MR SANG'S NEW TABLE OF LOGARITHMS TO 200 000. 527 



tions are sufficient for our purpose. The only intrinsic difficulty is this, that 

 the final differences change irregularly in the last place ; wherefore, in using 

 any machine for computing logarithms, the operator must set the final difference 

 by hand preparatory to each step. The machine thus cannot properly be called 

 self-acting ; it is liable to errors caused by mistakes of the operator, who is 

 under the necessity of examining each result. He dare not venture to overpass 

 several steps, because one error may have balanced another in the intermediate 

 work. If the instrument go only to the extent of the printed work the last 

 digit would thus be insecure. 



If, on the other hand, the instrumental work be carried to more places, in 

 order that minute errors may not tell, the second differences would be brought 

 into account, the machine would become enormously complex, and the expense 

 of it would exceed many times what, in another way, may produce as good a 

 result. Besides, the amount of attention, that is, of mental fatigue, would be 

 much greater, and would be accompanied by a loss of time. 



Again, the machine must not merely compute, it must record the results in 

 some solid form capable of transferring impressions to paper. Only two ways 

 have been proposed for this. One to cause the figures to be punched in a plate 

 of soft metal from which electrotype casts may be taken; the other, to arrange 

 moveable types by the machine. In the first way it is difficult to correct an 

 error otherwise than by going over the whole page. In the second plan a 

 wrong type may get into the group from which the figures are taken. In either 

 way the results have to be carefully watched. Thus, do what we will, the last 

 resort is to careful reading, and careful reading will accomplish the whole with- 

 out any machine. The determination, therefore, was to proceed by the ordinary 

 method of hand-setting. 



The course actually followed did not differ essentially from the usual process. 

 The types were set up in pages, proofs were taken, corrections made, and the 

 pages were then subjected to the process of electrotyping. In two respects 

 only did the course actually followed differ from the usual one. After the 

 electrotype has been taken, the page is unlocked, and the types are distributed 

 into their proper boxes to be ready for future use. The usual way is to make 

 use of these types, which lie in disorder in the case. Instead of using the types 

 directly after distribution, these types were set up in regular packets, so as to 

 permit of the examination of their faces. In this way the errors of distribution 

 were completely obviated. Moreover, the types were now placed in the case 

 all ready arranged and in the position most convenient for the compositor, who 

 was no longer obliged to examine the manner in which each individual type 

 happened to be lying in its box, and who could now take up the types without 

 almost looking off his paper. By this arrangement the errors in composition 



