( :i\v,) ) 



y.v -f ff// = (f {((,i; 4- .-i;/) 



wiil have to determine the same functions /(t) and r/,(;fi) as y = r/ (./■). 



Now the curve i/ = (/{,c) undergoes on account of the sul)stitutions 

 (33) a liomogeneous linear transformation, where therefoi-e the line at 

 infinity and the origin remain invariable. It is therefore a matter of 

 course that the bearing of the curve with respect to these einvariant 

 elements will come particularly to the fore. The form of the func- 

 tions 7(t) and q,{f^) will therefore be generally governed by the 

 mutual position of the points of contact of the tangents out of the 

 origin. Indeed, we read from (21)) 1. lliat q^ gets an inlinite value 

 in the points, for which at the same time holds F=zO and F~ = 0, 

 i. e. iji tl)e points of contact of tiie tangents out of the origin, 2. 

 that c/j vanishes in the points which satisfy at the same time 7^^=: 

 and z :^C), i. e. in the points lying at infinity whilst 3. q^ tends 

 to zero in the points indicated by 7^=0 and H=z{), i.e. in the 

 inflectional j)oiiHs. Ecpiation (32) on the other hand bhows us 

 that / becomes infinite in the |)oints lying at infinity, iji the points 

 of contact of the tangents out ofthe origin and in the inflectional points. 



That the part played l)y the points at infinity can be studied more 

 con\'eniently out of (29) and (32) than out of (18) and (23) is one 

 of the chief reasons why we have included the equation F{.i',t/)=zO 

 in our considerations. 



Geology. — "Xotes on the Sopoetidi Monntnins in tlw .}fin(fh((ssi(" . 

 (Second part). By Mr. M. Kopekbekg. (Communicated by 



Prof. C. E. A. WiCHMANN). 



(Communicated in the meeting of Sept. 30, 1911.) 



The eruption of 190(1 



According to the official telegram of the Resident of Menado and 

 a comminiicalion of Mr. A. Limburg, the meritorious observer of 

 the seismic plienomena at Tomohon, both (pioted in the Natuur- 

 kundig Tijdschrift voor Nederlandsch-lndië, Vol. LX VII, p. 5.5/58, 

 the sym[)toms of new volcanic activity in the Sopoetan-monntains 

 were fii'st observed on the J 7^'' of .lune early in the morning, in 

 the form of a dense colunni of snu)ke, afterwards accompanied by 

 occasional showers of ashes and nnid, among others at Amoerang and 

 at Tondano. After information from the initives a new ci'ater had opened 

 at about 800 M. distance from the Sopoetan-crater, about '/^ bouw 

 i. e. ± 1750 M.' in extent, measuring 45 to 50 M. in width, the 

 contour taken as a circle, from which sand or grit and stones in redhot 



