An Interview with Joe Brady

Joe Brady
JB = Joe Brady
GAM = George Michael

GAM: It's the 6th of September 1994, and we're talking to Joe Brady, one of the first people who came to the Laboratory and led a lot of activities inside the Computation Department. Joe, why don't you start by telling us when you came to the Lab, and what your first assignments were, and so on?

JB: All right. I came to work at the Lab early in 1953, I was interviewed by Bob Mainhardt, and I didn't start working until my clearance came through. When I came to work, I became the supervisor in charge of the CPCs. That is, I supervised the people who were working on the CPCs. The CPCs were in a room adjacent to the UNIVAC, and there were two of them. Each one had things called memory boxes. Do you remember this?

GAM: Yes.

JB: Each memory box had two rows of memory devices that could hold ten digits. So, each CPC had twenty, and each CPC had five boxes, so each CPC had one hundred words of memory. Now, this wasn't a stored program calculator; this was a card-programmed machine, if you wanted a loop, one had to put the cards in over and over again.

GAM: Yes, I remember that.

JB: And it was run from a printer that had a board in it that had to be wired by hand. There were two CPCs. I believe that one of them was replaced sometime later by an IBM 650, which was a decimal machine, not a binary machine.

The 650 was a decimal machine with floating point, which was wonderful. Whereas, the UNIVAC didn't have floating point, so you had to rescale the problem every so often.

GAM: Oh, yes, that's true.

JB: There was a little room off to the side of this 650 that held the keypunch operators, because everything was done on cards. After awhile, an IBM 701 arrived.

And it went into a new building-what was that building? Was it building 120A?

GAM: Right. I watched it being built.

JB: And it had so many windows off to the-what direction would that be?

GAM: South.

JB: There were so many windows off to the south that the air conditioning wouldn't keep the room cool enough for the computers. The windows had to be boarded up or somehow eliminated. And it was divided into two rooms: one had the 701; the other now had two 650s.

GAM: Yes, and it was a comfortable place, because it was the only place that had any air conditioning then. We used to go work in there during the summers.

JB: They were very nice machines, and they did a lot of computing. But the trouble was that the Computation Department was divided into groups by the machine that they were supposed to be using. So if you supervised a couple of dozen people on the 650, they might think it better to use the 701, or maybe the UNIVAC, but they couldn't because they were assigned to the 650!

If the problem couldn't be done on the 650, these people couldn't do it. This was changed by Sid Fernbach, sometime later, for the better, when they were divided into groups under a supervisor, but they could use any machine to do any problem, which is much more efficient.

I don't know what dates these would be; maybe you do.

GAM: Well, it's got to be '53 to '54. In '57 we had several 704s.

JB: OK. In 1955, Edna Vienop (later Edna Carpenter) started an n-body code for the IBM 704s, because I wanted to do the orbit of Halley's Comet and predict the 1986 return. [ed: See the references for Joe's publications on Halley's Comet and other topics.] To compute a comet orbit it is necessary to have the positions of all the planets. These were acquired on cards from the Naval Observatory. All we had to do was send them some IBM cards on which they would put the planetary data. The data on the cards was put on tape, one tape for each planet. It turned out that the coordinates for Mars were inadequate. The orbit of Mars was quite eccentric and difficult to do by the methods used in the Naval Observatory, known as General Perturbations. So, it was decided to use the n-body code to improve the orbit of Mars before starting the comet orbit.

In 1957 the United States was getting ready to launch the Vanguard satellite and Nevin Sherman wanted to use this n-body code to track it. For a satellite around the Earth it wasn't necessary to have coordinates of the planets. All that was needed was the effect of the Moon and the Sun and the oblateness of the Earth. So, this code was ready in October 1957 when Sputnik suddenly went up.

GAM: This was the THEMIS code?

JB: Yes. Soon after the launch Sid received a call from the Smithsonian Astrophysical Observatory asking him if the Lab would track Sputnik and predict what was going to happen to it. Smithsonian knew about the THEMIS code because I had given a paper describing it at a meeting in Boston in April 1957. Of course, we agreed to do it, if they would send us the observational data. So, we were given a Teletype over which the Smithsonian Observatory sent us the precise time when Sputnik transited the meridian of Washington, DC.

So we knew the time it took Sputnik to make a revolution around the Earth. Russia had refused to give us the cross-section of the satellite, so we couldn't compute the drag of the atmosphere. The density of the atmosphere was very poorly known in those days.

