The Ground Plan of the Nave
Equilateral triangles like that shown in red in Figure 4 relate the inward extremity of the pier bases to the centre line of the opposite arcade. This geometry was also used at Bristol. A square shown in green with side equal to one bay, edge aligned on the centre line of the south arcade gives the position of the glass in the aisle windows (Figure 4).
An equilateral triangle shown in blue in Figure 4 gives the length of three bays. It also defines the north-south extent of the piers. Let the length of the base of this triangle be d. Then the height = (√3/2) x d. From the measurements in note 21 below, d evaluates to 63'1".
Triangles like this may be drawn in the nave of Wells 19 and the Choir of Southwell, but in those places it gives the length of four bays.
A circle diameter d shown in red (Figure 5) passes through certain corners of the pier bases. The tangent shown in yellow defines the western extent of the thickening of the piers that support the towers, also the interior face of the east wall of the Jasper tower.
Another circle on the same centre shown in blue, with radius equal to the internal width of the west front or the distance apart of the inner faces of the arcade walls, with a pentagon inscribed, gives the position of the centre lines of the western half of the arcades, and the position of the east-west extremities of the piers (Figure 5).
The centre line of the south arcade is practically parallel with a 37' module line (Figure 5). The western half of the north arcade participates in the pentagonal geometry and is parallel with the south arcade. The two eastern piers of the north arcade have been made to conform to a 37' module line in their north-south placement. The fifth pier from the west is intermediate between the two lines. Its position is however justified by an equilateral triangle as shown in yellow (Figure 4).
The internal length of the nave from the west front to the sanctuary arch i.e. 150' 2" is another link with Wells, for 150' is the extreme width of the Wells west front including the plinths, also the external width of the transepts. 20 The extra 2" at Llandaff are used to ease the transition from the arcades to the West Front. Theoretically, half of a triplet shaft should be visible at the junction with the west front, but in practice, two shafts of the triplet are present, and the base can be seen to curve inwards before it meets the west front.
The geometry may have been developed in the following manner: First the 150' length of the nave was marked out from the centre of the Norman presbytery arch, then the length from the west face of the Norman presbytery arch to the west front was divided unequally into eight to give the bay length. The overall length available for the nave arcades was 146’8”. Assuming spaces of 6” were left at each end of the arcades, the remainder, divided by 8, gives 18’2½” for the bay length, which matches the calculated value exactly. 21 Measurement of the bay lengths leads to the conclusion that the north arcade was more loosely built than the south arcade. The close adherence of the bay lengths in the south arcade to the theoretical length rules out the possibility that the extra length of the first bay is due to poor measurement. The creation of substantial sub-arches in the bays next to the presbytery and the corresponding thickening of the piers (Figures 1, 10 ) is evidence that twin towers may have been intended at this point. The extra 6” allowed for these bays is consistent with the hypothesis. Apparently there was a change of plan for the eastern towers distinct from the change of design in the nave. All four towers would originally have been the same size, with the east walls of the east towers to have been built over the east walls of the Norman transepts, but the reduced eastern towers would have had east walls to the west of this position. An arch to support the east wall of the projected south east tower was inserted with considerable lack of aesthetic and structural sense immediately to the west of the entrance to the chapter house vestibule (illustrated below). Internal and external thickening of the adjacent aisle wall can be associated with this work. When the towers were abandoned, the extra thickness was chamfered off using any available stones. 22
The length d, not being an integer, is a derived measure. It may have been obtained as the height of an equilateral triangle with base equal to four bay lengths, and found to be close to the distance between the inner faces of the aisle walls. The centre used in Figure 5 was located. The equilateral triangle base d was set up, not in order to determine the bay length, but to give a measure for the north-south extent of the piers. From the discussion of the arcade geometry below, the east edge of the first pier from the west was to be a distance of 34½ inches from the north-south axis line of that pier. A north-south line of indeterminate length was marked out accordingly. To construct the pentagon, a line was drawn starting at the centre and inclined at an angle of 36° to the axis line. The point where this line met the north-south line defined the centre line of the arcade. The length of this line was taken as a radius of the pentagon, and also the distance between the inner faces of the arcade walls, so that the green triangle in Figure 5 is equilateral. Or perhaps a pentagon was inscribed in the larger circle and the north-south line was set up to intersect its radius.
