Velocity
of Light
Hansen | help from Turing |
measurement of length
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The velocity of
light was needed for the design of cavity wavemeters and still more urgently
for air navigation. The position of a plane can be found from its distances
from two known sites, the distances being calculated from the travel times of
radio signals from these sites to the plane multiplied by velocity. In practice
transmitters suitably situated give a worldwide coverage. The calculations are
of course all carried out on the instruments which give a continuous display of
the plane’s position as it flies.
Several detailed
reviews of all the measurements of velocity in the past led to the conclusion
that the value was within 4km/s of 299,776km/s. The value was based largely on
the results of Michelson and his co-workers, and particularly on his last
experiment made in 1935. This was performed with the encouragement and support
of international bodies, it was costly and widely publicised. One feature which
made it costly and was thought to be in its favour, was that the light path was
confined in an evacuated pipe 1.6km long to eliminated the effect of the
refractive index of the air which reduces the velocity by about 0.03%. Previous
measurements had all been made in air and corrected for refractive index which
was calculated from the atmospheric conditions at the time. The reviewers’
faith in the result was strengthened by the fact that four subsequent
determinations made by different scientists in different countries were in
close agreement with it.
A study of the
original papers convinced me that the value was not nearly so well established
as was thought. The actual precision of measurement was low and the results
were obtained as the average of many, sometimes thousands, of individual
measurements, always an unsatisfactory procedure. The authors themselves made
no great claims for their accuracy and pointed out that unexplained
discrepancies were present. My experience made me confident that the velocity
could be obtained far more accurately as well as far more simply by measuring
the dimensions and resonant frequency of a specially constructed cavity. The
setting to resonance is so precise that a single measurement would be more
accurate than the average of the large numbers taken in the optical
determinations and the high precision would make it possible to investigate and
eliminate the effect of small systematic errors. In view of its importance in
radio navigation I thought it was reasonable to include a velocity of light
determination in the programme of the Radio Department and no objections were
raised.
Hansen
A visitor from the
USA mentioned that WW Hansen at Stanford University was contemplating a similar
measurement. But it is no bad thing to duplicate work of this kind; and
although Hansen was one of the pioneers in cavity resonator theory the NPL was
better equipped on the technical side. We had then the best frequency standards
and microwave measuring experience in the world, a splendid workshop where the
resonator could be made and a metrology department where its dimensions could
be measured. All these facilities were situated in the same grounds and
collaboration between the staffs was encouraged. This latter point proved to be
most important. There was a slight discrepancy between some of the metrological
measurements which were discussed with the head of the department. In the
course of the discussions it occurred to him that there might also be a
systematic error. The internal diameter had been measured by their standard
method in which two small balls at the ends of the arms of feeler gauge slide
over the curved surface. The pressure of the balls on the surface causes a
slight depression which must be corrected for, and as the gauges usually tested
are all made from steel a standard correction is included in the calculations.
But our resonator was made of copper, a softer metal, and a larger correction
should be applied. His suspicions were correct and a small but significant
error was avoided through the close relationship between our departments.
The frequency
measurements were made with the help of AC Gordon Smith, a skilled and
meticulously careful experimenter. Our result was 16km/s higher than the
accepted value which was much more interesting than if it had been confirmed.
It did not surprise us but everyone else was very sceptical, even our Director,
who, while congratulating us on the work, suggested that we would no doubt get
the correct result when we had perfected the technique. The radar departments
in the UK and the USA who were the people most concerned, continued to use the
old value for several years showing that scientists can get fixed ideas on poor
evidence and refused to relinquish them. No result had been published from
Stanford but a report in a popular journal suggested that the result was going
to confirm the optical value. As I was visiting the USA our Director suggested
that I should go and see them. Unfortunately I found that Hansen was in
hospital with pneumonia which proved fatal. His colleagues were not in a
position to give a value, but when it was published in a short note later it
was quite near to the NPL result, being 3km/s lower.
