IMPROVEMENTS OF ARCHITECTURE, THE ELEMENTARY METHOD OF FORMATION EM- PLOYED IN THE SAME BEING ALSO FURTHER APPLICABLE FOR HARMONIZING FORMATION, AS OF URNS OR VASES
Year: 1847

page_text: TO ALL TO WHOM THESE PRESENTS SHALL COME, I, JOHN
ROBERTSON, of Tweedmouth, Berwick, Gentleman, send greeting.
WHEREAS Her present most Excellent Majesty Queen Victoria, by Her
Royal Letters Patent under the Great Seal of the United Kingdom of
Great Britain and Ireland, bearing date at Westminster, the Ninth day of
November, One thousand eight hundred and forty-seven, in the eleventh year
of Her reign, did, for Herself, Her heirs and successors, give and grant unto
me, the said John Robertson, my exors, admors, and assigns, Her especial
licence, full power, sole privilege and authority, that I, the said John Robertson,
my exors, admors, and assigns, or such others as I, the said John Robertson,
my exors, admors, or assigns, should at any time agree with, and no others,
from time to time and at all times during the term of years therein
expressed, should and lawfully might make, use, exercise, and vend, within
England, Wales, and the Town of Berwick-upon-Tweed, my Invention of
"IMPROVEMENTS OF ARCHITECTURE, THE ELEMENTARY METHOD OF FORMATION EM-
PLOYED IN THE SAME BEING ALSO FURTHER APPLICABLE FOR HARMONIZING FORMATION,
AS OF URNS OR VASES;" in which said Letters Patent is contained a proviso
that I, the said John Robertson, shall cause a particular description of the
nature of my said Invention, and in what manner the same is to be performed,
by an instrument in writing under my hand and seal, to be inrolled in Her
said Majesty's High Court of. Chancery within six calendar months next and
immediately after the. date of the said in part recited Letters Patent, as in
and by the same, reference being thereunto had, will more fully and at large
antear.

page_text: NOW KNOW YE, that, in compliance with the said proviso, I, the said
John Robertson, do hereby declare that the nature of my Invention, and the
manner in which the same is to be performed, are fully described and ascer-
tained in and by the following statement thereof, reference being had to the
Drawings hereunto annexed, and to the figures and letters marked thereon,
that is to say:-
I have to present a method of architectural formation-which I consider to
be the proper one for curvilinear formation, or formation in relief, and which
also affords the basis for proportioning the parts of rectilinear formation, which
may be connected with the same. A mere rectilinear and rectangular
formation does not in itself produce nor afford the principles of any gradations
of magnitude or relief of one part beyond another, nor of any proportions or
limitations of extension, but I have here to shew the practicability, and, so far
as I am able, the application, of a regular curvilinear formation, analogous in
its primary simplicity to that of the simplest rectilinear and rectangular
formation. The curves defining the formation will be divisible in the proper
directions into circular arcs of forty-five degrees, convex or concave, or the
same having more or less extension. The formation will be upon directional
right lines, which may include or be in planes including rectangular spaces,
or in some cases, as in the sloping of roofs, have a diagonal or a gradation of
a diagonal inclination. Exclusive of such inclined directions the directional
lines, which will be the axes of the curves, will, in an architectural structure,
be either vertical or horizontal, the horizontal being in two directions, which
in the accompanying representations or diagrams of elevations, which are
drawn or thographically, will be the one direction in or parallel with the plane
of the picture, and the other at right angles to it in the direction of view.
Figure 1 represents the elevation of a solid, the outer of the two concentric.
circles of Figure 2 being, the plan at its base and the inner at its summit,
the same letters referring to corresponding points in a plan or section as in
the elevation which they accompany. The outer circle of Figure 2 is in such
proportion to the inner that a square inscribed in the one will be described
about the other, or if the radius of the greater circle be as 100 that of the
lesser will be as 70, 71, nearly, and that of a circle, the next gradation less, in
the same proportion will be as 50, and so on through any number of grada-
tions, increasing or decreasing; and such in the following system are the
gradations of magnitude or of radius of formation considered independently of
extension. The two circles of Figure 2 are divided into arcs of forty-five
degrees by diameters, two directional A, B, and two diagonal B, D. By the
extension of an arc A, B, or of the same on the other side of the Figure piaced

