LECTURE IX. 
MEASUREMENT OF LIGHT AND RADIATION. 

74. Since radiation is energy, it can be measured as such 
by converting the energy of radiation into some other form of 
energy, as, for instance, into heat, and measuring the latter. 

Thus a beam of radiation may be measured by having it 
impinge on one contact of a thermo-couple, of which the other 
contact is maintained at constant temperature. A galvanom- 
eter in the circuit of this thermo-couple thus measures the 
voltage produced by the difference of temperature of the two 
contacts of the thermo-couple, and in this manner the temper- 
ature rise produced by the energy of the incident beam of radia- 
tion is observed. 

Probably the most sensitive method of measuring even very 
small amounts of radiation is the bolometer. The beam of 
the radiation (or after dissolving the beam into a spectrum, 
the wave length of which the power is to be measured) impinges 
upon a narrow and thin strip of metal, as platinum, and thereby 
raises its temperature by conversion of the radiation energy 
into heat. A rise of temperature, however, produces a rise of 
electric resistance, and the latter is measured by enclosing the 
platinum strip in a sensitive Wheatstone bridge. The rise of 
temperature of the platinum strip by the small power of radia- 
tion obviously is so small that it could not be observed by 
any thermometer. Electric resistance measurements, however, 
can be made with extreme accuracy, and especially extremely 
small changes of resistance can be measured. Thus a change 
of resistance of 1 in a million and, with very sensitive measure- 
ments, even many times smaller changes can be observed. As 
1 deg. cent, produces a resistance change of about 0.4 per cent, 
a change of one millionth corresponds to a temperature rise 
°f ?tfW deg. cent. Thus, by the bolometer, extremely small 
amounts of radiation can be measured, as, for instance, the 
power of the moon's radiation, etc. 

166 


MEASUREMENT OF LIGHT AND RADIATION. 167 

The total radiation energy of a body for a given time can be 
measured by absorbing it and measuring the heat produced by 
it, as; for instance, the amount of ice melted in a calorimeter. 
Any particular range of the total radiation, as, for instance, the 
total visible radiation, can be measured in the same manner 
by passing the radiation first through a body which absorbs 
that part which is not desired, for instance, a body transparent 
to visible, but opaque to invisible radiation. As no body is 
perfectly transparent to one, perfectly opaque to another radi- 
ation, the separation of the radiation by absorption is nec- 
essarily incomplete, and correction must therefore be made 
in the result. This makes this method rather inconvenient 
and inaccurate. Even when measuring the total radiation by 
absorption in a calorimeter, it is practically impossible to 
collect the total radiation without either losing some, or 
including energy, which is not radiation, but heat conduc- 
tion or convection. Obviously, by enclosing the radiator in 
the calorimeter, the latter would measure not only the radi- 
ation, but also the power lost by heat conduction, convec- 
tion, etc. 

Sometimes the power of radiation can be measured by meas- 
uring input and losses. Thus, in an incandescent lamp, the 
electric-power input is measured, and the power lost by heat 
conduction and convection estimated if not entirely negligible. 
In those cases in which all or most of the energy supplied is 
converted into radiation, as in an incandescent lamp, this 
method is the most exact. However, it can directly measure 
only the total radiation power. To measure the different parts 
of the radiation so as to determine separately the power in the 
visible, the ultra-red, and the ultra-violet range, the method of 
input and losses can be used to give the total radiation power, 
and, by bolometer or other means, the relative powers of the 
component radiations measured in a beam of light. From the 
total radiation and the ratio of its components, then, follows 
the values of radiation power of the components. 

75. Light, however, cannot be measured by any of the pre- 
ceding methods, since light, in the sense in which it is con- 
sidered photometrically, is not power, but is the physiological 
effect of certain wave lengths of radiation, and therefore can- 
not be measured, physically, as power, but only physiologically, 


168 RADIATION, LIGHT, AND ILLUMINATION. 

by comparison with other physiological effects of the same 
nature. 

The power of visible radiation obviously can be measured, 
and thus we can express the power of the visible radiation of 
a mercury lamp or an incandescent lamp in watts. But the 
power of visible radiation is not proportional to the physiologi- 
cal effect, and thus not a measure thereof. One watt of green 
radiation gives many times as great a physiological effect, that 
is, more light, as does one watt of red or violet radiation, and, 
besides, gives a different kind of physiological effect: a differ- 
ent color. 

