706 TRANSLATOR’S NOTES TO M. MENABREA’S MEMOIR 
mind that the inscriptions within any of the squares, are quite inde- 
pendent of the mechanism or workings of the engine, and are nothing 
but arbitrary memorandums placed there at pleasure to assist the spec- — 
tator. 
The further we analyse the manner in which such an engine per- 
forms its processes and attains its results, the more we perceive how 
distinctly it places in a true and just light the mutual relations and con- 
nexion of the various steps of mathematical analysis, how clearly it 
separates those things which are in reality distinct and independent, 
and unites those which are mutually dependent. A. A. L. 
Note C.—Page 677. 
Those who may desire to study the principles of the Jaequard-loom 
in the most effectual manner, viz. that of practical observation, have 
only to step into the Adelaide Gallery or the Polytechnic Institution. 
In each of these valuable repositories of scientific 2//ustration, a weaver 
is constantly working at a Jacquard-loom, and is ready to give any in- 
formation that may be desired as to the construction and modes of 
acting of his apparatus. The volume on the manufacture of silk, in 
Lardner’s Cyclopedia, contains a chapter on the Jacquard-loom, which 
may also be consulted with advantage. 
The mode of application of the cards, as hitherto used in the art of 
weaving, was not found, however, to be sufficiently powerful for all the 
simplifications which it was desirable to attain in such varied and com- 
plicated processes as those required in order to fulfil the purposes of 
an Analytical Engine. A method was devised of what was technically 
designated backing the cards in certain groups according to certain 
laws. The object of this extension is to secure the possibility of bringing 
any particular card or set of cards into use any number of times success- 
ively in the solution of one problem. Whether this power shall be taken 
advantage of or not, in each particular instance, will depend on the 
nature of the operations which the problem under consideration may 
require. The process is alluded to by M. Menabrea in page 680, and 
it is a very important simplification. It has been proposed to use it 
for the reciprocal benefit of that art, which, while it has itself no appa- 
rent connexion with the domains of abstract science, has yet proved so 
valuable to the latter, in suggesting the principles which, in their new 
and singular field of application, seem likely to place algebraical com- 
binations not less completely within the province of mechanism, than are 
all those varied intricacies of which intersecting threads are susceptible. 
By the introduction of the system of backing into the Jacquard-loom 
itself, patterns which should possess symmetry, and follow regular laws 
of any extent, might be woven by means of comparatively few cards. 
Those who understand the mechanism of this loom will perceive 
that the above improvement is easily effected in practice, by causing 
the prism over which the train of pattern-cards is suspended, to revolve 
backwards instead of forwards, at pleasure, under the requisite cireum- 
stances; until, by so doing, any particular card, or set of cards, that — 
has done duty once, and passed on in the ordinary regular succession, 
is brought back to the position it occupied just before it was used the ~ 
preceding time. The prism then resumes its forward rotation, and— 
thus brings the card or set of cards in question into play a second time. — 
This process may obviously be repeated any number of times. A. A. Le 
