100 REPORT — 1878. 



Theoretically it might supersede the difference engine, a majori; but 

 for reasons already stated, the specialization of the difference engine 

 would probably give it an advantage over the more powerful engine, 

 when the work was specially suited to finite differences. 



There would remain much work, tabular and other, for which diffe- 

 rences are not very directly suited. Among these may be mentioned the 

 determination of heavy series of constants and of definite functions of 

 them, such as Bernoulli's numbers, 2a; -n , coefficients of various expan- 

 sions of functions, and inversions of known expansions, solutions of 

 simultaneous equations with large numerical coefficients and many 

 variables, including, as a particular, but important case, the practical 

 correction of observations by the method of least squares. If all sorts of 

 heavy work of this kind could be easily and quickly, as well as certainly, 

 done, by merely selecting or punching a few Jacquard cards and turning 

 a handle, not only much saving of labour would result, but much which is 

 now out of human possibility would be brought within easy reach. 



If intelligently directed and saved from wasteful use, such a machine- 

 might mark an era in the history of computation, as decided as the intro- 

 duction of logarithms in the seventeenth century did in trigonometrical 

 and astronomical arithmetic. Care might be required to guard against 

 misuse, especially against the imposition of Sisyphean tasks upon it by 

 influential sciolists. This, however, is no more than has happened in 

 the history of logarithms. Much work has been done with them which 

 could more easily have been done without them, and the old reproach is 

 probably true, that more work has been spent upon making tables than 

 lias been saved by their use. Yet, on the whole, there can be no reason- 

 able doubt that the first calculation of logarithmic tables was an expen- 

 diture of capital which has repaid itself over and over again. So- 

 probably would the analytical engine, whatever its cost, if we could be 

 assured of its success. 



VIII. Possible Modification of the Engine. 



Without prejudging the general question referred to us as to the 

 advisability of completing Mr. Babbage's engine in the exact shape in 

 which it exists in the machinery and designs left by its inventor, it is 

 open to consideration whether some modification of it, to the sacrifice 

 of some portion of its generality, would not reduce the cost, and simplify 

 the machinery, so as to bring it within the range of both commercial and 

 mechanical certainty. The "mill,"'for example, is an exceedingly good 

 mechanical arrangement for the operations of addition and subtraction, 

 and with a slight modification, with or without store-columns, for multi- 

 plication. We have already called attention to the imperfection of the 

 existing machines, which show weakness and occasional uncertainty. It 

 is at least worth consideration whether a portion of the analytical engine 

 might not thus be advantageously specialized, so as to furnish a better 

 multiplying machine than we at present possess. This, we have reason 

 to believe, is a great desideratum both in public and private offices, as 

 well as in aid of mathematical calculators. 



Another important desideratum to which the machine might be 

 adapted, without the introduction of any tentative processes (out of 

 which the complications of the machinery chiefly arise) is the solution of 

 simultaneous equations containing many variables. This would include 



