8 SEC. 1. ARITHMETIC. 



29. Calculating Disc, size about 1 8 centimeters, with double 

 divided circle ; constructed on the system of Prof. Sonne, cf. 

 No. 4002. Landsberg and Wolpers, Hanover. 



30. Calculating Disc, with index of logarithms. 



Landsberg and Wolpers, Hanover. 



31. Calculating Disc, pocket apparatus. 



Landsberg and Wolpers, Hanover. 



32. Calculating Circle, O'OS meters in diameter, with single 

 scale of brass. Rudolf Weber, Aschaffenburg. 



33. Calculating Circle, 0*15 meters in diameter, with single 

 square and cubic scale. Rudolf Weber, Aschaffenburg. 



The circles are on account of their continuous scale more convenient and 

 more accurate than straight slide rules. They are, therefore, peculiarly 

 adapted as pocket instruments for practical purposes, and can be relied on to he 

 as accurate as logarithms to four places. 



34. Cubing Circle, 08 meters in diameter, for ascertaining 

 the cubical contents of trees in forests. 



Rudolf Weber, Aschaffenburg. 



The cubing circle is to be noted as giving the index numbers for obtaining 

 the cubical contents of standing (not felled) timber ; these have been ob- 

 tained from practical experiments carried out by the Government Department 

 of Forests in Bavaria on more than 40,000 trunks of different kinds of trees. 

 The circle may be relied on for great accuracy in forest valuation. 



35. Calculating Instrument, invented by Sir S. Morland. 



Bennet Woodcroft, F.R.S. 



35a. Calculating Planisphere. Royal College of Science. 



35b. McFarlane's Calculating Planisphere. 



The Committee, Royal Museum, Peel Park, Salford. 



36. Calculating Machine, designed by the Vicar Hahn 

 of Echterdingen, in 1770-1776 ; constructed by his son, Court 

 Mechanician in Stuttgart, in 1809 ; fourth specimen. 



Her Highness the Duchess of Urach. 



The machine which is exhibited is on exactly the same principle as that of 

 the one now in general use which was invented by Thomas, the only differ- 

 ence being that in Thomas's machine the numbers are placed in straight lines, 

 and in that of Hahn in a circle. It must have served as a model for 

 the machine of Thomas. The machine is to the present day in perfect order, 

 and works calculations up to numbers of 12 digits. 



37. Logarithmic Calculation Apparatus, with one folding 

 scale, 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 