The unit in which illuminating value of light, or its intensity, 
is expressed as the "candle-power," is, therefore, a physiological 
and not a physical quantity, and hence it has no direct or con- 
stant relation to the unit .of power, or the watt. The unit of 
light intensity has been chosen by convention: as the physio- 
logical effect exerted on the human eye by 5 sq. mm. of melting 
platinum, or by a flame burning a definite chemical compound 
— as amyl acetate or pentane — at a definite rate and under 
definite conditions, etc. 

Broadly, therefore, the conception of a chemical equivalent of 
light, that is, a relation between candle power and watt, is 
irrational, just as, broadly, a relation between time and distance 
is irrational; that is, just as distance cannot be expressed by 
the unit of time, so candle power cannot be expressed by a 
unit of power, as the watt. A relation between two such 
inherently different quantities can be established only by an 
additional conventional assumption, and varies with a change 
of this extraneous assumption. Thus stellar distances are 
measured in " light years," that is, by the distance traveled by 
the light in one year, as unit. So also the physiological effect 
of one definite color of light, as that of the green mercury line, 
or the yellow sodium line, or the red lithium line, can be related 
to the unit of power, or the watt, and we may speak of a me- 
chanical equivalent of green light, or of yellow light, or of red 
light. When doing so, however, we give to the term " mechan- 
ical equivalent" a different meaning from what it has in physics, 
for instance, as "mechanical equivalent of heat." The latter 
is the constant relation between two different forms of the 
same physical quantity, while, for instance, the "mechanical 


MEASUREMENT OF LIGHT AND RADIATION. 169 

equivalent of green light " is the relation between a physiolog- 
ical effect and the physical quantity required to produce the 
effect, and thus is not necessarily constant, but may, and does, 
vary with the intensity of the effect, the individuality of the 
observer, etc. It appears, however, that at higher intensities 
the relation is very nearly constant and the same with differ- 
ent observers, so that it is possible to express the physiological 
effect of a definite wave length of radiation, within the accuracy 
of physiological measurements, by the power consumed in pro- 
ducing this wave length of radiation; but it becomes entirely 
impossible to compare physiological effects of widely different 
wave lengths by comparing the power required to produce them. 

When speaking of mechanical equivalent of light, it thus 
must be understood in the extended meaning of the word, as 
discussed above. 

76. In photometry, and in general in illuminating engineer- 
ing, it is of essential importance to keep in mind this difference 
in the character of light, as physiological effect, and radiation, 
as physical quantity of power. This is the reason why all 
attempts to reduce photometry to a strictly physical measure- 
ment, and thereby bring photometric determinations up to 
the high grade of exactness feasible in physical observations, 
have failed and must necessarily fail; we cannot physically 
compare an effect as light, which is not a physical quantity, 
but somewhere in all photometric methods the physiological 
feature, that is, the judgment of the human eye, must always 
enter. 

Photometric tests therefore can never have the accuracy of 
strictly physical determinations. All attempts to eliminate 
the judgment of the human eye from photometry, by replac- 
ing it by the selenium cell, or the photographic plate, or 
Crookes' radiometer, etc., necessarily are wrong in principle and 
in results: some of those instruments, as the bolometer, the 
radiometer, etc., compare the power of the radiation, others, 
as the selenium cell or the photographic plate, the power of 
certain changes of radiation, but their results are comparisons 
of power, and not of physiological effects, and thus they can- 
not be of value in measurement of illuminating power. 

Measurements of light thus are made by comparison with 
an arbitrarily chosen conventional unit, a primary standard 


170 RADIATION, LIGHT, AND ILLUMINATION. 

of light, as " standard candle," or a duplicate or multiplicate 
thereof. Obviously, in measurements of light, usually not the 
primary standard of light is used, but a more conveniently 
arranged secondary standard of light, that is, a standard which 
has been calibrated by comparison, directly or indirectly, with a 
primary standard. 

77. The most accurate method of comparing lights is the 
zero method, as represented by the different types of photom- 
eters. The illumination produced by the two different sources 
of light — the one to be tested and the standard — are made 
equal by changing the relative distances of the sources. At equal 
illumination their intensities are proportional to the square of 
their distances. Thus, for instance, in the bunsen photometer, 
as shown diagrammatically in its simplest form in Fig. 55, the 


FIG. 55. 

two white screens A and B are illuminated, the one, A, by the 
light, L, which is to be tested, the other, B, by the standard S, 
as a calibrated or standardized 16-cp. incandescent lamp, and 
then either L or S or both are moved until, seen from (7, the 
two sides A and B of the screen become equal, that is, the divid- 
ing line C between them disappears. When this is the case, 
L -T- S = x2 -T- 7/2, where x and y are the two distances of the 
sources from the screen. 

