by Tom Bullough
‘Let us see with what exactness we can by this means form a conception of the distance which separates the Earth from the Sun.
‘Light – the propagation of which is the most rapid movement known, and which travels at the rate of 290,000 versts in a second of time – requires 8 minutes and 17 seconds to flash from the Sun to the Earth. If we suppose the intervening space to contain atmospheric air, a sound, with an intensity sufficiently great to put in motion a sphere of such enormous dimensions, would take fourteen years and two months to reach our ears, sound travelling, as we know, about 340 metres a second.
‘Finally, an express train going at the rate of about 50 versts an hour, leaving the Earth the 1st of January, 1866, would not arrive at the Sun until the year 2213, nearly 347 years after the day of its departure.
‘We can thus form an idea of the immensity of the chasm which lies between the Sun and our globe – an immensity, the measure of which is expressed by the round number, so simple in appearance, of 140 million versts. It is this number – this 140 million versts – which will henceforth form the unit, the “standard measure”, by means of which the other celestial distances will be expressed.’
Konstantin counted the seven zeroes, then counted them again. He considered how much further it was to the Sun than Vladivostok, and with a little rounding down and a sum on the back of his Latin grammar he came to the figure 23,333⅓, which still possessed almost no meaning for him at all. He twisted the scraps of moustache that sprouted at each end of his mouth, pulled his sheepskin tightly round his shoulders and turned to the open window of the classroom and the Sun itself, which burnt above the snow-shrouded roof of the prison and threw its light from every plane and contour of the embankments and the snow-bowed trees in Zasorny ravine. He looked askance, through the haze of the city’s smoke, and, by narrowing his eyes, he managed to see an orange disc about the same size as the Moon. He tried to imagine how big and fierce the Sun would appear if he were standing directly in front of it, but the exercise proved impossible, and so in the end he contented himself with the view from Mercury.
Finding the relevant page in The Heavens, he discovered that at 44,200,000 versts, the nearest point in Mercury’s orbit, the Sun would be 3¼ times larger than it appeared from the Earth: a furnace consuming the sky, its heat increased by 6 ⅔.
Although the day was calm, the smoke rising at a gentle angle from the chimneys across the ravine, still Konstantin failed to hear the bell that marked the end of the lesson. He knew it had rung only by the stirring of the other twenty-four boys, whose backs straightened, whose pencils vanished, whose arms returned to the sleeves of their coats. On the bench beside him, Ignat made a tapering pile of his books. In his place by the stove, Tomasz consulted the watch in the pocket of his thick woollen waistcoat. At the front of the room, the Latin master continued to pass back and forth beneath the meaningless characters on the blackboard, his voice a sequence of half-heard grunts, his step the same short-legged strut that had measured out the past hour, but already Konstantin could feel the next-door class disgorging on to the floorboards in the corridor – their footsteps evaporating as they reached the top of the long stone staircase.
Out on Kopanskaya Street, Konstantin left the crowds at the gymnasium gates – laughing, pushing one another, no doubt sending jibes in his direction. He hurried alone along the icy pavement, the Sun warm like candlelight on his downy left cheek, his nose grown distinctly sharp, his eyelids showing a tendency to droop. Turning on to Tsarevskaya Street, he paced out the distance between the streetlamps. He wondered how Amédée Guillemin could possibly know that it was 140 million versts from the Earth to the Sun, and as he passed beneath the fire wardens smoking in the bell tower of Tsarevo-Konstantinovskaya Church he tried to imagine some way to measure the size and distance of the Moon, and then to scale up these measurements, but by the time he reached Preobrazhenskaya Street he had rejected this idea, and he frowned to himself as he climbed the stairs to the apartment.
In the kitchen, Anna was preparing cabbage soup – one eye on little Stanislaw, who was scurrying after a spring-powered carriage.
‘One hundred and forty million versts away!’ Konstantin exclaimed.
‘What is?’ she asked.
‘The Sun!’
