THE CIVIL ENGINEER AND ARCHlTECrS JOURNAL. 



[April, 



eotasis, they are bo at their springing, which may perhaps be Vitruvius's 

 meaning, as lliere is no instance, except, I believe, the temple atTivoli, of 

 so great a declination as he describes. It was well known generally 

 among the ancients that such was the case. Cicero relates an amusing 

 story, in his oration against Verres, how Verres was very anxious to do 

 Bomelliing in the building way, and restore a certain temple of Castor at 

 Syracuse. He came into the temple, and on examining it, found every 

 thing sound and in good repair. He turned about him, and asked his 

 conlideulials what he should do. One of them jokingly said, '• Why, 

 Verres, you have nothing to do here, unless, perhaps, you would like to 

 set the columns perpendicular." That man (Verres), most ignorant on all 

 subjects, asks, " What do you mean by perpendicular ?" They answer 

 him, that there was hardly any column which could be perpendicular. 

 Then said he " By Hercules, let us do so, and put them perpendicular." 

 Cicero thus holds up Verres for derision, for being ignorant on matters of 

 taste. 



It seems to me that the following consideration suggested the inclina- 

 tion given to the columns : — In consequence of the diminution of the 

 columns, the upper spaces become larger than the lower, and as the eye 

 measures the whole length of the architrave by the sum of the inter- 

 columniations, it would appear longer than the step, and consequently the 

 columns would appear to diverge from the ground, unless such inclination 

 be given to the angular columns as shall correct this false impression. 



Vitruvius states that all Ihe members above the capitals should lean 

 outwards ■}^\h of their height. This, 1 believe (and 1 have seen some very 

 careful measurements of Mr. Scoles's, made with reference to this), does 

 not obtain iu any Greek building. The corona of the Parthenon, indeed, 

 has an inclination outwards of 1 in 100, but all the rest of the members lean 

 inwards in the direction of the columns ; it is clear that -j'jlh would be too 

 much, and especially at the angles would appear nearly J(h, which would 

 look preposterous. I have no doubt that the I'/h in the text of Vitruvius 

 is corrupt, or else Vitruvius must have generalized too much; I should 

 prefer the former hypothesis. 



There is a small dill'erence both iu the west front and east front. In 

 the outer intercolurauiations of the Parthenon, that to the south is in both 

 fronts about ^'jth ofafoot wider than the northern one. Can this have arisen 

 from a desire to make the intercolumniations towards Ihe south — which are 

 more seen, both on account of sun and situation — more nearly equal to each 

 other? In the temple of Theseus the same holds but vic^ versi. In both 

 cases the addition is given at the side which from its position is most com- 

 manding. 



The joint of the stone of the architraves next the angles is on both sides 

 made to lie a little within the centre of the column (or towards the centre 

 of portico), by means of which the two metopes next the angles are squares, 

 and the next two diflcr, by a small quantity, from that figure. It must 

 have been thought that it was more important to get the angular metopes 

 exactly symmetrical im each face, than two contiguous ones on the same 

 face. This adjustment, however, is not so apparent on the flanks and west 

 front as it is in the east front ; but the east was the principal front theo- 

 retically, though in the Parthenon the west front was seen more from the 

 town. 



There are some small and curious varieties in the abacus in different 

 parts of the Parthenon. The more ordinary one on the east, west, and 

 north sides is -['jth upper step. The abacus of Ihe angular column is Ij 

 Attic dactyli, or nearly j'jih greater. I divided ^J^th of the upper step of 

 the Parthenon (i. e. one Allic foot, according to Ihe Greek fashion) into 

 16 dactyli, and have found these divisions to agree very well with the 

 smaller dimensions, which were taken by myself as well as by others, and 

 with fragments in Ihe British Museum. 



If the abacus be divided into 30 parts, 28 such parts will give Ihe lower, 

 and 22 parts the upper, diameter of Ihe column. The angular abacus is 

 ^th the height of Ihe column; the thickness of this abacus is Jlh of its 

 breadth. On the south side every abacus is less by -2 feet than those on 

 the north side and fronts, and is equal to Cj' Olympic or Attic feet, or y-jjjof 

 upper step. 



