174} Mr Sang on an erroneous Method 



ever, of an order sufficiently high to induce inaccuracies in the 

 determination of the degree of the meridian, the oblateness of 

 the earth, and such hke. 



The arrangement of the readers, as described to me, is this : 



A 



A, being the principal one, another, B, is placed exactly oppo- 

 site to it, so that the two, A and B, form the ordinary system 

 of two readers. Again, two others, C and D, are placed each 

 120° from A, so that the three A, C, D, form the common 

 system of three readers. ^ 



The indications of these four having been taken, the average 

 of A and B is struck ; also that of A, C, and D ; and lastly, 

 the mean of these two averages is taken for the true reading. 



Putting a, 6, c, d for the four readings, this unique opera- 

 tion is thus represented in an algebraic form : 



a -\- b g + c 4- c ? 



2 



which is equivalent to 



12 



The evils of the method stand so prominently forward in this 

 expression, that there is hardly need for saying another word 

 on the subject. Yet it may be better to inquire into the real 

 amount of imperfection than merely to point out its source. 



If our instruments were perfectly graduated, and accurately 

 centred, one reader would be as good as two, three, or five, for 

 the readings by all would be exactly alike, and their average 

 the same as any one. Headers are multiplied for the sake of 

 correcting the error of excentricity, and of diminishing that of 

 graduation. Now, the error of centering is eliminated from 



^—x — , and also from - — ^ , so that it is necessarily corrected 



