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