At Los Alamos there was a brilliant British-born metallurgist named Cyril Smith who had made a career in the brass business, in which alloys are central to making different products. By trial and error he found that if you alloyed plutonium with gallium it stabilized the delta phase, and you could make a plutonium metal. From that day to this, no one knows why gallium works or what the stability of the alloy is over a very long period, something that is important for storing warheads. The use of this alloy is a crucial bit of information that is absolutely essential in the manufacture of plutonium-based nuclear weapons, and Fuchs was in a position to pass it on. When the Russian physicists learned his identity they nicknamed him Santa Klaus.
Fuchs, the son of a Lutheran minister, had been born in Rüsselsheim, Germany, in 1911. As a student he joined the German Communist Party and when the Nazis came to power he left Germany. He managed to get to Bristol University where he got his Ph.D. in 1937. When the war came, he was interned in Canada as an enemy alien but Max Born, one of his professors, got him released. He was then approached by Rudolf Peierls, who made the first calculation of the “critical mass” needed to make a uranium bomb, to work on nuclear weapons. From the time the Germans invaded Russia, Fuchs began giving information to the Soviets about the bomb. When Peierls joined the British delegation to Los Alamos, Fuchs was asked to go along. Recently, a remarkable letter to Peierls from James Chadwick who headed the British delegation to Los Alamos has emerged, in which he describes Fuchs’s reluctance to go. He thought that he could be more useful to the project staying in England. If he had, the subsequent history of the Russian atomic bomb might have been quite different. Once at Los Alamos Fuchs was at the center of the work. He knew everything and transmitted what he knew through the courier named Harry Gold.
The people at Los Alamos liked him. He was a solitary man, worked hard, and was always available as a baby sitter when the more sociable scientists needed one. After the war, the British were not allowed to take classified documents with them. In Fuchs’s case it didn’t matter, since he had a photographic memory and memorized the final design of the gadget, which he saw tested at Alamogordo. This was the same bomb design that destroyed Nagasaki a month later. In October of 1945, a report was delivered to Lavrenty Beria, whom Stalin had put in charge of the Russian bomb program, spelling all of this out. Of the plutonium it says, “The element plutonium of delta-phase with specific gravity 15.8 is the active material of the atomic bomb.”1 It is equally specific about the rest of the design.
How this information aided the Russians is a matter of some disagreement. Beria did not share it freely with the scientists. He probably did not entirely trust the source. There was at least one other source, a young physicist named Theodore Hall who also transmitted material independently from Los Alamos. The Soviet scientists were given information that surely had an effect. What the spies said about plutonium metallurgy and the use of gallium must have saved months of trial and error.
In any event, the first atomic bomb the Russians tested—which they called “First Lightning” and the US called “Joe 1″—was exploded on August 29, 1949. It was a duplicate of the gadget. The US intelligence services were caught completely off-guard. The Americans had no agent on the ground in the USSR and relied on a monitoring system using aircraft alleged to be on routine weather patrols. The planes were equipped to collect radioactive samples of the kind that a reactor accident or a nuclear explosion would produce. Until this data was collected and analyzed, which took several weeks, there was considerable disbelief—including that of President Truman—that the Russians had really tested an atomic bomb. Once it was verified that they had, the cold war nuclear arms race was on. Fuchs was identified in 1950 and served nine years in prison in Great Britain. He was allowed to return to Germany, and died there in 1988.
The reader may wonder why I have not mentioned the hydrogen bomb and any part that Fuchs might have had in the Soviet program to make it. So much of the relevant information is still classified that it is very difficult to arrive at a complete accounting of his contribution. In the case of the fission bomb this is possible because the relevant material is unclassified. We know that what Fuchs did was to supply the Russians with a blueprint of the plutonium implosion bomb that was tested at Alamogordo and dropped on Nagasaki. The Russians then copied this blueprint. Fuchs left Los Alamos in 1946 to return to England where he had an important part in the development of British nuclear weapons.
This took place before there was a breakthrough in the American hydrogen bomb program, owing to the work in 1951 of Stanislaw Ulam and Edward Teller. Nonetheless, Fuchs had been active in hydrogen bomb work before he left the US. In 1946, he and the Hungarian-born mathematician John von Neumann took out a patent on what they thought was a design for a hydrogen bomb.
