PROCEEDINGS OF THE AMERICAN ACADEMY OP ARTS AND SCIENCES. Vol. XXXVI. FROM MAY, 1900, TO MAY, 1901. BOSTON: PUBLISHED BY THE ACADEMY. 1901. Santijersttg }0rrss: John Wilson and Son, Cambridge, U.S.A. IS 1 f P/- CONTENTS. Page I. A New Fossil Crab from the Miocene Greensand Bed of Gay Head, Martha's Vineyard, with Remarks on the Phylogeny of the Genus Cancer. By Alpheus S. Packard 1 II. On the Thermal Diffusivities of Different Kinds of Marble. By B. O. Peirce and R. W. Willson 11 III. Geometry on Ruled Quartic Surfaces. By Frank B. Williams 17 IV. On Supposed Merostomatous and Other Paleozoic Arthropod Trails, with Notes on those of Limulus. By Alpheus S. Packard . 61 V. Certain Derivatives of Metadibromdinitrobenzol. By C. Loring Jackson and W. P. Cohoe 73 VI. On the Continuity of Groups generated by Infinitesimal Transfor- mations. By Stephen Elmer Slocum 83 VII. On Hardystonite and a Zinc Schefferite from Franklin Furnace, N. J. By John E. Wolff. With a Note on the Optical Constants of the Schefferite. By Dr. G. Melczer . . . Ill VIII. On the Thermal and Electrical Conductivity of Soft Iron. By Edwin H. Hall 119 IX. A New Conception of Thermal Pressure and a Theory of Solutions. By Gilbert Newton Lewis 143 X. International Atomic Weights. By Theodore William Richards 169 XI. Peripheral Distribution of the Cranial Nerves of Spelerpes bilin- eatus. By Mary A. Bowers 177 XII. On Certain Derivatives of Orthobenzoquinone. By C. Loring Jackson and Waldemar Koch 195 XII r. On the Action of Sodic Sulphite on Tribromdinitrohenzol and Tri- bromtrinitrobenzol. By C. Loring Jackson and Richard B. Earle 229 1^ CONTENTS. Page XIV. False Spectra from the Rotvland Concave Grating. By Theodore Lyman 239 XV. Investigations on the Composition of Petroleum. By Charles F. Mabery 1. On the Composition oj California Petroleum. By Charles F. Mabery and Edward J. Hudson 2. On the Chlorine Derivatives of the Hydrocarbons in Cali- fornia Petroleum. By Charles F. Mabery and Otto J. Sieplein 3. On the Composition of Japanese Petroleum. By Charles F. Mabery and Shinichi Takano 253 XVI. The Eclipse Cyclone and the Diurnal Cyclones. Results of Meteorological Observations in the Solar Eclipse of May 28, 1900. By H. Helm Clayton ,305 XVII. An Ajyparatus for Recording Alternating Current Waves. By Frank A. Laws 319 XVIII. Suggestion concerning the Nomenclature of Heat Capacity. By Theodore William Richards 325 XIX. Symmetrical Triiodbenzol. By C. Loring Jackson and G. E. Behr 331 XX. A Study of Groiving Crystals by Instantaneous Photomi- crography. By Theodore William Richards and Ebenezer Henry Archibald . 339 XXI. Design as a Science. By Denman W. Ross 355 XXII. The Occlusion of Magnesic Oxalate by Calcic Oxalate, and the Solubility of Calcic Oxalate. By Theodore W. Rich- ards, Charles F. McCaffrey, and Harold Bisbee 375 XXIII. Preliminary Diagnoses of Neiv Species of Laboulbeniaceae — ///. By Roland Thaxter 395 XXIV. A Study of Variation in the Fiddler Crab, Gelasimus pugilator Latr. By Robert M. Yerkes 415 XXV. The Development and Function of Reissner\y Cayley, Salmon, and others, but very little seems to have been done with the quartic cones, which, as will appear later, present some very interesting features. The consideration of curves in space has been the subject of a great many articles by the most eminent geometricians, but curves on ruled quartic surfaces in particular have received little attention. As early as 1861, Chasles I gave a method of describing curves of order 4 ?m + w, on * SuUe superflcie gobbe di quarto grado, Mem. della R. Istoria di Bologna, Series II., T. VIII. t Second and Third Memoirs on Skew Surfaces, Otherwise Scrolls. Coll. Math. Papers, Vol. V. and Vol. VI., respectively, and Phil. Trans., 1863 and 1869, respectively. t Description des courbes a double courbure de tons les ordres sur les surfaces regle'os du troisicmc et du quatricme ordru. C. K. LllI, 884-889. 20 PROCEEDINGS OF THE AMERICAN ACADEMY. ruled quartic surfaces, by means of a pencil of surfaces of order m and groups of n generators in involution. In 1897, Rohn * treated some of the properties of curves on the general quartic surface, considering also the surfaces that can be passed through these curves and presenting some theorems regarding the residual intersection. In 1883, Professor Story discovered a method by means of which he was able to classify all curves lying on a quadric surface and to give a formula for the number of intersections of these curves, thus obtaining, by a synthetic process, the results already found by Cayley.t Professor vStory applied his method to the cubic scrolls, classifying all curves lying on these surfaces and obtaining a formula for the number of intersec- tions of any two of these curves, analogous to that found for curves on quadrics. By an extension of the analytical method of Cayley, Dr. Ferry % suc- ceeded most admirably in treating analytically the " Cubic Scroll of the First Kind," verifying the results of Professor Story for this surface, and in a paper soon to be published, Dr. Ferry has also verified, in the same way, Professor Story's results for the other cubic scroll. It is the purpose of the present paper to consider the classification of curves on all ruled quartic surfaces ; to find the formula for the number of intersections of any two curves that lie on the same ruled quartic sur- face ; and to point out some of the most notable results obtained in the course of the investigation. The equations of many of the ruled quartic surfaces are so complicated that very serious difficulties arise when we attempt to treat them analytically, and it has been found most convenient to employ the synthetic method of Professor Story. 2. For convenience, we shall use the symbol S'^"'^ to denote a surface of order v, and S^*^' to denote a ruled surface of order jx. O^") will be used to denote a curve of order a lying on the ruled surface in question. By an arbitrary generator we shall mean any simple generator that bears no special relation to the curve in question, e. g. in considering a plane curve, it is any simple generator not lying in the plane of the curve. It must be proved, first of all, that every curve C<") meets each gen- erator of the surface on which it lies in a constant number of points, say * Die Raumcurven auf den Flaehen IVer Ordnung. Verliandlungen der K. Sachs. Gesell. der Wiss. zu Leipzig, 1897. t On the curves situate on a surface of the second order. Coll. Math. Papers, Vol. v., and Phil. Mag., 1861, pp. 35-38. X Geometry on the Cubic Scroll of the First Kind. Archiv for Mathematik og Naturvidenskab, B. XXI. Nr. 3, 1899. WILLIAMS. — GEOMETRY ON RULED QUARTIC SURFACES. 21 a points, equal to the number in which it meets an arbitrary generator. (If the curve goes through a point common to all the generators, e. g. the vertex of a cone, this point is not counted as one of the a points on any generator.) This furnishes us a method for classifying all curves on 2^'^), and we shall use the symbol «„ to denote a curve of order a that meets each generator of the surface on which it lies in a points, a being a constant. Similarly, b^ will denote a curve of order b that meets each generator /? times. Each generator is itself a plane curve of order 1, and since it is not met by any other generator except those lying in its plane, it is represented by Iq. In case S^'*) has more than one system of rulings, the lines of one system are chosen as the generators, with refer- ence to which the classification is made for all curves on that surface, and the lines of any other system are regarded simply as curves of order 1. We shall use the symbol (a^, bp) to represent the number of intersec- tions of any two curves «» and bp on the ruled surface. Professor Story * proved that for all curves lying on a quadric surface («a) bp) = a ^ + b a — 2 a /3, and for all curves lying on the cubic scrolls (Ga, bp) = a P + b a — 3 a ^, and stated that it is probably true that (tta, bp) — a P -\- b a — fji, a fS, for curves on a scroll of any order fi. It will be proved here that the formula is true for all ruled quartic surfaces, i. e. that we have (1) (a , bp) = a (3 + b a — i a j3, and when we say that this formula holds for a certain curve we shall mean that it gives the number of intersections of this curve with any other curve on the scroll. It must be borne in mind that these formulae for the cones of different orders give, in each case, the number of inter- sections of the curves aside from those at the vertex, since the vertex is not one of the a points on any edge. This will be proved for the quartic cones. 3. We shall first consider three general theorems,! which must be proved before the formula can be established. The first may be called the fundamental theorem and may be stated thus : 21ieorem 1. — If a be the number of points of C'"* on an arbitrary gen- erator, there are a points of C*"' on each generator. * On the Number of Intersections of Curves Traced on a Scroll of any Order. Johns Hopkins University Circulars, August, 1883. t These theorems were given by Dr. Story in his lectures, October to Decem- ber, 1899. 22 PROCEEDINGS OF THE AMERICAN ACADEMY. No general proof of this theorem has yet been found, and it must be proved for each of the ruled surfaces, separately. From Theorem I are readily deduced the other two theorems, as follows : Theorem II. — If aj is the complete intersection of 2(^) and S^''\ and if h^ is any curve on 2^^) that has no component in common with aa.-, then (fta, bp) = a, ft + b a — ixa fS. Proof. — The intersections of tta and b^ are simply the intersections of /S(^' and bp and are in number equal to b v, i. e. (ua, bp) = 6 v. Now since each generator meets S^"^ in v points, a = v, also a == yx v = /u. a, and we have a (3 -{- b a — fia/S^ixafi + bv — /x a ft = b v; therefore (Oa, h^) = a(3 + ba — fxa/3. Theorem III. — If «„ is irreducible and the partial intersection of S^*^) and *$("), a'a' being the residual intersection, and if the formula holds for each irreducible component of a'a' with an arbitrary curve b^ on S''^^ it also holds for a^ with bp. Proof. — The residual a'a' may break up into several curves, but b^, being arbitrary, does not in general contain any part of the inter- section of 2''*) and »S'(''). If a'a' is reducible, the order a' is the sum of the orders of the component curves, and the number of points a in which any generator meets a'a' is the sum of the numbers of points in which this generator meets the component curves. Since the complete intersection of S^*^) and 5('') is aa + a'a' we have, by Theorem II, (a„ + a'a , bp) = (a + a') (3 + b(a-h a')- fx {a + a') (3. By supposition {a'a, bp) = a' ft-\-ba' -fia' /?. Now the number of points in which b^ meets the complete intersection less the number in which it meets a'a' must be the number of points in which it meets «„ ; therefore («a, ^^) = a ft -{■ b a — fxaft. Corollary. — If the complete intersection of S^*^) and S(^) consists of two curves and the formula holds for one of these curves it holds for the other also. 4. In order then to prove the formula for any ^i") it suffices first to prove Theorem I, and then to show that every curve on S^*^) can be cut out by an »S('') such that the residual is a curve, or is composed of curves, WILLIAMS. — GEOMETRY ON RULED QUARTIC SURFACES. 23 for which the formula holds. Now the formula holds for every genera- tor, i.e. for a Iq, since Iq meets b^ in (3 points, and the formula gives (1q, b^) = 1.(3 + b.O — IX.0./3 — /3. Therefore, if every conic can be cut out by an S^''^ such that the residual is nothing but generators, if every cubic curve can be cut out by an S'^"^ such that the residual consists entirely of conies or generators or both, and in general, if every a^ on 2('') can be cut out by an S'-''^ such that the residual * is of order less than a or is composed of curves of orders less than a, the formula is true. 5. For certain species of C^^^'s it may be possible to choose v smaller than for certain other species, e. g. all the quartic curves lying on a quadric surface can certainly be cut out by cubic surfaces, but the " quartics of the first kind " can also be cut out by quadric surfaces. We shall first determine the lowest value of v for which we can be certain that an S^"') will cut out any species of €("'>. This can be done for a surface of any order, /x, without difficulty, but since we are here going to treat the ruled quartics only, we shall consider the case of (1 = 4 only. S'^"^ is determined by J (v + 1) (i/ + 2) (i/ + 3) — 1 arbitrary points.f When V ^ 5 we must take care that S^"') does not break up into 2'*' and a surface of order v — 4, i. e. of the points necessary to determine aS^"' we must take one more than enough to determine a surface of order i/ — 4 as not lying on 2'^' ; also, we must take a v + I points of S^") on C'"' in order that S'-"^ may contain this curve ; so that for i/ > 5 the number of arbitrary points of 2'*' through which we can make S^"^ pass is (2) . . . H'' + l)('^+2)(v+3)-l-^(v-3)(v-2(.-l)-(«i.+ l) = 2 u'^ — a V. For V = 4 we must take one point of *S'M not lying on 2'^ but then the term }^ (y - 3) (v — 2) {v - 1) = I ■ for v = 1, 2, or 3 we do not have to take any points of S^"^ off 2'^', but then the term i {v — 3) (u — 2) (i-— 1) = 0; therefore formula (2) gives the number of arbitrary points for all values of v, when /a = 4. We have, therefore, 2 i'^ — a v ^ 0, .... _ a which gives at once v >-; so that, for the lowest value of v, we have V = - when §!'') v + 1 times and therefore lies on /S''') ; but, if C'"* has an m-tuple point and v — m + 1 other points on L, even if L meets *S'(^) only once at this multiple point, m — 1 points not included in formula (2) are still at our disposal and may be taken on Z, so that v + 1 points of (S*") lie on L and L will therefore lie on .S'(''). Therefore, in considering whether a line can be made to lie on /S^') or not, we need not take account of the multiple points of C'"' that lie on this line, but may regard the line as meeting jS^''* in points of C'"' equal in number to the number of points on the line in which an arbitrary plane through the line meets C'"'. 6. We have seen that, when certain theorems can be proved, formula (1), p. 21, gives the number of intersections of any two curves on the same ruled surface. In special cases, where the curves bear a particular relation to one another, and in most cases where the multiple curve is involved, the result given by this formula requires a special interpreta- tion, namely : if two curves on 2'^' pass through the same point of the multiple curve, any bi'anch of either curve is regarded as intersecting only those branches of the other curve that lie on the same sheet with it, and two branches that pass through the same point of the multiple curve are not regarded as intersecting at that point if they lie on different sheets of S*'*' there. In particular, two generators through the same point of the multiple curve are not regarded as intersecting, when con- sidered as loci on that quartic surface. The double curve on a ruled quartic cannot be of order greater than three, and therefore a plane section can never have more than three double points on the double curve. If the plane section has a double point not on the double curve, this double point is a point of tangency of the plane, and, since a tangent plane to a ruled surface contains the gen- erator through the point of tangency, the section must be a degenerate quartic curve having at least one generator as a component. Therefore the section of a ruled quartic by a plane can never consist of two proper conies ; for the section would then have four double points, one of which must be a point of tangency of the p'lane, and therefore the plane would cut out a generator. Cayley * uses the general symbol S{tn,n,p) to denote a scroll gener- * Scconil Memoir on Skew Surfaces, Otherwise Scrolls. Coll. Matii. Papers, Vol. v., ami I'liil. Trans., ISO.I 26 PROCEEDINGS OP THE AMERICAN ACADEMY. ated by a line that meets each of three curves of orders m, n, and p once, S(^>n~,n) to denote a scroll generated by a line that meets a curve of order tn twice and a curve of order ?i once, and S (m^) to denote a scroll generated by a line that meets a curve of order m three times. In his symbols for the quartic scrolls he has also used a subscript, in most cases, to denote the order of multiplicity of the curve on the scroll ; but he has not, in all cases, adhered to his general method, and it seems best, while jjreserving his classification, to change his symbols, making them con- form to his general rule for such symbols. II. Qdartic Sckoll, with A Triple Linear Director and a Simple Linear Director, *S'(l3, 1, 4). (Cayley's Third Species, '^(13,1,4).) 1. This scroll has three sheets through the triple linear director, which we shall denote by T, and T is scrolar * on each sheet. Through each point of T pass three generators, one on each sheet, and if we pass a plane through two of these generators it will also con- tain the simple director, since each generator meets the simple director once, and therefore the third generator at the point lies in this same plane, for it meets it once at the point and once on the simple director; i. e. any plane through the simple director meets the scroll in this director and in three generators that intersect in the point where the plane meets T. 2. Proof of Theorem I. — Pass a plane through T; it meets the scroll in T aud one generator and meets C") in a points. Now if we revolve the plane about T it will cut out, in succession, each genera- tor of the scroll, and since the plane always meets C^") in the same num- ber of points, say t points, on 2] it meets C(") in the same number of points, say a points on each generator, where t -\- a ^ a. Since three ... , — a , _ 2tt generators lie m a plane a <; - and t > -— . o o 3. Plane Curves. — A plane that does not pass through any line on the scroll, i. e. an arbitrary plane, meets the scroll in a plane quartic curve having a triple point on T, and since an arbitrary generator meets the plane once, every plane quartic is a 4i. A plane through one and only one generator cuts out a plane cubic having a double point on 7\ through which the generator passes, making * Cajley culls a line scrolar on a surface when the tangent plane to the surface is different at each point along the line. WILLIAMS, — GEOMETRY ON RULED QUARTIC SURFACES. 27 a triple point on the complete intersection ; the generator meets the cubic again where the plane is tangent to the scroll. Since an arbitrary generator meets the plane once and does not meet the generator lying in that plane, it meets the plane cubic once, and therefore every plane cubic is a 3i. If a plane cuts out a proper conic, it must also cut out another conic, which must be an improper conic consisting of two lines through a point of the proper conic, since the section by the plane must have a triple point on T\ but the only lines on the scroll that pass through a point of 7', besides T itself, are generators, and we have seen that a plane through two generators also cuts out a third generator and the simple director ; therefore, there are no conies on this scroll. The triple director T is met once by each generator, and is, therefore, a Sj. The simple director is met once by each generator, and is, therefore, a li. P2ach of these plane curves is either the complete intersection of the scroll and a plane, or else the residual intersection consists entirely of generators, and therefore by Theorems II and III, formula (1) holds for every plane curve on the scroll. A plane quartic has a branch on each sheet where it crosses T, and therefore meets T' three times, as the formula shows, (4i , 30 - 4 + 3 - 4 =. 3. A plane cubic has a branch on each of two sheets where it crosses T, and therefore meets T twice, (S^ , 3i) = 3 + 3 — 4 = 2. The simple di- rector does not meet T', (Ij , Sj) = 1 + 3 — 4 = 0. The simple direc- tor meets a plane once, and therefore meets a plane quartic once, (li> 4i) = 1, but since it meets each generator once, it cannot meet a plane cubic, (Ij, 3i) = 0. Two plane cubics intersect in two points, on the line of intersection of their planes, (3i , 3i) = 3 + 3 — 4 = 2, the other two points, where this line meets the scroll, being the two points where each cubic is met by the generator that lies in the plane of the other. A plane cubic and a plane quartic intersect in three points on the line common to their planes, (3i , 4i) = 3 + 4 — 4 == 3, the fourth point where this line meets the scroll being the point where the generator in the plane of the cubic; meets the plane quartic. Two plane quartics meet in four points on the line of intersection of their planes, (4i,4i) = 4 + 4-4 = 4. 4. Ttvisted Cubic 3i. — We saw that when a is odd we can take V = — 2 — ' ^^■> ^^^ "^^ twisted cubic, v = 2, and by formula (2), p. 23, wc have two points at our disposal in the determination of this ((uadric, 28 PROCEEDINGS OP THE AMERICAN ACADEMY. S'^\ that cuts out the cubic. Since a < - we have a = 1 , and every twisted cubic is a 3i ; therefore t = 3 — 1 = 2, i. e. the twisted cubic meets T in two points, which must be distinct, since a twisted cubic cannot have a double poiut. Therefore the quadric that cuts out the twisted cubic meets T in two points on this curve, and since we can make the quadric pass through any two points we please that are not on the curve, we can make it pass through another poiut of T, and it will theu contain T. The residual intersection, which is of order 5, then consists of T, which counts for three lines, and two generators, since there are no conies on the scroll, and, moreover, each generator meets the quadric once on 5" and once on the twisted cubic, and cannot meet it again without lying on it ; and if a conic or the simple director formed part of the residual, an infinite number of generators would lie on the quadric, which is impossible. Since formula (1) holds for 2^ aud the generators, by Theorem III it holds for every twisted cubic. A plane through the simple director cuts out three generators and meets the twisted cubic three times, once on each generator, and there- fore the twisted cubic does not meet the simple director. 5. Twisted Quartic, 4j. — We have a = 4, v = - = 2, and r r= 4, where r is the order of the residual ; a = 1, and every twisted quartic is a 4j. Hence t = 3, and if the quartic has no double point on T there must be three distinct points of the curve on T, i. e. T meets the quadric that cuts out the quartic three times, and therefore lies on it. If the quartic has a double point on 7", it is a " quartic of the first kind," and we can pass a quadric through it and through any Arbitrary point not on the curve ; the (piadric already meets T twice on the quartic curve, and if we make it pass through another point of T, T will lie entirely on it. In any case, the twisted quartic can be cut out by a quadric such that the residual will consist of T and one generator, and, since formula (1) holds for T and all generators, it holds for every twisted quartic ; if T lies on the quadric the simple director cannot form part of the residual, since each generator already meets the quadric once on Tand once on the twisted quartic. The twisted quartic has a point on each generator, and therefore meets the simple director once, (4i, l^) ^^ 1. G. Twisted Curves, in general. — When a is odd we take v = — - — , a whence r = a -(- 2 ; and when a is even we take v ■= -, whence r = a. _ a _ 2 a We saw that « < q and t > — where r is the number of points on T, WILLIAMS. — GEOMETRY ON RULED QUARTIC SURFACES. 29 in which «„ is met by a plane through T. For a = 3, we saw that T could be made to lie on /S'<^', the quadric that cuts out the twisted cubic. Now for « > 3, V = — - — < T when a is odd and v = - < t when a is even. It follows at once, therefore, from what was said on p. 24, that we can always make J" lie on »S'(''). Therefore when a is odd the re- sidual can be made to consist of Tand a curve of order /• — 3 = a — 1, and when a is even the residual can be made to consist of T and a curve of order r — 3 = a — 3. Therefore, by Theorem III, if formula (1) holds for every curve of order less than a, it holds for every curve of order a ; but we have proved that it holds for all plane curves and for all twisted curves of orders 3 and 4 ; it therefore holds for every curve of order 5 and therefore for every curve of order 6 and so on, and it therefore holds for every curve on the scroll. 7. The above proof is also applicable to the Quartic Scroll, with a two-fold 3 (+1) -tuple linear director, S (I3, 1, 4). (Cayley''s Sixth Spe- cies.) This scroll is, in fact, the limiting case of the scroll just consid- ered, where the simple director has moved up into coincidence with the triple director. Cayley denotes this symbolically by drawing a bar over the two I's. The triple linear director on this scroll is torsal along one of the three sheets through it, i. e. the tangent plane to this sheet, along this director, is the same for every point of this director; the generator, lying on this sheet, that is cut out by this tangent plane, coincides with the simple linear director, and is regarded as intersecting the triple linear director at the point where the other two generators cut out by this tangent plane, one on each sheet, intersect. III. Quartic Scroll, with a Triple Linear Director, S {\s,2,2). (Cayley's Ninth Species, S (l^).) 1. The triple director, T, is scrolar on each of the three sheets that pass through it, and this scroll differs from the Quartic Scroll ^(l,.,, 1, 4) in not having a simple linear director, in consequence of which we have, on this scroll, three generators through each point of T that do not lie in the same plane. The plane of any two of these three generators meets the scroll otherwise in a conic that passes through their point of inter- section on 7\ making up the triple point of the complete intersection. TlKircfore, there are three conies through each point of T, one in each of the tliree planes that contain two generators through the point. 30 PROCEEDINGS OF THE AMERICAN ACADEMY. The proof of Theorem lis the same as for the Quartic Scroll S (I3, 1, 4), _ a p. 2G. Siuce two generators lie in a plane, « < k* 2. Fla7ie Curves. — As before, each plane curve is met once by an arbitrary generator, i. e. a = 1 for any plane curve. There is no Ij on this scroll. Each conic is a 2i, the triple director 7' is a 3i, and the other plane curves, 3i and 4i, are the same as for the Quartic Scroll S (1 3, 1, 4). Every plane curve is either the complete intersection of the scroll by its plane or else the residual is composed of generators, and therefore, by Theorems II and III, formula (1) holds for every plane curve. Two conies do not intersect ; even if they pass thi-ough the same point they lie on different sheets, and cannot be regarded as intersecting on the scroll ; the formula gives (2i, 2i) = 2 + 2 — 4 = 0; the line of inter- section of the planes of the two conies meets the scroll in the four points where the two generators in the plane of either conic meet the other conic. In the plane of a conic each of the two generators that lie in that plane meets the conic on T and at one other point where the plane is tangent to the scroll ; therefore the plane of every conic is a double tangent plane to the scroll. T meets each conic once, (S^, 2i) = 3 + 2 — 4=1. A conic meets a plane cubic once, (2i, 3i) = 1, and meets a plane quartic twice, (2i, 4i) = 2 + 4 — 4 = 2. a 3. Twisted Curves. — Since a < -, we have for the twisted cubic a = 1 and t = 2, where t is the number of points of intersection of the curve and an arbitrary plane through T that lie on T. By the same reasoning as that employed on page 28, we see that T can be made to lie on the quadric that cuts out the twisted cubic, and that formula (1) holds for every twisted cubic. When a is odd we take v = • Then, since two generators lie in a plane and a is an integer, a ^ — - — and t > — ;r — ; but by formula a A- \ (2) we have — - — = v points at our disposal in the determination of S^") and therefore we can make T lie on S'^^) ; the residual will then con- sist of T and a curve of order r — 3 = « + 2 — 3 = a— 1. iTTL • , ft — a ., _ a ^. a a When a is even we take v = -; a :p - and t > -. If a < -, t > -, 2 ^2 2 22 i. e. T > v, and it follows from what was said on page 24 that T can be made to lie on Si") ; the residual will then consist of T and a curve of order a — 3. If a = - = v, every generator meets S^"^ in v points, which WILLIAMS. — GEOMETRY ON RULED QUARTIC SURFACES. 31 are points of a^ ; if, then, any generator meets S'^") in an additional point it must lie on *SM, and therefore if any generator has on it a point of the residual it lies on /S^'') and is itself a part of the residual ; therefore, when a = - the residual consists entirely of generators which are a in number, since the residual is of order a ; and if the curve has no multiple points on T, there are - pairs of generators that pass through the - points where «„ meets T. We have shown then that every twisted curve of order a can be cut out by an S'^"^ such that the residual will consist of curves of orders less than a, and it therefore follows, as on page 29, that formula (1) holds for every curve on the scroll. IV. QuARTic Scroll, with two Double Linear Directors and WITH A Double Generator, S (I2, I2) 2). (Caylet's Second Species, ^'(Ij, lo, 4).) 1. Let us call the double linear directors D and U ; they do not intersect, and a plane through either of them cuts out also two generators that intersect in the point where the plane meets the other director, i. e. any generator A meets a definite generator B on D and another definite generator E on Z)', so that A and B lie in a plane through ZX and A and E lie in a plane through D, while B and E do not meet. In a special form of this scroll four generators may form a gauch-quadrilat- eral having two vertices on each double director, e. g. taking the gener- ators above, if A and B meet D at the point P, A and E meet D' at the point R, B meets D' at the point S, and E meets D at the point Q, the scroll may be of such a form that a generator i^will pass through Q and S, as can easily be shown analytically. It is also very probable that there are special forms of this scroll on which any even number of gen- erators, greater than four, form a gauch-polygon, but it is not the purpose of this paper to discuss these special forms. The double generator, which we will denote by G, arises from the fact that the plane quartic direct- ing curve has three double points, one on each of the double directors and one through which G passes ; a plane through G and either double director does not meet the scroll again. 2. Proof of Theorem I. — On any quartic scroll where the double curve is a twisted cubic, either proper or degenerate, we can prove Theorem I by passing a quadric through this twisted cubic. In the 32 PROCEEDINGS OP THE AMERICAN ACADEMY. present«case the twisted cubic is degenerate, consisting of D, D , and G. Let us pass a quadric through eight points, three on D, three on D' , one on G, and one on any generator A^ the last two points not being on D OT D' ; then D, D\ G, and A will all lie on the quadric and count for 7 lines in the intersection of the scroll and quadric, and therefore the quadric cuts out one more generator; the quadric passes through eight fixed points and we can make it pass through an arbitrary ninth point, so if we vary this ninth point continuously the quadric will cut out, in suc- cession, each generator of the scroll. Now C'"' meets the quadric in 2 a points, of which a fixed number lie on D, I/, G, and -4, and therefore the same number of points of C'"', say a points, lie on each generator. It is evident that there must be a points on A^ for if any other generator be chosen, through which the quadric is always to pass, then there is the same number of points, a, on A, as on each of the other generators. Since we can pass a plane through D and two generators, there are a — 2a points of fla on D, and, similarly, there are a — 2 a points of Qa on D' . A plane through D and G meets the scroll in these two lines only, and there are, therefore, 2 a points of aa on G, as is otherwise evi- dent from the fact that G counts for two generators. Since a twisted curve of order a cannot have a points on any line, 2a'. It is easy to see, by the aid of formula (1), how the other plane curves intersect. 4. Twisted Cubic, 3^. — We have seen that a < - for all twisted curves, and, consequently, every twisted cubic is a 3i. Also, if 8 be the number of points of the curve on D or D' , 8 ^ a — 2a = l for the cubic. The tw'isted cubic is cut out by a quadric ( v = — - — j, and we can make the (piadric contain B, since, by fornuila (2), we have two VOL. xxxvi. — 3 34 PROCEEDINGS OF THE AMERICAN ACADEMY. points at our disposal in determining the quadric. Every generator then meets the quadric once on the twisted cubic and once on D, and cannot meet it again without lying on it ; therefore, the residual consists of D and tliree generators. Since formula (1) holds for Z>and the generators, it holds for every twisted cubic on the scroll (Theorem III). 5. Twisted Quartic 4i. — Since a < ^r, every twisted quartic is a 4i; S = a — 2tt = 2;i. e. a plane through D ov 1/ meets the twisted quartic twice on that line. If the curve is a " quartic of the first kind " it may have a double point on D, D', or G, but in any case it has two distinct or consecutive points on one of the double directors, say D, and since we can pass a quadric through a " quartic of the first kind " and any arbitrary point, we may take this arbitrary point on D, and D will then lie on the quadric ; if the quartic has no double point on G the residual will then consist of D and G, and if the quartic has a double point on G the residual will consist of D and two generators, since each generator will then meet the quadric once on D and once on the quartic. If the curve is a " quartic of the second kind," it is more convenient to cut it out by a cubic surface, i. e. we take v = 3 ; the re- sidual then is of order 8, and by formula (2) we have six points at our disposal in the determination of ^S'^' ; since this quartic has no double point, it meets both D and D' in two distinct or consecutive points, and if we put two more points of \ G, and two generators. Since formula (1) holds for D, U, G, and the generators, it holds for every twisted quartic on the scroll (Theorem III). « + 1 6. Twisted Curves in General. — When a is odd we take v = — - — , and the order of the residual is r = a + 2. We have seen that a < s or 1 ^ tt < — - — , and that there is the same number of points, say 8 points, on each double director, where 8 = a — 2 a, i. e. 1 < 8 < a — 2. It has also been shown, p. 25, that we need not consider whether a^ has multiple points on D and D' or not. By formula (2), we have — - — points at our disposal, in the determination of ^S^"), and therefore we can WILLIAMS. — GEOMETRY ON RULED QUAKTIC SURFACES. 35 make both D and iX lie on *S(-) if 8 + —^ ^ "^ h 1, i. e. if 4 2 ^ _ a + 5 _ Za—6 _3a-5 8 > or a < ^ . lliererore for a ^ the residual 8 o 8 can be made to consist of D, U , and a curve of order r — 4 = a — 2. When a > r , at least one point of «„ lies on D, and since we have 8 — points at our disposal, we can make D lie on ^(''), and the residual will then consist of D and a curve of order r — 2 = a, say Wp, where p is the number of points of this curve on each generator; now formula (1) holds for Z), and if it holds for a^ it will hold for «„ (Theorem III), so we need only consider the curve Op ; each generator meets .SW in « + 1 . T\ ■ 1 • , V = — ;^ — points, once on x', a times on a^-, and p times on ap, so that 2 a+1 , a + l 3 (7 — 5 a+1 P = -y--l-a<-^--l 8— °'^< 8 ' 3 Q 5 i. e. p < ^ for a > 3, and Op is therefore a curve like that consid- 8 ered above, that can be cut out by an S^") such that the residual consists of curves of orders less than a. When a is even, it is convenient to separate the curves into two divi- sions, according as - is odd or even. If -- is odd we take v = - : then * 2 2 2 r =: a, a < -, and 8 must be even since 8 = a — 2 a ; if 8 > — h 1, i- e. a — 2 if a < — - — , both D and D' lie on *§■(") (or can be made to lie on *5('')), and the residual consists of D, I/, and a curve of order ?- — 4 = a — 4 ; a — 2 if a > — - — the residual is a curve of order a, say an ap, where a a « — 2 a -f 2 , a + 2 . p = - — a<- — , or p < — — — ; but — - — is an integer and p 2 2 4 4 4 -«+2 ,. _a — 2, IS an integer, and thererore p :< — 1, i. e. p :< — - — ; therefore, Op is a curve like that just considered, that can be cut out by an ^ + 2, _ a — 4 i. e. if a < — - — , both D and U lie on S^"^ (or can be made to lie on 36 PROCEEDINGS OF THE AMERICAN ACADEMY. /S^"^), and the residual then consists of D, D' , and a curve of order a — 4 ; \i a> ^ ~ , a > ^5 and when « > 2 ^^ residual is an Op, where n = n <^ orp^ , and a^ is therefore a curve that can be ^ 2 2 4 ^ 4 '^ cut out by an /S^") such that the residual will consist of curves of orders less than a ; finally, if a = - we take v = - + 1 ; then r = a + 4 and 8 = - ; if then we put two more points of aSW on D and two more on D' , both of these double directors will lie on *?'*'>, and this we can always do, since, by formula (2), we have a + 2 points at our disposal in the determination of -SI") and a > 4 ; then G will meet ^SW once on D, once on i/, and 2 a = - times on a^, and will therefore lie on S(v) ; each gen- a erator will meet jS^") once on D, once on Z>', and - times on Oa, and, con- sequently, if we put - more points of /S^") on any generator it will lie on 4 / a S^"') ; now we still have at our disposal a — 2>2l-l points, since a. > 4, and therefore we can make two generators lie on *§('); therefore the residual can be made to consist of D, D', C, two generators, and a curve of order r — 8 = a — 4. Therefore, on this scroll, we may divide all twisted curves into two groups, viz. group (1), those that may be cut out by an ^('') such that the residual consists of curves of orders less than a, and group (2), those that may be cut out by an S^''') such that the residual is a curve of group (1), with or without D. Now we have seen that formula (1) holds for all plane curves and for all twisted curves of order 3 or 4 ; it therefore holds for all curves of order 5 of group (1) (Theorem III), and it there- fore holds for all curves of order 5 of group (2) ; it then holds for all curves of order 6 of group (1), and therefore for all curves of order 6 of group (2), and so on. Therefore formula (1) holds for every curve on the scroll. 7. The above proof is also applicable to the Quartic Scroll, with a two-fold 2 (+ 2)-tvple linear director, and with a double generator S (I2, I2, 2), {Cayley^s Fifth Species, -S" (U, Ig, 4)), for this scroll is simply the limiting case of the scroll just considered, where one of the double directors has moved up into coincidence with the other. A plane quartic has a tac-node, where it meets the two-fold director and has' a double point on the double generator. A plane cubic, regarded as lying in the WILLIAMS. — GEOMETRY ON RULED QUARTIC SURFACES. 37 plane, is tangent to the generator in its plane where it meets the two- fold dii'ector, but regarded as lying on the scroll, it does not meet the generator there, for they lie on different sheets, and the generator meets the cubic in one point only, where the plane is tangent to the scroll — the formula giving (Iq, 3i) = 1. The system of conies is the same as on the scroll just considered. The two-fold director may be re- garded as a 42, since it has two lines on each of the two sheets through it and is met twice by each generator. A plane quartic has a branch on each sheet, and therefore meets the two-fold director four times, (4i, 42) = 8 + 4 — 8 = 4, while a plane cubic has a branch on one sheet only, and therefore meets this director twice, (3i, 43) = 6 + 4 — 8 = 2. V. Quartic Scroll, with two Docble Linear Directors and WITHOUT a Double Generator, S (U, I2? 4). (Cayley's First Species, »S(l2, I2, 4).) 1. We shall call the double directors D and 2/. They do not inter- sect, and if we pass a plane through either it cuts out two generators. The scroll is similar in many respects to the Quartic Scroll S (U, l2> 2) already considered, and what was said there in regard to gauch-polygons applies equally well here. But the scroll now under consideration has no double generator, the plane quartic directing curve having only two double points, one on each double director, and this is the only quartic scroll on which the multiple curve is of order less than three. 2. Proof of Theorem I. — A plane through D cuts out two genera- tors that meet in a point where the plane meets i)', and if we revolve the plane about D, it will cut out, in succession, all the generators of the scroll, two at a time. The plane meets C'"' in a points, of which a defi- nite number, say 8 points, lie on D, and therefore there are a — 8 points of C"' on the two generators in the plane, taken together ; for any given curve 0"\ the number a — 8 is a constant non-negative integer, say k. Let x and y be the number of points of 0"\ respectively, on the two generators lying in a plane through D ; theu as the plane revolves about D, we always have x -\- y =1 k, and since x, y, and k are all non- negative integers and k is constant, there is only a finite nund)er of values of x and of y that will satisfy this relation. Let us, for the moment, designate any generator by the number of points of C'"' on it, i. e. the generator x has x points of C'"^ on it, etc. To any value of x, say (/, there corresponds a certain value of y, say r/, such that ff + (J = k ; if then a plane through D cuts out a generator y, it also cuis out a gen- 38 PROCEEDINGS OF THE AMERICAN ACADE3IY. erator g'. As there is a finite number of pairs of values of x and y, we may arrange them in order of magnitude, calling g the greatest, i. e. we shall say that g is the greatest number of points of C*"* on any generator ; correspondingly, / is the smallest number of points of C'"' on any gen- erator, since g + g' = k. Now a plane through D' cuts out two genera- tors, and as we revolve the plane about i)' the number of points of C'"* on the two generators in the plane is constant and equal to a — 8', where h' is the number of points of C""' on U . If then we pass a plane through jy and a generator g' , having the least number of points of 6'"" on it, the other generator in this plane must have the greatest number g of poiuts of C'"> on it ; therefore g -Y g — a — 8', and since g ->r g' — a—h, we have 8 = 8', i. e. 6'"" meets each of the double directors, D and D', in the same number of points, 8. If now a plane be passed through a generator g and the director D it will cut out a generator g , and if through this generator g and U we pass a plane it will cut out another generator g, so that there are at least two generators g. Through these two generators g, the directors D and D (which four lines form a gauch-quadrilateral), and an arbitrary point we can pass a quadric ; D, D', and the two generators counting for 2 + 2 + 1 + 1 = 6 lines in the intersection of the quadric and scroll. Each generator meets the quadric in two points, one on D and one on U , and if we take the arbi- trary point on any generator, this generator will lie on the quadric, and tlie remaining intersection of the quadric and scroll will be another gen- erator. Thus by varying this arbitrary point all the generators of the scroll, two at a time, will be successively cut out by a variable quadric tliat always contains D, Z/, and the two chosen generators g. This quadric always meets C'"' in 2 a points, of which 2 8 lie on Z) and IJ and 2g lie on the two chosen generators g, so that the remaining 2a — 2h — 2g points lie on the other two generators cut out by the (juadric ; but a — h ^ g -\- g' and therefore 2 a — 2 8 — 2 ^r = 2 ^'. Now there is no generator that has fewer than g' points of C'"' on it and the number of points of C'"' on the two generators together is 2 ^' ; therefore each must have g' points of C"' on it. Therefore every gen- erator of the scroll, except the two chosen generators g, has g' points of C<") on it. In like manner, if we choose two generators g', through which the variable quadric is always to pass, we have the sum of the number of points of CW on the other two generators cut out by the quadric always equal to 2 a — 2 h — 2 g' =z 2 g, and, since no generator has more than g points of C(') on it, every generator on the scroll, except the two chosen ones, has g points of C'(") on it. Therefore g ~ g' and WILLIAMS. — GEOMETRY ON RULED QUARTIC SURFACES. 39 every generator meets (7<") in the same number of points, say a points. Two generators lie in a plane through D ; therefore, 8 = « — 2 a, and __ a 2. Plane Curves. — D and D' are both 2i's. There is no system of conies on the scroll, for there is no double generator, and a plane through two generators cuts out D or D' * A plane through one and only one generator cuts out a plane cubic, a 3i, that meets each double director once and has no double point, since the section has only three double points which are the points where the generator in the plane meets the cubic, one on each of the double directors, and one where the plane is tangent to the scroll. An arbitrary plane cuts out a plane quartic, a 4^, having two and only two double points, one on each double director. Every plane curve is, therefore, either the complete intersection of the plane and scroll, or else the residual consists entirely of generators, and consequently, by Theorems II and III, formula (1) holds for every plane curve on the scroll. 3. Twisted Curves. — It may be shown in exactly the same way as for the Quartic Scroll, S {\^, l2'2), pp. 33-36, that formula (1) holds for every twisted curve on the scroll. It will be observed that, in the proof referred to, the double generator is shown to be a part of the residual ; now, there is no double generator on this scroll, but disregard- ing the double generator the residual is still composed of curves of orders less than a, and the conclusion follows as before, without change. 4. The proof just employed is also applicable to the Quartic Scroll with a two-fold 2 (+ '2.) -tuple linear director and without a double gener- ator, S (lo, I2, 4), (Cayley's Fourth Species), which is the limiting case of the scroll .S' (lo I2 4), just considered, where one of the double linear directors has moved up into coincidence with the other. VI. Quartic Scroll, with a Double Conic and a Double Linear Director meeting it, S (I.,, 2o, 2). (Catley's Seventh Species, *S' (1, 2, 2).) 1. For convenience, let D represent the double linear director and let A' represent the double conic. Any plane through D meets A' in one more point, besides the intersection of K and 1), and this is a double point on the section by the plane. The plane therefore cuts out Z) and a * The section cannot consist of two proper conies. (See p. 25.) 40 PROCEEDINGS OF THE AMERICAN ACADEMY. conic having a double point on K, i. e. two lines that meet in this point, which are the two generators in the plaue. 2. Proof of Theorem I. — The double curve on this scroll is a degen- erate twisted cubic, consisting of the double conic K and the double director D. We can pass a quadric through nine arbitrary points, and if we take five of these on K and two on D, distinct from the point of intersection of ^and D, A' and D will both lie on the quadric and we shall still have two points at our disposal ; now every generator meets K and D, and if we take one more point of the quadric on any generator A, it will lie on the quadric ; the quadric will then intersect the scroll in K counted twice, D counted twice, and the generator A, and will, there- fore, cut out one more generator. Making the quadric always contain K, D^ and A, we have one point at our disposal, and by varying this point continuously we make the quadric cut out, in succession, all the gener- ators of the scroll. C'"' meets A', D, and ^ in a definite number of points, and as it meets every quadric in 2 a points it meets each generator in the same number of points, say a points. It is evident that A also meets C'"' in a points, for any other generator may be chosen as the one through which the quadric is always to pass, and then A will meet 6'*"' in the same number of points as the other generators, i. e. in a points. A plane through D cuts out two generators, and there are therefore a — 2a points of cia on Z). K is the complete intersection of its plane and the scroll, and there are therefore a points of aa on A", The number of points of a„ on D cannot be less than zero, and therefore a ^ -. 3. Plane Curves. — The double director D meets every generator once and is therefore a 2i. The double conic K is met once by each generator and is therefore a 4i. The section by a plane not through D or K has three double points on the double curve, one on D and two on K. We have seen (p. 25), that the section cannot consist of two proper conies, and we know that a plane through two generators that meet on A', cuts out Z), for each generator meets D ; therefore, if a plane cuts out a simple conic, it cuts out also two generators that meet in a point on D, for there are no lines on the scroll but the generators, and D and two generators meet only on K or D; conversely, through every point of D pass two generators and their plane cuts out a proper conic ; consequently, there is a system of conies that do not meet D, but meet A' twice, for clearly the plane cannot meet D again, and the section cannot have a triple point on D unless the plane contains Z> ; each of the two generators in tlie plane of any conic meets the conic twice, once WILLIAMS. — GEOMETRY ON RULED QUARTIC SURFACES. -ll in a point where the plane meets K and once where the plane is tangent to the scroll ; therefore the section has five double points and the plane is a double tangent plane. The conic and either generator lie on ditFer- ent sheets at the point where they meet K, and, regarding them as lying on the scroll, they do not intersect there. An arbitrary generator meets the plane once, and, since it does not meet either generator in the plane, it meets the conic once, and therefore every conic is a 2i. Any plane through one and only one generator cuts out a plane cubic, a 3i, having a double point on ^and passing once through each of the points where the generator meets K and D. Any plane that does not contain D, K, or any generator, cuts out a plaue quartic, a 4i, having three double points, two on iv and one on D. The double conic K is the complete intersection of its plane with the scroll, and every plane quartic is the complete intersection of its plane with the scroll, and therefore formula (1) holds for isT and for every plane quartic (Theorem II). A plane cubic is cut out by a plane through a single generator, D is cut out by a plane through two generators, and every conic is cut out by a plane through two generators, and therefore formula (1) holds for every plane cubic, for D, and for every conic (Theorem III). Formula (1) holds, therefore, for all plane curves on the scroll. 