Second smallest of the SIP range - and fitted with a conventional elevating saddle with a maximum vertical travel of 13.5"/325 mm - the 2P was of a similar general specification to the No. 1-H, though with a slightly less-accurate displacement accuracy of 0.0001". It's work-holding capacity was, however, considerably larger with its 27.5" x 12.5" (700 x 317 mm) table having travels of 16" longitudinally and 10" across with a maximum clearance of 19" (485 mm) vertically and a throat of 13.375" (340 mm). Like the No. 1-H, fully enclosed, wear-free precision standard scales with illuminated viewing screens, micrometer drums and verniers were used to indicate the table position to within 0.0001" (0.001 mm).
A machine of clean, modern design with all its control functions and drives fully enclosed, it had a table carried on ways relieved by spring-loaded rollers, thus ensuring both a particularly smooth motion and an accurate, stick-free repetition of settings. When used as a light milling machine (the rollers imposed an obvious limit on metal removal rates) a motorised, infinitely-variable-speed drive was used, the setting (from 2 to 47 inches per minute) being by rotating a dial. Control of the direction in which the table was to be moved was concentrated into a single joystick lever.
With a head carried on vertical ways set at right-angles to the table (the head could only move vertically, not in and out) the 2P used a relatively small internal spindle taper -  a No. 1 Morse taper socket - but a larger (1e) size of the special SIP external fitting. Driven by a motor held in the rear of the head, the spindle revolved in self-adjusting, high-precision ball and roller bearings of SIP manufacture with the quill having a travel of just over 5 inches (130 mm). Quill movement was by either a very sensitive handwheel or under power, with just two rates of feed: 0.00008" and 0.0025" (0.02 to 0.06 mm) per revolution with travel measured by a neatly engineered, built-in ruler scale, dial-indicator and gauge block mounting that allowed positions to be determined to within 0.0005" (0.01 mm) over the whole travel range. In order to improve sensitivity and eliminate backlash, the effective but old-fashioned solution was adopted of balancing the head and spindle with a single chain-suspended counterweight - though the effect was arranged to act on each separately, through a "differential lever", a clever system also used on some versions of the little Linley jig borer from the USA. Drive was by a ½ h.p. 3-phase motor with the eight speeds running through 200, 300, 440, 650, 980, 1400, 2100 and 3000 r.p.m.
Although the No. 2-P could bore a hole twice as big as the 1-H at 2.0625", the drilling limits remained unchanged at 9/16" (15 mm) in cast iron and ½" (12 mm) in steel. 
For the No. 2P a special No. 2 version of the Rotoptic Optical Circular Dividing Table was offered. With a 11.75-inch (300 mm) table this had, like the No. 1 model, readings shown on a viewing screen projected from a built-in circular ruler made to standard scale accuracy with angular settings down to 1 second of arc possible.
With an overall front-to-back measurement of 57.5" (1460 mm), a width of around 56" (1415 mm) the No. 2P weighed approximately 4450 lbs (2000 kg) net.
Like all SIP machines, the 2P was expensive costing  in, 1966, US$23,850 (UK price list £4058) plus another US$1,000 (£226) for the essential tooling. In other words, the cost of a very decent house in either Europe or the USA. The special rotary table made for the machine, the optical reader Rotoptic No. 2, was nearly US$3000 or, from the UK price list, £531 : 17s : 0d - with a 6-month lead time..

A single joystick lever was used to control the direction of table travel with a dial to set the speed of movement.

Guiding arm for the boring of very small holes. This was carried on a scraped prismatic surface on the lower part of the head and held interchangeable bushes the diameters of which corresponded to standard twist drills and milling cutters as listed in the maker's accessory sheets.

For the No. 2P a special No. 2 version of the Rotoptic Optical Circular Dividing Table was offered. With a 11.75-inch (300 mm) table this had, like the No. 1 model, readings shown on a viewing screen projected from a built-in circular ruler made to standard scale accuracy with angular settings down to 1 second of arc possible.

A kit of accessories recommended by the manufacturer to enable the machine to be put to immediate use: 12.5 X locating microscope; locating dial indicator; drill chuck and a set of adjustable boring tool holders