Different modifications of the bunsen photometer are most 
commonly used. 

As the sensitivity of the eye to differences of illumination is 
not very great, usually a number of readings are taken on the 
photometer, and then averaged. 

For testing incandescent lamps, L, as standard S, a calibrated 
incandescent lamp is used, operated on the same voltage supply, 
so that fluctuations of light caused by minor fluctuations of sup- 
ply voltage eliminate by appearing in both sources L and S. 


MEASUREMENT OF LIGHT AND RADIATION. 171 


For similar reasons, when testing gas lamps or other flames, 
L, as S, a flame standard, as the pentane lamp, is used, so that 
the effect of barometric pressure, humidity of the air, etc., 
appears in both lamps and thereby does not appreciably affect 
the comparison of their light. 

A quick and approximate method of comparison of sources 
of light is given by the shadow photometer by moving an 
object between the two lamps until the two shadows of the 
object give the same darkness. When this is the case, the 
illumination at the object is the same, and the intensities of 
the two sources are then proportional to the square of their dis- 
tances from the object. Street lamps can, in this manner, be 
rapidly compared, with fair 
accuracy, by pacing the 
distance from the one to 
the other, and noting when 
the two shadows of the 
observer are equal in dark- 
ness. If then at x steps 
from the one lamp, Llt the 
shadows are equal, and y 
further steps are required 
to reach the second lamp, 
L0, it is : 


0 


A very convenient form 
of photometer, which gives 
good results even where 
the two lights are of some- 
what different color, is the FlG 56 
paraffine photometer. A 

block of paraffine is cast, as shown in Fig. 56, divided by a 
sheet of tinfoil in the center C, and covered with tinfoil except 
at the top and on the sides A and B. It is advantageous to 
have the center sheet of tinfoil C perforated by a hole D. 

The block of paraffine then is held so that the side A is illu- 
minated by the one lamp, L, the side B by the other lamp, S, as 
shown in Fig. 57. As paraffine is translucent, the entire block 
then appears luminous, and a beam of light is seen traversing 


172 RADIATION, LIGHT, AND ILLUMINATION. 

the block from the hole D, on the side which receives less light. 
By moving the paraffine block between the lamps L and S, 
until both sides of it are of the same luminosity, that is, the 
dividing line C and the beam cast by hole D disappear, equality 
of the two illuminations can be located rapidly and with great 
accuracy. 


FIG. 57. 

78. When comparing lamps giving light of the same color, as 
incandescent lamps of the same filament temperature, that is, 
the same efficiency, exact comparisons can be made — within 
the limits of sensitivity of the eye for intensity differences — 
by the photometer by making the two sides A and B of the 
Bunsen photometer screen, or the two halves of the paraffine 
block, identical, that is, making the dividing line C disappear. 
If, however, the color of the two lights is not the same, as, for 
instance, when comparing a tungsten lamp and an ordinary 
incandescent lamp, no position of the photometer can be found 
where the dividing line C between A and B (Figs. 55, 57) dis- 
appears, but a color difference always remains. To make a 
comparison, it is therefore necessary for the eye to judge 
when the two sides A and B are of the same intensity while of 
different colors. If the color difference is small, as between two 
different types of incandescent lamps, this can be done with 
fair accuracy, though obviously not as accurately as the com- 
parison of lights of identical colors. If, however, the color 
difference is great, as between the mercury arc and the orange- 
yellow carbon filament lamp, the uncertainty of equality of 
the intensity of illumination becomes very great, and constant 
errors appear, due to the difference of the physiological effect 
of different colors, and differences also appear between differ- 
ent observers, so that the photometric comparison of light 
sources of greatly different colors is quite unreliable, and that 
not merely by inaccuracy, but by unknown and individual con- 
stant errors. 

In such cases, frequently lights of intermediary color are 
used to reduce the differences in each observation. Thus the 
carbon filament lamp is compared with the tungsten lamp, the 


MEASUREMENT OF LIGHT AND RADIATION. 173 

tungsten lamp with the carbon arc lamp, and the latter with 
the mercury arc lamp. Hereby the uncertainty of each obser- 
vation is reduced by the reduced color difference. In the final 
result, however, the comparison of the carbon incandescent- 
lamp standard and the mercury arc lamp no advantage is 
gained, because the errors of the successive measurements add. 
Especially is this the case with the constant errors, that is, 
errors due to the specific color effect, and in consequence thereof 
the inaccuracy of the final result is not much better than it 
would be by single and direct comparison. 

