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Htm York 1 4609 '■\a '..a^ f''6) *8? -0300 ■ Phone ^S ''6) 288 - 5989 fa^ Keiirintcil from I IIK A-l Ri'I'H VMi Al Im KNM, Vil. X\V. Ni ;, April 1907 "7 CO 1X1 THE CHARACTER OF THE STAR IMAGE IN SPECTROGRAPH IC WORK 1. S. I'LASKEIT I'KIMKI) M rilK t'NlVKRSirV OF CIllCAtiO IKh-S 'P i THK CHARACTKK OK THK STAR IMACJK IN SPKC TRO- (JKAIMIIC WORK liv J. S. I'l.ASKll r The object of this paiur is to descrihr sonic experiments on ilic size and form of the star ima^e fiiven hy the comliination of olijtctive and correcting lens, with an investigation into tiie i iiisis of the observed efficts and suggestions for the improvement of existing conditions. The equipment of the Dominion ( )i)Mrvatory, Ottawa, for radial- velocity work consists of a 1 5-inch telescope with a Hrashear visual ob";'ctive and photographic correcting kns, and a spectroscope of niversal type, also by Hrashear. The objictive for \isual pur- •.s is excellent, and the siKctroscope is admirably adajitcd for f^eueral sj)ectroscopic work, but, as the experience of others as well as myself has shown, is not suit,d)le for the accurate dt termination of radial velocities. Its design as a univers.d siactroscoiie dois not give sulTicient stability, and, in exinisures of any length, llexure will not only ruin the defmition, but is liable to introduce systematic errors in the velocities obtained. Pending the construction of a spectrograph specially designed for the reipiired purjuise, an attempt was made to render the |)resent instrumc nl capable of giving acdir.ite velocity values. The investigation and removal of the known sources of error led to thi' discovery of the aberrations to be pn>< ntly described. .\ brief description of the steps leading tlunto i. ,iy be of interest. Trusses connecting the various parts of the instrunnnt, where flexure could occur, with the supporting tul)es were applied to such effect that an initial displacement of the spectral !ini-s, equi\alent to a velocity of 30 km per second, occasioned by a movement of tele- scope and spectroscope through two hours in right ascension, was reduced to j\ km. The prisms were tirmly damped in place, without inducing strains in the glass, by screws ]iassing through '' v base of the i)rism-box and the minimum-deviation linkwork into he prism- cells. The slit-jaws, originally too thick on the edge, were reground, 1(/) J. S I'LASKFTT ;in(] the occulting (ii^q)lir;ij;ms for star ami spark lij;ht \m ri' r> moved from tlu' slit-hiail ami placed on m imirptmltnt franu' attached to the sup|K)rtinK tubes. ' '"' eomparison apparatus was renKxleled, the direction of the spark lieinf; made iransxcrse to, instead of parallel will), the slit jaws, and many otlur smaller di tails were (artfully attended to. After all known sources of error in the spectroscoj'e itself had lui n ovireonie, and after it had \mn jilaced in thoroiiuli adjusinnnt, it wasfoimd that test s])ectr.i of the standanlvi lot ity stars occasion.dlv };.ive Values dilTeritif^ hy as much as ? km jur si cond from those obtained by other ob^rMrs. As the probable i rror of the mean of thi' measured lines did not exceed four-tc nths of a kilometer, and .,s all the other known causes of systematic error had been overcome, it seemtd probable that this mij,'ht be I'iie to uns}nimetrical distribu- tion of tin Iacement of o. i mm from the focus, a distributioi. of the star li^;ht on the collimator objec- tive so that its center of intensity is 5 mm to one side of the axis, is sulVicient tocausea(lisi)lacem' nt of the spcctralline j^t X,'„ =7.1,,, mm e(|uivalent to a velocity of 1 .8 km i>er second. .\n examination of the illumination pattern on the collimator lens, both visual and pliotoj^rajihic showed how easily such or even greater displacements of the center of intensity could occur even with the utmost care in guiding. The illumination could never be made uniform, no matter how the relative positions of slit and corrccting- lens were altered. The jiattern was either a diametrical bar parallel to tile slit of a width about one-third or one-fourth the aperture, or else such a bar w ith the addition of a peripheral ring; while a very slight movement of the slit-jaws to one side or other was sufTicient to cause .sy.U" iMM.i: IS srixiKOiiKM'inc wokk ")7 om- side only of tlu' Inis to Ik- ilhitnin.ilcl, uiilmut iMiisin^' ,my a|'|>ri I i.iblf cli.iii^;f in the .ippiMr.inic ol tin ini.ii,'i' in tlu miiilint; lrli>"()|H', >;iiidin^» brin^ done by nifiins of li'^lil minitii; tiirou^li tlu' >lil. It istM>\ to SCI' how till' ctntirof^inltn-ity of tlu -t.ir li^lil miild bi' di^plicKl without the ol)Mrvi-r biini; ;iw,in of liu- f.nl, llui-' i.iii-,- inj? .1 (li>iil.utnu'nl of tlu' st.ir linrs unlr>-. tlu- plate utri- in ix.ict fotus. The :ii(p<-:irann' of this pattern and its bihi\ior for ihini^'c of >lil |K)>ition indiiMtiil >phiriial alurraliun of the Kindeii-^ini; >\>tein. I'hal aberrations of sonu' natiiri' '.vere present \\a^ inili( ati il luit only bv the loni; expo->ures retpiired ii]iw,ird of two hours for i star of the fourth |ihoto'4raphie niai;nituiu)wi'. '.y tlu- wide optiiiiii;, o.j, nun, of the slit requireil to obtain uniform illumination. An examination of the correi tint: Kns showed that part of ti\t' dilVuultv might arise from tlie aciidinlal in\ersion of the divertjin^ elenuiit, whieh iiad been so pl.ued in the eell that