4. Twisted Cubic, 3i. — Since a ^ -, every twisted cubic is a 3i. We have seen that there are a points of Oa. on K, i, e. there are three points of the twisted cubic on A', and, since we have two points at our disjjosal in the determination of the cpiadric that cuts out the twisted cubic, we can take these two points on iTaud thus make the quadric contain K. The residual, which is of order 5, will then consist of K, which counts for 4, and one generator, and therefore formula (1) holds for every twisted cubic on the scroll (Theorem III). 5. Twisted Qtiartics, 4^ and i^. — Since a < -, every twisted quartic is either a 42 or a 4i. A 42 may be cut out by a (juadric ; every generator will tlien meet the quadric twice on the quartic curve 42 and cannot meet it again without lying on it; consequently, every generator that has on it a point of the residual must lie on the quadric and form part of the residual, and the residual therefore consists of four generators; therefore formula (1) holds for every 42 (Theorem III). For the 4i, we take V = 3 ; then r = 8, and we have 19 — 13 := G points at our disposal in the determination of the cubic surface aS""'" that cuts out the 4i. There 42 PEOCEEDINGS OF THE AMERICAN ACADEMY. are four points of the twisted quartic 4i on K, and if we take three more points of ^S*^'* on A' -S'^^ will contain K; D meets »S'*'^' twice on the curve 4i, and if we take two more points of ^'^' on D, S^^^ will contain D ; every generator will then meet aS'''* once on D, once on A', and once on the curve 4i, and as we still have one i)oint at our disposal we can make aS'''** contain a generator ; this genei-ator, D, and K count for 7 in the order of the residual, and therefore aS''^' cuts out one more generator. The residual then consists of K, D, and two generators, and therefore formula (1) holds for the twisted quartic 4^ (Theorem III). Formula (1) holds, therefore, for every twisted quartic. 6. Twisted Curves in General. — When a is odd we take v = — - — ; then r =r a + 2, and, by formula (2), we have — - — points at our dis- posal in the determination of *S'(''). If K does not lie on *S'('''), it meets ^(i-) in 2 ( — - — j = a + 1 points ; but we have seen that there are a points of «„ on A", and consequently, if we take two more points of »S'('') on K, *S'('') will contain K; this we can always do, since the number of points at our disposal is — - — > 2 for a > 8. The residual will then consist of K and a curve of order r — 4 = « — 2. When a is even, we distinguish two kinds of curves according as - is odd or even. If - is odd we take v = - ; then r = a, and if 8 be the number of points of «a on D^ we have seen that 8 = a — 2 a : now, if 8 ^ ^- + 1, i.e. if a ^ , D meets »S<'') in at least - + 1 = v + 1 points,* and therefore lies on >SM, so that the residual consists of D and « — 2 a curve of order r— 2 = a — 2; if a> — - — , the residual either breaks up into curves of orders less than a, or else it is a curve of order a, say an «p, where p = - — a, since each generator meets jS'") in v = - a ~ 2 points, of which a lie on «„ and p on cfp ; then, suice a > — - — , « + 2, . . -,fl + 2. . ^ , ^ p< — - — : but p IS an integer and — - — is an integer, so that = «+2 . ^ a — 2 , ., „ p, p <; — -j 1, I.e. p <; , and Up is therefore one ot the curves * Or S^"^ can be made to pass through v + 1 points of D. (See p. 25.) WILLIAMS. — GEOMETRY ON RULED QUARTIC SURFACES. 43 just considered, that can be cut out by such an aS^") that the residual will consist of D and a curve of order a — 2. It - is even and ^ — -, the residual is of order a ; then 8 must be even, being equal to a — 2 a, and, if S = _ _}- 2, i.e. if a ^ — - — , D lies on /S^"), and the residual consists of D and a curve of order « — 2. If a > — - — , then a > . . When 4 4 a > - the residual either breaks up into curves of orders less than a, or 4 a . else it is a curve of order a, say an Op, where p = v — a < t , i-e. d 4 p ^ , and consequently a^, is a curve like that just considered, that can be cut out by an -S^") such that the residual will consist of D and a curve of order a — 2. Finally, when a = - , we take v = - + 1 ; then 4 2 7- = o + 4, and, by formula (2), we have « + 2 points at our disposal in the determination of -S'^''). If K does not lie on 6 for a > 4. Since a — - , 8 = - , and if we make S^"^ 4 2 pass through two more points of Z), not on aa. , S^"^ will cut out D. The residual will then consist of K, D, and a curve of order r — 4 — 2 = a — 2. The twisted curves on this scroll can therefore be divided into two groups, viz., group (1), those curves of order a, each of which can be cut out by such an S^"') that the residual will consist of curves of orders less than a, and group (2), those curves of order a, each of which can be cut out by such an aS^") that the residual will be a curve of order a and of group (1). Therefore, by the same reasoning as that employed for Quartic Scroll -S* (l^, 1^, 2), p. 36, Formula (1) holds for all curves on the scroll. VII. Quartic Sckoll, with a Double Twistk.d Cubic mf.t TWICE BY EACH GENERATOR AND WITH A SiMPLE LiNEAR DIREC- TOR, S{3^^,1). (Cayley's Eighth Species, ^(1, 3-).) 1. Let Q represent the twisted cubic, which is the double curve on the scroll. Through each point of Q pass two generators ; the plane of these two generators contains the linear director, since each generator 44 PROCEEDINGS OF THE AMERICAN ACADEMY. meets the linear director once, and therefore this plane cuts out also a third generator, i.e. any plane through the linear director meets Q in three points, say L, M, and N, and cuts out the three generators L M, 2. Proof of llieorem I. — We can make a quadric pass through Q by making it pass through seven points of Q ; and since ^ is a double cubic it counts for six in the order of the complete intersection of the quadric and scroll ; if the eighth point for the determination of the quad- ric be taken on any generator A, the quadric will contain A, since each generator meets Q twice ; the remaining intersection will be any gener- ator on which we choose to take the ninth point for the determination of the quadric, and if we keep the first eight points fixed and vary the ninth point continuously, the quadric will cut out in succession the differ- ent generators of the scroll. A fixed number of points of C^") lie on Q and the chosen generator A, and therefore every generator contains the same number of points of C("), say a points. Any generator, other than A, can be chosen, through which the quadric is always to pass, and therefore there are a points of (7(') on A. Since the quadric meets «„ in 2 a points, there are 2a — 2a = 2(a — a) points of tta. on Q. Three gen- erators lie in a plane through the linear director; therefore a <; -, and there are a — 3 a points of «„ on the linear director. 3. Plane Curves. — Since the section by a plane cannot consist of two proper conies (p. 25), a plane through a proper conic would either cut out two generators or the simple director and one generator; but we have seen that a plane through two generators or through the simple linear director cuts out three generators and the linear director ; there- fore there can be no proper conic on the scroll. A plane through one, and only one, generator cuts out a plane cubic, a 3i, having a double point on Q and passing once through each of the two points where the generator meets Q ; the generator meets the plane cubic in one other point where the plane is tangent to the scroll. An arbitrary plane cuts out a plane quartic, a 4i, having three double points on Q, and since any plane quartic is the complete intersection of its plane with the scroll, formula (1) holds for it (Theorem II). The simple linear director, a l^, is cut out by a plane through three generators, and every plane cubic is cut out by a plane through one generator, and therefore formula (1) holds for the simple linear director and for every plane cubic (Theorem III). Therefore formula (1) holds for all plane curves on the scroll. WILLIAMS.- — GEOMETRY ON RULED QUARTIC SURFACES. 45 The double cubic Q, although not a plane curve, will be considered here. We have seen that it is cut out by a quadric through two gener- ators, and therefore formula (1) holds for it (Theorem III). It is met twice by every generator, and is, therefore, a 62. A plane quartic has a branch on each sheet at each of the three points where it meets Q, and the number of its intersections with Q is 6, (62, 4i)=6 + 8 — 8 = G. A plane cubic meets Q four times, twice at the double point of the plane cubic and once at each of the other two points where the plane meets Q, (62, 3i) = 6 + 6 — 8 = 4. The linear director does not meet Q, (62,10 = 6 + 2-8 = 0. __ a 4. Twisted Cubic, 3i. — Since a < „, every twisted cubic is a 3i. We o take V = d; then r = 9, and we have 19 — 10 = 9 points at our disposal in the determination of /S'''^* that cuts out the twisted cubic. The number of points of the twisted cubic on ^ is 2 (a — a) = 4, and if we take 6 more points of aS*^' on Q, /S'^' will contain Q ; this leaves 9 — 6 = 3 points at our disposal, and, since each generator now meets ;S^'"' twice on Q and once on the twisted cubic, we can take one more point of >S''^' on each of three generators and *S'"' will then contain those three generators ; the residual will then consist of Q and three generators, and therefore formula (1) holds for every twisted cubic (Theorem III). Since three generators lie in a plane through the linear director, a twisted cubic does not meet the linear director, (3^, li) = 3 + 1 — 4 = 0. 5. Twisted Quartic 4i. — Since a < -, every twisted quartic is a 4i. o We take v = 3 ; then r = 8, and the number of points at our disposal in the determination of S^"'' is 19 — 13 = 6. There are 2 ((t — a) = 6 points of the twisted quartic on Q, and if we take four more points of /S''"^* on Q, -3-j since a < -. That aS^") may contain Q, it must o 0 46 PROCEEDINGS OP THE AMERICAN ACADEMY. pass through 3 v + 1 = — — points of Q, and therefore, if we take 3 a + 11 . _ a + 33 „ , . ,. - ^ rf/ \ Ml ~ ■ — o < — of tlie points at our disposal on Q, oa") will coii- tain ^; if X be the number of points left at our disposal, after making • ^ X = 3 a + 9 a + 33 . ^ = 4 a ^ ol"' contain Q, A ^ — -; — , i. e. A > —- 1. J\ow each 2 b o generator meets aS'') twice on Q and a times on «„, i. e. at least three a + 3 times since a > 1 ; if, then, we make aS^") pass through • — h 1 — 3 a — 1 . = — - — other points on any generator, that generator will lie on S^^'h ' . . 4fi We can, therefore, make at least two generators lie on »S'(''), since — 1 > 2 I • — - — |, and the residual will then consist of Q, two generators, and a curve of order r — 6 — 2 = a — 2. When a is even we take v = - + 1 ; then r = a + 4, and, by form- Li ula (2), we have a -f- 2 points at our disposal in the determination of _ 4a /S"'"). The number of points of a^ on ^ is 8 = 2 (a — «) > -5-- In o 3o + 8 2 2)oints of Q, and therefore in addition to the 8 points we must make ^>'') ,3a + 8 ^_a + 24 , . ,^ ,. pass through — — h :^ other pomts of Q ; this we can a + 24 always do, since the number of points at our disposal is a + 2 > — for a > 4. The residual will then consist of Q and a curve of order r - 6 = a — 2. We have shown, then, that every twisted curve of order a can be cut out by an aS'") such that the residual is composed of curves of orders less than a; we have also shown that formula (1) holds for every plane curve and for every twisted curve of order 3 or 4 ; it holds, therefore, for every twisted curve of order 5, and therefore for every twisted curve of order G, and so on (Theorem III); therefore formula (1) holds for every curve on the scroll. VIII. QuARTic Scroll, with a Double Twisted Cubic met TvriCE BY EACH GENERATOR, aS'(32^2). (CaYLEY's TeNTH Species, ^^(S^).) 1. Let Q be the double twisted cubic. Through every point of Q pass two generators. Tlie scroll differs from the Quartic Scroll ,S' {^.^, 1) order for /S'f'') to contain (?, it must pass through 3 v + 1 = WILLIAMS. — GEOMETRY ON RULED QUARTIC SURFACES. 47 in not having a simple linear director, in consequence of which a plane through two generators cuts out a proper conic. 2. Proof of Theorem I. — By passing a quadric surface through Q and any chosen generator, Theorem I is proved in exactly the same way as it is for the Quartic Scroll 8(^2^ 1)? P- 44., and if a be the number of points of O"' on each generator, we see, as before, that the number of points of aa, on ^ is 2 (a — a). Since two generators lie in a plane, _ a "<2- 3. Plane Curves. — Since there are no lines on the scroll except the generators, a plane through two generators cuts out a proper conic, and since the section has three double points on Q, the conic passes through each of the two points in which the generators meet Q, different from their point of intersection. Each conic is a 2i, and regarding the conic and generators as lying on the scroll, the conic is met once only by each generator in its plane, since at the point where the conic and gen- erator cross Q they lie on different sheets. The two points where the two generators meet the conic, not on Q, are points of tangency of the plane, and therefore through every point of Q there is a double tangent plane to the scroll. By Theorem III, formula (1) holds for every conic. There is no li on the scroll, and the other plane curves, the cubic, 3i , and the quartic, 4i, are the same as those of the same order on the Quartic Scroll S {Zo^, 1) and therefore formula (1) holds for all curves on the scroll. Since ^ is a double twisted cubic met twice by each generator, it is a Go. and since it is cut out by a quadric through two generators, formula (1) holds for it (Theorem III). We have seen that Q meets each conic twice, and the formula gives (62,20 = 6 + 4-8 = 2. 4. Twisted Curves. — It is proved in exactly the same way as for the Quartic Scroll S {d^^, 1) that formula (1) holds for every twisted curve on the scroll ; therefore, it holds for every curve on the scroll. IX. Quartic Developable. 1. This surface is formed by the tangents to a twisted cubic, E\ E is then a double curve on the surface, and from one point of view, this sur- face is the limiting case of the Quartic Scroll 'S'(32^, 1) whore the two points in which any generator meets the twisted cubic have become con- secutive ; the twisted cubic then becomes the " edge of regression " and the three double points of the section by a plane become cusps. 48 PROCEEDINGS OP THE AMERICAN ACADEMY. 2. Proof of TJieorem 1. — By passing a quadric through E, which is the cuspidal edge of the developable, and any chosen generator, Theo- rem I is proved in exactly the same way as it is for the Quartic Scroll S{^^, 1), p. 44, and if a be the number of points of C'(") on each gen- erator, E has 2 (a — a) points of «„ on it. Since E is cut out by a quadric through two generators, formula (1) holds for it (Theorem III). Being a double twisted cubic met twice by each generator, E is a G^, and formula (1) gives, for the number of intersections of E with a^, (62 ,«„)== 6 a + 2 a — 8 a = 2 (a — a). 3. Plane Curves. — A " plane of the system," i. e. an osculating plane of E, cuts out two consecutive generators and a proper conic* This conic, which is tangent to E,1[ can never break up, for there are no lines on the surface except the generators, and a plane cannot contain more than two generators (which must, moreover, be consecutive), since it cannot meet E in more than three points. Each conic is a 2i , and there is a conic through every point of E. A plane through one and only one generator cuts out a plane cubic, a 3i , that has a cusp at the point not on the generator, where the plane meets E, and has the generator for its real inflectional tangent at the point where the generator meets E; for, since the two consecutive points in which the generator meets E must be double points of the section of a plane through the generatoi", the plane cubic must pass through each of these points, i. e. it meets the generator in at least two points there ; but the generator at this point crosses from one sheet to the other, say from the upper to the lower, while the plane cubic crosses from the lower to the upper ; therefore they cross each other and intersect, in an odd number of points, and consequently they intersect in three points, i. e. the generator is the real inflectional tangent. Every plane quartic has three cusps, one at each of the three points where its plane meets E, and since it is the complete intersection of its plane with the developable, formula (1) holds for it (Theorem II). Every conic is cut out by a plane through two generators and every plane cubic is cut out by a plane through one generator, and therefore formula (1) holds for every conic and for every plane cubic (Theorem III). Formula (1) holds, therefore, for every plane curve on the developable. * Salmon's Geom. of Three Dimensions, § 339. t V. Jamet, C. R., 1885, Vol. 100, pp. 1332-35. WILLIAMS. — GEOMETRY ON RULED QUARTIC SURFACES. 49 4. Thoisted Curves. — It may be shown in exactly the same way as for the Quartic Scroll aS'(32-, 1), that formula (1) holds for every twisted curve on the developable. Formula (1) holds, therefore, for every curve on the developable. X. Quartic Cones. 1. Using the plane quartic curves as a base, we may say that there are ten different species of quartic cones, corresponding to the ten species of plane quartic curves.* But for our present purpose we need not distinguish between double edges and cuspidal edges, and it will be convenient to divide the cones into five groups, viz., (I) cones hav- ing a triple edge, (II) cones having three edges double or cuspidal, (III) cones having two edges double or cuspidal, (IV) cones with one double or cuspidal edge, and (V) non-singular cones, i. e. cones with no multiple edges. t A curve C(''), lying on a cone, has a i"-tuple point at the vertex, where 0 < ^, and any plane through the vertex meets C(") in k points there. 2. Theorem I. — Every edge of a quartic cone meets C(") in the same number of points, say a points (in addition to the k points at the vertex) ; the number of points of C^") on a double edge is 2 a, and the number of points of C(") on a triple edge is 3 a. Proof. — Consideriug group (I), if we pass a plane through the triple edge and revolve it about this triple edge, it will cut out, in succession, all the edges of the cone; the plane meets (7(") in k points at the ver- tex and in a fixed number of points, say t points, on the triple edge, and, as it meets (7(") altogether in a points, the same number of points, say a points, lie on each edge of the cone. An arbitrary plane through the vertex meets the cone in four edges, and therefore 4 a + ^- = a, i. e. 4 a = a — ^. Taking the plane through the triple line, we have a -|- T = « — X; = 4 a, i. e. t = 3 a. Consider now group (II), and pass a quadric cone through the three double or cuspidal edges and any chosen edge A of the quartic cone ; these count for seven edges in the intersection of the two cones, and * Salmon's Iliglier Plane Curves, § 243. t When not qualified by the words double, cuspidal, triple, multijile, etc., the word ed(/e will always moan a simple ed(je of the cone. VOL. XXXVI. — i 50 PROCEEDINGS OP THE AMERICAN ACADEMY. they must have one more edge in common ; if, then, we vary continu- ously the fifth arbitrary edge that determines the quadric cone, this cone will always pass through the three double or cuspidal edges and the edge A of the quartic cone, and will cut out all the edges of the quartic cone one at a time. Every quadric cone meets C(") in 2 a points, of which a definite number lie on the three double or cuspidal edges and the edge A, and therefore the same number of points of (7("), say a points, lie on each edge of the quartic cone ; it is evident that, if any other edge be chosen through which the quadric cone is always to pass, the edge A will have a points of C(") on it. If we pass an arbitrary plane through any of the double or cuspidal edges, it will also cut out two edges of the quartic cone, and, if 8 be the number of points of C(") on this double or cuspidal edge, we have 8+2a:=a — k=4:a, i. e. 8 = 2 a, since an arbitrary plane through the vertex cuts out four edges, giving 4a = a — k. To prove the theorem for group (III), we may employ a method analogous to that used for the Quartic Scroll 'S'(l2, Ig, 4), p. 37; corre- sponding to the planes there, through the double directors, we should use here the planes through the double or cuspidal edges, and instead of the quadric used there we should now employ a quadric cone. We shall not consider this proof in detail, but shall now give a proof of the theorem for groups (IV) and (V), — a proof which holds for the other three groups as well, and therefore for all quartic cones. If JO is the number of points of C^") on any edge of the cone, it is evi- dent that 0 < jD < a — 1, and p can have, at most, a different values. For convenience, we shall say that all the edges for which p has the same value belong to the same set ; and if there is an infinite number of edges in a set, we shall call it an infinite set, or, if there is a finite num- ber, a finite set. There are, at most, a different sets, and, since a is finite, at least one of these must be an infinite set. Let us suppose, first, that there is only one infinite set, and let a be the value of p for this infinite set ; we can then pass a plane through one of these a-edges (i. e. an edge having a points of C^") on it) and turn it about so that it shall not contain any edge of any finite set ; this plane will then cut out four a-edges, and as it meets C^") in a points, of which k lie at the ver- tex, we have 4 a -\- k := a, i. e. a — k ^= Aa. Now we can pass a plane through any edge of any of the finite sets and WILLIAMS. — GEOxMETRY ON RULED QUARTIC SURFACES. 51 turn it about so that it will not contain any other edge of any finite set, and this plane will then cut out three u-edges in addition to the chosen edge ; if )8 is the number of points of (7*°' on the chosen etlge, we have (3 -\- 3 a =^ a — /t = 4 a, i. e. y8 = a. Therefore every edge of the cone has a points of O"^ on it. If the cone has a double or cuspidal edge, an arbitrary plane through it will cut out two a-edges, and if 8 is the number of points of C'"' on the double or cuspidal edge 8 + 2 a =: a — Z: = 4 a, i. e. 8 = 2 a. • If the cone has a triple edge, having t points of C'"' on it, an arbitrary plane through this triple edge will cut out one a-edge, and we have T + a = a — k = 4 a, * i. e. T = 3 a. Therefore, the theorem holds when there is only one infinite set. Sup- pose now that any number of the a sets are infinite, and let a be the least value of p belonging to any of these infinite sets. Pass a cubic cone through nine of these a-edges; then, since the cubic cone meets C'"' in 3 a points, of which 3 ^- lie at the vertex and 9 a on the nine chosen edges, the remaining 3a — 3k — 9a points lie on the three other edges in which the cubic and quartic cones intersect, and at least one of these three edges must have as many as a — k — 3 a points of C"' on it. Keeping seven of the a-edges fixed, we can vary the other two in such a way that the cubic cone, determined each time by the nine a-edges, will have for its remaining intersection with the quartic cone tliree edges different from those of any other such cone previously deter- mined ; since there is an infinite number of a-edges, we get, in this way, an infinite number of such cubic cones, and therefore an infinite number of edges each having as many as « — ^' — 3 a points of C'"' on it ; hav- ing an infinite number of such edges, we can so choose two of them that their plane will not pass through any edge of any finite set, because there is a finite number of edges in all the finite sets taken together ; besides the chosen edges this plane will then cut out two edges belonging to the infinite sets. Now the number of points of (7'"* on the two chosen edges taken together is equal to or greater than 2a — 2^— 6 a, and if (3 and y be the number of points of C'-"\ respectively, on the other two edges in the plane we must have 2 a — 2k-C>a + l3 + y^a — k, and, since neither (3 nor y can be less than a, 2a-2^-— 6a-t-2a^'^-/C', 52 PROCEEDINGS OF THE AMERICAN ACADEMY. i. e. a — ^' ^ 4 a. If, now, we pass a plane through any edge of any infinite set and turn it about so that it will not pass through any edge of any finite set, it will cut out three other edges of the infinite sets. Let pi, p^, p^, and JO4 be the number of points of C'*"', respectively, on the four edges in this plane ; we have then />i 4- /'2 + />3 + i»4 = a — j{; < 4 a, and, since neither pi, p^, ps, nor p^ can be less than a, each must be equal to a ^nd a — ^ = 4 a. Therefore, every edge of every infinite set meets C'"' in a points, i. e. there is only one infinitive set, and we have proved that the theorem holds in this case. 3. On the cones, a curve CI"' is, as before, designated by the symbol fla, but a now means the number of points, other than those at the vertex, in which an arbitrary edge of the cone meets the curve C'"'. We shall now show that formula (1), {(1^-, b^) = a (3 + b a — 4 a ft, gives, for the quartic cones, the number of intersections of the two curves, Oa and bp, exclusive of the number of their intersections at the vertex of the cone. We have seen that a — ^- = 4 a, i. e. ^' = a — 4 a, where k is the number of branches of fta through the vertex, i. e. «„ has an (a — 4 a)- tuple point at the vertex. Let »„ be the complete intersection of S^''") and the quartic cone, and let b^ be an arbitrary curve on the cone ; the total number of intersections of «„ and b^ is the number of intersections a b of /S'"^ and b^, which is b v, and, since a = 4 i', 61/ = — - ; now, at the vertex, /S^") has a point of multiplicity (since eta. is the complete intersection of S^") and the cone and has an (a — 4 a)-point at the vertex), and b^ has a (6 — 4 ^) -tuple point, so that b^ meets /S^") in (^°)(*-*»=^*-(«fl+*a-4a/3) points at the vertex ; since the total number of intersections of b^ and /S'W is — , the number of their intersections exclusive of those at the 4 vertex, i. e. the number of intersections of b^ and «„ exclusive of those at the vertex, is— + (a ft + b a — 4: a (S) = o/3+ b a — 4 a /3, 4 4 which is the number given by formula (1). Since the formula holds when «„ is the complete intersection of the cone and S^''\ by Theorem III, it holds when a^ is the partial intersec- WILLIAMS. — GEOMETRY ON RULED QUARTIC SURFACES. 53 tion of the cone and aS'(''), provided we cau always cut out a^ by an S'-") such tliat the residual is of order less than a or breaks up into compo- nents each of which is of order less than a ; for we know that it holds for the number of intersections of any edge, a Iq, with an arbitrary curve 6fl, givinw (lo, S/s) = /S. Each edge is a Iq, each dovible or cuspidal edge is a 2o, and each triple edge is a 3o, since the edges and multiple ed'^es meet only at the vertex. Every multiple edge can be cut out by a plane such that the residual will consist entirely of generators, and therefore formula (1) holds for every multiple edge (Theorem III). Since the plane quartic cannot break up without the cone breaking up (unless it consists entirely of edges or multiple edges), the only plane curve, besides the edges and multiple edges, that can lie on the cone is a plane quartic which is the complete intersection of its plane with the cone, and therefore formula (1) holds for every plane curve. 4. Twisted Curves. — There is no cubic curve on a quartic cone, since 1 ^ a and 4 o < a, and, therefore, 4 ^ a. Every twisted quartic is a 4i, since a ^ - , and, since ^- = a — 4a = 0, it does not go through the vertex. Any twisted quartic can be cut out by a cubic monoid,* for we can pass the monoid through 19 — 4 = 15 arbitrary points, and if we take thirteen of these on the quartic curve, the monoid will contain it. The node of the monoid is taken at the vertex of the cone ; each edge of the cone then meets the cubic monoid twice at tht; vertex and once on the quartic curve, and cannot meet it again without lying on it ; therefore the monoid cannot meet the cone in any other curve, and the residual consists entirely of edges or multiple ed^es of the cone. Every twisted quintic is a Oj , and has one branch through the vertex, k ^= 5 — 4r=l; it can be cut out by a cubic monoid which can be passed through 15 arbitrary points; for the quintic meets the monoid twice at the vertex, and if we pass the monoid through 14 other points of the quintic, it will contain the quintic. Every edge of the cone meets the monoid twice at the vertex and once on the quintic curve, and there- fore the residual consists entirely of edges or multiple edges of the cone. Every twisted sextic is a Gi , and has two branches through the vertex, since ^ = 6 — 4 = 2; it can be cut out by a cubic monoid whose node is at the vertex of the cone ; for the sextic meets the monoid four times * A monoid of order /// is a surface of order m Iiavhig an (m — l)-tuple point. (Cayloy.) 54 PROCEEDINGS OP THE AMERICAN ACADEMY. at the vertex, aud if we pass the mouoid through 15 other poiuts of the sextic it will contain the sextic. The residual will then consist entirely of edges or multiple edges of the cone. In the same way it may be shown that all curves of order 7, and all curves of orders 8, 9, and 10 for which a = 1, can be cut out by a quar- tic monoid such that the residual will consist of edges or multiple edges of the cone. When a ^ 2 (for which a ^ 8), or when a ^ 11, i. e. for all curves not yet considered, we must take v > 5, where v is the order of the sur- face of lowest order that cuts out a^ such that the residual coysists of edges or multiple edges of the cone. We shall now show that such a surface can be found for any cia, and the value of v given in terms of a and a. Since the residual is to consist entirely of edges or multiple edges of the cone, an arbitrary edge must meet the required surface in V — a points at the vertex, i. e. the surface must have a (v — a) -tuple point at the vertex of the cone. Let M^_^ be the required surface. When V > 4 we must take care that M ' does not break up into the quartic cone and a surface which must be an Mj_^_^, i. e. a surface which has a (v — a — 4)-tuple point at the vertex; Mj_^_^ can pass through only K(i/-3)(i^-2)(v-l) - (i/-a-4)(v-a-3)(v-a-2)]-l arbitrary points, different from the vertex, and consequently if we make M _ pass through (A) ^[(v-3)(.-2)(.-l)-(./-a-4)(v-a-3)(v-a-2)] arbitrary points, not on the quartic cone, it cannot have the quartic cone as a component ; the number of arbitrary points remaining, to determine M , must be great enough to make it contain «„, which has a — 4a branches through the vertex ; consequently we have (3) . . . av+\ - {a- 4a)(v - o) < I \.{^ + 1) (" + 2) (,. + 3) -(;^-a)(v-«+l)(v-a+2) - (v - 3) (v - 2) (v - 1) + (i/ - a + 4) (,/ - a - 3) (i/ - a - 2)] - 1, from which we obtain the relation 1 +aa+ 4av — 4a2^4av — 2u^+ 4v— 4a — 3, i. e. ,,, a(n!-2a+4) + 4 (4)... v^ ^ , WILLIAMS, — GEOMETRY ON RULED QUARTIC SURFACES. 55 or the next greater integer. When v = 3 or 4 we saw that a = 1, so that the expression (A) that enters into eq. (3) vanishes for v = 3, as it should, and is equal to unity for ;/ = 4 ; therefore eq. (4) gives the correct value of v for all twisted curves on the cone. If then we take the value of v given by eq. (4), any twisted curve o.^ can be cut out by an Jt/''^ such that the residual will consist entirely of edges or multiple edo-es of the cone, and therefore formula (1) holds for all twisted curves on the quartic cones. In determining the above value of v, no account was taken of the actual multiple points, not at the vertex, that Wa iiiay have. We have seen (p. 24) that an m-tuple point reduces by m — 1 the number of points of a,, through which it is necessary to make M^}^ pass in order for it to contain «„) if this m-tuple point be taken as one of them ; therefore, if u (a — 2 a + 4) + 4 = 1 (mod. 4) and a^. has a double point not at the vertex, the value of v may be taken one less than that given by eq. (4) ; if a (a — 2 a + 4) + 4 = 2 (mod. 4) and (la has two double points or one triple point, not at the vertex, the value of V from eq. (4) is reduced by unity, and so on. If «„ has four double points, or two triple points, or two double points and a triple point, or a double point and a 4-tuple point, or one 5-tuple, not at the vertex, then the value of v is always one less than that given by eq. (4). We have shown, then, that formula (1) gives the number of inter- sections, aside from those at the vertex, of any two curves on any quartic cone. It is to be observed that any branch of «« through the vertex has an edge of the cone as its tangent at that point and that one of the two consecutive points, in which the edge meets the branch there, is one of the a points of «„ that lie on this edge ; if a double or cuspidal edge is tangent to a branch of «„ at the vertex, then two of the 2 a points of Ua that lie on it are consecutive to the vertex ; and if a triple edge is tangent to a branch of «« at the vertex, then three of the 3 a points of a„ that lie on it are consecutive to the vertex. If, therefore, «„ and ^,3 each have a branch through the vertex tangent to the same edge, i. e. a branch of «« tangent to a branch of b^ at the vertex, then one of these two intersections of the curves at this point is included in the number of intersections given by formula (1). In like manner, if «„ and b^ each have a branch through the vertex, and these branches have there a com- mon inflectional or cuspidal tangent or have any peculiar relation to one another, the excess of the number of intersections that these branches have there over the number of intersections that two arbitrary branches would have there is included la the number of intersections given by formula (1). 56 PROCEEDINGS OF THE AMERICAN ACADEMY. 5. We shall now consider the "twisted quartics more in detail. Every twisted quartic is a 4i, and, since it has at least two apparent donble points, the cone on which it lies must have at least two double or cus- pidal edges, i. e. no twisted quartic can lie on the cones of groups (IV) and (V) ; moreover, the cubic monoid, which cuts out the twisted quartic, has six * lines on it through the vertex, and these six lines must count for eight, the order of the residual intersection of the cone and monoid, and therefore the cone must have, at least, two double or cus- pidal edges with which two of the six lines coincide. Through a "quar- tic of the first kind" can be passed an infinity of quadrics, i.e. we can pass a quadric through a " quartic of the first kind " and any arbitrary point ; let this quadric be passed through the vertex. The " quartic of the first kind " has two apparent double points, and the two double edges, of the cone, on which they lie, meet the quadric twice on the curve and ouce at the vertex, and therefore lie entirely on it ; these double edges are, therefore, the two generators of opposite systems, of the quadric, through the vertex. The cubic monoid, in this case, breaks up into the quadric and a plane through the vertex. The " quartic of the first kind" may have an actual double point or cusp, in which case the cone has an additional double or cuspidal edge that meets the quadric only once at this double point or cusp and once at the vertex, and there- fore does not lie on it. The cone may have a cuspidal edge due to an apparent cusp on the quartic curve, i. e. if a tangent to the curve passes through the vertex, the curve when viewed from the vertex appears to have a cusp on tliis tangent, which is therefore a cuspidal edge of the cone (the apparent cusp replaces one of the apparent double points and the cuspidal edge is one of the generators of the quadric). If two tan- gents to the quartic curve pass through the vertex, the cone has two cuspidal edges and the curve has two apparent cusps. When the quadric that cuts out the quartic goes through the vertex the residual consists entirely of the two double or cuspidal edges on which the apparent double points or apparent cusps lie, but for every other quadric that passes through the " quartic of the first kind," the residual is another " quartic of the first kind " similar to the original quartic ; this may be shown as follows: since the quadric does not go through the vertex no edge or multiple can lie on it, and therefore the residual cannot break up, i. e. it must be a twisted quartic; moreover, every edge or multiple * Tliis is the number of common edges of its superior and inferior cones- Cay ley, Collected Papers, V. p. 8. WILLIAMS. GEOMETRY ON RULED QUARTIC SURFACES. 67 edge meets the quadric twice and no more ; then every double edge on which an apparent double point of the original quartic lies is met by the original quartic in two distinct points, and therefore the residual quartic must cross this double edge at the same two points, since there are two and only two branches of the complete intersection at these two points where the double edge meets the quadric ; therefore, for every apparent double point of the original quartic there is an apparent double point of the residual quartic. The double or cuspidal edge, on which au actual double point or cusp of the original quartic lies, meets the quadric only once there, and must meet it at one more point, which is, therefore, a double point or cusp on the residual quartic. A cuspidal edge due to an apparent cusp on the original quartic meets the quadric in two consecu- tive points, and the residual quartic must p.iss through these two con- secutive points, i. e. it has this cuspidal edge as a tangent and therefore the residual quartic also has an apparent cusp at this point. The re- sidual quartic is therefore a " quartic of the first kind " similar to the original quartic. Each of these two "quartics of the first kind" consid- ered as lying on the quadric, meets the generators of each system of the quadric in two points, and is therefore a 4o on the quadric ; the formula for the number of intersections of two curves «« and b^ on a quadric being (oa, bii) = a fi + b a — 2 a 13, the two quartics in question, con- sidered as lying on the quadric, intersect in (42, 42) = 8 + 8 — 8 = 8 points ; but on the cone these quartics are 4i's, and, since they do not go through the vertex, formula (1) gives the total number of their intersections, so that regarding these quartics as lying on the cone they intersect in (4i, 4i) = 4-|-4 — 4=r 4 points. This illustrates what was said (p. 25) in reference to the point of crossing of two curves on a multiple line not counting as a point of intersection of those curves, con- sidered as lying on the surface having the multiple line, when those curves lie on different sheets at this point of crossing. In the present case we have four such points, two on each of the two double or cus- pidal edges on which the apparent double points or cusps lie ; these four points count as points of intersection of the (juartics considered as lying on the quadric, because the quartics lie on the same sheet of the quadric, but they do not count as points of intersection of the quartics, considered as lying on the cone, because these curves lie on different sheets of the cone at these points ; these four points make U[) the difference in the number of intersections that the quartics have on the two surfaces. The "quartic of the first kind" nmy lie on a cone with a tac-nodal edge formed by the union of two double or cuspidal edges ; the i|uar- 68 PROCEEDINGS OP THE AMERICAN ACADEMY. tic then has an apparent tac-node equivalent to two apparent double points. The quartic that lies on the cone having a triple edge, is a " quartic of the second kind ; " for, if it were a " quartic of the first kind," we could pass a quadric through it and through the vertex ; the triple line would then lie on the quadric and be a generator of one system ; the generator of the other system that passes through the vertex would meet the cone four times at the vertex and at least once on the curve, and would there- fore coincide with an edge of the cone ; but an edge of the cone meets the quartic once only, and therefore the quartic would be met by the generators of one system of the quadric once only, and would not be a " quartic of the first kind " as supposed. Every " quartic of the second kind " has three apparent double points (or cusps), and cannot lie on a quartic cone with fewer than three double or cuspidal edges ; two of these may unite, forming a tac-nodal edge, or all three double edges may unite, forming a triple edge ; on the tac-nodal edge the quartic has an apparent tac-node equivalent to two apparent double points, and on the triple edge the quartic has an apparent triple point equivalent to three apparent double points. Through every '"quartic of the second kind " can be passed one and only one quadric, and, if the quartic lies on a cone with a triple edge, the quadric always passes through the vertex ; for, the triple line meets the quadric three times on the quar- tic curve, and therefore lies on it, being a generator of one system of the quadric ; the generator of the other system that passes through the ver- tex coincides with an edge of the cone, as we have seen, and therefore the residual consists of this edge and the triple edge. When the " quar- tic of the second kind" lies on a cone with three double (or cuspidal) edges, the quadric cannot go through the vertex (for if it did all tiiree double or cuspidal edges would lie on it), and the residual is therefore another " quartic of the second kind " because it has an apparent double point (cusp) on each of the three double (cuspidal) edges ; the points of crossing are the same as those of the original quartic, and the curves lie on different sheets at these points. Now, the generators of the quadric meet the cone four times, and, considering one system of generators, they must meet the cone three times on one quartic and once on the other quartic (since every '' quartic of the second kind " on a quadric meets the generators of one system three times and those of the other system once), i. e. on the quadric, one of the quartics is a 4,3, and the other is a 4i ; therefore, considered as lying on the quadric, these quartics inter- sect in 10 points, (43, Aj) — A + 12 — 6 == 10. But on the cone each WILLIAMS. — GEOMETRY ON RULED QUARTIC SURFACES. 59 quartic is a 4i, and these two qiiartics intersect in only 4 points, (4i, 4i) = 4. The six points, two on each double or cuspidal edge, where the branches of the two curves cross, do not count as points of intersection of the two quartics considered as lying on the cone, for the branches lie on different sheets of the cone at these six points, and this accounts for the difference in the number of intersections that the curves have on the two surfaces, — a further illustration of the principle already stated. The different species of twisted quartics that lie on the different cones can be tabulated as follows, where 8 is the number of actual double points, K the number of actual cusps, k the number of apparent double points, k the number of apparent cusps, and T the number of apparent triple points. Quartic Cone. Quartic Curves. Double Edges. Cus- pidal Edges. Triple Edges. First Kind. Second Kiud. S K h k h k T 2 0 0 0 0 2 0 1 1 0 0 0 1 1 0 2 0 0 0 0 2 2 1 0 0 1 2 0 2 1 0 1 0 1 1 1 2 0 1 0 0 2 1 0 0 1 1 1 3 0 0 1 0 2 0 3 0 0 0 3 0 0 1 0 2 0 3 0 0 0 1 0 0 1 5. Salmon* has divided twisted quintics into four groups, viz. group (I), having foiir apparent double points, group (II), having live ap[)ar- * Gconi. of Throe Dimen.si()ii.s, § 352. 60 PROCEEDINGS OF THE AMERICAN ACADEMY. eut double points, and groups (III) and (IV), having six apparent double points. Now, from an ordinary point on any curve of order m, the number of apparent double points of the curve is h — ^?^ + 2,* where h is the number of apparent double points of the curve from an arbitrary point; therefore, since every twisted quintic on a quartic cone has one branch through the vertex, the number of apparent double points from the vertex, i. e. the number of double edges of the quartic cone, is h — 3 > 1 ; moreover, since any twisted quintic can be cut out by a cubic monoid, the six lines of the monoid that pass through the vertex must count for seven, the order of the residual, and therefore the cone has at least one double (or cuspidal) edge with which one of these six lines coincides; therefore there is no quintic curve on the non-singular cone. There is a twisted quintic, which is not a special case of any of the groups given by Salmon, that has only three apparent double points, but it has an actual triple point, where the three tangents do not lie in the same plane, and the quartic cone on which it lies has a triple edge due to this actual triple point. All the quartic cones, except the non- singular cones, have species of twisted quiutics on them, and these may be tabulated in the same way as the twisted quartics. We have seen that any twisted sextic can be cut out by a cubic monoid, and, since the residual is of order six, the six lines of the monoid that pass through the vertex may be six edges of the cone, and therefore the non-singular cone, as well as each of the other cones, may have twisted sextics on it. Any twisted curve of order 7 can be cut out by a quartic monoid which has 12 lines that pass through the vertex, 9 of which may be edges of the cone, forming the total residual, and therefore a quartic cone of any group has on it some species of twisted curve of order 7. For a > 8 we have a > 2 for some species of a^, and therefore when a > 8, a quar- tic cone of any group has on it some species of a^. * Salmon's Geom. of Three Dimensions, § 330, example 2. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVI. No. 4.— July, 1900. ON SUPPOSED MEROSTOMATOUS AND OTHER PALEOZOIC ARTHROPOD TRAILS, WITH NOTES ON THOSE OF LIMULUS. By Alpiieus S. Packakd. PALEONTOLOGICAL NOTES, NO. VI. ON SUPPOSED MEROSTOMATOUS AND OTHER PALEO- ZOIC ARTHROPOD TRAILS, WITH NOTES ON THOSE OF LIMULUS. By Alpheus S. Packard. Presented May 9, 1900. Received May 22, 1900. Trails or tracks evidently made by paleozoic arthropods have occurred most abundantly in the Potsdam sandstone (Cambrian) of Canada and New York, also in the Hudson River or Cincinnati stage of the Ordovi- cian Period. We have now to add descriptions of tracks of a similar nature from the Chemung stage (Upper Devonian) and from the Upper Carboniferous. We will give the name trail to the entire series of foot- prints, and restrict the word track to the individual footprints. The trails discovered by Logan, and carefully described by Professor R. Owen,* were very large, being six inches wide and several feet long, and were evidently made by some large trilobite (as first suggested by Dana) with a caudal spine, as there is a well-marked median furrow. Whether the trilobite was a Paradoxides or not is uncertain, because the species of this genus are without a definite caudal spine, such as is to be seen in Dalmanites and certain other trilobites of a later period than the Cam- brian. But aside from this the tracks, in sets of seven and eight, seem most probably to have been made by an arthropod with numerous pairs of jointed cylindrical legs, such as we now know, through the researches of Walcott and of Beechcr, trilobites possessed. Professor Owen described six species of the tracks, for which he proposed the generic name of Protichnites, but we venture to suggest that it is not improbable that tliey were all made by a single species of trilobite, as observation has t;uight us that Linmlus may make tracks of very dissimilar shape. We would suggest that to trails consisting of sets of several, or as many as * Journal Geolog. Soc. London, VIII. pp. 199, 214. 1852. These trails, Protichnites septem-notnlus Owen, are figured on a reduced scale in Dana's Manual of Geology, Fig. 250; and P. oclonotatus Owen in the new edition of Bronn's Letliaja geognostica. 64 PROCEEDINGS OF THE AMERICAN ACADEMY. 7 or 8, individual tracks, the terra Protichnites be restricted. Logan's Climactichnites wilsoni, six and a half inches wide and thirteen feet long, also from the Potsdam sandstone, which Dana suggested may have been made by a large trilobite,* seems to be such. There is an interrupted median furrow ; the oblique furrows were probably made by the legs, and the lateral furrow bounding the track is much like that made by the cheeks or sides of the head of Limulus. We now come to similar but less comjjlex tracks described by O. C. Marsh, f also from the Potsdam sandstone near Port Kent, N. Y. This trail was about six feet long, and the tracks were separated from each other " by a space of about one and three-fourths inches, and having an extreme width between their outer edges of two and a half inches." In this trail there is no median furrow, no lateral ridge, and here and there are double tracks, as if they were footprints made by a second anterior pair of feet. The track has a decided merostomatous appearance, but was probably made by a trilobite, as there are no Limuloid merostomes known to have existed in the Cambrian, and the track could scarcely have been made by an Eurypterid. The next set of paleozoic trails are those described by Miller and Dyer \ in 1878, in a fine hard shale of the Cincinnati's stage of the Ordo- vician Period at Cincinnati. The originals are in the Museum of Com- parative Zoology at Cambridge, Mass., aud I am indebted to Dr. R. T. Jackson for the privilege of examining them. One of them is similar to that described below from Providence, but the trail is twice as wide, and the tracks not so wide. They were perhaps made by a trilobite ; there is no median furrow, or lateral ridges. § The trails of Limulus j^olyphemus. — Figs. 1, 2 (one-third natural size). The trail made by this merostome has been described and figured by the late Sir J. W. Dawson in the Canadian Naturalist, VII. p. 271. He gives three interesting figures of the trails left by a single small Limulus four inches wide on a sandy shore. In each of his figures the median furrow is distinct, but the lateral marks are furrows " with slight ridges exterior to these," while my example left only a ridge. The * Manual of Geology, p. 189 (first? edition), Fig. 259. t Araer. Journ. Sc. and Arts, XLVIII. July, 1869. Plate. \ Journ. Cincinnati Natural History Society, 1878. § The trails figured by Emmons (Agriculture of New York, I.) as Nereites jach- soni pipgnus and loomisii, appear to be Annelid trails, and none of those figured by James Hall (Paleontology of New York, II. Pis. 13-lG) seem to have been made either by trilobites or merostomes. PACKARD. — PALEOZOIC ARTHROPOD TRAILS. 