July 6, igi i] 



NATURE 



7 



values are the determinations most frequently useful 

 in forming a conclusion. 



The chemistry of the essential oils is no doubt 

 better and more widely known than that of the resins. 

 Nevertheless, in the interests of readers who are not 

 specialists in this branch of chemical work, a sum- 

 mary of the chief facts respecting the composition of 

 the essentials oils may not be unprofitable. These 

 oils, to which the characteristic odours of flowers and 

 plants are nearly always due, are composed of some 

 half-dozen groups of compounds, one or two of the 

 groups predominating in any particular oil. Tcrpcnes 

 constitute the bulk of many essential oils, but are 

 seldom the most useful portion. In fact, various so- 

 called " terpeneless " oils are now prepared, the re- 

 moval of terpenes serving in effect to concentrate the 

 odoriferous properties of the oil in the residual con- 

 stituents. Alcohols of various tvpes — open-chain, 

 aromatic, and sesquiterpene alcohols — with their cor- 

 responding aldehydes and ketones, are the important 

 compounds in many oils. Examples are the alcohol 

 gcraniol in otto of rose ; the aldehyde citral in lemon- 

 grass oil, and the ketone pulegone in oil of pennv- 

 royal. Bergamot, clove, and mustard oils respectively 

 owe their special properties to esters, phenols, and 

 sulphur compounds. Methods by which the propor- 

 tions of the various constituents may be determined, 

 usually with a fair approach to accuracy, are described 

 at length in the volume, which can be recommended 

 as well worthy of its place in the series. 



C. Simmoxds. 



MECHANICS, THEORETICAL AM' 

 TECHNICAL. 

 (i) Lelirbuch dcr technischen Physik. By Prof. Hans 

 Lorenz. Dritter Band, Technische Hydromechanik. 

 Pp. xxi + 500. (Munich and Berlin: R. Olden- 

 bourg, 19 10.) Price 14 marks. 



(2) Die Theorie der Krdftepldne. By Prof. H. E. Timer- 

 ding. Pp. iv+100. (Leipzig and Berlin: B. G. 

 Teubner, 1910.) Price 2.50 marks. 



(3) Vibrations of Systems having One Degree of Free- 

 dom. By Prof. B. Hopkinson. (Cambridge 

 Engineering Tracts, No. 1.) Pp. 54. (Cambridge : 

 University Press, 1910.) Price 2s. 6d. net. 



(4) Leerboek der Werktuigkunde. By F. J. Vaes. 

 Vol. i., pp. xii+152. Vol. ii., pp. xiv + 224. 

 (Schiedam : H. A. M. Roelants, 1910.) Price 1.40 

 gulden. 



THERE is probably no branch of science in which 

 such wide gaps occur between theorv and practice 

 as in the study of the motion of fluids. We have, on 

 one hand, the mathematical theory of hydrodynamics, 

 which is limited bv the difficulty of obtaining soluble 

 problems and building up integrals of the differential 

 equations of motion subject to given boundary condi- 

 tions. This difficulty alone restricts the scope of the 

 investigation mainly to the studv of perfect fluids, 

 thus immediately introducing a discrepancy, between 

 theory and observation. On the other hand, we have 

 the hvdraulics of the engineering student, the object of 

 which is mainlv to enable numerical calculations to 

 be made regarding such problems as town water 

 NO. 2175, VOL. 8/] 



supply, efficiency of turbines, pumps, propellers, and 

 ships. 



In endeavouring to produce a text-book on technical 

 hydromechanics (1) which should be satisfactory- both 

 from a theoretical and from a technical point of view, 

 Prof. Lorenz thus undertook a dutv of enormous 

 difficulty. It is not surprising that when he had half 

 finished the manuscript in 1906 he was so dissatisfied 

 with the result that he decided to start afresh, a task 

 which he did not commence until 1908, after re- 

 studying the subject and making a number of original 

 investigations. That such difficulties would exist was 

 shown not only by what he describes as the " step- 

 motherly " treatment of this subject in technical 

 colleges, but also by the absence of any comprehen- 

 sive treatise covering the required ground. Books on 

 hydraulics generally treated the subject entirely from 

 Bernouilli's principle, combined with the hypothesis 

 of parallel sections, nothing being said about Euler's 

 equations of motion in three dimensions, much less of 

 their modifications for viscous fluids. In one case 

 the treatment of hydraulics was preceded by an intro- 

 duction on hvdrodynamics, an order of treatment likely 

 to confuse rather than enlighten the "applied science" 

 student. On the other hand, we have purely theo- 

 retical treatises on hydrodynamics, where practical 

 applications are represented only by half a chapter on 

 the hypothesis of parallel sections, and this Cam- 

 bridge lecturers, at any rate formerly, told their 

 students to omit. 



The order of treatment adopted bv Prof. Lorenz is 

 probably the best that could be devised for the object 

 in view. Starting with analytical hydrostatics (in- 

 cluding the oscillations of floating bodies, and surface 

 tension) the author next deals with steady, and subse- 

 quently with variable, one dimensional motion treated 

 by the hypothesis of parallel sections. These chapters 

 constitute hydraulics proper, and contain applications 

 to flow over weirs and through sluices, pumps, 

 efficiency of turbines, and propellers, long waves in 

 canals, and tides. The extension of the investiga- 

 tion to three dimensional motion leads up quite natur- 

 allv to Euler's equations of motion of a perfect fluid, 

 problems in irrotational motion, both continuous and 

 discontinuous, vortex motion, and viscosity. In addi- 

 tion to such problems as are commonly treated in 

 hydrodynamics, we have discussions of the oscilla- 

 tions of ships, including a digression on the Schlick 

 gyroscope, approximate theories of the turbine, and 

 of the resistance of ships, and the equations of motion 

 of underground waters. The latter subject might with 

 advantage be brought more prominently than it has 

 been before mathematical students in this country. 

 It affords excellent examples of motion derived from 

 a potential, and the divergence between theory and 

 observation is probably less than in Eulerian irrota- 

 tional motion. Not the least important feature is a 

 concluding chapter on the history of hydrodynamics. 

 A few points in the book might be improved. The 

 proof of the permanence of irrotational motion on 

 p. 342 scarcely appears conclusive. The equation 

 shows that if the components of spin are ever zero 

 their rates of change will also be zero. This does not 



