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Symmetry is used to define alternative categorizations to which real atomic and molecular systems may correspond. By constructing idealized models to correspond to limiting cases, it becomes possible to decide what are the best approximations and starting points for making mathematlcal representations of the real systems. Tiffs is illustrated with two examples: atoms with two valence electrons, and multidimensional potential surfaces of atomic clusters. In the first example, the question is whether an independent-particle, quantum analogue of a solar system or a collective, rotor-vibrator model is more appropriate, ht the second example, the problem is finding enough about the multidimensional potential to describe the dynamics of the atomic motion, without becoming overwhelmed with irrelevant data.

In a recent paper on deviations from Matthiessen's rule for platinum Klemens and Lowenthal (1961) classified the deviation patterns, calculated for a number of different platinum resistance thermometers, into three groups, and reported that only one of these groups followed the pattern predicted by Sondheimer and Wilson's (1947) two-band conduction theory. They suggested that if resistors belonging to one particular group (though no matter which group) were selected for use in low temperature platinum resistance thermometry then the resistance-temperature relationship could be expressed accurately by a relatively simple formula. We believe that Klemens and Lowenthal's method of classifying the resistors into groups is open to serious objection and that consequently some of their important conclusions are not necessarily valid.According to Sondheimer and Wilson (1947) the resistivity p(T) for two-band conduction can be expressed in the following mann-er :(1) where p(T) and p(O) are the resistivities at temperature T oK and 0 oK respectively and the subscript i refers to ideally pure metal. The last term on the right-hand side represents the deviation from Matthiessen's rule and should always be positive. According to Wilson (1953) the quantities a and b should be of the order of unity and may be temperature-dependent.To evaluate the parameter a (in fact they preferred to use the reciprocal) Klemens and Lowenthal used the relation given below which was derived from equation (1) for the case where p;>p (O) :~~t:~:;:(~) (l-cu;(T))(1 +1/a), (2) and where for any given resistor cu(T) and cu(O) are the ratios of the resistivity at T oK and 0 oK respectively to the resistivity at 273 oK; the subscript T4 refers to their reference resistor T4. Their calculated values of 1/0, for 17 platinum resistance thermometers were found to vary among the different thermometers from -0·4 to +8·6 and in addition were usually temperature dependent for any particular thermometer. They then classified the resistors into three groups with group 1 having l/a both small and constant with temperature; group 2 having l/a small and increasing with temperature; and group 3 having l/a large and increasing with temperature. In conclusion, they stated that the two-