Such a bomb gets its energy from the fusion of light elements—possibly but not necessarily hydrogen—to make other light elements, with the consequent release of energy. This is the process that makes stars shine. From the beginning of the war, a number of scientists realized that if this process could be duplicated, one could make a weapon of almost limitless energy. The trick was to heat the fusible elements to temperatures like those of the interior of the sun. This was to be done in two steps by using the energy from a fission bomb. First, one had to “ignite” the fusing light elements; second, once ignited, the fusion reaction had to “propagate”—i.e., maintain the ignited state. This latter process was the hard part, and all the designs up to those of Ulam and Teller resulted in a cooling-off before they could propagate. This problem was not solved by Fuchs and von Neumann, but they did propose a novel form of ignition, which was a forerunner of the Teller-Ulam design, and this is what Fuchs gave to the Russians. There is no consensus on the extent to which the Russians used it; but there is increasing agreement that it was of significant help to their program.
I thought of all of this when I read the fascinating new book Spying on the Bomb by Jeffrey T. Richelson, a senior fellow at the privately funded National Security Archive and the author of other books on military intelligence. While some of this material has been available in other sources, it has never been put together so comprehensively. He has also interviewed some of the participants. The book begins with an account of US attempts during World War II to learn what the Germans were doing and goes on to describe its efforts to obtain information about the nuclear programs of the Iraqis, North Koreans, South Africans, Israelis, and Iranians. The one common theme is that if you do not have both agents on the ground and competent people to interpret what they have uncovered, you are playing a game of blindman’s bluff with very high stakes indeed.
So far as I know, the Germans never tried very hard to learn about our nuclear program. I think that they simply did not take seriously the possibility that the US had one. In the early summer of 1945, ten German nuclear scientists were confined in a manor house outside Cambridge, England, and their conversations recorded. When the bombing of Hiroshima was announced, their collective initial reaction was disbelief. On the other hand, we took the possibility of a German program very seriously. It was the British who first concluded from limited intelligence that there was no crash program in Germany to build a bomb. Professor Peierls told me that he was convinced of this because he had got hold of catalogs of courses in German universities and saw that the usual people were teaching the usual physics courses.
However, in the fall of 1943 there was a scare. That summer a German nuclear physicist named Hans Jensen had visited Bohr in Copenhagen. Jensen was not part of the German nuclear program but was close to people who were. He brought to Bohr news of what Werner Heisenberg and the people around him seemed to be doing. Bohr obtained from Jensen a drawing of something that he took to be a nuclear weapon. Who made this drawing was never clear. In October of 1943, Bohr escaped to England carrying with him the information he had learned from Jensen. In December of 1943, Bohr came to the United States and was debriefed by General Leslie Groves, who was in charge of the bomb project. He showed Groves the drawing and Groves became extremely exercised. He insisted that Oppenheimer stop everything he was doing and convene a meeting of experts in Los Alamos as soon as Bohr arrived. In the 1970s I was able to contact the scientists who had attended this meeting and were still alive, including Bohr’s son Aage, Hans Bethe, and Edward Teller. Teller told me that he had no recollection of the meeting but Bethe told me that he took one look at the drawing and saw that it was the drawing of a reactor.2 His first thought was that the Germans must be crazy. Apparently, he thought, they wanted to drop a reactor on London. What neither he nor any of the rest of those at the meeting realized was that the Germans were not crazy at all. By 1940, they understood that you could use plutonium as a nuclear explosive and that this was made in reactors. They never succeeded in making a workable reactor but they knew what to do with one.
In the fall of 1943, General Groves authorized the creation of an intelligence mission that was to follow the troops across Europe and learn once and for all what the Germans had done to produce nuclear weapons. The mission was called Alsos and its scientific leader was the Dutch-born physicist Samuel Goudsmit. By Christmas of 1944, Goudsmit had seen enough to be sure that the Germans never had a workable program. In his book he was somewhat derisive about their efforts. He even, quite incorrectly, chided Heisenberg for failing to realize that plutonium was a possible nuclear explosive. That Goudsmit could make a mistake like this shows just how difficult it is to gather and interpret intelligence.
