Se a a i ee A ek LOB teelg Ce oe a ee ie ey {ha bah wan, OCR eo AOTC NL A ee vite te. ' ; ae ae f TOC i, On Oe i Ce a 4 Cree tooge Sr RRC Ren) Ic ar ev Wr bY ids nee OE EAE Net BUY MANS SMS as Hi ealen wae Mt aks Coble be ns peyyey ' ‘ fo led pee VG CUM OW Oe et file Vey yee ah Qiee Thebes Aro fe La na Ped ty AA LT Ce er ey ety by, ren Le DY eels Dee RNC ae ‘ ental tee pal TOC NEE er MR rc era rh AY Cec ea week oe we Oe a pana VOCE ea see HE tte En tee oe ph te eae vee tee de ‘ a) Ye ode at Pa eree pp adewaa Ce er a Mee bbclben ; eft a ee RU Re OR ee ’ tot? Me ee We eet RN buikd ee Car ree rs Geer an a Oe a a Se | ae *¥r fore baa ae Phe aw aaeta COC ee Ue rade ee Wiese Owe 4 eee Lys felt 7 ia aa Mi ESA. UL, 88TH ES gO LF i BOO) ‘ Pw tabi pea a Sh Ye Stew 7 eee 4 i oan) Wt, a tea yy) be ' ' aia paras e SW tte hh ardeds ME ee oe) hoa sai 8 Meth nm ini m0 Hse a vas 7 rir pi ue cay e tetra teen Neo ee Me Rime ew aes ‘ ie? »* 7 oes ee ar TUL CR a he We PY Nina a a a ret | ‘nt oevsnne MeN nN MOE ET M TL a8 HA oe $55) ots mam aw Samia ascot aur reverts thar CL OEE EN EE ® Ate W Ohad bE eh Ee Ce Rem Bi is be Nite Seok HEB Ve ea 1 ' Veear aC Cn NOG nya tity ma - 4 ra ebe ‘ He aN wth Creek ey Mean e. Lhe ey BAe OW Tey c Pei e pda ee ha ee et OC A CN , aA CA ol Ce Df g 0 eek Ase Dog CO ek ne ee vera hd sty @ ve febee vite we tee wat ey rf . oer a de 9 DRO COC COC XE yew wt Cay sainge) : n ' fy : , PVN PN YY Vette a 000 ee otal wh ab aensat a nthe as a8 My uate aint nd ree yoad eae we Wine eat th Ot | Un aa ye ame tint ir v0 th Bey Aveewe. : ; ; Toe ee a DOU SI Toe hr WASH van Pandan Prey ra ° ¥ Fare ae eaeredmnaas 4 ety ‘ t 4 ' ' y Mee eh on een ey D yo A eye au ' re | weve i. ve JR ING D7 RH) pes ea : tt SA OM UNO teh ee Y Moet tee F re cab shea MKT RRS Vell We 977 Fore . bad a ras vs rir PRGA He ik : : i au " ; Kor _ Peary Die ere mad . 1 i ‘ eC ee ow yhy an — WEA Aa ty ee ain Meee et us ses Ye 1 ’ “yd re fers Cea N eee t “ at i YF ¥ £ toby ih Lewy boast wa De Vase Ute tekeg em aye F : Sua ts tp begs phat tens ’ ‘ ‘ neha re vngtte na tae nt Neern the ee .| va a he f 7 ' TUR GA he ho te RoE eh bi Matt Be sieeem » mime a gsigen Ge ben Ap Acne , Ais © ee ee Oe vi ane a ‘ Ae tsk ite herds tyaoar toa, Yue pos qevet ' RU rae PUR At oR ve Wri Lt ae Weta me fee, tem yh i i] Preedntebuese tet ere Yuta we ite ha tbe rt Ds 1 DAW De ete Ota We le dean Kou ea W tpes ' Ot ee ; na Pores Obit Ve a oP Oa tiny N StL Be We Pier ela le peyton iegiy ei, we a Pd F, rer aa ¥ truy be Cn er rer te A ee Oe ee PB ey { &e Wh 1. he Hm rhea VA Nath Fal Geli L Ta meek : page , Ga) Soup ue riay 7 Aa ay y Cr ee | ‘ ' bere, Gee ge ep ay dee ome Weis te eh RE Ld eee ee ers ot a bts DNA eth Die Wheel at dents w, iret st hit fy A no eT » be Uy ses fa ‘ fore eth eh ee PELE D bes Pee pe gee ke eetey Poh een ete ah M828) noe Wy '8 He te at nal hd cua : cached) 3 we YU ook © Oe fe Cowes oe EE Ly Weeds eg Pad ee ee ee PARE RR So Seth ny phe nel Me lena Mey Big itp g : wai ieca CT 1 he hee’ Oe Ba? wearatys Py Pe Pe dah tye te web ae POET DUNO TRE Bho te OR OO LOtUnnns pets tbe whites hi ' ch i Biv ; 1a hk Aga 4 pone PONS pte RT Uti bie Pen 1 Jy Vb whee mann s W, hods werbaOrte te ye Vee OM ee era b eer de abe PAD eos ee 8 WS tote WMemugchealuh tata nat be vad tae ' ; ' hey , “ A k ar Lae on) a . : c VV MOTs "5 40:30 4p ‘ r ‘ . v bee cm) Wh ati tidak WL eT ' Y bowen tt > in sto We We ibe eo oe ee ' rie ‘ U $ La 5 Ln % Ware d + Ru hath po Rnd ibe i) ’ ' hy We vote nh, Ponty Wake oh oh “ ra er i as te is $ 7 1 Raet Wt hts Bite tO Om fhem y 1 an ee ee ee ' PES PE LER DOV yas | el Ro oe el ee a | ‘ i} 1 ' ‘ “ ’ ot gy ‘ : Aly Tele peted: Pwrthgenes Wire aewar ‘9 ee ie | m4 ae Per ene 4 Phe eee ee F : » ek Sine y o8 ws . 4 adhe a th ptt aN ee LY ek a) ves , to 14 WPM Pa higet ‘1 R ' nnn Ss ay th hey VM he: pA he } ry v,¢ ‘ er vo ngs ein ‘ ele DN ge ast vt a GU | - i 00 fe) Ue ee See LL Oe Reel OL TORO a can ih : rai vai geo bud Dds we eee eee Ce ee ee be eee mee oe 4024 yD she ME ete ts te , : 7 % “on re ere dae mee Ly ‘eee a) Ao ey He Rem EDD Rhee We then ei hy 4 — ; ‘ ooyvr ped a ete | ree vw byt UNE PM bake Wow te eH, dy le yh RAM 8 Ve dette Wath aT 1M Aim ete My atlps a rtytte Bo Dive 7 “4 * ‘ ' ve f\p Woes by twee , yey real i ee Oe ee ee he eLearn) Me Dye eat ed ate Coreen : i' 1 f 14 peeps if ois Pures KGy acs evr PAT ey) A ay PORNBB Met ee cng 8 tr. . ‘ 2.) bab seen ‘ fan 4 1 ee ti VU NT b Ae 2 Pde Oe ele eb et eH be he » 1 ee Reaty { i | 1 var “ $7 % y ee fy wey PM Lae eaey dep & Heat & eh 8 ee ee by 1 ‘ ' ‘ . Og | ‘ re . ‘ * ' . ' ’ oa . , + yyy tye vu Vet Ve HEE Coe En yeh Hy ee fh Fi r { to ' ‘ ra Cn rs am | rt pu 4 ee oe es a TNT PR UL BEAN tee @hey y ‘ ey 3 . % ». of Lec 4 » 4 beg eV 7 ‘ Viva re gpa ee ee ee eS te Se WRU betes eemiehen acts 1 pet - R Saget : ty te sae a ‘ Y Yor nya na Bere eV Neg Va . ‘ Mos Met AP Wh abe ent T. va tik 4 sore ‘ ' ‘ Vd ' toe rye oy th 28en Ge aha a Sa a SIT ee a ee : bier aga ‘ a yoy nse ea A tht Wry ed bp’ 9 Win mh y te Weeteelh ayttntebn waahe ; ! ' ry ¥ ' oo re doney « bog ! ‘ | ’ +E eu aee bag ye et Ph my 5 ; we Raden te ye coy «ah Pe ese ed ae co ts NAL EAHA OY Sead ol, BNE tu Va ke fa) Pea iyy Paw 4 Vp eee eee YE a taste te by ' } ' \ re a ROE OR ICH SON bet he 3% ' ' reeewn rye yp bee ' eh Ht pe he bet , vey . +1 ' a4 ener tee Shite fel w tate 1 ‘ ‘ . ’ . i 1% ay bo ny ty We le : i ; * Ca Ce Wiece Ge ae WE rere Wed bore pe Umer ; . F ; ‘ rags HEM UTA Nn ben Wm hah : hel» whe po ’ city Pe TVR be Bm ye et ; Pi 7 treet rebynys ' 7 Blew nyt SEED Bd ely Veh ol by Any ' 4a h. & Tye ‘ . ' te eimwuis oo sh ws 99 is ae tay pst F i jt Peed ee Pg 4 rey A ee ad ey Aye # a { fo ' ee y ‘ yur ] J tht ita re ‘ : My Cif Aly, ok Wie toy "ys aa yey be ahh ih a, ; > : sus exer fps a) : wire yg Man Mea, ' 7 or ¢. Pequers wy at z . y eee she " #0 Ne As Be Me ay 14 y , } P ' ae ' 8 19, Ye ey Vs art tthe wes) vw ; bow . ‘ , yt 1 SOE ey she Ki : bepecg Sop ws Ae Nas ie als 9! Gh 4 hy Fi ' ty ’ wi hi’ eee Vik? MRM y's ‘ ‘ 74 ' ‘ . - oF : PY ane ; oe ; ? t ‘ roa 1 ! ‘ 7 Lee | J “ ; i) ey, Dae Ak , rhemis ey sda BEATE? yee cs ODE low oe ; 7 7 ae ee ae TY Oo PRT HED eye haben Feabnisd ints w Wino : : x ae a re ey ‘| ‘a4 ¢ i ‘ i ' res ‘ he tw Mg som hed es Ve tee Bis ey Crh ery k : ‘ ry « eg i Phi pee ' t-b QA ' , ; rete ny 22 NDA bench we abt t t ' 1 ty i ae A ‘ Die te berm y hte : : ‘ ’ , ; peu mh — t3 i" 3 8B hey ‘ a i c ye i ' ' ' } ’ t . 7 iM 1 oA ! share t Peer oth LAY! mf) ‘ eds ra babe Vebebe 4 ’ LJ 4 : ‘ai 7} § i} y | i nit A ; b's Wee & 4 i ; vi, ric tre ft 4 ' z } \ + 4 4 . 1 ' 1 4 he i 4 H toe ! ti . . ‘ ve b } ‘ 5 ‘ iv fan bay M4 oo + 4 ‘ 1 Vi ‘ ' ’ t ' : ‘ ‘ y} ' 4% or | ye.r ‘ a's ‘ ‘ : rod i af 8s ' , , J ta ‘ one : per ye Fed i i ‘ 4 ' ‘ . f 1 ’ ' ' . i . : ' . hans U ' ' i ) ' , 4 i A . ' ' ' Mite ate l ' * 4 1 ' i ‘ agian ie 4 ox wi ; ‘ Bhoersain i rae ak ' , ‘ { tra ‘ : é ' i i) ted ‘ ' ‘ ‘ ib tobe da ine ‘ i PEPE MPA DEO AP OTH EY wis ; 7 er Ae Tee Fite ae : j , t : 4 9 ok ae em Pie At Be! : : tT were dda tte ay PaaS eR an ‘ r | 2.5 ‘ a ! a ais Mar en ae», ' i iy ee Oy ” Bene. Pi F + Ne heb i 1 ; ' : i deo dail’ £4 ,, ey aye) . ; i ‘ Or a . ‘ io4 it + o« ‘ eh hn H F : yer A thane oe RR) i ; ’ i 1 ‘ Oe deta a, 44 sma bal “me Woy tate “wh ny f Mi F . mei kod, §deye bok te nite eh PR ED et BR ae aed too a . ae re ee oe Mee Bd , ue Wey Wi Pat wae gh . - A i wad ‘ to aed * yal ‘ 5 EE tate sie rive at . ; i -i4 B ane er Aa tte aie Pi oth wie WE ea Upwa i ' oat ata ot vd he Feeds Oh Pon thee ra ae) i ' car ‘ i>.a ia 4 Cree | “ i” ae CPretcrrt Peery yy te ' ‘ ii ' ‘ ou Hae ed es OS Titel tel ana eh { y i Naini de ae 4 vA eOwhe we why ’ i * 4 ' r, ‘ ’ : te 4 Bhi Ha ial ee ” Aaue r lee a ay ra . re Cth ea ae hae ood pent ay hed dew edorn bee i Seetin bee © sae me wate ’ i ola ‘ , Pabgdieotiiva Heooe | ; ” ’ ‘ oma Bieldside ay ancien ia wha ‘ tr 4 ' . ee or Qe bia Feb eed Oe he to 4 err we oy eee ig ee OE Bat ray o4 Ko bh bial yy Ree tk abies ale eek gh wwe Ci eee ee ee re ee ae | Veen ye ak Pee n ee wae Fabel bude dt bee ed ed el eg oa database h heidi gi Wad ahh Derr a wd < ‘ as yp Vad i at pues , 99h teeta i eer fe ee o . ia + ae ‘ mud bat ba ‘ ee ee ce ce eer er ‘ 1 it ‘ i | aii yoo mei me nt SPE beh 6 wre bb) ort ede dey £ 6h ii figs basin i IBLE MRE ah eo CUI ' fie’ y ‘ ‘ - fF didlineD ste bens 4a dt wb oe eee etenavene arts : A , Oe Obed thee thee Gade het Pe ed Pea rinedierisy " : ’ a kp died plea ebapb daa y a : ; Pe A eP ePyte PONS tal ; i $r-tce vi ewe hio wae Ot ' ‘ i rue reread bee eane See es th Pl id bbe ta Oe mE dee ae ly ' view Ga af od ‘ va gaat ade pile i aha Ya he bet eae st hy Be GS 19 top ne oe ' van 4 baw bg Le Oa OH GE aot hata 5 rae ‘ a a etal Maia a : bebe oy A ‘ pute $e oa ee ee “nu ear ere yr ir aie ; P weasie ee Lew tte Wha oh pa Cer ees om be Ame oer che bole rae ' ebbing ‘ : eee ee atin i) Pi itty 6 Pe nreardre seagate. bend re or ar Ure dr ine bawt LEME W NE br er Peal Mr beer COT tute iL Ft NOT em Heme ay fer Pr - : : what bot a dee (dvd deel bh Cd adyne br eee Hhe @diewme de pe thy i tvel G4 ‘ ot eveide en eee a eee ree ee ore ke tree iy eed Oe mae kate Loy tye ee i t rr i bicena Per ee ee ee eh ee rer ee ret ee erent mer y ot Whe Mame ne ' ‘ . aes ‘ Ce ee Ce ee ee ere ec en rere et PAPO ee ee eed at ‘ oe a “ ‘ ee ee An er een Yes ela a Ta es 48 ie oy v4 ' ' ‘ oe ae tows ‘ oe are Ok oe a ee eee | NWA dat kelly RR tad ’ ‘ ' i ‘ ‘ . i 1 wt et 4a ' 4ferrl ete @ 2h te Oe wee bbe ee week re MEM ty late ot chal + f . i] ta obe ‘ ‘ mar \ Ly ee oot ee i] - wide <7 Ca i] raedea * Ce ee ‘ Mbt. nM) ® AO Wi oe ve ‘ past i fo ban emit ' ho 7 inka + cktare oon ge eee wa sat eoakee PU CR Ae ! i, i ‘ ee DPN be ek ob oad wee rae ale o EG A aeh dh O69 dt dane js ‘ ' ibe W; i i ‘ fue ter wit we aad 4 veut ArT Fy 7 : ' hr Sy my idee RU BO ee eer Ty yen ow 1a or sed hae meee ‘ ar | . ‘ en ' sie wt ' Vad adm de tod ia ria readeat - sao . hf oe ow ‘ we i vr ot ' sees Sorte ta Pah rae e as iow ' pa ip i ha { 4 ba ' Cob bworte CEL OOD geht be pe week ote P ed Soba ya : he sas tad bade Bee en tb sy awee. fe fal ay ‘ ‘ PHA boobs 44 ' ond ’ Oa Te ae A was Laie be ae Ua boil of of ta hae ate dlare hay) nalbep er A ba ies ee Puetee bees aa te a hatisend nti mah yt hyip ‘ee retes ane eee h Yio es oe toe 4 ‘ ‘ ‘ ‘ ' ‘ ow ye i we iat aya ‘eoeehe mA ne eer Piebhdea 1 ‘ ' OUR 1g ee be oe hams My < Saw A rani 7 ova Wiae F ae ee fee me VHOe bi gare esreat ee , to ead f] i ‘vw v1 Pan ‘ but Matra Wye as CR A ' wey we” ' ‘ 1 ‘ wie ebte bead ihe we t n ' f i ' riwead on tau ify ey aut @a ty i is f nea ta ‘ ia in Ca edith orl petal: ’ ta v ‘ oo yoy ' re ae eae a dca a deaty ay v6 4 ie ia i ‘ a) m4 . se bbe Ce eee ee ee de ahriot 4 ie i bea wed tan fa’. oa Cerrar ek rie eT | TOC UCRIe OR CT wa i ‘ é Cot Pb ag tions thet sewn a) oh oa ei roe a | overage sro " ria | enna PRC REN OM LY BY eB hy Or re ' € tee ‘ fo : Pa beck a fm rer | RENN tou 4 pau ' Pepe ens Val Tan La 4 oh wil as ‘ ‘ . 1 ribs oes wana “erie Carirer a i) ve hocnvig 1 f°. 4. i beh i Ce ee re pera hoes ie UM. Ba 8d 1 eb ab ed as Cr a avd bike Dida f bY Ma a 1) er ee oe ee ee ee cer eee eee ee ee - omy et bie ‘ ' ie ke Tan a | ‘ Oe ee ee | ‘btw eve d wi vada gated ep deedu bbe 4 ~~ oe had . » of 's 7 a se. Lan - » ws ne : * he : | 3 ; . ut - G: — Sea hee eee ae eS ge eat OA He So _ ‘ “et wee es ee <> a ae we *=* ign, , ‘ } 4 , r, ¥ / 4 n ed i , Z j ‘ t * } i ‘ y ‘ j \ , ‘ 4 ? F ae ‘ * ’ ~ ‘4 : i Ae ‘ ‘ a , 4 ’ i i’ 1 } 4 ’ ? y y ) fy! i} + ! ad ’ ’ J 7 W : i 1, ia j ‘ " f 7 ‘ ; } — | bh} es ae, al Ay hb): i at % (oa ee. she ee iy + aks! so 5 a - ; | PIR eal i, f é i ee: ha 7 '- ee ; ) ; | oes ee eee ee s 4 . TRANSACTIONS ‘ ; ‘OF THE QONNECTICUT ACADEMY OF ARTS AND SCIENCES. VOLUME IX. NW. EEA EN’: PUBLISHED BY THE ACADEMY. 1892 to 1895. THE TUTTLE, MOREHOUSE & TAYLOR PRESS. " ma? Le sa¥} Vice-President. CHARLES S. HASTINGS. Secretary. SAMUEL L. PENFIELD. Librarian. ADDISON VAN NAME. Treasurer. WILLIAM W. FARNAM. Publishing Committee. ; HUBERT A. NEWTON, _ CHARLES S. HASTID GEORGE J. BRUSH, ADDISON E. VERRIL: RUSSELL H. CHITTENDEN, EDWARD S. DANA, ADDISON VAN NAME. S “>... Auditing Committee. ADDISON E. VERRILL, ADDISON VAN NAME C.O ONT Ene eS. isn On ADDITIONS TO THE. LIBRARY,.-_...-...- NG a Nee Art. I1.—MatueEmaticat INVESTIGATIONS IN THE THEORY OF VaLuE anD Prices. By Irvine Fisuer,-.--_-.-. -. IL—Strupizs 1n THE Hinerisho Mysrery Puays. By En AR Hci WAC TDG ON, 2 epee ies etc Ne UE ha IiI.—Paporp-picrestion. By R. H. Cuirrenpen,.--_------ TV.—ON THE CLASSIFICATION AND GEOGRAPHICAL DistTRI- BUTION OF THE LAMINARIACES. By W. A. Sxutcu- V.—ReEvIsION OF THE Faminies oF Loop-BpEarinc Bracnu- 1opopa. By C. KE. Brzcurr. Plates 1, 2,..--.---- VI.—Tue DEVELOPMENT OF TEREBRATULA OBSOLETA, DALL. Brg @r ie bnnemmr, Plates. 2.3/5. 22'.02 2220. <2. Via.—Canapian Spipers. By J. H. Emerton. Plates la, 2a, aes eh ce Pane Senn May ys alia Abed ENE Uy tl hed LG lS VII.—Own Some Birps anp Eaes coLttectep By Mr. Gro. Comer at Gouen Is~tanp, KercuELen IsLanp AND THE ISLAND OF SOUTH GEORGIA, WITH EXTRACTS FROM HIS NOTES, INCLUDING A METEOROLOGICAL REC- ORD FOR ABOUT SIX MONTHS AT Goucu IsLtanp. By Care urine ow ilaves 859. Oe tele. lk VIII.—On tHe Anatomy oF a spEctES or NEMERTEAN ( Cerebratulus lacteus Verrill), WITH REMARKS ON CER- TAIN OTHER SPECIES. By W.R.Coxz. Plates 10-15, [X.-—DESCRIPTIONS OF THREE NEW SPECIES OF NEw ENc- LAND PALHONEMERTEANS. By W. R. Con,---.--- ~~ X.—SuPPLEMENT TO THE MARINE NEMERTEANS' AND 298 3393 400 430 479 515 PLANARIANS OF New Enauanp. By A. E. Verritn, 523 ODITIONS Pe yik hiBRARY OF THE Connecticut Academy of Arts and Sciences, By GIFT AND EXCHANGE FROM JAN. 1, 1891, To Duc. 31, 1892. American Association for the Advancement of Science. Proceedings. Meeting XX XIX, XL, 1890-91. Salem, 1891-92. 8°. ALBANY.—WNew York State Library. Annual report. LUXXIII, 1890. 8°. Bulletin. Legislation, I, 1891; Additions, I, 1891; Library school, I. 8°. New York State Museum of Natural History. Annual report. XLIV, 1891. 8°. Bulletin. Vol. TL. 1,°1892,. 8°. ANNAPOLIS.— United States Naval Institute. Proceedings. Vol. XVII, XVIII. 1-3, 1891-92. 8°. AustTin.—Texas Academy of Science. Transactions. Vol. I. 1, 1892. 8°. BALTIMORE.—Johns Hopkins University. American chemical journal. Vol. XIII, XIV, 1891-92. 8°. Studies from the biological laboratory. Vol. V.1, 1891. 8°. Maryland Academy of Sciences. Transactions. Vol. J], pp. 213-228, 1892. 8°. Boston.—American Acadenvy of Arts and Sciences. Proceedings. Vol. XXV, XXVI, 1889-91. 8°. Society of Natural History. Memoirs. Vol. IV. 10, 1892. 4°. Proceedings. Vol. XXV, 1890-92. 8°. BRIDGEPORT.—Scientific Society, — List of birds found in the vicinity of Bridgeport, Conn. By C. K. Averill; dr. 1892. 8°. BUFFALO.——Society of Natural Sciences. Bulletin. Vol. V.3, 1891. 8°. CAMBRIDGE.—Harvard College. Annual reports of the president and treasurer. 1889-90, 1890-91. 8°. Astronomical Observatory of Harvard College. Annals. Vol. XXVI. 1, XXX. 1-3, XL. 1, 1890-92. 4°. Annual report. XLV-XLVII, 1890-92. 8°. Variable stars of long period. 1891. 4°. Museum of Comparative Zoology at Harvard College. Memoirs. Vol. XIV. 1, pt. 2?, XVII. 2, 1891-92. 4°. Bulletin. Vol. XVI.10, XVIII, XIX, XX. 6-8, XXI, XXII, XXIII. 1-4, 1890-91. 8°. Annual report. 1889-90, 1890-91. 8°. v1 Additions to the Library. CAMBRIDGE.—Entomological Club. Psyche. No. 177-187, 189-200, 1891-92. 89. New Englund Meteorological Society. Investigations. 1890. 4°. Bulietin. No. 1-59, appendix 1890. 8° and 4°. CHAPEL HILu.—Zlisha Mitchell Scientific Society. Journal. Vol. VII. 2, VIII, 1890-91. 8°. CINCINNATI.— Observatory. Publications. No. XI, XII, 1891-92. 8°. Journal of comparative neurology. Vol. I, II. 1-3, 1891-92. 8°. Society of Natural History. Journal. Vol. XIII. 4, XIV, XV. 1, 2, 1890-92. 8°. Des Mornes.—Jowa Academy of Sciences. Proceedings. Vol. I. 2, 1890-91. 8°. FRANKFORT.—Kentucky Geological Survey. , Report of progress from Jan., 1890 to Jan., 1892. By John R. Procter. 8°. Report ou the geology of Clinton county. By R. H. Loughridge. 8°. Report on the geology of Whitley and a part of Pulaski counties. By A. R. Crandall. 8°. Report on the geology of parts of Jackson and Rockcastle counties. By Geo. M. Sullivan. 8°. Report on the occurrence of petroleum, natural gas and asphalt rock in western Kentucky. By Edward Orton. 8°. GRANVILLE.—Deninison University. Bulletin of the scientific laboratories. Vol. VI, VII, 1891-92. §&°, HARRISBURG.—Second Geological Survey of Pennsylvania. Annual report for 1887. 8°. Report of progress, 1888-89. 8°. Seventh report on the oil and gas fields of western Pennsylvania for 1887, 1888. ~S°. Summary final report. Vol.I, II. 1892. 9°. Atlas of northern anthracite field. Pt. VI. 1889. 89°. Atlas of western middle anthracite field. Pt, III. 1S89. 8°. Atlas of southern anthracite field. Pt. III, 1V, IVB, V, VI. 1889-91. 89°. New general map of the anthracite region. 1890. 8°. Dictionary of fossils. Vol. II, III. 1889-90. 89. HarTFORD.— Connecticut Historical Society. Papers and reports, May 26, 1891. 8°. LittLeE Rocx.—Arkansas Geological Survey. Annual report, 1890. Vol. I, Il. 89°. MERIDEN.— Scientific Association. Transactions. Vol. IV, 1889-90. 89°. MINNEAPOLIS. —Minnesota Academy of Natural Sciences. Bulletin. Vol. III. 2, 1887-89. 89°, New YorkK.—Academy of Sciences. Annals. Vol. V, 9-12, extra no. 1-3, VI. 1-6, 1890-92. 8°. Transactions. Vol. X. 1-6, XI. 3-5, 1890-92. 89. ——American Geographical Society. Bulletin. Vol. XXII. 4, XXIII, XXIV. 1-3, 1890-92. 89, —— American Museum of Natural History. Bulletin. Vol. III. 2, 1891. 89°. Annual report. 1890-91. 89, Astor Library. Annual report. XLII, XLIII, 1890-91. 8°. ——- Linnean Society. Abstract of proceedings for year ending March 6, 1891. 8°. i Additions to the Library. vu New Yor«:— Microscopical Society. Journal. Vol. VII, VIII, 1891-92. 8°. Torrey Botanical Club. Bulletin. Vol. XVIII. 1-6, 8-12, XIX. 2-12, 1891-92. 8°. OBERLIN.—— Oberlin College. Laboratory bulletin. No. II, 1892. 8°. PHILADELPHIA.—Academy of Natural Sciences. Jounnaly Viol, Tx. 3, 18d 42° —— American Entomological Society. Transactions. Vol. XVII. 3, 4, XVIII, XIX. 1, 2, 1890-92. 8°. Franklin Institute. Journal. Vol. CKXXI-CXXXIV, 1891-92. 8°. POUGHKEEPSIE — Vassar Brothers Institute. Transactions. Vol. V, 1887-90. 8°. ROcCHESTER.— Academy of Science. Proceedings. Vol. I. 2, II. 1, 1891-92. 89°. SACRAMENTO.— California State Mining Bureau. Annual report of the state mineralogist. X, 1891. 8°. St. Lours.—Acadenvy of Science. Transactions. Vol. V, VI. 1, 2, 1886-92. 8°. Result of the observations made by the Washington University eclipse party at Norman, Cal., Jan. 1, 1891. Camb., 1891. 4°. Missouri Botanical Garden. Annual report. I, II, 1890-91. 8°. SaALeM.—TZssex Institute. Bulletin. Vol. XXII. 4-12, XXIII, XXIV. 1-6, 1890-92. 8°. San FrRaAncIsco.— California Academy of Sciences. Rroceeningss ser UW Voleiil. 1, 1sot. 8°: Technical Society of the Pacific Coast. Transactions and proceedings. Vol. VII. 4, 5, VIII, IX. 1-3, 10--11, 1891- Deh 82: University of Virginia. Leander McCormick Observatory. Publications. Vol. I. 4, 5, 1889-90. 8°. W ASHINGTON.— Bureau of Education. Report of the commissioner of education. 1888-89. 8°. Chief Signal Officer. Annual report. 1890. 89°. Department of Agriculture. Division of entomology. Bulletin. No. 23-27, 1890-92. 8°. Periodical bulletin. Vol. III. 4-12, IV, V. 1, 2, 1890-92. 8°. Report of the chief of the weather bureau. 1891. 8°. United States Geographical and Geological Survey of the Rocky Mountain Region. Contributions to North American ethnology. Vol. II, V. 1890. 4°. United States Geological Survey. Annual report. X, 1888-89. 8°. Bulletin. No. 62, 65, 67-81, 1890-91. 8°. Mineral resources of the United States. 1889-90. 8°. United States relief map. United States Naval Observatory. Astronomical and meteorological observations. 1885-88. 4°. Report of the superintendent. 1890, 1891. 8°. National Academy of Sciences. Memoirs. Vol. IV. 10, V. 4. 4°. —— Smithsonian Institution. Bibliography of the Algonquian languages. By James C. Pilling, 1891. f vill Additions to the Library. Catalogue of prehistoric works. By Cyrus Thomas. 1891. 8°. Omaha and Ponka letters. By James Owen Dorsey. 1891. 8°. WILKES BARRE.— Wyoming Historical and Geological Society. Notes on the tornado of April 19, 1890 in Luzerne and Columbia counties. By Thomas Santee. 1891. 8°. WORCESTER.—American Antiquarian Society. Proceedings. Newseries. Vol. VII, VIII. 1, 1890-92. 8°. AMIENS.—Société Linnéenne du Nord dela France. Bulletin. No. 211-224, 226-234, 1890-91. 89. AMSTERDAM.—Kon. Akademie van Wetenschappen. Jaarboek. 1890-91. 8°. Verslagen en mededeelingen. Afdeel. natuurkunde. 3de reeks. Deel VIE, 160, 9Se- Australasian Association for the Advancement of Science. Report. Meeting III, 1891. S°. AUXERRE.—Société des Sciences Historiques et Naturelles del Yonne. Bulletin. Tome XLIV, XLV, 1890-91. 8°. BaSEL.—Waturforschende Gesellschaft. Verhandlungen. Theil IX. 2, 1891. 8°. BaTavia.—Kon. Natuurkundige Vereeniging in Nederlandsch-Indié.- Natuurkundige tijdschrift. Deel L, LI, 1891-92. 68°. Magnetical and Meteorological Observatory. Observations. Vol. XII, XIII, 1889-90. 4°. BERGEN.— Museum. Aarsberetning. 1890. 8°. BERLIN.—Konigliche Sternwarte. Berliner astronomisches Jahrbuch. 1893, 1894. 8°. Veroffentlichungen des Rechen-Instituts. No. I, 1892. Naturae novitates. Jahre. X-XIII, XIV. 1-22, 1888-92. 8°. BoLoena.—f&h. Accademia delle Scienze dell’ Istituto di Bologna. Rendiconto, Anno 1889-90. 8°. BomBay.—Bombay Branch of the Royal Asiatic Society. Journal. No. XLVIII, 1891. 8°. Government Observatory. Magnetical and meterological observations. 1888-89. 4°. Bonn.—WNaturhistorischer Verein der preussischen Rheinlande, Westfalens und des Reg.-Bezirks Osnabriick. Verhandlungen. Jabrg. XLVII. 2, XLVIII, 1890-91. 8°. BorRDEAUX.—Académie Nationale des Sciences, Belles-Lettres et Arts. Actes. Année LI, 1889. 8°. Société Linnéenne. Actes. Tome XLIYV, 1890. 8°. ’ Société des Sciences Physiques et Naturelles. Mémoires. 3°¢sér. Tome V.2. 4°sér. Tome II. 1890-91. 8°. BRAUNSCHWEIG.— Verein fiir Naturwissenschaft. Jahresbericht. VI, 1887-89. 8°. BREMEN.—WNaturwissenschaftlicher Verein. Abhandlungen. Bd. XII. 1, 2, 1891-92. 8°. Meteorologische Station. Ergebnisse der meteorologischen Beobachtungen. Jahrg. I, 1891. 8°. BRESLAU.-—Schlesische Gesellschaft fiir vaterldindische Cultur. : Jahres-Bericht. LXVIII, LXIX, 1890-91. 8°. BRISBANE.— Queensland Museum. Annals. No. I, II, 1891-92. 8°. Additions to the Library. 1x BRISBANE.— Queensland Branch of the Royal Geographical Society of Australia. Proceedings and transactions. Vol. VII. 1, 2, 1891-92. 89. Brinn.—WNaturforscher Verein. Verhandlungen. Bd. XXVIII, X XIX, 1889-90. 8°. Bericht der meteorologischen Commission. VIII, IX, 1888-89. 8°. BRUXELLES.— Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique. Mémoires couronnés et mémoires des savants étrangers. Tome L, LI, 1889-90. 4°. Mémoires couronnés et autres mémoires. Tome XLIII-XLV, 1889-91. 8°. Bulletins. 3¢sér. Tome XVII-XXI, 1889-91. 8°. Annuaire. Année LVI, LVII, 1890-91. 8°. Catalogue de la bibliothéque. 2° partie. 1890. 8°. Société Hntomologique de Belgique. Annales. Tome XXXIV, XXXV, 1890-91. 8°. Société Royale Belge de Géographie. Bulletin. Année XIV. 3-6, XVI. 3, 1890-92. 8°. Société Royale de Botanique. Bulletin. Tome XXIX, i891. 8°. Société Royale Malacologique de Belgique. Annales. Tome XXIV, XXV, 1889-90. 8°. BucaRrEst.—Jnstitut Météorologique de Roumanie. Annales. Tome IV, V, 1888-89. 4°. Bupapest.—Kon. ung. Central—Anstalt fiir Meteorologie und Hrdmagnetismus. Jahrbicher, Jahrg. XVIII, XIX, 1888-89. 4°. Buenos Aires.—Museo Publico. Anales. Tomo III. 5, 6, 1891. 4°, Sociedad Cientifica Argentina. Anales. Tomo XXX.6, XXXI. 2-6, XXXII, XXXIII, XXXIV, 1, 1890-92. Se: ———Indice general, vol. I-X XIX, 1876-1489. 8°. El] Paramillo de Uspallata. Por German Avé Lallemant. 1890. 8°. CaEn.—Société Linnéenne de Normandie. Bulletin. 4¢ sér. Vol. III-V, 1888-91. 8°. CaLcuTTa.—Asiatic Society of Bengal. Journal. Vol. LIX, pt. i, no. 3, 4, pt. ii, no. 2-5; LX, pt. i, ii; LXI, pt. i, mo. 1, 2, pt. ii, no.1, 2: 1890-92. 8°. Proceedings. 1890, no. 4-10, 1891, 1892, no. 1-7. 8°. Geological Survey of India. Paleontologia Indica. Ser. XIII, vol. iv, pt. 2, 1891. 4°. Memoirs Vol. XXIII, XXIV. 3, 1890-91. 8°. Records. Vol. XXIII. 4, XXIV, XXYV, 1, 2, 1890-92. 8°. Index to the genera and species described in the Paleontologia Indica up to 1891. 4°. Contents and index of the first twenty volumes of the Memoirs. 1892. 8°. Contents and index of the first twenty volumes of the Records. 1891. 8°. Meteorological Department of the Government of India. Indian meteorological nemoirs. Vol. IV. 7, V. 1, 1891-92. f°. Report on the meteorology of India. 1889, 1890. f°. Report on the administration of the meteorological department, 1889-90 1890-91. f°. Meteorological observations recorded at seven stations in India. 1889-91, 1892, Jan.-Apr. f°. Cyclone memoirs. Pt. III, IV, 1890-91. 8°. CAMBRIDGE.—Philosophical Society. Transactions. Vol. XV. 1-8, 1891-92. 4°. Proceedings. Vol. VII. 3-6, 1890-92. 8°. x Additions to the Library. CaTANIA.—Accademia Gioenia di Scienze Naturali. Atti. Ser. IV. Vol. II, III, 1889-91. 4°. Bullettino mensile. Nuovaserie. Fasc. 15-25, 1890-92. 8°. CHERBOURG.—Société Nationale des Sciences Naturelles. Mémoires. Tome XXVII, 189i. §&°. CHRISTIANIA.—Norwegische Commission der Europdischen Gradmessung. Publication. Heft VI, VII, 1888-90. 4°. Norwegisches meteorologisches Institut. Jahrbuch. i888-90. 4°. Norwegian North-Atlantic Expedition, 1876-78. Publication XX, XXI, 1891-92. 4°. Videnskabs Selskabet. Forhandlingar. 1890. 8°. Cuur.—WNaturjorschende Gesellschaft Graubiindens. Jahres-Bericht. Neue Folge. Jahrg. XXXIV, XX XV, 1889-9i. 89. Danzic.—WNaturforschende Gesellschaft. Schriften. Neue Folge. Bd. VI. 3, 4, VIII. 1, 2, 1890-92. 8°. Dison.— Académie des Sciences, Arts et Belles-Lettres. Mémoires. 4° sér. Tome iI, 1890-91. 8°. Dorpat.—Gelehrte Estnische Gesellschaft. Sitzungsberichte. 1890-91. 8°. Verhandlungen. Bd. XIV, XV, XVI. 1, 1889-91. 89°. Naturforscher- Gesellschaft bei der Universitit Dorpat. Sitzungsberichte. Bd. IX. 2, 3, 1890-91. 89°. Schriften. VI, 1891. 8°. DRESDEN.—Naturwissenschaftliche Gesellschaft Isis. Sitzungsberichte und Abhandlungen. 1891, i892, i. 8°. Dus.Lin.— Royal Irish Academy. Transactions. Vol. XXIX. 14-16, 18, 19, 1891-92. 4°. Proceedings. Ser. III. Vol. I. 4,5, IL 1, 2, 1891-92. 89. Cunningham memoirs. No, VI, VII, 1891-92. 4°. EDINBURGH.— Botanical Society. ; Transactions and proceedings. Vol. XVIII, XIX, pp. 1-231, 1890-91. 8°. Geological Society. Transactions. Vol. VI. 2, 3, 1890-92. 8°. Royal Observatory. Catalogue of the Crawford library. 1890. 4°, Royal Physical Society. Proceedings. Vol. X. 2, 1889-90. §S°. Royal Society. Proceedings. Vol. XVII, XVIII, 1889-91. 4°. EmpEN.—WNaturforschende Gesellschaft. Jahresbericht. LXV-LXVI, 1889-91. 89°. ErFurt.—Kon. Akademie gemeinniitziger Wissenschaften. Jahrbiicher. Neue Folge. Heft XVII, 1892. 8°. FIRENZE.— Biblioteca Nazionale Centrale. Bollettino delle pubblicazioni Italiane ricevute per diritto di stampa. No. 120-167, 1891-92. 8°. FRANKFURT A. M.—Deutsche malakozoologische Gesellschaft. Nachrichtsblatt. Jahrg. XXIII. XXIV, 1891-92. 89, ——Senckenbergische naturforschende Gesellschaft. Abhandlungen. Bd. XV1. 2-4, XVII, 1890-92. 4°, Bericht. 1891, 1892. 8°. FRANKFURT A. O.—WNaturwissenschaftlicher Verein. Helios. Abhandlungen und monatliche Mittheilungen. Jahrg. VIII, IX, X. 1-3, 1891-92. 8°. —_— "3 Additions to the Library. xl FRANKFURT A. O.—Societatum litterae. Jahrg. V, VI. 1-8, 1891-92. 8°. FREIBURG IN B.—WNaturforschende Gesellschaft. Berichte. Bd. V, VI, 1890-92. 89°. GENEVE.—Jnstitut National Genevois. Bulletin. Tome XXX, XXXI, 1890-91. 8°. Société de Physique et @ Histoire Naturelle. Mémoires. Tome XXXI. 1, 1891]. 49. Volume supplémentaire. Centenaire de la fondation de la société. 1891. 4°. Museo Civico di Storia Naturale. Annali. Vol. XXVII-XXIX, 1889-90. 8°. GIESSEN.— Oberhessische Gesellschaft fiir Natur und Heilkunde. Berieht:. XXVIII, 1892: 82. GLASGOW.— Geological Society. Transactions. Vol. IX. 1, 1888-90. 8°. Philosophical Society. Proceedings. Vol. XXI, XXII, 1889-91. 8°. GOTEBORG.—Kon. Vetenskaps och Vitterhets Samhiille. Handlingar. Nytids. Haft. XX-XXV, 1885-91. GOTTINGEN.—Konigl. Gesellschaft der Wissenschaften. Nachrichten. 1890, 1891, 1892, no. 5-10. 8°. Gistrow.—Verein der Freunde der Naturgeschichte in Mecklenburg. Archiv. Jahrg. XLIV, XLV, 1890-91. 8°, HapBana.—Real Colegio de Belen. Observaciones magneticas y meteorologicas. 1888. ii, 1889.i 4°. HAuiFrax,—WNova Scotian Institute of Natwral Science. Proceedings and transactions. Vol. VII. Ser. II. Vol. I. 1, 1889-91. 8° HALLeE.—Kais. Leopoldinisch-Carolinische deutsche Akademie der Naturforscher. Leopoldina. Heft XXVI, 1890. 4°. Novaacta. Bd. LY. 4, 1890. 4°. Das Vorkommen der nattrlichen Kohlenwasserstoff- und der anderen Erdgase. VonC.F. Zincken. 1890. 4°. Naturforschende Gesellschaft. Abhandlungen. Bd. XV. 3, 4, XVIII. 1, 1892. 4° and 8°. Bericht. 1888-91. 89°. Naturwissenschaftlicher Verein fiir Sachsen und Thiiringen. Zeitschrift fiir Naturwissenschaften. Bd. LXIII. 4-6, LXIV, LXV. 1,2, 1890-92. 8°. HAMBURG.—Deutsche Seewarte. Archiv. Jahrg. XIII, XIV, 1890-91. 4°. Monatliche Uebersicht der Witterung. 1890, Juni-Dec.; 1891. 8°. Deutsches meteorologisches Jahrbuch. 1889, 1890. 4°. Ergebnisse der meteorologischen Beobachtungen, 1886-1890. 4°. Naturwissenschafilicher Verein. Abhandlungen. Bd. XI. 2, 3,1891. 4°, Wissenschaftliche Anstalten. Jahrbuch. Jahrg. VII, VIII, IX. 1, 2, 1889-91. HARLEM.— Musée Teyler. Archives. Série II. Vol. III. 5-7, 1890-92. 8°. Société Hollandaise des Sciences. ‘ Archives néerlandaises des sciences exactes et naturelles. Tome XXV, XXVI. 1, 2, 1891-92. 8°. Le Havre.—Société Géologique de Normandie. Bulletin. Tome XIII, 1887-89. 8°. HELSINGFORS.—Societas Scientiarwn Fennica. Acta, Tom. XVII, XVIII, 1891. 4°. xi Additions to the Library. Ofversigt af forhandlingar. XXXII-X XXIII, 1889-91. 8°. Bidrag till kannedom af Finlands natur och folk. Haft. XLIX, L, 1890-91. 8°. HERMANNSTADT.— Siebenbiirgischer Verein fiir Naturwissenschaften. Verhandlungen und Mittheilungen. Jahrg. XL, XLI, 1890-91. 8°. Hopart.—Loyal Society of Tasmania. Papers and proceedings. 1889-1891. §°. JENA.—Wedicinisch-naturwissenschaftliche Gesellschaft. Jenaische Zeitschrift fiir Naturwissenschaft. Bd. XXV, XXVI, XXVII. 1, 2, 1890-92. 8°. Kasan.—Société Physico-Mathématique de V Université Impériale. Bulletin. Tome II-VIII. 2¢sér. TomelI. 1-4. 1883-91. 8°. KHAaRKOW.—Société des Sciences Experimentales annexée a V Université de Kharkow. Travaux de la section médicale. 1890.i, 1891.i. 8°. Section physico-chimique. Supplément. Fasc. 1, 2, 1890-92. 8°. Kiei.—Kénigl. Christian Albrechts- Universitat. Schriften aus dem Jahre 1890-91, 1891-92. 8° and 4°. Kriev.—Kieuskie Obshchestvo Iestestvoispytateler. Zapiski. Tom. XI. 2, 1891. 89. KJOBENHAVN.—Kon. Danske Videnskabernes Selskab. Oversigt over forhandlinger. 1890. ii, iii, 1891, 1892. i. 89. Fortegnelse over de 1842-1891 udgivne videnskabelige arbejder. 1892. 8°. Naturhistorisk Forening. Videnskabelige meddelser. Aaret 1862-65, 1875-91. 8°. KONIGSBERG.—Konigl. physikalisch-dkonomische Gesellschaft. Schriften. Jahrg. XX XI-XXXII, 1890-91. 4°. Krakow.—K. k. Sternwarte. Materyaly do klimatografii Galicyi. Rok 1890, 1891. 8°. La PLata.—useo. Revista. Tomo I, IT. 1, 1890-91. 8°. Revista Argentina de historia natural. Tomo I. 1, 2,5,6, 1891. 89°. LAUSANNE.—Société Vaudoise des Sciences Naturelles. Bulletin. 3esér. No. 102-108, 1891-92. 8°. LEEDs.— Yorkshire Geological and Polytechnic Society. Proceedings. Newseries. Vol. XII. 1, 1892. 8°. LEIDEN.— Nederlandsche Dierkundige Vereeniging. Tijdschrift. Ser. IZ. Deel III, 1890-92. ‘8°. Catalogus der bibliotheek. Eerste vervolg, 1884-91. 8°. Sternwarte. Annalen. Bd. V, VI, 1890. 4°. Letpzic.—Astronomische Gesellschaft. Vierteljahrsschrift. Jahrg, XXV. 3, 4, XXVI, XXVII. 1, 2, 1890-92. 89. Catalog. Abth. I. Stiick III, V. 1890-92. 4°. Kon, sichsische Gesellschaft der Wissenschaften. Berichte. Math.-physische Classe. Bd. XLII. 2-4, XLIII. 1,2, 4,5, XLIV. 1, 2, 1890-92. 8°. Naturforschende Gesellschaft. Sitzungsberichte. Jahrg. XVII, XVIII, 1891-92. 8°. Verein fiir Hrdkunde. Mittheilungen. 1890-91. 8°. -Zoologischer Anzeiger. No. 351-407, 1890-92. 8°. LisBoAa.— Sociedade de Geographia. Boletim. Serie IX. 10-12, X, XI. 1-83, 1890-92. 8°. Lonpon.— Geological Society. Quarterly journal. Vol. XLVII, XLVIII, 1891-92. 8°. Linnean Society. Journal. Zoology. No. 124, 125, 145-151, 1891-92. §°. Additions to the Library. X1ll Journal. Botany. No. 175-6, 186-201, 1891-92. 8°. Proceedings. 1888-90. 8°. List. 1890-91, 1891-92. 8°. Mathematical Society. Proceedings. No. 391-448, 1891-92. 8°. Royal Historical Society. Transactions. New series. Vol. V, VI, 1891-92. 8°. Walter of Henley’s Husbandry, together with an anonymous Husbandry, Seneschaucie and Robert Grosseteste’s Rules. 1890. Royal Meteorological Society. Quarterly journal. Newseries. No. 77-80, 1891. 8°. List of fellows, 1890. 8°. Royal Microscopical Society. Journal. 1890. v, 1891, 1892. i-v. 5°. Charter and by-laws, list of fellows, 1892. 8°. Royal Society. Philosophical transactions. Vol. CLXXXI. A, B, CLXXXII. A, B, 1890- 91. 4°. Proceedings. No. 295-316, 1890-92. 8°. List of counciland members. 1890-91. 4°. Louvain.—La Cellule. Tome VI. 2, VII, VIII. 1, 1890-92. 8°. Lunv.— Universitet. Acta. Tom. XXVI, XXVII, 1889-91. 4°. Luxempoure. Institut Royal, Grand-Ducal. Publications. Section des sciences naturelles et mathématiques. Tome 2 DANN io) eet len Observations météorologiques. Tome V, 1884-88. 8°. Musée Guimet. - Annales. Tome XVIII-XXI, 1891-92. 4°. Bibliotheque des Gtudes. Tome I, 1892. 8°. Revue de Vhistoire des religions. Tome XXII-XXIV, XXV. 1, 2, 1890-92. 3°: Introduction au catalogue. 1891. 8°. MADRAS.— Government Observatory. Observations made with the meridian circle, i871-76. 4°. Results of the meteorological observations, 1861-90. 4°. MADRID.— Comision del Mapa Geologico de Espana. Boletin. Tomo XVI-X*YILII, 1889-91. 8°. Memorias. Descripcion fisica, geologica y minera de la provincia de Soria. Por D. Pedro Palacios. 1890. 8°. Real Academia de Ciensias Exactas, Fisicas y Naturales. Memorias. Tomo XV, 1890-91. 4°. MANCHESTER.—Literary and Philosophical Society. Memoirs and proceedings. Series IV. Vol. IV, V. 1, 2, 1890-92. 8°. MarsBure.— Gesellschaft zur Beforderung der gesammten Naturwissenschaften. Sitzungsberichte. Jahrg. 1890-91. 8°. Metz.—Académie. ; Mémoires. 38¢sér. Année XXII, 1887-88. 8°. MEx1c0.— Observatorio Meteorologico-Magnetico Central. Boletin mensuel. Tomo III. 1-4, 1890. 4°. Secretario de Komento. Memorias. Tomo I-VI, 1883-85. 4° and f°. Anales. Tomo IX, 1891, Boletin de agricultura, mineria e industrias. Ano I. 1-11, 1891-92. 8°. Estadistica general de la republica mexicana. Ano V, 1889. 8°. Xl1v Additions to the Library. Boletin semestral de la estadistica. Ano 1889, no. 3. 8°. La industria sericola en el estado de Jalisco. Por Marciano Barcena. L501 ).82: Mexico—Sociedad Cientifica ‘‘Antonio Alzate.” Memorias. Tomo IV. 3-12, V, VI. 1, 2, 1890-92. 8°. Sociedad de Geographia y Estadistica. Boletin. EpocalV. Tomo II. 1-5, 1890-92. 8°. Sociedad Mexicana de Historia Natural. La naturaleza. Ser. II. Tomo II. 1, 2. 1890-92. 4°. MIDDELBURG.—Zeeuwsch Genootschap der Wetenschappen. Archief. Deel VII. 1, 2, 1891-92. 89°. Levensberichten van Zeeuwen. Afi. IIT, 1891. 8°. MiLano.—Real Istituto Lombardo di Scienze e Lettere. Rendiconto. Serie Il. Vol. XXII, XXIII, 1889-90. 8°. Mopena.—fegia Accademia delle Scienze, Lettere ed Arti. Memorie. Serie Il. Tomo VII, 1890. 4°. Societd dei Naturalisti. Memorie. Serie III. Vol. IX. 2, X, XI, 1890-92. 8°. MONTPELLIER.—Académie des Sciences et Lettres. Mémoires. Section des lettres. Tome IX. 1,2, 1891. 4°. Section des sciences. Tome XI.2. 4°. Section de médecine. Tome VI. 2. 49. Moscovu.—Société Impériale des Naturalistes. Bulletin. Année 1890. ii-iv, 1891, 1892. i. 8°. Meteorologische Beobachtungen am Observatorium der landwirth. Aka- demie bei Moskau. Jahr. 1889. ii, 1890. 4°. MtncHen.—Kon. bayerische Akademie der Wissenschaften. Sitzungsberichte.- Philosph.-philolog. und histor. Classe. 1890, Bd. i. BS, ifs 4891) Bde dodo By 8: Mathemat.-physikal. Classe. 1890. iii, iv; 1891. i, ii. 8°. Die grossen Monarchien oder die Weltreiche in der Geschichte. Festrede von Ferdinand Gregorovius. 1890. 4°. Rerum coznoscere causas. Ansprache des Prasidenten Dr. Max vy. Petten- kofer. 1890. 4°. | Gedichtnissrede auf Wilhelm von Giesebrecht. Von Siegmund Riezler. i891. 4°. Kon. Sternwarte. Neue Annalen. Bd. II, 1891. 4°. . Munster.— Westfiilischer Provincial- Verein fiir Wissenschaft und Kunst. Jahresbericht. XVIII, XIX, 1889-90. 8°. Nanoy.—Académie de Stanislas. Mémoires. 5¢ sér. Tome VIII, IX, 1890-91. 89. Napour.—R. Accademia delle Scienze Fisiche e Matematiche. Atti Ser: Hf) Voll i¥, isat7 3 Ae. Rediconto. Ser, II. Vol. IV, V, VI. 1-6, 1891-92. 4°. NEWCASTLE-UPON-TYNE.—WNorth of England Institute of Mining and Mechanical Engineers. Transactions. Vol. XXXVIII. 6, XXXIX, XL. 1-5, 1890-92. 89. Report of the French commission on the use of explosives in the pres- ence of fire-damp in mines. Pt.3. 1891. 89. NURNBERG.—WNaturhistorische Gesellschaft. Jahresbericht nebst Abhandlungen, Bd. IX, 1892. 8°. OpeEssa.—Société des Naturalistes de la Nowvelle Russie. Zapiski. Tom. XV, XVI, 1890-92. 4°. Matematicheskoe otdielenie. Tom. XI, XII, 1891-92. 89. Additions to the Library. XV OrrawAa.—Geological and Natural History Survey of Canada. Annual report. New series. Vol. IV, 1888-89. 8°. Summary report. 1890. 89°. Contributions to Canadian micro-paleontology. Pt. 3. i891. 8°. Meteorological Service of the Dominion of Canada. Report. 1886-88. 8°. OxrorD.— Radcliffe Library Catalogue of books added during 1890. 8°. Radcliffe Observatory. Results of astronomical and meteorological observations. Vol. XLV, 1SSir2 8°. PALERMO.—R. Accademia di Scienze, Lettere e Belle Arti. Bulletino. Anno VII, VIII. 1-3, [X. 1-3, 1890-92. 4°. Paris.—LEvcole Normale Supérieure. Annales scientifiques. 3¢sér. Tome VII. 11, 12, VIII, LX, 1890-92. 4° Ecole Polytechnique. Journal. Cahier LX-LXII, 1890-92. 4°. —— Observatoire National. Rapport annuel. 1890, 1892. 4°. Société Nationale @ Acclimatation. _ Revue des sciences naturelles appliquées. Année 1891, 1892. 8°. Société Géologique de France. Bulletin. 3esér. Tome XVII.10, XVIII. 5-9, XIX, XX. 1, 1889-92. 8°. Société Mathématique de France. Bulletin. Tome XIX, XX. 1-5, 1891-92. 8°. Société Zoologique de France. Bulletin. Tome I-XVI, XVII. 1-6, 1876-92. 8°. Mémoires. Tome I-IV, V. 1-4, 1888-92. 89°. Pisa.—Societa Toscana di Scienze Naturali. Memorie. Vol. I, VI. 3, XI, 1875-92. 8°. Processi verbali. Vol. II. pp. 65-89, 256-287, III. pp. 197-272, VII. pp. 199-345, VIII. pp. 1-156, 1875-92. 8°. PotsDAM.—Astrophysikalisches Observatorium. Publicationen. Bd. VII. 1, 1892. 4°. PraG.—Kon. bohmische Gesellschaft der Wissenschaften. Abhandlungen der math.-naturwiss. Classe. Folge VII. Bd. IV, 1891. 4°, Sitzungsberichte. 1891. 8°. Jahresbericht. 1890-91. 8°. ——K. k. Sternwarte. Magnetische und meteorologische Beobachtungen. Jahrg. LI, LII, 1890-91. 4°. PuLKova.—WNicolai- Hauptsternwarte. Bericht, Mai 1887—Nov. 1889. 8°. QuEBEC.—Literary and Historical Society. Transactions. No. 20, 21, 1889-92. 8°. REGENSBURG.— Naturwissenschafilicher Verein. Berichte. Heft II, III, 1888-91. 8°. Historischer Verein von Oberpfalz und Regensburg. Verhandlungen. Bd. XLIV, 1890-91. 8°. Register zu Bd. I-XL, 1832-86. 8°. RicHMOND, SurREY.—Kew Observatory. Report of the committee. 1890. 8°. Riea.—Naturforscher Verein. Correspondenzblatt. Jahrg. XXXIV, XXXV, 1891-92. 8°. Xvi Additions to the Library. RIO DE JANEIRO.—ZJnstituto Historico, Geographico Brazileiro. Revista trimensal. Tomo LIV, LV. 1, 1891-92. 8°. Museu Nacional. Le muséum national de Rio de Janeiro et son influence sur les sciences naturelles au Brésil. Par Ladislau Netto. Paris, 1889. 8°. Ls ROCHELLE.—Académie des Belles-Lettres, Sciences et Arts. Annales de la société des sciences naturelles de la Charente-Inférieure. No. 26, 27, 1889-90. 8°. Roma.—JBiblioteca Nazionale Centrale Vittorio Hmanuele. Bollettino delle opere moderne straniere acquistate dalle biblioteche pubbliche governative del regno d’Italia. Vol. V. 4-12, VI, VII, 1890- 92.6 8°: Reale Accademia dei Lincei. Atti. Ser. IV. . Rendiconti. Vol. VI. il. 9-12, VII. 4, ti. 2=35geees Ser. V. Vol. I. i. 1-8, 10-12, 2, ii. 4, 5 -11, 1890-92. 40°. Memorie della classe di scienze morali, storiche e filologiche. Notizie degli scavi, 1890, 1891, 1892, no. 1-4, 9,11. 4°. Accademia Pontifica de’ Nuovi Linke Atti. Anno XLIII. 4-7, XLIV, XLV. 1. 2, 1890-92. 4°. Reale Comitato Geologico @ Italia. Bollettino. Vol. XXI, XXII, 1890-91. 8°. Societa degli Spettroscopisti Italiani. Memorie. Vol. XIX, XX, XXI. 1-11, 1890-92. 4°. Sr. GALLEN.—WNaturwissenschaftliche Gesellschaft, Bericht. Jahrg. 1888-89, 1889-90. 8°. S. PaoLo.—Commissav Geographica e Geologica do Estado de S. Paolo. Boletim. No. 4-7; 1890. 8°. St. PETERSBURG.—Comvité Géologique. Mémoires. Vol. IV. 2, V. 1, VIII. 2, XI. 2, XIIT. 1, 1890-91. 4°. Bulletins. Vol. VIII. 9, 10, 1X, X, XI. 1-4, 1889-92. 89°. Bibliothéque géologique de la Russie. 1889-90. 8°. Hortus Petropolitanus. Acta. Tom,)XI. 2, 1892. 82. Imp. Russ. Geograf. Obshtchestvo. Otchet. God 1890. 8°. Kais. Akademie der Wissenschaften. Repertorium der Meteorologie. Bd. XIII, XIV, 1890-91. 4°. Physikalisches Centralobservatorium. Annalen. Jahrg. 1890. 4°. Russisch-Kaiserliche Mineralogische Gesellschaft. Verhandlungen. Ser. II. Bd. XXVIII, 1891. 8°. SANTIAGO.—Sociéeté Scientifique du Chili. Actes. Tome II. 1, 2, 1892. Schweizerische noturforschende Gesellschaft. Verhandlungen. Jahresversammlung LXIII, LXIV, 1890-91. 5°. STocKkHOLM.—Lntomologisk Forening. Entomologisk tidskrift. Arg. XI, XII, XIII, 1890-92. 8°. STuTTGART.— Verein fiir vaterldindische Naturkunde in Wiirttemberg. Jahreshefte. Jahrg. XLVII, XLVIII, 1891-92. 89. SYDNEY.— Government of New South Wales. Year book of Australia. 1891, 1892. 8°. Statistical account of the seven colonies of Australia. By T. A. Coghlan. 1892. 8°, Free public library, Sidney. Report for 1890. 8°. Government Observatory. Results of meteorological observations made in New South Wales during 1889. 8°. Additions to the Library. Xvi Results of rain, river and evaporation observations during 1890. 89°. Sypngey.—Linnean Society of New South Wales. Proceedings. Series II. Vol. III. 2-4, 1888-89. 8°. Royal Society of New South Wales. Journal and proceedings. Vol. XXIV, XXV, 1890-91. 8°. Catalogue of scientific books inthe library. Pt.1.1891. 8°. TacuBaYyA.— Observatorio Astronomico Nacional. ; Anuario. Ano XII, XIII, 1892-93. 8°. Boletin. Tomo I. 1-12, 1890-92. 4°. THRONDHJEM.—Kon. Norske Videnskabers Selskab. Skrifter. 1888-90. 89. TiFLis.—Physicalisches Observotorium. Magnetische Beobachtungen. 1888-90. 8°. Meteorologische Beobachtungen. 1889-90. 8°. Beobachtuugen der Temperatur des Erdbodens, 1881-85. 8°. Toxy0.—Imperial University of Japan. Journal of the college of science. Vol. IV, V. 1, 2, 1891-92. 4°. Seismological Society of Japan. Transactions. Vol. XIV-XVI, 1889-92. 89. TorIno.—WMusei di Zoologia ed Anatomia Comparata. Bollettino. No. 87-93, 104-130, 1890-92. 8°. Toronto.— Canadian Institute. Transactions. Vol. I, I, 1890-92. 89°. Annual report. IV, 1890-91. 8°. Annual archeological report. 1891. 8°. Time-reckoning for the twentieth century. By Sanford Fleming. Wash. 1890). 82: An appeal to the Canadian Institute on the rectification of parliament. By Sanford Fleming. 1892. 89°. TouLOousE.-—Académie des Sciences, Inscriptions et Belles-Lettres. Mémoires. 9¢sér. Tome II, III, 1890-91. 8°. TRomMsO.— Museum. Aarshefter. XIII, XIV, 1890-91. 8°. Upsata.—Regia Societas Scientiarum. Novaacta,; Ser 11. Vok XIV. 2, 1891, 4°. Utrecat.—fon. Nederlandsch Meteorologisch Instituut. Nederlandsch meteorologisch jaarboek. Jahrg. XLII, XLIII, 1890-91. 4°, Provinciaal Utrechtsch Genootschap van Kunsten en Wetensshappen. Verslag van het verhandelde in de algemeene vergadering. 1890-91. 8°. Aanteekeningen van het verhandelde in de sectie-vergaderingen. 1890-91. VENEZIA.—Tstituto Veneto di Scienze, Lettere ed Arti. Atti. Ser. VII. Tomo I, II. 1-9, 1889-91. 8°. VICENZA.—Accademia Olimpica. Atti. Vol. XXII-XXIV, 1888-90. 8°. WELLINGTON.—WNew Zealand Institute. Transactions and proceedings. Vol. XXIII, XXIV, 1891-92. 8°. Wien.--Kais. Akademie der Wissenschaften. Sitzungsberichte. Mathemat.-naturwiss. Classe. Abth. I. Bd. XCVIII. 4-10, XCIX, C. 1-7, 1890-91, 8°. -—— K. k. Central-Anstalt fiir Meteorologie und Hrdmagnetismus. Jabrbiicher. Neue Folge. XXVI, X XVII, 1889-90. 4°. —. K. k. geologische Reichsanstalt. Abhandlungen. Bd. XIV, XV. 3, XVII. 2, 1890-92. 4°. Jahrbuch. Bd. XL. 3, 4, XLI. 1-3, XLII. 1, 1890-91. 8°. Verhandlungen. Jahrg. 1891, 1892, no. 1, 6-10. 8°. xvii Additions to the Library. Wien.—K. k. naturhistorisches Hofmuseum. Annalen. Bd. V. 4, VI, VII. 1, 2, 1890-92. 8°. ——K. k. Universitdts-Sternwarte. Annalen. Bd. VII, Supplementbd. I, 1890-91. 8°. -——--K. k. zoologisch-botanische Gesellschaft. Verhandlungen. Bd. XL. 3, 4, XLI, XLII. 1-3. 1890-92. 8¢ WIESBADEN.— Nassauischer Verein fiir Naturkunde. Jahrbiicher. Jahrg. XLITI-XLV, 1890-92. 8°. Witrzsure.—Piysikalisch-medicinische Gesellschaft. Sitzungsberichte. Jahrg. 1891. 8°. Ztricr.—Naturforschende Gesellschaft. Vierteljahrschrift. Jahrg. XXXIV. 3, 4, XXKV, XXXVI, XXXVII. 1, 2, 1889-92. 8°. Generalregister der Publikationen und Uebersicht ihres Tauschverkehres. 1892. 8°. Borsari, F. Etnologia Italica. Etruschi, Sardi e Siculi nel xiv° secolo prima dell’ era volgare. Napoli, 1891. 8°. —w-—Le zone colonizzabili dell’ Eritrea e delle finitime regioni Etiopiche. 1891. ae, Societa Americana d’Italia. Programmae statuto. Napoli, 1890. 8°. From Prof. F. Borsari. Chamberlain, J. 8. A comparative study of the styles of Composite. [New York, 1890.] 8°. From the Author. Douay, Léon. Etudes etymologiques sur l’antiquité américaine. Paris, 1891. Bek From the Author. Herzenstein, S. Ichthyologische Bemerkungen aus dem zoologischen Museum der Kais. Akademie der Wissenschaften. I-III. St. Petersburg, 1890- 92, .4°. — Ueber einen neuen russischen Wels (Exostoma Oschanini, Herz.) 1889. 4°. Wissenschaftliche Resultate der von N. M. Przewalski nach Central-Asien unternommenen Reisen. Zoolog. Theil. Bd. III, Abth. 2. Fische, von S. Herzenstein. Lief. 1-3. St. Petersburg, 1888-91. 4°. From the Author. Ives, J. E. Echinoderms and Arthropods from Japan. [Philad.,189i.] 8°. Echinoderms from the Bahama islands. [Philad., 1891.] 8&9. —-—Reptiles and Batrachians from northern Yucatan and Mexico. [Philad., 1891]. 8°. From the Author. Pickering, Charles. Chronological history of plants: man’s record of his own existence illustrated through their names, uses and companionship. Boston. 1889. 8°. From Prof. Hdward C. Pickering. Pihl, O. A. L. New stellar cluster of 7 Persei micrometically surveyed. Christ- iania, 1891. 4°. From the Author. Salisbury, Rollin D. Preliminary paper on drift and pleistocene formations of New Jersey. Trenton, 1892. 8°. —-The drift of the North German lowland, 1892. 8°. From the Author. mDDETIONS TO, TEE LIBRARY OF THE Connecticut Academy of Arts and Sciences, By GIFT AND EXCHANGE FROM JAN. 1, 1898, To JULY 1, 1895. American Association for the Advancement of Science. Proceedings. Meeting XLI-XLIII, 1892-94. Salem, 1893-95, 8°. ALBANY.—WNew York State Library. Annual report. LXXIV, LXXV, 1891-92. 8°. Bulletin. Legislation. .V, 1895. 8°, Regents’ Bulletin. No. 21, 24, 27, 29, 1893-94. 8°. New York State Museum of Natural History. Annual report. XLV, XLVI, 1892-93. 8°. Bulletin. Vol. III. 11-18, 1893-95. 89°. ANNAPOLIS.— United States Naval Institute. Proceedings. Vol. XVIII. 4, XIX. 2-4, XX, XXI. 1, 1892-95. 89. AustTiIn.—Texas Academy of Science. Transactions. Vol. I. 2, 1893. 8°. BALTIMORE.—Johns Hopkins University. American chemical journal. Vol. XV, XVI, XVII. 1-7, 1893-95. 8°. Studies from the biological laboratory. Vol. V. 2-4, 1892-93. 8°. University circulars. No. 102-120, 1893-95. 4°. Boston.—American Academy of Arts and Sciences. Proceedings. Vol. XXVII-XXIX, 1891-94. 8°. Society of Natural History. Memoirs. Vol. IV. 11-14, 1893-94, 40°, Proceedings. Vol. XXV, XXVI. 1-3, 1893-94. 8°, BROOKVILLE.—Indiana Academy of Science. Proceedings. 1891-93. 8°. BUFFALO.—-Society of Natural Sciences. Bulletin. Vol. V. 4, 1894. 8°. CaMBRIDGE.—Harvard College. Annual reports of the president and treasurer. 1891-92, 1892-93, 1893-94. 8°. Astronomical Observatory of Harvard College. momaiss “Vol Vi 2, Wie eV, AOD, XXXT. 1,2, XXXIT. 1, XXXV, XL. 2, 3, XLI. 1, 2, 1892-95. 4°, Annual report. XLVIII, 1898. 8°. Museum of Comparative Zoology at Harvard College. Memoirs. Vol. XIV, no. 1, pt. 3, XVII. 3, XVIII, 1893-95. 4°. Bulletin. Vol. XVI. 11-15, XXIII. 5, 6, XXIV, XXV. 1-8, 10-12, XXVI, XXVITI. 1, 1898-95. 8°. Annual report. 1891-92, 189%-98, 1893-94, 89, 2K Additions to the Library. CAMBRIDGE.— Entomological Club. Psyche. No. 188, 201-230, 1891-95. 8°. New Englund Meteorological Society. Annual summary of the New England weather service for 1893. 4°. CHAMPAIGN.—Lllinois State Laboratory of Natural History. Bulletin, Vol. I. 1, 2, 6, IL. 2-8, III. 1-14, IV. 1, 4, 1876-94. 80°. Natural history survey of Illinois. Ornithology. Vol. I. 1889. 8°. CHAPEL HiLu.—Llisha Mitchell Scientific Society. Journal. Vol. [X, X, XI. 1, 1892-94, 8°. Cuicaco.—Field Columbian Museum. Guide to the Field Columbian museum. 2. ed. 1894. 12°. Publications. Vol. I. 1, 1894. 89°. University of Chicago. Journal of geology. Vol. I, II, III. 1-3, 1893-95. 8°. CINCINNATI.— Observatory. Publications. No. XIII, 1895. 8°. Society of Natural History. Journal. Vol. XV. 3,4, XVI, XVII, 1892-94. 8°. DAVENPORT.—Academy of Natural Sciences. Proceedings. Vol. V. 2, 1885-89. 8°. Des Motines.—Jowa Academy of Sciences. Proceedings. Vol. I. 1, 3, 4, 1887-94. 8°. Iowa Geological Survey. [Publications.] I, II, 1892-98. 8°. GRANVILLE.—Dennison University. Bulletin of the scientific laboratories. Vol. VIII, 1898-94. 98°, Journal of comparative neurology. Vol. II. 4, III, IV, V. 1, 1892-95. 89. HARRISBURG.—Second Geological Survey of Pennsylvania. Geological maps of Schuylkill, Carbon, Berks and Dauphin Counties. Topographical map of Blue Mountain. Summary final report. Atlas. 1894. 89°. LAWRENCE.— University of Kansas. Kansas University quarterly. Vol. I. 3, II, III, 1893-95. 80°. LittLE Rock.—Arkansas Geological Survey. Annual report. 1890. iii, iv; 1891. i, ii; 1892. i, ii. 8°. Mapison.— Washburn Observatory. Publications. Vol. VI-VIII, 1890-93. 89°. Wisconsin Academy of Sciences, Arts and Letters. Transactions. Vol. IX, 1892-98. 8°. MERIDEN.— Scientific Association. Transactions. Vol. V, 1893. 8°. MINNEAPOLIS.—WMinnesota Academy of Natural Sciences. Occasional papers. Vol. I. 1, 1894. 8°. Minnesota Geological and Natural History Survey. Report of the state zoologist. I, 1892. 8°. Mr. Hamitton.—Lick Observatory. Publications. Vol. II, III, 1894. 8°. Contributions. No. III, 1893. 8°. New York.—Academy of Sciences. Annals. Vol. VI, 7-12, VII, VIII. 1-5, 1892-95. 8°. Transactions. Vol. X. 7, 8, XI. 1, 2, XII, XIII, 1892-94. 80°, ——American Geographical Society. Bulletin. Vol. XXIV. 4, XXV, XXVI, XXVII, 1, 1892-95. 8°, American Museum of Natural History. Bulletin. Vol. IV-VI, 1892-94. 89°, Annual report. 1892, 1893, 89, Additions to the Library. XxI New Yor«.—Linnean Society. Abstract of proceedings for year ending March 27, 1894. 8°. Microscopical Society. Journal. Vol. 1X, 1893. 8°. Scientific Alliance. Addresses delivered at the first joint meeting, Nov. 15, 1892. 8°. Proceedings of the second joint meeting. Mar. 27, 1893. 8°. Third annual directory. 1893. 8°. Torrey Botanical Club. Bulletin. Vol. XVIII. 7, XIX. 1, XX, XXI, XXII. 1-5, 1891-95. 8°, PHILADELPHIA.—Academy of Natural Sciences. Journal. Vol. X. 1, 2, 1894. 4°. American Entomological Society. Transactions. Vol. XIX. 3, 4, XX, XXI, XXII. 1, 1892-95. 8°. Franklin Institute. Journal. Vol. CXXXV-CXXXIX, 1893-95. 8°. University of Pennsylvania. Contributions from the botanical laboratory. Vol. I. 2, 1898. 8°. Wagner Free Institute. Transactions. Vol. III. 2, 3, 1892-95. 8°. ° POUGHKEEPSIE.— Vassar Brothers Institute. Transactions. Vol. VI, 1890-93. 8°. RicHMoND.— Virginia State Library. Calendar of Virginia state papers and other manuscripts. Vol. VI-XI, 1792-1869. Richmond, 1586-93. 4°. ROCHESTER.— Academy of Science. Proceedings. Vol. II. 2, 3, 18938. 8°. St. Lours.—Academy of Science. Transactions. Vol. VI. 3-18, VII. 1-3, 1892-95. 8°. Missouri Botanical Garden. Annual report. IV-VI, 1893-95. 89°. SaLEM.—SHssex Institute. Bulletin. Vol. XXIV. 7-12, XXV, XXVI. 1-6, 1892-94. 89°. Henry Wheatland, M.D. Sermon preached by Rev. Edmund B. Willson, Mar. 5, 1893. 8°. San FRANoIScO.— California Academy of Sciences. Memoirs. Vol. II, 3, 4, 1894-95. 8°. Occasional papers. III, IV, 1893. 8°, Proceedings. Ser. II. Vol. III. 2, [V. 1, 2, 1898-95. 8°. California State Mining Bureau. Report. XI, XII. Sacramento, 1890-94. 8°. Bulletin. No. 3-5. Sacramento, 1894. 8°. Catalogue of West North American and many foreign shells, with tbeir geographical ranges. Sacramento, 1894. 8°. Technical Society of the Pacific Coast. Transactions and proceedings. Vol. X.3, 4, 6-10, 12, 1893-94. 8°. Tacoma.— Academy of Science. Proceedings, Feb. 8, 1893. 8°. TopeKA.—Kansas Academy of Science. Transactions. Vol. XIII, 1891-92. 8°. Tufts College. Studies. I-III, 1894. 8°. University of Virginia. Leander McCormick Observatory. Publications. Vol. I. 6, 1893. 8°. WaAsHIneton.— Biological Society. Proceedings. Vol. IX. pp. 1-128, 133-188, 1894. 8°. xxl Additions to the Library. WasuHineton.— United States Department of Agriculture. Division of entomology. Bulletin. No. 28-38, 1893-95. 8°. Insect life. Vol. V. 3-5, VI, VII. 1-4, 1893-95. 8°. Report of the chief of the weather bureau. 1891-92. 8°. Bulletin of the New England weather service. No. 1-39, 1892-95. 4°. — United States Geographical and Geological Survey of the Rocky Mountain Region. Contributions to North American ethnology. Vol. VII, IX. 1890-93. 4°, . United States Geological Survey. Annual report. XI, XII, XIII, 1889-92. 8°. Bulletin. No. 63, 64, 66, 82-86, 90-111. 1890-93. -89. Mineral resources of the United States. 1891-93. 8°. Monographs. Vol. XVIJ-XXII, 1892-93. 4°. — United States Naval Observatory. Astronomical and meteorological observations. 1889. 4°. ——Smithsonian Institution, Bureau of Lthnology. ‘ Annual report. VII-XII, 1885-91. 8°. List of the publications of the Bureau of Ethnology, with index to authors and subjects. By Frederick W. Hodge. 1894. 8°. Bibliography of the Athapascan languages. By JamesC. Pilling. 1892. 8°. Bibliography of the Chinookan languages. By James C. Pilling. 1893. 8°. Bibliography of the Saliskan languages. By James C. Pilling. 1893. 89°. Bibliography of the Wakashan languages. By James (C. Pilling. 1894. 8°. Chinook texts. By Franz Boaz. 1894. 8°. Archeologic investigations in James and Potomac valleys. By Gerard Fowke. 1894. 8°. An ancient quarry in Indian Territory. By William H. Holmes. 1894. 8°- The Siouan tribes of the East. By James Mooney. 1894. 8°. The Pamunkey Indians of Virginia. By John G. Pollard. 1894. 89°. The Maya year. By Cyrus-Thomas. 1894. 8°. WILKES BARRE.— Wyoming Historical and Geological Society. Union services at the old Forty Fort church, Luzerne County, Pa., on June 15, 1888. 8°. WORCESTER.—American Antiquarian Society. Proceedings. New series. Vol. VIII. 2, 3, IX. 1-3, 1892-94. 8°. AMIENS.—Société Linnéenne du Nord de la France. Bulletin. No. 235-258, 1892-93. 89. AMSTERDAM.—Kon. Akademie van Wetenschappen. Jaarboek. 1892-93. 8°. Verslagen en mededeelingen. Afdeel. natuurkunde. 3de reeks. Deel 1D. be es Verhandelingen. Sectie I. Deel I, II. 1-6, 8, 1892-94. &°. — Sectie IJ. Deel I-III, 1892-94. 69°. Verslagen en zittingen van de wis-en natuurkundige afdeeling. 1892-93, 1893-94. 8°, AuGsBURG.—Naturhistorischer Verein fiir Schwaben und Neuburg. Bericht. XXXI, 1894, 8°. Australasian Association for the Advancement of Science. Report. Meeting IV, V, 1892-93. S°. AUXERRE.—Société des Sciences Historiques et Naturelles de Vv Yonne. Bulletin. Tome XLVI, XLVII, XLVIII. 1, 1892-94. 8°. BAMBURG,—WNaturforschende Gesellschaft. Bericht. XV, XVI, 1890-93. §&°. Additions to the Library. xxiii BASEL.—Naturforschende Gesellschaft. Verhandlungen. Theil IX. 3, X. 1-3, 1892-95. 8°. BATAVIA.—Kon. Natuurkundige Vereeniging in Nederlandsch-Indié. Natuurkundige tijdschrift. Deel LII, LILI, 1893. §°. Magnetical and Meteorological Observatory. Observations. Vol. XIV, XV, XVI, 1891-93. 4°. BERGEN.— Museum. Aarsberetning. 1891-92. 8°. BERLIN.—KoOnigliche Sternwarte. Berliner astronomisches Jahrbuch. 1895-97. 8°. Veroffentlichungen des Rechen-Instituts. No. 2, 3, 1893. 8°. Naturae novitates. Jahre. XIV. 23, 24, XV, XVI, XVII. 1-5, 1892-95. 8°. BoLoGna.—f&. Accademia delle Scienze dell’ Istituto di Bologna. Rendiconto, Anno 1891-94. 8°. BomBay.—Bombay Branch of the Royal Asiatic Society. Journal. No. XLIX, XLIX?, L, 1892-94. 89. Government Observatory. Magnetical and meteorological observations. 1891-98. 4°. Bonn.—Naturhistorischer Verein der preussischen Rheinlande, Westfalens und des Feg.—Bezirks Osnabriick. Verhandlungen. Jahrg. XLIX, L, LI. 1, 1892-94. 8°. BoRDEAUX.—Académie Nationale des Sciences, Belles-Lettres et Arts. Actes. Année LII-LIV, 1890-92. 8°. Société Linnéenne. Actes. Tome XLV, XLVI, 1892-93. 8°. Catalogue de la bibliothéque. Fasc.I. 1894. 8°. Société des Sciences Physiques et Naturelles. Mémoires. 3¢sér. Tome V.2. 4° sér. Tome I, IIT, LV, 1893-94. 89°. BRAUNSCHWEIG.— Verein fiir Naturwissenschaft. Jahresbericht. VII, 1889-91. 89. BREMEN.—WNaturwissenschaftlicher Verein. Abhandlungen. Bd. XII. 8, XIII. 1, 2, XV. 1, 1893-95. 8°. Meteorologische Station. Ergebnisse der meteorologischen Beobachtungen. Jahrg. III-V, 1892- 95. 4°. BRESLAU.-—Schlesische Gesellschaft fiir vaterldindische Cultur. Jahres-bericht. LXX, LX XI, 1892-93. 8°. BRISBANE.— Queensland Branch of the Royal Geographical Society of Australia. Proceedings and transactions. Vol. VIII, IX, 1892-94. 8°. Brounn.—WNaturforscher Verein. Verhandlungen. Bd. XXX-XXXII, 1891-93. 8°. Bericht der meteorologischen Commission. X-XII, 1890-92. 89. BRUXELLES.— Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique. Mémoires. Tome XLVIII, XLIX, L. 1, 1892-93. 4°. Mémoires couronnés et mémoires des savants étrangers. Tome LII, 1893, 4°. Mémoires couronnés et autres mémoires. Tome XLVI, 1892. 8°. Bulletins. 3° sér. Tome XXII-XXV, 1891-93. 8°. Annuaire. Année LVIII, LIX, 1892-93. 8°. Société Hntomologique de Belgique. Annales. Tome XXXVI-XXXYVIII, 1892-94. 8°. Mémoires. II, 1894. 8°. Société Royale Belge de Géographie. Bulletin. Année XVI. 4-6, XVII, XVIII, 1892-94. 8°. Société Royale de Botanique. Bulletin. Tome XXX, XXXT, 1891-92, 8°. XXIV Additions to the Library. BRUXELLES.—Société Royale Malacologique de Belgique. Annales. Tome XY. 2, XXVI, 1880-91. 8°. BucHAREST.—ZJnstitut Météorologique de Roumanie. Annales. Tome VI-VIII, 1890-92. 4°. BuDaPEst.—Kon. ung. Central-Anstalt fiir Meteorologie und Erdmagnetismus. Jahrbiicher, Jahrg. XX, XXI, 1890-91. 4°. BuENOS AIRES.—Sociedad Cientifica Argentina. Anales. Tomo XXXIV. 2-6, XXXV-XXXVIII, 1892-94. 8°. CaEN.—Société Linnéenne de Normandie. Bulletin. 4¢sér. Vol. VI-VIII, 1892-94. 8°. CaLcuTtTa.—Asiatic Society of Bengal. Journal. Vol. LXI, pt. i, no. 3,4 and 2 suppl, pt. ii, no. 3; LXII, pt. i, li, iii, no. 1-3; LXIV, pt. i, no. 1-4, ii, tii, no. 1; DL: XDY, pees 1892-95. 8°. Proceedings. 1892, no. 8-10, 1893, 1894, 1895, no. 1-3. 8°. Annual address, 7 Feb. 1894. 8°. Geological Survey of India. Paleontologia Indica. Ser. IX, vol. Il, pt. 1, 1893. 4°. Records. Vol. XXV. 3, 4, XXVI, XXVII, XXVIII. 1, 2, 1892-95. 89. Manual of the geology of India. By H. B. Medlicott and W. T. Blanford. 2 ed. revised and largely rewritten by R. D. Oldham. 18938. 8°. Meteorological Department of the Government of India. Indian meteorological memoirs. Vol. V. 2-6, VI. 1, VII. 1, 2, 1892-94. f°. Monthly weather review. 1891-94. f°. Rainfall of India. 1891-93. f°. Report on the meteorology of India. 1889, 1890. f°. Report on the administration of the meteorological department. 1891-92, 1893-94. f°. Meteorological observations recorded at seven stations in India. 1892, May-Dec., 1893, 1894. f°. Instructions for observers. By J. Eliot. 1894. 8°. CAMBRIDGE.—Philosophical Society. Transactions. Vol. XV. 4, 1894. 4°. Proceedings. Vol. VIII. 1-4, 1892-94. 8°. CaTania.—Accademia Gioenia di Scienze Naturali. Atti. Ser. IV. Vol. IV-VI, 1891-93. 4°. Bullettino mensile. Nuovaserie. Fasc. 26-35, 1892-94.. 8°. CHEMNITZ.—Naturwissenschaftliche Gesellschaft. Bericht. XII, 1889-92. 8°. CHERBOURG.—Société Nationale des Sciences Naturelles. Mémoires. Tome XXVIII, 1892. §&°. CHRISTIANIA.—Kong. Norske Universitet. Beskrivelse af en rekke Norske bergarter. Af Dr, Th. Kjerulf. 1892, 4°, Norwegische Commission der Huropdischen Gradmessung. Resultate der im Sommer 1893 in dem nordlichsten Thiele Norwegens ausgefuhrten Pendelbeobachtungen. 1894. 8°. — Norwegisches meteorologisches Institut. Jahrbuch. i891. 4°. — Norwegian North-Atlantic Hxpedition, 1876-78. Publication XXII, 1893. 4°. — Videnskabs Selskabet. Forhandlinger. 1893. 8°. Cuur.—Naturforschende Gesellschaft Graubiindens. Jahres-bericht. Neue Folge. Jahrg. XXXVI, XXXVII, 1891-94. 8°. CorDoBa.—Academia Nacional de Ciencias. Boletin. Tomo XI. 4, 4*, XII, XIII, XIV. 1, 1889-94. 8°. Additions to the Library. XXV Danzic.—WNaturforschende Gesellschaft. Schriften. Neue Folge. Bd. VIII. 3, 4, 1894. 8°. Dison.—Académie des Sciences, Arts et Belles-Lettres. Mémoires. 4° sér Tome II-IV, 1892-94. 8°. Dorpat.—Gelehrte Estnische Gesellschaft. Sitzungsberichte. 1892-94. 8°. Verhandlungen. Bd. XVI. 2, 1892. 8°. Naturforscher- Gesellschaft bei der Universitat Dorpat. Archiv fiir die Naturkunde Liy-Ehst-und Kurlands. Ser. II. Bd. X. 3, 4, 1893-94. Sitzungsberichte. Bd. X. 1, 2, 1892-93. 8°. DrespEn.—WNaturwissenschaftliche Gesellschaft Isis. Sitzungsberichte und Abhandlungen. 1892, ii, i893, 1894. 8°. Verein fiir Hrdkunde. Jahresbericht. XXII, XXIII, 1892-93. 8°. Literatur des Landes-und Volkskunde des Konigreichs Sachsen, hrsg. von Paul Emil Richter. NachtragI. 1892. 8°. Dusiin.— Royal Irish Academy. Transactions. Vol. XXX. 1-14, 1892-94. 4°. Proceedings. Ser. III. Vol, II. 3-5, III. 1-3, 1892-94. 8°. Cunningham memoirs. No. X, 1894. 4°. Todd lecture series. Vol. ILI-V, 1892-94. 8°. EpinBurGH.—Botanical Society. Transactions and proceedings. Vol. XIX, pp. 253-636, XX. 1, 1892-94. 8°. Geological Society. Transactions. Vol. VI. 5, VII. 1, 1893-94. 8°. Royal Physical Society. . Proceedings. Vol. XI, XII, 1890-94. 8°. — Royal Society. Proceedings. Vol. XIX, 1891-92. 8°. Emprn.—WNaturforschende Gesellschaft. Jahresbericht. LXXVII, LXXVIII, 1891-93. 8°. ErFurt.—Kon. Akademie gemeinniitziger Wissenschaften. Jahrbiicher. Neue Folge. Heft XVIII-XXI, 1892-95. 8°. FIRENZE.— Biblioteca Nazionale Centrale. Bollettino delle pubblicazioni Italiane ricevute per diritto di stampa. No. 168-226, 1892-95. 8°. — BR. Istituto di Studi Superiori Pratici e di Perfezionamento, Pubblicazioni. Sezione di filosofia e filologia. Maestri e scolari nell’ India Brahmanica. Saggio di Girolamo Donati. 188s; 82. —Sezione di scienze fisiche e naturali. Osservazioni continue della elettricita atmosferica fatte a Firenze nel 1884. Seconda memoria di L. Pasqualini ed A. Roito. 1885. 8°. Saggio sperimentale sul meccanismo dei movimenti volontari nella Testuggine palustre (Emys Europea), del Dott. Giulo Fano. 1884, 8°. — Sezione di medicina e chirurgia. Archivio della scuola d’anatomia patologica. Vol. III, ITV. 1885-86. 8°. FRANKFURT A. M.—Deutsche malakozoologische Gesellschaft. Nachrichtsblatt. Jahrg. XXV, XXVI, XXVII. 1-6, 1893-95. 8°. Senckenbergische naturforschende Gesellschaft. Abhandlungen. Bd. XVIII, 1892-95. 4°. Bericht. 18938, 1894. 8°. Katalog der Vogelsammlung. 1891. Katalog der Batrachier-Sammlung, 1892. Katalog der Reptilien-Sammlung. Theil I. 1893. XXV1 Additions to the Library. FRANKFURT A. O.—WNaturwissenschaftlicher Verein des Regierungsbezirks Frankfurt. Helios. Abhandlungen und monatliche Mittheilungen. Jahrg X. 4-12, XI, XII, 1892-94. 8°. Societatum litterae. Jahrg. VI. 9-12, VII, VIII, IX. 1-3, 1892-95. 89. FREIBURG IN B.—WNaturforschende Gesellschaft. Berichte. Bd. VIII, 1894. 8°. GENEVE.—Jnstitut National Genevois. Bulletin. Tome XXXII, 1894. 8°. Société de Physique et d’ Histoire Naturelle. Mémoires. Tome XXXI. 2, 1892-93. 4°. GENOVA.— Museo Civico di Storia Naturale. Annali. Vol. XXX-XXXIII, 1890-93. 8°. GIESSEN.— Oberhessische Gesellschaft fur Natur-und Heilkunde. Bericht. X XIX, 1893. 8°. GLAscow.— Geological Society. Transactions. Vol. IX. 2, 1890-92. 8°. Natural History Society. Proceedings and transactions. N.S. Vol. III. 1, 2, 1888-90. 8°. Philosophical Society. Proceedings. Vol. XXIJI-XXV, 1891-94. 89. Index to proceedings vol. I-XX. 1892. 8°. GORLITZ.— Naturforschende Gesellschaft. Abhandlungen. Bd. XX, 1893. 8°. GOTEBORG.—Kon. Vetenskaps och Vitterhets Samhdille. Handlingar. Nytids. Haft. XXVI-XXIX, 1891-94. 8°. GOTTINGEN.—Konigl. Gesellschaft der Wissenschaften. Nachrichten. 1893. Philologisch-histor. Klasse, 1894, i-iii, 1895, i. Mathe- matisch-physikal. Klasse, 1894, i-iii, 1895, i. Geschaftliche Mittheil- ungen, 1894, 1895, i. 8°. GuUstrow.— Verein der Freunde der Naturgeschichte in Mecklenburg. Archiy. Jahrg. XLVI-XLVIII, 1892-94. 89, HaBana.—Feeal Colegio de Belen. Observaciones magneticas y meteorologicas. 1889. ii, 1890. 4°. Hauirax,—WVova Scotian Institute of Natural Science. Proceedings and transactions. Ser. II. Vol. I. 2, 3, 1891-93. 8°. Department of Mines, Nova Scotia. Report. 1892, 1894. 8°. HAutLeE.—Kais. Leopoldinisch-Carolinische deutsche Akademie der Naturforscher. Leopoldina. Heft XXVII-XXIX, 1891-93. 4°. Novaacta. Bd. LIII. 1, LVII. 5, 1889-92. 4°, Naturforschende Gesellschaft. Abhandlungen. Bd. XVIII. 2, XIX, XX. 1893-94. 5°. Bericht. 1892. 8°. Naturwissenschaftlicher Verein fiir Sachsen und Thiiringen. Zeitschrift fiir Naturwissenschaften. Bd. LXV. 3-6, LXVI, LXVII, 1892-94. 8°. HampBurG.—Deutsche Seewarte. Aus dem Archiv. Jahrg. XV-XVII, 1892-94. 4°. Deutsches meteorologisches Jahrbuch. 1891-1893. 49. Naturwissenschaftlicher Verein. Abhandlungen. Bd. XII, XIII, 1892-95. 8°. HANNOVER.—WNaturhistorische Gesellschaft. Jahresbericht. XL-XLIII, 1889-93. 8°. HARLEM.— Musée Teyler. Archives. Série II. Vol. IV. 1-3, 1893-94. 89. Additions to the Library. XXVIL HARLEM.—Société Hollandaise des Sciences. Archives néerlandaises des sciences exactes et naturelles. Tome XXVI. 3-5, XXVII, XXVIII, X XIX. 1, 1892-95. 8°. HELSINGFORS.—Societas Scientiarum Fennica. Ofversigt af forhandlingar. XXXIV, 1891-92. 8°. Bidrag till kinnedom af Finlands natur och folk. Haft. LI, 1892. 8°. Institut Météorologique Central, Observations météorologiques faites a Helsingfors. 1884-92. 4°. Observations météorologiques (stations finlandaises). 1881-88. 4°. HERMANNSTADT.— Siebenbiirgischer Verein fiir Naturwissenschaften. Verhandlungen und Mittheilungen. Jahre. XLII, XLIII, 1892-94. §°. JENA.—Medicinisch-naturwissenschaftliche Gesellschaft. Jenaische Zeitschrift fiir Naturwissenschaft. Bd. XXVII. 3,4, XXVIII, XXIX. 1, 2, 1892-94. 8°. Kasan.—Société Physico-Mathématique de V Université Impériale. Bulletin. 2¢sér. Tome II, III. 2-4, IV. 1, 2, 1892-94. 8°. KHARKOW.— Université Impériale. Annales. 1893.i. 8°. Société des Sciences Hxperimentales annexée a V Université de Kharkow. Section médicale. Travaux. 1892-93. 8°. Section physico-chimique. Travaux. Tome XXI, 1893. Supplément III-VI, 1892-93. 8°. KieLt.—Konigl. Christian Albrechts- Universitat. Schriften aus dem Jahre 1892-93, 1893-94. 8° and 4°. Naturwissenschaftlicher Verein fiir Schleswig-Holstein. Schriften. Bd. ITI-IX, X. i, 1877-93. 89°. Kirv.—Kieuskie Obshchestvo TIestestvoispytatelei. Zapiski. Tom. XII, 1892. 8°. KJOBENHAVN.—Kon. Danske Videnskabernes Selskab. Oversigt over forhandlinger. 1892. ii, iii, 1898, 1894. i, ii. 8°. Naturhistorisk Forening. Videnskabelige meddelser. Aaret 1892-94. 8°, KONIGSBERG.—Konigl, physikalisch-dkonomische Gesellschaft. Schriften. Jahrg. XX XIII, XXXIV, 1892-93. 40°. Krakow.—k&K. k. Sternwarte. Materyaly do klimatografii Galicyi. Rok 1892, 1893. 8°. Stanwody na rzekach Galicyjskich. Rok 1891, 1892. 8°. La PLata.—Museo. Revista. Tomo III, IV, 1892-93. 8°. Anales. Seccion de arqueologia. I-III, 1890-92. foe. Seccion de historia Americana. I, II, 1890-91. f°. Seccion de historia general. I, 1892. f°. Seccion geologica y mineralogica. I, 1892. f°. Seccion zoologica. I, 1893. f°. Paleontologia Argentina. I, II, 1891-98. f°. LAUSANNE.—Société Vaudoise des Sciences Naturelles. Bulletin. 8esér. No. 109-115, 1892-94. 8°. LEEDS.— Yorkshire Geological and Polytechnic Society. Proceedings. Newseries. Vol. XII. 4, 1894. 8°. LEIDEN.— Nederlandsche Dierkundige Vereeniging. Tijdschrift. Ser. II. Deel IV, 1893-94. 8°. Sternwarte. Verslag. 1890-94. 89, LEIPZIG.—Astronomische Gesellschaft. Publication. XX, 1892. 4°. Vierteljahrsschrift. Jahrg. XXVII. 3, 4+, XXVIII, X XIX, 1892-94. 89, Catalog. Abth. I. Stiick VI. 1894. 4°. Xxviil Additions to the Library. LEIpzic.—Konigl. stichsische Gesellschaft der Wissenschaften. Berichte. Math.-physische Classe. Bd. XLIV. 3-6, XLV, XLVI, XLVII. 1, 1892-95. 8°. Verein fiir Hrdkunde. Mittheilungen. 1892-94. 8°. Wissenschaftliche Veroffentlichungen. Bd.II. 1895. 89. ‘Zoologischer Anzeiger. No. 408-477, 1892-95, 89. LisBoa.—Sociedade de Geographia. Boletim. Serie XI. 4-12, XII, XIII. 3-9, 12, 1892-94. 89. Lonvon.— Geological Society. Quarterly journal. Vol. XLIX, L, LI. 1, 2, 1893-95. 89°. List, Noy. 1, 1894. 8°. — Linnean Society. Journal. Zoology. No. 152-157, 1892-94. 8°. Journal. Botany. No. 177, 202-208, 1892-94. 8°. Proceedings. Nov. 1890-June 1893. 8°. List. 1892-93, 1893-94. 89. Mathematical Society. Proceedings. No. 449-508, 1892-95. 8°. Royal Historical Society. Transactions. New series. Vol. I. 2, 3, 1V, VII, VIII, 1882-94. 8°. Proceedings of the Gibbon commemoration, 1794-1894. Lond., 1895. 8°. Royal Microscopical Society. Journal. 1892. vi, 1893, 1894, 1895. i. 8°. Royal Society. Philosophical transactions. Vol. CLXXXIII, A, B; CLXXXIYV, A, B; 1892-93. 4°. Proceedings. No. 317-345, 1892-1895. 8°. | List of council and fellows. 1892, 1893. 4°. LovuvaIn.—La Cellule. Tome VIII. 1, 1X, X, 1892-94, 8°. Lunv.— Universitet. Acta. Tom. XXVIJI-XXX, 1892-94. 4°. LuxEMBOURG.—Jnstitut Royal, Grand-Ducal. Publications. Section des sciences naturelles et mathématiques. Tome XXII, XXIII, 1893-94. 8°. Lyon.—Académie des Sciences, Belles-Lettres et Arts. Mémoires. Classe des sciences. Tome XXX, XXXI, 1889-92. 8°. Sciences et lettres. 3¢ sér. Tome I, II, 1893. 8°. MADRAS.— Government Observatory. Results of observations of the fixed stars made with the meridian circle. Vol. VI-VII, 1877-87. 4°. Hourly meteorological observations, 1856-61. 4°. MADRID.—Comision del Mapa Geologico de Espana. Boletin. Tomo XIX, 1892. 8°. Memorias. Descripcion fisica, geologica y minera de la provincia de Viz- caya. Por D. Ramon Adan de Yarza. 1892. 8°. Mapa geologico de Espana. Hoja 1, 3, 5, 7, 9, 11, 13, 14, 15. Observatorio. Observaciones meteorologicas. 1890-91, 1892-93. 8°. Resumen de las observaciones meteorologicas efectuadas en la peninsula. TRDO0, SBA7 7 he 5 MANCHESTER.—Literary and Philosophical Society. Memoirs and proceedings. Series IV. Vol. VI, VII, VIII. 2, 3, IX. 1, 2, 1892-95. 89. MARBURG.— Gesellschaft zur Beforderung der gesammten Naturwissenschaften. Sitzungsberichte. Jahrg. 1892-93. 8°. Additions to the Library. Xx1X MaARSEILLE.—Faculté des Sciences. Annales. Tome I-III, IV. 1-3, 1891-94. 4°. MetTz.—Académie. Mémoires. 3¢sér. Année XVIII-XXI, 1888-92. 8°. MEXICcO.—Asociacion de Ingenieros y Arquitectos. Anales. Tomo III, 10-12, IV. 1-3, 1893-04, 8°. -Observatorio Meteorologico-Magnetico Central. Boletin mensuel. 1895, no. 1-3. 4°. Resumen comparativo. 1877-88. Secretario de Fomento. Boletin de agricultura, mineria e industrias. Ano I. 12, II. 1-9, 1892. 89. Sociedad Cientifica ‘‘Antonio Alzate.” Memorias y revista. Tomo VI. 3-11, VII, 1892-94. 89°. Sociedad de Geographia y Estadistica. Boletin. EpocalIV. Tomo II. 8-12, III, 1, 2, 1893-94. 89°. Sociedad Mexicana de Historia Natural. La naturaleza. Ser. II. Tomo II. 3-7, 1892-94. 4°. MIDDELBURG.—Zeeuwsch Genootschap der Wetenschappen. Archief. Deel VII. 3, 4, 1893-94, 89. Levensberichten van Zeeuwen. Afl. IV, 1893. 8°. Verslag over 1885-93. 8°, Mivano.—feal Istituto Lombardo di Scienze e Lettere. Rendiconto. Serie II. Vol. XXIV-XXVI, 1891-93. 8°. Indice generale dei lavori dalla fondazione all’ anno 1888, per autori e per materie. 1891, 8°. Reale Osservatorio di Brera. Pubblicazioni. No. XX XVIII, i895. 4°. Rassunto delle osservazione meteorologiche. 1894. 4°. Societa Italiana di Scienze Naturali. Atti. Vol. XXXIV, 1892-94. 8°. Memorie. Tomo V, 1895. 4°. MopENA.—Legia Accademia delle Scienze, Lettere ed Arti. Memorie. Serie II. Tomo VIII, IX, 1892-93. 40°. Societa dei Naturalisti. : Memorie. Serie III. Vol. XI. 3, XII. 1, 2, 1898. 8°. MONTPELLIER.—Académie des Sciences et Lettres. Mémoires. Section des lettres. ‘Tome [X. 3,4. Sér. II. Tome I. 1-4. 1892-94. 4° and 8°. Section des sciences. Tome XI. 3. Sér. II. Tome I, II. 1. 1892- 94. 4° and 8°. Section de médecine. Tome VI, 22, 2%. Ser. II. TomelI. 1. 1892- 93. 4° and 8°. Moscov.—Société Impériale des Naturalistes. Bulletin. Année 1892. ii-iv, 1893, 1894. i-iii. 8°. Mitnouen.—Kon. bayerische Akademie der Wissenschaften. Sitzungsberichte. Philosph.-philolog. und histor. Classe. 1891. iii-v, 1892, 1393, 1894, i. 8°. Mathemat.-physikal. Classe. 1891. iii, 1892, 1893, 1894. i-iii, 89. Ueber die Stoffe und die Wirkung der griechischen Tragodie. Festrede von N. Wecklein. 1891. 4°. | Ueber die allgemeinen Probleme der Mechanik des Himmels. Rede von Hugo Seliger. 1892. 49. Gedachtnissrede auf Wilhelm von Giesebrecht. Von Sigmund Riezler. 1892, 4°. Kurfiirst Maximilian I. von Bayern als Gemaldesammler. Festrede von F.v. Reber. 1892. 4°. ok Additions to the Library. MUNCHEN.—Ko6n. bayerische Akademie der Wissenschaften. Erkennen, Erleben, Erschliessen. Festrede von M. Carriere. 1893. 4°. Gedachtnissrede auf Karl von Nageli. Von K. Goebel. 1893. 4°. Ueber die Wege und Ziele der Hirnforschung. Festrede von N. Rudinger. 1893. 4+°. Die Lehre vom Tyrannenmord in der christlichen Zeit. Festrede von Max Lossen. 1894. 49. i MUnsTER.— Westfilischer Provincial- Verein fiir Wissenschaft und Kunst. Jahresbericht. XX-XXII, 1891-94. 5°. Nancy.—Académie de Stanislas. Mémoires. 5¢sér. Tome X, XI, 1892-93. 8°. NaPpoui.—f&. Accademia delle Scienze Fisiche e Matematiche. Atti. Ser. If. Vol. V, VI, 1892-93. 49. Rediconto. Ser. II. Vol. VII, VIII, 1893-94. 4°. Real Istituto d’ Incoraggiamento alle Scienze Naturali, ete. Atti. Ser. IV. Vol. V, VI, 1892-93. 4°. NEUCHATEL.—Société des Sciences Naturelles. Bulletin. Tome XVII-XX, 1889-92. 8°. NEWCASTLE-UPON-TYNE.—North of England Institute of Mining and Mechanical Engineers. Transactions. Vol. XLI, XLII. 1, 3-5, XLII, XLIV. 1-3, 1892-95. 8°. Account of the strata of Northumberland and Durham as proyed by bor- ings and sinkings. S-T. 1894. 8°. Report of the proceedings of the flameless explosives committee, 1894. 8°. NURNBERG.—WNaturhistorische Gesellschaft. Jahresbericht nebst Abhandlungen. Bd. X. i, 2, 1892-93. 8°. OpeEssa.—Société des Naturalistes de la Nouvelle Russie. Zapiski. Tom. XVII, XVIII. 1, 2, 1892-94. 4°. Matematicheskoe otdielenie. Tom. XIJI-XYV, 1891-95. $9. OSNABRUCK.— Naturwissenschaftlicher Verein. Bericht. IX, 1891-92. 8°. OTTawaA.— Geological and Natural History Survey of Canada. Annual report. New series. Vol. V, 1890-91. §&°. Catalogue of a stratigraphical collection of Canadian rocks, prepared for the Columbian Exposition, Chicago, 1893. By W.F. Ferrier. 1893, 8°. Catalogue of section I. of the museum. 1893. 8°. OxFORD.— Radcliffe Library. Catalogue of books added during 1892-94. 8°. ——-adcliffe Observatory. Catalogue of 6424 stars for the epoch 1890. Oxford, 1890. 4°. PALERMO.—. Accademia di Scienze, Lettere e Belle Arti. Atti. Ser, III, Vol. I, 1891. 4°. Bulletino. Anno X, 1893. 4°. Paris.—Ecole Normale Supérieure. Annales scientifiques. 3¢sér. Tome X, XI, XII, 1-6, 1893-95. 49, Ecole Polytechnique. Journal. Cahier LXIII, LXIV, 1893-94. 49. —— Musée Guimet. Annales. Tome XXII-XXV, XXVI. 1, 1892-94. 4°. Bibliothéque des ¢tudes. Tome II, IV, 1893-94. 8°. Revue de Vhistoire des religions. Tome XXV. 3, XXVI-XXVIII, XXIX. 1, 2, 1892-94. 8°. Muséum @ Histoire Naturelle, Bulletin. Année 1895, no. 1, 2. 8°. Additions to the Library. XXX1 PaARIs.— Observatoire National. Rapport annuel. 1893, 1894. 4°. Société Géologique de France. Bulletin. 38¢ sér. Tome XX. 1-8, XXI. 1-5, 1892-93. 8°. Compte-rendu. Année 1893, no. 1-7, 9-18; 1894, no. 1-38. 8°. Société Mathématique de France. Bulletin. Tome XX. 6-8, XXI, XXII, XXIII. 1-3, 1892-95. 8°. Société Nationale @ Acclimatation. Revue des sciences naturelles appliquées. Année 1893. 1-16, 18-24, 1894, 1895. 1-11. 8°. Société Zoologique de France. Bulletin. Tome XVII. 7-8, XVIII, XIX, 1892-94. 89°. Mémoires. Tome V. 5, VI, VII, 1892-94. 8°. PENZANCE.—Rfoyal Geological Society of Cornwall. Transactions. Vol. XI. 8, 9, 1894-95. 8°. Pisa.—Societa Toscana di Scienze Naturali. Memorie. Vol. XII, XIII, 1893-94. 8°. Processi verbali. Vol. VIII. pp. 157-241, IX. pp. 1-241, 1892-94. $9. PotspAM.—Astrophysikalisches Observatorium. Publicationen. Bd. VI. 2, VIII-X, 1893-95. 4°. PraG.—Kon. bohmische Gesellschaft der Wissenschaften. Sitzungsberichte der math.-naturwiss. Classe. 1892, 1893. 8°. Jahresbericht. 1892, 1893. 8°. K. k. Sternwarte. Magnetische und meteorologische Beobachtungen. Jahrg. LIII-LV, 1892-94. 4°. PuLKova.—JNicolai- Hauptsternwarte. Russische Expeditionen zur Beobachtung des Venusdurchgangs, 1871. Abth. I. St. Petersburg, 1891, 4°. Déclinaisons moyennes des étoiles principales pour l’époque 1885. St. Pétersbourg, 1893. 4°. Tables auxiliaires pour la détermination de l’heure par des hauteurs correspondentes de différentes étoiles. St. Pétersbourg, 1892. 8°. REGENSBURG.— Naturwissenschaftlicher Verein. Berichte. Heft IV, 1892-93. 8°. —Historischer Verein von Oberpfalz und Regensburg. Verhandlungen. Bd. XLV, XLVI, 1890-93. 8°. Riega.—WNaturforscher Verein. Correspondenzblatt. Jahrg. XXXVI, XXXVII, 1893-94. 8°. Rio DE JANEIRO.—Jnstituto Historico, Geographico Brazileiro. Revista trimensal. Tomo LY. 2, LVI. 1, 1898. 8°. Colombo. Poema por Manoel de Araujo Porto-Alegre. 1892. 8°. Christovam Colombo e o descobrimento da America, Por J. M. Pereira da Silva. 1892. 8°. : Homenagem. Sess&o extraordinario en commemoracgo do fallecimento de 8. M. o Snr. D. Pedro II., 4 Marco 1892. 8°. Museu Nacional. Archivos. Vol. VIII, 1892. 4°. La RocHEeLLE.—Académie des Belles-Lettres, Sciences et Arts. Annales de la société des sciences naturelles de la Charente-Inférieure. No. XXVIII-XXX, 1891-98. 8°. Roma.—Accademia Pontifica de’ Nuovi Lincei. Atti. Anno XLV. 3-6, XLVI, XLVII. 1-3, 1892-94. 4°. Reale Accademia dei Lincei, Atti. Serie [V. Memorie della classe di scienze morali, storiche e filolo- giche. Vol. VII, VIII: parte i, vol. i, VIII; 1890-91. 49°, Xxxll Additions to the Library. Roma.—Reale Academia Accademia dei Lincei. Atti. Serie V. Rendiconti. Classe di scienze fisiche, matematiche e naturali. Vol. I. ii, 12, IL. i, 1-5, 7-9, 12, III. i, ii, 1-5, 7-12, IV. i, 1-7, 9, 1892-95. 4°. Rendiconto dell’ adunanza solenne di 4 Giugno, 1893; 3 Giugno, 1894. 4°. Rassegna delle scienze geologiche in Italia. Anno II. 1-3, 1892. 8°, Reale Comitato Geologico @ Italia. Bollettino. Vol. XXIII, XXIV, 1892-93. 8°. Societa degli Spettroscopisti Italiani. Memorie. Vol. XXI. 12, XXII, XXIII, XXTV. 1-5, 1892-95. 4°. ROTTERDAM.—Bataafsch Genootschap der Proefondervindelijke Wijsbegeerte. Nieuwe verhandelingen. Reeks II. Deel III. 3, IV. 1, 1890-93. 49, St. GALLEN.—WNaturwissenschaftliche Gesellschaft. Bericht. Jahrg. 1890-91, 1891-92, 1892-93. 89°. St. Jonn.—New Brunswick Natural History Society. Bulletin. No. Il, [V—XII, 1883-94, 8°. S$. PaoLo.