412 



NATURE 



[March 5, (908 



The method of treatment adopted by the 

 author is one hkely to be very effective in 

 teaching ; new principles and processes, as they arise 

 in the natural development of the subject, are illus- 

 trated and driven home by the use of models, 

 diagrams, and repeated applications to suitable 

 ])roblems, so that the conscientious student is always 

 fuUv conversant with the reasons for his geometrical 

 constructions. The very excellent and suggestive 

 questions from the examination papers of the Board 

 of Education for the last five or six years are freely 

 employed, both in the text and as sample test papers, 

 affording a good criterion of progress. 



In addition to the ordinary geometrical solids, many 

 familiar objects the forms of which can be dissected 

 into simple geometrical figures are used as examples. 

 After the student has thoroughly mastered the 

 fundamental principles as set fortli in part i., he 

 should experience comparativeh little difficulty with 

 the three succeeding parts, which extend the subject 

 to lines and planes obliquely situated, to shadows by 

 parallel and divergent rays, and to reflections in hori- 

 zontal and vertical mirrors. The book will be very 

 acceptable both to teachers and students of this 

 interesting branch of applied geometry. 

 Strength of Materials. By W. C. Popplewell. Pp. 



X-I-180. (Edinburgh and London: Oliver aiid 



Boyd, 190;.) 

 Tins text-book, which is based on the notes of 

 lectures given by the author to day and even- 

 ing students at the Manchester Municipal School of 

 Technology, deals with the fundamental principles 

 which must be mastered by every student who wishes 

 to have a sound knowledge of machine and structural 

 design. Special attention has been devoted to the 

 effects of unequal distribution of stress, and in chapter 

 vii. the author gives details of his own experimental 

 work in connection with this branch of the subject. 

 The last three chapters give an account of the 

 methods adopted and appliances required in making 

 tests of the various materials used in constructional 

 work, and the important subjects of limit of elasticitv 

 and of the influence of previous loading, &c., upon 

 the limit are discussed. In an appendix is given a 

 table of strengths and weights of a large number of 

 different materials, and there is a collection of useful 

 examination questions for each chapter. 



LETTERS TO THE EDITOR. 

 ]The Editor does not hold himself responsible for opinions 

 expressed by his correspondents. Neitlier can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous communications.] 



Lithium in Radio-active Minerals. 



The recent results of Mile. Gleditsch {.Comptes rendus, 

 cxlvi., p. 331) corroborating those of Prof. McCoy, viz. 

 that lithium is generally, but not always, a constituent of 

 radio-active minerals containing copper, and that there is 

 no fixed proportionaHty between the copper and the lithium 

 in these minerals, must not be taken to have the exclusive 

 significance which their authors attribute to them. As 

 explained in our original communication to the Chemical 

 ^Society, we are inclined to believe that sodium, and perhaps 

 also potassium, are products of the degradation of copper 

 salts when in contact with radium emanation. As both 

 these metals are constituents of ordinary glass, and as the 

 experiments were carried out in glass vessels, the only 

 argument which was used was that the weight of the 

 residue from the treated was greater than that from the 

 imlreatcd copper salt. Lithium was mentioned because it 

 IS an unlikely constituent of dust, glass, copper, &c., 

 which were tested specially to prove its absence ; it was 

 certainly contained in the' treated residue. Inasmuch as 



NO. 2001, VOL. yj'\ 



the emanation in contact with water yields neon, on the 

 probable supposition that monatomic gases are produced 

 from the emanation, it would follow that the production 

 of any particular one is dependent on surrounding condi- 

 tions. It will be remembered that the gases from the 

 action of the emanation on a solution of copper sulphate 

 contained no helium, but probably argon. As sodium and 

 potassium are much more widely distributed than lithium, 

 it is more likely that they are the chief products from 

 copper, and that some modifying circumstance has deter- 

 mined the formation of a trace of lithium. Experiments 

 now in progress in silica vessels will settle this point. 

 Numerous chemical analogies might be adduced in favour 

 of this view. For example, the action of bleaching powder 

 on ammonia solution is to give nitrogen for the most part ; 

 if much ammonia be present, and if glue or some other 

 colloid be present, hydrazine is the chief product. One 

 can only be guided by such analogies in determining the 

 lines of future experiments. \\". R.\MS.\Y. 



Formation of Ground-ice. 



In Canada we have made an extended study of the 

 formation of ground-ice, or anchor-ice as it is called here, 

 and consequently I was interested to see a letter in Nature 

 of January 30 from Mr. Hampson asking for information 

 as to its origin. 



May I at the outset refer Mr. Hampson to four papers 

 published many years ago which are wonderfully interest- 

 ing to anyone studying the formation of ground-ice? Two 

 of the papers appeared in the Edinburgh New Philosophical 

 Journal, one by M. Arago, vol. xv., p. 123, 1833, and the 

 other by the Rev. Mr. Eisdale, vol. xvii., p. 167, 1834. 

 The two other papers were published in the Phil. Trans., 

 vol. cxxv., p. 329, 1835. and vol. cxxxi., p. 37, 1841, by 

 the Rev. James Farquharson, of Alford. 



In reply to the questions raised by Mr. Hampson, I 

 may say that (i) the essential conditions for the formation 

 of ground-ice on the bed of a river are clear weather 

 conditions at night with the water at or near the freezing 

 point, e.Kcessively low air temperatures by day, with no 

 sunshine and no surface ice or other cover such as over- 

 hanging weeds or a bridge to check the nocturnal radia- 

 tions. The answer to (2) is covered by the above. (3) A 

 flowing river becomes stirred by eddy currents, and hence 

 the cold surface layers find their way to the bottom. 

 We notice many of our large rivers flow with a rolling 

 motion. (4) The water is such a bad conductor of heat 

 that it is only by the mechanical action that the bed 

 of a river becomes cold enough to form ice on it when 

 aided by radiation, or, as I have shown, by a slight 

 supercooling in the water. (5) Ground-ice will form in 

 water of any degree of agitation provided either or both 

 of the causes mentioned in (4) are operating. In the 

 case Mr. Hampson cites of the mill, I should say the heat 

 generated by the water flowing through the mill would 

 tend to prevent the formation of ice on the lower side. 



In Canada we have anchoi*-ice formed in very large 

 quantities in all the waterways flowing too swiftly for 

 stirface-ice to form. In some parts of the .St. Lawrence 

 it grows 5 feet or 6 feet in depth, forming very rapidly 

 during the periods of intense cold and clear nights. On 

 bright days the sun's radiant heat brings large quantities 

 of it to the surface with much noise and disturbance. The 

 buoyancy of large masses of the ice is often great enough 

 to raise huge stones and boulders and carry them along 

 in the current, depositing by this means portions of the 

 river bed further down stream in the quieter waters . 

 Boatmen are very careful not to cross the river when 

 anchor-ice is rising, for fear of having a large mass come 

 up under them and carry the boat helpless into the rapids. 

 Under surface-ice, with its covering of opaque snow 

 crystals, anchor-ice does not form, and hence it causes no 

 trouble under these conditions. 



.Anchor-ice is known and studied in every country iit 

 the world where ice is formed, and there is much that 

 might be written about it. In Nature of January i7._ 

 iqo7, a careful review of my book on " Ice Formation." 

 with special reference to anchor-ice and frazil, was given, 

 and may help to answer some of the questions in the 

 " long list " mentioned by Mr. Hampson. My paper read 



