B L I 
this taMe ; and, by confequence, no arithmetical operation 
which one cannot execute upon it. Let it be propofed, 
for inftance, to find the film, or to work the addition, of 
the nine numbers followin 
f r • 
* 
1 
2 
3 
4 
5 
2 
3 
4 
5 
6 
3 
4 
5 
6 
7 
4 
5 
6 
7 
8 
5 
6 
7 
8 
9 
6 
7 
8 
9 
0 
7 
8 
9 
0 
1 
8 
9 
0 
1 
2 
9 
0 
i 
2 
3 
cl I exprefs them on the table in the order as they are 
dictated to me ; the firft figure at the left of the firft num¬ 
ber, upon the firft fquare to the left of the firft line ; the 
fecond figure, to the left of the firft number, upon the fe- 
xCond fquare to the left of the fame line; and fo of the 
reft. I place the fecond number upon the fecond row of 
fquares, units beneath units, and tens beneath tens, &c. 
1 place the third number upon the third row of fquares, 
and fo of the reft. Then with my fingers running over 
each of the rows vertically from the bottom to the top, 
beginning with that which is neareft to my right, 1 work 
the addition of the numbers which are exprefted, and mark 
the furplus of the tens at the foot of that column. I 
then pafs to the fecond column, advancing towards the 
left: upon which 1 operate in the fame manner; from 
thence to the third; and thus in fucceflion I finifh my ad¬ 
dition. 
“We may fee how the fame table ferved him for de- 
monftrating the properties of rectilineal figures. Let us 
fuppofe this propofition to be demonftrated, That paral¬ 
lelograms which have the fame bafis and the fame height 
are equal in their furfaces. He placed his pins accordingly, 
and gave names to the angular points, and finifhed his de- 
monftration with his fingers. If we fuppofe that Saun- 
derfon only employed pins with large heads to mark the 
limits of his figures, around thefe he might arrange his 
pins with fmall heads in nine different manners, all of 
which were familiar to him. Thus he fcarcely found any 
•embarraffment but in thole cafes where the great number 
of angular points which he was.under a neceftity of nam¬ 
ing in his demonftration obliged him to recur to the letters 
of the alphabet. We are not informed how he employed 
them. We only know, that his fingers ran over the board 
with aftonifhing agility ; that he undertook with fuccefs 
the longeft calculations; that he could interrupt the feries, 
and difeover his miftakes ; that he proved them with the 
greateft eafe ; and that his labours required infinitely lefs 
time than one could have imagined, by the exaftnefs and 
promptitude with which he prepared his inftruments and 
difpofed his table. 
“This preparation confided in placing pins wfith large 
heads in the centres of all the fquares: having done this, 
no more remained to him biit to fix their values by pins 
,of fmaller heads, except in cafes where it was necelfary to 
mark an unit; then he placed in the centre of a fquare a 
pin with a fmall head, in the place of a pin with a large 
head with which it had been occupied. Sometimes, in- 
ftead of forming an entire line with thefe pins, he con¬ 
tented himfelf with placing fome of them at all the angu¬ 
lar points, or points of interfeftion ; around which he tied 
filk threads, which finifhed the formation of the limits of 
his figures.” It may be added by way of improvement, 
that for the divifion of one feries of numbers from another, 
a thin piece of timber in the form, of a ruler with Which 
lines are drawn, having a pin at each end for the holes in 
the fquares, might be interpofed between the two feries 
to be diftinguiihed. 
By the notation here exhibited every modification of 
numbers may be expreffed/and of confequence every arith¬ 
metical operation fuccefsfully performed ; but we fliall 
•now deferibe another form of palpable arithmetic, equally 
VOL. III. No. 120. 