surfaces of unlike eLir\aluri' were adjacent to each otiit r ( )n in-.trtini; tiiis (oncavc element so that surfaits of like radius of curvature were in lont ut, the illumination i>attern became more uniform, the ri(|uirc d exjM)sure time was diminished by 50 per cent, and no irmrs of a jjreater m ij;ni- tude than should be expected with the dispi rsion imployed, apjicirtd in velocity determinations of standard stars. If tlu' diameter of the oi>ject-!:lass, 15 inc''es. and the linear dis]ler^ion of tlu- spiitrograiih, 18.6 tenth-meters ler miiiimeter at //*/, l)e taken inio account, the ex|)o>ures re(|uired less tii.m an hour for stars of the fourth l>hotographii magnitude com j)a'' very favorably with tliosi of other e<|uipnKnts. Notwitlistandin;; tlie great imjirovement shown, iihotograjihic tests of tile star focus for dilTerent tem])eratures indicated that the star >pectrum was much wider than could nasonably be accounted for by atmospheric disiuri)ance, and I was led to make thorough tests of the character and diameter of the image. To determiiH' whether a narrower spectrum lould be ol)tained bv a change in adjustment, a i)la!v w.is made for each of six settings of the correcting-lens, abovi' and below its computi'd position, over a range of four inches. \ simple device applied to one of the pl.ite- 198 /. 5. PLASKETT holders iniblftl ten succissivc star s| tra to Ix- made side hy siilc on iMcli of tlitsc plalis, at dilTcrint sitnnf^s of llu- slit jxjsition in the ncij;hlx)rhood of th«: star focus; the sixiy sjuitra forniinj^ a niord of the diameter of the star ini.iKe under x.iryin^ eoniiition>. To in>urc that the siKdrum had not Ijeen widened by a drift of the star image aloni; the slit, the s|KCtrosto|ie was turned in jiosiiion angle until the slit-jaws weri' parallel to an hour linle. \\\ ojuning the slit o. 2 mm, and by using a bright star, Vej^a, a fully exiK)sed linear sjiee- trum was obtained in eight or ten seconds, evidently with no chance of widening due to drift. The width of the narrowest part of the narrow- est spectrum on eacii plate, presumably where the star was in focus on the slit, was miasured, and these widths ranged from 0.085 '" ° "5 mm. As the camera and collimator objectivis are of the s;ime focal length, antl .is oni- second of arc in the focus of the refractor is e(|uiv- ulent to 0.OJ75 mm, the dianv.ter of the star image according to this test must be between V' iind 4.'5. The diameter of tlie central dif- fraction disk as given Ijy llie formula d " -— is, for a i^-indi objective and //> light, about 0^57, while the actual elTective diam- eter as obtained from the width of star spectra is live to eight times as great. This enlargement of thi d'lTraerion image may be due to three causes: (1) aberrations in the sjH'ctrosco])e; (2) atmospheric distur- bances; (3) aberrations in the system of objective and correcting-hns. I. Abfrrations in the spectroscope- l\. is a simph' matter to deter- mine whether the wide star spectra obtained :ire due to this cause, for by direct photography of the star image no aberrations in the s|)ectrosco[)e can atTect the result. ;\ series of star trails was there- fore made on ordinarv' ]ilates by the system of objective and correcting- lens. A small plate, held in guides in the slit-cap of the siKctroscope, could lie moved in these guides between e.\|x)sures so as to make a number of trails on each pl.ite. The (ollimator tube, carrying the l)late with it. was moved by the rack and pinion al)out a quarter of a millimeter between each exposure, to insure having one of the trails within an eighth millimeter of the focus. .\ plate each was made of six st;'rs ringing from the third to the sixth magnitude, and the width of the narrowest trail on each plate, corres|)onding to the S7 I A' nt U.I l\ .S77( I KiU.h: I/' II I 'AA I')') jKcilion wluTr 'hi- >t.ir \\;i> nm-t :ii.irl\ in Imti-. u.i- mr.,>iir. .1 .\lllii)ii^;li till iuti(liii(>n> nl sninu Imtli lor ir.nl- i^l 'imtr,! vm r. ,il>i'M- tlu' .iMMHc ,,'• ! ; in .1 M , lit 111 ;. tin ir.nl- \m ri nci . nniinu oil- l>ut liroki n ,inil ji^j^iil. owinn to .ilnto-iiln rii ili-turh.inn -, .itt'l llu nuM-iin iiunt- wirr in^nlc in two \\,iv>: I'lr-t, of I'u- wiilili oi n.irrow -liori p.iri-of tin ir ' • ulnri' ilu mi ini; h.nl Im iioiniiitariK stiMilv; and, -cionil.of the .,\(r,ij;<' wiilili ni a lon^^i r -trip ol tr.nl. In tlif rir>t si-rii-of niiM>-Mr(inrnt- tin- widiii^ \.irir(l from o 070 nini in ihr f linti r -i.irs too 110 mm in llu lirii.;liti r »t,ir-. wl.li tin at r i^t- wiilili^i of lonv;t r -iriif- wirt- .iIhuiI .'o \»r tint, '^rtii.i >ii\« 1 llu witltli of -ix'dri NMTf |.r,ntii.iliy tin -,nu. it i.> i\ii!. m ili.ii \U> i.iiHt' niu>l l)f >oiii;lit in llu- >l.ir im.iK> il-tif, .iml i- iu>i ilm to iln rr 1 tion- in llu ■']ii i iroM opt-. .'. Aliiiii^filicirii ilisliirl'iiiiit^ Ntu.iU in hi- p.i|it tin i|i-ii;n of >|>ti irojir.iph-' li.i> introilut I il .1 m ry um ;! »i>iu .on, iliil of inmor (ii-k-, .iml In -t.itt- ili.it almo-] lu -■■ ■! -!iiri>,itu t- tnl.irm- tlu- tl'liilivt- liianuti-r of l!u- ■~i,ir !n,,ii;i Si '• • nl..p.,'t nu nl ni.i\ Im- tliu- 1 iilur to boilih ili-i>i.iit nil III : In im;i:,'t .1 an ii> iiu ,in )"'-iiion or lii tlu- sprcailinj; i>iil of 1!" 1 1 riii.i. ma^'t- intt. .1 nrirr or It -- 1 Ap.itul {■i\ ili-k. lit- iDii-itltr- ih.ii tlu- .uiu.il tlTt-tt, -o f.ir ,i> yt-ttiiv.