5IO 



NATURE 



{March 29, 1888 



leading sub-types under each main type, is what I have tried to 

 indicate. Such a table makes clear at once not only the 

 passage of, say, syenites into trachytes, diorites into andesites, 

 but also that of trachytes into andesites, andesites into basalts, 

 &c., &c. 



A student who has attempted, with plenty of good sections to 

 work on, to draw a definite line between trachytes and ande- 

 sites, or augite-andesites and basalts, will probably not easily 

 again fall into the error of believing in hard-and-fast types ! 



Dr. Hatch has at once indicated two main points which will 

 strike petrologists as open to criticism in Rosenbusch's system : 

 the "dyke rocks," and the subdivision of the effusive rocks into 

 "palaeo-volcanic" and " neo- volcanic." With regard to the 

 former it deserves to be pointed out that it has not been found 

 possible to classify any reprefentafives of the diabases and 

 gabbros under the head of dyke rocks at all ; and one feels that 

 very considerable force has been used, in some other cases, in 

 order to get the rocks under this division into their proper 

 "pigeon-holes." 



Something of the same sort of strain and artificiality is felt in 

 some cases with regard to the two divisions of the effusive rocks, 

 and here again it is, perhaps, the equivalents of the diabases 

 and gabbros which most strongly exemplify this feeling— viz. 

 the augite-porphyrites and melaphyres, and the basalts. 



Many passages, in several parts of the book, show how fully 

 conscious Rosenbusch is of the weak places there are in his 

 system, as there must always be weak places in every system in 

 a young and rapidly growing science like microscopic petroiosy. 

 One does not know which most to admire — the wonderfully wFde 

 research and knowledge, and the skill and painstaking care and 

 labour, with which the system of classification has been evolved 

 out of the great amount of material to hand, or the great modesty 

 with which it is presented to us. 



It will be a thousand pities if a translation of the book does 

 not before very long find its way into the hands of all English- 

 speaking petrologists. A. B. 



Manchester, March 19. 



" The Mechanics of Machinery." 



Any errors— or what seem such— in a work of so high 

 character and repute as Prof. Kennedy's " Mechanics of 

 Machinery " may be conveniently noticed in Nature ; and 

 therefore no further reason need be offered for the following 

 remarks. 



(i) "If, then, a body is moving with a linear velocity of 

 V feet per second about a centre (permanent or virtual) at 



radius r feet, it is undergoing a radial acceleration of — foot- 



r 

 seconds per second, and the centrifugal force corresponding to 



this acceleration will be — pounds per unit of mass . . . ." 



r 

 (p. 228). 



Surely there is some confusion here between the virtual or 

 instantaneous radius, and the radius of curvature ; for it is of 

 course the latter which indicates the radial acceleration. 



It has always seemed to me that the common expression that 

 a body is turning "about," or, as Prof. Kennedy sometimes puts 

 it, "round," its virtual centre is very apt to mislead. All that 

 we are entitled to say is that at any given instant one point is at 

 rest ; and that all other points are moving in directions at right 

 angles to the lines joining them with that point, and with 

 velocities proportional to those lines. This being true also in 

 the simple case of motion in a circle we are apt to use the same 

 language to express it, with the inevitable suggestion of the 

 curvature being in correspondence. It need not be said that the 

 curvature may be zero (as when a circle rolls inside one of twice 

 its diameter) ; or that it may be aivay from the centre (as when 

 the former circle is more than twice the diameter of the second). 

 The beginner would find it hard to realize the latter case when 

 he has been taught to speak of the body "turning round" its 

 virtual centre. I do not know that any better description can 

 be adopted, but it ought to be introduced with emphatic cautions 

 that it is merely a convenient device of description. In any case 

 it seems to me that the old term "instantaneous centre" is more 

 likely to keep the truth before us than the "virtual centre" 

 preferred by Prof. Kennedy. 



(2) In a series of interesting discussions about train resistance, 

 the following passage occurs : "The brake resistance is 1200 

 pounds, but it has to be overcome through a distance it times as 

 great as that moved through by the train as a whole ....;" 

 this brake resistance having been described above as "the 

 frictional resistance at the periphery of each wheel." 



I cannot follow this. Surely if the circumference of the 

 wheel be x feet, by the time the train "as a whole " has run 

 over a rail-length of x feet, the brake has slid over a wheel- 

 circumference of X feet also.^ 



This need hardly have been noticed, but that the examples 

 seem always very carefully chosen, not as fancy problems, but as 

 being in accordance with practical experience. Either, there- 

 fore, the common impressions as to the time and distance re- 

 quisite for stopping must be wide of the mark, or the value 

 assumed, in this and a number of other examples, for the brake 

 resistance, must be about three times too small. 



(3) " If, for instance, the brakes had not acted promptly, and 

 had been put very hard on at the end, the velocity and accelera- 

 tion curves might have been as dotted, when the maximum 

 acceleration occurs almost at the end, a state of affairs very 

 uncomfortable for the passengers " (p. 205).^ 



Is this so certain ? I mean, is there any reason to suppose 

 that a sudden change oi acceleration, not of velocity — for of this 

 there is no question with any conceivable brake system — would 

 be felt as disagreeable ? 



The question must, one would think, have often presented 

 itself to speculative and scientific engineers ; but as I do not re- 

 member to have seen it discussed one would like to get their 

 opinion on the point. The way it strikes me is this. We cannot 

 practically suppose the acceleration /?</(?« instantaneously, for the 

 brake needs time to work ; but we can get as near as Nature 

 allows to the instantaneous when it is taken off. That is, if the 

 brakes are left on to the end, the velocity continues to diminish 



' In the Errata we are told to omit this passage ; but as the premises and 

 the conclusion, between which it formed the necessarj' connection, are left 

 unaltered, the need for it is as great as before. How else, but by such an 

 inference, can the conclusion be reached ? 



^ The curve of velocity here is a parabola, or nearly so, representing (on a 

 distance scale) a nearly constant "acceleration," with a constantly decreasing 

 velocity. 



