5o8 



NA TURE 



[March 30, 1905 



triangles. The definitions arc then extended to angles 

 of any magnitude, and formulae are established for 

 the sum and difference of angles, and for multiple 

 and submultiple angles, &c. There is a chapter on 

 logarithms, and a number of four-figure tables are 

 given. This work leads up to the properties and solu- 

 tion of triangles with applications. Inverse functions 

 are introduced, and general expressions established for 

 angles having given trigonometrical ratios. There are 

 a large number of examples, any necessary answers 

 to which are given at the end of the book. 



(5) Part ii. of Messrs. Baker and Bourne's excellent 

 algebra begins by formally establishing the laws of 

 operation of algebraical symbols. It contains chapters 

 on surds and indices, proportion, logarithms, pro- 

 gressions, series, scales of notation, permutations and 

 combinations, the binomial theorem, interest and 

 annuities, exponential and logarithmic series and 

 partial fractions. Tliere are numerous groups of 

 examples, and special sets of revision papers at 

 intervals, the answers being all given in an appendix. 

 .\ special feature of the book is the frequent use of 

 graphs and of geometrical illustrations. This text-book 

 must give satisfaction wherever used. 



(6) Clive's shilling arithmetic is intended for the use 

 of teachers who adopt almost entirely the oral method 

 of instruction, and who only require a class-book con- 

 taining concise statements of rules, with graduated 

 sets of exercises, and with the formal proofs of theorems 

 omitted. Thus a small volume is sufficient to cover 

 the range of subjects usually taught in schools, and 

 which this manual contains. The book can be ob- 

 tained with answers included at an extra cost of 

 threepence. 



(7) In the graphical statics of Messrs. .Alexander 

 and Thompson the authors first give a set of sixteen 

 graduated problems on coplanar forces, solved by 

 means of force and link polygons; these include 

 couples, centres of area and moments of inertia of 

 beam sections. Then follows a set of seventeen ex- 

 amples showing applications to roof trusses, girders, 

 walls, and masonry arches. The treatment is some- 

 what fragmentary and arbitrary, but, if supplemented 

 by the teacher, the course would prepare a student 

 for a systematic study of graphic statics, and the 

 book is intended more particularly as an introduction 

 to the author's "Elementary Applied Mechanics." 



SALT-BEDS AND OCEANS. 

 Ziir Btldiing der ozeanischen Salzahlagerungen. By 

 J. H. van 't Hoff. Pp. vi + 8s. (Brunswick': 

 Vieweg and Son.) Price 4 marks. 



T^HIS work will be welcomed alike by chemists, 

 -*- geologists, and oceanographers. It forms the 

 first instalment of the collection into one publication 

 of the results of some forty memoirs of the author 

 and his collaborators on the formation of double salts. 



The principal object of the work was the study of 



he problem of the natural salt beds. .As tliese beds 



ive in all probability been formed by the evaporation 



of a body of water comparable with the existing oceans, 



which certainly contain some of everything, it was 



NO. 1848, VOL. 71] 



necessary to set limits to the investigation. This 

 was effected by confining attention to the principal 

 constituents of the salt-beds. These are chloride 

 of sodium, in great preponderance, and the chlorides 

 and sulphates of magnesium and potassium with 

 their, water of crystallisation. The latter form a 

 series of more complex bodies which appear and dis- 

 appear with the changing equilibrium of the solution. 

 .After these come the calcium salts, such as anhydrite 

 and polyhalite ; but they are held over for treatment in 

 the next fascicule. 



The work is a gigantic exercise in physical chemistry, 

 which the author carries through on strictly scientific 

 lines, while at the same time touch is kept with the 

 important applications of his results in the economy 

 of nature, and chemistry is thus vindicated as a branch 

 of natural history. 



The experimental part of the work is of especial 

 interest to physical chemists, and the publication of 

 it in a connected and condensed form will be welcomed 

 by them. It is proposed here to notice only the ap- 

 plication of it to the occurrence of salts in nature in 

 beds and in solution. 



The experimental basis of the work is the deter- 

 mination of the solubility, at certain temperatures, of 

 the common salts of the sea, in water and in solutions 

 of each other. With the information so obtained, it 

 is possible to follow exactly the crystallisation of a 

 solution containing all these salts, as it gradually 

 loses water by evaporation at the temperature of the 

 experiment. The temperature most used is 25° C, 

 which is fairly representative of the temperature of 

 sea water evaporating in salt gardens, such as those 

 of Hyeres or Cadiz in summer. 



\\'hen average sea-water has been evaporated down 

 to the point at which chloride of sodium begins to 

 crystallise, the liquor contains (in molecular propor- 

 tions) 100 NaCl, 22 KCl, 78 MgCU, 38 MgSO,; 

 and this mixture of salts is associated with, roughly, 

 1000 mol. H^O (exactly 1064). On allowing this 

 liquor to evaporate at 25° C, the crystallisation follows 

 a definite route, which can be traced exactly, and 

 without difficulty, on one of those marvellous charts 

 representing the march of physical and chemical 

 phenomena with which the resourceful inventiveness 

 of van 't Hoff has familiarised us. 



The crystallisation takes place in four acts corre- 

 sponding to the regions in the chart. 



(i) Rock-salt : separation of chloride of sodium in 

 great abundance. Of the 100 NaCl present when 

 crystallisation began, only 4(1 NaCl remains dissolved; 

 the remainder, 05 NaCl, has been deposited. 



(2) Kieserite region : separation of chloride of 

 sodium, sulphate of magnesium, and kainite 



(MgS0,KCl3H„0). 

 The salt separated in this act consists of 442 NaCl, 



2 02 KCl, and 307 MgSO, ; or, 4 42 NaCl, 105 MgSO,, 

 and 2. 02 kainite. 



(3) Carnallite region : scp.iration of chloride of 

 sodium, carnallite (KMgCl ,,()H,0), and kieserite 

 (MgSOi.HjO), and the amounts separated are 



003 NaCl, O.I carnallite, and 035 kieserite. 



(4) Final liquor: what remains solidifies to 015 