65 footprints were slightly oblique series of four punctures, or pits, " deepest behind, in which the four marks left by the nails of the posterior feet were most prominent, and sometimes the only marks seen." FiGUKE 1. Figure 2. " When the Limulus creeps on quicksand, or on sand just covered with water, so that its body is partly water-borne, it appears principally to use its ordinary walking feet, and the footprints then resolve them- selves into a series of longitudinal scratches after the manner of Protich- nites I meatus" . . . " When placed in shallow water, just covering the body, the creature used its flat abdominal swimming feet, and though the impression made was very faint, and not readily observed under water, it was obviously very different from those before mentioned, agreeing with them only in the lateral and median grooves, while between these were series of fur- rows extending obliquely from each side of the middle groove, and re- VOL. XXXVI. — 5 66 PROCEEDINGS OF THE AMERICAN ACADEMY. sembling ripple marks (Fig. 3). These were produced by the sand swept up by the swimming feet." Dr. Dawson then compares the trail represented by his Fig. 3 with Logan's Climactichnites, and they are remarkably similar, except that the oblique furrows made by the legs between the median and lateral ridges are directed in the reverse direction. Of the tracks afterwards described and figured by Dr. Dawson * from the upper Carboniferous of Nova Scotia, none seem to me to be referrible to trilobitic or merostomatous trails. Protichnites carbonarius, as already remarked in these Proceedings, f appear to have been made by a crusta- cean, and we have referred them to a distinct genus, Ostrahiclmites. Some years ago I made some experiments with small Limuli by placing one in a shallow tin pan, in which the sand was about half an inch deep, and the water not deep enough to entirely cover the body. The animal, so far as I can now remember, used its ambulatory feet in walking, while the swimming or abdominal legs were partially used. The result may be seen in Fig. 1. The king-crab was about four inches (10 cm.) in width. The trail it made consisted, besides the tracks themselves, of an outer ridge made by the outer edge of the head or carapace ; this ridge (d) was about 15 mm. in width, and was due to the heaping up of the fine sand ; in section it would be low conical ; one would suppose that the action of the edofe of the head would make a furrow rather than an ele- vated ridge. The tracks (t) were opposite, and quite regularly concavo-triangular, the apex of the triangle rounded, and directed backwards, the sand being pushed slightly up on the jDOSterior edge of the track. The tracks of each side were directly opposite each other, and those of each pair directly in line with those of the pair in front. It was noticed that the distance apart of the tracks varied with the rapidity of the half- walking, half-swimming movements of the animal. It was seen that the tracks were made by the hindermost, or sixth pair, of limbs only, no im- pression being left in the sand by the feet in front. The triangular shape of the track was due to the spreading out of the two spatulate spines of the last segment of the leg. It should be observed that the distance apart, outside measurement, of the tracks is about two-thirds that of the entire trail. * Impressions and footprints of aquatic animals and imitative markings on carboniferous rocks. Amer. Journ. Sc. and Arts, 3d Series, V. Jan. 1873, pp. 16-24, Figs. 1-5. Also Acadian Geology, 2d edit. Supplement. 1878. t XXXV. AprU, 1900, p. 403. PACKARD. — PALEOZOIC ARTHROPOD TRAILS. 67 The four narrow furrows (f) intersecting the tracks were made by the lateral abdominal spines, which are bent down and trail in the mud or sand when the animal is walking or moving over the bottom. The large, deep, median furrow (c) was made by the caudal spine ; it was continuous, uninterrupted, during the continuous forward movements of the animal. Another trail is represented by Fig. 2. It will be seen that it pre- sents no resemblance to the other. Unfortunately I did not make any notes as to the relations of the animal to the bottom. So far as I can remember it was a smaller individual, and probably it moved rapidly. The indentations on the margin of the trail were evidently made by the feet, while the series of median furrows were made by strokes of the caudal spine. The trail was 3.50 cm. wide, 2Vie tracks of living terrestrial Isopod Crustaceans. — Fig. 3. In this connection it was interesting to ascertain the nature of the tracks made by Crustacea so much like trilobites in general shape as our terrestrial Isopods. One of our common Armadillo was cap- • , tured, its feet inked, and it was then set free and allowed to ' ' " make tracks " on a sheet of paper. It will be remembered that the Isopods have seven pairs of ambulatory legs, the . » extremities of which end in a single sharp point. The width • of the body is from 4 to 5 mm. It was noticed that the ' ' crustacean in running put down the feet of each pair at the . , same time, and that the legs, and especially the pointed ex- ' • tremities, were perpendicular to the surface over which it ' " ran. '. . The trail thus made was a very simple one, being a double ' row of slightly elongated dots, the individual tracks of each pair being exactly opposite to each other, as seen in the figure. • . When the feet dragged the dots became lines. The trail is t^ ^„ o ^^ rIGURE o. also nearly of the same width as the body itself, though a little narrower rather than wider. A specimen of our common Porcellio scaher was also compelled to undergo similar treatment and like evolutions with the same result. The trail differed in no essential respects from that of the other Isopod. It will be of much interest to experiment with macrurous and brachyu- rous Crustacea, in order that the results may throw light on the numerous tracks in the Triassic beds of the Connecticut Valley described by Hitch- cock in his " Ichnology." Merostomichnites beecheri n. sp. Fig 4. This trail is in a fine shaly sandstone of the Chemung beds at Warren, Pa. It covers an area 68 PROCEEDINGS OF THE AMERICAN ACADEMY. 3 cm. long and about 9 mm. wide. It is straight and short. The individual tracks are opposite each other, as in those of Limulus. The animal must have leaned more to the right side, as the tracks on this side are larger, deeper, and much more perfect than on the left side. The most perfect ones are in shape ajraost exactly like those made by Limulus when half walking and half swimming in very shoal water. A typical track may be described as forming a low triangle, the apex pointing backward ; it is hollow, the interior forming a hollow triangle surrounded by a raised ridge. There are six pairs of tracks, with traces of a seventh. The width of the trail is 9 mm., but probably if the entire trail were perfect on the left side it would have measured about 10 mm. in width. The tracks are opposite to each other. The largest and best marked individual track is 5-6 mm. wide and 3 mm. deep (or long) from in front to the apex or hinder part. The tracks of each pair are very near to each other, and those in the front part of the trail tend to be united into a simple trans- verse ridge. There are no secondary tracks in between the others, and in this respect the track differs from that of M. narragansettensis, and resembles that of Limulus. The original of this track is in the paleontological collection of the Peabody Museum of Yale University. I am indebted to the kindness of Professor C. E. Beecher, the curator, who did me the favor to send me an excellent cast, from which the above description has been made. Professor Beecher informs me that in the beds of the Chemung group at Warren, Pa., there are no remains of trilobites ; and he expressed his belief that the tracks were those of some merostome. It is to be observed that there is no median furrow or trail made by a tail or caudal spine, and no furrow or ridge made by the edge of the body or carapace. The merostome which made it most probably had no caudal spine. And yet the tracks are otherwise very similar to those of Limulus. It may be observed that all the Eurypterida are provided with a telsou, either broad or narrow and spine-like, and their trails would evidently include a furrow made by such a spine. The Limulidae were represented in the Devonian by Protolimulus eriensis Williams (" associated with typical Chemung fossils"). Was this track made by a young individual of this genus, with the caudal spine too short to make a trail ? If not, was it made by a Bunodes, which lived in the Upper Sihirian of Europe, but has not yet been discovered in America, and had no caudal spine ? But Bunodes vyould perhaps have left a lateral furrow made by the broad thin edge of PACKARD. — PALEOZOIC ARTHROPOD TRAILS. 69 Figure 4. FiGUltE 5. 70 PROCEEDINGS OF THE AMERICAN ACADEMY. its elliptical body. The trail seems to indicate the occurrence of a mero- stome of a group not represented by any known fossil genus, unless it should prove to be a young Protolimulus. Merostomichnites narragansettensis (Pack.). Fig. 5. Proc. Amer. Acad. Arts and Sci. XXXV. No. 20, April, 1900, p. 402. Three trails of this species were discovered by a member of my geological class, — Mr. H. H. Mason, of the class of 1900, — and kindly given to me, while doing field work under my direction in Providence, R. I., just north of the city and of the North Burying Ground. The trails occurred in a rounded pebble of dark arenaceous shale picked up from the mass of water-worn gravel and boulders constituting the body of a large rounded kame. It was split in two, so as to show the impressions and the relief of the tracks. The subglacial deposits at this point are derived from a region a few miles a little east of north, probably in the vicinity of South Attleboro, though I have not seen beds of this peculiar blackish sandy shale in place. There are three trails, — one separate, and the two others crossing each other. The long separate series is nearly straight, 6.50 cm. in length ; the other trail is sinuous, and is crossed by a third, shorter trail. The width of each trail is the same, being about 12 mm. outside meas- urement. The distance between the individual tracks of the same pair is about 9 mm., that between the footprints on the same side varies from about 2 mm. to about 4 mm. The tracks are opposite and not alternate. Along most of the length of the trail there is but a single series of tracks on a side, but in portions of the entire trail the footprints are double, there being an inner and an outer set on each side. If we select four of the tracks in a place where they are double, it will be seen that they are arranged in a very low trap- ezoid ; while the space between the two outside tracks is 9 mm., that between the two inner, a little in advance, is 5 mm. The individual tracks forming the trails are of quite uniform shape, the best marked ones being transversely oval or crescentic in outline, the mud having been pushed back by the animal's feet so as to leave a cres- centic ridge, the concavity pointing forward. The size of the impression in transverse diameter is about 3 mm., the longitudinal diameter 1.5, i. e. the tracks are about twice as broad as long. Thus they are not linear, and more or less parallel to the main series of tracks, as in those referred to the decapod Crustacea. In two or three cases the tracks are connected by a slight ridge curved forward in the direction the animal moved. PACKARD. — PALEOZOIC ARTHROPOD TRAILS. 71 While these tracks are certainly not Isopod tracks, they with still more certainty canuot be referred to impressious made by the feet of insects, vvliicli are always alternate, as in hexapod insects the legs of each pair are raised and put down alternately. The Providence carboniferous tracks were evidently made by an arthropod of the same group as Limulus, as the. tracks are opposite, and in general shape like those of Limulus, as may be seen by Fig. 1. The present tracks differ from those of Limulus in the absence of a caudal spine trail-mark, and in the fact that an additional anterior pair of feet made impressions. Trilo- bites are not known to exist in our Upper Carboniferous associated with Limulus. Limuloids of the genus Prestwichia with a short caudal spine exist in considerable numbers in tlie Upper Carboniferous of Mason Creek, Illinois, and in the Upper Carboniferous beds of Pennsylvania, though from a horizon hiirher than that of the Mason Creek beds. As the genus Belinurus has a very long caudal spine, and there are no traces of a median furrow in our trails, that genus should be ruled out as the author of these tracks. Now the adult Prestwichia is about two inches in diameter and its caudal spine nearly half an inch in length. It is, however, well known that in the freshly hatched Limulus, and even after the first moult, and wlieu the creatures are half an inch in diameter, the caudal spine is very short, too much so, probably, to leave a trail or median furrow. The Providence trails are considerably less than half an inch in diam- eter, and reasoning by analogy, and also in part by exclusion, it seems not impossible that these trails are the footprints of a young Prestwichia a little less than half an inch in diameter, with too short a caudal spine to leave a furrow. This conclusion is interesting as suggesting the occurrence of these Limuloids in the Narragansett basin during the later part of the Carbon- iferous Period. These tracks are so similar to those of the Chemung beds above described that they were probably made by Merostomes of the same family or genus, and may be referred to Merostomichnites rather than to Protichnites. The possibility tliat these trails could have been made by an Eurypterid seems excluded by the absence of a median furrow, or of any prints made by the large paddles of the hind feet, or by the paddles and chelae of the first pair of feet of such a form as Pterygotus. Bkown University. Proceedings of the American Academy of Aits and Sciences. Vol, XXXVI. No. 5. — July, 1900. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. CERTAIN DERIVATIVES OF METADIBROMDINITROBENZOL. By C. Loring Jackson and W. P. Cohoe. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. CERTAIN DERIVATIVES OF METADIBROMDINITRO- BENZOL. By C. Lorixg Jackson and W P. Cohoe. Presented December 13, 1899. Received June 4, 1900. The dibromdiuitrobenzol melting at 11 7°. 4 was made by Korner in his classical research on Isomerism of the Aromatic Compounds with Six Atoms of Carbon,* but its constitution has not been determined with certainty, Nietzki and Schedler f in a recent paper have proved that the dichlordinitrobenzol melting at 103° has the structure C]2l.3.(N02)2 4. 6, and as this substance is made from the action of fuming nitric acid on metadichlorbenzol, just as the dibrom compound is made from metadi- brombenzol, there is good reason to believe that they have the same constitution ; but we thought it necessary to prove that this was the case before we studied this dibromdinitrobenzol further. For this purpose we heated the substance with aniline, and obtained the dianilidodinitrobenzol melting at 186°, which Nietzki and Schedler had obtained from their dichlordinitrobenzol ; the dibrom substance therefore has the structure Br„ 1. 3. (NO.,)., 4. 6. If aniline acted on the dibromdinitrobenzol in the cold, a bromauilidodinitrobenzol, CcFLBrCellsNP^NOi)^, melting at 157° was obtained, and this occurs in a yellow and in a red modification which seem to differ in crystalline form as well as in color. This seems to be a case of dimorphism, as the two forms pass into each other with great ease. The yellow form is converted into the red by crystallization from benzol, the red into the yellow by heating to 135°. Similar phe- nomena have been observed in the cases of anilidotrinitrophenyltartronic ester I and trianilidodinitrobenzol. § * Gazz. Chim. 1874, 305. t B,er. rl. chem. Ges,, XXX. 1006 (1897). X -I.ickson and Bentley, Tliese Proceedirifrs, XXVI. 83. § Jackson and Herman, Ibid. XXVII. 2u3. 76 PROCEEDINGS OF THE AMERICAN ACADEMY. After the coustitutiou of the 1. 3.4. 6 dibromdinitrobenzol had been determined, we studied the action of sodic ethylate upon it, in the hope of encountering the replacement of bromine by hydrogen uuder the action of this reagent, which has been studied for some years in this Labora- tory. But no such behavior was observed ; the action ran iu the normal way, resulting in the formation of the diuitroresorcine diethylether melt- ing at 133", discovered by Warren and one of us,* and proved to have the symmetrica] structure by Koch and one of us t ; so that this observa- tion confirms the determination of the constitution of this body by the action with aniline. Sodic phenylate converted the dibromdinitrobenzol into diphenoxydi- nitrobenzol, which melts at 129°. The action of sodic malonic ester was tried on this compound to determine whether the phenoxy groups could be replaced by the malonic ester radical CH(COOC2H5)2 ; as it has been found t that the best way to make dichlordimalonicesterquinone CgCL[CII(COOC2H5)2].202 is by treating dichlordiphenoxyquinone with sodic malonic ester, and we wished to see whether the nitro groups would produce the same effect as the oxygen atoms of the quinone in promoting the replacement of the phenoxy groups by malonic ester radicals. We found that phenol was eliminated when the diphenoxy- diuitrobenzol was treated with sodic malonic ester, and from the very unmanageable product a sodium salt was obtained which contained an amount of sodium corresponding to CeH.,OC6H5CNa(COOC2H5)2(N02)2 ; so that we feel justified in assuming that the reaction has consisted in the replacement of the phenoxy by tlie malonic ester group. The dibromdinitrobenzol, when reduced with zinc dust and acetic acid, gave a dibrommetaphenylene diamine, wliich was identical with that melting at 135° obtained by the action of bromine on metaphenylene diacetamid. § It follows from our preparation of this base that it has the constitution Brg 1. 3. (NH2)2 4. G. In all this work we have been careful not to approach too near to the field reserved by Nietzki and Schedler in their paper on dichlordinitro- benzol. * These Proceedings, XXV. 170. t Ibid. XXXIV. 134. t Jackson and Grindley, Ibid. XXX 425. § Jackson and Calvert, Ibid. XXXI. 150. JACKSON AND COHOE. — METADIBROMDINITROBENZOL DERIVATIVES. 77 Preparation of Metadibromdinitrobenzol. Monobromacetanilid was first made by passing a stream of air laden with the vapor of bromine through five litres of water in which fifty grams of acetauilid were suspended. The end of the reaction was determined by tlie appearance of a lasting yellow color in the liquid and a distinct change in the appearance of the solid. In all our attempts to convert this 2)roduct into the dibromacetanilid by the action of liquid bromine on it when suspended in water, we observed the formation of a considerable amount of symmetrical tribromaniline (NHg 1. Brg 2. 4. G.), produced un- doubtedly by the action of bromine on the free base proceeding from the saponification of some of the bromacetanilid by the hydrobromic acid formed in the reaction. The monobromacetanilid was accordingly filtered out, and after being dried, suspended in glacial acetic acid or chloroform, to which a little more than the calculated amount of bromine was then added drop by drop. This method gave an excellent yield of the dibromacetanilid with little trouble. The dibromacetanilid was saponified by boiling it with sulphuric acid of specific gravity 1.44 in a flask with a return condenser, until the solu- tion of the solid, which was usually accompanied by a darkening in color, showed that the reaction was complete. The liquid was then allowed to cool, when most of the dibromaniline crystallized out, and what remained in solution was precipitated by the addition of a large quantity of water. To remove the amido group, 100 grams of the dibromaniline were dissolved in a mixture of 300 c.c. of alcohol and 120 c.c. of benzol, to which 20 c.c. of sulphuric acid had been added ; the mixture was heated in a flask on the steam bath, and 60 grams (a large excess) of solid sodic nitrite added as fast as the reaction would permit. The contents of the flask, which had taken on a reddish color, were boiled for an hour, and then allowed to stand over night, after which a large quantity of water was added, and the precipitated oily liquid distilled over with steam. A small amount of tribrombenzol is usually present, which appears as a solid in the condenser toward the end of the distillation with steam ; it is well to stop the distillation as soon as this solid appears. The distillate with steam was dried with calcic chloride and distilled, collecting for use the fraction boiling from 210° to 225°. A small additional amount of dibrombenzol was obtained by extracting with ether the aqueous portion of the steam distillate, but the increase of the yield in this way was so small that this extraction was hardly worth while. The dibrombenzol was converted into dinitrodibrombenzol by boiling 78 PROCEEDINGS OF THE AMERICAN ACADEMY. it with fuming nitric acid of specific gravity 1.52, or better a mixture of this acid and sulphuric acid. As soon as the oil had dissolved in the acid, the reaction was complete ; the boiling was stopped, and the prod- uct precipitated by pouring the acid lic^uid into a large quantity of cold water. The yellow crystals thus obtained were purified by crystallization from alcohol, until they showed the constant melting point 117°. Detebmination op the Constitution of Metadibromdinitro- BENZOL BY THE ACTION OF AnILINE. Two grams of the dibromdinitrobenzol melting at 117° were heated with an excess of aniline on the steam bath for half an hour. At the end of this time the excess of aniline was removed by treatment with dilute hydrochloric acid, and the ^^ellovv residue, after being washed thor- oughly with water, was recrystallized from a mixture of alcohol and benzol until it showed the constant melting point 185°, which is essen- tially identical with 186°, that of the dianilidodinitrobenzol prepared from dichlordinitrobenzol by Nietzki and Schedler.* As they established the constitution (NHC6H5)2 1. 3. (N02)2 4. 6 for this body, the dibrom- dinitrobenzol belting at 117° must have the corresponding structure Bra 1. 3. (NOo), 4. 6. Action of Aniline on Symmetrical Dibromdinitrobenzol in THE Cold : Bromanilidodinitrobenzol. Two grams of the dibromdinitrobenzol cooled by a freezing mixture were moistened with aniline, and the mixture was allowed to stand packed in ice for twelve to eighteen hours. The excess of aniline was then removed by dilute hydrochloric acid, and the dense yellow residue, after thorough washing with water, was purified by crystallization from alcohol and benzol until it showed the constant melting point of 157°> when it was dried at 100°, and analyzed, with the following result: — I. 0.0994 gram of the substance gave by the method of Carius 0.0558 gram of argentic bromide. II. 0.2138 gram of the substance gave 0.1229 gram of argentic bromide. Calculated for Found. C6H2BrC,5H5NU(N02)2 I. II. Bromine 23.67 23.89 24.46 * Ber. d. chem. Ges., XXX. 1G68 (1897). JACKSON AND COHOE. — METADIBROMDINITROBENZOL DERIVATIVES. 79 Properties of Bromanilidodinitrobenzol, CoHoBrCoH5NH(N02)2(Br 1. CeH^NH 3. (N0o)2 4. 6.). This substance crystallizes from a mixture of benzol and alcohol, sometimes in much modified short and thick flat prisms apparently of the monoclinic system, resembling certain crystals of felspar ; at other times in rhombic plates occasionally with some of the angles slightly bevelled, which pass into forms like rhombohedra ; all of these crystals have a full golden yellow color. Other crystals were distinguished from these by their brilliant red color and by appearing in square prisms modified on one of their angles or on two opposite angles. From these two colors, red and yellow, and the difference at least in crystalline habit, if not really in crj-stalline form, we infer that the substance appears in two closely related modifications. The yellow form, in which the substance is obtained from its preparation, becomes gradually converted into the red by crystallization from a mixture of alcohol and benzol, but several crystallizations are necessary to make this conversion complete. If, however, the yellow form is dissolved in benzol alone, the solution deposits, as it evaporates, a red oil, which on stirring solidifies to the red crystals. All the other common organic solvents except the alcohols also convert the yellow into the red form by a single crystallization. On the other hand, if ihe red crystals are heated in an air bath, they begin to assume a yellow color at 110°, and are completely converted into the yellow form at 135° ; this conversion is attended with no change in weight. The substance melts at 157°, forming a red liquid, which, when cooled and stirred, solidifies to the yellow modification. It is obvious that the melting point given above is that of the yellow form, since the red is converted into the yellow at 135°. The bromanilidodinitrobenzol is freely soluble in benzol; soluble in toluol or chloroform ; slightly sol- uble in ether, acetone, amyl alcohol, or hot ethyl alcohol. The best solvent for it is a mixture of benzol and alcohol. Determination of the Constitution of Metadibromdinitro- BENZOL BY TREATMENT WITH SoDIC EtHYLATE. One gram of the dibromdiuitrobenzol melting at 117° was mixed with an excess of sodic ethylate prepared by the action of sodium on a consid- erable excess of absolute alcohol, and after the mixture had stood for some time at oi'dinary temperatures, the excess of alcohol was allowed to evaporate spontaneously. The residue, after repeated washings with 80 PROCEEDINGS OF THE AMERICAN ACADEMY. hot water, was purified by crystallization from a mixture of ligroin and benzol, when it was found to melt at 133°, the melting point of the dinitroresorcine diethylether discovered by Warren and one of us,* which it also resembled in crystalline form. As Koch and one of us f have 2^roved that this dinitroresorcine diethylether has the constitution (00113)2 1. 3. (N02)2 4. 6, it follows that the dibromdinitrobenzol melt- ing at 117° has the constitution Br^ 1. 3. (N02)2 4. 6, — a result which confirms that already obtained from the action of aniline. Action of Sodic Phenylate with Symmetrical Dibromdinitro- benzol. The sodic phenylate for this experiment was prepared by adding five grams of powdered sodic hydi'ate to enough melted phenol to make a pasty mass. While this was still in the viscous state, five grams of the dibromdinitrobenzol were added little by little with constant stirring, the beaker containing the mixture being kept cool with ice water. The product, a dark brown solid mass, was treated with water, filtered, and the insoluble portion recrystallized either from slightly dilute alcohol, or from a mixture of benzol with a large excess of ligroin, until it showed tlie constant melting point 129°, when it was dried in vacuo, and ana- lyzed, with the following results : — I. 0.2494 gram of the substance gave on combustion 0.5563 gram of carbonic dioxide and 0.0903 gram of water. II. 0.3746 gram gave on combustion 0.8457 gram of carbonic dioxide. The water was unfortunately lost. Found. II. 61.59 Calculated for I. Carbon 61.38 60.82 Hydrogen 3.41 4.02 The method of making sodic phenylate given above was adopted because in alcoholic solution the sodic phenylate gave principally the dinitroresorcine diethylether, and in aqueous solution there was no action until high temperatures were reached, and then the yield was unsatis- factory. * These Proceedings, XXV. 170. t Ibid., XXXIV. 134. JACKSON AND COHOE. METADIBROMDINITROBENZOL DERIVATIVES. 81 Properties of the Dinitroresorcine Diphenylether, C,lh(OC,U,),(N0.2)2.({OC,U,\ 1. 3. (NOa). 4. 6.). This substance, when crystallized from a mixture of benzol and alco- hol, forms slender white prisms terminated by one slanting plane, or, when better developed, by two planes meeting at a very obtuse angle and modified by several smaller ones, so that a blunt end is formed. It melts at 129°. It is freely soluble in benzol; soluble in cold toluol or chloroform, or in alcohol, ligroin, or acetone when these solvents are hot; slightly soluble in ether or amyl alcohol. The best solvent for it was either dilute alcohol, or ligroin containing a little benzol. Some experiments were tried to determine whether the phenoxy groups in the diphenoxydinitrobenzol could be replaced by malouic ester radicals (CH(COOC.2H5)o), as a replacement of this sort had been ob- served in the case of dichlordiphenoxyquinone.* The solid diphenoxy- dinitrobenzol was dissolved in an alcoholic solution of sodic malonic ester, and the mixture allowed to stand at ordinary temperatures over night; afterward it was treated with dilute sulphuric acid, which precipitated an oil, and showed that phenol had been set free by the strong smell of this substance. The oily precipitate, after washing with water, was extracted with ether, which removed from it a pale yellow oily substance ; but as this did not solidify even after standing for several months, we tried to determine its nature by the analysis of a salt. A specimen of the oil was dissolved in alcohol and treated with an aqueous solution of sodic hydrate, which threw down a briglit red precipitate; this was washed with benzol, dried in vacuo, and analyzed, with the following results : — I. 0.1383 gram of the substance gave 0.0191 gram of sodic sulphate. II. 0.1476 gram of the substance gave 0.0228 gram of sodic sulphate. Calculated for Found. C6H,(N02)jOCoU5CNa(COOC2H5)2. I. II. Sodium 5.23 4.47 5.01 The results of these analyses, in connection with the elimination of phenol, prove that the reaction has run as was expected. The phenoxy- dinitrophenylmalonic ester separated from the salt as an oil, and there- fore we did not think it worth while to attempt a more careful study of it. * Jiickson anil Grindley, Tlicsc Proceedings, XXX. 425. VOL. XXXVI. — G 82 PROCEEDINGS OF THE AMERICAN ACADEMY. Reduction of Symmetrical Dibromdinitrobenzol with Zinc Dust and Acetic Acid. Twenty grams of zinc dust were placed in a flask fitted with a Bunsen valve and connected with a carbonic dioxide generator, acetic acid of eighty-five per cent was added, and then five grams of the dibromdinitro- benzol in small portions at a time, as under these conditions the reaction ran quietly and smoothly, although accompanied by blackening in every case. The reduction was carried on at first in the cold, but toward the end of the operation the mixture was heated gently on the steam bath. After two hours the reaction was complete, when the insoluble portion was filtered out, and extracted with dilute alcohol, which upon cooling deposited crystals melting even in the crude state at 131°. The filtrate from the insoluble reduction products was treated with an excess of sodic hydrate sutficieut to dissolve the zinc salts, the precipitate formed in this way filtered out, and extracted with hot dilute alcohol, which gave an- other portion of the crude product melting at 131°. After purification by crystallization from alcohol the melting point became constant at 134° ; it was dried in vacuo, and analyzed with the following result: — 0.1407 gram of the substance gave by the method of Carius 0.1976 gram of argentic bromide. Calculated for C6HoBr2(NH2),. Found. Bromine 60.15 59.78 This dibromphenylene diamine melts essentially at the same point ( 1 35°) as that prepared by S. Calvert and one of us * from metapheny- lene diacetamide and bromine. It also crystallizes like this in white needles, which turn brown on exposure to the air. As the constitution of our dibrorabinitrobenzol is Bro 1.3. (NOo).. 4. 6, it follows that this dibrommetaphenylene diamine must have the corresponding constitution Brol.S. (NH2)o'4. 6. * These Proceedings, XXXI. 150. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVI. Ho. 0. — August, 1900. ON THE CONTINUITY OF GROUPS GENERATED BY INFINITESIMAL TRANSF0R3IA TIONS. By Stephen Ei,mek Slocum. ON THE CONTINUITY OF GROUPS GENERATED BY INFINITESIMAL TRANSFORMATIONS. By Stephen Elmer Slocum, Fellow in Mathematics, Clark University, Worcester, Mass. Preseuted by Uenry Taber, May 9, 1900. Eeceived June 20, 1900. § 1. The publication of the results of Professor Sophus Lie's investigations in the theory of finite continuous groups, embodied in papers appearing from 1870 to 1898, chieily in the " Archiv for Mathematik og Naturvi- denskab" and the ''Forhandliugar i Videuskabs Selskabet i Christiania," and the systematic presentation of his theory in six large volumes, pub- lished during the years 1888-1893, opened to mathematicians a new and exceedingly rich field of investigation. As a creator and pioneer in this field. Professor Lie's aim was to outline his theory as broadly as possible, not stopping to obtain entirely rigorous demonstrations of his theorems ; and it is not surprising to find that certain of these theorems, and of the fundamental conceptions of his theory, require modification. Thus it appears from a discovery of Study's, mentioned below, that the chief tlieorem of Lie's theory holds, in general, only in the neighborhood of the identical transformation, and, as a consequence of this fact, that the con- ception of isomorphism, as developed by Lie, requires modification. The chief theorem of Lie's theory is that r independent infinitesimal transformations,* whose symbols are n g ■^i = 2^ t,ji {Xi . . . X„) 71 1 d X^ {{=1,2 .. . r) (where the ^'s are analytic functions of ?i independent variables a*i . . . x„) generate an r-parameter (r-gliedrige) group, in which each transformation * Lie terms the symbols of infinitesimal transformation X-^ . . . Xr independent if the I's satisfy no linear homogeneous relations of the form ei hi {x)+ . . . + e.. Ii, (x) = 0 simultaneously for i = 1, 2 . . . n, with coefficients e independent of the x's. 86 PROCEEDINGS OP THE AMERICAN ACADEMY. is generated by an infinitesimal transfornaation of the group, if and only if the Xi , . . X,. fulfil relations of the form where (Xj, X^ denotes the alternant X^ X^ — X^. Xj, and the coefficients Cj^s ^'*e quantities independent of the x's.* In Volume XXXV. of the " Proceedings of the American Academy of Arts and Sciences," jip. 239 et seq., 1 pointed out an error in the demon- stration of what Lie calls the first fundamental theorem,! upon which he bases the demonstration of his chief theorem. This error consists in neglecting conditions imposed at the outset upon certain auxiliary quan- tities [xi, ,U2 • • • Mr? introduced in the course of the demonstration. Thus in the " Continuierliche Gruppen," pp. 372-376 (and substantially in "Transformationsgruppen," III. pp. 558-564), Lie proceeds as follows: Being given at the outset a family with an 00"" of transformations 7\, de- fined by the equations X ^ ^=^ Ji \pCit • • • x„, cii , . . . cf,.j {1 = 1,2. . . n), containing the identical transformation, and such, moreover, that the x"s satisfy a certain system of differential equations, he defines by the intro- duction of new parameters /x a family of transformations ^ij_, X i =^ J*i{X I, . . . X ^, ^i, . . . fl^J {i = \,2. . . n), each of which is generated by an infinitesimal transformation. Lie then establishes the symbolic equation * Transformationsgruppen, III. 590; Continuierliche Gruppen, 211, 305, 390. t Transformationsgruppen, III. 503; Continuierliche Gruppen, 376. I If the equations defining tlie families of transformations 7',, and E^ are, respectively, x'.=/^{t, . . . x^, a, . . . a^) (; = i,2 . . . »), and x'.= F.rx\ . . . .r , Ml ■ • • M,.) {■, = 1,2 .. . n), the symbolic equation T^ E^ = T,^ is equivalent to the simultaneous system of equations SLOCUM. — FINITE CONTINUOUS GROUPS. 87 where the a's and /x's are arbitrary, and «-t = ^k (P-l • ■ ' H-n «i . . . Ctr) (X; = 1, 2 . . . r), the $'s being independent functions of the /x's. For (0) «i = «fc (i = 1, 2 . . . /■), the transformation Ta becomes the identical transformation ; and there- fore we have E = T((,)£J = T * where a* = 'Pi C/^l • • • A'rj «1 • . . «r ; (i- = 1, 2 . . . r). Thus every transformation of the family E^ is a transformation of the family T„. If, conversely, we could show that, for arbitrary values of the a's, every transformation T^ belonged to the family E^, it would follow that T, T^ = 7:„t that is to say, we should then have shown that the family of transforma- tions T^ forms a group. But, although the $'s are independent functions of the /a's, nevertheless the fx's in certain cases may be infinite for certain systems of values of the a's ; and infinite values of the /a's, by their definition, are excluded 5',=/i(^i . . . x^,di . . . a.), x'. - F^{x\ . . . x\^. Ml . ■ • M,.), (, r= 1, 2 . . . «), x'^=.f^{Xl . . . T^.ai . . . a^), or, to the functional equations F.(/, (x.a) . . ./Jx, a), mi • • • M,.) ■=f^(xx . . . x^.a-^ . . . a^) (; = 1. 2 . . . «)■ * That is, F.(Fi . ..x\, Ml . ■ . M,) = -f'tC/i (r, «'"') . . •/„ (x, a" ), Mi . ■ -M,.) -/j Ci'i . • • x ^, ai . . . u^.l (/ = 1, 2 . . . „), since J'. = /". (r, . . . x , rt, . . . a ) (/ = 1, 2 . . . «)• t That is /, (/i (■^. a) • • ■ /„ (-r, a), a, . . . a.) = /, (.ri . . . x^ , c/j . . . a,.) (, = 1, 2 . . . »). 88 PROCEEDINGS OP THE AMERICAN ACADEMY. at the outset* We cannot then assume that every transformation T^ belongs to the family E . We may, however, proceed as follows : For all values of the a's for which the functions ^x.^ = M^ (ai . . . a^, cti'*^- . • • a,-*"') 0 = 1> 2 . . . r) are finite, we have that is, /C/i(^5 «) • • -Ink^, »), ai . . . a,) = Fii^fi (x, a) . . . f„(x, a), ^j . . . /x^) (i = 1, 2 . . . n). Let /?!, ySo . . . be a system of values of the a's for which one, or more, of the corresponding yw's is infinite. Also let b^, bi . • . be the system of values assumed by the a's for a^. = /Sj. (^-=1,2... r). Since the functions / are continuous functions of the variables and parameters, and since we assume that the system of parameters /3 give a definite transfor- mation T^ of the tamily, we have fi C/i (^, a) • • ' fn (x, (i), ^1 • . • /S,) = ^'in- fi (/i {^> «)•••/« (^, «)> «! ' . • a,) = lim. /, (xi . . . x„, Ui . . . a,) =f^(xi... x„, b^ - . . b,) a z= h (1 = 1,2 .. . n), which is equivalent to the symbolic equation n T', = T, lim. T; = lim. T, T; = lim. T„ = T,. Consequently, the composition of two arbitrary transformations T- and Tp of the family is equivalent to a transformation T/^ of this family ; that is to say, the family of transformations 7^„ forms a group. The transfor- mation 7)^, however, may not be a transformation of the group that can be generated by an infinitesimal transformation of the group. Thus, every transformation of a group with continuous parameters and con- taining the identical transformation is not necessarily generated by an infinitesimal transformation of the group.f Professors Study and Engel were the first to point this out, and thus establish a distinction between a group with continuous parameters and a continuous group. J They found that not every transformation of the * These Proceedings, XXXV. 247. t Tliese Proceedings, XXXV. 483-485. I Engel : Leipzigcr Bericl)te, 1892. SLOCDM, — FINITE CONTINUOUS GROUPS. 89 special linear homogeneous group can be generated by an infinitesimal transformation of the group, and consequently this group is not properly continuous in the sense in which Lie uses the term. Since this impor- tant discovery, the subject of continuity has been investigated for the case of the general linear homogeneous group and its sub-groups, as well as for various other groups, by Professor Taber and his pupils, and from a geometrical standpoint by Professors Newson and Emch. * This paper contains an investigation of the relation of the continuity of a group generated by infinitesimal transformations to its structure {Zusammensetzung)^ and the classification of all possible types of structure of complex groups with two, three, and four parameters with reference to the continuity of groups of these types. All possible types of groups with two, three, and four parameters can be divided into three classes. Every group is continuous whose structure is of a type belonging to the first class ; every group is discontinuous whose structure is of a type drawn from the second class ; and of the groups whose structure is of a type belonging to the third class, some are continuous and some are discontinuous. The parameter group of a given group G,. has the same structure as G^ ; and every group of a given structure has the same parameter group. In every case which I have examined, the parameter group is discontinuous unless its type of structure is of the first class. I have considered not only complex groups, but also real groups generated by infinitesimal transformations. §2. The criterion for the continuity of an r-parameter group G,. is obtained as follows. Let Xj . . . X^ be any system of independent infinitesimal transformations of G>. The equations of Gr in their canonical form f are then (1) x'i =fi{xx . . . a-,,, «! . . . a,) (/ = 1,2 . . . 11), where f (x, «), for ^ = 1, 2 . . . w, is defined in the neighborhood of the identical transformation by the series * Taber: Am. Jour. Maths., XVI.; Bull. Am. Math. Soc, July, 1891, April, 1890, Jan. 1897, Feb. 1900; Matli. Ann., XLVI.; These ProceodinRS, XXXV. 577. Rettger: These Proceedings, XXXIII. 49.3-499 ; Am. Jour. Maths., XXII. Wil- liams; These Proceorlings, XXXV. 97-107. Newson: Kansas Univ. Quart., IV., V. 189G. Emeh: Kaiis.'is Univ. Quart , IV., V. 189G. t Transformationsgruppen, I. 171, III. 007; Continnierliche Gruppon, 454. 90 PROCEEDINGS OP THE AMERICAN ACADEMY. r 2 r »• Xi + 5^. a J Xj Xi + — : 2y 2^ a^- a^. X,- X* a^^ + . , . 1 ^ • 1 1 The transformation defined by equations (1) (the general transformation of this group) may be denoted by T^. For finite values of the parame- ters Oj, a2 • • • flrs t^G transformation 7'„ is generated by the infinites- imal transformation but for infinite values of a^, iu . . . a,., 7', is not generated by an infin- itesimal transformation of the group unless 7^, = T^^ the parameters ai, tta . . . a,, being all finite.* The transformation 1\ is defined by (2) x'\=f^{x\ . . . x'„,b, . . . b,.) (( = 1, 2 . . . n); and the transformation Ti, T„, obtained by the composition of the trans- formations Ta and 7),,t is equivalent to a transformation T^, defined by (3) X i =/^ (Xi . . . x„, Ci . . . Cj.) (i = 1, 2 . . . n), where (4) Cfc = gPjt (^1 . . . a,, ii . . . b,) [k=\,2 . . . r). If the c's can be taken finite for every finite system of values of the «'s and S's, the group is continuous. If, however, it is possible to assign finite values to the a's and S's sucli that in each system of values of tiie c's one (or more) of the c's becomes infinite, the transformation Tf^ T^ cannot be generated by an infinitesimal transformation of the group, and consequently the group is discontinuous. t A transformation which cannot be generated by an infinitesimal transformation of the group may be termed essentially singular. % If the parameters a and b are taken suf- ficiently small, the transformation T^ T^ can always be generated by an infinitesimal transformation, and, consequently. Lie's chief theorem holds in the neighborhood of the identical transformation. * Taber: These Proceedings, XXXV. 579. \ T.T will denote the transformation obtained by applying to the manifold (r, . . . .r ) first the transformation T and then the transformation T,. Lie denotes this resultant transformation by T^ T^ . % Cf. Rettger: Am. Jour. Maths., XXII. § Taber: Bull. Am. Math. Soc, VI. 199-203; These Proceedings, XXXV. 580. SLOCUM. — FINITE CONTINUOUS GROUPS. 91 If the system of equations (4) be written in the form (5) a\— *(«'! ■ . • «'., A • . . i^r) we have (i- = 1, 2 . . . r). (") «"i- = 0ii(«i • • • «,j yi • • • yr) where (i- = 1, 2 . . . /■), (8) y7 = ^^ ("1 • • • «-■> /5l • • • /5r) (>=1,2 . . . ;•). The group thus defined is termed the 'parameter group of the group C,. .* Since the equations defining the transformations of the parameter group involve the functions 0, this group is especially important in the study of groups generated by infinitesimal transformations. In general there is more than one system of functions such that provided Cj = (fij («! ... a,., ^1 ... 5^) (7 = 1,2 .. . r). But it may happen that the equations defining one group of a given structure restrict the functions c to fewer systems of values than in the case of another group of the same structure. Thus it is possible that of two groups of a given structure one shall be contirmous and the other discontinuous.! These statements are exemplified by a consideration of two groups G2 and G2' , whose infinitesimal transformations are, respectively, />i, x^Pi, and P2, x^p.2 -\- pi-X Both of these groups have the structure * Transformationsgruppcn, I. 401 ct srq. t Cf. Bull. Am. Matii. Soc, VI. 202. t Throughout; this paper Lie's notation will be followed, in accordance with which _ ^ — d — d 92 PROCEEDINGS OP THE AMERICAN ACADEMY. (Xi, X.) = Xi . The cauonica! form of tlie finite equations of the group pi, ^iPi is (9) .'. = .„. + !-(,.= _,), 3? 2 -— ■''2 • These equations define the transfornoation T^ of (?2 • Similarly, the equations defining the transformation Tf, of Cg are (10) x^ = .^.'=+ I (.'.-!), The transformation Tf, T^, obtained by the composition of the transfor- mations 7], and 7\, is defined by 00 x" x" «2 2 =^ 3^2 ; (e"^ _ 1) e''= +r:(«"- 1), and, if this is equivalent to a transformation T,. of the group, we have also (12) Therefore m x'\ x\ = Xx e . + _(..- 1). (13) ci == «2 + ^2 + 2 i g"2+''2 _ IT "V/— - 1 02 01 (^n 'e'-- - 1 )] , ^-2), C2 = «2 + ^2 + 2 /; TT V— 1 > = 02 («1 ) ^2 1 ^1 ) ^2)? where ^' is an arbitrary integer. Consequently for G^ there is more than one system of functions . Provided a., + h is not an even multi- ple of TT V— 1; every system of values of Ci and c^ is finite. For a., + b.2 = 2 KTT V — 1, C2 is finite, but the denominator of Cj becomes zero. In this case, however, that system of values of r^ corresponding to ^- = — « is finite. Consequently the parameters c^ and C2 can always be chosen finite, and therefore G2 is continuous. For the group G2 , whose infinitesimal transformations are j}^, x.,p2 -f pu T,^ is defined by x\ = x^ -\- a.,, (14) a:'2 = X2e''= + -(e"^-l), (In SLOCUM. — FINITE CONTINUOUS GROUPS. 93 and 7; by X '\ = x\ + b.„ (15) J J. I *i fJ>, x'\:=.x'.e'^- + j{e''^- 1). Consequently the transformation Tf^ T„ is defined by X"i r= Xj + flo + b.., (16) , x"o = X. e"^ + *' + e''^- (e"' - 1) + r i^'' - ^)i «2 «2 whence, if 7; T„ = T„ [e'^- (e"= - 1) + P (e^= - 1) ]= c^i («i, a^, i^, b,), ao + 6. . «! IN , ^1 /J, e"2 + ^2_ 1 *- a2^ ^-z (17) _ C2 = Oo + &2' = <^2 (^''ij 'J'2) ^1) ^2)' In this case there is but one system of functions ^. If, now, a.^ + 62 is an even multiple of tt -\/— 1? <^2 is finite, but Cj is infinite ; that is, there is no finite parameter c^ corresponding to tliis choice of the parameters a and b. Consequently, if a^, -\- b^ ■= 2 k it \/— 1 =1= 0, T^ T^ cannot be generated by an infinitesimal transformation of the group, and therefore G2 is discontinuous.* Lie states that two groups having the same structure are (holohedri- cally) isomorphic ; but the groups G.y and Gi are not properly isomor- phic, except in the neighborhood of the identical transformation, since one is continuous and the other discontinuous. Whence it appears that the conception of isomorphism, as developed by Lie, requires modification. The parameter group of G^ is defined by the equations ^ ^ a2 + a2-f2^-^V-l a, _ 1) ^ (^„, _ i)-j (13 a) a 2 «2 + 02 + 2 Z: TT V— 1» For the group -1^, \(x\V\ — x ^i> h)' and. if r;^ + ft.j = 2 (2 k + 1) t /\/— 1, where /c is an integer, r^ is always infinite. Consequently this group is also discontinuous. 94 PROCEEDINGS OF THE AMERICAN ACADEMY, where k is any integer, and of Gj by ihe equations (I [e'^.'ll (j,-2 _ 1) + ^(e'X3_i)]^ (17 a) a 2 '=■ (^2 "^ '^2' (1) Nevertheless, for any value of k, the parameter group of G.y is identical with the parameter group of G^, . For let S^ denote the transformation (21 defined by equations (13 a), and S^ the transformation defined by equations (17 a). Tiien for any system of values of ai, a^, and for any value of k, we have, by properly choosing ^i, /J^, ^a — ^^ '■> which symbolic equation persists for /3i, (i^i and k arbitrary, if ai, as are properly chosen.* Let Tg^ be.an arbitrary transformation of G^, defined by the equations r \ r r X'i = X^-\- 1j aj X, Xi + — 2^- 2^ aj Ujt Xj X^Xi+ . . . (( = 1, 2 . . . n). The transformation T~ , inverse to Ta, is then defined by the equa- tions which we obtain on replacing aj, ag . . . by their negatives, f Compound the transformation T^ and its inverse with each transforma- tion Ta of G> so as to obtain the transformation TJ1\T'^ , which is also a transformation of G^ ; and let (18) T^.^TJaT-\X Let (19) T„„= T,T,„T-\ Then, if (20) T^^1\T^, we have (21) 7;,,= TTJ — 1 V * Equations (13 a) may be regarded as defining a group with three parameters a^, a,, and i, of which two, a^ and oo, vary continuously, and one, namely A-, takes only integer values. But this group is not a mixed group, since we have shown that h is unessential, that is, it is immaterial what value is assigned to k. t Transformationsgruppen, I. 52, 5.3. J The transformation 7",,' is said by Lie to be obtained by tlie application {Aus- fuhninij) of T^ to the transformations Ta of Gr ■ Cf. Lie : Continuierliche Grup- pen, 445 et sc(j. SLOCUM. — FINITE CONTINUOUS GROUPS. 