MriTATHLN lU'LES. 



ADDITION OK Si T.TKA< TIOV. Ascertain from the stated object of 

 the work the percentage accuracy desired. If this is about 



One per cent, or worse, carry the result to four (4) places of signifi- 

 cant figures; 



One-tenth per cent, or worse, carry the result to five (5) places of 

 significant figures; and so on, and carry each component quantity to 

 that place of decimals which would correspond to this required place in 

 the result, that is, stand in the same column with that place. 

 nj>!<'s: 6-8, page xix. 



THE DESIRED ACCURACY is NOT STATED, inspect the data 

 to find the component whose first uncertain place is furthest to the left, 

 i.e. whose deviation measure (page xlii), in units, not percentage or 

 fractional, is greatest. Retain this component to two uncertain 

 places, and all other components to the place which would stand in the 

 same column with this second place. 

 Examples : 6-8, page xix. 



N. B. If the number of components approaches 20, care may 

 well be taken in refined work that an unusually large rejection error 

 does not enter through a special combination of rejected figures. 

 The rules are, however, sufficient for the worst possible case. 



The computer should notice that the percentage precision of a 

 result which is the difference of two or more quantities will usually 

 be smaller, and may be much smaller, than that of any of the 

 component quantities. 



Numerical Substitution in Formulae. A large number of f ormulaB 

 may be represented by the type 



a-b c-d ... 



07 = 



p-qr>s ... 



where a, b, c, d, etc., represent numbers to be multiplied, divided, 

 added, or subtracted, etc., as indicated. Any one or more of the 

 factors and terms may be wanting ; or, there 'may be several in place 

 of two ; and so on. 



Obviously, in order that the result x shall be accurate to a speci- 

 fied per cent, both numerator and denominator must be at least of 

 that accuracy, and each should therefore be carried out to the num- 

 ber of places of significant figures needed in x. Then as the numer- 

 ator consists of two or more terms ab and be added or subtracted, 



