( 'i9^^ ) 



to a far greater (le})lli and when they liad been taken ont of it, they 

 (lid not so easily regain tiieir former snpijorl. 



DuRAND (1845) gave the exphination whieii a large, old seedling 

 on mercnry snggested to him. It had stayed so long on it, that 

 an adhesixe layer had been forinetl on the mercury of snfticient 

 thickness to fasten the plant to some extent. That therefore all 

 seedlings whose roots penetrate into mereniy, should stiek to it by 

 such a layer is not true. The peiietration takes [)laces after a short 

 time Avhen the mercury is still bright. 



DuTKOCHKT (1845) accepted Durand's explanation and made expe- 

 riments on the formation of the sticky layer. Hut he did not put to 

 himself the question whether in all the obser\ed cases such a 

 "plaster" had been present. 



WiGAND (1854) has undoubtedly obtained Pinot's results. In his 

 discussion however he confused and complicated the question as 

 Mulder had done. For this reason later imestigators did not bestow 

 much attention to the paradox which he had so clearly pronounced. 

 Where he speaks of peneti-ation into dry mercur}', this must cer- 

 tainly not be taken literally; the soaked seeds retain a layer of water. 



HoFMEiSTER (1860) Studied the penetration of roots in relation with 

 his theory of the plastic apex. He did not obtain the result of Pinot 

 and WiGAND and acce[)ted Durand's explanatioji which also I )rTKO(iiET 

 had accepted. 



Later investigators all followed Hofmeister's o[)inion. 



Mathematics. — ''The harmoaic curves hi']o)i<i'ni<i fo a ^jiri'ii it/ttz/c 

 cubic curve.'' By Prof. Jan de Tries. 



1. The "harmonic" curve of a given })oinl I* with resi)ect to a 

 given plane cubic curve /■'' is the locus of the i)oinl H se})arated 

 harmonically from P by two of the points of intersection A^,A.^,A^ 

 of k^ and PH^). We shall determine the equation of the harmonic 

 curve /i' wdien k^ is indicated by the equation 



«'2 = ^''.l = («l '^'1 + «2 ''>'■! + <'3 •'^'zf^^ ~ ^' 



and P by the coordinates (//i, y.^, yO- 



^) Tliis ciu'vc appeal's in Steiner's frcali^^e : "Ufbor solclio algclti-aisclic Ciirvcn, 



welclie einen Millelpunkt hahon, " (J. of Crcllc, XLVIl), and is Uicrc more 



generally spcciued as a curve of order v. Slereomctrically it has Iteen determined 

 by Dr. H. de Vuies in liis dissertation: "Over do resldoor.snede van twee volt-ens 

 ecne vlakke kromme persp:_H'livisclie kegels, en over satclliclkioiiinicir', Amsterdam 

 I'JOl, p. G and 88. 



