1887.] Mr A. W. Hare on the Purity of Water. 
313 
immediately above, and again immediately below a source of sewage 
contamination. The results obtained by this method in the case of 
a rapid river with gross sewage contamination will be detailed in 
the second part of this paper, where special attention will be drawn 
to the way in which this test is of value in associating special forms 
of microbes with special conditions of organic decomposition, thus 
acting as a qualitative test of some degree of definite value in deter- 
mining the purity of water. 
(e) Another biological method is an extension of the preceding. 
Having found by the preceding method what organisms are usual 
inhabitants of a river, the introduction of a foreign organism at a 
certain point, and its recovery from the stream at another by plate 
cultivations, may give valuable evidence as to the condition of the 
river-water between these points. The organism so employed must 
be perfectly distinctive in its mode of growth, and its relation to 
other organisms well known, as also its powers of survival and mul- 
tiplication in a variety of conditions. Given these data, much may 
be learned from its behaviour in various areas of the river examined. 
In the second part of the paper such an experiment will be described. 
In the present state of our knowledge of water testing, it would 
be unwise to discard the methods of chemical examination for any 
one, or a combination, of the above biological tests. But some of 
them, and particularly that of Koch, are capable of affording strong 
corroboration of the results obtained by chemical tests; and since 
it is its vital rather than its purely chemical contaminations that 
render water a source of danger to the health of the human subject, 
it may safely be predicted that, when extended and rendered yet 
more exact, these biological tests will become an essential element 
in the experimental determination of the purity of water. 
4. Alternants which are Constant Multiples of the 
Difference-Product of the Variables, By A. H. 
Anglin, Esq., M.A. 
