# Page:Passages from the Life of a Philosopher.djvu/150

194 SOLUTION OF EQUATIONS.

But here a difficulty arises : saocessiye powers of ten are to be sabstitated for a; in the equation^ until a certain eyent happena A set of cards may be provided to make the snb- stitation of the highest power of ten, and similarly for the others ; but on the occurrence of a certain event, namely, the change of a sign fix)m + to — , this stage of the calcula- tion is to terminate.

Now at a very early period ol the inquiry I had found it necessary to teach the engine to know when any numbers it might be computing passed through zero or infinity.

The passage through zero can be easily ascertained, thus: Let the continually-decreasing number which is being com- puted be placed upon a column of wheels in connection with a carrying apparatus. After each process this number will be diminished, until at last a number is subtracted £rom it which is greater than the number expressed on those wheels.

Thus let it be . 00000,00000,00000,00423 Subtract . . . 00000,00000,00000,00511

99999,99999,99999,99912

Now in every case of a carriage becoming due, a certain lever is transferred fix)m one position to another in the cage next above il

Consequently in the highest cage of all (say the fiftieth in the Analytical Engine), an arm will be moved or not moved accordingly as the carriages do or do not run up beyond the highest wheel.

This aim can, of course, make any change which has pre- viously been decided upon. In the instance we have been considering it would order the cards to be turned on to the next set.

K we wish to find when any number, which is increasing.

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