The tangent in yellow (Figure 5) passes along the upper edge of the chamfer of the pier base. The distance apart of the inner faces of the arcade walls is measured between the tops of the chamfers. The base line of the exterior of the west front (Figure 11) is also aligned, vertically in this case, with the top of the chamfer. It is probable therefore that the geometry of the pier bases relates to the tops of the chamfers. The inner line of the arcade was reflected in the centre line to give the outer line of the arcade, and the intersection of this line with the circle diameter d gave a corner of the upper edge of the chamfer. The other three corners were found by reflecting this point in the north-south and east-west centre lines of the piers.
Note:
The Norman presbytery arch has wholly disappeared, so its position can only be located by inference. The inner moulding immediately west of the 37’ line is represented by stones of the period of the nave on the north side of the arch, demonstrating that the inner moulding of the arch reproduces mediaeval design. The same is true of the outer moulding. The coursing of the lower part of this moulding on the south side is the same as that of the duplet shaft and the stub of the wall that runs past the back of the Bishop's throne, which are mediaeval features. The line of the outer moulding is the same as that of the west face of the wall above the arch. The line of the east face of the same wall is also taken up in a moulding on the north side of the arch, which too displays mediaeval stones. Some of these stones are common to the east face of the arch and to the half of a triplet shaft visible at the west end of the north presbytery arcade. This shows that the thickness of the wall, which is known to have been altered in the 18th, 19th and 20th Century restorations, is mediaeval at the latest. Geometrically, the east face of the wall is located by the blue transept square in Figure 2 (see also Figure 10: the dotted line to the right of the blue square in Figure 2 does not correspond with any stonework). Moreover, if the wall had been rebuilt or made thinner by repositioning the west face, this would have happened right at the beginning of building operations, causing major disruption to the Norman Cathedral, but we have seen that the new work left the presbytery, transepts and most of the nave undisturbed for as long as possible. The method of building an arch in an existing wall is demonstrated in the presbytery arcades. This procedure was also followed in the south arcade at Brecon, 23 and in the large arches cut into the inner walls of the Norman towers at Exeter. It is probable therefore that the mediaeval presbytery arch was cut into the east wall of the Norman crossing.
An equilateral triangle shown in blue in Figure 4 gives the length of three bays. It also defines the north-south extent of the piers. Let the length of the base of this triangle be d. Then the height = (√3/2) x d. From the measurements in note 21 below, d evaluates to 63'1".
Triangles like this may be drawn in the nave of Wells 19 and the Choir of Southwell, but in those places it gives the length of four bays.
A circle diameter d shown in red (Figure 5) passes through certain corners of the pier bases. The tangent shown in yellow defines the western extent of the thickening of the piers that support the towers, also the interior face of the east wall of the Jasper tower.
Another circle on the same centre shown in blue, with radius equal to the internal width of the west front or the distance apart of the inner faces of the arcade walls, with a pentagon inscribed, gives the position of the centre lines of the western half of the arcades, and the position of the east-west extremities of the piers (Figure 5).
The centre line of the south arcade is practically parallel with a 37' module line (Figure 5). The western half of the north arcade participates in the pentagonal geometry and is parallel with the south arcade. The two eastern piers of the north arcade have been made to conform to a 37' module line in their north-south placement. The fifth pier from the west is intermediate between the two lines. Its position is however justified by an equilateral triangle as shown in yellow (Figure 4).
The internal length of the nave from the west front to the sanctuary arch i.e. 150' 2" is another link with Wells, for 150' is the extreme width of the Wells west front including the plinths, also the external width of the transepts. 20 The extra 2" at Llandaff are used to ease the transition from the arcades to the West Front. Theoretically, half of a triplet shaft should be visible at the junction with the west front, but in practice, two shafts of the triplet are present, and the base can be seen to curve inwards before it meets the west front.
