**Practical Bud Observation,
Measurement and Analysis**

**Measurement**

**Manual Measurement**

**The path geometry** that appears to conform so very
well to the buds is discussed in full elsewhere.

**In this section**, we deal with the practical
application of that geometry to real buds—or, at any rate, to photographs of
them. We discuss what measurements need
to be taken, how to take them, and the difficulties that attend taking them. We assume that our bud images are suited to the
measurement process and of sufficient quality for it, as set out in the section
on Observation.

**We will in the first place be
concerned with a bud’s profiles.** We will want to know whether or
not—and if, then how well—the path geometry conforms to these profiles.

**To this end**, we suppose that the bud may be placed in an *invariant triangle* such that the tip of
the bud lies at one vertex and the base of the budlies at a second.

Although there is no absolute necessity that
it must, the third vertex is generally taken to lie at infinity, in a direction
at right angles to the line joining the first two vertices, those occupied by
the tip and base of the bud. This means
that the invariant triangle presents as two, parallel lines, traversed by a third
line at right angles to them—which, at first sight, may not seem to *be* a triangle, but is a triangle
nonetheless, as it has the requisite three vertices and three sides. In draughtsman’s terms, this triangle is a
“side elevation” of the full invariant tetrahedron that we suppose pertains to
our bud. It is the side view of a
tetrahedron with one real side and its two real vertices placed locally, and
with its other two vertices not only at infinity, but *imaginary* besides. We have
an edge-on sight from infinity of (or a vertical section through) a *semi-imaginary tetrahedron. *

**We usually speak of the
vertices** at the tip
and base of the bud as the “** Poles**”: one of these (and either at
will) may be thought of as a “source”, and the other as a “sink”, as if the
path curve were arising from one, proceeding along the bud’s profile, and
disappearing into the other

**The path is set by measures
and we want to find them**, but before we set about doing so, we must first be reasonably
confident that we have properly placed the poles, and when we come to attempt
it, we at once find that we have a problem.

**In
general, it is fairly evident **where the top, or high, pole should go. The tips of most buds are usually well-defined, and easy to locate with
precision, so we can for the most part be rather sure of where to put the high
pole. **The same is not true of the
base of the bud!** The bud attaches
there to its stem, or twig, and it is seldom easy to tell where the bud stops
and the twig begins.

**One approach is** **to select a “likely looking” place for the low pole on the bud, then
stick to it.**

**That is**,
we accept that the chosen place is probably not the “correct” one, but we suppose
that it is “not too far” from it—and we keep it there from photo to photo, day
to day.

**In adopting this approach**, we are in effect deciding that we are more interested in the**variation with time** *of our results than in their perfect precision, and our method reflects our supposition that we will see this variation best if we keep the Inter-Pole Distance (IPD) as constant as we can.*

**Sometimes** there is a convenient, well-defined natural mark or feature on the bud
upon which we can reasonably set the low pole. If there is no such feature (as will surely be the case with silhouettes),
then, if we are working by hand on photographs or prints, we can make up a
“graticule”, or template, on a slip of paper. In fact, this is worth doing even if there *is* a natural mark available, as the graticule does double duty: it
allows us to set off the IPD, if we need to, and to mark the heights at which
our measurements are to be taken. We
place the first mark of the graticule at the tip of the bud’s image, align the
graticule with the long axis, and mark the heights and the position of the low
pole on the image. It is quickly and
easily done on one image after another.

**As we proceed** through a sequence of images, we
may from time to time find reason to make a fresh graticule—the bud may be
elongating, for example—but each template will be found to serve for a good
many images in succession, certainly sufficiently many to justify the making of
templates!

**Also**, if we are working entirely by hand, rather than with computer
assistance, it can be useful to trace the outlines of the bud on tracing paper every
few images. When they are laid over
other images in the same sequence, these tracings reveal changes that might
otherwise go undetected, and help us to determine when a new graticule needs to
be made. If we are prepared to make pin
holes in our pictures, the functions of tracing and graticule can be combined:
we can use a pin to prick through the tracing paper, at the calibration marks
now on the tracing paper, into the image.

**Tracings** also improve the *lateral* accuracy and consistency of the
pole placements, as traced outline can be matched with new outline with an eye
to registration. But the holes in our
pictures are permanent, and this can be a nuisance if we want to review our
measurements, and perhaps make fresh ones. We must then somehow indicate on the image which set of measurements was
finally accepted. This can be awkward.

