On a Calculating Apparatus based on Napier's Rods. 191 



native arsenic in barytes : on a large crystal still on the spe- 

 cimen there is a plane between (2 1 2) and (1 1), developed 

 as in fig. 11. From measurement of a smaller crystal which 

 was removed from the specimen, the indices of this plane 

 would appear to be (4 1 4), the plane given by Dana. On 

 this same small crystal are two other minute planes, afford- 

 ing measurements which accord with (6 1 6), (1 5 1 1 5) : — 





Observed. 



Calculated. 



010.212 . . 



. 64 54 



64 59 



212.414 . . 



. 11 52 



11 53 



414.616 . . 



. 4 21 



4 18 



616.15 1 15 . 



. 5 8 



5 16 



15 1 15.101 . 



. 3 13 



3 34 



XXVI. On a Calculating Apparatus based on Napier's Rods. 

 By John Bridge, M.A.* 



[Plate VI.] 



THE ingenious contrivance known as Napier's rods or 

 bones is perhaps usually regarded as of some historical 

 interest, but as no longer of practical use. For half a century, 

 however, after its description in Rabdologia] it received much 

 attention ; and it has often been revived in various forms J. I 

 propose here to show that, by an improvement in manipula- 

 tion, it may still be made to give valuable aid by diminishing 

 labour and increasing safety and speed in calculation. 



Fig. 1 (PI. VI.) represents the apparatus, omitting some non- 

 essential points, diminished linearly as 4 to 1. SSBB is a 

 board on which, along its middle, a series of Napierian tablets 

 (I have discarded the form of rods) are to be arranged for use. 

 These have a notch at each end, so that they may be set in 

 their places by means of pairs of pins (figs. 1 and 2) fixed in 

 the board, which is about "1 inch higher between the pins than 

 elsewhere. 



The tablets, which carry on one side multiples of 0, 1, 2, 3, 

 4, carry on the other side multiples of 9, 8, 7, 6, 5, respec- 

 tively. They are kept arranged and instantly accessible in a 

 magazine which, when not wanted, is deposited in a cavity (M) 

 in the board. 



* Communicated by the Author. 



t The full title is, Rabdologice sen Numerationis per Virgulas Libri duo ; 

 cum Appendice de expeditissimo Multiplications Promptuario, Quibus ac- 

 cessit et Arithmetics Localis Liber unus. Authore et inventore Johanne 

 JXepero. 12mo. Edinb. 1617. 



\ See Bulletin de la SocieU de V Encouragement, 1851, p. 415. 



P2 



