202 Mr. T. T. Wilkinson's Additions to the late 



Questions 553 and 558 of the Repository. By the time he 

 arrives at page 129 his worldly prospects had been blighted by 

 the " dishonest relative " alluded to by Professor Davies ; for at 

 the foot of the page he remarks, " these are trities, but they 

 divert my attention from the dark clouds of my calamitous cir- 

 cumstances ;'' and a fortnight later, "5th May 1828," he adds, 

 " I do very little now ; — the poverty to which I and my children 

 are reduced by plundering villains has pi'ostrated all my enjoy- 

 ments and hopes. I have slaved for 33 years, and at 53 I am 

 destitute." With how many of our ablest geometers such has 

 been the case we need not here inquire : — poverti/ and mathe- 

 matics seem to be inseparable adjuncts to those of the Lanca- 

 shire and Yorkshire schools ; for amongst them, wherever a genius 

 for the latter has existed in an unwonted degree, the withering- 

 influences of the former have almost invariably been more than 

 ordinarily present. It was ever the case with Wolfenden and 

 Butterworth, and fortune has not been more favourable to some 

 of their illustrious contemporaries who still survive. 



In page 160 Mr. Swale notices with commendation a solution 

 by Mr. Jeremiah Ainsworth (the grandfather of the gifted novel- 

 ist, William Harrison Ainsworth), who was long the ablest and 

 favourite contributor to Burrow's Diary ; and in a subsequent 

 page, Mr. Richard Nicholson is alluded to with much tenderness 

 of feeling as his " early mathematical associate and an excellent 

 geometrician," who used to meet him " at Mr. Ryley's house in 

 Leeds to converse on mathematics." " I linger," he adds sub- 

 sequently, " among these problems and sketches as the pleasing 

 though melancholy reminiscences of days for ever gone and of 

 early acquaintances now silent and mouldering in the tomb." 

 Pages 197, 198 are occupied with the demonstrations of several 

 theorems which he afterwards applies (pp. 227-230) to the de- 

 teiunination of the general problem on "Inclinations;" but as 

 these were aftei'wards corrected and extended in a separate manu- 

 script, they need not at present be moi-e particularly described. 

 The subject of Inclinations is again resumed in pp. 233-235, 

 after another method, and two or three different consti'uctions 

 are given to each case ; but agreeably to J\Ir. Swale's usual prac- 

 tice, no demonstrations are added, which is the more to be re- 

 gretted since the methods are generally different from those in 

 common use. The Maxima and Minima of geometrical quan- 

 tities occupy pp. 251-257, which are treated with his usual ele- 

 gance : — from internal evidence I am led to think that a portion 

 of these were intended to follow those in No. II. of the Apollo- 

 nius, especially since page 252 supplies a correction to Mr. Wil- 

 liam Smith's elaborate solution to Question 69, No. X. of the 

 Mathematical Companion. Several of these investigations are 



