The President's Address. 
69 
informed,, cost fifty guineas, and on the writing machine Mr. 
Peters expended upwards of one hundred guineas, exclusive 
of the cost for cleaning and embellishing before presenting it 
to the Society, exclusive also of the handsome stand, mahogany 
table, and glass case, which are now before you. 
On a former occasion I gave a description of the principles 
and construction of the instrument (read April 25th, 1855 ; 
*^Tr. Mic. Soc.,^ London, n. s., vol. iii, p. 55). Since that 
time some alterations have been made in the details, the 
chief of these is that instead of the diamond moving over the 
glass, as formerly, it is now detached from the levers ; in its 
place a light stage, carrying a small piece of thin glass, is 
connected with the distal extremity of the combined levers, 
and is made to move over the diamond point, which is fixed 
and kept in contact with the under surface of the glass by the 
pressure of a spring nicely adjusted. Besides this alteration, 
some additions have been made to admit of its movements 
being guided by mechanism, instead of by the hand only; 
and now Ibbetson^s geometric chuck, which accompanies the 
instrument, can be connected with the proximal end of the 
levers, and, so combined, they suffice to produce the almost 
endless diversity of figures resulting from two circular move- 
ments, with circles of similar or difi'erent diameters moving 
with equal or different velocities, either in similar or opposite 
directions. The subject of the curves, generated by the 
motion of a point of one of these circles, has been studied and 
largely illustrated by H. Perigal, Jun., Esq., one of your 
Council, whose numerous figures of bicircloids are, no doubt, 
well known to you. All of these, and any combination of them, 
can be produced on a scale of exceeding minuteness, and 
beautiful and complex designs of this kind have been engraved 
on glass, with wonderful precision, in the space of a circle 
-^th of an inch in diameter. On this occasion I have only 
time to allude to a few of the marvellous results of the use of 
the instrument. Eor example, the Lord^s Prayer is written 
in a circle only -r^-o'th of an inch in diameter ; yet it is dis- 
tinctly legible with a half-inch objective, the writing having 
no appearance of crowding or of want of room. Few persons 
have a distinct notion of the space defined by a circle of -pro'th 
of an inch in diameter. Dr. Lardner, in his treatise on the 
microscope, has given a woodcat (p. 62) showing several 
disks of from -^th to -rs^irth of an inch in diameter, the latter 
of these to the unaided eye is not a disc, but literally a point ; 
the space occupied by this point, though smaller than the full 
stop of ordinary print, is still sufficient to contain five circles, 
each -j-o^ o^th of an inch in diameter ; and in a circle of that size 
