Many of his evenings were spent in the society of John Wigham, whose father occupied the Glebe farm at Benton close at hand. John was a fair penman and good arithmetician, and Stephenson frequented his society chiefly for the purpose of improving himself in writing and "figuring." Under Andrew Robertson he had never quite mastered the Rule of Three, and it was only when Wigham took him in hand that he made progress in the higher branches of arithmetic. He generally took his slate with him to the Wighams' cottage, when he had his sums set, that he might work them out while tending his engine on the following day. When too busy with other work to be able to call upon Wigham in person, he sent the slate by a fellow-workman to have the former sums corrected and new ones set. Sometimes also, at leisure moments, he was enabled to do a little "figuring" with chalk upon the sides of the coal-wagons. So much patient perseverance could not but eventually succeed; and by dint of practice and study, Stephenson was enabled to master the successive rules of arithmetic. John Wigham was of great use to his pupil in many ways. He was a good talker, fond of argument, an extensive reader as country reading went in those days, and a very suggestive thinker. Though his store of information might be comparatively small when measured with that of more highly cultivated minds, much of it was entirely new to Stephenson, who regarded him as a very clever and extraordinary person. Wigham also taught him to draw plans and sections, though in this branch Stephenson proved so apt that he soon surpassed his master. A volume of "Ferguson's Lectures on Mechanics" which fell into their hands was a great treasure to both the students. One who remembers their evening occupations says he "used to wonder what they meant by weighing the air and water in so odd a way." They were trying the specific gravities of objects; and the devices which they employed, the mechanical shifts to which they were put, were often of the rudest kind. In these evening entertainments the mechanical contrivances were supplied by Stephenson, while Wigham found the scientific rationale. The opportunity thus afforded to the former of cultivating his mind by contact with one wiser than himself proved of great value, and in after life Stephenson gratefully remembered the assistance which, when a humble workman, he had received from John Wigham, the farmer's son.