NAP 
531 
NAP 
ad Triangula Sphterica faciliore calculo refolvenda ; una 
cum Annotationibus doditiffimi D. Henrici Briggii in eas, 
et memoratam Appendicem ; publifhed by the author’s 
fon in 1619. 5. Rabdologia, feu Numerationis per vir- 
gulas, Libri duo, 1617. 6. A Letter to Anthony Bacon, 
the original of which is in the archbifliop’s library at Lam¬ 
beth, entitled, “ Secret Inventions, profitable and necef- 
fary in thefe days for the Defence of this Ifland, and with- 
ftanding Strangers,Enemies to God’sTruth and Religion,” 
dated June 2, 1596 , which the earl of Buchan has printed 
in the Appendix to his “ Account of the Writings and 
Inventions of Napier of Merchifton.” 
Of Napier’s method of Logarithms, and of other 
methods which arofe from it, we have given a full ac¬ 
count under that article, in vol. xii. It remains now 
to defcribe another curious and ufeful invention of his, 
called 
Napier’s Rods, or Bones, an inftrument whereby the 
multiplication and divifion of large numbers is much fa¬ 
cilitated. As to the conftrudftion of Napier’s rods ; fup- 
pofe the common table of multiplication to be made upon 
a plate of metal, ivory, or pafteboard, and then conceive 
the feveral columns (Handing downwards from the digits 
on the head) to be cut afunder; and thefe are what we 
call Napier's rods, or bones. But then there muft be a 
good number of each ; for, as many times as any figure is 
in the multiplicand or divifor, lo many rods of that fpe- 
cies (i. e. with that figure on the top of it) muft we have; 
though fix rods of each fpecies will be fufficient for any 
example in common affairs; there muft be alfo as many 
rods of o’s. But, before we explain the way of ufing 
thefe rods, there is another thing to be known, viz. that 
the figures on every rod are written in a manner fomewhat 
different from that in a common multiplication table; for 
the little fquare in which the feveral products of every 
column are written, is divided into two triangles by dia¬ 
gonals, in fuch manner as that the units are found in the 
right-hand triangle,and the tens in the left-hand triangle; 
the left-hand row of large figures is called the index-rod. See 
a complete let of rods at fig. 8. of the preceding plate. 
Uj'e of Napier's Bones in Multiplication.- —To multiply 
any given number by another; difpofe the lamellae in 
fuch a manner, as that the top figures may exhibit the 
multiplicand ; and to thefe, on the left-hand, join the 
index-rod, or lamella of units: in which feek the right- 
hand figure of the multiplicator ; and the numbers cor- 
refponding thereto, in the fquares of the other lamellae, 
write out by adding the feveral numbers occurring in 
the fame rhomb together, and their fums. After the 
fame manner write out the numbers correfponding to the 
other figures of the multiplicator; let them be difpofed 
under one another, as in the common multiplication, and 
laftly, add the feveral numbers into one fum. 
Example.—Suppoie the multiplicand 5978, _ 0 
and the multiplicator 937. From the outer- 
moft triangle on the right-hand of fig. 9. which 
correfponds to the right-hand figure of the 
multiplicator 7, write out the figure 6, placing 
it under the line. In the next rhomb, towards 
the left, add 9 and 5; their fum being 14, 
write the right-hand figure, viz. 4, againft 6 ; 
carrying the left-hand figure 1, to 4 and 3, 
which are found in the next rhomb. The 
fum 8, join to 46, already put down; after the fame man¬ 
ner in the laft rhomb, add 6 and 5, the latter figure of 
the fum 11, put down as before, and carry 1 to the 3 
found in the left-hand triangle; the fum 4 join as be¬ 
fore, on the left of 1846; thus you will have the faftum 
of 7 into 5978 ; and after the fame manner will you have 
the fa6lum of the multiplicand into the other figures of 
the multiplicator: the whole added together gives the 
whole produdl. 
Uj'e of Napier's Bones in Divifion. —Difpofe the lamellae 
fo, as that the uppermoft figures may exhibit the divifor ; 
to thefe, on the left-hand, join the index-rod as before. 
