We begin with Anthony Wood’s account of Wingate’s introduction of
Gunter’s scale into France.[5]
In 1624 he transported into France the rule of proportion, having a
little before been invented by Edm. Gunter of Gresham Coll. and
communicated it to most of the chiefest mathematicians then residing in
Paris: who apprehending the great benefit that might accrue thereby,
importun’d him to express the use thereof in the French tongue. Which
being performed accordingly, he was advised by monsieur Alleawne the
King’s chief engineer to dedicate his book to monsieur the King’s only
brother, since duke of Orleans. Nevertheless the said work coming forth
as an abortive (the publishing thereof being somewhat hastened, by reason
an advocate of Dijon in Burgundy began to print some uses thereof, which
Wingate had in a friendly way communicated to him) especially in regard
Gunter himself had learnedly explained its use in a far larger volume.[6]
Gunter’s scale, which Wingate calls the “rule of proportion,” contained, as
described in the French edition of 1624, four lines: (1) A single line of
numbers; (2) a line of tangents; (3) a line of sines; (4) a line, one foot
in length, divided into 12 inches and tenths of inches, also a line, one
foot in length, divided into tenths and hundredths.
The English editions of this book which appeared in 1623 and 1628 are
devoid of interest. The editions of 1645 and 1658 contain an important
innovation.[7] In the preface the reasons why this instrument has not been
used more are stated to be: (1) the difficulty of drawing the lines with
exactness, (2) the trouble of working thereupon by reason (sometimes) of
too large an extent of the compasses, (3) the fact that the instrument is
not readily portable. The drawing of Wingate’s arrangement of the scale in
the editions of 1645 and 1658 is about 66 cm. (26.5 in.) long. It contains
five parallel lines, about 66 cm. long, each having the divisions of one
line marked on one side and of another line on the other side. Thus each
line carries two graduations: (1) A single logarithmic line of numbers; (2)
a logarithmic line of numbers thrice repeated; (3) the first scale
repeated, but beginning with the graduations which are near the middle of
the first scale, so that its graduation reads 4, 5, 6, 7, 8, 9, 1, 2, 3;
(4) a logarithmic line of numbers twice repeated; (5) a logarithmic line of
tangents; (6) a logarithmic line of sines; (7) the rule divided into 1000
equal parts; (8) the scale of latitudes; (9) a line of inches and tenths of
inches; (10) a scale consisting of three kinds, viz., a gauge line, a line
of chords, and a foot measure, divided into 1000 equal parts.
Important are the first and second scales, by which cube root extraction
was possible “by inspection only, without the aid of pen or compass;”
similarly the third and fourth scales, for square roots. This innovation is
due to Wingate. The 1645 edition announces that the instrument was made in
brass by Elias Allen, and in wood by John Thompson and Anthony Thompson in
Hosier Lane.