124 Mr. Nixon on the Measurement {by Trigonometry) of the 



t' — ;•' ; and — the correct measure of the (constant) refrac- 

 tion in terms of the arc*. To insure success to the calcula- 

 tion, the smaller arc should be considerably inferior in mag- 

 nitude to the larger one, and be derived from very numerous 

 data. If we have given any number n of arcs with their re- 

 spective observed refractions, each affected by the unknown 

 error — x, the sum of the latter will contain — xxn; which 

 sum, divided by n, will give the true refraction minus xxl, 

 (or equivalent of the observed refraction) of the ?ith part of 

 the sum of those arcs. 



The sum of the 10 /; the sum of their u 



first arcs is 2509; refractions 46 neg. 



One-tenth 251; one-tenth... 4.6 neg. 



The sum of the 9 last the sum of their 



arcs is 7167; refractions 406 pos. 



One-ninth 796; one-ninth... 45*1 pos. 



Then, as the greater and its observed 



arc is 796; refraction 45*1 pos. 



And the lesser arc 251; 4*6 neg. 



The true refraction of 



their difference 545" will be equal to 49*7 pos. 



The constant refraction being evidently-— — , or very nearly 

 — th of the contained arc, it follows that the difference be- 

 tween that proportion of either the greater or lesser arc and 

 its observed refraction will be equal to the constant error of 



observation. Hence —■ - 45"- 1 ; or -~- - ~4'6 = 27"*5; 

 whence the formula must be — 27"'5. 



On comparing the observed refractions with the quantities 

 furnished by the formula, the deviations will be found, in al- 

 most every instance, to be not only trivial, but, what is equally 

 conclusive of the justness of the rule, they are alternately po- 

 sitive and negative, without regard to the extent of the arc. 

 The discrepancies exceeding 6" are but four in number, and 

 admit of considerable explanation. At Shunnor Fell the tele- 

 scope has in all probability been pointed at the top of the wall 



* On the same principle the index-error ot a box-sextant may be conve- 

 niently found. Let a terrestrial object A lie between two others B and C, all 

 the three, as well as the eye of the observer, being apparently in the same 

 plane. Measure the arcs AB, BC, and (their sum) AC. From the latter 

 subtract AB, leaving the correct value of BC, which will differ from its ob- 

 served measure by the amount of the index-error. 



on 