Actually, the density of the atmosphere not only changes by altitude but also changes between daylight and darkness. But it turned out that knowing the cross-section wouldn't have done us any good, because the satellite was tumbling in a random fashion and it would have been impossible to calculate the drag. All we could do was measure the decay in the period by the transit times. Sid and Teller decided we should have two 704s exclusively for 72 hours.

Initially, the period of Sputnik was 96 minutes. But the computer time needed to compute one revolution was also about 96 minutes-thus, the necessity for two 704s to perform the multiple integrations needed for the differential corrections. We used these 704s for seventy hours straight, only stopping to rush outside to see the satellite orbiting overhead. Do you remember this? We worked day and night.

GAM: Yes.

JB: We never went to bed for seventy hours. We finally arrived at the oft-quoted death date of Sputnik as December 1, 1957. Do you remember that?

GAM: Not that part, no.

JB: The last observed transit over the meridian of Washington, DC, was also December 1! In other words, the satellite reentered the dense layers of the atmosphere sometime on December 1. Nobody knows when or where. But at least we pinpointed the date. This was an extrapolation of 58 days from launch. It was a long time ago, wasn't it?

GAM: Yes, it was. Do you remember if you used the earlier versions of FORTRAN for this code, or some assembler?

JB: We used FORTRAN.

GAM: So, it's got to be post-'56 then.

JB: I don't know which version of FORTRAN it was, but it was '57 when we used the code for the Smithsonian.

GAM: Okay, yes. Well, Hans Bruijnes related something similar in his interview, and also said that they (NASA) asked for the code to be given to them. They took it back east to continue orbit calculations, because they didn't have anything inside of NASA that would do it.

JB: I don't remember giving the code. Maybe Hans gave his code, which was only single precision, whereas THEMIS was double. A UCRL report [1] early in 1958 mentioned four astronomical tracking codes that the Lab used to investigate the motion of astronomical objects. THEMIS was a double-precision integration, all-purpose code, and Hans Bruijnes' and Virginia Strehl's code was the SATELLITE code, a single-precision integration code developed mainly for Earth satellites and other objects requiring a small number of integration steps.

GAM: I always thought that, well, it was just a copy of yours. You know, he had more I/O features in it and so forth, but the basic heart and soul, the mathematical portion of the thing, was yours.

JB: After Sputnik, we got back to the Mars coordinates. We needed observations of Mars. The Royal Observatory on clear nights made observations of all visible planets, and these were published in many thick, big volumes for over two hundred years. The UC Berkeley Library managed to borrow a set of these volumes and we copied out all the Mars observations.

All the observations had to be processed, a rather elaborate job that required a lot of calculating. After this was finished, we started calculating the orbit. The Lab at Berkeley had just acquired a 700-series computer, and they couldn't keep it busy more than one shift. We sent our computer operators to Berkeley to work until they were cleared. So Sid said, "We'll use the other two shifts for your Mars orbit." And he gave that time to me.

So, I had that machine from five o'clock in the evening till eight o'clock in the morning. And our own operators were there helping me. One night's calculation produced the residuals (differences) between the observations and the calculated positions. So, I'd integrate Mars, get all these residuals, and then take them back to the Lab. I'd drive home, have breakfast with my children before they went off to school, and then I'd go out to the Lab. And von Holdt would help me do a least-squares solution on these residuals, producing new starting values which could be used the following night. And the next night, I'd go back. I don't know when I got sleep, but I never was sleepy. I never was tired or sleepy. It was just so thrilling to have all that machine to myself. And I finished. The resulting orbit of Mars was based on 2000 observations taken between 1830 and 1952, producing the coordinates at five-day intervals between 1800 and 2000.

In 1962, the Lab had them published in a 400-page volume titled, "Heliocentric Coordinates of Mars," by Joseph L. Brady and Edna Vienop. Molly Sanderson wrote the 650 program to process the observations. Ken Tiede wrote the IBM 7090 double-precision input-output routine. And Nevin was always involved. Most of the volumes were bought by NASA to use in its space program.

Now, we had all the planets on tapes, one tape for each planet, so we were ready to start computing the orbit of Halley's Comet. We no longer had the Berkeley machine. When we ran an integration we needed all the tape drives. Do you remember, on those 700 series each person was given a few minutes? It wasn't time-sharing, you just had a few minutes now and then.
Joe Brady

GAM: Right.

