REPORT OF A SURVEY OF THE DILAPIDATED PORTIONS OF HEREFORD CATHEDRAL, IN THE YEAR 1841 : BY THE REV. ROBERT WH^LIS, M.A., F.R.S., OF CAIUS COLLEGE, CAMBRIDGE, AND JACKSONIAN PROFESSOR OF THAT UNIVERSITY. HEREFORD : PRINTED BY THOMAS N. WEBB, 1842. The Dean and Chapter of Hereford, in giving to the Public this interesting and valuable report, cannot refrain from expressing their thankfulness to the Lord Bishop of Hereford, for having sug- gested a reference to Mr. Professor Willis, as a measure which could not be otherwise than satisfac- tory to all parties, and for his kind intervention in ob- taining the Professor's consent. To that gentle- man they cannot adequately express the sense they entertain of the zeal and ability which he evidenced in the investigation of their venerable Cathedral, and the obligation which they gratefully acknowledge for the laborious and indefatigable attention which he devoted to it. Hereford, March 1, 1841. Cambridge, September 22, 1841. Gentlemen, In compliance with your request, I have examined the Cathedral of Hereford, and have embodied the results of my observations in the accom- panying Report, in rvhich I have endeavoured to des- cribe the present state of the building, — especially of the tower and its piers, — as well as to trace the history of its several failures and repairs — an investigation which will, I hope, possess some interest for you. In pointing out the parts which require immediate resto- ration, I have not ventured to indicate the exact man- ner or extent of the repairs, which must of course be left to the judgment of your architect, whose skill has been already so successfully exerted in the similar cases of Rochester and Armagh. Should I not have succeeded in making myself intelligible in any portion of the following pages, I shall have great pleasure in supplying the required explanations, and remain. Gentlemen, Yours most sincerely, R. WILLIS. The Very Rev. the Dean and Chapter of Hereford. ON THE PRESENT STATE OF THE CATHEDRAL OF HEREFOED. AND ON THE CAUSES WHICH HAVE LED TO IT. Every part of the building exhibits settlements and consequent distortions to a much greater degree than is generally the case with buildings of the same age. Thus^ the eastern gable of the choir inclines considerably to the east, and the south wall of the Lady Chapel to the south ; the walls of the north transept inchne northwards and outwards in all du-ections, and the buttresses of its western wall are also thrust northwards. The north porch, com- monly attributed to Bishop Booth, is also considerably inclined to the north, and the piers of the nave to the west ; in short there is scarcely a vertical wall or pier in the whole building, with the exception perhaps of the Audley Chapel. When these several settlements are carefully examined, 6 they appear to be of such a nature as would arise more from compression of the ground or foundation upon which they stand, than from weakness of the walls themselves, for these walls and piers are not bent into a convex form, as they would be if they had given way from constructive weakness, but are thrust bodily over, sinking into the ground on the yielding side. This may, for example, be observed in the piers of the nave, near the great tower, both on the north and south sides. The greater part of these settlements however, can be shewn to be of great antiquity, having as might be expected, taken place very soon after the building was finished, and there is no fear of their going any further, except in those cases in which the original settlements may have so weakened the walls, by fracturing and displacing their materials as to allow them to sink under their own weight or that of the subsequent additions. For the purpose of examining the nature of the founda- tions, excavations have been made by Mr. Cottingham, at the bases of the piers on the south side of the nave, and about that of the northern piers of the tower. From these, as well as from an excavation in the centre of the nave, it appears that at a depth of about seven feet below the present pavement, there is a firm bed of gravel, which, from deeper sinkings in the neighbourhood of the Cathedral, is ascer- 7 tained to extend to a great depth, forming what must be con- sidered to be an unexceptionable foundation ; and since the new work of Mr, Wyatt, as well as the Audley chapel re- mains perfectly upright, it is thus shewn that the ground when properly treated admits of a solid bearing. Again, as the settlements might have been supposed to have arisen from springs of water immediately under the building, search and enquiry has been directed to this point without discovering any. Immediately upon the surface of the bed of gi-avel, a wall about five feet high is placed. The stones of which it is built are rough from the quarry and are in seven courses; they are from 15 to 18 inches long at the lower part, and rather less at the upper, and the breadth of the wall is about four feet greater than the bases of the piers which stand upon it ; two of these walls appear to extend from one end of the Cathedral to the other — from west to east, — the one receiving the northern and the other the southern range of piers as well as the piers of the central tower. The squared masonry of the bases of the piers rests upon the upper surface of these walls. Of course the rough structure of the walls prevents the detection of any settle- ment or displacement ; but I am of opinion that it is rather this basement wall, than the gravel below which has given way, and allowed the piers to sink down and lean over as they do at present. 