—Commissavo Geographica-e Geologica do Estado de S. Paolo. Boletim. No. 8, 9, 1891-93. 8°. Secc4o meteorologica. Dados climatologicos. 1891, 1892. 8°. St. PETERSBURG.—Uomité Géologique. Mémoires. Vol. IV. 3, V. 5, VIII. 3, [X. 2, 3, X. 1, 2, XII. 2, 1898-94, 40, Bulletins. Vol. XI. 5-10, XII, XIII. 1-3, 1892-94. 8°. Bibliotheque géologique de la Russie. 1891, 1892. 8°. Hortus Petropolitanus. Acta. Tom. XII, XIII, 1892-94, 8°. ——AImp. Russ. Geograf. Obshtchestvo. Izviestiya. Tom. XXIX, XXX, 1893-94. 8°. Otchet. God 1892-93. 8°. ; Beobachtungen der russischen Polarstation auf Nowaja Semlja. Theil I. Magnet. Beobachtungen. 1891. 4°. Kais. Akademie der Wissenschaften. Bulletin. Tome XXXVI.1,2. 5esér. Tome I, II. 1, 2, 1893-95. 409. Mémoires. 7e sér. Tome XX XIX. 2, XL, XLI, XLII. 1-6, 1892-94, 40. Repertorium der Meteorologie. Bd. XV-XVII, Supplementbd. VI, 1892-94. 4°. Physikalisches Centralobservatorium. Annalen. Jahrg. 1891-93. 4°. Russisch—Kaiserliche Mineralogische Gesellschaft. Verhandlungen, Ser. I]. Bd. XXIX, XXX, 1892-98. 8°. Materialien zur Geologie Russlands. Bd. XVI, 1893. 8°. San SALVADOR.— Observatorio Astronomico y Meteorologico. Resumen de las observaciones. 1892. 89. Observaciones. 1895. 4°. SAnTIAGO.—Société Scientifique du Chili. Actes. Tome II. 1, 4, III, IV. 1-4, 1892-94. 8°. Universidad di Chile. Anales. Tomo LX XXII. 6-9, 1892-93. 8°. Schweizerische naturforschende Gesellschaft. Verhandlungen. Jahresversammlung LXXV-LXXVII, 1892-94. §°. STAVANGER.—Museum. Aarsberetning. 1892. 8°. SrocKkHOLM.—Zntomologisk Forening. Entomologisk tidskrift. Arg. XIV, XV, 1893-94. 8°. ——-Kongl. Bibliotek. Sveriges offentliga bibliotek Stockholm, Upsala, Lund, Goteborg. Accessions-katalog, I-IX, 1886-94. 8°. Additions to the Library. XXXlll StocKHoLM.—Kongl. Svenska Vetenskaps-Akademie. Handlingar. Ny foljd. Bd. XXII-XXV, 1886-92. 4°. Bihang till handlingar. Bd. XIV—XIX. 1889-94. 8°. Ofversigt af forhandlingar. Bd. XLVI-L, 1889-93. 8°. Lefnadsteckningar. Bd. III. 1, 2, 1891-94. 8°. Ledamoter. 1890-93. 6&9. Meteorologiska jakttagelser. Bd. XXVII-X XXII, 1885-90. 4°. StuTTGartT.— Verein fiir vaterlindische Naturkunde in Wiirttemberg. Jahreshefte. Jahrg. XLIX, L, 1898-94. 89. SyDNEY.— Government Observatory. Observations of the transit of Venus, 9 Dec. 1874. Sydney, 1892. 4°. Results of astronomical observations, 1879-81. $°., Results of double star measures, 1891. 8°. Results of meteorological observations made in New South Wales during 1890. 82 Results of rain, river and evaporation observations during 1891-93. 8°. Sypney.—Linnean Society of New South Wales. Proceedings. Series II. Vol. IV, V, 1889-90. 8°. Royal Society of New South Wales. Journal and proceedings. Vol. XXVI, XXVII, 1892-938. 8°. TACUBAYA.— Observatorio Astronomico Nacional. Anuario. Afio XIV, XV, 1894-95. 8°, Boletin. Tomo I. 13-21, 1893-95. 4°. THRONDHJEM.—Kon. Norske Videnskabers Selskab. Skrifter. 1891, 1892. 89. TiFLis.—Physicalisches Observotorium. Beobachtungen. 1891. 4°. _ Beobachtungen der Temperatur des Erdbodens, 1886-89. 8°, ToKyo.—IJmperial University of Japan. Journal of the college of science. Vol. V. 3,4, VI, VII, VIII. 1, 1893-95. 4°, Calendar. 1893-94. 8°. Torino.—WMusei di Zoologia ed Anatomia Comparata. Bollettino. No. 26-32, 131-192, 1887-94. 8°, TorontTo.— Canadian Institute. Transactions. Vol. III, IV. 1, 1892-94. 8°. Annual report. V, VI, 1892-94. 8°, TOULOUSE.-—Académie des Sciences, Inscriptions et Belles-Lettres. Mémoires. 9¢ sér. Tome IV—VI, 1892-94. 89°, TRIESTE.— Osservatorio Astronomico-Meteorologico. Rapporto annuale. Vol. VII-IX, 1890-92. 40°. Tromso.—Museum. Aarsberetning. 1892. 8°. Aarshefter. XVI, 1894. 89°, UrsaLa.—Kongl. Universitet. Arsskrift. 1892, 1898. 8°. Bulletin of the geological institution. Vol. I, 1-8, 1892-98. 8°. Inbjudningsskrifter till de hégtidligheter hvarmed trehundraarsminnet af Upsala mote kommer att firasi Upsala den 5-7 September, 1893. 8°. ——-Regia Societas Scientiarum. Nova acta. Ser. III. Vol. XV. 1, XVI, 1892-93. 40, Utrecut.—Kon. Nederlandsch Meteorologisch Instituut. Nederlandsch meteorologisch jaarboek. Jahrg. XLIV, 1892. 4°, ——Provinciaal Utrechtsch Genootschap van Kunsten en Wetenschappen. Verslag van het verhandelde in de algemeene vergadering. 1892-94. 8°, Aanteekeningen van het verhandelde in de sectie-vergaderingen, 1892-94, XXX1V Additions to the Library. VrNEZIA.—Istituto Veneto di Scienze, Lettere ed Arti. Atti. Ser. VIE. Tomo II. 10, 111, TV, V. 1-8, 1891-94. 82: WELLINGTON.—New Zealand Institute. Transactions and proceedings. Vol. XXV, XXVI, 1893-94. 89. WIEN.--Kais. Akademie der Wissenschaften. Sitzungsberichte. Mathemat.-naturwiss. Classe. Abth. I. Bd. C. 8-10, CI, CII, CIII. 1-3, 1891-94, 8°. K. k. Central-Anstalt fiir Meteorologie und Erdmagnetismus. Jahrbiicher. Neue Folge. XXVIII, 1891. 4°. —— K. k. geologische Reichsanstalt. Abhandlungen. Bd. VI, XVII. 3, XVIII, 1898. 4°. Jabrbuch. Bd. XLI. 4, XLII. 2-4, XLITI, XLIV. 1, 2, 1891-94. §9. Verhandlungen. Jahrg. 1888, no. 7; 1890, no. 14-18; 1891, no. 1; 1892, no. 2-5, 11-18; 1893; 1894, no. 5-18; 1895, no. 1-5. 89. ——-K. k. naturhistorisches Hofmuseum. Annalen. Bd. VII. 3, 4, VIII, IX, 1892-94. 8°. —— K. k. Universitdts-Sternwarte. Annalen. Bd. VIII, IX, 1892-93. 89°. —— kK. k. zoologisch-botanische Geselischaft. Verhandlungen. Bd. XLII. 4, XLII, XLIV, XLV. 1-4, 1892-95. 8¢, WIESBADEN.—Wassauischer Verein fiir Naturkunde. Jahrbicher. Jahrg. XLVI-XLVII, 1893-94. 8°. Witrzpure.—Prysikalisch-medicinische Gesellschaft. Sitzungsberichte. Jahrg. 1892-94. 89°. Ztricu. —Naturforschende Gesellschaft. Vierteljahrschrift. Jahrg. XXXVII. 3, 4, XXXVIII, XXXIX, XL. 1, 1892-95. 8°. Aquilera, J. G. and Ordonez, E. Datos parala geologia de Mexico. Tacubaya, 1894. 8°. From the Authors. Arnoux, Gabriel. Essais de psychologie et de métaphysique positives. Arith- métique graphique. Les espaces arithmétiques hypermagiques. Paris, 1894. 8°. From the Author. Bickerton, A. W. Some recent evidence in favor of impact. Christchurch, 1874. 8°. Copy of letters sent to ‘‘Nature’’ on partial impact. Christchurch, i ford Meg soice From the Author. Cobb, N. A. Host and habitat of the Australian Fungi. Sydney, 1893. 8°. Diseases of the sugar-cane. Sydney, 1893. 8°. Contributions to the knowledge of Australian rusts (Uredinew). Sydney, 1894, 8°. Tricoma and other new Nematode genera. Sydney,1893. 8°. From the Author. Duerden, J. E. On some new and rare Irish Polyzoa. Dublin, 1893. 8°. Report on the Hydroida collected by the Royal Irish Academy Survey of the south-west coast of Ireland, 1885, 1886 and 1888. Dublin, 1893. —The rock pools of Bundoran. Dublin, 1895. §$°. On the genus Alicia. 1895. 8°. From the Author. Fritzsche, H. Ueber die Bestimmung der geographischen Lange und Breite und der drei Elemente des Erdmagnetismus. St. Petersburg, 1893. 8°. From the Author. Gilbert, G. H. The moon’s face, a study of the origin of its features. Wash- ington, 1893. 8°. From the Author. Gilpin, Edwin, Jr. The use of safe explosives in coal mines. Pt. i, ii. Halifax. S Additions to the Library. XXXV Report of the department of mines, Nova Scotia, Jan.-Sept., 1893. 8°. From Mr. Edwin Gilpin, Jr. Hasperath, L. Chemische Briefe V. 500 Thesen uber die Welt-Bildung. Buenos Aires, 1894. 8°. From the Author. . Herzenstein, 8. Apercu sur la faune malacologique de l’océan glacial russe. 8°. From the Author. Klossovsky, A. Organization de |’ étude climatérique spéciale de la Russie et problémes de la météorologie agricole. Odessa, 1894. 4°. Distribution annuelle des orages a la surface du globe terrestre. 4°. From the Author. Kuntze, O. Geogenetische Beitrage. Leipzig, 1895. 8°. From the Author. Le Jolis, A. Remarques sur la nomenclature hépaticologique. Cherbourg, 1894, Sey From the Author. Macfarlane, A. The fundamental theorems of analysis generalized for space. 1893. 8°. From the Author. Mouret, G. Démonstration du principe de l’ équivalence. Niort, 1894. 8°. From the Author. Miller, F. Max. An offering of sincere gratitude to my many friends and fellow labourers for their good wishes on the first of September, 1893, the fiftieth anniversary of my receiving the Doctor’s degree in the Univer- sity of Leipzig. 1893. 8°. From the Author. Pihl, O. A. L. On oceulting micrometers and their value as applied to exact astronomical measurements. Christiania, 1892. 4°. From the Author. Russell, H. C. Physical geography and climate of New South Wales. 2. ed. Sydney, 1892. 8°. | President’s address, Royal Society New South Wales, May 4, 1892. Sydney, Welan TIS From the Author. Wadsworth, M. E. The Michigan mining school. Lansing, 1894. 8°. From the Author. [The following memoir is in substance the writer’s thesis for the degree of Ph.D. at Yale University, 1891. ] ]. — MATHEMATICAL INVESTIGATIONS IN Pome TERORY OF VALUE AND PRICES. By Dr. IRVING FISHER. [Read April 27, 1892. ] PREACH. John Stuart Mill* asserted that he had left nothing in the laws of value for any future economist to clear up. Until 1871 this state- ment doubtless had much the force of dogma. Even Jevons made preliminary obeisance before proceeding to break the ground afresh with the mathematical instrument. Jevons with characteristic can- dor expressly disclaimed finality ;+ but few of his followers have realized with his clearness and honesty the need of further analysis along the lines which he laid down. The truth is, most persons, not excepting professed economists, are satisfied with very hazy notions. How few scholars of the lit- erary and historical type retain from their study of mechanics an adequate notion of force! Muscular experience supplies a concrete and practical conception but gives no inkling of the complicated dependence on space, time, and mass. Only patient mathematical analysis can do that. This natural aversion to elaborate and intri- cate analysis exists in Economics and especially in the theory of value. The very foundations of the subject require new analysis and definition. The dependence of value on utility, disutility, and commodity, the equality of utilities, the ratio of utilities, the utility of a commodity as a function of the quantity of that commodity solely, or of that commodity and others conjointly, are subjects, the neglect of which is sure to leave value half understood, and the mastery of which claims, therefore, the first and most patient effort of the economic scientist. These form the subject matter of the following memoir which is a study by mathematical methods of the determination of value and prices. Much germane to the subject has been omitted because already elaborated by others. Cases of discontinuity belong to almost every step, to modify or extend the continuous case. But the appli- cation of this correction has been thoroughly worked out by Auspitz und Lieben. Multiple equilibrium and monopoly value are omitted for a similar reason. The two books which have influenced me most are Jevons: ‘“ Zhe- ory of Political Economy,” and Auspitz und Lieben: “ Untersuch- ‘Pol. weon,; bk, IIT, Ch: I, $1, + Pol. Econ., Pref. 3rd ed. 4 Prefuce. ungen weber die Theorie des Preises.”” To the former I owe the idea of marginal utility and of mathematical treatment in general, to the latter the clear conception of the “symmetry” of supply and demand and the use of rate of commodity in place of absolute commodity, © and to both many minor obligations. The equations in Chapter IV, § 10, were found by me two years ago, when I had read no mathematical economist except Jevons. They were an appropriate extension of Jevons’ determination of exchange of two commodities between two trading bodies to the exchange of any number of commodities between any number of traders and were obtained as the interpretation of the mechanism which I have described in Chapter IV. That is, the determinate- ness of the mechanism was expressed by writing as many equations as unknowns. ‘These equations are essentially those of Walras in his Eléments d’économie politique pure. The only fundamental differences are that I use marginal utility throughout and treat it as a function of the quantities of commodity, whereas Professor Walras makes the quantity of each commodity a function of the prices. That similar results should be obtained independently and by sepa- rate paths is certainly an argument to be weighed by those skeptical of the mathematical method. It seemed best not to omit these ana- lytical portions of Part I, both because they contribute to an under- standing of the other portions of the work and because they were in a proper sense my own. Three days after Part II was finished I received a saw for the first time Prof. Edgeworth’s Mathematical Psychics. 1 was much interested to find a resemblance between his surface on page 21 and the total utility surfaces* described by me. The resemblance, how- ever, does not extend far. It consists in the recognition that in an exchange, utility is a function of both commodities (not of one only as assumed by Jevons), the use of the surface referred to as an inter- pretation thereof and the single phrase (Math. Psych., p. 28) “and similarly for larger numbers in hyperspace” which connects with Part I, Chie ss There is one point, however, in which, as it seems to me, the writer of this very suggestive book has gone far astray. Mathe- * His result, which translated into my notation is dU dU feo (sa) (ae )ic e& \(&)= becomes by transposition and division identical with part of the continuous pro- portion, Part I, Ch. IV, $3. Preface. 5 matical economists have been taunted with the riddle: What is a unit of pleasure or utility ? Edgeworth, following the Physiological Psychologist Fechner, answers: “Just perceivable increments of pleasure are equatable” (p. 99). I have always felt that utility must be capable of a definition which shall connect it with its posi- tive or objective commodity relations. A physicist would certainly err who defined the unit of force as the minimum sensible of mus- cular sensation. Prof. Edgeworth admits his perplexity: “It must be confessed that we are here leaving the terra firma of physical analogy” (p. 99). Yet he thinks it is “a principle on which we are agreed to act but for which it might be hard to give a reason ;” and again: [such equality] ‘‘it is contended, not without hesitation is appropriate to our subject.” This foisting of Psychology on Economics seems to me énappro- priate and vicious. Others besides Prof. Edgeworth have done it. Gossen* and Jevons appeared to regard the “calculus of Pleasure and Pain” as part of the profundity of their theory. They doubt- less saw no escape from its use. The result has been that “ mathe- matics” has been blamed for “restoring the metaphysical entities previously discarded.” t These writers with Cournot,$ Menger,|| and Marshall] appear to me to have contributed the most to the subject in hand. With the exceptions noted I have endeavored not to repeat them but to add a little to them, partly in the theory of the subject and partly in the mode of representing that theory. Readers to whom the subject is new will find the present memoir exceedingly condensed. In the attempt to be brief, the possible uses of the diagrams and mechan- isms have been merely sketched, and elaborate explanations and illustrations have been omitted. I have assumed that my readers are already familiar with (say) Jevons, Walras, Menger or Wieser where illustrations and explanations regarding “final utility” abound. Much of Part II and Appendix I may not be thoroughly intelligible to those not familiar with higher geometrical analysis. These parts are made as brief as possible. My especial thanks are due to Prof. Gibbs and Prof. Newton for valuable criticism. IRVING FISHER. * Menschlich Verhehr., Braunschweig, 1854. + Jevons, p. 23, also pp. 8-9. ¢{ Dr. Ingram. $ Théorie des Richesses, Paris, 1838. | Volkswirthschaftslehre, Wien, 1871. {| Prin. of. Econ., Macmillan, 1890. PART 1. CHAPTER J, CHAPTER II, SYLLABUS. UTILITY OF EACH COMMODITY ASSUMED TO BE DEPENDENT ONLY ON THE QUANTITY OF THAT COMMODITY. Utility as a Quantity. 1. Psycho-economic postulate, Definitions of equal and unequal atilities, 3. Application of these definitions to an equation of exchange, : : Definition of the ratio 2: two utilities, Analogy with other mathematical definitions, Marginal utility, unit of utility, Exact meaning of a utility curve, : z Total utility, utility-value, gain or consumer’s rent, Element of time, 10. Utility curves for a time- aa bag for an ‘inate 11. A yearly utility curve implies no exact foreknowledge of amounts consumed, $12. Theory of probabilities Paely, eliminates increas influences except as regards ‘‘ gain,” 13. Infinitesimals appropriate though non-existent, | 14. The preceding definitions of utility absolve the econ- omist from psychological and metaphysical disputes, $15. Summary of Chapter I, CH CH CD vo ODD OM CO th) CD 7 COD CO) Mechanisin. § 1. Mechanical analogy common in economic thought, § 2. Ideal suppositions concerning the market, S$ 8. A new utility diagram. Its related cistern (Fig. 2), § 4, A single commodity and a single consumer, S 5. One commodity—one producer ; disutility cia and cistern (Fig. 3), S$ 6. One commodity—many consumers (Fig. 4), § 7. Analytical interpretation of § 6, Aggregate commodity, 2 One commodity—many geedades (Fig. 5), Preceding simply gives exactitude to the common imagery of thought, _ = CH) CH CMa co ce 23 23 Syllabus. CHapTeR III. One consumer (or producer)—many commodities. Distribution of income, Mechanism (Fig. 6), 3 : The three determining conditions of chok Snibrinay: Analytical interpretation of §3, Aggregate income, One producer—many a arnoditioe (Fig. a); CHAPTER IV. m commodities—n consumers (or producers). OD Ch WT DQ? ca v7 CO zy OS CO Be Geo. 8 10. ed: 1 Relative points of view of Chapters II, III, and IV, These points of view compared exactly and analyti- cally, : Equaiity of marginal utilities now gives way to their proportionality, Mechanism (Figs. 8, 9, 10, 11), Equilibrium automatic, The various magnitudes popuchantent Two simple relations of these magnitudes, Complex interdependence traced, 1. Equal incomes, 2. One income increased, , 3. One income increased, one decreased, 4. One commodity increased, ; 5. One commodity increased with rant in- come-increase, 2 6. All commodities increased, 7. All incomes increased, ; 8. Change in individual characteristics, Aggregate cisterns impossible, Analytical, ‘ m commodities—n Pracalect (Figs. ips 13), CHAPTER V. Production and consumption combined. at Interdependence of production and consumption must not be overlooked, Assumptions, : One individual consuming rae that adantiee of a given commodity which he himself produces (Fig. 14), Analytical, n individuals—m A onan antics (Figs, 15, 16), Analytical, CuapTeR VI, The component processes of production. a1. § 2. & 3. Retailing (Fig. 17), Analytical, Further subdivision of 7 pr paieied! co =p) co CO on) Hy He wo won is 60 61 63 8 Syllabus. PART II. UTILity OF ONE COMMODITY A FUNCTION OF THE QUANTITIES OF ALL COMMODITIES. CHAPTER I. Two commodities with interrelated utilities. Page & 41) introduction, < : . : 64 § 2. Interdependence of ntilibies common, : : : 65 § 3. Effect on the cistern-analysis, . : 4 65 § 4. Competing and completing commodities aefineas ee § 5. Cistern-analysis correct but incomplete, . A : 66 § 6. The third definition of utility (Part I, Ch. DT, . : 67 § 7. Twocommodities, . : . : 67 § 8. Impossible combinations of two oomiencatitiee ; : 69 § 9. Curves of utility, : : : ‘ : ; : 69 §10. Indifference curves, . ‘ : : 70 §11. Partial income line fanaa to jniiarnne CURVE; ae 71 $12. Different sensitiveness of competing and completing commodities, . . ‘ : : 73 $13. Good and poor qualities of ne same commode : 73 $14. ‘‘Maximum directions,” . : 74 $15. ‘‘Maximum directions ” of all consumers pansies ; 75 §16. Production, : : : : ‘ : : ‘ 75 $17. Production and consumption, . : ‘ : : 76 © CHAPTER II. Three or more commodities. § 1. Construction in three dimensions, . : : : 76 § 2. Complicated dependence of utilities, : : ; 7 § 8. Equilibrium if only three commodities exist, . z 78 S$ 4. Passage to two dimensions by plane sections, . é 79 § 5. m dimensions requisite, . : Tey : : 79 § 6. mdimensions used, . é : 4 : ; : 80 § 7. Conditions of equilibrium, : d ; 80 § 8. Passage to lower dimensions by ‘ fat » soahiones : 81 § 9. Analytical (vector analysis), ; : : : Y 81 $10. Peculiar cases of marginal utility, . : : : 82 CuHapTerR III. Mechanical analogies. §1. Mechanical analogies discussed, : : 4 85 §2. Analogies in parallel columns, . : 3 ; , 85 CHAPTER IV. Utility as a quantity. $1. No need to compare two persons’ utilities, . 4 : 86 § 2. How such a comparison might be made, . : : 86 § 3. How it could be applied to statistics, . : ; 87 §4. Definition (8) (Part I, Ch. I) unessential in Part I, : 87 §5. ‘‘Maximum directions” alone important. . ; : 88 §6. Integration of total utility probably impossible for in- terrelated utilities, . : : : 5 i : 88 $7. Arbitrary constants unessential, . : 89 $8. Four attributes of utility unessential in the speeae in- vestigation, : ; 4 : ; ; ; — 89 Syllabus. APPENDIX I. MISCELLANEOUS REMARKS ON Part I. I. Failure of equations, Il. The cisterns and diagrams of Part I compared with the diagrams of Jevons and of Auspiz und Lieben. $1. Possible geometrical representations of commodity and utility, : : §2. Scheme comparing the een copedsitntcs with “tics of Jevons and of Auspitz und Lieben, $3. A linear assumption, $4. The relative value of the adorns) §5. Properties essential to the cisterns, $6. Meaning of the abscissa, $7. Total utility and gain, Ul. Gain a maximum, $1. For one individual, : 3 : §2. For one commodity and in what sense true, §3. For whole market and in what sense true, $4. Under what conditions would the total market gain te maximum if we could obtain the ‘‘ true” equivalence between two persons’ utilities, IV. Elimination of variables, Each price is the quotient of two determinants, and all equa- tions can be reduced to a single set involving commodities only. APPENDIX IJ. LiImiIvTaTIONS OF THE PRECEDING ANALYSES. 1. The suppositions were ideal, 2. Utility a function of many variables, : 3. Articles not homogeneous nor infinitely divisible, 4, Discontinuity in time, 5. Statics and Dynamics, 6. Population, 7. No perfect individual Pecan dion a ducing (as consuming) at any point, No perfect knowledge of prices, : 9. Production different from consumption in many im- portant respects, ; : : - $10. Marginal utility and aeanialiey a may Pagatonnllty vary in a manner opposite to that which has been sup- posed, : A ' : : ‘ §11. Markets are not culate and there is no perfect market, De C2 Uh Ch CF WI YW @ Page 98 98 101 106 106 10 Syllabus. APPENDIX III. THE UTILITY AND HISTORY OF MATHEMATICAL METHOD IN ECONOMICS. Page $ 1. Its utility is of same kind as the utility of mathemat- ical method elsewhere, . 4 106 S$ 2. Mathematical method distinguished fein insithoataee 505507, : : : ; : : : i : 107 S 3. Utility of mathematical method is relative to the user, : : : : ; ; 107 S$ 4. Mathematical mpitieds is for Hehse economics, * : 108 § 5. Has mathematical method come to stay? . : c 109 S$ 6. What has it already accomplished? . A 110 S$ 7. Quotations in favor of mathematical sapthed’ fea Whewell, Cournot, Gossen, Jevons, Walras, New- comb, Launhardt, Wicksteed, Foxwell, Auspitz und Lieben, Edgeworth, Marshall, and Cunynghame, . 112 § 8. Quotations opposed to mathematical method from Anonymous, Cairnes, Wagner, Ingram, and Rab- berio, with comments, . : : : : ; 116 § 9. A reason for opposition, . : : : : ; 119 §10. Conclusion, : : : ; ; : 119 APPENDIX IV. BIBLIOGRAPHY OF MATHEMATICO-ECONOMIC WRITINGS. $1. Scope of bibliography, : : : q 120. §2. List selected from Jevons’ piblioneaphy: ; : ; 120 $3. Extension of Jevons’ bibliography, . : ‘ ; 122 Part I.—UtTimiry oF EACH COMMODITY ASSUMED TO BE DEPEN- DENT ONLY ON THE QUANTITY OF THAT COMMODITY. CHAPTER I. UTILITY AS A QUANTITY. ae Tue laws of economics are framed to explain facts. The concep- tion of utility has its origin in the facts of human preference or decision as observed in producing, consuming and exchanging goods and services. To fix the idea of utility the econumist should go no farther than is serviceable in explaining economic facts. It is not his province to build a theory of psychology. It is not necessary for him to take sides with those who wrangle to prove or disprove that pleasure and pain alone determine conduct. These disputants have so mangled the ideas of pleasure and pain that he who follows them and their circular arguments finds himself using the words in forced senses. Jevons makes utility synonymous with pleasure. Cairnes* objects and claims that it leads to a circular definition of value. The circle is however at the very beginning and vitiates psychology not eco- nomics; the last dollar’s worth of sugar (we are told) represents the same quantity of pleasurable feeling as the last dollar’s worth of dentistry. ‘This may be true as a mere empty definition, but we must beware of stating it, as a real “‘synthetic proposition,”t or of connecting it with the mathematics of sensations{ as did Edgeworth.§ The plane of contact between psychology and economies is des?re. It is difficult to see why so many theorists endeavor to obliterate the distinction between pleasure and desire.|| No one ever denied that economic acts have the invariable antecedent, desire. Whether the necessary antecedent of desire is “pleasure” or whether indepen- dently of pleasure it may sometimes be “ duty” or “fear ” concerns a phenomenon in the second remove from the economic act of choice and is completely within the realm of psychology. We content ourselves therefore with the following simple psycho- economic postulate: Leach individual acts as he desires. Mm Pol. Heon., p. 21. + Kant, Critique Pure Reason, Introduction. { Ladd, Physiological Psychology, p. 361. S See above (Preface). || See Sidgwick, Methods of Ethies, Chap. IV. 12 Irving Fisher— Mathematical investigations The sense in which utility is a quantity is determined by three definitions: (1) For a given individual at a given time, the utility of A units of one commodity or service (@) is equal to the utility of B units of another (4), if the individual has no desire for the one to the exclu- sion of the other. | A and B are here used as numbers. Thus if the first commodity is sugar and the second calico and if the individual prizes 2 pounds of sugar as much as 10 yards of calico, A is 2 and B is 10. (2) For a given individual, at a given time, the utility of A units of (a) exceeds the utility of B units of (0) if the individual prefers (has a desire for) A to the exclusion of B rather than for B to the exclusion of A. In the same case the utility of B is said to be less than that of A. The third definition will be given in § 4. The two preceding definitions are exactly parallel to those of any other mathematical magnitude. Thus: two forces are equal if at the same time they alone act on the same particle in opposite directions and no change of motion results. One is greater when additional motion is produced in its direction. Again: “two masses are equal which if moving with equal velocities along the same straight line in opposite directions and impinging on each other are reduced to rest by the collision.”* Two geometrical magnitudes are equal if they can be made to coin- cide, ete., ete. Just as coincidence is the test of equality and inequality of geo- metrical figures, and the tip of the scales the test of equality and inequality of weights, so is the desire of the individual, the test of the equality and inequality of utilities. It is to be noted that in each definition of equality the word “no” or some equivalent occurs. A standard mode of cancellation is thus designated. § 3. Let us see how these definitions of utility apply to an act of pur- chase. An individual I enters a market with fixed prices to ex- change some of a commodity (a) for another (6). We may sup- pose prices to be such that he gives one gallon of (a) and receives two bushels of (4), then a second gallon for two more bushels and so on * Price, Calculus, vol. iii, p. 316. in the theory of value and prices. 13 until finally he has given A gallons and received B bushels. At what point does he stop? Although the “exchange values” of A gallons of (a) and B bushels of (6) are equal, their wtzlities (to I) are not. He prefers b to the exclusion of A, for his act proves his preference (postulate). Therefore by definition (2) the utility of B exceeds that of A. We may write: ut. of B > ut. of A. Why then did he cease to buy (0)? He sold exactly A gallons for B bushels. By stopping here he has shown his preference to buy no more (postulate). Hrgo the utility of a small increment, say another bushel of (4) is less than the utility of the corresponding number of gallons of (a) (Def. 2). Likewise he prefers to buy no less. Firgo the utility of a small decrement, say one less bushel is greater than the gallons for buying it. Now by the mathematical principle of continuity, if the small increment or decrement be made infinites- imal dB, the two above tnequalities become indistinguishable, and vanish in a common equation, viz: Ui. of 7d Be ut: of dA dB and dA are here exchangeable increments. But the last incre- ment dB is exchanged for dA at the same rate as A was exchanged for B; that is By ge where each ratio is the ratio of exchange or the price of B in terms of A. or EE reesei dB dA multiplying this by the first equation, we have: ut. of dB ut. of dA Gi ors Sig TEN = which may be written :* aU _ aU dB dA The differential coefficients here employed are called by Jevons “final degree of utility,’ and by Marshall “marginal utility.” Hence the equation just obtained may be expressed: For a given * Cf. Jevons, Pol. Econ., p. 99. + Jevons, Ibid., p. 51. { Marshall, Prin. of Econ., Preface, p. xiv. 14 Irving Fisher—Mathematical investigations purchaser at the time of purchase the quantity of the commodity purchased multiplied by its marginal utility equals the like product for the commodity sold. Or again: for a given purchaser the utili- ties of A and B, though actually unequal would be equal if every portion of A (and also of B) were rated at the same degree of utility as the last infinitesimal. This hypothetical equality underlies, as will subsequently appear, the notion of the equality of values of A and B. S 4. But the two definitions (1) and (2) do not fully determine the sense in which utility is a quantity. To define when the “ grades” of two parts of a highway are equal or unequal (viz: when they make equal or unequal angles with a horizontal), does not inform us when one shall be twicé as steep as the other. It does not oblige us to measure the “grade” by the sine of the angle of elevation, or by the tangent, or by the angle itself. If the two highways were inclined at 10° and 20° respectively, the “grades” have a ratio of 1°97 if measured by sines, of 2°07 by tangents, and exactly 2 by angles. For a long time philosophers could define and determine when two bodies were equally or unequally hot. But not till the middle of this century* did physicists attach a meaning to the phrase ‘“ twice as hot.” It is here especially that exactitude has been hitherto lacking in mathematical economics. Jevons freely confesses that “ We can seldom or never affirm that one pleasure is an exact multiple of another.”’+ Now throughout Part I the assumption is made that the utility of any one commodity (or service) depends on the quantity of that commodity or service, but is independent of the quantities of other commodities and services. This assumption is preliminary to the definition we seek. Our first problem is to find the ratio of two infinitesimal utilities. If an individual I consumes 100 loaves of bread in a year the utility of the last infinitesimal, or to fix our ideas, the utility of the last loaf is (presumably) greater than what it would be if he consumed 150 loaves. What is their ratio? It is found by contrasting the utilities of the 100th and 150th loaves with a third utility. This * The first thermodynamic definition of one temperature as a multiple of another was made by W. Thomson in 1848. See Maxwell, Theory of Heat, p. 155. + p. 13. in the theory of value and prices. 15 third utility is that of oil (say) of which let B gallons be consumed by I during the year. Let / be that infinitesimal or small increment of B whose utility shall equal that of the 100th loaf. Now in sub- stituting the hypothesis of 150 loaves let us not permit our individ- ual to alter B, his consumption of oil.* The utility of the 150th loaf will be pronounced by him equal (say) to the utility of 4 f. Then the utility of the 150th loaf is said to be half the utility of the 100th. | That is, if: ut. of 100th loaf = ut. of /, B being the total, and ut. of 150th loaf = ut. of 6/2, B being the total again, the ratio is defined : ut. of 100th loag § 6 _ 5 iteor 150th loah se 6/220 It is essential to observe that if the 100th loaf is twice as useful as the 150th when their ratio is defined as above in terms of incre- ments of oil, it will also be twice as useful when the ratio is defined by any other commodity ; also that it matters not what total quan- tity (B) of oil or other commodity is employed. This theorem may be thus stated: Given (1) ut. of 100th loaf = ut. of £, B being total, and (2) ut. of 150th loaf = ut. of (6/2, B being total, also (3) ut. of 100th loaf = ut. of y, C being total, To prove ut. of 150th loaf = ut. of 7/2, C being total, where C is the quantity of another commodity (c) consumed by I in the same period and y is such an increment of C that its utility shall equal that of the 100th loaf. We may write from (1) and (3): ut, ol. 100th: loaf = ut, of 6 = ut. of 7, (100 loaves, B and OC, being totals). Now, if the first total (100 loaves) be changed to 150, B and C being unchanged, the above equation, dropping the first member, will still be true, viz: ut. of Pi == nt, of 9, (150 loaves, B and C, totals), for, by our preliminary assumption these utilities are independent of the quantity of bread. * As a matter of fact an individual who, if consuming 100 loaves of bread would consume B gallons of oil might, if consuming 150 loaves, use also more oil. But this fact in no wise hinders our inquiring how he would reckon utili- ties if he used the same amount. 16 Irving Fisher—Mathematical investigations Since £ and y are infinitesimal it follows from the mere mathe- matical principle of continuity that: ut. of 6/2 = ut. of v/2, (B, C, totals), by aay ut. of 150th loaf = ut. of y/2, (150 loaves, C, totals) Q. HE, D. Hence our definition becomes: ut. of 100th loaf _ i aoa ut. of 150th loaf —y/2 Likewise: ut. of 100th loaf ‘o} of 150th loaf ut. _ete., etc., all of which results harmonize. Since C is any arbitrary quantity it follows that the definition of the above ratio is independent not only of the particular commodity employed as a means of comparison but also of the total quantity of that commodity. It is to be noted here that if the utility of one commodity were dependent on the quantities of others, two applications of the defini- tion would yield discordant results.* 7 We may state our definition in general terms as follows : (3) The ratio of two infinitesimal utilities is measured by the ratio of two infinitesimal increments of the same commodity respectively equal in utility to the two utilities whose ratio is required, provided these increments are on the margin of equal finite quantities : In general symbols this becomes : ut. of dA PGES IE iia n:—if ut. of dA = ut. of ndM (M total), and ut. of dB = ut. of dM (M also total), where 7 is any finite number, positive or negative, whole or frac- tional. This definition applies not only to infinitesimal utilities of the same commodity (as of the 100th and 150th loaves of bread) but to those of different commodities or services. * We shall afterward see how this affects our notions of utility (Part II, Ch. IV. in the theory of value and prices. 17 S 5. Definition (8) is perfectly analogous to other mathematical defini- tions. To define equality of forces does not fix their proportionality. This property is found in the additional definition: “The ratio of two forces is the ratio of their mass-accelerations.” Before me- chanics was a science, “force” stood for a “‘common sense” notion resolvable in the last analysis into a muscular sensation felt in push- ing and pulling.* But to construct a positive science, force must be defined with respect to its connection with space, time and mass. So also, while utility has an original “common sense” meaning relating to feelings, when economics attempts to be a positive science, it must seek a definition which connects it with objective commodity.t 8 6. (4) Zhe marginal utility of a commodity (as implied in § 8) és the limiting ratio of the utility of the marginal increment to the magni- tude of that increment. Hence the ratio of two marginal utilities is the ratio of the utilities of two marginal increments divided by the ratio of these increments. If the units of the commodity are small, the marginal utility is practically the utility of the last unit—for bread, of the last loaf, but if this loaf is sliced into 10 parts and these slices have different utilities, the marginal utility of bread is more nearly the utility of the last slice divided by ;1,, and so on ad infinitum. It is now an easy matter to find a unit of utility, the lack of which has been the reproach{ of mathematical economists. The utility of the 100th loaf per year may be regarded as the unit of utility. Or in general: * Spencer, First Principles, p. 169. + Jevons, Marshall, Gossen, and Launhardt, omit indicating in any way what they mean by the ratio of utilities. Yet each of them embody the idea in their diagrams. Edgeworth (Math. Psych., p. 99) thinks ‘‘ just perceivable increments [of pleasure] are equatable” and uses this ‘‘minimum sensible” as a unit in terms of which any pleasure is to be measured (in thought at least). His defini- tion and mine show perhaps the very point of departure between psychology and economics. To measure a sensation, the minimum sensible is perhaps the only thinkable method (see Ladd, Physiological Psychology, p. 361). Here the phenomenon is subjective and so is its measure; while in economics the phe- nomena are objective and likewise their measure. ¢t Dr. Ingram, Article: Pol. Econ., Ency. Brit., xix, 399. TRANS. Conn. AcAD., VOL. TX, 2 JULY, 1892. 18 Irving Fisher— Mathematical investigations (5) Lhe marginal utility of any arbitrarily chosen commodity on the margin of some arbitrarily chosen quantity of that commodity may serve as the unit of utility for a given individual at a given time. This unit may be named a wiz. Any unit in mathematics is valuable only as a divisor for a second quantity and constant only in the sense that the quotient is constant, that is independent of a third quantity. If we should awaken to-morrow with every line in the universe doubled, we should never detect the change, if indeed such can be called a change, nor would it disturb our sciences or formule. § 7. With these definitions it is now possible to give a meaning to Jevons’ utility curve, whose abscissas represent the amounts of a commodity (say bread) which a given individual might consume during a given period and the ordinates, the utilities of the last (i. e. the least useful) loaf. For if corresponding to the abscissa 100 loaves an ordinate of arbitrary length (say one inch) be drawn to stand for the utility of the 100th loaf, we may use this as a unit (wtil.) For any other abscissa as 85 loaves whose marginal utility is (say) twice the former, the ordinate must be two inches, and so on. For any other commodity as oil the marginal utility of A gallons being contrasted with the utility of the 100th loaf of bread and this ratio being (say) three, an ordinate of three inches must be drawn. In all the curves thus constructed only one ordinate is arbitrarily selected, viz: that representing the utility of the 100th loaf. § 8. Only differentials of utilities have hitherto been accounted for. To get the total utility of a given amount of bread we sum up the utilities for the separate loaves. Or in general: (6) Zhe total utility of a given quantity of a commodity at a given time and for a given individual is the integral of the mar- ginal utility times the differential of that commodity. That is: ut. of (x) = ut. (dz,) + ut. (dz) + .... + ut. (da,) 4 ¥ zs a ut. (dx) 0 ne ] if = ‘a aU dx. w/ 0 dx: in the theory of value and prices. 19 (7) Lhe name vvTiLity-VALUE of a commodity may be given to the product of the quantity of that commodity by its marginal utility or du The name is suggested from money-value which is quantity of commodity times its price. (Cf. § 3). (8) The Gain or consumers rent is total utility minus utility value. That is: - Gain = f- “Y tase e On ae dx It is the actual total utility diminished by that total utility which the commodity would have if it were all rated at the same degree of utility as the last or least useful increment. It is to be observed that total utility and gain are not experiences in time but the sum of increments of utility swbstitutionally succes- sive. The individual is to assign the marginal utility for the 90th loaf on the hypothesis that he were consuming 90 loaves per year, and then abandoning this supposition to substitute successively the hy- pothesis of 91 loves, 92, 93, etc., all for the same year. That is, a number of mutually exclusive hypotheses for the same period are thought of. . § 9. The preceding definitions have been expressed relative to a par- ticular instant of time. This was because in actual life purchases are made by separate instantaneous acts. But the important com- modity-magnitudes in economics are “tons per year,” “yards per day,” etc., bought, sold, produced, consumed. In order to make our definitions applicable to such quantities the element of time must be introduced. Hence the following supposition : During the given period of time (that is, the period for which commodity-magnitudes are considered) the marginal utility to a given individual of a given commodity is the same at all instants at which he buys or consumes it or sells or produces it. This involves supposing that prices do not vary, for prices (as we shall see) are proportional to marginal utilities. A housewife buys (say) 10 Ibs. of sugar at 10 cts. per pound. As she closes the bargain she roughly estimates that the last or tenth pound is about worth its price. She did not stop at five pounds for she wanted a sixth more than the 10 cts. it cost her. She may not buy sugar again for a fortnight. When she does, we shall suppose 20 Irving Fisher—Mathematical investigations the price to be the same, so that the last pound she then buys has the same utility as the last pound she previously bought. She may buy fifteen pounds. A fortnight later only five, all depending on her plans for using it. The whole yearly purchase may be 250 lbs. and we may write : ut. (10th Ib.) Jan. 1 = ut. (15th lb.) Jan. 15. = ut. ( 5th lb.) Jan. 30. = ete. ut. (250th lb.) for whole year. Thus: Zhe marginal utility of a certain quantity of a commodity for a given period (say a year) is defined to be the marginal utility of that commodity on all occasions during that year at which it is bought or consumed, the sum of the individual purchases being the given yearly purchase and consumption. l $10. In the hypothetical case the marginal utility of 250 pounds per year equalled the marginal utility of 10 cts. In the same manner we may practically estimate the marginal utility of 200 pounds by supposing the price to be such that our housewife would buy 200 pounds. Thus a number of alternative suppositions are made for the same period. By means of these a utility curve can be con- structed, one of the codrdinates of which is the yearly consumption of sugar. To do this statistically is of course quite a different and more difficult though by no means hopeless proceeding. Curves of this nature are the only ones to be here considered. But it is clear that there also exist utility curves for each time of purchase.* These would differ both from the “yearly” curve as well as from each other. $11. To meet a possible objection it must be pointed out that the use of a ‘yearly ” utility curve assumes no nice calculation on the part of the individual as to his future income and receipts. He may even be and generally is totally ignorant of the number of pounds of butter he consumes per year. He creeps along from purchase to purchase and only at these individual acts does he estimate his needs and his abilities. Yet if he always completes his purchase with the same estimate of marginal utility as measured against other com- * They would be the curves of Fleeming Jenkin: Graphie Representation of Supply and Demand. Grant’s Recess Studies, p. 151, Edinburgh, 1870. in the theory of value and prices. 21 modities, this must be the marginal utility for the year and the total yearly purchase is the quantity which bears this marginal utility. This marginal utility or “final” degree of utility of the commodity for the year is clearly not the utility of the last amount chrono- logically (that is Dec. 31), but the utility of the least useful part of any and each of the separate purchases. § i2. It may further be objected that there is a fitful element in the problem which the above supposition ignores. We have supposed prices do not vary during the given period and also that the indi- vidual’s utility-estimate does not vary. It may justly be claimed that not only do prices vary from day to day, but even if they did not, the individual’s estimate of utility is fitful and, although at the instant he closes a bargain his estimate of utility must be regarded as corresponding to the given price, yet he is likely gen- erally and certain sometimes to regret his action so that if he were to live the year over again he would act very differently. This objection is a good illustration that a microscopic view often obscures the general broad facts. As a matter of fact the use of a period of time tends to eliminate those very sporadic elements objected to. First, though prices vary from hour to hour under the influence of excitement and changing rumors, and from season to season under causes meteorological and otherwise, yet these fluctua- tions are self-corrective. ‘The general price through the year is the only price which is independent of sporadic and accidental influences. This general price is not the arithmetical mean of the daily prices but a mean defined as such that had it been the constant price during the period the amounts bought and sold would have been just what they actually are. Secondly, the individual caprice is self-correc- tive. If a man lays in too large a stock of provisions this week he will buy less next. The theory of probabilities therefore substan- tially harmonizes the theoretical and the actual. The apparently arbitrary suppositions regarding constancy of price, etc., may be looked upon as convenient definitions of an ideal average as just described. One observation however must not be overlooked. Although accidental variations of price or choices of caprice afford both posi- tive and negative errors and thus largely cancel each other, yet the effect on the total utility and the gain is always to diminish them. To buy too much or too little, to sell too cheap or too dear will be 22 Irving Fisher—Mathematical investigations equally sure to diminish gain. Herein lies the virtue of insur- ance and the vice of gambling. Neither alters (directly) the amount of wealth. But insurance modifies and gambling intensi- fies its fluctuations. Hence the one increases the other decreases gain. $13. Again it may be objected to the foregoing definitions that the use of infinitesimals is inappropriate since an individual does not and cannot reckon infinitesimals. The same apparent objection attaches to any application of the calculus. We test forces by weights but cannot weigh infinitesimal masses nor do they probably exist; yet the theory of forces begins in infinitesimals. We apply fluxions to the varying density of the earth, though we know that if we actually take the infinitesimal ratio of mass to volume we shall generally get zero since matter is discontinuous. The pressure of a confined gas is due to collisions of its molecules against the containing vessel. As each molecule rebounds the change of momentum divided by the infinitesimal time is the pressure. Yet at any actual instant the value of this fluxion is quite illusory. But these facts do not mil- itate against the use of fluxions for a thinkable theory of forces, density and gaseous pressure. In cases of discontinuity fluxions have important applications though infinitesimals may not exist. The rate of increase of population at a point in time is an impor- tant idea, but what does it mean? It is convenient to define it as infinitesimal increase of population divided by the infinitesimal time of that increase though we know that population increases discon- tinuously by the birth of whole individuals and not of infinitesimals. Practically we can find the approximate marginal utility of a commodity just as we approximately find the rate of increase of population by taking small increments in place of intinitesimals. In actual fact inequality of utilities is the rule and absolutely equal utilities never exist. Instead of a curve of utility we should draw a belt (fig. 1) whose limits are ill-defined and whose width in general depends on the amount of antecedent atten- tion which the individual has bestowed on the alternative amounts and modes of consumption. iM O in the theory of value and prices. 23 $14, Utility as defined in the preceding sections does not involve the economist in controversy as to the laws of the subjective states of pleasure and pain, the influence of their anticipation as connected with their probabilities,* the vexed questions whether they differ in quality as well as in intensity and duration,t whether duty can or cannot exist as a motive independently of pleasure,{ ete. It does not follow that these discussions have no meaning or im- portance. Doubtless pleasure and pain are connected with desire and doubtless they have an important biological and sociological function as registering “healthful” or ‘ pathological” conditions.§ But the economist need not envelop his own science in the hazes of ethics, psychology, biology and metaphysics. Perhaps utility is an unfortunate word to express the magnitude intended. Desirability|| would be less misleading, and its opposite, undesirability is certainly preferable to dis-utility. “ Utility” is the heritage of Bentham and his theory of pleasures and pains. For us his word is the more acceptable, the less it is entangled with his theory. $15. This chapter may be thus summarized: Postulate : Each individual acts as he desires. Definitions of utility. (2) and (1) ut.of A = ut. of B if the given indiv. at the given time prefers A to B or neither. ut. of dA id ut, of dB ” if ut. of dA=ut, of ndM (M total) and ut. of dB=ut. of dM (M also total). le lioada Pom Me aa af (4) WA = Marginal utility. (5) a = Unit of utility (wéi/.) (A being given). * Jevons, p. 72. + Jevons, p. 28, ete. ¢{ Darwin, Descent Man, I, p. 76, Sidgwick, Methods Ethics, Ch. IV. § Marshall, Prin. of Econ., p. 181, Spencer, Data of Ethics, p. 79, L. Stephen, Science of Ethics, p. 366. || Marshall, Prin. of Econ., p. 306. 24 Irving Fisher—Mathematical investigations (6) ys av. 4% Be ban An dA = Total utility. dU wea eet (7) A. ae = Utility-value. A dU dU Heep CHA ax dA—A. 7A _ = Gain. Assumption: a = Function of A only. Corrollaries: From (1) and (2) and postulate, when B is ex- changed for A dU dU 7 P=7* From (8) and assumption, in the equation: ut. of dA/ut. of dB=n, the value of » is independent of the particular commodity and of its quantity M used in the definition. CHAPTER. IL. MECHANISM. Si. Scarcely a writer on economics omits to make some comparison between economics and mechanics. One speaks of a “rough cor- respondence” between the play of “economic forces” and mechan- ical equilibrium. Another compares uniformity of price to the level- seeking of water. Another (Jevons) compares his law of exchange to that of the lever. Another (Edgeworth) figures his economic “system” as that of connected lakes of various levels. Another compares society to a plastic mass such that a “pressure” in one region is dissipated in all ‘‘directions.” In fact the economist bor- rows much of his vocabulary from mechanics. Instances are: Equi- librium, stability, elasticity, expansion, inflation, contraction, flow, efflux, force, pressure, resistance, reaction, distribution (price), levels, movement, friction. The student of economics thinks in terms of mechanics far more than geometry, and a mechanical illustration corresponds more fully to his antecedent notions than a graphical one. Yet so faras I know, no one has undertaken a systematic representation in terms of me- chanical interaction of that beautiful and intricate equilibrium which manifests itself on the “exchanges” of a great city but of which the causes and effects lie far outside. in the theory of value and prices. 25 a2. In order to simplify our discussion the following preliminary sup- positions* are made : (1) A single isolated market large enough to prevent one man’s consciously influencing prices. (2) A given period, say a year. (3) During this period the rate of production and consumption are equal and such that stocks left over from last year and stocks held over for next may have an influence which is unvarying or which is not a function of quantities produced and consumed during the year. Their influence is accounted for in the form of the curves to be employed just as is the influence of climate, population, polit- ical conditions, ete. (4) Each individual in the market knows all prices, acts freely and independently and preserves the same characteristics during the period, so that the forms of his utility curves do not change. (5) All articles considered are infinitely divisible and each man free to stop producing and consuming at any point. (6) The marginal utility of consuming each commodity decreases as the amount consumed increases, and the marginal disutility of pro- ducing each commodity increases as the amount produced increases. (7) As stated in Chapter I, §4, the utility of each commodity is independent of the quantities of other commodities and likewise for disutility. § 3. In fig. 2 let the curve MN be drawn with axes OK and OA. This curve is such that the shaded area represents any amount of the given commodity consumed 2. by the given individual in the given period of time, and the ordinate (drawn downward) from O to R represents its marginal utility. The figure evidently interprets the fact that as the quantity of commodity increases its marginal utility de- creases and wice versa.t OA indicates what the marginal utility would be if only an infinitesimal quantity of the commodity were consumed. Furthermore let a glass cistern (fig. 2) be formed having the figure OAMN for its front 4 * These are (essentially) those of Auspitz und Lieben. + For the further properties of the curve MN and its relation to the curves of Jevons, Auspitz und Lieben and Fleeming Jenkin, see Appendix I, Division I. 26 Irving Fisher— Mathematical investigations face and a uniform thickness of unity so that the volume of liquid contained is always equal numerically to the area on the face. Hence the amount of liquid in the cistern may represent commodity and the distance of its surface from O, its marginal utility. Va) 4, ONE COMMODITY (A)—ONE CONSUMER (I). Let fig. 2 represent the utility cistern for I relative to A. Let us select as a unit of utility the marginal utility of money supposing this to be constant. Thus the cistern is (say) one inch in thickness ; the number of cubic inches of water represents the number of units of the commodity (yards, gallons, or pounds, etc.) consumed by the individual during a given period (say a year) and the ordinate OR (in inches) represents the number of dollars at which the individual prizes the last yard or gallon (say) of the commodity. Since the market is large enough to prevent any conscious influ- ence on the price by the individual I, he acts with reference to a fixed price (p dollars). He will therefore consume such an amount of A that its marginal utility in dollars equals that of the price p, that is, the cistern will be filled tilOR=yp. This is evident, for if less should be consumed OR would be greater than p, that is, a little more commodity would be valued more highly than the dollars exchanged for it and so would be purchased, and if more should be consumed, reverse considerations hold. If the price rises OR will increase and less be consumed but if it falls, more. If the price falls to zero as is the case for water and air the quantity consumed fills the whole cistern up to the horizontal axis. This volume is therefore the quantity of maximum satisfaction. If the price rises to OA the individual will cease consuming. This price is therefore the limiting maximum price at which he will buy. The liquid contents of the cistern may be regarded as made up of successive horizontal infinitesimal layers each representing an incre- ment of commodity. The height or distance of each layer from the origin represents the degree of utility of that layer. The last or top layer is on the margin of the whole and its vertical distance from the origin is the degree of utility of that marginal layer or inere- ment of the commodity or briefly its marginal utility. Thus the margin of consumption has in the cistern an actual physical analogue. in the theory of value and prices. 27 8 5. ONE COMMODITY—ONE PRODUCER. The definitions of utility in Chapter I apply also to negative util- ity or disutility. Corresponding to all that has been said relative to consumption are analagous remarks for production. a Thus we may construct a disutility curve and cistern (fig. 3) marginal disutility (O R) being measured upward from the origin. If utility be measured in money as in the last section, O A represents the minimum price at which the individual will produce the commodity, O R the current price and the shaded | area (or the cubic contents behind it) the output. ana TRS The marginal disutility of production is here represented as de- creasing as the amount of the product increases. This assumes a “law of diminishing returns.” It is true that this law is seldom if ever rigorously true when applied to small amounts ; that is, the cost or disutility of producing the first unit is not less but greater than that of producing the second. But the marginal disutility con- tinues to decrease only up to a certain point, after which it increases. This is usually true even of manufacturing. American bicycle fac- tories are now running behind their orders. If they attempted to run their factories at a higher velocity the cost of the additional product would become greater than its price. In general at the actual rate at which a concern produces, the law of increase of dis- utility applies. It would be possible by looping the curve MN near the bottom to make a cistern of such a form as to represent correctly both the law of decrease and increase, but as we are chiefly concerned with the point of equilibrium and as at equilibrium the law of increase usually apples such complicated curves are not here drawn. If a producer has such a productive capacity as to consciously in- fluence prices by a variation of his product, he may find his maxti- mum gain by restricting his output even at a point where the law of decreasing disutility applies ; for if he should extend his production, his price might decrease faster than his cost. These considerations together with the important one that in a productive enterprise the expenses are classified as ‘“‘fixed” and “running,” make many interesting cases of instability and indeter- minateness and lead to the discussion of monopolies, combinations, rate wars, etc., etc. These each require special analysis. In the 28 Irving Fisher—Mathematical investigations present memoir, however, attention is confined to those features of production which are strictly analogous to consumption. (See Ap- pendix IT, § 8.) § 6. ONE COMMODITY—MANY CONSUMERS. Let fig. 4 represent the utility cisterns for all individuals I, II, Ill, 1V,...N, in the market and let utility be measured in money St ~~ Yo TE | as before, the marginal utility of money being considered constant (say 1 util.). The water in the connecting tubes (represented by oblique shad- ing) does not stand for commodity. The water will seek its own level. This is exactly what happens in the economic world and may be stated in the theorem: A given amount of commodity to be consumed by a market during a given period will be so distributed among the individuals that the marginal utilities measured in money will be equal. Furthermore the margi- nal utility thus determined will be the price. This follows, for there can be but one price, and each individual will make his marginal utility equal to it, as shown in § 4. If the stopper,* 8, be pressed, more liquid (commodity) flows into the cisterns, there is an inevitable change in level and the price de- creases. When it cheapens to 2, II begins to indulge. It is for the first time “within his reach.” | It is to be noted that from the Standpoint of a single individual the existence of the general price level is an unalterable fact and the amount which he consumes is accommodated to it, just as the gen- eral water level in several hundred cisterns may be said to determine * A rubber compression ball would be used in practice. Throughout the de- scriptions, the mechanisms are those simplest to delineate and in many cases not those which might be actually employed. in the theory of value and prices. 29 the amount in any particular cistern. But, for the system as a whole, the price level is a consequence of the amount of commodity marketed. What appears as cause in relation to effect to an indi- vidual is effect in relation to cause for the whole market. The quantities of commodity and the marginal utilities mutually limit and adjust themselves, subject to three conditions, (1) that due to the forms of cisterns, (2) that due to the total amount of commod- ity marketed, (3) uniformity of price, or of marginal utility. § 7. ANALYTICAL. The algebraic interpretation of the preceding mechanism or of the economic phenomena themselves is as follows : Let A,, A,, A,,... A, be the (as yet unknown) quantities of the commodity consumed by I, II, II],...N. Let dU dU dU CON EO SG be their (unknown) marginal utilities. Then the three conditions mentioned in § 6 become : : (The unit of utility (util.) is that of the marginal dollar.) son OL ) 7x = F(A) au ie a Rips ee | # equations. (1) 4 a r | 2 2 unknowns. dU | ( dA. = EVA) J x 1 equation. (2) EARS Sa RO oe ae on new unknowns. (Unit of utility is that of marginal dollar.) (3) Cs eels | Sa ats 4 alae dU ) n—1 independent equations dA, oe 1 aR —~ A, J no new unknowns. Hence the number of equations is : m+1+(m—1)=—2n and of unknowns : 2n+0+0—2n. Therefore the numbers of equations and unknowns are equal and all quantities and utilities are determinate. 30 Irving Fisher-—Mathematical investigations § 8. AGGREGATE COMMODITY. Let C, fig. 4, be the average curve* of all the individual curves, I, II, I1],.... N, and let the new cistern have a thickness equal to the sum of the thicknesses of the individual cisterns. Then as much water will be in the aggregate cistern as in all the others.* The water in the aggregate cistern may be regarded as a repetition of the con- tents of the individual cisterns. It represents no new commodity. In cistern C it is almost too evident to require mention that an in- creased supply of this commodity (indicated by pressing the stopper) reduces the price while a diminished supply increases it. This fact is all that is usually exhibited in “demand curves” such as of Fleeming Jenkin.t § 9. Fig. 5 and completely analogous explanations apply to production cisterns. > 5 RI A [| s Y < |~ = ZL ee aa “4 j \ ot ee NS ee N = y s WS 5 oats ———— = SS g Sy 4 — 3 SSS Se Z es —— Y Z N== 4 — —————— y Y f > as A as SS Y Y 4 I A ee es SSS y Z RS Am ——————— Z g pee, y 7 j j y a 7 j = Z Z Z 4 — Z Z Yj Yj Yj Z g g as hau é o a se Z Y Y y Z LLLTYTL TTETEPLTILLT TILT TIV EDS R IED E SEE OL OSTE DLS TELA ISITIT ISIS jj, AE, rene: * Formed as follows: Select pts. of like price on the individual curves, that is, pts. of like ordinates (as y1, Yo, Ys, .. . Yn) and using the same ordinate for the new ordinate, take the average of their abscissas for the new abscissa and make the thickness of the new cistern equal to the sum of the thicknesses of all the in- dividual cisterns. Then if in such a cistern liquid be allowed to flow to the level of the individual cisterns the amount of liquid contained in it will equal all that contained in the individual cisterns. For evidently the free surface of the water in the large cistern equals in area the total free surfaces in the small, and as such equality of horizontal infinitesimal layers or laminz holds true at all successive levels, it holds true of the sums of the layers. + The Graphic Representation of Supply and Demand. Grant’s recess studies, p. 151. in the theory of value and prices. 31 § 10. The mechanism above described simply gives exactness to a com- mon imagery in economics, such as ‘‘margin,” “price levels,” “planes ” of demand (and supply) and: “a plentiful supply brings the commodity ‘ within reach’ of consumers.” The notion of a cistern is also natural. Says Adam Smith: “The demand for food is limited by the capacity of a man’s stomach.” Not only is there a “limit,” but the demand for food has varying intensities according to the degree in which the stomach is filled. The economic man is to be regarded as a number of cisterns or stomachs, each relative to a particular commodity. CHAPTER III. ONE CONSUMER (OR PRODUCER)-MANY COMMODITIES. alle The next problem is that of the distribution of an individual’s in- come over all the commodities in the market. The income-spender considers not only the price of a given article in determining how much of that article he will take but also the relative advantages of using the same money for other things. The manner in which this consideration affects the mechanism de- scribed in Chapter II is through the utility of money.* In the last chapter, while the price varied in relation to the quan- tity of commodity, each individual’s valuation or marginal utility of money was regarded as constant. This is nearly true when only one commodity is considered. In the present chapter, on the other hand, the individual valuation of money varies in relation to the quantity of money income, but the prices of all commodities are re- garded as constant. This is nearly true when only one individual is considered. * This sort of interaction, especially when extended to several consumers and several commodities (as in the next chapter), presented the most difficulties to the Auspitz und Lieben Analysis; on p. 63 in $16 they say: ‘‘ Welche Aende- rung eine Hinzelkurve erleidet wenn sich die Vermégensverhiiltnisse des be- treffenden Individuums iindert, liisst sich im allgemeinen nicht verfolgen. Wenn auch in der Regel die Ordinaten der kurven linger werden, wenn das Individuum -wolhabender wird, so wird dies doch keineswegs gleichmiissig der Fall sein, vol- lends nicht, wenn wir verschiedene Artikel betrachten.” 32 Irving Fisher—Mathematical investigations § 2. _ Let the individual I distribute his income over the commodities Fe NLer igh © DaRe a seas oa xm M. Let the thickness of each cistern in fig. 6 be proportional to the price of the commodity it contains. Thus if A bears a price of $2 per yard, B $1 per gallon and C $4 per pound, the thickness of cistern B is 2, of B 1, and of Ch. Let the unit of area on the front surface of each cistern represent a unit of commodity, yards for A, gallons for B, ete. Then the volume of liquid will evidently indicate the money value of the commodity, for it equals the front area times the thickness, that is, the quantity of commodity times its price. Moreover the sum of all the water will indicate the whole* income in dollars. The unit of volume thus represents not a yard, gallon, pound, etc., but a dollar’s worth in each case. For A it would be 4 yard, for B 1 gallon, for C 2 Ibs., ete. Accordingly let the curves which limit the cisterns be so con- structed that the ordinates shall represent marginal utility per dollar’s worth not per yard, gallon, ete. § 3. The liquid will seek its own level corresponding to the economic proposition : A consumer will so arrange his consumption that the marginal utility per dollar’s worth of each commodity shall be the same. : * Saving is here regarded as a form of spending, the commodity purchased being capital. The analysis implies that the marginal utility of saving a dollar equals the marginal utility of the dollar spent in other ways. This would be elaborated from another standpoint in a theory of distribution. Cf. Launhardt ; Volkswirthschaftslehre ; B6hm-Bawerk ; Kapital und Kapitalzins. in the theory of value and prices. 33 This follows because if the individual should vary his consumption from such a distribution, by expending an extra dollar on A he would divert that amount from another article or articles, say B. Then the level in the A cistern would be higher than in the B, which interpreted, is the dollar spent on A had less utility than if it had been devoted to B. If the stopper be pressed, i.e. if the individual had had a larger income, the valuation of the last dollar’s worth of each commodity decreases, or the marginal utility of money decreases. If it becomes at the maximum marginal utility of B he begins to spend on B. As it is in the figure he “ cannot afford it.” The amount spent on any particular commodity depends on the general water level, i.e. the valuation of a dollar, while reversely the valuation of money depends on the total amount to be spent on all commodities. Three conditions suffice to make the distribution determinate : (1) that due to the forms of the cisterns, (2) the condition that the total income equals a specified amount, (3) uniformity of marginal utility (per dollar’s worth) of each commodity. § 4. ANALYTICAL. Let A, B, C, . . . M be the (unknown) quantities of various com- dU OM Ba ane their (unknown) mar- ginal utilities. Let p,, p,, .. . Pm be their (known) prices. Then the above three conditions become : modities consumed by I, and (The unit of commodity is the dollar’s worth.) (au ’ | rae rT dU : —. =— H/(B m equations, (1) : d dB (B) ‘I | 2nr unknowns. dU é. | emt i | A A B Rie ie | 1 equation, ©) Pee Wea es {no new unknowns. TRANS. Conn. ACAD., VOL. TX. 3 JULY, 1892. 34 Irving Fisher—Mathematical investigations (Unit of commodity is dollar’s worth.) ; sh Un Us _ dU Lae independent equation. (3) (dA ~ dB~ °° * ~ aM Sno new unknowns. Number of equations = m+1+m—1= 2m. dg “ unknowns = 2m+0+0 = 2m. Hence the system is determinate. Sig. AGGREGATE INCOME. Let I, fig. 6, be the average curve* of all the separate commodity curves A, B, C,. . . M, and let the new cistern have a thickness equal to the sum of the thicknesses of the original cisterns. Then the water in the resultant cistern equals the sum of that in the com- ponents.* 7 The liquid in the new cistern represents the money collectively considered and the ordinate the utility of the last dollar. If this income increases, its marginal utility decreases and de- creases in a law whose relation to the laws of utility for the separate commodities is shown by the relation of the resultant cistern to the components. * In this case the average is not a simple arithmetical mean but a weighted average. Select points of like utility on the component curves, that is, points of equal ordinates. Average their abscissas, multiplying each by the ratio of the thickness of its cistern to that of the resultant cistern (viz: the sum of the thick- nesses of the original cisterns). Thus if the thicknesses are p, p,,.. . p,, and the abscissas «,, #,,. . . « , the resulting thickness and abscissa (P and X) are: P= Pp, Se eae ae LP, te, Pir... +e p ay pit peas If in a cistern thus formed liquid enters to the level of the component cisterns, the liquid in the resultant cistern equals the total in the component. For the sum of the free surfaces in the component cisterns is CP +e, pit... +e p and the free surface in the resultant is Paes : ed Te Dera. Rime), pp ee m Since these two expressions are equal and this equality holds of infinitesimal layers at the free surface and so successively at all levels it must hold of the sums of these layers. in the theory of value and prices. 35 § 6. An analogous discussion applies to fig. 7. In place of a given in- come we must suppose a given amount of expenses to be met by the &y Ns Meat [11 \ 8 ESSUSSSSSSS SS SSS SSS SSNS production of various commodities.* It is at this point that an im- portant distinction between production and consumption enters, viz: in civilized life men find it advantageous to consume many things but to produce few. The discussion of this difference pertains to Part IT. CHAPTER IV. M COMMODITIES—N CONSUMERS (OR PRODUCERS). Sl. We have seen the laws of distribution of commodities from two points of view, by first restricting our discussion to one commodity among many consumers and afterward to one consumer among many commodities. Our discussion is like a tourist’s view of a great city, who glances up each east and west street while riding along the same avenue and then takes a “cross town” course and sees each avenue from a single street. We are now to seek a bird’s-eye view. The variables and their variations which have been described are comparatively simple. But the possible variations in the more gen eral case are so complicated that they can scarcely be seen or de scribed without the aid of a mechanism. * Borrowing capital is to be here regarded as a form of producing. The dis- utility of borrowing the last dollar equals the disutility of producing the last dollar’s worth of goods. See foot note to § 2. 36 Irving Fisher—Mathematical investigations > 2. Wo First of all an analysis will serve to set the two preceding diseus- sions in a common point of view. In any purchase the last infinitesimal commodity bought has a utility equal to that of the money given, that is: ut. of dA=—ut. of dm ‘ dU dU or: 7A dA) == aes dm (see Ch. I, § 3.) dU 2 dU dm ea dA” dm dA - a _ a ts dA dm’? where p, is the money price. That is, the marginal utility of a commodity (per pound, yard, etc.) equals the marginal utility of money (per dollar) times the ratio of exchange of money for commodity : This equation is fundamental In our first discussion (one com- modity, various consumers) the marginal utility of money was sup- posed constant so that GAP oe or the marginal utility of a commodity is measured by it price. In the second discussion the other factor, the price, was supposed constant, and: dU 2 dU dA dm or the marginal utility is measured by the valuation of money. In the present chapter we are restricted to neither of these special suppositions. For the individual I, we may write dU _ dU dA,” dm, "De w _ aw dB dm Ps qu _ dU in the theory of value and prices. 37 whence, since the marginal utility of money to I is the same in each case, Since this is true for every individual and the prices to all individ- uals are the same, we may write: oO OU dU ORY UA men Pa = aA. : aB, sAepitieie : aM, Bs Cu au ; dU Tis Wee sean, dM Ee aU de dU 7. “GEA nba ema dM, These equations express in the most general way the theory of marginal utilities in relation to prices. This theory is rot, as some- times stated, “‘the marginal utilities to the same individual of all articles are equal,” much less is it “the marginal utilities of the same article to all consumers are equal,” but: Zhe marginal utilities of all articles consumed by a given individual are proportional to the marginal utilities of the same series of articles for each other con- sumer, and this uniform continuous ratio is the scale of prices of those articles. The idea of equality is inadequate and must be replaced by the idea of proportionality. The problem which confronts the individ- ual must be figured as to so adjust his consumption of all commodi- ties that the utilities of the last pound, yard, gallon, etc., shall bear the ratio which he finds their prices do, while the market as a whole must cause such prices to emerge as will enable each individual to solve this problem and at the same time just take off the supply. § 4. This notion of a ratio is introduced into the following more com- plicated mechanism (fig. 8). Fig. 9 (an elevation of fig. 8) shows the various cisterns of various commodities for the individual I. The ordinates represent marginal utility per wnit of commodity. It corresponds to fig. 6, except that in the latter the utility is per dollar’s worth of commodity. The tops of the cisterns are no longer at the same level. The cisterns are now to float like boats in a 38 Irving Fisher— Mathematical investigations | iF ae il °o aed a Sreteek fi in the theory of value and prices. 39 ~ tank* and free to move only vertically (being so constrained by a telescope arravgement beneath and not shown in the diagram). A glance at fig. 8 or fig. 10 (a plan of fig. 8) will show that any right and left row of cisterns is rela- tive to a single individual 10. and corresponds to fig. 6 and that any front and back row is relative to a single commodity and corresponds to fig. 4. The water in these cis- terns must be subjected to two sets of conditions, first: the sum of all the contents of IA, ITA, IITA, etc., shall be a given amount (viz: the whole of the commod- ity A consumed during the given period) with a like given sum for the B row, C row, etc., secondly : the sum of IA, IB, IC, ete., each multiplied by a coefli- cient (the price of A, of B, of O, etc.), shall be given (viz: the whole income of I during the period) with a like given sum for the II row, III row, ete. * The level of water in each cistern is intended to be that of the level in the tank. The only constant cause which will make the levels different is the differ- ence between the weight of the whole cistern and the weight of the water dis- placed by its walls (partly wood) which difference is slight, may be plus or minus, and is equal to the weight of the excess or deficit of water in the cistern above or below the outside level. 