^ li^hl tlirouuli llu- -lit of a -pit irour.ipli i- tonttrnnl. i- tlu- -anu- a- if llu- ima,i;t tiin-i-li-(l of a untral tort- from 1" to j" in ilianu It r -iirronnilt d l)v a mori- t)r li— ililTu-t- ami ^'railu..ll\ illmini-liini^ porliiui. llu- wliol-- (lianitti-r lu-ini; in llu nt iuliKorliootl of \" or :;". If \\t .m t pi Ni-wall's r-timalt- a- tDrn-tt. .ind if \m- rtnuiiilni ill, it in no i.i-i- \va- a -iiflu it-nllv lon^' i-\po-iiri- i;i\t-n lo allow llu millvinu p.iri- of llu- irtiimi ili-k to inirt-a-t- llu- witlili of -pi-tirum or trail, llun ilu- ili.inu ii-r of llu- imaiii- i^ivi-n l)\ llu- 'ii " 1 liji-t ,i\t ,inil lorrtiiini;- it-ns, (.-vt-n allowing tlu- i-\trt-nu- limit ,i--ii.;iutl hv Ntwall tor .iimo- phi-rit (li-turhani t-. i- nt-.irl\ i\\ it t- .1- L;ri-.it ,1- it -hoiiM Im-. Il i- also a simplf malttr lo u-i ilii- lotulu-ion f\pt-rinit nt.illy . .\- llu- ohji-ttivi- i,'i\*'"' i-N* till lit \i-ual ill linition, it m,iy Im sifily a— uniftl llial llu- \i-ual -1 r im.,L;t- i-of norm. 1 ili.inu it r. .\ mt.:-iiri nu-nt of tilt- w iillh of -pt-t ir,i ,m 1 trails i)r(«iiit 1 il 1>\ ilu \ i-ii.il im.iL'r, anil a iomp:iri-on with tlu- wiilth- i;iv(-n l)y ohjniiM- ami mrrniiiiu It-ns in plioto.i;raphii li.i^hl, -houM ,it onti- ilu it It whitlu r llu oh-t r\til ' M.nilhly .\,ili,,y 65, So.s. i.)c 5 200 J. S. PLASKETT clTcct is due to atmosi)heric tri'mor. The correctinK-li-ns was thiTi-- forc ri'iTiovid, the spictroscopc was adjustid for yillow li^ht, and spictra wiTc made similarly to the previous ones, lliou^ii on Cramer Isoehromalic plates, whicli have a jjronounced l)and of sensitiveness almost identical in wave-kn^th witli the turning-{)oint of the color-curve of the objective. The widths of the spectra ])ro(luced varied between 0.050 and 0.065 mm, about 2", Init as the seein.i; was very unsteady (about i\ in scale of 5), these widths are doubtless about 25 ])er cent, f^reater than would be the case with good seeing. Kor the star trails the same make of plate was used, light of shorttr wave- length than X. 5000 l)eing al)S(irl)e(l by a yellow screen of ])lane glass placed in contact wilii thi' ])l.ite. Owing to the insensiliveness of the ])late to light of wave-lengllis betwtcn \ 5000 and \ 5 100, and to longer waves than X 5800, only the light wiiit h is elTective in forming the visual image c^'n act in producing the trails. As befori', the width of the trails varied with tlie brightness of the stars, ranging from 0.025 mm in faint trails to 0.055 f""! 'i^ stronger trails, or from i" to 2", while the average width over a longer stri|) of trail was ai)out 20 per cent, greatir. .Xotwithstanding the bad seeing, both trails and sjjcctra were much more sharply detmed than those made with the correcting-lens in pliotographic light and of only half the width. These e.\[)erimenls conclusively prove that the abnormal width of spectra and trails in photogra])hic light is not due to aberrations in the s])ectr()scope nor to atmos])iieric disturbances, and clearly jjoint to aberrations in the condensing system as the cause of the obsirved elTects. .\ sliort summary of the experimental data will render this more evident. The theoretical diameter of the central disk, or ralhir of the first dark ring, for \ isual light \ 5600, is o.'74, for pliotographic light, \ 4,^40, is o."57. The actual width of visual spectra and trails is from 1" to 2", or one and one-half to three times the theoretical diameter. Thi' actual width of photographic spectra and trails is from }i" to 4.' 5, or live to eigiit times the theoretical diameter. Some further information regarding the si/e and character of the pliotogra])hic image may be gained by considering its elTectivc diameter under anotluT aspect, that of the loss of liglit at the slit. Referring again to .^'ewall's pa])er, and taking, as he does for an example, a tremor-disk of 5" diameter with a core of 2", we find that STAR IMAGE IX SPECIROaKAPIIlC WORK 201 a slit 0.025 mm wide will tnmsmit ,^i [ur ctiit. i)f tlu- inridirt star li}^ht; a slit 0.0,^7 mm, 44 jht ant.; a slit 0.05 mm, 58 pt .nt.; and so on. I am indiliud to a suggestion hy I'rofts.sor Campbell for a method of testinj^ this theoretieal result experimentally. .\ series of star sjH'ctra were m.ide at dilTennt slit -widths, and the resulting inim-vities were comjiared. .\s it is practically imiKissiblc to make .. number of wide spectra of uniform intensity thr(iu<^h()Ut their width, photometric measurmients c.innot be relied ui)on and recourse must Ik " ad to visual estimates. Sudi estimatis can be made more accurately if the exi)Osures are so re};ulate(l as to give spectra of e(jual inttnsity, an;reat extent avoided. The spectrum of n Lyrar. the star usid, is ]iraclic.ii'y continuous exce]it for the If series, and is therefore well suited for the estimation of intensities, while its brif^htness is such tiiat only short exix)sures are re([uired. Ten ilitTerent slit-widths between 0.012 and 0.25 mm were used, and ten spectra, one throui;h each si it -opening, were made ~ide l)y side on the same plate. The ex]K>sures were so regulated as to render the resulting spectra as nearly ecpially intense as possible, and the tmal estimate is the mear from a number of ]ilales and from spectra of dilTerent widths. To render the comi)arisons more direct, slit-widths will be rejiresented by divisions, a single division corre- sponding to 0.025 mm, and ttie relative exjKisure limes will be reducerl