8 The walls of the Audley Chapel are, as already stated, perfectly upright, but the south wall of the Lady Chapel, agamst which it is erected, and into which its masonry is bonded, declines very considerably to the south ; plainly, therefore, this settlement must have existed before the Audley Chapel was erected, and cannot have increased since the year 1500 ; on the other hand, the eastern gable of the Lady Chapel is in a state of ruinous disintegration, and re- quires immediate repair to save it from the fate of the west end of the Cathedral. The inclination of the walls and buttresses of the north transept, and of Booth's Porch, are original settlements, and nothing is to be apprehended from them or from that of the eastern gable of the Choir, the en- tire ponderous Norman wall of which, has evidently gone to the east, and possibly its upper gable may have been re- duced to such a ruinous condition as to have justified the rebuilding of it by Mr. Wyatt. But my attention has been more particularly directed to the state of the tower, and to understand the result of ray observations, it will be necessary to say somewhat of the history of its erection. It is clear that the piers and the four great arches that rest upon them are of Norman work, and that at some sub- sequent period, the present tower, which rises above the roofs, was added. Whether a Norman tower was ever carried 9 above the roof, and consequently taken down to make way for the present erection, is uncertain; I am inchned to think not. The line of demarcation between the Norman wall and that of the added tower is easily traced. The up- per limit of the Norman work is marked by a string course, ornamented with a double row of little arch-heads, and the additional work commences just above this, in a manner that will be described below. The erection of this tower is not recorded, but from the style of its ornaments, may be fixed at the beginning of the fourteenth century. The date usually assigned to it is a century earlier — it being sup- posed the work of Bishop de Braos ; but this date, repeated by every successive historian, merely rests on a passage of Godwin, who in his biography of this Bishop,* says, " That his effigy has a model of a tower in its hand, whence he conjectures that he must have been the builder of the cen- tral tower." This date is thus founded upon no document, and being contradicted by the now well-understood archi- tectural style of the tower, may be dismissed as possessing no authority. It is much to be regretted that the period of erection of no one part of this Cathedral has been recorded, with the exception of its first foundation. It is established, however, that Bishop Cantilupe died in 1282 and was bu- ried in the Lady Chapel, that his reputed sanctity and the * De PrsESulibu?, 1616, p 536. B 10 miracles which were said to have been wrought at his tomb, brought considerable sums to the church, and that his body was removed to the north transept in 1287 ; also that he was canonized in 1307. The style of the north transept agrees with the suppo- sition that it was erected for the reception of the shrine of Cantilupe, between his death and the translation of his body; and the superior magnificence of the design be- speaks the increase of riches and consequence which this event had brought to the Cathedral. To the same source and the same circumstances may be attributed the new tower, of which, if we place the date at about 1300, or a little later, it will appear to have been undertaken imme- diately after the completion of the north transept, and pro- bably from the funds which still arose from the same pro- fitable source. And this may account for the omission of any recorded founder or benefactor in connection with either the work of the north transept or of this tower ; for it may be generally observed, with respect to the buildings of the middle ages, that when they were carried on by their monasteries, no record is preserved of the work, but only when some considerable portion of it, as a tower, a transept, or the vaulting of an aisle, was undertaken at the expense of an individual. Thus it happens in the pre- sent instance, that the building of the Lady Chapel and its vestibule, the clerestory and vault of the choir and nave. 11 all of them works of the twelfth and thirteenth centuries, are not recorded. To be sure Leland has recorded of Bishop de Vere, who died in 1199, that he constructed many remarkable edifices (on the authority of his epitaph), and we may assign some of these works to him, if we please. To return however to the tower ; it is evident that at the time of the addition of the present tower, the piers and the four great