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



the same time, I am inclined to think that it was never suffi- 

 ciently made known to the mathematical public ; and probably 

 the neglect of " agents " was the chief cause. This at least I 

 know, that I could not procure a copy two or three years after 

 either tlirougli the regular channels or any irregular channel 

 either — till Mr. Swale himself presented me with a copy several 

 years later. I had meantime been at the trouble of transcribing 

 the entire book for my own use from a borrowed copy, that copy 

 itself Jiaving been obtained after much seai'ch. 



He, however, like many other mathematicians, ardent for the 

 promotion of their science, commenced a periodical to be pub- 

 lished annually. This he called the " Apollonius." Probably 

 he thought the usiial contributors to works of the class would 

 at least supjiort the undertaking, so as to be, if not remimerative, 

 at least self-supporting. Whether this project failed for want of 

 business-tact, like the "Amusements," in not being made suffi- 

 ciently kno^^^l and easily procured, I do not know ; but at all 

 events, I myself did not know of its existence till long after it 

 had been discontinued, though I was one of the class that should 

 have been apprised of it. 



This work, however, of which only two numbers were printed 

 in 1823 and 1824, is quite as scarce (at least the first number), 

 and was till lately as little known as the " Geometrical Amuse- 

 ments." Mr. Gaskin and Mr. Potts are the only writers who 

 have mentioned this work (with the exception of what I have 

 elsewhere said respecting it), and they appear to have seen only 

 the second numljer — at least they only refer to it. 



For its miscellaneous matter, the work is of little value (and 

 not always quite orthodox) ; but its geometry is of a. very high 

 order, and worthy of the most careful study. The papers on the 

 tangency of circles, and on polygons inscribed in circles or in 

 other polygons, are masterpieces of geometrical research. In- 

 deed, the same may be said of the whole of this part of the work, 

 as far as the subjects admitted. Theorems occupy a due portion 

 of this, as problems did the whole of the former ; and this leads 

 me to think that much of the matter (in perhaps a concentrated 

 form) intended for the " Amusements " was transferred to the 

 " ApoUonius." 



IMr. Swale had, however, been known from the early part of 

 the present centuiy as a contributor to the mathematical annuals, 

 and to some local publications devoted to mathematics. He 

 never seems to have cared to compete with others, either by 

 sending solutions to all questions alike, or by proposing and 

 solving the most difficult only ; his rule appearing to be to send 

 only wiien and what seemed to himself to be worthy of himself, 

 om its novelty of principle or simplicity of result. Yet his 



