696 TRANSLATOR’S NOTES TO M. MENABREA’S MEMOIR 
and is incapable of developing, tho Analytical Engine can either tabu- 
late or develope. 
The former engine is in its nature strictly arithmetical, and the re- 
sults it can arrive at lie within a very clearly defined and restricted 
range, while there is no finite line of demarcation which limits the 
powers of the Analytical Engine. These powers are co-extensive with 
our knowledge of the laws of analysis itself, and need be bounded only 
by our acquaintance with the latter. Indeed we may consider the 
engine as the material and mechanical representative of analysis, and 
that our actual working powers in this department of human study will 
be enabled more effectually than heretofore to keep pace with our 
theoretical knowledge of its principles and laws, through the complete 
control which the engine gives us over the executive manipulation of 
algebraical and numerical symbols. 
Those who view mathematical science not merely as a vast body of 
abstract and immutable truths, whose intrinsic beauty, symmetry and 
logical completeness, when regarded in their connexion together as a 
whole, entitle them to a prominent place in the interest of all profound 
and logical minds, but as possessing a yet deeper interest for the human 
race, when it is remembered that this science constitutes the language 
through which alone we can adequately express the great facts of the 
natural world, and those unceasing changes of mutual relationship which, 
visibly or invisibly, consciously or unconsciously to our immediate phy- 
sical perceptions, are interminably going on in the agencies of the 
creation we live amidst: those who thus think on mathematical truth 
as the instrument through which the weak mind of man can most 
effectually read his Creator’s works, will regard with especial interest 
all that can tend to facilitate the translation of its principles into ex- 
plicit practical forms. 
The distinctive characteristic of the Analytical Engine, and that 
which has rendered it possible to endow mechanism with such extensive 
faculties as bid fair to make this engine the executive right-hand of 
abstract algebra, is the introduction into it of the principle which Jac- 
quard devised for regulating, by means of punched cards, the most com- 
plicated patterns in the fabrication of brocaded stuffs. It is in this that 
the distinction between the two engines lies. Nothing of the sort exists 
in the Difference Engine. We may say most aptly that the Analytical 
Engine weaves algebraical patterns just as the Jacquard-loom weaves 
flowers and leaves. Here, it seems to us, resides much more of origi- 
nality than the Difference Engine can be fairly entitled to clam. We 
do not wish to deny to this latter all such claims. We believe that it 
is the only proposal or attempt ever made to construct a calculating 
machine founded on the principle of successive orders of differences, and 
capable of printing off its own results; and that this engine surpasses 
its predecessors, both in the extent of the calculations which it can per- 
form, in the facility, certainty and accuracy with which it can effect 
them, and in the absence of all necessity for the intervention of human 
intelligence during the performance of its calculations. Its nature is, 
however, limited to the strictly arithmetical, and it is far from being 
the first or only scheme for constructing arzthmetical calculating ma- 
chines with more or less of success. 
The bounds of arithmetic were however outstepped the moment the 
