538 Transactions. — Chemistry and Physics. 



If further approximation be desired, the next systematic 

 step would be to reduce the deviations at the odd-eighth 

 points of x by means of quintic, hexic (somewhat different 

 from the tabulated sample, obviously), heptic, and octic func- 

 tions ; and so on. 



The same operations might possibly be considered easier if 

 performed by simple algebra, but we should then lose the 

 analytical power of judgment which is the vital advantage of 

 the " standard " method. 



With reference to the computation of values of Y from 

 formulas, the values of the standard functions up to the 

 quartic degree may be computed by writing down the datum 

 values of x ; (1 — x) ; and (1 — x) — x, or (1 — 2x), and form- 

 ing the proper products. Up to the octic degree we should 

 need also (1 - 4x) and (3 - Ax), or 2(1 - 2a;) + 1. It is clear 

 that if computation is to proceed by means of an arithmo- 

 meter the labour of computation will not materially differ 

 from that in which simple powers are used. With logarithms 

 it will be necessary to enter the table once extra for each 

 factor required. 



