DAYLIGHT
MEASUREMENTS
IN UTRECHT

G, W. POSTMA

BIBLIOTHEEK DER
RIJKSUNIVERSITEIT
UTRECHT.

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DAYLIGHT MEASUREMENTS IN UTRECHT

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DAYLIGHT MEASUREMENTS
IN UTRECHT

PROEFSCHRIFT
TER VERKRIIGING VAN DEN GRAAD VAN
DOCTOR IN DE WIS- EN NATUURKUNDE
AAN DE RIJKSUNIVERSITEIT TE UTRECHT, OP
GEZAG VAN DEN RECTOR MAGNIFICUS
DR, C. W. VOLLGRAEF, HOOGLEERAAR IN DE
FACULTEIT DER LETTEREN EN WIJSBE-
GEERTE, VOLGENS BESLUIT VAN DEN SENAAT
DER UNIVERSITEIT TEGEN DE BEDENKINGEN
VAN DE FACULTEIT DER WIS- EN NATUUR-
KUNDE TE VERDEDIGEN OP MAANDAG
8 JUNI 1936, DES NAMIDDAGS TE 3 UUR

DOOR

GERRIT WILLEM POSTMA

GEBOREN TE ROTTERDAM

BIBLIOTHEEK OER
RIJKSUNJVERSITEIT
UT R ECHT.

AMSTERDAM - 1936
N.V. NOORD-HOLLANDSCHE UITGEVERSMAATSCHAPPIJ

. lt;é

Aan mijn Moeder.

Aan mijn aanstaande Vrouw.

Lik».

Promotor: Dr. L. S. ORNSTEIN.

Aan Prof. Ornstein betuig ik mijn groote erkentelijkheid voor zijn vele
steun en belangstelling.

Aan mej. Dr. J. G. Eymers, Dr. D. Vermeulen en J. H. Heiërman
mijn hartelijke dank voor de samenwerking.

M

W't

introduction.

A few years ago the town-council of the Hague requested Prof. Ornstein
to give his advice on the lighting-system to be applied in the Municipal
Museum of that town, designed by Dr. Berlage the architect.

While the plans were in course of preparation, it turned out, that the
data necessary for the plani^ing of any adequate lighting-system, namely
those concerning the intensity and the spectral distribution of daylight,
did not exist for our country. This induced us to enter upon a preliminary
investigation of the constitution of daylight. This investigation showed us
the advisability of attacking the whole subject more systematically than it
had been possible to do in the time available for sending in our plans.

The outcome of this was that intensity-measurements in the visible part
of the spectrum were carried out by us for nearly a year at a stretch. In
Chapter I of the present publication the method of measuring and the
way in which we described the meteorological conditions are explained.
Chapter II contains the raw material and the optical and meteoroligical
details belonging to it. Chapter III outlines the treatment of the material
according to certain leading aspects and gives analytical expressions,
comprising the results. The latter are divided into two principal groups,
namely, those concerning the total illumination (due to the scattered light
from the sky the direct light from the sun) and those concerning the
indirect illumination (due to the scattered light from the sky only).
Chapter IV contains the observed values (arranged according to the
solar altitude arid the degree of covering) expressed in lux-units and
further tables giving for every month of the year and for certain hours of
the day the average value to be expected, of the total as well as of the
indirect illumination.

In Chapter V we considered the influence of the atmosphere from a
more theoretical point of view.

CHAPTER L
Method of measuring.

The illumination of an object by daylight is effected by radiation, which
either reaches the object straight from the sun or has been previously
affected by scattering, reflection, diffraction etc. The illumination is,
therefore, dependent on the position of the sun with respect to the earth,
on the atmospherical condidons and on the surroundings of the illuminated
object. The latter influence is variable in many ways. We shall not include
it in the present considerations and study only the influence of the sun
and the atmosphere; indeed we must first know how the light reaches the
earth before we can form a complete picture of the illumination by daylight,
in which the surroundings also play their part.