page_text: in a concave position between the same extreme points, I mean the extension
in the direction of its diameter of direction or axis A, A, E, or of its sine B, B,
which is the measure of its first or original extension, the versed sine A, B, being
the measure of its depth; the other diameter of direction, in a line with which
and perpendicular to its axis is its base or a line parallel with the same,
passing through the other extremity of the arc, may also be considered as a
base. Then, by increasing or diminishing the extension or length of an arc as
to 6 or b, I mean doing so equably from either base in the direction of its axis
or diameter of direction, and by increasing or diminishing the depth of an arc
I mean doing so equably in the direction of its base. The arcs which are
upon vertical axes I shall call ascending arcs, and the arcs upon horizontal
axes I shall call lateral arcs.
Having explained some of the terms which I shall use, I return to the
representation of a simple solid in Figure 1, whose summit as well as base is
flat and horizontal, and which is bounded all round, or its diametrical sections
are bounded by ascending arcs of forty-five degrees of the same magnitude
and extension as the arc A, B, of the plan, and their axis rises vertically from
the centre C of the plan, and intermediate lateral arcs, cutting the ascending
arcs in their corresponding points, will encircle the figure horizontally. In
Figure 3 this form is altered by each of the ascending arcs B, D, which
bound its diagonal sections, having its extension diminished so as to equal the
first extension of an are one gradation less, and the intermediate ascending
arcs between these and the ascending arcs A, B, having their extensions
diminished so that the curve B, D, joining their upper extremities shall
present upon the plane of the picture an arc of forty-five degree of the same
magnitude and extension as the arc B, D, of the plan, which it likewise will
still do upon the horizontal plane, and the ascending arcs B, D, will present
the same upon the plane of the picture; and also upon a transverse section of
it, for their apparent depth, as so viewed, is diminished in the same proportion
as their extension has been diminished, and thereby B, D, B, D, B, presents,
as viewed in front, a semicircle of the same magnitude as that signified by the
same letters in the plan. The arcs A, B, which bound the directional sections
retain their original extension. The intermediate lateral arcs also taking a
curvature downward, so as still to cut the ascending ones in their corresponding
points, will become arcs corresponding with the ascending ones in the same
positions on each face, of the form. Completing the semicircle A, B, A, B, A,
the outline of another face of the figure is given, and doubling the figure, in
Figure 4, the form which is the primary capital of this system of formation
is completed. It has six similar faces, each of which presents, as viewed in
as

page_text: front, a circle B, D, B, D, &c., and which is of the next gradation less than
the outer circle A, B, A, B, &c., which is that of a directional section of the
whole form. All the arcs defining the surface of the form are of equal depth
in the directions of the diametrical sections which they bound, and are equal
in that respect to the arc A, B, their differences being in extension. I have
especially described this form because it appears to me that the practicability
of this system of formation principally depends upon the practicability of this
formation of the primary capital, that is to say, of a form the directional
diametrical sections of which are circular, as if of a sphere, whilst at the same
time the outline of each of its six faces presents, as viewed directly in front,
upon the plane of the picture a circle which is of the next less gradation of
magnitude according to this system. This primary capital is to be considered
as holding the corresponding place in a curvilinear formation which a cube does
in a rectilinear and rectangular formation. If three cylinders, one vertical and
the other two horizontal, cross one another, their axes cutting one another at
right angles in the same point, then the lines where the surfaces of the
cylinders cut one another will be the outlines of the faces of the primary capital;
but, instead of right lines bounding the surfaces in the directions of the axes
of the cylinders, arcs of forty-five degrees, having the same axes or directional
diameters, are to be used, commencing from the outlines of the faces of the
capital, and defining the surfaces of the continuations of the formation as of the
shafts of columns below and above the capital, which in the latter instance is
the base, and of what I shall call architraves, in this system proceeding from
the side faces of the capital of Figure 5, which shews the elevation.
Figure 6 shews the halves of the transverse sections through the middle of
the architraves, and also of the curtain or cove of the wall which may be filled
up between the shafts and architraves, also of so many of the grades of a
pyramidal or cupola coping, which may be placed upon the capitals and
architraves, also of a capital and base of double curvature, with corresponding
architraves, and to which I shall presently further advert; and Figure 7 is the
plan of the sections. In this elevation, Figure 5, the shafts and architraves
are of the least extension consistent with not using any arcs bounding the
directional sections of less than the first or original degree of extension.
A, B, are capitals; C, D, bases; E, E, shafts; F, G, architraves of the base.
As there are also capitals or part capitals of the base, the perpendicular part
beneath which, H, may be called a sub-base. K, L, are architraves; M, one
half of the curtain or cove of the wall filled in; N, the same, with half of a
rectangular window cut out of it; O, so many grades of a pyramidal coping,
and P of a cupolar one; according to this system, lessening by gradations of

