Coal was the main fuel during the 18th and 19th centuries and coal mining provided the means for industry to flourish. It certainly played a vital part in French industrial progress, and schools such as the École des Mines provided training for mining engineers who learnt the scientific principles behind efficient and safe mining. Many mathematicians were trained at the École des Mines and in this article we discuss Poincaré's career as a mining engineer.
Poincaré entered the École des Mines in October 1875. As part of his studies he undertook field work in Normandy in 1876 and then travelled abroad on trips organised by the École, going to Austria-Hungary in 1877 and to the several Scandinavian countries in the following year. Following his first trip, Poincaré wrote two memoirs, one on the exploitation of the coal mines of Staatsbahn in Hungary, and the other on the metallurgy of tin in Banat in eastern Europe. After his second trip, he wrote two memoirs on mining in the Scandinavian countries. None of these memoirs survive.
He graduated as a mining engineer from the École des Mines on 28 March 1879 and immediately received an appointment in the Corps des Mines as an inspector of mines at Vesoul in the Franche-Comté region of eastern France. Poincaré had explicitly asked for an appointment which would let him be close to his family in Lorraine. He arrived at Vesoul to take up his new job on 3 April 1879 and immediately began to make inspections of the mines. He had responsibility for the mines of Ronchamp which was due east of Vesoul.
What sort of things was Poincaré looking for in his inspections? Each mine had to be assessed for its potential for future production. Mines had to be kept working as efficiently as possible so Poincaré had to report on likely areas where gas might build up and, very importantly, on how the gas could be removed so that it did not cause problems. Ventilation was of the utmost importance, both to bring fresh air into the mine and also to remove dangerous inflammable gases. Miners working down the mines which Poincaré inspected used a pick to break the coal loose from the coal seam. Because of the danger of inflammable gases, providing lighting which would not ignite gas while miners went about their tasks was essential. The Davy safety lamp, invented about 1815, provided the solution at the time Poincaré worked. It consisted of a flame enclosed in a double layer of wire gauze which prevented any inflammable gas from igniting. However, although ventilation was vital, nevertheless too strong air currents made the Davy lamp unsafe.
For the first few months Poincaré carried out inspections which were routine. He descended into each mine, made a careful inspection, then wrote a report. For example he carried out a routine inspection of the Saint-Charles mine on 4 June 1879. However on 1 September 1879 there was an explosion at the Magny pit, which had only been operational from 8 July 1879, and Poincaré was quickly on the scene to assess the cause. There were twenty-two men in a shift and the explosion occurred at 3.45 in the morning killing sixteen of the twenty-two men who had descended the shaft in the cage at 18.00 the previous evening to begin work. Two men had just come up from the mine while four men, who were in the cage at the time of the explosion, were able to get to the surface. One other was found alive but died of his injuries in hospital on the following day. The others had all died almost instantly where they were working at the time of the explosion. The rescue operation began immediately with the off-duty chief miner M Juif, searching for survivors. Poincaré descended the shaft into the mine to start his investigation of the cause of the explosion on 1 September while the attempted rescue operation was in progress. The bodies were not all recovered until 3 September.
As one might imagine, Poincaré's report is a remarkably carefully argued document where he details a whole series of possible causes and lists the evidence for and against each. First he gave a general description of the mine and its two shafts which allowed air to ventilate the mine. The nearest coal to the surface was 650 metre down and it was only that seam which was being worked. Poincaré then gave a precise description of the lengths of the three galleries and the accurate measurements of the underground passages. He then described the method of ventilation employed which used a temporary machine. He attached a graph to his report which gave the results of experiments carried out on the volume of air produced on 26 July and 21 August, only days before the accident. Poincaré also reported that the company monitored its miners closely, in particular ensuring that they did not damage their lamps.
