[king] DETERMINATION OF AVOGADRO'S NUMBER 61 



may be remarked that these relations may be obtained in a very general 

 manner independently of any assumptions regarding the atmospheric 

 gradients of temperature and pressure, provided that the planes of 

 equal density be parallel to the earth's surface. 



The accuracy of the experimental measure of the zenith trans- 

 mission a = e- C * rests ultimately on the ratio of two galvanometer 

 deflections, or the measurements of two ordinates of a holograph 

 record, quantities measurable to well within one per cent. Owing 

 to the occurrence of the ratio only, corrections due to the imperfect 

 reflecting powers of mirrors, absorption by prisms, slight refection 

 from the bolometer-strip, etc., do not appear. The determination of 

 the remaining observed quantities, zenith distances of the sun, wave- 

 lengths and barometric pressures are all measurable to a high degree 

 of accuracy, so that it does not seem too much to say that the zenith 

 transmission can be determined over a considerable range of wave- 

 lengths to an accuracy well within one per cent. 



Data on atmospheric extinction recently made available by the 

 publication of Vol. III. of the "Annals" of the Smithsonian Astro- 

 physical Observatory are given in terms of the zenith transmission a, 

 for the most part over a range of ten wave-lengths, avoiding regions of 

 selective transmission. The average zenith transmission a is deter- 

 mined for a large number of days each year; unfortunately it is not 

 quite exact to derive the mean coefficient of attenuation as loge a ; 

 the error committed is difficult to estimate beforehand but will be 

 negligible only when the attenuation coefficients are small or when 

 they deviate very little from their mean value; actual trial shows 

 that the error committed may amount to as much as 2 or 3 per cent. 

 In addition, there is the probability that the constants 13 and y are 

 independent variables; for these reasons it seemed advisable to the 

 writer to determine and y independently from each day's observa- 

 tions from the constants of the line of closest fit (calculated by least 

 squares) corresponding to the formula C x = y + ^ 4 , taking as 

 variables C x and X -4 measured in units chosen according to a suitable 

 scale. The computations were very ably carried out by Mr. A. A. 

 Scott, M.Sc, and Mr. Etienne S. Bieler, both of McGill University, 

 working under a grant from the Rumford Fund of the National 

 Academy of Sciences. The daily determinations of /3 and y have 

 now been extended to all the transmission observations as yet pub- 

 lished by the Smithsonian Astrophysical Observatory. Comparison 

 with theory is most conveniently made by calculating n according to 

 the preceding formulée. For each selection of wave-lengths a value of 

 ( JUo _ 1)2 lighted according to X -4 was employed, while the baro- 



