68 



NA TURE 



[November 20, 1902 



this with a protecting layer of porcelain paste and after drying 

 to bend the whole into spiral form by means' of a blowpipe. 

 The glower, which is composed of a mixture of zirconium oxide 

 with the yttria-erbia oxides, is, of course, while cold a non- 

 conductor of electricity. Heated, however, by the heater it 

 begins to conduct, rendering itself hotter by its own current 

 energy, getting hotter and hotter until it reaches its normal 

 brilliant state of incandescence. The glower current flowing 

 through the coils of the cutout magnetises the same, causing it 

 to pull in its armature and break the heater current at c. 



An unfortunate feature of the Nernst glower is that at the 

 necessary state of incandescence the voltage across it decreases 

 with increase of current. If one wished to express this mathe- 

 matically, one would say its 5i>/$a (z'i= volts, a = amperes) is nega- 

 tive. A conductor possessing this property placed across supply 

 mains of constant voltage is. however, in an unstable state of 

 equilibrium and will not burn properly. The function of the 

 series resistance R is to correct this. This consists of a very 

 fine iron wire placed inside a glass bulb containing hydrogen gas 

 at low pressure. The thickness of the iron wire is so chosen 

 that at the normal current it is just at its critical stage, i.e. at 

 that point, just under the red heat, where its5z'/5rzis highly posi- 

 tive ; the instability of the glower by itself is thus compensated 

 and the whole glower circuit across the mains is rendered 

 staMe. 



Ttie smaller lamp, used for all candle-powers below fifty) 

 conists of essentially similar parts to the larger model already 

 described. 



As to the economy of the Nernst lamp, the following table 

 shows the result of a test carried out by the PhysikalischeTech- 

 nische Reichsanstalt, of Berlin : — 



Mean of five lamps. Pressure 220 volts. 

 Time(hours). Candle-power. Watts p eJ candle. 



o . ... 35"i ' 6 5 



50 3 2 '4 177 



100 32-3 177 



200 30-1 1-85 



300 27-5 193 



400 26'S 197 



Mean during 400 hours 30/1 ... ... 183 



The average life was 380 hours. The heaters were not 

 damaged. 



Unfortunately, no information is given as to the source of 

 upply on which these tests were made. Experience already 

 acquired shows that this is of great importance as determining 

 the life of the glowers. Of course, on the basis of I '8 watts 

 per candle, for a life of 400 hours, the Nernst lamp works out 

 at a saving of about 40 percent., first cost and renewals included, 

 over ordinary incandescent lamps. 



We believe that the lamp is finding, or will find, considerable 

 commercial application, and we anticipate for it a very useful 

 and prosperous future. C. C. Garrard. 



I 



NATURAL PROPORTIONS IN 

 ARCHITECTURE. 1 



T is well known that formal decoration must be based upon 

 exact geometrical construction. The history of art and 

 architecture shows that the most beautiful buildings and formal 

 ornamental motifs are those depending upon definite and 

 regular principles. The symmetry of architecture consists 

 of the rhythmical repetition of certain parts of a design in 

 relation to a plan or scheme as a whole, or uniformity as 

 regards the answering of one part to another. The symmetrical 

 forms of Nature have the same interdependence of detail. If a 

 flower is examined which possesses a definite and unmistakable 

 symmetrical adjustment of part to whole, it will furnish a case in 

 point. If even a glimpse could be obtained of the manner in which 

 Nature made the adjustment of her detail, it seemed not unreason- 

 able to expect that the principles involved would be of assistance 

 to design. Even a casual examination showed that much of the 

 harmony of relationship of parts in regular objects could be 

 expressed graphically by geometrical lines. It was found by 

 experiment that this expression was very simple. In most cases, 

 a few circles described concentrically would entirely satisfy 



1 Abstract of a paper read before the Hellenic Society on November 4 by 

 Mr. Jay Hambidge. 



NO. 1725, VOL. 67] 



zones of symmetry involved in some forms. In addition to the 

 formal plans disclosed in plants, with their leaves, flowers and 

 fruit, the author investigated the beautiful curves of the wings 

 and bodies of butterflies, beetles, moths and bees. He found 

 that in all such examples, these curves were best satisfied by the 

 tangent arcs of circles which had their radii determined by a 

 simple ratio. This ratio almost invariably was a double or 

 binary one, the unit being obtained from the length of the 

 subject's body. With such a unit as a radius, a circle would be 

 described ; the diameter of it would be taken as a radius for 

 another, the radius of this for still another, and so on. This 

 progression would be continued until enough arcs had been 

 secured to satisfy all the curves involved. The tangent arcs of 

 circles so related would satisfy these curves, so that it would be 

 impossible for the eye to detect any difference between the 

 approximated and the actual form. 



The circles used to satisfy curves of natural objects in this 

 manner may be termed binary circles. They are really circles 

 having radii which form a geometrical progression with a ratio 

 of two. By describing these binary circles concentrically, many 

 proportions involved in the plans of certain forms were 

 accounted for. There were other proportions, however, which 

 these circles did not explain, but the three simple figures which 

 compose the regular polyhedra are involved in the construction 



Fig. 



A A 

 B B 

 CC 



DA 

 □ B 



Primary Circle 1. 



Circle I derived from in A. 



Circle 2 ,, ,, □ in A. 



Q in Circle A. 

 The symmetry expressed formally. 



Cross section of young 

 fruit and contained 

 seeds of the verbena. 



to satisfy them. There are but five possible regular polyhedra, 

 and the three simple figures which compose their faces are the 

 equilateral triangle, the square and the regular pentagon. Once 

 having obtained the primary circles, these simple regular figures 

 may be inscribed in any one of a binary series and a side of 

 each used as a radius to describe others concentrically. 



With this simple geometrical formula, it is possible to account 

 for every possible combination of symmetry and proportion. 

 Snow crystals and mineral crystals furnished, so to speak, the 

 converse aspect of the curved forms of organic nature. The 

 straight lines used in the graphic expression of the form of a 

 crystal of any system may be shown to be connected with circles 

 such as have been described. The precision with which this 

 formula analyses the symmetrical shapes of Nature is very 

 remarkable. 



If the master architects and decorative artists of the past 

 were guided by Nature, we ought to find an agreement between 

 the proportions of curve and straight line which they employed 

 in their plans and the plans of regular natural objects. This is 

 exactly what a general analysis of architecture and formal art 

 has disclosed. As the designer has used good or bad propor- 

 tions in his architectural and decorative compositions, there 

 may be found, by this method of analysis and comparison, 

 harmony with the proportions which Nature employs. 



The fact that the simple figures of the polyhedra are involved 

 in all symmetrical forms of Nature has naturally suggested that 

 their proportional properties be investigated. If these figures 

 are considered as representing elements of symmetry and the 