Norman arches, upon which it was placed, were in a state of great dislocation and settlement. If the south-east pier be examined in connection with the east Norman wall of the south transept, it will be seen that the masonry of the latter wall near this pier, has been dragged downwards by the settlement of the pier. This is very visible on the inside of the building above the vault, as well as on the outside of the clerestory. It is also shewn by the bending downwards of the string mouldings in the interior of this transept, and also by the difference of level of the opposite impost mouldings of the small Norman arch, which opens between this south transept and the south aisle of the choir ; for we may assume that all these things, namely, the courses of the masonry, the string mouldings, and the two imposts of the arch, were originally respectively level. But when the respective downward dislocations of these three things are carefully measured, they are found to be exactly the same, namely, three inches and a half ; and 12 as thejr are situated at difFerent altitudes, we may conclude that this pier has sunk bodily downwards into the founda- tion through the vertical space of three inches and a half with respect to the wall of the south transept which is of the same age as itself ; but as the foundation is thus shewn to be compressible, it must be supposed that the wall itself must have sunk, although in a less degree, than the pier, and therefore that the actual sinking of the pier must have been greater than three inches and a half In fact, by levelling the courses of masonry in the clerestory wall of this transept, immediately above the vault, I find a dif- ference of level of about ten inches between the southern and northern extremities, which is manifestly due to sinking, and not to inaccurate workmanship, because the courses run nearly level over the piers, and sink in stages over the window heads. A great settlement or subsidence is thus shewn to have taken place between the Norman pier and the Norman wall in connection with it, as well as a positive sinking of each into the foundation. The Norman waU of the choir has also sunk to the same extent, and as the Early English string moulding of its clerestory exhibits the same depression, we must either suppose that the depression happened after the clerestory was added, or that this string moulding was laid upon the Norman wall without levelling it, a supposition which is not inconsistent with the known roughness of the 13 work of that age. The settlement of the south wall of the south transept cannot now be measured, because a large Perpendicular window was inserted on this side, and the wall over it entirely rebuilt during the fifteenth century ; most likely because this part of the wall had been entirely shattered by the subsidence of the tower. Neither can the settlements of the tower piers, with respect to the walls of the nave, be ascertained, in consequence of the entire re- building of the clerestory and triforium by Mr. Wyatt. The two southern piers of the tower being in immediate connexion with walls of their own age, their subsidence is thus as it were recorded for our information. But the two northern piers are now connected with the northern or Cantilupe transept, which was built more than two cen- turies later, and probably replaced a Norman transept similar to the southern. The eastern clerestory wall of this north transept, is, however, not at all disturbed by dragging downwards with the pier, and we may therefore conclude that the subsidence of the piers had ceased before the year 1300, for it will be shewn that the two northern piers had in themselves suf- fered quite as much, if not more, from settlements than the southern ones. If then, their j unction with walls two cen- turies later, exhibits no signs of relative motion, we may plainly infer that all the subsidence of the piers had taken 14 place before these walls were connected to tliem. It is true that the western wall of the north transept, exhibits a great dislocation of form ; the entire mass of masonry which forms the southern side of the lofty window, forty feet high, has shrunk and slipped away from its junction with the Norman wall, and settled downwards and northwards, bulging out and bending the iron bars of the window, and rendering an immediate repair necessary. But this is a local settlement, unconnected with that of the Norman pier and occasioned by the difficulty of establishing a firm bond between new work and old, for the clerestory and the upper part of this wall between the roofs exhibit no signs of having been dragged downwards by the tower pier. When the great piers themselves are examined below, especially the two western, it is evident that they have suffered great disturbances. The greater part of the original Norman ashlering is now either covered by subsequent casing, or has been removed and rebuilt ; nevertheless, the Norman capitals, from which the four tower arches spring, remain, and on several faces of the piers, the position of the corresponding shafts can be ascertained. This is the case with the southern face of the north-western