95 The symbolic equation (18) may be regarded as defining a transfor- mation between the parameters a and a' of G,., and is equivalent to r equations of the form (22) «',-=i^,(«i . . . a.,ai . . . a,) (J = 1, 2 . . . /•). Similarly, (19) is equivalent to «", = F, (a\ . . . a%, ^1 . . . /S;) (j = 1, 2 . . . r), and (21) to «"^ = ^j("i • • • «r, yi • • • yr) (; = 1, 2 . . . r), and, in virtue of (20), y> == ;■ («! • • • Or 5 ^1 • • • ^r) (j = 1, 2 . . . r). Thus equations (22) define a group T, which is termed the adjoined of G,..* The number of variables of the group F is r, and it contains r parameters, but these are not necessarily all essential. The number of essential parameters in T is less than r by one for each independent infin- itesimal transformation of G,. commutative vpith each of the infinitesimal transformations Xi . . . X^.-f Thus, if G^ contains just s such independ- ent infinitesimal transformations, T is an (r — s)-parameter group. The canonical form of the equations defining the transformation T^ of C^' is (9 a) ^. = .,."^ + ^(.«^-l), and consequently, if T,^, = T^T,^T~ , we have (23) "2 _ a^ Fi («! . 'Vo, «!, fZo), a'2 = Oo -\- 2 k TT V— 1 = F2 {' be denoted by e% that is, let e"' = e" '" '^, where ai = a + 8 f y = aj Xi -f «2 ^2 + • . • + o^ X^. Applying the infinitesimal transformation e repeatedly, we thus obtain the equations a, a BIfi a„ a, olfi a 251B a, an S'B a 33/S a,,_i 5,'^ a h5/S For n infinite, n^t is finite, and may be taken equal to unity ; thus a,, a S Consequently, if A does not va,nish for any system of values of a^ . . . a^, in which case A is a constant,* then the composition of an arbitrary transformation e" with finite pararaetei's with an arbitrary transforma- tion e" = e with finite parameters, gives a transformation of the group with finite parameters which is generated by an infinitesimal trans- formation. The form of A depends only on the structural constants, and thus A is the same for all groups of the same structure. Therefore, if the A cor- responding to a given structure is a constant, the composition of two arbitrary transformations of any group of this structure gives a transfor- mation of the group with finite parameters, that is, a non-singular transformation of the group, and consequently every group of this structure is continuous.! If the A corresponding to a given structure vanishes for certain systems of values of a^ . . . a,., some groups of this structure may be continuous and others discontinuous. For example, the two groups 6*2 and GT, con- sidered above, page 92, both have the structure (Xi , X.2) = Xi . The * For complex groups A is either unity, or else vanislies for certain systems of values of flj . . . «,. . See the expression for A as a product on page 104. t This criterion of continuity is due to Professor Taber. 102 PROCEEDINGS OP THE AMERICAN ACADEMY e- — 1 determinant A corresponding to this structure is A = , and this a.7 vanislies for ao an even multiple, not zero, of tt V— !• Nevertheless the group Cj is continuous, whereas the group Go is discontinuous. The symbolic equation e"' = e""*" '^ is equivalent to the system of equations <^k = «'i ■ + S if c* (^■=l,2 . . . r), which define the infinitesimal transformation of the parameter group. But the infinitesimal transformation of the parameter group is defined by the equations r «!' = «A- + ^j^kj{a)h^*' (^■ = 1,2... r)* Therefore r c* = ^j ^Kj (a) bj {k=l,2 . . . r). If A =1= 0, equations (28) give ^A — -^J » ^3 1 A (^- :- 1, 2 . . . r). Therefore, if ^i . . . ^^ denote the symbols of infinitesimal transforma- tion of the parameter group, we have 1 d a^ 1 A d flj (i = 1, 2 . . . r).t To illustrate what precedes, consider the two-parameter structure Equation (26) gives bi Xi -\- b.2 Xo, — Ci Xi + Co Xo, — ^ (oi Co, — a.2 Cj) X^ — -^^ («i c, — rto Cj) Xi — T-f («1 ^2 — «2 Ci) Xi — ^ (Oi Cg — «2 <^l) -^'l — • • • whence follows b\ = fl ^ (^ ' — «2 — 1) ^2> (29) ^2 n 2 Z>2 = Co. * Transformationsgruppen, I. 55, 65. t Engel and Schur, Transformationsgruppen, TIT. 754 el seq. and 788 et seq. SLOCUM. FINITE CONTINUOUS GROUPS. 103 Cousequently A /' - 1 3 0, a -V(/^-«,-l) For a^ an even multiple, not zero, of it -v/— 1, A vanishes. Thus it is possible that some group of the above structure shall be discontinuous. Equations (29) give Cl /> 2 1 « o 1 (30) = b. = ^J ^2j («) f^j Therefore the infinitesimal transformations of the parameter group are «2 5 ^i = T- I e l9ai _ «! (e"^ — «2 — 1) 5 9 ^2 = TT — ^rr + As a second example, take the three-parameter structure (Xi,X) = 0, {X\,X,) = 0, (X,X3) = Xi. Equation (26) gives bi Xi + &o X2 + bsXs = Ci Z] 4- c. X + cg X3 — I (flfg C3 — as c.^) X^ . Therefore a» Oj (31) and A = "i "-■l ' 2 " 2 b.= is discontinuous, G^ itself, and all groups having the same structure as 6?^, are discontinuous. The adjoined group corresponding to the above structure is, however, continuous, and consequently not every group of this structure is necessarily discontinuous. Nevertheless, the group px, /?,, Xip^, — x^pi -|- p^, of the above struc- ture, is discontinuous.* Its finite equations in the canonical form are x\ = I (e"^'-' + e-"^'-') - "-^-^^ (/'^ -1 - e~"^'-^) _ x,^/-\ ^^„3,'— 1 _ ^-.3^^) _ ilL (e'-a^'^ + ^-"3^1 - 2), X g = a?3 "T f^?,' * Tliis is one of the real groups of Euclidean movement in three dimensional space. Cf. Transformationsgruppen, III. 385. SLOCUM. — FLNITE CONTINUOUS GROUPS. 107 If this transformation is denoted by T^^^ then from the symbolic equation Tf,Ta^^ T^ we obtain the five relations (28) e-3 »^i _ ,- <-3 * ~i == I (e'3 ^^i + ,- 's * ^^ (, s v " i _ ,- "3 v^) (29) c, = a,-]-b,, (30) ^ (."3 * - 1 + e- '■3 *'- 1 - 2 ) - ^^^ (/3 *'- 1 _ .- '-3 « - 1) 2 C3 2 C3 = # («''^'~' + e- '^'^ - 2) - ^L^;^ (,'3^-i _ e-*3v-i>> ^3 ■^ •'a X ( :^ (e"3 *'-! + .- "3 ^'^1 - 2) - ^i^' (/3 ^ =^ _ ,- "3 ^'^) I I2a3^ ^ 2a3 ^ ^j + ^(e''-''-'-e-^^^-') 2 X {-'-^("^■■'-'--"*^)-2^/'"'''-' + »-'''"'-^)}=X. (31) ^(/.'-> +,-'.'-l_2) + ?l^^(2) ^2i»i — X1P2, and these only, are discontinuous. The first of these groups is the special linear homogeneous real group, and has the structure (Xi, X,) = — 2 Xi, (Xi, X3) = X.2, (Xo, X3) = — 2 X3. The determinant A corresponding to this structure is e 2 \'a\ -t- rti"3 _ J e~^ 2 » u\ + "i"3 J 2 ■\/o^2 + '''1 a-i — - Va% + «i «3 This vanishes if the a's are so chosen as to satisfy the condition 2 I 7 2 2 a 2 + «i f/3 = — A TT", where k is an arbitrary integer.* The second of the above groups has the structure (Xj, Xo) = Xg, (Xi, X3) ^ — X2, (Xo, X3) = Xi. The A corresponding to this structure is * Tlie special linear homogeneous comjilex group has been shown to be discon- tinuous by Professor Sturlj', Leipziger Berichte, 1892; and the vpdl group by Professor Taber, Bull. Am. Math. Soc, April, 1890. The general linear homogene- ous (real or complex) group is continuous. Thus a group may be continuous and yet have a discontinuous sub-group. • SLOCUM. — FINITE CONTINUOUS GROUPS. 109 A = and this vanishes if the a's satisfy the condition a^i + «"2 + a% = 4 ^^ tt^, where ^' is an arbitrary integer. The adjoined of this group is c) d d d a a and is discontinuous. Consequently, every group of this type is discon- tinuous. In the table on pages 391-397, Vol. XXXV., of These Proceedings, as mentioned above, I have marked by an asterisk those types of structure for which all real groups are continuous ; and by a dagger those types of structure for which I have found at least one real group that is discontinuous. Proceeding's of the American Academy of Arts and Sciences. Vol. XXXVI. No. 7. — August, 1900. CONTRIBUTIONS FROM THE HARVARD MINERALOGICAL MUSEUM. YIIL — ON HARDTSTONITE AND A ZING SCHEFFERITE FROM FRANKLIN FURNACE, N. J. By John E. Wolff. WITH A NOTE ON THE OPTICAL CONSTANTS OF THE SCHEFFERITE. By Dr. G. Melczek. CONTRIBUTIONS FROM THE HARVARD MINERALOGICAL MUSEUM. VIII. — ON HARDYSTONITE AND A ZINC SCHEFFERITE FROM FRANKLIN FURNACE, NEW JERSEY. By John E. Wolff. WITH A NOTE ON THE OPTICAL CONSTANTS OF THE SCHEFFERITE. By Dr G Melczer. Received June 21, 1900. a. Hardystonite. The new mineral hardystonite described in these Proceedings * was found in small grains in a mass of zinc ore and isolated by handpicking and the use of heavy solutions, while the (tetragonal) crystal system was determined by the study of thin sections of the grains. When visiting the mine in September, 1899, I received from the mine officials pieces from a large mass of neai-ly pure Hardystonite, several inches in diame- ter, which had been found in the same workings as the original mineral. The material is grayish-white in color, often streaked or clouded by faint pinkish tints, and breaks into angular fragments owing to the presence of several cleavages ; the lustre is glassy on the more perfect cleavages, elsewhere faintly resinous. It was easy to select material for thin sec- tions oriented parallel to the basal and prismatic cleavages and for pol- ished plates parallel to the base, from which the indices of refraction were determined and the original statement confirmed; namely, that the mineral is tetragonal and optically negative, has a basal cleavage and primatic cleavages parallel to the prisms of the first and second orders — iu addition, traces of a pyramidal cleavage were observed. By means of the Abbe total rellectometer the indices of refraction were determined on a plate parallel to the base as follows : * Tliese Proceedings, XXXIV. 479, 1899. VOL. XXXVI. — 8 114 PROCEEDINGS OF THE AMERICAN ACADEMY. For Na oj = 1.6691 e= 1.6568 For Uw= 1.6758 ± .0002 c = 1.6647 ± .0002 The figures for Li are inaccurate in the fourth decimal to two or more places, owing to the indistinctness of the boundary line. Unlike the original material, the mineral gives a strong sodium flame, and the following analysis of the new material (I) was therefore made : * I. II. III. IV. V. SiOa 37.78 37.73 624 624 38.10 AI2O3 FegOs ZnO 0.91 0.43 23.38 0.91 0.43 23,35 8 2 286 >313 J 0.57 24.30 MnO 1.2G 1.25 17 J 1.50 CaO MgO 34.22 0.26 34.19 0.26 610 6 J 610 33.85 1.62 K.,0 Nap 0.78 1.10 0.78 1.10 8 17 J 25 .... Ig 0.34 .... . . . • • • 0.52 100.46 100.00 . . . . . . 100.46 I. Analysis of new material. II. Analysis of new material reiluced to 100 omitting Ig. III. and IV. Molecular proportions. V. Analysis of original material. It is seen that the alkalies replace in part the Ca and Mg, but that there is still a molecular excess of the alkalies. The thin sections show, in addition to numerous fluid inclusions, the presence of frequent small grains of an undetermined mineral to which the content in alkalies may be partly due. * Both analysis and optical determinations were made by me in the Miner- alogical Institute at Munich. WOLFF AND MELCZER. — HARDYSTONITE AND SCHEFFERTTE. 115 b. Zinc Schefferite. While visiting the mine in September, 1898, my attention was called by Mr. Van Mater, Superintendent at North Mine Hill, to a peculiar pyroxene which was then coming out from the workings at the Parker Shaft, and abundant material was then secured from the ore sorting belts in the concentrating mill. The mineral occurs in large foliated masses, associated with franklinite, willemite, and small grains and masses of a white zinc mineral (to be described in the future), which often lies in thin films parallel to the basal jilanes of the pyroxene. The latter has a light-brownish red color in the large masses, while another variety occur- ring in small grains in the zinc ore has a deep brown color. The most striking physical feature is the (apparent) basal cleavage, which is as perfect as that of feldspar, in addition to the ordinary prismatic pyroxene cleavage. The angle between the two prismatic cleavages was determined by the reflecting goniometer as 92° 59', between the basal cleavage and the prism as 79° 02'. In a thin section parallel to (010) the angle /? between the basal cleavage and c' was determined as 74° 25'. It is readily seen in this clinopinacoidal section that the apparent cleavage parallel to the base is due to the development of gliding planes, for the basal cleavage planes enclose thin lamellae which are evidently in the position of twins parallel to the base with reference to the main mass of the mineral. The thin sections show the usual optical character of monoclinic py- roxene,— one optic axis is approximately perpendicular to the base; on the clinapinacoid the axis of least elasticity c makes an angle of 40° 35° with c', lying in the obtuse angle /?. The following analysis shows that the mineral is a zinc schefferite ; it was found impossible to completely decompose the mineral with IIF, hence FeO was not determined. SiO., 52.8G FeoOa+Al-A 1.08 MnO 5.31 ZnO 3.38 MgO 13.24 CaO 24.48 Ig 0.45 100.80 Sp. Gr. 3.31 116 PROCEEDINGS OF THE AMERICAN ACADEMY. Optical Constants of the Schefperite. By Dr. Gustave Melczer. The indices of refraction were determined on polished phites, prepared hy Voigt & Hochgesang, by means of the Abbe total reflectometer and with the application of the differential method proposed by Viola.* There were used (1) a plate approximately perpendicular to the acute bisectrix, (2) a thin section similarly oriented, and (3) and (4) two plates parallel to the base (001). Since the plates were not transparent, the boundaries of the total reflection could only be measured with the reduc- ing telescope, but with this, especially in the case of the last two plates (owing to their excellent polish), the limits could be fixed within 1 to 3 minutes. By reading every 15 degrees and in the vicinity of the maxima and minima every 5 degrees (which according to my experience com- pletely suffices with the reducing telescope), the boundary curve was constructed, and the following maxima and minima determined for Na light : (1) t 64° 261' and 64° 22' 62° 56' and 62^ 26' (2) ? ? 62° 57|' 62° 271' (3) 64° 25' 64° Ij-' 62° 55' 62° 23^' (4) 64° 20|' 64° 1' 62° 51|' 62° 23' The boundaries for the comparison prism were determined, after each pyroxene determination, by five readings 90° apart, as follows : (1) 62° 11' (2) 62° loy (3) 62° llf (4) 62° 11^' The cause of these noticeable differences in w of the prism cannot lie in the temperature, for this only differed by 3° on the different days when the measurements were made, nor can it be due to lack of homo- geneity in the glass hemisphere, for in using the enlarging telescope the mean of two readings in diametrically opposite positions of the horizon- tal circle were only 15 seconds apart. The cause can therefore only lie in the use of the reducing telescope itself, the accuracy of which, even with the sharpest boundaries, is only within 1 to li minutes, while with the enlarging telescope the same boundaries can be determined within 10 to 15 seconds. * Zeit. fiir Krjst, XXX. 438 and XXXII. 313. 62° 571-' and 62° 29' 62° lOi' 62° 54^' 62° 24i' 62° 12' 62° 512-' 62° 211' 62° 11' WOLFF AND MELCZER. — HARDYSTONITE AND SCHEFFERITE. 117 As regards the differences between the boundary angles of the individual plates, these are too large to be ascribed to indefiniteness of the boundary lines, for as already mentioned these were sharp, especially in (3) and (4). In order to be quite sure I repeated the measurements on three plates and found : Prism. (1) t 64° 273-' and 64° 23}/ (2) 64° 21' ... (3) 64° 21' ... There the above supposition was correct. Since the refractive index of the glass of the Abbe hemisphere, accord- ing to one of my previous determinations, is 1.8903 for Na light, and that of the glass prism used 1.6724, there follows from the boundary angles given above for the individual plates : Tna /^na ''''na (1) and (2) 1.7060 ± 0.0002 1.6840 ± 0.0002 1.6766 ± 0.0004 (3) 1.7050 ± 0.0005 1.6834 ± 0.0001 1.6757 ± 0.0001 (4) 1.7045 ± 0.0001 1.6827 ± 0.0001 1.6752 ± 0.0002 and as a mean : y — ^ = 0.0218 /3- a = 0.0075 y - a = 0.0293 These variations of the indices in the individual plates could perhaps be referred to local variations in the chemical composition of the zinc schefferite, or to the uneven distribution of pigment. The latter is not noticeably different, and yet it is known that for certain minerals at least very small variations produce such differences in the indices. If from the above values we take as the mean of the indices y = 1.705 )8= 1.683 a= 1.676 then by calculation 2 Va for sodium = 59° 29|:'. For the direct measurement of the axial angle the plate (1) could not be used, for although one optic axis and the middle of the figure could bo seen, and therefore, Hj might have been measured, yet the geometric orientation of the surface could not be determined ; the thin section (2) gave both hyperbolas, but somewhat indistinctly, so that they could only 118 PROCEEDINGS OF THE AMERICAN ACADEMY. be centred withiu J° accuracy. The plate was immersed in monobrom- ouapthalin whose temperature during the measurement was 19° and whose index of refraction was determined by the Abbe total-refracto- meter as: n^^^ = 1.6597. AVith the thin section the following values were determined in the axial angle apparatus : Li Na Tl Hi 37° 30' 37° 20' 36° 50' Ho 24° 10' 23° 40' 23° 40' whence, as to^ for the section was found to be 62^ 57' 45" and li= 1.6842 : 2 Va for sodium = 60° 0' and p > v. Munich, April, 1900. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVI. No. 8. — August, 1900. ON THE THERMAL AND ELECTRICAL CONDUCTIVITY OF SOFT IRON. By Edwin II. Hall. Investigations on Ligut and Heat made and published wholly or in part with Approprl\tions FROM the RuMFORD FuND. ON THE THERMAL AND ELECTRICAL CONDUCTIVITY OF SOFT IRON. By Edwin H. Hall. Received May 9, 1900. Presented July 17, 1900. The general method used in the investigation of which this paper is to eive an account is set forth with much detail in two articles already published.* Certain more or less important changes of apparatus or procedure will be described and discussed later; but the main results will first be given. The metal studied was Taylor (Yorkshire) wrought iron, recommended to me by an engineer friend of much experience as the softest wrought iron to be found in the Boston market. Chemical analysis showed the following composition : — Iron 99.93 % Carbon 0.059 The density was about 7.785 at 0°C. The values which I find for the thermal conductivity, k, of this iron are at 0.1528 28°. 2 C. " 0.1514 58°.3 C. if the specific heat of water at each of these temperatures is called 1. This would give for the temperature coefficient 0.0003, very nearly. If the values of k are revised in accordance with the values proposed by Winkelmaiin f for the specific heat of water at the given tempera- tures, they become at 0.1513 28°.2 C. " 0.1511 58°.3 C. * Thermal Conductivity of Mild Steel, by E. IT. Hall, These Proceedings, XXXI. 271, 1896; On the Thermal Conductivity of Cast Iron, by E. II. Hall and C. H. Ayres, XXXIV. 283, 1899. t Part 2 of Vol. II. p. 340. 12'2 PROCEEDINGS OF THE AMERICAN ACADEMY. and the temperature coefficient deduced therefrom will be too small to be worth writing down, 0.0000 ?, let us say. But the recent work of Calleudar and Barnes * gives for the specific heat of water 0.9992 at 25° C. 0.9987 " 30° C. 0.9992 " 55° C. 1.0000 " 60° C. If these values given by Callendar and Barnes are adopted as correct, my first values of k will stand almost without change ; and I shall there- fore leave them for the present without correction for variation in the specific heat of water. My value for the temperature coefficient, 0.0003 or a little less, is, so far as it goes, a corroboration of the substantial accuracy of the tempera- ture coefficient found by Lorenz, 0.0002282, although it may be doubted whether the last three figures of this number are of much significance. This agreement is eminently satisfactory to myself; for a comparison of the work of Lorenz with that of other investigators has convinced me that his value of the temperature coefficient is entitled to an especial degree of confidence. Measurements of the electrical resistance of the iron were made on nine cylinders, each 2 cm. long and about 0.23 cm. in diameter, cut from the same great bar as the disk on which the measurements of k were made. The length of the cylinders, like the thickness of the disk, was taken parallfel to the length of the bar ; and the cylinders were cut from a part of the bar adjacent to that from which the disk was cut. The extreme difference in the specific resistances of these cylinders was apparently about 5 per cent. The mean specific resistance was found to be 12240 at 18° C. The mean specific conductivity, x, at the same temperature would, therefore, be 817 X 10"^ C. G. S. " The ratio ^ -f- x is about 1716 at 0°C. The " thermo-electric height " of this iron, as compared with copper, is about 1028 X 10-« volts at 26°. 6 C. 980 " " " 41°.3 C. 936 " " •' 54°.5 C. 870 " " " 71M C. * Physical Review, April, 1900. HALL. — CONDUCTIVITY OF SOFT IRON. 123 The relation of the values here giveu for k and x to those found by others who have studied the thermal and electrical conductivities of soft iron, I have set forth in the " Physical Review" for May-June, 1900. The following details of ray work are perhaps unnecessarily extended and tedious ; but a considerable study of the literature of thermal con ductivity has convinced me that most experimenters in this field have omitted important matters in the printed description of their investiga- tions. It is my hope that those who may have to deal with problems similar to, though not exactly like mine, will find what is here written worthy of their attention. The iron used for tlie expei'iments on thermal conductivity was in the form of a disk cut from the end of a five-inch cylinder and turned down at first to a diameter of 10.5 cm. The thickness of the disk was about 1.996 cm., the greatest thickness indicated by the calipers being 1.998 cm., and the least 1.995 cm. TREA.TMENT OF THE DiSK. The disk was coated with copper electrolytically on both faces by a method substantially the same as that previously described. Spots which, because of slight flaws in the surface, appeared not to be taking the copper well from the preliminary cyanide bath, were rubbed with the point of a lead pencil to give them a coating of graphite, after which they speedily became coppered like the rest. In the sulphate bath the convex surface of the disk was protected as before by rubber bands ; but outside these bands was now placed a band of paraffined paper about 5 cm. wide, the object of which was to impede the deposit at the edge of the faces of the disk and so make it keep better pace with the rate of deposit at the centre of the faces. As before, it was occasionally neces- sary during the progress of the deposit, which lasted about a week, to remove the disk from the bath in order to break off or file off projecting pimples, or corals, of copper. The final coating of copper on each face, after being turned down nearly to a plane, was about 0.2 cm. thick. The whole curved surface was now turned down until the diameter of the disk was 10.00 cm. Mounting and Use of Disk and Adjacent Apparatus. Figures 1 and 2 of an article already mentioned, " On The Thermal Conductivity of Cast Iron," indicate with accuracy in most particulars 124 PROCEEDINGS OF THE AMERICAN ACADEMY. the method of mounting and using the disk now under consideration. Certain small changes, however, must be imagined in Figure 2, in order to make it accord perfectly with the latest developments of the apparatus. Thus, the water stream entering beneath the disk is no longer allowed to flow without restriction straight against the centre of the lower face. A little affair shaped somewhat like a three-legged stool is placed at the top of the admission tube, just beneath the point marked by the letter C, and most of the water escapes laterally between the legs of the stool, although a small part of it runs through a hole in the top straight against the disk. This device was adopted in the hope that it would make the temperature more uniform over the lower face of the disk. With a similar purpose regarding the upper face of the disk, the hard rubber block HH has been replaced by one having a somewhat more gradual curvature, so as to make a thinner and more rapid stream over the central parts of the disk. It is doubtful whether these changes have done much good, on the whole, although they appear to have made the difference of temperature between top and bottom of disk at the centre very nearly equal to the mean difference at other parts, as numbers presently to be given will show. Another attempt to improve the distri- bution of temperature, by making the flow of water more nearly equal along different radii of the upper face of the disk, affected the manner of admission of the water to the funnel FF ; but, as it was of doubtful utility, it need not be described. The air-vent leading up from the funnel FF by the tube w has been considerably enlarged ; but the small escape of water which had previously been maintained at this vent is no longer permitted. The small copper wires, extending from the copper coatings of the disk, are now protected fi'om actual contact with the hard rubber plugs Ki, K2, etc., and with the soft rubber packing surrounding these plugs, by a wrapping of oiled silk, with the purpose of preserving tlie wires from the destructive action of the sulphur emitted from the rubber ; but, after all, the wires cannot be depended upon for more than a few months. Stops about 0.16 cm. thick, placed at the edges of the faces of the disk, prevent the blocks HH and H'H' from approaching these faces so near as to endanger the safety of the small wires or cut off the flow of water. The parts marked Jj and Jo in Figure 2 of the former paper now contain spirals of platinum instead of thermo-electric junctions of copper and German silver, change of resistance of platinum having been substi- tuted for change of thermo-electromotive force as a means of measuring HALL. — CONDUCTIVITY OP SOFT IRON. 125 the change of temperature of the stream of water which flows over the upper surface of the disk. More will be said of this later. The parts surrounded by the water-jacket are carefully and thickly wadded with cotton-wool so as to make a nearly cylindrical body, about 18 cm. in diameter, up to the plugs J^ and Jo. The plugs also are covered with cotton-wool, as well as the slot in the top of the jacket. Around the disk itself the wadding is so thick as barely to allow the jacket to enclose it. The copper wires leading out from the plugs Jj and J2 ran, after July 17, outside the cotton-wool wrapping, but without touching the jacket. Determination of the Difference of Temperature OF THE Two Faces of the Disk. As before, this is effected by thermo-electric means, the iron disk and its two copper coatings being used as a thermo-electric couple. As be- fore, thirteen fine copper wires lead off from as many points on the upper coating, and similar wires from cor- responding points on the under coat- ing. Each pair of corresponding wires can be used singly, or all the thirteen pairs can be joined and used in multiple by an arrangement described in a preceding paper. The distribution of wires over either coating is shown in Figure 1, the numerals being alongside the points of attachment to the coating. In the arrangement of these points there was an attempt to make the various areas represented respectively by the individual points as nearly equal as practicable. Point 13 is intended to be at the centre of the disk ; points 3, 6, 9, and 12, 2.55 cm. from the centre of the disk ; points 2, 5, 8, and 11, 3.80 cm. from the centre of the disk; points 1, 4, 7, and 10, 4.60 cm. from the centre of tiie disk. No great accuracy is attained in placing these points ; and, in fact, each attachment is rather a line, about 0.5 era. long, than a point, each such line, except No. 13, crossing nearly at right angles the radius upon which it lies. Figure 1. 126 PROCEEDINGS OP THE AMERICAN ACADEMY. It is, of course, desirable to make the flow of water along the two faces of the disk such that the indication received from any one pair of wires, one above and one below, shall be about the same as that given by any other such pair of wires, and much thought has been given to the attain- ment of this end. The result is not quite all that could be wished for ; but it is such that any important error from the inequalities observed is very unlikely. The following tables show the I'esults of tests made under conditions as nearly uniform as it was found practicable to keep them. The galvanometer deflection credited to each pair of junctions is the mean obtained from two short sets of observations, the various pairs being used first in the order in which they are here given, and then in the reverse order. Between these forward and back series of observa- tions with single pairs a short set of observations with all the pairs in multiple was made, and the mean deflection from this set, corrected for the difference of resistance of the multiple and single arrangements, is also given below. Temperature about 28° C Junctions. 13 and 13' 1 and 1' 4 and 4' 7 and r 10 and 10' 2 and 2' 5 and 5' 8 and 8' 11 and 11' 3 and 3' 6 and G' 9 and 9' 12 and 12' Deflections. 11.1 11.0 X 11.1 f 12.0 12.2^ 10.9 N 10.8 ( 11.7 ( 11.6 ^ /■11.6 10.6 X 10.7 ( 10.5 ( 11.1 ' 11.3 10.7 Mean, 11.2 Along radii 1 and 1' 11.0 2 and 2' 10.9 3 and 3' 10.6 4 and 4' 11.1 5 and 5' 10.8 6 and 6' 10.7 7 and 7' 12.0 8 and 8' 11.7 9 and 9' 10.5 10 and 10' 12.2 11 and 11' 11.6 12 and 12' 11.1 10.8 10.9 11.4 11.6 All in multiple, 11.3 HALL. CONDUCTIVITY OF SOFT IRON. 127 Temperature about 57° C. Junctions. Deflections Along radii. 13 and 13' 10.4 10.7 1 and V 11.5 4 and 4' 9.5 7 and r 10.8 10 and 10' 10.8 2 and 2' 11.5 5 and 5' 9.5 8 and 8' 10.6 11 and 11' 11.3 3 and 3' 11.0 6 and 6' 9.7 9 and 9' 9.9 12 and 12' 10.6 Mean, , 10.5 10.7 10.3 1 and 1' 11.5 . 11-5 ^11.3 11.0 ) 2 and 2' 3 and 3' 4 and 4' 9.5 ^ 5 and 5' 9-5 [ 9.6 6 and 6' 9.7 ) 7 and 7' 10.8 \ 8 and 8' 10.6 [lOA 9 and 9' 9.9 ) 10 and 10' 10.8 ^ 11.3 M9.0 10.6 ) 1 1 and 1 1' 12 and 12' All in multiple, 10.4 It seems likely that the differences between the different radii are due ill part to inequalities of water-flow caused by the lodging of air-bubbles at various points on or near the surfaces of the disk. The agreement between the deflection obtained with all junctions in multiple and the mean of those obtained with the pairs used singly ap- pears satisfactory, in view of the not very rigid character of the test by which the comparison is made. The resistance of each individual pair of wires, out to the point where all were connected in multiple, is shown in the following table, as it was found July 12th, 1899 : — 13-13' 0.56 ohm 1- 1' 0.55 " 4- 4' 0.55 " 7- 7' 0.56 " 10-10' 0.56 '' 2- 2' 0.55 " 5- 5' 0.56 " 8- 8' 0.56 ohm 11-11' 0.56 " 3- 3' 0.55 " 6- 6' 0.56 " 9- it' 0.55 " 12-12' 0.56 '' The deflections noted above are those of a rather sensitive astatic gal- vanometer, the sensitiveness of which was fnicjucntly determined by means of a potentiometer and a standard Carliart cell, or rather, two 128 PROCEEDINGS OP THE AMERICAN ACADEMY. such cells, which differed from each other iu electromotive force about 1 part in 500. The mean difference of temperature of the two streams of water on entering the apparatus was about 8° at low temperatures and about 7°. 6 at high temperatures. The mean difference of temperature between the two surfaces of contact of the iron and copper, as indicated thermo- electrically, was about 1°.42 at low temperatures and about ]°.58 at high temperatures, which shows that heat is communicated more readily from the water to the copper coatings, and vice versa, at high temperatures than at low temperatures, other things being equal. In order to determine the difference of temperature, just mentioned, between the surfaces of contact of the copper with the iron disk, it was of course necessary to find the thermo-electromotive force corresponding to a known difference of temperature of two similar junctions. This datum was obtained by the method described in Appendix I of the paper on the " Conductivity of Cast Iron," to which paper a number of refer- ences have already been made in this writing. Some jDarticulars of the present case follow. A second disk about 2.5 cm. thick was cut from the same end of the same cylinder of Yorkshire iron that had furnished the disk already de- scribed. This second disk was then cut into two half disks, and from one of them was taken a slice, thickness-wise, about 11 cm. long, 2.5 cm. wide, and 0.3 cm. thick. This slice was then sawed up, crosswise, into thirty-three bars. All but ten of these bars were then reduced by filing and milling to a diameter of about 0.16 cm., and the length of each was reduced to 2.0 cm. The remaining ten were reduced in the same way to a thickness of 0.23 cm. and a length of 2 cm. The bars were then numbered from 1 to 33 in the order of their original position in the slice from which they had been cut. Numbers 1, 4, 7, 10, 13, 20, 23, 26, 29, and 32 were placed end to end, in the order just given, in the bore of the wooden cylinder of the thermo-electric test apparatus shown in Figure 5 of the article on " Conductivity of Cast Iron." No essential change has been made in this apparatus or in the manner of using it since the de- scription given in the article just mentioned was written, except in these particulars, that the electrical resistance * of the end-to-end row of bars * This resistance was likely to be as much as 2.5 or 3 ohms when the pres- sure, about 3 kgms., was newly applied to the row, but a gentle rocking, from side to side, of the copper blocks, kept well seated, would in tlie course of a few min- utes reduce this resistance to less than 1 ohm, the end pressure remaining un- HALL. — CONDUCTIVITY OP SOFT IRON. 129 aud copper end-pieces has been dealt with more carefully and successfully in recent experiments than in earlier ones, aud that in some cases the bars have been placed in a glass tube instead of a woodeu one. The results of these thermo-electric tests, subject to slight corrections for pecu- liarities of the thermometers* used, are given below. The temperature put down for each case, in the second column, is the mean of the ther- mometer readings in the two copper blocks at the ends of the row of iron bars. The third column, headed A, gives for each case the mean differ- ence of temperature of the two thermometers. The fourth column, headed E, gives for each case the thermo-electromotive force corresponding to a difference of 1° between the two thermometers, each of which thermome- ters is supposed to indicate with sufficient accuracy the temperature of the copper-iron contact neighboring to it. Date T A B June 3, '99 2o°.8x 7°.04\ 1041 x IQ-S " 7, " '27°.7I 7°.52i 1017 " 30, '' 25°. sl ^'-^HT-^n ^^^* July 3, " 2G°.5r'' '^ 8°.22r '^^ 1042 " 4, " 26°. 41 6°.64\ 1031 •' 6, " 27°.8j 6°.79j 1012 June 6, " 40^5^ 7°. 44^ 979 " 7, " 44°. T)/ 7°.23/ 964 July 3, " 40°.6>4l°.3 7°.79>7°.19 982 " } 978 X 10-^ " 4, " 38°. si 6°.94\ 990 " 6, " 42°. oj 6° .57; 976 June 6, " 55°. 6^ 7°.03^ 926 " 7, " 56°.5/ 6°.95/ 930 July 3, " 52°.2>54°.5 7°.60>6°.89 941 " > 934 X IQ-^ " 4, " 53°. 8 1 6°. 64 1 938 " " 6, " 54°. ej 6°.25J 933 26° .6 ,,„'^_,y°.30 _,.. ^^ )1028xl0-8 volt a u a June 3, " 69°. 0\ 6°.07n 885 " " 7, " 74°.5) 6°. 24/ 850 " " 30, " 69°.4f 6°.18f 865 " v «7i ^ 10- July 3." 70°.6r^ -^ 7°.04r -^^ 874 " >«'1X1U " 4, " 71°. 3\ 6° .041 879 " " 6, " 71°. 9J 6°.66j 870 " clianged, and, fxcept during the moments of measurement of resistance, no electric current flowing tlirougli the row of bars. * Baudin, Nos. 10,286 and 10,287, as in previous work. VOL. xx.xvi. — 9 130 PROCEEDINGS OF THE AMERICAN ACADEMY. Applying to the raeau values of E, found above, certain small correc- tions which take account of errors in the graduation of the therinometers, we get, — T • E 26°.6 1028 X 10-« volt ir.3 980 " " 54°.5 936 71°.! 870 " '^ These numbers plotted, with temperatures for abscissas and electro- motive force per degree for ordinates, indicate a curve wliich descends with very gradually increasing slope with rise of temperature. Indeed, this curve is so nearly a straight line that its curvature cannot be satisfactorily shown in a small figure. It would be almost perfectly straight if the numbers given under E were 1028, 975, 929, and 870. The minute examination which I was obliged to give to the individual small cylinders, during measurements of their electrical resistance, led me to notice defects and possible distortions which might, I feared, have affected their thermo-electric quality. Accordingly, several months after tests just described were made, I undertook a similar test with ten of the somewhat larger cylinders already mentioned, which had apparently suf- fered much less in the process of milling. In this later test I found it convenient to enclose the bars in a tube of glass instead of a tube of wood. This test gave 1064 X 10"^ for E at 15°.4 C. The earlier tests, above described, did not run so low in temperature, but by extrapolation they give, for 15°. 4 C, E = 1065 X 10~^, or some- thing very close to that, a satisfactory agreement. Determination of the Difference op Temperature of the In- going AND Outgoing Water at the Chamber above the Disk. It has been already stated that a differential platinum thermometer was used for this purpose instead of the two copper-German-silver thermo- electric junctions which had been employed in the preceding investiga- tions. This change was the result of a conviction, the fruit of much experience and vexation, that no suitable permanent protection can be found for the thermo-electric junctions against the action of hot water. A thin layer of shellac well dried on appears to be the best coating ; but this is liable to give way at a most inconvenient time and bring to naught HALL. — CONDUCTIVITY OF SOFT IRON. 131 the labor and observations of hours. The platinum thermometer method is not without ditficulties, as the following pages will show ; but it ap- pears preferable to the other. Figure 2 represents one of the platinum spirals, S, in position for use. It consists of about 22 cm. of wire, 0.012 cm. in diameter. The diameter of the coils is about 0.45 cm. The ends of this platinum wire are soldered V<>:^<^^<^'>'->^ Figure 2. to copper wires, C and C, each about 1.6 m. long and 0.1 cm. in diameter, which extend through the hard rubber plug R. Each of the copper wires is soldered at the outer end to a copper rod 5 era. long and 0.6 cm. in diameter, which is well amalgamated at the free end and serves to make connection with a mercury well of a Carey Foster bridge. Care was taken to make the length of the wire very nearly equal in the two spirals, and equal care to make the copper wires, all of which are from the same piece, all alike at first. The parts of Figure 2 which are in solid black represent metal ; the parts cross-liatched thus / represent soft rubber. The resistance of each spiral was about 1.4 ohms, and that of its con- necting copper wires about 0.1 ohm. Trial showed that one spiral with its connecting wires had a resistance about 0.0006 ohm greater than that of the other spiral and its connections. Slight changes in the copper wires reduced this difference of resistance to something like 0.000025 ohm. As the original difference of resistance was probably nearly all in the spirals, these continued to differ, at the temperature of the room, by something like 0.0006 ohm, which would correspond to about one- seventh part of a degree difference of temperature. No attempt at a 132 PROCEEDINGS OF THE AMERICAN ACADEMY. closer adjustment of the spirals was made, as the method of experimen- tation was expected to eliminate from the result any considerable error arising from this inequality. That this expectation was finally justified will be shown later, although more difficulty was encountered than at first appeared, the fact being, apparently, that the two spirals, although made from the same piece of wire, did not have quite the same tempera- ture coefficient of resistance, so that the difference of resistance between them was not constant when their temperature was varied,* but increased when the spirals were heated. Calibration of Differential Platinum Thermometer. In order to calibrate this diff'erential platinum thermometer, the two spirals were placed in streams of water, the temperatures of which were measured by means of the same thermometers that were used in studying the copper-iron thermo-electric junctions, and the difference between the electric resistance of spiral No. 1, with its connecting wires, and that of spiral No. 2, with its connecting wires, was measured by means of a Carey Foster bridge. The conditions under which this trial was made resembled very closely those under which the spirals were to be used in the main experiment, the plugs bearing the spirals being inserted in the same sockets in which they were afterward to be used, which sockets were temporarily removed from the main apparatus and fitted to brass tubes through which flowed the streams of water employed for the test ; these tubes were wrapped around with cotton wadding, and sockets and tubes together were surrounded by the same water-jacket that was used later to surround the main apparatus. The copper connecting wires led down between the cotton wadding and the water-jacket, and then out beneath the latter without touching it ; this detail is mentioned because the temperature of the connecting wires is by no means a matter of in- difference in some parts of the investigation. In this calibration test each stream flowed past the thermometer bulb before reaching its spiral, and past the spiral before reacliing the ends of the copper wires which carried the spiral. The distance from each thermometer bulb to the * The wire from which the spirals was made was annealed by drawing it through a flame, wliich treatment may have introduced into it some lack of uniformity. After the spirals were formed and soldered to the copper they were kept in a bath of melted paraffine, in the neighborhood of 145° C, about two hours, with the object of removing inequalities of condition caused by tlie bending to whicli the wire liad been subjected. HALL. CONDUCTIVITY OF SOFT IRON. 133 spiral beyond it was perhaps 2 cm. The velocity of the stream between the bulb and the spiral was some 30 or 40 cm. per second. One stream was usually about 6°. 7 warmer than the other. The method of alterna- tion was used ; that is, if the stream passing spiral No. 1 was during one set of observations, kept a certain number of degrees warmer than the other stream, the streams were exchanged at the end of that set and an- other set was then made, the difference of temperature and the mean tem- perature remaining nearly as before, and no part of the apparatus suffei'ing change of place except the cock by means of which the change of flow was affected. The combination of the two complementary sets of obser- vations gave a result from which errors due to disagreements of the ther- mometers and lack of perfect equality of the spirals was practically elim- inated. Sets of observations were made at various mean temperatures, and, in order to make the results at these various temperatures com- parable, slight corrections, amounting at the most to less than one-half of one per cent, were made in certain cases because of errors in the graduation of the thermometers, the combined diameters of the bores being slightly greater at some temperatures than at others. Similar cor- rections made in calibrating the copper-iron thermo-electric junctions have already been referred to. Each of the horizontal lines, numbered from 1 to 8 in the table below, gives the result of two complementary sets of observations, such as have been described above. T is the mean temperature of each pair of sets ; A is the mean difference of temperature of the streams ; L is the mean length of bridge wire included between the two points of equilibrium correspond- ing to the two positions of the commutator of the Carey Foster bridge. Date T A L L -h A May 5,1899 20°.77 6°. 68 20.,30 cm. 3.039 (1) " 6, " 36°.72 6° .33 19.21 " 3.032 (2) " 11, " 70°.41 G°.5o 19.80 " 3.032 (3) « 11, " 21°. 32 6°.99 21.20 '' 3.033 (4) " 12, « 76M2 6^63 20.21 " 3.048 (5) " 17, " 51°.60 6° .80 20.57 " 3.024 (6) " 26, " 52°.46 6°.96 21.01 " 3.018 (7) " 26, " 37°. 69 7°. 15 21.59 " 3.019 (8) The mean resistance of the bridge wire used in this test was 0.001491 ohm per cm., the material being German silver and the diameter about 0.2 cm. The mean resistance of the bridge wire, German silver about 0.4 cm. in diameter, employed in later experiments, when the spirals L -H A I 3.036 17.77 3.026 17.71 3.021 17.68 3.040 17.79 134 PROCEEDINGS OF THE AMERICAN ACADEMY. were used to determiue the change of temperature of water in the heat- conduction apparatus, was 0.0002548 ohm.* With these data we get from the table above : — Mean of T (1) and (4) 21°. 1 (2) " (8) S7°.2 (6) " (7) 52°. 0 (3) " (5) 73°.3 Here / stands for (L -f- A) X (0.001491 -^ 0.0002548), that is, the length of bridge wire, used in the main experiments, corresponding to a difference of 1° in the temperature of the spirals. Values of / for temperatures intermediate between those here given were found when needed by interpolation between the values of I here given. It will be observed that there is a maximum difference of 11 parts in 1770 between the given values of I. Rigid constancy of I would mean rigid constancy of the mean of the temperature coefficients of the two spirals with ref- erence to the mean scale of the mercury thermometers used. Such con- stancy was hardly to be expected. Use op Differential Thermometer in the Main Experiments. In the main experiments the plugs bearing the spirals were at first placed in their supporting sockets according to Figure 2, which repre- sents the spiral placed in the incoming stream. The water, therefore, on entering the apparatus, passed the first spiral before reaching its copper connections, but on leaving the apparatus it passed the copper connections of the second spiral before coming to the spiral itself. Ac- cordingly, any net conveyance of heat by the copper wires into or out of the stream was superposed on the action of the conducting disk to produce the difference of temperature noted by the spirals. Any such effect of the copper wires would probably be very small except at high temperatures ; and at such temperatures the effect would be, in large measure, eliminated from the result by the practice, always maintained, of combining one set of observations in which the disk carried heat to the upper stream with another set of observations in which the disk car- ried heat from the upper stream, the mean temperature of the disk re- * Each bridge wire was calibrated by finding what length upon it corresponded to the difference between the resistance of a 1 ohm coil and that of a similar coil shunted by a known, niuch larger, resistance. HALL. — CONDUCTIVITY OF SOFT IRON. 135 maining nearly unchanged throughout the two sets.* The elimination, however, would not be perfect ; for the reason that the temperature of the stream which we are considering is not quite the same in the two complementary sets of observations just described, being about 8° warmer in one set than in the other. The question at issue comes, therefore, very nearl}' to this, whether the amount of heat carried away from the stream by the wires, when the stream is 8° warmer than the room, is negligible in comparison with the amount carried away by the disk, the difference of temperature of the two faces of the iron being, as we have seen, usually 1°.4 or more. This question can be answered in the affirm- ative ; for the aggregate cross-section of the four copper wires is little, if any, more than 0.03 sq. cm., and the length of each wire, from the spiral out to the point where it is exposed to the temperature of the room, is not far from 30 cm. The carrying power for heat of a rod of copper 30 cm. long and 0.03 sq. cm. in cross-section, the thermal conductivity of copper being taken as eight times that of iron, would be about one five-thousandth part of the carrying power of the iron disk for a given difference of temperature, and not more than one eight-hundredth part, if the difference of temperature were 8° for the rod and 1°.4 for the disk. Nevertheless, after a considerable number of trials had been made with the spirals placed as in Figure 2, the plugs bearing the spirals were put in at the other ends of the supporting sockets, so that any changes of temperature produced in the stream by the copper wires must now occur either before or after the change of temperature noted by the spirals. The mean of the results obtained after this change of arrangement was slightly different from the mean of those obtained before ; but it is un- likely that the difference was due to this change. In the observations of July 31 and thereafter a loop of each copper wire was kept in a pocket containing oil on the outside of the water-jacket, so that each wire had at this point a temperature not more than one or two degrees different from that of the spiral with which it was connected. Another question was whether the heat carried in or out by the copper wires affected the temperature of the spirals directly by metallic conduc- tion, so as to keep them at a temperature different from that of the water passing them. The reasons for thinking that any such effect was neg- ligible are given in the Appendix to this paper. It has been stated that there was a difference of resistance between the two spirals at any given temperature, and that this difference in- * Tfie time between the exchange of the water streams and the beginning of the next set of observations was usually rather more than twenty minutes. 