Honorary Research Follow
UNIVERSITY OF TASMANIA OCCASIONAL
Wholly set up and printed by the Printing
Section, University of Tasmania
ISBN 0 85901 051 1
Dr Grote Reber graduated from the
Illinois Institute of Technology in 1933 and for the next ten
years, while he pioneered the field of radio astronomy, was employed
as an engineer by a Chicago radio corporation. He designed and
built the world's first radio telescope and during this period
was the only active radio astronomer. He arrived in Tasmania
in 1954 and has spent much of his time since then making low frequency
radio astronomy observations at various sites in the Tasmanian
midlands. He has published many scientific papers in radio astronomy
and also in other fields. In 1962 he was awarded the Catherine
Wolfe Bruce Gold Medal by the Astronomical Society of the Pacific.
Endless, Boundless, Stable Universe
is the text of a lecture
delivered by Dr Grote Reber in the University of Tasmania on Wednesday,
8 September 1976.
Requests for copies of this publication
should be addressed to Information Services, University of Tasmania,
Box 252C GPO Hobart, Tasmania 7001.
According to modern mysticism*, the radius of the universe is 10.4 x 1022 kilometres, corresponding to a symbolic time of 1.1 x 1010 years. The radius of the earth is 6.38 x 103 kilometres. The ratio of the former to the latter is 1.63 x 1019.
When the Hubble variable was discovered** in 1926 it had a value of 500 kilometres per second per megaparsec. During the past halfcentury this variable has gradually declined*** to 50.3 kilometres per second per megaparsec. The radius of the universe is inversely proportional to the magnitude of this variable. Accordingly the universe is expanding by a factor of 100 per century. Dividing this factor into the above ratio discloses that the expansion began here on earth 961 years ago, or 1015 AD during the dark ages. Obviously, western cosmology was born in the dark and has been there ever since.
*Halton Arp, 'Extragalactic Astronomy', Science, 17 Dec. 1971, vol. 174, p. 1189.
**R.H. Baker, Astronomy, Ist ed. 1930, p. 497
***M. Rowan-Robinson, ëExtragalactic
Distance Scaleí, Nature, 16 Dec. 1976, vol. 264,
The Doppler Shift
Johann Christian Doppler1
worked in Vienna as a mathematical physicist during the first
half of the nineteenth century. During 1842 he predicted a shift
in observed wavelength would be caused by relative motion between
the source and an observer. When the two are approaching the
wavelength will be shorter. When the two are separating the wavelength
will be longer. This was confirmed experimentally for sound by
Buys Ballot in 1845. The optical confirmation had to wait until
1871 when the phenomenon was observed in Fraunhofer lines using
solar rotation, about 0.1 angstrom in the red. In 1901 Belopolsky
verified the effect in the laboratory using a system of rotating
During the latter half of the nineteenth century there were great improvements in telescopes, spectrographs and photography. By the turn of the century, the Doppler effect was being used to study very close double stars. These are pairs of stars rotating about a common centre of mass. See Fig 1. Usually the two stars have different spectra. When star A moves toward the observer its spectrum is shifted toward blue. Simultaneously the star B is moving away from the observer. Its spectrum is shifted toward red. Half an orbit later the two spectra A and B are shifted oppositely toward red and blue respectively. Any observed red shift is always accompanied by an equal and opposite blue shift. The magnitude of these shifts varies widely. It is dependent on the spacing between stars A and B. The closer they are, the greater the shifts. On the average the shifts are independent of the distance from the pair to the observer.
A decade later the motion of the sun
among all the other stars was being studied using the Doppler
phenomenon. The stars in front of us appear to be approaching
and have a blue shift. The stars behind us appear to be receding
and have a red shift. See Fig 2. Again, the magnitude of these
shifts varies widely because each star has its own peculiar motion.
However these motions are random. On an average there are just
as many blue shifts from stars in front of us as there are red
shifts from stars behind us. The magnitude of the shifts is not
dependent on distance.
By 1920 the rotation of our galaxy, the Milky Way, was being examined using the Doppler phenomenon. See Fig 3. The farther it is from the centre of the galaxy, the slower does material rotate. In quadrant A the inside material is catching up with us. We are catching up with material in quadrant C. Thus objects in quadrants A and C show dominantly blue shifts. Similarly, material in quadrants B and D show dominantly red shifts. There is a large scatter because all the material has its own peculiar random motion. However, on the average, the shifts are independent of the distance from the source to the observer.
