Direct Counting Methods

Because physiological deterioration is generally accompanied by an increase in bacterial population, as pointed out by Nielsen, Wolford, and Campbell (33), estimation of bacterial numbers might serve as the basis of a test for condition. Obviously, the plate count method is not adaptable because of the time limitations imposed. Direct microscopic count would be much more appropriate, especially if a positive field count were substituted for cell count as suggested by Wolford (39). 

Laser diffraction is most suitable for analyzing dilute emulsions that are fluid, and therefore competes directly with electrical pulse counting methods, which are applicable to similar systems (see Alternate Protocol). Most laser diffraction instruments can cover a wider range of particle sizes (i.e., 0.01 to 1000 pm) than electrical pulse counting instruments (i.e., 0.4 to 1000 pm using a number of different aperture sizes), and do not require the presence of electrolyte in the aqueous phase, which could destabilize some electrostatically stabilized emulsions. Nevertheless, electrical pulse counting techniques are considered to have greater resolution. 

There are two methods of estimating the number of cells in a suspension. Using a haemocytometer the number of cells in a given volume is counted by direct microscopic examination. Using electronic counters, e.g. the Coulter counter, the cells in a given volume of suspension are drawn through an orifice and registered electronically. 

Another advantage of the differential photon counting method of detection is that the measurement uncertainties can be estimated directly from photon statistics. Schippers [11] has demonstrated that the standard deviation, a, of gium detected by the differential photon counting method can be related through Poisson statistics to the total number of photon counts, N, by the simple formula... 

The electron pulses (Raman signal) from the PM tube may be processed by the direct-current (dc) amplification or a photon-counting method. In the former, the electron pulses from the PM tube are averaged over time, and the resulting dc current is amplified directly and measured by a picoammeter or electrometer. However, this method is no longer used because the photoncounting method gives much better sensitivity. 

High energy / emitters, particularly 32P, can be counted directly in aqueous solutions without recourse to stintillation cocktails, since electrons with energies > 0.5 MeV excite water molecules to emit blue light which can be observed by the photomultiplier. This, so-called Cerenkov counting method, has an efficiency of about 40 %. 

U-series nuclide activities can be measured directly by detection of their emitted nuclear particles, e.g., alpha particle counting by solid-state detectors (Ivanovich and Harmon, 1992). In contrast, measurements by mass-spectrometry do not require waiting for Nature to take its course. Atoms of the sample are ionized and accelerated so that charged particles of the nuclides themselves can be measured by Faraday cups or electron multipliers (see Goldstein and Stirling, 2003). Mass-spectrometry is hence a more rapid technique. Typically mass-spectrometry measurements take tens of minutes to hours, while counting methods require days to weeks. 

Methods for calculating these quantities are discussed in detail in the book by Holbrook, Pilling and Robertson [29]. These methods fall into several basic categories - classical approximations, inversion of the partition function, direct count methods and Monte Carlo methods, each of which is introduced briefly. 

Comparison with direct count methods for systems of harmonic oscillators indicates that the classical density of states is generally an underestimate. However, it is so convenient to have an explicit formula for the density of states that more accurate semiclassical approximations have been developed. 

Gordon and Davison136 initiated the path counting method. In the path counting method the number of Kekule structures Kof a benzenoid B is equal to the number of the mutually self-avoiding directed peak-to-valley paths 138,139... 

Figure 21. Vibrational density of states (pv b) versus vibrational energy (Evib) in anthracene calculated using a direct count method and the frequencies of Refs. 64. Given in the Figure are characteristic times for IVR in the absent, restricted, and dissipative regimes.

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