\\ COMPUTATION KlLES. 



[Deduced from Lanza's ' ; Applied Mechanics," page 336. Tlie several con- 



j. if. u. and jjooo would of course be combined into a single constant 

 in a working formula, but they are here left separate for purposes of better 

 illustration.] 



w many places of significant figures should the quantities, result, and 

 various steps of the computation be carried out to assure against a computation 

 ernr in the result, sensible as compared to one per cent? 



S ''ifiitn. In this and all similar problems, where the expression consists 



number of factors in the numerator and denominator ^either or 



both), without additions or subtractions, the solution of the si-niticant figure 



;n can be made without any knowledge of the magnitude of the component 



quantities, such as <7, /, JV, etc! In this example, as the result is desired to one 



the rules it should be carried to four places of significant 



Ibnee. according to the rule, page xiii, or to Proposition II, page xii, 



each factor of the whole expression should be carried to four places. Jn this 



~in every quantity is a factor, either in the first or a higher power, viz. 2, 



\". 1 6, 12, and 33000. Each, therefore, should be carried to four 



Hence, also, if direct multiplication be employed in the solution, each 

 product and quotient must be carried to four places. If logarithms are used 

 (they should be) four-place tables should be chosen. AVhcn a quantity enters 

 as a factor of the nth power this is equivalent to its entering n times as a simple 

 factor or as n separate factors, all with the same percentage error of the same 

 sign. See also note under example 3. 



The constants 2, 16, 12, and 33000 do not require to be carried to more 

 places than they are here given because they are complete as they stand, that is, 

 all further figures are known to be zero as a matter of definition or mathematical 

 fact. If either of them had been an experimental constant , that is, determined 

 by measurement, it should have been carried out to four places even if the last 

 figure or two were zero. For instance, if experimental, the 16 should have been 

 written 16.0, 16.00, 16.000, and so on according to the number of places to which 

 it wa> known (see rule, page xii). Failure on the part of those who write such 

 formuhe to adhere to this convention, or to indicate in some clear way the 

 degree of accuracy possessed by such constants, is a serious source of annoyance 

 and trouble to those who use them. 



As elsewhere it must not be inferred if certain of the quantities, e.g. d or/, 

 in this expression cannot be carried out to this desired number of figures, that 

 consequently the result will not have the accuracy desired in the given case. 

 The outcome of such a condition would merely be that these factors would be 

 liable to introduce more than a safe computation error. For instance, if/ were 

 given as 10100 Ibs. per square inch, we should have no certainty that it was 

 carried far enough. The presumption would be that it was correct to but three 

 places, and therefore not exact enough. If, however, from a knowledge of the 

 subject we were aware that the best known value was 10110, we should know 

 that the error from using 10100 was only i in 1000 or o.i per cent, and hence 

 admissible. On the other hand, if we know that the best value was 10050, we 

 should know that the computation error in the result from using 10100 was 0.5 

 per cent, and hence by no means safe in the above problem. 



More complete methods for ascertaining the exact accuracy needed in each 

 component measured quantity in such formulae, are given in the author's 

 " Precision of Measurements." It is to be remembered that we are now dealing 



