ai'^ 



NA rURE 



[March 2, 1899 



As a simple illustration of earthquake radiation, we may 

 i.nagine a disturKince to originate at O as a single impulse, the 

 resulting vibrations spreading in all directions through the earth, 

 and in all directions over its surface. The former of these may 

 be regarded as elastic vibrations, whilst the latter have the 

 character of surface undulations influenced by gravity. At any 

 station l'| the first arrivals would be preliminary tremors, chiefly 

 compressional in character. These would be suddenly eclipsed 

 by vibrations, prob.ibly distortional, originating by refraction 

 beneath the crust in the vicinity of P,. The first of them we 

 should expect to find serrated, whilst their followers emerging 

 between I', and T.j would be smoother in outline and larger in 

 amplitude. The last and largest members of the series would 

 be those which have travelled practically as free .surface-waves 

 through the crusi. The result of such radiation as exhibited on 

 a seismogiam would be to show tiue preliminary tremors, 

 suddenly lollowed by a series of larger waves, which would 

 gradually grow in size. If at the origin there were several 

 impulses, then these latter precursors would arrive in groups. 

 An alternative hypothesis is to assume that all the vibrations 

 recorded at a station 1' arrived along their peculiar brachisto- 

 chronic paths through the earth, an important fact supporting 

 which, is that up to the present we have not with any certainty 

 identified waves which may have reached V pas.sing outwards 

 from O round our world in opposite directions. Although it is 

 not likely that I shall be able, in the tremor-haunted, damp, 

 dark stable where I work, to catch the waves which have taken 

 the longest route to my observing st.ition, that there are such 

 surface undulations radiating in all directions from an epifocal 

 area there is but little doubt. Xear to an origin you see the 

 little waves come rolling down a street, whilst at distances of 

 yx> miles the ground swell may be so heavy that I and many 

 others have been seized with nausea. What proportion of 

 seismic energy escapes round the surface of our earth, as 

 compared with that which passes through the same, I do not 

 know ; but if the experiment were made, I should not be sur- 

 prised to find that at the lime of large earthquakes, mountains 

 swayed like the masts of ships on a slowly heaving ocean. 



All that has here been suggested is clearly very far from being 

 above criticism. It indicates a want of knowledge respecting 

 the researches of the elastician, whilst the facts are few. 

 Although the observations may lie characterised by their poverty, 

 I often see in the rough-headed mobs of earthquake precursors 

 rhythmical repetition ; and I trust that, if my story of their 

 creation and long duration is not the true one, it may at least 

 induce others to ariempt better hypotheses. John Miine. 



The Orbit of Witt DQ. 



The extreme eccentricity of the orbit of Witt's planet suggests 

 some interesting speculations. Assuming the aphelion and 

 perihelion distances in terms of the earth's mean distance are 

 respectively I 79 and 112, the planet approaches the sun in 

 322 days, a distance of sixty-one million miles, an average of 

 200,000 miles a day. 



Practically this may be considered as a fall, during the half- 

 revolution, of this distance. Now if the planet were a perfectly 

 plastic body, and we knew all its elements, it would be per- 

 fectly possible to deterinine the deforming forces acting on it 

 during the ))assage It is evident that the force ol gravity acting 

 on the forward point of the syzygial axis would always be in 

 excess of that on the rear, and in consequence that the tendency 

 would be to continually lengthen that axis in a proportion 

 referable to the S()uares cf the distances fallen. On the other 

 hand the force of internal gravitation towards its own centre 

 would always tend to restore the sphericiiy, and the result would 

 be that a body starting as a sphere from aphelion would find the 

 syzygial axis prolonged and its shapi. deformed into an increas- 

 ingly prolate spheroid, till on its arrival at perihelion and its 

 commencement to retreat the reverse phenomenon would occur, 

 and the planet on its return become again a sphere. 



Now, of course, we have no reason to suspect that III,) is a 

 plastic body, and the comparative insignificance of its size, 

 would, were it to be composed of matter of equal rigidity 

 with ordinary rocks on the surface of the earth, enable it to suc- 

 cessfully lesist these deforming influences. We may, however, 

 imagine a case where the strains would be sulVicient to break up 

 an ordinarily rigid body, if the eccentricity exceeded a certain 

 amount, and the conseijuenl dilTerential action of gravity became 

 sufliciently great. 



