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                     THE FIFTEEN WATT TUNGSTEN LAMP

                                   BY

                         CLAIR ELMORE ANDERSON

                  B. S., University of Illinois, 1911

                                 THESIS

      Submitted in Partial Fulfillment of the Requirements for the

                               Degree of

                           MASTER OF SCIENCE

                       IN ELECTRICAL ENGINEERING

                                   IN

                          THE GRADUATE SCHOOL

                                 OF THE

                         UNIVERSITY OF ILLINOIS

                                  1912




[Illustration:

  UNIVERSITY OF ILLINOIS
  THE GRADUATE SCHOOL

  May 31, 1912

  I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY
    CLAIR ELMORE ANDERSON ENTITLED THE FIFTEEN WATT TUNGSTEN LAMP BE
    ACCEPTED AS FULFILLING THIS PART OF THE REQUIREMENTS FOR THE DEGREE
    OF MASTER OF SCIENCE IN ELECTRICAL ENGINEERING

  Ernst Berg
  In Charge of Major Work

  Ernst Berg
  Head of Department

  Recommendation concurred in:

  Morgan Brooks
  Ellery B Paine
  J M Bryant
  Committee on Final Examination]




                                CONTENTS


                                                    Page

                 I. Introduction,                   1

                II. Description of Lamps and Tests, 2-4

               III. Characteristic Curves,          5-12

                IV. Spherical Candle Power,         13-15

                 V. Phenomena of “Overshooting”,    16-18

                VI. Theories of “Overshooting”,     19-20

               VII. Amount of “Overshooting”,       21-22

              VIII. Curves of “Overshooting”,       23-26

                IX. Conclusions,                    27

------------------------------------------------------------------------




                       THE 15 WATT TUNGSTEN LAMP




                            I. INTRODUCTION.


Since the introduction of the tungsten lamp some five years ago, the
manufacturers have attempted continually to produce smaller and smaller
units in the standard voltages. The latest lamp offered today is the 115
volt, 15 watt, tungsten, and it is the purpose of this paper to show the
characteristics of this lamp, how it compares with the larger units as
to life under different conditions and its behavior in general.

First of all, it must be borne in mind that these tests have been made
upon a comparatively small number of lamps, and for that reason the
results should not be taken as absolutely conclusive. For the life
tests, at least 100 lamps should have been used under each condition,
but this was impossible because of the expense.

Special attention has been given to the phenomenon of “overshooting”. An
entire year could have easily been spent investigating this subject, and
the writer regrets that lack of time has prevented more elaborate and
comprehensive tests of this strange phenomenon.




                  II. DESCRIPTION OF LAMPS AND TESTS.


The total number of 15 watt lamps tested was 24, one half of which was
obtained directly from the manufacturer and the other half bought in
open market. It is well to mention at this time that this may have been
the cause of the different qualities as brought out by the life tests.

The lamps were rated at 1.31 watts per horizontal candle power and were
supposed to have a useful life of 1000 hours. The voltage ratings of
those obtained from the factory were 114 - 112 - 110 and those bought in
open market were 115 - 113 - 111. The correct efficiency of the lamps as
found by test was 1.34 watts per candle power. A shot diagram follows
which shows the actual rating of the lamps at high efficiency.

All readings were made by a Lummer-Brodhun photometer and the voltmeters
and ammeters used were carefully standardized. The ammeter was placed
beyond the voltmeter in order to get the true current taken by the lamp.
The drop across the ammeter was taken into account in the voltmeter
readings.

Life tests were made under two conditions, namely, a shock test where
the lamps received severe vibrations and a test under ideal conditions,
i.e. no jar and constant voltage. In order to obtain vibrations for the
lamps upon the shock test, a small motor, with its shaft pulley off set,
was screwed rigidly to a table. The lamps were placed in a normal
position upon the table by means of wooden frames. The result was that
when the motor was running it had a pounding effect, thus putting the
table, consequently the lamps, in a state of severe vibration. The
filaments of the lamps could be seen violently shaking for some
distance. The test was indeed a hard one, and one that would not be
found in many actual cases. It is very doubtful if railway lamps are
subjected to such a strain and they are of the heavy filament low
voltage type. The following photograph shows the arrangement above
described. Ten 15 watt lamps were used on this test, the remainder shown
being 20 and 25 watt and carbons.

