313 



the tirst alloy would iilso have veiy cippioximatclj the yume value 

 (Vol. II, p. 314), whereas accordnig- to the measurements of the 

 Duti'li Commission the difference in expansion of the metres 19 and 

 23 is too small to l)e observable. (Vol. II, p. 314, 315). This is 

 not quite in accordance with Fizeau's results (Vol. II, p. 323) obtained 

 at 12°, 42°. and (32°, as these give for 19 and 27 somewhat difïerent 

 values. But if the quadratic term is taken into account, the coeffi- 

 cients of expansion at 40°, the mean temperature used by Fizeau 

 in his measurements, would be according to his formulae 8'^74 for 

 19, and 8''.75 for 27, so tiiat in connectiou with the equality men- 

 tioned above of the expansion of the 4 first-named metres of the 

 "metal du conservatoire" and the equality of the expansion of J 9 

 and 23 found by the Dutch Commission it may be inferred, that all 

 the metres of the firsf alloy have also the same coefficient of expansion. 



The next question is, what the difference is between the coefficients 

 of expansion of the first and second alloy. 



According to measurements by Benott and Guillaume with Metre 

 6 of the 2"'^ alloy the mean expansion between and 20" per 

 degree and per metre is 8'^617; according to measurements by 

 FiZEAU the mean of the same expansion for metres 19 and 27 of 

 the first alloy is b.'^537, i. e. a difference of O.'^OB. It is necessary, 

 however, to observe, that the two values were obtained by altogether 

 different methods, that of BexNOit and Guillaume by ordinary measure- 

 ments of length at different temperatures, that of Fizeau by his 

 well-known interference-method. 



Against these we have the determinations of the differences in 

 expansion of metre 6 of the 2'"^^ and of metres 1, 3, 12, and 13 of 

 the 1st alloy (Vol. Ill p. 77) all from ordinary measurements of 

 length at different temperatures. As the result of these 0^02 is 

 obtained as the average of the differences. 



Taking into account, that, where the methods of observation differ, 

 systematic errors in the differences are possible, it seems to me 

 probable, that the latter result is the more trustworthy. 



In the reduction of the Dutch metre 27 to the International metre 

 the difference in length of metres 23 and 27 also plays a part. 

 For this difference two values have been determined ; in 1879 the 

 Dutch Commission found 27 -23 =0-.92 ± 0^031 (Vol. II, p. 297) 

 and in 1880 the same commission found 27 — 23 = 0".41 ± 0^073 

 (Vol. II p. 334). Of the latter value no further use has been made 

 by Bosscha; it seems to me, however, that it is preferable to use 

 the mean of the two results, taking into account the respective 

 weights. In that case the result is 



