f 488 ) 



radius of llic niolenile), then avc iiiav also snv, tliat avp must dimiiiish 

 I^ \\\\\i liair tlic couihiiKMl xoliiiiics df ilic dislaiicc s|)lier('s. \\ liieli 

 (|iiaiitily is iisiiallv denoted Uy />, or by //y. if wc ^^ isli to take into 

 aceoinit iIk^ \arialtilily of llio ('«(rreclioii in cojisecinence of xaiialion 

 in density. Varions nietliods Iiaxe heen follo\\'ed in order lo inx'estiLiate 

 tliis iiilhuMice: all these melliods yielded a conforinaltle result, so lliat 

 no reasonal>le douht can exist as to the (-(U'reetness of this slatenienl. 

 We slioidil he inclined to deduce from this, that the iidlneiice may 

 he correctly allo\\e<l for in second a|)|>ro\iniation hy diminishinu; 

 I^ \\\\\\ half the \oluine i-eally occu|»ie(l \)\ the distance sjdieres, in 

 which a se.uinent which twd di>tance s|iliere> liax'c in common, is 

 counted only once, or what (-(unes to the same, hy wriliii;^' Ay- — 2i<S 

 iiislead of Ay- , J!i'-'^' ri'|)resi'iitin,ü- the sum of all the seunienis which 

 arc covered hy two distance spheres at the same tim(\ 'I'he correc- 

 tion has heen intioduced in this w ay hy Prof. .1. D. \ an i»kk \V \ \i,s ') ; 

 and Dr. .1. .1. van Laaij') has made a calculation of a second correc- 

 tion term, xvhicli i> hased (Ui a similar supposition. I \\'\\\ howcxcr 

 conline myself to the discussion of the first coi-rectioii term, for whicdi 



1 7 a; . , 



\\p Ijnd in this way ^ ? . I he ipiestion whether the lii-st correction 



lei-ni is c(»rrectly found iii this x\ay has not heen answcied un- 

 animously ill the aflirmati\e. IIoi.t/ma.nn ') follows (piite a dilferenl 



;; //-■ 

 method for calcnlatiiiu- it and linds "^ . 'riioutih Uoi.tz.mann in his 



8 \ 



communication in lhe.se Proceed iiiii's expressed the wish that his 



puhlicarion of this result diirerini:- fi'imi my father's would uive rise 



to a discussion \)\ which this donhtfnl point mi,uhl i»e elucidated, 



no discussion has lollowo<l hy which liie (pieslion has he(>n settled 



coiiclusi\('l\ . Now I think 1 can sli(»w that there is no reason lor 



inlrodiicinu' di(^ correction in tlu' wa\ which \ ields the \alue ;,,,-• 



and at the same time 1 will uive a reasoning, hy which the term 



o ƒ "- 



^^_ is derived in a shorter wav than that followed h\ I)OI.tzm\nn. 



8 V ■ 



The simplest wav to show clearly what supposition we must 



17//;, 

 make in order to uel the correction term ^^ ; is to start Ironi tjic 



1) Versl. Kon. Akad. v. \\'flensL!i. V. \). 150. Oct. 1890. 

 -) Tliese Proct'eding.s V(.l. I. p. 273. Jan. 1899. 



3) These Pruceediiigs Vol. 1, p. 398. March 1899; and -Vorlfsungen iiber 

 Gastheorie" II, p. lol. 