pier. The lower portion of the pair of Norman shafts remains with the bases, and one of them still exists to the height of thirty-three feet. These shafts are still vertical, but the capitals, which undoubtedly were originally placed imme- 15 diately over them, are now removed by settlements, together with the entire western arch of the tower, through the enormous space of ten inches and a half to the west. Also two cylindrical piers of the nave on each side, and con- tiguous to the piers of the tower are pushed bodily over, so that their impost mouldings are now four inches and a half to the west of their true position ; in fact every pier of the nave has gone to the west in a slight degree. The Norman nave-arches which rest upon them have suffered a corresponding distortion of form, which is the most evident in that arch which connects the first cylindrical pier on the north side, with the half column that projects from the tower pier ; for the half column has remained up- right while the cylindrical pier has been pushed over as- already described. The Norman triforium aud clerestory which once sur- mounted these piers, were destroyed by Mr. Wyatt, but the nature of the settlements just described — namely, that the capitals of the tower piers have gone so considerably to the west, while the lower half of the same pier remains vertical, and yet that all the piers of the nave are also driven to the west, — demonstrates that the upper part of the pier must have separat(id itself from the lower, by a diagonal fis- sure extending from the upper eastern portion to the lower westera, and that the western half of the mass so separated, must have slipped downwards, and by pressing 16 against the walls and columns of the nave, have produced their present change of position. And that the upper part of this pier with the entire western tower arch sank in this manner downwards and west- wards, will also be shewn from the present state of the Nor- man string course over the great tower arches. I should also mention that the capitals of the shafts on the western face of the north-eastern pier have been similarly driven to the north about four inches, and that the south-western pier has undergone nearly the same settlement as the north-western. Now the upper extremities of the great piers having thus moved from their true position, the four great Norman tower arches which rest upon them, are necessarily distorted in a very great degree. Two of these arches, the north and south, are smaller than the east and west: the respective spans being about nineteen and thirty-one feet. Immediately above these arches, a Norman string course projects from the wall ; this was of course horizontal when first executed, and its deviations from horizontality serve to mark the extent of the dislocations of the arches below it. The western arch appears to have preserved its form tolerably well, and in fact, as the two piers upon which it rests have gone together towards the west, without diverging, this arch appears to have settled bodily with them without change 17 of form. The other three arches have suffered great dis- turbance ; their original semicircular outline being now converted into an ellipse by the sinking of the crowns, occasioned by the divergence of the piers ; for since the capitals of the north-west and south-west piers have each moved ten inches to the west, and that of the north-east four inches to the north, it follows that all the four arches, except the west, have spread at tlie feet, and therefore must have sunk at the crown. I have levelled and examined the present state of the Norman string course, and I find that its north-west extremity is seven inches lower than its north-east, shewing the sinking of the north-west pier, which has been already detected from other appearances. Also the north-east end is two inches higher than the south-east end, and on this side the string course has sagged in the middle so as to fall about six inches lower in the centre than at the two ends, this is produced by the sinking of the crown of the eastern arch j again, the south-east angle is one inch and a half higher than the south-west, and the string sags about four inches in the middle; over the western arch the string course has been removed, but the south-western angle is three inches and a half higher than the north-western. These differences are too great to be attributed to bad workmanship, and they all point to the c 18 same facts that have been attested by the other appearances described, namely, that the piers have all subsided and that the north-western has suffered the most ; besides these appearances, the masonry of the spandi-els — ^that is, of the walls included between the Norman arches below, and the string course above, — is ia a frightful state of disloca- tion ; for the change of form in the arches has twisted and fractured the stones in all directions, besides drawing them asunder so as to open the joints in many places to the extent of two inches or more. The rubble work in the heart of the wall has lost aU cohesion. Upon these arches, however, and in this state of ruin or very nearly so, did