708 TRANSLATOR’S NOTES TO M. MENABREA’S MEMOIR 
zero is substituted. At the end of a ealculation, therefore, every 
column ought as a general rule to be zero, excepting those for results. 
Thus it will be seen by the diagram, that when m, the value on Vo, is — 
used for the second time by Operation 5, Vo becomes 0, since m is not 
again needed ; that similarly, when (mm 2’ — m' 7), on V,., is used for the 
third time by Operation 11, V,. becomes zero, since (mn — m'n) is 
not again needed. In order to provide for the one or the other of the 
courses above indicated, there are éwo varieties of the Supplying Vari- 
able-cards. One of these varieties has provisions which cause the — 
number given off from any Variable to return to that Variable after 
doing its duty in the mill, The other variety has provisions which 
cause zero to be substituted on the Variable, for the number given off, 
These two varieties are distinguished, when needful, by the respective 
appellations of the Retaining Supply-cards and the Zero nig 2 orang 
We see that the primary office (see Note B.) of both these varieties of 
cards is the same; they only differ in their secondary office. 
Every Variable thus has belonging to it one class of Receiving Vari- 
able-cards and @vo classes of Supplying Variable-cards, It is plain 
however that only the one or the other of these two latter classes can 
be used by any one Variable for one operation ; never both simultane- 
ously ; their respective functions being mutually incompatible. 
It should be understood that the Variable-cards are not placed in 
immediate contiguity with the columns, Each ecard is connected by 
means of wires with the column it is intended to act upon. 
Our diagram ought in reality to be placed side by side with M. Me- 
nabrea’s corresponding table, so as to be compared with it, line for line 
belonging to each operation. But it was unfortunately inconyenient to 
print them in this desirable form. The diagram is, in the main, merely 
another manner of indicating the various relations denoted in M. Mena- 
brea’s table. Each mode has some advantages and some disadvantages, 
Combined, they form a complete and accurate method of registering 
every step and sequence in all calculations performed by the engine. 
No notice has yet been taken of the wpper indices which are added 
to the left of each V in the diagram; an addition which we haye 
also taken the liberty of making to the V’s in M, Menabrea’s tables of 
pages 681, 684, since it does not alter anything therein represented 
by him, but merely adds something to the previous indications of those 
tables. The lower indices are obviously indices of locality only, and 
are wholly independent of the operations performed or of the results 
obtained, their value continuing unchanged during the performance of 
calculations. The upper indices, however, are of a different nature. 
Their office is to indicate any alteration in the value which a Variable 
represents ; and they are of course liable to changes during the pro-— 
cesses of a calculation. Whenever a Variable has only zeros upon it, 
it is called °V; the moment a value appears on it (whether that value 
be placed there arbitrarily, or appears in the natural course of a caleu- — 
lation), it becomes 'V. If this value gives place to another value, the 
Variable becomes *V, and so forth. Whenever a value again gives — 
place to zero, the Variable again becomes °V, even if it have been »V the 
moment before. Ifa value then again be substituted, the Variable ; 
becomes "+!V (as it would have done if it had not passed through the — 
intermediate °V); &c. &c. Just before any calculation is commenced, — 
and after the data have been given, and everything adjusted and pre-— 