to a unit of 100 witli a slit-widtli of one division, 0.025 ™'''^' "•■ o'9t. the normal width with the disjKrsion eniployeil here. The following table slu)ws that the exposure miuin-d is inversely proiM)rtional to the slit-width until this reaches 0.1 mm. Ir.iving out of accoimt widths less than a single division, where dilTracticmal loss within the collimator plays an imi^ortant part. It also shows that with normal slit-width less ih.m 17 per cent, of the light incident on the slit is transmitted. In Newall's hy|K)thetical rase ,?i per cent, would be transmitted. The experimental data given above, using Newall's metliod of calculation, indicate a tremor disk H" or 10" in diameter with a core of about _v'5. Jm'l. as the previous exixriments have shown, this is much larger than can l)e accounted for by atmos- jiheric disturbances. 302 J. S. I'LASKF.TT Loss lAiiii: I lit I.Tc.iir Ai Si tt CourAKAlUK TlMK FOR I'jVM l\it N>!rv I)i«. Mm Sfcs. IxiKrimcnlal ("onipulcd; i O OI J 45 .qoo ■ o.?? <)t 100 100 li ■°,(7 1 .\> '>7 70 .050 I Sj 50 5 I ■075 2-7,? .V< '•.'< . 100 3 "4 28 U 5 US 4 55 i"! ,^i ft .150 5 45 21 7 \i « .200 / ■ * # . .M lO .250 0.07 If.. 7 ,?• Tlu- ;il)ovc cxpirinunts i>()int (.oncliisivily lo abirmtions in the systim of objective and correctinj^-lens, w lit-n used with i)hotogra])hic liglit, ah the cause of llie observed elTects, but lliey give no information concerning the nature of these aberrations beyond indicating in a general way, from the appearance of out-of-focus i)hotograi)hs of spectra and trails, that spherical aberration is ])resent. It was decided therefore, to make quantitative tc-ts to ascertain if j)()ssible the nature and magnitude of the al;errations and the best means of removing them. The most simi)le and accurate method of determining the zonal errors and axial astigmatism of a telesco])e ol)jec!ive is Hartmann's melliod' of extra-focal measurements. The ])rinciple of the method and tlie measuremenls and reductions mcessary are extremely sim])le, while it gives accurate values with tlie expenditure of com|)arativelv little time and without the use of any appliances exce])t such as can be rea'(l at two jioint:-, om- witliin and oni- without tl\f focus, the ])oiiU of interseetioti of llie luneils, and lonseiiuently the foeus lor the particular /one in (|Uebtion. can be at once ol)tained from similar triani^les. For let (/., Fi^. i, be the distanci' between llie pencils at the scale readinj; .1, within tlu- focus, il, the tance at the scde- readin^ .1^ bevond the focus. Evidently then tiie scale rtailini; for the focus .1 "'*•'>"'(,/'.'/)*•*' ■''^- ""' '•'^'•'"'^''^ '^ ■'"'! ''1 mav be determined directly by mii ronieter me.isuremt nts on the pencils from a star or distant artiticial point source, or by makiii'^ exposures on photoj;raphii' platis in tlie two ])osilions and mea?urin,i; the distances between tile n-ultinj^ imai^es by a ineasurini; microscope. The latter method is j ire l< Table and was used e\clusi\'l\ . except that tile photoi^rajihic determinations were checked by micrometer measures. A /.one plate .1, Fig. 2. similar to that (>, S;, io|. i_\:;, i |j, .do, and 17S mm. In order to determine the aslis^matism alont; liie axis, each pair of open- 304 J. S. PLASKITT ings is (luplicatL'd hy a second similar ])air at rii,'lit anj^ks, so that the foius of lach zone of the oljjcctivi' is (lilcTmimd for two iKminls lKT|nndicular to i()pi', and can be readily moved u|) and down tlirough a range of ai)<)ut 20 cm. Experience showed tiiat the images weri' most shar])ly defmid, and the best measurements could bi' oljtained when the jilalis were between 6 and 10 cm from tlie focus. .\s the pliolographic focus was to be tested, an ordinary Seed 27 plate was IJrst tried; but it was not found possible to make very accurate settings, as the ]iencils from the zone ])late were spread out into radial spectra owing to the long range of wave length (^A.30CX3 to the limit passed by t!ie object-glass, siy A. 3600) to which such a plati- is sensitive. Siveral means of overcoming this dillkulty were tried. .\s a yellow screen in front of an ordinary I)late did not imiirove matters, tlu' dispersion of the pencils must evidently be ciiietly due to tlie light around II iS. .\n ordinary lantern plate, which is sinsitivi' from about X )()00 down, was therefore next tried, and gave good images capable of at curate measurement; while if a yellow screen weri' usid with suili a plate tile resultant images were again ilongaled, showing tha ]ir()l()ng((l ix]iosure entailed tlurebv h;;d extended the action on the jilate toward the rid and nintroduied the lirst ilifliculty. .A yiUow or red star was used in preference to a white or blue, as limiting the action in the \iolet, shortening the it'fective range ( lectrum, and thus giving images with les. spectral dispersion and with no apparent elongation. .s/.iA' /.i/.i(.7-: IS srrxi Kihh.M'iiic \\(^kk JO!; FoUfM tsof i\tr,i foial platis win- m.idr whiih.oii luini,' inc,i-'tiriiti()n> i)f tin- nitu- /diks as lahulattil liilow I'l'ahlc 11 1. Ml l'i>ur nuasurcs ar<' in substantial aKnt-niint, whidi dI ioutm' i> ilo-t-r for llic outrr /oms wluri' tlu- (■()nv(rf,M;;v of ilir juniii-- i- i^rratcr. 