A photometer which is sometimes used for comparing lights 
of different color, and is based on a different principle from 
either of the above discussed instruments, is the flicker pho- 
tometer. In its simplest form it consists of a stationary disk, 
illuminated by the one lamp, and a rotating half disk or sector 
in front of it, which is illuminated by the other lamp. At slow 
rotation a flicker shows, which disappears if the speed be- 
comes sufficiently high. It is obvious that the more nearly 
equal the effect on the eye of the two illuminations — that of the 
stationary disk and that of the revolving sector — the lower is 
the speed at which the flicker disappears, and, by adjusting the 
distances of the two lamps so as to cause the flicker to dis- 
appear at the minimum speed, the instrument indicates equality 
of the effect of the two successive illuminations on the eye. 
This is frequently considered as representing equality of the 
illumination, and the instrument in this manner used to com- 
pare illuminations. There is, however, no reason why this 
should be the case, but, on the contrary, it is improbable. As 
the persistence of vision, and in general the physiological effects 
of different colors, are different, the flicker photometer must be 
expected to have a constant error which increases with color 
difference; that is, it does not compare lights of different color 
by their illuminating values, but by some other feature not 
directly related thereto. 

79. The photometer thus cannot satisfactorily compare lights 
of different colors. After all, this is obvious: the photom- 
eter compares by identity, but lights of different colors can- 
not be identical, and thus two such lights cannot be more 
broadly compared than any other two quantities of different 
character; that is, a green light can no more be equal to a red 


174 RADIATION, LIGHT, AND ILLUMINATION. 

light than a piece of stone can be equal to a piece of ice. A 
comparison of quantities of different nature is possible only 
regarding particular features of the quantities which they have 
in common. Thus a piece of stone and a piece of ice can be 
compared regarding their weight, or their density, etc. In the 
same manner, two different colors of light, or in general two 
different frequencies of radiation, can be compared by any 
feature which they have in common. Thus, for instance, the 
photographic plate compares them in their chemical activity, 
the bolometer by their physical energy. 

Light is used for seeing things by, that is, distinguishing 
objects and differences between objects. Regarding this feature, 
the distinction of objects given by them, different colored lights 
can be compared, and a green light can be made equal to a red 
light in illuminating value. 

It thus means that any two lights, regardless of their color, 
have the same intensity if, at the same distance from them, 
objects can be seen with the same distinctiveness, as, for in- 
stance, print read with equal ease. The only method, therefore, 
which permits comparing and measuring lights of widely differ- 
ent color is the method of " reading distances," as used in the 
so-called luminometer. It after all is the theoretically correct 
method of comparison, as it compares the lights by that prop- 
erty for which they are used. Curiously enough, the lumi- 
nometer, although it has the reputation of being crude and 
unscientific, thus is the only correct light-measuring instrument, 
and the photometer correct only in so far as it agrees with the 
luminometer, but, where luminometer and photometer disagree, 
the photometer is wrong, as it gives a comparison which is 
different from the one shown by the lights in actual use for 
illumination. 

The relation between luminometer and photometer for meas- 
uring light intensity, therefore, is in a way similar to the relation 
between spark gap and voltmeter when testing the disruptive 
strength of electrical apparatus: while the voltmeter is fre- 
quently used, the exact measure of the disruptive strength is 
the spark gap and not the voltmeter, and, where the spark gap 
and voltmeter disagree, the voltmeter must be corrected by the 
spark gap. In the same manner the luminometer measures 
the quality desired — the illuminating value of the light — but 


MEASUREMENT OF LIGHT AND RADIATION. 175 


FIG. 58. 


the photometer may be used as far as it agrees with the lumi- 
nometer. 