In order to ascertain this, our measuring arrangement was mounted on
the roof of the Physical Laboratory — a rather high building in the town
of Utrecht; from this roof a considerable part of the sky is visible. In
measuring the illumination, we must distinguish between the illumination
by direct sunlight {direct illumination) and that by the scattered hght from
the sky {indirect illumination). It is the direct sunlight that causes in the
majority of cases a marked shadow. The direct and indirect illumination
together give the total illumination. In our experiments the daylight
illuminates a nearly horizontal white surface and the brightness of the
latter, which is determined with the aid of a spectral pyrometer, i) serves
as a measure for the illumination. If the illumination is to be readily
obtained from the observed brightness (i.e. the one in the direction of the
pyrometer), the latter must be dependent only on the total amount of
energy incident on the observed surface-element and not on the direction
of incidence. For, if this condition is complied with, the illumination is
simply proportional to the observed brightness. Now, a magnesium-oxide
surface meets these demands very satisfactorily for all wavelengths within
the range of the visible spectrum, provided the angle between the surface
and the direction of incidence be not too small. Accordingly, our white
surface consisted of a layer of magnesium-oxide, precipitated on a flat
metal plate. The factor of proportionality between brightness and
illumination is readily determined by illuminating the white surface by a
standardized lamp from the Utrecht Institute, and by then measuring
the brightness corresponding to that known amount. The spectral pyro-

1) L. S. ornstein, Miss J. G. EymeRS, D. Vermeulen. Zeitschr. f. Phys. 75,
575 (1932).

controlling the lamp. The way it works is as follows. The lens L^ forms
an image of the white surface W on the filament of L, bent in the shape
of a reversed U, which lies in a plane perpendicular to the optical axis of
the system Ly, L2, L^. The lens Lg forms an image of the filament and
therefore also of the white surface very near the prism of the monochro-
mator; finally, the prism P and the lens L4 form a spectrum on the lid of
the second monochromator tube. In this lid is an aperture D. Through it
the filament and the white surface are seen in the light of the wavelength,
determined by the position of the prism. By turning the latter, any part of
the spectrum can be brought to fall on the diaphragm. The filament is
part of an electrical circuit, which further contains a 4 volt accu, an
adjustable resistance and a milliamperemeter. To a certain current
corresponds a certain brightness in each part of the wavelength-region.
When we look through the diaphragm at the filament and the surface, we
see each with its own brightness, so that, when the filament is brighter we
see it light against a dark background. When the surface is brighter, we
see the filament dark against a light background. If they are equally bright
that part of the filament, for which the brightness is constant cannot be
distinguished from the background. In order to measure the illumination of
the white surface, we must adjust the current in such a way, that the
filament becomes invisible, and we must know the amount of energy per
cm2, per A and per second, incident on the white surface, corresponding
to the current, adjusted in that way. To that end the surface is illuminated
by an absolutely standardized lamp (that is to say, one of which the
amount of energy radiated per unit of solid angle, per A and per second is
known for the various wavelengths) and the current corresponding to that
illumination is then measured. In this way a set of curves is obtained.

representing the connection between the pyrometer current and the
illumination of the white surface.

By the use of this white surface, errors are avoided, which otherwise
might arise from the fact that daylight is partly polarized, whereas the
standardizing is performed with ordinary light. For, by the reflection at the
white surface, the light is completely depolarized so that by this device the
spectral pyrometer receives ordinary light when the daylight is measured,
as well as when the standardizing takes place. The precision of our
determinations depends on the precision with which the radiated energy
of the standardized lamp is known and on the precision of our adjustments
and readings. As regards the former, the error is certainly less than 2 %
of the amount of energy, actually brought into account; as for the latter,
the error in the adjustment on equal brightness of filament and background
is less than 0.2 of a scale division of the mA meter and the error in the
reading of this instrument less than 0.1 of a scale division. Now, an
error of 0.2 of a scale division corresponds in the central parts of the
standardizing curves to a relative energy deviation of less than 2%. We
may, therefore, safely assume the total error to remain, in general,
under 5 %.

