The Clock That Gains in Winter
The tower clock at Saint Ninian's is eight minutes fast by Christmas every year, and the treasurer wants a 2,400 euro radio-controlled motor in its place. The parish assistant will not say the clock is broken. From three weekly readings against the phone's time (0:00, +0:37, +1:14) it gets 5.3 seconds a day, and from the tower thermometer (2.4 C against 12 C when it was last set) a steel pendulum rod predicts 5.0. The cure is one division on a rating nut, about 0.08 mm, and the same turn back in April.
The tower clock at Saint Ninian's had gone fast every winter for as long as Dermot Hannay had wound it, which was thirty-one years, and every spring it had come back to the right time by itself, the way the swallows came back, and nobody had ever asked why.
This year Priya Nair asked. She was the parish treasurer, thirty-four, an accountant, and she had a quotation open on the vestry tablet for a radio-controlled drive that would hold the hands to the second, for two thousand four hundred euro, with a grant form attached.
"It was ten past eleven on the church clock when I came out of the shop on Thursday," she said, "and it was five past by my phone. Every year people say it, at the Christmas Mass. I'd like to stop them saying it."
"I'd like to look at it with you before you spend that," said the assistant. "I am not saying you shouldn't. I'm saying that nobody has yet measured what the clock is doing, and I think the measurement may be cheaper than the quotation. Dermot, may I ask you to read me the clock against your phone, at the same time of day, on Saturdays?"
Dermot was sixty-nine and did not like phones. But he liked the clock, and he said he would.
He read it on the sixth of December, on the thirteenth and on the twentieth, at noon, standing in the ringing chamber with the lantern in one hand and the phone in the other. The first Saturday he set the hands to the phone's time, to the second, and the second Saturday they were thirty-seven seconds ahead; the third, a minute and fourteen.
"That's thirty-seven seconds a week, and thirty-seven again," said the assistant. "Between five and six seconds a day: 5.3. A steady rate, not a jump. That matters. A clock that is broken tends to lurch. This one is merely wrong by a fixed amount, which means it is keeping something very regular, just at the wrong pace."
"It's a pendulum clock," said Dermot, with the faint offence of a man whose clock has been called a thing. "It's a seconds pendulum. It's a steel rod and a lead bob."
"Then I think I can tell you what it's doing, and you can tell me if I've got it wrong. Is there a thermometer in the tower?"
There was: a min-max one, hung on a nail by the weights since the nineteen-eighties. Dermot read it out. For the week to the twentieth the average of the minimum and the maximum was 2.4 degrees.
"And the clockmaker's book?" It was in a biscuit tin on the shelf. "When was it last set to time?"
"April. The seventh. It says twelve degrees in the tower, in his hand."
"Good. Then here is the whole of it. A pendulum's period goes with the square root of its length. For a pendulum that beats seconds, the swing from one side to the other and back takes two, and the length is a little under a metre: nine hundred and ninety-four millimetres, from the pivot to the middle of the bob. Cold shortens a steel rod. Steel shrinks by about twelve millionths of its length for every degree. A shorter pendulum swings faster, and a faster pendulum makes the clock gain."
"Everyone knows that," said Priya, who had not known it a minute ago.
"What's less obvious is how much. The rate changes by half the fractional change in length. From twelve degrees down to two and a half is nine and a half degrees: that's about one part in nine thousand in length, so one in eighteen thousand in time, and in a day of eighty-six thousand four hundred seconds that comes to about five seconds. Five point zero. Dermot has measured five point three."
Dermot said nothing. He was looking at the pendulum.
"They agree to within six per cent," said the assistant. "I'd be suspicious if they agreed exactly. The thermometer hangs by the weights, not by the rod; the rod is warmer near the roof; there will be a bit of friction and air I have not allowed for. But that match means the rod is steel, as you said, and that the cold is the whole explanation. Nothing is wrong with the clock. It is a thermometer that tells the time."
Priya was quiet for a bit. Then she said, "So it will get worse as it gets colder."
"At minus one in the tower, which on the clockmaker's log has happened, the difference is thirteen degrees from April and the clock gains about six and three quarter seconds a day. Over the ninety days from the end of November, that is eight to ten minutes, if nobody touches it. What you hear at Christmas, eight minutes, is the January figure arriving early in the story. And in August, at twenty-two degrees, the same clock loses five seconds a day."
"Then it is right twice a year."
"Twice, and in between wrong by an amount you could write on a card." The assistant had the answer on the screen for the three of them to look at, in plain figures. "Now what the clockmaker did, and what I would do, is move the bob. The rod ends in a rating nut under the bob, with a thread of a millimetre to a turn. Raise the bob one millimetre and the pendulum is shorter by one millimetre, and the clock gains forty-three seconds a day. Lower it and it loses forty-three. That is 0.5 times 1 over 994, times 86,400. So the 5.3 seconds a day the clock is gaining wants the bob lowered by 0.12 of a millimetre."
"That's nothing."
"It is an eighth of a turn. Is there a scale on the nut?"
There was: twelve fine marks around the rim, each a twelfth of a turn, a twelfth of a millimetre, which is three and a half seconds a day. "One mark and a half," said the assistant. "Take it down one mark, and do not take it two. One mark is 3.6 seconds a day; the clock will still gain, by about 1.7. Then read it again for a week. The thing I would not do is turn it by feel, on a Sunday, because the clock is wrong on Sunday morning and the Mass is at ten."
"And in April?"
"Up one mark. Or one and a half. The card will say."
Dermot lowered the nut himself that same Saturday, the twentieth, by one mark, with the clockmaker's spanner and the tip of his tongue between his teeth, and stopped the pendulum for no more than the time it took, and started it with two fingers. The clock lost its half-minute on the stop and was reset.
By Christmas night it was eleven seconds ahead of the phone: five days at about two seconds a day. On Christmas night the church clock, which had been eight minutes fast every year since 1991, was still within a quarter of a minute when he rang the first bell, and he told nobody, and did not mention the phone.
He wrote the card himself, in the biscuit tin's own pencil, and pinned it on the nail with the thermometer. October, down a mark. April, up a mark. Read it Saturdays. Do not touch it on a Sunday.
Priya came to look at it in January, and she was not displeased. She took the quotation off the screen. She asked whether the radio drive could be kept in the file, for the day Dermot stopped climbing the tower, and the assistant said that it could, and that it would be a fair thing to buy then; the rate fix cost nothing, but it did not wind itself.
"No," said Dermot, from the stair. "It does not."