page_text: .
magnitude until they terminate in a point or line. It must be obvious that
as arcs of forty-five degrees are used, whether with more or less extension and
in a continuous formation, the extremity of one arc joins that of another, and
the conjoined arcs are upon the same axis. They must be of the gradations
of magnitude, considered independently of extension; as already stated; two
united arcs having the same directional axis, either repeating the same gra-
dation of magnitude, or one being a gradation of magnitude greater than
the other. Thus the shaft E is of the next gradation less magnitude or
breadth of formation than the base C, and the capital A is a repetition of
that magnitude of the shaft. The architraves are bounded laterally or
longitudinally with concave arcs of 90°, with more or less extension, and
being of the next less magnitude of formation than the arcs of the capital
of which they are continuations, and the lateral arcs of the curtain of the
wall are also concave, and are of the next less magnitude of formation than
those of the shaft of which they are continuations or conjoined, and upon the
same axes, whilst the ascending arcs of the curtains of the wall, by which, of
course, I am always meaning which define the superfices, are convex arcs of the
next less gradation of magnitude than the continuing arcs of the architrave
of the base, and of the same gradation with those of the architrave above,
or architrave proper.
In the same manner as an architrave springs from the
side face of a capital, so will the roof or cieling between the architraves, spring
from the side faces of the architraves, the curves being concave and of the
next less gradation of magnitude to those of the architraves which they join,
and with which they are upon the same axes or directional diameters. Thus,
Figure 8 represents either the upper or under side of a roof or ceiling (or
it may be of a floor, unless the same be levelled in or off), also the corre-
sponding under or upper faces of the four architraves, from the side faces of
which it springs, the diametorical lines of the architraves and of the capitals.
from which they spring forming a rectangle, and rectangular spaces may be
unclosed either by only four columns and their walls and roof and floor, or by
ranges of columns, the architraves of which may, where they cross one another,
spring from the sides of suspended capitals not supported by shafts, but
shewing their under faces in the ceiling; a flat cieling may also be formed,
having a cornice of similar formation to the coping upon the upper faces of
the capitals and architrave of Figure 5, but springing from the lower half
of their side faces; and other varieties may be practiced, analogous to those
practised in other methods of architecture; for upon the whole it will be
found that this method gives the due capability of conjunction of parts for the
forming of varieties. But I must now proceed to consider some general

page_text: principles of proportions and adaptations of 'this system, not having time
nor being prepared to enter into minor details, nor to state anything specific
regarding them.
Figures 9, 10, and 11 are for the purpose of explaining the grounds upon
which I consider the heights of the columns, and their distances from one
another, should be proportioned. Figure 9 also shews some coincidences
bearing upon the same, and derived from the properties of the circle. On
one side of Figure 9 the columns are in a regular sequence of gradations
of height from the first or nearest gradation, as shewn in the Figure, the
breadth of the column lessening by gradations without its height being
lessened. If the breadth of its shaft at the base be in the sequence
20.71-29.29-41.42-58.58, &c., then, with the same breadth of shaft
retained, the gradations of heights of the column, measuring always from the
centre of formation of the base to that of the capital, will be in the sequence
of two of these quantities which are proximate to each other, united, as
20.71 +29.29 = 50, the next greater gradation of height to which is
70.71, the next 100, the next 141.42, and so on. And the gradations
of distance beginning from the nearest between the columns will be terms of
the same sequence as that of their heights; and a greater distance will be
divisible into lesser distances, which will be equals or halfs or quarters,
and so forth of one another; thus a breadth of 200 may be divided. into
four breadths of 50; or say a portico may be formed of four columns,.
the centre distance between them, that is, of their axes, being as 100,
and the side ones as 50. This I call the first sequence of gradations of
heights and breadths. On the other side B, of Figure 9, the heights and
greater distances are compounded of two proximate terms of the first
sequence of heights and distances, as 50 + 35.355-85.355, 70.71+50.
= 120.71, a facade formed of these as great distances will be divisible
into lesser distances of the first sequence. Taking a great arch whose
inner semicircle is one gradation less than its outer, then the shaft of a
column in the second sequence of heights and distances may with its breadth
at the base occupy the thickness of that arch, whilst its height and the greater
or undivided distance between its columns will coincide with the height and
span of the arch. In the first sequence on the side A, of Figure 9, the
centre-line of the shaft must be placed on the outer semicircle of. the arch,
as if the shaft would divide itself also with another arch. In Figure 10
there is a succession of capitals or half capitals and bases connected by
what may be called epistyles; if these successions were continued at the same
proportions of distance diminishing they would meet at a point in which they