'I'lu re thr jn-olMMr ; rror of a >int;lf (Ktcrminatioii of tin focus docs not ixiird o.i mm, wiiiU' mar till' nnlir it may hi a> f^rrat as 0.5 mm. It will ln' notiiid tiial till' forus for tin- td^;i' of the ol>jicti\r and torrii linu' U ns i> u|i\vard of 2 mm lon^'ir than the fo( us mar the nnlir, and if a>tii;matism hf takin into aicoiint also, thr ditTinncc is ),'riat- ])indi(l stall- ri|irt>inun)^ millimrtirs. 1 In liori/.ont.d line is drawn in the [Mj-itionof foius 75.;^4that j^ivo the >malU>l i inks of lontuMon, in this lasi- 0.04 mm in diamcttr. The astium.iti>m will iniriaM- this to sonu' ixtint. so th.it proliahly tlu di.inutcr will he marly 2". L'nli>- the >lit is xt ixaitly at this niian jiosiiion, whiih i> not likily, thi' diannttr of the ronfusion disks will l>i- still furtht r im nax-d, >o that we mav ion>idi r .•" as a modrrati- istiinati. It mii>t In- n r iiin- hiTid. how I \ IT. that in sjnakini^ of i in It- of ( (infu>ion the com t piions of ^comi triial ojitiis aloni ari- luin;^ lonsldind. and no aiiount is taken of dilTraition ]ihinonniia. whiili may ha\c some ilfnt on the m'omctriially lali'ulatid dimin>ion> of tin Mar di>k n-^ultini; from ahirralions of tin- n.a.^nitudi' htre ]>risiv'|y that the iiholo.tjraphii; imaije was alunit 2" j^reatcr in diameter than tile visual im; u'e, ]iresuniat)ly unalTeitid hy ..herrations. and this aj^ries with the Ljeometriial theory. To determi'.ie wliere tile aberrations ari>e it is necessary to aieu- ralelv eompare the |ierformanee of the ohjeilive used visually w ith the ])erforniame of the olije(ti\i- and (oTediim Uns in the ]ihoto,i;r,i]ihic part of tile siieetruni. /ond ti^ts were therefore made of the ohjer- tive alone. I'or tin- ])ur]M.-e the wa\e lent;th ol the lit^'ht Used niu^t he limited to X- 5 )00 X 5S00, tile ran.Ue to which the eye is mo>t sensitive, whltli i^ the most luminous in tiie >iieitrum, and wiiidi coincides with the turning; iH)ini of the iitivene>s of Cramer Isociiro- 206 J S. Pl.ASKI.n lAHi.i; II ZiiSM liMi (IF 15 Is( II ()iin( n\K I >i))K< i[\t \NI) I'okKl- ti\..l -KNi .,1. nv> Ai >Nt, — .^ 'll'.l.H.kAI'Mlf \|>I »L /..St. h; li;i Mr.iu .\'UKm.iii>ni IVn us Mr.ui Abli|{n UliMIl . -^ — -. . 2S 45' 7.^ 54 — . io io().4( — ■05 '15 7.? <)4 7.! 74 -i- .•0 lofi 54 I06,4,S -1- 06 47 71 ID r .o,s lo-S-.V^ .- 42 DO 74 0^ 74 H — o,S 107 51 107 '),? - 4i 66 :^ / > 51 -- ■.1.0 io(. (,7 — 1.1 ■,>.-i 7 i U 75 >4 ^ ■.io tOt< D,i 106 So . '.* >*5 7t 15 . 1 1 106,42 . 2(1 DO ■ i Dl 71 f-l — . 10 105 D' 10'' ') — ■ -5 IC| n 71 'S - -'.i io() 15 — oS ■vS /'5 1 I 71 ■-^•-^ ■ -',< Id ,(1 IO(. 2i -I- oS '-',i 75 OS 22 io(> 20 Od 1 <)o 75 - 5 75 4'' -'I 10(1.02 1 06 11 - .0() 14-' " * 5 7^ D,i -'4 1 06 . oS -+- 20 0- . -, -> i-' - .V '°5 77 — . 1 1 11 -' ^ 75 "7 — 02 105 .K2 — .06 f '57 5 75 ^,i 75 'M >4 105 Si 105 ss — °5 \ix> ! 15 75 5-"^ — 15 105 Dl 04 '.i5 7s ss 75 7 ^ 15 105 s^ 105 S7 -■ 04 17,H 1 7" 1 1 -t~ Jf 105 (i; - 01 iSo- 75 (H, 75 '1'^ ~ 31 "'S ')5 IDS 04 t 01 Mr.Mlf... U^ 106 01 niatic |>l;it(.< almost ixailly loimidis with ilu' .^ami' ri'j.;ion, all that is iHTi'ssa ry in order to oljtain iiliotoi^rapliic test plates is to absorb the blue and violet li^'ht by a suitable screen, ami thus eonfine the action to the visud part of the sjiectrum. A dee]) yellow screen with plane parallel surlaies was used in contact with the plate. Althou),'h the ])eprils from the /.one plate are displaced slif,'h!ly on passing through this screen, these disi)lacements are projiortional, and the onlv elTect will be tolengtlun the focus for all the /.ones by the same amount, about one-third the thi( kness of the screen, witliout in the least alter- ing the relative ]M)>itions of the pencils. .\n e.\|)osure of about a minute on ('apclln. ilirough tlie screen, with thi plate from Oo to loc mm from tiie focus, gives a negative of good intensity in whidi tlie images of the pencils are ipiite round and free from any noticeable spectral elongation, thus allowing accurate measurement. Five sets of e.xirafocal e.\|K)sures were made in the visual i)art of the si>ectrum. and tiu- n.ean values resulting from the nieasureniint and reduction of these plates are given in Table II and plotted graphi- 5/MA' /U.K./; /.Y SI'ECl H(H:K.\rillC \\(^KK In.. ;. -AitKil OilTiTcnci s cf Incus callv in t un t' /•' of Kig. ,^ An examination of tliis curvf shows that no point or focus is at a j^nati-r (iistance than o. 2 mm from thi' iK)sition 20S J. S. ri.ASKr.TT of ini'Mn f()( us, shown by the hori/ont.il line, i\(r])i ;i smiill rii;ion nt.ir tin- ( cnicr of ilu' ohjictivc wliirli lias a l()ni,'ir fonis. Thf ilTci t of this n 1,'ion on llic ]>( rforni ncc of the ol)jiiti\r nuisl, Iiowimt, \w i\cnilint,'ls- sm ill, owini^ to its small ari'a, K>s than om-tinth of tlu' ()l)ji(ti\f, and to till- uiak ( oiUAT-^cnry of llu' pmiils ]pro(i'i(lint^ from it. In f.iit if H.iriminn's iriirrion 7' as to the (|iiality of an ()l>jiili\i' 1)1- ii)ni|)iitiiar only whin it is usid in lonjunition with an auxiliary lornitor for s|>iitroj,'ra|>hic work. Whithir the .ihrrriiions tluri' ])risi'nt arc dui- to the lornilinj^ lins, or to the ohjrilivi' whin usid in the iiii()to,!.,".,|ihic i>art of tlii' s|if( truni, remains to lie ditirmined. For thi> jpurpose a further aipjiliealion of Mart- niann's method was necessary to Imd the color curves of the ohjeclive ah)ne, and of the system of ohjeclive a.nd correi tinj;-lens for a number of /ones. It was iiopid that such ohserv.itions would throw liijht on the cause of the al)errations and suj,'f,'esl a [tossihle remedy. They would also serve as a che( k upon tile /.one-pl:ite determinations, as, in this case, no spectral iiisiHr>ion .if the pencils could alTect the accu- racy of setting;. 