186 



niSCOVERY 



Billington (John Richardson, London, about 1820), it 

 is stated that the principal nave of St. Peter's is 610 

 feet in h-ngth and the transverse is 457 feet. These 



a- -BUI' 



£Ej 



FIG.l. 



FIG.2. 



F1G.5 



FIG. 7. 



F1G.6. 



figures are within eight inches of absolute agreement 

 with the ratio of 4 to 3. 



In the grottoes of Benihassen, on the Nile, are two 

 chambers whose measurements are given as length, 

 52 feet 5 inches ; breadth, 39 feet 4 inches. The floors 

 of these chambers thus form rectangles in the ratio of 

 4 to 3, with a discrepancy of only one-third of an inch. 

 (For measurements, see Narrative of a Journey in Egypt, 

 b}' Thomas Legh, M.P. : Murray, 1816.) 



The houses at Priene usually occupied a space of 

 80 feet by 60 feet {The Planning of Hellenistic Cities, 

 Professor Percy Gardner ; Transactions of Town Plan- 

 ning Conference in London, 1910). At Silchester the 

 remains of the old streets can be traced, and are laid 

 out at right angles, with one large rectangle in the 

 proportion of 4 to 3 for the central part of the town 

 (Professor F. Haverfield, in above Transactions). 



In English black-and-white buildings the prevalence 

 of this root figure is very marked in the proportions of 

 windows, timber-framing, roof gables, and sizes of rooms. 

 E.xamples will be found in Hall-i'-th'-Woods, Bolton, 

 illustrated in Building World, November 27, 1915 ; 

 Bamfurlong Hall, in Building World, January 22, 1910 ; 

 Old Clergy House, Alfriston, in Building World, 

 November 25, 191 1. Other examples might be added 

 from French and Italian work. 



By another combination of the root triangles, in the 

 manner shown in Fig. 2, a rectangle in the proportion 

 of 8 to 3 is obtained. In the Bottom Chamber in the 

 Great Pyramid the end wall is said to measure 27 feet 



by 10 feet 6 inches, which is within 4J inches of the 

 above proportion. The measurements are taken from 

 Chambers's Encyclopcsdia. 



The main hall at Hampton Court is described in 

 Cresey's Civil Engineering as measuring 106 feet by 

 40 feet. This is within 3 inches of the theoretical 

 length calculated from the above ratio. 



The arrangement shown in Fig. 3 gives a rectangle 

 measuring 6 by 4, or li to i. It can be traced in 

 Moorish work, but an interesting English example is 

 the crypt of Kipon Cathedral, which, according to 

 Bell's Cathedral Series, measures 11 feet 5 inches by 

 7 feet 7 inches. In this case the cedculated width is 

 within one-third of an inch of the recorded width. 



In Fig. 4 is shown how the triangles are combined to 

 form a rectangle measuring 9 by 4, a ratio which is 

 sometimes found in ancient work. Thus, in the 

 Journey of Mr. Thomas Legh, referred to above, the 

 excavated temple at Guerfeh Hassan is said to measure 

 34 feet 6 inches by 15 feet 6 inches. The discrepancy 

 here is 2 inches from the theoretical width. 



An extremely interesting example of this proportion 

 is afforded by the Parthenon at Athens. The measure- 

 ments of this building, as given in Harmsuorth's Ency- 

 clopcsdia, are 227 feet by loi feet. By calculation the 

 wddth is found to be within ij inch of the recorded 

 width. 



/I 



; \ 



FIG.8. 



A remarkable use of the root figure is shown in 

 Fig. 5, where three right-angled triangles, each with 

 sides in the ratio of 3, 4, and 5, are combined to 



