332 MR. CMYK CUTHBERTSON ON THE 



a large extent allowed for by observing the position of the bands when the 

 preliminary shift ceased and counting the time procession of bands from this starting 

 point. 



It is probably owing to this cause that the experiments in which the number of 

 bands was small yielded the most discrepant results. 



Leaks. In the case of the tube which remained in connection with the manometer 

 a leak could not remain undetected. In the tube containing the substance a leak 

 would produce a discrepancy between the number of bands observed in the upward 

 and downward grades of temperature, and the concordance of the two observations is 

 the test by which such a source of error could be detected. 



A considerable leak would, in the cases of mercury and phosphorus, produce solid 

 compounds visible to the eye. No experiment was accepted as trustworthy in which 

 these tests did not give negative results. 



Reading the Bands. With the aid of a pointer in the field of view the position of 

 the bands could generally be estimated to \ of their breadth, and sometimes I believed 

 my reading to be accurate to yy of a band. 



Weighing. The substances used were weighed on a good long-armed balance, 

 accurate to '01 of a milligramme, or -^JQ part of the smallest quantity ever employed 

 (usually much less). The weight of mercury was obtained from the difference of the 

 weights of a capillary tube empty and full of mercury. The sulphur and phosphorus 

 were weighed by BORDA'S method. 



Corrections. 



Inequality in the Length oftlie Tubes. When an experiment was performed with a 

 tube which had been broken and mended, the two tubes sometimes differed in length 

 by as much as a millimetre, and a correction had then to be made for the variation of 

 the retardation of light in passing through a layer of air equal to this difference, as 

 its density varied with the temperature. 



If the difference of length was 1 millim. and the limits of temperature 1 5 C. and 

 270 C., the correction only amounted to ^ of a band, so that the error due to an 

 inaccurate estimate of these limits is inappreciable. 



Change of Dimensions ivith Change of Temperature. The refractivity is directly 

 proportional to the volume of the tube when the temperature is highest, and inversely 

 to its length ; and since both these measurements are made at the temperature of the 

 air, the observed refractivity has to be multiplied by l+2a(^ ^,), where a is the 

 linear coefficient of expansion of glass and t^ and t* the limits of temperature. 



Unfortunately, the coefficient of expansion was not measured for each tube at the 

 time, and, as the numerous tubes all ultimately broke and the upper limit of 

 temperature was not exactly known, the correction cannot be made accurately. But, 

 as its gross amount does not exceed ^ per cent., we shall not err by 1 part in 1000 by 