40 Irving Fisher—Mathematical investigations To realize these two sets of conditions each cistern is divided into two by a vertical partition of wood. The front compartments are all of unit thickness one inch (say). All front compartments belonging to the same front-and-back row are mutually connected by tubes (in the tank but not in connection with the water of the tank) thus ful- filling the first set of conditions. The thickness of the back compartments is adjustable but is (as will soon appear) constrained to be always equal to the price, thus if the price of A is $1, of B $3 and C $1.20, the thickness of all cisterns in the A row will be 1, in the Brow 3 and in the C row 1.2 (inches). Since the thickness of the front compartment is unity, the con- tents of each back compartment equals the contents of the front multiphed by the number of inches of thickness of the back cistern, that is the back compartment contains a volume of water equal to the amount of the commodity multiplied by its price. It contains therefore the money value of the commodity. The double cistern represents the double light in which each commodity is commonly regarded—so many pounds, yards, etc. and so many dollar’s worth. All back compartments of the same right and left rows are mutually connected by tubes—that is the sum of their contents is given—thus fulfilling the second set of conditions. | The back compartments can change their thicknesses, as the walls at the right, left and bottom are of flexible leather; the back plane is kept parallel to the wood partition by two double “ parallel rules” not diagramed. There remains to be described the system of levers. The purpose of these levers is to keep the continuous ratio of marginal utilities, the same for all individuals and equal to the ratio of prices. First there is a system of oblique* levers (F12, etc., fig. 9) con- nected by sliding pivots with the tops of the cisterns and having their lower extremities hinged to wooden floats F, the hinges being on the level of the water of the tank. These floats are free only to shift laterally. It is evident from the similar triangles FR1 and FR2 in fig. 9 that the ordinates of the two cisterns IA and IB are proportional to the distances of the A and B rods R and K from the hinge in the left float F. Likewise in the row behind, the ordi- nates are proportional to the same distances. Hence the four ordinates are proportional to each other and in general all the * A convenient angle for each lever can be assured by a careful selection of commodity units. Thus if the marginal utility per pound gives inconvenient ordinates in the A row, reconstruct the cisterns in that row so that the ordinates are lengthened to represent marginal utility per ton or shortened for the ounce, in the theory of value and prices. 4] ordinates of the front row are proportional to those of the row next behind, also of the second row behind and so on. Remembering that each ordinate is a marginal utility we have: ow dU Ema inlige eased) e: RM a A ea Be et which is the required condition that marginal utilities must be pro- portional ($3). Secondly there are the horizontal levers (F34, etc., fig. 10) lying on the surface of the water in the tank. These relate to prices. The sliding pivots 3, 4, etc. are connected with rods RRR, which in turn are connected by vertical pins with the rear walls of the cisterns. A motion of one of these rods causes all back compart- ments in that row to expand or shrink in unison. The pivots 3, 4, ete. are so situated on these rods that if the levers F34, etc. should assume a right-and-left position along the dotted line FI’, the back compartment of every cistern would be completely closed. Hence R3 equals the thickness of each back compartment in the A row, R4 the corresponding thickness in the B row and so on. By the similar triangles FR3 and F34 in fig. 10, it is clear that the lines R3 and R4, and consequently the rear thickness in the A and B rows are proportional to the distances of the A and B rods R and RF from the float F. But we have just seen that the ordinates of IA and IB are proportional to these same distances. Hence the thicknesses of the back compartments of the cisterns are propor- tional to the ordinates of those cisterns, that is to marginal utilities. Hence we are free to call the thickness of each back compartment, the money* price of the commodity to which that cistern relates. * Money is here tied solely as a measure of value. It is not one of the com- modities in the market. The high or low price of commodities in terms of this money is dependent entirely on the amount of it at which we agree to rate the yearly consumption of the market, that is the amount of liquid originally in the back cisterns. We are so accustomed to regard money as the medium of exchange and therefore as a commodity that we may not observe that it is per- fectly possible to have a measure of value which is not a commodity at all. Thus we might agree to call the consumption of the United States for a year $10,000,- 000,000, and this agreement would immediately fix a measure of value, though the new dollar need have no equality to the gold or silver dollar. It would be easy to translate between such an arbitrary standard and any commodity standard, Thus if statistics showed that the consumption measured in gold dollars was $12,000,000,000, the agreed standard is at 120 compared with gold and by means of this factor we can reduce the prices of all commodities. In the mechanism the aggregate amount of liquid in the back cisterns corresponds to the $10,000, 000,000. If we take it so and if the amount of liquid in the I row is given at $1,000, this means that (in whatever standard) the consumption of I is one-ten” millionth in value the aggregate consumption, 42 Irving Fisher— Mathematical investigations It is to be observed that the cisterns are free to move only verti- cally, the rods and rear cistern walls only forward and backward, the wooden floats can shift only sidewise right and left while the levers assume such positions as the mechanism compels. 8 5. Let given quantities of water be introduced into each front-and- back-row of front cisterns and into each right-and-left row of back cisterns. The system will attain a stable equilibrium and the level of water in each cistern will be that of the tank. The front cisterns of a front-and-back row must have’a uniform level on account of their mutual connection. The back cisterns of a right-and-left row must preserve a uniform level for a similar rea- son. The movable rear walls allow the pressure of the outside water in the tank to keep the back cisterns at the same level as the front. Without taking account of the levers the cisterns would thus all have the same level as the tank. But it would be possible to arrange their vertical positions and their rear thicknesses in many arbitrary ways. The levers simply specify or determine this arrange- ment. BiG. It may be needful to restate carefully the magnitudes, their units and the conditions which determine them. The magnitudes are: 1. The quantities of each commodity consumed by each individual during the year. These are represented by the quantities of water in each front compartment. 2. The given total quantities of each commodity consumed by the whole market—represented by the fixed amount of water in each front and back row of front comparments and registered on scales* A, L, CU, at the rear of the tank. Hach commodity-water may have a distinguishing color. 3. The money paid for each commodity by each individual—rep- resented by the water in each back compartment. 4. The total. money income of each individwal—represented by the fixed amount of water in each right-and-left row of back com- partments, and registered on scalest I, II, III, at the right of the tank. * The stoppers A B, C regulate this amount of water. The stoppers are each directly connected with the pointers on the scales A, B, C, and so arranged that when the stopper is withdrawn so that the scale reads zero, the water entirely disappears from the cisterns. + The stoppers I, II, III are also directly connected with pointers on the scales L, a, a: in the theory of value and prices. 43 5. The marginal utility of each commodity to each individual —represented by the ordinate of each cistern, 1. e. by the distance from its top to the water level. 6. The money price of each commodity — represented (in any cistern in the same front-and-back-row) by the thickness of the back compartment, and registered on scales* p,, pi, p. at the rear. (The relation of price to marginal utility will recur.) 7. The prices of commodities in terms of each other—represented by the ratios of their ordinates. 8. The marginal utility of money to each individual — repre- sented (in any cistern in the same right-and-left-row) by the ratiot of the ordinate of that cistern to the ny thickness of its back compartment and registered on scalest UI, U II, U III at the right. The units of these magnitudes are : 1. The unit of commodity is a ton, yard, gallon, ete., and is repre- sented by (say) a cubie inch of water. 2. The unit of money is (say) a dollar and is represented by (say) a cubic inch of water. 3. The unit of price is one dollar per ton, yard, gallon, etc., and is represented by one inch. 4. The unit of marginal utility for each individual is the marginal utility of (say) 100 tons of A. It may be called a util and by a proper * The rods RRR are each connected by a cord and pulley with the pointers of the scales p, p,, D,- + This ratio is evidently the marginal utility of money (‘‘ valuation of money ’’) 4 dU dU ae hed eee) because as seen in chapter IV, § 2, ey gle Ee au dU i ROLE oe ordinate of cistern whence : se ein pe Se : ; dm p, thickness of its back compartment { Fig. 11 (which views the outside of the right wall of the tank) shows the device by which this is accomplished. Evidently from the labels dU a dA dU —— or « = - 1 p adm a The pointer obviously varies with x. It is so arranged as to register zero when w = 0, 44 Irving Fisher—Mathematical investigations adjustment of the breadth of each cistern may be represented by one inch. ‘That is, if 100 cu. in. of water are put im each A cistern the ordinate must be one inch. This apphes as well to the utility of money, so that the scale U at the left indicates the number of wtéls at which the individual values the last dollar of his income. It should, however, be noted that the variation of utils is only valuable in the same register, that is, for the same individual. There is no important meaning attached to the ratio of the scale readings U for two individuals. If that of lis 1 and of II 2 it means simply that II values his last dollar twice as much as his 100th ton of A, while I values his last dollar just as much as his 100th ton of A. It is in- teresting to observe that analogously the price registers are not to be compared, for while one indicates price per ton the other indicates price per yard, etc. Thus the mechanism is independent of any common measure of utility for different individuals and any common measure of prices for different commodities. § 7. It will be observed that the numbers on the various registers are so connected that the product of the register of A by that of its price added to the like products for B, C, ete., will equal the sum of all the income registers. Moreover if each cistern is provided with a graduation to show marginal utility, this number will be found to be the product of the number for price in its front-and-back row, by that for valuation of money in its right-and-left row. . § 8. The mechanism just described is the physical analogue of the ideal economic market. The elements which contribute to the determination of prices are represented each with its appropriate réle and open to the scrutiny of the eye. Weare thus enabled not only to obtain a clear and analytical picture of the interdependence of the many elements in the causation of prices, but also to employ the mechanism as an instrument of investigation and by it, study some complicated variations which could scarcely be successfully followed without its aid. Its chief uses may be briefly classified as follows : 1. Arrange the stoppers I, II, III, etc., so that the money incomes of J, I, [1], are all equal. The differences of distribution of the commodities will depend on individual characteristics, that is, on in the theory of value and prices. 45 the character of the cisterns. If all the A cisterns are alike and also all B cisterns, all C cisterns, etc., then each commodity will be distributed in equal parts among the individuals. . 2. Press stopper I. This amounts to increasing the income of I. It does not increase the amount of commodities in the market but gives a larger share to I. The total money value of the same aggre- gate commodities in the whole market has increased by the amount of liquid added by depressing the stopper. The added water in the back cisterns of the I row will make the back compartments in this row fuller than the front. The back level will be temporarily above the water level of the tank and (as the cisterns will sink) the front level will be temporarily below. The effect of the former is to bulge out the movable rear wall in the I row, to extend the rods and to cause the same expansion in the back compartments of the II, II, etc. rows. This makes the back liquids in these rows lower and the front liquids higher than the tank level. Hence the front cisterns of the II, III, etc. rows pour part of their contents into the I row whose level as we have seen is below that of the tank. In economic language to give a greater money value to one indi- vidual causes for him smaller marginal utilities (cisterns sink), a lower marginal utility of money, and increased consumption of com- modities. For other individuals it increases marginal utilities (cis- terns rise), decreases consumption, increases prices (back cisterns expand), and may increase or decrease their marginal utility of money-income according as marginal utilities (ordinates) increase faster than prices (back thicknesses) or the reverse. So much for the effect on different individuals. Now as to the effect on the various commodities. Prices in general have risen but not necessarily of all articles. Suppose article C is consumed little or not at all (cistern narrow) by the enriched individual I but is ex- tensively used by those whose valuation of money has increased. Then since the valuation of money to II is-equal to the quotient of the ordinate of ILC divided by the thickness of the back cistern of IIC, and since this ordinate has not lengthened by any appreciable loss of commodity C from II to I, the thickness must have, lessened, that is, the price has been reduced. Not only may there be such exceptional commodities but there may be exceptional individuals. Thus a man may be the principal consumer of just those commodities and those only whose price has fallen. His consumption will increase, his marginal utility of money 46 Irving Fisher— Mathematical investigations decrease. He is benefited not injured by the increase of income of his neighbor I. 3. Press stopper I and raise III. I, II, II now represent a wealthy middle class-and poor man respectively. We observe first that this change causes the poor man to relinquish entirely some things (luxuries) as C while decreasing his necessaries slightly; second that the rich man increases his luxuries enormously and his necessaries slightly, and thirdly that slight modifications will appear in the prices and hence in the middle-class consumption. The nature of the effect on prices depends on the character of the cisterns of I and III, and on the magnitude of the changes in their incomes. In order that prices may not change, one condition (neces- sary but not sufficient) is that the amount of money income added to I must equal that taken from III, for if the amounts of com- modities are not to change, nor their prices, their total values cannot. If all prices rise it proves a net increase of money income in the whole system. If the increase of income of I equals the decrease of that of II, so that the total money value in the market is unchanged, and if furthermore all the cisterns of J and III have straight walls on the right and have their breadths* proportional, there will be no change in price. For if the cistern breadths of the III row are each, (say) half the corresponding ones in the I row, equilibrium will clearly be satisfied by shortening each ordinate of the I row by a uniform per- centage (say 102), and lengthening those of the III row by just twice the amount of shortening in the corresponding I ordinates. This will evidently cause the lengthening of the III ordinates to be uniform (say 15%). The ratio of marginal utilities has thus been preserved and hence the prices. Obviously the contents added to IA equals that taken from IIIA and equilibrium is reéstablished by a simple transfer from III to I. In this case there is no effect on II or any individual save J and IIL. * The breadth of a cistern is evidently the differential of its area divided by the differential of the ordinate that is the fluxion of commodity in reference to its marginal utility. It is a magnitude important in the discussion of distribution of commodities. Involving as it does the second differential of utility it has no perfectly distinct recognition in popular language. A narrow cistern means that a slight reduction of its contents causes its ordinate to increase much, i. e. causes it to be greatly desired. The individual is very sensitive to a change in that commodity. He misses a little less of it and appreciates a little more. Reversely a broad cistern signifies that it is hard to satisfy the man by increase and hard to annoy him by decrease. These two sorts of cisterns may be called ‘‘ sensitive” and ‘‘ callous” (see Appendix I). in the theory of value and prices. 47 More generally in a redistribution of incomes without altering their aggregate, in order that no prices may change (1) no condition is necessary for those whose incomes have not changed; (2) for those whose incomes have changed the geometrical character of the cisterns must be such that a proportional shortening of the ordinates for each and every richer man will absorb in the aggregate, the same additional commodity of each sort as is lost in the aggregate by the poorer through a proportional lengthening in the ordinates of each of them. If the enriched man or men absorb more of a given commodity than this requirement its price will rise, if less it will fall. If the increase of income of I equals the decrease of III effects on prices must be compensatory. If one rises some other or others must fall. If IA is much broader than IIIA but IB is much nar- rower than IIIB, the price of A may rise and of B fall unless counteractions come from other commodities. For if we were to suppose prices unaltered, the cistern TA would absorb from IIIA so much and IB from IIIB so little that the ordinate of IIIA would be too long and of IIIB too short for equilibrium. In order to partially permit this lengthening and shortening there must be a corresponding lengthening and shortening in the whole A and B rows respectively and prices must be proportioned to these ordinates. In this case it is to be noted furthermore that a change in prices causes a change in the distribution of the income of II and all other individuals. The marginal utility of money for I decreases, for III increases, and for II may slightly rise or fall, owing to the change of prices. With the breadths of the cisterns properly adapted to the changes in prices there may be no change™* in the valuation of money for I. * If the prices of only two commodities A and B change and AII and BIT are straight walled, and if their breadths are inversely proportional to the difference of the squares of the old and the new prices, there will be no change in the valu- ation of money. For, let p and p’ be the old and new prices, let x and x, be the breadths (for II) of the A and B cisterns and let y,, y, and y,’, y,’ be their old and new ordinates. Since the marginal utility of money is not to change nor the prices of C, D, etc., their ordinates cannot and therefore their quanti- ties (for II) cannot change. Hence the added expenditure (by Il) on A must equal that taken from B, i.e. : Ys Py — CY Pa = CYP, — DY, DP, - But since the valuation of money is to be kept constant, Be Wy Y, Y," ted ps fi P, ‘el P, i Py, * 48 Irving Fisher— Mathematical investigations If the price of A rises slightly and of B falls relatively more while the breadth of IIA is less than of IIB, the valuation of money to II will fall. For if not then the ordinates of IIA and IIB must change pari passu with the thickness of the back cisterns. The thickness and ordinate for ITA are, say each increased 10% and for IIB reduced 50%. There is clearly not room in IIA for all the money poured out of IIB. This surplus will spread over all A, B, C, ete., and reduce the ordinates and reduce the money valuation of II. These artificially exact cases obviously stand for more general and approximate economic theorems. ‘There are no such delicate adjust- ments in the actual world as here presented, but through ideal cases we study real tendencies. 4. Depress stopper A. The chief effect will be to lower the price of A. If it is a necessary* a relatively large share of the increase will go to the poor. It will probably occur that while the total money expenditure by the poor for this commodity will increase, that for the rich will decrease.t The marginal utility of money in general decreases especially for the poor man. Most other commodities will rise in price if A decreases in price faster than it increases in quantity. For there will be a saving in the expenditure for A which must be made up elsewhere. But an exceptional commodity may fall in price. Thus if B happens to be extensively used (cisterns deep and broad) only by those who use A slightly, these persons will not save materially in the expenditure p 72 — oS he n2 Hence x kp? —x kp? = «kp, —2x,kp,?. of Me gh A. gh 9 Hence ae 2 ie, co he ee which is the condition required. More generally in order that the valuation of money to an individual shall not change, the cisterns of II must be so formed that when the money saved on some articles equals the extra spent on the others the ordinates may all change proportionally with the prices. If the ordinates increase more than this requirement or decrease less, the valuation of money will rise. In the reverse cases it will fall. * A necessary may be defined as a commodity whose cistern is relatively deep and narrow. I. e. a very small quantity has a very great utility and a slight addition gives satisfaction very rapidly. A luxury has the reverse properties. + When commodity begins to flow into a cistern its money value (the contents of the back cistern) increases in about the same rate as the commodity—it matters little how much the price (thickness) falls. Contrariwise when the cistern is nearly full a fall of price decreases the money value at about the same rate—the increase of commodity matters little. The dividing point is where the commod- ity increases at the same rate as the price decreases. These characters are more plainly shown in the diagrams of Auspitz und Lieben, p. 48, ete. in the theory of value and prices. 49 for A, but will be compelled to pour much money into C, D, etc. of which the prices have risen. This will cause a rise in their valuation of money and as the quantity of B does not decrease its price must. Moreover there will be slight changes in all other quantities IB, “TIC, etc. If (say) IIC decreases, it is due to one or both of two causes, a rise in price of C or a rise in valuation of money of II. In general the valuation of money will decrease. The decrease will be relatively great for the poor as compared with the rich, but (as just seen) will not necessarily decrease for all persons. If A is a “luxury ” the fall in its price will be small relatively to the feregoing case. Most of the increase of A will go to the rich. The total amount of money spent on it will probably increase which will in general decrease the price of other articles. Exceptions can be found analogous to that in the former case. The valuation of money will in general decrease, most perhaps for the middle class and more for the rich than the poor, but not necessarily for all. 5. The cases just discussed assume that the additional production of A is such that the incomes of I, I, III, ete. are not disturbed. To represent the case in which I produces all of A, after depressing A a given amount, slowly depress I until the difference of income as registered on the I scale shall equal the final reading on the A scale multiplied by the price of A minus the former A by its former price. The chief change to any one article will be in the price of A which will decrease. The chief change to any one person will be to I whose income is increased (especially if the commodity is a luxury), whose expenditure for most other articles will increase though not necessarily for all, and whose valuation of money will decrease, owing both to an increase of income and to a decrease in price of other articles consequent on the withdrawal of money from them to be spent on A. Only exceptional articles will increase in price if their chief consumers sufficiently decrease their expenditure for A. But it may be that the increase of A will so greatly depress the price that the value of the total will decrease. This is generally true of necessaries. The producer I will lose income, that is stopper I must be raised instead of depressed. His valuation of money will increase doubly, owing to the contraction of his income and the rise in price of other articles. The money* return to such a benefactor * Monopoly price is not treated here. It is interesting to note that the Dutch East India Co. used to destroy a part of their spices to prevent a great fall of price. The same thing has been done by the Japanese in silk-worm eggs. TRANS. Conn. ACAD., VOL. IX. 4 JULY, 1892. 50 Irving Fisher— Mathematical investigations is therefore not even roughly proportioned to his benefaction. If the exact shares among I, IJ, III, etc. in the old and new produe- tion of A are known, the proper combination of stopper-positions may be made and the reactions, now exceedingly complicated, may be watched. 6. Depress each stopper A, B, C, etc, There will be a general fall in prices. But it will not be true that if the quantity of each com- modity is doubled its price will be halved, and the price of one commodity in terms of another unaltered as Mill* apparently thought, for the ratios of exchange are not the ratios of the con- tents of the cisterns but of their ordinates. Nor will the ratios of distribution of commodities remain the same. If however all cis- terns in each front and back row are geometrically similar and their filled portions also similar (a most unreal condition), the ratios of distribution of commodities will be unaffected+ and if furthermore all cisterns are similar, the ratios of prices will be unaltered.{ In the actual world aside from differences in the shapes of cisterns there are more important differences in the way in which they are filled. Those for necessaries are relatively full as compared with those for luxuries and those for the rich as compared with those for the poor. Hence the effect of a proportionate increase of produc- tion in all commodities will depress the price of necessaries much more than of luxuries. The effects on the valuation or marginal utility of money will be more complicated. If we suppose the depression of the stoppers to begin when they are far extended, the effects may be roughly described as follows. At first the valuation of money inereases since the prices decrease faster§ than the marginal utilities, reaches a maximum (which is different for each individual and depends on the initial distribution), and decreases when the decrease of ordin- ates is faster than that of the thickness of the back cisterns. These * Pol. Econ., Bk. III, Ch. XIV, § 2. + For proportional increase of the contents of the cisterns in the same front and back row will reduce their ordinates proportionally and shrink the back com- partments alike, thus restoring equilibrium. + For in addition to the above consideration the reduction of ordinates in all rows will be alike. § Because when a cistern is relatively empty, a rise in the surface of its con- tents diminishes the long ordinate by only a slight percentage but very materially contracts the back compartment. hyo in the theory of value and prices. 51 - changes in the valuation of money are of course subject to the con- dition that each income measured in money remains the same. 7. Depress all income stoppers proportionally, i. e. increase all incomes in the same ratio. Then will all prices increase and the valuation of money decrease exactly in this ratio. There will be no change in the distribution of commodities. There is merely a depreciated standard of money. Formerly the whole marketed commodity was valued at a given number of dollars, now this number is increased. We have seen under number 1, that an increase in the money income of a single individual without an increase in commodities is a benefit to him, but such an increase when universal is bene- ficial to no one. 8. Remove cistern IA and replace it with a shallower one, i. e. suppose a change in the taste of I for A, making the article less attractive. It is as if we raise the bottom of the original cistern IA. More of A will flow to other consumers and more of ’s money will flow to the purchase of other commodities. A will fall in price, most other articles will rise. I’s valuation of money will fall. For those who consume A extensively the valuation of money will fall. For others it may rise. If all of the [ cisterns grow shallower there will be a fall in the valuation of money for I, but either prices will not change or their changes must be compensatory, for the quantities of commodities have not been altered nor their aggregate value. If all of the I row cisterns change so as to admit of a uniform percentage shortening of ordinates without any commodity flowing out of any cistern, no commodity will flow out, no prices will change and there will be no change whatsoever in the distribution of commodities nor in the valuation of money to other people. If one cistern shortens more than this requirement, the effects will be analogous to those just described for a single cistern. If all the cisterns of the A row are made shallower the price of A will decrease.* That of other articles will in general increase. In order that the distribution of commodities may not change, the A cisterns must be so changed as to admit of a shortening of ordin- * Otherwise while the A ordinates shorten and their ratio to other ordinates lessens, the back cisterns would have a relatively too great thickness compared with the other thicknesses. Irving Fisher— Mathematical investigations or bo ates in a uniform percentage without loss or gain of commodity. In this case the price of A will decrease while that of all other articles will increase exactly alike.* The valuation of money will be re- duced since the ordinate of a B cistern (say) has not changed while its back thickness has increased. The changes just considered may be brought about if A suddenly goes out of fashion. Perfectly analogous changes occur if a cistern or cisterns become narrower. The individual is then more keenly “sensitive” to changes of quantities. This change may occur through a discovery by which a little of the commodity is made to “go farther” than before. Reverse changes occur if cisterns are broadened or deepened. § 9. It is impossible to combine all the A cisterns into a single demand cistern for A as was done in Ch. II or to combine all the I cisterns into an income cistern as in Ch. III, for we can no longer overlook the influence of other commodities and other individuals. The analysis therefore which treats of but one commodity at a time and constructs a demand curve for it is a superficial one for it does not reach all the independent variables. § 10. ANALYTICAL. Suppose there are 7 individuals and m commodities in our given — isolated market during the given period and suppose the amounts of the commodities A, B, C, etc., are given K,, K,, K., ete., and the given incomes of I, II, III, etc. are K,, K,, K,, etc. Then the con- dition that the commodity-sums are given is: 3 eH 2M 2 Ge GaP eae See ee pAs=Ko LEON GS ii gt Ae oe noes eee +B,=K, Cae Oe ©) OTS Stare Sener +C,=K, m equations. Wee ap eceeber ee dae AE Le tS =) ae r mn unknowns. M,+M,+M,+....... +M,=K,, J * For their mutual ratios cannot change since the ordinates to which they are proportional do not. in the theory of value and prices. The condition that the incomes are given is: BU Pers 0; + pee ° pt Bb, ‘ Pot | Seca A, ‘ Pat B,, j Jha evens le J Se) Cee Ys: ete, The utility functions (the cistern-forms) are: dU era 1: dU , Sa eae Sa (ML dA, B(A,); dB, BOB 5 ? dM, H(M,) | x au eee tee au | mn equations. da, 1 As); 7B, B(B.)s 5) 7. Pree ‘ Mn new i unknowns dU ek |. dU —F(B,); _ aU —F(M,) | Sia eo ) \ ae dB, n} 9 ? a Mak n J The principle of proportion is ov dU dU. CM in ) dA, dB,’ dO, dM, | n (m—1) dU dU 0g ia : independent L, = a ant?” \ equations. .- 22 2 oe earee aia = | no new ae aU © cae) er ean | unknowns. dA, F dB, 5. 14 WEL KOE ENS ba dM, =Pa: Por Per +++: ‘Pin J Total number of equations: m+n+mn+n (m—1) = 2mn+m “4 oS unknowns mn + m+mn+0 = 2mn+m 53 nm equations. m new unknowns (prices). Therefore all magnitudes are determinate and the number of these magnitudes as well as the number of the equations is twice the num- ber of commodities times the number of individuals plus the num- ber of commodities. The valuation of money for each individual can be found from the equations: : dU dU dA, ae = me (Ch. IV, § 2.) dU dm, 54 Irving Fisher— Mathematical investigations $1 For production the treatment is precisely parallel to the foregoing (figs. 12, 13). Nee et, RD | ae a] = , | CHAPTER V. PRODUCTION AND CONSUMPTION COMBINED. $1. Hitherto it has been assumed that the quantities of commodities and incomes (or expenditures) have been given. But these quanti- ties have themselves been determined by economic causes. Jevons* arranges the sequence as follows: “ Cost of production determines supply, Supply determines final degree of utility, Final degree of utility determines value.” * Pol. Econ., Ch. IV, p. 166. f Ries Ce Ge hy ee ee dora eed in the theory of value and prices. 55 This represents the chronological order but only part of the causa- tion. Cost of production is not the sole determinator of supply. Production is prophetic. When prices are steady the certain future price is an unquestionable regulator of supply. Auspitz und Lieben appear to me to deserve much credit for showing how all these facts harmonize. Price, production, and consumption are determined by the equality of marginal utility and marginal cost of production.* Their clear exposition of this theory not only exhibits the “ funda- mental symmetry of supply and demand,” but reconciles in a captivating manner the old one-sided and seemingly contradictory theories of value making them fall in place as opposite facets of the same gem. It is discouraging to find the old fight still going on. Dietzelt attempts to play the peacemaker by the makeshift of dividing the field between the contesting theories. The apparent conflict grows out of an inadequate conception of mathematical determinateness. As the quantity of any commodity increases its marginal utility to consumers decreases while its mar- ginal disutility to producers increases. If the latter exceeds the former the price which consumers will give is less than what pro- ducers will accept. Production is contracted and the utility and disutility approach each other. If the quantity is too small the machinery acts in the reverse way. The equilibrium though always miscalculated is constantly sought and its more delicate and rapid deflections are corrected by a special functionary, the speculator. Se, It is assumed that the rate of production during the given period is exactly equal to the rate of consumption. This is asserting an ideal equilibrium. The expenses of transportation and retailing are included in “ pro- duction.” | The principle of proportion previously explained is now extended. The marginal utilities of consuming and the marginal disutilities of producing are in the same continuous ratio for each individual—the ratio of prices. § 3. As the simplest case of combining production and consumption, suppose an individual to consume himself just that quantity of a given commodity which he produces. * Auspitz und Lieben, § 5, p. 17. + Die Klassische Werttheorie und die Theorie vom Grenznutzen. Conrad’s Jahr- buch, 20. 56 Irving Fisher—Mathematical investigations 14. quantities in the cisterns for production and consumption, respect- ively, are so connected as to move together, keeping the quantities in the two cisterns equal. Furthermore the water pressure on them from the tank keeps the level of all three liquids the same—that in the tank and those in the two cisterns. The lever keeps the mar- ginal utility equal to the marginal disutility, for its pivot is a fixed one and is placed midway between the axes of ordinates. The resulting determinate equilibrium is subject to three sets of condi- tions : (1) The quantity consumed equals that produced—a condition pro- vided for by the duplicate pistons. (2) There must be a relation between the quantity produced and its marginal disutility and between the quantity consumed and its marginal utility—the character of the cisterns. (3) Marginal utility and disutility are equal—the lever. § 4. ANALYTICAL. If A_ and A, be the quantities of A produced and consumed, respectively, the conditions of equilibrium are : ) 1 equation. 1D. 8 ; ) 2 unknowns. dU ) — = F(A dA. (4,) | 2 equations. dU 2 new unknowns stey! = F ; We dA, (A,) | dU _ ___ dU } 1 equation. dA, — dA, J no new unknown. No. equations: 1+2+1=4. No. unknowns: 2+2+0—=4. * In practice a more intricate frictionless bellows would be used. oe ™ eee in the theory of value and prices. 57 $5. In the more general case there are m individuals and m com- modities. 15. Fig. 15 simply connects fig. 9 and fig. 12 by a series of new levers like that in fig. 14, so that for each individual the ordinates of the production cistern and its consumption cistern shall be equal. There are also analogous horizontal levers (fig. 16) to keep the price for 16. consumers equal to that for producers. The stoppers are all duplicate asin fig. 14 for each commodity. Moreover there are analogous duplicate pistons to keep each individual’s incomes and expenditures equal. The industrial machinery is now seen to be self-regulative. There is no arbitrary assignment of incomes or of commodities. The only 58 Irving Fisher— Mathematical investigations changes possible are effected by change in the forms of the cisterns or by changing their nwmber, that is by changing the “ cost” of pro- duction or the utility of consumption, or by changing the population (which changes, we may remark, go together). By making the cisterns removabie and replaceable the effects of varied conditions can be studied as in the preceding chapter. - However, this equilibrium is indeterminate in one respect. Unlike the former it does not fix the unit of value. income-cistern-contents is arbitrary. expenditure-pistons are simultaneously depressed all incomes proportionately, the equilibrium will will the distribution of commodities be affected. will simply dilate in uniform*® ratio. changed. The sum of the If all duplicate income-and- so as to increase not be upset nor The rear cisterns The money standard has alone This may be remedied by making the thicknesses of all back eis- terns for the commodity A equal to unity. A thus becomes the stand- ard of value, and henceforth all prices are in terms of this com- modity. This is what is done in the actual world. ANALYTICAL. § 6. AL +A oF. Seay See PSN Pts Naas t= nee te Bo be Se 4: Ma a gee Kit Ye ty iia SM < pitee Br ahe e ds etiesereat es ae one Asi pet wc. BM, 4 Drea Pare ee ee Pn dU pT Ne) FINE zsokl 1 2 Oa oe yee a aM, == BMS) | dU | aH Lie SE | Fi re sh ON tee oe rh Be F(M,.,) i | av Signe Rs ast air x : | | Aes. 0 B(A, a P > dad M.., ‘ark Hi Mies) ‘ ' dU dU | | peas Bias) eine F(M,,,,) ee ») m equations. 2mn unknowns. (n—1) inde- pendent equa- \ tions. | m new un- ) knowns (prices) , 2mn equations. mn new w- knowns (marg. ut.). * Of. Ch. IV, §8, number 7. ete ee ah nk fp BT or ate : * " in the theory of value and prices. 59 ee: CO bee dU A A od Ur ati i AU.) >) Bi i Me Pe Me omy)» meee Ui AU oa ge aU indepen- ME DB id Mins dA etsy OMe | gant aes Sects te OS nah ea eters ge se Pe oe equations. Mer dire GUE. "ta Ur ae een or, aa Uw no new meee Beis od @A ss aR + dM) inkiowns: ee os re ee PO Py ED, ; No. equations: m+(n—1)+2mn+(2m—1) n=4mn+m—1 No. unknowns: 2muv+m+2mn+0 =4mn+m. There are just one too few equations. It may not be evident at first why the second set does not contain » independent equations instead of (7—1). ‘The point is that any one of these equations can be derived from the others together with the equations of the first set. Thus multiply the equations of the first set by p,, Pi, -- + Dm respectively and add the resulting equations arranging as follows : eee 1: Py 1 CMS pee | +A_..p,t Blo. p+... +M_»-. p+ me | feersieh a eis 7 hates SEND 90, 4 a ea Se Pat Bs C 5 Crh +M,.. OR a | a) Se IA RNG MN oy aR Ee mt att ( +A n- Pat Bon. Pot. -.- + Mon: Pm- Subtracting from this equation the sum of all but the first (say) of the second set, our result is : Pee Be pt EM pe Ae ee Pee «Ps te fe Mis Dm which is the first equation of the second set. This equation is there- fore dependent on the others, or there is one less independent equa- tion than appears at first glance. Hence we need one more equa- tion. We may let: 1a This makes A the standard of value (cf. § 5). No such limitation applies to the equations in Chapter IV. 60 Irving Kisher—Mathematical investigations CHAPTER VI. THE COMPONENT PROCESSES OF PRODUCTION. § 1. Without dwelling on the economic applications of the mechanism just described we hasten on to the description of a more complicated mechanism. Production usually consists of a number of successive processes. The last of these is retailing. Let us group all other processes under the head of production. The price for production and con- sumption are no longer equal. : Hitherto we have had two sets of cisterns, the production set and the consumption set. Separate now, these sets far enough to introduce a third set for exchange or retailing as in fig. 17. Li: The exchange set is a series of double cisterns each related to a particular commodity, and a particular person. Consider the cistern IA, for instance (the sub-letter for exchange or retailing). In the front compartment is the quantity of A which I buys and sells or transfers from producer to consumer. The back compartment con- tains the money pay for doing it. These exchange cisterns are connected with each other and with the production set by levers precisely as if they were so many new commodities produced. in the theory of value and prices. 61 So also the rods maintain a constant money rate for exchange; in- stead, however, of the former simple relation between the producers and consumers there is now the following that the sum of the ordin- ates of Al, and A I,, equals the ordinate of AI,, and likewise for II, III, etc., also that the thickness of the back cisterns of A, plus that of A, equals that of A,. These results are effected by parallel rulers, those for the former purpose being represented in fig. 17. The new machinery required for the exchange process consists then (1) of triplicate pistons* which necessitate that the same quantity of A shall be produced, exchanged, and consumed ; (2) the additional rods and levers (horizontal and inclined) to make the marginal disutilities of producing and exchanging proportional to the recompense and which also maintain a constant price for exchang- ing the same thing; and (3) the special contrivance to add the marginal disutilities of producing and exchanging for any individ- ual so as to equal that of consuming, and also equate the sum of the prices of producing and exchanging to that of consuming. 52. ANALYTICAL, eee Ne EASA tt A LE SES ae a ar eee i equations. ( 3 mn 2m Kn Meee MM + ...+M.,=Mi+.-.+M,, J unknowns. A... Pay Tees 4M Prix as A. Paye Tees +M,, Pig Pre Hier secs M1 Pre i Par a sacle a i ae Pryx se Ae Dis at ie ne Me ee Pax a5 Sat a6 ju pe Pin n—1 independent equations. 3m new unknowns (prices). dU dU hen eee aM dU dU ae H(A, tee ) aM. sa Ld) | | dU dU Se ee A 1) 3 ; ae at M.. dA, (4,1) dM,., ( ) 3 mn equations. ee) oe hen me oo ieee elle 3 mn new unknowns gu) : Ok (marg. ut.). otis 1h Galan aa we a oe. g dU dU i B(A,,,) 5 3 au, = FM) dU dU dA im F(A,») ’ OB that is A is cheaper than B, for OA and OB are the quantites of A and B pur- chasable for the same money. If the prices of A and B were equal so that OA = OB, it would not be tangent to an indifference curve unless on the B axis and A would go out of use. Moreover it is evident that a slight variation in the relative prices of A and B will change greatly the position of I for a poor man but will not change materially that of I’ for a rich man. If the poor consumers predominate the line AB will follow the general trend of the curves near the origin. If the rich consumers predominate the line AB will become steeper (as in the dotted posi- tions). That is the two prices of the two qualities separate widely. This interprets the fact that in a rich market like New York City a slight difference in quality will make an enormous divergence in price while in some country towns different grades either do not exist or sell for nearly the same price. In the country districts of “ the west ” all cuts of beef sell for the same price (about 10 cts. per Ib.). In the cities of the west two or three qualities are commonly dis- tinguished, while in New York a grocer will enumerate over a dozen prices in the same beef varying from 10 to 25 ets. per lb. $14. In fig. 25 if the individual III attempts to change the position of - II he may do so in many different ‘‘ directions.” If he changes in the direction III a, he will increase his con- sumption of A without alter- ing that of B or if toward B, IIL 7, without altering A, if in an intermediate direction, III 6, he will increase both A and B and in the ratios of the components of that direc- tion (III a and III f). The direction of maximum in- crease of utility is perpendicular to the indifference curve.* We may figure III 6 asa force. If III were in any other position the force would evidently have a component along the line A, B, and would move III back to the position of equilibrium III. 20. * For between two infinitesimally distant indifference curves the shortest route is on their perpendicular. in the theory of value and prices. — 15 We: may call the perpendicular direction iI 6 the “ maximum direction.” It has the important property that its components III a and III / are proportional to the marginal utilities of A and B. This follows from a theorem* of vector calculus or thus: III @ and Ill / are inversely proportional to OA, and OB,, that is directly proportional to the prices of A and B and therefore proportional to their marginal utilities. Sil If (fig. 25) the separate curve systems of all individuals I, II, ete. are drawn, and the lines AB drawn in each case, they will be paral- lel. For the prices are uniform among all individuals and OA and OB in each case are inversely as the prices. Since the normals to these lines will also be parallel, this theorem may be stated: The “maximum directions” of all are alike. $16. These methods apply to the comparison of any two commodities and afford a means of graphically representing statistical relations connecting the demands for two articles so far as the variations in the quantities of other articles can be eliminated. The same principles apply to the production of two articles. Hides and tallow are completing articles from a producer’s standpoint. Likewise coke and coal gas, mutton and wool, and in general any article and its “ secondary product.” On the other hand most articles are competing or substitutes from a producer’s point of view. The difficulty of producing cloth is greatly increased if the same individual produces books. This is the root.of the principle of division of labor and leads to that im- portant contrast between production and consumption once before alluded to. This and other contrasts will be mentioned in Appen- dix II, §8. Marshall and others are fond of using the expression “fundamental symmetry of supply and demand.” ‘This notion must be supplemented by that of a “ fundamental asymmetry.” As social organization progresses each man (and each community or nation) tends to become producer of fewer things but consumer of more. * Gibbs, Vector Analysis, $$ 50-53. III a@ 0p OB; Pa + For by similar triangles: il ~ itt \ Galaihed 0 Salama 76 Irving Pisher—Mathematical investigations Fig. 26 shows the usual sort of indifference production curves. 26. B is here laid off to the left and A downward ; the line AB is the locus of production combina- tions of A and B which can be sold for the same money, say $1,000. The point of tan- gency™ lis the point at which the individual can produce the required $1,000 worth of A and B with the minimum disutility. The curves are such that the points of tangency will be gener- ally at or near the axes, especially if the amount of production is large i. e. if the line AB is far from the origin. If B becomes cheaper (OB longer) the point of tangency will change but slowly until presently there are two points of tangency and if B becomes still cheaper the individual will change his profession suddenly from the position I to a position in or near the A axis. The numbers on the indifference curves for production increase in- definitely negatively. There is usually no maximum or minimum point. $17. Finally an article consumed may be competing or completing to another produced. *% “Snone: | “ - td f-4.) SGhnLe “« B8a—(n_ +n, +7,), Es 2 iF “« fourth “ 8n—(n,+n,+7,), ce ce ce ce fifth 74 none b) or 6n—2(n,+7,+%,) altogether. From the above agreement it appears that there can be no indeter- minate case under the suppositions which were first made. Let us look at this somewhat. more closely. in the theory of value and prices. 91 . 3m In the fourth set of equations there are really n(sm—1)(=y separate equations but only (3m—1) are independent. Which shall be selected is a matter of convenience. We may make every equa- tion contain p,, for instance and write Bee eae OU ean oe es, 2B Ce Pax ° Peja = etc. we Cle er ref .0) ve) hes sen 8 gio van Oe; se Pee Ce eS ee OL Ae Ol Os Oo oO. 6) 64 6 eae See Oe) Aw oe, Ve (eee. ors! Senay Ve Now from the first two equations we may derive by division 2 al ee ab. dOL,? 1 but we might wish to use this last as one of the (3m—1) indepen- dent equations, if A,_ should “fail.” From the n(38m—1) ss sepa- rate equations we are at liberty to select for use any 2(3m-—1) inde- pendent ones; and if in this selection there occur any which by some change of quantities fail, we are compelled to change our selection so that the new »(3m—1) equations shall avoid the “failing” magni- tudes. This is interpreted in the mechanism as follows: when a cistern is wholly above the surface of the tank (as IIIC fig. 8) and so con- tains nothing, the quantity of commodity and its utility “fail.” The levers which keep the ordinates in proportion to the corresponding ordinates of other individuals may be far more numerous than the levers pictured in former diagrams. Thus for four cisterns there may be six levers (by joining each pair) but only three are neces- sary. The “ failure ” of any magnitudes will not invalidate any system of levers originally selected ; it will simply make their num- ber greater than necessary. II. THE CISTERNS AND DIAGRAMS OF PART I COMPARED WITH THE DIAGRAMS OF JEVONS AND OF AUSPITZ UND LIEBEN. N 1A In order to represent geometrically the relations between quantity of commodity, marginal utility, total utility, and gain (any two of which four magnitudes are determined by a specified relation between 92 Irving Fisher— Mathematical investigations the other two) it is only necessary to have a plane curve of appro- priate form and to represent any two of the above economic magni- tudes by any two geometrical magnitudes determined by the posi- tion of points in the curve. | Out of the numerous possible methods thus included, the one se- lected for the preceding discussion was to represent marginal utility by the Cartesian ordinate and commodity by the area included be- tween the curve, the axes of codrdinates, and the abscissa drawn from the point. S.2. In order to show the connection between this system of codrdi- nates and those of Jevons and of Auspitz und Lieben, the followmg scheme is presented : Jevons. Auspitz & Liehen. “The new curves. Commodity ..-- = %; == ws = eg Marginal } di = Bp mei) 2 = = tan 60 = mle Ty Yi dx, es y Total Ae — OS OF ee == utility eC ee Sy let Ya Jyndy : dy, Gain) ssh Lc Sy da—ay, = Fee, ae = fyady —yfady 29. FT 8 ar dl. 32. ) | A MN F OX in the theory of value and prices. 93 30. 34. These curves are shown in figs. 29 and 30 (Jevons), 31, 32 (Aus- pitz und Lieben), and 33, 34 (new). The first in each case is for consumption the second for production.* If Jevons’ curve for consumption becomes a straight line, fig. 35, its equation is:+ “+ Gy; = mM. Using the preceding table substituting for 2, and y, we get in Auspitz und Lieben coérdinates : 35. 36. 37 which integrated gives 29Y, = 2mx,—2,'-+C. Since the curve must evidently pass through the origin, C = 0, and using new constants we may write ei Yo = ax, — Sax,’, which is a parabola (fig. 36). * Jevons used no production curve. The one drawn is inserted to complete the comparison. Fleeming Jenkins’ ‘‘Demand and Supply” curves are the same as Jevons save that price replaces marginal utility. } Gossen, Launhardt, Whewell, and Tozer (the last two use no geometric analy- sis) employ such a linear supposition, though the meanings of their variables are not identical, { Launhardt’s equation. 94 Irving Fisher—Mathematical investigations For the new codrdinates the substitutions from the table give : Jedy+qy =m, which reduces to L == = i, a straight line parallel to the axis of ordinates (fig. 37). The Auspitz und Lieben curve does not reveal to the eye the spe- cial supposition (that commodity and marginal utility change pro- portionally). If we suppose that marginal utility decreases at a con- stant rate in relation to constant second differences of commodity, the new diagram reduces to a straight line : w= qy—m = 0, while the other curves would be: (y.+ Aw,+B)* = C(D—-a,)* and e, = H-Fy,—Gy;. 8 4. The value of Jevons’ diagram consists in the use of a simple and familiar system of coordinates (the Cartesian) as representing the two chief economic quantities, and is probably the best for elemen- tary purposes. The value of Auspitz und Lieben’s diagram together with a “ derivative ” curve* not shown above consists chiefly in the ease with which maxima are discovered and the clear association of maxima with equality of marginal utilities. It is believed that the third | method will, by means of its applicability to the mechanisms of Part I, more clearly reveal the interdependence of the many com- modities of many individuals and of their many utilities. Cn 5. The properties which are essential to the curve we have adopted are:— First, That the curve shall never admit of being intersected twice by a horizontal line (i.e. that it shall not cease to run in a general up and down manne?), ¢o express the fact for consumption that mar- ginal utility decreases as quantity of commodity increases and for - production that marginal disutility increases as the quantity of com- modity increases. BS 4 eh dYa * Whose Cartesian codrdinates are a, and Yq —. in in the theory of value and prices. 95 Second. That the curve shall approach the axis of ordinates asymptotically and in such a manner that the whole area between it and the axis is finite, to express the fact that marginal utility becomes infinitely minus for consumption of, and infinitely plus for production of finite limiting quantities of commodity.* Third. 'The curves begin (have commodity equal to zero) at a finite vertical distance from the origin. (These assumptions are less generally true of production than of consumption, but they have been here employed throughout.) § 6. It is evident that in comparing the forms of curves for different articles their differences and peculiarities are determined in a most delicate fashion by the form of the curve . . . far more delicately than, with our present statistical knowledge, is necessary. Observe, then, what the abscissa of our curve stands for. An infinitely thin layer «dy is the amount additional demanded (or supplied) in response to an infinitesimal decrease (or increase) dy in marginal utility. The abscissa # is the ratio of the infinitesimal layer xdy to the infinitesimal change of price, dy. it is therefore the rate of increase of quantity demandedt (or supplied) in relation to change of marginal utility. AM (figs. 2 and 3) is the initial rate. Consulting II, § 2 of this appendix, we see that af ay Hence, dx, = «dy But y = y, and dy = dy; Hence oS ao a dy; That is the abscissa of our curve is the tangential direction in Jevons’ curve, considered with respect to the axis of ordinates. Hence if Jevons’ curve be subjected to the condition of being convex, the new curve must have the simple condition that succes- sive absvissas diminish, ete., etc. § 7. » Hitherto nothing has been said as to the mode of representing total utility and gain. If y, is the marginal utility (which may be figured in money) at which a consumer actually ceases to buy, y, that at which he would * Cf. Auspitz und Lieben. pp. 7 and 11. + Cf. foot note Ch. IV, § 8, div. 3. 96 Irving Fisher—Mathematical investigations just begin to buy, then his consumer’s rent or gain is (see Ch, I, § 8) Gaff yedy—y, f* ae dy Yk Yr or measuring this gain in the given commodity as valued at y, cents Ff Lady [a ay, Y; y, 9 Yi This may be interpreted by a simple geometrical construction. In‘fig, 38 OA = y, and OR =y.. (say) per unit, Selecting the point 3 make the evident dotted construction deter- mining a point 5. 75 O5 O7 y y Kvidently: —= = 2 = ase j= in =H {= . : NIC CHLY: 7a: adie ON ae aye ae (Z x ) Let 3 assume all positions from M to 6. Then 5 will trace a curve 26. The area described by the moving line 73 is evidently Ye The area described by the moving line 75 is evidently /M(4 x Jay, Fi : _ Hence area described by the moving line 35 is the difference of these expressions or G/y,. That is the area M62 represents the gain measured in commodity. Thus suppose a person buys corn measured by RAM6 and let corn at the valuation RO be the unit of utility. It is only the last layer R6 on which no gain is felt. For any preceding layer 75 the price really paid is OR while the price which it is worth to him is O7.. The layer 73 may be considered as lengthened in his eyes by that in the theory of value and prices. 97 ratio O7/OR so that by getting it at less than he was willing to pay, he has gained the element 35 measured in corn. His gain is mazi- mum when he purchases such a quantity that its final utility equals its price. Fig. 39 applies to “ producer’s rent” or “gain,” substituting | sale” for “purchase ”; “sell ” for “ buy.” To express the gain in money the area M26 must be multiplied by the price. On each cistern construct the curve 62 (fig. 38) and con- sider the area RA26 to move front and back one unit (say one inch) so as to trace a volume (fig. 40) adjacent to the front cistern and again to move p inches further back so as to trace a volume adjacent to the back cistern. The front volume gives again the total utility measured in com- modity. ‘The back volume gives the total utility measured in money. That is the whole back cistern and its adjacent volume represent the money which if the individual paid he would neither gain nor lose, provided his marginal valuation of it is unchanged by the operation. The cistern portion is the money he actually pays and the outside volume 7, 10, 12, 9, 8, 11 is his “gain.” Likewise for the producer. III. GAIN A MAXIMUM. = 1. In the case of a single individual distributing a fixed income over -various commodities under fixed prices the distribution actually TRANS. ConN. ACAD., VOL. IX. 7 JULY, 1892. 98 Irving Fisher-—Mathematical investigations attained and specified in Part I yields the maximum total utility, for, since (Ch. IV, § 2): ef icra 26 dU _ dU dA, dm, 8"? 08 — dm” at rel therefore : dU dU dU a ae ae ; Pweg Duinciin ok (1) The numerators are the marginal utilities per unit of commodity. To divide by the price is to make the unit of commodity the dollar’s worth. Each fraction is thus the marginal utility per dollar’s worth. The equation expresses the fact that the rate of increase of utility from spending more money on any one commodity equals the rate of increase for any other. Hence by a familiar theorem of the cal- culus the total utility must be the maximum attainable by any dis- tribution of a fixed income. Im like manner the individual dis- tributes his production so that the marginal disutilities in all modes of producing dollar’s worth of commodity are equal so that his total disutility is a minimum. Hence the difference between his total utility and total disutility or his economic gain is a maximum. § 2. In the distribution of a single commodity over many individuals since : aU. dU OU Sead. a dU Se dA dm,” he dA, dm Pod+ ++ GA > i therefore, dU dU dU dA, ts aA? _ @A, 2) GU a Pe a ee dm. dm. dm, . 2 that is, the marginal utilities (when the unit of utility is the marginal utility of money for each individual) are equal and the total utility is maximum. In like manner the total disutility is a minimum and gain therefore a maximum. aM d The first continuous equation may be divided by = and the in the theory of value and prices. 99 second by p, and since the first members will become identical we have a common continuous equation: dU dU dU dA. ABs dA, ir. 3 == al wat SG bed == 1 Een == etc. (3) dim,” Pa dm, Dp dm, sate he that is, the marginal utilities of all commodities to all consumers are equal when the unit of utility is the marginal utility of money and the unit of commodity the dollar’s worth. Hence the total utility in whole market thus measured is a maximum.* § 4. However it may justly be objected that the marginal utility of money to one person is not equatable to that of another, that is that it is unfair to use the unit of utility for the poor man the high mar- ginal utility of his small income and add the small number of such large units in a poor man’s gain to the corresponding rich man’s gain in which the unit of measure is small and the number of units large. If we suppose by some mysterious knowledge an exact equiv- alence of utilities were possible between different individuals (see Part II, Ch. 1V, $2) and by some equally mysterious device of socialism we could without changing the aggregate commodities alter their distribution so as to make the whole market utility a maximum our condition would be | aN: = ah = Cte. (4) ad&, dA, This could be brought about by a change in the relative incomes, taking from the rich and giving to the poor until AU al j dm, ~ dm, Sarit which applied to equation (3) will evidently afford the required (4), or by breaking down the condition of uniformity of price and mak- ing each man’s price inversely as his marginal utility of money, which applied to (3) will evidently yield (4). To interpret equation 4 in the mechanism we may alter the posi- tion of the stoppers in tig. 8 until the ordinates in each front and back row are equal. (This will not be when “incomes are equally divided” nor when “gains” are equal, for persons differ in their power of enjoyment, and it would still be true that those whose * Cf. Auspitz und Lieben, p. 23 and 435. 100 Irving Fisher—Mathematical investigations capacities for pleasure were great would consume the most in order to make the aggregate gain in the whole market a maximum). Or we may destroy all the levers and re-arrange the rear thicknesses until the front and back ordinates are made equal. In like manner the minimum disutility would be attained if all marginal disutilities were equal. The maximum gain would then result. This is the maximum gain obtainable when the amounts of each commodity consumed and produced are fixed and given. If we are permitted to rearrange these amounts also, we shall secure the maximum gain when the marginal utilities equal the marginal disutilities ; 1. e. dy ad Die tiara, dk js Under such a socialistic regime more “necessaries” and less “luxuries” would be consumed and produced than previously. The “rich” or powerful would produce more and consume less than previously ; the poor or weak would consume more and produce less. Yet for each the marginal utilities and disutilities would be = Ste; equal. It is needless to say that these considerations are no plea for socialism, but they serve to clear up a subject sometimes discussed by mathematical economists and reconcile Launhardt’s contention* that utility is not a maximum with Auspitz und Lieben’s that it is. The former unconsciously has reference to equation (4) which is not true, the latter to equation (3) which is.t IV. ELIMINATION OF VARIABLES. The four sets of equations, Part I, Ch. IV, § 10, can be reduced. du. 3 rhe: We may substitute for 7A its value F'(A,) and thus eliminate all mar- 1 ginal utilities. Moreover we can get an expression for p,, ~, ete., in terms of commodities. First, if m= the second set of equa- tions are easily solved.by determinants} giving :§ * Volkswirthschaftslehre under ‘‘ Widerholte Tausch.” + Auspitz und Lieben appear to overlook this difference of standpoint. Preface, p. XXV. ¢ Burnside and Panton. Theory of Equations, p. 251. § This equation does not mean that any arbitrary values can be assigned to A,, Bi, ete., and the resulting price of A be so simply expressed ; only when Aj, B,, etc. satisfy all the conditions of Ch. IV, $10 will the price be expressible as the quotient of the two determinants. in the theory of value and prices. 10] (es B, M, | ek: B, M, | ie 3 M, | PAs B: M, | Qa Se a r [a eet ae | [2 Gage | | K, B, M, [ ay B, M, | in which obviously in general a change in A will produce a greater influence on p, then an equal change in B, ete. But it shows clearly that p, is not a function of A alone. Usually n >> m. Hence we may use the first m equations of the second set, or in fact any m equations. The resulting determinant- quotients must be equal and must equal also the several like determinates for production. The corresponding values of p,;, p,, ctc., may be found and may be substituted in the fourth set. If wherever A, now occurs in the fourth set, we substitute K,—A, — A,—... —A, from the first set, and likewise for B,, etc., the resulting fourth set is self-sufficient. We have thus eliminated the variables S etc., p,, etc., A,, B,, etc., and have gotten rid of the first, second and third set of equations. We can proceed no further, however, until the explicit forms of the functions F(A), eté., are given. | APPENDIX IL. LIMITATIONS OF THE PRECEDING ANALYSIS. Sor, No pretense is made that the preceding analysis is perfect or ex- haustive. There is no such analysis of any phenomena whatever even in physics. The suppositions in Ch. II, § 2 of Part I, are of course ideal. They only imperfectly apply to New York City or Chicago. Ideal suppositions are unavoidable in any science. In fact it is an evidence of progress when the distinction between the ideal and the actual arises.* Even in hydrostatics the assumption of per- fect fluidity is never fully realized. The physicist has never fully explained a single fact in the universe. He approximates only. The economist cannot hope to do better. Some writers, especially those of the historical school are disposed to carp at the introduc- tion of a refined mathematical analysis. It is the old story of the * See Prof. Simon Newcomb, 'The Method and Province of Pol. Econ., N. Am. Rey., CCXI, IX. 102 Irving Fisher— Mathematical investigations “practical” man versus the scientist. A sea-captain can sail his vessel and laugh at the college professor in his elaborate explanation of the process. What to him is all this resolution of forces and velocities which takes no account of the varying gusts of wind, the drifting of the keel, the pitching and tossing, the suppositions which makes of the sail an ideal plane and overlook the effect of the wind on the hull? ‘There is no need to point the moral. Until the economist is reconciled to a refined ideal analysis he cannot profess to be scientific. After an ideal statical analysis the scientist may go further and reintroduce one by one the considerations at first omitted. This is not the object at present in view. But it may be well to merely enumerate the chief of these limitations. ; § 2. In Part I the utility of A was assumed to be a sole function of the quantity of A, and in Part II a function of all commodities con- sumed by a given individual. We could go on and treat it as a function of all commodities produced and consumed, treating not net production for each article, but the actual amounts separately produced and consumed by the given individual. Again we could treat it as a function of the quantities of each commodity produced or consumed by all persons in the market. This becomes important when we consider a man in relation to the members of his family or consider articles of fashion as dia- monds,* also when we account for that (never thoroughly studied) interdependence, the division of labor. This limitation has many analogies in physics. The attraction of gravity is a function of the distance from the center of the earth. A more exact analysis makes it a function of the revolution of the earth, of the position and mass of the moon (theory of tides) and finally of the position, and mass of every heavenly body. Articles are not always homogeneous or infinitely divisible. To introduce this limitation is to replace each equation involving mar- ginal utilities by two inequalities and to admit an equilibrium inde- terminate between limits. As an extreme case we may imagine an article of which no one desires more than a single copy as of a book. The utility of (say) Mill’s Pol. Econ. is considerably greater than * See David Wells, Recent Economic Changes, on Diamonds. + Auspitz und Lieben, 117-1386 and 467. in the theory of value and prices. 1038 its cost, but the utility of a second copy is considerably less than its cost. In the aggregate market, however, there will be a mar- ginal person whose utility is very close to the price. A change in price will not alter the amount purchased by everyone, but will alter the number of purchasers.* § 4. Producing, consuming and exchanging are discontinuous in time. The theory of utility when applied to a single act of production or consumption or of sale or purchase, is independent of time, or rather the time element is all accounted for in the form of the utility function.t But an analysis of a number of such acts must take account of their frequency. The manner in which the time element enters has puzzled not a few economists. An example from physics may not be amiss. In the kinetic theory of gases the pressure on the walls of the containing vessel is explained by its continual bombardment by molecules. But an apparent difficulty must be observed. A rebound of a molecule involves the idea of momentum only while that which we wish to explain is pressure or force which is not by any means momentum, but momentum divided by téme. How does this time enter? By regarding not one but many molecules and taking account of the Srequency of their collision. The average momentum of each blow divided by the average interval between the blows is the pressure sought. So a produce exchange is a channel connecting production and con- sumption. Instead of an even flow of one bushel per second, the machinery of the exchange is such that by an instantaneous blow of a bat, so to speak, a thousand bushes are knocked along. Time is in- appropriate to explain the single blow but necessary to explain the many. § 5, The ideal statical condition assumed in our analysis is never satis- fied in fact. 3 No commodity has a constant yearly rate of production or con- sumption. Industrial methods do not remain stationary. ‘Tastes and fashions change. Panics show a lack of equilibrium. ‘Their explanation belongs to the dynamics of economics. But we have * The analysis of H. Cunynghame in the Ec. Jour., March ’92, applies to this case, + Cf. Jevons, 63-68. 104 Irving Fisher— Mathematical investigations again a physical analogue. Water seeks its level, but this law does not fully explain Niagara. A great deal of special data are here necessary and the physicist is as unfit to advise the captain of the Maid of the Mist as an economist to direct a Wall street speculator. The failure to separate statics from dynamics appears historically* to explain the great confusion in early physical ideas. To make this separation required the reluctant transition from the actual world to the ideal. The actual world both physical and economic has no equilibrium. ‘‘ Normal”t+ price, production and consumption are sufficiently intricate without the complication of changes in social structure. Some economists object to the notion of ‘‘ normal” as an ideal but unattainable state. They might with equal reason object to the ideal and unattainable equilibrium of the sea. The dynamical side of economics has never yet received system- atic treatment. When it has, it will reconcile much of the present apparent contradiction, e. g. if a market is out of equilibrium, things may sell for “more than they are worth,” as every practical man knows, that is the proper ratios of marginal utilities and prices are not preserved. S 6. We have assumed a constant population. But population does change and with it all utility functions change. An analysis whose independent variable is populationt leads to another department of economics. Inthe foregoing investigation the influence of popnla- tion was included in the form of the utility function. So also with all causes physical, mental and social not dependent on the quantities of commodities or services. S 7. Individuals are not free to stop consuming or producing at any point. Factory operatives must have uniform working hours. The marginal undesirability of the last hour may for some workmen equal, for others exceed or fall short of the utility of its wages. 8. So No one is fully acquainted with all prices nor can he adjust his actions to them with the nicety supposed ; both these considerations are starting points for separate discussion. * Whewell, Hist. Induct. Sci., I, 72-3 and 186. + Marshall, p. 84. t See article of Prof. J. B. Clark. Distribution as determined bya law of rent. Quart. Jour. Econ., Apr. 91, p. 289. in the theory of value and prices. 105 § 9. The “fundamental symmetry of supply and demand worked out by Auspitz und Lieben should not bind us to the fundamental asymmetry. The symmetry enables us to investigate the general dependence of consumption and production but special investigation of production, e. g. of railroad rates should be independently pur- sued. (1.) Production of a commodity always precedes its consumption. (2.) The maximum advantage in production involves few com- modities for each individual, in consumption many. . (3.) Increasing social organization intensifies the former fact not the latter. (4.) There are more successive steps in production than consump- tion. (5) Social organization intensifies this distinction. (6) Owing to (4) and (5) service rather than commodity becomes increasingly the unit in production. (7.) Freedom to leave off consuming at any point is greater than for producing. (8.) Social organization intensifies this. (9.) Combination and monopoly are more feasible and frequent in production than in consumption. (10.) In production the distinction of fixed charges and running expenses often plays an important réle. This deserves a separate treatment. The transportation charges on a steamship are not what it costs to transport an extra ton but it is this quantity plus the pro- portionate share of that ton in the fixed charges (interest, insurance, etc). That is, the marginal cost of service involves the margin of capital invested as well as the marginal cost of running the ship) (which is purely nominal). This is so in theory of railroad rates but the railroad investor cannot foresee the results of his enterprise as well nor can he change his road when built from one route to another as a steamship can do. To apply the theory to railroads assumes that railroad projectors know what the traftic will be. Con- sequently the proper discussion of railroad rates, assuming that the railroads are already built, takes no account of fixed charges but becomes formulated as “ what the traffic will bear.”* A complete theory of the relation of cost of production to price in its varying and peculiar ramifications is too vast a subject to be treated here. * See Hadley, Railroad Transportation. 106 Irving Fisher—Mathematical investigations § 10. ? It has been assumed throughout this investigation that marginal utility decreases as quantity of commodity increases. This is not always true, e. g. it is obviously not true of intoxicating liquors. A study of the liquor traffic would require a somewhat different treatment from that of most other commodities. Still less is it always true that marginal cost of production always increases as the quantity produced increases. It is clearly not true that it costs _ more in a shoe factory to produce the second shoe than it costs to produce the first. Yet it is probably quite generally true that at the actual margin reached in business the disutility of extending the | business grows greater. When this is not true and when it is not true that marginal utility decreases as quantity of commodity in- creasess an instability is the result. The matter of instability is one element at the bottom of the present industrial tendency toward trusts and pools. Sia i There is no isolated market. Not only this but a “market” itself is an ideal thing. The stalls in the same city meat market may be far enough apart to prevent a purchaser from behaving precisely as if he stood before two counters at once. The relation of the counters ten feet apart differs in degree rather than in kind from the relation of London to New York. APPENDIX IIL THE UTILITY AND HISTORY OF MATHEMATICAL METHOD IN ECONOMICS. SEE Mathematics possesses the same Aind though not the same degree of value in every inquiry. Prof. B. Peirce,* in his memorable Linear Associative Algebra, says: ‘‘ Mathematics is the science which draws necessary conclusions. * * * * * Mathematics is not the discoverer of laws, for it is not induction, neither is it the- framer of theories for it is not hypothesis, but it is the judge over both. * * * * * It deduces from a law all its consequences. Mathematics under this definition belongs to every inquiry, moral as well as physical. Even the rules of logic by which it is rigidly bound could not be deduced without its aid. The laws of argu- * Amer, Jour. Math,, IV., p. 97. in the theory of value and prices, 107 ments admit of simple statement, but they must be curiously trans- posed before they can be applied to the living speech and verified by observation. In its pure and simple form the syllogism cannot be directly com- pared with all experience, or it would not have required an Aristotle to discover it. It must be transmuted into all the possible shapes in which reasoning loves to clothe itself. The transmutation is the mathematical process in the establishment of the law.”* I make this quotation for I believe many persons, especially econo- mists, do not understand the character of mathematics in general. They imagine that a physicist can sit in his study and with the eal- culus as a talisman spin out some law of physics. Some economists have hoped for a similar mysterious use of mathematics in their own science. Sr We must distinguish carefully between what may be designated as mathematics and mathematical method. The former belongs, as ° Prof. Peirce says, to every science. In this sense economics has always been mathematical. The latter has reference to the use of symbols and their operations. It is this which is to be discussed here. A symbol] may be a letter, a diagram, or a model. All three are used in geometry and physics.t By an operation on symbols is meant arule the formulation of which depends on the mention of those symbols (as the operation of differentiation). To employ mathematical method is to pass from what is given to what is required by the aid of sucharule. To avoid mathematical method is to do it without the rule. Symbols _and their operations are aids to the human memory and imagina- tion. § 3. The utility of mathematical method is purely relative, as is all utility. It helps greatly some persons, slightly others, is even a hindrance to some. Before a schoolboy studies “mechanics” he is usually given in his arithmetic problems of uniform motion. It would sorely puzzle him if he were compelled to use the formula s=wt. The employ- ment of symbols has for him only disutility. But when in —- - = ee ——E— * Cf. Grassmann, Ausdehnungslehre, Introduction. + Few are aware how important models sometimes are in the treatwent of these sciences. Maxwell’s model to represent the relations of volume, entropy and energy in thermodynamics is an excellent example. 