of Whatman No. | paper was +3.9%; 
mean density was 8.785 mg/cm? 
The effect of a +10% variation 
on the self-absorption and on the 
corresponding corrections in the assay 
of some typical isotopes was calculated 
by means of Libby’s self-absorption 
equation (8). The results are shown 
in Table 1. Even in the case of the 
soft beta emitters, it is unlikely that 
this variation will seriously impair 
quantitative work. 
Resolution. When two or more 
labeled components are incompletely 
resolved, one must decide arbitrarily 
how to divide the area of the plotted 
radiochromatogram. Alternatively, 
an ingenious technique developed by 
Keston et al. (4) may be useful. In 
this method, one of the unresolved 
components is labeled by means of a 
second isotope of sufficiently different 
radiation characteristics to enable its 
boundary on the chromatogram to be 
determined by selective scanning. 
Corrections for recorder drum 
speed, rate of scanning, and back- 
ground. The radiochromatogram is 
plotted by the recorder as counting 
rate (ordinate) against distance along 
the strip (abscissa). In Eq. 1, the 
activity or rate of count a will be 
constant (neglecting statistical fluctua- 
tions and decay) for each exposed 
section; Za is therefore proportional 
to the area A enclosed by each radio- 
activity peak of the radiochromato- 
gram. Thus w= K’A, where K’ 
depends upon the over-all counting 
efficiency (observed rate of count per 
absolute disintegration rate) and upon 
the units in which A is measured. 
In practice, it is convenient to adjust 
the recorder drum speed (provision is 
made for this in the majority of re- 
corders) so that radiochromatograms 
plotted from R,=0 to Ry =1 at 
different scanning rates will be repre- 
sented by equal or comparable dis- 
tances along the recorder paper. The 
scanning rate will be varied (by altering 
the timer-controlled intervals between 
pulses fed to the scanner solenoid) 
according to the level of activity on the 
paper strip. For example, as discussed 
later, low activities require a lower 
scanning rate than will high activities 
for the same statistical accuracy. 
Corrections for differing recorder 
drum speeds and scanning rates in 
quantitative work are then made in 
the following manner: Suppose, in the 
calibration of the apparatus for quan- 
titative work, a known weight w of a 
labeled substance is scanned. Let s 
be the scanning rate, d the recorder 
drum speed, and r the rate of count 
corresponding to unit scale (ordinate) 
of the recorder. Let A be the area 
enclosed by the radioactivity peak 
corresponding to the labeled substance 
of the radiochromatogram. This area 
on the recorder paper may be measured 
in any convenient unit (to suit a par- 
ticular planimeter, for example). 
Area A must be corrected for decay 
in the usual way and for background, 
which is simply the observed counting 
rate over that part of the strip free of 
labeled material. Then K’ = w/A. 
A second strip containing an un- 
known weight w’ of the same labeled 
substance is now scanned at a rate s’ 
and recorder drum speed d’. Let A’ 
be the corresponding net area on the 
radiochromatogram, and r’ the rate of 
count equivalent to unit scale ‘of the 
recorder. It follows that 
F a ast. 
w = KA lee (2) 
In the apparatus described above, 
r’/r will be 10**, where n is 0, 1, 2, 3, 
etc., corresponding to the sensitivity 
ranges of the ratemeter. The fraction 
s’/s may be more conveniently replaced 
by t/t’, where ¢ is the timer interval or 
time of exposure of each section, and 
will therefore be a simple multiple of 
one second or of one minute. 
Precision in quantitative work. In 
radiometric assays, one rarely tries 
to determine a labeled substance by 
calculating the absolute disintegration 
rate from the observed counting rate. 
Assays are usually based on the rate of 
count observed with a known weight 
of the substance under standardized 
conditions. 
In the methods described here, 
assays are similarly based on radio- 
chromatograms obtained with known 
weights of labeled material. Under 
these circumstances, mean recoveries 
are complete, and precision or repro- 
ducibility becomes the important point. 
The principal factors affecting preci- 
sion, apart from manipulative errors 
such as micropipetting on to the paper 
strip, are self-absorption, statistical 
errors (9) inherent in all random 
particle counting, and geometry. 
The effects of self-absorption have 
been discussed. The statistical coeffi- 
cient of variation of a net count ob- 
tained as the difference between the 
total count Nr and the background 
count N»g over the same interval of 
time is 
It can be shown that the coefficient of 
variation of an assay by scanning is 
+100./d(Ar + Az)/(Ar — As) 
where Ar and Az are the total and 
background areas in em/cps and d is 
the recorder drum speed in cm/sec. 
The particular contribution of geo- 
metrical factors to variation, such as an 
asymmetrical distribution of active 
material over an exposed section, has 
not been investigated. 
Data are available, however, on the 
over-all variation due to all errors, 
including those due to manipulation, 
incomplete chromatographic — resolu- 
tion, etc., as a result of some resolution 
experiments with Br**-labeled deriva- 
tives. Single labeled substances or 
simple mixtures were resolved on 
reversed phase paper chromatograms 
(3) and scanned. In one case, the 
separated components were activated 
after chromatography. All recoveries 
were estimated in terms of a reference 
strip run with a known weight of pure 
substance and scanned. The results 
are shown in Table 2. They are not 
intended to demonstrate the sensitivity 
of the methods. In all cases, fairly 
active samples were used, and weights 
of the order of 1/100 or 1/1,000 of 
those given could have been assayed 
with comparable accuracy. 
* * * 
The authors are indebted to Mr. W. K. 
Cordaroy for constructing the escapement 
mechanism and scanning frame and to the 
E.R.D. Engineering Company for construct- 
ing the specially designed lead castle. 
This paper was first presented in London 
to the Physical Methods Group of the Society 
of Public Analysts in May, 1951, and 
acknowledgments are due to the editors of 
The Analyst for permission for its publica- 
tion in Nucteonics. The contribution is 
made by permission of the Department of 
Scientific and Industrial Research. 
BIBLIOGRAPHY 
1. A, A. Benson, J, A. Bassham, M. Calvin, T. C,. 
Goodale, V. A. Haas, W. Stepka, J. Amer. 
Chem. Soc. 72, 1710 (1950) 
2. F. P. W. Winteringham, P. M. Loveday, A. 
Harrison, Nature 167, 106 (1951) 
3. F. P. W. Winteringham, A. Harrison, R. G. 
Bridges, Nature 166, 999 (1950) 
4. A. S. Keston, S. Udenfriend, M. Levy, J. Amer. 
Chem. Soc. 69, 3151 (1947) 
65. R. M. Fink, C. E. Dent, K. Fink, Nature 169, 
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6. F. P. W. Winteringham, J. Chem. Soc. S416 
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