All three of the above examples are
correct interpretations of spectral shift caused by relative motion
between the source and the observer. There are always equal and
opposite blue and red shifts. The magnitude of shifts is independent
of the distance to the source, and usually represents a few to
a few tens of kilometres per second velocity.
During the eighteenth century, telescopes improved in power and image quality. Soon it was found that all celestial objects are not point dots of stars. Some are diffuse irregular low surface brightness patches which resemble comets but do not move. Messier was an avid comet hunter who found these fixed patches a nuisance. He compiled a list of over a hundred objects and their positions for ready reference of objects to be excluded during his searches for comets. His numbers are still in use today.
The nature of these objects was a matter of conjecture for many years. About 1923 George Ellery Hale organized the Shapley-Curtis debate as to whether the fuzzy patches were part of our own Milky Way or external thereto. Lack of evidence prevented any conclusion. They became known as nebulae.
The problem finally succumbed to data from the 100 inch telescope at Mount Wilson operated by Edwin Hubble2. He was able to resolve several nebulae into stars of types familiar in our own Milky Way and demonstrate that the nebulae are separate stellar systems of comparable size. Using a boot-strap operation, distances were secured far beyond anything dreamed of in the past. The remarkable story is excellently told in his Observational Approach to Cosmology. When discussing these subjects before various astronomical gatherings and university departments I have asked for a show of hands by people who have read this book. The results have been trivial. The old masters deserve more direct attention. This book should be required reading for all young astronomers. It is good literature with fine style.
As early as 1913 V. M. Slipher3
had secured spectra of light from some of these fuzzy objects
and noted the similarity to background light from unresolved stars
in the Milky Way. Milton Humason followed up these data with
observations using large reflectors at Mount Wilson. The unexpected
and disconcerting finding was that the spectra showed only red
shifts. These shifts were directly proportional to the distance
of the object as determined by Hubble. Furthermore, by 1934 the
shifts were up to 13 or 14 percent equivalent to a symbolic velocity,
about 25,000 miles per second. The results were startling partly
because of the magnitude of the phenomenon, but partly because
no blue shifts were encountered. Clearly the interpretation of
these spectral shifts as representing relative motion was dubious.
If a light photon gains or loses energy this is manifested by a change in wavelength respectively toward the blue or the red. A photon may lose energy during its travel through intergalactic space. The energy loss would be proportional to the distance traveled. Thus the lengthening of the wavelength, as measured by the shift, would be proportional to distance, as observed. Hubble concludes on page 30 ëLight may lose energy during its journey through space, but if so, we do not yet know how the loss can be explainedí. He makes frequent reference to this dilemma on pages 2, 21, 26, 31, 43, 63. Finally he closes on page 66: ëWe seem to face, as once before in the days of Copernicus, a choice between a small, finite universe, and a universe indefinitely large plus a new principle of natureí.
I met Hubble only once. It was 1952,
the year before he died. I had gone to see him about another
matter but could not help mentioning the subject his name is so
closely connected with. He seemed only mildly interested and
appeared to feel that everything possible to say had already been
said many times over. Furthermore, if future progress were to
be made it would require some new and different kind of evidence.
Pursuing existing techniques would merely lead farther down a
dead-end road. I asked him what kind of new and different observation
should be made. He had no suggestion to offer. Perhaps I am
giving an impression of an aging man.
Cosmology has been a philosophical
football since time immemorial: about 500 BC Parmenides4
inferred that the universe had no beginning. Most modern speculation
or theories are on a par with those of the ancient Hindus. The
earliest discussion I have found about tired light is by Fritz
Zwicky5. He has several vague ideas. The deSitter6
universe is based on imaginary fabrication of a repulsive force
varying directly with distance. J.Q. Stewart7 searches
through a table of universal constants and comes up with the following
He wants someone to write and tell
him why this is so. Apparently the editor of The Physical
Review did not bother to dimension the above. The left side
of the equation is a pure dimensionless number. The reader can
dimension the right side as a fireside exercise. Fred Hoyle8
proposed continuous creation where hydrogen atoms are made out
of nothing by unspecified black magic. After being talked out
of this Fred9 now suggests masses of fundamental particles
are increasing with time. Finlay-Freundlich10 opts
for photon-photon encounters but does not explain how they work.