The problem with so much of Konstantin’s reading was the endless words that he did not understand. The language of mathematics seemed to come to him naturally – even cube roots and cosines needed minimal explanation – but as he sat at his father’s desk in the drawing room, opened The Heavens and turned to a chapter named ‘Celestial Measurements’, on the very first page he encountered the words ‘inaccessible’, ‘stellar’, ‘parallax’, ‘unacquainted’, ‘enunciating’ and ‘incredulity’. He might have abandoned the book altogether had he not spotted, on the following page, a picture of a man in a field beside a river, measuring the distance to the top of a church tower with a mysterious, three-legged instrument.
Konstantin considered this instrument, a theodolite, with interest. He rummaged through The Heavens but, finding no further information on the subject, he turned to the shelves that held his father’s dust-covered manuscript and various books on science, mathematics and natural history. On page 4 of Adolphe Ganot’s Elementary Treatise on Physics, he discovered that a theodolite measured angles, but it was only in a book named Practical Geodesy that he found a description of sufficient detail to start work.
He took his father’s protractor from the desk drawer and, with a piece of sealing wax, attached a length of string to the meeting point of the radial lines. He tied a kopeck coin to the end of the string and opened the window. As he understood it, the principle of the theodolite was to make a geometric shape in actual space just as you would draw one on paper. If he called the windowsill A, the pavement directly beneath the window B, and the foot of the tower of Tsarevo-Konstantinovskaya Church C, then he had a right-angled triangle with one side that he could measure easily with the tape that his father used on the logs at the sawmill. Breathing uncomfortably, Konstantin lay on his belly so that his head poked outside into the sunlight. He unrolled the tape until its end touched the ground and measured 4.81 arshins to the corner of the frame. He realized at once, however, that it was impossible to use the theodolite at that level, and so he measured an additional 0.19 arshins to make five, crouched down, checked the level again, propped his elbows inside the window in the manner of a tripod, peered along the flat edge of the protractor until it was aligned with the point where the tower met the crumpled snow, and clamped off the string against the notches of the angles.
Konstantin closed the window and took down the tangent tables from their shelf. If the angle A was 89.3°, he concluded, then the angle C was 0.7°, the angles of a triangle making 180°. He ran a finger down the columns of tiny printed figures and wrote in chalk on his slate:
Tan 0.7° = 0.012218
∴ 0.012218 = 5 ÷ distance to tower
∴ 5 ÷ 0.012218 = distance to tower
He pondered a moment, then divided 50,000 by 122 and wrote on the slate:
409.8 arshins.
Standing on the pavement some minutes later, when only the dormer windows of 19 Preobrazhenskaya Street still reflected the afternoon sunlight, Konstantin tied his ankles together with string so that his feet were precisely one arshin apart. He set one heel against the pink brick wall beneath the neighbours’ kitchen window, waited for a government clerk to pass on a pair of skis, took a sight along his left arm and set out into the Thursday traffic.
He progressed slowly, keeping one foot exactly in front of the other, glancing back from time to time to check his path in the snow. Dimly, he was conscious of the noises around him. He knew that the peasants were stopping to watch him, laughing, mimicking his walk in their spotless market-day shoes and stockings, but his experiment exercised all of his attention and even when the girl from number 23 appeared at her front door in a blue velvet cloak, Arctic in her beauty, he was able to abs
orb her in a universal mosaic of circles, rhombi, trapezoids and triangles.
March 1873
‘The ear trumpet,’ wrote Adolphe Ganot in Elementary Treatise on Physics, ‘is used by persons who are hard of hearing. It is essentially an inverted speaking trumpet, and consists of a conical metallic tube, one of whose extremities, terminating in a bell, receives the sound, while the other end is introduced into the ear. This instrument is the reverse of the speaking trumpet. The bell serves as mouthpiece; that is, it receives the sounds coming from the mouth of the person who speaks. These sounds are transmitted by a series of reflections to the interior of the trumpet, so that the waves, which would become greatly developed, are concentrated on the auditory apparatus, and produce a far greater effect than divergent waves would have done.’
April 1873
Even by his own standards, Eduard Ignatyevich looked grim and preoccupied. In the three and a half years since the death of his wife, he seemed to have weathered like an exposed pine, bent by the wind and bowed by the snow so that even during the fine, brief summers he was unable to recover his previous shape. In the late-spring sunlight flooding through the south-facing window of the drawing room, he stood grey-faced, red-eyed, considering through the perpetual miasma of his cigarette smoke a letter written in a formal hand.
