46 i?. S. Woodward —Iced Bar Base Apparatus. 



Data for length of 100" 1 comparator. 



Observation equations. 



mm mm 



D + 20£ — 20B 17 — .'39-272= + 0M34 

 D — 20j»— 20JB 17 — 39191 = + "149 

 D + 20x— 20B 17 — 39*394=+ -012 

 D — 202 — 20B l7 — 39-320=+ -020 

 D + 20^— 20B 17 — 39-432 = — '026 

 D — 20cc—20B 17 — 39-369 = — '029 

 D + 20SC— 20B 17 — 39-422 = — -016 

 D — 20aj—20B 17 — 39-370=— -030 

 D + 20cc— 20B 17 — 39-512 = — -106 

 D — 20a; — 20B„ — 39"449 = — -109 



The normal equations from this group are : 



Date 



Direction of 



1891. 



measure. 



Sept, 24 



WtoE 



24 



W to E 



Oct. 2 



W to E 



2 



WtoE 



2 



E to W 



2 



E to W 



6 



W to E 



6 



W to E 



6 



E to W 



6 



E to W 



whence 



10D+ 0a?=10(20B„ + 39) + 3-731, 



+4000 =■• +6 660; 



D = 20B 17 + 39 373±0-019, 

 x= 1^7±l^-0. 



The probable error of an observed quantity of weight 1, or 

 the probable error of one measure without interchange of 

 observers, is dz61 i ". 



The values of D resulting as above from the two groups of 

 determinations differ by 0'149 mm , a quantity which is about ten 

 times the average of the probable errors of the separate values. 

 It seems most probable, in view of our experience on the 

 standard kilometer, that this difference is due to a movement 

 of the end marking stones of the comparator. The residuals 

 of the second group of measures indicate a progressive change 

 of this sort. 



The data of Oct. 2 and 6 indicate that measures made in 

 the direction west to east give smaller lengths than measures 

 in the opposite direction. Thus the lengths for Oct. 2 are : — 



ram 



Direction \V to E 20B 17 + 39-357, 

 " E to W 20B J7 + 39-400, 



Their difference is 43 1 " and the corresponding difference for 

 Oct. 7 is 84*". They show an average difference of 64*", which 

 is equivalent to an error of l'"-6 per bar length relatively to 

 the mean of a forward and backward measure of a line. 



Results of measures of standard kilometer. — In the meas- 

 ures of the kilometer the observers always interchanged posi- 

 tions in reading on the bar. The results may then be regarded 

 as free from personal equation except so far as such equation 