Richelson has much to say about the report of an alleged nuclear explosion that could never be confirmed. His story depends not on eyewitnesses but on information from “Vela” satellites, i.e., those equipped with a “bhangmeter”—an optical sensor that can register light fluctuations that last no longer than one thousandth of a second. Such meters are crucial in detecting the initial flash of a plutonium bomb explosion, which lasts only about a thousandth of a second. What is interesting about this episode is that while some kind of explosion was thought to have taken place on September 22, 1979, there is still no agreement about what it was. No eyewitnesses have been found. On that day a Vela satellite detected the two light events that are characteristic of an atmospheric nuclear explosion. The satellite was not equipped to detect the precise location of the presumed explosion, although later it was established that the light flashes were at a spot in the Indian Ocean near Prince Edward Island.
Up to that point, the Vela satellites had an impeccable record for detecting nuclear explosions, so it was natural to assume that this is what it was. But who set it off? There were two possible candidates, Israel and South Africa, and perhaps the two jointly. Although the Israeli program was by then well known, few realized that South Africa also had a nuclear weapons program, one that it finally abandoned in 1991 when it signed the nuclear nonproliferation treaty, which opened the program up to international inspections.
Apart from South Africa having sold some uranium to Israel, it was never established what the connections, if any, between the Israeli and South African programs may have been. Later on, in September of 1979, US experts concluded that South Africa did not have enough weapons-grade nuclear material for a bomb, but in 1979, this still was regarded as a possibility. If either Israel or South Africa had actually tested a weapon this would have had very serious diplomatic consequences, so it was decided that the Vela information had to be examined very carefully. A high-powered panel of experts was assembled under the direction of Jack Ruina, a professor of electrical engineering at MIT. The Vela satellite in question was running past its expected lifespan at the time of the detection, so that its results were suspect.
The general conclusion of the panel was that there was reason to be wary of the Vela results.3 However, there were other observations involving ocean acoustic waves and disturbances in the ionosphere that might indicate that a nuclear explosion had occurred. Still, no radioactive fallout was observed. That it was a solo Israeli test seemed implausible since that would have involved a naval expedition, which seemed beyond Israel’s capacity. As far as I can tell, the prevailing opinion is that the Vela satellite observed something else, although it is not clear what this was. This again illustrates the proposition that without agents such as Fuchs and Hall in place, reliable information is hard to come by, especially if the country in question is both clever and deceitful. When it came to nuclear weapons, the Israelis exhibited both of these qualities.
The Israeli program is nearly as old as the state itself. Ben-Gurion authorized it in 1952. The Israelis soon developed new methods for extracting heavy water from ordinary water and for transforming uranium into a gaseous form so that it can be enriched and used as fuel for an explosion. They managed to interest the French in this project, and Israeli physicists started to visit Saclay, outside Paris, which was the center of the French nuclear program. When he visited the US, I met the late Amos de Shalit, a very distinguished Israeli theoretical nuclear physicist who, after spending some time at MIT, worked at Saclay for four months. I was always tempted to ask him if he had picked up any tips about nuclear weapons from such MIT scientists as Victor Weiskopf who were both Los Alamos veterans and supporters of Israel. I never could quite bring myself to do it. On the other hand, I did have a chance to talk about nuclear matters with Benjamin Netanyahu at a small social gathering in New York. This was long before he became an important member of the Israeli government. I was introduced to him as someone who had worked in nuclear physics and had been a summer intern at Los Alamos. Not surprisingly, the subject of the Israeli bomb came up. He told me that if the survival of the country was at stake, the Israelis would use it and worry about the consequences later.
In the late 1950s, with French assistance, the Israelis had begun to construct a large reactor in the Negev and a facility for processing the fuel rods needed to make plutonium. Then, in 1959, De Gaulle became president of France and said French assistance could continue only if Ben-Gurion gave public assurance that the reactor would be used solely for peaceful purposes. This he did, while knowing full well that the reactor was going to be used to make plutonium for nuclear weapons. The reactor was completed in 1963. During this time the Israelis and the Americans engaged in a kind of theater of the absurd. The Americans demanded inspections and the Israelis came up with one ingenious maneuver after another to avoid them. For example, the Americans were informed that the nuclear complex at Dimona was a textile factory. Before he was assassinated, President Kennedy and his experts came close to a finding that a nuclear reactor was being used to make plutonium. The Israelis went on maintaining the fiction that they had not manufactured nuclear weapons. What brought an end to this farce was the testimony of an immigrant Moroccan Jew named Mordechai Vanunu.
