This paper is concerned with the queuing process which arises when one imposes nonzero crossover times on a nonpreemptive priority system with two classes of customers. The objective is to derive the Laplace-Stieltjes transform of the waiting-time distribution function and the queue-size generating function for each class of customers. The results are obtained by first analyzing a simple single queue model with walking time and then extending this model to fit the two queue problem by an appropriate choice of variables.

; deceased, May 1958. This review was completed by the junior author, who takes responsibility for the accuracy of the text and citations, and for any omissions.

1. Of 585 strains of lactose-fermenting aerobes each isolated from faeces of a different person, 501 did not utilise citrate or ferment cellobiose; 20 were citrate negative and cellobiose positive; 27 were cellobiose negative and citrate positive; and 37 were positive to both tests.2. Almost 10 per cent, of the strains isolated were indol negative.3. One culture was methyl-red negative and Voges-Proskauer positive. Two were positive to both tests. The rest were methyl-red positive and Voges-Proskauer negative.4. It is concluded that the results are not favourable to the use of the citrate or the cellobiose test in routine water analysis.5. A discussion of the taxonomy of the lactose-fermenting aerobes is given. Only two species,Bacterium coli(Escherich) L. and N., andBacterium aerogenes(Escherich) Chester, are recognised.

The Eijkman test (1904) is designed to detect fecal pollution of water. Water is inoculated into glucose-peptone broth which is incubated at 460, and gas production is assumed to indicate fecal pollution from warm blooded animals. Bacterium coli and Bacterium aerogenes strains of non-fecal origin or from feces of coldblooded animals are not supposed to grow, or at least not to produce gas under these conditions. Although much has been written in its favor and much against the test, it would seem that the fundamental question as to whether or not most of the colon bacilli from human feces are able to grow and produce gas at a temperature of 460 has not been satisfactorily answered. A review of both sides of the question will be found in the papers of Leiter (1929), of de Magalhaes (1932), and of the authors (1930). The latter, by using the dilution method, showed that in many samples of feces, at least half of the bacteria capable of producing gas from lactose at 37.5°refused to produce any at all from glucose at 460, and that in some samples of feces very few, even less than 1 per cent of the fecal B. coli, were able to produce gas under the conditions of the Eijkman technique. The Bulir test (1907) is a modification of the Eijkman test, and consists in using a mannitol-peptone beef infusion broth at 460.

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