II. - CALCULATING MACHINES. 9 



37. Logarithmic Calculation Apparatus, with one folding 

 scale, equivalent to five meters in length. 



Prof. Gustav Hermann, Aix-la-Chapelle. 



Calculation by means of this instrument is effected with the use of only one 

 scale. The two revolving arms are used like a compass. When the logarithm 



a 

 of a quotient has been fixed between the arms, the plate must be 





turned until the one arm is brought to a factor c, the product , c will then be 



read on the other arm. This arrangement admits of the scale being made as 

 long as may be necessary by breaking it into lengths, without rendering the 

 instrument inconvenient. In the exhibited instrument ten circles are used, 

 by which means the scale attains a length of five meters, and is accurate up 

 to 16 06 . In using the instrument care must be taken to mark the number 

 of each scale circle, which can be fixed by small sliding buttons. The 

 number of the circle on which the result is to be read is found by the same 

 rules as the characteristic of a logarithm, on the supposition that the ten scale- 

 circles form a graphic table of logarithms of all the natural numbers, the base 

 of the system being ^ 



38. Arithmetical Disc, a very simple calculating machine, 

 with accompanying description. Prof. Prestel, Emden. 



39. Calculating Machine, of the last century. 



The Royal Gcwcrbe Academy, Berlin (Director, Prof. 



Rculcaux). 



This calculating machine formed part of the legacy of Hofrath Beireis, 

 the well-known ph} r sicist and chemist in the 18th century, and is very 

 similar to the calculating machine, No. 36. The following description 

 which accompanies this calculating machine is especially interesting, as it 

 was probably drawn up and written by the maker. 



On the Use of the Calculating Machine. 



There are on the small number-discs [Zahlen-Scheiblein] in the smallest 

 [circles], as well as on the large, in the great circles, the numbers 1, 

 10, 100, 1,000, and so on ; these indicate that the numerals on the first disc,. 

 where the (1) is marked, are units, on the second disc, where the numeral (10) 

 is marked, the tenfold of the numbers, and on the third, the hundredfold, 

 and so on ; and this applies also to those arcs on the largest circles. And if 

 on its first six discs respectively the following numerals were placed, 357,862, 

 they would indicate multiples of the numbers 1, 10, 100, which are on the 

 respective discs. On the sixth disc, where the numeral (3) is placed, is to 

 be found the number 100,000 ; thus indicating three times a hundred thousand. 

 On the fifth disc the numeral 5 represents 50,000, similarly the numeral 7, 

 7,000, and so on ; this would, in the first place, be " ciphering.'" 



Now follows, iu the second place, addition. In calculating use is made of 



the same numbers that are placed in the openings on the number disc, the 



black numbers on the large discs are used for addition and multiplication, 



and at the commencement noughts must be placed in all the apertures. As 



q , an example, the following numbers will now be added together. 



These numbers must be placed on those arcs which are found con- 



r* secutively in the outer circle. The handle must then be turned, 



when the numerals 352 will have come in the place of the noughts, 



~7~~ on the three first large discs under the opening. Then the second 



_'__ an( i Aird row are placed on the discs and by turning the handle 



added to the preceding. 