JB: Well, it would take us five minutes to mount all the tapes. We lost half our time just mounting tapes! And we used to come in before our time was scheduled, and that would bug those who were already there, because we'd start messing with the empty tapes. There was always a problem getting the previous user off when his time was up. Sometimes you had to push the "clear" button for them.

GAM: That's a marvelous story! Well, I think for the record we ought to notice that you're the author of that famous remark, "Anything that's got science in its name, isn't." Do you remember that? We used to argue about computer science?

JB: I remember that.

GAM: You were pooh-poohing computer science, and I think rightly so. I think that now I'm more comfortable with the idea of computational science or computing science, which is some sort of happy mixture of mathematics and logic and things of this sort. But the stuff that's passing for computer science in many schools today is maybe not as elegant as it should be, you know?

JB: Well, in those days, there was no such thing as computer science, really. Most had degrees in mathematics or physics or astronomy.

There was no such degree that you could get at that time. And the best programmers that we had were often-look at Tom Haratani-he had a degree in biology. And who was that guy who was a machine operator, and then became a programmer, and had a Ph.D. in something?

GAM: Well, there was Roger Fulton. He had a degree in history.

JB: And yet he was mounting tapes, and he was a machine operator for a while. And then he became a programmer.

GAM: Well, why don't you tell us a little bit about your adventures with Planet X? How did that come about?

JB: Before I can talk about Planet X, I should talk about Halley's Comet, because the problems that arose from working on Halley's Comet were the reasons for Planet X.

I wanted to compute the 1986 return of Halley's Comet. Appearances of comets have been recorded for over three thousand years. Over fifty of them are probably Halley's Comet and go back to 2347 B.C. All but the last four apparitions-in 1910, 1835, 1759, and 1682-were seen before Galileo discovered the telescope, and so had to be very bright comets visible to the naked eye. Since Halley's Comet has an average period of 76 years, the next apparition was probably going to be around 1986.

In order to make an exact prediction, which means the instant when the comet is closest to the Sun, the positions of all the planets are needed. The planetary positions that we had from the Naval Observatory and from our own Mars coordinates only went back to 1800 and forward to 2000. Therefore, when we used the THEMIS code, we could only reproduce the last two apparitions, with no guarantee that a third apparition would be correct. But, fortuitously, in 1967, J. Lieske at the Jet Propulsion Lab produced all the starting values needed to integrate the nine planets forward and backward as far as we wished. Thus, if we had the observations of Halley's Comet we could try to reproduce them computationally, and then we would have confidence in a forward integration to predict the 1986 return.

To do this meant we needed a new code that would integrate ten bodies, the comet and nine planets. Frank McMahon agreed to write the required n-body code, and a beautiful program it was. But while this was being done we had to get the observations of Halley's Comet.

Sid Fernbach let me go to Washington, DC, to work at the Library of Congress for a while to get the observations. The librarian gave me a stack pass, and told me to find what I could and they would make photographic copies. Actually, some of the books were so old and crumbly that they couldn't be copied. They sent me to the Harvard College Library in Cambridge where I found older documents than at the Library of Congress. Many of these were in foreign languages and had to be translated. My wife could translate some of them like French, Italian, and Spanish, but the Chinese, Korean, Egyptian, and German observations had to be sent out by the Lab for translation.

GAM: How many observations?

JB: I came home with over five thousand observations. Not all could be used due to uncertain times or dates of the observations, or sometimes due to ambiguities from language problems in the published reports. Most of them were from 1682 to 1910 and were more or less accurate observations. Before the discovery of the telescope, Halley's Comet was only visible for a few days. In 1682, it was observed for 24 days. In 1910, it was observed for twenty months. But some observations were very ancient and were just hints of when the comet was visible, with no indication of where in the sky it was seen. And there were problems with the various calendars used in early cultures. For example, Wen Shion Tsu reported in his Chinese history that during the tenth year of the reign of Tsin Tsao Kung (467 B.C.) a hui (comet) was seen. The computed time of this apparition was 468 B.C., on July 16.047.

Each observation had to be reduced to a common coordinate system and this was a very big job. To do this required knowing the latitude, longitude, and altitude of the observatory. And this information was sometimes lost and unrecoverable. To get an idea of what to expect in errors, the reduction of an observation is a very complicated task and probably not what you are dying to know about. A lot of people were involved-Edna Carpenter, Dick von Holdt, Nevin Sherman, Don Freeman, and others, I'm sure.