the architect of the tower in 130O proceed to erect his work. That this was the case is shewn by the following evidence : — The masonry of the new tower begins at the level of the Norman string or a little above it, the junction of the two works being very easily traced. About four feet above the Norman string, a second or gothic string course is placed at the same level as the passage or gallery which rims in the thickness oi the wall all round the tower, and upon this string course is supported the singular row of piers which constitute the interior lining of the tower. Now the Norman string course has been shewn to be completely out of level at the corners, besides sagging in 19 the middles. But this gothic string course on the contrary, is now so nearly level with respect to the comers, that the difference may be attributed to errors of workmanship, and it has only sagged in the centre about half an inch on the east and north, and not at all on the other two sides. Also the lower bed of the first course of gothic masonry which rests upon the Norman wall, is exactly shaped to accomodate the sagging already described, but its upper bed is straight and level, proving decidedly that the entire present settlement of the Norman work had taken place before the tower was added, with the exception of a slight subsequent disturbance, of which I shall speak presently. On the north and south walls, immediately above the Norman string course, may be traced a regular series of apertures in the face of the wall, about eleven inches square, in which were evidently once inserted the beams of a floor or ceiling. These apertm-es follow the sinking line of the Norman work, and not the level line of the tower work ; con- sequently they indicate the position of the original Norman ceiling, which is now replaced by a vault of the fifteenth century. As the lines of this vault cut through the level of the floor, this last was necessarily removed to make way for it. These holes on the north side, have been rudely stop- ped up with blocks of tufa — the light substance used in vaulting — from which, we may suppose that the beams were 20 removed and the holes stopped when the vault was in pro- gress, and consequently this material at hand. At all events, the jointing of the masonry shews very clearly that the floor beams were not removed at the time the walls were carried up ; for it is evident that the new masonry was built roimd and about the beams, in a way that it is not easy to describe without drawings, but which plainly shews that the beams were left undisturbed. At each angle of the tower, and at the same level as these beam holes, is a diagonal aperture higher than they are, and extending nearly through the wall ; now the pur- pose of the beam holes cannot be mistaken, and we have seen that the new masonry was built round them without disturbing them, and I conclude that these similarly diago- nal holes also received some timber work, which in like manner was allowed to remain undisturbed. The interior walls of the tower are of a very singular construction : twelve piers of compact masonry on each side, beside angle piers, are carried up to the height of twenty-six feet, and connected half way up by a horizon- tal course of stone, in long pieces, and by an iron bar, which runs all round immediately imder this bonding course. Upon these gigantic stone gratings, if I may be allowed the expression, the interior wall of the tower rests; and they also carry the entire weight of the bell- 21 cliamber and bells. I believe this construction was entire- ly adopted for the sake of lightness. It is clear that it was never intended to be seen from br/7t To Svnm /ookmc/ Hasf . LETTEES FROM THE VERY REV. THE DEAN OF HEREFORD, AND THE REV. PROFESSOR WILLIS, IN REPLY. Letter from the Dean of Hereford TO Mr. Professor Willis. Deanery^ Hereford, July 12th, 1842, My dear Mr. Professor, I learn from the Bishop that he sent ;you a newspaper, in which was a Report of our Pro- jceedings at the County Meeting; it was of course, a very j imperfect Report, and did not fully detail our humble « efforts; however, the result has more than answered our (expectations, as it has removed the doubts and prejudices Awhich existed in many quarters. 40 My object in now writing to you is to request that you will give me a little explanation of one point in your admirable and most valuable Report, which has caused me some little embarrassment. You say in the last page, after declaring the necessity of further examination behind the casings of at least two of the Norman piers, " I do not think it neccessary or expedient to restore the original form of the Norman piers. The repairs, which are as I have shewn, themselves of sufficient antiquity to claim respect, have so far ad- vanced the faces of these piers in many places, and removed the Norman shafts in others, and the settlements have so disturbed the capitals from their true positions that any attempt to restore their original form and replace the shafts must be attended with very great expense." Now, as it is obvious that at least two of the piers must be in great measure refaced, and