It appeared that the solution of a secret of the chain line lies in an exponential function. In the XVIII century it was still a novelty, and now each eighth-grader has to know it. It is function of a type of y=ax where an – any positive number not equal Calculations showed that for creation of the chain line it is most convenient to accept an equal to the so-called Napierian number designated by a letter e. It received the name in honor of the Scottish mathematician John Napier – one of inventors of logarithms. Number it is almost so well-known, as well as number; its approximate value taken to within 0,0005:e2,71
How to find the line equation in a case when for these points of subweight of A and B length of a chain 2l' does not coincide with length 2l arches of AB belonging to a curve of y=1/2 (ex-e-x)? In search of the answer we will lean on the fact noted above that all chain lines are similar among themselves.
If to use negative indicators of degrees, the last function can be presented in the form y=e-x. Now it is clear that both schedules are symmetric each other concerning ordinate axis, as finds drawing.