'I'o Imd such color-curves, the pencils of lifjht coming from a /one jilale fall on llie spectroscope slit, and the distance between the resulting; spectra taken with the slit within and beyond the focus ^ives a measure, cilcul ited in llie same way as before, of the focal position of any desired wave length for any |).irticular zone. It w.is decided to determine the color curves of eijjht zones of ,^8, 57. 76, 05, 114, I},!,, i-,2, 171 mm radius; and, to ])revent the spectr.i from merf^ini; into one anotlur, two /one jilates were rec|uired, one (H), Fii^. 2, ol the four /ones of 57, 05, i ;;,^. ami 171 mm radius, and the other (C), Fig. 2, of the remaininj^ four. The central open- inj^s were each 20 mm sijuare, and the outer 20 by 25 nmi. The /one plates were so placed on tlie objective that the row of openings w.is parallel to an hour circle, and the spectroscope was turned in * /eitsfhri/t jttr Instrumcntnikitndt', 24, 40, 1904. STAR l.\t.U;i: l.\ SPECTRtHiKM'im \\i>KK .•0() |X)situm iin^li' until tlu' -lit was i)ar,ilitl to tin opmini;^. in onhr that imj^uLiritii's in driving wouM not w idi n tin >i»itra. I u iliniin ish the t'X|><)surcs as mm li as jKissihli-, lirii^ht siar>, l'<,i,''/ .mil Sinus, wiTf usrd and thr slit was widily o(Hni.d. , s no in. uur.,i> would In- thiTi'bv intRMlnct-d in thf dist.incc liilwun tin ^]>ntr.i. Tlu > xpo sun-s win- madi- on a nii^hl wntn ihi' trmpt ratun- w..s m-. ri\ -iiiion ary.and wrrt'.irr.in^id in thr following order: I'latr i; /"iir I'l.ili- iH) \in. J. >lit ,il«.ut 50111111 williiii llu l"i ii^ .; iD " ■' ;o ' " 5; (C') " " 40 " Ih\.'Ii1 4; («) " •' 40 This imjcedure was followed to avoid a> f.ir is iio".-il>li' any n la • tivc (Usi)l;icemenl of the foc.il deiermin.itions of the two m 1 ,, due lo slight changes of temjieniture of the ohjeetive. That no nu iMir.ihle displacement has occurred is shown by the continuity of tlie /.on.il curves of Fis^. ,^ dniwn from the comhin.ition of the two ^epar,lte determinations, and by their af;reenunl with tlioM- m.ide by tiie re^^ular /.one-plate method. Each of these plates cont.iins ei;;ht sjiectr.i sidi by side, one from each light i)encil transmitted by the /.one )>l.ite. .md the po-ition of the focus for each zone and for any desired wave lenu'th in the ran^,'e on the plate can be determined in ex.ictly the same w.iy ,is before. The hvdrogen lines, in the I'lr.st type stars usdi, >erve as d.itum marks for the identil'ication of wave leni^llis, and me.i>urement> w( re m.ule .it eleven [wsitions between X. .^gjo and X. SO.iO- 'll'*' corresjxindin^' focal iwints, as calcul.ited from these me.isurements, are given in Tat . Ill for eight zones of the objective alone, and in T.ible IV for the same eight zones of the objective with corni ting lens, the hitter being about 40 mm nearer the focus than its computed [H):,ition. Tile reason for using the correcting lens below its computed position at (mce appears on inspection of Fig. 4, which represents, in their correct relative jjositions, the color-curves of a medi.m /.one of 108 nmi radius, determined in exactly tiie same way as above. Curve .1 (Fig. 4) is the color-curve of the visual objective between the limits \ 6250 and X 3()70, which shows that the minimum focus i^ at about \ 5(100, exactly in its computed ])osition. Curvi' B is the color curve of the system of objective and correcting-lens between \ 6250 and 3IO J. s. PLASKirr >TC A s 1 lie 'M h 30 / / / 1 .- / to k- — ., , — 70 €0 \ ^ "V D «, ^ ^ _^*'-- ,-^' , h" .-^ 4C Wto d i Hi Hi H5 Fli".. 4. — Ciilor-Curves for a Modian Zone A. 3970, wliich shows that llic minimum focus is at about //^, instead of //7, its computed jMJsition. When the correcting-lens is moved STAR IM U.F. I\ SricrfH^CKM'IIIC UCAA. 'I I I Mil I III ('iiIllR (1 kX 1-. I't ' •IMI' I r- I \liiS) W A\ I I I N , i" 1' lit 4.S(.| 4M0 4< 0. 444 > lly 411 • 41 .«■' ,S5 57 HI, ^7 llll " si; (0 nil <,o HH lis •1- r-} 1)4 ^'S ')!' tK^ ion -u s'( ^4 s^ 7.S SS 7" ')! 01) il( (1; ,,'. \'l >l'l *}> S( (.; s; t- SS 41 i|0 S.* • l< 5'' .,(. M 'J'l 114 **» .(« ■■^s 7''* .s.s (iS i|> I'l '» > ^7 ,,(. 77 WW lU ,S4 7> X'i 'M HS (.,S 1)1 CS Oi -' ■■*> o(< St< .'!) S.) IS 'M 1') 'It 41 'i7 4-' IlV^ 1 71 .si; t' S(i S; s,, ''5 *)-* <^\ '!> c-' ,|S ol inl ',, |:-| //^ ■^ ■*' i i^ ^ 71 S ' u "> 5 ' f. 71 //t 1 AlUI l\ CiilliR (1 K\ ^^ liK < IMIM nVh W IJ ( '1 iK H c I 1 Si . I.I \-- W \\> It \. .ril ■ Hi son 4H'il 4^»So 4440 414" 4i50 ;S 55 ij 54 7S >i II >i I** ^■^ ''5 r^'^ ')-' 5- 'i' >' i7 5' !'' 5i ''•'' .^i '" -•,: ii (S ,; ■'^'i ;■• i;; ^i 'i"* =;i -t 5' f't ?'" ''" =;' ■" .^ ' "^ '' '^ ^ ''• 7" 51 51 5* ''7 >■ ^t ii '"' ^1 ") ii 'I '' "' >' " .^' ■' " ■" ''' '■' ■'' 115 ;; 57 51 ^7 55 K' 5-' 4'' 5i 'i5 5i 70 51 '-^ ;i 71 5' ■><' 5- *o ^-' "'' 111 ;5 45 54 ■**-' 55 ''-' 55 '-• 5-7'' 5.' 5'i 5-" ''5 ^-' 7'' ^^ '^ < ^< •' • ^' *' 1(5 55 04 55 10 55 >"< 55 5 55 °'' 5- '"^'i ^-' ''< 5> '> 5i i' =■ < '* ^i 75 15.' ;:; S| 55 15 5» 05 5! 5» 55 -''' 55 "7 '^ ^ -^ 5^ i^ >i 1'' 171 5(>.o5 55 ;.| 51 .(S 5< i)0 5;. '10 55 55 5i 5'' 5i 'i7 5i i5 51 - (!.