The filament of the pyrometerlamp may not be run at a higher current
than corresponds to 130 scale divisions, in order to prevent changes in its
condition invalidating the standardizing i). In the case of short wavelengths
the brightness of the wire is often insufficient for a direct comparison with
that of the white surface. The latter brightness is then diminished by
means of a reducer V, inserted in front of the lens L^. In order to obtain
the most advantageous conditions, we made use of two reducers of unequal
transmission-powers. We ascertained, by measuring, that they were nearly
grey, i.e. that the reduction factor was nearly the same for all the
wavelengths that concerned us. (The reducers were made by some time
exposing a photographic plate to the light and by then developing and
fixing it.) The reduction factor depended also on the position of the
reducer in front of the lens.

The actual measuring was carried out as follows: We began to measure
without reducer the brightness at the various wavelengths from 1 = 6800 A
downward, until the mA meter read somewhere between 120 and 130
scale divisions. The brightness at the corresponding wavelength was then
again measured with the reducer inserted and the reduction factor obtained
from these two measurements was applied to the determinations (with the
same reducer inserted) of the brightness at the wavelengths further down
to 2 = 4500 A. By this way of proceeding the results are liable to errors

1) It is necessary to re-standardize from time to time in order to ascertain, whether
the standardizing curves must be altered on account of certain alterations in the condition
of the filament connected with the life-time of the lamp and with the strength of the
current which the filament has had to stand.

since the illumination is under certain conditions of the weather not
constant while the set of measurements is being obtained, but may fluctuate
considerably in a short interval.

The white surface was protected from rain by a bellglass. That part of
the glass, which the radiation from the surface actually passed on its way
to the pyrometer was protected against trickling water by a small glass
roof. The reduction factor of the bellglass was found to be 1.2 (whether
wet or dry). The observed brightnesses must therefore be multiplied by
1.2 to allow for the influence of the bellglass. In order to be able to
measure the total, as well as the indirect illumination, the direct light from
the sun could be intercepted by means of a wooden screen placed at some
distance from the surface. This screen intercepted also a certain amount
of scattered light from the sky in the immediate vicinity of the sun, but
this amount can be neglected.

The pyrometer and accessories were mounted in a wooden shed on the
roof of the Physical Laboratory where there are comparatively few
obstacles. When the sun was low in the western sky the pyrometer shed
itself was in front of it, and in midwinter the sun set behind the shed
belonging to the heliostate of the hehophysical department somewhat
further away on the roof. But towards the north, the east and the south
the view was practically unobstructed.

The white surface formed a small angle with the horizontal plane — as
did also the optical axis of the system Lj, Lg and Lg so that the surface
could be conveniently observed through the pyrometer.

Since there appeared to exist a distinct connection between the
illumination on the one hand and the solar altitude and the cloudiness on
the other hand, we tried to determine the data concerning the latter
quantities more closely. Now, as regards the solar altitude, this is
completely determined by the time at the moment of measuring. As regards
the cloudiness, notes were made of the degree of covering, the type of
clouds and their height. The degree of covering was estimated in tenths
of the total hemisphere i), the type of the clouds was assigned to them in
the usual way according to their shape and level.

At all levels we distinguished between cumulus- and stratus-types. We
denoted by quot;cumulusquot; more or less isolate clouds, in the majority of cases
of rounded shapes and vertical sides; by quot;stratusquot;, clouds extending like
a sheet over part or over the whole of the sky, without clearly marked
individual clouds. Between these extreme types there are various inter-
mediate ones. We distinguished three levels.

In the lowest level we distinguished between cumulus, stratocumulus and
stratus. Stratocumulus is intermediate between stratus and cumulus, it
shows clearly separate formations in the layer of clouds, though distinct

1) In estimating the degree of covering we chiefly considered the zenithal part of
the sky.

vertical sides are as yet not present. This level reaches as high as 2000
to 2500 M.

