The great secret has already been revealed that this mysterious symbol , which is after all only a long , merely means “the sum of,” or “the sum of all such quantities as.” It therefore resembles that other symbol (the Greek Sigma), which is also a sign of summation. There is this difference, however, in the practice of mathematical men as to the use of these signs, that while is generally used to indicate the sum of a number of finite quantities, the integral sign is generally used to indicate the summing up of a vast number of small quantities of indefinitely minute magnitude, mere elements in fact, that go to make up the total required. Thus , and .
Any one can understand how the whole of anything can be conceived of as made up of a lot of little bits; and the smaller the bits the more of them there will be. Thus, a line one inch long may be conceived as made up of pieces, each of an inch long; or of parts, each part being of an inch long;