Anyway, I had to throw some observations out. You see, you never knew what the observer had done to the observations. He may have made some of the corrections, or he may not have. If the literature didn't tell you exactly-there was one observatory I couldn't even find-it was some eastern college that had made these observations. I talked to the college and they said, "That observatory has long since been torn down. We don't even know where it was on campus. We can't give you a location!" I had to throw those out, and all those made in Egypt were so bad, and the errors were so big, that I threw them out.

GAM: Yes. Oh, wait a minute, are you saying that here's a college which covers a certain number of acres, and you couldn't just approximate the location of the observatory?

JB: I could, and sometimes I did. Often a college observatory isn't even on the campus.

GAM: You could say it was at the center-I mean, this is an error of maybe a mile or so.

JB: Well, it makes a difference.

GAM: It does?

JB: Oh, yes!

GAM: One mile? Come on!

JB: Oh, yes! Well, I'm talking about the eighth decimal place. An error of one mile is an error in the eighth decimal place. When working with double precision you don't want to introduce errors in the eighth decimal place. You have to be as accurate as possible. A comet observation, even today, is often not precise. The computed position refers to the center of gravity of the comet, which is assumed to be the nucleus. But the nucleus is often hidden in the bright coma, so an observer picks the center of light-which may not be the nucleus. And sometimes, when the comet is close to the Sun, tidal forces have broken the nucleus into several pieces.

GAM: So, you've made all these corrections, and you still had to throw out some observations.

JB: Yes. We ended up with about 3000 observations for 1910, 1500 for 1835, 250 for 1759, and 13 for 1682. And then I integrated the orbit. Each apparition had be integrated as a separate problem to determine the probable error for that era. In 1835, there were no reflectors larger than 30 inches and no refractors larger than 15 inches. Even in 1910 the largest reflectors were the 61-inch at Harvard and the 60-inch at Mt. Wilson. In 1910, they didn't have any 100-inch or 200-inch reflectors. I forget what the size of the telescopes were back in 1682, but the telescope was very small. And primitive. So, I would have to take each of the four apparitions, and integrate those and reduce the errors to as small as possible, and do that separately for each apparition.

Once the observations had been reduced and their probable errors determined, starting values for the comet were chosen. The n-body integration then determined the error between the calculated positions of the comet and the observed positions of the comet, each weighted by the probable error of that apparition. By a least-squares solution of the several thousand observations, the comet's starting values could then be recalculated. And the process was repeated over and over until the errors ceased to change. But it turned out that it was impossible to get a reasonable fit for more than two adjacent apparitions. The next apparition was always off by approximately three days. So it was impossible to predict the 1986 apparition closer than three days. To get a better fit for a prediction, we decided to put an empirical term into the equations of motion, a small force-

GAM: A force?

JB: A little force that depended on the time, and could be adjusted to obtain a fit to as many apparitions as possible. There is a precedent for this in the history of astronomy. Newton's theory of gravitation could never explain the motion of the planet Mercury and an empirical term was used to correct the orbit. However, in 1917, Einstein's general theory of relativity was successful in explaining the discrepancy. And when I integrated Halley's Comet again using this empirical term, I was able to fit not only the last four apparitions, but all of them reasonably well. In fact, I could go back and back a thousand years, and fit even the visual Chinese observations. I had a lot of Chinese observations, and Korean.

There was a Chinese man who had translated them. They use different constellations than we do.

GAM: Fascinating.

JB: They had totally different names for the constellations. He translated those into our constellations. So, when I had this little empirical force in there, I could fit all these observations beautifully, within the probable errors that I had determined.

This orbit was then used to predict the 1986 return, which turned out to be correct within a few seconds of arc. In the years that followed this prediction several articles were published. One was titled, "Halley's Comet: A.D. 1986 to 2647 B.C.," which described all the known observations prior to 241 B.C. And with the empirical term, the orbit was then used to integrate forward, and it produced a search ephemeris from 1982 to 1989. The time of perihelion was predicted to be 1986 February 09.39474.

GAM: You were off by a few minutes or something like that, or a few seconds of arc?

JB: A few seconds of arc. Let's start with Planet X again. So now, after the predicted 1986 return of Halley's Comet, there was a question as to what the empirical term meant. One answer was that it could mean a missing planet: the mass of a missing planet affecting a comet, an unknown planet beyond Pluto.

