B. S. Woodward — Iced Bar Base Apparatus. 45 



D + 2Cte — 20B ]7 — Q= v, 



while for tlie reverse position tlie equation is 



D — 20ce — 20B l7 — Q = v . 



The following table gives the data furnished by the first 

 group of measures of the comparator. These data include 

 the observations for personal equation, which give rise to 

 observation equations involving the quantity x only. Although 

 the latter equations should have somewhat greater weight than 

 the others they are all treated as of equal weight in this purely 

 preliminary statement. 



Dal a for length of 100 m comparator. 



Observation Equations. 



Date 



Direction o 



1891. 



Measure. 



1 30 



W to E 



30 



W toE 



30 



W toE 



30 







31 



W to E 



31 





J- 3 



W to E 



3 



.. 



4 



WtoE 



4 



W to E 



4 







7 



W toE 



7 



W to E 



July 30 WtoE D + 20.T — 20B 17 — 39"532= + 



D + 20.T— 2()B 17 — 39-574= + 

 D + 20a:—20B n — 39-660= — 



+ 20.X '— 0-049= + 



D + 20sc — 20B 17 — 39-548= + 



+ 10a; '— o-04()= — 



io-. 3 W to E D + 20aj—2nB JT — 39-643 = 



+ \i)x — 0-061 = — 



D + 20sc— 20B 17 — 39-624 = — 

 D — 20a;— 20 B 17 — 39-476= — 



+ 2()x . . . '— 0-022= + 

 D + 20ck— 20B I7 — 39-528= + 

 U — 20a; — 20B 17 — 39-424= + 



The resulting normal equations are : 



052 

 •010 

 •076 

 •013 

 •036 

 •008 

 •059 

 •029 

 •040 

 •016 

 •040 

 •056 

 •036 



whence 



9D + 100a; = 9(20B 17 + 39 ram )+ 5-009, 

 100+4600 = 100(20B 17 +39 mm ) + 66-610 ; 



D = 20B 17 + 39-522 mra ±0-0H mm , 

 x =+3^-l±0^-5. 



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

 of a single measure of the comparator without interchange of 

 observers to eliminate personal equation, is ±30^. 



Later in the season (Sept. 24 to Oct. 6) a second set of meas- 

 ures of the comparator interval was made. In each of these 

 measures the observers interchanged positions, and on two 

 dates the interval was measured in the direction east to west 

 as well as in the direction west to east. The results of these 

 measures are given in the following table which is arranged in 

 the same form as the preceding table. 