the estimate of the architect includes the restoration of the shafts and piers, would it not be a pity to reconstruct them in their present form, would not the original form be equally or probably more efficient to bear the weight, when so restored, and if so, would not the uniformity of the whole four piers in their original style be most desirable, especially as the capitals, with one exception only, are perfect, and portions of the shafts projecting and visible, I am of course aware that these 41 must be restored to their perpendicular line. I should be glad to know whether your remarks are merely in reference to the question of expense, or to the safety of ' the process of restoration, or the efficiency of the piers to bear the weight when restored to their original form as now intended by the architect, who proposes so to restore them, feels confident of the practicability and safety of the process, and has calculated the costs to meet the under- taking. If there were funds for it would it be objectionable to do it ? I confess I have no love for the mended por- tions, and would gladly see the restoration if possible, but I wish to be prudent, and shall be most thankfiil for your explanation. If you could give it to me before the diocesan meeting of the 21st, at Ludlow, it would be the more valuable to me. I think 1 before asked if you would allow your Report to be printed with other docu- ments — ^you cannot fully know how much I value the in- defatigable labour which you devoted to the investigation of our fabric, and how thankful we all of us feel to you for such important assistance, and remain. My dear Mr. Professor, Yom' obhged and faithful servant, JOHN MEREWETHER. 42 Mr. Professor Willis TO The Dean of Hereford. Parker's Piece, Cambridge, January 20, 1842. My Dear Mr. Dean, My object in writing the Report was to confine myself as closely as possible to the questions of structure and history, with a view to discover how much was to be feared from the present state of the building, and how much was absolutely required in the way of repair under the circumstances of very limited funds. Beheving as I do, the south-eastern pier to be in a perfectly sound state, and the north-eastern pier to be also quite safe, I did not think myself justified m recommending the expenditure of any portion of the funds upon them. Whether, sup- posing an ample sum to be raised, these piers should be restored to the Norman form is a question of taste about which much might be said. I have endeavoured to shew in the Report that the ashlaring of these two piers is of considerable antiquity, and that in all probability it is not a casuig under which the original Norman work remains, but a replacing of the Norman ashlaring. These piers will also be covered to a considerable height by the stall work. In Hereford Cathedral, as in many 43 others, there is a mixture of all styles. The choir is Nor- man below and Early English above ; the north transept Early Decorated ; the vault of the tower and of the Norman sonth transept of Late Decorated work and so on, and all these dissimilar portions are seen at once and do not admit of being changed so as to make the whole Norman in style. For this reason I do not as a question of taste see the necessity of restoring the Norman face and form of piers which are in a sound state. But as the north-western and south-western piers, especially the for- mer, are in a very unsightly garb and unsafe, the experi- ment of restoration may be tried upon one of them, and it will then be found whether the internal state of the piers and the appearance when finished is such as to justify the expenditure, and also how far the estimate may be relied on, for in works of this nature it is not easy to predict all the sources of expense as in the case of a new building. I am delighted to hear that my labors have in any shape contributed to the fiirtherance of so good a work. I can assure you that I always look back with pleasure upon the investigation, which has been to me a source of the greatest possible interest. Pray send it to press if you think that by its publication it will attract any additional interest towards the works. I shall merely request that the proof sheets be sent to me for correction ; as, in all probability, 44 there may be errors and redundancies which have escaped me in the haste of writing. I have only now returned from London, and I feai- this letter will be too late for your meeting. I remain, yours most sincerely, R. WILLIS. PRINTED BY T. N. WEBB, HEREFORD. linirrCij at Stationers' liall. A KEY TO PROPORTIONS OF THE PARTHENON, " This perfect recovery of the hght that guided the Athenian artists, can alone raise the arts connected with the geometry out of the errors that ages of darkness have cast around them ; this alone can restore them to their true position among the exact sciences, and eventually place the arts of Europe on a level with the present advanced state of general science." — John Pennethorne, 1844. It is left to others to determine the cause hitherto, of the general very great " want of perception " of the necessity for a public exhibition of diagrams, models of curved solids, numerous simple apparatus and their curved results, consecutively and per- manently arranged in a Gallery for inspection and comparison — for " experiment and observation " — for a far more extended knowledge of practical geome- try than an individual unaided can ever accomplish; to instruct the mind and the eye, in reference to proportion and form of definite curved lines and curved surfaces, and their intersections, and projec- tions, especially applicable to architecture ; for unless true principles are accurately known, they cannot justly be either appreciated, or with strict propriety be introduced in design. 