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XXXIII. On a new Instrument for the Mechanical Trisection of 
an Angle ; and on the Multisection of an Angle. By Tuomas 
Tate, Esq.* 
ee trisection of an angle is a subject of historical celebrity, 
and, apart from its utility, must always be interesting to 
the mathematician. Some years ago, Professor Christie invented 
an instrument for the mechanical trisection of an angle, which 
consists of four rods, kept at equal angles apart from each other 
by means of linkwork. Although simple in principle, this in- 
strument is somewhat complicated in construction, and therefore 
necessarily, to some extent, inaccurate as regards its application. 
This instrument contains four rods, ten links, ten axes, and two 
sliding-pieces ; whereas the instrument which I have made con- 
tains only two rods, four links, four axes, and two sliding-pieces. 
Both instruments are mathematically correct in principle. 
The instrument : 
which I have con- 
structed is represent- 
ed in the annexed 
diagram. AB and 
AC are two rods 
turning on the axis 
A; DE, DF, DH, 
and DG are four 
links, each equal in 
length to AE or AF, 
turning on a common 
axis D, DE being 
connected with AB 
by an axis at E, and 
DF with AC by an 
axis at F. The pin 
G, of the link DG, 
slides in the slit ab 
formed in the rod 
AB in the line of 
the axes A and E; ~ 
and the pin H, of 
the link DH, slides 
in the slit ec formed in the rod AC in the line of the axes A 
and F. The inner edges of the four links, DE, DF, DH, DG, 
are in a line with the centres of their respective axes, as shown 
in the diagram. The rods A B and AC are connected by a half- 
lap joint at A; and similarly the four links are connected at D 
by half-lap joints, so that the pieces all lie flat upon the surface 
* Communicated by the Author. 
Phil. Mag. S. 4. Vol. 19. No. 127. April. 1860. T 
