80 Intelligence and Miscellaneous Articles. 



one or two units near the fifth decimal place, by either of the formulae* 

 (n — 1-52642)(\ - 1-5182 x 10" 5 ) = 7-7733 x 10-7, 



(n'—l-53519)(\— 1-5504 x 10~ 5 ) = 7-8594 x 10-7 . 

 calculated by taking the mean of the very concordant measurements 

 of the indices made by Rudberg, Mascart, and Van der Willigen, 

 taking for the wave-lengths the means of the measurements made 



o 



by Mascart, Ditscheiner, Van der Willigen, and Angstrom ; the 

 latter numbers were transformed so as to correspond to the wave- 

 length X D2 = 5-888 x 10 - 6 adopted by M. Mascart. The constant 

 of the grating having been determined each time so as to satisfy 

 this condition, we see that the thicknesses are provisionally 

 measured as a function of what M. Mouton calls Fraunhofer's 

 millimetre. 



II. A double correction for temperature must be introduced in 

 the thicknesses thus calculated. If by 6 we denote the tempera- 

 ture to which correspond the indices given by the f ormula) above, 

 by t that at which the measurements were made, the thickness e , 

 at 0° of the plate, should be calculated by the formula 



2e (l + kt)(n+vd-vt—l)=p>\; 



k, v, and v being coefficients determined, the first by M. Benoit, 

 the two others by M. Dufetf . It is more simple and just as exact 

 to correct the thickness e , originally calculated by one or other of 

 the two simplified formulae, 



e = 0-999741(l -0-0000019 t)e ordinary rays, 

 or e = 0-999709(1 -0-0000001 t)e extraordinary rays. 



These two formulae J apply to the case in which the plate is cut 

 parallel to the axis. 



III. I applied this method to two quartz plates cut parallel to 

 the axis made by Hoffmann. The thinnest of them measured 

 directly (123 bands observed, ordinary rays) gave 



e = 0-402958 cm. +0-000001. 

 On the other hand, we measured the difference in thickness of two 

 plates (123 bands observed, extraordinary rays). From this was 

 deduced for the thickest plate, 



<? = 0-602316 cm. ±0*000003. 



IV. "We may add that this method may lead to a new determi- 

 nation of the absolute value of the wave-length of the ray D 2 . The 

 thickness of the second plate, which M. Benoit kindly measured 

 with the apparatus of the Bureau international des Poids et 

 Mesures, was found equal to 0*60236 to within 1m- or 2^. From 

 this we get for the wave-length of the line D 2 , the number 



A=5-8884xl0- 5 , 



o 



which is exact to within -^Vim and is very near that of Angstrom 

 (5-8889). — Comptes Bendus, June 2, 1885. 



* Cornu, Annates de I'Ecole Normale superieure, vol. ix. p. 42 (1880). 



t Journal de Physique, 2nd series, vol. cxi. p. 252 (1884). 



X It has been assumed that = 20°. As this temperature is scarcely 

 known to within 4° or 5°, there is an uncertainty of about ^-joo- 



