317 



2. /S — S' . Tiiking into account the precision of the niicro- 

 metrical measurements and the small intluence ot' the systematic errors 

 in the measurements made at Delft, as appears from the values of the 

 mean errors, that term may also be neglected in tryinj^ to explain 

 the great value of ^L. 



3. 4|iA^. 4,i is about 34" and A^ is the difference in the errors 

 of the mean temperatures of the metre, determined at Breteuil and 

 at Delft. When we assume, that in the perfectly constructed 

 comparator at Breteuil the error in the mean temperature of the 

 metre was zero, the effect of an error of 0°,1 in the mean tem])e- 

 rature of the metre at Delft on its length is 3'^4, and in order to 

 get a positive value of AL the temperature of the thermometer 

 laid on the surface of the metre must be lower than the tempe- 

 rature of the metre itself. 



During the measurements the temperature of the metre was slowly 

 I'ising, it is therefore improbable, that the temperature of the thernio- 

 meter should be systematically lower than that of the metre, and it 

 is difficult to explain the positive value of AL, either totally or for 

 the greater part by an error in A^f. 



4. 4A/. I cannot say, what is the real value of A/, the error 

 of the difference I adopted between the length of metre N". 27 and the 

 International metre. The mean erroi' of the adopted value of 4A/ 

 is =b l.'^8. It is therefore possible that a part of the AL may be 

 accounted for by an error in the adopted difference, but it is 

 improbable, that it should explain the whole value, 8". 7 of AL. 



5. 4/A/?. We can determine a' fairly probable value of that 

 term. According to a telegram from Monsieur Bf.noit, the mean expan- 

 sion for J° between 0° and 15°, used in the reduction of the 

 measurements of the [)rolotype. made of the second alloy, is 8'',662, the 

 mean expansion per degree between the same limits adopted in my 

 reductions of the length of N". 27 made of the first alloy is 8''^,493 ; 

 the difference between the two is 0'^169. As a result of direct 

 comparisons, the mean difference of the expansion of the metres of 

 the first and second alloy is 0",02, as I stated above. 



If we assume, that the coefficients of expansion of the metres 

 of the second alloy are really equal and that it is the same with 

 the metres of the first alloy, which assumption after the researches 

 of Bosscha is very probable, the erro!' Ai would be ecpial to 0.169 

 — 0.02 =0//,15. As t is about 15°, the term 4^A,i is 9^ almost 

 equal to the value 8",7 found for AL. 



Although I do not pretend, that the assumptions made in order 

 to explain the difference betw^een the results obtained in Breteuil 