Hesitantly, Konstantin rose from the desk, directed his ear trumpet towards his father’s lips.
‘What is that, Konstantin?’
His voice was so plain that he might have been speaking directly into his ear.
‘It’s … It’s an ear trumpet, Father.’
‘An “ear trumpet”,’ he repeated, tonelessly.
‘Yes, Father …’
‘Yes.’ Eduard Ignatyevich took a step forwards. His eyes turned momentarily to the long tin shaft, the funnel bell, the knotted bands of wire taken from the heaps of crinoline that Konstantin had bought for kopecks at the flea market. ‘Well, Konstantin, it will come as no surprise to you to learn that you have failed the second year for a second time, which means, of course, that you will receive no qualification. I am afraid that I can see no alternative to an apprenticeship.’ He removed his spectacles, rubbed his eyes with hard, blunt fingers. ‘Given the sacrifices I have made to pay your fees at the gymnasium, I need hardly tell you how disappointed I am in you. If you had dedicated a fraction of the energy to your schoolwork that you have wasted on these toys of yours …’ He indicated a carriage of wood and tin, which sat on the grubby grey blanket covering the green velvet couch.
Konstantin lowered his eyes, opened his mouth.
‘Do you have something to say for yourself?’
‘They’re … They’re not toys, Father. They’re models.’
‘I hardly see that it makes any difference.’
‘But … models are essential to an understanding of physics, that’s what Adolphe Ganot says.’
‘Indeed?’ Eduard Ignatyevich collected the carriage, revolved it in his hands. ‘So, tell me, what physical principle does this little car demonstrate that is more important than your school certificate?’
‘It’s a reaction machine, Father … It’s propelled by a jet of steam, so it … it demonstrates the Third Law of Isaac Newton.’
His father looked again at the neat wooden wheels, the firebox, the slim tubulure that jutted from the back of the cylindrical boiler.
‘Explain,’ he said, after a moment.
‘Well, Father,’ said Konstantin, haltingly. ‘It moves because of the reactive force of the vapour expelled by the boiling water, which proves … that for every action there is an equal and opposite reaction.’
Eduard Ignatyevich extinguished his cigarette in the fireplace. Through the clearing smoke, the sunlight found a trace of blue in his eyes.
‘Then … how do you explain the others?’
‘Well, Father …’ Konstantin turned to the jumble of models in the corner. ‘I’ve … I’ve made a carriage driven by a spring, which … demonstrates the principle of potential energy, and a theodolite, which makes extremely accurate angular measurements, and I’ve built a lathe, and a pendulum clock, and … I’ve tried to make a hydrogen balloon to demonstrate the buoyancy of a gas less dense than air, but unfortunately I have no caou … no caoutchouc varnish so I have not yet been able to stop the gas from escaping. And I’ve made lots of inventions too! I’ve made a new type of string instrument with a bow you can work with a pedal! And I’ve made a new type of carriage powered by a windmill, with a special tail so that the sails will always face into the wind!’
Sitting in the stern of one of the broad, shallow boats at the wharf beneath the big hotel, Konstantin watched as the ferryman seized his oars and began to pull with quick, fierce strokes – angling his course into the current. He felt a shudder in the hull as the first ice-trimmed log collided with the gunwale. In the prow, he saw the three women returning from the Sunday market with their unsold figurines and penny whistles cross themselves, lower their heads, and so, to provide a distraction, he rolled his reaction machine first one way then the other across the lid of a brightly painted chest. When he looked up, he saw that he had attracted the attention of the women and the ferryman alike, but such was the roar of the wind and the river in his ear trumpet that he was unable to hear any trace of their questions. He watched as his father explained the principle of reaction, while, above his old black hat, the spires of Feodorovskaya Church, Pyatnitsky Church, Spassky Cathedral and Holy Resurrection Cathedral emerged from the glimmering, snow-strewn escarpment – as if ascending into the heavens.