In the middle level we find the altocumulus and altostratus type.
Altocumulus does not show definite vertical parts. The clouds give the
impression of rounded crowded masses, hanging more or less loosely
together. Altostratus often shows very little detail. (Height about 3000 M.)

The highest clouds are the cirri, subdivided into cirrostratus, cirrus and
cirrocumulus. The cirrustype has often a kind of filigree structure. As an
effect of perspective, the threads of clouds seem at times to meet in one
point. Cirrostratus covers the sky like a transparant veil. Cirrocumulus
often occurs together with altocumulus. The cirri produce the halos round
the sun and the moon.

Generally speaking the same type of clouds is lower in winter than in
summer, so that one cannot suffice with simply assigning to each of the
three levels one definite height above the surface of the earth.

For the lower level clouds we have added the estimated height above
the earth of their lowest parts. The clearness of the atmosphere in a
horizontal direction was expressed by the degree of visibility of the horizon
— varying from quot;very clearquot; to quot;invisiblequot;. Particulars, such as rain or
snow etc. were duly registered.

chapter ii.

In this chapter the measurements concerning the illumination are given,
obtained during the interval from Aug. 1932 to July 1933 inclusive.
We shall give a fev^ comments and an explanation of the abbreviations
used in connection with the various terms separately.

Time: Time is recorded in Amsterdam time = G.M.T. cx, 20 min.
Solar Altitude. The altitude is determined with an accuracy of about 2°.
Total or Indirect. By Indirect (I) are denoted those observations during
which the direct radiation of the sun was intercepted at about 2 m from
the white surface by a screen of about 20 X 40 cm.

Cloudiness. The cloudiness for the observations 1—180 is only occasion-
ally, but for the observations 181—706 it is stated regularly by a. the degree
of covering in tenths of the whole hemisphere, b. the type of clouds and c.
the height (in m) above the earth of the cloud basis — as far as the lower
types (st, cu, stcu, ni) are concerned. The meaning of the abbreviations is :

St = stratusnbsp;ast = altostratus ci = cirrus

stcu = stratocumulus acu = altocumulus cist = cirrostratus
cu = cumulusnbsp;cicu = cirrocumulus

ni = nimbus
(See also Chapter I.)

For the other observations we have introduced the distinctions:
a. heavily clouded sky (h), b. moderately clouded sky (m), and c.
slightly clouded or cloudless sky (1, no cl). Again br. sun means, that the
sun was shining brightly and continuously, and occ. sun that it was shining
at intervals.

Horizon. The indications here given refer to the visibility of the horizon.
The meaning of the abbreviations is:

inv. = invisiblenbsp;v. cl. = very clear

v. hazy = very hazynbsp;m. cl. = moderately clear,

m. „ = moderately hazy
si. „ = slightly hazy

Wavelength. The wavelength of the hght of which the intensity is
determined, is given in A (1 A=10—« cm).

Illumination. Owing to the way our instruments are read, the illumination
is expressed in relative units.

1 relative unit corresponds to 1.39 X IQ-« W/A cm2. The fact that a
reducer is used (B, weak; G, strong) is indicated by the reduced amount
of energy in brackets under the computed actual amount. All values

following such a one are obtained with that same reducer inserted, while
the reducing factor is taken to be constant as regards the wavelength.
A few observations were carried out with the reducer apphed from the
beginning: this is duly mentioned under: quot;remarksquot;. Whenever the bellglass
has been used in case of rain or other atmospherical condensationproducts,
special mention has been made. The reducing factor 1.2 has already been
accounted for in the values given.

From observation No. 222 onward, the result from a new standardizing
of the pyrometer was employed, which differed from the old one by the
constant factor 1.17. The results from the observations 1—222 have been
put in line with those of the others, by multiplying them by this factor, since
we had reason to consider the last standardizing as the most accurate.

Our measurings were always begun at = 6800 A and finished at
I = 4500 A.

Class. The observations are divided into three classes A, B, C, and a
further group of unreliable or incomplete observations indicated by?. (For
more details see Chapter 111.)

23
19 Aug

10.15
46°
I