September 13, 1901.] 



SCIENCE. 



395 



usual hypothesis that the path is a parabola. 

 The body was moving nearly in the plane 

 of the ecliptic, and caught up with the 

 earth, which was traveling less rapidly in 

 the same general direction . The search for 

 fragments will continue. The paper will 

 be illustrated by a large map showing the 

 meteor's path across the country, and by a 

 drawing exhibiting the relation of its orbit 

 to that of the earth. It will be published 

 in Popular Astronomy . 



' Divergent and Conditionally Convergent 

 Series whose Product is Absolutely Con- 

 vergent ' : Professor F. Cajori, Colorado 

 College. 



In an article on ' Divergent and Condi- 

 tionally Convergent Series whose Product 

 is Absolutely Convergent/ in the Trans, of 

 the Am. Math. Soc, Vol. II., pp. 25-36, were 

 given special cases in which an absolutely 

 convergent series is obtained as a result of 

 multiplying two conditionally convergent 

 series together, or one conditionally con- 

 vergent series by a divergent series. But 

 the sum of one of the two factor- series of 

 each pair given in that article is zero. In 

 the present paper it is shown that this is 

 not a necessary property of conditionally 

 convergent series whose product is abso- 

 lutely convergent, and that the nth sum of 

 such series may be of the degree — r, with 

 respect to n, where ^ < r ^ 1. 



' The Application of the Fundamental 

 Laws of Algebra to the Multiplication of 

 Infinite Series ' : F. Cajori. 



The behavior of infinite series with re- 

 spect to the laws of algebra may be consid- 

 ered under two heads : An inquiry into 

 the validity of the laws ; (1) when applied 

 to the terms of an infinite series ; (2 ) when 

 applied to the infinite series themselves. 



The second inquiry, when made for 

 the multiplication of series, leads to 

 the conclusion that in this operation 

 (assuming Cauchy's definition for the 

 product of two infinite series), the asso- 



ciative, commutative, and distributive laws 

 are obeyed. 



The two series obtained by removing the 

 parentheses from the series, 



' ~p^o \4j9'- + 1 4j)'- + 4 "^ 4^'- + 1 



^\ 



4/ +4/' 



p=oc / 



42f + 4 4:f-\-4: 



1 



Af + 1 



4:f + 1 



) 



where |^<;r^l,are conditionally conver- 

 gent, but their product is absolutely con- 

 vergent. 

 Hence, 



{S^S2){S^S2){S^S2) is abs. convergent. 

 But 



{SyS,){S^S.;) {S,S,) = ^1^ . ^^3^ and 



;S'/ and S^ are each divergent when r < f. 

 Hence, when ^ < ^ < f , 'S'/ and S.^^ are two 

 divergent series whose product is absolutely 

 convergent. 



' On Systems of Isothermal Curves ' : Pro- 

 fessor L. E. Dickson, University of Chicago. 



The object of this paper is to give an 

 elementary geometrical definition of a sys- 

 tem of isothermal curves in the plane. The 

 definition is readily extended to families of 

 curves on any algebraic surface. Two fami- 

 lies of curves are discussed at length. From 

 these the general definition is apparent. 



' The Plane Geometry of the Point in 

 Space of Four Dimensions ' : C. J. Keysek, 

 Columbia University. 



The space under investigation is the point 

 (in 4-space) regarded as the assemblage of 

 all the lineoids (t. e., ordinary 3-fold spaces), 

 planes and lines containing it. This space 

 is 3-dimensional in lineoids and in lines, the 

 lineoid and the line being reciprocal ele- 

 ments ; it is 4-dimensional in planes, the 

 plane being self-reciprocal. The plane being 