On the narrow beach at Dymkovo, Konstantin and Eduard Ignatyevich walked among keeling boats, men casting lines and boys scavenging for planks in the ocean of logs that spread upstream from the boom at Simonovsky Island. They passed teams of horses dragging logs up the bank on long, looped ropes – following the principle of the pulley. They passed gangs of peasants loading firewood on to sledges whose runners made streams in the ruined ground. They passed bonfires tall as two-storey houses, a pair of rails where men pushed logs on wagons towards the hulking shed of the sawmill itself – its tall black chimney boiling smoke, its circular saw screaming so plainly that, for a moment, Konstantin almost thought that his hearing had returned.
Overlooking this infernal activity, a bare-cheeked, yellow-haired figure was smoking on the veranda of a small, grimy office. He was dressed in polished leather boots and a suit in the German fashion – a golden ribbon between his lapels – and he lifted his hat when he saw them approaching between the stacks of boards and beams, bowing ceremonially.
‘Eduard!’ he exclaimed. ‘And what do we have here? A bugler?’
Konstantin glanced questioningly at his father.
‘Matvei Ilyich,’ said Eduard Ignatyevich. ‘May I present my son, Konstantin? I am afraid that he is rather hard of hearing. He is employing an ear trumpet of his own invention.’
‘Of his own invention!’ The foreman raised an eyebrow. ‘A boy after my own heart! And tell me, young man, what is that extraordinary-looking carriage you have there?’
‘It’s … a reaction machine, sir,’ said Konstantin.
‘Is it indeed?’
‘Yes, sir …’
‘The Third Law of Isaac Newton, eh?’
‘Yes, sir …’
‘I should say so!’ Matvei Ilyich chuckled amiably. ‘I hope you will honour me with a demonstration?’
So thick were the soot and the sawdust on the windows of the office that, despite the bright spring sunshine, a lantern was burning on the leather-clad desk, which was largely concealed by an enormous technical diagram. The light caught the spines of the fat, dusty ledgers in the bookcase. It shone from a portrait of Alexander II and a recent, framed cutting from the St Petersburg Vedomosti.
‘Tell me, Matvei Ilyich,’ said Eduard Ignatyevich when they were all sitting down. ‘How was your reception with the governor?’
‘It was, I believe, a success …’ The foreman produced a silver ciga
rette case. ‘Of course, Mikhail Yakovlevich is not a scientific man like ourselves, but he is a politician and a reader of the newspapers. He has given me his assurance that he will speak to Prince Kuznetsov on our behalf.’
Konstantin held a match to the crumpled paper in the firebox of the reaction machine and blew on the woodchips until they were burning fiercely. He set the model on the floorboards, and turned his attention to the diagram on the desk. It took him several moments to identify a pair of giant wheels at the heart of its labyrinth of struts, levers, ropes and regulatory instruments – vertically arranged, strung with a belt of neat little barrels. So far as he could tell, the right-hand side of this belt was immersed in a tall thin reservoir of water, while a drive shaft led from the lower of the two wheels, passed through a system of gears and concluded in a minute circle, which was, he realized, the blade of the sawmill itself.
Konstantin frowned and restored the ear trumpet.
‘And since it seems a certainty, Matvei Ilyich,’ his father was saying, his cigarette pinched between his fingers, ‘that your machine will need to be replicated throughout the country, even throughout the world, it occurred to me that … that perhaps the time has come for you to consider employing an … apprentice. As you see, my son shows considerable technical potential.’
The foreman nodded, joined his hands beneath his naked chin.
‘Sir?’ asked Konstantin, cautiously. ‘May I ask you a question?’
‘By all means, my boy!’
‘Sir, I … I am not sure that I fully understand this diagram. It seems to me that the machine is propelled by the barrels rising through the tank of water, and if this is the case then it should continue …’
‘Perpetually,’ said his father, with satisfaction.
‘Perpetually,’ Konstantin repeated. He looked again at the diagram. ‘But, sir, I am afraid that I do not yet understand the principle. You see … My understanding is that the buoyancy of an object, either in air or water, is the result of the difference in pressure between its upper and lower surfaces? That is to say, if you have an empty barrel immersed in water then the pressure on the lower surface will be greater than the pressure on the upper surface, which causes an overall upward force …’