514 



Mr. J. W. L.*Glaisher on the 



[June 15, 



The question of the variation of (1) the direct and (2) the diffused 

 radiation is next discussed. On comparing the curve representing the 

 chemical intensity of diffused light with the curve-of solar obscuration, it 

 is found that the rate of diminution in chemical action exerted by the dif- 

 fused light is up to a certain point greater than corresponds to the portion 

 of eclipsed sun, whilst from this point up to totality the rate of diminution 

 becomes less than corresponds to the progress of the eclipse. The same 

 rapid diminution in the chemical action of the diffused daylight during the 

 early periods of the eclipse was also observed at Jamkandi ; it is doubtless 

 due to the dark body of the moon cutting off the light from the brightly 

 illuminated portion of sky lying round the solar disk. 



The results of the observations at Catania are then compared with those 

 made at Moita, near Lisbon, and communicated to the Society in 1870. 

 This comparison shows a striking coincidence between the two sets of ob- 

 servations. In each case it is seen that the relation between solar altitude 

 and total chemical intensity is represented by a straight line, although the 

 Catania observations slightly exceed, by a constant difference, those made 

 at Moita in conformity with the slight difference in latitude, and with the 

 fact that the former determinations were made at a greater elevation above 

 the sea-level. 



The Catania observations further confirm the fact which we formerly 

 announced, that for altitudes below 50° the amount of chemical action 

 effected in the plane of the horizon by diffused daylight is greater than that 

 exerted by direct radiation, and also that at altitudes below 10° direct sun- 

 light is almost completely robbed of its chemically active rays. 



VII. "On the Calculation of Euler's Constant." By J. W. L. 

 Glaisher, B.A., F.R.A.S. Communicated by James Glaisher, 

 F.R.S. Received June 6, 1871. 



The main object of the present communication is to correct some inac- 

 curacies both of reasoning and calculation contained in two papers by Mr. 

 Shanks, viz. " On the Extension of the Value of the Base of Napier's 

 Logarithms ; of the Napierian Logarithms of 2, 3, 5, and J ; and of the 

 Modulus of Briggs on the common System of Logarithms ; all to 205 

 places of Decimals," in the Proc. Roy. Soc. vol. vi. p. 397; and "On 

 the Calculation of the Numerical Value of Euler's Constant," in the Proc. 

 Roy. Soc. vol. xv. p. 429 (1867). 



For the calculation of the constant Mr. Shanks has used (as, indeed, 

 has every calculator who has computed the value of the constant during 

 the present century) the semiconvergent series 



,,1,1 ,1 , 1 . B, B 2 , B ' 

 ya=l-f- + -. . . +-- -loea?— \- — \.— — + — -~ . . . , (i) 



r 2 3 as to 2eo 2a? 4a? 4 6a? 8 w 



y being the constant, and B p B 2 , B 2 . . . Bernoulli's numbers. 