He proposes an empirical formula
Shift = AT4d where T is
the temperature of the radiation field.
This is placing the desired answer into the hypothesis, so the correct result is inevitable. Even so he seems to have reservations or gets cold feet. On page 318 we learn ë... light must be exposed to some kind of interaction with matter ... in intergalactic spaceí. No mechanism, details or comment are given.
Shelton11 and his opponents engage in desultory contests involving tired light produced by Compton transitions. The discussion fizzles out because no one can point to evidence for the existence of intergalactic material. They do not know how to handle low energy Compton transitions, and only Shelton realizes a ësingle effect (deflection) ... would be very minute, and ... be compensated by an equally minute diversion in the opposite directioní. This is a problem in two-dimensional random walk. Mathematical ability to handle it may not have been available at that time. On page 171 Shelton says ëDr. Hubble never committed himself to the theory of the expanding universeí. The late Dr. R.A. Millikan told me thus in a letter dated 15 May 1952, and added ... ëPersonally I should agree with you that this hypothesis (tired light) is more simple and less irrational for all of usí.
Mansfield12 imagines that gravity is not constant but increases with time. Malin13 suggests the mass of particles varies inversely as the fourth dimensional radius of the curvature of the universe. Brush14 thinks that gravity is in fact merely longwave radiation pushing masses together. However the best of these speculations is given by Hubble on page 44. 1 have not stumbled across his unstated source which he characterizes as ëspecial pleadingí. Time runs at variable speed. In the distant past time ran faster and much was accomplished. See Genesis 1.
Today the spacious universe has a
much slower rhythm. I am sure many readers believe this unknown
pleader has things backwards. Getting from 10 to 15 years old
seemed an interminable time. From 55 to 60 years is a frighteningly
short time. During the past half century a vast amount of paper
has been expended on this kind of material as sensed by Kellerman
The Astronomical Society of the Pacific has bumper stickers with various astronomical slogans. See Figure 4.
How did this myth get into the text
books? The cause lies in an assumption, always present but rarely
mentioned or even implied. This worrisome assumption can be seen
in remarks by Zwicky, Freundlich, Shelton and others.
The assumption is that intergalactic space is a void. By definition
a void lacks contents. Light cannot interact with a void. By
making this assumption, the door is closed to all physical phenomena.
The only possible explanation of shifts of spectral lines in
light from distant nebulae becomes relative motion. This assumption
is based on an anthropocentric view of our surroundings. If a
person cannot hear, smell, feel or see an object, this object
does not exist. Only recently has it been realized, even among
the scientific community, that ëabsence of evidence is not
evidence of absenceí16. Until a few years ago,
I had little interest in cosmology. It seemed immersed in hokus-pokus
and humbug, all rather dull. I was injected through the back
door by chance.
Hectometre Radio Astronomy
By the early 1950s radio astronomy was becoming respectable. Dishtype radio telescopes were being installed at several places. The march to ever shorter wavelengths in search of ever greater angular resolution was under way. The science seemed to be in good hands. I decided to try for observations of cosmic static at long wavelength simply as an exploratory search. Whatever the wavelength it must arrive at the observer on the surface of the earth. As the wavelength increases beyond twenty metres, the ionosphere becomes increasingly important. The ionosphere is a mirror for radio waves, silvered on both sides. A man-made wave will be reflected back to earth allowing long distance radio communication around the curvature of the earth. A celestial radio wave will be reflected back into space. See Figure 6A. At wavelengths greater than 100 metres, the ionosphere is the dominant feature of the experiment. As the name implies, the ionosphere is a layer of ions 200 to 300 km above the surface of the earth. However, not the ions but the associated free electrons are
more effective the ionosphere becomes as a shield for long-wave cosmic static. Obviously, if observations of cosmic static at hectometre (hundred metre) waves are to be successful, the electron density must be as low as possible. Fortunately measuring characteristics of ionosphere had become a popular scientific fad, so data was available at scores of places around the earth. Furthermore I had access to this vast mass of observations and I was not associated with any institution committed to long-term microwave studies and a resultant freezing of resources. Also, my past engineering experience was at long wavelengths; and I was not inhibited by any preconceived ideas about what was to be looked for. All this independence put me in a very preferred position. The situation was rather similar to that I enjoyed at Wheaton, Illinois, during the 1930s.