80. The luminometer can hardly be called an instrument, 
but it is merely a black box, as shown in Fig. 58, to screen off 
all extraneous light, and 
allow only the light of the 
source which is to be ob- 
served, to fall on the print. 
The print obviously must 
be black on white, that is, 
complete absorption and 
complete reflection, so as 
not to discriminate in 
favor of particular colors. 
No great accuracy could 
be reached by merely com- 
paring the ease of reading 
the same kind of print with different sources of light. A high 
accuracy, however, is reached by using a print which does not 
give definite words — in which letters which are not clearly 
seen cannot be guessed from the sense of the word or sentence 
— but a jumble of letters, capitals and small letters, arranged in 
meaningless words. 
Such a luminometer chart is given below: 

Amhof dirito amritu, Lisno ladse pemrane odo Ulay 
Foresca 1598720 woleb noitaidar. Ybod ergy may 
Pewos ex Idetnera, bsor poge Morf Tenscerophop War- 
dog; Omsk whykow efforau tespo ygnew col Brispo 
Monas albo darmosphor? Cottef vol Demno myo 
36802 Erbtomy, quot Hiaworu pio Nio cuguab Qaphla- 
qua H 530 K b n q; 267 Lloysir baraka nunc, cinq 
Viamara W x 4 zoliaq kama nambosi erianoscum. 
Zaraz didym fore ik yiquia Fumne. 

With such a printed chart in the luminometer, the observer 
moves towards the light or away from it — or the light is 
moved, with the observer stationary — until a point is found 
at which the large letters, as the capitals, can be clearly dis- 
tinguished, but the small letters are indistinguishable. This 
point can be found with great sharpness, and the accuracy of 


176 RADIATION, LIGHT, AND ILLUMINATION. 

observation by the luminometer when used in this manner is 
nearly as great as that of the ordinary photometer, but, unlike 
the photometer, the luminometer gives consistent and reliable 
readings even with widely different colors of light. 

The comparisons made by the luminometer of widely differ- 
ent colored lights by different observers agree remarkably 
well, showing that the distribution of color sensitivity is prac- 
tically the same in different human eyes. Only occasionally a 
person is found with abnormally low sensitivity for some par- 
ticular color — this obviously is not a fault of the instrument, 
but in the nature of the measured object, which is a physiologi- 
cal effect, and as such may be different in different persons. 

The luminometer can be still further improved by illuminat- 
ing one half of the printed chart from the one, the other half 
from the other, source of light, and then moving the two sources 
to such distances that the small letters on both sides of the chart 
become indistinguishable, while the capitals are distinguishable. 

As well known, the luminometer is largely used for measuring 
street illumination, as it is very simple and requires no special 
technical training. Such observations, where the distances are 
measured by pacing, are crude, and, to get exact results by the 
luminometer, the same care is required as when using the pho- 
tometer. 

The limitation of the luminometer, as generally used, is that 
it compares lights at constant and relatively low intensity of 
illumination. The relative intensity of light sources of differ- 
ent colors changes however over a wide range with the inten- 
sity of illumination at which they are compared, as discussed 
in Lecture III. A complete comparison of different colored 
lights therefore requires measurements at different intensities 
of illumination. 

With a photometer, the intensity of illumination can usually 
be varied over a wide range by bringing the light sources 
nearer to the screen or removing them farther. In the lumi- 
nometer, only a moderate change of the intensity of illumina- 
tion, at which the comparison is made, can be produced by 
using different sizes of print, and the interpretation of such 
tests is difficult. 

A wide and definite range of intensities of illumination, at 
which comparison of the light sources is made by the lumi- 


MEASUREMENT OF LIGHT AND RADIATION. 177 

nometer, can be secured by using gray print on white back- 
ground, and lights of different colors thereby compared over 
a wide range of illuminations. 

With a luminometer chart of gray letters, of albedo a, on 
white background, the illumination or light flux density, at 
which the luminometer readings are made as described above, 
is: 


where i0 is the illumination or light flux density when using 
black print on white background. 

81. Since light is a physiological effect, the measurement of 
this effect requires a physiological unit, which is more or less arbi- 
trarily chosen. Such a unit may be a unit of light, that is, of 
light intensity or light flux, as a flame, or it may be a unit of 
light-flux density or illumination, that is, of light flux per unit 
area. 

Thus, a fairly rational unit of light-flux density or illumination 
would be the illumination required at the limits of distinguish- 
ability of black print of a specified type, on white back- 
ground, that is, the light flux per unit area by which, with such 
black print on white background, the capitals and large letters 
can still be distinguished, while the small letters are indistin- 
guishable. 

