MB. A. E. TTJTTON ON A COMPENSATED INTERFERENCE DILATOMETER. 349 



represents the complementary fraction to that to be added to the punctures of the 

 first interval, so this fraction is set, by exception, over the top of this particular 

 puncture rather than alongside it. It is convenient to actually make this puncture, 

 because the total number of punctures made for the two sets of observations then 

 represents the actual number of dark bands which have made their transit between 

 the starting temperature and the highest limit. 



Three quantities are the result of these observations : 



(a.) The number of whole bands and fraction of a band which have passed the 

 point of reference between the starting temperature and the first higher limit 

 (about 70 C ). This is given by the number of punctures for the first interval plus the 

 initial and final fractions for that interval. 



(b.) The number of whole bands and fraction of a band which have passed the 

 reference point between the first higher limit and the highest limit (about 120). 

 This is equal to the number of punctures for the second interval minus one, plus the 

 initial and final fractions ; or, which is the same thing, the number of punctures plus 

 the final fraction for this interval minus the final fraction for the first interval. 



(c.) The number of bands and fraction of a band which have made their transit 

 past the reference point between the starting temperature and the highest limit. 

 This is given by the sum of the total number of punctures and the initial and last 

 fractions. Naturally, c = a -\- b. 



If we retain FIZEAU'S symbol, f, for the number of bands and fraction of a band 

 passing the reference point during a given interval of temperature, the alteration of 

 thickness of the air film denoted by the observations for that interval is approxi- 

 mately equal to/^X, where X is the wave-length of the particular light employed to 

 generate the bands. The wave-length of the green mercury line is 0'00054GO millim. 

 The word approximate is introduced because there is a correction to apply for the 

 alteration of the refractive index of air, and consequent variation of the wave-length 

 involved, due to change of temperature and pressure. The result of this alteration 

 in the wave-length is that the number of bands actually observed to pass the fixed 

 point is slightly different to the number which would have been observed if no 

 change in the wave-length had occurred. This correction is very small, only a small 

 fraction of a band, when the air film is thin, as is usually the case ; but it is very 

 considerable, amounting to a tenth of the whole value, when the thickness is 

 relatively great, as it is during the determination of the expansion of the tripod. 

 The nature and extent of this correction have been fully discussed by both BENOIT 

 and PULFKICH (loc. cit.), and the formulae arrived at by each of these observers 

 lead to the same result. After employing both, the author finds the form of 

 expression given by PULFBICH (' Zeits. fur Instrumentenkunde,' 1893, p. 456), rather 

 more convenient, as the values of several of the factors can be taken directly from 

 LANDOLT'S, ' Physikalisch-Chemische Tabellen.' The formula is as follows : 