First the ionosphere data was perused. The lowest electron density was found to be near the minimum solar activity, during winter at night between latitudes 40o and 50o, near the agonic line where compass points true north. The most auspicious places are near Lake Superior in the northern hemisphere, and Tasmania in the southern hemisphere. The former looks out on the northern sky and the periphery of the Milky Way. The latter looks out on the southern sky and the centre of the Milky Way, a more interesting region.
Before doing anything it seemed wise
to consult assorted pundits and experts, self appointed and otherwise.
This produced a psychological situation. Asking for advice is
a form of flattery: the recipient feels he must rise to the occasion.
Advice is provided which under more sober circumstances would
probably be declined. Also, most people have their own pet hobbies
which envelop their lives. A stranger comes and proposes something
different. Obviously it cannot be much good, or they would have
thought of it first. Consequently the advice is negative. I
was informed that hectometre waves could not possibly get through
the ionosphere and even if they did there would be a large, variable
and unknown absorption. There would also be unknown and variable
bending of rays of cosmic static by refraction. Furthermore I
would have great difficulty locating an empty channel because
of the huge number of transmitters. Finally if I could find an
empty channel, I would be swamped by atmospherics. After listening
to these Cassandras it was obvious none had any idea of circumstances.
Clearly, hectometre radio astronomy was an excellent opportunity
to do new, different and fundamental research.
This large island off the southeast corner of Australia seemed a likely place to choose. I examined Physics Abstracts and found a paper about ëZí echoes by G.R.A. Ellis, now Professor Ellis. This seemed a likely contact with someone of similar experience and interests. I wrote explaining briefly my ideas and requesting comments and suggestions. His prompt reply disclosed that the ionosphere station had been recently moved from Cambridge to Mount Nelson. The old hut with phone, power and water was available plus some tall poles with cage antennas. Only suitable electronic apparatus for measuring cosmic static was needed.
Events proceeded and I arrived in Sydney on 1 November 1954 aboard the Orion with ten cases of electronic apparatus in the hold. The wharfies promptly struck. Only passengers and personal baggage were unloaded by the crew. The Orion then left for New Caledonia with my cases. Eventually I got to Hobart toward the end of November and my cases followed in a few weeks.
It was summer time, so observations were deferred until the middle of March. One afternoon the equipment was set to an apparently empty frequency near 2130KC and left operating. Three days later we returned and examined the recordings. Daytime showed low level station interference which increased in magnitude along with atmospherics toward evening. About 1 a.m. on the first night, the electron density of F layer decreased enough so that a transparent hole in the ionosphere appeared at 2130KC. See Figure 6B -The pen rose to a high level, about three-quarters full scale and continued smoothly until sunrise when the hole closed due to increasing electron density in F layer. The two following nights the hole opened partially in an erratic manner between midnight and dawn. During the first night when the hole was open, all man-made interference and atmospherics went out through the hole into space. The cosmic static came in without attenuation and had unexpectedly great strength. The Cassandras were wrong. Here was a new and interesting aspect of radio astronomy which should be followed up.
We made observations all winter using
additional frequencies near 1400KC, 900KC, and 520KC from time
to time. Some cosmic static was secured every night at 2110KC,
and on fewer occasions at lower frequencies. A few partial openings
of the hole were observed at 520KC. The antennas were
pairs of dipoles, so directivity was meagre. The opening and
closing of the hole as determined by cosmic static recorders was
checked by the ionosphere recorder on Mount Nelson. Very close
agreement was found. These results were published17
early in 1956. Solar activity was rising, so observing conditions
were deteriorating. Our ways diverged. Ellis took a post in
Queensland. I returned to the United States. In retrospect,
the solar activity minimum of 1954-5 produced lower electron densities
than the minimum of 1964-5. The recent minimum has been even
poorer for hectometre radio astronomy. Observations at II 55KC
during winters of 1974, 1975 and 1976 have been a complete failure.
Not even one partial opening of the hole has been observed.
