30 SCIENTIFIC APPARATUS. 



of crystallography are never very considerable. In the case of 

 some organic bodies the number of equivalents that enter into the 

 formula has to be counted by hundreds ; but in all such instances, 

 owing to the imperfection of the methods of chemical analysis, the 

 determinations that have been given must be regarded as open to 

 correction. The " indices " of any face of a crystal actually 

 occurring in nature rarely exceed ten. 



(2.) The geometrical and mechanical appliances for aiding in 

 the operations of arithmetic, as applied to continuous magnitude, 

 are not very numerous, and possess in most cases a theoretical 

 rather than a practical importance. 



A very ingenious instrument of this kind, and one that has been 

 extensively used, is the slide rule, which may be described as an 

 apparatus for effecting multiplications and divisions by means of 

 a logarithmic scale ; the requisite additions and subtractions being 

 performed without calculation by a proper adjustment of the instru- 

 ment itself. The principle on which it depends admits of being 

 applied in various ways, and thus there are slide rules of very 

 various forms, and adapted to very different purposes. But the 

 card of four figure logarithms is a formidable competitor to any 

 logarithmic scale, and it may be doubted whether at the present 

 time these really beautiful contrivances are in as common use as 

 they deserve to be. The Exhibition contains a complete series of 

 them by Messrs. Aston and Mander; besides the Estimator of 

 Dr. F. M. Stapff, and the Pocket Calculator of General De Lisle. 



Instruments for solving triangles and for finding the roots of 

 quadratic and higher equations may next be noticed. Some of them 

 are remarkable for their ingenuity ; some are useful as educational 

 appliances, because they serve to illustrate, in a very beautiful 

 way, the connection between arithmetic, or algebra, and geometry. 

 Others again are of great interest from the difficulty of the pro- 

 blems which they propose to solve, and the profound character of 

 the principles which they employ in the solution. To this last 

 class belongs the interesting application by Professor Sylvester 



