A Mathematical Question. 115 
in the usual mode of water-carriage induces many tradesmen to 
have goods by that more expensive conveyance, the waggon ; and 
others are subject to much inconvenience by having their goods 
detained for a month or six weeks, by the prevalence of westerly 
and south-westerly winds. The only steam-vessels I have had 
an opportunity of seeing are those used on the ‘Thames, which 
being constructed for passengers chiefly, are not adapted for 
goods, being deficient of stowage :—besides, from their having 
such an extended width of deck, to cover the paddle-wheels, it 
is conceived these vessels, or any enlarged vessel on such a mo- 
del, would be unsafe in the Channel. 1 have therefore subjoined 
a sketch of the plan on which it is proposed to construct our 
vessel (see Plate II. figs. 3 and 4}. The form intended is that 
which may be most approved for stowage and sailing, or rather 
that will move through the water with the least resistance. The 
paddie-wheels are proposed tobe placed at the stern, for the fol- 
lawing reasons. First, to obviate the inconvenience of the in- 
crease of deck by their being placed over the sides. Secondly, 
by placing them at the stern, the diameter or breadth of the 
wheels can be much increased without causing the roll such 
ponderous weights would occasion when on the sides, Thirdly, 
the machinery and boiler occupying the aftermost part of the 
vessel, will not interfere with so much valuable stowage. F. ourthly, 
the vessel will lie by the side of a wharf for the purposes of 
taking in and discharging her cargo without injury to the wheels. 
And lastly,—and which for this port, is a matter of more import- 
ance than the preceding, having to pass through two locks of a 
navigable river,—the paddle-wheels must ctherwise be contrived 
to take off, to admit the vessel through.— My object in this ad- 
dress is th gain the opinions of your more experienced readers, 
and to adopt such hints.as may be gathered from others who 
have made this subject their study. 
I am, sir, 
~ Your most humble servant, 
Exeter, July 29, 1817. 
—— 
XVI. A Mathematical Question. By A CoRRESPONDENT. 
To Mr. Tilloch. 
Sir, — Concinmane, how many able Mathematicians read 
your truly scientific Work, and often correspond with you, it has 
somewhat surprised me, that so few of them have appeared to 
notice, and take a part in the elaborate and curious researches, 
relating to Musical Intervals, which have been occasionally sent 
to you for insertion, in your last 24 volumes, by Mr. Farey sen. 
H 2 within 
