“Quite wrong, Kingsley. I’m going up to Cambridge for a Trinity Feast.”
Kingsley, still acutely conscious of the execrable dinner he had just consumed, pulled a wry face.
“Always amazes me the way those Trinity beggars feed themselves,” he said. “Feasts on Mondays, Wednesdays, and Fridays, and four square meals on each of the other days of the week.”
“Surely it’s not quite as bad as that. You seem quite put out today, Kingsley. In trouble of any sort?”
Metaphorically the Astronomer Royal was hugging himself with delight.
“Put out! Who wouldn’t be put out, I’d like to know. Come on, A.R.! What was the idea of that vaudeville stunt this afternoon?”
“Everything that was said this afternoon was plain sober fact.”
“Sober fact, my eye! It would have been much more sober if you’d got up on the table and done a clog dance. Planets a degree and a half out of position! Rubbish!”
The Astronomer Royal lifted down his brief case from the rack and took out a large file of papers on which a veritable multitude of observations was entered.
“Those are the facts,” he said. “In the first fifty or so pages you’ll find the raw observations of all the planets, day-by-day figures over the last few months. In the second table you’ll find the observations reduced to heliocentric co-ordinates.”
Kingsley studied the papers silently for the best part of an hour, until the train reached Bishop’s Stortford. Then he said:
“You realize, A.R., that there isn’t the slightest chance of getting away with this hoax? There’s so much stuff here that I can easily tell whether it’s genuine. Can I borrow these tables for a couple of days?”
“Kingsley, if you imagine that I would go to the trouble of staging an elaborate — hoax as you call it, primarily with the object of deceiving you, of taking a rise out of you, then all I can say is that you flatter yourself unduly.”
“Let’s put it this way,” answered Kingsley. “There are two hypotheses that I can make. Both at first sight seem incredible, but one of them must be right. One hypothesis is that a hitherto unknown body with a mass of the same order as Jupiter has invaded the solar system. The second hypothesis is that the Astronomer Royal has taken leave of his senses. I don’t want to give offence, but quite frankly the second alternative seems to me less incredible than the first.”
“What I admire about you, Kingsley, is the way you refuse to mince matters — curious phrase that.” The Astronomer Royal reflected thoughtfully for a moment. “You should go in for politics one day.”
Kingsley grinned. “Can I have these tables for a couple of days?”
“What do you propose to do?”
“Well, two things. I can check the consistency of the whole business and then I’ll find out just where the intruding body is located.”
“And you’ll do this how?”
“First I’ll work backwards from the observations of one of the planets — Saturn might be the best one to choose. This’ll determine the distribution of the intruding body, or intruding material if it isn’t in the form of a discrete body. This’ll be much the same thing as the J. C. Adams — Le Verrier determination of the position of Neptune. Then once I’ve got the intruding material pinned down, I’ll work the calculation forwards. I’ll work out the disturbances of the other planets Jupiter, Uranus, Neptune, Mars, etcetera. And when I’ve done that, I’ll compare my results with your observations of these other planets. If my results agree with the observations then I’ll know there’s no hoax. But if they don’t agree — well!”
“That’s all very fine,” said the Astronomer Royal, “but how do you propose to do all this in a couple of days?”
“Oh, by using an electronic computer. Fortunately I’ve got a programme already written for the Cambridge computer. It’ll take me all tomorrow modifying it slightly, and to write a few subsidiary routines to deal with this problem. But I ought to be ready to start calculating by tomorrow night. Look here, A.R., why don’t you come to the lab after your Feast? If we work through tomorrow night, we ought to get the matter settled very quickly.”
The following day was most unpleasant; it was cold, rainy, and a thin mist covered the town of Cambridge. Kingsley worked all through the morning and into mid-afternoon before a blazing fire in his College rooms. He worked steadily, writing an astonishing scrawl of symbols of which the following is a short sample, a sample of the code by which the computer was instructed as to how it should perform its calculations and operations:
T
z0A23 
1U11
2A 2F3U13
At about three-thirty he went out of College, thoroughly muffled up and sheltering under his umbrella a voluminous sheaf of papers. He worked his way by the shortest route to Corn Exchange Street, and so into the building where the computing machine was housed, the machine that could do five years of calculation in one night. The building had once been the old Anatomy School and was rumoured by some to be haunted, but this was far from his mind as he turned from the narrow street into the side door.
His first move was not to the machine itself, which in any case was being operated by others just at that moment. He still had to convert the letters and figures he had written into a form that the machine could interpret. This he did with a special kind of typewriter, a typewriter that delivered a strip of paper in which holes were punched, the pattern of the holes corresponding to the symbols that were being typed. It was the holes in the paper that constituted the final instructions to the computer. Not one single hole among many thousands must be out of its proper place, otherwise the machine would compute incorrectly. The typing had to be done with meticulous accuracy, with literally one hundred per cent accuracy.
It was not until nearly six o’clock that Kingsley was satisfied that everything was satisfactorily in order, checked and double-checked. He made his way to the top floor of the building where the machine was housed. The heat of many thousands of valves made the machine-room pleasantly warm and dry on this cold damp January day. There was the familiar hum of electric motors and the rattle of the teleprinter.
The Astronomer Royal had spent a pleasant day visiting old friends, and a delightful evening at the Trinity Feast. Now at about midnight he felt much more like sleeping than sitting up at the Mathematical Laboratory. Still, perhaps he’d better go along and see what the crazy fellow was up to. A friend offered to take him by car to the lab., so there he was standing in the rain, waiting for the door to be opened. At length Kingsley appeared.
“Oh hello, A.R.,” he said. “You’ve come at just the right moment.”
They walked up several flights of stairs to the computer.
“Have you got some results already?”
“No, but I think I’ve got everything working now. There were several mistakes in the routines I wrote this morning and I’ve spent the last few hours in tracking ’em down. I hope I’ve got them all. I think so. Provided nothing goes wrong with the machine, we should get some decent results in an hour or two. Good feast?”
It was about two o’clock in the morning when Kingsley said:
“Well, we’re nearly there. We should have some results in a minute or two.”
Sure enough five minutes later there was a new sound in the room, the chatter of the high-speed punch. Out of the punch came a thin strip of paper about ten yards long. The holes in the paper gave the results of a calculation that it would have taken an unaided human a year to perform.
“Let’s have a look at it,” said Kingsley as he fed the paper tape into the teleprinter. Both men watched as row after row of figures were typed out.
“The lay-out isn’t very good, I’m afraid. Perhaps I’d better interpret. The first three rows give the values of the set of parameters I put into the calculations to take account of your observations.”
“And how about the position of the intruder?’ asked the Astronomer Royal.
“Its position and mass are given in the next four rows. But they’re not in a very convenient form — I said the lay-out isn’t very good. I want to use these results to calculate next what influence the intruder should have on Jupiter. This tape is in the right form for that.”
Kingsley indicated the paper strip that had just come out of the machine.
