1882.J 
Analyses of Books. 
559 
waters, we find that the author recommends determination of 
potassium, sodium, magnesium, calcium, chlorine, sulphuric and 
silicic acids, organic and volatile matter, total solids, hardness, 
and oxygen required for the oxidation of organic matter. We 
do not find any reference to the possible presence of phosphates, 
nitrates and nitrites, ammonia, and nitrogen in organic combina- 
tion — omissions to be regretted, since these substances, if found, 
are the chief indications of animal pollution, and serve as a 
pabulum for any germs of microbia which may be incidentally 
introduced. Nor are there any hints as to the possible occur- 
rence and determination, if needful, of certain heavy metals, 
such as lead and copper. 
In the analysis of milk Dr. Bolton recommends the deter- 
mination of water (adding washed and ignited quartz-sand for 
the desiccation-process), fatty matter, sugar, total solids, and 
proteine compounds, the last item being found as difference. 
Under Petroleum we note a circumstance with which we have 
been often struck in American technological and chemical 
treatises, — the preference given to Baume’s hydrometer. We 
are not aware that this instrument possesses any special or pecu- 
liar advantage, whilst it is open to the serious objection that its 
degrees cannot be converted into diredt specific gravity by a 
simple calculation. 
A Treatise on the Theory of Determinants, with Graduated Sets 
of Exercises for Use in Colleges and Schools. By Thomas 
Muir, M.A., F.R.S.E. London: Macmillan and Co. 
The objedt of the author of this work has been to furnish a full 
exposition of the theory of Determinants in a form suitable for 
students. The book is divided into four chapters, the first of 
which is merely of an introductory nature. The second chapter, 
devoted to determinants in general, furnishes their definition and 
all their important properties. The third chapter treats of special 
forms of determinants, such as continuants, alternants, sym- 
metric determinants, skew determinants and Pfaffians, compound 
determinants, &c. ; whilst the fourth chapter gives the history 
and bibliography of the subjedt from the Leibnitz downwards. 
An Appendix gives the results of the Exercises. 
