September 11, 1896.] 



SCIENCE. 



345 



The large discrepancies in photometric 

 measures of colored stars led the author, 

 who employs the method of extinctions in 

 his photometer, to investigate the absorp- 

 tion of three principal colors— red, yellow 

 and blue — by differently colored shades. 

 The relative proportions of the three colors 

 in the light of any particular star were 

 measured, and corrections were deduced so 

 that the effect of color was very largely 

 overcome in observations by the method of 

 extinctions. 



Motion of the Great Bed Spot and Equatorial 

 Belt of the planet Jupiter from 1879 to 1896 : 

 By G. W. Hough. 



From the comparison of his micrometrical 

 measures (not mere drawings) of definite 

 points upon the visible disk of the planet, 

 the author obtained the (changeable) rate 

 of rotation of the spot about the planet's 

 rotation-axis, and he showed charts and 

 diagrams of the motions of the belt both in 

 latitude and longitude. No theory of the 

 nature of the spot was advanced. The 

 paper will be printed in the Monthly Notices 

 of the Royal Astronomical Society. 



On the direct application of a rational dif- 

 ferential equation to a series of points whose 

 coordinates represent observed physical prop- 

 erties : By Robert B. Warder. 

 The theory for the speed of chemical 

 action gives rise to differential equations, 

 which are usually integrated before being 

 applied to test a series of measurements. 

 As the theoretical ' constant ' often proves 

 to be variable (showing that the assumed 

 rational formula does not fully represent 

 the processes of Nature), the character of 

 the variations must be determined by one 

 of several modes of calculation. The paper 

 was mainly an inquiry as to the best 

 methods of computing the required quanti- 

 ties. Three methods had been tried in an 

 application to Lichty's determination of the 

 speed of esterification of monochloracetic 



acid, and a further paper (offered with 

 this for publication in the Journal of Physical 

 Chemistry) was read before Section C. 

 A proposed fundamental integral-transcendent : 



By James McMahon. 



A large number of transcendent integrals 

 are reducible to the fundamental form 



/log 



sec X dx. 



which may be computed from a series and 

 tabulated for different values of x. Let the 

 function ils x (integral-log-secant x) be de- 

 fined by the equation 



I log sec X dx = ils x, 



then ils x may be computed and tabulated 

 from the development 



2 ., TTx „x^ . S, x^ . SeX^ , 8a x^ 



V^i^T^^^^s + Ts + sv + lQ--;- 



(where S"' = -^ + -^+-^ ad inf.j 



which is convergent when x <^ 1, and can 



be used when the argument — lies between 



and—, — a sufl&cient range, since ils-^= 

 2 2 



00 and ils = 0. 



Numerous integrals were given which are 

 expressible in terms of ils re, of which we il- 

 lustrate by only three : 



(1) I log cos a; (Zx = — ils a;. 



log tana; (Zx = ils ( — — a; j +ilsa; — 2ils j-. 



(This may be denoted by ilt x, integral- 

 log-tan X.) 



( 11 ) C fT^z^^ = i^* (*^^ ~'^)' ^^^ 



Analogous relations are found for hyper- 

 bolic functions. The paper will appear in 

 the Annals of Mathematics. 

 On the Level of the Sun-Spots: By Edwin B. 



Frost. 



The correctness of the Wilsonian doctrine 

 that Sun-spots are depressions in the solar 