136 PROCEEDINGS OP THE AMERICAN ACADEMY. creased with rise of temperature. This difference, if constaut at each temperature, would be eliminated by combining two sets of observations made at the same mean temperature, one set being made with spiral No. 1 the warmer, and the other with spiral No. 2 the warmer. Sets of observations were, it is true, combined in pairs, but in each such pair it was the meau temperature of the disk that was kept nearly constant, while the mean temperature of the spirals was seven or eight degrees warmer in one set than in the complementary set. Accordingly, the mean result of a pair of sets, taken without individual correction for the inequality of the spirals, would have been subject to the error caused by ignoring the variation of this inequality through a rise of, we will say, 8 degrees in mean temperature. This error would have been about 1.5 per cent of the final result at any temperature. To prevent such an error, corrections, based on careful observations made for this specific purpose, were applied in each individual set of observations for conduc- tivity ; and, after these corrections had been applied, the complementary sets were put together for a mean result at any given temperature of the disk. By this means the error in question was probably reduced to very small dimensions. It appeared likely that some part of the apparent difference of resist- ance of the spirals at high temperatures was due to difference of resist- ance of the copper connecting wires, which near the spirals and for some distance away from the latter were considerably heated. As the experi- ments went on, increasing care was taken to make the condition of the wires leading to one spiral as nearly as might be the same as the condi- tion of those leading to the other spiral, in order that the differential changes of resistance should be confined to the spirals themselves. The result was a progressive diminution of the correction for isothermal ine- quality of resistance at high temperatures ; but this correction remained large and somewhat uncertain to the end, so that the value of the con- ductivity calculated from any one set of observations, unbalanced by its complementary set, was liable to a considerable error, as the details presently to be given will show. If I were to go through such work again, I should try to reduce the importance of temperature changes in tl>e copper connecting wires by increasing the resistance of the spirals or the change of temperature of the stream between them. Heating and Flow of Water. The method of heating and controlling the flow of the streams of water has been describe0.1528 " u a 28°. 1 27°.8 0.1539 0,1513 28°. 0 0.1526 « 27, " 27°. 4 27°.5 0.1580 0.1510 27°. 5 0.1545 ^ « 31, '* 27°.7 27°,4 0,1465 0.1529 27°, 6 0.1497 . Aug. 2, » 28° ,3 28°,2 0.1543 0,1573 28°.3 0.1558 ^ ^'^^"^^ }- 0,1526 0.1530 2«°.2 0.152« July 18, " 58° .8 58°. 6 0.1531 0.1529 58°. 7 0.1530 " 22, " 58° .9 58° .8 0.1608 0.1441 58°. 9 " " " 58°. 6 58° .7 0.1593 0.1420 58°. 7 " 27, " 56°. 2 57°. 6 0.1552 0.1490 56°.9 m^ rOA521 u.ioyu-x 0.1525 ( 0.1507 ( 0.1521 ^ Aug. 2, " 58° ,3 58°, 6 0.1568 0,1432 58°.5 0.1500 J ^' 31, '' 57°.8 57°. 7 0.1510 0.1498 57°.8 0.1504 , ' " 1502 0.15G0 0.1468 58°.3 0.1514 138 PROCEEDINGS OF THE AMERICAN ACADEMY. The values of K given above take no account of the variation in the specific beat of water between 28°. 2 and 58°. 3. The temperature coeffi- cient of K obtained from the trials made July 31 and August 2 after a change in the arrangement of the spirals, which change was supposed to make for greater accuracy of results, is decidedly greater than that ob- tained from the trials which preceded this change; but the considerable diffei'ence between the values of K at low temperature found July 31 and August 2 makes it unsafe to give especial weight to the value of the temperature coefficient calculated from the trials of these two days. The best course appears to be to take the mean of all the results at low temperature and compare it with the mean of all those at high tempeia- ture ; and this has been done, with the result stated at the beginning of this paper. Measurement of the Electrical Resistance. A satisfactory determination of the mean electrical resistance of the iron was a work of considerable difficulty. I attemp'ed it at first by use of several little cylinders, each taken singly, such as had been used in testing the thermo-electric quality of the iron (see p. 128). I found, however, that the last milling which these cylinders had been subjected to had left them somewhat irregular in diameter, so that it was impossible t^ measure this dimension accurately, even when calipers with jaws meeting along a narrow line were used. Accordingly I used the some- what larger cylinders, already mentioned, which had suffered much less from the imperfections of the milling process. These were about 0.23 cm. in diameter, and could be measured with satisfactory accuracy. The straight thick wire of a Carey Foster bridge having been replaced by two stout brass rods lying in line, with a gap between their ends, which were amalgamated, one of the iron cylinders was placed end to end between these rods and firmly held there under considerable pressure. Then the resistance of a certain measured length, 1.472 cm., of the iron bar was determined in the usual way by means of the bridge and the accompany- ing low resistance coils. Four cylinders were tested in this way, and their mean specific resistance was found to be 12430, C. G. S., at 22° C. Later the resistance of the same length of each of these bars and of five other similar bars, held as just described, was measured by a poten- tiometer method, the potentiometer wire being of copper drawn especially for this test. The mean specific resistance of the nine bars, as found by this latter method, was 12240, C G. S., at 18° C, the value given in the beginning of this paper. HALL. — CONDUCTIVITY OF SOFT IRON. 139 Appendix. Does the conductive action of the copper wires attached to the platinum thermometer spirals introduce error hy preventing these spirals from taking the temperature of the water flowing past them'l If the warming or cooling produced by the action of the copper wires were equally great at the two spirals, no harm would result, as it would not affect the difference of their temperatures, which is the quantity measured ; but this perfect compensation can hardly be, for all of the copper coimections are subjected to very nearly the same temperature conditions outside the supporting hard rubber plugs, while the spirals themselves differ in temperature about 0°.5. The differential effect, upon which alone the possibility of sensible error depends, is very much the same as if one of the spirals were at the same temperature as its connect- ing wires outside the plug and the other spiral 0°.5 warmer or colder than its connecting wires outside the plug. It is possible to make a very roufjli estimation of the maximum amount of error which could arise from such a condition. For the purpose of this calculation it may be assumed that the hard rubber plug is a non-conductor of heat, — an assumption which tends to magnify the effect under discussion. The length of the plug, that is, the length of the wire from air to water, is 2.5 cm., the diameter of the wire about 0.1 cm., the length of each copper wire exposed to the water about 1.6 cm. The length of the platinum wire in each spiral is about 22 cm., and its diameter about 0.012 cm. The point of attachment of the platinum to the copper is near the middle of the part of the copper exposed to the water. We will discuss the action of a single copper wire, and assume that one half of the plat- inum wire was attached to this by one end, the other end being free. For this purpose it will be necessary to know something about the " surface conductivity " of copper immersed in running water. Fortu- nately the main experiment with the copper-coated disk gives us some information in regard to this, — very inaccurate information, no doubt, but sufficient for the present purpose. In this main experiment, with a mean temperature t in the disk, and with a temperature < -|- 4 in the stream on one face and t — ^ \x\ the stream on the other face, the two meeting surfaces of copper and iron had respectively temperatures about t + 0.8 and t — 0.8, we will say. Assuming the thermal conductivity of copper to be eight times that of iron, and remembering that the copper coatings are each 0.2 cm. thick while the disk is 2 cm. thick, we get for the temperatures of the two outer 140 PROCEEDINGS OF THE AMERICAN ACADEMY. copper surfaces, in contact with the water, the temperatures t + 0.82 and t — 0.82 respectively. This makes each copper coating to have a tem- perature gradient of 0°.l per cm., with a difference of 3°. 18 between its outer surface and the water stream flowing across it. The ratio of the u ^2 temperature gradient to the external difference is therefore about According to this we may infer that a stream of water flowing across one face of a copper wire, with a speed equal to that of the flow across the surface of our disk, and with a temperature t degrees above the tem- perature of the face of the wire, will maintain within that wire a gradient of temperature equal to ^ -f- 32, all lateral action being excluded. The point of attachment of the platinum wire to the copper is about midway of the exposed part of the copper, and is as much as 3.0 cm. from the outer end of the plug. If the copper wire terminated at this point of attachment, and suffered conductive contact with the water only at its terminal surface, the change of temperature from the outer end of the plug, supposed non-conductive, to the end of the wire would accord- ingly be about ^^, ^^, as great as the difference of temperature between the end of the wire and the water flowing past it. If, therefore, the wire at the outer end of the plug exceeds in temperature the stream ol water by 0°.5, as we will assume, the fall of temperature within the wire would be about 0°.04, and the end of the wire would be about 0'^.46 above the temperature of the stream. This conclusion, however, is based on a false assumption as to the area of contact of the wire with the water ; in fact, this area of contact is about sixty times as great as the cross-section of the wire, and the point of attachment of the platinum is near the middle of this area, so that we shall not be very far from the truth in assuming that the temperature of the copper at the cross-section next the point of attachment of the platinum is the same that it would be if the wire had contact with the water only at this cross-section but had sixty times as great a surface conductivity as such an area really has in contact with the stream. This leads to the conclusion that the fall of temper- ature within the wire, from the outer end of the plug to the point of attachment of the platinum, is about f ^ times as great as the difference of temperature between the point of attachment and the stream. This last difference would therefore be rather less than 0°.l, but we will call it that. The problem now is to find how much the mean temperature of a plat- inum wire 0.012 cm. in diameter and 11 cm. long will exceed that of the water stream in which it is placed, if one end of this wire is kept 0°.l above the temperature of the water. This problem is of a faiuiliar sort, HALL. — CONDUCTIVITY OF SOFT IRON. 141 and is easily dealt with if we know the ratio between the thermal con- ductivity, jfiT, of the platinum and its " surface emissivity," E, in the stream of water. Assuming E to be the same for platinum as for copper, and A" to be ^ as great for platinum as for copper, we get iov E -=r A the value \. We now have (see Preston's " Heat," p. 513) or /x = 9 in round numbers. Then, using the formula ^ = ^q ^ ~ '^'^j where 6o is excess of temperature of the heated end of wire above temperature of water, 6 the excess of temperature at any point distant x cm. from this end, and c the Napierian base, we have, reckoning 6 in per cents of a degree : — X 0 0 10 0.1 cm. 4.1 0.2 " 1.7 0.3 " 0.7 0.4 " 0.28 0.5 " 0.11 Mean 2.4 % of 1° Accordingly the mean excess of temperature of the wire along its first 0.5 cm., less than oV of its whole length, would be about 5 % of the usual difference of temperature, about 0°.5, between the two spirals; and beyond this point the excess would be very small ; so that the error made by neglecting the difference of temperature between the spirals and the water is not important, provided the calculation just made is tolera- bly accurate. The most uncertain element in this calculation is probably the value of the " surface emissivity," which is based on observations made on the behavior of the disk and the streams across its face. But as the velocity of the water in passing the spirals is probably ten times as great as its mean velocity across the disk, it seems altogether likely that a sufficiently low estimate of emissivity has been used in the calcula- tion, and that the possible error from the source in question has been overestimated in the discussion just given. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVI. No. 9. — October, 1900. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. A NEW CONCEPTION OF THERMAL PRESSURE AND A THEORY OF SOLUTIONS. By Gilbert Newton Lewis. A NEW CONCEPTION OF THERMAL PRESSURE AND A THEORY OF SOLUTIONS. By Gilbert Newtox Lewis. Presented by Theodore W. Richards. Received July 19, 1900. Introduction. For an understanding of all kinds of physico-chemical equilibrium a further iusiyiit is necessary into the nature of the conditions which exist in the interior of any homogeneous phase. It will be the aim of the present paper to study this problem in the light of a new theory, which, although opposed to some ideas which are now accepted as correct, yet recommends itself by its simplicity and by its ability to explain sev- eral important phenomena which have hitherto received no satisfactory explanation. The theory suggested itself in the consideration of certain remarkable general laws which treat of heterogeneous equilibrium in which the several phases are subject to different pressures. These laws will be discussed in the first section of this paper, an/es Spelerpss. Plate l. &Keisel.«li«* EXPLANATION OF PLATES. All figures .are reconstruction drawings from sagittal sections of Spelerpes hi- linedtns. Tlie colors employed follow the scheme adopted by Strong, viz. : Black for lateral line {also for optic n), Pink for fasciculus communis, Yellow for general cutaneous, Blue for motor. IT. . . III. . . III. ob. inf. III. rt. i. III. rt. inf. III. rt. su. I V. ob. su. Va . . Va^ . . TV . . V0 .. . Vy . . vs . . Fe . . V.l.n. . V. I. na. . V. m. na. V. md. . V. md. ex. V. md. i. V. mx. . V. opt. . V. rx. V. rx. mot. VI. . . VI. ret. bl. VI rt. ex. VI. rx. viot. VII hue. VII. hoi. VII. hoi-md VII. md. ex VII. md. ex.' List of Abbreviations. Opticus. Oculomotorius Branch of III. to ni. obliquus inferior. " " " rectus internus. •■ inferior. " " " " superior. Trochlearis to m. obliquus superior. Dorsal branch from ophthalmicus trigemini. Small branch of To. (follows m. rectus superior). " " " (to skin of dorsum). Branch of r. mandibularis V. (to m. masseter). " " " " (to ra. temporalis). " " " " (to skin posterior to angle of jaw). " " " " (to skin of lower lip). Erroneously engraved in Fig. 1 for V. I. na. Ramus lateralis narium. " medialis " " mandibularis trigemini. " " " externus trigemini. " " " internus " maxillaris trigemini. " ophthalmicus trigemini. Ascending root of the trigeminus. Motor Abducens. Branch of VI. to m. retractor bulbi. " " " rectus externus. Erroneously engraved in Fig. 1 for VII. rx. mot. Ramus buccalis facialis. " hyoideus " " hyomandibularis facialis. Branch of ramus m.mdibularis externus (or mentalis) facialis. EXPLANATION OF PLATES. VII. md. i. VII opt. snf. VII. pal. '. VII. rx.fas. com. VII. rx. In. I. VII rx. mot. VJII.rx. . /Xl + 2 . . IX.S + * . . IX. rm. Ing. A.i — A.5 . X. rml. vsc. oe. X. rml. vse. oc. X. rm. vsc. . a cl. fjn. . . el. gn.' . . coms. . . . gn. IX. + A'. gn. ac-fac. gn. Gas. . gn. spi.2 . h'gls. . . t.' . . . m. . . . p. . . . rm. aur. . rm. brn. . rm. comn. IX.- \ 11. rm. d. spi.i . . . ?■/«. d. spi.o ■ rm. I. . . rml. amp. a. rml. amp. ex. rml. amp. p. rm. lav. . . rm. phy. . ■ rm. pry. . rm. scop. (?) rm. sv'tp. rm. V. spi.i . rx. d. spi..2 . rx. spi-i . . rx. V. spi-z ■ Ramus mandibularis internus (or alveolarie) facialis. " oplithalmicus superficialis facialis. " palatinus facialis. Fasciculus-communis rout of the facialis. Lateral-line root of tlie facialis. Motor root of the facialis. Root of auditory nerve. Anterior root of the ninth cranial nerve. Posterior " Ramus lingualis glossopharyngei. Roots of the tenth cranial nerve. Branch of visceralis vagi to the oesophagus. Erroneously engraved in Fig. 1 for X- rml. vsc. oe. Ramus visceralis vagi. Anterior. , Ganglionic cells of oculomotorius. " " " abducens. Commissure between the r. palatinus VIL and the r. ophthal- micus V. Ganglion of the glossopliaryngeus and the vagus nerves. Ganglion acustico-facialis. Gasserian ganglion. Ganglion of second spinal nerve. Hypoglossus nerve. Lateral. Median. Posterior. Ramus auricularis. " branchialis. " communicans glossopharyngei ad facialem. Dorsal branch of first spinal. Note. — In Fig. 2 the dotted line has been omitted ; it should have run to the left and downward from the letters rm. Dorsal branch of second spinal. Ramus lateralis. Ramulus ampullae anterioris. " " externae. " " posterioris. " laryngeus. " pharyngeus. Erroneously engraved in Fig. 1 for r?n. phy. Ramus scapularis (?). " supratemporalis. Ventral branch of first spinal. Dorsal root of second spinal. Root of first spinal. Ventral root of second spinal. Bowers - Cranial Nerves Spelehpes. For the sake of convenienee in comparing Fig. 1 with Fig. 3, and Fig. 2 with Fig. 4, Plates 1 and 2 have been bound in facing each other. PLATE 1. Fig. 1. View of the roots, ganglia, and branches of the cranial nerves of the left half of the head, as if seen from the left side projected on to the sagittal plane. The ear capsule and tiie eyeball are represented in outline, and the contour of the brain by a line accompanied by a tint on one side of it. X 72. Fig. 2. Dorsal aspect of the roots, ganglia, and branches of the cranial nerves of the right half of the head projected on to tiie frontal plane. The drawings were made from reconstructions of the left half of the head, but in engraving were reversed for the sake of readier comparison with Fig. 4. Outlines of eye, ear, and brain represented as in Fig. 1. X 72. PLATE 2. Fig. 3. View of the branches of the cranial nerves in the vicinity of the left eye, seen from the left side, projected on to the median plane, to show especially the eye-muscle nerves in relation to the II. and certain branches of the V. and VII. cranial nerves. X 72. Fig. 4. Dorsal view of the nerves shown in Fig. 3, but from the right side of the head, projected on to the frontal plane. Compare also with Fig. 2. The super- ficial ophtlialmic VII. has been only faintly shaded, instead of being printed in black, in order to allow the course of the underlying nerves to be seen. The distal end of IV. oh. su. has not been colored blue, owing to a mistake of the lithographer. X 163. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVI. No. 12. — November, 1900. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. ON CERTAIN DERIVATIVES OF ORTHOBENZO- QUINONE. By C. Lorixg Jacksox and "Waldemar Koch. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. ON CERTAIN DERIVATIVES OF ORTIIOBENZOQUINONE* By C. Lorixg Jackson axd Waldemau Koch. Presented May 9, 1000. Received October 17, 1900. Attempts to prepare the orthobenzoquinone have been mentioned, so far as we can find, in only two papers. The first is that by Ziiicke,t in which he describes tetrabromorthoquinone and tetrachlorortlioquinone, but says that a number of attempts to make the unsubstituted orthoquiuone have failed to produce the desired result. The second is by Hinsberg and Himraelschein,t who obtained ortho- dioxydiphenylsulphone by the action of potassic dichromate on a mixture of pyrocatechine and benzolsulphinic acid, and draw the inference that the formation of this substance probably was preceded by the formation of orthoquiuone. They add that all their experiments to isohite ortho- quinone have failed because of its strong tendency to condensation and polymerization. It seemed to us that one probable cause of the ill success of these experiments was the sensitiveness of the orthoquinone to oxidizing agents ; this view was confirmed by the observations of Cousin, § that trichlorpy- rocatechine and dibrompyrocatechiue give only red resinous products with * Tlie work described in tliis paper formed part of a tliesis presented to the Faculty of Arts and Sciences of Harvard University for the Degree of Doctor of Philosophy by Waldemar Koch. t Bcr. d. chem. Ges., XX. 1776 (1887). t Ber. d. chem. Ges., XXIX. 2025 (IBOG). § Annales de Cliim. et de Fhys., [7J XIIL 485. 198 PROCEEDINGS OF THE AMERICAN ACADEMY. nitric acid, whereas the trichlor- or tribrom-homopyrocatechiue gives under the same conditions an orthoquinone ; and also by some experiments undertaken by H. A. Torrey and one of us on the action of hydric diox- ide or electrolytic oxygen on pyrocatecliine, which led to unpromising black products. Accordingly we searched for a method which would produce a quinone without the use of an oxidizing agent, and found one in the action of iodine on the lead salt of the dioxybenzol. After having shown that the method converted liydroquiuone into quinone, we applied it to pyrocatechine ; but our first experiments led to no result, because we used alcohol as our solvent, which attacks the orthoquinone as soon as it is formed. Upon replacing the alcohol by chloroform we succeeded in obtaining a dark garnet red solution, in which the presence of ortho- benzoquinone was established by a number of tests given later in this paper. From this solution we nest tried to isolate the solid orthoquinone, but after trying every method we could devise, which gave even a remote promise of success, we have failed to obtain a trace of solid orthoquinone, and are forced to the opinion that it cannot exist in the solid state, or even for any length of time in solution. The products obtained in place of the orthoquinone in every case were a black substance insoluble in chloroform, and a brown substance, or mixture of substances, which dis- solved in chloroform ; this brown product we have not attempted to inves- tigate, but we have studied the black insoluble product, and can give a fairly complete account of its nature in spite of its unmanageable proper- ties. It begins to form in the chloroform solution of the orthoquinone in less than an hour, and is best obtained by allowing the solution to stand in a corked flask for not more than thirty hours. A combustion of the sub- stance gave results corresponding to the formula CigHgOs ; the analysis of a lead salt prepared in a somewhat different way indicated the same for- mula, and this was confirmed by two analyses made by H. A. Torrey of his product from the electrolytic oxidation of pyrocatechine, which seemed to be identical with ours, and by an analysis of the benzoyl derivative of our black substance ; we have, therefore, five analyses of four different samples, all of which agree with each other, and leave no doubt that the substance is a definite compound, and has the formula CioHgOs. This formula indicates that the compound was formed by the union of two molecules of orthoquinone with the introduction of an additional hydroxy! group, a view which is confirmed by the analysis of the lead salt CioHeOsPb, in which there are evidently two benzol rings to each atom of lead. When we consider the manner in which these two benzol rings JACKSON AND KOCH. — DERIVATIVES OP ORTHOBENZOQUINONE. 199 are united, two theories seem especially worthy of attention : first, the two rings may be joined directly, so that the compound is a substituted di- phenyl, (I.) 02(HO)H2C6-CoH3(OH)2 ; or second, they may be united by two atoms of oxygen forming a substituted pyrocatechine ether according tothisform.da: (II.) (HO) H3C6=02=C6H2(OII)o* The first (diphenyl) formula is rendered much more probable than the second by the anal- ogy between our orthoquinone and the orthonaphthoquinone, whicli is converted by dilute sulphuric acid into dinaphthyldiquiuhydrone,t 02H5Cio"CioH5(OFI)2. a black powder like our alteration product; this has been proved by Korn t to be a dinaphthyl body by conversion into a-a dinaphthyl and diphthalylic acid, (COCO)(CeH4COOH)2. The support of the diphenyl formula by this analogy is so strong that we should feel it was hardly worth while to consider the second (ether) formula, if it were not for the fact that we have observed an oxygen attachment similar to that in Formula II. in a derivative of tetrabrom- orthoquinone, described later in this paper. To decide between Formula I. and Formula II. we studied the action of reducing agents on the black substance, as, if it were an ether (Formula II.), it should be reduced to a mixture of pyrocatechine and a trioxybenzol ; whereas a diphenyl com- pound (Formula I.) would only take up two atoms of hydrogen without decomposition. § We selected as the reducing agent sodium amalgam and water, because this had proved effective in breaking up the pyrocate- chine ether containing bromine already alluded to; but, even after long continued action on our black alteration product, not a trace of pyrocate- chine could be detected ; the only reduction product was a black substance evidently as complex as the original body. This I'esult, therefore, de- clares decisively in favor of the diphenyl structiwe (Formula I.). The action of beuzoylchloride on the black substance in presence of so- dic hydrate converted it into a tribenzoyl derivative, Ci2lIi;0203(COCoH5)s, thus proving the existence of three hydroxyl groups in the substance ; and this benzoyl derivative, and also the original black compound, gave new substances with phenylhydrazine, which contained nitrogen, as was shown by the analyses. Unfortunately the percentage of nitrogen found in both cases was far below that required by the probable, formulas, which * In both these formulas the third hydroxyl group may be attached to the other benzol ring. t Steriliouse and Groves, Ann. Chem. (Liebig), CXCIV. 205. t Ber. d. chem. Ges., XVII. 3020. § Korn dill not succeed in splitting dinaphthyldiquinliydrone into simpler bodies by reduction. — Ber. d. chem. Ges., XVII. G02i. 200 PROCEEDINGS OF THE AMERICAN ACADEMY. is undoubtedly accounted for by the difficulty in purifying these amor- phous and infusible substances ; our analyses, therefore, amount only to qualitative proofs of the presence of nitrogen. The introduction of the nitrogen, however, makes it highly probable that both the original substance and its tribenzoyl derivative contain oxygen atoms in the quinone position. We feel justified from the results of the foregoing experiments in assigning to the black alteration product the formula 02(110) H2C6-C6H3(OH)2, in which two of the hydroxyl groups are prob- ably in the ortho position to each other, since the substance forms a stable lead salt when treated with plumbic acetate. We have made no progress toward determining the position of the third hydroxyl group, which may even be attached to the other benzol ring. The introduction of this third hydroxyl group is not without analogy, since the dinaphthylorthoquinone C10H5O2-C10H5O2 is converted by the action of the air on its solution in weak alkali into the dioxy compound C10H4OHO0-C10H4OHO2.* In our case, however, the oxygen of the air took no essential part in the reaction, as the same alteration product was formed in an atmosphere of carbonic dioxide ; and this is not surprising, as we have had frequent occasion to observe that the orthobenzoquinone is a mucb stronger oxidizing agent than the orthonaphthoquinone, so that one portion of it might easily oxidize the other during the polymerization. The portions of the orthoquinone which gave up oxygen during the formation of the black body were undoubtedly converted into the brown substances soluble in chloroform, which made up about half of the total product. Although, as has been already stated, we could not obtain the ortho- quinone in the solid state, many of its properties can be determined from the study of its solution in chloroform ; thus, there can be little doubt that it has an intense red color and little if any odor, as the solution smelt of nothing but chloroform, whereas a smell as strong as that of paraquinone could have been detected even in presence of the amount of chloroform used. Its very slight stability has been dwelt on at sufficient length already, but we should add that it seems to be decomposed at once by even small quantities of water or alcohol. We turn next to the reactions of the solution on which is based our inference that it contained orthoquinone. Hydrochloric acid converted it into monochlorpyrocatechine, which, however, was mixed with a little pyrocatechine, as would be expected, since Wichelhausf has shown that * Korn, Ber. d. chcm. Ges., XVII. 3021. t Ber. d. chem. Gcs., XII. 150i. JACKSON AND KOCH. — DERIVATIVES OP ORTHOBENZOQUINONE, 201 the action of hydrochloric acid on parabenzoquinone consists in the formation of hydroquinone and chlorine, which subsequently react to- gether, and in this corresponding case part of the pyrocatechine formed could well have escaped the substituting action of the chlorine. Re- ducing agents like ammonic sulphide or sulphurous dioxide produced pyrocatechine from this chloroform solution. Bromine formed with it tetrabrompyrocatechine, the reduction of the orthoquinone being achieved in this case by the hydrobromic acid formed in making the substituted quinone. When the chloroform solution was added drop by drop to a solution of benzolsulphinic acid also in chloroform, an orthodioxydiphenylsul- phone, CeHaSOaCc 1^3(013)2, melting at 153° was formed, which should be identical with that obtained by Hinsberg and Himmelschein * by oxidizing pyrocatechine in presence of benzolsulphinic acid, but the properties of the two substances show they are different. Hinsberg and Himmelscheiu's substance contained water of crystallization, and melted at 117°, if this were not driven off; at 143° to 145° after heat- ing in the steam-bath; and at 164° if completely dried by previous fusion; our compound contained no water, and melted at 153°, whether dried at ordinary temperatures or by previous melting. We have not succeeded in finding the conditions under which Hinsbers: and Him- melschein's compound is formed, so that we were unable to compare the two substances, and must consider with our present knowledge that they are isomeric. With aniline the chloroform solution gave a dianilidoquinoneanil, C6Ho(C6H5NH)20(CcH5N), which melted at 203°, and by this and a careful comparison of its other physical properties was proved to be identical with the body prepared by Zincke and von Ilagen f from paraquinone by the action of aniline and acetic acid. As this sub- stance has previously been made only from paraquinone, it has always been supposed that it contains the oxygen and anil group in the para position to each other, but after our preparation of it from ortho- quinone it is also possible that it is a derivative of orthoquinone ; and some weight is given to this view by the fact that it is formed easily from the orthoquinone by aniline alone, whereas it can be prepared from the paraquinone only with difficulty, and by the combined action of aniline and acetic acid. On the other hand, it seems hanlly prob- * Ber. d. chem. Ges., XXIX. 2025. t Ber. (1. chem. Ges., XVIII. 785 202 PROCEEDINGS OF THE AMERICAN ACADEMY. able that a derivative of orthoquiaone would be so stable as this ; and the beta-naphthoquinone forms with aniline and alcohol a correspond- ing auilidouaphthoquiuoneanil, CioH50(C6H5NH) (CeHgN), which is undoubtedly a derivative of alpha-uaphthoquinone. Zincke * also has obtained recently from the azimidodichlororthoquinone by warming it with aniline an azimidoanilidomonochloroxyparaquinone, and similar cases of conversion of orthoquinones into derivatives of para- quinones are not rare. We are so strongly of the opinion, therefore, that our dianilidoquinoneauil is a para body with the constitution 0, 1. CeHgN, 4. (CeHsNH)^, 2. 5, that we have not thought it worth while to submit the question to an experimental investigation, which would of necessity occupy much time. Assuming that the constitu- tion given above is correct, the body would be formed from the ortho- quiaone by the following series of transformations, which are modelled after those worked out by C. Liebermann f for the corresponding case of beta-naphthoquinone : — II. III. IV. aH,NH o 0 C«H.,NH -'6 "5 NHCeHg OH CeHsNH NCfiHs The replacement of the two hydrogen atoms of the orthoquinone by the anilido groups to form II. takes place under the oxidizing influence of another portion of the orthoquinone, which takes up hydrogen to form pyrocatechine (always formed in our process) ; II. then passes by isomerization into III., which is converted into IV. by the further action of aniline. Upon treating the solution of orthoquinone with orthophenylene- diamine no phenaziue was formed, but the reaction seemed to consist only in the oxidation of the diamine. We have also devoted some attention to the study of the tetrabrom- orthoquinone, and have obtained from it two derivatives. The first of these was prepared by treating tetrabromorthoquinone with tetrabrom- pyrocatechine dissolved in acetic acid and water; it was a beautiful red * Ann. chem. (Liebig), CCCXI. 276. t Ber. d. chem. Ges., XIV. 16G4. JACKSON AND KOCH. — DERIVATIVES OF ORTHOBENZOQUINONE. 203 body, which was soluble only in warm nitrobenzol. Its formula was Ci2Br604, and it was formed by the following reaction : C6Br4(OH)o + CfiBrA = Ci2Br604 + 2HBr, as was shown by the detection of hydrobromic acid as one of the prod- ucts of the reaction, and the fact that a good yield was obtained only when the two reagents were used in equal amounts. This formation of the substance is most naturally explained by supposing that the two benzol rings are united together by two of the atoms of oxygen forming a substituted pyrocatechine ether, C6Br^=0./C6Br202, but it is also possi- ble that the union took place directly between the two benzol rings forming a diyhenyl compound with this formula, OaBrgCe-CeBrgOs, the two atoms of bromine removed in this reaction combining with the atoms of hydrogen of the pyrocatechine, and thus oxidizing it so that the body contains two orthoquinone groups. To decide between these two formulas the substance was submitted to reduction with sodium amalgam, as under these circumstances the pyrocatechine ether should be split into two molecules of pyrocatechine, while the diphenyl com- pound should be reduced without splitting the molecule. The princi- pal product of this reduction was a chocolate brown substance, which contained an amount of bromine nearly identical with that of the oriofi- nal body, and was converted into it again by nitric acid. With it there was always formed a certain amount of pyrocatechine, and this seemed to us strongly in favor of the ether formula, but it could not be considered conclusive, as the amount of pyrocatechine was much less than that of the brown product. In the hope of increasing the yield of pyrocatechine we submitted the brown product again to the action of sodium amalgam, but found it was entirely unaffected ; we accordingly oxidized it to the original red body, — a reaction which takes place quantitatively, — re- duced this again by sodium amalgam, obtaining fresh quantities of pyro- catechine and the brown body, and continued these alternate reductions and oxidations until the original specimen of the red body had been completely converted into pyrocatechine. Although we could wish that this conversion had taken place by reduction alone, the use of the oxida- tions cannot be held to vitiate the argument, as they gave a quantitative yield of the original substance, and we feel justified, therefore, in infer- ring that the two benzol rings are united by two atoms of oxygen, and that the substance is a pyrocatechine ether. The brown product formed by the action of sodium amalgam was also obtained by tbe action of tribrompyrogallol on the tetrabromorthoqui- 204 PROCEEDINGS OF THE AMERICAN ACADEMY. none, and of hydrochloric acid at 160° to 175° on the red pyrocatechine ether. There seems no doubt, therefore, that it is formed from the red body by the conversion of two orthoquinone oxygen atoms into hydroxyl groups ; in other words, tliat it is the pyrocatechine corresponding to the red orthoquinone ; and this view is coufirmed by the oxidation of the brown substance to the red by nitric acid. The reaction of the hydro- chloric acid is especially instructive in regard to the constitution of these two bodies, as it is the familiar conversion of a quinone to a hydroqui- none by this reagent. The red color of the original substance also points to the presence of orthoquino oxygen in it, whereas the lighter color of the reduction product (brown when crystallized, but {purplish white when amorphous) confirms the view that it is the hydroxy compound. We therefore assign the following formulas and names to these sub- stances, — red compound, Br4C6=02='CeBr202, hexabromorthoquinopyro- catechine ether; the brown reduction product, Br4C6=02=C6Br2(OH)2, hexabromdiorthoxypyrocatechine ether. The only observed fact not in accordance with this last formula is that the substance does not dissolve in a solution of sodic hydrate, as we should expect it to do considering that it contains two phenol hydroxyls ; this may, however, be explained by the very slight solubility of the substance (soluble only in warm nitrobenzol), which might prevent the solution of sodic hydrate from coming into sufficiently close contact with it to react. The hexabromorthoquinopyrocatechine ether was formed when acetic acid or alcohol was used as the solvent, but none of it was obtained when the tetrabromorthoquinone and tetrabrompyrocatechine were mixed in solution in chloroform or ether. In this latter case the residue left after the evaporation of the solvent was a reddish white mass, apparently a mixture of the unaltered reagents, which contained none of the hexa- bromorthoquinopyrocatechitie ether. This is strange, as Zincke by mix- ing the two substances in ethereal solution obtained a black crystalline substance. An attempt will be made in this laboratory next year to find the conditions under which this black compound is formed. "We have succeeded also in obtaining a reaction similar to that just described from tribromresorcine and tetrabromorthoquinone. The other phenols tried acted simply as reducing agents. The product proved to be a ditribrommetoxyphenyldibromorthoquinophenylene ether, (C6HBr30HO)2C6Br202. This substance melts at 217°, and like the reduction product just de- scribed, does not dissolve in a solution of sodic hydrate, in spite of the two JACKSON AND KOCH. — DERIVATIVES OF ORTHOBENZOQUINONE. 205 phenol hydroxyl groups it contains, according to its most probable for- mula. We should explain this anomaly in the same way as before, althouorh this substance is much more soluble than the reduction compound. With glacial acetic acid the tetrabromortlioquinone C6Br402 formed a white compound, to which we have given much attention, but of which we can only give a very imperfect account. Zincke * in his paper on tetrabromorthoquinone noticed that it was attacked by glacial acetic acid, but did not isolate the product ; on the other hand he obtained a white body by crystallizing tetrabromorthoquinone from ether and ligroin, which we have not succeeded in encountering. When tetrabromorthoquinone is evaporated to dryness with glacial acetic acid, a small amount of the red hexabromorthoquinopyrocatechine ether is formed, but the greater part of the quinone is converted into a white crystalline body melting at 230°, the analysis of which led to one of the two following formulas, CiiHgBrgOs or Ci^BrgOs. The first would be formed by the union of two molecules of the tetrabromorthoquinone with one of acetic acid, one molecule of water being eliminated, thus : — 2C6Br402+C2H402= CnHsBrsOs+HsO. The second would be formed from the first by removing two atoms of hydrogen, which could be done by the oxidizing action of another portion of the tetrabromorthoquinone, and the tetrabrompyrocatechiiie thus formed would then give rise to the red body, which always accompanied the white product ; but the amount of this red compound always fell far below that which should be formed, if it had taken such an important part in the reaction (10 grams of tetrabromorthoquinone should give 5 grams of the red product, whereas the usual yield was only 0.8 gram), and, as the amount of hydrogen found in the white compound was dis- tinctly larger than should have been given by a body free from that element, we have decided to adopt provisionally the formula CHlLiBrgOj. We had hoped to settle this question by studying the decomposition prod- ucts of this substance, but so far it has either been unaffected or com- pletely decomposed by all the reagents we have tried. We hope that in the coming year the study of this body will be completed and the work carried on in various other directions in this Laboratory. * Ber. d. chem. Ges., XX. 1777. 206 PROCEEDINGS OF THE AMERICAN ACADEMY. Experimental Part. Action of Iodine on the Lead Salt of Hydroquinone. These experiments were tried to test the efficacy of this method of makin"' quinones. An aqueous solution of ten grams of hydroquinone was ti'eated with the calculated amount of sodic hydrate in a flask, to which the air had access only through a tube containing an alkaline solution of pyrogallol ; to the sodium salt thus formed an aqueous solution of plumbic acetate was added, which gave a white precipitate of the lead salt. As this blackened rapidly on exposure to the air, no attempt was made to filter it, but an alcoholic solution of five grams of iodine was added directly to the precipitate suspended in the liquid, when plumbic iodide was formed, as shown by the appearance of a yellow color. After the reaction seemed to have come to an end, the insoluble substances were filtered out, and the filtrate, which had a strong odor of quinone, extracted with ether. This ether extract left on evaporation yellow crystals with a strong odor of quinone, which under the microscope showed the characteristic form of this substance, and after purification by sublimation melted at 11 2° -11 3°, which, although distinctly below the melting point of quinone, 115°. 7, is near enough to it to prove in con- junction with the otlier properties that quinone was formed. To prove that this quinone was formed by the action of the iodine on the lead salt and not by the oxidizing effect of the air, a specimen of the salt mixed with water was exposed to the air for several hours, until it was thoroughly blackened ; upon filtration a red solution was obtained which had no odor of quinone. Extraction with ether did not remove the red color, and on the evaporation of the ether, crystals of hydroqui- none were obtained, recognized by the melting point, but no quinone. Upon adding an alcoholic solution of iodine to a similar specimen of the lead salt blackened by exposure to the air, the sharp odor of qui- nine was observed at once, and a considerable amount of this body was obtained from the filtrate. The method, therefore, is applicable to the production of quinones, but naturally would be used only in cases where oxidation is inadmissible. We also tried some experiments with iodine and the lead salt of resor- cine, but as it was evident that the purification of the product would be a matter of great difficulty, we have postponed the continuation of this work until we have finished the study of pyrocatechine. JACKSON AND KOCH. — DERIVATIVES OF ORTHOBENZOQUINONE. 207 Orthoquinone. Action of Iodine on the Lead Salt of Pyrocatechine, Preparation of a Solution of Orthoquinone. To prepare the lead salt of pyrocatechiiie two grams of pyrocate- cliiue dissolved iu 150 c.c. of water were added gradually, with constant stirring, to a boiling solution of 7.5 granas of plunabic acetate in 250 c.c. of water. The precipitated lead salt was allowed to settle, filtered out, and washed five times with hot water. It was then dried at 100°, and finely pulverized. It is not advisable to use more than two grams of pyrocatechine at a time in making the lead salt, as with larger amounts it was found to be hard to wash out all the impurities. Ten grams of this lead salt were thoroughly moistened with chlo- roform in a 500 c.c. glass-stoppered Hask. The salt must be absolutely dry, and the chloi'oform free from water and alcohol, as these sub- stances decompose orthoquinone. A boiling solution of five grams of iodine in 200 c.c. of chloroform was then added to the lead salt and the whole shaken well for five to ten minutes ; after which, upon fil- tering through a dry Gooch crucible, a garnet red solution of orthoqui- none was obtained. The amount of iodine used in this experiment is a little more than half that required by the theory (one molecule to each molecule of the lead salt). This large excess of the lead salt was used to avoid as far as possible the presence of iodine in the chloroform solution, and in this we were fairly successful, as a sample of it, when tested with a fresh specimen of the lead salt of pyrocatechine, showed only a trace of plumbic iodide. This chloroform solution contained orthobenzoquinone, CeH^Oo 1.2, as is proved by the experiments described later in this paper, and it must have been a nearly pure solution of this body, since the only other sub- stance which could have been present was iodine, and the amount of this was very small, as shown in the preceding paragraph. It had a dark garnet red color, and no odor could be perceived except that of the chloroform. Within an hour from the time of its preparation it began to show signs of alteration by depositing a black precipitate, and after twenty-four to thirty hours all the orthoquinone had disappeared from the solution. We have made numerous attempts to isolate the solid qui- uone from its solution in chloroform, of which the following is a brief summary : Evaporation spontaneously at ordinary temperatures ; evap- oration at— 12° ; evaporation in vacuo of a solution in pure chloroform made from chloral, so as to avoid all traces of alcohol which decomposes 208 PROCEEDINGS OP THE AMERICAN ACADEMY. the orthoquinone ; evaporation by a stream of dry air, or dry carbonic dioxide passed through the solution cooled by a freeziug mixture ; pre- cipitation with ligroin at — 5° ; precipitation with tetrachloride of carbon at — 20° ; we had great hopes of this last attempt, as we had not succeeded in making any of the orthoquinone, when tetrachloride of carbon was substituted for chloroform in the preparation, and we inferred from this that the quinone probably was insoluble in this substance ; but this, as well as all the other experiments mentioned above, did not lead to the de- sired result. The product in every case was the black alteration product already mentioned, the nature of which will be discussed presently, so that we are forced to the conclusion that the orthobenzoquinone cannot exist for any length of time, if at all, in the solid state. Study of the Alteration Product of Orthobenzoquinone. This substance was most conveniently obtained by allowing the chloro- form solution of orthobenzoquinone, prepared as already described, to stand at ordinary temperatures in a corked flask from twenty-four to thirty hours.* The black precipitate thus formed was not easy to purify, for although it was soluble in alcohol and some other solvents, all our attempts to crystallize it have failed; we finally decided to depend for its purification on its insolubility in chloroform and benzol. Accordingly, after filterius it out from the chloroform in which it was formed, we washed it thoroughly with chloroform, and afterward extracted it three times with hot benzol. About 40 per cent of the orthoquinone used was converted into this black product. In calculating this yield we assumed that the amount of orthoquinone in the chloroform solution cor- responded to the amount of iodine used in making it. The black sub- stance, after it had been purified by extraction with benzol, was dried in vacuo and analyzed with the following results : — 0.2041 gram of the substance gave on combustion 0.4684 gram of car- bonic dioxide and 0.0696 gram of water. to' Calculated for Calculated for Pnnnd C],H^0„(0H)2. Ci,H50o(OH)3. TUUUU. Carbon 66.67 62.07 62.59 Hydrogen 3.70 3.45 3.79 These numbers would indicate that the substance has been formed by the union of two molecules of orthoquinone with the introduction of a * The solution sliould not be allowed to stand more than tliirty hours, as in that case the product is contaminated with a brown impurity. JACKSON AND KOCH. — DERIVATIVES OF ORTHOBENZOQUINONE. 