90 Scientific Proceedings, Royal Dublin Society. 



two Variables of tweuty figures each iu about 1 secouds, and tlieir 

 addition or subtraction in about 3 secouds. Tlie time taken to divide one 

 Variable by another depends on the degree of couvergeuoy of the series 

 derived from the divisor, but IJ- minutes may be taken as the probable 

 maximum. When constructing a formula-paper, due regard should there- 

 fore be had to the relatively long time required to accomplish the routine 

 of division ; and it will, no doubt, be found advisable to use this process as 

 sparingly as possible. The determination of the logarithm of any number 

 would take 2 minutes, while the evaluation of «" (for any value of n) by 

 the expotential theorem, should not require more than 1| minutes longer — 

 all results being of twenty figures.^ 



Tiie machine, as at present designed, would be about 26 inches long, 

 24 inches broad, and 20 inches high ; and it would therefore be of a 

 portable size. Of the exact dimensions of Babbage's Engine I have no 

 information; but evidently it was to have been a ponderous piece of 

 machinery, measuring many feet iu each direction. Tlie relatively large 

 size of this engine is doubtless due partly to its being designed to 

 accommodate the large number of one thousand Variables of fifty figures 

 each, but more especially to the fact that the Variables were to have been 

 stored on columns of wheels, which, wliile of considerable bulk in themselves, 

 necessitated somewhat intricate gearing arrangements to control their move- 

 ments. Again, Babbage's method of multiplying by repeated additions, 

 and of dividing by repeated subtractions, though from a mathematical 

 point of view very simple, gave rise to very many mechauical compli- 

 cations.' 



To explain the power and scope of an Analytical Maolune or Engine, 

 I cannot do better than quote the words of the Countess of Lovelace : 

 " There is no finite line of demarcation which limits the powers of the 

 Analytical Engine. These powers are coextensive with the knowledge of 

 the laws of analysis itself, and need be bounded only by our acquaintance 

 with the latter. Indeed, we may consider the engine as the material and 

 mechanical representative of analysis, and that our actual working powers 

 in this department of human study will be enabled more effectually than 

 heretofore to keep pace with our theoretical knowledge of its principles and 

 laws, through the complete control which the engine gives us over the 

 executive manijDulations of algebraical and numerical symbols."^ 



A Committee of the British Association which was appointed to report 



' The times given include that required for the selection of the Variables to be operated on. 



- See Report Brit. Assoc, 1S7S, p. 100. 



2 R. Taylor's "Scientific Memoirs," 1S43, vol. iii., p. 696. 