**Once we have our marks** we are *nearly* in a position to take our measurements. We want to measure the whole widths of the
bud at the marked heights, at right angles to the line joining the poles—but
how are we to lay off the right angle? We use a graduated set square and a straight edge. The technique is as follows:

**Lay** the straight edge on the image, approximately parallel to the axis if
the bud, and so that the entire bud remains in view.

**Place** the set square against the straight
edge, then, on the horizontal, graduated edge of the set square, locate a
graduation mark close to the bud axis.

**Slide** the set square back and forth along
the straight edge and, while doing so, adjust the position of the straight edge
until the graduation mark selected above is seen to run exactly along the bud
axis—**at which moment the straight edge
will be accurately parallel to, and the graduated edge of the set square will
be accurately at right angles to the chosen bud axis, and we can take our measurements.**

**While
holding** the
straight edge firmly in the place found for it, move the set square to a height
mark.

**Note
(that is, measure)** where the left and right profiles of the bud intersect the set square at that
height.

**Subtract** the lesser measurement from the
greater. **This is the whole width of the bud at that height.**

**Remembering **to hold the
straight edge firmly in place, repeat the previous three steps for all the height
marks.

**When** all the height marks have been
visited in this fashion, we will have our list of bud widths, and can go on to
do the path curve calculations based upon them.

**The accuracy** of our measurements is chiefly affected
by the degree of enlargement of the photographs, or print-outs: clearly, the
enlargement should be as great as practically possible. But the choice of unit is a factor, too, and *that* choice is affected by personal
preference! Some prefer to use inches,
and tenths-of-inches. Others prefer to
use millimetres. Those using inches
report that they can measure to plus or minus about two hundredths of an inch:
those using millimetres say that they manage plus or minus around one tenth of
a millimetre.

**The method** of measurement described above is
effective, but basic. It is susceptible
to all sorts of refinement: for example,
the author has incorporated a vernier calliper into a set square, with which
measurements accurate to one hundredth of a millimetre were easily obtained—that
is, if the image of the bud was sufficiently sharp. Now it happens quite often that it is not,
and in fact there is a practical limit to precision, set by the quality of the
images, beyond which an increase in the native precision of our measuring
instrument does not lead to a corresponding increase in the precision of our
data. When all is said and done and
tried, the precision available from the basic arrangement depicted above is
probably adequate.

**There is a basic decision to
be taken** about the
number of heights at which we intend to take measurements. It might be argued that we should take as
many as can be physically managed, and so we would, were it not so that many of
these would fall near the low pole and be measurements of twig or stem rather
than of bud, and that many others might fall on local, and quite possibly
spurious, imperfections.

**As to that**, sober reflection must present us
with the thought that, even if they are basically of path curve nature, and
even if no imperfections are present, the profiles of a real bud are likely to *consist* of variations, however slight, on
a *theme* of “path curve”. Discussion of the full practical and
scientific implications of this is certainly in order. This will come in the section on “*Analysis*”. For now, we simply remark that multiplying the
number of measurement heights eventually leads to the obliteration of useful by
useless data. In the language of the
communications engineer, we eventually worsen the “signal-to-noise ratio”.

**Finally**, there is the question of how much
time and labour can be devoted to the measurement of a single bud image.

**In pre-computer days**, when Lawrence Edwards (and the
author) did all measurement by hand, the number of measurement heights finally
settled on was seven, and this has remained the “default” even in these computerised
times, though occasions do arise on which other numbers are used.

**In any case, **choose** **an odd number of heights (not
including the heights of the poles). This
ensures that a measurement height falls exactly mid-way between the poles. There are two methods of analysis in use; the
so-called *Projective* method, developed
by Lawrence Edwards, and the so-called *Regression* method, developed by the author. The
former requires the middle measurement height. The latter does not, but can use it if it is there, so if we make sure
that the centre height is present, both methods will be available for the same
bud.

*1. It is helpful
to think of a path curve like this—that is, both in terms of motion, and at one
and the same moment as a whole thing, “there” in its entirety. The motional aspect reminds us of the
rhythmic transformation from which it springs, whereas the wholeness draws
attention to the fact that there is a point *already at* every stage of the journey from source to sink. The form of the curve stays the same: it is
the invariant path that all points take. One might think of a pilgrimage of the faithful, winding single-file
along an ancient, well-beaten trail.*