108 Irving Fisher—Mathematical investigations ‘“‘mechanics” proper a few years later the same boy studies “ falling ' bodies ” he finds it helpful to use the formula v = gt which contrasts. with the preceding formula only in that space (s) is replaced by space per unit of time (v) and velocity (w) by velocity acquired per unit of time (g). The increased complexity of the magnitudes makes a formula relatively desirable. Yet for some minds the latter formula is of no use. Experience in teaching this very subject has convinced me that there are a few who understand it better without the aid of the formula, but they are just those individuals whose comprehension of the relations involved is the vaguest and the weakest. The formule, diagrams and models are the instruments of higher study. The trained mathematician uses them to clarify and extend his previous unsymbolic knowledge. When he reviews the mathe- matics of his childhood, the elementary mechanics is to him illumined by the conceptions and notation of the calculus and qua- _ternions. To think of velocity, acceleration, force, as fluxions is not to abandon but to supplement the old notions and to think of momentum, work, energy, as integrals is greatly to extend them. Yet he is well aware or ought to be that to load all this on the beginner is to impede his progress and produce disgust. So also the beginner in economics might be mystified, while the advanced student is enlightened by the mathematical method. § 4. The utility of a mathematical treatment varies then according to the characteristics of the user, according to the degree of his mathe- matical development and according to the intricacy of the subject _ handled. There is a higher economics just as there is a higher phys'es, to both of which a mathematical treatment is appropriate. It is said that mathematics has given no new theorems to economics. This is true and untrue according to the elasticity, of our terms- The challenge of Cairnes might be answered by a counter challenge to show the contents of Cournot, Walras, or Auspitz und Lieben in any non-mathematical writer. If I may venture a speculation, those who frown on the mathe- matical economist because he “ wraps up his mysterious conclusions in symbols” seem to me in some cases to point their finger at those “conclusions ” which when “unwrapt ” of symbols they recognize as old friends and lustily complain that they are not new; at the same time they seem to ignore completely those ‘ mysterious” conclu- in the theory of value and prices. 109 sions which are new because they think the former and admitted theorems exhaust all that is important on the subject. Why should the mathematician be obliged to vindicate the exercise of his science by overturning economics or by deducing some “ laws” more funda- mental than those already admitted ? Elementary physics is the fundamental physics and it can be taught with little or no mathematical symbols. Advanced physics is relatively less popular while more mathematical. By actual count Ganot’s elementary physics of 986 pages contains a formula for every three and one-third pages. The chapter on electricity and magnetism of 320 pages, a formula for every 43 pages, while the profound treatise of Mascart and Joubert on Electricity and Mag- netism, vol. I, of 640 pages, contains 3% formule for each page or 15 times as many per page as the same subject in Ganot. Similarly in economics, mathematical treatment is relatively use- ful as the relations become relatively complicated. The introduction of mathematical method marks a stage of growth—perhaps it is not too extravagant to say, the entrance of political economy ona scien- tific era. § 5. Has the mathematical method attained a firm footing? Before Jevons all the many attempts at mathematical treatment fell flat. Every writer suffered complete oblivion until Jevons unearthed their volumes in his bibliography. One chief reason for this is that these writers misconceived the application of mathematics. I think this was true even of the distinguished Whewell. Jevons thinks it is so of Canard though his work was crowned by the French institute. The second reason for this oblivion is that the world was not pre- pared for it. The movement was too advanced and premature. Cournot certainly, Gossen possibly, now exert considerable influence on economic thought. Marshall, whose recent book is acknowledged to be to modern economics what Mill’s was to the economics of a generation ago repeatedly expresses his admiration for and obliga- tion to Cournot. Thus the mathematical method really began with Jevons in 1871. Up to this time pol. econ. had been the favorite field for those per- sons whose tastes were semi-scientific and semi-literary or historical. But the scientific and literary temper are seldom equally balanced and as might have been expected after once beginning to divide they have steadily differentiated. On the one extreme is the histori- 110 Irving Fisher—Mathenatical investigations cal school of Roscher and Leslie, on the other the mathematical, _ deductive, or so-called Austrian school of Jevons, Menger and Walras, while the “orthodox” economists the legitimate successors of Adam Smith, Ricardo and Mill constitute the central body from which both have split. This cleavage is, however, largely a division of the field of research rather than opposed theories or methods on the same field. The mathematical economics apparently has its warmest adherents in Austria, Italy and Denmark. France occupies the next position, while England, America and Germany have their individual enthu- siasts but are still restrained largely by classic traditions. Prof. Pantaleoni thinks “the most active movement in Italian pol. econ. is that of the new school styled rather inexactly the “ Aus- * while Graziani says that the utility theory of value “seems to close the evolutionary cycle of Italian thought.”* In England, Prof. Edgeworth, noted for his enthusiasm on mathe- matical economics, has recently been elected to the chair of pol. econ. at Oxford, while Prof. Marshall is carrying forward the same movement at Cambridge. There has been a great increase in mathematico-economie litera- ture since 1871. Just two decades have passed by since Jevons’ epoch-making books appeared. Of the mathematico-economic writingst appearing in this period which here come to my notice, the number in the first decade was 30, representing 12 writers, while in the second decade it was 66, representing 23 writers. From all apparent evidence the mathematical method has come to stay. trian,” 70) 6. We can see why this is so if we glance at the work which the mathematical method has already accomplished. It is perhaps fair to credit the idea of marginal utility to mathematical method. This idea had five independent origins with Dupuit, Gossen, Jevons, Menger, and Walras. All except Menger presented this idea and presumably attained it by mathematical methods. No idea has been more fruitful in the history of the science. This one achievement is a sufficient vindication of the mathematical method. * Article on Economics in Italy, by Prof. Ugo Rabberio, Pol. Sci. Quart., Sept., 1891, pp. 439-473. +I have not even included here Menger, B6hm-Bawerk and other writers of the Austrian school, who in spite of a mathematical tone have omitted to use math- ematical symbols. in the theory of value and prices. 111 To pass in review all that has been done in expanding and apply- ing the idea of marginal utility (and most of this expansion has been purely mathematical) would not be possible here, nor would it be possible to state all the other notions which have grown out of a mathematical treatment. It has corrected numerous errors and con- fusion of thought. This correcting function has really been the ~ chief mission of mathematics in the field of physics though few not themselves physicists are aware of the fact. ‘ In fact the ideas of marginal utility and disutility may be re- garded as corrections of two old and apparently inconsistent theories of value—the utility theory and the cost of production theory. Utility was first thought of as proportional to commodity. (That this was never explicitly assumed is a splendid illustration of how without a careful mathematical analysis in which every magnitude has definite meaning, tacit assumptions creep in and confuse the mind). It was next pointed out that utility could not explain price since water was useful. So “utility” and “scarcity ” were jointly privileged to determine price. It was Jevons’ clear and mathemat- ical exposition of utility which showed the shallowness of the for- mer discussion and brought to light the preposterous tacit assump- tion, unchallenged because unseen, that each glass of water has an inherent, utility independent of the number of glasses already drunk. Jevons laid emphasis on demand. Many who accepted his work were still applying the analogous errors to supply. Ricardo* had indicated the idea of marginal cost. But even Mill did not perceive its extension beyond agricultural produce. Considerable credit belongs to Auspitz und Lieben for working out the legitimate con- sequences and showing by a beautiful mathematical presentation that the marginal utility theory and the marginal cost theory are not opposed but supplementary. In fact the “margin” itself is determined by the condition that the utility and the cost of final increments shall be equal (when measured in money). Mathematical method is to be credited with the development of the ideas of consumers’ and producers’ rent or gain so ingeniously applied by Auspitz und Lieben and so conspicuous in the orig- inal article of Prof. J. B. Clark on the law of the three rents.t The intimate and mathematically necessary relation between the equality of marginal utilities and disutilities and the maximum sum of consumers’ and producers’ rent, a theorem emphasized by Auspitz und Lieben, and Edgeworth, is of course due to the mathematical instrument. ‘ * Pol, Econ., Ch. 2. is ; + Quart. Jour. Econ., April, 1891. 1h2 Irving Fisher— Mathematical investigations Mathematical method is making a new set of classifications based on mathematical properties. ‘Thus the classification by Auspitz und Lieben of all commodities into three groups* is, I believe, a new one, and one suggested by, and readily discussed by the use of their diagrams. The classification of capital into free and sunk is one which is emphasized by the mathematical writers, as Marshall, and is bearing fruit.t , I believe therefore that mathematical method has made several real contributions to economics, and that it is destined to make more. To verify this statement I would refer the reader to the books men- tioned in the bibliography among recent writers, especially Walras, Auspitz & Lieben, Marshall, Edgeworth, Wicksteed and Cunyng- hame ; also, if it is proper to include those writers, who while avoiding mathematical language are interpreting and extending the same ideas, Menger, Wieser, BOhm-Bawerk, Clark and Hobson. § 7. It may not be amiss to present a list of quotations from those who have pursued or admired the mathematical! path : Whewell{ says: [Mathematical method in mechanics saves scien- tists three errors, viz:] “They might have assumed their principles wrongly, they might have reasoned falsely from them in conse- quence of the complexity of the problem, or they might have neglected the disturbing causes which interfered with the effect of the principal forces. * * * It appears, I think, that the sciences of mechanics and political economy are so far analogous that some- thing of the same advantage may be looked for from the application of mathematics in the case of political economy.” Again :§ “This mode of treatment might be expected to show more clearly than any other within what limits and under what conditions propositions in political economy are true.” Cournot -|| L’emploi des signes mathématiques, est chose naturelle toutes les fois qwil s’agit de discuter des relations entre des gran- deurs ; et lors méme quwils ne seraient pas rigoureusement nécess- aires, s’ils peuvent faciliter exposition, la rendre plus concise, mettre sur la voie de développements plus étendus, prévenir les écarts * Page 46. +See Cunynghame, Geom. Meth. of treating exchange value, monopoly, and rent. Econ. Jour., March, ’92, p. 35. + Cambridge Philosophical Transactions, 1830, p. 194. § Cambridge Philosophical Transactions, 1856, p. 1. || Principes math. de la théorie des richesses, 1838. Preface, p. viii. — in the theory of value and prices. 113 dune vague argumentation, il serait peu philosophique de les rebuter, paree qwils ne sont pas également familiers 4 tous les lecteurs et qu’on s’en est quelquefois servi 4 faux.” Gossen :-* Was einem Kopernikus zur Erklirung des Zusammen- seins der Welten im Raum zu leisten gelang, das glaube ich fiir die Erklirung des Zusammenseins der Menschen auf der Erdoberfliche zu leisten. * * * Darum ist es denn eben so unmodglich, die wahre Nationalékonomie ohne Hiilfe der Mathematik vorzutragen, wie dieses bei der wahren Astronomie, der wahren Physik, Mechanik u. 8. W.” Jevons -+ “JT have long thought that as it deals throughout with quantities, it must be a mathematical science in matter if not in language. J have endeavored to arrive at accurate quantitative notions concerning utility, value, labor, capital, etc., and I have often been surprised to find how clearly some of the most difficult notions, especially that most puzzling of notions value, admits of mathematical analysis and expression.” Walras -}, “Je crois bien que les notations qui y sont employées paraitrout tout d’abord un pen compliquées; mais je prie le lecteur de ne ponit se rebuter de cette complication qui est inhérents au sejet et qui en constitue d’ailleurs le seule difficulté mathématique. Le systéme de ces notations une fois compris le systeme des phé- nomenes Gconomiques est en quelque sorte compris par cela méme.” Newcomb :§ “To ultimately expect from pol. econ. results of such certainty and exactness, that it can present the legislator with numerical predictions like those we have described is by no means hopeless.” * * * * “ Mathematical analysis is simply the application to logical deduction of a language more unambiguous, more precise, and for this particular purpose, more powerful than ordinary lan- guage.” Launhardt || “Es ist ja die Mathematik nichts anderes als eine Sprache, welche in strenger Folgerichtigkeit die Beziehungen mess- bare Dinge zu einander darstellt, was durch die gewohnliche Sprache entweder gar. nicht oder doch nur in weitschweitiger ungenauer Weise erreicht werden kann.” * Menschlicher Verkehr. Preface, p. v. + Preface to first edition, p. vii. { Econ. pol. pure, 1874, Preface, p. vt. S$ The method and province of pol. econ. [Review of Cairne’s logical method in pol. econ.|, N. Amer. Rev., No. CCXLIX, 1875, p. 259. || Volkswirthschaftslehre : Preface, p. v. TRANS. CONN. ACAD., Vou. IX. 8 JULY, 1892, 114 Irving Fisher—Mathematical investigations Wicksteed :* “'The diagrammatic method of studying economics may be regarded from three points of view: (I) many teachers. find in it a stimulating and helpful appeal to the eye and use it asa short and telling way of making statements and registering results. (II) a few students treat it as a potent instrument for giving pre- cision to hypotheses in the first instance and then for rigorously analysing and investigating the results that flow from them. (III) a very few investigators (among whom I think we must rank Jevons), have hoped ultimately to pass beyond the field of pure hypotheses and analysis and to build up constructive results upon empirical curves of economic phenomena established by obserya- tion.” | Foxwellt [speaking of the mathematics of Jevons and Marshall] : “Tt has made it impossible for the educated economist to mistake the limits of theory and practice or to repeat the confusion which brought the study into discredit and almost arrested its growth.” Auspitz und Lieben:} “ Wir haben uns bei unseren Untersuch- ungen der analytischen Methode und namentlich der graphischen Darstellung bediehnt, nicht nur weil sich diese Behandlungsweise iiberall, wo sie tiberhaupt anwendbar ist, und namentlich in den naturwissenschaftlichen Fichern glinzend bewihrt hat, sondern hauptsiichlich auch darum weil sie eine Prazision mit sich bringt, — welche alle aus vieldeutigen W ort-definitionen entspringender Miss- verstiindnisse ausschliest.” Edgeworth :§ * * * “the various effects of a tax or other impedi- ment, which most students find it so difficult to trace in Mill’s labori- ous chapters, are visible almost at a glance by the aid of the mathe- matical instrument. It takes Prof. Sidgwick a good many words to convey by way of a particular instance that it is possible for a nation by a judiciously regulated tariff, to benefit itself at the expense of the foreigner. The truth in its generality is more clearly contemplated by the aid of diagrams. * * * * There seems to be a natural affinity between the phenomena of supply and demand, and some of the fundamental conceptions of mathematics, such as the April, ’89, p. 298. +The Economic Movement in England, Quart. Jour. Econ., Oct., ’88. + Untersuchungen. Preface, p. xiii. § Address before Brit. Assoc. as president of the section on economic science and statistics. Published in Nature, Sept. 19, 89, p. 497. in the theory of value and prices. 115 of the differential calculus; especially in its application to the determination of maxima and minima.” [It seems to] “supply to political economy what Whewell would have called ‘appropriate and clear’ conceptions. * * * Algebra and geometry are to ordinary language in political economy somewhat as quaternions are to ordinary algebraic geometry in mathematical physics” (Quotes Maxwell on quaternions: ‘‘I am convinced that the introduction of the ideas as distinguished from the operations and methods * * * will be of great use.”’) Again :* “JT do not mean that the mathematical method should form part of the curriculum as we make Greek obligatory for the students of philosophy. But may we not hope that the higher path will sometimes be pursued by those candidates who offer special subjects for examination.” Marshall:+ “It is not easy to get a clear full view of continuity in this aspect without the aid either of mathematical symbols or diagrams. * * * * experience seems to show that they give a firmer grasp of many important principles than can be got without their aid ; and there are many problems of pure theory, which no one who has once learnt to use diagrams will willingly handle in any other way. | The chief use of pure mathematics in economic questions seems to be in helping a person to write down quickly, shortly and exactly, some of his thoughts for his own use: and to make sure that he has enough, and only enough, premises for his conclusions (i. e. that his equations are neither more nor less in number than his unknowns). But when a great many symbols have to be used, they become very laborious to any one but the writer himself. And though Cournot’s genius must give a new mental activity to every one who passes through his hands, and mathematicians of calibre similar to his may use their favorite weapons in clearing a way for themselves to the center of some of those difficult problems of economic theory, of which only the outer fringe has yet been touched; yet it is doubtful whether any one spends his time well in reading lengthy translations of economic doctrines into mathematics, that have not been made by himself. A few specimens of those applications of mathematical language which have proved most useful for my own purpose have, however, been added in an Appendix.” * An introductory lecture on pol. econ. delivered before the University of Oxford, Oct. 23d, 1891, published in Economic Journal, Vol. i, No. 4, p. 629, +Prin. of Econ. Preface to first Ed., p, xiv; in 2d ed. 116 Irving Fisher—Mathematical investigations Cunynghame:* “But curves play in the study of pol. econ. much the same part as the moods and figures play in logic. They do not perhaps assist in original thought, but they afford a system by means of which error can be promptly and certainly detected and demonstrated. And as in logic so in graphic pol. econ. the chief difficulty is not to solve the problem, but to state it in geometrical language.” § 8. Contrast with the preceding the following statements from a few who can see nothing good in mathematical method : A writer in the ‘Saturday Review” (Nov. 11, 1871), quoted by Prof. Edgewortht says of Jevons: ‘The equations, * * * assum- ing them to be legitimate, seem to us to be simply useless so long as the functions are obviously indeterminable.” [Mathematics studies relations as well as calculations. Numerical indeterminability is common even in mathematical physics. | Cairnes:{ “ Having weighed Prof. Jevons’s argument to the best of my ability, and so far as this is possible for one unversed in mathematics, I still adhere to my original view. So far as I can see, economic truths are not discoverable through the instrumentality of mathematics. If this view be unsound, there is at hand an easy means of refutation—the production of an economic truth, not before known, which has been thus arrived at ; but I am not aware that up to the present any such evidence has been furnished of the efficiency of the mathematical method. In taking this ground, I have no desire to deny that it may be possible to employ geometrical diagrams or mathematical formule for the purpose of exhibiting economic doctrines reached by other paths, and it may be that there are minds for which this mode of presenting the subject has advan- tages. What I venture to deny is the doctrine which Prof. Jevons and others have advanced—that economic knowledge can be ex- tended by such means; that mathematics can be applied to the development of economic truth, as it has been applied to the devel- opment of mechanical and physical truth ; and, unless it can be * Geometrical methods of treating exchange value, monopoly and rent. H. Cunynghame. Econ. Jour., March, ’92, p. 39. + Math.-Psychics, p. 119. + The Character and Logical Method of pol. econ. New York, 1875. Preface, See also, p. 122; also: Some leading principles of pol. econ. newly expounded, Preface. in the theory of value and prices. 117 shown either that mental feelings admit of being expressed in pre- cise quantitative forms, or, on the other hand, that economic phe- nomena do not depend upon mental feelings, I am unable to see how this conclusion can be avoided.” ['There are examples in Cournot, Walras, Auspitz und Lieben, Marshall, etc., which I think are fair instances of the “production of an economic truth, not before known.” It is admitted, however, that each of these truths could have been discovered without ‘mathematical method” by some remarkably clear headed reasoner. but the same is true in physies. The deduction used in every physical truth could be reasoned out without diagrams or formule. A railway will best convey a man from New York to San Francisco though it is perfectly possible to walk. Cairnes certainly has an erroneous idea of the use of mathe- matical method in physical investigations. Mathematics afford the physicist a complete and precise view of his subject, and this con- dition of mind permits and facilitates his discovery. The discovery is only indirectly due to mathematics though it might never have been made without it. Cairnes apparently thinks that physical truth has been discovered by the manipulation of equations. The history of physics will not bear him out. So far as I know only one physi- cal discovery was made in that way—a discovery in light. See the quotation from Peirce at the beginning of this appendix. | Wagner* [in reviewing Marshall’s Prin. of Econ.]: “I do not believe that this mode of treating the subject has an independent value of its own for solving our problems. Indeed Marshall himself admits as much [does he? Cf. preceding statement of Marshall. ] * * * He has used diagrams and formule only for purposes of illustration and for greater precision of statement.” {Diagrams and formule are never used for any other purpose yet they surely have an independent value in (say) physics. Cf. § 1.] Ingram :-+ “There is not much encouragement to pursue such researches, which will in fact never be anything more than academic playthings, and which involve the very real evil of restoring the metaphysical entities previously discarded.” Also, ‘ Units of animal or moral satisfaction, of utility and the like are as foreign to positive science as a unit of dormative faculty would be.” [See Part I, Ch. I]. Also:§ “ Mathematics can indeed formulate ratios of exchange when doy * Quart. Jour. Ke., April. 91, p. 327. + Ency. Brit., 9th ed. Vol. xix, p. 399. { Ency. Brit., 9th ed. Vol. xix, p. 386. § Hist. Pol. Econ., New York, 1888, p. 182. Wee Irving Fisher—Mathematical investigations they have once been observed; but it cannot by any process of its own determine those ratios; for quantitative conclusions imply quan- titative premises and these are wanting. There is then no future for this kind of study, and it is only waste of intellectual power to pursue it.” [What a “therefore”! Why require mathematics to predict prices in order to be admitted into good society with the his- torical school? No mathematical economist has ever tried to do this. Dr. Ingram does not discuss what mathematics has done or attempted, but complains loudly that it cannot do everything and therefore has no future. | Rabberio* in speaking of Prof. Pantaleoni’s Principi di Economia Pura says: “As a monument of abstract logic, it bears fresh witness to the unusual qualities of the author’s genius; but it is based on a method which, frankly speaking, I consider dangerous. In the face of pressing practical problems of every kind, both in production and in distribution, economic thought is drawn off into the field of bar- ren abstractions. Under an attractive semblance of mathematical accuracy these abstractions conceal much that is really false; for they do not correspond in the least to the complexity of concrete facts. While they distract the student with an imaginary logical construction, they lessen his interest in that positive study which tells us what is, whereas logic by itself gives us only what is thought. Thus in last result they deprive economic science of that great practical importance which it should have in society.” [I am not acquainted with Prof. Pantaleoni’s book nor with any Italian writer. As to the criticism on mathematical method, however, I may say that experience in other sciences shows that “in face of many practical problems” it is wisest to ‘‘draw off thought ” for a time to pure theory. Before solving the problems of cannon pro- jectiles it is best to solve the problem of projectiles in general. Before an engineer is fit to build the Brooklyn bridge or to pro- nounce on it after it is built it is necessary to study mathematics, mechanics, the theory of stress and of the natural curve of a hang- ing rope, etc., etc. So also before applying political economy to railway rates, to the problems of trusts, to the explanation of some current crisis, it is best to develop the theory of pol. econ. in general. When these special “practical problems” are examined the mathe- matical instrument will, I believe, often be the one to get the best results. Iam far from denying, however, that some mathematical econo- mists have exhibited a “false accuracy.” It has been due to * Economics in Italy, Prof. Ugo Rabberio, Pol. Sci. Quart., Sept. 1891, p. 462. in the theory of value and prices. 119 making special assumptions not with the purpose of facilitating economic investigation but for permitting algebraic transformation. A writer who intentionally parades his mathematics really does the cause of mathematical economics much harm. I venture to think that Launhardt’s Volkswirtschaftslehre which contains some excel- lent things would have exhibited these excellencies better if the author had contented himself with solving problems in all their generality]. § 9. I cannot refrain from venturing an opinion the application of which may not apply to all of those writers just quoted but which certainly applies to many: Mathematics is looked upon as an intruder by those students of economics who have not had the mathematical education to understand and make use of them, and who are unwilling to believe that others enjoy a point of view unattainable by themselves. A friend of mine much interested in economics asked me what was the service of mathematics in the subject. On hearing my reply ke said: “Well, I don’t like to admit that I can’t understand economics as well as those who have studied higher mathematics.” Thus part at least of the opposition to mathematical method is a mere incident to its novelty. It must be remembered that the character of economists is itself a variable and from generation to generation those choose or reject the pursuit of economics according to what it is at the time of choice. It may not be rash to expect that the next generation of the theoretical (as distinct from histori- cal) economists will have fitted themselves by mathematical training for this mode of treating their theme, and that they will be such men as by natural aptitude can so fit themselves. S$ 10. The effort of the economist is to see, to picture the interplay of economic elements. The more clearly cut these elements appear in his vision, the better; the more elements he can grasp and hold in mind at once, the better. The economic world is a misty region. The first explorers used unaided vision. Mathematics is the lantern by which what before was dimly visible now looms up in firm, bold outlines. The old phantasmagoria disappear. We see better. We also see further. 120 Irving Fisher— Mathematical investigations APPENDIX IV. BIBLIOGRAPHY OF MATHEMATICO-ECONOMIC WRITINGS, He A bibliography of mathematico-economic writings was constructed by Jevons and extended* by his wife up to 1888. This list con- tains a number of works mathematical in tone only. I have selected out of the whole number (196), those 50 which are either undoubt- edly mathematical or are closely associated logically or historically with the mathematical method. ‘Thus Menger, though his writings are not explicitly mathematical, is included for he founded the ** Austrian School” which has ever since been allied with the mathe- matical method. Jn this selected list the references are much abbre- viated and only the first edition of each work is cited. The second list is intended to be an extension of that of Jevons up to the present date. I shall be indebted for information as to inac- curacies and omissions. A star has been placed opposite those writ- ings in which mathematical method is employed only occasionally or whose mathematical character is not explicitly expressed in symbols or diagrams. In the case of Italian and Danish writings, with which I am wholly unacquainted and in the case of a large number of others - which I have not been able to see and examine, I have been guided by book notices or the wording of the title. The list in Jevons’ appendix and the second list here given may be taken as a reasonably complete bibliography of mathematico- economic writings in the broadest sense, while the unstarred writings in the abridged list of Jevons here quoted together with the un- starred writings in the second list represent the economic literature which is strictly and avowedly mathematical. The distinction between these two classes is tolerably well marked. S 2. SELECTED FROM JEVONS. 1711 Crva—De re nummaria quoad fieri potuit geometrice Nactata. 1765 Brccarta—Tentativo analitico sui contrabandi. Etc. 1801 Canarp—Principes d’economie politique. 1824. THompson—Instrument of Exchange. 1826 von THtnen—Der isolirte Staat, etc. > * Pol. Econ., Appendix I to third edition, 1888. 1829 1838 1838 1840 1840 1844 1844 1847 1849 1850 1850 1854 1856 1863 1864 1867 1870 1871 1871* 1872 1873 1874 1874 1874* 1875* 1875% 1876 1876 1876 1878* 1879 1881 1881 1883 1884 1885 1886 1886* 1886" 1886 1886 1887 1887 1887 1888 in the theory of value and prices. 127 WHEWELL— Mathematical Exposition of some Doctrines of Pol. Econ. Cournot—Recherches sur les principes math. de la théorie des richesses. TozeR—Math. Investigation of the Effect of Machinery, etc. ANONYMOUS—On Currency. TozER—On the Effect of the Non-Residence of Landlords, etc. Dupvuit—De la mesure de l’utilité des travaux publics. Hacrn—Die Nothwendigkeit der Handelsfreiheit, etc. Borpas—De la mesure de l’utilité des travaux publics. Dupvuir—De l’influence des péages sur l’utilité des voies de communication, LARDNER—Railway Economy (chapter xiii). | W#HEWELL—Mathematical Exposition of Certain Doctrines of Pol. Econ. Goss—en—Entwickelung der Gesetze des menschlichen Verkehrs, ete. BennER—Théorie mathématique de l’economie politique. Manco.tpt—Grundriss der Volkswirthschaftslehre. Fauveau—Considérations math. sur la théorie de l’ impot. Favuveau—Considérations math. sur la théorie de la valeur. JENKIN—The Graphic Representation of the laws of Sup. and Demand, ete. JEvons—The Theory of Political Economy. Mencer—Grundsitze der Volkswirthschaftslehre. LaunHarpt—Kommerzielle Trassirung der Verkehrswege. PocuEtT—Géométrie des jeux de Bourse. W axLras—Principe d’une théorie math. de l’échange. WaLras—Eléments d’économie politique pure. Lrerort—De V’application des math. 4 étude de l’econ. pol. Darwin—The Theory of Exchange Value. Boccarpo—Dell’ applicazione dei metodi quantitativi, ete. W aLras—Equations de l’échange, etc. WaALRAS—Equations de la capitalisation. WESTERGAARD—Den moralske Formue og det moralske Haab. Wetsz—Die mathematische Methode in der Nationalékonomie. Watras—Théorie math. du billet de banque. Epcrwortu—Mathematical Psychics. Watras—Théorie math. du bimétallisme. Launnarpt—Wirthschaftliche Fragen des Kisenbahnwesens. WiEsSER—Hauptgesetze des wirthschaftlichen Werthes. Launnarpt—Math. Beegriindung der Volkswirthshaftslehre. GrossmMan—Die Math. im Dienste der Nationalédkonomie. I Lieferung. Nerwcomp—Principles of Political Economy. Boum-BawERK—Theorie des wirtschaftlichen Gititerwerts. ANTONELLI—Teoria math. della economica politica. Grossman—Die Math. im Dienste der Nationalékonomie. II Lieferung. Van Dorsten—Math. onderzoekingen op het gebied Staathuishoudkunde. WeEsterRGAARD—Math. i Nationalékonomiens Tjeneste. PantaLEont—Teoria della pressione tributaria, etc. WickstEED—The Alpbabet of Economic Science. TRANS. Conn. ACAD., VOL. IX. 9 JuLY, 189°. 122 Irving Fisher—Mathematical investigations § 3. EXTENSION OF JEVONS’ BIBLIOGRAPHY. 1867 WurrsteIn—Mathem. Statistik. Hanover. 1882 PantTaLEeont (M.)—La Traslazione dei Tributi. Rome. Paolini. 1884 ScHROEDER (E. A.)}—Das Unternehmen und der Unternehmergewinn vom historischen, theoretischen und praktischen Standpunkte. Wien. 92 pp. 1884* Sax (E.)—Das Wesen und die Aufgabe der Nationalékcnomie. 1887* Sax (E.)—Grundlegung der theoretischen Staatswithschaft. 1887 Prcarp (A.)—Traité des Chemins de fer. 4 vols. Paris: Rothschild. 1888 EpcGeworts (F. Y.)}—New method of measuring variations in general prices. Jour. Stat. Soc. London, p. 347. 1888* Sax (E.)—Die neusten Fortschritte der national6konomischen Theorie. Vortrag gehalten in Dresden miarz. Leipzig: Duncker & Humblot. 8vo. 38 pp. 1888* MenGER (C.)—Contribution a la théorie du Capital. [Trans. from Jahrb. fiir Nat. Oek., by C. Secrétan.] Rev. d’Econ. Pol., Dec. ’88. 1888* SaLERNO (Ricca)—Manuale di Scienza delle Finanze. Florence. Barbera. 1888 Hap.ry (A. T.)—Railroad Transportation, its History and its Laws. New York and London. 269 pp. [Appendix IT. ] 1888 Gossen (H. F.)—Entwickelung der Gesetze des menschichen Verkehrs. [New edition.] Berlin: Prager. 8vo. 286 pp. 1888* MrncGeEr (C.)—Zur Theorie des Kapitals. Jahrb. Nat. Oek., 17 Heft 1. 1889 PantTaLeoni (M.)—Principi di Economia Pura. Florence. Barbera. 1889 AvusPITz unD LizrBEN—Untersuchungen iiber die Theorie des Preises. Leipzig: Duncker & Huinblot. 535 pp. 1889* ZucKERKANDL (R.)}—Zur Theorie des Preises mit besonderer Beriick- sichtigung der geschichtlichen entwicklung der Lehre. Leipzig. 548 pp. 1889* WHESER (F. von)—Der natiirliche Werth. Wien. 287 pp. 1889* B6umM-BAWERK (E.)—Kapital und Kapitalzins. Translated into English by Wm. Smart. 1890. London and New York: Macmillan. 1889* Leur (J.)—Wert, Grenzwert, und Preise. Jahrb. Nat. Oek., 19 Heft 1. 1889 Suprnc (C.)—La Teoria del Valore e la Legge del minimo mezzo. Giorn. degli Econ. Aug. ’89. 1889 Watras (L.)—Théoreme de l’Utilité maxima des Capitaux Neufs. Rev. d’Econ. Polit., June 89. 1889* MactEop (H. D.)—The Theory of Credit. Vol. I. London: Longmans & Co. 8vo. 342 pp. 1889 Str. Marc (H.)—Les Procédés d’Analyse Graphique & l’Exposition Uni- verselle. Rev. d’Econ. Polit., Aug. ’89. 1889 Vireo (F.)—La Statistica Storica e Mathematica. Giorn. degli Econ., Aug. 89, concluded Oct. ’89. 1889* Hearn (W. E.)—Plutology ; or, The Theory of the Efforts to satisfy Hu- man Wants. [New edition.] Melbourne: Robertson. S8vo. 486 pp. 1889* KomMaRzYNSKI (J.)—Der Werth in der isolirten Wirthschaft. Wien. Manz. 8vo. 105 pp. 1889 Rossi (G.)}—La Mathematica applicata alla Teoria della Ricchezza Sociale : Studi Bibliografici. Storici, e Critici. Vol. I, fase. 1. Reggio Emilia Artegianelli. S8vo. 103 pp., 4 charts. asl in the theory of value and prices. 123 1889* BoumM-BaweEeRK (EK. von)—Une Nouvelle Théorie sur le Capital. Rev. Econ. Pol., April, 1889. 1889* Boum-Bawerxk (E. von)—Kapital und Kapitalzins. Zweite Abteilung: Positive Theorie des Kapitals. Innsbriick. 8vo. 1889* Cuark (J. B.)—Possibility of a Scientific law of Wages. [Publ. of Am. Hcon, Assoc.] Baltimore. 8vo. 82 pp. x 1889 WicksTEED (P. H.)—On certain Passages in Jevons’ ‘‘ Theory of Political Keonomy.” Quart. Jour. Econ., April, ’89, p. 2938. 1889 EpGrwortsH (F. Y.)—On the application of Mathematics to Pol. Econ. Journ. Stat. Soc. London, Dec. S89. 1890* DierzEL—Die Klassische Werttheorie und die Theorie vom Grenznutzen. Conrad’s Jahrbuch N. F. Band 20. pp..561-606. 1890* Macteop (H. D.)—The Theory of Credit. Vol. I], Part I. London: Longmans. 8vo. 1890 MarsHaty (A.)—Principles of Economics. Vol. 1, 1st ed. London: Macmillan. 770 pp. [Mathematical Footnotes and Appendix. | 1890 PantraLeont (M.)—Principi di Economia Pura. Florence: Barbera. 16mo. O46 pp. 1890 JuriscH (K. W.)—Mathematische Diskussion des Kutwickelungsgesetzes der Werterzengung durch industrielle Produktionsgruppen. Véiertelj. f. Volksw. 27 Band 3, 1. Second paper, same title, 27 Band 3, 2. 1890 Vauruier (L. L.)—Quelques Considérations Elémentaires sur les Construc- tions Graphiques et leur Emploi en Statistique. Jowrn. de la Soc. Sta- Gst., June, 90: 1890* Auspirz (R.)—Die klassische Werttheorie und die Lehre vom Grenznutzen. Jahrb. Nat. Oek. 21 Heft 3; reply to Dietzel, same journal, 20 Heft 6. 1890* ZucKERKANDLE (R.)—Die klassische Werttheorie und die Theorie vom Grenznutzen. Jahrb. Nat. Oek. 21 Heft 5. Reply to Dietzel. 1890 Coxson (G.)—Transports et Tarifs. Précis du Régime, Lois Economiques de la Détermination des Prix de Transport, Tarifs de Chemins de Fer, etc. Paris: Rothschild. 8vo. 479 pp. 1890 Launnarpr (W.)—Theorie der Tarifbildung der EHisenbahnen. Berlin: Springer. 8vo. 84 pp. 1890 WersterGaarpD (H.)—Die Grundztige der Theorie der Statistik. Jena: Fischer. 8vo. 286 pp. 1890 Cossa (E.)—Le Forme Naturali della Economia Sociale. Milan: Hoepli. 1890 MarsHauu (A.)—Principles of Economics. Vol. I, 2nd ed. London: Macmillan. 770 pp. [Mathematical Footnotes and Appendix. | 1891* Hogson (J. A.)—The law of the three rents. Quart. Jowr. Econ., April, 1891, p. 263. 1891* CLarKk (J. B.)—Distribution determined by a law of rent. Quart. Jour. Econ., April, 1891, p. 289. 1891 Ena@eworts (F. Y.)—Osservarioni sulla Teoria matematica dell’ Economia Politica con riguardo speciale ai Principi di Economia di Alfredo Mar- shall. Giorn. degli Econ., March, 91. 1891* Smarr (W.)—An Introduction to the Theory of Value on the lines of . Menger, Wieser and Bbhm-Bawerk. London and New York; Maemillan. 16mo, 88 pp. 124 Irving Fisher— Mathematical investigations, ete. 1891* Ciark (J. B.)—The statics and the dynamics of Distribution. Quart. Jour. Heon., Oct. 797, p. 111. 1891* Wieser (F.)—The Austrian School and the Theory of Value. Hconomic Journal, March, ’91. 1891* BoumM-Bawerk (E. von)—The Austrian Economist. Annals of Am. Acad. bf Pont. Set, , son. 91. 1891 EpGEeworts (F. Y.)—La Théorie Mathematique de l’Offre et de la Demande et le Cotit de Production. Rev. d’Econ. Polit., Jan. 91. 1892* BOuM-BAWERK (EK. von)—Wert, Kosten und Grenznutzen. Jahrbiicher fiir Nationalékonomie und Statistik, Dritte Folge, Dritter Band, Drittes Heft, pp. 321-378. 1892 BitGcram (H.)—Comments on the ‘‘ Positive Theory of Capital” [of Béhm-Bawerk]. Quart. Jour. Econ., Jan. ’92, pp. 190-206. 1892 Grossman (L.)—Die Mathematik in Dienste der National6konomie unter Beriicksichtigung auf die praktische Handhabung der Finanzwissenschaft und der Versicherungstechnik [schluss Lieferung]. Vienna. 1892* WueserR (F. von)—The Theory of Value. A reply to Prof. Macvane. Ge a , ct > i 0 high eet Se Grape ree ale eae —y "hae WA 5 ag ote ; 77° UY- AL ~ “ aa > ‘ Charles Davidson—English Mystery Plays. Orléans, XII Century. ARMIGER reversus salutat regem ; flexo genu dicat: Vivat rex in zeternum ! HERODES : Salvet te gratia mea ! ARMIGER : Adsunt nobis, Domine, tres viri ignoti, ab oriente venientes, novum natum quemdam regem queritantes. Tunc mittat HERODES oratores vel inter- pretes suos ad magos, dicens : Leti inquisitores, qui sunt inquirite reges, Affore quos nostris jam fama revolvit in oris. INTERPRETES ad Magos: Principis edictu, reges, preescire veni- mus Quo sit profectus hic vester et unde profectus ? MAGI : Regem quesitum, duce stella signifi- catum, Munere proviso, properamus eum ven- erando. ORATORES, reversi ad Herodem : Reges sunt Arabum ; cum trino munere natum Querunt infantem, quem monstrant sidera regem. HERODES, mittens Armigerum pro Magis: Ante venire jube, quo possim singula scire, Qui sunt? cur veniant ? more requirant ? quo nos ru- ARMIGER : Quo mandas citius, rex inclite, profi- cietur, ARMIGER ad Magos: Regia vos mandata vocant, non segniter ite. ARMIGER, adducens Magos ad Herodem: Kn Magi veniunt, et regem natum, stella duce, requirunt. TRANS. CONN. AOAD., Vou. IX. 14 181 1The normal form of this episode prob- ably differs from both of these. The num- ber of actors appears to have confused the authors. OCTOBER, 1892. io 8) Charles Davidson—English Mystery Plays. Rouen, XIV Century. Freising, X Century. REX ad internuntium : Ante venire jube, quo possim singula scire, qui sint, cur veniant, quo nos ru- more requirant ...iude...aut... dic... suavisex,.. REX ad Magum primum : Tu mihi responde stans primus in ordine, fari! Respondeat PRIMUS : Impero Chaldeis dominans rex omnibus illis. Ad Secundum : Tu, autem, unde es? Respondeat SECUNDUS : Tharsensis regio me rege . . . Zoroastro. Ad Tertium : Tute.... unde es? Respondeat TERTIUS : TRG isis Arabes, mihi parent usque fideles. REX: Regem, quem queritis, natum esse, quo signo didicistis ? Respondeant; ~- Tilum natum esse didicimus in oriente ; stella monstravit. REX: Ex quo illum regnare creditis, dicite nobis. Nune respondeant : Hune regnare fatentes, cum maysticis muneribus de terra longinqua adorare venimus. PRIMUws :! Auro regem. SECUNDUS: Thure deum. TERTIUS: Mirra mortalem. REX ad milites: Vos mei sinistri, accite disertos pagina scribas prophetica. Charles Davidson—English Mystery Plays. Orléans, XII Century. HERODES, ad Magos : Que sit causa vie? quivos? vel unde venitis ? Dicite. MAGI: Rex est causa vie; reges sumus ex Arabitis ; Hue querimus Regem regnantibus im- peritantem, Quem natum mundo lactat Judaica virgo. } HERODES : Regem quem queritis natum esse quo signo didicistis ? MAGI: Illum regnare fatentes, Cum mysticis muneribus De terra longinqua adorare venimus Ternum Deum venerantes tribus cum muneribus. Tunc ostendant munera ; PRIMUS! dicat: Auro regem. SECUNDUS : Thure Deum. TERTIUS : Myrrha mortalem. Tune HERODES imperat sinistris qui cum eo sedent in habitu jwvenili, ut addu- cant Scribas qui in diversorio parati sunt barbati : Vos, mei sinistri, Legisperitos ascite, Ut discant in prophetis Quod sentiant ex his. 183 1 At Limoges given in song with action while advancing through the choir, before the star has been seen. 184 Charles Davidson—English Mystery Plays. Rouen, XIV Century. Freising, X Century. MILES ad scribas : Vos legis periti,1 ad regem vocati, cum prophetarum libris properando venite. REX, ad scribas : O vos scribe, interrogati dicite, si quid de hoe puero ; scriptum habetis in libro. Respondeant SCRIBE : Vidimus domine in prophetarum libris, nasci Christum in Bethlehem civitate, David propheta sic vaticinante. Antiphona Bethlehem. REX’ ad scribas : ... finem spectat prudentia rerum ? Vadite cum vestris.. . estis! et projiciat librum. REX ad proceres : Consilium nobis, Proceres, date laudis, honoris... 4% ARMIGER? ad regem: Audi que facias, rex, audi pauca sed apta! mox des dona Magis, ne..... morari, ut noviter nato quem querunt rege reperto, rex, per te redeant ut te ipse scias quod adores. REX ad armigerum: Abdue externos citius, vasalle, tyrannos. ARMIGER ad magos: Regia vos mandata vocant. Charles Davidson—English Mystery Plays. 185 Orléans, XII Century. SINISTRI ad Scribas, et adducant eos cum libris prophetarum : Vos, legisperiti,’ 1 This incident seems to have been exactly Ad regem vocati, copied from one original. Cum prophetarum libris Properando venite. Postea HERODES interroget Scribas, dicens : O. vos, scribe, Interrogati dicite, Si quid de hoc puero Scriptum videritis in libro. Tune SCRIBZ diu revolvant librum, et tandem inventa quasi prophetica, dicant : Vidimus, Domine, etc., et ostendentes cum digito regiincredulo tradant librum : Vidimus, Domine, in prophetarum Lineis, nasci Christum In Bethleem Judz civitate, David propheta sic vaticinante. Chorus. Bethleem non est minima, etc. Tune HERODES,” visa prophetica, furore ‘ et : d prop iS 2 Here there is variation again. The wrath accensus, projiciat librum,; et FILIUS js the same, but the wording is different. ejus, audito tumultu, procedat pacifica- turus patrem, et stans salutet eum : Salve, pater inclite, Salve, rex egregie, Qui ubique imperas, Sceptra tenens regia. HERODES. Fili amantissime, 3 The soldier in F gives the advice upon Digne laudis munere, which the king acts ; in O he acts without advice. The introduction of the son seems Rendi f audis ee ee to have led the author astray. Tuo gerens nomine, Rex est natus fortior, Nobis [que] potentior ; Vereor ne solio Nos extrahet regio. Tune FILIUS despective loquens, afferat se ad vindictam, cdicens : Contra illum regulum, Contra natum parvulum, Jube, pater, filium Hoe inire preelium. Tunc demum dimittat HERODES Magos ut inquirant de puero, et coram eis spondeat regi nato, dicens : 186 Rouen, XIV Century. Dum autem processio navem Ecclesie in- trare ceeperit, corona ante crucem pendens in modum stelle accendatur, et MAGI stellam ostendentes, ad imaginem sancte Maric super altare crucis prius positam cantantes pergant : Kece stella in Oriente przevisa! iterum precedit nos lucida,’ ete. Hoc finito, Duo® de majori sede cum Dal- maticis et utraque altaris parte stantes, suaviter respondeant : Qui sunt hi qui, stella duce, nos adeun- tes inaudita ferunt ? MaAGI® dicunt : Nos sumus, quos cernitis, reges Tharsis et Arabum et Sabe, dona ferentes Christo regi nato, domino, quem, stella deducente, adorare venimus. dy Paes i. 7 ' Charles Davidson—English Mystery Plays. Freising, XX Century. Ite, et de puero diligenter investigate, et, invento, redeuntes mihi renunciate, ut ego veniens adorem eum. MAGI aspicientes stellam canant : Kece stella in oriente preevisa! iterum precedit nos lucida. MAGI? ad pastores: Pastores, dicite, quidam vidistis ? PASTORES : infantem vidimus pannis involutum. ANGELUS :5 Qui sunt hi qui stella duce, nos adeun- tes inaudita ferunt ? MAGI® respondeant: Nos sumus, quos cernitis, reges Tharsis et Arabum et Sabeze, dona ferentes Christo nato, regi domino, quem, stella duce, adorare venimus. # i. Charles Davidson—English Mystery Plays. Orléans, XII Century. Ite, et de puero diligenter investigate, Kt invento, redeuntes michi renunciate, Ut ego veniens adorem eum. Magis egredientibus, preecedat stella eos, que nondum in conspectu Herodis appa- ruit, quan IPSI sibi mutuo ostendentes, procedant. Qua visa Herodes et filius minentur cum gladiis. Kecce ! Iterum preecedit nos lucida. stella in oriente preevisa! Interim PASTORES, redeuntes a preesepe, veniant gaudentes et cantantes in eundo. O regem cceli! Ad quos MAGI :3 Quem vidistis ? PASTORES : Secundum quod dictum est nobis ab angelo de puero isto, invenimus infan- tem pannis involutum et positum in presepio, in medio duum animalium. Postea, pastoribus abeuntibus,* MAGI procedant post stellam usque ad pre- sepe, cantanies : Quz non prevalent propria magnitudine, Coelum, terra, atque maria lata capere, De virgineo natus utero, Ponitur in presepio, Sermo cecinit quem vatidicus : Stat simul bos et asinus. Sed oritur stella lucida Preebitum Domino obsequia, Quem Balaam ex Judaica ’ Nasciturum dixerat prosapia. Haec nostrorum oculos fulguranti lu- mine perstrinxit lucida, Kt nos ipsos provide ducens ad cuna- bula resplendens fulgida. Tunc OBSTETRICES® videntes, Magos allo- quantur : Qui sunt hii qui, stella duce, Nos adeuntes inaudita ferunt ? MAGI :° Nos sumus quos cernitis reges Tharsis et Arabum et Saba, Christo nato, regi Domino, quem, stella ducente, adorare venimus. dona ferentes 187 1 Here the procession and Herod episode closing, the three plays agree again. 2 Given in full by Du Méril, p. 155. 3 In O the shepherds have an appropriate introduction, in F none. 4 The introduction of this song is one of many proofs of the higher artistic finish of O. 5 Presbyters, evidently. 6 These lines would seem to argue a com mon dramatic origin. 188 Rouen, XIV Century. Tunc DUO DALMATICATI aperientes corti- © nam, dicant: Ecce, puer adest quem queritis. properate adorare, quia ipse est redemp- tio mundi. Jam Tunc procidentes REGES ad terram simul, salutent puerum, ita dicentes : Salve Princeps szeculorum. Tune UNUS a suo famulo aurum acci- piat, et dicat: Suscipe, rex, aurum. SECUNDUS Rex ita dicat, et offerat: Tolle thus, tu vere deus ! TERTIUS ita dicat, et offerat: Myrrham, signum sepulture. Interim fiant oblationes a clero et pop- ulo, et dividatur oblatio predictis Canonicis. Tune Magis orantibus, et quasi somno sopitis, QUIDAM PUER alba indutus, et quast Angelus, in pulpito® illis dicat hance antiphonam : Impleta sunt omnia quz Prophetice dicta sunt. Ite ab viam remeantes aliam ne delatores tanti regis puniendi eritis.* Hoe finito, CANTOR incipiat ad introitum Chori responsorium : Tria sunt munera.® Versus.’ Salutis nostre auctor. Ad Missam tres Reges Chorum regant, qui festive cantent : Kyrie Fons bonitatis, Alleluija. Sanctus, et Agnus. Officium: Ecce advenit. Charles Davidson—English Mystery Plays. Freising, X Century. OBSTETRICES : Ecce, puer adest quem queritis. Jam properate et orate quia ipse est redemp- tio mundi. Intrantes MAGI: Salve princeps seculorum. PRIMUS :? Suscipe, rex, aurum ! SECUNDUS : Tolle thus, tu vere deus! TERTIUS : Mirram, signum sepulture. ANGELUS ad prostratos magos: Impleta sunt omnia que prophetice dicta sunt. Ite, viam remeantes aliam, ne delatores tanti regis puniendi sitis. MAGI redeuntes antiphonam canant : O regem celi.® INTERNUNCIUS : In eternum vive domine ! Magi viam redierunt aliam. REX prosiliens : Incendium meum ruina extinguam !§ ARMIGER : Discerne,? domine, vindicare iram tuam et stricto mucrone querere jube pueros ; forte inter occisos occidetur et puer. REX gladium versans armigero reddit dicens : Armiger eximie, pueros fac ense pe- rire ! Charles Davidson—English Mystery Plays. Orléans, XII Century. OBSTETRICES ostendentes puerum : Kece, puer adest quem queritis. Jam properate et adorate, quia ipse est redemptio mundi. MAGI: Salve, rex seeculorum !! Salve, Deus Deorum ! Salve, salus mortuorum ! Tune procedentes MAGI, adorent Puerum et offerent. PRIMUS’ dicat : Suscipe, rex, aurum, regis signum. SECUNDUS : Suscipe myrrham, signum sepulture. TERTIUS : Suscipe thus, tu vere Deus. Istis factis, Magi incipiant dormire ibi ante prcesepe, donec ANGELUS desuper apparens, moneat in somnis ut redeant im regionem suam per aliam viam : Impleta sunt omnia‘ que prophetice scripta sunt. Ite viam remeantes aliam, nec delatores tanti regis puniendi eritis. MAGI evigilantes : Deo gratias! surgamus ergo, visione moniti angelica et, calle mutato, lateant Herodem que vidimus de puero. Tune MAGI abeuntes per aliam viam, non vidente Herode, cantent : O admirabile commercium ! Creator omnium. Tune venientes choro, cdicent : Gaudete, fratres, Christus nobis natus est, Deus homo factus est ! Tune CANTOR incipit : Te Deum, etc. 189 1 Another proof of artistic superiority in O. 2 An episode common in earler ritualistic plays, probably the invention of one author there. 3 A platform necessary as in Sens resur- rection play, p. 191. 4 Nove.—Then the three kings go through the side aisles out of the church and reénter by the left door into the choir. 5 Given in full by Du Méril, p. 152. § The closing of Fis evidently a reminis- cence of some play of the slaughter of the innocents. 7 The closing of R shows its affinity to the church service. 8 The Sallust tag which occurs also in ‘Interfectio Puerorum’ and in ‘ Ordo Rach- elis.’ Sallust is quoted also in the second journée of Saint Didier, and other classics elsewhere.—Julleville, Les Mystéres, vol. 1, p. 261. 9 Agrees with ‘Interfectio Puerorum.’ 190 Charles Davidson—English Mystery Plays. Here we close the second step of our investigation. We have seen the simple liturgy of the early church grow into an elaborate symbolism, which presented the life and work of Jesus so indirectly that the hearts of men were seldom touched by its teachings. This symbolism the new faith in a daily sacrifice revivified, and through it men’s hearts were again melted by the tragedy of the cross. In the Western church the desire to view concretely that which had touched the heart so profoundly, led to theatrical representation of the highest dramatic moments of the ritual. Two groups of such moments we have followed down : the first, until we found it pass- ing over to the vernacular, a sure sign of severance from the church offices ; the second, until single plays became but scenes or episodes in a more complicated drama, another sign of approaching inde-. pendence, since such plays could no longer hold their appropriate places in the church calendar.’ As these plays conform more and more to the popular taste, the sphere of their influence broadens, and their volume expands. Soon they will supplant the chanson de geste in the affections of the French, and the literati of a nation will express through them the mocking spirit of the Gaul, cutting with its satire the foibles of church and nation. It is no part of our present plan to seek in these later plays of the continent for testimony concerning medieval thoughts and manners, nor to examine, except cursorily, into their development or stage- setting. We are nearing the time when the English plays, evidently the outcome of long-established literary traditions, will present themselves fully developed, the most sympathetic exponent of the popular life of England in their day, and will offer to us, in the question of their literary ancestry and relationships what, to my mind, is the most interesting literary problem of the Middle Ages. Some knowledge, however, of the impress of the national spirit upon the cyclic plays of the continent, as shown in their form and in the manner of their presentation, will give increased significance to many features of the English plays. Accordingly, we turn again to the continental plays to learn how cycles were built up, with something of their content and dependence upon the devices for their presentation. It will be necessary, also, to consider the atti- tude of the church towards the plays while they remained within the church edifice, as well as after they had passed out from under clerical authority, and to notice in passing the organizations, liter- ary and otherwise, that made them their care. 1 It must be borne in mind that the simple plays of the church offices held their own until the Reformation, side by side with the expanded plays, and that sometimes clergy and laity were in active competition. Charles Davidson— English Mystery Plays. 191 2G THE STAGE AND THE PLAY IN FRANCE. In the Orleans and Freising plays we have seen one method of combination by which single and ritual plays formed a continued drama. A related development is connected with the evolution of the stage. In the Mont St. Michel and Sens resurrection plays we are informed that the angel had a station ‘super altare,’ ‘in pulpito.” In the ‘Officium Peregrinorum’ of Rouen are these words: ‘Et ita cantantes, ducant eum usque ad tabernaculum in medio navis ecclesiz, similitudinem castelli Emau preparatum.” In the Orleans play we read as a stage direction: ‘‘ Parato Herode et ceteris personis,” and in the Freising play :* “ Ascendat rex et sedeat in solio.” From these directions it is evident that all the actors took their assigned positions upon the stage at the opening of the play, and were conventionally absent when not performing their parts. Thus we read in the Orleans play:* “Tune Magi abeuntes per aliam viam, non vidente Herode;” so, in ‘Interfectio Puerorum,’* “ Joseph abiens, non vidente Herode.”’ The greater number of the actors did not move about the stage, but held fixed stations which were marked out upon the platform’— here a throne and palace hall, there the interior of a dwelling—while one or two actors passed from group to group, connecting through their action the different episodes, each of which embodied a single ritual play. These platforms were originally erected in the nave ; at Rouen,* “in medio navis ecclesiz.” Upon the platform the sta- tions,’ at first but slightly marked off, were afterwards defined by upright posts and cross-beams, the platform extending farther down the nave as the stations increased in number. ‘The plays seem often to require an unobstructed view across the stage, which would necessitate stations without sides, and as nearly as possible free from theatrical furniture and scenery.* How these primitive theatrical arrangements were used we learn from certain miracle and mystery plays. In the ‘Secundum Mirac- ulum Sancti Nicholai’ of the Orleans’ MS., there is one station, the house of Senex. ‘he action is as follows: 1 See p. 189. 2See p. 174, 3 See p. 189. 4 Wright. 5 Ebert, vol. 5, p. 68. 6’ Du Cange, Peregrinorum Officium. 7 Cp. Julleville, vol, 1, p. 388. 8 Mone, vol. 2, p. 158. ® Wright. 192 Charles Davidson—English Mystery Plays. The traveling students approach, converse, enter, dine, and go tosleep. Their death is planned and in some way, probably by dumb show, represented. St. Nicholas applies for admission, enters, in dining brings conviction to Senex by his words, prays that the students may be restored to life, and students and all join in the closing ‘Te Deum laudamus.’! In the ‘Quartum Miraculum Sancti Nicholai,’ of the same MS..,’ the stations have grown to three. On one side Rex Marmorinus sits enthroned, with armed guards ; on the other side Rex Getron with wife, son, and attendants ; in the centre stands the church of St. Nicholas. The action is carried on principally by messengers, is brief, and illustrates the use of fixed stations. The attendants salute Rex Marmorinus: ‘‘ Salve, princeps, salve, rex optime!” The king orders them to go forth, subjugate the world, and slay those resisting them. Getron with wife, son, and priests goes to the church as to some church festival. At the sight of the guards of Marmorinus, who are carrying out their lord’s mandates by an advance upon the church, Getron flees, leaving the boy behind, who is led in triumph by the soldiers to their king, to whom they announce: ‘‘ Quod jussisti, rex bone, feci- mus.’’ The king ascribes praise to Apollo and inquires of the boy his parentage. This ques- tion gives occasion for six quatrains, rhyming in couplets, in which the king affirms: ‘*Deus meus Apollo Deus est,’’ and the boy stoutly maintains: ‘‘ Deus tuus mendax et malus est.” Meanwhile, Getron’s wife, discovering her loss, returns to the church in search for her son, and now bursts forth into lamentations. Her attendants seek to comfort her, and she prays to Nicholas for the return of her son: ‘ Nichole, pater sanctissime, * * * * * * Fac ut meus redeat filius. It seems that she then returns home, although the stage direction is lacking, and her husband in four quatrains, rhyming in couplets, advises dependence upon Nicholas. They then arise, go to the church, and she again prays to St. Nicholas. Afterwards they return home, and the table is spread with bread and wine, of which the clergy and beggars partake,—possibly a hint to the lookers-on of the proper treatment of the stu- dent actors. About this time, Rex Marmorinus decides that he is hungry, and calls for food, which his attendants bring. Water also is brought; the king washes his hands, and eats. He is thirsty, and bids the son of Getron bring wine. The boy sighs heavily, the king demands the cause, and emphasizes the impossibility of rescue. Incidentally, the boy states that he has been prisoner a year. Now enters “ aliquis in similitudine Nicholai,” and leads the boy out of the king’s house. This, in spite of the attention centered upon the boy, no one discovers! A citizen of Getron’s dominions, who for unexplained reasons is in hostile territory, asks the lad’s name, and runs to Getron with the news: Gaude, Getron, nec fleas amplius; Extra fores stat tuus filius. Nicholai laudat magnalia, Cujus eum reduxit gratia. The mother hurries to her son, kisses him repeatedly and praises God and St. Nicholas. — The play ends, ‘* Chorus Omnis.” 1 The Salisbury Missal of 1534 has a picture of St. Nicholas, with the children rising from atub, where their members have been placed in pickle by the inn-keeper.—Hone’s Ancient Mysteries, p. 191. 2 Wright. Charles Davidson—LEinglish Mystery Plays. 193 Such plays make us conscious of the feeble beginnings from which dramatic art has arisen. This play reads like a children’s play for an improvised theater. The playwright succeeds fairly well in the capture, though the absurdity shown in the confidence of the soldiers that such a capture fulfilled such a command is appar- ently not evident to the author. The child is now in the king’s power; how to contrive a reasonable escape would seem a diffi- cult problem, but it does not trouble our dramatist. The boy is reintroduced through his conversation with the king, though this expedient would seem to make his unobserved escape a difficult matter. Not at all; an invisible St. Nicholas enters and sets the boy over the threshold, when he is free to go where he will: The infancy of art alone possesses such resources. Rex Marmorinus does not leave his seat during the play, and Rex Getron simply walks to the. church and back. Such simplicity of action requires a narrative play with no complexity of situation and but few lead- ing characters. To such requirements the Bible story readily adapts itself, as we shall now see in the condensed cyclic play found in the earliest extant Italian mystery play, and in one of the thir- teenth century in Germany. _ Dal THE STAGE AND THE PLAY IN ITALY. According to Klein the oldest Italian plays,’ known as “ Devo- zioni,” were designed, the first for Maundy Thursday, the second for Good Friday.” An analysis may be given as follows : The scene opens with the meal at the house of Lazarus six days before Easter.4 Christ enters as from Jerusalem. Mary, followed by Mary Magdalene and Martha, goes to meet Him, embraces Him, and conjures Him not to return, as the Jews will kilt him. Christ answers that He must do the will of His Father, but that she must not be sad, as He will tell her before He goes. They embrace again. At that the meal is served. Mary remains standing by Christ, saying continually, ‘*“My Son, My Son.” Inthe meal Lazarus takes part. At the close Christ calls Mary Mag- dalene to his side and informs her, while she kneels before Him, that He will go to-day 1 Dialect old and mixed; Palermo, as referred to by Klein, vol. 4, p. 165. Date in first half of fourteenth century.—Klein, vol. 4, p. 165. 2The only Italian representative of this step of development.—Ebert, vol. 5, p. 66. The play not in the liturgy but acted during service.—Ebert, vol. 5, p. 67. 3 The following abstract follows Klein 4, p. 157 ff., and Ebert in Jahrbuch ftir Roman- ische und Englische Literatur 5, p. 58 ff. 4 Wbert believes that there was a scaffold in the middle aisle, upon which Bethany and the Mount of Olives were located.—Kbert, vol. 5, p. 68; cp. p. 104. 194 Charles Davidson—English Mystery Plays. to Jerusalem, where He will suffer the death of the cross. He commends to her care His mother, who will beso deeply troubled. She herseif is to keep this news a secret until He is taken.t Mary Magdalene promises this, then kisses His feet. He, thereupon, retires and joins the rest of the company, but Mary Magdalene remains. Mary comes to Mary Magdalene and wishes to know what her Son has said, but Mary Magdalene declines to tell. Both, then, go to Christ. Mary would kneel to Him, but is prevented by Him. She asks why He is so sad, and shows great anxiety. Christ now tells her that for the redemption of the world He goes to His death. Mary swoons. Reviving, she bewails her fate. ‘Call me henceforth no more Mary, since I have lost Thee, my Son!” At the close of the conversation both fall inaswoon. They rise and embrace. Christ then goes to His seat.2 Mary kneels to Judas, begging him not to forsake Jesus, if He should fall into the hands of the people.2 Judas permits her to kneel, and replies ambiguously, “It is not necessary to entreat me more, as I know what I have to do.’’ She then kneels to Peter, who will not permit it, and vows that he will protect Christ against the world. Now go Mary, Mary Magdalene, Martha, and Lazarus to Christ, who embraces His mother, and offers to depart. Mary Magdalene prays that they may accompany Him to the gate of the city, to which Christ assents. They proceed together to Jerusalem. When they reach the gate, Mary declares that she is unwilling to leave her Son. He insists, but promises to send to her the angel Gabriel until John can come. Instantly the angel appears. Mary blesses her Son. Again they swoon. Jesus rises and ‘“‘steps through another door into Jerusalem.” Mary Magdalene and Martha raise and support Mary while she speaks to the people: O Figlio mio tanto amoroso O Figlio mio, due se’ tu andato ? * * * * ¥ x * Ditemi, o done, per amore de Dio, Dov’ é andato el Figlio mio ? She then turns to the angel, and entreats him to tell her all] the sorrows of Christ, that through the hearing she may find death. Mary Magdalene entreats Mary to return to Bethany and await John’s arrival. Mary beseeches the two sisters not to leave her, kneeling before them. They now return to Bethany, Mary speaking touching words to the women by the way.‘ All enter Bethany together.4 Forthwith, the scene of Christ’s prayer upon the Mount of Olives begins. He takes with Him Peter, James, and John, commands them to rest but watch, while He goes to pray. He kneels down, takes the cups in His hand, and, lifting up His eyes, prays. He returns to His followers, as in the Bible narrative. The second time, Christ puts a stone under His head and sleeps a little. After the third prayer an angel appears. Christ now wakens the three young men while, according to the stage direction, the armed men prepare to take Him prisoner. Christ goes to the other apostles. The thief-catchers with Judas come. *‘Quem quzritis?’’ and the following words of Christ are in Latin. Thearrest follows. Fastened by a thong, Christ is led away, while all His’ followers forsake Him. Here ends the play, but there is little break between this and the ‘Devozion’ of Good Friday which, beginning when the preacher comes to the passage where Pilate commands that Christ shall be scourged,’ is as follows : 1 Note that Jesus informs His mother soon after, and this requirement of secrecy seems to be satisfied by Mary Magdalene’s refusal to tell Mary. 2 The conventional exit. Cp. Julleville, vol. 1, p. 389. 3 One of the most artistic touches in the early dramas. 4 This consciousness of an audience appears elsewhere in this play, notably where John reminds the women of their sons. 5 A conventional exit. 6 The prostrations, kissing, blood, and cup are all liturgical traces.—Ebert, vol. 5, p. 70. 7 The lesson for the day was Chaps. 18 and 19 of John’s Gospel, the nineteenth begin- ning, ** Then Pilate took Jesus and scourged him.’’—Ebert, vol. 5, p. 67. 4 a Charles Davidson—English Mystery Plays. 195 Christ enters, stripped for the scourging, with His tormentors, who lead Him through the throng to the assigned spot where the column stands. John stands near Christ. The scourgers strike Him a little reverently, and listen to Christ’s words to John, who kneels before Him. He bids John call the Virgin. The men now strike and revile Christ and lead Him away. John asks the people where Mary is. He shows a black garment which he would carry to her, and seeks to rouse feeling by reminding the women of their own sons.1 Mary Magdalene now comes from the women’s side of the church to the stage? and steps before John while she bewails the sad news she has heard. John prays her to. accompany him to Mary, as he has not the heart to go-alone. Meanwhile Mary appears on the other side and they go to her. She laments when she sees the black garment. Mary Magdalene informs her of Christ’s captivity, and invites her to take the garment. Christ now appears bearing His cross, accompanied by a throng of women, to whom He teaches the words of the Bible. Meanwhile, He approaches the spot where Mary, Mary Magdalene, and John stand. Mary hastens to Him to embrace Him. The Jews drive her away. Christ drops His cross. Mary, bemoaning her fate, would take the cross,3 but the Jews drive her back. She falls fainting, and Christ passes on to Golgotha. Mary revives, seeks for her Son, inquires of the women, then goes with Mary Magda- lene and John to the place of execution. Now the preacher‘ explains the situation, and at a signal from him the Jews nail Christ to the cross and lift it up. Christ speaks, and prays for His enemies. Mary addresses the cross. ‘Bow down thy branches that thy Creator may find rest.” Inclina li toi rami, 0 croce alta, E dola [dona] reposo a lo tuo Creatore; Lo corpo precioso ja se spianta ; Lasa la tua forza e lo tuo vigore. Here again the preacher speaks, while the play pauses until he gives the sign, when Christ's speech with the robbers follows. Now the deadi arise. Three of these speak to Jesus, declaring that the souls in Hell expect Him, the Patriarchs and Prophets; one has also come to stand by Mary and serve her. The preacher finds it necessary to explain this. Again at the signal the play goes on. The Virgin prays Mary Magdalene to direct Christ’s attention to her, saying that He had spoken to the robbers, but not a word'to her.6 Mary Magdalene complies, and Christ commends His Mother to the care of John, who, kneeling and kissing Mary’s. feet, strives to comfort her. Mary laments, embraces the cross, and faints.7 The preacher takes up his discourse until Jesus cries out, ““My God, My God, why hast Thou forsaken me ?’’?’ Meanwhile, God says to His angels that they must strengthen His Son.8 The angels prostrate themselves, withdraw and descend.9 Theyexamine to see which is the Son. Meanwhile, the devil appears and approaches the cross upon the right side. One of the angels now descends fully, to receive the blood of Christ. Jesus thirsts. The Jews hand Him with jokes the vinegar mingled with gall, and He refuses to taste it. Mary bewails the malice of the Jews. Jesus exclaims, *‘ It is finished.”’ 1 See note 4, p. 194. 2 The stage is only one location. The actionis in different parts of the church.—Klein, vol. 4, p. 164. 3So Mary desires to take the cross in the Woodkirk Mysteries. The Towneley Mys- teries, p. 212. 4 Compare the preacher with the expositor in the Chester plays. 5 See cut, p. 199. 6 This complaint Mary addresses to Christ in the Coventry Mysteries, p. 322. 7 Note the author’s repeated recourse to this as an expedient for removing Mary tem- porarily from the action. 8 Ebert believes there was a scaffold in the choir which represented Heaven, that there was a Hell mouth anda post for scourging, but that some action took place in the aisles of the church.—Ebert, vol. 5, p. 68. *9 There must have been a stairway from Golgothato Heaven, or some means for paus- ing midway. a ee ~Se > 3 196 Charles Davidson—English Mystery Plays. The preacher againexplains. Ata sign the devil speaksin humble tone, trying to per- suade Christ to resign the world to him and save himself from death. Christ turns from him—‘'Thou wilt never see me rest until I have driven thee out.’? The devil speaks louder and more threateningly, promising him the lordship of the world. The lance thrust of Longinus! follows, his healing and gratitude. Jesus again speaks, com- mending His spirit to God, at which the devil throws himself upon the ground. Again the preacher speaks to the people. Mary and John address the people, bewailing Christ’s death. Joseph and Nicodemus enter, and take Christ from the eross. They ask of Mary permission to bury Him. She grants it, but will first embrace Him. This isa touching scene. Joseph stands at Christ’s head, Mary Magdalene at His feet. Mary kisses the limbs of Christ, His eyes, cheeks, mouth, sides, and feet, while she speaks touching words to the others or they to her. She shows John the lacerated hands. “ These are the holy hands wherewith He blessed all,” says John. The angel Gabriel appears to comfort Mary and advise her to permit the burial. Mary grants it with much lamentation. Joseph and Nicodemus carry Christ to the grave, while Mary, John, and Mary Magdalene go down the women’s aisle. Mary turns and shows the peo- ple the nails of the cross which she carries. Mary Magdalene exhorts them to resist the devil as Jesus had done. Here they enter Jerusalem and the play closes. XII. THE STAGE AND THE PLAY IN GERMANY. The following play is of the thirteenth century.” It shows an intermixture of Latin and German, similar to that observed in the Ludus de Nocte Pasche.* A comparison of the German and Ital- ian plays will serve to show how widely accepted were the same literary conventions among the writers of mysteries. The fixed stations, the continual presence of the actors, their supposed absence when sitting, the avoidance of any complexity of action, such as the advancement of plot through bye-play ; all are common charac- teristics. In development the German play is evidently the older, since it is still largely in Latin. It also lacks many of the dramatic features of the Italian, adhering closely to the Biblical narrative where the Italian artist strikes out a path of his own. The following abstract was made from Hoffmann’s edition of the play : Pilate and wife with soldiers take their places, then Herod with his soldiers, then the priests, the merchant and his wife, lastly Mary Magdalene. Afterwards, the *‘dominica persona’4 goes alone to the shore to call Peter and Andrew, and finds them fishing. The Lord says to them, ‘“ Follow me; 1 will make you fishers of men.” They reply, ‘** Lord, what thou wishest, we will do.” Then the Lord goes to Zaccheus, and a blind man meets him,—‘t Domine Iesu, fili David, miserere mei.” Jesus heals him. He then bids Zaccheus descend from the tree, as he would tarry at his house.5 Jesus passes on. 1 Longinus, the centurion, stood by the cross. The Gospel of Nicodemus. [II.] Longinus, the soldier, pierced Christ’s side.—The Gospel of Nicodemus. [1I.] 2 Hoffmann, vol. 2, p. 245. 3 See p. 149; also Hoffmann, vol. 2, p. 272. 4 Of. ‘Figura’ for the Almighty in ‘Adam.’ 5 He does not visit Zaccheus, however. 4 Charles Davidson—English Mystery Plays. — 197 Children strew branches and garments before him, singing Gloria and Laus. Now the Pharisee invites him to dinner. He accepts, and the Pharisee urges his servants to, hasten the preparations.1 Mary Magdalene? sings in Latin of the joys of this world, and seeks the merchant with her girl companions to buy for herself ointment. The merchant offers his wares in Latin. Mary sings a German love song with the chorus: Seht mich an, junge man, Lat mich eu gevallen. She now enters the house, and an angel announces to her that Jesus, the Nazarene, who forgives the sins of the people, is dining with Simon. She rises, and again sings her song of the delights of life,—‘* Mundi delectatio dulcis est et grata,” etc. A lover enters, whom Mary salutes. They converse, then Mary sings to the girls: Koufe wir die varwe da, Die uns machen schoene unde wolgeténe. She now appeals again to the merchant, who tenders his wares this time in German. The ointment purchased, she again enters the house, and the angel meets her as before, and disappears. She rises once more and repeats her song of the pleasures of the world, then falls asleep, and the angel appearing repeats his song of Jesus who for- gives sinners. Mary awakes and breaks into lamentation: ‘‘ Heu vita preeterita, vita plena malis,” ete. The angel appears and says: ‘“‘I declare unto you that there is joy in Heaven over one sinner that repenteth.”’ Mary scorns her secular garb and lays aside her robes, putting on a black garment. The lover and the devil retire.2 She goes again to the merchant, seeking precious ointment,4 which the merchant sells her for a talent of gold. The chorus sings: ‘‘ Accessit ad pedes.’’5 Mary now enters the house of Simon, and, weeping, approaches Jesus. Asshe anoints his feet she sings one stanza in Latin, followed by two in German. The Pharisee utters the well-known words, and Judas bewails the waste. Jesus declares the work a good one, addresses to Simon Peter his question about the debtors, asking which of those for- given would love the more. Peter replies, and Christ announces to Mary the forgive- ness of her sins. Mary, at this, retires lamenting : Awé, awé daz ich ie wart geborn. Jesus now departs to raise Lazarus and is met by the sisters,6 wailing for their brother. There is no expansion of the Biblical narrative. The incident closes with ‘*‘ Lazare, veni foras,’’? after which there is a chant by the clergy. Judas, meanwhile, hastens to the priests exclaiming, ‘“*O Pontifices, 0 viri magni consilii, lesum volo nobis tradere.”’ The bargain is struck, the sign is agreed upon, and the Jews follow Judas with swords and lights. 1 This requires four stations, beginning at the sea-shore. Peter and Andrew appar- ently follow Christ to the house of the Pharisee. He crosses the boundary and sits down. 2 Evidently rises from her place and advances to the merchant’s station. 3 It would seem that the lover has been sitting in the house since his first entrance, although he has said nothing. The devil is hard to account for. 4It is there supposed that some time has elapsed, and that her precious purchase is exhausted. 