209 hydroxyl group, but it is obvious that the composition of a body like this, which is amorphous, and has uo definite melting point, can be determined only by the analysis of several samples prepared by different methods. Accordingly we undertook the preparation and analysis of the lead salt, which should be insoluble and stable, if the substance contains two hydroxyls in the ortho position to each other, as would be the case if it is formed from two molecules of orthoquinone. Further, as we thought that the additional hydroxyl indicated by the analysis might have been introduced by the action of the oxygen of the air, we repeated the prep- aration in an atmosphere of carbonic dioxide. The solution of ortho- quinone was made from the lead salt of pyrocatechine and iodine in a flask filled with this gas, and was separated from the plumbic iodide by means of a rose filter with an asbestos film without exposing it to the air. Upon standing over night still in an atmosphere of carbonic dioxide, a black precipitate was formed identical in appearance with that obtained by the ordinary process. This was purified in the way already described, and then converted into its lead salt as follows : 0.3 gram of this black bodv dissolved in 40 c.c. of alcohol was added to a boiling solution of one gram of plumbic acetate in 400 c.c. of water; this large amount of water is necessary to prevent the alcohol from precipitating plumbic acetate, which, becoming imprisoned in the lead salt, could hardly be removed by washing. The jet black lead salt thus obtained was washed five times with hot water, dried at 100°, and analyzed with the following result : — 0.2352 gram of the salt gave 0.1645 gram of plumbic sulphate. Calculated for Calculated for „ , C,2H,;0„02l'b. CijHcO.OHOjPb. tound. Lead 49.17 47.39 47.76 This result shows that the oxidizing agent, which introduces the ad- ditional hydroxyl, is not the oxygen of the air, but the orthoquinone itself, and this view is confirmed by the fact that the chloroform solution, from which the black compound has separated, contains brown substances probably formed from the orthoquinone in oxidizing the insoluble prod- uct, but which were so unmanageable that we were unable to determine their composition. We would add here two analyses made by H. A. Torrey some years ago in this laboratory with a body agreeing with our black compound in its properties, which he had prepared by the electrolytic oxidation of pyrocatechine. Tiiey gave the following results : — VOL. XXXVI. — 14 210 PROCEEDINGS OF THE AMERICAN ACADEMY. I. 0.1275 gram of the substance gave on combustiou 0.2940 gram of carbonic dioxide and 0.0436 gram of water. II. 0.0608 gram of the substance gave 0.1401 gram of carbonic dioxide and 0.0230 gram of water. Calculated for C,2HA(OH)3- Fc I. >und. 11. Carbon 62.07 62.88 62.85 Hydrogen 3.45 3.80 4.20 The substance is obviously the same as that previously analyzed, although not so pure. We have, therefore, four analyses of three samples of this substance prepared or purified in different ways, and, as these agree, there can be no doubt that the black alteration product of the orthoquinone is a defi- nite compound, and has the composition C12H8O5. Properties of the Black Alteration Product of Orthohenzoquinone (^Orthodioxyphenyloxyorthoquinone,* C6H3(OH).2C6H20H02). — It forms an almost black amorphous powder, which does not melt, but decomposes gradually at temperatures above 170°. It is easily soluble in cold alco- hol, ether, or glacial acetic acid ; insoluble in benzol or chloroform, whether cold or hot. Strong acids have no apparent action on it, but alkalies dissolve it. The following experiments were undertaken to determine the constitu- tion of the black alteration product. Reduction of the Alteration Product. The formula of the substance CioIIgOs indicates that it contains two benzol rings, and these may either be united directly, forming a diphenyl compound, or they may be united by two atoms of oxygen, forming a substituted pyrocatechine ether, [C6H30H]02[C6H2(OH)2]. The di- phenyl formula, (HO)02H2C6-CeH3(OH)2, is rendered probable by the formation of the dinaphthyldiquinhydrone t under somewhat similar cir- cumstances from beta-naphthoquinone, which has been proved to be a dinaphthyl compound ;t the pyrocatechine ether formula, on the other hand, is in harmony with a derivative of tetrabromorthoquinone, which is described later in this paper. Reduction seemed the easiest way to de- * This name and formula for the substance are established by the work described later in this paper. t Ann. Chem. (Licbig), CXCIV. 205. X Ibid. 206. Korn Ber. d. cliem. Ges., XVII. 3020. JACKSON AND KOCH. — DERIVATIVES OF ORTHOBENZOQUINONE. 211 cide between these formulas, as the ether should be split iuto pyrocate- chine and a trioxybenzol, while the diphenyl product would be reduced without splitting apart the two benzol rings. Upon treating the black alteration product with sodium amalgam and water in an atmosphere of carbonic dioxide for several days, an uninviting black solid was obtained on acidification, which was soaked in water, and this water as well as the acidified filtrate from the reduction extracted with ether, but not a trace of pyrocatechine was obtained. As the bromether, which we have ob- tained in another part of our work, gives a large quantity of pyrocate- chine by this treatment, we infer that the black alteration product is a diphenyl derivative. Action of Benzoylchloride on the Blach Alteration Product. Haifa gram of this substance was dissolved in 10 c.c. of a solution of potassic hydrate (1 : 5), and to the warm solution benzoyl chloride was added drop by drop, until the product of the reaction rose to the surface as an oily mass, leaving the liquid clear. This was then treated with sodic hydrate, in which it did not dissolve, and thoroughly washed with water. The tarry mass thus obtained was dissolved in chloroform, the solution filtered, and the filtrate mixed with an excess of alcohol, which preciptated out the substance. After drying in vacuo it was analyzed, with the followins: result : — » 0.2210 gram of the substance gave on combustion 0.5933 gram of carbonic dioxide and 0.0744 * gram of water. Calculated for Calculated for „ , C,oH„03(0C0C„U5),. CoU^O.COCOC.ns),. *^°"°<^- Carbon 70.91 72.79 73.21 Hydrogen 3.64 3.08 3.74 The substance is therefore a tribenzoyl compound, and the original black body must have contained three hydroxyl groups. This henzoxyorthoquino- orthodibenzoxydiphenyl, C6H2(OCOCgH5)OXcH3(OCOC6H5)2, t forms a light yellow amorphous powder without a definite melting point. It is easily soluble in chloroform ; insoluble in alcohol or water. Alkalies do not dissolve it. The fact that only three benzoyl groups are taken up by the black alteration product indicates that two of its five atoms of oxygen do not * A little water was lost in this analj-sis. t Tlie distribution of the benzoxy groups in tliis substance has not been determined. 212 PROCEEDINGS OF TBE AMERICAN ACADEMY form part of hydroxyl groups ; from the formation of the substance these two atoms of oxygen must either belong to a quiuone, or be the connect- ing atoms of a pyrocatechiue ether, and, as our work on the reduction of the alteration product has shown that it is probable they are not pyro- catechine ether oxygen atoms, there can be little dcubt that they occur in the quinone configuration, which indeed was the more probable supposi- tion of the two. We tried to confirm this inference by the formation of hydrazones both from the original black alteration product and its ben- zoyl derivative, but without satisfactory results. When jDhenylhydrazine in excess was added to a solution of 0.5 gram of the black alteration body dissolved in 10 c.c. of alcohol, the dark blackish color of the so- lution was discharged, and on pouring the product into acidified water a golden yellow precipitate was formed ; but an analysis of the substance gave 6.39 per cent of nitrogen, whereas the most probable formula, C12H8O4NNHC6H5, requires 8.70 per cent of nitrogen. The tribenzoyl derivative of the black substance was dissolved in chloroform, and boiled with an excess of phenylhydrazine for several minutes ; a new com- pound was formed, which was obtained by allowing the chloroform to evaporate spontaneously, treating with an acid to remove the excess of phenylhydrazine, dissolving the residue in cold alcohol, and precipi- tating the substance from this solution with water. After drying in vacuo it was analyzed, and 3.19 per cent of nitrogen found instead of 4.42 per cent of nitrogen required by the formula of the hydrazone, Ci2H50(NNHC6Hi3)(OCOC6H5)3. It is evident from these results that phenylhydrazine acts on both of these substances, and that the product in each case contains nitrogen. The results, therefore, as far as they go, confirm our inference that there are two quinone atoms of oxygen in the black substance, but they are of little value, because the exceedingly unman- ageable nature of both of these substances prevented us from purifying them sufficiently to determine their composition with certainty. The work just described establishes the following points with tolerable certainty. The black alteration product is a diphenyl compound, and contains three hydroxyl groups and an orthoquinone group ; it may there fore be called orthodioxyphenyloxyorthoquinone, and receive the formula C6H3(OH)2C6H2(OH)02, although the three hydroxyl groups may be attached to the same benzol ring, as we have not determined the position of the third hydroxyl experimentally. JACKSON AND KOCH. — DERIVATIVES OP ORTHOBENZOQUINONE. 213 Experiments with the Solution of Orthobenzoquinone. Action of Hydrochloric Acid on the Solution of Orthobenzoquinone. Dry hydrochloric acid gas was passed through a fresh cliloroform solution of orthoquinone (prepared from iodine and the lead salt of py- rocatechine), until it fumed strongly. After filtering out a slight tarry precipitate, a large part of the chloroform was recovered by distillation, and the concentrated solution thus obtained allowed to stand over night in an open vessel. The residue, which was usually oily, was heated on the steam-bath to drive off the last traces of the solvent and a slight impurity of iodine, and then extracted with a hot mixture of three parts chloroform with one of ligroin, which left behind a large quantity of a black oil. The solution became milky on standing, and deposited an oily substance, followed, when it had cooled, by the formation of crystals. As soon as these crystals began to appear the clear solution was decanted from the oil and allowed to crystallize in a separate vessel. The residual oils by a similar treatment with chloroform and ligroin yielded an additional amount of the crystals. The crystals were dissolved in benzol, and treated with bone-black, after which they were purified by repeated crys- tallizations from the mixture of chloroform and ligroin. They showed the melting point 84° to 85°, which was not quite constant, indicating that the substance was not perfectly pure ; but in spite of this it was dried in vacuo, and analyzed with the following result : — 0.2005 gram of the substance gave by the method of Carius 0.1865 gram of argentic chloride. Calculated for -p , Chlorine 24.57 23.00 This result indicates that the body is monochlorpyrocatcchine, but that it contains some pyrocatechine, as would be expected if the reaction ran in the same way as that of hydrochloric acid on parabenzoquinone, since Wichelhaus * has shown that in this case hydroqninone and chlorine are formed in the first instance, and that the substitution com- pounds, which form the final product, are made by the action of the chlorine on the hydroquinone. We have not attempted to purify the chlorpyrocatechine more thoroughly, as much time and labor would be necessary to obtain sufficient material for this purpose, and the forma- * Ber. d. cliem. Ges., XII. 1504. 214 PROCEEDINGS OF THE AMERICAN ACADEMY. tiou of chlorpyrocatechine under these conditions is confirmed by the following analysis of the lead salt, made by adding plumbic acetate to an aqueous solution of the product of the reaction of hydrochloric acid on the solution of orthoquinone. 0.3867 gram of the salt gave .03306 gram of plumbic sulphate. Calculated for ■d'„„_j CoHjClO^Pb. ^°'^°'^- Lead 58.98 58.55 Tlie mouochlorpyrocatechine in the slightly impure state in which we obtained it crystallized in white pearly plates, which are easily soluble in water, alcohol, ether, benzol, chloroform, or acetone ; insoluble ia ligroin. With an aqueous solution of plumbic acetate it gives a lead salt. It blackens quickly if exposed to the air after treatment with an alkali. The melting point observed by us is of course of no value, on account of the presence of the impurity of pyrocatechine. Behavior of the Solution of Orthohenzoquinone with Reducing Agents. Amnionic Sulphide. — Some of the solution of orthoquinone in chloro- form was shaken with about one third of its volume of the ordinary laboratory solution of amnionic sulphide. The red color of the ortho- quinone disappeared, and the aqueous solution took on a dark color. The two liquids were separated by means of a drop funnel, and the chloroform was extracted twice with water, the extracts being added to the amnionic sulphide solution at first obtained. The mixed aqueous portion was then heated on the steam bath, acidified with hydrochloric acid, allowed to stand until the precipitated sulphur had settled, filtered, and the clear dark colored filtrate extracted with ether. The residue left on the evaporation of the ether was recrystallized twice from benzol, when it was found to melt constant at 103° -104°, and to show all the other properties of j)yrocatechine. In order to be certain that the pyro- catechine, detected in the product from the action of ammonic sulphide on the orthoquinone solution, was formed from the orthoquinone, it was necessary to prove that this solution contained no free pyrocatechine ; for this purpose a small amount of it taken before the reduction was shaken with water, the water evaporated, and the residue extracted with benzol ; the benzol extract was evaporated to drj'ness, the very slight residue dissolved in water, and tested with plumbic acetate, when it gave no precipitate, showing that no free pyrocatechine was contained in the chloroform solution. JACKSON AND KOCH, — DERIVATIVES OF ORTHOBENZOQUINONE. 21-3 Action of Sulphurous Dioxide. — Dry sulphurous dioxide was passed through the chloroform solution of orthoquiuone uutil it was saturated; the principal product was a black unmanageable precipitate, probably a compound of orthoquiuone and pyrocatechine corresponding to chinhy- drone ; but the filtrate from this left on evaporation crystals, which were recognized as pyrocatechine by their properties and the formation of the lead salt. Action of Bromine on the Solution of Orthohenzoquinone. An excess of bromine was added to the solution of orthoquinone in chloroform, the chloroform allowed to evaporate spontaneously, and the crystalline residue, after being heated gently to drive off the excess of bromine, was spread on unglazed porcelain to remove oily impurities. After recrystallization from benzol it showed the constant melting point 191°, which is near enough to 192°-193°, that given by Zincke* for tetrabrompyrocatechine to leave no doubt as to the nature of the sub- stance. For greater certainty the substance was analyzed with the fol- lowing results : — I. 0.1835 gram of the substance gave by the method of Carius 0.3210 gram of argentic bromide. II. 0.1509 gram of the substance gave 0.2637 gram of argentic bromide. Calculated for Found. C6Br4(OH)2. I. II. Bromine 75.11 74.44 74.39 These numbers are sufficiently near to show that the product of the action of bromine on the orthohenzoquinone is tetrabrompyrocatechine. Behavior of the Solution of Orthohenzoquinone with Benzolsulphinic Acid. The chloroform solution of orthoquinone was added drop by drop to a solution of benzolsulphinic acid, t also in chloroform, until the color began to disappear less rapidly, and the solution of the sulphinic acid had as- sumed a decided reddish tint. After standing over night, the liquid was filtered, the filtrate evaporated to dryness, and the residue allowed to solidify. The solid residue was next treated with hot benzol, which * Ber. a. clicm. Ges., XX. 1777. t Iftlie conditions were reversed, and the solution of benzolsulpliinic acid was added to the solution of orthoquinone, none of the desired sulplione was obtained ; we ascribe this difference in behavior to the oxidation of the sulphinic acid by the excess of orthoquinone. 216 PROCEEDINGS OF THE AMERICAN ACADEMY. dissolved all but a slight black residue. On allowing the benzol solu- tion to evaporate a crystalline substance was obtained, which was puri- fied by crystallizations with the aid of bone-black at first from water mixed with a little alcohol, finally from water alone, until it showed the constant melting point 153°, when it was dried at 100°, and ana- lyzed with the following results: — I. 0.2353 gram of the substance gave on combustion 0.4931 gram of carbonic dioxide and 0.08G2 gram of water. II. 0.1454 gram of substance gave by the method of Carius 0.1418 gram of baric sulphate. Found. II Carbon Calculated for CoH3(OH)2SOAHc. 57.60 I. 57.14 Hydrogen 4.00 4.07 Sulphur 12.80 13.39 As this body must be a substituted pyrocatechine, it should give a lead salt, and upon trying it with a solution of plumbic acetate we obtained one, which was analyzed with the following result : — 0.2601 gram of the substance gave 0.1729 gram of plumbic sulphate. Calculated for ifniiiifl Lead 45.50 45.39 There can be no doubt, thei-efore, that the substance is a pyrocate- chinesulphone or orthodioxydiphenylsulphone. Properties of Orthodioxydiphenylsulphone, C6H3(OH)oS02CgHj. — It crystallizes from alcohol and water in short, thick, well-formed, white prisms terminated by two planes at an obtuse angle to each other. It contains no water of crystallization, and melts at 153°. It is easily soluble in alcohol, ether, chloroform, or glacial acetic acid ; very slightly soluble in cold water, or benzol, freely soluble in either of these liquids when hot; essentially insoluble in ligroin, either hot or cold. Alkalies dissolve it with a yellow color. Ferric chloride gives a bluish green color with it, which changes to red on the addition of sodic carbonate. As has been already mentioned, its aqueous solution gives a precipitate with plumbic acetate. This substance has the same composition as the orthodioxydiphenyl- sulphone made by Hinsberg and Himmelschein * by oxidizing pyrocate- * Ber. d. chcm. Ges. XXIX. 2025. JACKSON AND KOCH. — DERIVATIVES OF ORTHOBENZOQUINONE. 217 chine in presence of benzolsulj-hiuic acid, and we should expect that the two bodies would be identical, but, strangely enough, they seem to be isomeres, since Hiusberg and Hinimelschein's compound contains water of crystallization, and melts in presence of this at 117° ; when dried in the steam oven, at 143°-145° ; when previously fused in the air, at 164°; whereas our substance contains no water, and melts at 153°, whether dried at ordinary temperatures or by previous fusion. We made five attempts to prepare their body according to Hiusberg and Himmel- schein, but did not succeed in finding the conditions under which it is formed, which must lie within very narrow limits ; and, as in doing this we had devoted more time to the subject than we could afford, we were obliged to abandon our intention of making a comparative study of the two compounds. Action of Aniline on the Solution of Orthobenzoquinone. The solution of orthoquinone in chloroform was heated with an excess of aniline for five minutes on the steam-bath ; the chloroform was then allowed to evaporate, and the residue, after having been freed from ani- line by treatment with hydrochloric acid and washing with water, was purified by recrystallization from a mixture of two parts of alcohol to one of benzol, until it showed the constant melting point 203°, when it was dried at 100°, and analyzed with the following result : — 0.2909 gram of the substance gave 28.2 c.c. of nitrogen at a tempera- ture of 22° and a pressure of 774 mm. Calculated for „ , CoH,(C„H5NU)„0„U5NO. *°"'°'^- Nitrogen 11.51 11.27 The substance is therefore a dianilinoquinoneanil. When the aqueous wash waters obtained in the preparation of this substance were extracted with ether, pyrocatechine was obtained, recognized by its odor and lead salt. Properties of the dianilinoquinoneanil, CgH2(C6H5NII).,C(5H5NO. — Crystallized from alcohol and benzol it forms bronze-colored small needles melting at 203°, although thev begin to draw totiether some- what at 198°. The melting point of this substance is identical with that (202°-203°) given by Zincke and Hageu * for the dianilinoquinoneanil made from paraquinone by the action of aniline and glacial acetic acid, * Ber. d. cliem. C.es., XVIII. 787. 218 PROCEEDINGS OF THE AMERICAN ACADEMY. and, as a comparison of the two substances showed they crystallized in the same form, there can be no doubt of their identity. The formation of a paraquinoue derivative from our orthoquinone has been already explained in the introduction to this paper. In the hope of obtaining a phenaziue the solution of orthoquinone was treated with orthophenylene diamine ; a reaction took place, tlie principal products of which consisted of uninviting black substances and pyrocate- chine recognized by the formation of its lead salt. From the appearance of the pyrocatechine we inferred that the reaction consisted principally in the oxidation of the diamine by the orthoquinone, and as even after trying the experiment under several varying conditions no more prom- ising results were obtained, this line of work was abandoned. Phenol also gave with the solution of orthoquinone such an uninviting product that we did not attempt to study it. Sodic hydrate gives with the ortho- quinone solution a green coloration similar to that obtained by the action of sodic hydrate on tetrabromorthoquinoue. Derivatives of Trtrabkomorthobenzoquinone. The tetrabromorthoquinoue used in this work was prepared as follows : 20 grams of pyrocatechine were dissolved in 50 c.c. of glacial acetic acid, and 37 c.c. of bromine added gradually from a burette. The mix- ture was allowed to stand over night, after which the product was puri- fied by recrvstallization from 200 c.c. of glacial acetic acid. In this way forty grams of pyrocatechine yielded 118-126 grams of recrystallized tetrabrompyrocatechine ; that is, between 75 and 80 per cent of the theo- retical yield. To convert this tetrabrompyrocatechine into tetrabrom- orthoquinoue thirty grams of it were dissolved in 300 c.c. of glacial acetic acid by heating on the water-bath ; the solution was then cooled to 16°, or until the glacial acetic acid began to solidify, and eleven grams of fuming nitric acid of specific gravity 1.5 diluted with 60 c.c. of glacial acetic acid added rapidly, the mixture being kept cool and stirred vig- orously daring the addition ; after standing for five minutes 300 c.c. of water were added, and stirred in thoroughly. If the jji'ocess had run successfully, the tetrabromorthoquinoue settled to the bottom in a glis- tening mass of dark red crystals, which were filtered ofi^, and dried. The product thus obtained melted at 14o°-147° instead of 150°-151°, but was pure enough for our work, which was fortunate, as recrystallization from glacial acetic acid is attended by a great loss of material. Thirty grams of tetrabrompyrocatechine gave eighteen grams of tetrabromortho- quinone, which amounts to about 60 per cent of the theoretical yield. JACKSON AND KOCH. — DERIVATIVES OF ORTHOBENZOQUINONE. 219 As has just been stated, the crystallization of tetrabromorthobenzo- quinone from glacial acetic acid cannot be effected without considerable loss, which we found was due to the conversion of the tetrabromorthoqui- none into two new bodies, one of which was red, the other white. * A more careful study of the conditions under which the red body was formed showed us that it was produced by the action of the orthoquinoue with tetrabrompyrocatechine, either existing as an impurity in our tetra- bromorthoquinoue, or formed from it by reduction. After this the study of this red product was carried on with comparatively little difficulty. Preparation of Hexahromorthoquinopyrocatechirie Ether, Ci.2Br604. Eleven grams of tetrabroraorthoquinone and ten grams of tetrabrom- pyrocatechine were dissolved in 470 c.c. of glacial acetic acid by heating the mixture on the steam-bath, 180 c.c. of water were then added, which produced no immediate precipitate, and the mixture allowed to stand in a warm place for twenty-four hours. During this time a red precipitate was formed, which was filtered out, and washed with hot alcohol to re- move unaltered tetrabromorthoquinone and pyrocatechine. In tliis way 10.7 grams were obtained ; that is, somewhat over 60 per cent of the theoretical yield. The purification of the substance offered at first some difiiculty because it was insoluble in all the common solvents, but later we found that it dissolved to a limited extent in hot nitrobenzol, and pro- ceeded as follows : Two grams of the crude red body were dissolved in 150 c.c. of nitrobenzol by heating the mixture on the steam-bath (at higher temperatures more of the substance will dissolve, but the solution is attended with decomposition). Upon cooling, the solution deposited about 0.7 gram of crystals, which were submitted to a second similar crystallization from nitrobenzol at 100°, after which the product was extracted several times with hot alcohol to remove adhering nitrobenzol, dried at 100°, and analyzed. As the substance does not melt, we had no means of determining whether this treatment had been an efficient purification. I. 0.1809 gram of the substance gave on combustion 0.1374 gram of carbonic dioxide and 0.038 125°-175° 175°-225° 225°-275^ 655 790 1175 900 700 Grms Further distillation of the lower fractions gave, after the fourth dis- tillation, the following weights, with smaller proportions at temperatures between : — MABERY. — COMPO SITION OP PETROLEUM. 275 96°-98° 116=-1202 136M40^ 158^-162^ les'-iTP 178M823 78 40 45 37 43 35 Grms The Torrey oil contained more of the lower distillates than any other of the specimens examined. Several grams collected below 40°, and at 6o°-70°, 30 grams came together. The unpurified distillate 65°-70° gave as its specific gravity at 50°, 0.6981, which was reduced only to 0.6926 after agitation with fuming sulphuric acid. The specific gravity of hexane boiling at 68° is 0.6630. Analysis of the purified oil gave the following results: — I. 0.1551 grm. of the oil gave 0.4768 grm. CO^ and 0.2138 grra. H2O. II. 0.1995 grm. of the oil gave 0.6146 grm. CO.. and 0.2769 grm. HgO. III. 0.1369 grm. of the oil gave 0.4248 grm. CO2 and 0.1888 grm. H^O. Calculated for Found. C„H]2. C„H,4. I. II. III. C 85.70 83.72 83.85 83.93 84.63 H 14.30 16.28 15.32 15.41 15.33 In analysis III. every precaution was taken to avoid loss of the oil after weighing, and the temperature of the combustion was maintained as high as the tube would stand. Probably the coincidence in the per- centages of hydrogen is due to retention of unsaturated hydrocarbons in the sulphuric acid. Apparently, as in the Fresno oil, the hydrocarbon at 68° is a mixture of hexane and hexamethylene. HePTAMETHYLENE, C7HJ4. The fraction 96°-98° had the specific gravity at 20°, 0.7496, which was scarcely changed by treatment with fuming sulphuric acid, 0.7430. Analysis I. was made of the crude distillate, and analysis II. of the purified product : — I. 0.1222 grm.. of the oil gave 0.3810 grm. CO., and 0.1602 grm. IT.O. 11. 0.1530 grra. of the oil gave 0.4801 grm. CO^ and 0.1974 grm. H^O. Calculated for Found. C7H,4. I. II. c 85.70 84.97 85.60 H 14.30 14.56 14.34 This product is, therefore, fairly pure hoptamethylene. The fractions in the vicinity of 110° were shown to be composed for the most part of toluol by the formation of nitro-products. 276 PROCEEDINGS OF THE AMERICAN ACADEMY. OCTONAPHTENE, CgHig. The specific gravity of the crude distillate 118°-120° was 0.7598, and after purification with fuming sulphuric acid and sodic hydrate, 0.7530. A combustion of the unpurified oil gave 86.21 per cent of carbon and 13.35 per cent of hydrogen, A combustion after purification indicated octonaphtene, although the percentage of hydrogen is somewhat too high, probably on account of accidental moisture : — 0.1470 grm. of the oil gave 0.4598 grm. COg and 0.1976 grra. H2O. Calculated for CgHig. Found. C 85.70 85.34 H 14.30 14.93 The distillates 135°-140° consisted largely of the xylols. Dekanaphtene, CioHao- The specific gravity of the crude fraction 158°-160° was 0.7742, and after purification with the fuming acid and sodic hydrate, 0.7742. Car- bon and hydrogen were determined in the purified oil : — 0.1455 grm. of the oil gave 0.4583 grm. CO2 and 0.1804 grm. HgO. Calculated for Cjo Hjo. Found. C 85.70 85.91 H 14.30 13.78 The specific gravity of the crude distillate 168°-170° was 0.7928, and 0.7840 after treatment with fuming acid and sodic hydrate. A combustion of the purified oil gave 85.98 per cent of carbon and 13.69 per cent of hydrogen. The fraction 178°-182° had the specific gravity before treatment, 0.8006, and afterward, 0.7924. A combustion of the oil after treatment gave 85.97 per cent of carbon and 13.51 per cent of hydrogen. The fraction 198°-200° had the specific gravity of 0.8133, and after treat- ment, 0.8069. The following percentages of carbon were given by com- bustion: carbon, 86.51 ; hydrogen, 13.54. The low proportions of hydrogen and high proportions of carbon alluded to before are especially apparent in the Torrey oil. Whether this be due to a higher series or to benzol homologues not easily MABERY. — COMPOSITION OP PETROLEUM. 277 removed will appear later in the composition of the higher vacuum distilltites. The Torrey distillates 140°-220°, 50 mm., showed a larger proportion of oxygen and nitrogen compounds than any other of the crude oils. Scott's Hill (Sespe District) Oil. The specimen of petroleum from Scott's Hill was lighter than the Torrey oil ; its specific gravity at 20° was 0.8782. It contained 1.25 per cent of nitrogen. Two determinations of sulphur gave (I.) 0.38 and (11.) 0.49 per cent. 8260 grms. of the crude oil gave the following weights on distillation in vacuo : — -150°At. Pr. -160° 160°-208=' 208°-275° 1220 495 930 880 The distillate -150° was collected under atmospheric pressure, the others under 70 mm. The portion -150° was subjected to further dis- tillation collecting at first within 5°, and twice within 2°. The fractions collected in larger quantities within the following limits : — ee^-TO^ Se'-QO^ 96^-100^ 116^-1202 135^-140° 156°-160° ITO^-lTl'- 1780-182° 190°-192° 26 38 35 37 38 62 41 38 41 Continuing the distillation of the higher fractions in vacuo, after the third distillation within limits of 2°, the larger quantities collected within the following limits with smaller quantities between : — 144°-148° 164°-1G83 182°-186° 210°-214:° 60 55 65 • 23 In distilling corresponding fractions from other fields in vacuo a tendency to collect within the same limits was observed. After agita- tion with fuming sulphuric acid, the fraction 66°-70° atmospheric pres- sure gave as its specific gravity at 20°, 0.6984; the specific value much higher than the specific gravity of hexane, 0.6630(17°5). A combus- tion gave percentages of carbon and hydrogen corresponding to a mix- ture of hexamethylene and hexane : — C5I1,.. Calculated for C„II,«. Found. c 85.70 83.72 84.67 H. 14.30 16.28 15.15 278 PROCEEDINGS OF THE AMERICAN ACADEMY. The distillates 65°-70° from Torrey, Scott's Hill, and Fresno oils were put together and carefully distilled a number of times in order to separate so far as possible the hydrocarbon boiling at 68° or 69° from other admixtures, and the fraction 68° -69° was thoroughly treated with fum- ing sulphuric acid, warming gently and allowing it to stand with the acid over night. Before treatment the specific gravity at 20° was 0.7005, and after treatment, 0.6929. The following results were obtained by analysis : — I. 0.2-122 grm. of the oil gave 0.7596 grm. COo and 0.3234 grm. HoO. Calculated for CeHio. C13H14. Found. I. c 85.70 83.72 85.50 H 14.30 16.28 14.84 In this analysis the combustion tube was filled with oxygen before the oil was volatilized, and the temperature was kept as high as the tube would stand. There seems therefore to be little doubt that the hydro- carbon in California petroleum boiling at 68°-69° is composed chiefly of hexamethylene. Since small quantities of distillates remained in the vicinity of 90°-91°, it suggested the possibility that isoheptane might form a part of this product. But its high specific gravity, 0.7303 at 20°, isoheptane 0.6819 (17°. 5), and the composition showed by analysis, excluded isoheptane in any considerable quantity. 0.1273 grm. of the oil gave 0.3987 grm. COo and 0.1665 grm. HgO. C7H18. Found. c 85.70 84.00 85.40 H 14.30 16.00 14.53 Especial precautions were taken in this analysis to have the tem- perature of the combustion as hot as possible, and the tube was filled with oxygen before the oil volatilized. The proportions of carbon and hydrogen indicating the absence of isoheptane could not have been due to the presence of benzol, since the oil was treated several times with fuming sulphuric acid. The volatile portions of California petroleum, therefore, contain at most very small proportions of the hydrocarbons, C„H2„+2, and these if present consist almost exclusively of members below normal hexane. Further confirmation of these formulae is given by the chlorine derivatives, which will be described in another paper. MABERY. — COMPOSITION OF PETROLEUM. 279 Hei'tamethylene, C^Hi4. The fraction 96°-98° gave as its specific gravity at 20°, 0.7479, and after purification with fuming sulphuric acid, 0.7436. A combustion of the purified oil gave the followiug results : — ■ 0.1530 grm. of the oil gave 0.4801 grm. CO, and 0.1974 grm. HoO. Calculated for C,IIu. Found, c 85.70 85.60 H 14.30 14.34 These values leave no doubt that this constituent was heptamethylene. OCTONAPHTENE, CgHig. A determination of the specific gravity of the fraction 118°-120° at 20° gave 0.762S, and after agitation with fuming acid and sodic hydrate, 0.7569. Determinations of carbon and hydrogen were made both before and after purification. I. 0.1644 grm. of the unpurified oil gave 0.5196 grm. COo and 0.1975 HoO. 11. 0.1470 grm. of the purified oil gave 0.4600 grm. CO2 and 0.1976 grm. HoO. Calculated for Found. CsHie. I. II. C 85.70 86.21 85.34 H 14.30 13.35 14.93 Although all these oils were dried over sodium, the hydrogen in analysis II. is somewhat too high, probably on account of a trace of moisture. No further examination of the higher fractions of this oil below 160° was made, except of the portions collected at 135°-140°, to show that large proportions of the xylols were contained as in the other specimens examined. DeKANAPHTENE, CioIl20- The specific gravity of the fraction 158°-160° was found to be 0.7848, and after agitation with the fuming acid, 0.7751. The propor- tions of carbon and hydrogen were determined by analysis : — 280 PROCEEDINGS OF THE AMERICAN ACADEMY. I. 0.1444 grm. of the oil gave 0.4575 grm. COo and 0.1885 grm. H2O. II. 0.1451 grm. of the oil gave 0.4533 grm. CO2 and 0.1848 grm. HoO. Calculated for Found. C,„H,o. I. II. C 85.70 85.65 85.24 H 14.30 14.22 14.33 UnDEKANAPHTENE, C11H22. The specific gravity of this fraction without purification was 0.8093 at 20°, and after treatment with the fuming acid and sodic hydrate, 0.7952. A combustion gave the following percentages of carbon and hydrogen: — 0.1458 grm. of the oil gave 0.4593 grm. CO2 and 0.1817 grm. H2O. Calculated for C]iH22- Found. C 85.70 85.90 H 14.30 13.85 Assuming, which is probable, that the benzol homologue was com- pletely removed, these proportions of carbon and hydrogen point to the presence of a hydrocarbon of a series containing less hydrogen. A similar result was obtained with the fraction 194°-196°, specific gravity crude, 0.8145, and after treatment, 0.8022. Combustion of the purified oil gave the following percentages : — I. II. C 85.52 ' 85.85 H 13.97 13.92 While the percentages of carbon in these analyses are satisfactory for the formula Q.Ho,,, the percentages of hydrogen are less satisfactory. The deficiency of about one half of one per cent in the sum of the carbon and hydrogen has appeared in many of the analyses of products that could be reasonably accepted as to their formula. With the greatest care in the details of analysis, we have also found difficulty in obtaining the total carbonic dioxide evolved by combustion of the oil in the ordi- nary method of analysis. This subject has received attention in another paper on this method of analysis. TrIDEKANAPHTENE, C13H26. After the separation of distillates in vacuo from the crude oils, the fractions may be distilled at temperatures which would cause decomposi- MABERY. — COMPOSITION OF PETROLEUM. 281 tion of coustituents of the crude oil. It is therefore possible to continue the distillation of the hydrocarbons even as high as tridekanaphtene under atmospheric pressure after the first distillation. In continuing the distillation, 35 grams collected at 230°-232°, specific gravity 0.8511. After purification with fuming sulphuric acid it gave as its specific grav- ity 0.8134 at 20°. A combustion gave the follovping results : — 0.1511 grm. of the oil gave 0.4733 grm. CO2 and 0.1937 grm. UoO. Calculated for CiaH,^. Found. C 85.70 85.41 H 14.30 14.24 This formula was also verified by a determination of its molecular weight : — 1.2712 grm. of the oil and 25.24 grms. benzol gave a depression of 1°.370. Calculated for CisHjg. Found. 182 180 A determination of the index of refraction gave 1.4745, and the molec- ular refraction 60.254; calculated for CigHge, 59.839. TeTRADEKANAPHTENE, C14H28. A considerable quantity of distillate collected at 144°-146°, which gave as its specific gravity before purification 0.8428, and after purifica- tion 0.8154. A combustion gave percentages of carbon and hydrogen required for the formula C^U^n. 0.1462 grm. of the oil gave 0.4600 grm. CO2 and 0.1824 grm. HA Calculated for 0,^2^. Found. C 85.70 85.81 H 14.30 13.87 A determination of molecular weight at the freezing point gave a value required for tetradekanaphtene : — 1.3356 grm. of the oil and 24.22 grms. benzol gave a depression of 1°.394. Calculated for CjiHoj. Found. 196 194 The index of refraction of this hydrocarbon was found to be 1.4423, and the molecular refraction 63.75 ; required for ChHjs, 64.44. 282 PROCEEDINGS OF THE AMERICAN ACADEMY. PeNTADEKANAPHTENE, C15H30. From each of the California oils, distillates in vacuo collected at 160°-162°, 50 mm., corresponding nearly to 260°-262°, atmospheric pressure. The specific gravity of the fraction from Scott's Hill oil was 0.8600, and after purification with fuming sulphuric acid, 0.8171. A combustion gave the following values for carbon and hydrogen : — 0.1454 grm. of the oil gave 0.4558 grm. COg and 0.1829 grm. HgO. Calculated for C15H30. Found. C 85.70 85.47 H 14.30 13.97 The percentages of carbon and hydrogen in the analysis of the two hydrocarbons last described indicate a falling off in the proportions of hydrogen. The deficiency in the analysis is more probably due to loss of carbonic dioxide than of water. Similar variations have been noted in connection with some of the lower hydrocarbons in other crude California oils. The deficiency in hydrogen may indicate, as mentioned heretofore, the presence of hydrocarbons composed with more than one methylene ring, which would require prolonged distillation for their complete removal. From the heavier California oils composed, it appears, largely of asphaltic hydrocarbons, the fixlling off in the proportion of hydrogen and consequent increase in carbon indicates the presence of hydrocarbons with the formula C„H2„_2. Such differences do not appear in determina- tions of molecular weights, but are shown by analysis. There are wide variations in the specific gravity of the distillates of California oil above 230° from different sources. This may indicate a certain proportion of hydrocarbons of a lower series than C,;Ho,„ and the higher percentages of carbon and lower percentages of hydrogen in some of these oils indicate the possibility of hydrocarbons C„Ho„_2. For faithful assistance in this work the following gentlemen should receive credit: Messrs. Shaw, Ames, Richards, Cushing. From this examination of California petroleum, the following conclu- sions may be drawn : — An essential characteristic is the relatively small proportions of the distillates below 225°. The main body of the crude oils from the jjrin- cipal fields distilling below 225° is composed of methylenes whicli resem- ble those identified in Russian oil, in boiling points and in specific gravity, except undekanaphtene, CnHos, dodekanaphtene, C10H24, and trideka- naphtene, C13H265 which differ in boiling points. The proportion of the MABERY. — COMPOSITION OF PETROLEUM. 283 aromatic hydrocarbons is much larger, apparently, in California oil. The homologues of benzol form a considerable proportion of the distillates, especially of those with lower boiling points. In the distillate 221°- 222° from Puente oil so much naphtaleue was present that the distillate became solid at 0°. California petroleum differs totally from the Eastern oils, — Pennsyl- vania, Ohio, Canadian, etc., — and also materially from Russian oil, in not containing members of the series C,jH2„_,.2' I" this respect, and in respect to the large proportion of aromatic hydrocarbons, California petroleum is unlike any other petroleum that has been examined in this Laboratory. Incidentally it may be mentioned that California petroleum differs from other petroleums hitherto examined in the large proportions of oxygen and nitrogen compounds which it contains. These bodies are under investigation in this Laboratory. Study of the portions with high boiling points, which is now in prog- ress, will have an especial interest, since, when they are separated with- out decomposition, they form the most valuable constituents of lubricating oils and asphalts that have been separated from petroleum. In some of the high distillates, such as those from Summerland oil, hydrocarbons of the series C„H2„_2 and the series C„H2„_4 have been identified. No. 36. —ON THE CHLORINE DERIVATIVES OF THE IIYDRa CARBONS IN CALIFORNIA PETROLEUM. By Charles F. Mabert and Otto J. Sieplein. In further confirmation of the composition of the hydrocarbon 68°-70° described in tlie previous paper (Mabery and Hudson), the chlorine de- rivatives were formed by exposing the hydrocarbon over water to the action of chlorine, in ordinary daylight. After washing and drying, the chlorine product was fractioned under atmospheric pressure until it col- lected at 125° -130°, and for the most part at 126°. It distilled con- stant under normal conditions with the mercury all in the vajior at 12o°.5. The specific gravity at io was 0.9255; at f^o, 0.9239 ; at l^o, 0.9143; and at 5^3, 0.9044. The coefficient of expansion calculated from the average of these determinations is 0.000918. 284 PROCEEDINGS OF THE AMERICAN ACADEMY. A chlorine determination gave the following percentage : — 0.1572 grm. of the oil gave 0.1872 grm. AgCl. Calculated for CeHnCl. Found. CI 29.92 29.50 The molecular weight was determined at the freezing point of benzol. 1.164:1 grm. of the oil and 19.92 grm. benzol gave a depression of 2°. 482. Calculated for C,-,IIjiCl. Found. 118.5 118 The index of refraction at 20° was found to be 1.416, and the molecu- lar refraction, 33.29. Required for CcHnCl, 32.54. Hexamethylene is, therefore, the principal hydrocarbon with this boiling point. In distilling the portions of California petroleum below 100°, it has always been observed that a distillate collected at 90°-91°. To ascer- tain whether a hydrocarbon were really present with this boiling point, distillation of the fractions 85°-100° was continued through a tall Hempel column until a larger portion collected at 89°-90°. The specific gravity of this fraction without purification was 0.7295, |^o. After thorough treatment first with common sulphuric acid, then with fuming acid, the specific gravity was not changed, 0.7295. The index of re- fraction of this hydrocarbon at 20° was 1.411, and the molecular refrac- tion 33.35 ; calculated for C7H14, 32.22. The molecular weight at the freezing point was found to be as follows: — 0.8669 grm. of the oil and 17.62 grms. of benzol gave a depression 2°.547. Calculated for C^Kl^. Found. 98 99 "With the mercury column all in the vapor. Bar. 745.3 mm., this hy- drocarbon distilled completely at 90°. 4. The chlorine derivative of this hydrocarbon was formed by the action of chlorine over water. After washing, drying, and distillation under atmospheric pressure, the chloride came together at 145°-150°, for the most part at 147°. A determination of chlorine gave a value required for the mono- chloride : — ■ MABERY. — COMPOSITION OF PETROLEUM. 285 0.1605 grm. of the oil gave 0.1 GOG grm. AgCl. Calculated for C;Hi3Cl. Found. CI 26.77 2G.13 The specific gravity of the chloride at l^o was 0.9332 ; at ^o, 0.9316 ; at ^o, 0.9231 ; at fjo, 0.9138. The coefficient of expansion for one de- gree calculated from these results is 0.000973. A determination of the molecular weight at the freezing point gave the following value: — 0.9318 grm. of the oil and 19.98 grms. of benzol gave a depression of 1°.744. Calculated for OjHijCl. Found. 132.5 131 The index of refraction at 20° was found to be 1.441, and the molec- ular refraction, 37.57; calculated for C7H13CI, 37.11. These results are sufficient to establish the formula for this hydro- carbon as C7H14. It is probably dimethylpentamethylene. It differs in its properties from methylhexamethylene, boiling point 99° -100° ; its chloride boils at 147°, while methylhexamethylene chloride boils at 141°-142°. Methtlhexamethtlene Chloride, C7H13CI. To ascertain the correct boiling point of heptamethylene, the dis- tillates 95°-l00° were carried through a series of distillations until the greater portion collected at 98°-100°, and this product distilled for the most part at 99°-100°, Bar. 745°. 3, with the mercury column wholly in the vapor. The empirical formula of this hydrocarbon has been ascertained in the distillates from various specimens of California oils, by analysis and de- terminations of molecular weight. The boiling point of hexahydrotoluol, prepared by the addition of hydrogen to toluol, was given as 97°. Mark- owuikoff found that the same hydrocarbon separated from Russian petroleum, and also the synthetically prepared heptanaphtene, boiled at 101°. For further identification of our product it seemed advisable to study its derivatives. The chlorine derivative was first formed by passing chlorine into the hydrocarbon over water until the greater part was converted into the chloride. This reaction takes place very readily in y 286 PROCEEDINGS OF THE AMERICAN ACADEMY. ordinary daylight, and with a large generator the action of chlorine 'may be made continuous, saving much time in the chlorination. This method seems to be more advantageous than that formerly used by us in which dry chlorine was allowed to act on the vapor of the dry oil. The chlorinated oil was washed, dried over calcium chloride, and frac- tioned. After five distillations through a Hempel column, a consider- able portion collected at 141°-142'', which proved to be the monochloride, and more remained above 160°, which was doubtless the dichloride. A determination of chlorine in the fraction 141°-142° by the method of Carius gave a value required for C7H13CI: — 0,1863 grm. of the oil gave 0.2025 grm. AgCI. Calculated for C7H13CI. Found. CI 26.77 26.88 The molecular weight was also determined by the Beckman freezing point method : — 1.1960 grm. of the oil and 25.8960 grms. benzol gave a depression of 1°.701. Calculated for C7H]3C1. Found. 1f> -'^ X TOO oZ.o loo The specific gravity of the monochloride at 20° was found to be 0.9310. For further confirmation of the formula, the index of refrac- tion was determined with the aid of a Pulfrich refractometer, and from the density and molecular weight the molecular refraction was calcu- lated. The index of refraction found was 1.441, and the molecular refraction : — - Calculated for C-H13CI. Found. 37.11 37.57 The theoretical value was calculated on the assumjjtion that all the carbons are singly connected. In order to ascertain whether the chlorine atom enters the ring or side chain, the nitril was formed by heating the chloride with alcoholic potassic cyanide for several hours. There was an abundant separation of potas- sic chloride, and on diluting the solution the nitril separated as an oily liquid above the water. This oil had the characteristic odor of the nitrils. Its specific gravity at 20° was 0.9253, and its index of refraction, 1.45. The molecular refraction, assuming the molecular weight, was MABERY. — COMPOSITION OP PETROLEUM. , 287 35.78, calculated from the elements, assigning to the cyanogen group the value 5.33, which was determined from ethyl cyanide, CoII^CN. The theoretical molecular refraction for the nitril calculated on the same hasis is 36.45. The nitril was saponified by heating it to 110° with concentrated hydrochloric acid. The acid formed had the odor of alphatoluic acid, but the amount obtained was not sufficient for complete examination. When heptamethylene chloride was brought together with metallic sodium, a vigorous action soon set in with the evolution of great heat, sufficient to cause the decomposition of the products unless it was con- trolled by cooling. This reaction was best carried on by dissolving the chloride in ether, adding the sodium in slight excess over the calculated amount, and keeping the solution cold. In two hours the reaction was complete. The products included an unsaturated hydrocarbon, boiling point 97°, and another hydrocarbon, boiling point approximately 220°- 230°. That the hydrocarbon boiling at 97° was unsaturated was shown by the formation of a bromine addition product ; bromine added readily in the cold with no escape of hydrobromic acid. A Carius determina- tion of the bromine in this product gave the following result : — 0.2045 grm. of the oil gave 0.3023 grm. AgBr. Calculated for CyllisBr,. Fonnd. Br 62.5 62.9 The specific gravity of the dibrora-derivative at 20° was 1.648. A determination of its molecular weight was made : — 0.9238 grm. of the oil and 25.3 grms. of benzol gave a depression of 0°.725. Calculated for. C7Hi2Br2. Found. 256 247 The odor of the unsaturated hydrocarbon was very sharp and pene- trating, very different from that of the paraffine and methylene hydro- carbons, but resembling the olefines. In further proof that it contained doubly bonded carbon, it was titrated with the Hlibl reagent, an alcoholic solution of iodine and mercuric cliloride. The amount of iodine absorbed was approximately equivalent to two atoms of iodine for each molecule of the hvdrocarhon. When heated witli hydriodic acid, the monoiodide was readily formed. The specific gravity of the unsaturated hydrocarbon weight was : — CgHoCHa. Calculated for ^6Hl0=CH2. 30.06 31.77 288 . PROCEEDINGS OF THE AMERICAN ACADEMY. at 20° was 0.7472. Its molecular weight was ascertained by the freezing point method : — 0.7116 grm. of the oil and 25.19 grms. of benzol gave a depression of 1.420. Calculated for C,H],. Found. 96 98 The index of refraction with sodium light was found to be 1.416. The molecular refraction calculated from the density and molecular Found. 