CALCHAS, the most famous soothsayer among the Greeks at the time of the Trojan war, was the son of Thestor. He foretold to the Greeks the length of time they would be engaged in the siege of Troy, and when the fleet was detained by adverse winds, at Aulis, he explained the cause and demanded the sacrifice of Iphigenia. When the Greeks were visited with pestilence on account of Chryseis, he disclosed to them the reasons of Apollo’s obtained by subtraction, it is quite evident that by reversing the process we shall obtain the original table. Suppose we are given the first terms of N, ∆ 1 , and Δ 2 , i.e., 1, 3, 2. If we add 3, the first term of ∆ 1 , to 1, the first term of N, we get 4, the second term of N; and if we add 2, the first term of Δ 2 , to 3, the first term of ∆ 1 , we get 5, the second term of Δ 1 ; and this added to 4, the second term of N, gives us 9, the third term of N. Similarly we obtain 16 by adding 9, 5, and 2 together, and 25 by adding 16, 7, and 2. Hence, given 1, 3, 2, we can, by a process of additions, obtain the series of square numbers. All numerical tables can be calculated entirely by this method or by repetitions of it.

The main characteristics of the difference engine, designed and partially constructed by Babbage, are these :— It consisted of several vertical columns of figure-wheels anger. After the return of the Greeks from Troy he is said to have retired to Colophon. According to the story, his death was due to chagrin at being surpassed in a trial of soothsaying skill by one Mopsus. It had long been predicted that he should die whenever he met his superior in divination.