The IBM 701 Defense Calculator (1952) was IBM's first production computer. It was designed primarily for scientific calculation and included "microsecond circuits installed at critical locations ... to send electrical impulses from one unit to another at a speed faster than one-millionth of a second" devised at Columbia University's Watson Lab . It rented for about $16,000 per month. In all, 19 units were manufactured, most of them for US national laboratories, the US Weather Bureau, aircraft manufacturers, etc, and big companies like GE. The first unit was installed in 1952 at IBM Headquarters in New York City, replacing the SSEC. The 701 came in eleven pieces:
Plus card punches, readers, and recorders, a printer, a magnetic tape unit (the world's first), and a drum.
The IBM 700 series were binary (as opposed to decimal) vacuum-tube logic computers with 36-bit words. The 704 was a 701 with core (rather than CRT) memory, floating-point arithmetic, and a bunch of new instructions; 123 of them were sold from 1955 to 1960. There was also a 705 with a 35-bit (not 36-bit) word. The 709 succeeded the 704, adding overlapped i/o, indirect addressing, and decimal instructions. The 7090 was a 709 with transistor, rather than vacuum-tube, logic. The 7040 and 7094 were scaled-down and -up 7090 variations. The 36-bit 700- and 7000-series were IBM's scientific computers from 1952 until the appearance of the 32-bit System 360 in 1964. 
Ronald Reagan and Watson Laboratory's Herb Grosch at an IBM 701 in 1954.
According to Herb Grosch's book, Computer, Bit Slices from a Life , the photo is from Bill Bell's book on electronic data processing (the first such book ever published by McGraw-Hill), taken in the General Electric 701 machine room, Evendale, Ohio. The book is: William Bell, A Management Guide to Electronic Computers, McGraw-Hill Book Company, New York, 1957. Reagan was host of CBS General Electric Theater.
Photo from an IBM ad in CACM Vol.18 No. 8, Aug 1975, caption: "Bill Stringfellow explains how the use of a special tool, an eight-tube pluggable unit, was set into a 701 computer. Alongside is an integrated circuit many times smaller, which performs comparable logic functions thousands of times faster in today's System/370."
The IBM 700 Series lives on in the terminology of the LISP programming language. From Bob Clements at BBN:
"CAR" stands for "Contents of Address part of Register", and similarly for CDR and "Decrement".
The relevant instructions on the 7090/7094 had two 15-bit (not 18 bit) fields (Address part and Decrement part) for those values.
The other 6 bits were a 3-bit opcode field and a 3-bit "which index register" field. Laid out as (L to R) OP, DECR, IDX, ADDR.
There were just a few ops with that layout. They used the high opcode bit (or maybe two bits?), being ones as an escape from the normal opcode map, allowing that big field for the Decrement. Like the high digit "7"being I/O ops on the DEC machines.
On the PDP-6 (et seq) LISP's CAR and CDR were 18-bits, of course, due to all the half-word data manipulation instructions.
On the 7090, there were three index registers, named 1, 2 and 4. If you lit more than one bit in the index field, it caused the two or three index registers to be OR-ed together to get the actual value. I remember seeing that used once, in a routine that translated punch card codes somehow. One of the indexes contained either 0 or 1 at that point, depending on something or other (zone punches? who knows).
On the 7094, there were 7 index registers, 1 thru 7, and there was a mode bit you could set to switch between 7090 compatibility (three OR-ed or 7 index regs).
IBM photo and roster courtesy of Bruce Gilchrist
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Updates: Thu Jan 1 16:07:14 2004; Sat May 13 10:56:53 2006.