Usually so-called " primary standards " have been chosen as 
units of light intensity. Violle recommended as standard the 
light at right angles from 1 sq. cm. of melting platinum. (Ap- 
proximately 20 cp.) This unit has never been introduced, 
partly due to the difficulty of producing it, partly due to the 
unsuitability of platinum for this purpose: platinum gives 
gray-body radiation, therefore any impurity, as a trace of car- 
bonized dust, may increase the light. 

Candles have been largely used for standards, as the name of 
the unit implies, made and burned under definite specifications. 
As individual candles vary widely in their light, the use of the 
candle as standard necessarily is very crude and inaccurate, 
and thus unsatisfactory. 

The only primary standard which has found extensive and 
international use is the amyl-acetate lamp of Hefner. This is 
a lamp burning arnyl acetate at a definite rate, with a definite 


178 RADIATION, LIGHT, AND ILLUMINATION. 

height of flame and definite conditions regarding air pressure 
and humidity. This Hefner lamp, or German candle, equals 
about 90 per cent of the British candle and equals 90 per cent of 
the international candle. Amyl acetate has been chosen, as it 
can easily be produced in chemical purity, and gives a good 
luminous flame. The flame, however, is somewhat reddish, thus 
markedly different from the color of the carbon incandescent 
lamp, and departs still much more from that of the tungsten 
lamp. Instead of amyl acetate, pentane has been used and is 
still used. It gives a somewhat whiter flame, but the pentane 
lamp is not as constant. 

However, the Hefner lamp, while universally used as pri- 
mary standard, is altogether too inconvenient for general pho- 
tometric use, and, for this purpose, usually incandescent lamps 
are employed which have been compared with, and standard- 
ized by, the Hefner lamp. In reality, from these standard 
incandescent lamps, by comparison, other incandescent lamps 
have been standardized, and so on, until of late years the 
Hefner lamp has been finally abandoned as primary standard of 
light, and we have no primary standard; but the standard of 
light is maintained by comparison with incandescent lamps 
kept for this purpose; that is, it is maintained by duplication of 
samples, and by international agreement an incandescent lamp 
unit has been adopted as the standard or " international candle." 

82. A number of primary standards have lately been pro- 
posed, but none has yet been much developed. 

Some work was done on the acetylene flame, burning in 
oxygen. It has a very suitable white color, but its intensity is 
very sensitive to slight impurities of the acetylene, and such 
impurities, as hydrogen, are difficult to avoid. 

A suitable unit appears to be the normal temperature radiation 
at specified temperature, and the temperature could be defined 
by the ratio of the radiation power of definite wave lengths. 
Thus, such a unit would be an incandescent lamp, radiating x 
watts at such temperature that the power radiated between wave 
lengths 45 and 55 bears to the power radiated between wave 
lengths 60 to 70 the ratio y. The radiated power x could prob- 
ably be determined from electric power input and losses. Such 
a unit would probably be replaceable with considerable exact- 
ness, but would still be arbitrary. 


MEASUREMENT OF LIGHT AND RADIATION. 179 

A further possible unit would be the light given by one watt 
visible radiation, by normal temperature radiation at a definite 
temperature — the latter specified and measured by the ratio 
of radiation power of two different ranges of wave length. 
Such definition would base the physiological effect, under speci- 
fied conditions of temperature, on the unit of power, or the 
watt, as unit of light. Its disadvantage is the difficulty of 
measuring the power of the total visible radiation, since at the 
ends of the visible spectrum the power is high and the physio- 
logical effect low, and a small error in the limits of the spectrum 
would make a considerable error in the result. 

More satisfactory, therefore, appears the derivation of a 
primary standard of light by combining three primary colors of 
light in definite power proportions. Thus, choosing three lines 
of the mercury spectrum — in the mercury arc in a vacuum, 
perfect steadiness and high intensity can easily be produced — 
in the red, green and blue, about equidistant from each other, 
these three radiations would be combined in definite propor- 
tions — chosen so as to give the desired color of the light, 
probably a yellowish white — and in such qualities as to 
give one watt total radiation, or, if as unit the illumination 
is used, to give one microwatt per sq. cm.; that is, the 
standard of illumination would be the illumination produced 
by one microwatt of radiation power, composed of the three 
wave lengths of the three chosen mercury lines, in definite 
proportions. 

Such a standard, derived by combination of definite wave 
lengths, which are easily reproducible, appears the most satis- 
factory in regard to permanence. It would incidentally give a 
numerical expression to color values, as any color then would 
be represented by the numerical ratio of the power of the three 
standard spectrum radiations, which, mixed together, give the 
color.* 

83. Light is produced for the purpose of illumination. The 
raw material used in illumination is the flux of light issuing 
from the illuminant. The important characteristic of the illu- 
minant, by which it is judged, thus is the total flux of light 
issuing from it, and its measurement one of the main objects 
of photometry. 