The minors were then named and the duties that they undertook that night were carefully recorded. Details of the rescue were precisely recorded. In particular Poincaré praised the bravery of the off-duty chief miner M Juif:-
This man, who was off duty, did not hesitate to rush to meet the danger. It was his presence of mind that must have avoided a second catastrophe, because clothing which he extinguished could have caused a fire and a second explosion. Although he was nearly 60 years old, he remained in the mine for eighteen hours without a break. He went everywhere, so that the engineers were obliged to hold him back. This man appears to me to deserve a reward.Where did the explosion occur? First Poincaré stated the well known fact that in a gas explosion, miners were burned upstream in the air flow while those downstream suffocated. All the miners in the Magny disaster died from burns, so the explosion was upstream of them all. This however left two possible sites for the explosion which, on this evidence alone, were equally likely. Looking at where the tunnels had caved in because of the force of the explosion reinforced the case that the explosion occurred at one of these two sites but failed to distinguish the correct one. To obtain strong evidence for which was the correct site Poincaré examined the miners' lamps. It was highly likely that the gas was ignited by one of the lamps so they were examined for damage. Each lamp had been numbered and signed out to a specific miner at the start of the shift and this information recorded. Two of the lamps were never found, presumably buried under cave-ins, and one was totally destroyed. Those which were slightly damaged showed signs of that damage being the result of the explosion.
Lamp number 476, however, had a slit in it which was consistent with having been caused by a miner's pick. But there was a puzzle. Lamp 476 was recorded as being given to Auguste Pautot but was not found close to his body. Rather it was hanging from a support 15 centimetres above the ground and close to the corpse of Emile Perroz. Now Perroz was loading coal onto trucks and had no pick, while Pautot had been working with a pick. Poincaré deduced that Pautot had hit his lamp with his pick but had not noticed that he had damaged it. At this time there was no problem as no gas was present in the mine. Pautot went, for some unknown reason, to talk to Perroz and when he returned to where he had been working he took Perroz's lamp by mistake. When there was a release of firedamp from a seam an initial explosion occurred when it came in contact with the damaged lamp. The gas, partially burnt and still alight, reached the main tunnel where the flow of air was strong and a second explosion occurred. Poincaré wrote:-
The Company had done all that was humanly possible to prevent the accident. The catastrophe was caused by the awkwardness of Pautot, who paid with his life for one moment of carelessness. This man was not a bad workman and nobody ever complained about him; but similar mistakes are often made by the best minors.He also noted that:-
There are in all 9 widows and 35 orphans of which the oldest is over 17 and 6 others are over 12. The Company immediately distributed 40 francs to each family ... The Relief Fund ensures each widow a pension of 25 francs per month, and each orphan a pension of 8 francs per month. However, the generous efforts of the Company will perhaps be insufficient to relieve so much misery.Roy and Dugas note in  that Poincaré's report:-
... is a model of its kind.They also note that Poincaré does not mention his own role in the rescue:-
But one must underline the silence of Poincaré on his personal role, although he was certainly present at this rescue which was to last three days ...Poincaré returned to the Magny mine on 29 November 1879 to report on a new ventilation system which had been put in place. His report on this visit was signed on 30 November and then on 1 December he was given a lectureship in mathematics at the Faculty of Sciences of Caen. He did not undertake any more work as a mining engineer but he did continue to hold a position in the Corps des Mines. He was promoted to chief engineer on 22 July 1893, then to inspector general on 16 June 1910.
He wrote an article in 1912, the year of his death, on mining. In it he wrote:-
A spark is enough to ignite an explosive mixture of air and firedamp, and then I refuse to describe the horrors which follow ...In the same article he wrote:-
There are mines where there is no firedamp; one is still not safe there; sometimes the atmosphere is filled with a fine dust, and this dust, mixed with air, can cause explosions just like gas ...It is clear that the horrors of the Magny explosion stayed with Poincaré for the rest of his life.
Article by: J J O'Connor and E F Robertson
MacTutor History of Mathematics