in the vacuum ultraviolet regions. Another common application is to identify lines of impurities which are mixed with lines of known elements. A third application is to locate a line of a given wavelength. To do this, one simply watches the calculator display for the wavelength as the plate is moved. The controller is set for the shortest display duration so that one can quickly arrive at the wavelength region of interest. Examination of the plate image at tha t point will indicate if the line of interest is present.

ACKNOWLEDGMENTS We wish to thank John G. Conway and Ralph Mc-

Laughlin for their interest and suggestions and espe- cially John A. Mendes for his technical assistance in the design and development of the unit.

A S i m p l e T e c h n i q u e for C o a t i n g C a r b o n A t o m i c A b s o r p t i o n A t o m i z e r C o m p o - n e n t s w i t h P y r o l y t i c C a r b o n

D. D. Siemer, Ray Woodriff, and Bruce Watne

Chemistry Department, Montana State University, Bozeman, Montana 59715

(Received 5 February 1974; revision received 6 May 1974)

INDEX HEADINGS: Pyrolytic carbon; Nonflame atomizers; Techniques, atomic absorption.

Recent l i terature is replete with evidence tha t carbon nonflame atomizers used for atomic absorption or atomic fluorescence analysis are improved by the use of pyrolytically coated graphite or vitreous carbon in lieu of the more common (and cheaper) forms of carbon. The reasons lie in the permeability of the usual spectroscopic graphites to gases and solutions. This permeability allows actual loss of sample atoms through

• the walls of the atomization chamber and shortens the

582 Volume 28, Number 6, 1974 APPLIED SPECTROSCOPY