CHAPTER XIV.
"SUPPOSED IMPOSSIBILITIES" It was only to be expected that the announcement of a lecture with such an alluring title by such a distinguished scholar and scientist as Professor Franklin Marmion should fill the theatre of the Royal Society, as the reporters said tritely but truly, "to its utmost capacity." The mere words, "An Examination of Some Supposed Mathematical Impossibilities," were just so many bomb-shells tossed into the middle of the scientific arena.

The circle-squarers, the triangle-trisectors, the cube-doublers, the flat-worlders, and all the other would-be workers of miracles plainly impossible in a world of three dimensions jumped--not incorrectly--to the conclusion that their favourite impossibility would be selected for examination, and, perhaps--blissful thought!--demonstration by one of the foremost thinkers of the day, to the lasting confusion of the scoffers.

Learned pundits of the old school, who were firmly convinced that Mathematics had long ago said their last word, and that to talk about "supposed impossibilities" was blasphemy of the rankest sort, came with note-books and a grim determination to explode Franklin Marmion's heresies for good and all.
Dreamers of Fourth Dimensional dreams came hoping against hope, for the Professor was known to be something of a dreamer himself; and added to all these there assembled a distinguished company of ladies and gentlemen who looked upon the lecture as a "function" which their social positions made it necessary for them to patronise.

The reader's personal friends and acquaintances, including Prince Oscarovitch and Phadrig, were naturally among the most anxiously interested of the Professor's audience.
It is almost needless to say that Hoskins van Huysman had donned all his panoply of scientific war, and had armed himself with what he believed his keenest weapons; and that Professor Hartley looked with amused confidence to a veritable battle royal of wits when the lecture was over and the discussion began.

The Prince and Phadrig were keenly anticipative, and the latter not a little nervous.
A verbatim report of that famous lecture would, of course, be out of place in these pages.