March 30, 19 16] 



NATURE 



^9 



to the line hi, but exceeding^ by a square ; that is, 

 to hi apply a line such that when multiplied by 

 itself and by hi the sum will be equal to the pro- 

 duct of zh and 61," the explanatory clause being" 

 possibly Dr. Archibald's; but however that may 

 be, this sentence is a good illustration of the 

 contrast between Greek methods and others. 



The editor's work seems to be very well done. 

 There is a historical introduction (pp. 1-28) ; the 

 restoration of the treatise (pp. 30-77), which gives 

 a translation of Woepcke's version of the Arabic, 

 and a close paraphrase of Leonardo's proofs when 

 they exist, with supplementary matter by the 

 editor indicated by brackets or different type ; and 

 a bibliography (1539-igii) which gives references 

 to works on "division" problems covering a very 

 wide range— some, for instance, leading" to 

 transcendental equations. 



If the Cambridge Press would issue this work, 

 to teachers at any rate, in a paper wrapper at 

 half-a-crown, it might have a larger circulation. 

 The book deserves to be well known on account 

 of its ingenuity and the light which its history 

 throws on the different phases of geometrical 

 theorv. G. B. M. 



OVR BOOKSHELF. 



A Laboratory Manual for Work in General 

 Science. By O. W. Caldwell, W. L. Eiken- 

 berry and C. J. Pieper. Pp. xi + 134. (Lon- 

 don: Ginn and Co., 1915.) Price 25. 6d. 

 This little manual, emanating from the School of 

 Education of the University of Chicago, gives 

 outlines of experiments and demonstrations for 

 use "in the first year of the high school." The 

 experiments adopted are stated to be the "result 

 of the co-of>erative work of several high school 

 teachers through a period of years." Their pur- 

 pose is "to direct the pupils into the habit of 

 finding out about many kinds of comm.on prob- 

 lems in science." Useful as some of the experi- 

 ments are to create a healthy interest in every- 

 day phenomena, the cours'e described covers so 

 many different fields and the experiments follow 

 each other with so little regard to sequence, that 

 the net result would probably be to impart very 

 unreal and superficial knowledge. In successive 

 experiments we have such abrupt transitions as 

 the following : No. 23. Does a liquid fill all the 

 space which it appears to fill? No. 24. What are 

 the parts of a flame? And, again. No. 43. How 

 do bacteria act on milk, and how may milk be 

 preserved? No. 44. What changes in volume 

 take place when water freezes? No. 49. Does 

 water evaporate in a plant? No. 50. How does 

 •a siphon work? 



I Exercises such as No. 61. What is the relation 

 ! between water supply and disease? No. 6ia. 

 I What is the significance of the local death-rate 

 I from typhoid? No. 62. How is sewage disposed 

 !of tn your community? are examples of later 

 jproblems. These are followed by exercises dealing 

 .with the use of pulleys and machines, experiments 

 NO. 2422, VOL. 97] 



on the soil, the growth of plants, the nature of 

 foods, and so on. Finally we have a statistical 

 study of the question, "Are variations in parents 

 transmitted to offspring? " 



In the reviewer's opinion, far too much is 

 attempted in the course laid down for it to be of 

 much real educative value. W. A. D. 



Archaic Sculpturings : Notes on Art, Philosophy, 



and Religion in Britain, 2000 B.C. to 900 A.D. 



By L. M. Mann. Pp. 52. (London : W. Hodge 



and Co., 1915.) Price 2s. 6d. net. 

 The object of this pamphlet, reprinted from the 

 Proceedings of the Dumfries and Galloway 

 Natural History and Antiquarian Society, is to 

 examine three groups of sculptures in that dis- 

 trict : Pagan, consisting of cup and ring mark- 

 ings of the Neolithic and Bronze Ages, and dia- 

 grams on slate of the Middle Bronze Age; transi- 

 tional designs, mostly of the Iron Age; and the 

 earliest Christian monuments. The scheme is 

 wide, probably too wide for treatment within the 

 limits of a single paper. The most interesting^ 

 part of it is the investigation of cup and ring 

 markings. The current theories of their origin 

 and purport being far from satisfactory, Mr. Mann 

 tells us that some years ago he began to recognise 

 that these figures, when plotted on paper, were 

 found to be "arranged in a most precise, mathe- 

 matical, and geometrical manner." He recog- 

 nises two main systems of lines fitting- into the 

 salient parts of the sculpturing. "One system 

 narrowly misses coinciding with the other. One is 

 related apparently to the actual pole, and the 

 other to the pole star of that period." He be- 

 lieves that many of them " embody primitive astro- 

 nomical motives mixed up with ideas of worship 

 of a Supreme Central Force which were wide- 

 spread over most parts of Europe during the first, 

 probably the second, if not also the third millen- 

 nium before Christ." 



The scheme is worked out with considerable in- 

 genuity. But the student will probably demand 

 further evidence, beyond the carvings themselves, 

 to show that these beliefs were current among the 

 sculptors, some precise dating of the ornamenta- 

 tion, and a more extended survey of similar mark- 

 ings bevond the area treated in this paper. The 

 theory is, at any rate, interesting, and those who 

 are in a p>osition to examine these stones might 

 bear it in mind. 



Warwickshire. By J. Harvey Bloom. Pp. xi-f 

 144. (Cambridge : At the L^niversity Press, 

 1916.) Price 15. 6d. net... 

 This little volume exhibits all the excellences we 

 have learnt to associate with the Cambridge 

 county geographies. Visitors to Warwickshire 

 will find here a concise and well-illustrated account 

 of the relief, geology, natural history, climate, 

 and industries of the county, in addition to other 

 interesting particulars about one of the most 

 beautiful parts of England. The coloured oro- 

 graphical and geological maps add greatly to the 

 value of the guide. 



