November 20, 1902] 



NA TURE 



69 



peculiar manner in which they lend themselves to subdivision 

 or multiple expansion is examined, it will be seen that they are 

 inseparably connected with circles which have their radii related 

 in the manner described. Study of these figures will enable one 

 to tell, by merely looking at a proportioned object, the order of 

 its symmetry or character of its plan. For instance, in a 

 cross-section of the young fruit and contained seeds of the 

 verbena, certain circles are involved in relationship to a square. 

 Without making any measurements from the fruit, the plan can 

 be accurately formulated (Fig. i). 



This construction is simple, but it involves principles which 

 are far-reaching. The ground plan of the Parthenon is an 

 instance of architectural construction where the detail is co- 

 ordinated in much the same manner. 



The basal projection of the crystal of topaz (Fig. 2) involves 

 all the proportions which occur in regular forms. There are the 

 primary circles the radii of which form the geometrical progression 

 with the binary ratio, and the secondary circles as derived from 

 the sides of the equilateral triangle, the square and the regular 

 pentagon. This example also includes the odd proportion 

 derived from the perpendicular of an equilateral triangle. This 



! 



Fig. 2. — Crystal of topaz — basal projection. 

 A A Primary circle 1. 

 BB ,, „ 2. 



C C ., „ 3. 



Distance of point □ A from centre determined by CJ in A. 



„ ,, A A „ „ ,, A in A. 



„ < B „ ,, „ in B. 



,. □ B ,, ,, ,, D in B. 



i, „ JB ,, „ „ J in B. 



,. „ OC ,, „ „ O in C. 



This crystal base contains the entire scheme of proportion and symmetry 



as found in the Parthenon. 



is the only proportion found in symmetrical natural form which 

 seems to be connected with an arithmetical progression. 



The Greek and Gothic styles of architecture furnish the most 

 satisfactory results in a comparison of their curves and pro- 

 portions with the curves and proportions of natural symmetrical 

 forms. In the finest example of the former, the Parthenon, the 

 agreement is so extraordinary that all its proportions and curves 

 may be obtained with no other instrument than a string and a 

 couple of sticks. A surface of levelled earth would furnish a 

 place to make the simple constructions. The beautiful curves 

 found in this building, which so simulate those of conic sections 

 as to deceive the expert mathematician, can be accounted for by 

 this method. In (act, there is no curve in Greek formal art 

 which may not be simply, rapidly and accurately drawn with a 

 compass, and when so drawn, the circles used will be found to 

 possess a definite relationship one to the other. This method 

 would seem to furnish a simple explanation as to how the Greek 

 architects used these curves so long before their supposed 

 discovery. The agreement between the plans of the regular 

 forms of Nature and the plans of the best buildings would seem 

 to suggest that the great architects possessed a formulated or 

 intuitive knowledge of simple principles of proportion which are 

 unknown to us. 



1 J is the symbol for the perpendicular of the equilateral triangle. 



MO. 1725, VOL. 67] 



EARTHQUAKES AND EARTH PHYSICS. 

 OROF. J. MILNE, F.R.S., read apaper on " World-shaking 

 *■ Earthquakes" before the Royal Geographical Society on 

 November 11. In the course of his paper, he remarked that 

 earthquakes may be divided into two groups — first, those which 

 disturbed continental areas, or even the world as a whole, which 

 he called macroseismic, and, secondly, local earthquakes dis- 

 turbing a few miles' radius, or not more than 100 or 200 miles, 

 which he called microseismic. Evidence of the existence of 

 large earthquakes was sometimes afforded, even though they 

 could not be felt ; for example, in 1755, the motion of the water 

 in lakes and ponds observed in England, Scandinavia and North 

 America was attributed to the earthquake at Lisbon. Another 

 form of evidence was sometimes discovered by astronomers, as 

 in May, 1877, M. Nyren observed disturbances in the level of 

 the axis of the transit at Pulkova, which were held to be due to 

 an earthquake about an hour and a quarter earlier at Iquique. 

 The first instrumental record obtained by the writer of an earth- 

 quake which could not be felt was in March, 1SS4. This and 

 others were referred to as " slow earthquakes." A long series of 

 observations justified him in saying, in 1883, that every large 

 earthquake might be recorded at any point on the land surface 

 of the globe. Thus a new field was open to seismologists, and 

 recording stations were now to be found in many countries, 

 the most complete organisation working in connection with 

 a committee of the British Association. A large earthquake 

 seemed to propagate a series of waves in all directions through 

 and in all directions over the world's surface. Describing 

 in detail the character of this motion, he said that the large 

 waves of earthquakes seemed to pass beneath a country like 

 ours with the character of an ocean swell. The character 

 of these waves was still in process of investigation, and there 

 were reasons for and against any conclusions which might 

 be reached. It would appear that the effective rigidity of the 

 world was about twice that of steel, and it was easy to measure 

 the difference in time between the arrival of preliminary, 

 tremors and of large waves — the former reaching a place 80 

 from their origin in about fifteen minutes, whilst large waves 

 took about fifty minutes. From these differences in times of 

 arrival of different waves, distances of origins could be obtained, 

 and from the distance ascertained from several distant stations 

 the origin might be easily located. Another method of ascer- 

 taining origin was the difference of the times of arrival at dif- 

 ferent stations of large waves, and by these methods the origin 

 of the world-shaking earthquakes for 1899, 1900 and 1901 had 

 been determined. Prof. Milne established a relationship be- 

 tween the distribution of the origins of large earthquakes and 

 the pronounced irregularities of the surface of the earth by a 

 number of illustrations taken from the Alaskan region, which- 

 had yielded large seismograms to the Cape of Good Hope, 

 which was antipodean to Alaska, the Cordillerean region, the 

 Antilles, the Andes, Japan, and other parts of the world. 

 He also gave an historic account, dating from 1692, of the 

 mass displacements which had been cau ; ed by great 

 earthquakes. As examples, in 1855, ln New Zealand, 

 4600 square miles were raised I foot to 9 feet ; and in 1897, in 

 Assam, according to Mr. R. D. Oldham, 10,000 square miles of 

 country were displaced po?sibly 16 feet along a thiu-t plane. 



The connection between large earthquakes and volcanic 

 activity was considered ; and instances were given of the 

 seismic convulsions which apparently resulted in reliefs of 

 volcanic strain. So recently as the early part of last sum- 

 mer, the symptoms of volcanic and seismic activities in the 

 Western Hemisphere culminated in the terrible explosions 

 in Martinique and St. Vincent. Prof. Milne also gave 

 the result of inquiries into the relationship between world- 

 shaking earthquakes and unusual movements of magnetic 

 needles. At certain stations, the unfelt waves of large earth- 

 quakes disturb magnetic needles, but this is not the case at all 

 stations. This difference in behaviour is not explicable on the 

 assumption that the movements are due to tilting of the instru- 

 ments, but it is possible that they may be due to magnetic in- 

 fluences. The stations at which movements are observed, Prof. 

 Milne suggests, may be nearer to the magma in which the 

 large waves are propagated than the other stations where move- 

 ments are not observed. Inasmuch as this magma is not only 

 magnetic, but is also dense at the former stations, the observed 

 value for g would exceed that at the remaining stations, 

 caete> is paribus. In support of this view, figures were adduced. 

 References were made to small changes in latitude. When 