5 An evidence of intimate connection with the service. 6 Evidently Mary withdrew to join her sister in the Bethany station. Such examples of preparation for future situations are comparatively rare. 1 Lazarus probably did not appear upon the stage. The symbolic nature of this inci- dent illustrates the intimacy existing between the symbolism of the ritual and the realism of the play. In the six lines given to the scene, three are chanted by the clergy: it is practically a leaf of the church service slipped into the drama, and seems to have satisfied author and audience, although the motived utterance, ‘* Lazare, veni foras,”’ leads to no issue. TRANS. Conn. ACAD., VOL. IX. OCTOBER, 1892. 15 198 Charles Davidson—English Mystery Plays. Meanwhile, Jesus does ‘as is the custom at a feast.’1 Now he takes four disciples, ascends Mount Olivet, and enacts this scene in the words of the Biblical narrative. The Jews appear, and Jesus asks: “Quem queritis?’? They reply: ‘“‘Jesum Nazarenum.” Jesus replies: ‘‘ Ego sum,”’ and the crowd falls back. When he is taken, ali the apostles except Peter and Judas leave him. Peter forthwith denies him twice. The priests chant appropriate Bible verses. Jesus is led to Pilate, then to Herod who clothes him in white and returns him to Pilate. The action passes on in the fewest words possible till Jesus is led out for scourging,? when he is clad in purple and crowned with thorns. Pilate says: ‘‘Ecce homo.” The Jews cry: ‘‘Crucifige, crucifige eum.” The dialogue in short Bible verses continues until Pilate washes his hands, and Jesus is led away for erucifixion. Now Judas comes penitent, weeping, to the priests, who reject him. The devil ap- pears and persuades him to hang himself. The women follow Jesus,4 weeping. Heis placed upon the cross and the title affixed: ““Tesus Nazarenus Rex Iudzorum.’’ The Jews object, and Pilate answers: *‘ Quod scripsi scripsi.”’ The Virgin now enters with John and, lamenting, beholds the crucified. ‘‘ Awé, awé mich hiut unde immer mé” begins the lamentation of Mary, so similar to those of earlier date.5 This is continued in Latin, as, smiting her breast, she addresses the weep- ing women. She concludes by embracing John and speaking eight lines while holding him in her arms, concluding: Immolemus intimas Lacrimorum victimas Christo morienti. The direction here reads: ‘‘ Et per horam quiescat sedendo,’’6 after which she again rises, addresses John, and John replies. Jesus now says, while John supports the Virgin: **Mulier, ecce filius tuus,’’ and to John: ‘‘ Ecce mater tua.” i John and Mary withdraw from the cross.7 Jesus thirsts, tastes the vinegar and cries, “Tt is finished.’’ Longinus appears and pierces Christ’s side. Jesus cries: ‘ &li, Eli, lamma sabacthani,’’ and expires. Longinus gives his testimony in Latin and German. Vere filius Dei erat iste. Dirre is des waren Gotes sun, adding, Er hat zeichen an mir getan Wan ich min sehen wider h4n,8 while the Jews tarry to see whether Elias will come to help him, and one closes the scene with: ‘‘ Alios salvos fecit, se ipsum non potest salvum facere.”’ An epilogue of sixteen German verses closes the play; of these Joseph of Arimathea sings the first eight, and Pilate concludes the song. 1 Jesus must have returned to the Jerusalem station, adjoining which Mount Olivet was probably situated. This bye-play during the performance of a leading action is very rare in these early plays. 2 Since the mocking, though brief, is represented, it is probable that the scourging was also. 3 Compare with the appearance of the devil in the Italian play, p. 195. 4 In the former play Jesus teaches the women, p. 195. 5 See p. 145. 6 This must mean that the play is suspended for a sermon, the priest explaining at once the whole mystery instead of interposing his remarks as in the Italian play. 7 Does Mary withdraw because of the improbability of her silence during agonizing moments while others carry on the play? In the Italian play she swoons at such moments. 8 Compare the Italian play, p. 196. Charles Davidson—English Mystery Plays. ‘199 XIII. THE OUT-DOOR STAGE. If we compare the above abstracts of action with the following sketch of the open-air stage of the sixteenth century, as found attached to a MS. of the fifteenth century Easter Play,’ we shall obtain an idea of the use of fixed stations in the developed cycle, sufficiently clear for our purpose. A, B, C. The three divisions of the the stage.2 1. The first door. 11. The house of Annas. 2. Hell. 12. The house of the Last Supper. 3. The Garden of Gethsemane. 13. The third door. 4, Mount Olivet. 14, 15, 16,17. Graves from which the dead 5. The second door. arise. 6. Herod’s palace. 18, 19. Crosses of the two thieves. 7. Pilate’s palace. 20. Cross of Christ. 8. The pillar of scourging. 21. The Holy Sepulcher. 9. The pillar upon which stands the cock. 22. Heaven. 10. The house of Caiaphas. The three divisions of the stage correspond to the three divisions of the church: the nave, choir, and sanctuary.* The action begins in the nave, and passes, station by station, through the choir into the sanctuary. The distribution of stations bears some relation to the sanctity of the division. The cross and Heaven are in the sanctuary, Hell isin the nave. This remoteness of position was not objectionable for the Inferno, as it was customary for the devils to make excursions about the stage and even among the audience. This we see in the Norman play of Adam, York Plays, etc. They even acted as police within boundaries,‘ and the unlucky wight who crossed the line became the prey of the devils, to the amusement of the audience. In regard to the genesis of the out-door stage for the mystery plays, I cannot agree with Mone,* who derives the scaffold from the i Mone, vol. 2, p. 156. 2Cp. Julleville, vol. 1, p. 392. 3 Cp. Julleville, vol. 1, p. 398. At Rouen in 1474, paradise was in the east or sanctuary end of the church. 4 Mone, vol. 2, p. 129. 5 Mone, vol. 2, p. 159. 200 Charles Davidson—fnglish Mystery Plays. remains of the Roman amphitheater, then existing in France. This theory, as it seems to me, is founded upon two. misconceptions : first, that the German plays were later than the French and bor- rowed from them ; but we have found them of about the same date, and, while slower of development, not by any means servile imita- tions of the French ; secondly, that the French plays were survivals of the Roman, a favorite theory with the French, but now rejected by their most careful writers, except so far as it applies to the early, unformed comedy. On the contrary, the form of the stage, its traditions and customs, point directly to the platform within the church. When the plays were taken out of the church, whether , because of clerical prohibition, into which we will look shortly, or because space was too limited for the crowds and the platform, or for other reasons, the stage was simply transplanted, and suffered change no more rapidly than the developing plays demanded. I am aware that we cannot fully solve the problem of seating such vast audiences’ so that all could see and hear. It is very possible that all the audience did not have favorable positions. Such conditions have existed at anniversary meetings and foot-ball games without seriously diminishing the audience. Yet a familiar play, upon a platform erected in a public square surrounded by houses whose roofs’ and windows would furnish a favorable outlook for many, could be seen satisfactorily by thousands. * This stationary platform, often of great size and sometimes of three stories,* with Hell beneath and Heaven above, and crowded with persons® and paraphernalia, was a distinctive feature of the continental play. To this the English cycles presented a marked contrast. The gild plays of England changed the station of the continental stage into a movable pageant, or platform, and instead of calling the population of a city to the stage, rolled the platform through the streets in orderly succession from audience to audience. 1 At Reims in 1490, it is said, there were 16,000 spectators.—Julleville, vol. 1, p. 409. 2 A portion of a house, upon whose roof many people sat as spectators, fell, killing 33 men.—Hofiman, 2, p. 248, referring to Flégel, Geschichte der komischen Literatur, vol. 4, Th. S. 250. 3 At Lyons in 1540 one Jean Neyron erected a vast theatre with balconies and boxes, where plays of the Old and New Testaments were acted for two or three years on feast- days and Sundays.—Julleville, vol. 1, p. 357. The French, in the 15th and 16th centuries, built boxes for the aristocratic spectators and placed benches for others, at great expense, which was partly met by entrance fees.—Julleville, vol. 1, pp. 401, 405. 4 Not immediately over each other necessarily, but with Hell covered over at one end of the platform, and Heaven rising at the other end.—Julleville, vol. 1, p. 388. 5 A Resurrection Play in the library of Lucerne, MS. date 1494, employed 40 persons; one of Frankfort, date 1498, 265 persons; one of Seurre on the Sadéne, date 1496, 163 persons.— Mone, vol. 2, p. 123. Charles Davidson—Einglish Mystery Plays. 201 Of this movable stage I have found no trace upon the continent, except in the Jew plays of Italy, where, on wagon-stages drawn by oxen, the Jew in effigy was mocked, tormented, and finally burned,’ and in the representations upon chariots, given by the Basoche in the provinees, but unknown in Paris.’ XIV. EVIDENCES OF EARLY ITALIAN AND SPANISH PLAYS. Such aid as the continental plays, prior to the date of the extant English plays, can give towards the study of the English cycles has, according to my knowledge, been presented ; not in its detail, which _will serve better as illustration when taken with the English plays, but in the general outline, as showing the trend of development in the various stages of advancement and severance from the church ritual. Our reliance has been almost entirely upon the French and German plays. The notices of the Italian drama, prior to the “ Devozioni” that we have outlined, are quickly given. We hear of Italian plays first in 1244, the records stating that on that date a Passion and Resurrection Play was presented.* On Whit- suntide and the two following days, in 1238, according to the chron- ile of Julianus, Canon of Cividale, the Passion, Resurrection, Ascension, and Outpouring of the Holy Spirit’ were acted,’ form- ing a cycle of no mean proportions. But already other portions of the Bible narrative, which the church linked with the Advent plays as prophetic or explanatory of Christ’s coming, were claiming atten- tion, and six years later, according to the same authority, the Creation of Adam and Eve, the Annunciation, and Birth were played. Thus we find in Italy as early as 1306, in two cycles, probably written in Latin, and surely played under the direction or patronage of the highest clergy, the principal scenes of the future world-cycle that should extend from the Creation of the Angels to the Last Judgment. It is evident that the mystery plays must have arisen in Italy as in France, although but scanty remains of the liturgical plays are extant ; otherwise cyclic dramas so early as 1298 would be impossible of explanation. That they also had a recognized standing in the 1 Klein, vol. 4, p. 239. 2 Julleville, Les Comédiens, p. 133. 3 Ebert, vol. 5, p. 51. 4 Rvidently the Passion, Resurrection, Ascension, were considered as forming a fitting introduction to the Giving of the Holy Spirit of which the celebration was a com- memoration. 5 Ebert, vol. 5, p. 54. 202 Charles Davidson— English Mystery Plays. Spanish church as early as the thirteenth century is proved by the code of Alfonso the Tenth, of about 1260, which, while forbidding buffoonery plays, expressly states that ‘‘ Exhibitions there be, that clergymen may make, such as that of the birth of our Lord Jesus Christ, which shows how the angel came to the shepherds and how he told them that Jesus Christ was born, and, moreover, of bis appearance when the Three Kings came to visit him, and of his resurrection, which shows how he was crucified and rose the third day.”’* It adds, however, that these should be in the cities under the eye of the bishop or archbishop, not in the villages, nor to gain money thereby. But in Spain, through adverse circumstances, the development of the play was arrested, and when at last, in 1496, the early dramatic type for Spain was set by the Representaciones of Enzina,’ its direct inspiration was the Latin pastoral rather than the liturgical drama. In Italy, on the contrary, the influences were favorable. Com- mercial cities and wealthy patrons fostered literature. Monasteries and religious brotherhoods lavished wealth upon their Rappresenta- zioni, in. some respects, it must be confessed, to the injury of the plays, since their prodigal expenditure encouraged spectacular effects to the detriment of dramatic power. In brief, then, as we turn to the more specific problem of the English plays, we shall look to Spain for little assistance, to Italy for much ; but our most important aids will be found in Germany and France. ‘The French church plays furnished the models for the liturgical plays of England. The German plays will afford most instructive illustrations of the gradual intrusion of the Teutonic humor, so evident in the York and Woodkirk Plays. The universality of tradition in ecclesiastical literature gave rise to uniformity of treatment, and to the choice of similar, oftentimes of the same, literary motives, throughout the Roman church. The result may be monotonous as literature, but is invaluable as supplying a common starting point for national literatures. Upon this material the folk-spirit impressed its individuality. In the changing treat- ment and interpretation we detect the compelling influence of suc- cessive phases of thought. From this vast store-house, as from a quarry, the later generations have selected according to their needs and fashioned according to their taste. Here the students of mod- ern literature stand on common ground, and, viewing each several stream on its divergent course, can take note of each deflection due 1 Ticknor, vol. 1, p. 230. 2 Ticknor, vol. 1, p. 245. Charles Davidson—English Mystery Plays. 203 to a foreign cause, of each break or eddy that betokens the vexation, dubiety, or sudden illumination of the national life that lies at the bottom of, and is faithfully mirrored in, every literature worthy of the name. DEVE THE ATTITUDE OF THE CLERGY TOWARD THE PLAY. There still remain for our consideration, before we turn to England, the question of the divorce of the play from the church, and that of the status of the writers of these later plays, whose number is legion and whose prolixity’ appals the reader. The writers upon mystery plays agree with great unanimity that the plays were driven out of the churches by the disapproval of the higher clergy. It is stated that the introduction of lay actors, of the vernacular speech, and, above all, of burlesque and comic epi- sodes, scandalized the devout and provoked the prohibitions of popes and councils. It seems to me that the statement is true only in a much narrower sense. In the first place the plays did not leave the churches,’ but, in their less developed ritualistic form, remained a part of the service until the Reformation, and indeed in many countries or sections long after. The people delighted in pageants, masques, and shows of every kind, and the church did not yield its right to make the ser- vice attractive by tableau, puppet-show, and liturgical drama, although such plays received comment less often than the open-air plays. If, then, these plays survived in the churches, it must have been understood that the clerical prohibition was not directed against every species of mystery play, for no play within the church could have withstood for centuries the uniform opposition of the higher clergy. A glance at the attitude of the church toward plays before the mystery arose may aid us in understanding the situation, for the Roman church has usually kept in touch with its earlier tradi- tions. From the beginning of the third century, when Tertullian wrote his De Spectaculis, until the tenth century, the church held con- 1The history of Joseph in the ‘Viel Testament’ fills 7000 verses. Les Actes des Apotres, par Arnoul et Simon Greban, is given in 61,908 verses. The Mystére de Sainte Marguerite contains 10,000 verses. 2 Julleville, vol. 1, p. 78. 204 Charles Davidson—English Mystery Plays. sistently a condemnatory attitude. In 610, at the second council of Braga, so in 813, and again in 816, the councils spoke in no uncer- tain tone. They condemned absolutely the performances of the Histriones, Musici, and Mimi. These continued the traditions of the Roman stage, which had adopted the Greek drama of intrigue, and exhibited realistically what the earlier drama had but insinuated. The Fathers use clear language, and show unmistakably that they condemn these because they teach immorality and all manner of iniquity. Indeed, St. Augustine carefully makes a distinction be- tween the mimes and the comedies and tragedies, “ the latter class being at least free from filthy language, while their study is approved by elders in their scheme of liberal education.” The plays of the day pandered to the lowest imaginations of man. The classic drama had been relegated to the closet. The attitude of the broader- minded of the clergy—of those who did not consider all mental activity a sinful waste when not devoted to the offices of the church —was a reasonable one, distinguishing between lasciviousness of motive and salutary instruction and diversion by theatrical repre- sentation. We have seen’ that these licentious and comic plays survived until the time of the mystery, and that in France they formed a partial fusion with the sacred drama, giving rise to certain abnormal devel- opments, such as the Feast of the Ass. When, therefore, we find the church condemning certain plays and classes of actors under the names of histriones, joculatores, etc., it is necessary to infer that the same classes of play and actor are meant as aforetime, that their intrusion into the church is reprobated, and that mystery plays that have the taint within them are condemned. In the northern countries, as in France, the popular festivities of the national holidays continually sought expression within and about the church edifice. The church had made itself the centre of all communal interests, so with the quickening of the national spirit an expression was sought within the walls of the church home. But this brought irreverence and indecorum. The hobby-horse in Eng- land, the Schimmelreiter in Germany and other ‘ monstra lavarum ’* must keep out of the churches. This will explain various interdicts, and will serve to show how in the Middle Ages many a distinction 1 See p. 166. 2Ina MS. of the twelfth century at Strasburg is a drawing of a ‘ Ludus monstrorum ; it isa puppet-show. For the use of monsters, dragons, giants, etc. in religious proces- sions see Magnin, Histoire des Marionettes, pp. 61, 66, 213. Charles Davidson—English Mystery Plays. 205 was made of which we lose sight because our knowledge of their life is vague and general. ) The primary cause for the departure of the play from the church must, as it seems to me, be sought for elsewhere. We have studied the gradual expansion within the church of the mystery from the rudimentary play of the ritual to the independent but condensed eyclic play. Either development must stop here or the play must leave the church. The nave could not contain the necessary stage, nor the edifice the audience. Great numbers brought confusion and disorder. As a consequence the play moved out of the church into the churchyard, as shown in the Norman play of Adam, or into the open space about the monastery, as the direction ‘‘ad januas mon- asterii” of the Orleans play’ indicates. Other motives, as is usual, emphasized a tendency. The longer play led to the introduction of interludes and comic scenes to relieve the tedium. The development of devil-play put upon the fiends, through the traditional license of devilish behavior, the onus of enlivening the people when wearied by the continued play. Their language might be plain, and to us blasphemous, but it was not lascivious, and often contained a telling moral lesson. If we make allowance for the frank realism of the day, we must accept these plays as devout in nature, with the purpose to instruct the people and promote religion. Therefore the priests could encourage them, take part in them, or write them. They could be made the vehicle for sermons upon morals of which the instances, especially in Eng- lish plays, are many, and the papal benediction could be sought and given, as was, probably, the case with the Chester plays.” Furthermore, as the commercial spirit grew, the concourse of peo- ple at the church on sacred festal days offered facilities for barter, and booths became fairs. These festal days were also the days of the mystery play, and thus in England a connection between play and fair was established; not, as Warton maintains, that the play was fashioned to draw to the fair, but fair and play depended upon the church holy day. No one will doubt but that merchants and monks were shrewd enough to turn both to their advantage, when once the connection was established. 2m a 2 The text of prohibitions is given by D’Ancona, Origini del Teatro in Italia, vol. 1, p. 51. Hoffmann, vol. 2, pp. 241-4; Mone, vol. 2, pp. 367-8; Wright, p. XII, taken from Hoffman. The subject is discussed in Smith’s Dict. of Christian Ant. under Theatre, Actor, closing, however, before the rise of the mystery; Prynne’s Histrio-Mastrix is important for clues, but the author’s bias must be borne in mind. 206 Charles Davidson—English Mystery Plays. bi THEWPUyY: The agencies that took part in the composition and representation of the plays, after they ceased to be liturgical, are many. As has been shown, the church did not take an attitude of opposition unless certain objectionable features were present.’ Therefore monkish and other religious authors often wrote plays,’ and even acted léad- ing roles.* Again, monasteries often bore the burden of presentation. This was most frequently the case in Italy.* The religious brother- hoods® that spread over Catholic Europe as early as the twelfth century were oftentimes the promoters of the mystery play. IH, as seems probable, the craft gilds had a religious origin,® or assumed functions akin to those of religious brotherhoods, their connection with the play is easily understood. Through connection with the craft gilds the Meistersinger of Germany also shared in the develop- mental history of the drama. Indeed, Mone attributes the downfall of the mystery in Germany—though probably other agencies were more potent—to the prolixity of the Meistersinger plays, involving the introduction of so many actors and so much machinery that the unskilled craft players could not successfully present the action. In France, the Puy, that shadowy literary academy of the Middle Ages, was the immediate successor of the clergy.’ These Puys, semi-religious, semi-literary, were very numerous in the West and North of France. During the eleventh and twelfth centuries they were devoted to the service of the Virgin, and the members com- posed verse in her honor, but in the thirteenth century the influence of the lay members led to a broader literary life, and they cultivated zealously the religious drama. To some Puy the cycle of Notre Dame is attributed. In the Puy d’Arras, it is believed, the comedies of Adam de la Halle were played. These literary societies, about the fifteenth century, turned to other lines of literary activity, to morali- 1 In France, the play passed from the hands of the clergy in the twelfth century, but they were interested in it even in the fifteenth century.—Julleville, vol. 1, p. 347. 2 Julleville gives sketches of the eighteen known authors of French mystery plays. Among these there were nine religious or ecclesiastical authors, one lawyer, one notary, one physician, two valets de chambre, and one princess.—Les Mystéres, vol. 1, p. 314 ff. 3 Julleville, vol. 1, p. 367. 4 Ebert, vol. 5, p. 56. 5 Compagnia de Battuti of Treviso established 1261, Ebert, vol. 5, p.52. Compagnia del Gonfalone of Rome, Hase, p. 18, and Ebert, vol. 5, p. 53. Brethren of St. Luke of Ant- werp, artisans, Hase, p. 18. 6 Wilda, Gildenwesen im Mittelalter; also Gross, Gild-Merchant, p. 175. 7 Julleville, vol. 1, p. 115 ff. Charles Davidson— English Mystery Plays. 207 ties, farces, chansons, chants royaux, etc., the mystery falling to the various societies of confréres of which the Confréres de la Passion, of Paris, was the most famous. The sources and makers of the English plays will be the subject of the following chapters. XVII. PAGEANTRY IN MEDIAEVAL ENGLAND. As we enter the English field, we are confronted by a confusion of names that is bewildering. It would seem as though writers classed everything from a wrestling bout to a mystery as a play. Some do not hesitate to affirm that pageant and play were synonymous terms.’ So little regard has been paid to classification by such writers as Warton, Collier, and Ward, that the student cannot trust their conclusions, but must patiently gather his data for himself at first hand, and classify them as his conception of the medieval life of England becomes clearer. Gradually he will perceive that society in that day was a great stickler for tradition, that the custom found in a given city in one century probably existed there in but slightly altered form in the next century, that the customs in a given city were many and various, and were, within certain limits, sharply defined and kept separate. England was, indeed, Merrie England in those days, but she went about her amusements as though they were very serious, and usually very thirsty, business. It would take me too far from my theme to attempt to describe all the shows and plays that formed part of a city’s life for even one year. ‘The royal entries, the ridings of different social or religious gilds, the church processions in which the laity took part with their pageants of tableaux, their giants and monsters, the plays in the churches, by the craft gilds, at the entertainment of notables, the setting of the watch, the May-day festivities, etc., if faithfully por- trayed for a single city, would till a thesis, and give a new and valuable picture of civic life. If to this we add the direct literary influence of France upon the nobility and court society of England at a time when England and a large part of France were politically one, the subject of amusements in medixval England assumes vast proportions and becomes exceedingly intricate. As a result, writers upon this subject have failed to observe distinctions that were clear 1 Collier says that in 1502 pageant was only another name for a play. 208 Charles Davidson—English Mystery Plays. to the people of that day, and, still further misled by the frequent use of a single favorite name for different. species of amusements, have included in their discussion of mystery plays’ much that was but indirectly related to the matter in hand. It becomes, then, our task to attempt to disentangle some threads, and to segregate the plays of the craft gilds which were presented on movable scaffolds, or pageants, from the multitude of similar but not closely connected phenomena. I. The Puy and the Gild of Parish Clerks in London. We have noted in France the rise of the Puy, and its position as a cultivator of the mystery. England at this time contained many French ecclesiastics, and it would not be surprising if we found, where sufficient numbers were congregated, something similar to the French Puy on English soil. The following points of similarity seem to me to establish at least a strong presumption in favor of kinship between the Puy and the Gild of Parish Clerks in London. These are characteristics of the Puy: | 1. Date, the eleventh and twelfth centuries. 2. In the thirteenth century admitted lay members. 3. In the thirteenth century cultivated the mystery.’ 4. In the fifteenth century abandoned the mystery. 5. Was dedicated to the Virgin. 6. Object, the cultivation of literature, probably music also, and sometimes had philanthropic features. | 7. Most numerous in the West and North of France. 8. Often formed of parish clerks with or without lay members.* 9. Sometimes given to playing in honor of Saint Nicholas.* These are the characteristics of the Gild of Parish Clerks: 1. Incorporated as a gild by Henry III about 1240.° 2. Formed of ecclesiastics and lay members.’ ) 3. Object, the cultivation of church music and literature.* It had, also, philanthropic features.* 1 Collier, vol. 1, p. 52, considers what was probably a French shepherd play presented before the Queen, a French woman, a mystery play. 2 The Miracles de Notre Dame in the fourteenth century were the work of a Puy.— Julleville, vol. 1, p. 120. 3 The Puy de l’Assomption at Douai was formed about 1330 under the name of the Confrérie des Clercs Parisiens, called ‘clerecs parisiens’ because they spoke French.— Julleville, vol. 1, p. 119. 4 As the Saint Nicholas of Jean Bodel of the Puy d’Arras.—Julleville, La Comedie, p. 27. 5 Hone, p. 208. 6 Survey of London, ed. 1842, p. 64. Charles Davidson—Hnglish Mystery Plays. 209 Dedicated to Saint Nicholas.’ Played stationary plays at Skinner’s Well.’ In 1390 a three days’ play at Skinner’s Well.® In 1409 an eight days’ play at Skinner’s Well. Plays attended by most of the nobles and gentry of England. In 1554, feast at Guildhall College, with singing, playing, and the next day a great procession.” — a oe as Among the points to be considered are the following : I. The social or religious gilds of England are, in general, a century later in origin. ‘Thus, to cite a few illustrations— 1327. Fraternity of Corpus Christi in Skinner’s Company in London.*® 1348. The Gild of Corpus Christi at Coventry.° 1358. The Gild of Corpus Christi at Kingston-upon-Hull.’ 1355. The Gild of St. Mary at Beverly.° 1378. The Gild of St. Elene at Beverly.’ II. Their plays followed continental, not English, traditions. a. They were stationary plays as were all the plays of France. 6. They continued three and eight days, as did the continental plays. e. They were especially patronized by the nobility. One might venture to say that they were probably in the French language. Ill. The most marked discrepancy is that touching the patron saint. On the continent the Virgin seems to have been universally adopted, but the Puys later did not hesitate to write in honor of St. Nicholas, and, finally, after the opening of the fifteenth century, to cultivate profane poetry. Il. The Royal Entry. Nothing illustrates better the community of custom and literary standards among the nobility of England and France than the cere- monies observed when the King, or a high church or state official, entered a city. Indeed, we need not limit our study to England and France, as the same customs obtained in the Netherlands and in Scotland. Two elements of the royal entry concern us here, the pageants and the ‘riding.’ 1 Hone, p. 208. 2Survey of London, p. 7; given as 1391, p. 36. 8’ Survey of London, p. 143; given as 1490 by Hone, and 1407 by Pollard. 4Strype, vol. 3, chap. 138, p. 121; given as 1651 by Hone. 5 Herbert, vol. 2, p. 299. 6 English Gilds, p. 282. 7 English Gilds, p, 161. 8 English Gilds, p. 149. 9 English Gilds, p. 148. 210 Tharles Davidson—English Mystery Plays. These pageants were originally stationary, mute mysteries, placed upon stages of elaborate construction along the route which the King would take within the city. That these shows should be sta- tionary is reasonable, since in such case the King and his retinue need be detained no longer than they wished. That they should be mute, though usually indulging in pantomimic action, is more strange, but of the fact there is abundant evidence. It will aid us to understand the progress from pure mystery to allegory, if we con- sider somewhat at length these mute mysteries. 1313. A mute play of the history of Jesus Christ from Nativity to Passion was exhibited at Paris before Edward II and his wife Isabella.’ 1377. At the coronation of Richard II, a castle was erected by the goldsmiths on Cheapside. Of the pageants exhibited two are described by Herbert.” 1420, Dec. Ist. In the entry of Charles VI and Henry V into Paris, a mute mystery, consisting of stationary pageants represent- ing a connected story, the Passion of our Savior, was shown,—a bas-relief of living figures counterfeiting a bas-relief of stone.* 1424, Sept. 8th. The pageant at the entry of the Duke of Beau- fort into Paris was described by an eye-witness in these words : “Devant le Chastelet, avoit ung moult bel mystere du Vieil testa- ment, et du Nouvel, que les enffens de Paris firent ; et fut fait sans parler ne sans signer, comme ce feussent ymaiges enlevez contre ung mur.” | 1430. At the entry of Henry VI into London there were many stationary pageants, some with verses attached and some where per- sonages spoke.* We have passed over a century, recording here and there one of the royal entries. All are alike, stationary, mute, and representa- tions of some portion of the Bible story. I find earlier a curious exception, as though uniformity of custom had not established itself prior to 1300. 1293. To welcome Edward I upon his return from Scotland, the London Gilds held a procession, with what appears to have been moving pageants indicative of trade.° But very early in the four- teenth century the type became fixed, and we find little variation until the time of Henry VI. Before 1430 the pageants had been taken from the Bible story, and were easily recognized by all in their conventionalized form, 1 Julleville, vol. 2, p. 188. 2 Herbert, vol. 2, pp. 217, 221. 3 Julleville, vol. 2, p. 189. 4 Julleville, vol. 2, p. 190. 5 Fabyan, pp. 603-7. 6 Herbert, vol. 1, p. 89. Charles Davidson—English Mystery Plays. 211 but now we find that other subjects are crowding in, breaking the sequence of the story, and rendering some designation necessary to interpret them to the beholder ; for this reason verses were attached. But when the necessity of choosing a Biblical theme was no longer present, the artist naturally selected some subject that would be complimentary to the high personage in whose honor the pageant was set up. Affixed verses he could not easily read, so the compli- mentary address to the King arose, or a laudatory conversation was carried on between actors. This is approaching very near to the borders of the spoken drama, but I have found no instance of royal entry where a genuine, spoken drama was acted. Further, it would seem that this development of the pageant arose earlier in England than in France. ; 1431, Dec. 2. Of the entry of Henry VI of England into Paris this description is given : “‘Depuis le poncelet en tirant vers la seconde porte de la rue Saint Denis avoit personnages, sans parler, de la nativité Notre Dame, de son mariage et de l’adoration des trois Rois, des Innocents’ et du bonhomme qui semoit son blé.” 1432. Entry of Henry VI into London after his coronation at Paris. Allegorical pageants with verses by Lydgate.” 1445. Entry of Queen Margaret into London. Seven pageants with verses by John Lydgate.* 1461, Aug. 31. Entry of Louis IX into Paris,—“‘y avoit une passion par personnages et sans parler, Dieu estendu en la croix, et les deux larrons a dextre et a sinistre.* 1461, Sept. 20. Entry of Louis IX into Orleans. Twelve pa- geants, stationary, laborers, moral virtues, David and Goliath,* ete. 1498, July 2. Entry of Louis XII into Paris. All the pageants were allegorical except those of the Confréres de la Passion who presented The Trinity, Abraham’s Sacrifice, and the Crucifixion.” So, fifty years after London, Paris bows to the popular demand for allegory. 1514, Nov. 6. Entry of Mary of England into Paris. 1515, Feb. 15. Entry of Francis I into Paris. 1517, May 12. Entry of the Queen into Paris, In these three the subjects were allegorical.° 1521. Entry of the Emperor, Charles V, into London. 1 Julleville, vol. 2, p. 191, quoting Enguerrand de Monstrelet. 2 Fabyan, p. 603, fol. 190. 3 Stow, p. 385. 4 Julleville, vol. 2, p. 196. 6 Julleville, vol. 2, p. 201. 6 Julleville, vol. 2, pp. 205-6. 212 Charles Davidson— English Mystery Plays. The London Drapers resolved to have no Midsummer pageant, because there were so many pageants ready standing for the Empe- ror’s coming into London, but they afterwards agreed to renew the old pageants and to establish a new one of the Golden Flees, also to bring out their giant, Lord Moryspys,' and to present a morys dance.” This item furnishes us one clue to the absence of plays by the craft guilds of London. The royal entries called for frequent and costly pageants from the gilds. These pageants were preserved, and refurbished when occasion demanded them. OS NUU SO = OS! 000 UO V— Vv mHKOS JU ababababedeced. 9S = OS OSU ae ae O= US UV = O— FU — vv — ee Ve 0S Tipe OO omc © mest Ee oe The author is evidently experimenting, since he misses through the insertion of the first line of the cauda a favorite riming form of the Coventry and Woodkirk plays, a type that had at a later date a profound influence upon the septenar stanza. The alliteration is excessive, but the iambic movement is fairly regular, and rime tests, as we shall see later, go to prove this play the work of the author of X and VIII. Comparison with play XXVI, which follows, will immediately reveal the difference in stanza, although the riming is the same. Ex. 21. York Plays. No. XXVI. Stanza 4. NS ae OC C—O 0 Oi eG a Vil =—<—V VO= OY U=s—VUVUOS 1U =e VOUS OE 0 — OO C= VUUGa SO 9 = iE SE ee ababababcdcced. OVGOsm 868 S—sb6 = Ul = 0UO— Oo —UNU= O— Ob = 60 O = VOUS VU MS oe a eee) ee Fe C—O pie Charles Davidson—English Mystery Plays. 243 The direction of the deterioration is evident. All stressed sylla- bles but two, and four unstressed syllables, have alliteration in this stanza. Such overloading with alliterative sounds destroyed all sense of their proper function. ‘The first half-verses have passed the bounds of anapestic movement. The voice naturally places a stress upon the first. unstressed syllable, thus transforming the verse into a 5-stress line and destroying the stanza. It is significant that this quasi 5-stress line was considered the most suitable for royal person- ages. Many instances might be cited of this anticipation of ‘ Mar- lowe’s mighty line.’ UES: CERTAIN STANZAS OF THE MYSTERY PLAYS. The later forms of the septenar stanza do not particularly concern us, as they lie outside of the Mystery Plays. I will therefore pass over them rapidly, giving the stanzaic schemes for completeness of view and for comparison with the Southern stanza toward which they gravitated. Ex. 22. Prologue to the EHighth Book of the Aineid by Gawain Douglas, date 1513." Last stanza. YUU, YUU oOUuUYU OOira 0 == VOU UV UU = 00 U—— 96s OU SUNVU => 0S 9 =— 0000 — UW US 00 COC =— 98 = 10 == 08 = G80 — =— V0 U0 = U0 = ababababcdddce.2 O98 = VU == UU 10 = =— 9 — UO US UO NU a OU GO = U0U =U On O— 00 oe ee) ee ee oS = Pe) O— UO ——\— Vi gpeesnn Qe Si 2 Lines 4 and 5 have the same alliterative letter, the letter s. Ex. 23. The Howlate of Holland, date 1450-54.* Stanza 2. 1 Schipper, vol. 1, p. 221. 2In the first line, the macrons (—) should each be read as double macrons (=), and another one should be inserted just before the ceesura. 3 Pinkerton, vol. 3, p. 147. 244 Charles Davidson—English Mystery Plays. Vy SV" Sy =v" = 20. — oe V0 =—000S==19 =v" = ¥ 990 =—0 0 =U == UU = 0000 Us HU HO VvVVU0= UGz== Ht — OU — 8 Se eee ababababcddde. == 8 OS Vl US UU 0== VU =v It == VU = v—vVvV = O09 Oo } 0 oo——ou = Vv UN Lines 3 and 4 have the same alliterative letter, the letter b; lines 5 and 6 have 1; lines 12 and 13 have b. Ex. 24. Gawan and Gologras,’ date about 1500. Stanza 3. vv =Svv—"v SS 4 VU SOU P—t 01 0 6 ee — Le © eo Oo CN ee = UU =v =00 00 =U = 00 =V7YU = = eouU = VO 00 Ue YD een te ababababcddde.3 == 00 OO CO Xex 65 © as (go On . 2 ———— Lines 1 and 2 alliterate on f, lines 5 and 6 on h, lines 7 and 8 on t, line 9, 10, and 11 on w. ‘The introduction of feminine rimes is worthy of remark. Ex. 25. The Anturs of Arthur at the Tarnewathelan,* date about 1350.° Stanza 3. CuO) —— =—— -—#»—=—00 "0 U=—0uU = t VVU=— —_ vuo= VU = twuVU — O——() o= U0 =v O00 = UU = 000==— YU = =U 00 =— — COG=—— Gy ——PFit =—_ VI— O00 =—voOv =I"! —= vu U— ababababcddde. o=—V00VU=— VU! 0 = 00> Vu=s=9yu"u=—= " 9 = OCO= GO ==vu0== vovo— wo} YU aaa U0 == 1In the sixth line the two macrons after the caesura should be read as one long macron. 2 Pinkerton, vol. 3, p. 69. 3 Breve at end of seventh line. 4 Robson. 5 Given by Hohlfeld, Anglia 11, p. 249, as on the authority of ten Brink. al Charles Davidson—English Mystery Plays. 245 Lines 1 and 2 alliterate on g, lines 3 and 4 on b, lines 5 and 6 on 1, lines 8 and 9 ont, lines 12 and 13 on b. So similar are examples 22, 23, and 24, that I do not hestitate to pronounce them products of the same school. Examples 23 and 24 were possibly by the same author, and written in the neighborhood of Carlisle. It would seem, then, from the evidence of the stanza, that 1500 is too late for Gawan and Gologras, and 1350 a date much too early for the ‘ Anturs.’ Ex. 26. Of Saynt Jobn the Euaungelist,' date about 1440.’ Stanza 1. Sow ig UV0=S== = OV 10 =— VU — = YUN = "0 — UUU = 00 == OO = !! =—=00 = ss U0 See OOD SS . = 09 == Ou UE O00 OV = "UO =— == Be tO Pa iis. ababababccdeced. Qos UG = - O==— VO ey OO = Woy = 9y=— UU = empany CN NOOSE Each alliteration is carried through two lines. The first short line recasts the thought of the last long line. It is impossible to deter- mine with certainty whether these more corrupt forms are de- scendants of the septenar stanza, or are offshoots from the Southern stanzaic forms. Ex. 27. Susanna,* date about 1360.* Stanza 1. VeU = YUU =S en ©) —— 000O=S=- i = —>—°oUOU= Ogg 000 =00= LE ——— CGO= (EO) SP (0 “o==- s- - OU == O=s=00Ss=— VU NboO = = — ~¢ —700 = o> v= 09== SU OO ababababcddde.s 0 =—90 = U0 U=UU UU — 0ot-_—_ OURO = 0vW0O= OO =—Vvu4u = oO — VY = JV = 1b. E. T.S. No. 26. 2 Schipper, vol. 1, p. 220. 3 Anglia, 1, p. 93. 4 Schipper, vol. 1, p. 219, given on the authority of Horstmann. 5 Insert a breve before last breve of sixth line. TRANS. Conn. AcaAD., Vou. IX. OCTOBER, 1892. 18 246 Charles Davidson—English Mystery Plays. This poem is assigned by Horstmann’ to the Northern dialect, by Morris, as stated by Horstmann, to the West-Midland. The stanza is found in the Woodkirk plays in ‘The Conspiracy’ and ‘The As- cension.’ It is one of the favorite stanzas in the so-called Coventry cycle, occurring in the following plays— The Prologue, II. The Fall of Man, IV. Noah’s Flood, i X. Mary’s Betrothment, XII. Joseph’s Return, XVI. The Adoration by Shepherds, XXII. The Baptism of Christ, XXII. The Temptation. XXVI. The Entry into Jerusalem, XXVIII. The Last Supper, XXIX. King Herod, XLIi. The Assumption of the Virgin, XLII. Doomsday. These Coventry plays are probably of East-Midland origin.* The same district appears to have been the locale of this stanza, which is found also in ‘The Castell of Perseverance.’* It would appear, therefore, that the poem of Susanna should be assigned to a poet south of York, whose style was affected by Northern extravagances in alliteration. . The stanza was also of late date, since it passed into the Morali- ties. ; From a fusion of the septenar stanza with this East-Midland stanza arose a new type with the following characteristics— 1. Alliteration in greatest excess. 2. So great an overplus of unstressed syllables that the recitation must have simulated chanting when the integrity of the stanza was preserved. 3. Surreptitious stress increased the accents to five and six in a line. 4, The rime of the East-Midland stanza was adopted. This measure, with the reiteration of alliteration, was considered the proper introduction for persons of dignity, and is used in all four cycles, although the Ch and the Co soften greatly the alliteration. As the actor of royal rank usually appears at the beginning of the 1 Anglia, 1, p. 93. 2 Pollard, p. XX XVIII. 3 Pollard, p. 64. Charles Davidson—English Mystery Plays. 247 play, modification of the play in compliance with the taste of the period was an easy matter. This stanza, with various modifications, appears in York plays XXVIII, XXIX, XXX, XXXI, X XXIII, and stanzas or portions of stanzas, formed unmistakably upon the same verse pattern, are found in the Woodkirk, the so-called Coventry, and even in the Chester plays. This stanza, as the earlier septenar, had a life history of change and deterioration. Sometimes the excessively long lines broke into two, with riming cesuras and the development of new stresses. Such verses, in process of resolution, exist in Pilate’s speech in the Ch play, ‘The Resurrection :’ For [ am prince pearles, Most royal man of riches, I may deale and I may dresse, My name is Sir Pilate. In these lines the alliteration has suffered injury, and the rime has been lost. They are a weak imitation, almost a prose version, of such lines as York XXXII: For sir Pilate of pounce as prince am y preued As renke most royall in richeste array— and the Woodkirk ‘ Flagellation :’ Say, wote ye not that I am Pylate, perles to behold ? An earlier form of the same appears in W, ‘Consp. & Captio :’ Cayphas. Syr Pilate, prince of mekylle price, That prevyd is withoutten pere— which lines form the beginning of anababababeded stanza, Furthermore, the bonds of rime were loosened, and sometimes the long lines passed towards the boundaries of rhythmical prose. This is illustrated by Y XX XI, “And drawe to no drofyng, but dresse you to drede, with dasshis,” where “drede” rimes with the second line below, and “dasshis” with the fourth; also by Y XXXII, |. 10, where “To knawe” has no affiliation with the verse structure, and calls to mind similar versification in legends and romances. Again, the breaking of stanzaic structure by the indefinite exten- sion of the pedes of the stanza, as in Y XXXII, stanza 2; in Co XV, in Joseph’s second speech; in Sir Gawain and The Green Knight, and elsewhere, led to the establishment of a species of verse, riming in most cases it is true, but with an irregular suc- cession of stresses and tending toward a rhythmical prose. An investigation of the transformation and relationship of this stanza would yield rich results, but we must leave it as a task for others. 248 Charles Davidson—English Mystery Plays. A fourth stanza invites our attention. In the French a simple 4-accent couplet was popular at an early date. Ex. 27. MS One Spee Ni Ve — esr em Vy — toa In this measure were written the ‘Roman de Brut’ of Wace, the ‘Roman de Rou,’* ‘Guillaume D’Engleterre,’ and many others. In English it is preserved in such ballads as ‘A mery Ballet of the Hawthorne Tree,’? and in other styles of verse too familiar for reference. These couplets were early fashioned into stanzas by the insertion of a short line, riming with the second couplet, and became popular in the 15th century with the French writers of Miracles. The stanza- occurs repeatedly in ‘ Les Miracles de Notre Dame.’ Ex. 28. DS A. =e So eS VB — 9 YY — Oo eet © ie PU vu vu ee ee This type probably gave rise to the English stanza— Ex. 29. AT oo ae a ne oe Sa Bie a Ve Oi | ——" 2» VS 0 SS a Vv— V —— but the method of riming is, regularly in English, the riming of sim- ilar verses, never in a succession of stanzas, as in French, by ‘con- catenatio.”® This stanza is found in the Woodkirk plays as follows— I. Creation, the character of Deus. X. Annunciation, the play exclusive of Deus. XI. Mary and Elizabeth. XII. Tlf Crucifixion, together with other stanzas. XXVIII. The Incredulity of Thomas, with other stanzas. It is used also for the second part of ‘Sir Ferumbras,’* for ‘The Woman of Samaria,’® for Minot’s ‘Edward in Brabant,’® and else- where. 1 Bartsch, col. 111, col. 143. 2 Ritson, vol. 2, p. 44. © 3 Cp. Schipper in index. 4K. E. T.S. No. 34. 5K. E. T. S. No. 49, p. 84. 6 Poems of Lawrence Minot, p. 18. ‘ 4 4 . 1 ‘ ‘ Charles Davidson—English Mystery Plays. 249 With the more difficult rime a ab aa b, this stanza occurs also in the Woodkirk plays— VIL. The Prophets. IX. Cesar Augustus. XXII. The Flagellation, in the part of the Dorsnoneuis Also in the Chester play, The Shepherds, among other stanzas. This stanza is interesting as the germ of the metrical-romance stanza, which was possibly rejected by the writers of drama as too monotonous. The following partial lists will illustrate its use— aabaabccbecb. Romance of Duke Rowlande and of Sir Ottuell of Spayne.* aabaabccbddb. Amis and Amiloun,’ Libius Disconius,’ The King of Tars,* Mary Legend, No. IL.* aabccbhddbeeb. The Romance of Athelston,” Emare.’ Romance of the Emporor Octavian,’ Erl of Tolous and the Emperes of Almayn,’ Le Bone Florence of Rome,’ Sir Isumbras.”° Rouland and Vernagu,” Torrent of Portyngale,” The Wright’s Chaste Wife,” Sir Amadace,”™ etc. Certain other stanzas were of wide-spread use, and appear in the different cycles of Mystery Plays. Of their origin it is sufficient to say in general that they sprang, for the most part, from the Latin stanzaic forms of the church service, especially from the service of song. Some of them, also, show evident marks of French influence, TBE. 8. INO: 85. 2KO6lbing, No. 2 3 Ancient English Metrical Romances. 4 Horstmann, p. 503.—Note. Kd6lbing’s criticism, Amis and Amiloun, p. XIV, of Horstmann’s statement concerning the rime, is itself incorrect, as Horstmann speuks of the Mary Legend, No. II, but Kélbing of the Mary Legend, No. I. 5 Reliquee Antique, vol. 1, p. 85. 6 Ancient Metrical Romances, vol. 2 1J.0O. Halliwell. 8 G. Liidthe. 9 Ancient English Metrical Romances. lo J. O. Halliwell. 11K. EK. T. 8S. No. 39. 12H. E. T. 8. Extra Series, No. 51. 13H. BE. T.S. No, 14. l4 Robson. 250 Charles Davidson—English Mystery Plays. and it is probable that the sources of some are to be sought for in the Provengal. A general view, as exhaustive as seems necessary for our purpose, is appended. aabab. Ex. 30. VI eaE ay, vV— UY UY = Sa a Se v—v —v is found in six stanzas spoken by Lucifer, W I. aaabab. York VI, XXII, XXX VIII, XLII. Woodkirk XIV, X XVII, XX XIT, XX VI (in the part spoken by Jesus). aaabaaab and aaabeceb. Woodkirk XVII, XXIII (Mary’s lament), XXIV. (the Torment- ors), XXIX (certain stanzas). | Coventry XIV (a portion of the play), XVI (stanzas by shep- herds), XVII (stanzas by Magi, and certain 2-accent stanzas), XIX (one stanza), XXVII (by Judas in part), XXXII (by Jews and others), XX XIII, XXXIV (by Nychodemus), XXXV (in 4-accent and 2-accent verses), XX XVI (in part). . Chester. The whole Chester cycle was written by a poet who at- tempted to use the stanza aabaab, but frequently resorted to aabcecb as an easier stanza, and sometimes lost his footing com- pletely. aaaabece b. Woodkirk III, XII, XT, XVI, XX, XXII, XXII, XXIV (certain stanzas), XXX (in stanzas by demons). Many modifications of* these stanzas appear infrequently in the plays. We note in closing our review a favorite stanza of the Cov- entry plays,a babbcebe, from which it is but a step to Spenser. Finally, we form from the foregoing examination of the stanzas of English in the medizval period certain conclusions—- 1. A distinctive stanza, formed from the septenar line, obtained in the district—to speak in general terms—extending from the Hum- ber to the Forth ; and was not used, except in a much altered form, outside of those limits. 2. The characteristics of this stanza were— a) Two 4-verse, 4-stress pedes ; a 4-verse or 6-verse 3-stress cauda. b) The pedes rimed in two riming quatrains ; the cauda originally rimed alternately, but variation was permissible. c) The verse kept carefully the iambic movement. Charles Davidson—English Mystery Plays. 251 d) The cesura was uniformly placed after the second stress, ex- ceptionally after the first and third.’ ¢) Cesuras and verses were masculine. jf) Alliteration was structural, i. e. confined to three stressed sy]- lables in the verse. ‘ 3. This stanza suffered direct change in three ways— a) By continual increase of alliteration. 6) Through the inordinate multiplication of unstressed syllables, especially in the first half-verses. c) Through innovations in the riming of the cauda. 4. These changes were so pronounced in type and limited in time, that the stanza affords important evidence in dating poems relatively to each other.’ 5. A stanza riming ababababcdddece was cultivated in East Anglia at a date somewhat later than that of the Northern stanza of pure type. 6. The Northern stanza, under the influence of the contiguous East Anglian stanza, formed a second distinct type. 7. This derived stanza developed as follows a) By the loosening of the bonds of stanzaic structure, the pedes were indefinitely extended, and the composition approached the bounds of rhythmical prose ; or, b) The voice failed to carry the excessive number of unstressed syllables, surreptitious stresses created a 5-stress line, or the verse broke into two lines with the development of new stresses. 8. A stanza aabaabecbecb was formed for rhythmical narrative, and became the vehicle of the metrical romance. 9. Other stanzas appear as directly dependent upon church sources and French influences. 10. A stanza ababbecbe closes the medieval period. This statement applies more directly to the district immediately north of the Thames. The cycles of Mystery plays present certain metrical characteris- tics as individual cycles—’ 1, The York cycle, with the exception of a few plays,* retains one stanzaic structure through a play, or, in some cases, through a scene. 2. The Woodkirk plays show an attempt to adapt the stanza to the character, or at least to limit the use of a given stanza to one char- acter in a given play. 1Cp, Ex. 19. 2Cp. Ex. 24. 3 Op. York XIT, XIII, XVI, XXIX, XXXI, XXXII, XL. 252 Charles Davidson—English Mystery Plays. 3. The Coventry plays exhibit prevailingly an interchange of three stanzas, the choice apparently influenced only by a desire for variety. 7 4, The Chester plays are, as uniformly as an author of limited © poetical resources could make them, cast in the mold of one stanzaie form. ; : The importance of the foregoing conclusions in determining the structure of the cycles of plays is evident. We proceed now to the defense of certain propositions relating to the cycles themselves. XX, A SURVEY OF THE CYCLES OF MYSTERY PLAYS. In considering the cycles of plays as wholes, certain general struc- tural characteristics appear. A discussion of these will prepare us for a more minute investigation of cycle construction. I. The York cycle contains plays of widely different styles and vocabulary. Such plays as X and XI have little in common with XXXI and XXXII, and still less with XLVI. The differences are not such as arise from an unskillful re-working of an old play. Such scribal changes are found in Woodkirk ‘ Pharao,’ when compared with York XI. They lead to the distortion of the stanza— a) By the insertion of extra-stanzaic verses, as the quatrain in W after the first stanza, or the two verses separating the cauda from the pedes in stanza 22. b) By the breaking of rime, as in stanza 25. c) By the disarrangement or obliteration of the alliteration through the displacement of alliterative words by non-alliterative synonyms, as through the substitution of ‘ words’ for ‘saws’ in 1. 17, or by the complete loss of alliteration in ]. 23. d) By the destruction of the iambic movement, as in lines 21, 39, 52, 53, ete. ‘ e) By the loss of a stress, as in line 28. The differences between the above-named plays are not of this character, but fundamental. They concern— a) The structure of the line, which in XXXI and XXXII is ex- cessive in alliteration, inordinate in length, irregular in rime, and contains occasionally an unusual tag, as line 10, XX XII. Charles Davidson— English Mystery Plays. 253 b) The riming, as in XLVJ, where the repetition of ‘hym,’ ‘us,’ and the frequent use of words ending in ‘ioun’ is a habit unknown to the author of X and XI. ce) The vocabulary of the writer, in cases where there is no ques- tion of the substitution of a more familiar synonym. Examples of such usage are ‘bewscheris’ and many quasi-French words (cp. line 257, XX XI), and the employment of words of Latin origin which were used in riming as an ornament of style,,especially such as end in ‘ioun.’ These affectations in riming we recognize, from later plays and from other poetical works, as the ornaments of style at a period later than the origin of plays X and XI. The municipal books of York show that expansion or contraction of the cycle, according to the present needs of the different crafts,’ was of common occurrence. Such changes were made by the inser- tion or excision of whole scenes, or of whole plays, never by the fusion of plays. This will become clear as we proceed to the more minute analysis. If. The Woodkirk cycle* is a collection of plays drawn from various sources. ‘The compiler was a man of small poetical ability. His original verse was confined to couplets, with an occasional at- tempt at quatrains. He did not hesitate to appropriate good work wherever he found it, or to do violence to rime or measure, if he con- sidered the thought unclear or contrary to accepted traditions. As illustrations of his methods we cite— 1. For transition between selected parts of plays, the sixteen verses by cherubim between the first speech of Deus and that of 1 York plays, pp. XIV to XX VI, notes. 2 Hall, Englische Studien, vol. 9, p. 449, argues that Y is derived from W because it contains more alliteration! He arrives at this conclusion by trusting implicitly to Skeat’s *“‘ Law of progress in alliterative poetry.”’ Preface to Joseph of Arimathea, p. X. If, as Skeat formulates it, the progress is *‘from lines with two alliterated letters to lines with three, and in very late instances, to lines with four,” from irregularity to regular- ity—although he admits that some of the latest examples of alliterative verse relapses into irregularity ;’—then I do not see how Hall’s conclusion can be escaped. But the law seems to run as well from no alliteration to two alliterated words. In that case the re-creation of the old alliteration after the literature containing it had been buried for centuries would be little short of a miracle. On the contrary, the old laws of alliteration were preserved by the North in continu- ous tradition. A sharp division must be made between structural alliteration, which conforms to ancient law, and alliteration for ornament, which gradually broke down the tradition of the fathers by swamping the essentials in a multitude of detail. We have already traced the progress of demoralization, and need only note that it, in con- formity with other evidences, makes W the later dependent cycle so far as concerns the older plays of the collection. 254 Charles Davidson—English Mystery Plays. Lucifer in Creatio. These couplets seem to be a condensation of some unknown play. 2. For introduction, the four couplets introducing the call of Deus, “ Abraham, Abraham,” in the play of Abraham. | 3. For expansion of thought or to convey indirectly a lesson, many quatrains—sometimes only three verses—that are usually introduced between stanzas, as in ‘Pharao’ after 1. 13,’ 1. 108, 1. 120; in ‘ Pagina Doctorum? after loa 73.1, 174, 175: 4. For plays of transition where the compiler desired that certain incidents of the Bible should be made prominent, and could find no suitable play, the drama of Isaac—Isaac blessing Jacob—and that of Jacob—when Jacob was named Israel. 5. For plays that are formed from two or more plays by the use of selected stanzas or varts of stanzas, ‘ Flagellacio’ and ‘ Extractio Animarum.’ To this compiler, however, we are indebted for the preservation of the second ‘Shepherd Play,’ our earliest farce, and for the ‘ Judicium,’ which, in the part of Tutivillus,* contains a satire on the fashions and manners of the day. III. The Chester plays are, as Hohlfeld has well said, the work of a translator.® I incline, however, to the opinion that the cycle was not French, but Anglo-Norman. The agreements with the other cycles are significant. They include— 1. ‘The Salutation,’ which shows agreement among Ch, Y, W, and S & T of Co. 2. ‘The Purification, which shows agreement among Ch, Y, W, and W of Co. . 3. The Song of Jesus, where there is agreement between Ch and W. 4. In ‘Christ Betrayed’ the agreement between Ch and W in two lines accompanying the stroke of the sword. To these may be added the distinctively English passages— 1. The gossips’ song, Ch I, p. 53. 2. The part of Mulier, Ch II, p. 81. It may be admitted that the Song of Jesus and the gossips’ song are later additions, that ‘The Purification’ is an adaptation of the York play ; still, ‘The Salutation’ is in the stanza of the cycle and probably by the same translator; therefore not all of these agree- ments arose from the late adoption of plays from other cycles. 1 The verse-numbers apply to the corresponding York play. 2 Cp. Tuteville in Rodentiner Osterspiel, pp. 49, 50. The coincidence appears to arise by independent derivation from ‘toute-vilain.’ 3 Anglia, vol. 11. Charles Davidson—English Mystery Plays. 255 The wide agreement in these plays seems to me to argue a common knowledge of models existing in England. These models may have been in part Anglo-Norman, as the cycle of the Parish Clerks of Lon- don probably was. Most of them were undoubtedly church plays, would be often in Latin, possibly sometimes in Anglo-Norman, and often in English.’ The continual presence of plays in the churches upon appropriate festival days must be assumed. Few remains of such plays are ex- tant, but the known opposition of the reforming party to these plays, and the efficient zeal of King Henry’s spoilers, would satisfac- torily account for their destruction with the dispersion of libraries that were their proper repositories. The repeated enactment of im- perative laws’ forbidding plays in the churches, the presence of sep- ulchres in many churches to-day, and the occasional references to them in hostile writings,’ are conclusive evidences of their presence. A mistaken interpretation of phenomena presented by the plays has often arisen through the failure to give due weight to two facts that concern the church customs of that day. It may be well to in- terrupt for a moment the course of this discussion to present those facts. First, the solidarity of custom, as well as of belief, throughout the churches of England and France. ‘This gave rise to a uniformity of method and expression in the mystery plays, which resulted in such striking similarities between plays formed on models used in the churches of England and those that arose from other models on the continent, that oftentimes direct dependence of the English play upon the French has been asserted, when, very possibly, each author knew no plays but those of his own cathedral church and immediate neighborhood. Churches are conservative bodies, slow to change their customs ; therefore the church plays would diverge from their common type very slowly. ‘They were viewed almost as parts of the liturgy. 1See the *‘ Mystery of the Burial of Christ,’ ‘Off the Wepinge of the Thre Maries,’ and the ‘Mystery of the Resurrection,’ given in Wright’s Reliquize: Antique, vol. 1, pp. 124-161. These are English church mysteries, which have been passed by without remark by writers upon this subject. 2 The chief trace tbat the old hierarchy left of its dramatic existence was the acting of plays in the churches, which was finally ordered to be discontinued by proclamation in 1542, but was continued by choristers of St. Paul and of the Chapel Royal until the time of Chas. I.—Hone, p. 229. In 1603, canon 88 of the canons of the Church of England enacted that church-wardens should not suffer plays in churches, chapels, or church- yards.—Encyclopeedia Britannica s. v. Theatre. 3‘'The Beehive of the Romish Church” speaks of the shows of Burial, Resurrection, etc.—Hone, p. 221. 256 Charles Davidson—En glish Mystery Plays. Secondly, if the tradition was preserved through acted chureh plays rather than through the importation and re-casting of texts, the agreement between plays will be different in kind. The corres- pondence arising through the remodeling of plays we can study in the Woodkirk cycle, when compared with the York. They are found throughout the body of the text, usually in whole stanzas or in considerable portions of stanzas, wherever the thought seemed pleasing to the compiler. The agreements, arising from the recollec- tion of the play as acted, will lie in certain notable actions that are conventionally present in every church play, and in the appropriate speech that goes with such action. A few examples, drawn from French and Italian sources, and placed in comparison with the English plays, will illustrate my posi- tion. F In J,* p. 5, Dieu takes Adam and Eve by the hand and tells them of the tree. In V T,’ vol. 1, p. 34, Dieu takes Adam and Eve by the hand, pronounces benediction of marriage, and shows them the tree. In W, p. 6, Cherubyn takes Adam by the hand and the Lord speaks about the tree. In Ch, vol. 1, p. 24, God takes Adam by the baad after the dis- course fs causes him to lie down.? Eve’s address to Adam when offering him the apple— In J, p. 8, Adam, chier compains et amis. In Ch, vol. 1, p. 28, Adam, husbande, life and deare. In Co, p. 28, My semely spouse and good husband. In W the play is lost. Adam eats—exclaims, then @) accuses Eve, or 0) perceives naked- ness, or c) combines the two. In J, pu 9, Ha hay! je suy mal avoiez. Ce morcel ne puis avaler. In V TI, p. 49, O vray Dieu, de moy te souvienne! Poore maleureux, que ay je fait? Te, XY jis 25; Allas! what haue I done, for shame! Ille counsaille woo worthe the! A! Eve, Pou art to blame. 1J stands for Mystéres inedits par Achille Jubinal. 2V T stands for Viel Testament. 3 A similarity here with V T leads to the supposition that God also led Adam into Paradise and showed him the tree. Charles Davidson—English Mystery Plays. 257 In ChI, p. 29, Out! alas! what aylith me? I am nacked well I see; Woman, cursed moth thou be. mae Co, p. 27; Alas! alas! ffor this fals dede, My flesly frend my fo I fynde, Schameful synne doth us unhede, I se us nakyd before and behynde. In W the play is lost. The exclamations of devils in torment— In J, p. 24, Belgibuz,—Harou, je suis tout forsonnez. In V. T, vol. 1, p. 18, Lucifer,—Harau, Harau! je me repens. In Y, p. 5, Lucifer,—Owte, owte! harrowe! helples, slyke hote at’ es here. In W, p. 4, Demon,—Alas, alas, and wele-wo! In N,’* Diabolus,—Put off Harro, and well away. In Ch, vol. 1, p. 17, Demon,—Out! harrowe! wher is our mighte. The salutation— In J, Gabriel — Ave Maria gratia plena. Marie, Dieu te sault, Marie. In D,° vol. 1, p. 188, Gabbriello,— Salviti Dio, che se’ di grazia piena: Teco si trova il gran Signore Dio. In Y, p. 98, Angel—Hayle! Marie! full of grace and blysse, Oure lord god is with pe. In W, p. 74, Gabriel— Haylle, Mary, and welle.thou be, My lord of heven is wyth the. In oy vol. 1, p. 94, Gabriell— Heale be thou, Marye, mother ffree, Full of grace, God is with thee. In Co, p. 112, Gabriel— Ave Maria gratia plena, Dominus tecum ! Heyl, fful of grace, God is with the. Mary’s consent — In J, p. 50, Ainssy soit fait com tu me dis. In D, vol. 1 p. 189, Ecco PAncilla del Signore Dio: Sia fatto a me secondo il tuo dir pio.’ 1 The use of the pronoun ‘at’ shows the expression to be old, otherwise the seribe would have changed it as elsewhere. The evident introduction of ‘heiples’ to alliter- ate with ‘harrowe’ shows that the favorite expletive was considered necessary. 2N stands for Noah’s Ark, Newcastle-on-Tyne, Sharp’s Diss. p. 224. 3 D stands for A. D’Ancona, Sacre Rappresentazioni. 4 See the extract of the church service on p. 179 of the same work. 258 Charles Davidson—English Mystery Plays. In Y, p. 99, Goddis handmayden, lo! me here, To his wille all redy grayd. la. Wp. 75, I am his madyn at his hand. In Ch, vol. 1, p. 95, Loe! Godes cossen meklye here. In Co, p. 114, Se here the hand-mayden of oure Lorde, Aftyr thi worde be it don to me. The stage direction— In J, p. 50, Cy descende 1 coulom qui soit fait par bonne maniére. In D, p. 189, Allora lo Spirito Santo discende sopra di lei, ed in cielo si fa grandissima festa, e ’ Angelo ritorna in cielo. In Co, p. 114. Here the Holy Gost discendit with iij. bemys to our Lady, the sone of the Godhed vest with iij. bemys to the Holy Gost, the fadyr Godly with iij. bemys to the sone, and so entre alle thre to her bosom, and Mary seyth. It is absurd to suppose, because of the above coincidences, that the writer of each English play had the Italian and French plays be- fore him. The Bible narrative was familiar to each writer. This sometimes necessitates the action, sometimes the language seems the natural outcome of the situation ; both reasons would operate as con- servative agents to prevent change in the church play. I think one is forced to admit that there must have been a uniformity of action and of expressions closely connected with action, in the important situations in church plays, similar to that obtaining in the liturgy itself, and that, in many instances, the agreements of plays in short passages and in the sequence of action is due to the essential identity of the church models from which these plays sprang. But further, if it can be shown that the action of the Chester plays agrees with the action of other English plays at points where all or several disagree in action or accompanying words with the continen- tal plays, a divergence of the English church plays from the customs of the continent will be established, and the Chester plays will fall into the category of English plays, though in the Anglo-Norman tongue. Unfortunately, the French texts necessary for the settlement of this question are not accessible to me. I can simply contribute one ~ item, and must pass on to other matters. 57:3 a c. With boiled blood-fibrin,—10 grams contained 3°692 grams of dry proteid (110° ©.). Digestions were warmed at 45° C. for 9 hours. Boracic Acid. Weight of undigested residue. Proteid digested. 0 (Neutral) 2°6397 grams 28°5 per cent. 2°0 per cent. ON COD aes 24°9 rt d. With coagulated egg-albumin,—10 grams moist coagulum con- tained 1:5143 grams of dry proteid (110° C.). Digestions. were warmed at 45° C. for 12 hours. Boracic Acid. Weight of undigested residue. Proteid digested. 0 (Neutral) 0°6503 gram 57°0 per cent. 2‘0 per cent. DOORS ee" 60°2 ei 310 Rh. H. Chittenden— Papoid-digestion. With the exception of the single experiment with boiled blood- fibrin, all of the results show that the proteid-digesting power of papoid is distinctly increased by the presence of boracic acid, at least by the percentages of acid indicated. Consequently, it is plain that the combination of boracic acid with papoid will not inhibit the action of the ferment, but will, on the oe increase its pro- teid-dissolving power. Influence of Acetic and Lactic Acids on Papoid Digestion of Raw Beef Proteids. The 10 grams of moist, prepared beef contained 2°8508 grams of dry proteid (110° C.). The digestions were warmed at 45° C. for 64 hours. Reaction. Pane te ee cece Neutral 0:9538 gram 66°5 per cent. 0°5 per cent. Acetic acid 1°6115 ‘“ 43°43 af | tae ae bo TG eX 43°98 Osa eiee Lactieacid 61 a196) + 5176) 45 ouae were 5 16823 —“ 40°9° The percentages of the two acids used in this experiment are somewhat high, considering the strength of the acids, but the object in view was especially to ascertain the probable effect on the ferment of admixture with an organic acid, such as might be developed in large quantity in the stomach in a case of strong acidity from lactic or butyric acid fermentation. The results show that the ferment is inhibited somewhat in its digestive action by the pres- ence of these large percentages, although not to any very great extent. Possibly, the addition of smaller quantities of these acids might lead to an increase in digestive power over that of the neu- tral solution. Influence of Lime Water on Papoid Digestion of Raw Beef Proteids. The 10 grams of prepared beef contained 2°707 grams of dry proteid (110° C.). The mixtures were warmed at.45° C. for 64 hours. Weight of Proteid Medium. undigested residue. Digested. 25 c. c. Water 0'7175 gram 73°4 per cent. 123 c. c. Water 08076 « "Od 3 123 ‘* Lime eater Here, the percentage of lime water was quite large, but the object in view was to ascertain quickly whether, under any ordi- * A saturated aqueous solution of calcium hydroxide. R. H. Chittenden— Papoid-digestion. 311 nary circumstances, as in the peptonization of milk, the presence of this weak alkali would offer any hindrance to the digestive action of papoid. The results show that when lime water is present to the extent of even 50 per cent. of the total volume, digestion is not materially interfered with. Indeed, in another experiment, where papoid was dissolved directly in 25 c. c. of lime water and no other fluid added, 53°7 per cent. of the raw beef proteid was converted into soluble products, while in the control digestion (papoid in water) 66°5 per cent. of the proteid matter was dis- solved ; thus showing that lime water, even when present in large amount, has little power to hinder the proteolytic action of papoid. b. Influence of Temperature. Animal ferments, especially those concerned in the ordinary pro- cesses of digestion, act most energetically, as is well-known, at approximately the body temperature. Raising the temperature to near 60° ©. quickly brings about a diminution in digestive action, followed by a gradual destruction of the ferment. Lowering the temperature below that of the body is likewise accompanied by a diminution in digestive action, although ordinarily less marked than the inhibition caused by a rise of temperature. With the animal proteolytic ferments, pepsin and trypsin, digestion 1s very slow at, say 20° C. With diastase, the vegetable amylolytic fer- ment, the most rapid conversion of starch into sugar takes place at about 55° C. A study of papoid digestion, with reference to this point, has revealed a very interesting peculiarity of this ferment, viz: a great resistance towards inhibition of digestive action by high tempera- tures. Thus, in an acid solution (boracic acid), a larger amount of cooked beef proteids is dissolved at 70° C. than at any lower tem- perature, while even boiling the ferment solution fails to destroy entirely the action of the ferment ; a fact which is especially true of an alkaline (sodium bicarbonate) solution of papoid. Further- more, at a comparatively low temperature, 20° C., digestion is very pronounced in both a neutral and acid solution of the ferment, while in an alkaline fluid, digestive action is almost as great at 20° C. as at 45° C, The three following series of experiments, illustrative of these points, were made at the same time and under exactly the same conditions, excepting the specified variations in temperature and reaction. Each digestive mixture contained 0°5 gram papoid, 10 312 hh. H. Chittenden — Papoid-digestion. grams of prepared cooked beef and 25 c. c. of fluid; the latter con- sisting of water alone in the neutral series, of 2°0 per cent. boracic acid-solution in the acid series, and of 20 per cent. sodium bicar- bonate-solution in the alkaline series. The digestions were continued at the given temperatures for 6 hours, the fluid itself being brought to the required temperature before the proteid was added. The 10 grams of cooked beef contained 3°5538 grams of dry pro- teid (dried at 110° C.). NEUTRAL SOLUTION. Temperature. Weight of undigested residue. Proteid digested. 20° C. 2°2445 grams 36°8 per cent. 40 147438. <* 58°5 ie 45 1°5640 ‘“ 50°9 = 60 ATS) 40% 66°S ci 70 thas 5 +s ee 66°3 — Solution first boiled and then 3°2286 =< pe es kept at 45°C. J ALKALINE SOLUTION. Temperature. Weight of undigested residue. Proteid digested. a Bley 1-4776 grams 58°4 per cent. 40 tots || Alina 635°C. a 45 1°3054** 632-205 60 1:0080 * 716 VS 70 14081 os 68°B. Sas Solution first ) boiled and then kept at 45° C. 24708 <* Se AcIp SOLUTION. Temperature. Weight of undigested residue. Proteid digested. 20° C. . 2°2153 grams 37°6 per cent. 40 14895: ** 58°6 oi 45 1°5240 = 57°1 x 60 1°3184 ** 65°7 i: 70 1:0804 ‘ 69°5 rae Solution first boiled and then 3°1560 ‘* 11:1 - kept at 45° C. The results brought out by these three series of experiments can be more readily seen by a direct comparison of the percentages digested under the different conditions, as shown in the following table : R. H. Chittenden— Papoid-digestion. 313 Proteid digested. Temperature. Neutral sol. aiaaenareainahs tle meklenline sol. 20° C. 36°8 per cent. 37'6 per cent. 58°4 per cent. 40 58°5 58°6 63'9 45 59°9 571 63°2 60 66°8 65:7 71°6 70 66:3 69°5 68°8 ’ Solution first 9-1 boiled and then i hes 30°4 kept at 45° C. We notice first in these results a repetition of what has been already demonstrated, viz: that in an acid solution (boracic acid), papoid is slightly more active than in a neutral fluid, while in an alkaline solution (sodium bicarbonate) the activity of the ferment is increased very greatly. We now see that this statement holds good practically for all temperatures. The most striking facts, however, brought out by these experiments are: first, the marked activity of the ferment at the comparatively low temperature of 20° OU. (the temperature of the room at the time the experiment was tried), especially in an alkaline fluid; and secondly, the retention of proteolytic power after the solution of the ferment has been actually boiled. Here, too, the alkaline solution appears to exert a certain protective influence upon the ferment, which is difficult to explain. Certainly, sodium bicarbonate alone will not dissolve a coagulated proteid to any great extent, as has been already demonstrated in connection with other experiments. Hence, we are forced to the conclusion that in an alkaline fluid especially, papoid is extremely resistant to the inhibitory effects of low and high temperatures, so characteristic of most known ferments. ‘This being true, it is ob- vious that papoid in the presence of sodium bicarbonate possesses special advantages in cases where it is desired to soften or digest tissue or other proteid matters, at comparatively low temperatures. In view of the importance of this fact, a duplicate experiment was tried, in which the digestive action of papoid was again tested at the room temperature (21-22° C.) on cooked beef proteids, in a neutral solution, and in the presence of boracie acid and sodium bicarbonate. The 10 grams of: prepared beef contained 38°7550 grams of dry proteid (dried at 110° C.). The digestions were con- tinued for 6 hours, at the given temperature. Reaction, Weight of undigested residue. Proteid digested. Neutral 2°4053 grams 35'9 per cent. 2°0 per cent. Boracic acid 2°23894 — *§ £0°875)./"' 2°0 Re Bicarb. soda M3 5 48°5 Without papoid. 2°0 per cent. Bicarb. soda Se GiGl, * B Gn ss 314 Rh. H. Chittenden— Papoid-digestion. Here, the same results are to be seen as in the preceding experi- ment, although the difference between the acid and the alkaline digestion is not quite as pronounced. Still, the results certainly warrant the conclusion already advanced, that in papoid we have a proteolytic agent especially adapted for the digestion of proteid matter at comparatively low temperatures. At the same time, it is a ferment very resistant to the ordinary destructive effects of high temperatures, and is especially characterized by exhibiting its maxi- mum digestive power at about 70° C. c. Influence of various Therapeutic Agents and other Substances on the Proteolytic Action of Papoid. In this connection, those substances have been chosen which might naturally be combined with papoid in its application as a therapeutic agent, either internally or externally, or which might perchance exert some modifying influence upon the action of the ferment as a general proteolytic agent. The experiments have been conducted in the same manner as those already described ; each digestive mix- ture containing 0°5 gram papoid, 10 grams of prepared beef pro- teids, raw or cooked, and 25 c. c. of water, together with the speci- fied percentage of the substance to be tested; the digestive action in each case being compared with that of a control digestion com- posed of papoid, proteid, and water alone. SALICYLIC ACID. The mixtures were warmed at 45° C. for 8 hours. The 10 grams of raw beef proteids contained 2°743 le of ane proteid (110° C.). Salicylic acid. Weight of undigested residue. Proteid digested. 