246 



NA TURE 



[January 10, 1901 



than upon the real genetic and morphological relations 

 of the deposit. Hence it is that Dr. Beck places the 

 pyritic deposits of Rio Tinto, Mount Lyell, &c., in quite 

 a different group from those of Sudbury, although most 

 authorities prefer to group them together. Moreover, it 

 is only in very few of the examples cited under this head 

 that the magmatic origin of the deposit can be said to 

 be in any degree probable. 



The class of the stratified ore deposits is better defined, 

 although it would have been preferable to have either 

 excluded altogether deposits that consist of ores dis- 

 seminated through an otherwise barren bed, or else to have 

 included all forms of this mode of occurrence ; the 

 attempt to class impregnations amongst the epigenetic 

 deposits, and to include in the present class only such 

 disseminations as were formed contemporaneously with 

 the bed in which they occur, is necessarily unsatisfactory, 

 for there are very few instances in which the true mode of 

 origin of such deposit has been proved beyond the possi- 

 bility of dissent. Another source of weakness in this 

 classification is the inclusion here of typically lenticular 

 deposits, whenever the lens lies parallel to the stratifica. 

 tion. Here again a relatively accidental character has 

 been emphasised whilst the real geological relations of 

 the deposit have been lost sight of. 



Dr. Beck is perhaps at his best in his classification of 

 veins, although the method here adopted is purely empiri- 

 cal. Such important geological relations as those of the 

 vein to the country rock are utterly disregarded, contact 

 veins are not distinguished from true fissure veins, &c., 

 whilst the classification relies entirely upon the mineral- 

 ogical character of the vein filling. This is the old 

 Freiberg classification, revised and extended, and though 

 it is less satisfactory when applied to the world as a whole 

 than it was when restricted to the Freiberg district, it 

 is nevertheless interesting, and, to a certain degree, even 

 useful. By far the worst portion, and the only one that 

 is wholly unsatisfactory, is the attempt to classify the 

 gold-bearing veins, the distinctions here drawn being 

 far too artificial, and the lines of demarcation too 

 imaginary. 



It maybe noted, by the way, that the well-known Sheba 

 deposit is here classed as a vein, whilst the bulk of what 

 is known about it tends to show that it is certainly a bed. 

 It is also doubtful whether the majority of the cinnabar 

 deposits are really vems, as they are here designated. 



In pointing out that many and grave faults can be found 

 with Dr. Beck's classification of ore deposits, nothing 

 more is intended to be conveyed than that Dr. Beck has 

 not succeeded where every one else has failed. It may 

 be doubted whether any one has yet evolved a classi- 

 fication of ore deposits that satisfied anybody — even its 

 author ; the inherent difficulties of the subject are so 

 great and so manifold that a satisfactory solution of the 

 problem may, in the present state of the science, fairly be 

 declared to be impossible. Classification apart. Dr. 

 Beck's work forms a contribution of the utmost value to 

 the study of ore deposits; his descriptions are concise 

 ' and clear, and his illustrations are well selected, especially 

 as regards German, Austrian and Scandinavian deposits. 

 The section on faults is eminently satisfactory, and indeed 

 it would be hard to point to any work in which this 

 complicated portion of the subject has received better 

 NO. 1628, VOL. 63] 



treatment. It is difficult to pass judgment on half a 

 book, but it may fairly be said that if the remainder of 

 the work is only equal to the first half, it will constitute 

 one of the best works available on the subject of ore 

 deposits, provided that it is furnished with thoroughly 

 complete indexes, and not with the apology for an index 

 that usually does duty in German works. As the ore 

 deposits described are arranged in accordance with the 

 author's own system of classification, a complete alpha- 

 betical subject- index, together with a complete alpha- 

 betical index of geographical names, are needed to make 

 Dr. Beck's work the highly useful book of reference that 

 its other merits entitle it to become. H. Louis. 



THE THEORY OF ''SCREWS." 

 A Treatise on the Theory of Screws. By Sir Robert 



Stawell Ball, LL.D., F.R.S. Pp. xix -f 544. (Cam- 

 bridge University Press, 1900.) 

 SIR ROBERT BALL'S "Theory of Screws" is one of 

 the most notable modern extensions of theoretical 

 dynamics. It is based on Poinsot's discovery that every 

 set of forces, regarded as acting on a rigid body, is re- 

 ducible to a force along one definite line and a couple 

 round the line ; combined with Chasles's discovery that 

 every instantaneous motion of a rigid body is reducible to 

 rotation round one definite line and translation along it — 

 in other words to a screwing motion. The modes of 

 reduction in the two cases are strictly analogous ; a force 

 along a line being the analogue of a rotation round the 

 line, and translation in any direction being the analogue 

 of a couple whose axis has this direction. 



The theory of screws treats of these two subjects in 

 conjunction. The definite line along which the force acts, 

 or round which the body rotates, is regarded as the axis 

 of a screw, and the ratio of the couple to the force in the 

 one case, or of the translation to the rotation in the other, 

 is called the pitch of the screw. The sign of the pitch 

 indicates whether the screw is right-handed or left-handed, 

 and IS not altered by reversing the screw end for end. 



It would be convenient to have some general name for 

 anything which follows the laws of combination employed 

 in these reductions. Clifford called it a motor. It might 

 well be called a screw-actor. The resultant of two screw- 

 actors may be called their sum. 



When the screw-actor is a set of forces. Sir R. B^l 

 calls it a wrench — a name which is not suggestive of a 

 statical concept, but rather of force combined with motion. 

 The ndiVixt. forcive seems more appropriate. 



When the actor is a screw motion. Sir R. Ball calls it a 

 twist, and the name twist-velocity is given to a screw- 

 velocity. The twists considered in the theory of screws 

 are, in general, supposed to be so small as to admit of 

 simple superposition, quantities of the second order being 

 negligible. 



Five numbers are required for specifying a screw. Two 

 will give the direction of the axis, two the intersection of 

 the axis with a fixed plane, and one the pitch. From 

 another point of view a screw is defined by the five ratios 

 of the six components of a screw-actor. 



The theory of screws lends itself with special readiness 

 to the discussion of the movements of a body with a given 

 number of degrees of freedom. A body with one degree 



