October igth, ip/J.] PROCEEDINGS. xiii 



was self-taught. All the leisure that could be spared from 

 weaving was devoted to his beloved geometry, and with infinite 

 toil he studied Euclid, Simpson's, and Emerson's "Exercises " and 

 finally Newton, whose " Method of Prime and Ultimate Ratios " 

 formed the basis of most of his work. He also studied Mechanics 

 and Astronomy to good purpose, and was in fact, among the 

 mathematicians of the second rank in the early 19th century. 



In place of the " bridge problems," and other unproductive 

 puzzle-competitions of the modern press, there were at that time 

 a sufficient number of amateurs to fill pages of the " Ladies' 

 Diary," the "Gentleman's Diary," "Burrow's Diary," "Whitley's 

 Mathematical Delights," and other periodicals with problems 

 often requiring much ingenuity, and Wolfenden contributed to 

 these for upwards of sixty years. He proposed and solved 

 such problems as the following : — " Given the base and vertical 

 angle of a triangle, to construct it when the rectangle under 

 the line bisecting the vertical angle and the difference of 

 the sides is the greatest possible." " Suppose the sun and 

 moon in the equinoctial, and the ratio of their forces to raise 

 the tides given, to find by geometry the elongation when the 

 interval or intercepted arc between the place of high water 

 and the moon is the greatest possible." This last had been 

 investigated by Bernoulli, by the aid of fluxions, but Wolfenden 

 founded his solution on a Lemma to a proposition in Simpson's 

 " Select Exercises." This was a kind of " tour de force " and 

 shewed the power of geometry in capable hands. Newton, 

 of course, was pre-eminent in this branch, but it was largely 

 abandoned by his successors in favour of less severe methods. 



He had many friends and admirers, and corresponded with 

 a number of mathematicians, who were deeply impressed by his 

 personality and attainments. If a large number of his letters 

 had not been used by his grand-daughter to cover jampots, 

 many interesting details might have been revealed, though 

 several letters are quoted in extenso in Wilkinson's memoir 

 already referred to. 



Wolfenden pursued his humble occupation till he was 62 