NO. I 53 I, VOL. 59] 



A hypothetical planet moving in an orbit of high eccentricity, 

 for instance, between Mars and Jupiter might, so long as it 

 continued plastic, preserve its condition as a single coherent 

 body. If, however, it were cooled to an extent sufficient to In- 

 come enveloped by a rigid crust, there might come a time when 

 the deforming forces would cause deep and continually proceed- 

 ing fractures. I-;ventually we can conceive that these fractures 

 would split the body into fragments, each of which from its own 

 intrinsic rigidity would be able to maintain its shape and co- 

 hesion. In such a case each of the fragments would proceed to 

 take up an independent motion of its own. lience, perhaps, we 

 may .see our way, without calling in any extraneous factor, to 

 account for the present zone of asteroids, as well as explain ihc- 

 small size of the individuals. 



This tallies, moreover, with observation. The great planets 

 have all orbits approaching a circle ; Jupiter, the greatest of all, 

 has, with one exception, the smallest maximum of eccentricity ; 

 and Mercury, the smallest, has actually the greatest. The 

 Leonids move in a still more elongated orbit, and they are 

 amongst the smallest celestial objects with which we .are 

 acquainted. Altogether the minuteness of the planet and the 

 eccentricity of the orbit have some connection in fact ; this con- 

 nection I cannot believe to be fortuitous, and it seems not alto- 

 gether presumptuous to refer it to a common law, which we 

 know pervades the universe. This is my excuse for attempting 

 to venture into a hitherto unexplored region of physics, but one 

 pointing to vast possibilities, amongst others in geology. 



Shanghai, January 17. Thos. \\ . IviNGSMll.t. 



The Teaching of Geometry. 



I AM sure that all mathematical teacheis can thoroughly en- 

 dorse Prof. Minchin's letter. The difficulty of making a change 

 lies in the University and Civil Service examinations, which still 

 prescribe P^uclid. On the continent Euclid has been super- 

 seded by modern books, some of which might serve as a basis 

 for a thoroughly reformeil English text-book. 



I am convinced that the deplorable weakness .shown by almost 

 all boys in the solution of geometrical problems, arises in great 

 measure from Euclid ; they are utterly confused by its prolixity 

 and verbiage. 



And it is not as though this prolixity meant any greater 

 accuracy or better logical sequence. It is not proved till 

 Book iii. that a circle can only cut a straight line in two points ; 

 but in (i. 12) this property is quietly assumed, otherwise several 

 perpendiculars could be drawn. I. 13 simply asserts that 

 II 4- (1^ -t- c) = [a + 6) + c, but is unintelligible to beginners 

 through its verbiage. In i. 16 we practically make an angle 

 equal to the interior one, against the exterior angle, and then 

 ask the pupil to see for himself that one is greater than the 

 i>ther, which is suspiciously like yV////c /;•/;.■.////. In the second 

 Book we have a ntnnber of cumbersome proofs, some of which, 

 indeed, are now shortened to an algebraic form. (I have 

 never been able to understand the Cambridge regulation that 

 the sign -f may be used, but not the sign - . ) The Euclidean 

 definition of proportion is quite unintelligible to beginners, 

 while the conception of similar figures and of s,a/c is easily 

 grasped. To insist on young boys entering on the subtleties of 

 the subject, is much as though one made a child beginning; 

 arithmetic re.id, say, the first chapter of Weber's .Mgebra. 

 What is wanted is thorough ready knowledge of the properties, 

 of lines and circles. .\nd for this I would strongly recommend 

 pnulkal gioin/liy. I believe it could very easily be made a 

 means of imparting a knowledge of geometry in its highest .and 

 widest sense. R. J. D.\t.l..\s. 



15 Pemberton Card ens, N. 



American and English Winters. 



Wmi.K we, in the south of England, this February, have 

 been enjoying weather of extraordinary mildness, we have re.id 

 in the daily papers of bitter frost in .\merica, and the miseries 

 of a ferocious blizzard. It is by no means uncommon to find 

 opposite winter weather, at the same lime, east and west of the 

 Atlantic. Can we form any exact idea as to frequency of the 

 occurrence ? 



By way of .seeking light on this, I have lately comiiared 

 Chicago and (,!recnwich weather in the first quarter of the year, 

 in the fifty-one years 1S41-91 ; presenting the facts by a variety 

 of the graphic method, which I do not remember to have seen 



I 



