338 



A' A rURE 



[August i, 1901 



MgSOj^HoO and MgCl;.6H„0 respectively ; the point E, 

 which corresponds to the point c in Fig. i, represents a sohuion 

 saturated simultaneously with regard to IMgClo.6H20 and the 

 hydrate 4MgS04. 5IUO. The broken curve joining A and E 

 has reference to solutions which are saturated with one or other 

 of the hydrates of magnesium sulphate, but not with magnesium 

 chloride. 



If a solution containing equivalent quantities of these two 

 salts and represented by the point a is evaporated at 25" C, 

 then, as in the cases already considered, separation of salt, viz. 

 MgS0j.7H,,0, will lake place when the index point moving 

 along o a reaches the curve c A, 



As the concentration of the magnesium chloride in the solution 

 increases, we move along the curve A c until at the point c this 

 concentration has attained such a magnitude that the transition 

 temperature MgSOj.7H„0->MgSOj.6H.,0 has been lowered 

 from 47' C. to 25° C. the separated MgS04.7H„0 in contact 

 with the solution is now transformed into MgSOj 6H,0, and by 

 further evaporation the index point moves along the curve c D, 

 a further quantity of MgSOj.SH.iO crystallising out. At D the 

 system undergoes a similar change to that which took place at 

 c; MgSOj.sH.p crystallises out and the MgSOj.eHoO now 

 disappears. Further changes of like character (not indicated in 

 the diagram) are experienced as the magnesium chloride con- 

 centration increases, whereby MgSOj.4HoO and MgS04. 2H.,0 

 appear successively. At the point E the hydrate 4MgS04. 5 HoO 

 displaces the dihydrate and the solution then becomes saturated 

 also with regard to MgC1.2.6H.,0. These two salts now 

 crystallise out together until the solution completely disappears ; 

 the point E represents the crystallisation end point of all solu- 

 tions containing the sulphate and chloride of magnesium. As 

 before, the arrows indicate the course of the crystallisation for 

 any given solution. 



The above crystallisation phenomena may be regarded as 

 typical for solutions containing two salts with a common ion. 



The phenomena are much more complex if the solution con- 

 tains four different ions, as in a solution of the chlorides and 

 sulphates of magnesium and potassium. The four simple salts 

 and their various hydrates, as well as several double salts, may in 

 general crystallise out from such a solution. The course of 

 crystallisation of the solution referred to has been carefully 

 worked out by van 't Hoff, Meyerhoffer and their pupils. The 

 phase rule serves as a safe and sure guiding principle ; solubility 

 determinations and measurements of the vapour pressures of 

 solutions supply the data which, when graphically represented 

 in a .suitable manner, enable us to follow the various phases of the 

 crystallisation process with almost the same ease as in the simpler 

 cases. The diagram representing the various saturated solutions 

 formed by the system composed of water and the sulphates and 

 chlorides of magnesium and potassium .has been tested by a 

 qualitative and quantitative study of the products of isothermal 

 evaporation, and the course of crystallisation is found to agree 

 perfectly with that indicated by the motion of the index point 

 on the diagram. In this short article it is not possible to treat 

 of this more complicated case in detail ; suffice it to say 

 that all solutions containing the above-mentioned salts deposit 

 in the last stage of crystallisation a mixture of carnallite, 

 MgCU.6H„0 and 4MgS04.5H.,0. 



The above sketch gives some idea of the preliminary work in 

 connection with the problem of explaining, on a physico-chemical 

 basis, the formation of the oceanic salt deposits. It indicates the 

 initial stages of the synthetic method pursued by van 't Hoff in 

 his treatment of this highly interesting problem. 



H. M. Dawson. 



BOOMERANGS} 



"DOOMERANGS may be studied for their anthropological 

 ■""^ interest as examples of primitive art,-' or for the manner in 

 which they illustrate dynamical principles.^ But there is ex- 

 traordinary fascination in making and throwing them, and in 

 watching the remarkable and always graceful curves described 



^ This paper is Iieie publislied by permission of the editors of the 

 Physikalischr- Zeitschrift, for which it was -originally written. A German 

 translation has appeared in that journal, and from its publishers the 

 accompanying illustrations have been obtained. 



■■! " The Native Tribes of Central Australia," by B. Spencer and F.J. 

 Gillen (1S99), Ch. ,tix. 



3 E. O. Erdmann, Ann. d. Phvs. n. Clteniic, vol. cxxxvii. p. i (iE6q) ; 

 E. Gerlach, Zcitschr. il. D. Vo'eins z. Fdi-d. d. Luftschifffahrt, Heft 3 

 (1886) ; G. T. Walker, London Phil. Tyitns., vol. c.\c. p. 23 (1897). 



in their flight ; accordingly, my chief object in the following 

 paper has been to diminish the practical difficulties of the subject 

 by giving some of the results of ten years' experimental acquaint- 

 ance with it. 



The Australian weapons vary enormously in shape and size, 

 while the skill of the natives in throwing them is great in some 

 districts and very small in others. The marvellous flights that 

 were described by former travellers are but rarely seen to-day, 

 and although it is undeniable that many a native can make a 

 boomeiang go So metres away before returning to his feet, I 

 know of only one trustworthy account of a much more sensa- 

 tional throw.' In this the boomerang described five circles in 

 the air, travelling to a distance of about 90 metres from the 

 thrower and rising to a height of 45 metres. 



For present purposes it will be convenient to consider two 

 types of implements. The first (Fig. I) is about So cm. in 

 length, measured along the curve, is bent (at B) almost to a right 

 angle, and has the cross section shown in Fig. 2. It is about 



65 cm. wide and I cm. thick in the centre at B, and the 

 dimensions of the cross section diminish slightly towards the 

 ends A and c ; the weight is about 230 grams. The arms are 

 twisted froiu the plane .IBC after the njanner of the sails of a 

 windmill, being rotated through 2° or 3" in the direction of a 

 right-handed screw about the lines n.\, BC as axes. This devia- 

 tion from the plane is subsequently referred to as the '* twist," 

 and the peculiarity that, as seen in the cross section of Fig. 2, 

 one face is more rounded than the other, is called the 

 "rounding." 



Boomerangs of the second type (Fig. 3) are about 70 cm. long 

 and 7 cm. wide, and have a cross section similar to that of 

 Fig. 2. The " twist" is in the opposite direction, involving a 

 left-handed rotation of about 3° ; the axes of rotation are now 

 DE, FE instead of ED, EF. 



Reltiriiing Flights. — An implement of the first type is held 

 with the more rounded side to the left and the concave edge 



forwards. It is thrown, with plane vertical, in a horizontal 

 direction and as much rotation as possible is given to it. The 

 plane of rotation does not remain parallel to its original direc- 

 tion, but has an angular velocity (i) about the direction of trans- 

 lation, and (2) about a line in its plane perpendicular to this. 



The effect of (2) is that the path curls to the left ; while 

 owing to (i) the plane of rotation inclines over to the tight (i.e. 

 rotates in the direction of the hands of a clock facing the 

 thrower) and its inclination to the vertical becomes comparable 

 with 30' in two seconds. The angular velocity (2) will now 

 imply that the path bends upwards as well as horizontally round 

 to the left. 



When the boomerang has described a nearly complete circle 

 its pace has diminished, and it falls to the ground near the 

 thrower. (See Figs. 4, 5, in which projections on a horizontal 

 and on a vertical plane are given; the direction of the axis of 

 rotation is indicated by giving the projections of a line of 



■ Ml. A. W. Houitt, NATt;RE, July 20, 1876. 



NO. 1657, VOL. 64] 