[Illustration: photograph, arrangement of tungsten lamps]




[Illustration: _Shot diagram for 15 watt lamps_]




                      III. CHARACTERISTIC CURVES.


Figure 1, Page 8, shows the variations of the candle power with the
voltage, current and watts. Figure II shows the relation between candle
power and the efficiency, watts per horizontal candle power, and also
the variation of the candle power with the resistance.

An empirical formula for the candle power expressed as a function of the
watts is cp = KW^x where K is a constant of the lamp and W denotes the
watts. From the curve when cp = 5, watts = 11.1 and when cp = 15,
watts = 17.5 dividing

                    cp_{1}/cp_{a} = KW_{1}^x/KW_{a}^x

substituting

                         5/15 = 11.1^x/17.5^x

and

                    log 3 + x log 11.1 = x log 17.5
                    .4771 + 1.0453x = 1.2430x
                    .198x = .4771
                        x = 2.41

solving for the constant K

                            5 = K 11.1^{2.41}
                            5 = 332 K
                            K = .0150

and the final equation for the candle power is

                          cp = .0150 × w^{2.41}

In the same way, the candle power may be expressed in terms of the
voltage and this is found to be

                       cp = 334 × 10^{-9} E^{3.68}

This formula checks precisely with the one used in the engineering
department of the General Electric Company at their lamp works,
Harrison, N.J.

The horizontal distribution curve of a lamp with its filament mounted as
is the modern tungsten is nearly a circle. This is not true, however, in
the case of vertical distribution and this curve is shown, Figure III.
As will be noted, the tip candle power is only about 23 per cent of the
horizontal.


                              Life Tests.

The results of the life tests were very surprising. The lamps upon the
test under ideal conditions, namely, no vibrations and constant voltage,
had only an average life of 460 hours, while every one of those upon the
shock test are still burning at the present time, having been burned 300
hours. In order to make the test still more severe, the lamps were
subjected to vibrations without voltage being impressed, and as yet, not
a filament has broken, the total time being 400 hours. It was impossible
to give more time to these lamps as was done for those under ideal
conditions, for the reason it was thought unadvisable to leave the
motor, which gave the vibrations, running over night.

The curves have the same general form for the two conditions but the
variations are far more great for the lamps which were upon the shock
test. The reason for this is that the vibrations were so severe as to
shake parts of the filament together thus giving a partial short
circuit, causing great variations in candle power.

[Illustration:

  _Fig I_

  _Characteristic Curves for 15 watt tungsten lamps_
  _Lamp of average rating used_]

[Illustration:

  _Fig II_

  _Characteristic Curves for 15 watt tungsten lamps_
  _Lamp of average rating used_]

[Illustration:

  _Fig III_

  _Vertical Distribution for 15 watt 115 volt Tungsten lamp_]

[Illustration:

  _Life Tests_
  _15 Watt 115 Volts Tungstens_
  _Conditions Ideal_
  o—_Burned Out_]

[Illustration:

  _Life Tests_
  _15 watt 114 volts tungsten_
  _Shock Conditions_
  _All lamps still Burning_]




                      IV. SPHERICAL CANDLE POWER.


Owing to the absence of an integrating photometer, the mean spherical
candle power has been found by Kennelley’s graphical method. This method
is very simple as compared with Rousseau’s and has the advantage of
yielding the mean spherical intensity as a one dimensional quantity.
This dispenses with the use of a planimeter or equivalent measuring
surface device. It consists essentially in determining graphically from
the given polar curve an evolute and the involute of the same and then
projecting this involute upon a vertical line. Half the length of the
projection is equal to the mean spherical intensity to the same scale as
the original polar curve.

Figure IV shows the method and is explained thus: The polar curve
O A H B corresponds to the distribution of intensity from an inverted
incandescent lamp having its base at V and tip at V´. This is not
precisely true but the only variation to speak of is that the tip candle
power does not fall off so much as the curve between B and O. This
variation is slight, however. The mean horizontal intensity is OH, the
diameter of the circle, and in this case is equal to 12.4 candle power.
In the diagram the construction is adapted to zones of 30° and the radii
of the midzones found i.e. at +75°, +45°, +15°, -15°, -45° -75°. These
are marked by dotted lines O t, O s, O r, O r´, O s´, O t´ respectively.

