A fourth operation of reasoning done by punch-card machines is finding that one number is greater than, or equal to, or less than another. This operation is done in the collator and may be called _sequencing_. For example, suppose that we have a file of punch cards for cities, showing in columns 41 to 48 the number of people. Suppose that we wish to pick out the cards for cities over 125,000 in population. Now the collator has a mechanism that has 2 inputs and 3 outputs (Fig. 17). We may call this mechanism a _sequencer_, since it can tell the sequence of two numbers. What goes into the _Primary_ input is a number: let us call it _a_. What goes into _Secondary_ is another number: let us call it _b_. An impulse comes out of _Low Primary_ if _a_ is less than _b_. An impulse comes out of _Equal_ if _a_ equals _b_. An impulse comes out of _Low Secondary_ if _a_ is greater than _b_. [Illustration: FIG. 17. Sequencer.] In the language of logic, if _p_, _q_, _r_ are the three indications in Low Primary, Equal, and Low Secondary, then: _p_ = _T_(_a_ < _b_) _q_ = _T_(_a_ = _b_) _r_ = _T_(_a_ > _b_) Returning to our example, we punch up a card with 125,000 in columns 43 to 48, and we put this card into the Secondary Feed. We take the punch cards for cities and put them into the Primary Feed. In the plugboard, we connect the hubs of the Secondary Brushes (that read the card in the Secondary Feed), columns 43 to 48, to the Secondary input of the Sequencer. We connect the hubs of the Primary Brushes (that read the card in the Primary Feed), columns 41 to 48, to the Primary input of the Sequencer. Then we connect the Low Primary output of the Sequencer to a device that causes the city card being examined to fall into pocket 1. We connect Equal output and Low Secondary output to a device that causes the city card being examined to fall into pocket 2. Then, when the card for any city comes along, the machine compares the number of people in the city with 125,000. If the number is greater than 125,000, the card will fall into pocket 1; otherwise the card will fall into pocket 2. At the end of the run, we shall find in pocket 1 all the cards we want. NEW DEVELOPMENTS We may expect to see over the next few years major developments in punch-card machinery. It would seem likely that types of punch-card machines like the following might be constructed: A punch-card machine that performs any arithmetical or logical operation at high speed and may perform a dozen such operations in sequence during the time that a punch card passes through the machine. A punch-card machine that uses loops of punched paper tape, which express either a sequence of values in a table that the machine can consult or a sequence of instructions that govern the operations of the machine. Punch-card machinery that uses a larger card than the 80-column card.