286 HYDROGRAPHICAL SURV EYING [chap. xii. 



be remarked that the latitude obtained from south stars 

 diminishes as the altitude increases, and vice versa with the 

 north stars. This is wholly attributable to the centring 

 error, and from these observations a very fair idea of that 

 error for each altitude may be obtained, as explained on 

 p. 9. It is therefore well, though the result will not be 

 affected, to apply the centring errors if known. 



In the example given only the direct mean was taken, 

 though the second pair was open to suspicion, the seconds 

 of both north and south stars being somewhat out of the 

 order observable in the remainder. 

 Valuing If, however, the observations had been less uniform, and 

 ®^" ^' there were not sufficient pairs manifestly better than others, 

 by which we could elect to stand, value would be assigned 

 by some such system as the following. 



Assume a number as perfection, say 10, and give to each 

 pair its value in that scale. Then the sum of the products of 

 the value and the seconds of latitude by each pair, divided by 

 the sum of the values, will give the mean seconds of latitude. 

 The values should not be given by the results, or we shall 

 arrive at pretty much the same conclusion as we should by 

 assuming the latitude directly, but by the circumstances of 

 observation of each star, and the number of observations, 

 remembering that reasons to doubt one star wdU as equally 

 affect the pair as if both stars were bad. 



Values must also be given wlien meaning the results by 

 different observers ; but here again, if one observer is ad- 

 mittedly the best, and liis observations are also good, a more 

 probable result will be obtained by ignoring the latitudes of 

 the others altogether. They will not be totally lost, as ex- 

 perience in good observing is only to be obtained by plenty cf 

 practice, and a young observer is more likely to take pains 

 when there is a chance, if his observations turn out well, of 

 having them included in the operations of the survey, than 

 when merely observing for what one may term barren 

 practice. 

 "Probable To determine the " probable error " and the value of the 

 "°'^" result of one set of observations as compared with others, 

 for the purpose of meaning the whole, we may proceed as 

 follows : 