GAM: You'd found that the perturbations could be explained by having another planet and so forth?

JB: Yes, so the problem was to find a hypothetical planet that would work as well as the empirical term. It was 1970 or 1971 when the computational search for this transplutonian planet began. It would be the tenth planet and so was called Planet X. The work was done using Frank McMahon's n-body code on the CDC 6600. It was a long, iterative process, and when it was finally finished it worked as well as the empirical term, in some ways better.

There were two other comets similar to Halley's Comet which had been observed at three apparitions. They were Comet Olbers and Comet Pons Brooks. Both had aphelion distances and eccentricities similar to Halley's Comet, and their orbits had errors of three or four days like Halley's Comet. But there the resemblances ceased. They both move in direct orbits, while Halley's Comet moves in a retrograde orbit. They are at perihelion when Halley's Comet is at aphelion. Yet, they must feel the effect of the transplutonian planet. The orbits of these two comets were integrated in the same manner as Halley's Comet, with and without the hypothetical planet. Happily, Planet X corrected their errors as well as Halley's Comet. So that's the story of Planet X.
Joe Brady

GAM: Well, not quite all the story. Didn't you make a prediction about Planet X?

JB: Yes.

GAM: The tenth planet. And there was, in fact, some experimental work that went on to try and find it?

JB: Yes. There were two searches made-one at Mt. Hamilton, at the Lick Observatory, and one at the Royal Observatory at Herstmonceux outside of London. They both searched down to the thirteenth magnitude, and couldn't find it. Planet X was predicted to be more massive than Saturn, so it should have been quite bright and easy to find. But, you know, when Pluto was predicted by Percival Lowell, it was long after his death when it was found and it was much smaller than the mass predicted. One astronomer wrote me that "there may be two planets out there-maybe even three" When Uranus was discovered, people were saying, "Well, that's it. That's the end of the solar system. There can't be any more." But along came Neptune and Pluto.

I knew there were two possible positions for Planet X, and they were 180 degrees apart. One of these two positions had been searched for Pluto, very carefully, back in the '30s when Pluto was discovered. But the other position hadn't been searched. So, that's the position I gave out.

GAM: Produced the ephemeris.

JB: Yes, I had given out the position for it, and I assumed that was the position it would be. It still could be the other position.

GAM: Well, it could now be also that you'd find it, because we have far more sensitive observational instruments, now and so forth.

JB: But my predicted planet would have to be very bright. It's massive. It's between Jupiter and Saturn in mass. It's a very massive planet to do what it has to do, and it would be very bright. So, they searched down to the thirteenth magnitude. Well, that's plenty.

When publicity about a possible new planet got out, I received a call from Glenn Seaborg, head of the Atomic Energy Commission. He said that since the chemists had dutifully named newly discovered elements after the planets-atomic number 92, uranium; number 93, neptunium; number 94, plutonium-that it was our turn to name a new planet "America" after element number 95, americium.

GAM: That's a wonderful story. All right. Well, Joe, let's continue. After finishing with Planet X, what did your career take on next?

JB: Sid assigned me to the problem of new hires for the Computation Department. This took about half of my time so I could work on astronomical problems, things I'd rather talk about.

I had to review the files sent to us by Personnel. I guess Personnel must have reviewed them to a certain extent first. I would look at them and decide whether to invite them for interviews. And then I would set up the interviews with the appropriate supervisors. A secretary would get the interviewee from Personnel, where he had been fingerprinted and talked to, and bring him to the Department, where I would meet him. The interviews were friendly and informal, and I hope we made the interviewee comfortable. I would talk to him and tell him what was going to happen, give him a list of the people who would talk to him and what jobs would be available. I also took him to lunch at the cafeteria. At the end of the day I would quiz him about the interviews and tell him he would hear from us one way or the other. Of course, if the guy had a degree in astronomy, I'd hire him immediately.

Occasionally an interviewee would say he didn't want any of the jobs that were available. And interviewees often asked about involvement with weapons work. If they were not from California, they always asked about earthquakes. One man, who had degrees from Harvard, Princeton, and MIT, worked at MIT and wanted to work on computers. I thought it important to hire him, so I took him home to have dinner and stay the night at my house. We happened to have artichokes for dinner that night. He had never seen one and didn't know how to eat it. Ah well, so much for an Ivy League education. My wife took him to the airport the next morning. He wrote me that he had decided to stay at MIT. Another man turned us down because he said he had learned that California was a cesspool of microwaves. Another man turned us down because he had explored Livermore and found there was not enough kosher food available. But the overwhelming majority of offers were accepted.

