A t twelve o'clock on a bright summer day Mr. Brook drove up in his dog-cart, with two gentlemen, to the Vaughan mine. One was the government inspector of the district; the other, a newly-appointed deputy inspector, whom he was taking his rounds with him, to instruct in his duties.  
"I am very sorry that Thompson, my manager, is away to-day," Mr. Brook said as they alighted. "Had I known you were coming I would of course have had him in readiness to go round with you. Is Williams, the underground manager, in the pit?" he asked the bankman, whose duty it was to look after the ascending and descending cage.
 
"No, sir; he came up about half an hour ago. Watkins, the viewer, is below."
 
"He must do, then," Mr. Brook said, "but I wish Mr. Thompson had been here. Perhaps you would like to look at the plan of the pit before you go down? Is Williams's office open?"
 
[Pg 223]
 
"Yes, sir," the bankman answered.
 
Mr. Brook led the way into the office.
 
"Hullo!" he said, seeing a young man at work making a copy of a mining plan; "who are you?"
 
The young man rose—
 
"Jack Simpson, sir. I work below, but when it's my night-shift Mr. Williams allows me to help him here by day."
 
"Ah! I remember you now," Mr. Brook said. "Let me see what you are doing. That's a creditable piece of work for a working collier, is it not?" he said, holding up a beautifully executed plan.
 
Mr. Hardinge looked with surprise at the draughtsman, a young man of some one or two-and-twenty, with a frank, open, pleasant face.
 
"Why, you don't look or talk like a miner," he said.
 
"Mr. Merton, the schoolmaster here, was kind enough to take a great deal of pains with me, sir."
 
"Have you been doing this sort of work long?" Mr. Hardinge asked, pointing to the plan.
 
"About three or four years," Mr. Brook said promptly.
 
Jack looked immensely surprised.
 
Mr. Brook smiled.
 
"I noticed an extraordinary change in Williams's reports, both in the handwriting and expression. Now I understand it. You work the same stall as Haden, do you not?"
 
"Yes, sir, but not the same shift; he had a mate he [Pg 224]has worked with ever since my father was killed, so I work the other shift with Harvey."
 
"Now let us look at the plans of the pit," Mr. Hardinge said.
 
The two inspectors bent over the table and examined the plans, asking a question of Mr. Brook now and then. Jack had turned to leave when his employer ceased to speak to him, but Mr. Brook made a motion to him to stay. "What is the size of your furnace, Mr. Brook?" asked Mr. Hardinge.
 
"It's an eight-foot furnace," Mr. Brook replied.
 
"Do you know how many thousand cubic feet of air a minute you pass?"
 
Mr. Brook shook his head: he left the management of the mine entirely in the hands of his manager.
 
Mr. Hardinge had happened to look at Jack as he spoke; and the latter, thinking the question was addressed to him, answered:
 
"About eight thousand feet a minute, sir."
 
"How do you know?" Mr. Hardinge asked.
 
"By taking the velocity of the air, sir, and the area of the downcast shaft."
 
"How would you measure the velocity, theoretically?" Mr. Hardinge asked, curious to see how much the young collier knew.
 
"I should require to know the temperature of the shafts respectively, and the height of the upcast shaft."
 
"How could you do it then?"
 
"The formula, sir, is M = h(t'-t) 480+x, h being the height [Pg 225]of the upcast, t' its temperature, t the temperature of the exterior air, and x = t'-32 degrees."
"You are a strange young fellow," Mr. Hardinge said. "May I ask you a question or two?"
 
"Certainly, sir."
 
"Could you work out the cube-root of say 999,888,777?"
 
Jack closed his eyes for a minute and then gave the correct answer to five places of decimals.
 
The three gentlemen gave an exclamation of surprise.
 
"How on earth did you do that?" Mr. Hardinge exclaimed. "It would take me ten minutes to work it out on paper."
 
"I accustomed myself to calculate while I was in the dark, or working," Jack said quietly.
 
"Why, you would rival Bidder himself," Mr. Hardinge said; "and how far have you worked up in figures?"
 
"I did the differential calculus, sir, and then Mr. Merton said that I had better stick to the mechanical application of mathematics instead of going on any farther; that was two years ago."
 
The surprise of the three gentlemen at this simple avowal from a young pitman was unbounded.
 
Then Mr. Hardinge said:
 
"We must talk of this again later on. Now let us go down the pit; this young man will do excellently well for a guide. But I am afraid, Mr. Brook, that I shall have to trouble you a good deal. As far as I can see [Pg 226]from the plan the mine is very badly laid out, and the ventilation altogether defective. What is your opinion?" he asked, turning abruptly to Jack, and wishing to see whether his practical knowledge at all corresponded with his theoretical acquirements.
 
"I would rather not say, sir," Jack said. "It is not for me to express an opinion as to Mr. Thompson's plan."
 
"Let us have your ideas," Mr. Brook said. "Just tell us frankly what you would do if you were manager of the Vaughan?"
 
Jack turned to the plan.
 
"I should widen the airways, and split the current; that would raise the number of cubic feet of air to about twelve thousand a minute. It is too far for a single current to travel, especially as the airways are not wide; the friction is altogether too great. I should put a split in here, take a current round through the old workings to keep them clear, widen these passages, split the current again here, and then make a cut through this new ground so as to take a strong current to sweep the face of the main workings, and carry it off straight to the upcast. But that current ought not to pass through the furnace, but be let in above, for the gas comes off very thick sometimes, and might not be diluted enough with air, going straight to the furnaces."
 
"Your ideas are very good," Mr. Hardinge said quietly. "Now we will get into our clothes and go below."
 
So saying, he opened a bag and took out two mining [Pg 227]suits of clothes, which, first taking off their coats, he and his companion proceeded to put on over their other garments. Mr. Brook went into his office, and similarly prepared himself; while Jack, who was not dressed for mining, went to the closet where a few suits were hung up for the use of visitors and others, and prepared to go down. Then he went to the lamp-room and fetched four Davy-lamps. While he was away Mr. Brook joined the inspectors.
 
"That young pitman is as steady as he is clever," he said; "he has come several times under my attention. In the first place, the schoolmaster has spoken to me of the lad's efforts to educate himself. Then he saved another boy's life at the risk of his own, and of late years his steadiness and good conduct have given him a great influence over his comrades of the same age, and have effected great things for the place. The vicar and schoolmaster now are never tired of praising him."
 
"He is clearly an extraordinary young fellow," Mr Hardinge said. "Do you know his suggestions are exactly what I had intended to offer to you myself? You will have some terrible explosion here unless you make some radical changes."
 
That evening the inspectors stayed for the night at Mr. Brook's, and the next day that gentleman went over with them to Birmingham, where he had some business. His principal object, however, was to take them to see Mr. Merton, to question him farther with regard to Jack Simpson.
 
[Pg 228]
 
Mr. Merton related to his visitors the history of Jack's efforts to educate himself, and gave them the opinion he had given the lad himself, that he might, had he chosen, have taken a scholarship and then the highest mathematical honours. "He has been working lately at engineering, and calculating the strains and stresses of iron bridges," he said. "And now, Mr. Brook, I will tell you—and I am sure that you and these gentlemen will give me your promise of secrecy upon the subject—what I have never yet told to a soul. It was that lad who brought me word of the intended attack on the engines, and got me to write the letter to Sir John Butler. But that is not all, sir. It was that boy—for he was but seventeen then—who defended your engine-house against the mob of five hundred men!"<............