June, 1904.] 



KNOWLEDGE c^- SCIENTIFIC NEWS. 



1 1 1 



(i.f., rouii.. ;; .1^.;^, ... rew-axes, &c.) necessitates or pre- 

 vents the existence of other elements. For example, if a 

 medium is brought to self-coincidence by a gliding- 

 reflexion in a plane, it must be also brought to self- 

 coincidence by a translation parallel to that plane. It is 

 assumed that every crystalline medium is brought to 

 self-coincidence by three very small but linite translations 

 not lying in the same plane — a fundamental hypotiicsis 

 which is justified by remembering that the physical 

 properties of a homogeneous crystalhne medium in a _i;inn 

 direction are the same in every part of the medium. It 

 follows from this assumption that the angle a. of move- 

 ments (2), (3), (7) must be a multiple of 60 ' or of 90". It 

 may be shown that the number of distinct arrangements 

 of symmetry-elements is 230 — a geometrical problem 

 solved independently by Fedorow, Schoenllies, and 

 Barlow. One such arrangement is shown in figure 2. 

 The system of molecules there given is supposed extended 

 indefinitely in the plane of the diagram, and over and 

 under it at distances 2/,, 4Z, 6z, . . . are placed 

 similar and similarly situated systems so as to fill all 

 space. It is evident that tlie collection of molecules so 

 formed has the lines perpendicular to the plane of the 

 paper, and passing through the points marked o and 9 

 as rotation-axes (a = 120"), has the planes parallel t<j 

 these axes, and passing through any two adjacent points 

 marked O for symmetry-planes, and has the planes half- 

 way between these symmetry-planes as gliding-planes. 

 Such a collection of molecules is one of the six different 

 geometrically possible ways of representing the structure 

 of a medium (such as tourmaline, potassium bromate, 

 &c.), which crystallizes in polyhcdra having a rotation- 

 axis for which a = 120' and three symmetry- planes 

 through that axis making angles of Go" with each other 

 (and having no other symmetryelenient). 



Again, suppose that half-way between two neighbour- 

 ing systems of molecules in the collection just described, 

 we insert the system obtained by rotating figure 2 through 

 180^ about one of the points marked O. The collection 

 has the lines perpendicular to the plane of the diagram, 

 and passing through the points marked • as rotation 

 axes for which a = 120°, the lines perpendicular to the 

 planes of the diagram, and passing through the points 

 marked O as screw-axes for which a = Go" and t = z, 

 and the lines half-way between any two adjacent rotation- 

 axes as screw-axes, for which a = 180' and t = z. The 

 collection has the same symmetry-planes and gliding- 

 planes as in the previous case, and has also gliding-planes 

 through the screw-axes perpendicular to the symmetry- 

 planes. The collection is one of the four different 

 geometrically possible ways of representing the structure 

 of a medium (such as zincite, wurtzite, iodyrite, &c.), 

 which crystallizes in polyhedra having a rotation-axis 

 for which a = to' and six symmetry-planes through that 

 axis making angles of 30'^ with each other. 



It must be remembered that it has not been proved 

 that a collection of molecules, such as has been described, 

 is one which can exist in stable equilibrium under the 

 influence of the mutual attractions of the molecules. On 

 the dynamical theory of crystal structure hardly any work 

 has yet been done, but the geometrical theory is now 

 fairly complete. 



Gkksham College Lectukes. — A course of lectures on 

 "Recent Solar Researches" was delivered at Grosham Col- 

 lege during Whitsun week by Mr. E. Walter Maunder, 

 F.R.A.S. The subjects of the lectures, delivered on succes- 

 sive evenings, were " Changes and Movements of Siinspots," 

 " The Structure of Sunspots," " The Solar /Vtmosphere," and 

 " Solar Periods and Influence." 



Aeroplane Experiments 

 at the CrystOLl PoLlaLce. 



r>y Major liADiiN-l'oWKLL. 



Ir has often bee'ii supposed that one of the greatest 

 difficulties to be overcome before successful aerial navi- 

 gation can be achieved is the practical balance of the 

 apparatus in mid air. Whether or not this will really 

 prove a stumbling block it is impossible, with our present 

 experience, to state with irertainty. Several inventors, 

 it is true, have had considerable dillicultics in the initial 

 starting of their machines, which have had a way of toppling 

 over as soon as they ha\e been launched into the air. It 

 seems just possible, however, that if the machine could 



Starting. 



be properly trinuned before starting, all such dilhculties 

 might be overcome. We know that small models, if 

 dropped from the hand or lightly thrown forward, will 

 easily upset, if not properly balanced, but which, if the 

 weights be carefully adjusted beforehand, will fly steadily 

 enough on their downward course. But it is extremely 

 difficult to calculate the position of the centres of gravity 

 and of pressure, and practical trial is the only certain 

 method of getting this balance, ilow, then, is it possible 

 to test practically the balance of a machine which we are 

 loth to launch into mid air because we are afraid of its 

 toppling over ? 



With a parachute or surface dropping perpendicularly, 

 the weight should, of course, be in the centre of area ; 

 but if a more or less flat surface be progressing through the 

 air horizontally, it is found that the centre of pressure ad- 

 vances towards the front edge, and, therefore, if the weight 

 be in the centre, the plane will rapidly rise in front, and will 

 soon overbalance and shoot down backwards, liut the 

 more rapidly the machine is travelling, the more does the 



