NATURE 



May 2, 1872 



case. Exp. 5, p. 10, does not clearly show that the heat 

 due to chemical union is independent of the heat caused 

 by the lamp ; while statements 6 and 7, if taken to- 

 gether, produce in the pupil's mind a confusion between 

 cause and effect. In pp. 23, 25, the allusions to acid and 

 alkali, both new names to the student, might easily be 

 accompanied by a marginal reference to p. 65, where the 

 terms are explained. In Exp. 17, p. 27, it is not made 

 evident in words that the hydrogen has passed from the 

 one bottle into the other. Exp. 22, p. 34, and Exp. 40, 

 p. 68, would gain in value if the action of the text, as well 

 as its result, were described, such explanation of the first 

 experiment being actually given later on at p. 87. In 

 Exp. 29, pp. 44, 45, the diction of the first two paragraphs 

 is confused and confusing, and it is doubtful if any lecturer 

 would be able to conduct Exp. 3 1, p. 48, so as to retain the 

 heated filings on the magnet. In Exp. 35, p. 56, the 

 numbers on the drawing do not tally with those of the 

 description. The explanation of the Davy lamp, p. 57, 

 to which further reference is made in Physics, p. 86, is, to 

 say the least of it, incomplete : and that of the safety 

 matches on p. 72 is quite unintelligible. The definition 

 of an Element, p. 58, and the phrase " difficultly fusible " 

 on p. 99, suggest purely verbal criticisms. 



In the Physic Primer, p. 2, force and motion should 

 hardly be called qualities" of dead matter. In Exp. 13, 

 p. 22, the " simple arrangement " for moving the hori- 

 zontal piston might be indicated. In p. 23 the large and 

 small piston are not lettered in the description. In Exp. 17, 

 p. 26,a shrewd pupil would inquire why the upward pressure 

 should not, from all that appears in the text, expel water 

 from the higher aperture as strongly as the downward 

 pressure expels it from the lower aperture. In pp. 40, 41, 

 some allusion to the Aneroid, if not to the Hypsometer, 

 might fairly be expected, and in p. 46 it is not easy to see 

 why the Syphon is described if its principle is not to be 

 explained. In p. 65 there is an allusion to " the mercury 

 in the bulb of glass," which is, in fact, there mentioned 

 for the first time, and is it not true that in Exp. 52, p. 105, 

 a principle of converse action is laid down on the evidence 

 of a specific and almost a solitary instance ? 



It is possible that to criticise these points as blemishes 

 suggests stupidity to the critic ; if so, his stupidity is pro- 

 bably typical, and the authors would be the first to wish 

 that their explanations should be self-sufficing, even to 

 the obtuse. In any case we tender them our hearty thanks 

 for work which marks a stage in the advance of scientific 

 education. Its lingering progress hitherto has been owing 

 to the want, not of zealous champions, but of united 

 action. The labours of its advocates are now beginning 

 to converge. The leaders of science and the leaders of 

 education are drawing close together— on the one side 

 eager to impart, on the other ready to receive, advice and 

 guidance. By the publication of these books the most 

 serious of the obstacles which have kept them separate is 

 removed. W. Tuckwell 



06-7? BOOK SHELF 



Astronomy and Gcolo'ZV compared. By Lord Orma- 



thwaite. (London : J. Murray, 1S72.) 

 This little volume is the product of a thoughtful and 

 observant mind. Its main object is to contrast the 



certainty of the conclusions of astronomy, the ex- 

 actitude with which eclipses can be foretold, and 

 with which other astronomical phenomena recur, and 

 the vagueness which hangs round many geological 

 theories, as, for instance, those connected with the age of 

 the various strata. A large portion of the volume is 

 directed against the theories of Mr. Darwin in natural 

 science, and Mr. Buckle in morals, theories which the 

 author considers, in consequence of the vagueness of 

 geological conclusions, to rest upon insufficient data. 

 With the general mode in which the argument is con- 

 ducted, we have little fault to find. Occasionally, how- 

 ever. Lord Ormathwaite's zeal on behalf of orthodox 

 theology betrays him into injustice, as when he says ; — 

 " There is one feature common to the writings of Mr. 

 Darwin and Mr. Buckle which is to be regretted — they 

 both of them seem to ignore, if they do not altogether 

 deny, the existence of a First Cause. .Secondary causes 

 are always with them the only springs of motion " With 

 this we may contrast the following sentence from the 

 " Origin of Species": — "To my mind it accords better 

 with what we know of the laius impressed on matter by 

 the Creator, that the production and extinction of the 

 past and present inhabitants of the world should have 

 been due to secondary causes, like those determining the 

 birth and death of the individual." Lord Ormathwaite 

 pleads bodily infirmities as an cxciise for any inaccuracies 

 or mistakes in the book, and we very willingly allow the 

 plea. 

 The Use and Origin of the Arrani^ements of Leaves in 



Plants. By Chauncey Wright. (American Academy 



of Science and Arts.) 

 This is an elaborate and ingenious attempt to apply the 

 principles of Natural Selection, or the Survival of the 

 Fittest, to the observed phenomena of Phyllotaxy, or the 

 arrangement of leaves on the stems in plants. Stating 

 in the outset very clearly the distinction between this 

 theory, according to which every organ, and every 

 arrangement of organs, must be of some practical (though 

 possibly undiscovered) utility to the plant, and that of 

 " types," which requires no such hypothesis. Dr. Wright 

 proceeds to investigate how the origin of the phenomena 

 under investigation can be accounted for on the former 

 theory. It must be assumed in the outset that the two 

 principal modes of the arrangement of foliar organs, of 

 which all others are modifications, the spiral and the 

 verticillate, are modifications of a single original type. 

 Investigating the actual arrangements on mathematical 

 principles, he finds th.it the various angular distances of 

 leaves on the stem are resolvable into the geoeral form of 



the continued fraction — ; — 



«+ I 



i + r 



I -f,&c., 

 in which a may have the values i, 2, 3, or 4. The actual 

 fractions thus resulting are when 



" = I • • J f ? I T3. &c. 



<7 = 2 . . ^ M I /s, &c. 



« = 3 • • ^ i ? iV A, &c. 



« = 4 . • \\% A A. &c. 

 each fraction being obtained by adding together the 

 numerators and denominators in the two preceding frac- 

 tions. Practically it is found, however, that certain only of 

 these fractions occur in nature, while of those that arefound 

 some are much more frequent than others. The approxi- 

 mate ultimate value (/•) of this continued fraction, when 

 a= I, iso'6i8o, X- possessing the property that any power is 

 equal to the difference between the two next lowest powers, 

 or /•" = k"-'' — ,('"-'. On this peculiar arithmetical pro- 

 perty of k depends the geometrical one of the spiral 

 arrangement which it represents, namely, that such an 

 arrangement would effect the most thorough and rapid 