In 1977, after a short course in the essentials of atomic weapons production, Vanunu got a job as manager in the graveyard shift at the nuclear plant, working between 11:30 PM and 8:00 AM. Vanunu’s clearance gave him access to all levels of secure sites at the plant, including those in which materials that might be used for a hydrogen bomb were manufactured. Vanunu was a political activist who attended rallies at which both Communists and Arabs were present. He was warned not to involve himself in such political matters, but he kept on doing so until 1985, when he was fired. He went to London with his story of Israel’s nuclear program and photographs to back it up. These were published in the London Sunday Times and created a sensation. Vanunu was lured to Rome by a young woman, an Israeli agent, and kidnapped by the Mossad; he was taken back to Israel where he spent the next seventeen years in prison, partly in harsh solitary confinement. He is now living under tight security in Israel. It was clear from what he revealed, Richelson writes, that Israel, which has been making nuclear weapons for decades, has a very considerable and varied nuclear arsenal.
About the Chinese, Indian, Pakistani, and Iraqi programs, Richelson points out that what they all have in common is that foreign intelligence failed badly to detect them, a failure caused in part by the successful deception practiced by these countries. In the Iraqi case, American and other intelligence services failed twice to find out about its nuclear progress. After the Israeli air raid that destroyed Iraq’s so-called Tammuz 1 reactor in June of 1981, foreign intelligence agencies assumed that the Iraqi program had been successfully stopped. As far as the manufacture of plutonium was concerned this was largely true. But the Iraqis had a very sizable program to separate uranium isotopes that had not been affected by the raid. They also had a group of bomb designers equally unaffected. Neither of these had been detected by American intelligence. Only after the first Gulf War, and after a good deal of resistance by the Iraqis, were international inspectors finally able to pin down the extent of the program. They concluded that if it had not been interrupted it might have produced a bomb within a year or so. In short, Saddam Hussein’s abortive invasion of Kuwait had an unintended consequence of depriving him of a nuclear weapon.
The misreading of the intelligence before the latest Iraq war has been much discussed, but a reader who wants a compact summary will find it in Richelson’s book. What the reader will not find is an explanation of why Saddam Hussein gave up the program in the early 1990s yet did not fully cooperate with the inspectors who would have verified that he had done so. If he had supplied adequate information at first, the war might well have been avoided; he might have reconstituted the program, although I have seen no hard evidence that he planned to do so. If inspections had been allowed to continue under Mohamed ElBaradei and Hans Blix in 2003, as many nations preferred, the absence of nuclear weapons and other weapons of mass destruction would have been increasingly clear, and in Blix’s view war would probably have been avoided. What has been hardly mentioned in the controversy over whether Saddam Hussein might have revived a nuclear program is Blix’s statement in his book Disarming Iraq that while he informed the Security Council that “neither governments nor inspectors would want disarmament inspection to go on forever,” he
reminded that Council that, after verified disarmament, a sustained inspection and monitoring system was to remain in place to strike an alarm if there was any sign of revival of forbidden weapons programs.4
In his failure to make full disclosure, Saddam Hussein’s worst enemy was Saddam Hussein. He may, Blix and others have speculated, have been reluctant to admit that he didn’t have the weapons with which to intimidate Iran and others in the region.
As for the Indians and Pakistanis, they simply lied about their intentions. The US had no informants on the ground, so when they tested their first nuclear weapons Americans were taken by surprise. Until 1959 the Russians and the Chinese collaborated on nuclear development, and Chinese scientists were sent to the Soviet Union to learn about nuclear technology. The Russians had agreed to supply the Chinese with fissionable material and, more remarkably, with a sample bomb and the plans that went with it. But then the two countries had a falling out and the cooperative program was stopped before any samples arrived. The Chinese were on their own. US intelligence services made a very substantial effort to follow developments, but they assumed incorrectly that, like the other countries, the Chinese were going to make a plutonium bomb, so they made an unsuccessful search, mainly from the air, for nuclear reactors that would produce plutonium. Not finding any, they came to the conclusion that no Chinese bomb was imminent.
The Chinese, however, had decided to make a uranium bomb but one with a novel design. In a bomb the fissionable material passes through three stages; subcritical, critical, and super-critical. In the subcritical stage fissions do take place but they do not produce a self-sustaining chain reaction. When the material becomes critical the chain reactions become self-sustaining and when it goes super-critical the material becomes explosive. In the Hiroshima bomb what happened was that a subcritical mass was fired into another mass, producing first a critical and then a super-critical mass. This device was not tested before it was used at Hiroshima.