With radius O r and center O, the arc hra is described through an angle
of 30°. The radius Oa is drawn at the end of the arc. A distance Ab is
measured from a along a O equal to O s, the second midzone radius. With
a center b and radius O s, the arc ac is described through an angle of
30° so that bc makes an angle of 60° with the horizontal OH. The line bc
is drawn at the end of this arc. From c towards b, a distance cd is
marked off equal to Ot, the third midzone radius. With center d and
radius O t, the arc ce is described through an angle of 30° so that de
makes an angle of 90° with the horizontal OH. The line de is drawn.

The arc ha´c´e´ is extended from the horizontal to the vertical beneath
in the same manner as above by steps of 30° with centers O, b´, and d´,
and radii Or´, OS´ and Ot´ respectively. The curve ecarr´a´c´e´ is now
continuous and complete. A vertical line QQ´ is drawn through the
convenient point H and the points e c a a´ c´ e´ are projected upon the
same. The length HQ, is the upper hemispherical intensity and the length
HQ´ the lower hemispherical intensity. Their arithmetical mean is the
mean spherical intensity. Since in this case the upper and lower
hemispheres are symmetrical HQ = HQ´ = QQ´/2 = mean spherical intensity.
By measurement this half length is found to be 3.125 inches and from the
scale used this corresponds to 9.67 candle power. The spherical
reduction factor for these lamps is, then

                            9.67/12.4 = 78%

[Illustration:

  _Fig IV_
  _Kennelly’s Diagram for Spherical C. P._]




                    V. PHENOMENA OF “OVERSHOOTING”.


The singular property of the tungsten lamp to “overshoot” or to give
temporarily a higher initial than normal candle power, was first
discovered by John B. Taylor and is explained in the following
manner:—The filament of the carbon incandescent lamp possesses a
negative temperature coefficient; that is to say, a rise in voltage
causes a more than corresponding rise in current and when the lamp is
connected to a source of constant potential, the current starts at a
comparatively small value and increases to a maximum when the lamp has
attained full candle power.

In the case of the tungsten lamp, the situation is just the reverse,
since tungsten has a positive temperature coefficient. When the lamp is
connected to a constant potential supply the current is a maximum when
the lamp is cold and decreases to a final value when the lamp reaches
full brilliancy. The most important difference between the two lamps due
to these different characteristics is that while a tungsten lamp reaches
full candle power the instant the current is turned on a carbon
incandescent lamp comes up to full candle power only after a perceptible
period of time.

The apparent temporary increase in the candle power of a tungsten lamp
was observed early after the lamp was invented but it was generally
ascribed to some possible physiological action due to the slow
contraction of the pupil of the eye.

The following curve was obtained by means of the oscillograph and shows
clearly the rush of current for the first instant after the lamp is
turned on. The break in the curve is due to an imperfection in one of
the operating switches and has nothing to do with any characteristic of
the lamp. The cycle wave was put on merely to obtain the time.

[Illustration: photograph, current after lamp is turned on]

In order to prove that this overshooting occurs, an actual photograph of
the intensity has been made. This was obtained by making a box
1´ × 1´ × 3´ absolutely light proof and arranging a lamp inside so that
it could be turned on and off at will. A slit, fitted with a shutter,
was cut in one end of the box which permitted the light to fall upon a
revolving oscillograph film. The film holder was attached to the box
with thin metal strips and revolved by means of a small motor. As is
seen the whole arrangement was nothing more than a large camera.

The following photograph shows the phenomenon quite clearly, point A
denoting where the lamp was turned on.

[Illustration: photograph, intensity of light, overshooting]




                    VI. THEORIES OF “OVERSHOOTING.”


The theory given by Taylor to account for the “overshooting” of tungsten
lamps is based on the fact that there is a small amount of residual gas
in the lamp, which is attracted to the walls of the lamp when it is
cold; and when the lamp is lighted and warms up, this residual gas is
driven off lowering the vacuum. With a high vacuum, practically all the
energy must be radiated from the filament; conversely, on a lowering of
the vacuum, some of the heat is carried away by convection and
conduction. When all the heat is carried away by radiation the filament
runs at a higher temperature and will give more light.

Another theory is that a cold tungsten filament lamp absorbs and
occludes certain gaseous substances from the low pressure space within
the chamber. Owing to the presence of these gases the filament shines
more brightly when first brought quickly to incandescence, but after the
gases have been driven off by the heat, the extra luminescence
disappears and can be regained only by prolonged cooling and rest.