32.34 These values indicate that the unsaturated hydrocarbon contains a double bond between the side chain carbon and a carbon atom in the ring, confirming the position of the chlorine atom in the side chain which is indicated by the ease with which it is replaced in the reaction with potassic cyanide. The form that the chloriuation takes doubtless de- pends on the fact that the hydrogen in the side chain is less firmly bound than the hydrogen atoms in the methylene ring. The unsaturated con- dition C6Hiij=CH2 is shown by the action of halogens and haloid acids, and confirmed by the molecular refraction, which corresponds to the sum of the atomic refractions assuming the double bond. This constituent of California petroleum is therefore identical with methyl hexamethylene, which maybe formed by the addition of hydrogen to toluol. The hydrocarbon with a boiling point 220^-230°, formed by the action of sodium on methyl hexamethylene chloride, doubtless contains two metliylene rings : — CeHiiCrTo-CH.Ce-Hu. The quantity of this product formed was too small for identification, but it evidently affords a means for building up the higher methylene hydrocarbons containing more than one methylene ring. That it was a condensed hydrocarbon was shown by its high specific gravity, 0.8872. DiMETHYLHEXAMETHYLENE ChLORIDE, CsHijCl. The formula of dimethylhexamethylene was ascertained, as shown in tlie previous paper, by analysis and determination of its molecular weight. The formula was still further verified by the formation of the chlorine derivative. As in the chloriuation of methylhexamethylene, chlorine MABERY. — COMPOSITION OF PETROLEUM. 289 was allowed to act on the hydrocarbon over water in ordinary daylight until it was nearly all converted into the chlorine derivative. After washing and drying, the product was distilled under atmospheric pressure ; after several distillations the monochloride collected in larger part ac 168°-170°. The specific gravity of this product at 20° was found to be 0.9358. A determination of chlorine gave the following result : — 0.2034 grm. of the oil gave 0.1973 grm. AgCl. Calculated for CgHuCI. Found. CI 24.21 24.01 The molecular weight of the chloride was determined by the freezing point method. 0.7293 grm. of the oil and 25. G6 grms. benzol gave a depression of 0°.982. Calculated for CgHiBCl. Found. 146.5 142 The index of refraction in sodium light at 20° was 1.455, and the mo- lecular refraction : — Calculated for CgUisCl. Found. 41.69 41.60 That the chlorine enters a side chain in this reaction, as in the case of methylhexamethylene, appears from the ready formation of the nitril by heating the chloride with alcoholic potassic cyanide. On diluting the solution the nitril separated as an oil, with the characteristic odor of the nitrils. It was saponified by heating with aqueous potassic hydrate. On acidifying the solution, a solid was precipitated, with an odor characteristic of the alpha-toluic acids; but the quantity obtained was not sufficient for identification. It was probably raeta-methyl, alpha-toluylic acid. Trimethylhexamethylene Chloride, C9H17CI. This chloride was also formed, washed, dried, and fractioned under atmospheric pressure. It came together in larger quantity at 186°-188°; its specific gravity at 20° was 0.9380. The percentage of chlorine was determined. 0.2300 grm. of the oil gave 0.2041 grm. AgCl. Calculated for CgHi,Cl. Found. CI . 22.10 21.94 VOL. XXXVI.- -19 290 PROCEEDINGS OF THE AMERICAN ACADEMY. The molecular weight was also ascertained at the freezing point. 0.8672 grm. of the oil and 25.03 grms. benzol gave a depression of 1°.090. Calculated for C9H17CI. Found. 160.5 - 156 In further support of the formula of the chloride, the index of refrac- tion was determined, 1.462, and the molecular refraction calculated. Calculated for CgHjjCl. Found. 46.3 47 When sodium was allowed to act on trimethylhexamethylene chloride, a vigorous reaction set in that could be controlled by cooling. By carry- ing on the reaction in an ethereal solution, on standing over night in water the reaction was complete. The product of the reaction consisted for the most part of an unsaturated hydrocarbon, and a smaller quantity of a heavy oil, doubtless formed by the union of two methylene rings. The boiling point of the unsaturated hydrocarbon was 135°-140°. Its unsaturated condition was shown by the readiness with which it united with iodine in Hiibl's reagent, absorbing approximately two atoms of iodine. The specific gravity of the unsaturated hydrocarbon at 20° was 0.7762. The molecular weight at the freezing point was determined. 0.8572 grm. of the oil and 22.45 grms. benzol gave a depression of 1°.571. Calculated for CgHjg. Found. 124 120 The index of refraction was found to be 1.431, and the molecular refraction : — Calculated for TrnnTid C^K,(ms)3. CeH8(CH3)2=CH2. '°''°''- 39.26 40.97 41.46 Dekanaphtene Chloride, C10H19CI. In confirmation of the formula of dekanaphtene, the index of refraction was determined and the molecular refraction calculated. With the den- sity 0.7898, and the index 1.4325, the molefular weight gave the following value: — Calculated for CmHjo. Found. 46.10 46.00 MABERY, — COMPOSITION OF PETROLEUM. 291 The chlorine derivative of this hydrocarbon was formed by passing in chlorine over water. After washing, drying, and fractioning in vacuo, the chloride collected in larger quantities at 105°-110° (50 mm.) An- other portion collected at 140°-145°, probably a dichloride. The specific gravity of the monochloride at 20° was 0.9470. A determination of chlorine gave the following value : — 0.1840 grm. of the oil gave 0.1476 grm. AgCl. Calculated for CioHigCl. Found. CI 20.33 19.80 The molecuIaY weight of the chloride at the freezing point of benzol was also determined : — 1.2536 grm. of the oil and 21.29 grms. benzol gave a depression of 1°.689. Calculated for C,oHiyCl. Found. 174.5 171 A determination of the index of refraction of this chloride gave 1.468. The molecular refraction calculated as follows : — Calculated for CioHjaCl. Found. 50.89 51.34 On account of the small quantity of the dichloride obtained, it was not possible to purify it completely by distillation. But a determination of chlorine gave 31.53 per cent; required for C10H18CI2, 33.90. A deter- mination of molecular weight gave 199 ; required for the dichloride, 209, The molecular refraction calculated from the index was 56.98 ; calculated from the formula, 55.81. On account of the differences between the theoretical values for the mono- and di-chlorides, these values are sufficient to show that the dichloride was formed and separated in nearly a pure form. Under ANAPHTENE Chloride, CnHoiCl. The index of refraction of this hydrocarbon was found to be 1.4403, and the molecular refraction : — Calculated for CuIIjj. Found. 50.70 50.63 This determination was made in the distillate 190°— 192°, which was used for all work on this hydrocarbon. 292 PROCEEDINGS OF THE AMERICAN ACADEMY. The chlorine derivative was prepared in the same manner as those of the hydrocarbons previously described. On fractioning it in vacuo at 35 mm. it collected for the most part at 125°-130°. Its specific gravity was found to be 0.9583 at 20°. A chlorine determination supported the formula of the monochloride. 0.1560 grm. of the oil gave 0.1179 grm. AgCl. Calculated for CnHjiCl. Found. 18.81 18.69 The molecular weight was determined at the freezing point of benzol. 0.6055 grm. of the oil and 17.37 benzol gave a depression of 0°.890. Calculated for CnHjiCl. Found. 188.5 192 The index of refraction was found to be 1.476, and the molecular refraction : — Calculated for C,iH„iCl. Found. 55.48 54.32 The composition of its chloride, together with its molecular weight and molecular refraction, all show that undecane has for its boiling point 194°-19G.° DODEKANAPHTENE ChLORIDE, C12H03CI. The index of refraction of dodekanaphtene was found to be 1.4649, and the molecular refraction : — Calculated for C12H24. Found. 55.38 55.24 The chlorine derivative was formed, washed, dried, and fractioned in vacuo. It collected for the most part at 130°-135° (17 mm.) Its spe- cific gravity at 20° was 0.9616. A determination of chlorine gave the following result : — 0.1657 grm. of the oil gave 0.1153 grm. AgCl. Calculated for C12H23CI. Found. CI 17.52 17.20 The molecular weight was also determined : — MABERY. — COMPOSITION OF PETROLEUM. 293 0.7172 grm. of the oil and 19.04 grms. benzol gave a depression of 0.925. Calculated for O^j^zsC^- Found. 202.5 204 The index of refraction was 1.480, and the molecular refraction : — Calculated for Ci^fl^fil. I'ound. 60.77 59.96 Tridekanaphtene Chloride C13H25CI. The index of refraction of this hydrocarbon as determined is 1.4745, and its molecular refraction : — Calculated for CiaHjg. Found. 60.25 59.84 The chlorine derivative was formed by the action of chlorine, dried and fractioned under 17 mm. ; it came together for the most part at 140°-145°. Its specific gravity at 20° was 0.9747; a Carius deter- mination gave the following percentage of chlorine : — 0.1 G74 grm. of the oil gave 0.1137 grm. AgCl. Calculated for C13U25CI. Found. 16.38 16.78 In the chlorine derivatives of the higher hydrocarbons the weight of oil that can be taken for analysis is limited, since as in the last analysis the pressure of the large volume of gases formed is more than the tube can stand. The molecular weight of tridekanaphtene chloride was determined at the freezing point of benzol : — 0.4447 grm. of the oil and 17.88 grms. benzol gave a depression of 0.763. Calculated for C13H25CI. Found. 216.5 217 Tetradekanaphtene Chloride, C14H07CI. Tetradekanaphtene chloride was readily formed by passing chlorine into the hydrocarbon over water in ordinary daylight ; if the action was stopped with a small portion of the hydrocarbon unacted on, the product consisted for the larger part of the monochloride. After washing and drying, the chlorine derivative was separated by continued distillation in 294 PROCEEDINGS OF THE AMERICAN ACADEMY. vacuo under 13 mm. ; it came together for the most part at 150°-] 55°. The specific gravity of the monochloride was 0.9748 |jo ; at Do 0.9730 ; at 50°, 0.9661 ; and at ^o, 0.9579. The mean coefficient of expansion, within 20°-40°, from these results, is 0.00078. A determination of chlorine gave a value required for the mono- chloride : — 0.1559 grm. of the oil gave 0.0989 grm. AgCl. Calculated for Ci4H27Cl. Found. CI 15.39 ' 15.80 As mentioned above, the decreasing proportion of chlorine in these derivatives with the increasing molecular weight, and the consequent larger volumes of gases, beyond the strength of the ordinary Carius tubes, gives a smaller weight of silver chloride than could be desired, but the accuracy of the method permits of sufficiently reliable results, even with the small weights. The molecular weight of the chloride was determined at the freezing point of benzol : — 0.8923 grm. of the oil and 17.76 grms. benzol gave a depression of 1°.094. Calculated for CiiHjjCl. Found. 230.5 225 The index of refraction was found to be, 1.493, and the molecular refraction 68.67 ; calculated for C14H27CI, 69.37. The boiling point of this chloride cannot be accurately determined under atmospheric pressure because it is rapidly decomposed at the higher temperature and in presence of air, although it may be distilled indefinitely in vacuo. Probably the boiling point under atmospheric pressure is not far from 275°. Pentadekanaphtene Chloride, C15H29CI. This chloride was prepared from pentadekanaphtene, which had been well fractioned in vacuo. These higher chlorides are formed as readily as the lower ones. After washing and fractional distillation under 14 mm. this monochloride came together for the most part at 170°-175° without decomposition. Its boiling point under atmospheric pressure is probably near 300°. Its specific gravity at ^o was 0.9771 ; at |]o 0.9753 ; and at 550, 0.9714; and at ^o, 0.9643. The coefficient of expansion calcu- MABERY. — COMPOSITION OF PETROLEUM. 295 lated from these values is 0.000576. A Carius determination gave the required percentage of chlorine. 0.1536 grm. of the oil gave 0.0923 grm. silver chloride. Calculated for CisHjgCl. Found. 14.51 14.85 A determination of the molecular weight supported the same formula. 0.9073 grm. of the oil and 18.93 grms. benzol gave a depression of 0°.984. Calculated for C15H29CI. Found. 239 244.5 The index of refraction was 1.493, and the molecular refraction, 72.90 ; calculated for C15H29CI, 73.97. Attempts will be made to form the chlorides of the higher hydro- carbons in connection with the study of the composition of these bodies. No. 37. —ON THE COMPOSITION OF JAPANESE PETROLEUM. By Charles F. Mabery and Shinichi Takano.* The oil fields in Japan are the most promising and are under the most rapid development of any recently discovered oil territory. The output in 1891 was 56,000 bbls. annually; in 1899 it was 1,000,000 bbls. The oil territory in Japan is contained in the province of P^chigo, at least to the extent of 90 per cent, on the northern coast of the Sea of Japan. This province is surrounded in part by a mountain chain which * Mr. Takano has spent three years in tlie study of petroleum in tliis country, having been sent for this purpose by the Japanese Government. He is thoroughly familiar with the geologj- of the oil territory in Japan, having given especial at- tention to this subject in a thesis which he presenteil for a degree in the University of Tokio. Besides a thorough knowledge of the composition of petroleum from a chemical point of view, which he has gained during the two years he has spent exclusively in the study of this subject in this Laboratory, Mr. Takano spent one year as a laborer in different refineries, where he took charge by actual manipula- tion of every process in the preparation of commercial products. The work pre- sented in this paper formed the subject of a thesis by Mr. Takano for the degree of M.S. 296 PROCEEDINGS OP THE AMERICAN ACADEMY. encloses a section of country 140 miles long by 150 miles broad, rising gradually from the sea to the mountains with a varying altitude from 150 feet to 500 feet. Oil is found chiefly in the Upper Eocene of the Tertiary formation, where it is held under pressure between impervious layers of slate and sandstone. Nodules of calcite are frequently found embedded in the sandstone, and crystals of calcite twinned, resembling those found in the Ohio Tren- ton-limestone, oil-bearing rock. The oil strata are full of sea-shells, a good indication as to the origin of the oil formations. There are great variations in the depths of the wells. For example, the wells of the Amaze field are approximately 2000 feet in depth, while those of the Miyagawa field, only six miles distant, are 700 feet deep; the wells of the Niitsu field are still shallower, 600 feet. The Nagaoka wells are 800 feet in depth. Nevertheless the oil strata at the different depths are essentially of the same formation. The sandstone in wiiich the Nagaoka oil is found is coarser than that of the other fields. On the surface of the Niitsu oil territory are immense beds of peat which are used f^or fuel. Although the oil fields of Japan are situated in close proximity, speci- mens of oil from the different fields differ as essentially in composition as the variations in specific gravity indicate. As will appear later, the Amaze, Miyagawa, and Hirei fields yield parafRne in considerable quantities. While the hydrocarbons above C7H14 do not include mem- bers of the series C„H2,j+2) ^t least so far as it appears from analysis of distillates prepared on a laboratory scale, the lower distillates do con- tain members of the paraffine series. The paraffine hydrocarbons with low boiling points, such as the butanes, pentanes, and hexanes, have an agreeable sweetish odor that is easily recognizable, and quite different from the pungent harsh odor of the methylenes. The odor of the paraffines is more apparent in the Miyagawa oil than in any other of the Japanese oils we have seen, and somewhat less in the Amaze oil. When these hydrocarbons with low boiling points are present, the crystalline paraffine hydrocarbons C„H2„+2 are usually to be found. Considerable quantities of gas were formerly obtained from the Amaze oil territory, but the supply now seems to be exhausted, at least so far as wells have been bored; some gas escapes from the shallow Miyagawa wells, more from the shallow wells of the Niitsu territory. As wells are sunk deeper in this territory it is probable that lighter oils will be found. On account of the friable condition of the oil rock and the danger of MABERY. — COMPOSITION OF PETROLEUM. 297 clogging the wells by loose material, " shooting " the wells after boring is not practised. The flow from the wells is irregular ; frequently it will amount to 300 barrels a day for a week, and then stop, and the oil must be pumped. The oil territory in Japan includes the following fields : — Amaze, Nagaoka, Niitsu, and Hiyama. The different sections of the oil terri- tory may be classified as follows: — Amaze Amaze I ^liyagawa \ green oil Gendogi Hirei Kitatani Katsudo Koguchi Kusodsu Hiyama { Hiyama Nagaoka Niitsu dark oil } dark green oil The Amaze field is the oldest ; the Hiyama field has been most re- cently developed; both these oils contain paraffiue. The crude oils from the different fields differ essentially in their prop- erties, as shown by the different specific gravity, the different percentages Amaze. Hirei. Katsudo. Kitatani. Koguchi. Kusodsu. Miyagawa. Specific Gravity . . . 0.8245 0.8622 0.8771 0.8952 0.9435 0.9210 0.8911 Per cent Sulphur . . 0.23 0.41 0.82 0.61 0.49 0.37 0.32 Per cent Nitrogen . . 0.35 0.74 0.07 0.75 1.34 1.23 0.55 Iodine Absorption . . 0.0 0.84 7.66 0.82 9.79 0.62 1.63 Coefficient of Expansion 82.5 78.5 70.5 79.5 67.5 61.5 74.5 ] Percentages c >F Distillates. Amaze. Hirei. Katsudo. Kitatani. Koguchi. Kusodsu. Miyagawa. - 150° 22.8 21.8 22.2 14. 0.0 0.0 15. ISOO-SOO" 40.2 38.3 38.8 38.8 25.0 25.0 36.8 4- ?.00° . . 37 39.0 39. 47.2 75. 75. 48.2 298 PROCEEDINGS OF THE AMERICAN ACADEMY. of sulphur, nitrogen, and the different proportions in which they distil at different temperatures. There are also marked differences in iodiue ab- sorption, and in the coefficients of expansion. The latter were determined by ascertaining the specific gravity at 5°, 10", 20°, and 25°, and divid- ing the differences in specific gravity at the different temperatures by five and multiplying the quotient by 100,000, the method described in Kedwood's treatise on petroleum. In the development of oil territory hitherto, no attempts have been made to ascertain the series of hydrocarbons which compose the main body of the crude oil. Beside the work of Pelouze and Cahours, Schoelemmer, and Warren on the Pennsylvania and Canadian oils, and the work carried on in this Laboratory, no attempts have been made to determine the form of the hydrocarbons in the lower distillates of American oils, and nothing whatever beside the unpublished work of this Laboratory on the determination of the composition of the portions with higher boiling points. Beside the work of Markownikoff on the Russian oils and the work of Warren and Storer on Rangoon petroleum, very little has been done in this direction on oils from other fields. On account of the ease in the ^preparation of commercial products from the lighter oils of Pennsylvania and Ohio, the ultimate composition was of less importance than it is now becoming in the development of oil fields that yield heavier crude oils, such as the oil territory in California, Texas, South America, Japan, and numerous other fields recently dis- covered. The methods that must be applied to these heavy oils are essentially different from the methods that have been universally in use since the beginning of the oil industry. In Japan, the promoters of those oil fields will have the advantage not only of all former experience in oil refining, but the further advantage of a knowledge of the hydro- carbons which form the main body of the crude oils. Japanese petro- leum apparently differs from other heavy petroleums in that it contains smaller amounts of the benzol homologues. Benzol and its homologues were found in the Amaze oil, and some of the other crude oils, but fuming sulphuric acid failed to reduce materially the specific gravity of several of the distillates that should yield benzol hydrocarbons, if they were present. Constituents of Petroleum from the Amaze Field. The lightest oil from the Japanese fields is found in the Amaze terri- tory. It consequently contains the largest projjortion of more volatile MABERY, — COMPOSITION OF PETROLEUM. 299 constituents. A combustion of Amaze crude oil gave 84. 6 G per cent carbon and 13.22 per cent hydrogen. After several distillations under a Hempel column, fractions collected in larger quantities at 68°, 98°, 119°, 135°, 62°, 96°, 216°. No attempts were made to ascertain the form of the hydrocarbons below 68°. The distillate collected at 68° gave as its specific gravity 0.7343, which indicated that hexane was not present in any considerable quantity. But nothing further was done toward identifying hexamethylene, which no doubt is the principal hydrocarbon in this distillate. The distillate collected at 98°-l 00°, after purifying with fuming sul- phuric acid, gave as its specific gravity at 20°, 0.7450. A combustion gave the following percentages of carbon and hydro- gen : — 0.1347 grm. of the oil gave 0.4221 grm. COo and 0.1721 grm. H2O. Calculated for C^IIij. Found. C 85.70 85.45 H 14.30 14.20 Its index of refraction was found to be 1.4174, and the molecular refraction, 33.14 ; calculated for C-,Hi4, 32.22. This hydrocarbon was therefore methylhexamethylene. The distillate 118°-120'^, after purification with fuming sulphuric acid, gave 0.7621 as its specific gravity at 20°. A combustion gave the following percentages of carbon and hydrogen : — 0.1406 grm. of the oil gave 0.4378 grm. CO2 and 0.1812 grm. HoO. Calculated for CgHig. Found. C 84.70 84.94 H 14.30 14.33 A determination of the index of refraction of this oil gave 1.4256, and the molecular refraction, 37.68 ; calculated for C^Uu, 36.82. This hydrocarbon was therefore dimethylhexamethylene. The distillate collected at 134°-135° was purified with fuming sul- phuric acid and analyzed. 0.1528 grm. of the oil gave 0.4805 grm. CO2 and 0.1950 grm. HgO. Calculated CyK^^. Found. C 85.70 85.76 H' 14.30 14.29 300 PROCEEDINGS OF THE AMERICAN ACADEMY. It gave as its specific gravity at 20°, 0.7787. The refractive index of tliis oil was found to be 1.4348, and the molecular refraction, 42.27 ; calculated for CgHig, 41.42. This con- stituent was therefore trimethyihexamethylene. A distillate collected in considerable quantity at 160°-162°, which was purified with fuming sulphuric acid and analyzed : — 0.2055 grm. of the oil gave 0.6445 grm. CO.2 and 0.2556 grm. HoO. Calculated for CiqHjq- Found. C 85.70 85.50 H 14.30 ■ 13.82 This oil gave as its specific gravity at 20°, 0.7902. Its index of refraction was 1.4418, and its molecular refraction, 46.94; calculated for CioHoo, 46.03. The distillate at 190°-192°, after purification with fuming sulphuric acid, gave as its specific gravity at 20°, 0.8061. Its composition was determined by analysis ; — 0.1612 grm. of the oil gave 0.5046 grm. COo and 0.2025 grm. HoO. Calculated for C,iH22- Found. C 85.70 85.35 H 14.30 13.96 The molecular weight of this hydrocarbon at the freezing point of benzol was 156; calculated for CnHo.,, 154. The index of refraction at 20° was 1.4482, and the molecular refraction 51.24; calculated for CuHoo, 50.63. The distillate 212°-214°, purified with fuming sulphuric acid, gave as its specific gravity at 20°, 0.8165. A combustion gave the following proportions of carbon and hydrogen : — 0.1875 grm. of the oil gave 0.5879 grm. COo and 0.2451 grm. HgO. Calculated for CijIIjj. Found. C 85.70 85.51 H 14.30 14.52 A determination of its molecular weight at the freezing point gave 172; calculated for C10H04, 168. Its index of refraction was 1.4535, and the molecular refraction, 55.76 ; calculated for CjoHo^, 55.23. MABERY. COMPOSITION OF PETROLEUM. 301 Composition of the Portions of Japanese Petroleum with High Boiling Points. Japanese petroleum from different sources differs materially in its com- position. From such oils as the Hirei no crystalline solids can be sepa- rated, even at low temperatures. But from others, such as the Amaze, Miyagawa, and Hiyama, crystalline solids separate from the higher fractions. The fraction 310°-315° atmospheric pressure, from Amaze crude oil became solid on cooling. The solid portion was separated by cooling and filtration ; it was washed, pressed, and warmed with gasoline which removed all color. Melting point, 68°. The fractions above 22o° were collected in vacuo under 30 mm. The purified solid from 225°- 230° melted at 70°, that from 2o0°-275° at 73°, and that from 2G0°- 265° at 74°. The solid from 225°-230° gave, by combustion, values showing it to belong to the series Cn^2n+2. 0.1535 grm. of the oil gave 0.4890 grm. CO2 and 0.1787 grm. HgO. Calculated for „ , p TT p XT Found. C 85.14 85.70 85.29 H 14.86 14.30 14.99 The fraction 250°-260°, 30 mm., from the Amaze oil gave the follow- ing percentages by combustion, also showing the series C„H2„+2 • — 0.1654 grm. of the oil gave 0.5161 grm. CO2 and 0.2233 grm. H2O. C 85.03 H 15.00 A combustion of the fraction 265°-270° gave values required for a hydrocarbon of the series C„H2„+2 • — 0.1750 grm. of the oil gave 0.5469 grm. COo and 0.2346 grm. H2O. C 85.21 H 14.81 In determining the molecular weight of this liydrocarbon at the boil- ing point of benzol, the following result was obtained: — 0.4190 grm. of the oil and 24.3 grms. benzol gave a rise in boiling point of 0.126. Found. 367 367 302 PROCEEDINGS OF THE AMERICAN ACADEMY. Determinations by the boiling point method of hydrocarbons vvitli such high molecular weights are of necessity somewhat uncertain on account of the slight rise in boiling point. The question of the molecular weights of these solid hydrocarbons will receive more attention with the constitu- ents of Pennsylvania and California petroleums with high boiling points. The specific gravity of the solid 250°-260° is nearly the same as that of the corresponding hydrocarbon from Pennsylvania petroleum : — Japanese, 250o-260^3Umm. I 292 •enusjivania,* :^-295 ', 50 mm, 60 0.7977 70 0.7943 0.7950 80 0.7920 0.7943 90 0.7918 The specific gravity of the Japanese solid at 60° could not be deter- mined, because it was not liquid at that temperature. MiTAGAWA Petroleum. Althougli this oil is from a field situated only six miles from the Amaze field, it differs essentially in its specific gravity, and in the pro- portions in which it distils, from the Amaze oil. The crude oil was distilled under atmospheric pressure, and the distillation of the lower portions continued until they came together in larger quantities at tem- peratures at which distillates were collected from the other oils. The specific gravity of the distillates after treating with concentrated sulphuric acid is as follows : — 98 -100\ 118'^-120^. 134^-136^. 160^-162°. 194°-196°. 212^-214°. 228°-230^. 0.7364 0.7631 0.7772 0.8088 0.8493 0.8674 0.8770 The last three fractions were also treated with fuming sulphuric acid and the specific gravity determined : — 194:'='-Jm°. 212°-214°. 228='-230°. 0.8412 0.8650 0.8720 The slight change after the thorough treatment with fuming sulphuric acid shows that no benzol homologues were present in these portions, yet the specific gravity of the hydrocarbons above 196° is considerably higher than of those from Amaze oil or from Hirei oil. The distillates * Unpublisliod data. MABERY. COMPOSITION OF PETROLEUM, 303 collected under atmospheric pressure were thoroughly treated with fuminc sulphuric acid, washed, dried, and their molecular refractiou determined : — Distillate. l.'efractive Index. Molecular Refraction. Calculated. Required. 9S°-100° 118°-120o 134°-] 36° 160°-162° 194°- 106° 214°-2I6° 1.4117 1.4163 1.4261 1.4463 1.4605 1.4706 33.14 36.92 41.51 46.26 50.27 51.34 32.21 36.82 41.42 46.03 50.63 55.23 HiREi Petroleum. A combustion of Hirei crude oil gave 82.28 per cent of carbon and 13.19 per cent of hydrogen. In the distillation of the Hirei oil, fractions collected within the same limits of temperature as those from the other crude oils. The distillate collecting in the vicinity of 98°, after treat- ment with sulphuric acid, gave 0.7412 as its specific gravity. Its molec- ular weight at the freezing point of benzol was 98 ; required for C7H14, 98. Its index of refraction was 1.4095, and its molecular refraction, 32.77; required for C^IIi4, 32.22. The fraction 118°-120° gave as its specific gravity 0.7523. Its mo- lecular weight was 114 ; required for CgHie, 112. Its index of refraction was 1.4151, and its molecular refraction, 37.34; required for CgHig, 36.82. The fraction at 135° gave as its specific gravity 0.7676. Its molecu- lar weijrht was 128; required for CyHis, 126. Its index of refraction was 1.4372, and its molecular refraction, 42.12; required for CgHig, 41.42. The fraction 162° gave for its specific gravity 0.7887. Its molecular weight was found to be 137; required for CjoHjo, 140. Its index of refraction was 1.4372, and its molecular refraction, 46.60 ; required for C10H20, 46.03. The specific gravity of the fraction at 196° was 0.8192. Its index of 304 PROCEEDINGS OP THE AMERICAN ACADEMY. refraction was 1.4516, and its molecular refraction, 50.78; required for C11H20, 50.63. The specific gravity of the fraction 216° was 0.8327, and the molecu- lar weight, 172; required for C12H24, 168. Its index of refraction was 1.4599, and its molecular refraction, 55.22; required for C12H04, 55.23. The specific gravity of these distillates from Ilirei oil is somewhat higher than was found in the corresponding distillates from Amaze oil, and the differences inci'ease with increasing molecular weights. It was at first thought that this was due to incomplete removal of benzol hydro- carbons, but still further treatment with fuming sulphuric acid failed to diminish these values. It is probable that the oil contains hydrocarbons with more than one methylene ring. The results of this examination show that Japanese petroleum is com- posed for the greater part of hydrocarbons of the series C^Ho,,, — the methylene hydrocarbons. Probably the very heavy oils contain hydro- carbons with two or more methylene rings, of the series C„H2„_2 or C,jH2„_4. Some of the oils contain solid paraffiiie hydrocarbons, others do not. The proportion of benzol derivatives in the oils examined is relatively much smaller than in California petroleum. The proportion of nitrogen compounds and of sulphur compounds is quite variable. In some of the oils the percentages were nearly as large as any found in California petroleum, in others the amounts were much smaller. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVI. No. 16. —January, 1901. THE ECLIPSE CYCLONE AND THE DIURNAL CYCLONES. Kesults of Meteorological Observations in the Solar Eclipse of May 28, 1900. By H. Helm Clayton. THE ECLIPSE CYCLONE AND THE DIURNAL CYCLONES. Results of Meteokological Observations in the Solar Eclipse of Mat 28, 1900. « By H. Helm Clayton. Presented November 14, 1900. Received December 12, 1900. The path of total solar eclipse in the United States on May 28, 1900, was visited by a number of experts and trained observers, who took meteorological observations as a part of the program on the day of the eclipse. These included Mr. A. Lawrence Rotch and Mr. S. P. Fer- gusson at Washington, Ga. ; Mr. O. B. Cole at Centerville, Va. ; Mr. G. W. Pickard at Virginia Beach, Va. ; and myself at Wadesboro, N. C. These observations were sent to the Blue Hill Meteorological Observatory and given to me for discussion. Besides these I obtained records from a number of well-equipped observatories in North America. These in- cluded the Toronto Observatory, the New York Central Park Observa- tory, the Blue Hill Observatory, the Belen College Observatory of Havana, the McGill College Observatory of Montreal, the Meteorological Station at Cornell University, the City Engineer's Office at Providence, R. I., and observations by Mr. Eddy at Bayonne, N. J. These obser- vations were all within the area of partial eclipse, and the data were furnished by the kindness of the directors. The details of the discussion of the observations are published in a Bulletin of the Blue Hill Meteorological Observatory.* The results embody certain conclusions of general interest which I am permitted to present to the Academy. The meteorological changes due to the eclipse were separated from other changes of greater length, such as the diurnal and cyclonic, by interpolating a uniform change between the beginning and the end of the eclipse and subtracting this from the observations. For example, in Figure 1 is plotted the observations of temperature at AVadesboro, N. C. * Annals of the Astron. Observatory of Harvard College, XLIII. No. 1. 308 PROCEEDINGS OF THE AMERICAN ACADEMY, The outside vertical lines B and E show the beginning and end of partial eclipse, and the central vertical lines T show tlie times of total eclipse. The dotted straight line connects the observed temperature at the begin- 7 A.M 8 A.M. 9 A.M. 10 A.M. Figure 1. ning and end of the eclipse, and represents the interpolated uniform change. The observed temperatures are shown by the unbroken curved line, and the departures of these from the values represented by the dotted line is assumed to be the depression of temperature arising from the eclipse. The pressure, humidity, and vapor tension were treated in the same manner. In order to obtain the eclipse wind in velocity and direction, the observations were treated in the following manner. In the accompanying diagram, Figure 2, let A B represent the direc- tion and velocity of the wind prevailing independent of the eclipse, and Figure 2. A C the wind observed at any moment during the eclipse ; then com- pleting the parallelogram of forces, A D will represent the eclipse wind in direction and velocity. The prevailing wind was derived from the mean of the winds immediately preceding and following the penumbra, or, what was found to be practically the same thing, from the mean wind direction durhig the passage of the penumbra, since the eclipse wind was CLAYTON. — THE ECLIPSE CYCLONE. 309 from opposite directions during this time. The penumbra is used to indicate the area of partial eclipse, and the umbra to indicate the area of total eclipse. The mean wind and the eclipse wind were at first deter- mined graphically for all the stations ; then as the results seemed to be of importance, they were rigidly computed for all the stations where the observations were sufficiently accurate to warrant it. These results, when plotted, indicate very clearly an outflow of wind from around the umbra, and an inflow around the borders of the penumbra. But there are certain irregularities due to the normal irregularities of the wind. In order to diminish the effect of these, I smoothed the observations by the formula . These winds were plotted at their proper places on maps of the United States for 8.15 a.m., Toth meridian time, when the umbra was about to enter the American conti- nent from the Pacific, and also plotted for 9 a.m., when the umbra had passed off the coast of the United States on to the Atlantic. These maps are shown in Figure 3. The position of the umbra is shown on each map by a dark circular area. The depressions of temperature by the eclipse are shown by numerals on the maps, and isotherms are shown by dotted lines. The weather conditions are indicated by symbols, and the direction and velocity of the eclipse wind are indicated by the direction and length of the arrows. The winds were practically reversed in direc- tion as the umbra moved from one side of the continent to the other, but both charts show a distinct anticyclonic circulation and an outflow of air extending from the umbra, or central area of the eclipse, to a distance of about fifteen hundred or two thousand miles. In the 8.15 a.m. chart the outer limit of the outflow appears to be in New York, beyond which there is an inflow. In tliis chart the stations of observations are so far in advance of the central area of the eclipse that no appreciable depres- sion of temperature is shown ; but in the 9 a.m. chart, which coincides with the greatest depression of temperature at Wadesboro. Washington, and Virginia Beach, there is a central area shown by the isotherms where the depression of temperature exceeds 8° F. This area of greatest cold lags behind the umbra about five hundred miles. The charts in Figure 3 show only a portion of the eclipse area, or penumbra, which was about iive thousand miles in diameter. Hence the charts do not give an idea of the winds on the outer area of the penum- bra, or the successive changes which occurred at any one station as the eclipse passed over it. A view of these changes is obtained by plotting the winds, temperature, etc., at given stations when they were successively 310 PROCEEDINGS OF THE AMERICAN ACADEMY. OCLEAR;eFAlR: e CLOUDY. ri(;rRK o. CLAYTON, — THE ECLIPSE CYCLONE, 311 in different portions of the eclipse area. The eclipse shadow travelled with a velocity somewhat greater than two thousand miles an hour. By- placing the stations at their proper distances from the path of the umbra and plotting the successive fifteen minute observations at intervals of about five hundred miles, a synoptic chart is obtained showing the conditions observed at any given station or group of stations when they were in dif- ferent portions of the eclipse area. In this way Figure 4 was constructed. In this diagram the direction and width of the path of the umbra is Figure 4. shown by parallel lines forming a long arrow. The central shaded area shows the umbra, and the outer unbroken circle shows the outer limit of the penumbra. The data north of the path of the umbra are derived from the mean of the observations at Ithaca, Toronto, and Blue Ilill ; the data along the path are derived from the mean of observations at Washington, Ga., and Wadcsboro. N. C. ; the dita south of the path are from Havana, 312 PROCEEDINGS OF THE AMERICAN ACADEMY. Figure 4 indicates distinctly an anticyclonic circulation of the wind around the centre of the eclipse extending out to a distapce of about fifteen hundred miles from the umbra. Outside this area there is an equally distinct cyclonic circulation about one thousand miles in width extending out to and beyond the edge of the penumbra. Beyond this there are indications of another ring of outflowing winds. The inner circle of broken lines in the diagram represents a probable ring of low- air pressure. The outer circle of broken lines surrounding the penumbra represents a probable ring of high pressure. The isotherms are shown by dotted lines. They show an elliptical area of cold air central about five hundred miles in the rear of the umbra. The greatest depression of temperature is north of the track of the umbra. This was chiefiy due to the continental efi'ect. The diiFerence may also have been due in part to the fact that the sky was partly cloudy at Havana. On comparing stations similarly situated as regards the eclipse, it was found that the depression of temperature due to the eclipse was less at stations where it was cloudy, and that it also diminished with height above the sea. This indicates that the cooling is chiefly in a thin stratum of air very near the earth's surface. The analogy to the diurnal change of temperature would also indicate that this must be true. The shape and position of the areas showing the humidity departures are so similar to those of tem- perature that it is not deemed necessary to reproduce them. The chief difference is that in one case the departures are plus and in the other minus. In other words, during the eclipse there is a rise of absolute and relative humidity and a fall of temperature. The observations indicate very clearly a lowering of the air pressure during the eclipse, the minimum of pressure occurring soon after the minimum of air temperature. This is shown by records made at Wash- ington, Ga., at Toronto, and at Blue Hill. The accompanying diagram Figure 5. shows a record made by an " aerograph," or air barometer, at Toronto. This barograph, devised by F. Najjier Deuison, has its air-chamber buried eight feet below the surface of the ground to protect it from CLAYTON. — THE ECLIPSE CYCLONE, 313 external changes of temperature. The curve is traced from the record, and is o-ivea on the same scale without correction in any way. The eclipse be^an at Toronto about 7.47 a.m. and ended about 10.18 a.m. A straight dotted Hue is drawn through the curve connecting the pres- sure recorded at the beginning and end of the eclipse. It is seen that the pressure was generally below the dotted line throughout the eclipse, but there was an upward swell between 8 and 9 a.m., shortly preceding the middle of the eclipse. Immediately preceding and following the beginning and end of the eclipse the curve rises above the dotted line, indicating a ring of high pressure surrounding the umbra, and thus agreeing perfectly with the distribution of pressure demanded by the wind circulation. I find that when the changes of pressure observed during previous eclipses are separated from the normal diurnal changes, they show changes very similar to those given by the curve for Toronto, except that the rise in pressure near the middle of the eclipse is greater for stations in the path of total eclipse. This central rise of pressure is due to the increased d-ensity of the air from cold, and on it depends the outflow of air surrounding the umbra. Hence in normal eclipses there is a central area of relatively high pressure ; surrounding this is a ring of minimum pressure, and beyond this, outside the edge of the penumbra, is a ring of maximum pressure. The low temperature, the circulation of the winds, and the form of the pressure curve accompanying the eclipse of May 28, 1900, all pro- claim the development by the eclipse of a cold-air cyclone, the theory of which has been so well worked out by Ferrel that no better descrip- tion of it could be given than in his own words. Ferrel maintains from theoretical considerations that cyclones necessarily have an inner area of low pressure, surrounded by a ring of high pressure, which Professor Davis has named a pericyclone. Ferrel further maintains that a cyclone may liave its origin either in a high temperature increasing toward a central area, or in a low temperature decreasing toward a central area. The one he calls a cyclone with a warm centre, the other a cyclone with a cold centre. Of cyclones with a cold centre he says : — " If for any reason the central part of any given portion of the atmos- phere of a somewhat circular form is maintained in any way at a lower temperature than the surrounding parts, and the temperature gradient on all sides is somewhat symmetrical, we have approximately the conditions which give rise to a cyclone. In this case it is readily seen that there must be a vertical circulation, as in the ordinary cyclone, but that it is reversed, out from the centre below, and in toward the centre above. 314 PROCEEDINGS OP THE AMERICAN ACADEMY. with a gradual settling down of the air in the interior to supply the out- ward current beneath. This vertical circulation, as iu the case of the ordinary cyclone, gives rise to a cyclonic motion in the interior and an anticyclonic in the exterior part of the air under consideration, but in this case the gyratory velocity is greatest above and is less at lower alti- tudes, diminishing down to the earth's surface, where it is least. In the anticyclonic part the reverse takes place, the gyratory velocity being least above and greatest down near the earth's surface. The distance from the centre at which the gyratory velocity vanishes and changes sign, is greatest above and gradually becomes less, with decrease of alti- tude down to the earth's surface, where it is nearest the centre. . . . The conditions of a cyclone with a cold centre which are the most nearly perfect are those furnished by each hemisphere of the globe, as divided by the equator, in which the pole is the cold centre, and the temperature gradient from the pole toward the equator is somewhat symmetrical in all directions from the centre. . . . The easterly motions in the higher latitudes and the westerly ones in the lower latitudes, in the one case, correspond to the cyclonic in the interior and the anticyclonic in the exterior part, and the belt of high pressure near the tropics to that of high pressure in the case of any cyclone with a cold centre. . . . The centre of a cyclone with a cold centre may or may not have a minimum pressure, according to circumstances. A certain amount of temperature gradient, and of pressure gradient which is independent of the gyratory motion, as explained in the case of the general circulation of the atmos- phere, is necessary to overcome the friction in the lower strata and to keep up the vertical circulation, upon which the cyclone depends ; and the pressure gradient, which depends upon the temperature gradient and is independent of the gyrations, may be such that the increase of pressure in the central part due to this cause may be greater than the decrease of pressure arising from the cyclonic gyrations, especially where surface friction is great." * The eclipse cyclone is of especial interest from a theoretical point of view, because its origin, clearly connected with the fall of air tempera- ture attending the eclipse, is freed from all questions of condensation of vapor or of the dynamic effects due to the meeting of air currents whose possible influence complicates the question as to the origin of the ordinary cyclone. The eclipse may be compared to an experiment by Nature in which all the causes that complicate the origin of the ordinary * A Popular Treatise on the Winds, pp. 337-3:J9. CLAYTON. — THE ECLIPSE CYCLONE. 315 cyclone are eliminated except that of a direct and rapid change of tem- perature. The results derived from the observations by eliminating the influence of other known phenomena give quantitatively the effects of a oriven fall of temperature near the earth's surface in a given time. They show that a fall of temperature is capable of developing a cold-air cyclone in an astonishingly short time, with all the peculiar circulation of winds and distribution of pressure which constitute such a cyclone. They show, furthermore, that a fall of temperature of the air does not act primarily to cause an anticyclone but a cyclone, and the anticyclone is a secondary phenomenon, or rather a part of the cyclone. The eclipse cyclone shows no apparent lag or dynamic effect due to the inertia of the air. To keep pace with the eclipse shadow moving about two thousand miles an hour the eclipse cyclone must continuously have formed within the shadow and must have dissipated in the rear almost instantly. In this way its motion may be considered to have a certain analogy to wave motion. Any given particle of air moving with the velocity of the eclipse winds could not have moved more than Ave miles as a maximum during the passage of the eclipse. Hence all the changes of pressure must have been derived from the deflective influence of the earth's rotation acting on air moving this distance. In brief, the meteorological effects of the eclipse are important — (1) Because they confirm so fully P^errel's theory of the cold-air cyclone ; (2) Because they show the wonderful rapidity with which cyclonic phenomena can develop and dissipate in the atmosphere ; and (3) Because they show that cyclones do not necessarily drift with the atmosphere, but move with their originating cause, which in the eclipse had a progressive velocity of about two thousand miles an hour. The DruRNAL Cyclones. The discovery that the brief fall of temperature attendiug a solar eclipse produces a well-developed cyclone which accompanies the eclipse shadow at the rate of about two thousand miles an hour, suffsests that the fall of temperature due to the occurrence of ni^ht must also produce or tend to produce a cold-air cyclone. Since the heat of day produces or tends to produce a warm-air cyclone, there must tend to occur each day two minima of pressure, one near the coldest part of the day, and an- other near the warmest part of the day, with areas of high pressun; between them due to the overlapping of the pericyclones suirouiiding the 31G PROCEEDINGS OP THE AMERICAN ACADEMY. cold-air and the warm-air cyclones respectively. These causes must produce entirely or in part the well-known double diurnal period in air pressure. At any rate, in view of the fact that an eclipse causes a cy- clone over half a hemisphere, it will be necessary before rejecting such a theory to show that the fall of temperature at night does not produce a cyclone, or that this cyclone and the corresponding warm-air cyclone of the day do not appreciably influence the barometer. The points in favor of the theory that the double diurnal period in pressure is due to two diurnal cyclones, one developed by the cold of night and the other by the heat of day, may be stated in brief as follows. The theory is based on well-known physical laws. The possibility of a cold-air cyclone under conditions similar to the diurnal cyclone is con- firmed by the eclipse cyclone. The theory explains the annual oscilla- tion of the time of maxima and minima of pressure in the diurnal period; and explains the occurrence of a third maximum in high northern lati- tudes in winter. The theory also explains why the warm-air cyclone is well developed over continents, and on clear days, and causes a marked fall in the barometer during the afternoon, while the morning minimum of pressure over continents does not attain an excessive development as compared with that over oceans where there is slight retardation of the air movements on which the fall of the barometer in the cold-air cyclone depends. The diurnal cyclones move from east to west, contrary to the motion of ordinary cyclones in temperate latitudes. Their velocity of motion is about one thousand miles an hour at the equator, and diminishes toward the poles. The two charts in Figure 6 indicate the circulation of the surface winds and upper currents in the diurnal cyclones. In these charts the ordinates represent the hours of the day, and the abscissas represent distances from the equator. The data for the surface winds are derived from observations at Blue Hill, lat. 42° 13' N., long, 71° 7' W., and Cordoba, Argentina, lat. 31° 25' S., long. 64° 12' VV.* The directions of the arrows represent in the usual way wind directions, and the position of the arrow shows the time of maximum frequency of each wind. Thus the greatest diurnal freciuency of southerly winds occurs at Cordoba at 7 a.m., and at Blue Hill between 7 and 8 p.m. There is also a second maximum frequency of southerly winds at Blue Hill about 10 a.'m. The wind arrows at Cordoba and Blue Hill are, in general, * Annals of the Astron. Observatory of Harvard College, XXX. I't. iv., 415 and 419. CLAYTON. THE ECLIPSE CYCLONE. 