N D. n 7 
comprehenfive and much more fitnple than that of Saun- 
derfon, the invention of Dr. Moyes. He fpeaks of it in 
the following terms: 
“ The following palpable notation I have generally ufed 
for thefe twenty years to aflift my memory in numerical 
computations. When I began to ftudy the principles of 
arithmetic, which I did at an early period of life, f Yoon 
difeovered, to my mortification, that a perfon entirely de¬ 
prived of fight could fcarcely proceed in that ufeful fei- 
ence without the aid of palpable fymbols reprefenting the 
ten numerical characters, Being at that time unacquainted 
with the writings of Saunderfon, in which a palpable no¬ 
tation is defcribecl, 1 embraced the obvious, though, as 
I afterwards found, ini perfect, expedient of cutting into 
the form of the numerical characters thin pieces of "wood 
or metal. By arranging thefe on the furface of a board, 
I could readily reprefent any given number, not only to 
the touch, but alfo to the eye ; and by covering the board 
with a lamina of wax, my fymbols were prevented from 
changing their places, they adhering to the board from the 
flightert preflure. By this contrivance, I could folve, 
though (lowly, any problem in the fcience of numbers : 
but it foon occurred to me, that my notation, confifting of 
ten fpecies of fymbols or characters, was much more com¬ 
plicated than was abfolutely neceffary, and that any given 
number might be diftinCtly exprefted by three fpecies of 
pegs alone. To illuftrate my meaning, imagine a fquare 
piece of mahogany a foot broad, and an inch in thicknefs; 
let the fides be each divided into twenty-four equal parts ; 
let every two oppofite divifions be joined by a groove cut 
in the board fufficiently deep to be felt witli the finger, 
and let the board be perforated at each interfeCtion with 
an inftrument a tenth of an incli in diameter. The fur- 
face of the board being thus divided into 576 little fquares, 
with a fmall perforation at each of their angles, let three 
fets of pegs or pins be fo fitted to the holes in the board, 
that when (tuck into them they may keep their pofitions 
like thofe of a fiddle, and require fome force to turn 
them round. The head of each peg belonging to the firft 
fet is a right-angled triangle about one-tenth of an inch in 
thicknefs ; the head of each peg belonging to the fecond 
fet differs only from the former in having a fmall notch in 
its Hoping fide or hypothenufe ; and the head of each peg 
belonging to the third fet is a fquare of which the breadth 
fhould be equal to the bafe of the triangle of the other 
two. Thefe pegs fhould be kept in a cafe confifting of 
three boxes or cells, each cell being allotted to a fet, and 
the cafe mu ft be placed clofe by the board previous to the 
commencement of every operation. Each fet fhould con- 
lift of fixty or feventy pegs (at lead when employed in long 
calculations); and, when the work is finifhed, they fhould 
be collected from the board, and carefully reftored to their 
refpeCtive boxes. 
“Tilings being thus prepared, let a peg of the firft fet 
be fixed into the board, and it will acquire four different 
values according to its pofitron refpeCting the calcula¬ 
tor. When its (loping fide is turned towards the left, 
it denotes one, or the firft digit; when turned upwards, 
or from the calculator, it denotes two, or the fecond di¬ 
git; when turned to the right, it re prefects three; and 
when turned downwards, or towards the calculator, it de¬ 
notes four, or the fourth digit. Five is denoted by a peg 
of the fecond fet, having its (loping fide or hypothenufe 
turned to the left; fix, by the fame turned upwards; fe- 
ven, by the fame turned to the right ; and eight, by the 
fame turned direCtly down, or towards the body of the 
calculator. Nine is exprefted by a peg of the third fet 
when its edges are directed to right and left; and the fame 
peg expreffes the cypher when its edges are directed up 
and down. By three different pegs the relative values of 
the ten digits may therefore be diftinCtly exprelfed with 
facility ; and by a fufficient number of each fet the fteps 
and refult of the longeft calculation may be clearly repre- 
fented to the fenfe of feeling. It feems unheceffary to il¬ 
luftrate this by an example; fuflice it to exprefs in our 
H li characters. 