These interviews were almost a daily chore. Sometimes, taking the interviewee to lunch was embarrassing. The Lab gave me a chit to pay for his lunch-but not mine. All I would want was a bowl of soup or a sandwich. But he, knowing the sky was the limit, would often get so many things, two or three desserts, that he'd have to put some of them on my tray. The girl at the cash register was sure I was trying to get away with something!

GAM: I meant to ask you at the beginning to roughly outline your college training experience. Where did you go to school, what did you major in, and so on?

JB: After the war, I went to UC Berkeley and majored in astronomy. I had gone to UCLA for two years and then transferred to Berkeley. Nevin Sherman and I both worked for Dr. Cunningham, who was a professor of astronomy at Berkeley. We shared an office in the old astronomy complex. It was a little brown-shingle building among the other brown- shingle buildings that surrounded a quadrangle near the north gate. We also shared the office with the first computer that IBM ever made, called the 602A.

GAM: Yes, I've heard of that.

JB: We computed orbits for Dr. Cunningham. He paid us a few pennies an hour, and every now and then he'd give us a raise, but it was out in the third decimal of a penny. He had small research grants but he hired Nevin and me, and sometimes Alice Roemer. Do you remember John Howard? John and Alice were married, and John worked at the Lab for many years. John is dead now. I see Alice occasionally.

GAM: Yes.

JB: We had to work at night because those were the hours Dr. Cunningham kept. He'd come in about one or two in the afternoon, teach his classes, and then stay on through the night. Near midnight, he would take us out the north gate to a little store and buy us an ice cream cone. Nevin lived in the co-op up the street from the north gate, and he had a noontime job in the kitchen. He would bring a cauldron of soup down to our office where we kept it warm. The afternoon classes lasted three hours, and when we got a fifteen-minute break, everybody would come in our office and get a bowl of soup. I lived on the south side of the Berkeley campus, and I would get home at dawn and have breakfast with my wife and children. My wife was teaching school. Then I would sleep until noon and go back to my graduate school classes. It was a nice department, quite different from the rest of the campus.

When Nevin and I would compute an orbit, the results were sent to a central clearinghouse at Harvard, and they would be published on what was known as the Harvard Announcement Cards. Of course, Cunningham's name would be at the bottom of the card as the author. But if we elected not to be paid for the work our names would be at the bottom. Sometimes, if only one of us worked on the orbit, Cunningham would say, "You can take credit for this, but you don't get paid." So every now and then, if we thought we could afford it, we would take credit for the orbit.

GAM: That's beautiful. Did you finish your graduate training and get a degree?

JB: I got a Master's degree. I could have kept on working for Dr. Cunningham, but I couldn't afford it.

GAM: I understand. Well, where did you meet Edna? At the Lab?

JB: At the Lab, yes. When I first went there, we were on this screened porch. And, you know, she was so willing to help people. When I was supervisor, she was my assistant supervisor. Did you read this little blue pamphlet about "The Mars Stars-Heated Discussions"? It was written by Sid's secretary, Kathleen Ehlers.

GAM: No, not yet.

JB: Joe Brady and Dick von Holdt would go to Edna Carpenter's office, across the hall from Sid's office. Do you remember, over in that other building? A little two-story, with a long hall-Building 116.

GAM: Yes.

JB: Sid was way down at the end of the first-floor hall, and Edna was right across the hall from him. So, we'd go to Edna's office. The men would talk about, and then scream about, their different viewpoints on Halley's Comet. Edna would listen quietly, but always made her point. For years, the secretaries in Building 116 affectionately referred to the trio as "our Mars stars." That's Edna for you. So I went to work at the Lab, and because of Sid Fernbach's constant support and encouragement and, much later, John Ranelletti's support, I spent thirty happy years at the Lab.

[1] UCRL-5240-T, "UCRL Codes for the Motion of Astronomical Objects in the Solar System," by Richard Levee and Joseph L. Brady (LLNL, 6/2/58). The details of the THEMIS code are in Vienop and Brady, "Themis Code, an Astronomical Numerical Integration Program for the IBM 704," UCRL Report #5242 (LLNL, 5/20/58); see also UCRL-5288-T, Report #2, by Brady and Levee (LLNL, 6/58).