1 80 Mr Sans: 07i an erroneous Method 



•& 



in both cases. What is the efFect" of our peculiar mode of ar- 

 rangement ? On reversion, the two readers A and B merely 

 change places, but C and D go to new parts of the limb. The 



average then takes the form 



- 



that is, four times as much importance is attached to each of 

 the readings at A and at B as to any of those at the other 

 points ! ! 



Applying the general formula to this case, we have 

 « = 4, ^ = 4, y = 1 , 5 = 1, s = 1, ^ = 1, i = 6 

 and 



That is to say, just as much precision (in correcting the inequa- 

 lities of the limb) is obtained by eight readings as might have 

 been had from four, and the reversion, instead of doubling the 

 exactitude, has only reduced the chance of error from oi ^^ ok • 



Nay more, if the reader B had been entirely left out, the pre- 

 cision w^ould have been augmented, the chance of error being 



then only 24. • 



Thus the surveyor has added greatly to his field and house 

 labour, and has enormously complicated his operations in order 



to augment the chance of error from g to ^ ! 



Here it may be worth while to inquire, what values should 

 be given to the arbitrary coefficients a, /3, 7, &c., in order to 

 render the determination as exact as possible. In the formula 



if we suppose 2 a to be constant, we must seek so to divide it 

 as to render the sum of the squares of its parts a minimum ; 



this gives cc=z(3=d — — -r-, that is to say, the best value 



for a, /3, 7 is unit, and therefore we have here a complete de- 

 monstration of the impropriety of regarding one reading more 

 favourably than another. Some crude ideas concerning the 

 superiority of one reader over another have been urged in sup- 