These capitals, being always seen either from the city below, or from the 

 very narrow space between the temple and ihe wall, on the platform itself 

 of the Acropolis, in quick perspective, a large portion of their under sur- 

 face would be seen, which would give them a greater appearance of size 

 than the others, which are not generally viewed from a similar situation, 

 and which would, therefore, appear more as in elevation. The abacus in 

 the British Museum is from the south side. 



1 now come to the entasis of the columns. In the Parthenon it is so 



slight as merely to correct the false impression which the eye always 

 receives from columns wnose sides are really straight lines, for the eye 

 naturally fixes upon and measures the column at the neck, and the spring- 

 ing or base, but has nothing to compare it with in the middle, so it loses at 

 that point in importance and requires compensation. 



The entasis of the columns of Ihe Parthenon is about that which would be 

 given in an Ionic column of Ihe same height, according to Vitruvius's rule, 

 viz., the thickness of the fillet of one flute. I have found, from measure- 

 ments taken at the edge of the flutes, that this curvature results from the 

 columns being hyperboloids of revolution. The generating hyperbola has 

 a principal axis equal to I Attic foot, a focal distance equal to 30 Allic 

 feet ; i. «., the distance between foci is equal to CO Attic feet, the line 

 of the foci at a distance of twice the abacus below the upper step. 



It is well known that the conic sections have been used very generally 

 in these Greek buildings, but 1 am not aware that the exact nature of the 

 entasis has been before demonstrated. In confirmation, I will only appeal 

 to Mr. Scoks. Hearing that he had some accurate measurements of one 

 of the columns, I asked him for his vertical measurements, and promised 

 to bring him Ihe horizontal diameters corresponding. On comparing these 

 with his measurements the coincidence was so striking that I am morally 

 certain that 1 have obtained the true nature of the curve. I have also 

 consulted the dimensions of the columns of Ihe Parthenon, given in the 

 supplement to " Stuart's Athens," wiih a highly satisfactory result ; I 

 have also found the columns of the Theseus.to be hyperbolic. A curve 

 obtained geometrically with line and rule, owing to the unequal action of 

 the elasticity of Ihe string, gives a trifling deviation from the curve obtained 

 by calculation, and approximates still nearer to Ihe entasis of tlie columns. 

 It is not to be supposed that, in forming their columns, the Atheniaa 

 artists struck the hyperbola full size, for then they would have required a 

 straight-edge about fifty feet long, which would have been very unmanage- 

 able ; but any hyperbola, constructed with the same principal axis, viz., 

 = 1013 feet, will have its horizontal abscissa full size, and the vertical 

 ordinates in some proportion, which can be easily determined. Conse- 

 quently, to obtain any number of dimensions for constructing a column 

 like those of the Parthenon we should proceed thus :— 



Take a straightedge H h, about 

 five feet long ; fix a string at one 

 end of this straightedge /i, and let 

 the other end traverse, upon a table 

 or drawing-board, round a fixed 

 point, H, by means of a pin or 

 awl. Let the siring be cut off 

 exactly 2025 feet shorter than the 

 length, H A, of the rod. The string 

 being fixed to the moveable end of 

 the rod h, and to a fixed point S at 

 some convenient distance H S, 

 from H, viz., about three feet. 



Now let the straight-edge revolve about H , and keep the string tight 

 against it with a pencil, as alQ ; thus will an hyperbola, P Q A, be traced 

 on the board, having all its horizontal dimensions equal to the real size, and 

 its vertical according to some scale which can be very easily determined :— 



Draw A V perpendicular to H S, aud, at 



a distance, N P = 



10 13 feet 

 been using, v 



11 



-=•092 feet, draw 



J 



P F parallel with A Y. Then set off 

 FQ = 'G9G feel, which is equal the entire 

 diminution of the column, and the segment 

 Q P will be proportional in height to the 

 shaft of the column, and if it be divided so 

 as to represent 31-4 feet, the scale so ob 

 tained will give the full size entasis at any ^ 

 point required. jj 



A somewhat similar method may be used 

 to obtain any desired entasis for any column that may be required, having 

 first fixed upon the amouut of the entasis and the diminution of Ihe column 

 by first drawing the curve as here described, with any convenient axis and 

 foci, and then applying a straight-edge until we get exactly or approxi- 

 mately the amount of entasis and dimiuulion required; dividing the length 

 of the arc so obtained for a vertical scale of Ihe column ; but as this im- 

 plies something of Uie loose natur e of a tentative process, itwould of 



