Least count

When we look at the residuals carefully, we are likely to find unexpected appearances. This seems to be true in our example here. Table 6 gives us a rather hard look at two sets of residuals, both of which seem to show some tendency toward relatively regular clumping. Inquiry of Dr. Lide as to whether there was a least count of 0.04 cm"1 to 0.05 cm"1 (40 or 50 in the units of Table 5) in the wave numbers either in measurement or calculation brought a response that this was not to be ruled out. While the discovery of such an effect at the time when the data were being analyzed might have been quite helpful, neither the suggestion nor a possible proof of its existence today can be of importance. 

To present a list of apparatus and instrumentation to be used, including the instrument ranges, least count, and identification numbers. 

The most successful technique for the stable species has been microprobe sampling followed by mass spectral analysis (alternatively by gas chromatography or other microanalytical techniques). The most successful microprobes have been pencil-like quartz tubes drawn down to orifices a thousandth of an inch in diameter or less. Because of the strong pressure drop (samples are pumped off at 10 atm), the probes act as miniature supersonic nozzles and the gas residence time in the probe is very short. The reactions are quenched by the rapid pressure drop (10- second and temperature drop (lO °K/second) due to adiabatic expansion in the nozzle. Reactions with half-lives as short as a few microseconds will be quenched. It is not necessary to cool the probes because of the short residence times. The effect which such a probe has on a flame is minor because of the small size of sample withdrawn (1-2 jag/sec). The aerodsmamic disturbance is minimized because the probe sucks off its own bow wave. The thermal disturbance is small because the probe wall temperature is only slightly below that of the flame. With such probes, it has been possible in favorable cases to make reproducible and reliable composition measurements with a precision of 2% and a least count of 10 mole fraction with a spatial reproducibility of 10 inches and resoution of 2 X 10 inches (see Figs. 3 and 5a). The scope and limitations of such composition measurements are discussed in Chapter IX of Fristom and Westenberg (1965). 

A reading is the single determination of a value at one point on a measuring scale. Generally, a reading can be estimated to one-half of the smallest I I I I I I I I division (least count) on a measuring scale. In the I case of the ruler in Figure 11.6, half of the smallest... 

Tbe least count is the smallest division that is marked on the scale of the apparatus. For example, a 50 cm burette will have a least count of 0.1 cm, and an electronic chemical balance giving up to three decimal places of a gram (e.g. 1 g reads as 1.000 g) will have a least count of 0.001 g, that is, 1 mg. For a digital reading, such as on an electronic balance, the random uncertainty is the least count. Hence, the random uncertainties in this burette and this balance may be reported as 0.05 cm and 0.001 g. 

Analogue scale Rulers, voltmeters, colorimeters, volumetric glassware (half the smallest scale division (least count)) ... 

With modern detectors and electronics most Enei -Dispersive X-Ray Spectroscopy (EDS) systems can detect X rays from all the elements in the periodic table above beryllium, Z= 4, if present in sufficient quantity. The minimum detection limit (MDL) for elements with atomic numbers greater than Z = 11 is as low as 0.02% wt., if the peaks are isolated and the spectrum has a total of at least 2.5 X 10 counts. In practice, however, with EDS on an electron microscope, the MDL is about 0.1% wt. because of a high background count and broad peaks. Under conditions in which the peaks are severely overlapped, the MDL may be only 1—2% wt. For elements with Z < 10, the MDL is usually around 1—2% wt. under the best conditions, especially in electron-beam instruments. 

An improvement of this method—the so-called biased sampling [55] (or inversely restrieted sampling)—suggests to look ahead at least one step in order to overcome the attrition. Consider a SAW of i steps on a -coordination number lattice. To add the / + 1st step one first checks which of the = q — neighboring sites are empty. If k qQ > k>0) sites are empty one takes one of these with equal probability 1 /A if A = 0 the walk is terminated and one starts from the beginning. This reduces the attrition dramatically. Now each A-step walk has a probability PAr( i ) = Ylf=i so that dense configurations are clearly more probable. To compensate for this bias, each chain does not count as 1 in the sample but with a weight... 

In addition to the 4 stable isotopes sulfur has at least 9 radioactive isotopes, the one with the longest half-life being which decays by activity (Kmax 0.167 MeV, 87.5 d). can be prepared by Cl(n,p), S(n,> ) or S(d,p) and is commercially available as SeicmcQt H2S, SOCb and KSCN. The radiation has a similar energy to that of C ( mav 0.155 MeV) and similar counting techniques can be used (p. 276). The maximum range is 300 min in air and 0.28 mm in water, and effective shielding is provided by a perspex screen 3-10 mm thick. The preparation of many - S-containii compounds has been... 

The general problem simplifies considerably in the finite field. F[2. Because circuits are always counted at least twice, their number contributes a factor = 0 (mod 2) we see from equation (5.14), therefore, that the only structural information necessary to obtain Pi x) is that of the parity of disjoint edge distributions. Moreover, since there is no way to distribute disjoint edges among an odd number of vertices, equation (5.13) gives... 

The assignment of oxidation states has more a formal character in the sense of electron counting rules [145]. In this context it should, however, be justified to use at least the term low valent silicon. 

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