217
TABLE 79.
10 kore oF more
values, so the calculation need be carried out only once.
From the expression
A(M2/C)
AC/C
Puin
1 torr
experiments.) One can arrange to work with relative
Limits or Error Systematic
Max
Min
Max
Min
0.04
—0.06
0.016
—0.020
0-02
— 0-04
0.011
—9.015
aC _ 1 3 ac |
He SLY
CONF OYs
make the calculations tractable by basing them upon
p are given double weight because they represent the
Bypartial differentiation of Eq. (2), dy can be computed for any combination of dp/p, de/e, and dP/P for
find out how the LS solution relates, through the dy’s,
the values of dC/C and d(M’/C) to any small varia-
y’s by certain coefficients that come out of the least
where A,;; and B;; are independent of the y;;. Thus
squares solution. The uncertainty due to random errors
should then be added to that due to systematic errors.
Such a procedure in our case, however, is not completely
Ay; and B;; can be evaluated by comparing two LS
solutions that are exactly the same except for a variation in yij-. (A set of nine such solutions required 18
valid, inasmuch as some of the errors we have treated as
seconds of computing time.) The numerical work was
carried out for Mj/Co = 0.105, a median value, and
with QLCoPmin 80 chosen as to yield a typical range of
the y:;. (The range tends to be much the samefor all
He
systematic can also contribute to the RMS deviation of
the data points.
Our standard practice has been to accumulate counts
until y has been determined with a statistical accuracy
cyCaH,
nGallio
nC
iCatlio
ee CoH
ais CoH30H+(CHs)z °
CeHe
+
CHAQH
nCgg
NH3+
nCsHio
ne Hig
+
neoCeHio cyCgHig
nC7Hig
: +
7
Hieco
CHa
H20 +
c/n 3
~
"|
co
+
Haeof PHs
2
+
:
C02
Fou
Ar
erst
Ne
cre
Xe
2
:
|
Ket
}
7
l
io
L
18
,
ment such as noise, statistical errors in counting, and
chance errors in reading instruments. According to the
theory of the method of least squares, the uncertainty
in our values for M? and C’ should be given by multiplying the root mean square deviation of the individual
M = >Biya 5
+
oP; P;
(3)
The term random errors is generally applied to errors
as linear functions of the y;;:
CHa
y |
“Jy.
that arse from truly capricious aspects of an experi-
related with P, it also carries the index /.
The least squares method (LS) expresses M’ and C
Ho
Op: pi
0y;; dP;
RANDOM ERRORS
tion of p, «, and P. Because of the correlations of the
errors, it is convenient to label the y’s with indices 2, 7
to represent momentum 7, pressure 7. Because e is cor-
4 t++ He le (Ho)
(H
;
A(M’/C) can be evaluated. The results of the calculation are given in Table 79.
the individual points. As shown below, one can then
ana
we
2
_1
2
4dC
d(M*/C) = (aw
M ic’
middle half of the field.
CoH
Oy. dpi
one can compute the error AC/C that results from any
combination of the errors Api/p1, Ap2/po. +--+ @&, €3 5 the
limit of error is found by choosing the combination of
signs that maximizes the magnitude of AC/C. A relation
analogous to (3) for dM’ can be written, and from
the eight points indicated bycircles. Each point represents an area; the points at the intermediate value of
C= DAaya
|
|
26
1
36
42
n= TOTAL NUMBER OF ELECTRONS
Fic. 168.—Experimental results for C
bo
54
58