0 (neutral) 1:1070 grams 59°6 per cent. 0-1 per cent. 09536 =‘ 65°2 re 0:2 = 09253.“ 66°3 oS From these results, it is evident that salicylic acid in small quanti- ties tends to increase the proteolytic action of papoid over that of a neutral solution. As is well known, a 0:2 per cent. solution of sali- cylic acid is amply strong to act as an efficient antiseptic, prevent- ing the appearance of putrefaction in an organic fluid, even under the most favorable circumstances for its development. Consequently, salicylic acid and papoid might well be combined where application of the ferment to morbid or suppurating growths is desired. r Rh. H. Chittenden— Papoid-digestion. 315 CARBOLIC ACID. The mixtures were warmed at 45° C. for 64 hours. The 10 grams of raw beef contained 2°8508 grams of dry proteid (ite? C:). Carbolic acid. Weight of undigested residue. Proteid digested. 0 (neutral) 0°9588 gram 66°5 per cent. 0:5 per cent. 11441“ 59°8 a 10 aH AZa Om 2 <8 56°9 ae Hence, carbolic acid inhibits slightly the proteolytic action of papoid, but not to any great extent ; the ferment will still act vigor- ously, even in the presence of 1°0 per cent. of the acid. MERCURIC CHLORIDE. The 10 grams of prepared raw beef contained 2°6996 grams of dry proteid (dried at 110° C.). ‘The mixtures were warmed at 45° C. for 64 hours. Mercuric Chloride. Weight of undigested residue. Proteid digested. 0 0:9758 gram 63°8 per cent. 0:05 per cent. 1EOGGCO pee: 60°5 ee In another similar experiment, but with 0:1 per cent. mercuric chloride, 57°3 per cent. of the proteid matter was dissolved, while in the control digestion 59°6 per cent. was converted into soluble pro- ducts. Hence, mercuric chloride or corrosive sublimate, when present in a neutral solution of papoid to the extent of 0:1 per cent., does not materially interfere with the proteolytic action of the fer- ment. This seems somewhat remarkable, and in conjunction with the two preceding experiments makes clear that papoid, as a proteo- lytic agent, is not checked to any extent in its digestive action Me three of the best known antiseptics. CHLOROFORM. The 10 grams of prepared raw beef contained 2°743 grams of dry proteid (110° C.). The mixtures were warmed at 45° C. for 8 hours. Chloroform. Weight of undigested residue. Proteid digested. 0 11070 grams 59°6 per cent. 4°) per cent. 1-201 4‘ 56°2 . 0) 0:9758 gram 63°8 _ 8 0 per cent. 1:3423 50°2 ae In the second experiment, with 8 per cent. of chloroform, the two mixtures were warmed at 45° C. for 7 hours, and the 10 grams of e 316 RR. H. Chittenden— Papoid-digestion. raw beef proteids contained 2°6996 grams of dry proteid. Obvyi- ously, in these experiments a portion of the chloroform evaporates during the seven or eight hours, but the greater portion remains to exert such influence as it possesses. The results show some inhibi- tion of ferment action, but it is not very pronounced unless the amount of chloroform is raised to more than 4 per cent. THYMOL. The 10 grams of prepared raw beef proteids contained 2°8508 grams of dry proteid (110° C.). The two mixtures were warmed at 45° C. for 7 hours. Medium. Weight of undigested residue. Proteid digested. Water 0-8988 vram 68°4 per cent. Water and thymol 1°0250 <“< 64:0 i= A few drops of thymol solution (20 per cent. thymol in alcohol) were added to the one digestive mixture from time to time, in such quantity that there was always a strong odor of thymol, and a thin film of the substance floating on the top of the fluid. As is well known, thymol is widely used in artificial digestion experiments, to prevent possible putrefaction, as it, like chloroform, ordinarily exerts only a minimal interference with the action of the unorganized fer- ments or enzymes. The above result shows that thymol has only the same slight inhibitory effect on papoid digestion. HYDROGEN PEROXIDE. There is no very satisfactory way of measuring the exact influence of hydrogen peroxide on the digestive action of papoid, or any other like ferment. The only way available was to dissolve the 0°5 gram of papoid in 25 c. c. of the peroxide solution (Marchand’s), and then to add the 10 grams of prepared raw beef. Naturally, the peroxide solution produced an immediate and pronounced change in the character of the proteid, and doubtless such diminution of diges- tive action as is apparent from the result is attributable to an altera- tion in the proteid, rather than to any change in the ferment itself. The experiment may therefore well be taken as illustrative of the extent to which a comparatively large amount of hydrogen peroxide will convert the easily digestible proteids of raw tissue into more difticultly digestible products. A control experiment, with 25 ¢. ¢. of the peroxide solution alone, shows that a small amount of the raw proteid is dissolved by this agent itself. = Rh. H.:Chittenden— Papoid-digestion. 317 The 10 grams of prepared raw beef contained 2°7071 grams of dry proteid (dried at 110° C.). The mixtures were kept at 40-45° C. for 7 hours. Medium. Weight of undissolved residue. Proteid dissolved. Papoid & water 0-9828 gram §3°6 per cent. Papoid & hydro- e 7p ‘ ; ie gen peroxide. | oe ee Hydrogen per-) ; ‘ : rr, oxide alone. § ONL Ue With cooked beef proteids, hydrogen peroxide so alters the char- acter of the material, that papoid cannot exert any solvent action whatever upon it, and the peroxide solution alone is not able to dis- solve any of the altered proteid. POTASSIUM CHLORATE. The 10 grams of raw beef proteids contained 2°707 grams of dry proteid (110° C.). : The mixtures were warmed at 45° C. for 64 hours. Potass. Chlorate. Weight of undigested residue. Proteid digested. 0 0-7175 gram 73°4 per cent. 1:0 per cent. 08245 ** Girone" 2°0 se 00-7948 ‘ USO ates Here, we see a very slight inhibitory action, so shght as to have little significance. Practically, potassium chlorate is without any marked hindering action on papoid digestion. SODIUM CHLORIDE. With this salt, three distinct series of experiments were tried, in order to ascertain its influence on the activity of the ferment in neutral, acid and alkaline fluids. The proteid material employed was prepared cooked beef, 10 grams of which contained 3°'7815 grams of dry proteid (dried at 110° C.). All of the mixtures were warmed at 45° C. for 54 hours. a. In neutral solution. Sodium chloride. Weight of undigested residue. Proteid digested. i) 1:9017 grams 49°7 per cent. 1°0 per cent. VB0Gks rts 52°1 & Bees 6 17506 .* j 53°4 ih 6 el Lesa 458° 52°7 fs Trans. Conn. AcApD., Vou. IX. DECEMBER, 1892. 23 318 R. H. Chittenden— Papoid-digestion. b. In alkaline solution, 2:0 per cent. sodium bicarbonate. Sodium chloride. Weight of undigested residue. Proteid digested. 0 1°6233 grams d7°7 per cent. 1:0 per cent. L637 Oui s* 566 Pee wap | eae GIF O Hees 006, s;arue 40 * 17450 Hs ao c. In acid solution, 0:1 per cent. hydrochloric acid. Sodium ‘chloride. Weight of undigested residue. Proteid digested. 0 2°7567 grams 27-1 per cent. 1°0 per cent. De OGe, es 39°D eae BO ea 22100 — ** 39°7 ed 2 | 2°3344 38°2 e d. In acid solution, 0:2 per cent. hydrochloric:acid. The 10 grams cooked beef proteids contained 3:7767 grams of dry proteid (110° C.). Sodium chloride. Weight of undigested residue. Proteid digested. 0 3°2872 grams 12°9 per cent. 1:0 per cent. Fal 274 Vis yee ig eee o 11S8 se. ss 17°5 = aD hte a 10280" i) cs Percentages of Proteid Digested. Sodium chloride. ‘Neutralsolution. 2-0 p. c. Bicarb. soda. Ol per cent. HCl. 0:2 per cent. HCl. 0 49-7 per cent. 57°77 percent. 27:1 percent. 12-9 per cent. 1:0 per cent. 52:1 56°6 39 5 17°3 2°0 53°4 50'6 39°7 175 4:0 52°7 53°8 38°2 17-3 From these results, it is plain that sodium chloride or common salt increases slightly the solvent action of papoid on coagulated pro- teids in neutral solutions ; while in an acid solution, 0°1 per cent. and 0°2 per cent. hydrochloric acid, it increases very greatly the solvent power of the ferment. This action of the salt we shall see later is connected with a certain solvent power.on one or more of the pro- ducts of digestion, especially formed in acid solutions of papoid. Salt by itself, or in connection with dilute acid, has practically no power of dissolving the proteids of coagulated beef. In fact, the presence of salt diminishes decidedly the ordinary solvent action exerted by dilute acid alone. Thus, 0°2 per cent. hydrochloric acid by itself, at 45° C., will dissolve about 4°6 per cent. of proteid mat- ter from the 10 grams of coagulated beef in 53 hours ; while in the presence of 2:0 per cent. of sodium chloride, acid of the same strength, under like conditions, will dissolve only 2°6 per cent. of the proteid. The salt counteracts the swelling action of the dilute acid and thus diminishes its direct solvent power. Rh. H. Chittenden— Papoid-digestion. 319 In an alkaline solution of papoid, salt appears to inhibit very slightly the proteolytic action of the ferment. BISMUTH SUB-NITRATE. The 10 grams of prepared raw beef contained 2°707 grams of dry proteid (110° C.). ‘ The mixtures were warmed at 45° C. for 7 hours. Bismuth sub-nitrate. Weight of undigested residue. Proteid digested. 0 (Neutral) .0°9043 gram 66°5 per cent. 1:0 per cent. P4816 "540° Be aiteicer 2°0 ne 1°63824 ‘ aCe a This salt, as is evident from the results, diminishes quite decidedly the proteolytic action of the ferment, although digestion will still go on even when the salt is present in large excess. BIsMUTH AMMONIUM CITRATE (SOLUBLE). The 10 grams of raw beef contained 2°2628 grams of dry pro- teid (110° C.). The mixtures were warmed at 45° C. for 8 hours. Bismuth salt. Weight of undigested residue. Proteid digested. 0 (neutral). 0:'5468 gram 75'8 per cent. 1:0 per cent. 1:2583 44-3 mee *s sly AGED! 26 22 eed OO Rh ee 2) Cee Here, as with bismuth sub-nitrate, we see a decided falling off in digestive power in the presence of the bismuth salt. The apparent slight increase in digestive power coincident with the increase in the percentage of the salt is probably due to the somewhat greater alkalinity, which presumably counteracts, in part, the inhibitory action of the bismuth portion of the salt. PEPPERMINT OIL. The 10 grams of raw beef proteids contained 2°6996 grams of dry proteid (110° C.). The mixtures were warmed at 45° C. for 64 hours. Peppermint oil. Weight of undigested residue. Proteid digested. 0 (Neutral) 0:9758 gram 63°8 per cent. 4‘() per cent. 1:0483 GES ets Obviously, the above percentage of oil was not wholly dissolved, but it insured a fairly large excess present throughout the experi- 320 RR. H. Chittenden— Papoid-digestion. ment. This, as seen from the result, did not materially interfere with the digestive action of the ferment. STRYCHNIN AND BRUCIN SULPHATES. The 10 grams of prepared raw beef contained 2°707 grams of dry proteid (dried at 110° C.). The mixtures. were warmed at 45° C. for 64 hours. Alkaloid salt. Weight of undigested residue. Proteid digested. 0 0-7175 gram 73°4 per cent. 0:25 per cent. Strych. sulph. 1:2006 « 5076 oe 0:-D0'. 0:9089..; <<: G64, eee Onaga Brucin sulph. 08461 < ite hay Moni 2 ODO (2 “ a 0°8068 = ¢ 10D Sn These results show that the two alkaloidal salts have a tendency to diminish the digestive power of papoid; a tendency which is more pronounced with strychnin than with brucin, the inhibitory action in the latter case being comparatively slight. Doubtless, the in- crease in digestive action coincident with the increase in the per- centage of the alkaloids is due to the slight acidity of the salts, which presumably overcomes in part the retarding effect of the alkaloidal base. ANTIPYRIN AND ACETANILID. The 10 grams of prepared raw beef contained 2°6996 grams of dry proteid (110° C.). The mixtures were warmed at 45° C. for 64 hours. Medium. Weight of undigested residue. Proteid digested. Control 09758 gram 63°8 per cent. 1°0 per cent. Antipyrin 09500 <* 64:8‘ 2°0 “s oy 1:08038:> <* 59°9 4-0 oh rs 129920 5% 51°8 5 1°0 a Acetanilid 0-9102.> “* 66°22 8 2°0 « he E040 Tap ct 61°71 = These two drugs agree in producing a very slight increase in proteolytic action when present in the digestive mixture in moder- ate amounts, followed in the case of antipyrin by a decreased diges- tive action when the amount present reaches 40 per cent. QUININE SULPHATE. With this salt, there is, as the results show, a slight inhibitory action on the digestive power of the ferment, but not sufficient to materially interfere with its proteolytic action. kh. H. Chittenden— Papoid-digestion. aya The 10 grams of raw beef used in this experiment contained 2-707 grams of dry proteid (110° C.). The mixtures were warmed at. 45° C. for 7 hours. Quinine sulphate. Weight of undigested residue. Proteid digested. 0 0:9043 gram 66°5 per cent. 1°0 per cent. Li632'"** Gz bir a0 pees CI say G29 Lio In view of the results obtained in the majority of the preceding experiments, it would seem that papoid is characterized by a fair degree of resistance towards the usual inhibitory action of many common therapeutic agents. Certainly, the foregoing results show that papoid is able to exert its ordinary proteid-digesting power under many diverse conditions, a fact which gives it added value as a therapeutic agent. 4.—The products of papoid digestion. The foregoing experiments, taken collectively, testify to the pro- teid-dissolving power of papoid under a great diversity of condi- tions. They do not, however, show that this solvent power is neces- sarily akin to, or identical with, that of the ordinary digestive ferments. As is well known, the latter agents exert their solvent action by virtue of certain chemical changes they induce, as a result of which new and for the most part soluble products result, of which the proteoses, or albumoses, and peptones are the principal representatives. It is to be presumed, however, that papoid acts in a similar manner. Indeed, Martin* long ago pointed out that the proteolytic ferment of papaw juice, acting on blood-fibrin, formed large quantities of peptone, together with leucin and tyrosin, as products of its digestive action. Such experiments as I have tried bearing on this point clearly show that the proteid-dissolving: power of papoid is due to a genuine ferment action, whereby soluble prod- ucts are formed which, so far as ordinary chemical reactions will show, are closely akin to, or identical with, those formed in gastric and pancreatic digestion. Leucin and tyrosin are ‘likewise formed, thus showing in another way the resemblance of this ferment to the trypsin of the pancreatic juice. While, in a general way, the final products of papoid digestion are essentially the same under all ordinary circumstances, certain minor differences appear in the primary or side-products, coincident with * Journal of Physiology, vol. v, p. 225. 322 kh. H. Chittenden— Papoid-digestion. changes in the reaction of the digestive fluid, and in the nature of the proteid undergoing digestion. Some of these points may be briefly summarized. In the digestion of coagulated egg-albumin with an alkaline (2°0 per cent. sodium bicarbonate) solution of papoid, even when the digestion has been long continued (say 18 hours) at a favorable tem- perature, and the ferment solution strong, there invariably remains a fairly large undissolved residue. At first glance, this would naturally appear to be simply a residue of unaltered, coagulated albumin. On being tested, however, it is found soluble, at least in great part, in warm 0°2 per cent. hydrochloric acid, from which solution it is reprecipitated by addition of 0°5 per cent. sodium carbonate and redissolved by an excess of the alkaline fluid. This residue is, like- wise, directly soluble in warm 0°5 per cent. scdium carbonate, and reprecipitated by neutralization. These two reactions clearly indi- cate that the above residue cannot be composed of unaltered coagu- lated albumin, since this substance is wholly insoluble in dilute acid and alkali. The only plausible inference, therefore, is that the so- called undigested residue in this case is composed of an albumose-like body insoluble in 2-0 per cent. sodium bicarbonate, a possible primary or side-product of the papoid digestion of coagulated egg-albumin. It is evidently a somewhat unique body, differing from hetero- albumose, and from ordinary globulin, by being insoluble in salt solu- tion. Aside from this peculiar insoluble body, the other products of digestion isolated in the single experiment tried were a deutero- albumose, a fairly large amount of peptone and some leucin and tyrosin. Only a trace of protoalbumose was found, and no hetero. Neutralization of the clear, alkaline digestive fluid failed to give any precipitate, as did also boiling the neutralized solution. In fact, all of the ordinary primary products of digestion seemed in this case to be replaced by the above described insoluble albumose, compos- ing the so-called undigested residue. Of the soluble products, deuteroalbumose and peptone predominated. In the digestion of raw blood-fibrin with a neutral solution of papoid, a somewhat different condition of things was observed. The undissolved residue contained, perhaps, a small amount of the body so characteristic of the digestion of coagulated egg-albumin, but certainly not a large amount. The clear, filtered digestive fluid, however, gave evidence of the presence of a peculiar body which was wholly wanting in the digestion of the coagulated albumin. Thus, the addition of water to the clear neutral fluid gave R. H. Chittenden—Papoid-digestion. 323 a heavy white precipitate, of what was later proved to be an albu- mose-like body, readily soluble in a little 10 per cent. salt solution. Addition of 0°2 per cent. hydrochloric acid, likewise, produced a heavy precipitate of the same body, easily soluble in a slight excess of the acid. Boiling the neutral solution also gave rise to a heavy precipitate or coagulum, apparently the same body. as that precipitated by water and by dilute acid, slowly but com- pletely soluble in warm 0-2 per cent. hydrochloric acid, and in warm 0°5 per cent. sodium carbonate-solution. Hence, this body is a solu- ble albumose and not a coagulable globulin. It is completely pre- cipitable from a neutral solution by heat, and partakes of the general character of heteroalbumose, being insoluble in water but com- pletely soluble in salt solutions, as well as in dilute acid and alkali. In addition to this peculiar primary product of digestion, there was also found a large amount of more soluble primary and secondary albumoses, together with true peptone, leucin and tyrosin. Raw blood-fibrin, digested with a weak hydrochloric acid (0°05 per cent.) solution of papoid, yields the same products as those just described; the peculiar primary albumose making its appearance here in fully as large quantity as in the neutral digestion and apparently taking the place of acid-albumin, which in the single experiment tried appeared to be entirely wanting. In the digestion of cooked beef proteids with a neutral solution of papoid, as likewise with an alkaline solution of the ferment, the peculiar heteroalbumose-like body above described was wholly absent ; only the ordinary primary and secondary albumoses were observed, together with a large amount of peptone and some leucin and tyrosin. The above results, therefore, plainly warrant the statement that the power possessed by papoid of dissolving various forms of pro- teid matter is dependent upon an ordinary digestive action akin to, or identical with, that of digestive ferments in general, whether animal or vegetable. 5.—Action of Papoid on Milk. The action of papoid on milk is twofold. First, under suitable conditions, it brings about a curdling of the milk or separation of the casein, more or less complete according to the circumstances. This is followed by the ordinary digestive action of the proteolytic ferment, in which the precipitated casein is gradually converted, wholly or in part, into soluble products. 324 R. H. Chittenden— Papoid-digestion. The act of curdling, like the process of digestion, is modified more or less by the conditions under which the experiment is tried. Thus, under some circumstances the curdling takes place quickly and the separation of the casein is quite complete. Under others, the curdling takes place slowly and is very incomplete. These points are well illustrated by the following experiments: Each mixture had a total volume of 100 ¢. c., composed of 25 ¢.c. of milk, either fresh or boiled as indicated, 25 c. c. of an aqueous solution of papoid (0°5 gram papoid), and 50 c. c. of water containing sodium bicar- bonate as indicated, or else an equal volume of lime water and water as specified. Some of the mixtures were kept at a tempera- ture of 40-45° C., while others were allowed to stand at the room temperature, viz: 22-24° C. Following, are the results obtained under the different conditions : At 40-45° C. Character of the milk. Reaction of the mixture. Time of curdling. Boiled Neutral ; - 38 minutes Fresh ef 10 oe ee 10 per cent. lime water 11 me +e BOs arise “§ 12 ‘e a: 2 Ores Bicarb. soda* 19 ¥ a3 al! 70) ce 6 35 6<é us Dea ee aS 55 a Boiled 20) sat a 240 ee In the presence of 2°0 per cent. sodium bicarbonate, the boiled milk was very incompletely curdled ; apparently, the digestion of the casein was quite advanced before any sign of separation could be observed. In the neutral solution, on the other hand, the curd- ling of the boiled milk took place almost immediately, as noted, and was at the same time very complete, the casein separating as a fine flocky precipitate, leaving an almost clear fluid. On longer stand- ing at 40° C., the separated casein was, however, gradually dis- solved. In the presence of 0°5 and 1:0 per cent. sodium bicarbonate, the curdling of the fresh milk was not as complete as when 20 per cent. of the bicarbonate was present. This would naturally be ex- pected, since the longer the curdling is delayed the less unaltered casein will there be to separate. In all of the above cases where the curdling took place inside of 20 minutes the separation of the casein was fairly complete. * The percentages refer to the total amount of bicarbonate, or other substance, con- tained in the 100 c. c. of fluid. a R. H. Chittenden— Papoid-digestion. 325 At 22-24° C. Character of the milk. Reaction of the mixture. Time of curdling. Boiled Neutral 12 minutes. Fresh es MAS ies ss : 3 20 per cent. lime water Mab enaatadtat 2 s 90 « Bi b. sod \. the end of 4 nea ota hours. Fresh vig It is thus evident, from the above experiments, that the curdling of milk by papoid is greatly modified by the temperature of the fluid. It is not to be assumed, however, that while precipitation of the casein is delayed by a low temperature, digestion is equally retarded. Such is certainly not the case, for digestion of the casein, whether still in solution or precipitated by the curdling process, unquestionably goes on, although naturally at a slower rate than at a higher temperature. In other words, the rate at which curdling is produced is not necessarily to be taken as a measure of the prob- able rate of proteolytic action on the proteids of the milk. The two processes are, without doubt, wholly independent, and in the case of predigesting milk, where naturally a smaller proportion of papoid is used than in the above experiments, the necessary diges- tion is accomplished without any accompanying separation of the casein; whether it be carried on at a low temperature, or at a tem- perature of 45° C.; and in the presence of water alone, or in the presence of sodium bicarbonate, or lime water. Hence, in order to curdle milk, fresh or boiled, a fairly large pro- portion of papoid must be employed, while for the partial digestion of milk a far smaller proportion will accomplish the desired result, and that without necessarily causing any preliminary separation of the casein. From this we may infer either that the proteolytic fer- ment is present in larger quantity in papoid than. the rennet-like ferment, or else that it is far more active than its neighbor, the milk-curdling ferment. In predigesting milk with papoid, or any other ferment, the main object sought is the partial digestion of the casein ; this being, as is well-known, the most important proteid of milk, and at the same time the one most liable to cause trouble in the feeding of infants, and others, with weak digestion. In order to test the digestive action of papoid on this proteid, the casein was separated from fresh milk by precipitation with dilute acid, partially purified by re-solution in alkaline water, and reprecipitation with acid. It was then washed with water, and though still containing some adherent 326 h. H. Chittenden— Papoid-digestion. fat was reasonably pure. A series of digestions with papoid was then made in the manner already described ; i. e. each digestive mixture contained 0°5 gram papoid, 8 grams of the moist casein, and 25 c. c. of water with the necessary amounts of sodium bicarbonate, etc., to give the indicated percentages. The mixtures were warmed at 40-45° C. for 6 hours, and when ready for filtration each was made as near neutral as possible, in order to precipitate any dissolved casein not converted into pro- ducts soluble in water. The 8 grams of moist casein contained 2°1377 grams of dry pro- teid (dried at 110° C.). Following are the results obtained : Weight of Reaction. . undigested residue. Casein digested.* Neutral 1:5128 grams 29-2 per cent. 1:0 per cent. Bicarb. soda 1 22057 <5 42°9) es 2°0 ri PAGS € i. 768 Alf 4:0 af ne LesGdo: pit 36°35)" 25:0 es Lime water Le ZOTOe eee 41 Vee O-1 as Hydrochloric acid 1°6774 <“ 21:0 It is thus evident that papoid is able to digest precipitated casein under all the above conditions, but that, as with other proteids, digestion proceeds to the best advantage in the presence of 1-2 per cent. sodium bicarbonate. Itis also to be noted that lime water constitutes a particularly good medium for the digestive action of the ferment on casein. The digestive action of papoid on milk-casein was next tested in a somewhat different manner, milk itself being used instead of the precipitated casein. In this series of experiments, each digestive mixture had a total volume of 100 c. ¢., composed of 25 ¢. ¢. of fresh milkt and 75 c. c. of water,{ the latter containing 0°5 gram of papoid, and in some cases the requisite amount of sodium bicarbon- ate to give the indicated percentages. The solutions were warmed at 45° C. for 64 hours, when the undissolved casein was filtered off, washed, dried and weighed. In all of these mixtures, the papoid * The presence of adherent fat in the casein without doubt introduced some slight errors in the above results, as it was noticed when the mixtures were filtered, that some butyric acid had been developed, thus changing, for example, the reaction of the neutral solution to a distinctly acid one; but it is safe to assume that the above percentages at least approximately represent the rate of proteolytic action, under the given conditions. + In one mixture boiled milk was used, as noted. + In one mixture water and lime water, as indicated. Rk. H. Chittenden— Papoid-digestion. 327 produced a separation of the casein inside of an hour, and in much the same order of time as shown in a previous experiment ; the neutral solution of boiled milk curdling within 5 minutes, while the mixture containing the smallest percentage of sodium bicarbonate curdled last, viz: in 55 minutes. In each case, the initial separation of the casein appeared quite complete, although of course some little allowance must be made for possible error in this direction. ‘The digestive action of papoid was, however, quite apparent to the eye, the precipitated casein visibly diminishing in amount as the diges- tion proceeded. The 25 c. c. of milk yielded by precipitation with dilute acid (0:2 per cent. hydrochloric) 1:°6148 grams of casein dried at 110° C. Following are the results obtained: Weight of Casein Reaction. undigested casein. digested. Neutral 0:9328 gram 42-2 per cent. he (Boiled milk) LO Stly S(T a Va 0:5 per cent. Bicarb. soda 09868 ‘* Glow chiens 16 i Ee 0:°7473** Boule cack A ale is O97 os Obs Go RO-OL Lime water ISPS nal PAO Geant From these results, it is to be noted that while boiled milk in a neutral solution is more quickly curdled by papoid than fresh milk, digestion of the precipitated casein is somewhat less rapid. Further, in close agreement with the results found for precipitated casein, it is seen that digestion is most vigorous in the presence of 2°0 per cent. sodium bicarbonate. Somewhat peculiar, however, is the result obtained in the presence of lime water. Digestion in this case appears to have been remarkably slow; certainly not at all in conformity with the previous results with precipitated casein, and other proteids. It is evident, however, from all of the previous results, that papoid, especially in the presence of sodium bicarbonate, is particu- larly well adapted for predigesting milk, the casein being converted by it, as by alkaline trypsin solutions, into soluble and more or less diffusible products. 6.— Action of Papoid on Starch. In addition to the two ferments already described, viz: the pro- teolytic and rennet-like ferments, there is apparently present in papoid a third ferment; an amylolytic one, capable of exerting some action upon boiled starch. At all events, papoid added to 328 R. H. Chittenden— Papoid-digestion. starch paste, preferably in the presence of sodium bicarbonate at 40° C., slowly converts a portion of the starch into soluble starch, and into a more soluble dextrin. This reaction, though plainly recognizable by the iodine test, is neither rapid nor very pro- nounced. It is not at all comparable in intensity to the proteolytic action, but still it does exist and implies the presence of a starch- converting ferment. The best result is obtained in the presence of 2—4 per cent. sodium bicarbonate. A neutral solution of the ferment is also active, but even 0°05 per cent. hydrochloric acid will produce marked inhibi- tion. In the latter case, however, the ferment is not destroyed, but simply checked in its action, since neutralization of the acid fluid with sodium bicarbonate (or better, making it alkaline) is fol- lowed by a renewal of the amylolytic action. Experimentally, the most satisfactory method of demonstrating the starch-converting power is to use a mixture composed of 0°5 gram papoid and 25 «. e- of a 1:0 per cent. starch paste, in which is dissolved 0°5 gram sodium bicarbonate. : | So far as the writer’s experience extends, the amylolytic action is limited to the conversion of starch into soluble bodies giving little or no color with iodine, ordinary soluble starch being first formed. Little or no reducing sugar appears. 7.—Probable Action of Papoid in the Body. Experiments already recorded show that papoid is active in the presence of percentages of sodium carbonate far larger than nor- mally occur in any of the secretions found in the alimentary tract. In fact, in the presence of 0°5 per cent. sodium carbonate, the reputed average strength of the pancreatic juice, the proteolytic action of papoid is slightly increased. ‘The question naturally sug- gests itself, however, in this connection, whether the alkaline pan- ereatic juice might not digest and destroy papoid, thus checking effectually the latter’s action. This important question was an- swered by trying several experiments, one of which may be profit- ably reported. An -artificial pancreactic juice was prepared by warming at 40° C. 1 gram of trypsin (Fairchild’s) with 100 «. ¢. of a 1:0 per cent. sodium bicarbonate-solution and filtermg from the undissolved residue. With this solution, two digestions were made with cooked beef proteids; one with 25 c. c. of the prepared trypsin solution alone, the other with the same quantity of trypsin solution plus 0°5 gram papoid. hAs ee le eens Rh. H. Chittenden— Papoid-digestion. 329 The two mixtures were warmed at 40° C. for 6 hours. The 10 grams of cooked beef proteids contained 35707 grams of dry proteid (110° C.). Weight of Medium. undigested residue. Proteid digested. Trypsin sol. alone 1°5657 grams 56°1 per cent. as ‘* with papoid tbO 4d ee iS O90 =) <8 From these results it is evident that the two proteolytic ferments, trypsin and papoid, can work together in the same solution, the latter ferment contributing to the digestive strength of the former. At first glance, it might seem that in combining trypsin and papoid we should have, providing there is no destruction of the latter fer- ment, a proteolytic action numerically equivalent to that of the two ferments, but the concentration of the solution must be taken into account, as well as the inhibitory effects of the accumulated products of digestion, both of which cannot well help acting as a check to continued ferment action. Doubtless, with a weaker trypsin solu- tion the digestive action of papoid would be more strongly marked. Another point to be taken into account in considering the action of papoid in the intestine, is the influence of bile. Two experi- ments were therefore tried ; one with ox bile, the other with human bile obtained from a fistula. The 10 grams of raw beef proteids used in the first experiment contained 2°707 grams of dry proteid (110° C.). The mixtures were warmed at 45° C. for 7 hours. Dry ox bile. Weight of undigested residue. Proteid digested. 0 (Neutral) 0°9043 gram 66°5 per cent. 4°0 per cent. ie to aa bs Ou“ Dry human bile, 0 (Neutral) IctOsOee pan 2 2:0 per cent. 09295 « 66-1 « In the latter experiment, with human bile, the mixtures were kept at 45° C. for § hours, and the 10 grams of prepared raw beef con- tained 2°743 grams of dry proteid (110° C.). The human bile was quite strongly alkaline, which probably accounts, in part, for the increased digestive action noticed. Both results, however, clearly show that the presence of bile offers little or no obstacle to the action of papoid in the intestinal tract. The only remaining point to be considered is the probable fate of papoid in the stomach. In this connection, it has already been demonstrated that the ferment is only slightly inhibited in its action by the presence of 0°1 per cent. hydrochloric acid, and that even in the presence of 0°2 per cent. hydrochloric acid it exhibits a fair 330 — RR. H. Chittenden—Papoid-digestion. degree of activity ; both of which results clearly favor the action of papoid in the stomach. Further, while the presence of 0°1 per cent. hydrochloric acid lessens somewhat the action of the ferment, the latter is not destroyed ; hence, by neutralization of the acid the inhibitory effect is overcome and the ferment springs into renewed activity when brought in contact with an alkaline medium. By long-continued warming of the bare ferment with 0°2 per cent. hydrochloric acid, there is a pronounced destructive action. This destruction, however, is accomplished by the free acid ; free, because of the lack of pro- teids present for it to combine with, a condition of things not so liable to occur in the case of a full stomach, which is naturally the time when a digestive ferment would be administered. The above statements are illustrated by the following facts: Two portions of papoid, 0°5 gram each, were warmed at 40° C. for 5% hours with 25 c. c. of 0-2 per cent., and 0°1 per cent. hydrochloric acid, respectively. The two solutions were then neutralized and eventually made slightly alkaline with sodium bicarbonate. Their digestive action was then compared with that of a like amount of fresh papoid, dissolved in the same quantity of fluid and of the same reaction. The 10 grams of cooked beef proteids contained 3:4420 grams of dry proteid (110° C.). The mixtures were warmed at 40° C. for 6 hours. Weight of Conditions. undigested residue. Proteid digested. Fresh papoid 1°7930 grams 47°8 per cent. Previously ‘ F : ‘ : “< Tae Lo 1 per cent. HCl 1-8425 46-4 66 6é 0:2 66 66 2:9960 66 14:9 66 It is thus evident that, under the above conditions, 0°1 per cent. hydrochloric acid may hinder the digestive action of papoid, but will not destroy the ferment. With 0-2 per cent. hydrochloric acids however, when the acid is free and not combined with proteid matter, there is a marked destruction of the ferment; not complete, but doubtless sufficient to interfere somewhat with its action. In the presence of an excess of proteid matter, this destructive action is not so marked. The presence of pepsin does not appear, materially, to modify the action of the dilute hydrochloric acid on papoid. I do not think that gastric juice of a given acidity has any more deleterious effect on the ferment, than acid of the same strength alone. In any event, ase i Vea R. H. Chittenden— Papoid-digestion. 331 papoid will certainly exhibit marked proteolytic action in the pres- ence of 0-1 per cent. hydrochloric acid and pepsin, although the conditions may not be favorable for the best action of pepsin. This is illustrated by the following experiments: an artificial gastric juice was prepared by dissolving some commercial pepsin (Fairchild’s) in 0°1 per cent, hydrochloric acid, in the proportion of 0-1 gram pepsin to 25 c.c. of acid. Digestions were then made, with and without papoid, of raw and cooked beef proteids, with the following results: The 15 grams of raw beef used contained 4°0494 grams of dry proteid, while the 10 grams of cooked beef contained 3-9608 grams of dry proteid (110° C.). The digestions were kept at 40° C. for 6 hours. a. With raw beef proteids. Weight of Proteid Character of the fluid. undigested residue. digested. 25 c. c. pepsin—HCl alone 3°3626 grams 16°9 per cent. * mc if a5 . Oy 66 . 6é 0:5 gram papoid 1-482 63°3 b. With cooked beef proteids. , Weight of Proteid Character of the fiuid. undigested residue. digested. 25.¢. c. pepsin—HCl alone 3°8689 grams — 2°3 per cent. 66 ¢ 66 ee ; ie ‘ oe 0°5 gram papoid 32124 44°] The action of papoid is prominent here simply because the condi- tions are favorable for its action, while they are not well adapted to the action of pepsin. The two points to be emphasized are, how- ever, first, that the presence of pepsin does not interfere with the action of papoid in an acid medium, where the other conditions are favorable to the latter ferment; and secondly, that any direct com- parison of the digestive action of the two ferments cannot well be made, since they act under such totally different conditions as regards dilution, reaction, etc. Further, in studying the action of acids on any ferment we have to consider not only the influence of a given percentage of acid, but must also take into account the absolute amount of acid, both in proportion to a given quantity of ferment and the proteid matter to be digested. It is hardly neces- sary to detail the several experiments that have led to this conclu- sion; one alone will suffice. The following mixtures were warmed at 40° C. for 6 hours, with 10 grams of cooked beef proteids, with results as indicated: 332 R. H. Chittenden— Papoid-digestion. Digestive mixture. Proteid digested. 100 c. c. 0-1 per cent. HCl, 0-1 gram pepsin, 0 papoid 21-4 per cent. &é a4 sé ce 0:5 gram se 91°3 “< 50 c. c. 0'1 per cent. HCl, 0-1 gram pepsin, 0 papoid 8°2 per cent. = ¢ es ‘* 0°5 gram *“ 148 5 25 c. c. 0:1 per cent. HCl, 0:1 gram pepsin, 0 papoid 6°8 per cent. = ms ih [fo ara °F oe oy It is thus seen that 0°5 gram of papoid, acting upon 10 grams of cooked beef proteids, in the presence of pepsin and 0°1 per cent. hydrochloric acid, will digest a reasonable amount of the proteid when the volume of the acid fluid is only 25 ¢. ¢., the pepsin action being very slight. As the volume of acid fluid is increased to 50 c. ¢., then the papoid action diminishes almost 50 per cent., while the pepsin action shows a slight increase. Increasing the volume of acid fluid still further, to 100 c. ¢, the pepsin action becomes paramount. Hence, it is evident that the rate of action of papoid in the stomach hinges mainly upon the presence or absence of an excess of free acid. With only combined hydrochloric acid present, and an excess of proteid matter and salts, a condition of things generally prevalent especially in the early stages of digestion, papoid cannot well help exerting its peculiar proteolytic power. And in this con- nection, it is to be remembered that papoid acts to the very best advantage in a concentrated fluid, in the presence of an excess of proteid matter. From the foregoing experiments, the following conclusions may be drawn : 1. That papoid is a true, soluble, digestive ferment or mixture of ferments, of vegetable origin. 2. That it has marked proteolytic action in acid, alkaline, and neutral solutions and in the presence of many chemicals, antisepties, and therapeutic agents. 3. That it has a peculiar softening and disintegrating action on proteids, and that its general proteolytic action is that of a genuine digestive ferment, similar to the ferments of animal origin. 4. That it has a certain amount of amylolytic, or starch-dissolving power. 5. That it has a marked rennet-like action upon milk, and a pro- nounced digestive action upon milk-casein. 6. That it exerts its peculiar digestive power at a wide range of temperatures. 7. That the ordinary conditions of health and disease in the stomach and intestine are not liable to check its action, while certain possible conditions may accelerate it. TV.—On THE CLASSIFICATION AND GEOGRAPHICAL DISTRIBUTION OF THE LAMINARIACEZ. By WititAmM ALBERT SETCHELL. AccorpineG to Bory de Saint Vincent,’ the name Laminartius was first used by Roussel in his ‘‘ Flore du Calvados” which was pub- lished in 1796. Lamouroux was the first to use the name Laminaria distinctively,’ and he was the first to separate the genus from the old comprehensive genus Fucus. Bory established several new genera,’ and grouped them together under the name of Laménariées.* He included the genera Durvillewa, Lessonia, Macrocystis, Agarum, Laminaria, and Iridea as understood by him. He also established two subgroups, the one comprising those forms with branched stipes, the other to include the forms with simple stipes. Since Bory’s publication there have been several revisions of the Laminariacece and it will be best perhaps to consider these briefly at this point. De la Pylaie, in the “‘ Flore de Terre Neuve,” gave a systematic review of the kelps and created a number of new genera, only one of which, viz: Saccorhiza, remains established. In Decaisne’s ‘‘ Essais sur une classification des algues et des poly- piers calciféres de Lamouroux,”® the eight genera assigned to this group are arranged in the following order: Laminaria, Haligenia, Agarum, Capea, Alaria, Ecklonia, Lessonia, and Macrocystis. In this arrangement the nearly related genera are grouped together. Endlicher enumerates eleven genera in the “Genera Plantarum.’”’ He does not group them together into subtribes, but arranges them in the following order: Lessonia, Macrocystis, Nereocystis, Ecklonia, Laminaria, Capea, Haligenia, Alaria, Thalassiophyllum, Agarum, and Costaria. The most noticeable feature of this arrangement is the relative positions occupied by cklonia, Capea, and Alaria. Neither Chorda (Scytosiphon filum) nor Lgregia (Phyllospora Menziesiz) are included in this group by Endlicher. In the same year (1843) Kiitzing published his “ Phycologia Gene- ralis” in which he proposed three new genera and divided the family, as he called it, into three sections. In his “Species Alga- 1 Dict. Class. d’Hist. Nat., t. 9, p. 187, 1826. 2 Essai, etc, in Ann. du Mus. d’Hist. Nat., t. 20, p. 41, 1813. 3 Loe. cit.. pp. 192-194. * Loc, City p.- 191. 5 1829, 6 Ann. Sci. Nat., sér. 2, t. 17, p. 330, 1842. 7 Suppl. ITT, p. 26, 1843. TRANS. Conn. ACAD., Vou. IX. MARCH, 1893, 24 334 W. A. Setchell— Classification and Geographical rum,” he retains these three sections and presents the following arrangement :°— “Sxctio I. Laminariee genuine; nec cribrate, nec caulescentes.” 1. Phleorhiza. 2. Laminaria. 3. Hafgygia. 4. Haligenia. 5. Capea. 6. Alaria. 7. Costaria. “Srctio Il. Agarex; stipitate vel caulescentes, phyllomate gi- ganteo cribratim et regulariter perforato.” 8. Agarum. 9. Thalassiophyllum. “Srctio III. Macrocystez ; caulescentes, foliosi; folia ex divi- sion basilari phyllomatis oriunda.” 10. Lessonia. 11. Macrocystis, 12. Nereocystis. 13. Pinnaria. The first volume of J. G. Agardh’s “‘Species Algarum” appeared in 1848. He included the genera Adenocystis, Hook. et Harv. and Seytosiphon, Endlich. (which at that time included not only Se. Jilum, Ag., but also Se. lomentarius, J. Ag. and Sc. tomentosus, J. Ag.). He divided the order (as he termed it) as follows:— “+ Soris totam frondem investientibus.” 1. Adenocystis. 2. Scytosiphon. “++ Soris maculas ambitu indefinitas efficientibus * Fronde ecostata, integra aut vage fissa, terminali.” 3. Laminaria. 4, Saccorhiza.. «<** Hronde ecostata circa stipitem spirali.” 5. Lhalassiophyllum. sc *#** Hronde costata.”’ 6. Costaria. 7. Agarum. & Alaria, «aeek Wronde pinnatifida.” 9. EKeklonia. «xkeeeE Wronde foliosa, foliis ambitu definitis.” 10. Wereocystis. 11. Lessonia. 12. Macrocystis. _ This is the latest classification of the Laminariacee known to me. Since then however, there have been several works which have added not only to our knowledge of the morphology of the various species, but also in regard to the affinities of the various genera. 1 Leipsic, 1849, 2 Cf. pp. 573-584. Distribution of the Laminariacee. 335 A great impulse was given toward a closer examination and a more correct determination of specific differences by Le Jolis’s pub- lication in 1855-56 on the confusion existing in regard to the two European species of digitate Laminarie.’ In J. G. Agardh’s “ De Laminarieis,” there is a most able discussion of a number of points of resemblance existing between the genera of the group in connec- tion with the description of new points in the morphology of the species. Most important too, are the descriptions and remarks to be found in the fourth and fifth portions of the “ Observationes Phycologice” of J. E. Areschoug,® where a number of rare forms receive full treatment. Since then a considerable number of forms have been described by Kjellman, Foslie, Bornet, and others, and there has been a very active study of the different forms and varieties of the different species, particularly among the Scandinavian algologists. But, as yet, there exists no classification of the group as a whole, that is natural or complete. Consequently this subject together with some of the main features of distribution have been taken up by the writer in the present article. The order of the Laminariacee or kelps is one of the most dis- tinct and well-defined among the Phzosporee, or, even among Algz in general. The members of the order are all of comparatively large size, while the species of Macrocystis reach a length even sur- passing that of tropical “climbers” and those of Lessonia possess stipes which in size and grosser structure strongly resemble the trunks of the ordinary dicotyledonous trees of temperate climates. They all with the exception of Chorda, possess a distinct stem or stipe and an expanded leaf or blade. The principal meristematic region in all is intercalary,* being situated in all except the genus mentioned, at the place where the stipe passes over into the blade viz: at the transition-place (Uebergangstelle). The organs of fructification are essentially the same in all the species and are crowded together into broad patches or “sori.” In Chorda the sori completely cover the whole surface of the frond, but in all the other genera they are of much more limited extent, Acta, Bd. -25, II, 1856. 2 Tund’s Univ. Arsskrift, t. 4, 1867. 3 Nova Acta Reg. Soc. Sci. Upsal., ser. 3, Bd. 12, I and II, 1884-5. 4 Cf. Janczewski, Mem. Soc. Nation. Sci. Nat. de Cherbourg, t. 19, pp. 109-113, 1875. 336 W. A. Setchell— Classification and Geographical of unilocular zoosporangia and of unicellular paraphyses. In all the species except those of Chorda and Saccorhiza, the paraphyses possess a peculiar and characteristic hyaline appendage at the tip. The order of the Laminariacez, then, includes all those species of the Pheosporee having unilocular sporangia and unicellular para- physes compacted into sori. The plants belonging to it are all of comparatively large size and have the principal meristematic region intercalary. When we come to consider carefully the morphology of the vari- ous species of kelp, we soon find that they arrange themselves into three or perhaps four different groups on account of the resem- blances between the methods by which the complexity of form of the adult plants is produced. On careful examination we find that the region of active growth in length, at the transition-place, is the place where these differences arise and that good distinctive charac- ters may be drawn from the different modifications of the transition- places in the different groups. Almost any species of Laminaria represents well the simplest type of all. The stipe expands gradually, or, at times, more or less abruptly, into the blade and the transition-place is plane and un- modified. There is nothing in the external appearance of the transi- tion-place to indicate that at this region, the stipe is increasing in length at its summit and the blade at its base. We may call this type the Laminaria-type and the special tribe characterized by it the Laminariidee. In the Laminaria-type we have a very simple and unmodified transition-place and the resulting frond characteristic of the Lami- nariidee is simple and unbranched. But when we turn to the species of the genus Lessonia we find that the adult fronds are pos- sessed of a complexity of structure that warrants us in expecting to find also a more decidedly modified transition-place than we found in Laminaria. In Lessonia, instead of the unbranched frond of the Laminaria, we find numerous small blades borne at the extremities of the ramifications of the dichotomously branched stipe. Conse- quently there are as many transition-places as there are blades. If we examine carefully the different blades of a single specimen, we shall readily discover how the characteristic dichotomous branching of the stipe arises. A longitudinal slit appears in the central por- tion of the transition place at the base of a blade and as blade and stipe increase in length, extends (or appears to) both upwards and downwards until finally we have two blades each with its own short Distribution of the Laminariacee. 337 branch of stipe and each with its own transition-place. The posses- sion of this power of splitting longitudinally by the transition-place is characteristic of the members of a tribe of the Laminariacez which may be called the Lessoniidex, under which may be reckoned two subtribes, the Lessonex, represented by the genus Lessonia, Nereocystis, etc. and the Macrocystee which includes only the genus Macrocystis. These subtribes will be discussed more fully below. It is to be mentioned here, however, that the original blade does not persist but its place is taken by the blades split off from it, the place of these by others, and so on. There is but one other general type of frond to be noticed and that is well represented by the fronds of any species of Alaria. In these, there is not only a large terminal blade which persists and a simple stipe with the meristematic region situated at the transition- place, but there are also present on the upper portion of the stipe (or the rhachis as it is called) twvu rows of leaflets or sporophylls (so-called because they alone bear the sori). In Alaria, the sporo- phylls arise as outgrowths on the lower portion of the transition- place, grow larger and larger until they reach a certain definite size when they have come to be situated at some distance below the transition-place which has been carried upward and away from them by the growth of the stipe in length and their places on it have been taken, in turn, by newly formed sporophylls. In this way a simply pinnate frond is produced. The essential feature then, of the Alaria-type is the formation of a compound frond by means of these outgrowths from the meris- tematic region. The tribe of the Alariidez based upon this type contains three subtribes, the Alariew including Alaria and Pterygo- phora, the Egregiee to include Hyregia, and the Ecklonex includ- ing Leklonia, Hisenia, ete. Above we have glanced at the three general types of adult struct- ure and the modifications of the transition-place associated with each. We are now in a position to consider the details of variation of these types as illustrated by the different genera. LAMINARIIDEH.—The members of this tribe, with the exception of Thalassiophyllum Clathrus, P.&R., possess unbranched fronds and all possess unmodified transition-places, unless we except the peculiar scroll-like structures noted below in the case of Agarwm and Thalassiophyllum. Under this tribe we may distinguish two subtribes, the Laminariex and the Agaree. 338 W. A. Setchell— Classification and Geographical Subtribe 1. Laminariew.—To this subtribe belong the three genera Chorda, Saccorhiza, and Laminaria.’ They agree in possess- ing a frond which is neither ribbed, perforated, nor with bullate swellings scattered over it and whose transition-place is perfectly plane and unmodified. Chorda, Stackh. We have two species of Chorda which are well known. They both differ very much in habit from the other kelps in possessing long cylindrical fronds which arise from a dis- coidal hold-fast. The fronds are hollow with diaphragms at irregu- lar intervals. The fronds in both species are covered with hairs, which in QC. filum (L.), Stackh. are more scanty and colorless, while in C. tomentosa, Lyngb., they are plentiful and possess abundant chromatophores. One or two other species are described, but they are little known. It has been customary for the last fifteen years to place these ‘species among the Laminariacez, on account of their unicellular paraphyses and unilocular sporangia covering the surface of the frond. But Reinke® dissents from this view and places them in a special sub-family Chordee (under Phzosporex) near to the Scyto- siphonex, on account of the cylindrical thallus and the occupation by the zoosporangia and the paraphyses of the whole surface. Chorda resemble Scytosiphon very much in habit and in this, differs from the other members of the Laminariacez, all of which possess a distinction between stipe, blade, and hold-fast. . It differs from Scytosiphon in its unilocular sporangia and more abundant unicellular paraphyses and in these details it resembles more closely the ordinary kelps. But the paraphyses lack the hyaline appendage so characteristic of nearly all the Laminariacee. In this however, it agrees with the species of Saccorhiza whose paraphyses are almost identical in structure with those of Chorda. It seems best to the writer therefore, to retain Chorda among the Laminariacez, for the present at least.* Saccorhiza, DelaPyl.—There are two species of this genus that are well known and two or three species that are very uncertain. 1 Prof. Kjellman (UndersOkning af nagra till slagtet Adenocystis, Hook. fil. et Hary. hanforda Alger, in Bihang till k. Svenk. Handl., Bd. xv, Afd. III, No. 1, 1889), has referred the type of the genus Adenocystis, A. Lessonii, Hook. fil. et Harv. to the Laminariacee, placing it near Chorda. The writer has not been able to examine spe- cimens of this type. * Atlas Deutscher Meeresalgen, Heft 2, p. 41, 1891. 3 Cf. also Setchell, Proc. Am. Acad., vol. xxvi, pp. 211-212, 1891 Distribution of the Laminariacec. | 339 The better known species are S. dermatodea (DelaPyl.), J. Ag. and S. bulbosa, DelaPyl. SS. dermatodea is the simpler form. Its structure and development have been treated of by the writer in another place.’ The structure and development of S. dulbosa has been carefully described by Barber.’ The first or primitive hold-fast of S. dermatodea is discoidal but soon two successive whorls of hapteres appear from a swelling, the “rhizogen,” which appears just above this primitive hold-fast. The stipe is flattened and in young specimens expands gradually into the blade which is covered at this period with cryptostomata. The hold-fast therefore, as well as the blade and stipe are much more complicated than in the species of Chorda. Yet the two genera agree closely in possessing paraphyses destitute of the hyaline appen- dages found in all the other genera. The relationship of S. derma- todea to S. bulbosa is much nearer than might be supposed from the great difference in size and habit existing between the adult plants. Young plants of the two species are very similar and the earlier changes to produce the rhizogen is essentially the same in both. Only two successive whorls of hapteres are produced in S. derma- todea however, while in S. bulbosa whorl after whorl are produced and the rhizogen consequently becomes enlarged into the character- istic “bulb” of the adult plant. Both species also, possess charac- teristic sclerenchyma fibers in the medulla of both stipe and blade. Both species of Saccorhiza very closely resemble those of Lamin- aria in general habit, but differ sufficiently in structure to be kept in a separate genus. Laminaria Lam’x.—The species of Laminaria are at present in great confusion and it is very difficult to determine just how many there are. About 28 species are usually recognized but several of these are doubtful and little known. They may be separated readily into two groups, the simple Laminarie of which there are about 11 species and the digitate Laminarie, of which there are about 17. Although there are many important individual variations such as the possession of a creeping rhizome-like organ as in LZ. Sinclairii (Harv.), Farlow, and in LZ. Rodriguezii, Bornet, the simple, discoidal hold-fast in L. solidungula, J. Ag., the peculiar modification of the base of the blade in ZL. radicosa, Kjellm. or even of more general characters such ag the longitudinal splitting of the blade in the 1 Proc. Am. Acad, vol. xxvi, pp. 177-217, Pl. 1-2, 1891. ? Annals of Botany, vol. iii, p. 41, PJ. 5, 1889. 340 W. A. Setchell— Classification and Geographical digitate species and the presence or absence of mucilage glands in the stipe, which Kiitzing’ has used to separate Hafgygia from Laminaria, yet in general structure they are all similar and agree perfectly in the most important characters, viz: the perfectly un- modified blade and transition-place. The features just mentioned, although remarkable and important, are to be looked upon as the variations among individual species or small groups of species. Subtribe 2. Agareze.—The genera included under this subtribe are Agarum, Thalassiophyllum, Costaria, Cymathere, and perhaps also Arthrothamnus. Agarum (Bory), P.&R.—The genus Agarum, although occurring both in the northern Atlantic and the northern Pacific, probably con- tains but a single species. The individuals however vary greatly in size, outline of the frond, the size and shape of the perforations, etc., but it is hard to find fixed characters to separate them.* In Agarum Turneri, P.&R., we find a stipe of very variable length (from an inch or two up to a foot or more) which bears at its tip the heart-shaped blade. Where the blade arises from the transition-place, which appears here to form a portion of the stipe, it unrolls itself from two small conical scrolls, each of which is involute upon the stipe into a sort of spiral. These scrolls at the base of the blade are present even in young plants of about 2 inches in length and probably also in still smaller ones. J. G. Agardh noticed these scrolls, for he says on page 3 of “ De Laminarieis;” “Sunt in his frondes una pagina plus minus ab altera dissimiles; seepe basi convolute, gerunt unam internam, alteram externam faciem;” and a few lines farther on: “In Agaro est stipes revera ad ortum frondis canaliculatus et frondis lamina, secus margines stipitis decurrens, involuta.” This is the only mention of these scrolls known to the writer. The stipe is continued up through the blade as a sort of broad midrib. The blade is perforated with holes of various sizes, the development of which has been described by Humphrey.* Thalassiophyllum, P.&R. — Thalassiophyllum Clathrus, P.&R., the only representative of this curious genus, is a resident of the 1 Phyc. Gen., p. 346, Species Alg., p. 577, also Areschoug, 6bs. Phyc;, Pt. 4p * Of. P. & R., Il. Alg., Pl. 20-23, 1840. 3 Cf. Farlow, New Engl. Alg., pp. 96-97, 1881, as to variability of the New England species. 4 Proc. Am. Acad., vol. lxxiii, pp. 201-203, 1886. Distribution of the Laminariacee. 341 northern portions of the Pacific Ocean. It differs decidedly in general appearance from Agarum Turneri, yet in its essential feat- ures comes very close to it. It has the same peculiar perforations in the blade and they arise in essentially the same fashion as in Agarum.’ The blade unrolls itself from a scroll-like transition-place as in Agarum, only in Thalassiophyllum, there is only one, very large scroll and the resulting blade is one-sided and fan-shaped with a cuneate base. As the blade unrolls itself it dies away on the free margin and leaves behind itself upon the stipe a spirally twisted ridge-like scar which is different from anything found in any other species of the Laminariacee unless it be the scar on the stipe of Arthrothamnus Kurilensis, Rupr. which is mentioned below. The frond of Thalassiophyllum is branched, but the branches do not follow a regular order as they do in Lessonia nor do they arise by any similar process, but originate as proliferations from the mar- gins of newly formed perforations at the transition-place.° Costaria, Grev.—This genus also contains a single species, C. _ Turneri, Grev. which is peculiar to the northeastern portion of the Pacific. The stipe is short and the blade is broadly ovate. The Stipe expands gradually into the blade in the younger specimens but in the older specimens the base is decidedly cordate.* There are no scrolls at the base of the blade, but the transition-place is unmodified and is plane except where the ribs are forming. These ribs run longitudinally through the blade and are five in number. Both Agardh* and Areschoug” call them “plicae” and explain that they project on one surface of the frond and are hollowed in on the other. Furthermore they both agree that the stipe is 5-striate and that the ‘“‘plicae ” of the blade are continuations of these striae of the stipe. The writer has had the opportunity, through the kindness of Prof. W. G. Farlow of Cambridge, Mass., and of Mr. F. S. Collins of Malden, Mass., to examine both old and young herbarium specimens and is indebted to Dr. C. L. Anderson of Santa Cruz, Cal., for a fine series of younger specimens preserved in moderately strong alcohol. The examination of these specimens failed to show the striae on the stipe and also has shown that while the so-called “plicae” project on one surface of the blade owing to a thickening in the cortical 1 Cf. Rosenthal, Flora, Bd. 48, p. 140, 1890. * Cf. Rosenthal, loc. cit, p. 149, Pl. 7-8, f. 33a and 34a. 8 Of. Pi disRn, Ul. Alo; Pls 2a. 4 De Laminarieis, p. 3. 5 Obs. Phyc, Pt. 4, pp. 19-20. 542 W. A. Setchell— Classification and Geographical tissues just under that surface, the other surface is not at all fur- rowed but perfectly plane. Consequently the blade of Costaria is not really plicate but ribbed, and each particular rib is confined to one surface, there being three on one surface and two on the other. Besides the ribs, the blades of the older specimens possess bullate swellings and these swellings are sometimes perforated as in Ayarum. This is the rule in the var. pertusa, Harv.’ Cymathere, J. Ag.—This genus was established by J. Agardh to receive the Laminaria triplicata, P.&R. The holdfast is dis- coidal and in this it resembles L. solidungula, J. Ag. The stipe is short. The blade possesses three longitudinal “ plicae” according to J. Agardh’® and five according to Areschoug.’ These “ plicae” are crowded together in the central portion of the blade which is also thickened in this region. J. Agardh also says:* that the blade is ‘“‘inferne involuta” in the young fronds. The writer has had the opportunity of examining a Postels and Ruprecht specimen collected by the Liitke expedition and preserved in the herbarium of Prof. Farlow at Cambridge, Mass. It is a rather young specimen and shows the discoidal base and the blade with the thickened central portion. The longitudinal “ plicae” are not very distinct, and the transition-place seemed to be plane and not provided with scroll-like structures. ; Arthrothamnus, Rupr.—The species of this genus belong in the northern Pacific and are very little known. Ruprecht has figured the type’ A. Kurilensis and a figure of A. bifidus, J. Ag. (A. radicans, Rupr.) is represented in plate 15 of Postels and Ruprecht’s “Tllustrationes Algarum.” A. longipes, J. Ag., and A. Bongar- diana (P.&R.), J. Ag. are probably incorrectly referred to this genus. The blade in both A. Awrilensis and A. bifidus seems to be plane but at the base it unrolls, in each species, from two small scrolls similar to those in Agarum Turneri. The stipe of A. Auri- lensis is forked® and marked with a spirally twisted scar after the fashion of Thalassiophyllum. The stipe in A. bifidus is said to be decumbent’ and repeatedly bifurcate, emitting “roots.” A specimen of Laminaria bifida, P.&R., collected by the Liitke expedition, in Prof. Farlow’s herbarium shows a long undivided blade involute 1 Proc. Am. Acad., vol. iv, p. 329, 1859. * De Laminarieis, p. 3. *-Obs. Phye., Pt. 4£2p. 20. & Loe: Cit. dp. 3. > Mem. Imp. Acad. St. Petersb., t. 6, Pl. 17, 1848. 6 Cf. Ruprecht’s figure, loc. cit. 7 Cf. Areschoug, Obs. Phyc., Pt. 5, p. 14. Distribution of the Laminariacec. . 343 on both sides at the base, but the characters of the stipe were ob- scured in the specimen. In the subtribe Agarez then, we find four, or perhaps five genera whose relationships both to one another and to the Laminariez are both complex and interesting. The lack of available material further complicates this discussion as all the forms except Ayarum Turnert are rarely found in herbaria. Agarwm and Thalassio- phyllum although so different in habit, are, as shown above, very closely related and seem to be of a type thoroughly distinct from the Laminaria-type. But they are connected with it both by Cos- taria and by Cymathere. Costaria is the nearer to Agarum in general habit. It has peculiar swellings and perforations of the blade that are very similar to those in Agarum and in habit, color, and internal structure the two are very similar. In both, the blade is ribbed with the differences noted above. But Costaria lacks the peculiar scrolls by which the blade of Agarum unrolls itself at the base, and in this respect it resembles the Laminaria-type. Cymathere on the other hand seems to be between Costaria and Laminaria, resembling the former in possessing ribs (or ‘ plicae”), and yet probably destitute also of the scrolls at the transition- place. Arthrothamnus might perhaps be considered as intermediate between Agarum and Thalassiophyllum on the one hand and Laminaria on the other. The blade is neither perforated nor ribbed, and yet it possesses the involute scrolls of Agarum at the base and the spirally scarred stipe of Zhalassiophyllum. LxssonipE2.—Under this tribe are reckoned the tive genera; Dictyoneuron, Lessonia, Postelsia, Nereocystis, and Mucrocystis. All of these genera are much more complex than any of the Lamin- arlidez. The fronds in all except Dictyoneuron are branched and this branching originates in a splitting at the transition-place as mentioned above. As to whether this splitting divides the blade at whose base it occurs, equally or unequally, we have two subtribes established, viz: the Lessoniez, comprising the first four genera and the Macrocystee, including the genus Macrocystis. Subtribe 1. Lessoneee. The four genera Dictyoneuron, Lessonia, Postelsia, and Nereocystis form a very natural subtribe of the Les- soniidez., ‘Their relationships are briefly discussed below. Dictyoneuron, Rupr.—There is only a single species belonging to this genus. It inhabits the Californian coast and is rather rare. 344 W. A. Setchell— Classification and Geographical The blades are long and narrow and often curved. The surfaces are coarsely reticulated with prominent veins and the margins pro- vided with remote coarse teeth, The fissure appears in the transi- tion-place and divides the blade into two and the stipe almost to the very base so that there is very little of a common stipe left, and this soon disappears or becomes covered with “rootlets,”* so that we have finally what looks like a group of separate plants in various stages of fission. Lessonia, Bory.—There are about six species of this interesting genus, but most of them are rare or ill-represented in herbaria. The “leaves” split at the base into two equal parts each of which develops into a new leaf with it own portion of stipe, and by the repetition of this process the stipe becomes very regularly dichoto- mously branched, and the “ leaves ” or small blades are borne on the ultimate ramifications. The lower portion of the stipe thickens and becomes fairly stout, even in the smaller species, and in the larger ones it reaches such a size and imitates in its “rings of growth” so very closely the woody exogens, that the dead trunks thrown up on the beach have been mistaken for logs.’ Postelsia, Rupr.—In some of the species of Lessonia, the “leaves ” are borne on very short branches of the stipe and therefore form a more or less compact cluster at the top of the main stipe or ‘‘ trunk.” This is carried still farther in the form, to receive which Ruprecht proposed the genus Postelsta. In adult specimens of this plant, the trunk is hollow and reaches a length of about a foot and a half, with a diameter somewhat less than an inch. On the flattened top of the trunk grows a bunch of from 30-50 leaves which appear to spring directly from it. Each leaf is lanceolate, or somewhat gladi- ate, coarsely wrinkled longitudinally, and provided with a distinct stalk. Most of them are found in the process of dividing which occurs exactly as in Lessonia and Dictyoneuron. ‘The stipe of each blade splits to the very base, and so all trace of the branching is lost in the majority of the leaves. Occasionally, however, the split- ting does not continue to the very base of the stalk and this gives rise to a few short branches each bearing six or seven leaves. Ruprecht has given excellent figures of adult plants in his ‘“ Neue oder unbekannten Pflanzen aus dem nodrdlichen Theile des stillen Oceans.””* \ 1 Cf. Rupr., Mem. Imp. Acad. Sci. St. Petersb., t..7, p. 80, Pl. 7, 1852. ® Cf. Hooker, Flora Antarctica, Pt. 2, p. 458, 1347. 3 Mem. Imp. Acad. Sci. St. Petersb., t. 7, Pl. 6, 1852. Distribution of the Laminariacee. 345 Nereocystis, P,.&R.—There are two species of the famous “ blad- der-kelp ” of California, the one, WV. Liitkeana, P.&R. ranging from Santa Cruz northward to Behring Straits, the other WV. gigantea, Aresch., extending from San Diego southward along the coast of Lower California. The latter has been made the type of a new genus by Areschoug,’ viz: Pelagophycus; but there seems to be no adequate reason for separating it generically from WV. Liitkeana.’ Both species agree in having a very long stipe which is slender and solid at the base and broader and hollow above, while at the apex it expands more or less abruptly into a large globular or pear- shaped bladder upon which are borne two bunches of leaves. In NV. Littkeana the bunches are sessile upon the top of the bladder,’ while in WV. gigantea the leaves are borne upon two dichotomously branched stipes and are removed some distance from the bladder. In WV. Littkeana, the leaves are sessile and each one on splitting divides to the very base or nearly to it, but in VV. gigantea the leaves are provided with fairly long stalks, and in fission the stipes are not divided to the base, so that there results a JLessonia-like portion. The first leaf however must divide nearly to the very base of the stipe in order to give rise to the two sets of branches. Of the four genera which make up this subtribe of the Lessoni- idex, Dictyoneuron is the simplest and stands somewhat apart from the other three. As regards the modification of the transition-place it agrees well with the other genera, but in the details of the form and markings of the blade as well as in the decumbent, rooting stipe, it differs decidedly from the other three. But Lessonia, Postelsia and Nereocystis are very closely related indeed. ‘The smaller forms of Lessonia approximate to Poste/sta and the latter in its hollow stipe comes very near to Vereocystis. Subtribe 2. Macrocysteze.—This subtribe contains a single genus , which, however, has a wider distribution than any other genus of the Laminariacee. Macrocystis, Ag.—In the genus Macrocystis we find a single very variable species." While it possesses a compound frond which arises 1 Bot. Notiser, p. 49, 1881, Obs. Phyc., Pt. 5, p. 6. ? Cf. Farlow, Bull. Torrey Bot. Club, vol. xvi, p. 7, 1889. ° Of. P. & R., Ill. Alg,, Pl. 8 and 9. 4 Cf. Hooker, Flora Antarctica, Pt. 2, p. 461. 346 W. A. Setchell— Classification and Geographical through a process of splitting at the transition-place, yet there is such a fundamental difference in the details of this process from that found among the Lessonex, as to warrant our placing the genus in a subtribe by itself. The latest paper dealing with the morphol- ogy is one by Rosenthal.’ At the tip of the frond there is a broad scimitar-shaped blade at the lower, rounded edge of which are several (3-8 or more) parallel slits. These are situated toward the base of the blade and parallel also to the rounded edge. The new leaves are thus formed on one side only and follow one another in fairly rapid succession. In this way also the terminal blade is divided into two parts which are unequal not only in size but in their farther development. The portion cut off by the extension of the lowest slit, becomes an ordinary leaf, more or less lanceolate- ovate in shape, with ciliate-toothed margins and provided wh short stipe and bladder-like expansion at the base. The other por- tion, viz: the terminal blade or leaf repeats this process of cutting off a portion of its base and so on. This modification of the process of splitting affects, of course, the general habit of the plant. Instead of a regularly dichotomous stipe with leaflets of the same value, we have a plant whose axis is sympodial and is often unbranched, with leaves in a single row and secund. Branches arise somewhat irregularly and come into exist- ence when, in the process of splitting, a portion is split off which is equal to the portion left behind. The new blade becomes the ter- minal blade of a branch.” ALARIIDE&Z.—Under this tribe it seems best to distinguish three subtribes, the Alariez, the Egregiez, and the Ecklonierw. The plants of this group possess compound fronds, but these arise, not by any process of splitting as in the Lessoniidere, but by out- growths from the meristematic region at the transition-place. Subtribe 1. Alariew—This subtribe includes the genera Alaria, and Pterygophora. They are distinguished from the other genera ~ by having the sporophylls situated upon the stipe alone and con- sequently arising upon the stipe-forming portion of the transition- place. Pterygophora, Rupr.— Pterygophora Californica, Rupr. is the only representative of this genus. Old plants possess a fairly long (1-2 1 Flora, Bd. lxxiii, pp. 107-111, Taf. vii-viii, f. 1-3. 2 Cf. Rosenthal, loc. cit. pp. 108-109. Distribution of the Laminariacee, 347 feet) rather stout, flattened stipe which bears towards the top a bunch of leaves. . Younger specimens show the arrangement of these leaves better than older ones. At the top there is a long strap- shaped blade tapering gradually to the base and with the central portion thickened into a sort of indefinite midrib. Below this are two ranks of leaves along the stipe arranged with their blades in the same plane with the terminal blade. ‘These leaves are the sporophylls and are much the same shape as. the terminal blade but lack the midrib. They are eroded at the tip and appear to increase in length at their own transition-places. It may be seen from younger specimens that the sporophylls arise as outgrowths from the lower portion of the transition-place. Below these sporo- phylls are scars on the stipe where older sporophylls have been situated. Neither the terminal blade nor the sporophylls ever pos- sess cryptostomata. Alaria, Grev.—The genus Alaria contains between 15 and 20 species which are at present both little known and in a state of con- siderable confusion. ‘They agree very well in their general charac- ters, the species being founded on details which are likely to vary considerably in individuals of the same species. The terminal blade in Alaria is much elongated and possesses a very distinct midrib. It is also provided with abundant cryptosto- mata even in adult specimens. The sporophylls are in two ranks on the upper portion of the stipe and arise as outgrowths from the lower part of the transition-place. The sporophylls in Alaria seem to be of definite growth, 1. e. they grow to be of a certain definite size and then stop. Their distal ends are rounded and never eroded as in Pterygophora. They are destitute of cryptostomata except in rare and apparently abnormal specimens. After maturing the zoosporangia the sporophylls drop off and their office is performed by younger ones. Alaria differs from Pterygophora in possessing a more definite midrib and cryptostomata in the terminal blade and by the definite growth of the sporophylls. Subtribe 2. Hekloniez,—This subtribe contains three curious: and little known genera, viz: Ulopterya, Lcklonia, and Eisenia. They all possess pinnatifid fronds and the pinnae, on examination, are found to be sporophylls which arise at the base of the blade rather than at the tip of the stipe. This forms the distinctive fea- ture of the subtribe. 348 W. A. Setchell— Classification and Geographical Ulopteryx, Kjellm.—This genus contains a single species U. pinna- tifida (Harv.), Kjellm., which is found in Japan. Specimens are rare in herbaria and it is very difficult, therefore, to get material for study. Kjellman has given an excellent account and figure of the adult plant.’ The writer has also had the opportunity of ex- amining an excellent young specimen collected by Prof. K. Miyabe of Sapporo, Japan and preserved in the herbarium of Prof. Farlow at Cambridge, Mass. The blade possesses cryptostomata, a distinct midrib and is deeply pinnatifid on the margins with finger-shaped pinnae. The pinnae decrease in length towards the base of the frond and at the transi- tion-place are represented by mere protuberances. The stipe of the young specimen in Prof. Farlow’s herbarium is cylindrical and un- modified, but in the older fruiting specimen figured and described by Kjellman, it is plicately twisted above somewhat after the fashion of the stipe of Saccorhiza bulbosa, DelaPyl. Ecklonia, Hornem.