The geometry may have been developed in the following manner: First the 150' length of the nave was marked out from the centre of the Norman presbytery arch, then the length from the west face of the Norman presbytery arch to the west front was divided unequally into eight to give the bay length. The overall length available for the nave arcades was 146’8”. Assuming spaces of 6” were left at each end of the arcades, the remainder, divided by 8, gives 18’2½” for the bay length, which matches the calculated value exactly. 21 Measurement of the bay lengths leads to the conclusion that the north arcade was more loosely built than the south arcade. The close adherence of the bay lengths in the south arcade to the theoretical length rules out the possibility that the extra length of the first bay is due to poor measurement. The creation of substantial sub-arches in the bays next to the presbytery and the corresponding thickening of the piers (Figures 1, 10 ) is evidence that twin towers may have been intended at this point. The extra 6” allowed for these bays is consistent with the hypothesis. Apparently there was a change of plan for the eastern towers distinct from the change of design in the nave. All four towers would originally have been the same size, with the east walls of the east towers to have been built over the east walls of the Norman transepts, but the reduced eastern towers would have had east walls to the west of this position. An arch to support the east wall of the projected south east tower was inserted with considerable lack of aesthetic and structural sense immediately to the west of the entrance to the chapter house vestibule (illustrated below). Internal and external thickening of the adjacent aisle wall can be associated with this work. When the towers were abandoned, the extra thickness was chamfered off using any available stones. 22
The length d, not being an integer, is a derived measure. It may have been obtained as the height of an equilateral triangle with base equal to four bay lengths, and found to be close to the distance between the inner faces of the aisle walls. The centre used in Figure 5 was located. The equilateral triangle base d was set up, not in order to determine the bay length, but to give a measure for the north-south extent of the piers. From the discussion of the arcade geometry below, the east edge of the first pier from the west was to be a distance of 34½ inches from the north-south axis line of that pier. A north-south line of indeterminate length was marked out accordingly. To construct the pentagon, a line was drawn starting at the centre and inclined at an angle of 36° to the axis line. The point where this line met the north-south line defined the centre line of the arcade. The length of this line was taken as a radius of the pentagon, and also the distance between the inner faces of the arcade walls, so that the green triangle in Figure 5 is equilateral. Or perhaps a pentagon was inscribed in the larger circle and the north-south line was set up to intersect its radius.
The tangent in yellow (Figure 5) passes along the upper edge of the chamfer of the pier base. The distance apart of the inner faces of the arcade walls is measured between the tops of the chamfers. The base line of the exterior of the west front (Figure 11) is also aligned, vertically in this case, with the top of the chamfer. It is probable therefore that the geometry of the pier bases relates to the tops of the chamfers. The inner line of the arcade was reflected in the centre line to give the outer line of the arcade, and the intersection of this line with the circle diameter d gave a corner of the upper edge of the chamfer. The other three corners were found by reflecting this point in the north-south and east-west centre lines of the piers.
Note:
The Norman presbytery arch has wholly disappeared, so its position can only be located by inference. The inner moulding immediately west of the 37’ line is represented by stones of the period of the nave on the north side of the arch, demonstrating that the inner moulding of the arch reproduces mediaeval design. The same is true of the outer moulding. The coursing of the lower part of this moulding on the south side is the same as that of the duplet shaft and the stub of the wall that runs past the back of the Bishop's throne, which are mediaeval features. The line of the outer moulding is the same as that of the west face of the wall above the arch. The line of the east face of the same wall is also taken up in a moulding on the north side of the arch, which too displays mediaeval stones. Some of these stones are common to the east face of the arch and to the half of a triplet shaft visible at the west end of the north presbytery arcade. This shows that the thickness of the wall, which is known to have been altered in the 18th, 19th and 20th Century restorations, is mediaeval at the latest. Geometrically, the east face of the wall is located by the blue transept square in Figure 2 (see also Figure 10: the dotted line to the right of the blue square in Figure 2 does not correspond with any stonework). Moreover, if the wall had been rebuilt or made thinner by repositioning the west face, this would have happened right at the beginning of building operations, causing major disruption to the Norman Cathedral, but we have seen that the new work left the presbytery, transepts and most of the nave undisturbed for as long as possible. The method of building an arch in an existing wall is demonstrated in the presbytery arcades. This procedure was also followed in the south arcade at Brecon, 23 and in the large arches cut into the inner walls of the Norman towers at Exeter. It is probable therefore that the mediaeval presbytery arch was cut into the east wall of the Norman crossing.