Still another theory, and the one that seems the most logical to the
writer, is that the increase of resistance accompanying the rise of
temperature takes a certain small interval of time so that when the
temperature is rising at the rate of thousands of degrees per second,
the resistance lags perceptibly. The resistance does not suppress the
current as quickly as it should and an extra rush of current and heat
energy goes through the filament, raising the temperature above normal,
with a corresponding increase in brilliancy.




                     VII. AMOUNT OF “OVERSHOOTING”.


In order to determine the amount of over shooting, the writer has made
photographs as shown below. Number one was made with the lamp under
voltage, number two by using normal voltage and suddenly turning the
lamp on by means of a snap switch, thereby obtaining the overshooting,
and finally number three was made by impressing voltage above normal.
The pictures were obtained by using the photographic arrangement as
before described. All three prints were made from the same film, that is
the three pictures were made upon one film thus insuring the same
development and printing for all. The print has been cut merely to allow
a closer comparison of the intensities.

[Illustration: amount of over shooting]

It is seen that number three compares favorably with the overshooting as
shown by number two and the candle power corresponding was found to be
approximately 50% greater than normal. It is not claimed that every lamp
will overshoot this amount as the degree of vacuum or other factors of
individual lamps may play an important part in this phenomenon. There is
no doubt, however, that this strange fact really occurs and is not due
to physiological reasons.




                    VIII. CURVES OF “OVERSHOOTING”.


In order to prove that the law of resistances, namely, R = R_{o}(1 + αt)
does not hold for the first instance after closing the switch on a
tungsten lamp, the following curves have been plotted. Number V. has
been taken from the oscillograph record shown in the first part of this
paper and shows that about .024 second elapses before the current
becomes normal. Knowing the current at any instant as given by this
curve, it is easy to find the resistance at the same instant by Ohm's
law, the electromotive force being a constant and known value. Curve VI
shows this relation. Curves VII and VIII are approximate values and not
absolute. Now from the temperature curve, values are taken and
substituted in the formula for resistance, R = R_{o}(1 + αt), the
resulting curve being Figure IX. It is seen that curves VI and IX do not
take the same values at all until after a brief interval of time has
elapsed. Curve VI is absolutely correct, however, as these values have
been obtained from the oscillograph record. Consequently, the assumption
upon which curve IX is based must be incorrect for the first .024th of a
second and the conclusion is that the law of resistances does not hold.
This result tends to strengthen the theory of the lag of resistivity for
the “overshooting” of a tungsten lamp.

[Illustration: _Fig V_]

[Illustration: _Fig VI_]

[Illustration: _Fig VII_]

[Illustration: _Fig VIII_]

[Illustration:

  _Fig IX_
  _R = R_{o}[1 +αt]_]




                            IX. CONCLUSIONS.


The following conclusions may be drawn from the results of the tests.

1st, That the quality of the two sets of lamps was greatly different.

2d, That it is doubtful if the 15 watt, 115 volt, tungsten lamp as first
put upon the market met the guarantee as to life. This conclusion is
reached by tests in the laboratory and experience with lamps installed
in residences.

3d, That the tungsten lamp is subject to overshooting.

4th, That during this period the initial candle power may be as much as
50% above the normal.

5th, That the most probable theory of overshooting is the lag of
resistance behind the temperature.

------------------------------------------------------------------------




                           TRANSCRIBER’S NOTE


Italicized phrases are presented by surrounding the text with
_underscores_.

Superscripted characters are represented by preceding with a caret (^)
symbol. When longer than one digit, they are also surrounded in curled
brackets.

Subscripted characters are represented by preceding with an _underscore_
and enclosing in curled brackets.

Fractions are represented horizontally using the slash / symbol. The
original separated the numerator and denominator horizontally, separated
by a _ line.

Punctuation has been normalized. Except in the following cases,
variations in hyphenation, spelling and spacing have been retained as
they were in the original publication.

Chapter 2:

    Lumer-Brodhum photometer —> Lummer-Brodhun photometer

Chapter 4:

    What appear to be hand-drawn primes in the text have been confirmed
    as: The arc ha´ce —> The arc ha´c´e´.

    e c a a´ c e´ —> e c a a´ c´ e´

Figure IV

    There are two points b radiating from point O. The lower is likely
    to represent b´.

Chapter 5:

    inportant difference between —> important difference between