Mr. T. S. Davies on Geometry and Geometers. 539 



contributions (irregular as to time and place, as this would render 

 them) to these works are both numerous and remarkable. Where- 

 ever we see the name of " Swale " we are sure to meet with 

 something new and elegant, and often with specimens of un- 

 equalled resource and unexampled method of research. 

 ^ But why this eulogy on the author of works already in print ? 

 Simply, that I have been entrusted by his son with the perusal 

 of a series of jMSS., the remains of this extraordinary geometer, 

 of which I think some account should be given in the present 

 series of papers ; and I considered it needful to introduce the 

 subject by a short notice of the position which he occupied as a 

 geometer, and this deduced from a reference to his published 

 writings. Had they been better known, this trouble might have 

 been saved me ; but the circumstances of their publication ren- 

 dered it necessary to give these preliminary notices, for the in- 

 formation of my readers. 



The hfe of a schoolmaster is seldom marked by any events of 

 public interest, at least in this country ; though on the other 

 side of the Atlantic we have seen that there is no obstacle to his 

 rismg to the highest office of one of the most powerful nations 

 m the world. With us, his histoiy is that of officiating as 

 " usher " for a hw years, " here and there and everywhere," — 

 manying — toiling wdth a school of his own — for the most part 

 barely able to suppoi-t his family, and at best (and this rarely) 

 being able to scrape together by industiy and oeconomy a few 

 hundreds to support himself and his wfe in their age and decre- 

 pitude. Nor does the life of this distinguished geometer furnish 

 any exception to the rule ; though of the specialities of his early 

 hfe I am able to give no account. I find from a memorandum 

 in one of his books, that his two eldest children were born at 

 Idle, a village in the West Riding, and the subsequent ones at 

 Liverpool. His reputation in Liverpool as a teacher was very high, 

 and he had every prospect before him of securing a respectable 

 competence for his old age. About 1828, however, he lost his 

 entire savings (about £1200) "by a dishonest relative;" and 

 from various notes it would appear that he was involved in further 

 liabiUtics for that person, which absolutely left him without 

 resources. This so preyed upon his mind and feelings, that he 

 sunk into a misanthropic state from which he never fully re- 

 covered ; though he was fast recovering when seized with his 

 last and fatal illness. 



For what reason does not appear, but all the MSS. of a Sate 

 prior to 1 828 are absent. From this period to the end of his life, 

 they appear to be comjdete — and each entiy is regularly dated. 

 From one or two entries being entered as copi(!s of ohler scraps, 

 I am led to think that he had, under the moody feelings engen- 

 202 



