Observing that this question is now under discussion in your columns (a question which occurred to myself years ago, and for which I have never been able to meet with a satisfactory solution), I am anxious that your correspondents should be aware what the real difficulty of the question is. According to the statement of “T. J. Buckton, Lichfield,” the day is always commencing at some point or other on the globe; so that if one could travel round it in twenty-four hours, arriving everywhere exactly at midnight by the time of the place, we should find each place in a state of transition of name. But if for midnight we substitute mid-day we are at once involved in a difficulty. The case may be briefly stated thus:—Suppose yourself to start from London at mid-day on Tuesday, and to travel with the sun, thus reaching London again at mid-day on Wednesday. If at the end of every hour you ask the English residents in the place you have reached the name of the day, you must at last reach some place where the answer changes to Wednesday. But at that moment it is still Tuesday (one p. m.), at the place you left an hour before. Thus you find two places within an hour in time of each other, using different names for the same day, and that not at midnight when it would be natural to do so, but when one place is at mid-day, and the other at one p. m. Whether two such places exist, and whether, if they do exist, any communication can take place between them without utter confusion being the result, I shall not pretend to say: but I shall be glad to see any rational solution suggested for the difficulty as I have put it.—
A Mathematical Tutor, Oxford.