“About the same time there arrived in England an American lad named Zerah Colbourn, whose power in mental arithmetic was made the subject of public exhibition. As this was a department in which I had diligently exercised both myself and my pupils, I accompanied my father to the performance with great interest. We found that the boy’s power consisted chiefly in finding with great rapidity the factors of numbers, and square and cube roots. I naturally tried my ability against his, and I found that so long as low numbers were dealt with, I equalled and even surpassed him in rapidity, but that he could deal effectually with numbers so high as to be far beyond my management. Thus he would rapidly extract the cube root of a number expressed in nine figures, provided always it were an exact cube, for with other numbers he declined to deal. His mode of proceeding was a secret, which, with some other devices, his father declared himself willing to reveal so soon as a subscription of, I think, one thousand pounds or guineas should have been raised. As this did not seem to me a very hopeful project, I came to the conclusion that my only way of becoming acquainted with the secret was to find it out for myself. I accordingly went to work, and soon discovered a mode of performing myself that which I had witnessed with so much wonder; and not content with this, proceeded to consider whether means might not be found for mentally extracting roots without limitation to exact cubes. This was an incomparably harder problem, nor did I arrive at its solution till a year or two later. Each process, as soon as discovered, I taught to my pupils, who in the easier task—all that Colbourn ever attempted—became more rapid and far more correct than Colbourn himself; for with him, in extracting a cube root expressed in three figures, it was a common incident to fail in the second, an error which my pupils learned for the most part to avoid. I may add that some of them became so quick and accurate in both processes, that when on a public occasion, viz., at Midsummer, 1822, printed tables of cubes and their roots had been placed in the hands of examiners, and questions asked therefrom ranging up to two thousand millions, and of course without any limitation to exact cubes, the answers—fractions, however being disregarded—were given so quickly as to lead some sceptics, little aware of the monstrous absurdity of the hypothesis, to declare that the whole must have been previously learned by rote. I reduced my discovery to writing, intending to publish it in a contemplated manual of mental arithmetic; but unfortunately this, with other papers, was lost in a manner never fully known, and to repeat the discovery I fear I should now find quite impracticable.[39]
“While on the subject of mental arithmetic, I may mention that I brought the pupils in my class to perform mentally other difficult calculations with a facility that excited no small surprise. Thus they would readily find the moon’s age (approximately, by epacts) for any day of any year; also, the day of the week corresponding with any day of the month; and, by a combination of the two processes, ascertain the day of the month corresponding with Easter Sunday in any year.”
It was with some reason that Mr. Sargant, in describing his old school, writes: “Our arithmetic was amazing, even excelling, by our laborious acquisition of mental arithmetic, the success of the present Privy Council Schools.”[40] In surveying, also, the young teacher’s pupils made almost as much progress as in mental arithmetic. He had undertaken to make a complete survey of Birmingham:—
“I now made my first trigonometrical survey; taking my first stations on our own playground (which fortunately commanded a view of many of the principal objects in the town), and, as before, engaging my surveying class in the work, both for their instruction and my own assistance.
“This occupation led me to inquire into the great trigonometrical survey then carried on by Colonel Mudge, especially that part of it which related to the neighbourhood of Birmingham, my chief object being to ascertain what records would avail for our map, and what further steps it would be needful for me to take to complete the work. With this view I procured his report, and studied it with care, finding it more interesting than any novel. I read with particular interest the part describing the measurement of the great base line on Hounslow Heath by his predecessor, General Roy; and I gathered from it that my own base lines, taken one on our playground and the other on the opposite side of Birmingham, were far too short, the longer extending to only one hundred-and-thirty feet. I therefore resolved to recommence my work, and not only to take a much longer base line, but also to measure it as accurately as I could. I now give a passage taken from my Journal.
“‘I accordingly procured some long deal rods and three stools for the purpose of measuring a line with great accuracy. The stools are made to rise and fall, and somewhat resemble music-stools; this construction was necessary, in order to place the rods always upon the same level.[41]
“‘I chose Bromsgrove Street as the situation of the base, on account of its remarkable levelness, and the number of objects which are visible from different parts of it. The base extends from the corner of the Bell Inn, on the right-hand side of the Bristol Road, and opposite to the end of Bromsgrove Street, to the wall at the north-eastern end of Smithfield; being nearly half a mile in length, and so admirably situated with respect to the objects, that there is not a single obtuse angle upon it.
“‘Besides measuring with the rods, I surveyed the line twice with a land chain, properly adjusted, and after making every allowance for the elongation of the chain during the admeasurement, I found the difference in the total length of the base, which is nearly half a mile, to be only three-quarters of an inch. When the survey is completed, I intend to write an account of it, which will be found among my manuscripts.[42]
“‘I have thought of publishing parts of it in some of the magazines, particularly a relation of a new mode of using the theodolite, which I have invented. This mode increases its power exceedingly.’
“In performing this work it was of course necessary to avoid the daily traffic, which would have disturbed our operations; and, as my Journal shows, my class and I, during the three days occupied in the process, viz., May the 25th, 27th, and 30th, rose the first day at three, the second at five minutes before three, and the third at five minutes past two.