May 25, 1905] 



NA TURE 



75 



own preferences. The absence of answers makes the 

 book of no use to the private student who requires 

 some check on tlie work he does. On the whole, 

 we think that the utility of the book would be 

 increased by the addition of these ; or, if this is not 

 favoured, then by their publication in a separate 

 volume. 



The whole ground of physics is covered, including- 

 mechanics. The general difficultv is only slight. Bv 

 far the largest number of the problems could be tackled 

 by a first-year university student. In mechanics very 

 many are even of matriculation standard; thus, " The 

 Washington Monument is 169 metres high. In what 

 time will a stone fall from top to bottom? " Mingled 

 with these are a few requiring the calculus. Many re- 

 quire onlv a qualitative answer; thus, ' Explain why it 

 is difficult to walk up an icy hill." These remarks are 

 equally true of the other sections ; thus, in electricity, 

 the following is a commonly occurring type of ques- 

 tion : — "Two copper wires are of the same cross-section, 

 but one is twice as long as the other. Compare their 

 resistances." Indeed, this question illustrates the 

 general character of the book very well. Take each 

 clause of an ordinary te.xt-book and express it in ques- 

 tion form — that seems to have been the mode of 

 formation. We miss the bright sparkle of genius which 

 flashes out from the examination papers of many of 

 the examiners that we know. Still, we think, and we 

 have said, that many will find it a very useful book. 



Turning next to the hints, which, we think, might 

 be multiplied with advantage, these are not always 

 above criticism. Take, for example, the following : — 



" Prove that a gun free to move backward and the 

 bullet fired from it have the same momentum when the 

 bullet leaves the gun. Note : Action and reaction are 

 equal and opposite. Force on gun = force on bullet. 



M,A,, = M(,A(, [A = acceleration] 



Multiply by t 



M,,V, = M4V,,." 



We are of opinion that equality of the two momenta 

 is the fundamental fact which can be proved only by 

 experiment. The operation of changing from a variable 

 acceleration to the change in velocity is inadequately 

 represented by a multiplication by the time. 



The arrangement of the problems seems to have been 

 imperfectly attended to ; very many questions are to 

 be found in sections with which they have nothing to 

 do. For example, under the head " Colour " occur a 

 series of questions such as " Why does an object appear 

 equally bright at all distances from the eye? " 



A series of useful tables completes the volume. The 

 numerical constants given are not always scrupulously 

 exact. For example, log ir = o.497i5o and not 0-497149 

 (as given) when only six figures are to be retained. 

 -Again, why should a student (or teacher) be misled into 

 taking log vr^ as 0-994299 when the much simpler num- 

 ber 0.994300 is more exact? There are two other 

 examples of this on the same page. This is the kind 

 of number which, if quoted at all, ought to be checked 

 and re-checked until the author is sure that he has it 

 right. 



NO. 1856, VOL. 72] 



MATliEUAriCAL METAPHYSICS. 

 Principicn der Mctiiphysik. By Dr. Branisiv 



Petronievics. Vol. i., part i. Pp. xxxi + 44T 



(Heidelberg : Carl Winter, 1904.) Price 15 marks. 

 ^''HIS is the first instalment of a new work on 

 -L metaphysics. It discusses only general ontology 

 and the formal categories (in other words, the general 

 ontological and the quantitative problem). The second 

 part of the same volume, we are informed, will deal 

 with the qualitative and hyper-metaphysical problems, 

 and the second volume will then go on to cosmology 

 and psychology. 



The author's guiding principle is expressed in the 

 motto, " Correct mathematical ideas are the key for 

 the solution of the riddle of the universe." We doubt 

 if this will command the acceptance of any meta- 

 phvsicians whose interests are not primarily mathe- 

 matical. Mr. Balfour, in a well-known passage, has 

 pointed out how often the battles of theology are 

 decided beyond the borders of that study ; it is a little 

 hard if the metaphysician, who contemplates all time 

 and all existence, is to be fettered by the geometrical 

 views of his age, and before he makes any headway 

 in prima philosophia must study closely the hundred- 

 page account of the new geometry " with 3 tables 

 containing 56 geometrical figures." 



We doubt in particular whether ordinary meta- 

 physicians will ever accept the " discrete " or atomic 

 view of space here given, however fashionable it may 

 be among modern mathematicians. That view goes 

 back to the Arabic school of the Mutakallimun. Dr. 

 Petronievics adopts, with some slight differences, the 

 development of the theory advocated by Giordano 

 Bruno. He distinguishes two kinds of " point," 

 Mittelpiinkt (der reale mit Inhalt erfiillte Punkt) and 

 Zwisclicnpiinkt (der irreale die leere nichtseiende 

 Liicke darstellende Punkt). The discussion of time 

 follows the same atomic lines. The plain man won- 

 ders in what fashion precisely his old friend " Achilles 

 and the tortoise " is to be dealt with on these 

 principles. (That fallacy, it is true, appeals in the first 

 instance to those who combine an atomic view of 

 Time with a non-atomic view of Space, but it has 

 surely its difficulties for any who regard either Time 

 or Space as discrete.) The same guileless inno- 

 cent, while understanding readily the general data 

 which enable a Kelvin to calculate the appro.ximate 

 size of " atoms " of water, does not see quite so 

 readily how we can ever hope to reach the data for 

 determining the size of atoms of impalpable Time or 

 Space. Nor, again, does he see the special benefit 

 of abolishing the old Euclidean point in favour of the 

 new one endowed with both position and magnitude, 

 when to all intents he is compelled, a moment later, 

 to revive in the term Zwischenpunkt the " point " of 

 his earliest geometrical affections — " that which has 

 position but not magnitude"; and he recalls the 

 Horatian tag, " ExpcUes fiirca, tamen usque re- 

 ciirret." 



Still, the discussion contained in this volume is 

 stimulating, and considerable dialectic power is dis- 

 played. One will watch with interest in the later 

 volumes whether the author succeeds in dealing with 