—There are about six species of Ecklonia, of which it is difficult to get good material for study on account of the large size of the plants and their rarity in herbaria. Through the kindness of Prof. D. C. Eaton of New Haven, Conn., the writer has been able to examine a number of fine specimens of Ecklonia radiata (Turn.), J.Ag., collected by Baron F. von Miller of Melbourne, Australia. Some of these specimens were fairly complete and showed very well the characters of the adult plants. The blade is very broad and long, and its margins are deeply pinnatifid their whole length. The pinnae are broadly linear- lanceolate and arise as outgrowths at the base of the blade. As the blade increases in length, there is a tendency for the central portion to wear away faster than the pinnated margins, and consequently there is left on each side of the upper portion of the blade a narrow strip with pinne attached. The stipe in this species is short and solid, but in Z buccinalis (L.), Hornem. from the Cape of Good Hope, the stipe is swollen and hollow.” Eisenia, Aresch.—Lisenia arborea, Aresch. grows on the coast of California and is very scarce and local. Areschoug* compares it with Postelsia, but from his description it seems to be very different. The writer is indebted to Prof. W. G. Farlow of Cambridge, Mass., 1 Of Kjellman and Petersen, Om Japan’s Laminarier, in Vega Expeditionens Jaktta- gelser, Bd. 4, 1885. Or Posh, ae. Alp. E12: 3 Obs. Phyc., Pt. 5, p. 7. Distribution of the Laminariacec. 349 . -and to Dr. C. L. Anderson of Santa Cruz, Cal., for fine, large, dried specimens from Monterey, Cal., and to Prof. Carl Eigenmann of Bloomington, Ind., for an excellent younger specimen from San Diego, Cal., preserved in alcohol. In the older specimens the stipe is long and stout (about 2 feet long and 2 inches in diameter), terete below but compressed above. At the top, it divides into two stout branches (10 inches long in some specimens) which are sepa- rated from one another above by a broad rounded angle. The branches are very much flattened, rounded on the outer margin,’ but nearly acute on the inner (or upper). The medulla, in cross-section extends up to the inner margin and there ceases abruptly at the surface as if cut off at that point. At the apex of each branch is a bunch of leaves. The leaves are from one to two feet long, linear-lanceolate in outline, very coarsely and remotely toothed on the edges, and longitudinally wrinkled. They resemble very much the pinnae of Heklonia. ‘They decrease in size (and in age) as they approach the outer margins of the tips of the branches and finally diminish to mere protuberances, thus showing that they arise as outgrowths and that they are true sporophylls. A very young specimen in Herb. Farlow, collected by Mr. Daniel Cleveland of San Diego, Cal., shows a large terminal blade with the sporophylls arising at its base as in cklonia. A comparison with Lcklonia radiata suggests that the whole central part of the blade dies away early, leaving the more active margins at the base with the pinnae. This would make the “ branches ” belong partly to the thickened base of the leaf, and partly to the stipe and the appearance of the medulla in cross section, spoken of above, seems to warrant this explanation. However this may be, Hisenta seems to be worthy of generic rank and is related to Hcklonia rather than to Postelsia. Subtribe 3. Hgregieze.—The genus Agregia differs from all the other genera of the Alariidez in that the sporophylls arise along the entire length of both margins of the transition-place and therefore are arranged, when full-growth, on the margins of both blade and stipe. Egregia, Aresch.—Lgregia Menziesii (Turn.), Aresch. is one of the most variable and most complex species of the Laminariacex. Herbarium specimens show very varied forms so that it seems dift- 1 Aresch., loc. cit. Trans. Conn. AcaD., Vou. IX. MARCH, 1893. 25 350 W. A. Setchell— Classification and Geographical cult to believe that we are dealing with a single species. There are three sets of forms which are most conspicuous. The first has a perfectly smooth stipe, with smooth sporophylls usually very little dissected or even divided and often bearing large bladders. The second is a form with a smooth stipe and sporophylls, but with the latter very much pinnately dissected, often entirely divided up into long capillary divisions, and with slender elongated bladders. Finally a form occurs, in which the surfaces of the terminal blade, the simple sporophylls, and the stipe are roughened with small spines, which in old stipes are very closely set together. The blad- ders are large and swollen. This is the form figured by Ruprecht.’ It is impossible to tell from herbarium specimens how thoroughly distinct these forms may or may not be, yet very young plants are found having these different characters already present. Young plants possess a comparatively large terminal blade, which is at first entire, but soon protuberances appear at the base, and as growth proceeds the blade consequently becomes pinnately divided as in Ecklonia. The protuberances, however, are not confined to the blade but appear also upon that portion of the transition-place belonging to the stipe. The stipe increases enormously in length and is throughout its whole length beset on both edges with sporo- phylls, which are of definite growth, resembling those of Alaria. In two of the forms mentioned above the sporophylls are little dis- sected, but they are very much cut up in individuals of the third. The frond of Eyregia is irregularly branched. The branches are usually very long and arise from sporophylls which function as ter- minal blades forming new sporophylls at their own transition-places. The Lgregiew, on account. of the formation of sporophylls, both at the base of the blade and the top of the stipe are intermediate between the Alariez on the one hand and Ecklonee on the other, Synopsis of the Genera of the Laminariacee. Tribe I. LamrnarupE#.—Fronds simple (except in Thalassiophyl- lum.) Subtribe 1. Laminariez.—Fronds provided neither with ribs, nor with perforations. Transition-place plane and unmodified. 1. Chorda, Stackh.—Fronds cylindrical, hollow, with diaphragms at irregular intervals. Sorus covering the entire surface. Para- physes destitute of a hyaline appendage. * Mem. Imp. Acad. Sci. St. Petersb., t. vil, .Ply A: Distribution of the Laminariacee. 351 2. Saccorhiza, DelaPyl. — Frond possessing a distinct blade and stipe. Paraphyses destitute of hyaline appendages at the tip. Sori not covering the whole surface. 3. Laminaria, Lam’x.—Frond possessing a distinct blade and stipe. Paraphyses provided with hyaline appendages at the tips. Sori not covering the whole surface. Subtribe 2. Agarez.—Fronds provided either with ribs, or with seroll-like auricles at the base of the blade, or with both. 4. Cymathere, J. Ag.—Blade provided with three (or five?) ribs (or plicae ?) and destitute of perforations, bullate swellings, or auricles at the base; bilateral. 5. Costaria, Grev.—Blade provided with five ribs and bullate swell- ings which occasionally form perforations, but destitute of auri- cles at the base; bilateral. 6. Agarum, (Bory), P.&R.—Blade provided with a midrib, with perforations, and with auricles at the base; bilateral. 7. Thalassiophyllum, P.&R.—Blade unilateral, provided with per- forations and a scroll-like transition-place but destitute of a midrib. Frond irregularly branched by proliferation from the _ margins of the perforations. 8. Arthrothamnus, Rupr.—Blade bilateral, plane, with auricles at the heart-shaped base. Stipe dichotomous provided with a spiral scar, erect or decumbent. Tribe II. Lessontipe“.—Frond compound. New blades arising from the old by a splitting process at the transition-place. Subtribe 1. Lessoneze.—Stipe dichotomous. A. Stipes solid. 9. Dictyoneuron, Rupr.—Divisions few; stipe creeping and root- ing ; blades reticulately veined. 10. Lessonia, Bory.—Divisions numerous ; stipe erect, blades plane or wrinkled, sometimes provided with a midrib. B. Stipes hollow. 11. Postelsia, Rupr.—Stipe cylindrical throughout. 12. Nereocystis, P.&R.—Stipe expanded at the apex into a large bladder. Subtribe 2. Macrocystez.—Stipe sympodial. Branching irregular. 13. Macrocystis, Ag. Tribe HI. Anariupes. Frond pinnately compound. Sporophylls arising as outgrowths at the transition-place. Subtribe 1. Heklonez.—Sporophylls situated upon the blade. 14. Ulopteryx Kjellm.—Blade provided with a distinct midrib and with cryptostomata. | 352 W. A. Setchell— Classification and Geographical 15. Eeklonia, Hornem.—The main portion of the blade persisting, destitute of cryptostomata. 16. Hisenia, Aresch.—The main portion of the blade disappearing early destitute of cryptostomata. Stipe bifurcate, above in ali except very young specimens. Subtribe 2. Egeregiew.—Sporophylls situated upon both blade and stipe. 17. Egregia, Aresch.—Frond irregularly branched. Subtribe 3. Alariezw.—Sporophylls situated upon the stipe alone. 18. Pterygophora, Rupr.—Terminal blade provided with an indefi- nite midrib but destitute of cryptostomata. Sporophylls of indefinite growth. 19. Alaria, Grev.—Terminal blade provided with a distinct midrib and with cryptostomata. Sporophylls of definite growth. Geographical Distribution of the Laminariacee. As far as the writer is aware, nothing has been written on this subject as a whole. Hooker’ speaks at length, of the distribution of Macrocystis. Kjellmann in his “ Arctic Alge” treats of the dis- tribution of the northern kelps very carefully, in connection with the other alge of the Arctic Sea. But apart from these the refer- ences are scattered and the main features are left unemphasized. It is the desire of the writer to bring these more general facts of distribution together in one place. The kelps inhabit the colder waters of the globe, delighting in the marine waters of the frigid and colder temperate zones, and absent or all but absent from the warmer temperate and tropical oceans. In selecting, then, our regions to be considered, we can leave out practically all the middle portions of both the larger oceans as well as all the Indian Ocean, and confine our attention to the Arctic Ocean, the northern portions of the Atlantic and Pacific, and to the southern portions of the same oceans together with the Antarctic Ocean. The Northern Atlantic and Arctic Oceans.—We may distinguish under this head six different districts’ whose kelp-floras differ suffi- ciently to receive, each its special mention. The districts are those of northern Asia, northern Europe, western Europe, Spitzbergen, Baffin Bay, and New England. 1 Flora Antarctica, Pt. 2, pp. 461-465. ® These are merely geographical districts selected for convenience in dividing up the coast and not true provinces as regards similarity of inhabitants. Distribution of the Laminariacee. 353 The District of northern Asia includes that part of the Arctic Ocean lying just north of Siberia. The conditions over this district are unfavorable for the growth of algz and the algal flora is con- sequently very poor.’ The District of northern Europe includes the seas north of Europe, from the Kara Sea on the east to the northern coast of Norway on the west. The western parts are comparatively rich in kelps. The District of western Europe includes the coast of Europe from western Norway down to Portugal and into the Mediterranean Sea. The Baltic Sea and the seas about the British Isles are included in this district. The District of Spitzbergen includes the coasts of Spitzbergen, Iceland and eastern Greenland. This includes what Kjellman’ calls the Spitzbergen and Greenland Seas. The District of Baffin Bay includes the west coast of Greenland and the northern part of the Labrador coast. The District of New England includes the coasts of New Eng- land and Nova Scotia, as well as that of Newfoundland and the southern extremity of Labrador. The Northern Pacific Oceans.—In the northern Pacific we have the coasts of western North America and of eastern Asia. Both of these may be still farther subdivided and we have finally four dis- tricts to consider, viz: those of California, Alaska, Ochotsk Sea, and Japan. The District of California includes all of the western coast of the United States. The kelp-flora is sufficiently alike along its whole extent for us to consider it as a whole. From San Diego southward along Lower California, there are a few fairly important differences. The District of Alaska includes Alaska and the adjacent coasts of British America. Its kelp-flora appears to be rich and varied, but it is, as yet, very imperfectly known. The District of the Ochotsk Sea includes the eastern and western coasts of Kamtschatka and the sea inside of the Kurile Islands. Almost our entire knowledge of its kelp-flora comes from the works of Postels and Ruprecht. The District of Japan includes the ocean and seas about the Japanese Archipelago. ' Cf. Kjellm., Arctic Algwe, pp. 7, 26, 27, ete. 2 DOG, City, pee 354 W. A. Setchell— Classification and Geographical The Antarctic Ocean is not separated off into such distinct parts, but is open throughout its extent. We may distinguish five dis- tricts in the Antarctic and southern Atlantic and Pacific Oceans, viz: the districts of western South America, Fuegia, western —— Cape of Good Hope, and Australia. The District of western South America includes chiefly the coast of Chili and our knowledge of its kelp-flora is very inadequate. The District of Fuegia includes the region about Cape Horn and the Straits of Magellan, and also the Falkland Islands. We have excellent accounts of the kelp-flora in Hooker’s “ Flora Antarctica,” part second. The District of western Africa includes the Azores, the Madeira, and Canary Islands, and the coast of Guinea. The kelp-flora is scanty, but the district is interesting as an intermediate district. The District of the Cape of Good Hope includes only the region immediately about the Cape of Good Hope itself. The District of Australia includes not only the western and southern coasts of Australia where kelps are found, but also New Zealand and Tasmania. Whether any kelps are found on the northern coasts or not seems uncertain. Three intermediate regions are of interest. One is the Canary Islands already mentioned above; a second is St. Paul and the Crozet Islands, midway between the Cape of Good Hope and Aus- tralia, and the other is Tahiti and the other Society Islands in the middle Pacific Ocean, only a comparatively small distance south of the equator. In the following tables are given lists of all the species belonging to the Laminariacee so far as they are known to the writer, and imperfect as it undoubtedly is, yet it will probably serve the pur- pose for which it is inserted, viz: to give some tangible basis for a general discussion of the relative distribution of the genera and sub- tribes of the group. 300 wNariacee. Distribution of the Lam "(| “aDYUIYYVT “AL *) OoStouvay ug 04 (j UOSMAPUW TO *MT) ‘POPLATp A[O]BITSIp Sso] JO BLOW SI OPBIG oy} Udy UDAd 2e1njon44s 91 0G OF ST 4Nq ‘MOIR “WwWOSMapUP “T SB souary 4% peyNqrijstp Useq sey saloeds siqy, : 2°110§ “SpuBls-asvTionw AjUBOS ING 95.1] T9781 GIA papraAoid ‘aaoqe qryds Ajquonbaay ‘fiywoupnybu07 pPa}yUIwsn fijasipod ‘azyetpeys 10 978 [099UB[-SUOTQO ‘SUOT JooJ F-[ opRig_ “UOT}OOS-SSOLO UL [BOIAdIT[a odI4s 944 Jo BI[NpoW!W “‘spuels -9.SB[IONU JO 939N4I4Sep ,,°qI MOIS JO SSUII,, MOT B SULMOYS ‘possordul0o AT} U-S1]8 ‘SUO] SoyoUT 9-g odI4g ‘STIOYM AB[NSIII UL posuvsie a1B YOM ‘so.1ojdey poqouviq A[SnOmO,OYoIp A[Surreds ‘NOS JO posodu0o yseploH “(168L “0g “d ‘It *[OA ‘907 Ul UOSIopuy "T ‘0 ‘Jo) “wasyy ‘|TeyoIeg ‘uMojDy “Tz Fi % (E681 “LIS “d ‘AL “tag *BISIAIBION VAOUN VT UL “joy “Jo ‘IA *[OA ‘oryog, Jo OUIZBSBIY [BOIUBIOg ogy) BANUIBIO “YW AQ VMUO}9 SNUIS 9Y4 04 paarozor useq ysnf sBy ‘wel y ‘vsooupps “T ; Ad.19JUOW PUB ZNAD vIURY WOAT 4SBOD UBIULOJT VO OYJ SUOTR AOIVM AMO]|VYS SJIQUGUT 4] dIdoosoa1OIU PUB apeTq osOSna ATOSAvOO 871 Aq poaysinsurystp ATIpeV | TRY4eg ;‘WMOTIET SLO) Pests ""MOTIVY “(CAIGA) Larepourg oa sinus nese cee | eis ee ee oie eared Bac ereiee han en ee ee ache io ee es Ae ‘UM 'd ‘eyeraery ‘SV ‘f ‘SIUL.OjIsua SSheoy pos eaicea ae NO ones] Se eee eg mele ee lens |= aan eal iee. abe gaint ae Sei owt eg eee |e ae eae eae ene Se oS ee aot oe ‘uayjoly ‘eyeyng ‘ural y ‘ereSiyuap Bie ney ee aL | Ser es ae Se a esl o ees | ee Peet aera ‘uel y ‘euvtuesiejeg Be See Fo is ee Be ee ae Se erie ee aie nai | oe eae | eee ~--> uaypely ;“esoorper RReiae |Special ee ee eee eee ee eeehan et beeen ages lee ea ee ee a oe ae ‘eoruode er Re he ils se Need eprom icine ene ciated es ee + ‘TAge]eq ‘stinszo1suo0} Seles ste a + |" Sy pe “Cyy0eIG) sITAT tye a+ Si a ces ‘XULvT “BULIeqOoRS SSebse Ste eer enn eae Sonal ene eect eee Ss ae “‘eljoyrouno i Se ee aah ee ‘OV ‘f ‘e[NSunpryos ‘XUleVy ‘D1pUurUDvyT pay eis ee | ec net cee Sie picts ar cena Ire al ali is etna + + | swe ‘(Aq Req) vapojeurszap -- -- ese pakong cathe aa ae SaaS aR ae a Se I Soe pert ee CES omelets ip baae 7) 0 Aa SIG, ( Shree) cence ‘Agee ‘nz1y.00ang SSS ean oe ee ee ee rl (pace aa eee | eee SGN Race |e eee ae ne ae ‘qsudyT ‘vsojueui03 Seas Cpe siete eh ech ara ieee + + + $f o ooo Soege *(Cry) any ‘TYOVIS ‘ypwoyy ee em saw Tee aed | Keay eee tS | fn mm rns Jerse | a Yume m\“vud trues) | Pome teem esses fe Ta Ta oe Se | eee assem ewlescee ees |e ceo a ae te ae pe ea | ne ee A we cl he ifs | (Pam ngs toms eess on eon | bose aon Pace eee ce ee aS eee Newe eve | oo on. oe wm ewe Kg lem we He] Ce ew ew Bolly U194S9 A BLoon,y jo adeg U104S9 “BTUIOSTRC) ‘adorn ULY}.10 NT Avg ugyeg ‘purpsuy MON "B29 YS}OTOO ‘uasreqzyidg a . H ! i r em | as ee | | -————— J ——————__ | ——_ ed Ge Oe Ped Po ‘SV ‘¢ ‘(UITeTD) snpytq ie ed Cd es kd ee een Idny ‘sIsua[Lin yy -+ + ‘rdny ‘snumpnyzouy.uy Pe ee ee Pe ee ree To reespeo sees ise sarap (UITSUIH) SH.AU4ZeIO + "UM 'd “ungppliydorssnoy, See eee Pee ees es “i Sn ctamaarciaart emerie rig Gy. wae Leila yi ia A "yp" ‘(At0g) ‘wnunby Se PT Rt ea gil, eens cay ay ee agen crema nae aileron EOE : "ADIN “N1LDJ8SOD Re Se iaesaceeh(aearematilad din 7 eat nels cede Mois me po) fof 1p 9 _ 3 ¥ ‘Lf ‘ovayzoulio DS (oh oe Oe ee Se a ee On eer ee | ee ee wzaqreurme7} ee ei Pa Roa (En nen NS) ee Bes eens BSS ese “ADLD ‘eptped SRE Ph ai al Valores 4 [Jperecefeeeces [eee e ee fee eee efeee cee ]ee 22 = [eee e ee feo een feor eee |en eee |o ooo > apap ‘erp qdoqueuny si ie EG slg meas Se apa eee a hoe cdl doo) [Ser ersiss Steeise ate loes iene ge aso nme =| ad a an ee ome ene ~-----|------|------|------|---------------- ‘dV ‘SI[ISSOS ~--+--/------|------]------|-------- (‘yosary) yyqoordny ates ae fakes a aletel (alaalaialas a | [taal alia a MOTIB YT ‘TUOSIOpUYy Pee ae a foc | Ses ae SS eee lorie sai sens |e ese ae eee P si 25 cc i pera Ey ee ane Gene | cokes — saS|cscess| Sec sabe Speer srs pars sever fou So tS" “A ae Sener mcien = |s omen e [hoa ela weno para TORTS SERS TT RaS S| se sers ene seers 5) ane an ctmmna nee SeeRES | epee pone eees= | Aree nee | Perea | ee ree Sele Sera ee || MR ae f+ [ror crc[rctrcr isco" erpsog ‘(aum9) veroqred Aq ~~ 2---|------|------]------]--2-2-|]------ des BRS ean Rehr ere a eran Gaels, spe: [TIS o |S CSOT SaaS ay oie ee E fais eal ES SS Ue eA ae ee SV ‘pf “eAynzory7e TR wll re Seances fe Mer ay ema | ea eee po feneenef------] 4 fol Sinise ee seen (ciara Intensives takes 6d aie o ites |i mM Facade hah aaa yer Ir nln he Gols» a *‘JUIOIG ‘LOTOOSIp a av + |" ‘Sy-'p ‘Carepy) eT Aqdouegs RAY Steere ee eee tomer = + [oper aes] Soe ame Sse Olson “CIDOULLOImEE + + a ae xuery ‘(rT) B7VILSIp DILDUIUD'T se ee W. A. Setchell— Classification and Geographical | | TN | | TT | | | | LL "BOLI ‘adoiniy UIOT]}.10 Ny ‘odoiny U104S9 \\ 356 ‘CIS U19T]}10 N a ‘Aeg ue TI04S9 AA 8 ‘IoUry “0g WIOS9 \\ "BIUIOFITRO jo ode RITeISsny | ‘adoyH pooy "Bag YS}OTPIO "Ud.818qZ}1dg 357 Distribution of the Laninariacee. ee ed mw ecm emer lemme eee —— ee 8 SS Shea ‘(osery ‘ea1oqie ‘Yosaly “piuasiq wayyy “erposyey eS ak oh Mae ‘uel y ‘eavo a ee eae ‘tayelyy ‘stpoAo1q Sn cee weut1of ‘(‘T) styeuroong ea 3V ‘ff ‘(‘Uany) eyerper a iar ne Sal Bape SY ‘¢ ‘sedtaciq ‘UeUIOF “01Uu07yoq ‘uel y ‘epyiyeuurd ‘unpely ‘whuazdo7 Q —_——— ee *- | -:.:. se Oe | | OOOO | | | | a ocigee seen sesso w2a3sho01 eI] ‘oy ‘erojyitdd ‘Sy ‘syshoovonyy —-See ee e|eae ence ee a a ad "eITRIISUY jo ode ‘BOL Vy W10}S9 \\ —-—eene "BIULOFITEO ee | ee | | —_—_—_—~=—_OasvxXveoe_=—=—S I SS | ‘RIS UWI9T}.IO N ‘adoring UWI9T]}.10 N ‘odoin, U101S9 \\_ —-ee--—-5 _—_——_—— "Bag Ys}oyIO ‘Mas1oqzyidg - Tae ew ew MW Be ee ee we ee ee waluosse-] ‘Wosery ‘voyuesis ‘UR “BuvayqnyT ‘UM 'd ‘syshooasan ‘adny ‘stuojeetmyped ‘rdny ‘nisjajysogq “AIVFT®'YOOH ‘“ezeao A eg ee ‘Alog ‘sueoseosny pigs igen g oy Alog ‘susosea3tu 5 a Uy'd ‘soploewiieuruaey cena wees ‘SV ‘pf ‘Tlagng ‘AIOg *DiUOSsaT ‘rdny ‘wanomsojITe9 ‘adny ‘wounauohjoqg we ee ee ee ee lt Geographical ton ANC a es mje ewer |—-- eee a a o uh ae wee +++4+4++4+44 ee ee a) a eee ee ——s eer we lee ee ee eee eemew |e = wee —-- eee lew ee ee wore elon wwe = i ) Sys tale Oe eae S ‘uyjoly ‘esuojovad SERCH eae ne aa wayjelyy “eds peas ae | eontalataes ev ‘unjjoly ‘eye1uery Bie | Papa ce ‘tappolyy ‘e4soorze] Thi = cere ‘wuupjoly “eyeloooURy GE ane [ Aiea aia wyjely “eysnsue SCE Tete ee se We'd ‘vsoynysy SSS en WH’ qd “eyeuLsreuUL Bs Tl Tae earae ‘tuyjelyy “etpozisse.o Peace Mees pai *JULO.AYS ‘SIAV[[oCRy "JUIOIYSY ‘SLIvVOTITT pee sae ees, ‘uyjoly ‘ecuojqo ‘mel sy ‘voydiyye wos >> suntpelsy ‘srpoeyroyorjop 25k ae RPE LE RS ‘SV ‘ff ‘elpoyipuesas ce I oe ‘SV ‘f ‘eooRvURIquIeUL + jody pe “Cqeeq) rerdg gfe. =* ne = Ady ‘(‘T) ByuUeTNose hes oe pe faay EE RIelY ——- 6 CEU "ADL ‘D1UD) F W. A. Setchell— Classificat 308 i —— ee Ses eal ela gs ae egret ee ae oe millers Rea NU eget Ges lla ‘yosary ‘(‘UIN]) Mselzuey ‘yosory ‘nibauby “elTRIJSNW jo odeg Bolly y T19}S9 A\ BLoon ‘IaWV “Og 1.10489 \\ _——— ‘under BISV UI9T}.10 N “odoin | | | ‘uas1eqzyidg ‘Aegq ue ‘adoH poo = Distribution of the Laminariacee. 359 The districts enumerated above are the principal geographical districts in which kelps are found. There are however several more or less isolated kelp-localities which are of great importance when the causes of distribution are being discussed. Such localities are the Society Islands, Kerguelen Land, St. Paul Islands, the Crozets, and the Canary Islands, the latter of whose species have already been enumerated in the table among the species of western Africa. At Kerguelen Land, nearly midway between Australia and the Cape of Good Hope but decidedly to the South are found growing: Macrocystis pyrifera, Ag. Lessonia fuscescens, Bory, and at Heard Island, 250 miles south of Kerguelen Land are found Lessonia nigrescens, Bory. “« ovata, Hook. & Harv.’ At St. Paul and the Crozets, also approximately half-way between the Cape of Good Hope and western Australia but more to the north or west, are found: Ecklonia buccinalis (L.), Hornem. Laninaria pallida, Grev. Macrocystis pyrifera, Ag., and at Tahiti and the other Society Islands, midway in the Pacific Ocean and in the Torrid zone (10-20° S. long.) are found: Macrocystis pyrifera, Ag. Lessonia Suhrii, J. Ag. a nigrescens, Bory. The Laminariacez, as mentioned above, are inhabitants of the colder waters of the globe. At the north, they extend up so far as there is suitable bottom which is free from permanent or very nearly permanent ice; and in the south, they extend down so far as the ice will permit.? They do not occur in the tropical waters nor in those of the warmer temperate regions except as the tempera- ture of these waters may be brought down to the proper degree of coldness by the current from the polar regions. It is the temperature that limits the distribution of the kelps and that too, the summer temperature, as heat not cold is inimical to their growth. They can endure almost any degree of cold that occurs, even in polar waters but readily die and decay where the waters 1 Cf. Dickie, Jour. Proc. Linn. Soe., vol. xv, p. 47, 1876. ? Hooker, Flora Antarctica, Pt. 2, p. 465. 360 W. A. Setchell— Classification and Geographical are at all “warm.” So that the distribution of the kelps is limited toward the poles by the presence of ice for too long a portion of the year, and in the directions away from the poles by the limits of the various colder currents. The tropical currents and waters are interesting as acting as barriers against farther distribution in cer- tain waters. In studying the table of distribution just given, we notice certain features which are of interest and importance. It will be best, per- haps, to consider these general features of distribution, first by pro- vinces, and then by tribes and subtribes. The district of northern Asia (or of the Siberian Sea)* possesses four species of Laminaria and three of Alaria. Of the latter two are peculiar to this district and one is found also on the coast of Alaska. Of the four Laminarice, one is found also in Alaska, and the other three are found in the northern Pacific (Alaska or Sea of Ochotsk) and in the Arctic Sea, either in northern Europe or more northern, in Spitzbergen, or Baffin Bay. So that the kelp-flora of this district is related both to that of the north Atlantic and Euro- pean Arctic as well as to the northern Pacific. The districts of northern Europe, Spitzbergen, and western Europe are very much alike in general features. Their kelp-flora is made up of the members of the Laminariez and Alariee alone. Even Agarum, so abundant in Baffin Bay and New England, is not pres- ent. Altogether they possess twenty-one species, of which four ~ are common to all three, while nine species are common to northern Europe and Spitzbergen, on account of the colder waters of these districts. There are also eight species common to both northern and western Europe. In fact the differences between these districts is mostly one of colder and warmer water species. When we turn to the districts of Baffin Bay and New England, we find that not only are the Laminariee and the Alariee repre- sented, but also the subtribe Agaree. They have eight species in common. The four species common in northern Europe, western Europe and Spitzbergen are also found in these two districts. They have six species in common with Spitzbergen and northern Europe, . while New England has seven species in common with both northern ~ and western Europe. The possession of Agarum Turneri suggests a comparison with the district of Alaska, with which New England has seven species in common and Baffin Bay nine. 1 Cf. Kjeliman, Arctic Algae, p. 5. Distribution of the Laminariacee. 361 The northern Atlantic and Arctic Districts then are nearly related, the districts of Spitzbergen, western Europe and northern Europe being the most alike, the district of northern Asia having something in common with the northern Pacific, and New England and Baftin Bay having also a prominent genus in common with the northern Pacific. In the northern Pacific we have separated four districts, each of which has its peculiar interest. Two of these are on the western coast of North America and the other two are on the eastern coast of Asia. The species of all of these are in considerable confusion at present, but enough perhaps is certain to afford a fair basis for comparison. The district of Alaska is credited in the above table with 30 species and the district of California with 15. They have however but 3 species in common. This number may be so small because of our imperfect knowledge, but there can be little doubt that there is a great dissimilarity in the kelp-floras of the two districts. While Alaska possesses 14 species of the Laminariez and 10 Alariex, Cali- fornia has but 3 of the former and but 2 of the latter, 1 species of which is the peculiar Pterygophora Californica, Rupr. Alaska also possesses 5 species of Agareze while California has but 1. On the other hand Alaska has no representative of the Lessonez while Cali- fornia possesses 5, and no members of the Ecklonee against 2 be- longing to California. Alaska possesses members of the Laminariez, Agaree, Macrocystez, and Alariee while California has representa- tives of all the 8 subtribes along its coast. Of the 15 species credited to California, 10 are peculiar to it. Of the remaining 5, 3 are found also in Alaska, 1 also in Japan, 1 also on the shores of Kamtschatka, while 3 are species also found in the southern hemis- phere. ‘The only one found also in the northern Atlantic or Arctic Oceans is Alaria esculenta and it is doubtful whether this species as understood by Kjellman is really present in Californian waters. The case is much different with the district of Alaska. It has 6 species in common with Spitzbergen and 9 with Baffin Bay, while the only species it has in common with the southern Pacific is Macrocystis pyrifera, Ag. On the opposite side of the Pacific Ocean, in the districts of eastern Asia we find a somewhat similar state of things. Here we have a northern district, viz: the district including the Sea of ‘Ochotsk and Kamtschatka, and a southern district including the larger islands which belong to Japan. The Ochotsk district has 362 W. A. Setchell— Classification and Geographica 15 species and Japan has 13, but they have only 1 species in com- mon. Ochotsk has 7 species in common with Alaska while Japan has but 3, Ochotsk has,5 species in common with the northern Atlantic, and Arctic, and Japan has 3. Ochotsk has no Eckloniezx while Alaska has, and Japan has neither Macrocysteze nor Lessoniez while Ochotsk has both. Ochotsk is to be compared with the southern Pacific on account of the possession of Macrocystis and a species of Lessonia peculiar to it, while Japan is to be compared with the southern Pacific on account of its possession of 3 species of Ecklonia, none of which, however, are found anywhere else. - The relations between the alge of the Sea of Ochotsk and Behring Sea are discussed by Kjellman in the Botanisches Central- blatt,' where he expresses the opinion that the Sea of Ochotsk is only a more southern part of the same province with the Behring Sea.” We find therefore that, in the most northern part of the Pacific Ocean, we have a kelp-flora which is partly Asiatic, partly Ameri- can, while the more southern districts, both on the Asiatic, and on the American sides have marked peculiarities which separate them both from one another and from the more northern part. We find also that this northern part of the northern Pacitic has a consider-— able similarity to the northern Atlantic and Arctic in regard to its kelp-flora, while it possesses two genera and one species in common with the southern Pacific. The Southern Pacific Districts of the most prominence are three, viz: those of Fuegia, of Australia, and of the Cape of Good Hope. Their characteristics are, briefly, as follows: Fuegia is the place where the Wacrocystis forms are most abundant; is also the only place where the species of Lessonia are found in any considerable abundance and luxuriance; but the species of Ecklonia are either very scanty or are entirely wanting. Australia abounds in forms of Ecklonia, Macrocystis is also fairly abundant there, but Lessonia species are entirely wanting. The Cape of Good Hope is the home of the largest species of Ecklonia (Z. buccinalis (L.), Hornem.) and possesses also the Australian species Macrocystis is abundant, par- ticularly at the Agulhas Bank,* but less abundant than at Cape Horn or on the coasts of Australia.* The Cape of Good Hope how- 1 Bd, xli, pp. 168-170 and 198-199, 1890. * Loe. cit., p. 199. ° Cf. Hooker, Antarctic Flora, Pt. 2, p. 465. 4 Cf. Martens, Die Preussische Expeditonen nach Ost-Asien, Die Tange, p. 40, 1866 Distribution of the Laminariacee. 363 ever possesses a species of the genus Laminaria (L. pallida, Grev.) which is said by Areschoug’ to be nearly as abundant as Heklonia buccinalis (L.), Hornem. The only two districts in the list now remaining to be discussed are those of western Africa and western South America. The district of western Africa is very poor in species of kelp, only three being reported from it. One of these, Saccorhiza bulbosa (Huds.), DelaPyl. is reported from the shores of Guinea,’ and Zck- lonia buccinalis (L.), Hornem. and Laminaria pallida, Grev. from the Canary Islands. Macrocystis appears to be absent. In the district of western South America, which means really the shores of Chili, are found 8 species, 5 of which are common both to it and to Fuegia. The coast of Chili, then, has all the Fuegian species and 3 besides. The most interesting species quoted from Chili is the Laminaria himantophylla, P.&R., one of the digitate species, concerning which almost nothing, however, is known,*® and some doubt may be felt perhaps as to whether it really belongs to the genus Laminaria or not. Above, we have glanced at some of the important features of dis- tribution by districts and groups of districts, the next thing to con- sider, is the general distribution by tribes and by subtribes. The Laminarice are northern species as a glance at the table will show. Members of the group are found in all of the districts of the Arctic, the northern Atlantic, and the northern Pacific Oceans.. Alaska is the richest district possessing 14 species, western Europe, northern Europe, Baffin Bay, and New England have 10 apiece and Spitzbergen has 8. This subtribe is one of the most widely distrib- uted subtribes for 2 species occur on the western coast of Africa, another at the Cape of Good Hope, while still another is reported from the western coast of South America. But in spite of the occurrence of these southern localities for Laminariex, the group, as a whole is distinctively northern, and these southern forms are to be regarded as waifs derived in some fashion from the main sub- tribe which is circumpolar at the north. ‘This subtribe too has 38 species referred to it, which is double the number referred to the Alariec, the next largest subtribe. 1 Phyceze Novee et Minus Cognitz, ete., Acta Reg. Soc. Upsal, ser. 3, vol. vi, p. 361, 1866. ? Cf. J. G. Agardh, Spec. Alg., vol. i, p. 138. 3 Of. Postels & Rupr., Ill, Alg., p. 2, also J. Ag., Spec. Alg., vol. i, p. 136, Le Jolis, Nova Acta, vol. xxv, p. 590, 1856. 364 W. A. Setchell— Classification and Geographical The Agaree are a small tribe numbering only 6 species. Of these Alaska has 5, the Sea of Ochotsk District 4, or the two districts taken together’ possess the whole number of species. California and Japan each possess 1 species as do also Baffin Bay and New England. The distribution of this subtribe then belongs entirely to the northern Atlantic and Pacific Oceans. There are no southern species, nor any inhabiting either the European or Asiatic portions of the Arctic Ocean. The home of the subtribe seems to be in Behring Sea, whence are derived both the Californian and the Japanese species. The occurrence of a single species along the northeastern coast of North America is not so easily explained. The distribution of Lessonec presents a number of very interest- ing points. The home, as we might call it, of this subtribe seems to lie in the region neighboring to Cape Horn, where the three largest and most typical species of Lessonia are to be found. The western coast of America possesses the same three species and in addition ZL. Swhrii, J. Ag., which may be said to be characteristic of this coast. None of the subtribe are found either at the Cape of Good Hope or upon the shores of Australia. JL. fuscescens, Bory, it is interesting to note is rare at Christmas Harbor, Kerguelen Land,” in the Antarctic Ocean, and at Tahiti, just south of the cen- tral portion of the Pacific Ocean where it is associated with JZ. Suhrii, J. Ag. the Chilian species.* L. nigrescens, Bory, and J. ovata, Hooker, occurs at Heard Island just south of Kerguelen. Ii the northern Pacific there exists a peculiar species of ZLessonéa in the region of Behring Sea and on the coast of California there are 6 species belonging to the subtribe. The Californian species of Lessonia are very much confused and not well-known, both Z. fus- cescens, Bory, and L. nigrescens, Bory, have been spoken of as per- haps occurring upon the Californian coast,’ but the determination still remains undecided. ‘There is a species which occurs at Oregon and also one in the southern portion of California, which is referred to L. nigrescens, Bory, in the table. But the most striking feature among the Californian Lessonez is the existence of the four peculiar and characteristic species belong- ing to three genera represented nowhere else, viz: Dictyoneuron, 1Cf. p. 362. 2 Cf. Hooker, Flora Antarctica, Pt. 2, p. 457. 3 Cf. Grunow, Reise der Oeterreichischen Fregatte Novara, Bot. Th., Bd. i, p. 51, 1870. 4 Of, Farlow, Proc. Am. Acad., vol. x, p. 355, 1875. Rept. U. 8S. Fish Comm. for 1875, p. 707, 1876. Distribution of the Laminariacee. 365 Postelsia, and Nereocystis. ‘The 4 species of these genera are char- acteristic forms of the very peculiar kelp-flora of this coast. There are no Lessoniez in the northern Atlantic or Arctic Oceans. Macrocystis pyrifera, Ag. is the only representative of the Macro- cystece and has the widest distribution of any single species of kelp. Hooker’ has given such an exhaustive account of the main features of its distribution, that subsequent writers have had little to do but to copy his account almost verbatim. The Macrocystis completely encircles the South Pole, its southern limit being fixed by the ice. It is said by Martens’ to be most abundant at Fuegia (or Terra del Fuego), less so at Australia (or New Holland) and least abundant at the Cape of Good Hope. From these places the Macrocystis is carried in large masses (or “drifting islets”) through all of the Antarctic currents and has found a resting place on the shores of the various islands where the conditions have been favorable for its growth, viz: Kerguelen Land, Heard Island, Tristan d’Acunha, St. Paul Island, and the Crozets. It does not extend up on either coast of Africa to any extent nor on the eastern coast of South America. It follows the Humboldt current up on the western coast of South America, to the equator and finally “enters the cold waters which flow from the Arctic Islands of the Pacific,” and thus extends along the entire western coast of North America up to Alaska, and crosses over to the coast of Asia at Kamtschatka and the Sea of Ochotsk. It occurs also in the central portion of the Pacific at Tahiti and is credited to China by Hooker* to which sea he suggests it has been brought from the northern Pacific. It is not reported from the shores of Japan, nor does it occur at all in the northern Atlantic and Arctic Oceans. The Hcklonee are generally regarded as southern, and as belong- ing principally to Australia and the Cape of Good Hope, but Kjell- man has recently shown’ that Japan has an abundant supply of Ecklonice, made up of three distinct species peculiar to the country. Ecklonic occur at Fuegia and the western coast of South America but the references leave some doubt as to the exact specific deter- 1 Plora Antarctica. Pt. 2, p. 465. 2 Die Preussische Epeditionen nach Ost Asien, Die Tange, p. 49. 3 Loe. cit., p. 465. 4 Kjellman and Petersen, Om Japans Laminarier, Vega-Expeditionens Vetenskapliga jakttagelser, Bd. iv, pp. 269-275, 1885. TRANS. CONN. AcAD., Vou. IX. MARCH, 1893. 26 366 W. A. Setchell— Classification and Geographical minations and lead us to believe that they are not very abundant. One species of the genus is credited by Areschoug,’ to California, but it seems very doubtful whether this is correctly referred or not. The most interesting points of distribution of this subtribe are the occurrence of the peculiar genus “lopteryx* on the Japanese coast and of the peculiar genus “isenia on the coast of California.* The Egregiece contain the single species Lgregia Menziesii (Turn.), Aresch., which combines in itself the characteristics both of the Ecklonee and of the Alariez. It is found only on the coast of California and this limited distribution makes its systematic position even more interesting. The subtribe Alariew is the second largest subtribe of the order, containing at present about 19 species. Of these 18 belong to the genus Alaria and | to Pterygophora. The latter is peculiar to the coast of California. The species of Alaria are entirely northern and prefer the colder waters. Their distribution is similar to that of the members of the Laminariez. Alaska leads with 10 species credited to its coast; Spitzbergen has 6, northern Europe 4, northern Asia and Baffin Bay 3 apiece, the Sea of Ochotsk and New England have 2 each, while Japan and California each have 1. Although the regions most care- fully examined have the advantage as regards the greater number of species credited, yet there is little room for doubting that the Alarie are most abundant in the coldest waters and diminish as the waters become warmer. ‘This can be readily seen on the coast of New England. In Long Island Sound and the region south of Cape Cod there are no species of Alaria ,; on the coast of Massa- chusetts 1 species is found. On the coast of Maine there are at least 2 species; and in Baffin Bay there are at least 3. We find then that the subtribes of the Laminariacee may be divided into those characteristically northern and those character- istically southern. Of the northern subtribes both the Laminariez and the Alariez are circumpolar while the Agaree and Egregiez are more limited in their distribution. The Laminariee extend down along the western coast of Africa to Cape Horn and beyond to St. Paul Is., and perhaps also down along the western coast of South America. Of the southern subtribes, the Macrocystezx, and the Ecklonex are both circumpolar and the Lessonez very nearly so. These subtribes are not however confined as strictly to the southern hemispheres as 1 Obs. Phyc., Pt. 5, p. 1? 2 Of. p. 275. 3 Cf. p. 348. Distribution of the Laminariacece. 367 the northern subtribes are to the northern hemisphere. The Macro- cystez have the most extended range as far as latitude is concerned, extending from the southern point of South America to the north- western corner of North America. In the case of the other sub- tribes the distribution is not so continuous. The Ecklonez have pos- session of Australia and Cape Horn, but reappear in peculiar forms in California and Japan. The Lessonee extend up the western coast of North America and reappear on the western coast of North America in forms peculiar to that region. Arguing from the fact that certain species of alge are practically cosmopolitan, being found in almost all marine waters, we may readily believe that if an alga be of such constitution as to endure almost any condition of heat or cold, freshness or salinity, ete., which may be found in the ocean; such a species would be found almost everywhere. Consequently we may also believe that a more or less limited distribution means that the particular form is unable to endure certain conditions found along the borders of the area inhabited by it and that thus barriers are raised against its farther dispersion. Within a particular area, a species is dispersed by the various tides, currents, swells, etc. of the waters of that area. Apropos of this subject Hooker has said:’ “ We are accustomed to regard the ocean as so ever-active and powerful an agent in facilita- ting migration, and its uniform temperature is so conducive to the general diffusion of species, that it seems almost wonderful that Alge should have limits to their distribution, especially in waters which gird the globe on the same parallel of latitude, and whose unchecked swells and currents literally extend over every degree of longitude.” The temperature of the water has perhaps as much to do, as any one thing, in limiting the distribution, and yet this is not the only thing. Species may be carried across even fairly wide areas of water whose temperature is unfavorable to their growth, by currents passing from the areas which they inhabit. Hooker goes on to say: “The remarkable increase in temperature of the tropical over the polar seas of the Atlantic may, and probably alone does, check the progress of the Macrocystis in its course from Cape Horn to the equator in that ocean, for, . .. the same sea-weed can float with the colder currents of the Pacific from the same Cape to Behring’s Straits ; but no such obstacle prevents the fullest interchange of 1 Flora Antarctica, Pt. 2, p. 457. 368 W. A. Setchell— Classification and Geographical Cystoseiree between New Zealand and the temperate seas of South America. It, however, is the fact, that whilst this group literally abounds in certain latitudes and longitudes, which are those of New Holland and the west Pacific, they are nearly absent from analogous positions in the longitude of South America.” Besides the temperature of the water the temperature of the air affects such species of alge as are partially or wholly exposed at low water. This matter might affect the distribution of the kelps to a slight extent,’ but most of them grow below low water mark. Two other cases, more local than general, which affect the distri- bution of alge, are the nature of the bottom and the salinity of the sea. Both of these are discussed by Kjellman in a very satisfactory fashion.’ The configuration of the coast, the amount of light, the tides, etc., have their share in preventing or helping a form to get a foothold on a particular coast but the main general factor is the temperature of the sea. As has been stated previously the kelps are inhabitants of the colder waters® and decrease in numbers and luxuriance of growth as we go towards the equator and cease, as a rule, long before we approach either tropic. At the same time, they approach the poles as near as the permanent ice will permit. ‘They flourish in the Arctic Oceans where the temperature even in summer is scarcely above 0.0° C.,* and they may fruit and produce germinating zoo- spores at temperatures of — 1° to — 2° ©.° Prof. Kjellman, to whose work on the “ Arctic Algze” numerous references have been made already, has had magnificent opportunities for studying this subject in regard to the marine alge in general and has considered the subject in detail in his published works. The Laminariez, the Agarez, and the Alariez belong among the inhabitants of the very coldest waters. The MJacrocystis is found floating’ within 15° of the south pole and is abundant in the colder Antarctic waters as a floating plant. The Macrocystis, however, in- habits also the warmer waters and, as we shall see below, can endure a rapge of temperature unknown in the case of any other kelp. 1 Cf. Kjellman, Arctic Algae, p. 31. 2 Loe. cit., pp. 24 and 26. 3 Kjellman, loc. cit., p. 15, “The formation of Laminariacee is the best marked and most widely distributed vegetation in the whole Arctic Sea,” ete. 4 Cf. Kjellman, loc. cit., pp. 31, 61, 84, ete. 5 Of. Kjeilman, loc cit. pp. 82 and 84. 6 Cf. Hooker, Flora Antarctica, Pt. 2, p. 465. Distribution of the Laminariacee. 369 In discussing this subject of the limiting of the distribution of kelps by variations in temperature we must keep two things in mind. In the first place we shall be dealing entirely with the sur- face waters; and in the second place, the temperature which is to be considered is the summer temperature principally. Kelps do not descend very deep into the ocean, so that the surface waters, and those just below are the only ones influencing their growth. So that the temperature of the surface waters is the one principally concerned. In regard to the matter of season, it has been shown in the case of organisms extending from the tropics toward the poles, that it is the winter temperature which determines the limits of distribution’ and consequently in the case of organisms extending from the poles towards the tropics, it is the summer temperature that has the most to do with limiting the range of the species. Of course we find that there are several sets of species, the inhabitants of the coldest waters, then of the less cold, and then even of the warm waters but their distribution towards the equator is limited by the summer temperature while their distribution toward the poles, if limited by temperature at all, is limited in this case only, by the winter tem- perature. In studying ene on which the temperatures of the surface waters are given in both isotheral lines and isocrymal lines, it is interesting to note the limitations of the different subtribes.” The Laminariez, Alariez, and Agarez do not descend below the 20° C. isothere except in a few species which may extend over toward the 25° line, while the most luxuriant growth of this portion of the kelp-flora is found to be bounded towards the equator by the 10° isothere. In the northern hemisphere the waters about northern Norway and of Behring Sea possess what is probably the greatest numbers of individuals as well as species of these tribes and these are within the isothere of 10°. In the southern hemisphere, Fuegia which is wholly below the 10° line and Kerguelen Land oy the Crozets which are said ape Hooker’ to be the “ great nurseries” for Cf. J. D. Dana, Crustacea of the U.S. laine ‘Expedition, Pt. 2, p. 1452, 1852. ? The isotheral and isocrymal iines for surface waters are given in the ‘ charts show- ing the surface temperatures of the Atlantic, Indian, and Pacific Oceans,” published by The British Meteorological Council in 1884, in degrees of Fahrenheit, and in Berg- haus’s ‘‘ Physikalischer Atlas’ (1892) in degrees of the centigrade scale. The temper- atures used in this paper are of the latter. 3 Flora Antarctica, Pt. 2, p.-465. 370 W. A. Setchell— Classification and Geographical Macrocystis in the eastern hemisphere, are considerably to the south of it. The isothere of 20° seems to limit the species of the three sub- tribes named above more or less sharply. This line touches the western coast of Europe just above Gibraltar and the coast of eastern Northern America in the neighborhood of Cape Cod. The colder species of both coasts reach their limits somewhat to the north of these points, probably at about 18° of surface temperature and either go down into deeper waters or are found only at exposed points to the southward. Such is the case with Agarum Turneri> P.&R. on the Massachusetts coast’ and Laminaria digitata (Turn.)’ Lam’x, south of Cape Cod.’ : We find the same state of things in the northern Pacific. The characteristic Laminariez, Agarez, and Alariez stop at about Puget Sound which is the terminus of the isothere of 15°, but Costaria Turneri, Grey. and Alaria esculenta (L.), Grev. (as we still call the Californian form or forms) continue to Monterey nearly to the 20° line, although they are found only at “exposed points.” The typi- cal Laminarie of California are LZ. Andersonii, Farlow, L. Far- lowti, Setchell, and Z. Sinelairii (Harv.\, Farlow, whose range toward the north stops, as far as we know, below the isothere of 15°. An interesting case is that of Pterygophora Californica, Rupr. which is reported by Dr. C. L. Anderson, as growing at Monterey all the year round but is reported by Mr. Daniel Cleveland as oceur- ring at San Diego only from February until May and in deep water.* On the coast of Asia the isothere of 20° reaches the coast of Yezo and there stops the southward range of the species characteristic of Behring Sea. On the eastern coast of Nippon, however, are found the characteristic species of Laminaria Japonica, Aresch., L. Peterseniana, Kjellm., LZ. radicosa, Kjellm., and Alaria crassifolia, Kjellm. : Those members of the Laminariaceze which partake of the Eek lonia-type of structure seem to prefer warmer waters than the majority of the species of the three subtribes mentioned above. Eyregia is found only on the coast of California between the isotheres of 15° and 20°, mostly in the neighborhood of the latter and to the south of it. Evsenia has very nearly the same range. The species of Ecklonia are found on the south and west coasts of Australia between the isotheres of 20° and 30°, at the Cape of Good 1 Cf. Farlow, New England Algz, p. 96. ? Cf. Farlow, loc. cit., pp. 4 and 94. 3 Cf. Hervey, Sea Mosses, p. 89, 1881. Distribution of the Laminariacee. 371 Ilope in the neighborhood of the 25° line, and on the coast of Japan both north and south of the 25° line. Ulopteryx is found with the Ecklonie in Japan. At Terra del Fuego, Ecklonic are very scarce, probably because the isothere of 10° passes through the straits of Magellan. @ouaieaes Ridgeway. Ridgeway. Chord: of culmen 2 «eek Se ite. |4°35-4°50*| 4°62 4°40 4°50 Depiijol doll arbase ott 2 22 2 )1°70—-1°75 IsGt 1°54 150 Depth of bill at unguis.......--...- eae ee 1:00 0-97 1:00 Least depth of bill (near middle)___-; 1°10 0°88 0°88... ae Width ofebill atJbase-. 2.22 osc. 4225 1:20 1:02 0°95 1:00 Greatest width of culmen (at nostrils))...._.--- 0°40 040° ||.22s sae Width of culmen at: umguis_: io. | eee 0°30 0°30 | | 2.22 Middle toe with claw ---------.---- 5°00+ 4°49 4°44 4°25 Middlev@lany tre eae oe ae oN oN ea 66 "56 | |. 20. cee Outer woe Wat elawy 22. kao ee 4°75 4°35 4°32 4°00 (Ghuiter (Ghaws aeae ere 22 xr. Le Lat ee ees 0°45 035. |<20. eee Inner toe with claws o2-. 502 226. 2-2 4°25 3°75 3°75 3°75 Inner claw see sse: =e 2 pees ere eee at eee 0°49 042. | eee Tarsus tease eis Siete eh fot 3°25} 3°05 3°07 2°75 Wy tng sae er ee ea ese A Pos ae 20:0-21:0 19200 ot. We See 19:0 Wail 22028 gee teres tee Se oie 8°0-9°0 BO! Dy (tae eae 70 * “ Bill, 44,” Gould; culmen 4°7, Sharpe. + Without claw, 4°30-4°35, Ridgeway. ¢ 2°8, Sharpe, Zool. Kerg., p. 147. Gough, Kerguelen, and South Georgia Islands. 443 From the above description it will be seen that, though similar in general appearance, this species differs considerably from either of the others. The gray, or “blue,” head and neck is, I have no doubt, a constant character in this species, as Mr. Comer told me partica- larly that all the “molly mokes” at Gough Island were “blue-heads.” Then the pure white forehead and absence of the dark patch behind the eye distinguish it from most of the descriptions, but by the entire absence of any yellow on the lower mandible and by the red unguis, it can be known from the others of this genus at a glance.* That these characters are not individual variations is shown by both specimens agreeing in the color of the bill and in all points where a skeleton can agree with a skin. That they are not young birds is shown by the highly colored and well developed bills, by the charac- ter of the legs and feet, and by the condition of the skeleton. The difference between this and the other species in some of the measurements, too, is considerable. Mr. Ridgeway makes the length of the tarsus one of his main diagnostic points between culminatus and chlororhynchus, and in our specimens the length is about half-way between the two other species, though a little nearer to culminatus. The two outer toes are also quite noticeably longer in eximius than in chlororhynchus and the proportions are different, for in the former the outer toe, without claw, is actually longer than the middle toe ; the tail too, although, of course, a variable quantity, is 1°5 longer than in the latter species; and the bill is somewhat deeper at the base. It seems strange that two islands so near together as Tristan and Gough Island should each have a different species of Albatross breeding on it, but the bird that Mr. Moseley saw at the former and Nightingale Island, was certainly chlororhynchus, although he calls it D. culminata, for he speaks particularly} of the “ bright yellow edge to the gape,” and says that “‘the yellow shows out conspicuously on the side of the head.” Concerning the “molly mokes” Mr. Comer has the following notes: “There is but one kind, which are known as Blue-heads, on Gough Island. Back and heads light blue, top of wings dark, white breasts, top of beak yellow, while the lower part is black, feet white. On this island they lay separately, keeping well apart and scattered * In his original description of TZ. chlororhynchus (I. c.), (4melin says, ‘‘ carina man- dibulz superioris bagique inferioris flava.” ; + ‘Notes of a Naturalist on the Challenger,” H. N. Moseley, pp. 130, 134; Voy. Chal., Zodl., ii, p. 149. 444 G. EL. Verrill—Some Birds and Eggs collected at about the island, among tussocks and brakes, more like the albatross [D. exulans], but at South Georgia and most of the islands they build close to each other in rookeries.* At Gough Island they com- mence laying the 20th of September. They lay but one egg. If robbed they do not lay again but leave the nest and do not return tili another season. Nests are built the same as the Albatross [D. exulans|, only smaller.” In his journal at Gough Island, on Sept. 7th, Mr. Comer notes that, “The molly mokes have commenced to make their nests.” Again on Sept. 27th that he “ got a few molly moke eggs,” and from then on he frequently speaks of taking their egos. The shape of the 75 eggs is comparatively pretty uniform, as a rule more elongate, and nearer elliptical than the following species, most of them approaching an elliptical ovoid. Several are nearly perfect ellipsoids. The texture and surface of the shell is much like that of D. exulans, but finer and smoother in proportion to their smaller size. The ground-color is white, generally with a very slight grayish or dusky and sometimes reddish tinge, and the whole egg is covered with minute specks of a reddish brown, darker than in D. exulans ; in some they are even dark brown. These specks vary much in number and are, for the most part, in the small pits and depressions on the surface of the shell. About one-third of the eggs are otherwise unmarked, so that at a little dis- tance they simply have a dusky appearance. In the other two-thirds the specks become larger and thicker toward the larger end, often forming a more or less perfect zone about it, in other cases they run together and form a blotch which is, in some, quite heavy and con- spicuous. As in JD. exulans, the color is very superficial and many have larger spots or small blotches, unevenly distributed, that scale off when very dry, and like the eggs of the large Albatross, most of them, when held to the light, show spots and blotches of color iz the shell. Three are quite different from the rest in markings, two being heavily streaked over the whole egg with reddish brown, thickest at the large end. The other is streaked, not quite so heavily, with pale lilac, which is not so superficial. * This seems to me another point showing the difference between the species, as [ have no doubt the birds at South Georgia are 7. chlororhynchus:as Mr. Comer writes me that ‘‘they have a yellow streak on the upper part of the beak and another on the lower part.” Gough, Kerguelen, and South Georgia Islands. 445 The average size of the whole seventy-five eggs from Gough Island is 3°785 X 2°45 and the average cubic capacity is 180°. The following table shows the principal variations in size and shape. Bee. of long to Measurements. short axis. Remarks. ee 3 ee : bi nh Two largest, capacity of each 220°. 3°92 x 2°66 1 to 678 Broadest. 7 309) x 2°30 1 to ‘678 Smallest, nearly elliptical; capacity 135°¢. 4°04 x 2°34 1 to 579 4°06 x 2°37 1 to 584 Nearly elliptical. 383x247 | 3°65 x 2°52 Nearly elliptical. 4°26 x 2°44 ito) 1s Most elongate. 3°67 x 2°64 1 to ‘719 Broadest for length. 3°69 x 2°37 Streaked with lilac. 3°70 x 2°57 Streaked with brown. 3°78 x 2°45 About average. (3°785 x 2°45) | = 1 to °6473 Average of 75 eggs, capacity 180°°. 7. Pheebetria fuliginosa (Gm.) Sooty Albatross. ‘‘Peole.” ‘“ Pearr.”’ Diomedea fuliginosa Gmel., 8. N., L, ii, 1788, p. 568; Sharpe, Philos. Trans. Roy. Soc., vol. 168, p. 148; Saunders, op. cit., p. 165; Salvin, P. Z. 8., 1878, p. 740; id., Voy. of Chal., Zool., vol. ii, p. 148. Phebetria fuliginosa Reichenbach, Syst. Av., 1852, p. v.; Kidder and Coues, Bull. Nat, Mus., No. 2, p. 21; iid., op. cit., No. 3, p. 12. -One skin, a skeleton, and ten eggs from Gough Island and one egg from South Georgia. Mr. Comer says, “It is the most difficult bird of all to get at. They lay separately (not in rookeries), usually on cliffs or projecting rocks. The nests are built small and low, of grass and mud. They commence laying by the middle of September and lay one egg, but when killed have a number of small eggs inside. While sitting on their nests they keep up a continual cry similar to that of a young goat. Beak is dark with a yellow streak on each side. White rim on the eyelids around the eye.” The shape of the eggs is ovate, generally rather elongated, but two are much shorter and rounder, while two others much resemble the eggs of PD. exulans in general shape and markings, but are much smaller. The surface and texture of the shell is much like the preceding species and here I may say, that, so far as I am able to judge from our series, there is very little difference in the texture or surface of the eggs of the four species, aside from the color, markings and shape, either to the eye or touch except in direct proportion to the TRANS. Conn. AcAD., Vou. IX. MARCH, 1895. 31 446 G. EL. Verrili—Some Birds and Eqgqs collected at size, the large eggs of D. exulans having a correspondingly coarse texture and rough surface. The individual variation, however, in the different eggs of each species is. considerable, some being much rougher and coarser than others. The ground-color of the eggs of this species is white, with a slight grayish tint, much like that of the preceding species, but not so clear, and pure white, as in D. exulans. The whole egg is covered with minute specks of reddish brown of about the same tint as in the last species, and, as in that case, giving a dusky hue to the egg at a little distance, but the number of specks varies much in differ- ent eggs. In all but two, the specks become larger and thicker about the large end, occasionally forming a slight zone, but gener- ally simply darkening that end a little. In four specimens there are also a few larger spots, scattered irregularly over the egg, as in the other species and, as with them, they scale off when very dry. The single egg from South Georgia does not differ from the Gough Island eggs except in size, it being larger than the others. The following table gives the measurements of all the eggs of this species in the collection. Locality. Measurements. | Ratio of axes. Remarks. South Georgia} 4°20 x 2°72 1 to 605 Shaped like D. exulans, capacity 250¢¢. Gough Island} 4°23.x 2°52 1 to 596 Longest and narrowest. a 3°70 x 2°63 1 to ‘701 Shortest and smallest. we 3°86 x 2°68 1 to 694 - 4:22 x 2°53 1 to *600 at 4°00 x 2°60 1 to *650 it 4:04 x 2°65 1 to *656 ‘ Pa 4:00 x 2°74 1 to *685 Largest and broadest from Gough Is’d. ed 4°00 x 2°65 1 to 662 Capacity 226°. bi 4°09 x 2°64 1 to °645 % 4:05 x 2°57 1 to ‘635 ‘es F ; Average of above 10 eggs from Gough (4-005 x 2.62) | 1 to “6542 | Island, capacity 2206 88 8 The following table gives comparative measurements of the eggs of the different species of Albatross represented in these collections. The last two columns give the sizes of the eggs having respectively the greatest and least cubic capacity; for the extreme in any one measurement, see the special tables under each species. Gough, Kerguelen, and South Georgia Islands. vas } i D ip Se : | : ce a 6 & a zg | 38 a ies « o Ss o o re) | ~ Species. 4 S as ans ois az 3 s D aS) H 30 es . (2) orm ~~ | fo) oO > > SS 3 | g A = < Des a 12, 13) consists of a tube with thick muscular walls which are attached anteriorly to the muscles of the head just in front of the brain (Plate XI, fig. 2; Plate XII, figs. 1, 2). Although often nearly as long as the entire animal, it usually lies coiled up in the esophagal region and reaches only a short distance further back. In the Anopla and in many of the Anopla this organ has its blind posterior end attached by a slender fibrous ribbon to the dorsal wall of the proboscis-sheath. This attachment is readily observed in the living worm or in micro- scopic sections. In this species, although I have examined a great number of individuals with reference to this point, I have been unable to find any such attachment. In all cases the proboscis lay coiled up within its sheath, and its smooth, rounded extremity (Plate XII, fig. 10) showed no evidence of having had any connection with the pro- boscis-sheath. The wall of the proboscis shows a striking similarity to the body- wall both in the number and in the arrangement of the constituent layers. A comparison of the diagrams on Plate XII, figures 5 and 6, will serve as an illustration of this close resemblance. Of course the curvature of the layers is different; but this would not be the case when the proboscis is extruded. In the body-wall, fig. 5, we find an outer epithelium (é) ; an outer longitudinal muscular layer (dm’) ; a nerve-plexus (np) ; a circular muscular layer (em); and an inner longitudinal muscular layer (dm). Likewise the proboscis, fig. 6, is made up of an inner epithelium (é) ; an inner longitudinal muscular layer (7m) ; a nerve-plexus (mp) ; an inner circular muscular layer (cm) ; an outer longitudinal muscular layer (/m'); and an outer cir- cular muscular layer (¢m’), besides a delicate endothelium (e7) bathed in the fluid of the rhynchocelom. The inner epithelial layer (Plate XII, figs. 11, 12, 13 e) is thrown up into large, circular folds which are more or less broken up into rounded papille by irregular longitudinal folds. The epithelium is directly continuous with that of the rhynchodzum, and is made up of long columnar cells (Plate XII, fig. 3) which are mostly filled with glandular secretion. The cells (4) which clothe the immediate lumen of the proboscis have, in many cases, in their free, outer borders a cluster of slender, rod-like bodies (70) resembling the rhabdites of the W. R. Coe—Anatomy of Cerebratulus lacteus. 489 Rhabdocela. The inner portion of each cell is prolonged into a slender process, above which lies the nucleus as in the cells of the body-epithelium. The fine granular protoplasm above the nucleus contains minute particles of a transparent secretion. Between these ‘‘rhabdite-cells”, and especially among their bases, are many less elongated cells (a’) which are more or less completely filled witha transparent secretion often collected into globules of various sizes. The secretion of the proboscis-glands is exceedingly sticky, so that the proboscis adheres to any object with which it comes in contact. This organ may possibly aid the worm in‘securing its food. It is often thrust out as if to explore the surrounding objects. In the anterior portion of the proboscis (Plate XII, fig. 11), the epithelium is very simple and is made up of ciliated columnar cells like those in the rhynchodzum (Plate XII, fig. 8). A transverse sec- tion through this region of the proboscis shows only longitudinal muscular fibres, among which the nerves (pz) appear as two crescent- shaped masses similar in position to the lateral cords of the body.* In the middle portion of the proboscis (Plate XII, fig. 12), the epithelium is much folded and when the proboscis is not extruded the columnar cells partially overlap, so that in a section the epithe- lium appears to be stratified (fig. 4). In this region the muscular layers are very thick. Towards the posterior end (fig. 13) the epithelial cells become still more slender than in the middle region and among them are very few “ rhabdite-cells.” The cells are mostly glandular and are filled with a transparent secretion collected into little globules. The muscular layers are made up of muscular fibres which are con- tinuous with the interlaced fibres of the head. These are gathered up from all sides into compact and strong bundles as they pass, just in front of the brain, into the proboscis. ‘These muscles at first show no division into layers but all run parallel with the long axis of the proboscis (Plate XII, fig. 11). Gradually, however, a circular layer arises just outside the nerves, which divides the longitudinal muscles into an outer and an inner layer. As the circular layer (fig. 12, em) becomes stronger some strands of the muscle pass tangentially from * Hubrecht (7) describes and figures (Plate XV, fig. 3) a similar section from the proboscis of Cerebratulus macroren, although he states that the section was taken very far back in the proboscis. He states also that the nervous plexus has given place to two longitudinal nerve-stems and that the epithelium is flattened. It would be sur- prising if the anterior end of the proboscis in one species should correspond to the posterior end in another species of the same genus. 490 W. £. Coe—Anatomy of Cerebratulus lacteus. it, through the outer longitudinal layer, above and below, and unite with the thin, outer circular layer (cm’) just internal to the outer endothelium. Dorsally, these fibres leave the inner circular layer to the right and to the Jeft of the middle line and pass outwards in such a manner that the fibres from the right side cross those from the left, in the midst of the outer longitudinal layer, in the middle line. Ven- trally, the fibres from each side leave the circular layer in the median line. These crosses (¢o,co’) are wanting only at the anterior and posterior ends of the proboscis. The fibres making such crosses do not occur in a continuous sheet but pass out in bundles between the bundles of longitudinal muscles. For a considerable distance back from the anterior end, the internal longitudinal layer (im) is much more massive than the external, but the muscle-bundles are much more widely separated by the connec- tive tissue framework and gelatinous tissue. Towards the middle region of the proboscis this layer becomes much reduced, and near the posterior extremity it disappears altogether. The inner circular layer (em) continues nearly the whole length of the proboscis with- out noticeable change of character. The external longitudinal layer (4m') maintains nearly the same thickness throughout the entire length of the proboscis and continues back to the very extremity, after both the other principal layers have disappeared. The external circular layer (em') is made up of a few fibres lying imme- diately beneath the outer endothelium. The proboscis is innervated by means of a pair of nerves (Plate XII, fig. 11, pr) which arise from the ventral brain-lobes and pass with the muscles into the proboscis, where they at first occupy a lateral position (similar to that of the lateral cords of the body) in the midst of the muscle-bundles. Farther back they expand dorsally | and ventrally, inside the forming circular muscular layer, until each meets the other above and below to form a cylindrical nerve-plexus (fig. 12, np) analogous to that in the body-wall. Towards the pos- terior end this layer becomes much reduced and at length disappears. The outer epithelium, or endothelium, (en) rests upon a thin base- ment membrane and is made up of a single layer of flattened endo- thelial cells quite similar to those which clothe the proboscis-sheath (fig. 7). Each cell rests upon the basement membrane below, with its free surface bathed in the rhynchoccelomic fluid. As in the endothe- lial cells of the proboscis-sheath, the cell-boundaries are not to be readily distinguished. The anterior end of the proboscis forms a circular line of attachment to the cephalic tissues. This attachment W. R. Coe—Anatomy of Cerebratulus lacteus. 491 (Plate XI, fig. 2, Plate XII, fig. 1, 7) is quite thin and is easily broken by any sudden contraction of the muscular sheath: The Alimentary Canal. The alimentary canal may be divided into five principal regions : mouth, esophagus, intestine, rectum and anus. The mouth is situated on the ventral side of the body a little farther back than the posterior ends of the cephalic slits. “It is capa- ble of great variation in size and shape ; at one time appearing as a small, round hole, and at another, as a longitudinal slit. The epithe- hum of the mouth-opening is thrown up into numerous longitudinal folds (Plate X, fig. 4) continuous with those of the esophagus. It passes insensibly into the epithelium of the integument on one side and the csophagal epithelium on the other. There is an outer layer of ciliated cells beneath which are large gland-cells in several layers. Their granular contents stain with great intensity. There isa large blood-vessel, the buccal, and a large nerve, the vagus, on each side of the mouth. The esophagus (Plate XI, figs. 1, 3) also has the epithelium thrown up into great longitudinal folds but is entirely devoid of diverticula. It is supplied with a loose musculature (fig. 1, 7) consisting of a few circular and longitudinal fibres; there is also a system of radial fibres connecting these muscles with those of the circular layer in the body-wall. The esophagus is surrounded by a complex system of blood-vessels ramifying in all directions beneath the epithelium. They are supplied from the lateral blood- vessels and anastomose anteriorly with the buccal vessels. ‘There is a large number of these cesophagal vessels, as many as twenty being seen in each cross section. In most related species the cesophagus is surrounded by a comparatively small number of large lacunz instead of contractile vessels as in this species.* In the nephridial region the nephridial canals run parallel with the smaller blood-vessels. The anterior portion of the csophagus is innervated by the vagus nerves, and the remainder by radial fibres from the nerve-plexus in the body-wall. | The epithelium (oe) is made up of asuperficial layer of ciliated and glandular cells and a deeper, thick mass of glands arranged in clus- ters. There is also a thin layer of very large gland-cells situated beneath the musculature. Each ciliated cell (fig. 5) is swollen near * Cf. OC. Leydit, Plate XV, fig. 13. 492 W. &. Coe—Anatomy of Cerebratulus lacteus. its free border and has its opposite end continued into a slender, often branched, fibre-like process. The nucleus (7) is placed in the lower part of the upper, broadened portion of the cell. These cells are regularly arranged with all their oval nuclei at about the same level. Glandular cells are scattered among the ciliated cells.* Beneath the superficial layer are elongated clusters of gland-cells closely packed together. Each cluster of cells apparently has a single duct leading through the ciliated layer to the lumen of the cesophagus. The individual gland-cells are large, oval or elongated, and contain a small nucleus pressed to one side of the mass of deeply- stained secretion, similar to that often found in the duct. The intestine comprises much the largest portion of the alimentary canal, and to further increase its surface there are broad, paired diverticula of the main canal throughout its course. These intes- tinal ceca are often forked or lobulated distally, especially above and below the median horizontal plane (Plate XIV, fig. 10). The main canal (7) is comparatively small, and in transverse sections appears somewhat flattened and broadened above, while the narrow ventral border lies near the ventral wall of the body (Plate XI, fig. 4). The intestine lacks muscles almost entirely, the ceca being directly surrounded only by connective tissue, and although there is a double set of dorso-ventral muscles reaching between each pair of cea nearly to the main canal, these belong rather to the body-muscula- ture than to the intestine. The epithelium consists of long, columnar cells (Plate XIII, fig. 2) which are prolonged below into slender, often branched, processes. Many of the cells are ciliated, but those cells which are most characteristic of this portion of the alimentary canal are more or less completely filled with colorless, refractive granules (s) resembling globules of oil or fat. It often happens that in mounted sections these granules stain intensely and resemble minute nuclei. The nuclei (mz) of the cells are usually placed just above the filiform processes (w@). The granules occur most abund- antly above the nucleus, although they are sometimes found beneath it.t At the posterior end of the intestine the ceca become very small and shallow, and disappear entirely in the short rectwm which lies *JIn Carinella the arrangement and structure of these ciliated and glandular cells (Plate XIII, fig. 4) are easily made out. + In Micrura affinis (Plate XIII, fig. 3) these long, slender cells are arranged with great regularity about the intestinal lumen, and have conspicuous cell-walls, which is not the case in any sections of C. lactews which I could obtain. W. R. Coe—Anatomy of Cerebratulus lacteus. 493 between the intestine proper and the anus. The rectum is clothed with a single layer of columnar, ciliated epithelium. The anus is at the end of the body, just beneath the caudal papilla. The Blood-vascular System. The blood is contained in vessels with muscular walls and in thin- walled lacune. It consists of a colorless plasma in which float spherical corpuscles (Plate XIII, fig. 11) about .006™" in diameter, each with a spherical, deep-staining nucleus. As in all Schizonemer- teans the blood system (Plate XIII, fig. 1) consists chiefly of three longitudinal trunks reaching the whole length of the animal, and connected anteriorly by means of lacune and posteriorly by numer- ous transverse, anastomosing branches. Of these three main trunks, two are paired, being known as the lateral vessels (lv), and arise, one on each side, as posterior continuations of the lateral cephalic lacune (cl). They pass backwards through the esophagal region on either side of the proboscis-sheath and above the esophagus, to the walls of which they give off numerous branches-(ov). In the intes- tinal region they assume a ventral and lateral position beneath the intestine. The third, or dorsal, vessel (db) arises from the ventral commissure of the cephalic lacunez, described below, passes through the walls of the proboscis-sheath, and continues between the muscles of the same and its internal endothelium (Plate XI, fig. 3) to the intestinal region. Here it again passes obliquely through the proboscis-sheath, directly beneath which (fig. 4) it continues to the end of the body, giving off on the way a pair of branches, which anastomose with the lateral trunks, opposite each pair of intestinal ceca. * A description in detail of this system of vessels, taken from a series of transverse sections, each .025™" thick, may prove of inter- est. Near the tip of the head (section 18 in one series) there is observed a small, thin-walled lacuna lying just above the proboscis- opening. ‘This lacuna spreads out and bends downward on each side of the rhynchodzum, so that a section of the lacuna in this region is _horse-shoe shaped. A few sections farther back this lacuna divides into two portions, crescent-shaped in transverse section. These are * Joubin (11), in describing the anatomy of Nemerteans in general, figures these anastomosing vessels between the intestinal caeca and states, on p. 21, that such is their position. In all those speties which I haye examined, on the contrary, these vessels do not alternate with the intestinal ceeca but lie opposite them. Cf. Plate XTV, oes. §, 10, 12: Trans, Conn, AcavD., Vou. IX. JUNE, 1895. 34 494 W. R. Coe—Anatomy of Cerebratulus lacteus. the cephalic lacune (Plate X, fig. 1, cl) of which the first lacuna is really the anterior anastomosis. ‘The cephalic lacune enlarge as they pass backward, one on each side of the rhynchodeum, from which they are separated only by a very thin- mass of tissue, nearly to the attachment of the proboscis (sect. 98). At this point, thick bands of muscles encroach so much upon their space that the lacunze become very small and thin. Just back of the anterior portion of the brain (sect. 113) the two lacune enlarge again and become united beneath in a ventral commissure, so that a section here shows a second horse- shoe shaped space (Plate X, fig. 9), but this time with its ends point- ing upward. Near the side-organs (sects. 