• i ''4 1 54 down, a\v;iv from tlu- ()l)jirlivi-, some 40 mm wi' ^ti ( urvc C, and .it 70 mm. (urvf /). In curvt- C the minimum f(H u- is marly at //-/, and in D at X 44(10. Kvidi'ntly tlif lowirin;,' of tlu' corrtrlin^ li ns somt- 40 mm rlTi( tsconsidiTahlr iniiirovinunt in tin- color torrid ion without, as thi' earlier experiments showed, apiireciahly enbrtjinj; the ima^i', and the lens has been used in ihis position almost from the tirst. Althouf^h all the data in rej^ard to the eomjilete coloi rves :;re given in ''"ables 111 and IV, still the aitu.d curves dr.iwn from these figures show all the cimditions at a glance, and are hence v, ,.Mi giving. To jireAent too great a confusion of lines, tlie curves for four zones only (zone jilatc (B), Fig. i), of 57, 95, i,?.^ 171 mm radius, arc shown here in Fig. 5, the upper curves being of objective 312 J. S. PIASKEIT 1 " 1 r- ■ T" ■ ■ f - I'li;. 5. — t'liIorCurvis uf luur '/.mws of Objedive and uf Objective with (orrt-ctor alont', the lower of objective and correclor. These cunxs show at a glance that, in the photograjjhic part of the spectrum, the focus for .STIR /»/.!(,/ /.v .srtci K(h,K- \riii(- ln>^'^• -''.^ thr rili^f i>( tlu' oltjcdivi' i- lon^jiT ili.m tin loni- fur ilun iiii r. ili.il it his ni'i^itivf sphiTitMl iilurritinti. I lii- i limtn.itii (liiiVrnm of s]ihiTiiMl al>iTr ition ii intunut in two |i .rt ohji i ii\i'^ of tlii onlin.iry Hl;issi's, ;inil till' i»nlv niTicflv i> t. on tin inntrar\. incrcasid it sonuwtiat, and the foi u> for ni.irv;in..l ri\ • i- iipu n! of 2 mm lonpr than thf focus for untnl ri\-.. I hi> ai;rn- ahno^t fxuctly with thi' previous (Ictirniinition of tJK /oiial loi i of oliju live ;in(l corrector, and is jjcmmI evident i- i>l thi ^uli^taiuiil atiuraty of the determinations. Heft)re leavini; thf^e curt t> it ir.i\ Ik iMiinietl out tha' the crossing; of the curve from tin •i~ mm /one ovt r tiie oiin rs in pissing from sliort to lont; waves is ihii to tiie loni;t r t ii~ ol the central /.ones in the visu d part and is furih.r evidtU'i ai t,i\or of the aicuruv of ihe thtermin.ition^. To ohtain a s'iii more strikin'^ ti>mp,iri>on of l!if i.uit- .md mafjnitude of the aberrations present in tin ■•\>uni, ilu color < ur\. or the jiosifons of fot us. of tlie whole jihoiourapliii rt i;ion for ei^ht zones of the ohjectivi in Tahiti HI and I\'. and thi>e tan In rt, dily plotted in the same way and on the s.ime scale as .1 , ml 7'. Ki^;. ^ If such curves were plotlid for every w,i\i lePfZtll in t!it>e tahles, thev would show a striking aj.;reenient in form, hut 1 h:i\e ^atislud mysilf with representing; ih'- positions <.. lu lotus of t ii;lit /ones lor Uy, the wave-len,i,'th for wiiich the system w.o i ominiltil, .lud lor the mean of X^^^o, 4,^40, 4440. and 4,^50, the ran^e of s;iittrum umiI here in velocity di terminations. /•;, Fij,'. .^ is the t urve ft lly u( the ohjective alone; C is the curve tt>r Jlyni objective anil torrtilor. /) is the curve for \ 4250 to \ 4550 of the objettive : loni ; H i> the curve fur X. 4250 to X 4550 of the objettive and t orret tor. A ctnni)arison of curves /)and I: with /•' shows in a -trikini; manner the chromatic dilTerences of si>herical aberr.aion in the objittive when used with photoi,'raphic liLiht. If we leavt out of at count or allow for the deviations in the central /.oms, we see that the ftxus of the outer is about 1.8 mm lonj;er than the focus for the central 214 J. s. I'LASKJ/rr /.()nr>, ;i li,mirc tiiat af^rtts almost cxadly w illi the comjuitrd (lilfcnncc as fiirmVlnd nu' In I'rofissor Hastinf,'s. A ( omiiiri-on of dirvts .1, li. and (' willi P and /•,' shows that this dirunna', instiad of Ininp rimovfd or diminislud l)y llu- inlnnliK tion of llic corrn ting kni- lias on till- lonirary Incn incrtasid by alxmt 0.6 mm, sf ;hat \h (liffircnii in fom> hilwiin ouUr and (intral /.ones i.- now alioiu 2.5 mm, wliidi, a> hifori' slatid, will gi\i- a confusion disk marly 2" in dianutir. 1 wish lo jioint out, htforc li;,\in,u thisr iur\i>. how tiu' form of the curve is maintained throiifihout from /•' u\> lo .1 e.\ce])t that the axis of the curve is inclined downward hy tlii' chro- matic dilTerenci'S in the photoj^raphic region, and further tilted hy the introduction of the torrecting lens. To show this I have dotted in ap|iro\imati' ]iositions of su( h a.xes in tlu- lurves /•,' to .1 to corre- s])ond witii thi' horizontal axis in/''. It will hi' notind that the irregu- larities in til' visual curve an- continued throughout, hut in an int' n~it'ie(l form, as is to \n- expectid wlun it is considend that the ol)jetti\e was i()mi)Uted and figurid for visual work, and its use in the ])h()tograi)hic region wilii an auxiliary corrector was only a second- ary consideration. I see no reason to doubt, howiver, if sullicit'nt positive abi rr, lion were left in tlu' (oiieding lins to com])er,.-ate for the nig:. live aber- ration introduced by the chromatic dilTennces, that the jurformance of the system could be much improveil, although it is not likily, from the magnifying of the unavoidable zonal aberrations, th; t it would equal its visual quality. If the curve .1, Fig. ,^ representing the present condition of the s\stem, could be tilted through the angle between the horizontal and dotted lines, by such a change in the correcting-lens, the resulting confusion disk would certainly have a diameter less than half its present magnitude, while the ])ercentage of the ill' idem star light transmilled by the slit wouiil be consider.. bly increased, jirobably doubled, with a pro])orlionate diminution of the rei|uire(l exposuri' times for stellar spictra. Such an imprtnenient would be well worth considerable etiort, anil I ha\i ' vn in communication with the Urashear C'om]i.!ny and with I'tv essor Hastings to that end. With their well known willingness. I may even say anxiety, to ]>roduce the highc'-t quality of optical work and to make any im]irovements lliat may be suggested ^^S ..'