214 Mr. W. H. Walenn on Unitation. 



If tlie necessary data were known from experiment for all 

 bodies, we might then exhibit their behaviour in changing 

 state by a series of models — -just as certain of their properties 

 are naturally shown by their crystalline forms. 



Aaclien, June 28, 1877. 



XXX. On Unitation. — VIII. Practical Remarks thereon, 

 together with Examples. By W. H. Walenn, Mem. Phi/s. 



Soc. 



[Continued from vol. iv. p. 379.] 



29. IN the general formula for any integer number, given in 

 JL art. 28, namely 



a»V w ~ 1 + a w _if n ~ 2 + . . . + a B r 2 + a 2 r + a ly 



the suffixes to the coefficients which correspond to the digits 

 are so disposed as to show the number of digits at a glance. 

 They also show, by inspection, the place of any one digit in 

 the number, counting the unit's digit as the 1st digit, symbo- 

 lized by cti, the tens' digit as the 2nd digit, symbolized by a 2 , 

 the hundreds' digit as the 3rd digit, symbolized by a 3 , and so 

 on. This use of the suffix implies a law; and the law is an 

 extension upon that which has hitherto appeared in relation to 

 suffixes ; this extension involves a special interpretation of the 

 symbol a Q . 



In this place it must be noted that suffixes have not been 

 used with that attention to perfect congruity which should 

 accompany every mathematical work. In ordinary algebra, 

 these adjuncts to notation have most frequently been used for 

 the series of coefficients in the general formula for an equation, 

 or in an expression in which each term is presumed to have a 

 coefficient, either known or unknown. In these cases, for the 

 most part, the suffixes simply indicate the order in which the 

 coefficients follow one another : sometimes this order is from 

 the right hand to the left, and in opposition to the order of the 

 indices of the powers of the unknown quantity or variable ; and 

 sometimes it is in the same direction. A common use of the 

 suffix is to mark the index of the power of the variable to which 

 the coefficient belongs in any particular term. It is used in 

 this way in Hind's i Algebra' (second edition), chap. xi. p. 374, 

 for instance in the formula 



a m r m + &c. + a 2 r 2 + a x r + rt r° + a-i?' _I + a^ 2 r~ 2 + &c. 



Another use of the suffix is to mark the terms that disappear 

 when a particular operation is performed upon a general ex- 



