( 395 ) 



density along the ei'li{)tic w ill liii.iliy bo the same evervwhere M. 

 The adjoined fig. 1 repiesenls I Ik; luulion of the ensenil)le. Every 

 point ot* the originally h()ri/,()ii(al elcnieiihiry area nioxes upwards in a 

 vertical direction \y\\\\ conslani xelocily, so ihal Ihe extension always 

 occn[)ies a slanting area \\ilh an incliiialion <l(Mcnnined hy /i/t( = /. 

 The horizontal areas at dislances 'i.-r from each olher indicate 

 the parts of the extejision, which are in the same point of the ecliptic. 

 Originally these pai'ts haxe been in parts of th(» original area at 

 equal distances from each olhei*. These dislances become smaller and 

 smaller, the snrface elements becoming more mimerons and at the 

 same time smaller. 



I]istead of the constant (piantily S=z | \ I'loij I'tlhUo (/ thought to be 

 co]itinnous) \\c get a variable, when we immediately take together the 



surface elements wdiicli come to the same thing with respect to the 



place in the ecliptic. So we get the quantity Sf, -^ i P' lo;/ F' <il, in 



u 



which F' represents the quantity found per unit of length in the 



conjoint areas, of a width dl and at distances 2rr apart, which 



give the same placijig in the ecliptic. So iji the case referred to, that 



originally a horizontal area wdiose width is c//„ was occiqiied, 



dL dl , dL 



P' dl = V- ^Kji^ ai cot a = :E Pi~'~ so F'z=z^ :£ Fi, in which Fi re- 



1) Gf. POINCARÉ I.e. 