.J . -^.- m.i ' '■ ■, '■ STAR IM.iai-: /.V SPF.CTROCKM'HIC WOKS ■;»5 to tlum, thi' Hraslu'ur Company arc undrrtakini,' lo niakc a in w corrccting-lens to computations hy F'rofis>or Ilasiinu's, to wlumi I I ;im vcrv much indebted for criticisms and suu'i^i-iion^ on tlu- pn sent paper. 1 may say that I'rofessor llastinus finds a very markid uKrcement between his computed data of tlie objecti\f, lolor dirves. and chromatic dilTerences. and my observations, lie explains tlie failure of the correctint; lens to compensate for the cliromatie dilUr- ences of focus, which it was comi>uted to do, by tile l.,ct llial lliis lens has to correct the errors of an objective of marly tifty linies the area, that the small dej)artures of tlu- wave >urface> from ,i true suhere have grown enormously when tliese surfaces liaw contracttd to one-t'iftieth their original area, and that a very jxTfecl cornel ion by spherical surfaces can hardly be hoped for. lie tliink.-, iiowe\er, that considerable improvement can be effectee with the means of overcoming them, in ordir to sniootii the way for similar investigations into the character of the star image given by other svstems of objective and correcting Kns. It seems to me extremely probable that, in the major j)art if nut all of the telescoji. s employed in spcctrographic work, aberrations of the s inu- or a similar nature are present. If a correcting Kns compute! to compensate for the chromatic dilTerence fails in one case, it is jio.-sible, even imibable, that it may fail in others, .\nother basis for this bdicf is a comparison of the relative e.\po>uri- times re(|uirecl for different installations taking into account si/.e of object glass, slil-widlh, and disper>ic)n of the spectrograph. I am well aware that such a ccmipari- son mu>t necessarily be incomiilete, and the results reached subject to an uncertainty, say, of 23 per cent., owing to the dilfuulty of comparing dilTerent installations under ditferent conditions of seeing, etc. We have already seen how important a part is i)layed by atmos- pheric disturbances in enlarging the star image so that the linear T-H 2ib J. S. riASKETT (li iim lir of ilic imi.m' incruascs marly in pre ortion with tlu' focal kiVi,'lli. ami llurcfon' a|>|>r()\iiii itily, as llu- ratio of aiK-rturf to focal kni,'tli (Iocs not vary much in larj^'c instrununts, with the diameter of tlu- object j,'l ->. {'onsc<|iiently, the !'ecl!\e value of increase of ai)erlurt' is not proiiortion tl to the increase of area, Init mori' nearly to the increase of (liaineter, which w.is accord inj^l)- used in the compari- son. So far as rei; irds the relative dispersion of different instrununts, the I \po>ure time was taken as directly pro|)()rtional to the linear di>per~ioii, presuinini; the same iieij^ht of s]>ectrum in each case. No accouni w,is taken of tlu- difference in the loss due to al)sori)tion and rellection in tlu- prism train, allhouuli this may he quite important in >onie cas(-s. The (-\iio-~ure tinu- reijuind was taken as inversely |)rop()nional to the slit width, and this, as one- of tlu- e.\[K-rinu'nts iletailed al>o\e shows, is probably nearly in accordance with the facts. In the following Table \', data of llu- \arious cc|uipments whivli are and have been us(-d -. radial \elociiy work, so far as they were awiilable to the writer, appear, but thise .>S 1 'jUipltK lU ( )n.i\v.i 15 N'rrkfs 40 l.i(k \U l,..u,ll J I NiA.iil .'5 He inn 1 -■ I'lilkiiw.! ;o I,..nl I.'* Aitti.i! Kxposurt' Required '"^&- "Ir all..Ms lit tit lilf 1 I 1 S . (1 .o.'q I i^oni ^loni Om 2. (.7 - I 10 s o,!,S 0.42 7> ■ I."; 15 -' 1 5 7'' ' -• 5 o-.i 0.62 -' > ■ - ^ . 4.-' L - CJO 1 1)1 7> 75 15 2 -t-C I i C20 .Si) ("{ ' ".> !■; o.S,( (») iS (1 CJ^ 1 20 liO ' 60:- 4 Tlu- above comparison shows that the Lick, Bonn, and Lord etiuipnu-nts in pracl'uc ■.\y\ixum\\ more iu-arl\- the llu-ort-tical el'liciency than the Ottawa, but tlu- Verkes, Lowell, \ewall,and I'ulkowa depart farther from it. HPPHVI STAR ni.\GE 7.Y SPECTROGRArUIC WORK :^i: 'I'hcrf strms tluri'fori' rcasonahlc j^rouiiu for l)i lit\ itiLl that i "ii- si(lrral)lc imi)n)vi'nn'nt in tln' tlVuicmv, aiul lonsidrraMi- imrtasc in ihe r mi^L'of tlu' majority of siKctro,i;ra|ilii( ((iiiipnnnts i.ji hcatiaimd l)v ' )okini^ into llif i liarat tcr of the star ini...i^c j^ivcn l>y the coniimsin^; ss>ti'm. Although llu' lx u t i-lTicl of atniosphiric (li-turhann ■- on the I'lTfctivr dianu'tiT of thi' star inia^f is ditTKull of di li rminalion, I fnl satisfifl, if I can obtain a corrtc tini: lens tliat will '^ivc a -t ir ima^i' roasonahly free from alnrration, that the (\|i<)>iirr limr- n- (luiri'd hire can he very materially ndiuid, I hojie hy 50 )>« r unt., ;ind I see no reason wliy a similar or even j^nati r imiirovemi ni could not be elTected in some of the other e(|uiiinnnts. 1 acknowledfje with jiUasure my indel)tednes> to Or. \\ . I'. Kinj;, the Director of the Observatory, for hel|) and encoiirai^munt in tin- prosecution of the work, and to Mr. W. K. Harper for niakini,' diijili- cate measures for comparison purjxjses on some of tiie te^t plates. Dominion ()iiSKi;\ aiokv, (>iia«a January, 1^07