Help from Turing
There was now a post war reshuffle of staff
and I moved back to the Electricity Division where I was able to repeat the
velocity measurement with a different form of resonator. The weakest point of
the first experiment seemed to be the measurements of the dimensions. Apart
from the metrological difficulty it was known that the electric and magnetic
fields penetrated the surfaces increasing the effective size. For perfect
conductors the penetration is zero but it is not negligible for copper although
this is one of the best conductors we have. I calculated the correction factor
from transmission line theory, but Turing the computer genius, who was then
working at the NPL, repeated the calculation elegantly and rigorously for me
from wave-guide theory. Actually I found later that it had been calculated and
published in a French journal. In any case I managed to eliminate most of the
correction by a suitable design of cavity resonator. The length could be
altered by a piston and the wavelength found by the distance between two
successive resonances, thus eliminating the effect of penetration in the end
faces. Then by using a number of different frequencies and different modes of
resonance it was possible to eliminate the diameter from the calculations or,
expressed differently, to measure the diameter in terms of length and
frequency. It was clearly a more complicated and difficult experiment than
before and I was fortunate in securing the help and the full co-operation of
our excellent workshops and of EG Hope, another skilled electronic expert to
replace Gordon Smith, whom I had lost in the move.
Another change I
made – and I mention this to show how difficult it is to make the right
compromise – was to construct the resonator from steel, because being a harder
material it is easier to grind the diameter to an exact size and uniformity.
Against this advantage it is a poor conductor and, therefore, had to be
silver-plated. We had been assured that this could be done uniformly but the
result fell short of our expectations and it is doubtful whether there was any
overall gain in changing from copper to steel. The two ways of obtaining the
diameter, direct metrological measurement corrected for skin penetration, and
indirect measurement from lengths and frequencies were in good accord and the
final result agreed exactly with that obtained before with the limit of error
reduced to 1km/s.
Measurement of length
These measurements
had been made with the resonators in evacuated enclosures to give the value in
vacuum directly. This value was now known so accurately and microwave
techniques were so well advanced, that it became an attractive and realistic
idea to measure all distances and not just the long distances involved in air
navigation, by measuring the time of flight of radio waves. The head of the
Metrology Division appointed a young scientist, KD Froome, with the specific
object of developing a suitable instrument. As these measurements were made in
air, corrections for refractive index would have to be made and this set us
another problem. It was clear from the literature that although the value for
optical waves was well established this was not true for radio and microwaves.
Froome and I, therefore, decided to collaborate in a set of experiments to
determine its value for air and its constituent gases at a number of
frequencies, using a cavity resonator technique. Special resonators were
constructed and their resonant frequencies were measured first when they were
evacuated and then when they were filled with the appropriate gas. It was a
difficult experiment because although the frequencies did not present much of a
problem, maintaining the pressure of the gas at a constant value and measuring
it turned out to be fraught with difficulties, particularly in the case of
water vapour, one of the most important constituents as far as refractive index
is concerned. In dealing with these problems Froome proved himself to be an
exceptionally skilled experimenter. The work was completed to our satisfaction
and because of its taxing nature was, in my view, the most rewarding of all my
experimental work. The results have remained at the internationally accepted
values and in spite of a number of attempts no one has been able to improve
them or indeed equal the accuracy we achieved.
The instrument
developed by Froome was so successful that he was invited to use his laboratory
model to survey various new projects around the world such as dams and subways.
Most geodetic surveying is now performed with such instruments. A director of
the Ordnance Survey commented that they could now complete in a few days a
survey that would previously have taken months but added, rather regretfully,
that it had been a very pleasant way of spending those months. It is a pity
that modern methods of measurement often take the fun out of the work.
In order to check
the performance of the instrument Froome had used it first to measure short
distances which could also be measured directly in terms of our length
standards. These measurements could be regarded as velocity of light
determinations and after several small differences his final value agreed
exactly with that obtained with cavity resonators.
The outstanding
success of the quartz clock and my velocity of light result, which was
gradually confirmed by other workers and is, in fact, still the accepted value
though now with smaller limits of error, gave me an international reputation
and invitations to lecture and attend conferences throughout the world.
It is quite easy
to stop productive work in this way and I was determined not to become a
conference man. On the other hand it is important to attend as many as
necessary to keep abreast of one’s subject and I found it particularly fruitful
and enjoyable to visit laboratories doing similar work. I found that if one has
something to give, scientists discuss their own work openly and freely. Some of
the conferences I attended had special ladies’ programmes for wives but
unfortunately my own wife was too fully occupied with our four daughters to
make use of such facilities until late in my career. Money was a problem too,
because scientific success did not bring any financial reward. Indeed in order
to support the children through universities, Joan nobly took in paying guests
who, of course, caused extra work, although they were pleasant to have with us.