The sunspot numbers for three minima are quite similar, so they
are not a suitable indicator of ionosphere conditions. Perhaps
examination of the size of the solar corona observed during solar
eclipses will provide a more intelligent guide. If the corona
is large, interplanetary space has a high particle density. These
particles fall into earth's atmosphere creating high electron
density at night. The reverse situation of a small corona may
imply good observing conditions for cosmic static at hectometre
On the basis of success at Cambridge,
I decided to return to Tasmania and build a more elaborate structure
capable of being called a radio telescope. A large flat open
area away from man-made electrical interference was needed. By
good fortune, I contacted a sympathetic landowner, G.B. Edgell,
whose Dennistoun estate five miles north of Bothwell was suitable.
An array 3520 feet diameter comprising 192 dipoles was constructed.
It was a meridian transit instrument with a beam capable of being
adjusted along the north-zenith-south plane. Observations were
made during 1963-7 at 2085KC, or 144 metres wavelength. Enough
data were secured to make a map of the entire southern sky. See
Figure 5. Results were published19 in 1968.
The radio sky at metre and shorter
wavelengths is rather similar to the optical night sky. The background
is dark with some bright objects scattered over it. Across the
sky is a bright diffuse band caused by our looking out along the
plane of the Milky Way. The brightest area is near the galactic
centre. Examination of Figure 5 shows the reverse situation.
A very bright background exists with several darker patches along
the plane of the Milky Way. The darkest area having the lowest
intensity is at the centre of the Milky Way. Obviously, the bright
background is outside the Milky Way. The low intensity regions
are caused by clouds of ionized hydrogen within our galaxy. These
absorb the hectometre wave energy from outside. At first glance,
the absorbing regions seem most interesting. However a little
reflection suggests the background is more important.
This background appears to be radiation
from an electron gas pervading intergalactic space. At 144 metres
wavelength the gas becomes opaque at about 330 megaparsecs. The
gas has a density of about 0.01 electron per cubic centimetre.
The electrons must have some energy input to replace the energy
lost by radiation and maintain equilibrium. This puzzle seemed
unexplainable until I had the happy thought that the energy going
into these electrons might be energy lost by light photons during
their travel through intergalactic space. Further consideration
disclosed the most likely phenomenon as Compton transitions20.
Calculation showed that the suggestion of Shelton11
was tenable. Also, perhaps, here was the kind of thing Hubble
might be looking for. The electrons in intergalactic space act
as transducers of energy from light waves to hectometre waves.
These are absorbed by ionized hydrogen gas clouds within the
galaxies. The clouds are building blocks for making stars. Thus
the light energy from old hot stars is recycled into unborn stars.
Up to now I have discussed only intergalactic electrons. These are active material for radio waves. However, the intergalactic gas must be neutral, so an equal number of positive ions must be present. These ions are probably hydrogen nuclei, namely protons. Choosing suitable numbers for the size and spacing of galaxies, it turns-out that nearly all the material in the universe is still in its most primitive state of electrons and protons spread throughout space. Less than one percent has condensed into galaxies, stars, planets, you and me.
The intergalactic material will have small irregularities of density. Gravity will cause these to build up into immense blobs. As they build up, internal motion will probably cause smaller concentrations. These broken blobs are the building blocks for clusters of galaxies. Since intergalactic material is constantly being drained off into clusters of galaxies, some material must be replenishing that lost to the blobs. During the past couple of decades a variety of peculiar galaxies have been discovered as byproducts of radio surveys. Several show jets21 coming out of the nucleus. Why and how the jets form is still speculative. A galactic nucleus sling-shot is proposed22. In any case, these jets provide the necessary material to replenish intergalactic space.
Other evidence for intergalactic material is provided by tails found on galaxies by the Dutch23. The observations are at 1420mc and represent neutral hydrogen dropping to lowest energy state. This neutral hydrogen is probably some of the electrons and protons discussed above, which have combined. The relative amounts of free electrons and protons to neutral hydrogens is unknown. (Ed. Note: Grote indicates this paragraph needs to be rewritten.)
Further evidence is from dynamical studies of galaxies in clusters. These clusters are very old. The internal random motions are large. In order for the clusters to remain intact a lot of invisible mass24 is required to provide the necessary gravity. This missing mass is several times the mass of visible galaxies. It probably is the blob of intergalactic material discussed in a previous paragraph.
