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LXXX. On the Graduation of the Puntograph. By 
J. W. Woottear, Esq. Lewes. 
To Dr. Tilloch. 
Sir, — Tue instrument called the Pantograph is so well known, 
that a minute description of it may here be dispensed with. The 
principle of its operation depends upon the geometrical doctrine 
of similar triangles; but the mechanical construction has under- 
gone several modifications. In its early form, the fulcrum, pen- 
cil, and tracing point, occupied fixed positions on the bars, and 
the ratio of reduction, that is, the proportion of the original 
draught to the copy, was determined by varying the situation of 
the pivots. It was afterwards found that greater mechanical 
accuracy could he attained by causing the fulcrum and pencil to 
shift their positions on two of the bars, while the pivots remained 
invariable. To this latter construction, as it is represented on 
Plate 31 of Adams’s Geometrical and Graphical Essays, and as 
it is to be met with in the shops of the Londen makers, the pre- 
sent remarks are intended to apply. 
On the two left-hand bars, which carry the sliding tubes ap- 
propriated to the fulerum and pencil, are usually engraved eleven 
transverse lines, marked 4, 4,4, and soonto " By adjusting 
the sliding tubes to the corresponding marks on each bar, the 
pencil being attached to the short bar, the instrument will pro- 
duce a copy whose scale will be an aliquot part of the original, 
as indicated by the engraved fractional number. And if the 
pencil be attached to the lowermost division (marked 4) on the 
long bar, and the fulcrum occupy a corresponding place on the 
short bar, a copy will be traced of the same size with the ofi- 
ginal. 
So far, and no further, are we instructed in the uses of this 
important instrument, by Mr. Adams’s work above quoted, and 
by the other books which I have consulted. But there is an 
indefinite number of other proportions, which a copy may be 
required to bear to its original, between the ratio of equality 
and that of 1: 2, and between this last and that of 1: 12; and 
in fact, by far the greater number of cases occur, in which the 
required scale of the copy is mot an aliquot part of the original. 
How then is the instrument in these instances to be adjusted so 
as to produce the desired effect? 
‘¢ There are sometimes,’”’ says Mr. Adams, ** divisions of 100 
unequal parts laid down on the bars, to give any intermediate 
proportion, not shown by the fractional numbers commonly 
placed.”” This is exactly what is wanted; but then such divi- 
sions must be actually laid down on the instrument, and they 
Vol. 59, No, 290. June 1822, 3 E must 
