Report on the Calculating Machine of M. Scheutz. 547 



the differences for the smaller intervals would first have to be calcu- 

 lated from those for the larger ones by formulae in finite diflferences, 

 and then the setting and working of the machine would proceed as 

 before. 



It must be confessed, however, that except in the case of mathe- 

 matical tables like those of sines, cosines, logarithms, &c., it is not 

 ordinarily required to tabulate functions to intervals at all approach- 

 ing, in closeness, to those in the example selected. Hence it is 

 mainly, as it seems to us, in the computation of mathematical tables 

 that the machine of M. Scheutz would come into use. The most 

 important of such tables have long since been calculated; but 

 various others could be suggested which it might be worth while to 

 construct, could it be done with such ease and cheapness as would 

 be afforded by the use of the machine. It has been suggested to us 

 too, and we think with good reason, that the machine would be very 

 useful even for the mere reprinting of old tables, because it could 

 calculate and print more quickly than a good compositor could set 

 the types, and that without risk of error. 



G. G. Stokes. 



W. H. MiLLEK. 



C. Wheatstone. 

 V . R.Willis. 



P.S. Some time since, I received from Mr. Babbage, to whom I 

 had written for information on one point connected with his machine, 

 a letter, written subsequently to his first answer, in which he said 

 that he had forgotten to mention an addition to his machine which 

 enabled it to calculate a function when the last differences, instead 

 of being constant, were dependent on the functions then under cal- 

 culation in the other parts of the machine, provided the coefficients 

 of the variable part were small enough to be expressed by a mode- 

 rate number of digits. This was especially designed for the calcu- 

 lation of astronomical tables, where a difficulty occurs in the appli- 

 cation of a machine with constant differences, arising from the 

 circumstance that in the case of functions of short period the omitted 

 differences soon become sensible even though the coefficients be but 

 small. Mr. Babbage did not then recollect that this contrivance 

 was accessible to the public, but in a subsequent letter he pointed 

 out that such was the case. The following is an extract from this 

 letter : — 



" 1st. The portion at Somerset House contains axes specially 

 prepared for what (at this instant) I recollect to have familiarly 

 called * eating its own tail.' 



" 2nd. The drawings contain the modes of governing those axes 

 in the finished engine. 



•• These are public property, and open daily to public inspec- 

 tion, which I suppose must be considered as publication. On refer- 

 ring to the 9th Bridgewater Treatise, second edition, I find (p. 34) 

 that I have used as an illustration a scries computed by that very 

 machine. * * *." 