41846 
17934 
53802, 
5601386 
53802 
22118 
17934 - 
Defcend under the divifor, till you meet thofe figures of 
the dividend wherein it is firft required how oft the di¬ 
vifor is found, or at leaft the next ief's number, which is 
to be fubtradred from the dividend ; the number corref¬ 
ponding to this, in the place of units, write down for a 
quotient. By determining the other parts of the quo¬ 
tient after the fame manner, the divilions will be com¬ 
pleted. 
Example. — Suppofe the dividend r oc , 
5601386; and the divifor 5978 ;_fince 5978)5601386(937 
it is firft afked how often 5978 is found 
in 56013, defeend under the divifor 
(fig. 9.) till in the lowed: feries you 
find the number 53802, approaching 
neareft to 56013 ; the former whereof „ , 
is to be fubtradled out of the latter, , 
and the figure 9 correfponding thereto 
in the lamella of the units write down 
r 1 • r- 1 • I OOOOO 
for the quotient. To the remainder, 
2211, join the following figure of the divifor, 8 ; and the 
number 17934 being found, as before, to be the next lefs 
number thereto, the correfponding number in the lamella 
of units, 3, is to be written down for the quotient; and 
the fubtra&ion to be continued as before. After the 
fame manner the third and laft figure of the quotient will 
be found to be 7 ; and the whole 937. 
To make the ufe of the rods yet more regular and eafy, 
they are kept in a flat fquare box, whofe breadth is that 
of ten rods, and the length that of one rod, as thick as 
to hold fix (or as many as you pleafe), the capacity of the 
box being divided into ten cells, for the different fpecies 
of rods. When the rods are put up in the box (each fpe¬ 
cies in its own cell diftinguifhed by the firft figure of the 
rod fet before it on the face of the box near the top), as 
much of every rod Hands without the box as ftiows the 
firft figure of that rod; alfo upon one of the flat fides 
without and near the edge, upon the left-hand, the in¬ 
dex-rod is fixed ; and along the foot there is a fmall ledge; 
fo that the rods, when applied, are laid upon this fide, and 
fupported by the ledge, which makes the practice very 
eafy; but, in cafe the multiplicand fliould have more than 
nine places, that upper face of the box may be made 
broader. Some make the rods with four different faces, 
and figures on each for different purpofes. 
NAPIMO'GA, f. [from the Caribean name of the tree, 
napimogaU] In botany, a genus of the clafs polyandria 
order trigynia, natural order rofacea, Juff. Generic Cha¬ 
racters—Calyx : perianthium fuperior, of one leaf, fmall, 
concave, in fix roundifh, acute, permanent, fegments. 
Corolla : petals fix, ovate, villous, inferted into the re¬ 
ceptacle of the flower, oppofite to the calyx. Stamina : 
filaments eighteen, inferted into the fame part; anthers 
roundifh, of two cells. Piftillum : germen inferior, 
crowned by the calyx; ftyles three ; ftigmas obtufe. Pe- 
ricarpium and feed : unknown .—Ejfential Charafter. Ca¬ 
lyx in fix deep fegments ; petals fix, villous ; ftamens 
three to each petal ; germen crowned with the calyx. 
Napimoga Guianenfis, a Angle fpecies. This is a tree, 
whofe trunk rifes to the height of twenty-five feet, and is 
one and a half in diameter, with a reddifh wrinkled and 
cracked bark. The wood is white and foft. The branches 
fpread in every direction. Leaves alternate, on very fhort 
and flender ftalks, elliptical, fmooth, ferrated, with a 
blunt point. Stipules fmall, in pairs at the bale of the 
footftalks, deciduous. Flowers fmall, greenifh, in flen¬ 
der, axillary, long-ltalked, fpikes, each flower accompa¬ 
nied by a fmall feale-like brafte. This tree is a native of 
the woods of Guiana, flowering in November. Juflieu 
ranges the genus next after Homalium, to which it ap¬ 
pears to have fome affinity ; but the barbarous name can 
only be tolerated till enough is known of the plant to efta- 
blifh its generic charadler with certainty. Aubl. Guiatu. 
592. t. 237. 
NAP'LACH, a town of Carinthia, on the Moll: five 
miles eall of Velach. 
t NATLES, 