page_text: vanish in size. The same would be the case in the succession in Figure 11.
By that means the shaft, whether taken from the first, second, third, &c.,
capital and base, will always bear the same proportion in extension to the
magnitude of the capital and base from which it is taken, or which it conjoins.
On the side A of Figure 10 the distances between the capitals above are the
same as of those of the base on the side B; they are proportional to them,
and therefore one gradation less. This causes that on the side A,. the height
of a column from the centre of one of the bases to that of the corresponding
capital, will be a gradation of the second series of heights, but commencing
with a greater extension of shaft; thus, if the breadth of the shaft at the
base be as 20.71, the height of the column between the centres of the first
base and capital will be 170.71; between those of the second base and capital
241.42; and so on. The heights on the side B of Figure 10 will be com-
pounded of two proximate quantities of the second sequence, as .85.355 +
60.355 145.71, and so forth, and the heights in Figure 11 will be in the
same sequence, but commencing with a greater extension of shaft. I have
then here to do with three sequences or series of gradations of heights and
distances of columns as compared with their breadths, say, of their shafts at
the base. Always taking the breadth of the shaft as one of a series of quantities
of which 20.71 - 29.29 - 41.42, &c., are following gradations, then the first
series of heights and distances are 50-70.71-100, and so on; the second
series are 85.355-120.71-170.71, and so on; and the third series are 145.71,
and so on, increasing or decreasing in extension in the same proportions as
those of the gradations of magnitude of this system. Figure 12 is of the
second series of heights and of distance between the exterior columns, which
is divided into distances of the first series. Figure 13 is the same, of shorter
proportions, and on one side the coves between the epistyles and the
architraves beneath them are filled in, and also the curtains or coves of the
wall, excepting that rectangular windows and a door are again cut out of
these. Figures 14 are of the same proportions as Figure.12, but have a
basement entablature and pediment with some variations engrafted upon
them. Figure 15 is, on the other hand, of-the first series of gradations of
height and distance between the exterior as well as the interior columns of
the portico, which has a basement entablature and pediment, with a variation
of projection shewn in one of the side views. Figure 16 is of the third
series of heights, and second, of distance between the exterior columns, and
has an entablature, &c., engrafted upon part of it. The projecting grades of an
entablature or basement I generally make increments of magnitude according
to the gradations of this system, the distance from the line of the axis of the

page_text: exterior column being the measure of the magnitude upon which the incre-
ment of magnitude is taken, and the height or thickness of these grades may
either be the same as their projections or a gradation of the same, or the
thickness of two of the grades may be united. I consider that blocked
entablatures and other varieties may also be formed, and that some species of
entablatures may also rest upon the upper surfaces of capitals.
The gradations of the slopes of roofs in this system of proportions I have
represented in Figures 17 and 18, and which are the same in each Figure, but
with different numerals. I need not advert much to varieties of this system
of formation, which I cannot at present work out; but, besides coalesced or
clustered columns and capitals, many varieties, from varying the extension of
of the curves of capitals as well as of other parts, may also be effected. It
will easily be seen that domes or cupolas and pinnacles may readily be formed,
of which some examples have been given. If in a continued cupolar for-
mation the ascending arcs were crossed throughout by lines horizontally
rectilinear, the ill effect of this would be easily perceived, and the value of
the capability of giving the sectional planes bounded by the curves more or
less of a diagonal inclination be found, and of thus equalizing the principles
of formation for both directions for one as for the other, so as to obtain a fully
consistent curvilinear formation. There are advantages of this system which
may be considered isolatedly, as rendering pillars not extraneous to the wall,
but part of its formation, and allowing their front faces to be seen in relief;
also when the alternating concave of the curtain of the wall is filled in; also
the curved architraves appear to harmonize better with the profiles of the
shafts, and also to stretch more lightly from column to column than do flat
architraves.
I have also to observe the further applicability of this system for harmo-
nizing forms for other purposes, as urns or vases. Examples of these are
given in Figures 19 to 23, which will shew the easy applicability to such
purposes of nearly the architectural forms; and having searched much to
ascertain its novelty, I believe it will be found that a new element is intro-
duced in these formations as well as those of the architecture.
Having been much engaged in studying the principles of this system, I am
not at last able to go so much into nor to illustrate further its details, and
must here close my Specification.
In witness whereof, I, the said John Robertson, have hereunto set my
hand and seal, this Ninth day of May, in the year of our Lord
One thousand eight hundred and forty-eight.
JOHN (L.S.) ROBERTSON.

page_text: AND BE IT REMEMBERED, that on the Ninth day of May, in the
year of our Lord 1848, the aforesaid John Robertson came before our
said Lady the Queen in Her Chancery, and acknowledged the Specification
aforesaid, and all and every thing therein contained and specified, in form above
written. And also the Specification aforesaid was stamped according to the
tenor of the Statute made for that purpose.
Enrolled the Ninth day of May, in the year of our Lord One thousand
eight hundred and forty-eight.