* Proc. A. I. E. E., (1908). 


180 


RADIATION, LIGHT, AND ILLUMINATION. 


The photometer or luminometer, however, gives the light 
intensity in one direction only. Thus, to measure the total 
flux of light, the light intensity in all directions in space 
must be determined, and added, or averaged, to get the 
average intensity of light, usually called the "mean spherical 
intensity." 

If the light intensity were the same in all directions, one 
single photometric observation would give it, and therefrom, by 
multiplying with 4 TT, the total flux of light would be obtained. 
This, probably, is never the case. 

Many illuminants, however, give a symmetrical distribution 
of light around an axis, so that the distribution curve is the 
same in all meridians. This is practically the case with the or- 
dinary incandescent lamp with oval filament, and also with the 
tantalum and the tungsten lamp. Thus if the curve, shown in 
Fig. 59, is the distribution curve in one meridian, it is the same 


FIG. 59. 

in every other meridian, and for photometric test of the illumi- 
nant it is sufficient to measure the light intensities in one merid- 
ian only, for instance, from 10 to 10 degrees. To get herefrom 
the mean or average intensity, it would obviously be wrong to 
merely average all the intensities under equal angles, since the 
equatorial intensity covers a far greater area — a zone of 10 de- 
grees width and 2 x circumference — than the intensity of lati- 
tude <j>j that is, under angle <f> from the horizontal: the latter 
covers a zone of 10 degrees width and 2 it cos $ circumference, 
and the polar intensity covers only a point. 
To get the total flux of light, the intensity under each angle <£ 


MEASUREMENT OF LIGHT AND RADIATION. 181 

thus is to be multiplied with the area of the zone which it 
covers, 2 nd cos <j>, where d is the angular width of the zone 
(10 deg., for instance), and then added. The average or mean 
spherical intensity then is derived herefrom by dividing with 
the surface of the sphere, or by 4 re. 

Thus, to get the mean spherical intensity from the distribu- 
tion curve, the instantaneous values of intensity, taken under 

equal angles d, are multiplied each by cos <£, then added, and 
ft 

the sum multiplied by -, where d, the angular distance under 

2 

which observations are taken, is given in radians, that is, 

10 deg. gives d = — - TT. This usually is done graphically. 
180 

Occasionally, as in incandescent lamps with single-loop fila- 
ment, the light intensity is not the same in all meridians, but a 
maximum in two opposite meridians: at right angles to the 
lamp, and a minimum in the two meridians at right angles to 
the former, giving a horizontal or equatorial distribution of 


FIG. 60. 

light intensity about as shown in Fig. 60. In this case the 
horizontal distribution curve may also be determined photo- 
metrically, averaged so as to give the mean horizontal intensity 


182 RADIATION, LIGHT, AND ILLUMINATION. 

and the ratio of the mean horizontal intensity to the maximum 
horizontal intensity (or any other definite horizontal inten- 
sity); and the mean spherical intensity, as derived from the 
meridian of maximum horizontal intensity (or any other definite 
horizontal intensity), is multiplied with this ratio to get the 
real mean spherical intensity. Usually in this case measure- 
ments are taken only in one meridian, but during the test the 
lamp rotated around its vertical axis with sufficient speed, so 
that each observation in the meridian, under angle <£, in reality 
is the mean intensity in the direction <f>. Thus, in incandes- 
cent lamp tests, usually the lamp is revolved, so as to average 
between the different meridians. 

As the distribution of intensity in the meridian is the same, 
within the error of photometric test, for all incandescent lamps 
of the same type of filament, usually the distribution curve of 
one meridian is measured once for all, therefrom the ratio of 
horizontal to mean spherical candle power, the so-called spherical 
reduction factor, determined, and then in further photometric 
tests of lamps of this type only the horizontal intensity meas- 
ured, and from this, dividing by the spherical reduction factor, 
the mean spherical intensity is derived. Thus, while with the 
incandescent lamp the intensity varies in each meridian, and is 
different in the different meridians, the mean spherical intensity 
nevertheless is derived by a single photometric observation of 
the horizontal intensity with rotating lamp: the rotation aver- 
ages between the different meridians, and the spherical reduction 
factor translates from horizontal to mean spherical intensity. 
Reduction factors of incandescent lamps usually are between 
0.75 and 0.80. 