4 It is however some encouragement to persevere single handed, to be enabled to submit such a number of facts in immediate connexion, and these proved by geometrical construction and by calcula- tion, which place beyond a doubt that the ancient Greeks have recorded in the Parthenon, much knowledge which has been since long lost, that they had acquired of geometrical laws, and to which their unrivalled success in architecture and the arts must be attributed. Mr. Penrose's Measurements of Upper Step, ivith their differences and averages. Feet. Difference. 1. East end at top 101-34l\ ^^^^ West end at top 101-347 J 2)202-688 Average 101-344 2. North side at top 228-141 South side at top 228-154 2)456-295 Average 228-147 3. Inclination of upper step '023 Average of end on top 101*344 Average of end at bottom...^.J^101-367 5 4. Inclination of upper step '028 Average of sides on top 228*147 Average of sides at bottom .... 228*170 On Proportion, 4 : 9. These averages for the length of the bottom of the upper • step at the ends, and the sides, form a parallelogram of very nearly the proportion 4:9; which proportion it is considered from the general evidence the mason's lines by which the steps were set, in reality originally was. Therefore : To the average of ends at bottom Allow for space for mason's line to hang clear of work — for any minute error in original setting out and in workman- ship — also for alterations by time during more than 2000 years — and for any inaccuracy in the measurements by Mr. Penrose The calculated full length of ends as originally set out .... 101*367 •073 ! ! ! ! 101*440 6. Then the average of sides of upper step at bottom Allow for space for mason's line, &c., as before, for ends 228*170 long •073 ! ! ! ! 6 The calculated full length of sides as set out 7. The half of -073 = -036 ; or less than one half of an inch, being added all round bottom of upper step as measured by Mr. Penrose, gives a parallelogram for the mason's line of 101-44 feet by 228-24 feet in the exact proportion of 4 : 9. Setting off a Right Angle, &c. There are various v^ays by which a right angle may be formed, amongst which a right angled triangle can be made and such a parallelogram may be set off by the proportions 3, 4, and 6, geometrically ; or by figures thus : 1 produced 3 times = 3 = one leg. , ^ ^ I another leg and end '{ of parallelogram . 4 + 1 . = 5 = hypothenuse. 4 + 5 . =9 = side of parallelogram. Or, further, calculated from the full length of upper step at one end of the Parthenon, thus : Full length, equal j ^ 101-44 leg ^ • = 50-72 one | 2 50-72 = 25-36 one ^ 2 228-243 7 25-36 + 3- or I 50-72 4- 25-36) 101-44+ 25-36 76-08 another leg = 126-80 = Hypothenuse. 101-44 + 126-80 = 228-24 = length of parallelogram = upper step at side. Or, with one half, or one quarter, or any other definite proportion of the full length of the end upper step, between the mason's lines at the sides, the other measures can be calculated, a right angle formed, and the breadth and length of a parallelogram of the upper step set off in the proportion of 4 to 9. On the Curvature of Upper Step, Sgc. Having advanced thus far, and supposing that stakes or blocks of stone to be fixed outside at the four angles of the temple, and to and from these the mason's lines fixed and stretched, at ends and sides, by which to guide the workmen to set the blocks for the upper step:— the thought occurred to the author that, although on a horizontal plane, these mason's lines would appear as right lines ; yet, as they would swag, on vertical planes they would be catenary curves ; and that just as much as these may be below a horizontal line at every point, if set off" as much above, might give the delicate curve of the top of the upper step, at any number of points. This very simple method on trial has been found 8 to be correct. Exactly coinciding with Mr. Penrose s points. Thus the ancient Greeks knew and applied in architecture, catenary curves ! ! The curve the full length at East end of the upper step the author set off ; and also the curve of the Entasis the full length of a column, at the Architectural Museum, Canon Row, Parliament Street, Westminster, for a lecture on the 28th of May, 1855. The model still remains there for the inspection, and it is to be hoped, for the conviction of some of those who have doubted the very existence and have ridiculed the idea of such delicately varying lines having ever been applied in architectural constructions. Other delicate curves, as for