Precisely speaking, the North Pole is simply a mathematical point, and therefore, in accordance with the mathematical definition of a point, it has neither length, breadth, nor thickness.
If the question is asked, how closely can the Pole be determined (this is the point which has muddled some of the ignorant wiseacres), the answer will be: That depends upon the character of the instruments used, the ability of the observer using them, and the number of observations taken.
If there were land at the Pole, and powerful instruments of great precision, such as are used in the world's great observatories, were mounted there on suitable foundations and used by practised observers for repeated observations extending over years, then it would be possible to determine the position of the Pole with great precision. With ordinary field instruments, transit, theodolite, or sextant, an extended series of observations by an expert observer should permit the determination of the Pole within entirely satisfactory limits, but not with the same precision as by the first method.
A single observation at sea with sextant and the natural horizon, as usually taken by the master of a ship, is assumed under ordinary satisfactory conditions to give the observer's position within about a mile.
In regard to the difficulties of taking observations in the arctic regions, I have found a tendency on the part of experts who, however, have not had practical experience in the arctic regions themselves, to overestimate and exaggerate the difficulties and drawbacks of making these observations due to the cold.
My personal experience has been that, to an experienced observer, dressed in furs and taking observations in calm weather, in temperatures not exceeding say 40° below zero Fahrenheit, the difficulties of the work resulting from cold alone are not serious. The amount and character of errors due to the effect of cold upon the instrument might perhaps be a subject for discussion, and for distinct differences of opinion.
My personal experience has been that my most serious trouble was with the eyes.
To eyes which have been subjected to brilliant and unremitting daylight for days and weeks, and to the strain of continually setting a course with the compass, and traveling towards a fixed point in such light, the taking of a series of observations is usually a nightmare; and the strain of focusing, of getting precise contact of the sun's images, and of reading the vernier, all in the blinding light of which only those who have taken observations in bright sunlight on an unbroken snow expanse in the arctic regions can form any conception, usually leaves the eyes bloodshot and smarting for hours afterwards.
The continued series of observations in the vicinity of the Pole, noted above, left me with eyes that were, for two or three days, useless for anything requiring careful vision, and had it been necessary for me to set a course during the first two or three days of our return I should have found it extremely trying.
Snow goggles, as worn by us continually during the march, while helping, do not entirely relieve the eyes from strain, and during a series of observations the eyes become extremely tired and at times uncertain.