123-128) fibres pass from each side obliquely upwards and inwards across the lacuna to the proboscis-sheath, beneath which a portion of the lacuna is separated from the rest to form a median lacuna (fig. 3, m/l). A few sec- tions further back this median lacuna communicates with the lateral lacune, after which it divides into two trunks which supply the mouth and anterior portion of the esophagus, and to which the name buccal vessels may be given. From the broad ventral anas- tomosis of the cephalic lacune, and directly above the median lacuna, a small vessel also arises, which becomes surrounded with fibres of the proboscis-sheath and forms the dorsal vessel, described above. Just back of the brain-lobes the lateral lacune greatly enlarge, and finally completely surround the side-organs, except at their anterior borders, so that these organs project freely into the blood space. In the region of the mouth (Plate X, fig. 4) the lateral lacune become much smaller and pass backward through the csophagal region, on each side between the proboscis-sheath and the lateral nerve-cord, as the lateral vessels. These vessels give off to the walls of the esophagus a multitude of branches (Plate XIII, fig. 1, ov) which break up into minute, anastomosing twigs. In the nephridial region these branches run in close proximity to, and side by side with, the tubules of the nephridial system (fig. 5). Towards the posterior portion of the wesophagal region the lateral vessels are not larger than some of the esophagal vessels although their appearance varies greatly according to the state of contraction. Near the intestinal region the lateral vessels bend downward and occupy a position, for the remainder of their course, beneath the intestinal czeca, somewhat laterally to the median line. Throughout the length of the intestinal region a branch (fig. 1, av) is given off from each lateral vessel beneath every pair of intestinal cxca, to join the dorsal vessel beneath the proboscis-sheath. There is a union of W. R. Coe—Anatomy of Cerebratulus lacteus. 495 the lateral vessels with the dorsal vessel at the posterior end of the body. Histology.—The walls of the lacune, and of those vessels which are surrounded by the body-muscles, have a different structure than those of the vessels which are surrounded by the parenchyma. In general, the former are destitute of a muscular coat, while the latter (Plate XIII, figs. 13, 14) have more or less strong walls of circular muscles. All these vessels have a delicate endothelial lining (e7') in which the small, oval nuclei are quite conspicuous on account of their affinity for staining fluids. The cell-outlines, however, cannot well be made out. In most cases the endothelium is thrown up into minute folds. Outside this endothelial lining are a few delicate longitudinal muscular fibres, and a layer of circular muscles (7) made up of very fine fibres with exceedingly few nuclei. The thick- ness of this layer varies much in different vessels, and, as a rule, is greater in those vessels of the intestinal than in those of the cesopha- gal region. Outside the muscular layer is a coating of large, wedge-shaped parenchyma-cells (yc) having the thin ends attached close to the muscular wall, while the outer thickened ends with their rounded edges are surrounded by gelatinous tissue. These cells are not unlike the cells found throughout the gelatinous tissue, especially where it comes in contact with other tissues. They are also found about the nephridial vessels, though to a much smaller extent. Each cell is provided with an oval nucleus. Between the parenchyma- cells are fine fibres which connect the blood-vessels with the other tissues. In the lacune of the head the endothelium is separated from the cephalic musculature only by a thin sheet of connective tissue. No muscles or parenchyma-cells are found. The dorsal vessel (Plate XIII, fig. 9) is provided with a much thicker muscular wall than is found in any of the other vessels. Outside of the muscular wall, and beneath the much-folded endothe- lium of the rhynchocelom, is a thick layer apparently made up of a mass of elongated parenchyma-cells (yc) piled one on top of another, and which have a dense protoplasm and oval nuclei. Between the cells run bundles of fibrous tissue from the muscular layer of the vessel towards the endothelium of the proboscis-sheath (en). Soon after the origin of the dorsal vessel from the ventral commissure of the lateral lacunze, and while it is still surrounded by the muscular fibres of the proboscis-sheath, these parenchyma-cells appear around it. Likewise when the vessel leaves the proboscis-sheath in the pos- terior esophagal region a thick coating of these cells continues, and 426 W. R. Coe—Anatomy of Cerebratulus lacteus. this covering does not become single layered, as in the other vessels, until much farther back. The Nephridial System. According to Biirger (3) the Nephridial system in the Nemerteans was first noticed in 1851 by Max Schultze (12) who found a second pair of canals, which he designated as water-vessels, running parallel with the lateral blood-vessels. No one seems to have again noticed the nephridia until 1876, when Semper (13) found them in Malaco- bdelia. The next year von Kennel (4) described in detail the system in the same genus. More recently Hubrecht (8), Oudemans (9), and Biirger (3) have contributed more or less extensive articles devoted almost entirely to the subject. In this species the nephridia (Plate XIII, figs. 1, 5) occupy about the middle third of the csophagal region, and occur below and at the sides of the esophagus. They are not found above the csophagus nor near the proboscis-sheath, Leading to the exterior is a single pair of efferent ducts (we). Each duct is formed by the union of two longitudinal canals running in opposite directions near the lateral nerve-cords, and parallel with the longitudinal axis of the body. Of these the one in front of the efferent duct is the longer. Each longitudinal canal divides dichoto- mously into a large number of branches (w) which ramify among the blood-vessels surrounding the esophagus. Some of the smaller twigs run for considerable distances parallel with, and close beside the smaller branches of the blood-vessels. The excretory products con- tained in the latter may readily pass through, or between, the few cells separating the lumens of the two canals, be taken up by the glandular epithelium lining the nephridial canals, and be swept by the cilia to the outside of the body. The walls of the canals are made up of a thin layer of connective tissue supporting the simple ciliated epithelium (Plate XIII, fig. 8, e) lining the lumen. They are apparently destitute of muscular fibres. The deep-stained, oval nuclei of the epithelial cells are placed closely side by side. The cell-walls are indistinct in all the preparations. The efferent ducts (fig. 8) differ in their structure but slightly from the other canals except that the former are provided with a much thicker sheath of connective tissue (¢c). These ducts (Plate XI, fig. 8, we) are often slightly enlarged just outside the circular muscular layer and open by a small pore on the dorso-lateral surface of the body. | Hubrecht (7) states that he finds a direct communication between W. R. Coe—Anatomy of Cerebratulus lacteus. 497 the lateral vessels and the nephridia in Carinoma, and Oudemans (9) likewise in Carinella. Biirger (3) has carefully studied the nephrid- ial system in some of the small species of the Enopla by placing the living animal in a dilute solution of methylene-blue for a few minutes and then compressing it under a cover-glass. By this method he has been able to demonstrate that the vessels of the blood-vascular system stand in very close relation with the excretory canals, but there is no direct communication between the two systems in the Enopla. The canals of the nephridial apparatus are clothed with a ciliated epithe- lium and end in blind sacs (“‘ Kélbchen”) which are also clothed with a simple ciliated epithelium. Swinging in the lumen of each blind sac is a tuft of long cilia (“ Wimperflamme”). In C. Leydii, a species resembling C. /acteus in many respects, the cephalic lacune are quite like those in the latter species, but instead of the many small vessels with muscular walls in the cesophagal region, as is the case in C. lacteus, we find the lateral lacune (Plate XV, fig. 13, @) to continue without change of character through the entire cesophagal region, back of which they bend downward to form the lateral vessels beneath the intestine. They do not acquire muscular walls until far back in the cesophagal region. The csophagus is sur- rounded by large, anastomosing lacune (o/) instead of small, contrac- tile vessels. The nephridial system occurs in a similar part of the body, but it consists of a pair of longitudinal canals (Plate XIII, fig. 10, «) with few branches, lying so closely pressed against the walls of the lateral lacune (//) as to be partly covered by them. There is a single efferent duct near the posterior end of each canal. In C. luridus the large lateral lacune (Plate XIII, fig. 7, 77) in the anterior cesophagal region are covered on their outer borders with a mass of convoluted nephridial tubules (w). But one pair of efferent ducts was seen. The nephridial system commences in Lineus socialis (Plate XV, fig. 9) just back of the side-organs. From this point the nephridial canals. follow the lateral lacune far back into the csophagal region, giving off on the way numerous efferent ducts (Plate XIII, fig. 6, we) which are, for the most part, paired. The number of such ducts seems to vary in different specimens. Oudemans (9) has shown that the number of efferent ducts, in some species, increases with age, Throughout its course the nephridial canal lies closely pressed against the wall of the lateral lacuna which lies near the proboscis-sheath. In L. bicolor the cesophagal region is very short, and, although the nephridia commence just back of the mouth, the efferent ducts are 498 W. R. Coe—Anatomy of Cerebratulus lacteus. situated almost back to the intestinal region, or so far back that the dorsal vessel has left the proboscis-sheath and the epithelium lining the alimentary canal has assumed the granular appearance so charac- teristic of the intestine. ‘The only available specimen had two effer- ent ducts on one side and but one on the other. The cephalic lacune in Valencinia (Plate XV, fig. 14) are par- tially divided into a number of longitudinal spaces which, in the region of the brain, coalesce into two lacunz similar to those in Cerebratulus. There is a large number of efferent nephridial ducts. In one specimen the first pair of nephridia, with the efferent ducts, was entirely separate from the six succeeding pairs. There was one unpaired efferent duct. | The Nervous System. The central nervous system is situated, except in the head, between the circular and outer longitudinal muscular layers of the body-wall, and consists of (a) the brain, (6) the pair of lateral nerve-cords, (e) the median dorsal nerve, and (d) a nerve-plexus uniting 6 and «. Nerves to supply the esophagus, the proboscis, the integument, special sense organs, etc., constitute the peripheral nervous system. The brain (Plate X, figs. 7, 8) is made up of two large, ganglionic masses situated in front of the mouth and immediately back of the attachment of the proboscis (Plate XII, fig. 1). Each ganglion con- sists of a dorsal and a ventral lobe, and is connected with its fellow above and below the proboscis-sheath, so that this latter organ is, at its anterior portion, surrounded by a ring of nervous matter. The brain, with its commissures, and the lateral cords have a central fibrous core and a thick outer sheath of ganglion-cells. The dorsal lobes of the brain (Plate X, fig. 8, d@) are rounded and lie immedi- ately above the ventral lobes, with which they are directly continu- ous. Connecting the fibrous core of the dorsal lobe of one side with that of the other is a comparatively thin dorsal commissure (dc). A portion of the fibrous core continues back to the side-organs (so) which lie close behind the dorsal lobes. A multitude of small fibres pass from these lobes in all directions to the tissues of the head, including the rhynchodeum, cephalic slits, integument, etc. These nerves are for the most part sensory in their function. The elongated ventral lobes (Plate X, figs. 2, 8, v) continue directly backward into the lateral cords. There is a ventral commissure (fig. 2, vc) much larger than the dorsal, connecting the ventral lobes. The lateral cords (ic) are the direct posterior continuations of the ventral lobes, so that it is impossible to decide where the latter end W. R. Coe—Anatomy of Cerebratulus lacteus. 499 and the former begin. As an arbitrary point, however, I would sug- gest that the origin of the vagus nerves be taken as the posterior extremity of the ventral lobes. The vagus nerves, as described below, pass to the lateral borders of the mouth and csophagus. The lateral cords pass backward in the body-wall (Plate X, fig. 4), in a median horizontal plane, to the posterior end of the body without appreciable change except as to size. Throughout their length they are connected, both above and below, by a loose plexus of nervous tissue (Plate XI, fig. 1, 2p) which forms a complete cylinder just external to the circular muscular layer (cm). Most of the fibres which go to innervate the integument, body-muscles and other tissues first pass from the lateral cords into this plexus and thence to their destination. From this plexus multitudes of nerve-fibres pass peripherally, between the muscle-bundles, to the integument. Like- wise at short intervals fibres are given off to the digestive canal. Such fibres have to pass through the circular and inner longitudinal muscular layers. In the median line the plexus is thickened to form a more or less distinct dorsal, or medullary, nerve (Plate X, fig. 4, dn). Although this nerve is much less conspicuous in this than in many related species, it can be traced without difficulty to the dorsal commissure of the brain. A pair of large nerves, the vagus (Plate X, figs. 4, 6, 8, un ; Plate XV, fig. 8), arise from the internal borders of the ventral brain- lobes near the origin of the lateral cords. They are connected with a strong commissure (cv) and pass downwards and outwards along the edges of the mouth, to supply this organ and the anterior portion of the esophagus. The commissure is fully as large as either vagus nerve and is provided with ganglion-cells on its dorsal border. The proboscis is supplied with a pair of large nerves (Plate X, figs. 6, 8, pv) from the anterior border of the strong commissure of the ventral brain-lobes. From their origin these nerves run anteri- orly near the proboscis-sheath and enter the proboscis at its attach- ment to the cephalic muscles. After reaching the proboscis they appear crescent-shaped in transverse section and lie in the midst of the muscles on each side (Plate XII, fig. 11, yz). Their position in the proboscis is thus similar to that of the lateral cords in the body- wall. ‘The ends of the crescents elongate until they meet above and below to form a nervous plexus (fig. 12, np) between the circular and inner longitudinal muscular layers. Histology.—The nervous tissues of which the brain and lateral 500 W. R. Coe—Anatomy of Cerebratulus lacteus. cords are constituted consist of a central fibrous core covered with a delicate sheath of connective tissue, or neurilemma ; a thick layer of ganglion cells with masses of connective tissue peripherally ; and an outer sheath of connective tissue covering the whole. Birger (2) finds in some species of Nemerteans four types of ganglion-cells which differ more or less in size and shape and in their relations with each other. Of these four types of cells three only are met with in this species; the fourth type, the “ neurochord- cells,” not being present, or at least they have not been discovered. All ganglion-cells appear to be unipolar, and are surrounded by a loose sheath of connective tissue. The first type of ganglion-cells (Plate XV, fig. 7, gc!) seems to be characteristic of the dorsal brain-lobes. They are conspicuous from their small, deeply-stained nuclei which in the sections are packed so closely together that it would seem that very little space could be left between them for the cell-protoplasm which is seen with diffi- — culty, although from it a slender process can sometimes be made out. The cells occur most abundantly in the outer and posterior borders of the dorsal brain-lobes, but are also found in the dorsal commissures and among the tissues of the head, surrounding the duct leading to the side-organs. There are large masses of such cells in the side- organs themselves. In the dorsal brain-lobes these cells are packed together in large masses above and below the fibrous core. Cells of the third type also occur abundantly in the inner and anterior bor- ders of the dorsal lobes ; otherwise these lobes contain only those of the first type. As the majority of the organs of special sense, includ- ing the side-organs (and eyes in those species in which they are pres- ent), are supplied with nerves from the dorsal lobes, there is evidence that the cells of the first type are sensory cells and that the cephalic nerves are largely sensory in their function. The second type of ganglion-cells (Plate XV, figs. 3, 6) is charac- teristic of the ventral brain-lobes and lateral cords. They occur in large, radial clusters with their processes converging towards the fibrous core into which bundles of fibres from these cells pass at certain points. After entering the fibrous core the fibres spread out and are lost to sight among the other fibres of the core. In these cells, also, the nucleus is very large in porportion to the size of the cell, which, however, is much larger than that of the first type, although only about half as large as a cell of the third type, measur- ing about .008™™ by .015™™. Ganglion-cells of ‘the third type (Plate XV, figs. 3, 7, ge) are W. &. Coe—Anatomy of Cerebratulus lacteus. 501 abundant in the inner and anterior borders of the dorsal brain-lobes, on all sides of the ventral lobes, as well as in the lateral cords and in the ventral commissure of the brain-lobes. These cells are very large in comparison with those of the other types, measuring in mounted specimens .025™™ by .015™™. Each cell is pear-shaped and is provided with a large, spherical nucleus near the larger end. The smaller end is continued into a process which, although large and conspicuous, can be traced but a little way from the cell. These cells mostly lie nearer the periphery of the brain than those of the other types of cells. Surrounding each cell is a delicate sheath of connective tissue. The fibrous core (Plate X, fig. 6; Plate XV, fig. 3, fc) is made up of exceedingly fine and delicate fibres. In the brain this core swells out in the dorsal and ventral lobes. The cores of the two sides are connected by both commissures. Each dorsal lobe shows a partial division into an upper lobule which ends free posteriorly, and an under lobule which continues into the side-organ. Among the fibres occurs a delicate, supporting connective tissue with a few oval nuclei. Outside the fibrous core is a delicate inner sheath of connective tissue, or neurilemma (Plate XV, fig. 3; Plate X, fig. 6, es), through which the fibres from the ganglion-cells pass in bundles to spread out among the fibres of the core. Supporting the ganglion- cells is a loose network of connective tissue (c) which, in certain parts of the brain, notably on the inner borders of the ventral lobes and the upper borders of the dorsal lobes, occupies a considerable area which is devoid of ganglion-cells. Surrounding the ganglion- layers is an outer sheet of connective tissue (cs’) much thicker than the inner neurilemma and more or less broken up into broad bundles of fibres. The lateral cords (Plate X, fig. 5) are composed of a central mass of fibrous tissue (fc) surrounded by a sheath of connective tissue (cs) much thicker than the inner neurilemma of the brain. Delicate nucleated fibres from this sheath run in all directions among the nerve-fibres, and often cross from one side of the core to the other, so that a few connective-tissue nuclei are often met with in the mid- dle of the core. Outside this inner sheath, or neurilemma, the gan- glion-cells (gc) are arranged in a large mass above and one below the fibrous core. These cells are mostly of the second type with a few of the third type towards the periphery. On the outer and inner borders of the cord no ganglion-cells occur, the outer border having a broad band of loose connective tissue (¢) with a few longitudinal 502 W. &. Coe—Anatomy of Cerebratulus lacteus. muscular fibres, while the inner border of the fibrous core abuts closely against the circular muscular layer of the body-wall. Out- side the ganglion-layer is a loose and irregular sheath of connective tissue (cs’). From the ganglion-layer bundles of nerve-fibres run both into the fibrous core and into the nerve-plexus to be dis- tributed throughout the body. The nerve-plexus lacks ganglion-cells but contains, besides nerve- fibres, an abundance of nucleated connective tissue fibres. It appar- ently serves as the path through which the nerves from the lateral cords are distributed to the various organs of the body. The Cephalic Slits and Side-organs. The side-organs, posterior brain-lobes, or olfactory lobes, as they are variously called, are a pair of large, spherical organs lying in the cephalic blood-lacune, closely pressed against the posterior borders of the dorsal brain-lobes (Plate XI, fig. 2, so). Each has a thin external sheath of connective tissue and a delicate outer endothelium lining the blood-lacuna. Except where they are united with the tis- sues of the head in front and on the anterior ventral border, they are surrounded with blood. This fact led the observers of a few years ago to consider the side-organs as having a respiratory function. A large branch from the fibrous core of the dorsal brain-lobe passes directly into the middle of these organs, and bent about in their tis- sues lies a canal with sensory epithelium. This canal-opens to the exterior of the body near the posterior ends of the cephalic slits, and places these organs in direct communication with the water in which the animals live. Their function is still somewhat problematical, though it is undoubtedly sensory, and is most generally believed to be olfactory. . ‘‘The lateral cephalic slits (Plate X, figs. 1, 2, 3, 8, Zs) are large and deep, extending the entire length of the head and running for- ward close to and a little above the proboscis-pore, those of opposite sides not uniting together except by a very shallow furrow... . Their margins are thin and mobile, often undulated or curled back so as to open the slits widely and expose the deep posterior pits. .. . ”* These slits are furnished with an epithelium which is not very dif- ferent from that of the rest of the integument, except that the cilia are longer and more conspicuous. Among the bases of the elon- gated cells are, especially in the posterior portions of the slits, many * Verrill, (1) p. 434. W. R. Coe—Anatomy of Cerebratulus lacteus. 508 nuclei of cells which closely resemble those of the first type of nerve- cells found in the dorsal brain-lobes. I believe these to be nuclei of sensory cells, and the cephalic slits to be, for the most part, sensory in their function. In the region of the dorsal commissure of the brain the lateral slits become so deep (Plate X, figs. 2, 8, 7s) that they reach internally almost to the brain-lobes. After giving off the large canals (Fig. 3, cc) to the side-organs the slits become suddenly shallow, and end a short distance further back. The canal which thus arises from the poste- rior end of each lateral slit passes backward in the dmgle between the dorsal and ventral brain-lobes (fig. 3), to enter the side-organ at its lower, outer and anterior border. Soon after its entrance into the side-organ the canal bends sharply upwards to the dorsal border, where it bends at a right angle and runs in this position nearly to the posterior border. Here it again bends towards the inner side and ends blindly among the masses of gland-cells which occupy the pos- terior portions of the side-organs. The portion of the canal between the lateral slits and the side- organs has a much wider lumen than that within the side-organs. The lumen is lined with elongated columnar cells each bearing a cluster of long, coarse cilia on the free surface, while the opposite end is tapered to a slender, often branched, fibre. Among the bases of the cells occur many sensory cells similar to those of the lateral slits. At its entrance into the side-organ, the canal becomes decidedly smaller and the nuclei are farther removed from the lumen. Afterthe canal (Plate XIV, figs. 1, 2, cc) has reached the upper and outer bor- der of the side-organ, and throughout the rest of its course, there is a marked difference in the character of the epithelium on one side of the lumen. The columnar epithelial cells on the side of the canal nearest the outer border of the side-organ are replaced by a smaller number of very large and much modified cells. About six such cells (fig. 2) are usually seen in a cross section of the canal, and to these Dewoletzky (5) has given the name of “lateral cells.” Of these six cells the two outer (#) are much longer than the others (4’) and from each a cluster of long cilia, adhering together to form a single refractive column, projects a considerable distance into the lumen of the canal.* Each of these cells may contain two or more nuclei in its enlarged end which is farthest from the lumen. As Biirger (2) suggests, each of these “lateral border-cells” appears to be a consoli- *In Micrura affinis these cilia are not consolidated into a single column, although they are very long and are closely packed together. 504 W. R. Coe—Anatomy of Cerebratulus lacteus. dation and modification of two or more simple, epithelial cells. Each of the four cells between them bears a similar, but smaller, process and contains a single nucleus. Bounding the opposite two-thirds of the lumen, and separated from the lateral cells by a considerable space, are the less highly modified “median ” cells (fig. 2, me). These cells (fig. 3) are provided with long cilia reaching to the center of the lumen. A dark band is seen just above the bases of the cilia, which results from a thickening of each cilium in this part. The nuclei of the cells are far removed from the lumen. A large bundle of nerves (figs. 1, 2, fc’) from the dorsal brain-lobe ramifies among the bases of the cells. Surrounding this nervous core, which is really a direct continuation of the core of the dorsal brain- lobe, is a thick mass of nerve-cells (gc) not unlike those of the first type found in the dorsal brain-lobes, with which, in fact, they form a continuous sheet. Towards its posterior end the canal (cc’) loses its conspicuous lin- ing of elongated sensory cells and ends blindly among the masses of large gland-cells which make up the greater part of the posterior third of the side-organ. These large, oval gland-cells (g) are filled with a granular secretion which stains so deeply as to obscure the finer details of the cells. Another mass of gland-cells occupies the anterior border of the side-organ, and the two glandular masses are connected by a thin superficial layer of similar gland-cells, ‘These glands discharge their secretion into the ciliated canal, probably in the space between the median and lateral cells, or amongst the latter. The Reproductive Organs. The sexes, asin most Nemerteans, are separate and, in the breeding season, can be readily distinguished by their colors. Instead of the white or pinkish color characteristic of this species in the summer and early fall months, as the generative products develop at the approach of winter both sexes take on a decidedly reddish color. In Feb- ruary the males. become bright red, while the females are dull red in color; in some cases appearing almost chocolate-colored. These deep colors are confined mostly to the intestinal region where the generative products are developed. The genital products are fully matured in March and April, although living spermatozoa may © be found as early as November. The breeding season extends over a considerable period of time, some individuals depositing their products fully a month before others ; nor are all the products in a W. &. Coe—Anatomy of Cerebratulus lacteus. 505 single individual discharged at once, a specimen often showing a portion of its genital sacs to be empty, while other sacs are filled with mature ova or spermatozoa. By the first of May, in the vicinity of New Haven, nearly all the genital products have been discharged. The genital products are developed in flattened pouches, or sacs (Plate XIV, figs. 10, 11, gs), which alternate with the intestinal ceca. These sacs are closely bordered in front and behind by the double band of dorso-ventral muscles (dm) which lies between each pair of intestinal ceca. In the summer, before the genital products begin to develop, the sacs occupy only a narrow ~/-shaped space (fig. 10) just inside the body-muscles. One end of this space lies near the proboscis-sheath above, and the other near the lateral blood- vessel beneath the intestine. It isin this space that the genital products originate. As they mature, the sacs greatly enlarge and finally occupy (figs. 9, 11) fully one-half of all the space within the body-wall. They extend from near the body-muscles (/m) on three sides nearly to the proboscis-sheath and central canal of the intestine (z). Ina horizontal section of the body, the sacs are seen to be some- what thicker next the central intestinal canal than distally. They are also thicker above and below than in the middle. When the genital products are nearly mature each sac is pointed into the mus- cular layers of the body-wall at a point between the lateral cord and the median nerve, though somewhat nearer the latter. This pointed extremity forces its way through the muscular layers and the integu- ment, making a duct through which the genital products may be dis- charged. This duct is lined with flattened epithelium. The genital sacs are also lined with a flattened epithelium, certain cells of which are destined later to develop into ova or spermatozoa, while others apparently remain unchanged to form the follicles. These epithelial cells have small, elongated nuclei. The cell-walls could not be made out. In the female, when the ova begin to develop, the nucleus of the epithelial cell greatly enlarges and the cell acquires a more definite wall. The young ovum (Plate XIV, fig. 5, ov’) has a delicate investing membrane, or follicle (fo), and is imbedded on one side in the loose connective tissue forming the frame-work of the sac. As the ovum increases in size its nucleus develops into the large germinal vesicle which has many germinal spots, of which one or two are much larger than the others. The fully ripe, living ovum (fig. 4) is .09™™ to .11™™ in diameter and is surrounded by a gelatinous zona pellucida which swells up in contact with water to about twice the diameter of the ovum. The 506 W. R. Coe—Anatomy of Cerebratulus lacteus. substance of the ovum is largely made up of fine yolk-granules. The transparent germinal vesicle is about one-third the diameter of the ovum, and often contains a highly refractive germinal spot one-third as large as the vesicle itself. Spermatozoa develop from cells similar to those which form the ova. Ina section through a spermary (Plate XIV, fig. 6) in which the spermatozoa are developing rapidly we see, next the connective tissue framework of the sac, several rows of cells in which are very large nuclei (sc), and in which the cell-outlines are not readily made out. Above these are several irregular rows of cells with much smaller nuclei (sc’). In the next stage we find still smaller, oval or elongate, bodies which usually show anucleus at one end while the rest of the cell is filled witha clear protoplasm. These are, apparently, the developing spermatozoa, although I was unable to trace the whole course of development. These are followed by nearly ripe spermatozoa (sp) which completely fill the lumen of thesac. The mature spermatozoa (fig. 7) are long and slender, with a head-piece measuring about .012™" in length. This head-piece is tapered to an exceedingly fine point in front, while the opposite end is swollen into a bright globule, from which goes off a tail-piece fully three times as long as the head-piece. The writer wishes to express his gratitude for valuable criticism and advice, both to Professor A. E. Verrill, at whose suggestion and under whose direction this paper has been written, and to Professor S. I. Smith, in whose laboratory the work has been done. W. R. Coe—Anatomy of Cerebratulus lacteus. 507 LITERATURE. There is given below a list of a few of the more important recent papers on Nemer- tean anatomy which are referred to in the text: Arbeiten aus dem Zool.- 1. A. E. Verrill, The Marine Nemerteans of New England. Transactions of the Conn. Academy, vili, 1892. 2. Otto Birger, Unters. tiber die Anatomie u. Histologie der Nemertinen nebst Beitr. zur Systematik. Zeits. f. wiss. Zoologie, 1, 1890. 3. Otto Birger, Die Enden des Exkretorischen Apparates bei den Nemertinen. Zeits. f. wiss. Zoclogie, liii, 1892. 4, J.v. Kennel, Beitrage zur Kenntniss der Nemertinen. Zootom. Inst. in Wiirzburg, iv, 1877-1878. 5. Rudolph Dewoletzky, Das Seitenorgan der Nemertinen. Arbeiten der Zool. Inst. zu Wien, vii, 1888. 6. W.C. McIntosh, British Annelids; Part I, The Nemerteans. Ray Society, 1873. 7. A. A. W. Hubrecht, Voyage of H. M. S. Challenger, 1873-76. Zool., xix, 1887. 8. A. A. W. Hubrecht, Der Exkretorische Apparat der Nemertinen. Zool. Anzeiger;, 1885. 9. A.C. Oudemans, Circulatory Apparatus of the Nemertea. Sciences, xxv, 1885. Quart. Journ. Micros. Zeits. f. wiss. Zoologie, lix, 1895. Paris, 1893. Greifswald, 1851. Arbeiten 10. T. H. Montgomery, Stichostemma eilhardi. 1l. L. Joubin, Les Nemertiens. Faune Frangaise. 12. Max Schultze, Beitrage zur Naturgeschichte der Turbellarien. 13. C. Semper, Die Verwandtschaftsbeziehungen der gegliederten Thiere. aus dem Zool.-Zoot. Inst. in Wurzburg, iii, 1876-1877. 14. Neapel, xi, 1884. 15. W.Salensky, Bau und Metamorphose des Pilidiums. xliii, 1886. A. Lang, Die Polycladen des Golfs von Neapel. Fauna und Flora des Golfs yon Zeits. f. wiss Zoologie. EXPLANATION OF PLATES. With few exceptions the figures were drawn with the aid of a camera-lucida. On the plates the following reference letters are used: a, ‘‘ rhabdite-cell ” epithelium. a’, gland-cell from same. av, anastomosing vessel between lateral and dorsal vessels in intestinal region. b, blood-vessel. bb, buccal blood-vessel. be, ventral commissure lacunee. bm, basement membrane. br, brain. c, connective tissue. cc, ciliated canal in side-organ; cc’, pos- terior end of same. cé, ciliated epithelial cell. from the _ proboscis- of cephalic ci, cilia. cl, cephalic lacuna. em, circular muscles. cm’, outer layer of circular muscles in pro- boscis, and in body-wall in Carinella. co, dorsal cross of fibres in proboscis. co', ventral cross of fibres in proboscis. cs, inner sheath of connective tissue. cs’, outer sheath of connective tissue. cu, cutis. cv, commissure of vagus nerve. d, dorsal brain-lobe. db, dorsal blood-vessel. de, dorsal commissure of brain-lobes. dm, dorso-ventral muscles. 508 dn, dorsal, or median, nerve. e, epithelium; integument. em, epithelial musculature. en, endothelium of rhynchoccelom. en’, endothelium of blood-vessels. 7, split between intestinal czecum and sur- rounding gelatifous tissue. 7c. fibrous core in dorsal brain-lobe. fc’, fibrous core in ventral brain-lobe and in side-organ. fo, ovarian follicle. g, g, gland-cell; glands. gc, ganglion-cell. gc’, ganglion-cell of first type. gc’, ganglion-cell of second type. gc3, ganglion-ceil of third type. gd, gelatinous tissue. gd, genital duct. gs, genital sac. hm, horizontal muscles in the region of the mouth. 7, intestine; interstitial cells of body- epithelium. ic, intestinal ceecum. Ze, intestinal epithelium. j, zona pellucida. k, “lateral” cell of ciliated canal in side- organ. Ic, lateral cord. li, lateral lacuna. Im, longitudinal muscles: inner layer of longitudinal muscles. Im’, outer layer of longitudinal muscles. is, lateral, or cephalic, slit. lv, lateral blood-vessel. m, muscles. With the exception of Plate XIII, figs. W. R. Coe—Anatomy of Cerebratulus lacteus. mc, ‘‘median” cells of ciliated canal in side-organ. mf, vauscle-fiber. ml, median blood-lacuna. n, nucleus. np, nerve-plexus. 0, mouth. od, anterior commissure of cephalic lacune. oe, cesophagal epithelium. ol, cesophagal lacuna. ov, cesophagal blood-vessel with contractile walls, as distinguished from a lacuna. ov’, ovum. p, proboscis. pc, parenchyma-cell. pl. cavity, or lumen, of proboscis. pn, proboscis-nerve. po, proboscis-opening. ps, proboscis-sheath. r, rhynchodeum. rc, rhynchoccelom. rf, radial fibres. rf, fibres from ganglion-cells. ro, rhabdite-like bodies. rs, rhynchodeeum sphincter. s, secretion. sc, sc’, sc’, germinal epithelium. sp, Spermatozoa. tg, tubular gland in cutis. u, nephridial canal. ue, efferent duct of same. bd ud, root-like process of epithelial cell. v, ventral brain-lobe. ve, ventral commissure of brain, un, vagus nerve. x, point of attachment of proboscis. 3, 4, 6, 7, 10, and Plate XV, figs, 4, 5, 9, 11, 13, 14, all the figures are taken from Cerebratulus lacteus. « PLATES. Figure 1.—Transverse section through the anterior portion of the head in front of the brain. (Oye eS: The large cephalic lacunze (cl) are seen on each side of the rhynchodeeum Figure 2.—Transverse section through the head in the region of the brain-commis- sures; dc, dorsal commissure; vc, ventral commissure. are very small and compressed; x 8. The cephalic lacune (cl) Figure 3.—Transverse section through the head in the region of the brain; d, dorsal brain-lobe; v, ventral brain-lobe; ce, canal leading to side-organ. The dorsal blood-vessel is seen in the walls of the proboscis-sheath (ps); cl, cephalic lacuna ; mi, median lacuna; x 8. W. R. Coe—Anatomy of Cerebratulus lacteus. 509 Figure 4.—Transverse section through the head in the region of the mouth; 9, mouth; bb, buccal vessel; vn, vagus nerve; lc, lateral cord; dn, dorsal nerve; J, lateral lacuna; ps, proboscis-sheath. Above the mouth is seen a thick band of horizontal muscles (hm) connecting the two sides of the incomplete circular mus- cular layer (cm). The cutis (cw) in this region is very thick and the tubular glands are much elongated; x 8. Figure 5.—Transverse section of the lateral cord in the cesophagal region. A large mass of ganglion-cells (gc) is seen below, and a similar mass above, the fibrous core (fc); cs, inner sheath of connective tissue; cs’, outer sheath; c, loose con- nective tissue; m, a few longitudinal muscular fibres; x 110. Figure 6.—Horizontal, longitudinal section through the ventral portion of the brain. On the right-hand side, the proboscis-nerve (pm) is seen to leave the fibrous core of the ventral commissure. The vagus nerve (vm) originates from the inner border of the ventral brain-lobe; gc, ganglion-cells; mi, median lacuna; x 40. Figure 7.—Side view of brain and side-organ dissected from a small specimen pre- served in a dilute solution of formalin; x 20. Figure 8.—Diagram of the brain and large nerves of the head. Partly reconstructed from sections, and partly from a sketch of the organs in the living animal. The extent of the cephalic slits (/s) is indicated by a dotted line. The proboscis-nerves (pn) are seen to originate at the anterior border of the ventral commissure. After running forward a short distance they bend inwards to enter the proboscis. The dorsal brain-commissure (dc) is seen to be very weak in comparison with the ventral. The vagus nerves (vm) arise from the internal border of the ventral lobes and are soon joined in the vagus commissure (cv), back of which they sepa- rate widely to pass to the borders of the mouth; x 6. Figure 9.—Part of a transverse section through the head in the region of the brain, to show the ventral commissure (bc) of the cephalic lacunze (cl). In the section the single lacuna is horse-shoe shaped, surrounding the proboscis-sheath (ps) ; se, 1:0, PLATE XI. Figure 1.—Transverse section through the body-wall in the middle third of the cesophagal region, a short distance below the lateral cord; e, epithelium; em, epithelial musculature consisting of an outer circular, and an inner longitudinal layer; cu, outer portion of cutis with tubular glands and longitudinal muscles; cu’, inner portion of cutis made up of anastomosing radial fibres; gd, gelatinous tissue filling the Space between the cesophagus and the body-wall; m, muscula- ture of oesophagus; x 90. Figure 2.—Horizontal section through the head, to show the attachment of the pro- boscis at x The proboscis is partially everted, so that the walls of rhynchodeum are widely separated and the cephalic lacunze (c/) are much flattened out; /s, pos- terior end of cephalic slit from which the ciliated canal passes into the side-organ. The cephalic lacunz are seen to pass directly into the lateral lacuna (//) surround- ing the side-organ (so); x 18. Compare Plate XII, fig. 1,in which the proboscis lies in its normal position. Figure 3.—Part of a transverse section through the nephridial region to show one of the two efferent ducts (we) of the nephridial system. The main longitudinal canal (uw) is seen internal to the lateral cord (ic); x 15. TRANS. Conn, ACAD., Vou. IX. JUNE, 1895, 35 510 W. R. Coe—Anatomy of Cerebratulus lacteus. Figure 4.—Transverse section through the intestinal region. The genital duct (gd’) leads into the thin-walled genital sac (gs) from which all the genital products have been discharged. The dorsal vessel (db) lies beneath the proboscis-sheath (ps) and the lateral blood-vessels (Jv) occupy a position beneath the intestinal czea (ic) and on either side of the main intestinal canal; x 8. Figure 5.—Cells from the cesophagal epithelium isolated by maceration in a 0.2 per cent. aqueous solution of formalin and stained with Delafield’s hematoxylin. The cilia which cover the outer, free surfaces are not shown; x 150. PLATE XO: Figure 1.—Horizontal section through the head to show the attachment of the pro- boscis at x. The proboscis (p) is in its normal position and the cephalic lacunze (cl) are normally distended; x 20. Compare Plate XI, fig. 2, in which the proboscis is everted. Figure 2.—A portion of the same section nfore highly magnified. The sphincter (7s) is seen at the posterior end of the rhynchodzum (7) and separates this chamber from the cavity of the proboscis (pl); x, attachment of proboscis; br, brain (cut somewhat obliquely); cl, cephalic lacuna: rc, rhynchoccelom; x 55. Figure 3.—Macerated cells from the epithelium of the proboscis; a, “rhabdite-cell” with a row of rhabdite-like bodies in the upper portion; vo, some of the extruded ‘“ rhabdites;” a’, one of the gland-cells which usually lie somewhat below the “ rhabdite-cells ;” x 250. Figure 4.—Epithelium from the proboscis; ¢, epithelium; 6m, basement membrane. The outer row of nuclei are those of the ‘“rhabdite-cells,” the others belong mostly to gland-cells. The “‘rhabdites” are seen as a dark band near the free border; x 125. Figure 5.—Diagram of the principal layers of the body-wall; e, integument including cutis and epithelium; 7m’, outer longitudinal muscles; np, nerve-plexus; em, circular muscles; /m, inner longitudinal muscles. Figure 6.—Diagram of the layers in the proboscis for comparison with those of the body-wall in figure 5; e, epithelium lining the lumen of the proboscis; /m, inner longitudinal muscles; np, nerve-plexus; cm, circular muscles; /m’, outer lon- gitudinal muscles; cm’, outer circular muscles; en, endothelium bathed in the thynchoccelomic fluid. Figure 7.—Part of a transverse section of the proboscis-sheath. The endothelium (en) rests upon a very thick basement membrane (bm); lm, thick layer of longitudinal muscles; cm, circular muscles separated from the outer longitudinal muscles (lm’) by a layer of loose connective tissue (c); x 140. Figure 8.—Ciliated epithelium of the rhynchodzum. The cells are arranged with great regularity, with their nuclei near their bases; x 175. Figure 9.—Corpuscles from the rhynchoccelomic fluid. Figure 10.—Posterior extremity of the proboscis of a small specimen; x 4. Figure 11.—Transverse section through the anterior end of the proboscis. Ciliated columnar epithelium (e) lines the four-lobed Jumen (pi). The muscles (m) are all longitudinal, and the nerves (pz) are situated to the right and to the left of the lumen in the midst of the muscles; en, outer endothelium; x 18. W. FR. Coe—Anatomy of Cerebratulus lacteus. 511 | Figure 12.—Transverse section through the middle of the proboscis; co, co’, dorsal and ventral crosses of muscles. The epithelium (e) is thick and much folded. The nerves have spread out to form a nerve-plexus (np) between the circular and inner longitudinal muscular layers. The thin, outer circular layer (cm’) lies immediately beneath the endothelium; x 18. Figure 13.—Transverse section of the proboscis near its posterior end. The epithe- lium (e) is very thick, while the two inner muscular layers are much reduced. The nerve-plexus cannot be made out in this portion. The outer longitudinal muscular layer (/m’) remains comparatively strong; x 18. PLatTeE XIII. Figure 1.—Diagram of the blood-vascular and nephridial systems. The two large cephalic lacunae (cl) are united in front, above the rhynchodzeum, by a small commissure (02). The ventral commissure is much larger, and from it arise the buccal vessels (00) and the dorsal vessel (db). The dorsal vessel passes backward within the pro- boscis-sheath to the point « without branching. At this point, which is at the posterior end of the cesophagal region, the vessel leaves the sheath and gives off a pair of branches (av), which anastomose with the lateral vessels (Jv) opposite each pair of intestinal ceca. The nephridia occur in the middle portion of the cesophagal region, and have a single pair of efferent ducts (we). Figure 2.—Cells isolated from the intestinal epithelium by macerating in a dilute solu- tion of formalin; 2a, a ‘goblet-cell” with its highly refractive secretion in small particles; 2c, more slender cells but having a similar secretion. In 2e the secretion has collected into globules (s) of considerable size; , nucleus ; wd, fibre-like process which is attached to the basement membrane; x 300. Figure 3.—Epithelium from the intestine of Micrura affinis. The slender cells are partly filled with the characteristic colorless secretion in small globules; x 150. Figure 4.—Epithelium from the cesophagus of Carinella. The ciliated cells are very little elongated and among them are found many “goblet-cells” filled with a mucus-like secretion; x 150. Figure 5.—Diagram of a portion of the nephridial system as shown in figure 1, enlarged. The nephridial canals (w) are cross-striped while the blood-vessels are only outlined: Jv, lateral vessel with branches about the cesophagus. Figure 6.—-Diagram of a portion of the nephridial and blood-vascular systems of Lineus socialis. One main nephridial canal (w) with several efferent ducts (we) is seen close beside the lateral lacuna (il). There are few branches either from the nephridial canals or from the lateral lacunee. Figure 7.—A portion of the vascular system in Cerebratulus luridus from a horizontal section. The nephridial canals break up into many small twigs (vw) which wind about on the outer border of the large, lateral blood-lacuna (VU). Figure 8.—Longitudinal section of the efferent nephridial duct as it passes through the body-wall. Neither the cell-walls nor the cilia could be made out. Beneath the thin basement membrane is seen a thick layer of connective tissue (c); m, muscles of the body-wall; x 200. Figure 9.—Transverse section of the median, or dorsal, vessel showing the inner endo- thelium (en’) with the muscular coat (m) made up mostly of circular muscle-fibres ; pe, the thick layer of elongated parenchyma-cells, bordered on the outside by the endothelium (en) of the proboscis-sheath; x 50. 512 W. R. Coe—Anatomy of Cerebratulus lacteus. Figure 10.—Cross section of the main longitudinal nephridial canal (w) and its close relation with the lateral lacuna (Il) in Cerebratulus Leydii; x 225. Figure 11.—Blood-corpuscles; x 500. Figure 12.—Cross section of a small nephridial canal. The section is rather thick and the nuclei of the cells do not appear as regular as is often the case. Cilia or cell-walls are not seen; x 225, Figure 13.—Cross section of a contractile blood-vessel with its regular coating of parenchyma-cells (pc). The muscles (m) outside the endothelium (en’) are con- nected with radial fibres of connective tissue (7/) which hold the vessel in place ; x 225. Figure 14.—Longitudinal section of a blood-vessel. The parenchyma-cells do not appear so sharply marked off as in a cross section; x 225. PLATE: XD. Figure 1.—Horizontal section of the side-organ showing the ciliated cana] (cc) cut trans- versely in its ascending portion ; ec’ posterior portion of same canal cut obliquely. The fibrous core (/c’) is directly continuous with that of the dorsal brain-lobe. Large areas of ganglion-cells (gc), like those of the first type in the brain, are seen on the right and left sides. A thick mass of large gland-cells (g) occupies the anterior and posterior borders; c, sheath of connective tissue covering the whole; x 150. Figure 2.—Section of the ciliated canal, more highly magnified ; n, nuclei of the greatly elongated ‘“‘median” cells (mc), far removed from the lumen of the canal (cc). Around the lumen of the canal are two dark lines, the inner being caused by the thickening of the cilia at this point, and the outer being made up of the borders of the cells; &’, inner ‘‘ lateral” cells; &, outer ‘“‘lateral” cells; fc’, fibrous nerve-core ; x 250. Figure 3.—One of the “median” cells macerated in formalin; x 300. Figure 4.—Nearly ripe, living ovum after being pressed from the body of the animal; j, zona pellucida. The transparent germinal vesicle contains a large germinal spot; x 50. Figure 5.—Portion of an ovary with developing ova. The large ova (ov’) lie against the connective tissue framework (c) and are surrounded by a follicle (/o) of flattened epithelial cells; x 50. Figure 6.—Portion of a spermary with developing spermatozoa. The layers of cells are commonly much thicker than is here represented (only the nuclei of the cells are shown); sc, several layers of large ‘‘ mother-cells ” internal to the connective tissue framework; sc’, smaller cells derived from the division of the ‘‘mother-cells ”; sc’” smaller, somewhat elongated cells which probably develop directly into spermato- zoa which fill the lumen of the spermary; x 500. Figure 7.—Ripe spermatozoa; x 800. Figure 8.—Sagittal section through a portion of the intestinal region of the body; ic, intestinal czeca, separated by thick bands of dorso-ventral muscles (dm); av anastomosing blood-vessels seen above and below each intestinal czecum (these are paired vessels uniting the dorsal with the lateral vessels: see Plate XIII, fig. 1); gd, gelatinous tissue; /m, inner layer of longitudinal muscles of body-wall. From a small specimen; x 40, W. R. Coe—Anatomy of Cerebratulus lacteus. 513 Figure 9.—Sagittal section through a portion of the intestinal region of a male speci- men with ripe spermatozoa. The genital products have developed between the double bands of dorso-ventral muscles (dm) and filled up most of the space occupied by the gelatinous tissue (gd, fig. 8). In this section the spermatozoa are develop- ing from the germinal cells (sc) above and below the intestinal ceca (ic). These czeca are much flattened and the space between them is filled with ripe sperma- tozoa (sp); av, anastomosing vessels; dm, internal longitudinal muscular layer of the body-wall; x 20. Figure 10.—Part of a median horizontal section through the intestinal region of a specimen in which the genital products are just beginning to develop; 7, intestinal canal; zc, intestinal czeca, one of which is bilobed; av, anastomosing vessel; 7, split between intestinal czecum and gelatinous tissue; ze, columnar cells of intesti- nal epithelium; dm, dorso-ventral muscles in two thin, vertical bands which unite near the intestinal canal; gs, genital sac in which the ova are just beginning to develop; x 20. Figure 11.—Horizontal section through the intestinal region of a female specimen in which the ova are nearly ready to be discharged; 7, intestinal canal opening into the cecum (7c); gs, enlarged genital sac filled with nearly ripe ova (ov). The genital sac lies between the two bands of dorso-ventral muscles (dm); x 20. PLATE XV. Figure 1.—Part of a transverse section through the integument in the cesophagal region; é, ciliated and gland-cells of epithelium; 7, interstitial cells among the bases of same: bm, underlying basement membrane; em, epithelial musculature con- sisting of an outer circular and an inner longitudinal layer; lm, longitudinal muscles of cutis; rf, radial nerve and connective tissue fibres, the latter forming a framework for the tubular glands (tg) which discharge their contents to the exterior among the epithelial cells; c, connective tissue occurring abundantly in the lower portions ofthe cutis; x 150. Figure 2.—Macerated cells from the body-epithelium. The cilia (ce?) of the ciliated cells (ce) are somewhat thickened near their bases. There are two varieties of gland- cells: g, cells which secrete a homogeneous, semi-solid substanve; and g’, those which have a coarse, granular, and deep-staining secretion; x 300. Figure 3.—Transverse section of the brain just back of the ventral commissure. The fibrous core (fc) of the dorsal lobe is surrounded above and at the sides by gan- glion-cells of the first type (gc’), with scattered cells. of the third type (gc*) peripher- ally. The fibrous core of the ventral lobe (/c’) is provided with cells of the second type as well as with those of the third type; c, masses of connective tissue ; cs, inner sheath of connective tissue surrounding the fibrous cores: cs’, outer sheath of connective tissue enclosing the whole brain; x 40. Figure 4.—Body-epithelium in Micrura affinis ; g, gland cells among the ciliated cells; 25. Figure 5.—Transverse section through the posterior portion of the cesophagal region of Carinella pellucida. The nephridial canal (uw) lies near the large lateral blood- vessel (lv); that of the left hand side is seen to open to the exterior. The lateral cords (Ic) are situated immediately beneath the thickened integument (e) and out- side the outer circular muscular layer (cm’); em, inner circular layer; lm, longi- tudinal muscular layer; x 50. 514 W. R. Coe—Anatomy of Cerebratulus iacteus. Figure 6.—Part of a radial cluster of ganglion-cells of the second type with fibres (/r’) passing to fibrous core of ventrallobe; x 300. Figure 7.—Ganglion-cells of the first (gc!) and third types (gc*). The cell-walls are not readily made out. Each cell is surrounded by a sheath of connective tissue, Ta, a single cell of the third type; x 300. Figure 8.—Portion of a transverse section through the head to show the origin of the vagus nerves and their commissure (cv); cl, cephalic lacuna; d dorsal brain-lobe v, ventral brain-lobe; x 12. Figure 9.—Transverse section of Lineus socialis through the region of the mouth; u, nephridial canal in close relation with the lateral blood-vessel (jv). On the left hand side is shown an efferent nephridial duct; 0, mouth; ic, lateral cord; e, integument; cm, circular muscles. From a small specimen; x 40. Figure 10.—Transverse section of a muscle-bundle. The nucleated fibres (m/f) are each surrounded by connective tissue, and the muscle-bundle by a sheath (c) of the same tissue; x 500. Figure 11.—Transverse and longitudinal sections of muscle in Carinella; x 200. Figure 12.—Transverse sections of three muscle-fibres from the anterior end of the proboscis-sheath. The flattened nucleus (n) is seen at one side of the contractile substance. But few nuclei are commonly seen; x 1000. Figure 13.—Transverse section through the cesophagal region of Cerebratulus Leydit. The efferent nephridial duct (we) joins the main nephridial canal near the lateral blood-vessel (lv). Branches of this blood-vessel appear as large lacune (0/) sur- rounding the cesophagus (oe); Ic, lateral cords; x 18. Figure 14.—Transverse section through the anterior portion of the head of Valencinia to show the cephalic lacunz (el) partially divided into many small spaces by thick strands of muscular tissue; x 25. IX.—DEscrRIPTIONS OF THREE NEW SPECIES OF NEw ENGLAND PALZONEMERTEANS. By WesteEy R. Cor. Since the publication of Verrill’s monograph on the Marine Nemerteans of New England, in vol. viiiof these Transactions, the three following species of Palzeonemerteans, which I believe to be undescribed, have been found on this coast. Carinella Johnston, Loudon’s Mag. Nat. Hist., vi, 1833 (t. McIntosh). Carinella Birger, Nachr. von der K. Ges. der Wiss. zu Gottingen, 1892; Joubin, Faune Frangaise, 1893. Head truncate in front, broader than the body, from which it is often separated by. shallow, transverse grooves. Intestine without ceca. The lateral cords lie between the basement membrane of the integument and the outer circular muscular layer of the body-wall. The side-organs are but slightly developed, and consist of a pair of epithelial pits which seldom become so deep as to penetrate a dis- tinct lobe of the brain. There are but two longitudinal blood-vas- cular trunks. Carinella pellucida sp. nov. Body slender, almost filiform, slightly flattened es Head broader than the body, somewhat flattened, often contracted so as to become emarginate in front. Head marked off from the body by a slight constriction formed by a pair of shallow, lateral, transverse grooves. Mouth small, placed ventrally, near the tip of the head. Ocelli none. Color pale grayish white or translucent, often with a slightly yel- lowish tinge. A small species, the sexually mature animals being only about 25™" long and having a diameter of about .5™™. Most of the specimens found are much smaller and in alcohol rarely exceed 5™™ in length.* The sexual products mature early in July. Savin Rock, near New Haven; not uncommon at low water among the tubes of annelids (Potamilla). * Verrill has figured, without descriptions, on Plate xxxviii, figs. 11, lla, in vol. viii of these Transactions, a species of Nemertean, from Vineyard Sound, which he designated as Lineus sp. (?), and which is probably identical with this. 516 W. R. Coe—New Palewonemerteans. The epithelium of the integument (Plate xv, fig. 5, ¢) is composed of columnar, ciliated cells and unicellular glands.* The former are the more superficial and form an almost complete layer ; the flask- shaped gland-cells lie among the bases of the ciliated cells and are mostly filled with a secretion which stains deeply. A delicate base- ment membrane lies beneath the epithelium. No cutis is present ; the basement membrane of the integument resting directly upon the body-muscles. There are three layers of body-muscles: a thin, outer circular layer (cm'), a strong longitudinal layer (dm), and an inner circular layer (cm). The proboscis-sheath is but slightly developed and reaches but a little way back into the intestinal region. Its wall is made up of an outer layer of circular muscles directly continuous with the internal circular layer of the body-wall, and an inner layer of longitudinal muscles made up of a single layer of fibres. The endothelium rests upon a well-developed basement membrane. The proboscis is attached to the tissues of the head just in front of the ventral commissure of the brain-lobes. The rhynchodzeum bends downward and opens on the ventral side near the tip of the head. The layers of the wall of the proboscis repeat, as in Cere- bratulus, the layers of the body-wall, consisting of a thin external circular, a longitudinal, and an internal circular muscular layer. There is a delicate, outer endothelium bathed in the rhynchoccelomic fluid, and a layer of columnar epithelium lining the proboscis-cavity. Between this epithelium and the internal circular muscular layer les a pair of nerves in a position similar to that of the lateral cords in the body-wall. The proboscis terminates posteriorly not far back in the intestinal region. The epithelium gradually disappears and then the circular muscular fibres, leaving only the longitudinal fibres which form a slender retractor muscle. This muscle is attached to the dorsal wall of the proboscis-sheath. At the point of attachment, the wall of the proboscis-sheath thickens up and the muscular fibres of the retractor become interlaced with those of the circular layer of the sheath. The epithelium of the cesophagus (Plate x11, fig. 4) consists of ciliated and glandular cells, many of the latter being filled with a clear, mucus-like secretion. These cells are columnar and are * In this genus, owing both to the larger size of the cells and to their more simple arrangement, the cell-structure of the various tissues is much more readily made out than in other genera of Nemerteans which I have examined. W. R. Coe—New Palwonemerteans. 517 arranged with great regularity. The cell-walls and the cilia are very distinct in most preparations. The intestine is without ceca, although the lumen is more or less lobulated. Its epithelium is made up of long columnar, ciliated cells filled with a secretion in small globules, most of which contain a single deeply-stained, spheri- cal granule. The blood-vascular system consists of two longitudinal trunks (Plate xv, fig. 5, Jv) lying on the inner side of the longitudinal mus- cular layer of the body-wall, near the lateral cords. They are united in front and behind. In the anterior part of the head is a single large lacuna which divides into two at the anterior end of the rhyn- chodeum. ‘The lateral vessels are narrow in the esophagal region, but are commonly enlarged farther back. There are many small lacunze about the esophagus. The two nephridial canals (uw) lie close against the dorsal wails of the lateral blood-vessels. There is a sin- gle efferent duct at the posterior end of each canal. The central nervous system lies between the outer circular muscular layer and the basement membrane of the integument. It consists of a four-lobed brain, a pair of lateral cords (dc), and a median dorsal nerve. ‘The brain-lobes are united by a dorsal and a ventral com- missure, of which the former is much smaller and lies in front of the latter. The dorsal nerve is well developed. It arises from the dorsal commissure and may be followed well back in the intestinal region. The pair of vagus nerves to supply the mouth and anterior portion of the wsophagus arises from the internal borders of the ventral _brain-lobes, as in Cerebratulus. They lie just beneath the epithelium at the sides of the mouth. The only indication of side-organs is a slight modification of the epithelium on the lateral borders of the dorsal brain-lobes. In some specimens there is a minute, shallow pit in this situation. The reproductive organs develop in sacs closely packed together above the lateral blood-vessels. Hach sac opens to the exterior on the dorso-lateral surface of the body. Parapolia, gen. nov. Body stout, cylindrical in front; intestinal region flattened. Head cylindrical, directly continuous with the body ; rounded in front ; without lateral, horizontal slits but provided with a pair of lateral, transverse furrows near the tip. Ocelli absent in the type species. Proboscis-opening sub-terminal. Mouth situated but a short dis- tance farther back, althongh it lies behind the brain. 518 W. R. Coe—New Palwonemerteans. The body-wall is made up of integument, and outer longitudinal, circular, and inner longitudinal muscular layers. The lateral cords lie just outside the circular muscular layer. Basement layer of the integument but little developed ; the cuti- cular glands extend into the outer longitudinal muscular layer. Proboscis without muscular crosses ; provided with an outer longi- tudinal, a circular, and an inner longitudinal muscular layer. The side-organs, though small and flattened, form distinct lobes of the brain. They are imbedded in the muscles of the head near the dorso-lateral borders of the dorsal brain-lobes. This genus is nearly related to Hupolia,* but the latter differs especially in having the head broadened and not directly continuous with the body ; in not having the intestinal region much flattened; in having a distinct layer of connective tissue, or basement layer, between the outer muscular layer of the body-wall and the glands of the cutis ; in the structure of the proboscis ; and in the position of the side-organs. Parapolia aurantiaca sp. nov. Body large, stout, rounded in the esophagal region, flattened and broad beyond. Im alcohol the anterior portion of the body is cylin- drical. The esophagal region decreases in diameter towards its pos- terior end. At the commencement of the intestinal region the body suddenly flattens and widens, and is thus divided into two distinct regions. In the intestinal region there is a conspicuous dorsal ridge above the proboscis-sheath. Head blunt, rounded in front, cylin- drical, continuous with the esophagal region. It is provided with a narrow, annular constriction near the tip. This constriction is made up of two lateral, transverse furrows into which the ciliated ducts leading to the side-organs open. In alcohol the transverse furrows are united above and below, although in the living animal they are probably separate. In the center of the constriction, in a sub-ter- minal position, is a small dimple marking the position of the mouth and the opening of the rhynchodeum. The latter is a minute pore situated on a slight prominence in front of the small, elongated mouth. No eyes were observed nor can any be detected in micro- scopic sections. * Eupolia Hubrecht, Voyage of the Challenger, xix, 1887. Polia (delle Chiaje) Hubrecht. Notes from the Leyden Museum, i, 1879 (non Quatre- fages, Ann. des Sci. Nat., vi, 1846). Eupolia Birger, Nachr. von der K. Gesellschaft der. Wiss. zu GOttingen, 1892 ; Joubin, Faune Francaise, 1893. W. R. Coe—New Palwonemerteans. 519 Length, more than 250™™, Csophagal region about 6™™ in diam- eter ; intestinal region 10" wide by 4™™ in thickness. Color, bright orange. The mucus secreted by the integument is excessively tena- cious. - Living in sand at low water. Wood’s Holl, Mass., 1894. The genital products are mature in August. This species, described from two incomplete specimens, presents a very striking appearance on account of its large size and its gorgeous orange color. A complete animal, judging from the fragments obtained, would probably measure at least two feet in length. Integument much as in Cerebratulus. The cutis is not provided with an underlying layer of anastomosing radial fibres and, conse- quently, its longitudinal muscles are not distinctly separated from the outer longitudinal muscular layer of the body-wall into which the tubular glands of the cutis extend. In the intestinal region the cutis is thin, and the epithelial musculature is well developed. The muscles of the body-wall consist of three principal layers, as in Cere- bratulus, although the inner longitudinal layer exceeds the circular ‘layer in thickness. The dorso-ventral muscles are rather poorly developed. The proboscis-sheath is provided with a strong muscular wall in the anterior cesophagal region, but is thin and delicate farther back. At the attachment of the proboscis, just in front of the brain, the rhynchodzum makes a sharp turn and opens to the exterior on the ventral side, near the tip of the head. The proboscis-sheath is pro- vided with an inner layer of longitudinal, and an outer layer of circu- lar muscles. The endothelium rests on a very thick basement mem- brane of gelatinous connective tissue. The musculature of the proboscis at its anterior end is made up almost entirely of longitudinal fibres. Farther back a circular layer arises, which divides the longitudinal muscles into a thin outer and a thick inner layer. The columnar, ciliated cells of the epithelium are separated from the muscles by a thin basement membrane. The epithelium is thrown up into slender papilla, more conspicuous towards the posterior end of the proboscis. A layer of connective tissue of considerable thickness lies between the outer endothelium and the muscles. Ata point about one-third the length of the pro- boscis from its posterior end the muscular layers become very thin. Back of this point the inner longitudinal layer disappears while the 520 W. R. Coe—New Palewonemerteans. circular and outer longitudinal layers increase in thickness. A sec- tion through the posterior third of the proboscis, therefore, shows only an inner circular, and an outer longitudinal layer of muscles. The epithelium of the esophagus is composed of an outer layer of ciliated cells with gland-cells beneath. The musculature is thin but is easily made out. ‘The intestinal ceca are mostly lobed or forked distally, above and below. In the head there is a large, median lacuna which is partially divided into many small spaces by strands of muscles which pass in various directions through the lacuna from one side to the other. Where these fibres come in contact with the blood they are clothed with a layer of endothelium. Thus, instead of the two definite lacunze which occur in Cerebratulus, we find the tissues of the head to be permeated by an irregular series of anastomosing blood-spaces which, farther back, unite into two large lacune. These, the lateral lacune, pass backward through the cesophagal region at the sides of the pro- boscis-sheath and give off branches which surround the cesophagus, except on its dorsal surface. They form large, anastomosing lacunez which occupy nearly all the space between the esophagus and the body-wall, so that there is very little gelatinous tissue developed. The dorsal vessel, soon after its origin from the anastomosing lacunz of the head, passes through the muscles of the proboscis-sheath, as in Cerebratulus. In the posterior portion of the csophagal region the vessel leaves the sheath, beneath which it passes to the posterior end of the body. The nephridial system begins a short distance back of the mouth and continues nearly to the intestinal region. Near the middle of the cesophagal region there is a single pair of efferent ducts from which canals run both forward and backward, giving off numerous branches which lie close against the walls of the csophagal blood- lacunee. The four-lobed brain is provided with a thin dorsal, and thick ventral commissure. The side-organs are flattened and but little developed. They lie just above the outer borders of the dorsal brain- lobes, from the fibrous cores of which they are supplied with nerves. A ciliated canal runs forward and opens into the transverse cephalic slit on each side of the head. The side-organs do not come in con- tact with the cephalic lacune, but lie imbedded among the muscles of the head. The lateral cords are united by a delicate nerve-plexus. The dorsal nerve is but slightly developed. The genital products develop in sacs which alternate with the W. R. Coe—New Palwonemerteans. 521 intestinal ceca. They are discharged through ducts opening on the dorsal surface of the body. Many parasitic worms were found imbedded in the muscles of the body-wall and occasionally in the proboscis-sheath. They occurred coiled up in spherical or oval cap- sules about 1™™ in diameter. Valencinia Quatrefages, Annales des Sci. Naturelles, vi, 1846; Birger, Nach. von der K. Gesellschaft der Wiss. zu Gottingen, 1892; Joubin, Faune Frangaise, 1893. Head pointed in front, without lateral slits. Ocelli absent or few in number. The proboscis-opening lies far back, nearly to the brain- lobes. The body-wall consists of four layers: integument, outer longitudinal, circular, and inner longitudinal muscular layers. The lateral cords lie outside the circular layer of muscles. Valencinia rubens sp. nov. Body almost cylindrical, slightly flattened posteriorly. Head flat- tened, elongated, sharply pointed in front, marked off from the body by ashallow, annular constriction. Proboscis-opening minute, situ- ated far back, just in front of the brain. Mouth small, placed a short distance back of the proboscis-opening. Ocelli none. No lateral slits. On each side of the head there is an inconspicuous pit into which the canal of the side-organ opens. Color pinkish anteriorly, deep red tinged with yellow posteriorly.* A single specimen, from which the posterior end was missing, was collected in the sand at low water at Wood’s Holl, Mass., in Aug., 1894. The length of the esophagal region of this specimen was about 35™™, and of the intestinal region only about 25™™ remained. The diameter was about 3™™. The glandular layers of the integument are not separated from the outer longitudinal muscular layer of the body-wall. The circular and inner longitudinal muscular layers are much as in Cerebratulus. The proboscis-sheath is thin, but it reaches far back. Proboscis short, composed anteriorly of a circular and an inner longitudinal layer ; farther back an outer longitudinal layer arises outside this circular layer. ‘There are three longitudinal blood-vascular trunks. The dorsal vessel runs in the proboscis-sheath about two-thirds the length *This species bears a close external resemblance to V. longirostris Quatrefages (Annales des Sciences Naturelles, vi, 1846) of Europe. It appears to differ, however, in the structure of the proboscis, and in other anatomical details. 522 W. R. Coe—New Palewonemerteans. of the esophagal region. The lacunz about the esophagus are very large. The cephalic lacune and nephridial system are briefly described on p. 498. Brain well developed, the four lobes distinct. Lateral cords small, closely pressed against the circular muscular layer. Side-organs well developed, united with the posterior ends of the dorsal brain- lobes. Their internal borders are separated from the lateral lacune only by a thin band of tissue. Cs ZNO ry" Giger oe Ce ys (cc 8 ay" 55 3. | Pu @ ol oly. a ee 7 ZOU un x “WN E ae Cp, Z| Gwyn Leite Oat Aa YD ® Gw yuiform Guogrifarm ——$<—$<———— ne TEREBRAPELLIDA. E Crisand, lith, New Haven, Ct. i=) _ PLATE IL. LTTE SEN EE dR YL : team Conn Acad. Sci vol 1X. ee ee : ee a w Haven, Ct E. Crisand, lith., N' iy . ' s . ' * ’ = - . . . Sad : . PEATE A - Trans.Conn Acad.Sci. Vol. 1X. E. Crisand, lith., New Haven, Ct a ee ee ee re Si Sey eee r J.H.Emerton, from nature. ete , lhith , New Haven, Ct, Trans.Conn. Acad.Sci. Vol IX ee Pin te ee ail : \ \ . SSX N | A iil SSN)\ ead : \\ Nea | Wy = SSNS CT SS = F ff SV \ } S Wo of \ y Whe . ISS \ ILS N @ P\ ay 7). MWA My ("yz ¥ i" \ Y/ y, ‘ p Yy FU ZG i y a Mai MUD i i ( M y nae MM Stent nrenetsnestenenesnenseee Se | PLATE IIL. 4 Le e ee, ; sf BE feo WIN 4. O) Z ’ J.H.Emerton, from nature. Lk E. Crisand, lith., New Haven, Cr: Trans.Conn. Acad. Sci. Vol-IX. PLATE IV. 4 NUNN Un da t | jee wa \ ] | a Dae a ae a ail Fey Sit ay aie yee a “il! Reomeeer 1 ieee a Yael ‘Whi ; 7 ea haa ii (gp < J.H.Emerton, from nature. E. Crisand, lith., New Haven) Ct, PLATE VIL New Haveia, Ut bh Mey LLU 1sand, wet A won es Le A.H.Verrill trom nai Pe Pewee rk Set Py Th Sey tis oe ea a re *o a ‘ ‘ Pare 60 * K 7 eG 4 ‘ re > € : . 2 $= s . . . a —. ‘ . 4 — 5 ; e « ‘ } ) f ' ‘ a J j VG f e a 7 7 Kid a j i: i a a ie ‘ | or ‘ Pp 4 ? ° » - ‘ » + ‘ , 2 A a i g | Fn * ol - = 3 f i = - “ ‘ j © \ i ie a j x rh ; ® ‘ie i mvpee TAP ' i We : i y let y ee | As ¥ J At H \ . * A i ‘ F : = i - * A‘ } A \d i 5 i © Ln aug CE MMP RE PPT a Lite: Carns ; y Fi ; af adn ~" f ¢€. ii ' { A BNL et UE a ie Pe NE RE ees Aut On Tier ae ee PLATE DC A.H Verrill from LLatUPe By. CLES iG, LLih ,New Haven, Ct h \ t - ' / ) ‘ ‘ ' ‘ reas t 4 Fi : » ay ‘ ‘ ‘ ’ i ¥ | : : ‘ ' Hy Wy = a aN us ' * * . Sars i if } i vas . ig " ~ ' ' f « . ' . x « ‘ 4 ' *F ‘ rw ' © bi j ele . Teeth Lt ' . ‘ j r + ra ‘ ‘ 4 Ff § i 4 4 +t i ; ' rt F Ae | gy { . \ i i 4 hee ineey ny oa a 4 we @ Trans.Conn. Acad.Sci: Vol.1X. eB 2S = A> = g Aye A W.R.Coe, del. A hee E. Crisand, lith., New Haven, Ct ie of Oe ee PEATE 2ol E. Crisand, lith., New Haven, Ct, BSR: : ‘ tb in at Wan. t Pracesra nnn PACU A here jhe (aS. ss 0.8) BS al Trans.Conn Acad. Set Wolo W.R.Coe, del. Ae ‘Trans. Conn. Acad.Sci. Vol PLAVE, XIL ——— NS ene nee mn Ty Tea pibaa pT RAN ie, pret he @ x BiG ER iV ee Eicon 2. New Haven, Ct i E. Crisand, lit W.R.Coe, del. PLANE, Zee ‘ans.Conn. Acad.Sci. VolLX. T oh t o 2.9 >> 9 O06 02880" = oo ae s GHEE Crisand, lith: New Haven, Ct, E W.R.Coe, del. Trans. Conn Acad.Sci. Vol.LX. eo i. W.R.Coe, del. E. Crisand, lith., New Haven, Ct. ; — St ” oe Ag We } Sr» ‘Trans.Conn. Acad.Sci. Vol. IX. Ne SS => ir xu) UT Sty os os [erie Ligep iss W.R.Coe, del. PART 1. Lae | - eae — > x i ACADEMY. 7 UBLISHED bod tae . : nis oa Ragly k S - Pon : Meee a= ee ag hd pan sane i" CONTENTS. List oF ADDITIONS TO THE Liprary ART. UF —Maruemaricar faves IN THE Turory or VALUE AND Prices. By Irvine Fism | Arr. IJ.—Strupies In THE EnciuisH Mystery Prays. : CHARLES .DAVIDSON 22 = e502 Arr. IIL—Paporp-prexstion. By R. H. CuITrEeNDEN ne price by the (areas Secretary, Addison Van Name, to on all-communications ronportitig exchange of publications should bea Volume I, Part 1,:1866. 246pp.and 3 plates..--..-.-.- Volume _I,. Part 2, 1867-71. . 367 pp. and 7 plates_______._... Volume II, Part 2,187). 208 pp. and_ 7 plates_-..-.--2.__.... Volame II, Part 2, 1878. 202 pp. and 11 plates.-_.-.--....._._ Volume III, Part 1, 1876. — 248 pp. and 87 plates. __ Bere Volume III, Part 2, 1878. 260 pp. and 28 plates___-.------. Volume . IV, Part 1, 1877. . 242 pp. and 2 plates <-> oe = Volume IV, Part 2, 1882. 100 pp. and 11 plates.__.__-- cies Volume IV, Part 3, (in press). Se Volume V, Part 1, 1880. 267 pp. and 26 platés...-_..-...- Volume _ V, Part 2, 1882. 341 -pp. and 88 plates....-.--.--- Volume VI, Part 1, 1884. --294 pp. and 32 plates....-.. _... Volume VI, Part 2, 1885. 228 pp. and 17 plates-..-----. ce Volume VII, Part 1, 1886.: 259 pp. i Volume VII, Part 2, 1888. 263 pp. and sie oe eee Volume VIII, Part 1, 1890. 204 pp. and 8 plates --..-_. Volume VIII, Part 2, 1893. 816 pp. and 36 plates... Ean Volume ~ IX, Part 1, 1892. © = 882 pp.2-- 80.225 sh TRANSACTIONS OF THE ) CONNECTICUT ACADEMY | || ARTS AND SCTENCES. VOLUME IX, PART 2. NEW HAVEN: PUBLISHED BY THE ACADEMY. 1895. THE TUTTLE, MOREHOUSE & | TAYLOR PRESS. 9) ates eR eae, Sh ne, Ag ale iat, ea oo al le fees a endian [me wll . fae ‘TION OF THE. arsine BF W. A. SETOHELL,. 2... 3833 an. V. —RnvIsION OF ‘THE oe OF LOOP-BEARING BRaCHIO- nv — Tie Daverorwent OF EM ea OBSOLETA, DALE me mle = oe ee ne ee ee nl woe lena aren tere een ene ee eee nen enn ee ene 2 ene vA | ann, ‘VI. ON Somn Brrps AND EaaGs COLLECTED BY MR. pice ‘ % - Comer AT GoucH ISLAND, KERGUELEN. ISLAND AND THE IstAND Aas Fa OF ‘Sour Guorera, WITH EXTRACTS FROM HIS NOTES, INCLUD- 4 ING A METEOROLOGICAL RECORD FOR ABOUT SIX MONTHS ar ; ‘ Gover eee Lae By VERRILL. Plates 8, 9,. | es " SPECTHS. By W. R. Cor. ‘Biatod TODD Best ema Preteens. | ie Arr. XS DascRIPTTONS: OF THREE NEW SPECIES OF NEw ENGLAND | Any of the peuee pation aii of the Transactions of the Connecticut ‘Aecdenme ~y or. ftis and Sciences will ay sent post-paid on Saale of the pr ice bs the ardent 5 Pages. Plates. Price. ) Vol. Part. Pages. Plates. Price. | eae 1866. | 1246 3 $2.50} Vi," 2, 1882. pT reed = mena 02S T, 2, 1867-71. 367 ees ON NPE (1, TRB os URI ek 3.50 | I, 1, 1870. ae B00 | Wie Be 1685. = FRR BE 00 Aysa@eOrae <6 ROR SL has. 004% VoD 1 1886: 259 “s be ‘1, 1876. {> 248 37 3.50| VII, 2, 1888. MB oe a 2,60) — IM, 2, 1878. 260° °° 28 2.50} VIAT, 1, 1890. 204. 8 2502 DEV eee 18 yif 5.) 6242S Be So BON WITT 8. 1808. 88h 1 eS: 3.50 EN, 22,1882. LOO ts SR AE ME, 1802; 832 Me OE ie ‘IV, 3, (in press.) IX, 2, 1895. 210 15 3.00 | |. RD V (acta BRO.) By 26. 8.00 ‘ a eS ery me bs - / -_—« tf S ‘ : ‘ f= = rar ee ete Re aS se > a Sa wane WW 3 9088 01354 2279