( 662 ) 



Tims the pntjeclioiis on the .///-piano of the cMirvcs (>' are of two 

 (listiiR'l eatejiories. To the first heh»iiü' tlie straiuht lines ,r=zii, i/=^/i, 

 reu'iilarlv dix idinu t.lie ry-plaiie in etpial s(|nai'e> of side niiitv. The 

 second category is formed liv siraiuht lines issninu' from theNcrtiees 

 of these scpiares and which, if j)i-odnfed. xNould pass thronuh the 

 oriiiin. The nnmUei- of these lines, which lia\<' llieir poiiMs of issne 

 inside llie scpiare. honnded hv the .r-a\is. the y-axis and 1>\ the lines 

 ,i!=iii, 1/ = i> i^ '^ceji to l>e '22l(/{/i) ^), thai is on an a\('i-a,U(' e(|iial to 



I/-, riierehn-e llic partial surlaees remote from the oi-iiiin nltimaleh' 



.T 



take the form of iidinitelv narrow strijts. the length of which varies 



IVcmi I to I '2. 



In order to lower as far as possible the deiii'ce of (lie snrface S, 



we slionld take /,■ =z \ an<l we liax'e from (\') and ( VIj 



1 

 1 /• l"=r'J /u,f\ 1 1 ,-' 



12 J I „=i \.vj 2 ] // 







A c(nn|)arison with I \' makes it e\ident that for inte.U'oi" \alnes 

 of .r aii<l // the (pianlilv : still becomes e(|nal to the urealest common 

 di\isor. The snrface N is of the (>''' dejii'ce, the |)arlial surfaces still 

 lianu' louether evervwliere Inii in this case tliev ha\ e no contact alonjx 

 the cnrves C'. 



Physics. — "(hi iiitl.riiiKi tllid iiniiinni of iiili'listi ij sonicfnins ulisrr- 

 ri'(/ ii-ilhiii tin' sIkkIiiki i<t stroiiiflij ii'idi'in'd sjxrlrd! hill's^ ^) 

 \\\ Prof. W. II. .In.ns. 



While e.xamininLi a series ot' |»hoto,i!rapli> of the solar spectrnm, 

 mad(> l)v Uowi.wn in IH(S<S and 1S81). .Ikwkm, discovered one plale 

 on which the shading' of // and A' was hroken np into a s\'.stem 

 of faint, neltnlons lines, svmmelricallv arranged ahont the central 

 absorption lines''). The distances apart of the component lines of 

 the series increaM'd as the distance fnmi the centj'al line increased. 

 On some other pliologra|)hs of the solai' spectrnm, taken hv Iv()\vi,a.nd 

 and bv himself, he onlv fonnd feeble indications of these series: bnt 



^) y (ii) denutes llie iiuinl)or ot integers less than n and prime to n. 



-) l^ait, uf the (oiileiiLs ot this comniuuication lias already been sliorlly menlioned 

 in a iool-iuite which was added to the English translation of a former paper 

 (Proc. Roy. Acad. Amsl. IV, p. (>01) but did not occur in the Dutch original of 

 the same. 



•5) L. E. Jewell, AsUuphysical Journal, III. p. lUS, t^W, and VUI, p. 51— 53, 1898. 