By chance on 24 March 1976, 1 met an old friend, Richard Wielebinski, at Socorro, New Mexico. He is a product of Tasmania and is now associate director of Max Planck Institute for Radio Astronomy at Bonn, West Germany. Their main instrument is the world's largest movable dish 100 metres in diameter. He showed to me an assortment of observations made at decimetre waves on the subject of Faraday rotation. Many of these objects are outside our Milky Way. Free electrons are required to produce Faraday rotation. Since the rotation is not related to direction within our galaxy, the electrons must be the inhabitants of intergalactic space. Pulsars are rather feeble sources of radio waves. All known pulsars are within our Milky Way. When a pulsar is discovered in a neighbour galaxy, the dispersion of pulse will give some idea of the density of free electrons between the galaxies.
Another bit of evidence is from x-ray astronomy. The entire sky seems covered by weak diffuse energy having a peak 30 to 50 angstroms. This is readily explained by free-free transitions among the intergalactic electrons and protons.
These developments are not surprising.
Up to the end of the nineteenth century interstellar space was
considered vacant. Now it has electrons, protons, gas, dust,
magnetic fields, cosmic ray particles etc. By the end of the
twentieth century, intergalactic space will probably be similarly
populated. ëAbsence of evidence is not evidence of absence16í.
Time is merely a sequence of events.
There is no beginning nor ending. The material universe extends
beyond the greatest distances we can observe optically or by radio
means. It is boundless. The energy from hot material
is recycled by electrodynamic (not thermodynamic) means. The
material from dying galaxies is recycled into new galaxies. Details
of material and energy distribution change on a small scale.
Over any large volume and long time the gross features of the
universe remain stable. I am not offering a finished product.
I am attempting to instill thinking about the Endless, Boundless,
3. Lowell Observatory Bulletins
4. F.N. Magill, Masterpieces of
World Philosophy, pp. 16-22, Allen and Unwin, London 1963
5. F. Zwicky, ëRed Shift of Spectral
Linesí, Proc. Nat. Acad Sci., 1929, vol. 15, pp.
6. R.H. Baker, Astronomy, 1st
ed. 1930 p. 497, 3rd ed. 1947 p. 284
7. John Q. Stewart, ëRed Shift
and Universal Constantsí, Phys. Rev. 1 Dec. 1931,
vol. 38, p. 2071
8. R.H. Baker, Astronomy, 7th
ed. 1959, p. 531
9. Virginia Trimble, ëFrontiers
of Astronomyí, Science, 24 Oct. 1975, p. 368. Contrary
evidence in New Scientist, 26 Aug. 1976, p. 438, and Physics
Today, Sept. 1976, p. 17
10. E. Finlay-Freundlich, ëRed Shifts in Spectraí, Phil. Mag., March 1954, P. 317. See also H.S. Shelton, Observatory, Dec. 1954, p. 252; and G.J. Whitrow, Observatory, June 1954, pp. 100-2, and in Monthly Notices
Roy. Astro. Soc., 1954,
vol. 114 pp. 180-90. It has been resurrected by J.C. Pecker,
Nature, 1972, vol. 237, p. 227 and 12 Jan. 1973, p. 109
11. H.S. Shelton, ëRed Shift
in Spectra of Distant Nebulaeí, Observatory, April
1953 p. 84, Aug. 1953 p. 159, Dec. 1953 p. 243, Aug. 1954 pp.
12. V.N. Mansfield, 'Cosmologies with
Varying Gravity', Nature, 17 June I976, p . 560
23 March 1911, vol. 86, pp. 130-2
15. K.I. Kellerman, ëRadio Galaxies, Quasars and Cosmologyí,
Astronomical Journal, Sept.
1972, vol. 77, pp. 531-42
16. Attributed to Martin Rees, Institute for Astronomy, Madingley Road,
17. G. Reber and G. R. Ellis, ëCosmic Radio Frequency Radiation near
One Megacycleí, Jnl Geophys.
Res., March 1956, vol. 61, pp. 1-10
18. M. Waldmeier, ëPredicted and Observed Coronal Structureí, Nature,
17 Feb. 1977, p. 611 and Z.
Astrophysik, 1955, vol 36, p. 275
1968, vol. 285, pp. 1-12
History Publication, Neale
Watson, New York 1975
vol. 123, pp. 550-1
1973, vol 85, pp. 5-23
23. G.K. Miley et al., ëExtragalactic Radio Sourcesí, Nature, 1972, vol.
257, pp. 269-72