When the plutonium bomb was first considered, scientists proposed to use the same design. But when the first plutonium was delivered to Los Alamos from the reactors in Hanford, Washington, it was found to contain an unwanted isotope of plutonium that spontaneously fissioned. This could set off the fission reaction in the bomb before enough material was assembled, thus producing a “fizzle.” Thus a different method was needed. This consisted of imploding a sphere of plutonium by wrapping shaped high explosives around it. This worked much faster and solved the isotope problem. What the Chinese did was to use implosion for their uranium bomb, which they exploded on October 16, 1964. This design was much more efficient than the one the US used at Hiroshima, so it used less fissionable material. The test again caught our intelligence services totally by surprise.
The last part of Richelson’s book deals with Iran and North Korea. Here events, especially in Iran, are moving so quickly that Richelson’s account has to be supplemented by information released by the International Atomic Energy Agency and reported by the press. Of the two countries, in my view, the prospects of an Iranian bomb are the more serious. The North Koreans probably have a small, untested nuclear arsenal. My guess is that sooner or later, under Chinese and other international pressure, Kim Jong-il may accept an offer of economic and other rewards in return for giving up his nuclear program. Meanwhile, the principal concern about the North Koreans is that they do not try to sell their technology to terrorists. They may have little else to sell.
What makes the Iranian situation so difficult is that they have oil to sell, which makes them less vulnerable to economic sanctions. Indeed, when they are threatened the price of oil tends to go up, making the Iranians richer. The Chinese at the moment get about 14 percent of their oil from Iran, which is why they are so unwilling to apply pressure. To add to the difficulties, the Iranian president often speaks of eliminating Israel, although it is a question whether he has the authority to try to do so. In any case, if the Iranians eventually make one or more bombs, the logic of mutual deterrence would apply: use of the bomb against Israel would very likely result in a disaster for Iran. Meanwhile, the Israelis seem to mean it when they say they would not allow the Iranians to have nuclear weapons; the Iranians, one can surmise, are as aware of this as anyone else, just as they must be aware of the alleged American contingency plans for an attack on Iran recently reported by Seymour Hersh.5
The themes of this review have been twofold. In order to have really reliable intelligence about the atomic program of a foreign country a necessary, but not sufficient, condition is to have agents on the ground. In the examples I have given the necessity is clear. Countries can hide their nuclear programs even from satellites and other sophisticated detection instruments. The Chinese hid their program because the satellites were looking for the wrong signals. Until Vanunu, an agent on the ground, unmasked the Israeli program the Israelis hid it by deception. But even with an agent on the ground mistakes can be made. Samuel Goudsmit was selected as the scientific leader of the Alsos mission in part because he did not know anything about ours. He often said that if he had been captured by the Germans he could not have told them anything. Since he did not know about our plutonium program, he did not look for the German program and made the erroneous assertion that there was none.
The second theme is that in almost all cases the predictions have erred on the side of conservatism. Countries have acquired nuclear weapons well before they were supposed to. The example of the Russians is the most graphic. This happened because Fuchs gave them a blueprint for the US plutonium bomb and the Russians had the technological capacity to follow it more or less literally. With the Iranians we are almost in the worst possible case. We do not, it seems, have agents on the ground so not only do we not know what they have done—except for what they have chosen to tell us—but we do not even know their technological capacities. To take an example, it is rumored that the Pakistani nuclear merchant A.Q. Khan has sold them the plans for an implosion bomb. As the people at Los Alamos discovered, making an implosion bomb was a very difficult technological feat that required the enormous assembled talents of almost the entire laboratory. Do the Iranians have the people to do this, even if they have the plans? We simply do not know.