84. Far more difficult is the matter with arc lamps : in the ordi- 
nary carbon arc lamp, the intensity also varies in the meridian, 
and is different in the different meridians, but not with the 
same regularity as in the incandescent lamp, and, further- 
more, the intensity distribution between the different meridi- 
ans, as well as, to a lesser extent, the total light flux of the 
lamp, varies with the time. The arc is not steady and con- 
stant in position, as the incandescent filament, but wanders, 
and the light intensities on the side of the lamp, where the arc 
happens to be, thus are greater than on the side away from the 
arc. The meridians of maximum and of minimum intensity, 


MEASUREMENT OF LIGHT AND RADIATION. 183 

however, do not remain constant in position, but continuously 
change with the wandering of the arc. Therefore, by measure- 
ments in a single meridian, the distribution curve of maximum 
and that of minimum intensity can be determined by waiting 
during the observation for the arc to come around to the 
side of the observer — maximum — and go to the opposite 
side — minimum — intensity. Such curves are shown in Fig. 61. 


FIG. 61. 

This, however, carried out for every angle in the meridian, 
makes arc-light photometry rather laborious, especially as 
the total intensity pulsates with the time, and therefore a 
considerable number of readings have to be taken in every 
position. 

Therefore, for arc light photometry, integrating photometers 
are especially desirable, that is, photometers which, by a single 
observation, determine — more or less accurately — the mean 
spherical intensity; that is, the average intensity, in all directions. 
With such an integrating photometer, by taking a number of 
successive readings and averaging, so as to eliminate the varia- 
tion of total intensity with the time, the mean spherical inten- 
sity, and thus the total flux of light, can be derived more 
rapidly. 

Such an integrating photometer is the Matthews photometer. 
It consists of a circle of inclined mirrors, which surround the 
lamp and reflect the light in all — or, rather, a certain number 
of — different angles into the photometer, and there the differ- 
ent reflected beams are by absorption reduced in the proportion 


184 RADIATION, LIGHT, AND ILLUMINATION. 

of cos (f> and combined on the photometer screen. Obviously, 
the Matthews photometer does not average the intensity in all 
directions, but only in two meridians opposite to each other; 
however, by averaging a number of successive readings, very 
accurate results can be derived. 

A method of averaging in all directions is based on a similar 
principle as that by which the radiation from the interior of a 
closed sphere of constant temperature was found to be black- 
body radiation: if the lamp is located in the center of a closed 
sphere (perforated only at the place where the photometer 
enters) of perfectly white reflecting surface, then the light in- 
tensity throughout the entire inner surface of the sphere is 
uniform, and is the mean spherical intensity of illumination at 
the distance of the radius of the sphere. The reason is : every 
element of the interior of the sphere receives light directly from 
the lamp, and also light reflected from all the other elements 
of the sphere, so that the total light received at every element 
of the sphere is the same, hence is the average illumination. 
By enclosing the test lamp in the center of such a photometric 
sphere of sufficient size, its mean spherical intensity thus can be 
determined by a single reading. Such an arrangement has the 
further advantage that it allows a direct measurement of mean 
spherical intensity — or light flux — of such illuminants as the 
mercury lamp, in which the radiator is of such extent that it 
cannot be considered as a point without going to excessive 
distances. 

85. Photometrically, and in illuminating engineering, only 
the mean spherical intensity — which represents the total flux 
of light — and the distribution curve — which represents the 
distribution of this light in space — are of importance. The 
"horizontal intensity7' has been used as a conventional rating 
of incandescent lamps, but is merely fictitious, as it does not 
mean an actual average horizontal intensity, but the horizontal 
intensity which the light flux of the lamp would give with the 
standard mean spherical reduction factor, if the filament had 
the standard shape. 

Downward candle power and maximum candle power obvi- 
ously have no meaning regarding the light flux of the lamp, 
but merely represent a particular feature of the distribution 
curve. 


MEASUREMENT OF LIGHT AND RADIATION. 185 

Hemispherical candle power is used to some extent, especially 
abroad. It is a mixture between light flux and distribution 
curve, and as it gives no information on the total light flux, nor 
on the actual distribution curve, and may mislead to attribute 
to the lamp a greater light flux than it possesses — by mistaking 
it with mean spherical candle power — it has no excuse for exist- 
ence, and should not be used.