G. B. Grant on a new Difference Engine. 115 
a second order can be formed from the first, a third from the 
second, and ultimately an order of differences will be reached, 
which is: constant or nearly so. For example, take a table of 
the cubes of the natural numbers, and forming the several 
orders of difference, it is found that the third order is invaria- 
Six. 
Table. 1st order, 2nd order. 3rd order. 
l 7 12 6 
8 19 18 6 
27 a 24 
64 61 
125 
It is plain that with nothing but the first terms 1, 7, 12 and 
6, the table might be constructed to any extent by simple addi- 
hon. A difference engine is nothing but a machine to operate 
this method, using several orders of differences, and a large 
number of decimal places. 
In logarithmic, trigonometrical, and in fact in the greater 
n 
h start must then be taken, and the table completed by a 
number of such operations, _ 
This engine, like both the others, consists of a calculating 
and a printing part. In the printing part, the calculated results 
are stamped into a sheet of lead, wax or other plastic substance, 
from which a stereotype plate is taken for printing the table, 
thus avoiding constant error in copying the numbers and set- 
Ung them up in type from manuscript. No description of this 
Part is given, as it contains nothing new of importance. 
; , The calculating part consists of the main wheels, A, on which 
the first terms are set up, the additions made, and from which the 
five inches in diameter, all turning on the sam ), in t 
a direction independently of each other, the axis being 
0 
They ‘are arranged in sets of two, three or more, according 
as the first, snehal ca higher order is designed to be constant. 
There are as many of these sets as there are decimal places in 
the largest number to be used. Hach wheel is furnished 
one edge with twenty teeth, and on the other with two cams, 
2 and a’, which project a little farther from the wheel than the 
ps e spaces between the teeth are stamped with the ten 
Tumerals, zero to nine, twice in succession. 