What we do know is that the Iranians have had a nuclear energy program for many years. We know that in the fall of 2002, the Russians began assembling a large nuclear reactor at the port city of Bushehr. This reactor has not yet been put into operation. It is what is called a “light water” reactor, which means that it uses ordinary water as a coolant. Such a reactor cannot operate with natural uranium—the kind you get out of a mine. It has to be enriched. How is this done? Like all elements, uranium comes in several isotopes. The isotopes differ from each other in the number of electrically neutral particles—neutrons—in their nuclei. The number of positively charged particles in the nucleus—protons—is the same for all these isotopes. This means that it is extraordinarily difficult to separate these isotopes chemically. Methods must be employed that take advantage of the tiny differences in mass between the nuclei of the isotopes. Soon after fission was discovered in 1938 Niels Bohr realized that it was the isotope uranium-235—i.e., with 235 particles in its nucleus—that was fissioning. But in natural uranium, which consists mostly of uranium-238, only 0.7 percent consists of uranium-235. Bohr understood how difficult it would be to separate these isotopes by physical means and declared that nuclear weapons were practically impossible because it would take resources on a national scale to carry out this separation. He was roughly right about that, but wrong about the impossibility.
There are a number of ways in which the separation can be carried out, all of them difficult. During World War II most of the separation was done using electromagnetic fields. If you put a charged particle in a magnetic field it will have its orbit deflected by an amount that depends on the mass of the particle. This was what was done at Oak Ridge where the wartime separation of uranium-235 was carried out. To have an idea of what was involved, the Hiroshima uranium bomb consisted of two subcritical parts. The “target” within the bomb consisted of 38.4 kilograms of 80 percent enriched uranium while the “projectile” that was designed to hit the target inside the bomb consisted of 25.6 kilograms of 80 percent enriched uranium. This design was considered to be such a sure thing that it was never tested before it was dropped on Hiroshima. If the Iranians can make a uranium implosion bomb of the kind that the Chinese first tested, they would need only between fifteen and twenty kilograms of highly enriched uranium.
The Iranians have chosen to do this enrichment by using centrifuges. These are long cylinders stacked in parallel. The cylinders can rotate at 50,000 to 70,000 rotations per minute. Uranium is introduced in the cylinder in the form of a very corrosive gas—uranium hexafluoride—and it is estimated that by late February of 2006 the Iranians had produced about eighty-five metric tons of uranium in this gaseous form. It would take about five metric tons of this uranium gas to produce enough enriched uranium to make one bomb.6 This assumes an implosion bomb.
In the centrifuge the heavier isotope, uranium-238, is spun to the outside leaving the lighter isotope, uranium-235, in the middle. This residue can be used as the stock for the next stage of enrichment, which is why the centrifuges are connected together in what is called a cascade. Once one obtains say a 50 percent enrichment, going to a full weapons-grade enrichment requires much less effort.7
So far this is mainly physics with a minimum of speculation. What is largely speculation is how far the Iranians have gotten with the enrichment process. It has been known for some time that they have had 164 so-called P-1 centrifuges in a cascade in their facility in Natanz in central Iran. “P-1” is short for “Pakistan-1.” Beginning in 1997, they were supplied by the A.Q. Khan network. If remnants of this network are still operating they may still be active in Iran.
Since August of 2005 the Iranians have been running the Natanz centrifuges without external inspection or supervision. Very recently they announced that they had enriched some uranium of the type that can be used in a reactor. Normally this means an enrichment of about 3 percent. This would be consistent with the claim of the Iranians that the only use they will make of enriched uranium is for nuclear electrical power. But no external observer has been allowed to see how much and to what percent. We simply do not know. The rotors of the P-1 centrifuges are constructed from aluminum. But there is a next generation—the P-2—which is made out of a specialized steel. These are much more efficient. In some of their statements the Iranians have talked about making a cascade of 54,000 P-2 centrifuges. If this very difficult task can be achieved—and we don’t know just how long it would take—and the cascade can be kept running for a year, the Iranians will have enough material to make more than one nuclear weapon.
—April 26, 2006
May 25, 2006
For the full text see http://nuclearwea-ponarchive.org/News/Voprosy2.html. ↩
The late Robert Serber gave me copies of the documents, including a letter from Oppenheimer to Groves that described the meeting and included a list of participants. ↩
I am grateful to Richard Garwin, who was a member of the panel, for discussions. ↩
Hans Blix, Disarming Iraq (Pantheon, 2004), p. 210. ↩
See The New Yorker, April 17, 2006. ↩
This estimate can be found in David Albright and Cory Hinderstein, “The Clock Is Ticking, But How Fast?” Isis, March 27, 2006. ↩
I am grateful to Norman Dombey, Carey Sublette, and Peter Zimmerman for many very helpful comments and suggestions about this. ↩