Invention of the Circular Parts. 351 
lished by Napier. I do not mean that Torporley gave his 
theorems in as elegant a form as Napier, nor do I deny that 
Napier abbreviated Torporley: what I say is that, of that 
abbreviation which is usually attributed entire to Napier, a con- 
siderable part belongs to Torporley. Nor am I by any 
means convinced that Napier had seen Torporley’s work : 
but, according to the rule established in such cases, the first 
publisher must take precedence of all subsequent ones, whether 
independent discoverers or not. 
Napier’s circular parts are in his first mathematical pub- 
lication, the Mirzfict logarithmorum Canonis descriptio, 1614, 
which is most easily seen in the reprint by Baron Maseres 
(Seriptores Logarithmici, vol. vi.). ‘The circular parts are in 
pp- 511, 512 of the last-named volume. 
Torporley’s work is Diclides Coelometrice, seu valve astro- 
nomice universales, omnia artis totius munera Psephophoretica 
in sat modicis finibus duarum Tabularum methodo nova, generali, 
et facilima continentes. Praeunte directionis accurate con- 
sumata Doctrina, -Astrologis hactenus plurimim desiderata. 
Authore Nath. Torporlao Salopiensi in secessu Philotheoro. 
London, 1602. An account of Torporley may be seen in 
Anthony Wood’s Athene Ovxonienses, or in the article Vieta 
in the Penny Cyclopzedia. An account of his work is in De- 
lambre’s Astronomie Moderne, vol. ii. p. 36. It is very strange 
that Delambre should not have seen that the very description 
which he gives almost amounts to stating Napier’s rules: 
but it is to be remembered that these circular parts, so cele- 
brated in Britain, have hardly ever been used abroad. De- 
lambre himself (Astronomy, vol. i. p. 205) says that he pre- 
fers to remember the six equations at once: a preference in 
which I heartily concur. 
There never was, perhaps, a more ludicrous mnemonical 
attempt than that of Torporley. His rules are first diclides, 
they then become valve. These valves, six in number, then 
receive names: they are Carcer, Hasta, Forfex, Siphon, Corvus, 
and Funda, ‘These six valves, namely the prison, the spear, 
the shears, the siphon, the crow (a pickaxe), and the sling, 
are then mounted on two mitres; Carcer, Siphon and Funda 
on one; Corvus, Hasta and Forfex on the other. This he 
calls mitrospherica memorabilis. But we have not done with 
metaphor yet: for as soon as the valves, under their new 
names, are fairly established on the mitres, one of each set 
becomes the mother, and the other two the daughters. Here 
is the reduction of the six cases to two. ‘lorporley then 
gives rules for the reduction of either daughter to the mother, 
and discovers the necessity for using the complements of the 
