Mr. J. Edmondson on Calculating Machines. 15 



made in England and this country since the conclusion of 

 my experiments ; but as few results by this method are at hand, 

 I publish it as a slight contribution to the history of this vexed 

 subject. 

 Marlborough, N. Y., April 15, 1885. 



II. Summary of Lecture on Calculating Machines, delivered 

 before the Physical Society of London, March 28, 1885, by 

 Joseph Edmondson, of Halifax*. 



CALCULATING machines are of two classes, the automatic 

 and the semi-automatic. The former were invented by 

 Mr. Charles Babbage between 1820 and 1834, and were de- 

 signed mainly for the computation of tables. When the primary 

 factors of a table are placed on such a machine, it will calcu- 

 late the table and impress it line by line upon a stereo-mould 

 with great celerity and absolute correctness. Mr. Babbage's 

 machine, so far as it was completed, is in the South Kensing- 

 ton Museum ; and another machine by M. Scheutz (for the 

 principles of which he confessed his indebtedness to Mr. Bab- 

 bage) is in the office of the Registrar General at Somerset 

 House. These machines proceed by the method of Differences, 

 and are therefore termed " Difference-Engines." Their work 

 is limited to addition, but they indirectly perform subtraction 

 by adding the complement of the subtrahend. 



If it be required to construct a table (of cubes for instance), 

 the law of its growth must be found by reckoning mentally 

 the first few terms of the table. Placing them in a line, the 

 difference between each term and its successor is placed under 

 the former. This process is repeated with the differences 

 until at last a line is reached in which all the differences are 

 cyphers. Thus : — 



216 



Table . . . 



A 



1 



8 



27 



64 125 



1st difference 



B 



7 



19 



37 



61 91 



2nd „ 



C 



12 



18 



24 



30 



3rd „ 



D 



6 



6 



6 





4th 



B 















The machine may now be set to work by placing the first 

 column of figures in their respective places upon it. During 

 the first half of the first revolution of the machine, the wheels 

 containing the terms A and C have the terms B and D added 

 on to them and become 8 and 18 respectively. During the 

 second half-revolution, B and D have the terms C and E added 

 on to them, becoming 19 and 6 respectively, and the second 

 column is complete. Each succeeding revolution of the 

 * Communicated by the Physica Society. 