the architrave above the columns, &c., may be set off in the same way, with facility and great accuracy. Such curves, although perfectly distinct on the full sized scale, and even on a very minute scale, the eye may be instructed to observe very delicate variations in lines, they cannot well be represented on the paper of a book. On the peculiar arrangement of the exterior Columns surrounding the Parthenon. In order that the positions of the columns at the sides and the ends of the Parthenon should per- fectly harmonize, it was seen to be necessary to make centres of fourth openings between columns 9 at the sides, at the same distance from the angles, as from the angles to the centres of the ends ; also in counting from sides the middles of fourth open- ings. By setting off one half the length of the end of the parallelogram from each angle along the sides, the sides are thus divided into three spaces ; viz., 50-72 + 126-8 + 50-72 = 228-24 = the full length of a side = the longest leg added to the hypothenuse The ends into two 50-72 + 50*72 = 101-44. Then the = 14-08888 = the general dis- tance from centre to centre of columns. There are 14 of these equal divisions on each side; therefore 14-08888 x 14 = 197-24444 = distance between the centres of second columns from the ends ; and there are 5 of these equal divi- sions at each end, therefore 14-08888 x 5 = 70-4444 = distance between second columns from each side. Now, 228-24 — 197-24444 = 30-99555. and, 101-44 — 70-4444 = 30-99555. asain 99555 __ ^5. 49 •777 — the distance from o 2 corner of the upper step (mason's line) to the centre of the second column, both at the sides and at the ends. Next, 15-49777 — 14-08888 ] and 14-08888 = 1-40888. 10^ J ^ This, thus, twice derived number, is proposed to be called the pivot. 10 On the eocact position and dimension of the surrounding Columns. This number 1*40888, is the difference between the sides of an inscribed and a circumscribed square to a circle : and 1*40888 is also the side of a square; the diagonal of which is 1*9922; and 1*9922 + 1*40888 = 3*4011 = the distance from the mason's line to the line of centres of all the columns at the sides and the ends of temple ; and also = to the side of the inscribed square ; the diagonal of which is = 4*8099 = the side of circumscribed square, and = the top diameter of intermediate columns. Again, 4*8099 + 1*40888 = 6*2188 = diameter of intermediate columns at hottorn. Further, the sum of the sides of the inscribed square = 3*4011 x 4 = 13*6044 ; and the sum of the sides of the circum- scribed square = 4.8099 x 4 = 19*2399 ; Sum of sides of both squares = 32*8444 Then 82*8444 — 1*40888 = 31*4355 = height of shaft of column, and 81*4355 + = 88*1360 = height to abacas ; next 32*8444 + 1*40888 = 34*2538 = full height of column to top of abacas. Further, 3*4011 x 2 6*8022 = breadth, or side of square of abacas. And, 34*2538 — 31*4355 = 1-40888 x 2 = 2*8177 = height of curved portion of capital. To conclude, — ^ = -70444 = varsed-sine to the chord, the side of inscribed square ; also it is the side of a square, formed by producing sides of I 11 iniscribed square to sides of circumscribed square. 6'2 1 8 8 TFhe diagonal of this square = -9961, and — ^ — 4*8099 = 3-1094 = radius at bottom ; and last, — — = 2- 4049 = radius at top of column. All this, when set out geometrically full size, beecomes simple and quite obvious : or by diagrams maay be illustrated. By the process described every necessary dimen- sidon is obtained for more than fifty thousand super- fidcial feet of the surface of the Parthenon being eaxecuted accurately ; or if the whole of the parallel- opgram enclosed by the upper step be taken, more thhan seventy thousand superficial feet! and, all this inn proportion for a building of any other size, may boe obtained by the same process from any given leength for end upper step : and doubtless all the pDrocess to execute every other proportion in the teemple may now be rediscovered. Very much of what is now given might be set ODut and exhibited full size temporarily, at the Archi- tdectural Museum ; and permanently, as well as the ccurves of the upper step and the entasis of the ccolumns, be placed in the British Museum, for which sppace can be pointed out, in connexion with the re- ranains of the Parthenon there ; for the inspection and iiinstruction of the tens of thousands who visit that TTemple of Knowledge. The following comparison of Mr. Penrose's mea- sisurements with the author's calculations it is hoped ^^^vi\\ make this process distinct. CO o CO CO 00 o 00 CD CO o t— 1 00 1—1 o >o cb do o ^ CO 11 ^ s 00 ^ g O (U 03 ^ rjq ^ 0,00 S ~ ai CO y ID CD CTS T-i r7-i O C5 ^3 3 a* o o o C3 00 O O o ^ :g ;g 'jH (L_ «*H y o O O CD 10 o 53 CO CO tc 03 a; ^ rjq § H -Go §_§ § t„ ^ CO IV, O a> C3 O Oh c5 C8 (M* o CO X'^ 00 oT 00 h 00 § S §^ y XD r- 1 1X5 11:2 u s o,.- . O O e<-i OJ O ITS Eh '''^ O t<_| o O T3 ' o 1^ 0) o a + 3 ^ ^ CT' O O be 02 03 a> 05 p3 S 02 CO O 3 a •^3 Sh O CO ceo CO 00 CT> «3 .-I O CO ^ CO C<> CO 00 CD CO C5 C<1 r— I 1— I T-H CO CO CO r- 1 CO (N tJ^ ^ r)H 01 (M T}H CO 01 O r-l Tj< 05 O O 00 00 O 05 I-I ^ CO (M CO CM : : ^ UO • • •