317 UPPER WIN'DS, 2000 - 10,000 METERS _I2 2 4 6 A.M. 8 10 12 2 4 6 P.M. 8 10 l2 o 00 Z q: vc to Ui o o - < q: tn ® t < VO CO 1^ > . ^ -' ,-> 2 *4 r « V 9 .0 9 1 « 1 '■•1 ? > 1 c - \ : .<^' \ ■• — * * • 1 0 / * ■* 0 ' t 0 1 ^s * * ^ ^-^ ^ ) » J \ •' -> • « * 1 1 1 / 1 0 > 0 * 1 < c u > u ^ C > Q POLE o t-1 318 PROCEEDINGS OF THE AMERICAN ACADEMY. in opposite directions, and distinctly indicate a circulation of the wind around two cyclonic centres passing along the equator, and an outflow from high pressures half-way between them. The lower chart, headed " Upper Winds," shows the hours of greatest frequency of each wind direction in the upper air between 2,500 and 10,000 meters. These times were determined by observations of clouds at Blue Hill, and from hourly wind records on the Siintis in Switzerland. Cloud strata at three different levels between 3,000 and 1 0,000 meters above Blue Hill each gave a result similar to the other. This is indicated by heavy arrows in the chart.* The observations on the Santis at an elevation of 2,500 meters are indicated by the light arrows in the same diagram. There are no observations available at these heights south of the equator, but the observations north of the equator indicate a circulation very different from that at the earth's surface. There is apparent at this height only one cyclonic and one anticyclonic circulation. The low pressure in the cold-air cyclone of night persists at these levels, and probably with in- creased intensity, while the low pressure in the warm-air cyclone of day has been replaced by a high pressure and an anticyclonic circulation. * Annals of the Astron. Observatory of Harvard College, XXX. Ft. iv., 415 and 419. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVI. No. 17. — January, 1901. CONTRIBUTIONS FROM THE PHYSICAL LABORATORY OF THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY. J..— AN APPARATUS FOR RECORDING ALTERNATING CURRENT WAVES. By Frank A. Laws. With a Plate. CONTRIBUTIONS FROM THE PHYSICAL LABORATORY OF THE ASSACHUSETTS INSTITUTE OF TECHNOLOGY. L. — AN APPARATUS FOR RECORDING ALTERNATING CURRENT WAVES. By Frank A. Laws. Presented May 10, 1900. Received December 15, 1900. FiGl The apparatus formiug the subject of this communication was con- structed at the Rogers Laboratory in 1898, and has proved of sufficient vahie to merit a short description. In brief, the arrangement gives us a modification of the " contact method," by which the record is rendered continuous and traced photographically. Tlie necessary electrical connections are shown in the diagram. Kx and Ko are two rigidly connected contact wheels of ebonite. Into the periphery of each wheel are set four brass blocks. These are accurately placed 90° apart. Upon each wheel a brush and collector ring give per- manent contact with the blocks. Another brush resting on the periphery of the wheel completes electrical connection as the blocks pass under it. The brushes are so placed that contact is made and broken at Kg before Ki closes. The contact wheels are driven by a synchronous motor, which gives one rev- olution for four complete alternations of the E.M.F. G is a dead-beat galvanometer, and C is an adjustable condenser. The leads a and b are carried to the points between which the P.D. is to be investigated. By inspection of the diagram it will be seen that once on each wave and at a definite point the condenser C is charged to the potential existing between a and 0. As the charge is determined by the breaking of the contact, the blocks may be of sufficient width to eliminate the effect of the jumping of the brushes. Also the resistance at the contact will not be of suffi- cient magnitude to prevent complete charging of the condenser. VOL. XXXVI. •21 322 PROCEEDINGS OF THE AMERICAN ACADEMY. The function of Ki is to discharge the condenser through the galva- nometer after Kg has broken circuit. The instrument would ordinarily experience a constant deflection, but Kj and Kg are rigidly connected and mounted on a radial arm, which is geared to the shaft so that it moves very slowly. The effect is to gradually move the contact point over the wave. The deflection of the galvanometer will at any instant be proportional to the P.D. between a and b at the instant of breaking at'Ka, or in other words, the deflection follows the wave form. The actual arrangement is shown in Figure 2 (see Plate), where the contact device, the synchronous motor, and the direct current motor used for starting the apparatus will be seen. By use of worm gearing the wheel train necessary for moving the brushes is made very compact ; the reduction for the instrument shown is 7200 to 1. I have found Sullivan's Universal Galvanometer to be a most satisfac- tory instrument for use with the apparatus. This galvanometer, of the D'Arsonval type, has a carefully balanced coil, so that it is not very susceptible to mechanical disturbances ; also the magnetic damping is most carefully adjusted. The instrument is not of great sensitiveness, but owing to the stiff suspension the zero is perfectly definite. The camera used for recording the curves is shown in Figure 3 (see Plate). The plate is contained in an ordinary plate holder. This is moved vertically by a fine wire which is wound on a drum, seen in Fig- ure 2, just in front of the lower worm-wheel. This drum can be thrown in at pleasure by a pin clutch. The slide of the plate holder is held sta- tionary by a pin, so that the plate is exposed as the holder is drawn up. The front of the camera, shown removed, is provided with a narrow slit about jIq of an inch wide. In front of it are projecting lips 9 inches long and ^ of an inch apart. They are blackened within and serve effect- ually to shut out extraneous light, and thus prevent fogging of the plate. The spot of light used was the sharply focussed image of the filament of an incandescent lamp. An alternative arrangement is to use a plate of ground glass in the holder, and to have a straight-edge fastened across the guides. It is then easy to keep the point of a pencil in contact with it and upon the spot of light. The arrangement described is of course a device for obtaining the average wave, and unsuitable for recording transient phenomena. The time taken in recording a wave at 120 cycles per second is about 14 minutes. The adjustable condenser allows one to adapt the apparatus to vary- ing conditions, so the E.M.F. curves may be taken directly, and the LAWS. — Recording; Alternating Current Waves. Figure 2. Figure 3. LAWS. — RECORDING ALTERNATING CURRENT WAVES. 323 Figure 4. — Potential difEerence between the carbons of an enclosed arc, in series with reactive coil. The curves were taken about one minute apart witii a view to testing the con- cordance of tiie readings. Figure 5. — yl, potential difference between the terminals of a small alternat- ing current motor. B, current through motor. Figure 6. — Curve A is E.M.F., and B is current in one phase of a quarter- phase synchronous motor running idle with the field adjusted for iniiiinuim ciirreiit. Source of power was a three-phase dynamo with phasing transfornifrs arraiiiied on the Scott system. current curves by the use of a drop wire, as indicated in Figure 1. In starting the arrangement it is very easy to determine when the proper 324 PROCEEDINGS OF THE AMERICAN ACADEMY. speed for synchronism has been attained by watching the spot of light, or by listening to a telephone which is inserted in place of the galva- nometer. With the latter one hears slow beats as the contact moves over the wave. Opposite are given some examples of the records obtained with the device. Rogers Laboratory of Physics, June, 1900. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVI. No. 18. — January, 1901. SUGGESTION CONCERNING THE NOMENCLATURE OF HEAT CAPACITY. By Theodore William Richards. SUGGESTION CONCERNING THE NOMENCLATURE OF HEAT CAPACITY. By Theodore William Richards. Received December 19, 1900. Presented January 9, 1901. The word " calorie " has come to have so many significations as to have lost definite meaning, unless qualified by an explanatory phrase. For this unfortunate condition of affairs, which is due primarily to the varia- bility of the specific heat of water, the best remedy seems to me to be the general use of a new standard for the measurement of heat capacity. The growing tendency to refer all energy measurements to the centi- meter-gram-second basis makes it fitting that heat also should be meas- ured directly in these terms. It is not unusual to do this, as far as heat-energy is concerned ; but the practice is hampered by the fact that the standards of temperature and heat-capacity have no rational relation to the so-called absolute units. One calorie equals about 42,000,000 ergs, or 4.2 joules. Would it not be a convenience to arrange the standards of heat measurement so that the direct product of heat ca- pacity and change of temperature would be expressed in joules ? Nearly ten years ago Ostwald pointed out some of the advantages of such a practice,* but the suggestion does not seem to have received the attention which it deserves. One way to accomplish the desired result would be to construct a new scale of temperature with degrees about f^ the size of the present cen- tigrade degrees, and to retain the specific heat of water at a definite temperature as the unit of capacity. This course retains one of the disad- vantages of our present system, and is open to several other objections, the chief of which would be the variability of the degree with each new measurement of the value of the mechanical equivalent. Another obvious course is to retain the centigrade degree, measured by the hydrogen or helium thermometer, as final, and to choose for the unit of capacity that capacity which is warmed 1 degree centigrade by * Zeitschr. phys. Chein., 9, 577 (1892). 328 PROCEEDINGS OF THE AMERICAN ACADEMY. 1 joule (1 watt-second, or 10'^ ergs). Here the unit of capacity will vary with each new increase in accuracy in the determination of the mechanical equivalent ; but capacity is a less tangible dimension than temperature, and its variation would cause less instrumental confusion. This convenient unit of capacity would be nearly represented by the heat capacity of a gram of magnesium at low temperatures (—50°), or that of a gram of aluminum at high temperatures (about 290° C). At ordinary temperatures an alloy of zinc and magnesium containing about 5.5 per cent of zinc would probably have the desired capacity. Specific heats are frequently spoken of in terms of calories, thus con- founding heat capacity with energy. As a matter of fact, the idea of specific heat is mathematically nothing but a simple ratio like specific gravity, — a pure number without physical dimensions. The unit sug- gested here is rather to be compared with density ; it has the definite dimension of energy divided by temperature. It seems to me that a name for this unit would greatly assist the beginner to discriminate between energy and capacity. Would not the name " mayer," in honor of the unfortunate Julius Robert Mayer, one of the discoverers of the first law of energy, be a convenient and fitting term for the centimeter-gram-second -r- centigrade unit of heat capacity ? On this basis the heat capacity of a gram of water at twenty degrees centigrade is about 4.181 mayers, and that of a gram of liquid mercury is .0333 X 4.18 = 0.139 mayers. The gas constant becomes 8.32 mayers, if the atomic weight of oxygen is taken as ] 6 ; and the Dulong and Petit constant or gram-atomic heat capacity becomes about 26.5 mayers on the same basis. These numbers are all of convenient magni- tude. For larger values, such as the heat capacities of solutions used in thermochemistry, the kilomayer is a convenient unit. F'or instance, the capacity of HCl + 100 HoO is 7.41 kilomayers, while that of a similarly dilute solution of 40 grams (a mol) of sodic hydroxide is 7.42 kilomayers. The solution produced by mixing these two has a capacity of 15.02 kilo- mayers. In order to show how convenient these figures are as a basis of calculation, it is only necessary to point out that this difference of 0.19 kilomayer between the capacities of factors and product indicates that the heat of neutralization will vary 0.19 kilojoule * for each degree of tem- * Ostwald lias pointed out the convenience of the kilojoule as a unit in thermo- chemistry, in the latest edition of the "Grundriss der allgemeinen Cliemie" It seems to me that it would be well to represent this useful unit by kj., in analogy to km. and kg., ratlier than by J., which might be mistaken as an abbreviation for joule. Kilomayer maybe abbreviated to kmy. RICHARDS. — NOMENCLATURE OF HEAT CAPACITY. 329 perature, according to the well-known equation (7y, — C.j. = rp, _ rp ' where capacities are represented by C, heats of reaction by U, aud temperatures by T. Since entropy has the dimensions of heat capacity, it too may be measured in mayers. This application of the new name may lend concreteness to an idea which has been to some a stumbling-block. The greatest gain to be derived from the consistent use of the " abso- lute " unit of heat capacity is to be found in the field of electrochemistry. Here even teclmical men have used for several years the admirable system of units resting upon the centimeter-gram-second basis. The increasing use of both the thermodynamic and osmotic equations of electrochemistry will make the ready application of these units to heat and gas energy almost a necessity. Cambridge, Mass., October 31, 1900. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVI. No. 19. — January, 1901. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. SYMMETRICAL TRIIODBENZOL. By C. Loring Jacksox and G. E. Behr. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. SYMMETRICAL TRIIODBENZOL. By C. Loking Jackson and G. E. Behr. Presented December 12, 1900. Received December 20, 1900. So far as we can find, three triiodbenzols have been described in the chemical literature, but the constitution of only one has been established thoroughly; this is the unsymmetrical (1.2.4) isomere melting at 76° obtained by Kekule * from the action of iodine and iodic acid on benzol. More recently Plantzsch f has also made it from the diioddiazobeuzol iodide prepared from diiodaniline and found that it melts at 77°. The other two isomeric triiodbenzols were made by Istrati and Georgescu t by heating together benzol iodine and concentrated sulphuric acid. Unfortunately their original paper is not at our disposal, so that we know their work only from the abstracts of it in the " Jahresbericht liber die Fortschritte der Ch'emie " and Beilstein's Ilandbuch (third edition). From these it appears that they ascribed the unsymmetrical constitution (1 . 2 . 4) to their compound melting at 85°, and the adjacent structure (I . 2 . 3) to that melting at 182° to 184°, but there is no statement that they determined these constitutions experimentally. The experiments of Kekule and Hantzsch just cited prove that the unsymmetrical isomere melts at 77° (or 76°), and, therefore, their compound melting at 85° cannot have this structure. Under these circumstances it seemed worth while to prepare the symmet- rical triiodbenzol and to prove its constitution by experiment ; accordingly we made the triiodaniline by the method of Michael and Norton, § that is, treating chloride of aniline with monochloride of iodine ; and replaced the amido group in this body by hydrogen by means of the diazo reaction. * Ann. Chem. (Liebig), CXXXVII. 164 (1866). t Ber. (1. chem. Ges., XXVIIL 684 (1895). t Buletinul d. Soc. d. Sciinte Fiz. d. Bucuresci, I. 62. Jarhresb. Chem. 1892, 1063. Beilstein's Handbuch (3d Edition), III. 73. § Ber. d. chem. Gee., XI. Ill (1878). 334 PROCEEDINGS OP THE AMERICAN ACADEMY. The triiodbenzol thus obtained melted at 181°, which suggested that it was identical with the substance made by Istrati and Georgescu melting at 182° to 184°, and this was proved to be the case by treating it with fuming nitric acid, which converted it into a triioddinitrobenzol melting at 210°, whereas Istrati and Georgescu* under similar conditions ob- tained from their substance a dinitro derivative melting at 210°-212°, That our triiodbenzol had the symmetrical constitution (I .3.5) was very probable, because the trichloraniline and the tribromaniline made under similar conditions are symmetrical compounds ; but, as we felt it was necessary to give an absolute proof of its structure, we treated the triioddinitrobenzol with aniline, when it formed a trianilidodinitrobenzol melting at 181°. The symmetrical trianilidodinitrobenzol made by Palmer and one of us f from symmetrical tribromdinitrobeuzol melted at 179°; in spite of the difference of two degrees in these melting points there can be no doubt of the identity of the compounds, and it follows, therefore, that the triiodbenzol melting at 181° has the constitution I3 1 . 3 . 5. This would leave only the structure 1.2.3 for Istrati and Georgescu's triiodbenzol melting at 85° ; but in view of the fact that this compound was isolated from a mixture of the two triiodbenzols and two tetraiod- benzols, it seems to us possible that it may be the unsymmetrical isomere (1.2.4) (melting at 77°) contaminated with some of these less fusible substances. We had hoped to prepare several derivatives of the triiod- benzol, but were unable to do so in the time at our disposal, and, as we cannot continue our work together, think it well to publish this account of the results so far obtained. Preparation op Triiodaniline. The triiodaniline was prepared by the method of Michael and Norton t slightly modified. Ten grams of aniline were dissolved in dilute hydro- chloric acid, and diluted with water at 15° or a higher temperature to the volume of seven litres. This solution was then treated with a rapid stream of air charged with the vapor of monochloride of iodine by pass- ing it through a flask containing somewhat more than the required amount of this substance heated to about 60° by immersion in warm water. After thirty or forty minutes the action had come to an end, and the liquid was filtered as quickly as possible to remove a heavy black precipi- * Bui. Soc. Sci. Fiz., I. 66. t These Proceedings, XXIV. 111. I Bar. d. cliem. Ges., XI. Ill (1878). JACKSON AND BEHR. — SYMMETRICAL TRIIODBENZOL. 335 tate which had formed; the filtrate was allowed to stand for several hours, when it deposited a flocculent bulF-colored precipitate, the weight of which varied from 10 to 20 grams in different operations ; that is, 20 to 40 per cent of the theoretical yield. An additional amount of the triiod- aniline could undoubtedly have been obtained from the black precipitate, which was filtered out at first, but this was so impure that it seemed more time would be lost in purifying it than in preparing fresh quanti- ties of the second bufF-colored precipitate, which without further treat- ment was pure enough for the manufacture of the triiodbenzol. That it was the triiodaniline was shown by an analysis of the substance purified by crystallization from glacial acetic acid and alcohol with the aid of boneblack, which gave 81.25 per cent of iodine instead of the 80.87 per cent required by the formula. Its melting point was 185°. Michael and Norton give 185^°. The monochloride of iodine used in this work was made by the action of chlorine on iodine according to one of the methods given by Hannay,* and used later by Bornemann.f Bunsen's t method, which consists in boiling iodine with aqua regia, gave a less good result. Distillation of iodine with potassic chlorate, recommended by Schutzenberger § and Hannay,|| was not tried. Forty-two grams of powdered iodine (the amount needed for ten grams of aniline) were treated with dry chlorine in a flask, until they had gained 12 grams; in addition to the reddish brown liquid monochloride a considerable amount of the brilliant yellow crystalline trichloride of iodine was formed, which was converted into the mono- chloride by adding a small excess of iodine and heating the flask gently on the steam bath under a short air condenser, until the yellow crystals had disappeared. The monochloride of iodine solidified in fine gray crystals, if cooled below 10°, and in this solid state could be kept for some time without decomposition. Its tendency to solidify made it necessary in the preparation of triiodaniline to use the solution of chloride of aniline at a temperature of at least 15° in order to avoid the danger of having the tube stopped up with monochloride of iodine. Although tliis substance melts at 24°. 7 (Hannay), we found no trouble from solidi- fication with a solution at 15°, which can be explained by the marked tendency of the monochloride to remain litjuid after it has been melted. * I'roc. Lond. Chcm. Soc, XXVI. 815 (187.3). t Ann. Chem. (Liebig), CLXXXIX. 184 (1877). t Gmelin-Kraut's Handbucli, I. 2, p. 410. § Zeitschr. d. Cliem., VI. 1. W Proc. Lond. Cliem. Soc, XXVI. 815 (1873). 336 PROCEEDINGS OP THE AMERICAN ACADEMY. Symmetrical Triiodbenzol, CeHalg. This substance was prepared as follows : Ten grams of the bufF- colored triiodaniline, made as described in the previous section, were boiled with 125 c.c. of benzol and 25 c.c. of alcohol, and disregarding the undissolved portion, 5 c.c. of commercial sulphuric acid were added, and then 5 grams of finely powdered sodic nitrite were sifted into the liquid as quickly as possible. As soon as the evolution of nitrogen had slackened sufficiently, the liquid was boiled for some time on the steam bath, until a large part of the solvents had passed off ; during this boil- ing a bright yellow solid, which formed on the particles of sodic nitrite as they entered the liquid, changed its color to a light grayish brown. After the solution had been boiled, it was allowed to stand over night, and then the deposit was filtered out and washed, first with alcohol and afterwards with hot water, to remove the inorganic salts. The amount of this crude product rarely fell below 50 per cent of the theoretical yield. The product, obtained as described above, was next sublimed from a large watch-slass heated on the sand bath, and covered with a funnel which stood on a piece of filter paper above the substance. If this sub- limation was carried on slowly enough, as much as 80 per cent of white glistening crystals was obtained, but if it was urged too fast, the impuri- ties also sublimed, and the crystals were yellow, or even in extreme cases light brown and sticky. When proper care was used, white crystals were obtained by this sublimation, even from very impure products, such as those recovered by evaporating the liquid portion of the product of the diazo reaction. The white sublimed crystals were not, however, pure, and to remove from them a persistent impurity we found repeated recrystallizations from alcohol were necessary, which finally raised the melting point to 181°, where it remained constant. The sub- stance was then dried at 100°, and analyzed with the following results : — I. 0.1187 gram of the substance gave by the method of Carius 0.1838 gram of argentic iodide. II. 0.1453 gram gave 0.2249 gram of argentic iodide. Calculated for Found. C6H3I3. I- II- Iodine 83.54 83.66 83.60 Properties of 1.3.5 Triiodbenzol — This substance crystallizes from alcohol at first in radiating groups composed of a few slender prisms, which develop later into long white prisms frequently tapering, but JACKSON AND BEHR. — SYMMETRICAL TRIIODBENZOL. 337 always terminated by a single plane at an oblique angle to the sides of the prism. It melts at 181°, and sublimes easily. It is freely soluble in benzol, or carbonic disulphide even in the cold ; in chloroform it is moderately soluble in the cold, freely soluble when hot ; in ether it is moderately soluble, whether hot or cold ; in glacial acetic acid or ethyl acetate it is somewhat soluble in the cold, freely soluble when hot ; in alcohol or acetone it is slightly soluble in the cold, moderately soluble when hot ; it is apparently insoluble in water, hot or cold. The best solvent for it is alcohol. Strong hydrochloric acid has no apparent action on it, even when hot ; strong nitric acid also has little or no action on it, but fuming nitric acid acts on it in the way described in the next paragraph. Strong sulphuric acid, when heated with it to its melt- ing point, causes a partial decomposition, taking on a dark color ; at higher temperatures the triiodbenzol sublimes out of the mixture. A strong solution of sodic hvdrate seems to have no action on it, even when boiling. An attempt was made to prepare triiodnitrobenzol ; for this purpose five grams of symmetrical triiodbenzol were boiled with 140 c.c. of a mixture consisting of four parts of fuming nitric acid with one part of common nitric acid. On cooling light yellow crystals appeared, and an additional amount of the product was obtained by pouring the acid liquid into about a litre of water, when a pale yellow flocculent precipitate was formed, which was filtered out, after it had stood some time, and with the crystals weighed 5.-3 grams. This was purified by crystallization from a mixture of four parts of alcohol with one of water, until it showed the constant melting point 210°. This indicates that the substance is triioddinitrobenzol, since Istrati and Georgescu * obtained a triioddini- trobenzol melting at 210°-212° from their triiodbenzol melting at 182°-184°. For still greater certainty the substance was dried at 100°, and analyzed with the following result : — 0.2049 gram of the substance gave by the method of Carius 0.2614 gram of argentic iodide. Calculated for C„HI.., (NO,),. Found. Iodine G9.77 69.76 The substance, therefore, is a dinitro compound, although obtained from fuming nitric acid somewhat diluted with common nitric acid. We * Bui. Soc. Sci. Fiz., I. 66. VOL. XXXVI. — 22 338 PROCEEDINGS OF THE AMERICAN ACADEMY. did not have time to try whether the mouoiiitro compound could be obtained with a still more dilute nitric acid. The agreement between the melting points of our triiodbenzol, 181°, and triioddinitrobeuzol, 210°, with those obtained by Istrati and Georgescu, * 182°-184° and 210°-212°, establishes the identity of these substances beyond a doubt. The triioddinitrobeuzol also gives us the means of proving their constitution. For this purpose 0.5 gram of the triioddi- nitrobenzol were heated with 0.5 gram of aniline ; this proportion gives about six molecules of aniline to each molecule of the dinitro compound. The heating was carried on for two hours on the steam bath, and the product, a dark red solution, was freed from the excess of aniline by washing with dilute hydrochloric acid, when it formed a dark red sticky mass, which was purified by working it well with a rod under dilute hydrochloric acid and then crystallizing it from alcohol. It showed the constant melting point 181°, which agrees sufficiently well with 179°, that given by Palmer and one of usf for the trianilidodinitrobenzol made from the tribromdiuitrobenzol Brg 1.3.5, (N02)2 ^ • '^- This proves, therefore, that the triiodbenzol melting at 181° has the iodine in the position 1.3.5, as would have been inferred from its preparation from triiodaniline, which according to the analogy of the chlorine and bromine compounds should have the symmetrical constitution. * Bui. Soc. Sci. Fiz., I. 62, 66. t These Proceedings, XXIV. 111. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVL No. 2U. — March, 1901. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. A STUDY OF GROWING CRYSTALS BT INSTANTANEOUS PHO TOMICR 0 GRAPH Y. By Theodore William Richards and Ebenezer Henry Archibald. With Three Plates. Investigations ox Light and Heat, made and published wholly or in part with Approprlations from the rumford fond. CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF HARVARD COLLEGE. A STUDY OF GROWING CRYSTALS BY INSTAN- TANEOUS PHOTOMICROGRAPHY. By Theodore \yiLLiAM Richards and Ebenezer Henry Archibald. Received January 7, 1901. Presented January 9, 1901. Countless observers have watched the growth of crystals under the microscope. As long ago as 1839 attempts were made to study also the birth of crystals, in order to determine in what manner the new phase makes its entrance into the system. With a microscope magnifying GOO diameters, Link* thought he could detect the formation of minute glob- ules at the moment of precipitation, — globules which soon joined and assumed crystalline form. Schmidt, f Frankenheim, t and especially Vogelsang, § made similar observations some years later, and several more recent accounts of this phenomenon have appeared. Modern investi- gators have been more concerned with the sjoeec? of separation from super- saturated or su[)ercooled liquids than with theybrm of the first separation. || Ostwald, in 1891, accepted the interpretation of these data, which as- sumes that crystallization is always preceded by the separation of an initially licjuid phase, consisting of a supersaturated solution of the former solvent in its former solute.** This explanation is indeed a plausible one, and undoubtedly holds true in cases like those studied by Schmidt and Vogelsang, where a sub- stance separates at a temperature not far below its melting point, and often where a substance soluble in one liquid is precipitated by the * Link, Pogg. Ann., 46, 258 (1830). t Schmidt, Lieb. Ann., 53, 171 (1815). J Frankenheim, Pogg. Ann., Ill, 1 (18G0). § Vogelsang, Die Krystalliten (Bonn, 1875). See Lehmann, Molccularpliysik, I. p. 730 (1888). II Gernez, Compt. Rend., 95, 1278 (1882); Moore, Zeits. pliys. Clieni., 12, 545 (1893) ; Friedliinder and Tammann, ibid., 24, 152 ( 1897) ; Tanimann, ibid., 25, 441 ; 26, 307, 367, 28, 96; Kiister, ibid., 25, 480, 27, 222; Bogajavlensky, ibid., 27, 585. ** Lehrbucli, L 1039 (1891). 342 PROCEEDINGS OF THE AMERICAN ACADEMY. addition ofaconsolute liquid in which the substance is insoluble. For examples, phenol always separates from aqueous solution in the form of a liquid, and manganous sulphate forms at first two liquid phases when alcohol is added to its aqueous solution. On the other hand, the separa- tion of a high-melting salt like baric chloride from its solution in pure water is much less liiiely to take place in this way. The admixture of water necessary to lower a melting point from 900° to 25° would be so large as to make the new phase, a solution of water in baric chloride, supersaturated to an improbable extent. It is hard to guess where the line between probability and improbability should be drawn. Ostwald has shown that an exceedingly small jiarticle of solid is capa- ble of starting crystallization,* — a fact which may not be wholly foreign to the present discussion. In any case, the matter seemed worthy of further experimenting. Ost- wald says, " Die erste Bilduug der Krystalle lasst sich bei Salzlosungen und dergleichen microscopisch nicht verfolgen, weil gewohnlich im Ge- sichtsfelde an einer bislang gleichformigen Stelle plotzlich ein Krystall- chen erscheint." While this is true as far as the human eye is concerned, instantaneous photography, an art unknown in Link's time, seemed peculiarly fitted for the unprejudiced recording of the circumstances at- tending the genesis of crystals. An attempt in this direction is described below. The problem resolved itself into the taking of a number of successive instantaneous microphotographs of a suitable mixture at the point of crys- tallization. This problem presented some difficulties, however. In order to secure a sufficiently brief exposure, very great illumination is needed. The greater the magnifying power of the lenses of the microscope-camera, the more intense must be the source of liglit. The difficulty is increased by the fiict that most crystals are so transparent as to absorb but little light, and reflection is possible only in certain directions. Hence it is hard to obtain a distinct image even in a strong light. Moreover, the macliinery necessary for shifting the plates must be so frictionless in con- struction, and so firmly fixed, as to impart no vibration to the camera or the mobile subject of study. These difficulties were at least partially overcome by two different ar- rangements, the first of which caused the successive impression of a bright image in a dark field, and tlie second registered dark images in a succes- sion of bright fields. Obviously the former was the more economical as * Ostwald, Zeits. phys. Chem., 22, 289 (1897). RICHARDS AND ARCHIBALD. GROWING CRYSTALS. 343 regards expenditure of sensitized film, and the more simple in execution ; for when the field is dark, successive images can be obtained by a very slight motion of either object or film, while, when the field is light, the whole previously exposed surface must be replaced by a fresh surface before each exposure. The apparatus consisted of a good compound microscope fitted above with a vertical folding camera, which was supported by two massive steel pillars on the heavy stand. It was, in short, the regular photomicro- graphic outfit made by Bausch and Lomb. Between the microscope and camera, in a suitable light-tight box, was placed a revolving shutter, which allowed an exposure equal to one fifth of the time of its revolution. Thus, when the shutter ma* = kt. represents equation D- = kt. The unit of time is tlie time of one revolution of the shutter, or 1.25 seconds. The substance was potassic iodide. The inspection of the fifjure show.s at once that the curve is similar in general .shape to one represented l)v iIr; ('(|iiati<)n D" = /•/, wliere /) is RICHARDS AND ARCHIBALD. — GROWING CRYSTALS. 351 the diameter of the crystal, t the time from the birth of the crystal, and h a constant. The only question is as to the magnitude of w. The curves which result from the assumptions n = 2 and n == 3 are given above, for comparison with the experimental curve. It is clear that the curve with the latter value, n = 3, is the nearest, possessing the same gen- eral curvature, and deviating from the average less than the individual measurements do. This is equivalent to saying that equal increments of time correspond to equal increments of volume, instead of equal increments o{ surface, as one might have supposed. Of course a law based upon such merely approximate data cannot be considered as definitely settled ; but clearly the general character or tendency of the curve is established. It is probable that under the necessarily ill-defined conditions of our experi- ments the growth follows no one law with precision ; supersaturation, convection, diffusion, and evaporation must all influence the result. The crystal which seems to have deviated most widely from the average is that depicted in Figure 10; this crystal grew at first less rapidly than usual, and finally came almost to a standstill. It is possible that an in- creasing solubility due to increasing temperature may have caused this delaying tendency It is interesting to compare this average, calculated on the assumption that the crystal starts in the middle of the dark interval, with a few sin- gle cases which appear to have begun to crystallize very near the begin- ning or end of the interval. In these cases, the first image of the crystal will appear either almost as large as the second image, or very small compared with it. It will appear almost as large as the second image when the preceding exposure has just not caught the beginning of the crystal, which has thus had a whole interval for growth ; or very much smaller than the second image when the first impression has registered a crystal only a very small fraction of a second old. Marked examples of the former case are to be found in Figure 11, and of the latter in the largest crystal in Figure 9, and the smallest crystal in Figure 15. The times of revolution represented by Figures 9 and 11 are the same, 1.25 seconds, and the other conditions also were identical, hence we may compare these with accuracy. Careful measurements of the sizes in Figure 9 showed the first large impression of the crystals to be about eighty per cent of the diam- eter of the next impression, and approximately the same relationship ap- pears in Figure 11. In order to find if this relationship corresponds with the equation D^ = kt, the larger diameter is assumed to be 0.93, the the- oretical value corresponding to two intervals of time, if that correspondintr to two and one half intervals is taken as unitv- Hence the smaller one 352 PROCEEDINGS OF THE AMERICAN ACADEMY, becomes 0.75, corresponding to one interval of time, a value, marked in a circle on the diagram, which is surprisingly near the cubic curve. Hence the equation D^ = kt is confirmed. That the same curve holds approximately for the further growth of the crystal is manifest by a quantitative study of Figure 9 (Plate II.). In this connection it is interesting to note that the crystal seems often to grow at first in the same proportion in all directions. Even the very minute image in the centre of the second exposure, given in Figure 9, shows itself under the microscope to be elongated like the crystal which grows from it. In the next exposure this crystal had the proportions 0.02 mm. X 0.0125 mm., and after four more exposures it still had almost exactly the same pro()orti()ns, being 0.035 mm. X 0.022 mm. After two or three more seconds the form given in Figure 9 began to change slightly, the crystal becoming slightly less elongated in shape ; but by this time the neighboring crystals had grown so much as to apjjroach it, and hence to alter the conditions. A similar constancy in proportion may be observed in many other series here given. The diagram shows how exceedingly fast the diametric growth of the crystal must be in the first tenth of a second of its existence. Hence we have an explanation for the suddenness of its appearance to the eye of an observer, and for the blurred edges of its photographic image. It is true that another cause may contribute to the blurred effect ; namely, the irregular refraction caused by the convection of the lighter solution which has just deposited part of its load ; but the speedy growth alone is capa- ble of explaining the observed indistinctness. Interesting as the rapid initial growth in diameter may be, it places a serious bar in the way of more precise study of the birth of crystals. One clearly needs not only high magnifying power, but also great speed; and these two together require very intense light. Whether or not we shall be able to obtain more positive knowledge with the present apparatus, is a questionable matter. The same phenomenon casts a measure of doubt over some of the observations of Link and his followers. Is it not possi- ble that the subjective effect of the rapidly growing crystal might be mis- taken for that of a globule of liquid ? Even upon the photographic plate there is a slight resemblance, and in one or two cases deliberate study is needed to detect evidence of structure in the smallest crystals. In conclusion, the report of the foregoing pages may be summarized as follows. It has been found possible to take very frequent photomicro- graphs of crystals during their birth and growth. An enlargement of over four thousand diameters was obtained, and both common and polar- RICHARDS AND ARCHIBALD. — GROWING CRYSTALS. 353 ized light were used. Only substances with liigh melting points were ex- amined, and the crystallization was always from aqueous solution. No properly focused image on any of the plates seemed to be devoid of crys- talline structure. The growth in diameter during the first second of the crystal's life was found to be vastly greater than during the subsequent period. Not the diameter itself, but a power of the diameter, was propor- tional to the time under the conditions used in our experiments. This exceedingly rapid initial diametric growth accounts for a lack of definition noticed in the first images, — a lack of definition sufficient to have misled the eye, but not enough wholly to obscure the photographic evidence of crystalline structure. Hence we may conclude that whatever theoretical reason there may be for believing that crystals always develop from a transitory liquid phase, the present experimental evidence is inadequate to prove that these globules attain a size visible in the microscope, except in the case of substances which melt at temperatures not far from the temperature of crystallization. The present paper is to be regarded rather as the sug- gestion of a mode of study than as a finished treatment of the subject, however. The apparatus might be used to obtain a series of kinetoscopic pictures of insects or other small animals or plants, and is now being used for the study of the change in structure of steel at high temperatures. Cambridge, Mass., October, 1898, to October, 1900. VOL. XXXVI. — 23 Richards and Archibald — Growing^Crystals Plate ' "•^:T*?'///?^,i Figure 2. Baric chloride ; 30 diaiii. : exposure 0.04 sec. Figure 3. Baric chloride; 30 diam. exposure 0.08 sec. FiGuino 4. Sodic nitrate ; 30 diam. exposure 0.10 sec. >%^*-«^' 'iv > < Figure 5. Sodic nitrate; 30 diani.; exposure 0.12 sec. ■^^' v\ut kill. Figure G. Baric cidoride; 110 diam.; exposure 0.10 sec. FiGiRT". 7. ( 'M]iric suliihatc; 110 diam.; exposure 0.12 sec. Richards and Archibald — Growing Crystals Plate II «f t ^ nO *^ -^ii urn 1 1, *mg^ Figure 8. Sodic nitrate ; 110 Jiani. ; exposure 0.12 sec. Figure 9. Potassic ioilide ; 100 diaiii. ; exposure 0.'2u sec. Richards and Archibald — Growing Crystals Plate III ' " .. ' 't-'J*L-.'. ^ ^ •^: FiGUKE 10. Potiissic iodide; 580 diiiiii. ; exposure 0.17 sec. FiGCRK 11. Potassio iodide ; 580diani.; e.xposure 0.25 sec. Figure 12. Potassic iodide ; 580 diaiii. ; exposure 0.17 sec. m "% l'"ii;iri!K \". Potassic iodide ; 580 diani. ; exposure 0.17 sec. l"ii;iui: 14. Potassic icnlide ; obOdiaru.; exposure 0.17 sec. Figure 15. Potassic iodide ; 580 diam. ; exposure 0.17 sec. Proceeding's of the American Academy of Arts and Sciences. Vol. XXXVI. No. 21. — Maucii, 1901. DESIGN AS A SCIENCE. By Denman W. Ross, Ph.D., Lecturer on the Theory of Design in Harvard Universitv. DESIGN AS A SCIENCE. By Denman W. Ross, Pii. D. Presented January 9, 1901. Received January 12, 1901. Art may be defined as the expression of Life, or, more specifically, as excellence in the matter of expression ; and excellence, in this case, may be defined as consistency, a consistency in forms of expression. Consist- ency has many manifestations, but they fall under three principal heads : Balance, which is a consistency of oppositions (antitheses) ; Khythm, which is a consistency of association (joint action or movement) ; and Harmony, which is a consistency of character (likeness). If art is con- sistency in forms of expression, Balance, Rhythm, and Harmony are its principles. They are also the principles of Beauty. We have no other definite conception of beauty. It is a perfect relationship or connection of parts in one organic whole. We find this unity in nature, when we seek it, and we find it in the art of man, homo additus naturae. Wher- ever and whenever we find it, we have the perception of beauty. The idea which the Greek philosophers had of art was as nearly as possible the one which I have given as the major premise of this argu- ment, and it is in the art of the Greeks that I have found its most perfect illustration. See Plato, in the Gorgias (§ 504) : " The artist brings all things into order, making one part to harmonize and accord with another, until he has constructed a regular and systematic whole ; this," Socrates says, " is true of all artists." Aristotle expresses the same idea when, in his Poetics, he speaks of poetic imitation having " as its subject, a single action, whole and complete, with a beginning, a middle, and an end. It will thus," he says, " resemble a living organism and produce its proper pleasure." See Poetics, xxiii. 1. While consistency in forms of expression may be regarded as a defi- nition of art, it is not, of course, a definition of what is significant or im- portant in art. We can take a few lines and put them together so that they shall be absolutely consistent, expressing one idea, unmistakably. The result is a work of art, but the work is unimportant. It is an easy thing to do. The work of art is important in proportion to the number 358 PROCEEDINGS OF THE AMERICAN ACADEMY. and variety of elements which are reconciled and united in its idea. Consider, for example, Raphael's Dispute of the Sacrament. Think of the number and variety of the elements united in that great composition. Such a design is an achievement representing intellectual power of the very highest order. So we discover, as the principal factor in art, the mind of the artist, and the measure of this is observed in his ability to see in many things one idea, and to express in one idea many things. Beyond this power of the mind to grasp and express many things in single ideas, a power which we can analyze, understand, and appreciate, lies some- thing which defies analysis, something which we may appreciate, but which we cannot understand. This is the strictly personal element which goes into the work of a man, whicli stamps it as his, which dis- tinguishes it from the work of other men. This personal element, when it is important, we call genius. The genius of the artist in his art is con- stantly mistaken for the art itself. It seems to me that the genius of the artist is something which lies beyond his art. His art is simply the technique in which, and through which, his genius finds expression. In speaking of art, therefore, I am speaking of the technique of expression and nothing more than that. That is a matter of precise definition and analysis. There is a passage of Plato in the Philebus (§ 55), where Socrates says, " If arithmetic, mensuration, and weighing be taken from any art, that which remains will not be much." In talking about art and its principles, I mean art in this definite sense. There is a passage in the eleventh canto of the Inferno of Dante which is significant in this connection : "If you read your physics attentively [Dante refers here to the physics of Aristotle], you will discover, after not many pages, how your art follows that [physical science] just as far as it can, as the disciple follows the master." There are many arts, the different modes and forms of expression : gymnastics (including dancing) ; music, speech (including poetry) ; con- struction (including architecture) ; modelling (including sculpture) ; and painting (inchuling design). The particular art to which your attention is called in this paper is the art of painting, in its highest form, Design. Painting may be defined as expression by spots of paint, paint being in this case any coloring material, no matter what it is, that may be used. Design is painting with particular reference to the principles of art. We have painting as Design and painting as Representation, which is the defi- nition of visual impressions, a description of things seen, remembered, or known, and we have Design in Representation. Design in which there is no representation, or in which the elements of representation are not ROSS. — DESIGN AS A SCIENCE. 359 considered as such, may be called Pure Design. This may be defined as the arrangement or composition of spots of paint for the sake of balance, rhythm, and harmony; for the sake of consistency, unity, beauty. Pure Design appeals to the eye just as music appeals to the ear. The term of expression in music is the sound; the term of expression in design is the spot of paint. Tlie spot of paint is three things : it is a tone, a measure, and a shape. By tone I mean the pigment material used in drawing the measure of the spot and its shape. By measure I mean the area covered by the spot, its size. By shape I mean its outline, or contour. Put a spot of paint upon a piece of paper, then change (1) its tone alone ; (2) its measure alone ; (3) its shape alone ; (4) its tone and measure, leaving its shape unchanged ; (5) its measure and shape, leaving its tone unchanged ; (6) its tone and shape, leaving its measure unchanged ; (7) change its tone, its measure, and its shape, producing an altogether different spot. Taking the spot of paint as the subject of my investigation, I will con- sider, first, the element of tone, then the element of measure, and, lastly, the element of shape. In order to study the element of tone we must eliminate all differences of measure and of shape, which might be confus- ing. Producing as many different tones as we can, in circles of half an inch diameter, we find that we can produce a very great number and a very great variety. Looking over the tones we have produced, we ob- serve that every tone is relatively light or dark. It has what is called value. It is a measure of light in the white-to-black scale. Observe, also, that every tone has a color. It is red, or green, or violet, or some other color, and the color which it has is relatively intense or neutral, or it m^y be quite neutral. We shall find it convenient to regard the neu- tral as a color. It is the color of white, or gray, or black. Tone means, according to these observations, two things, — value and color. We will consider, first, the element of value, afterwards, the element of color. In considering values alone we must eliminate all differences of color which might be confusing. Take the neutral pigments, white and black, and see how many neutral values you can produce in circles of half an inch radius. You can produce seventeen certainly, and perhaps a few more. You will observe that in producing as many as seventeen neutral values you are nearing the limit of visual discrimination, the limit of dis- tinct definition, or expression. Observe that every value which you have produced is a force drawing attention to itself. Observe that different values exert different degrees of attractive force, that this force is deter- mined iu each case (other things, measure, shape, and color, being equal) 360 PROCEEDINGS OF THE AMERICAN ACADEMY. by its contrast with the ground-tone upon which it has been drawn. If the ground-tone is white paper, the value having the greatest attractive force is black ; if the ground-tone is a half-tone between white and black, the forces of white and of black are equal. What is the result of all these forces of attraction, as they act upon the eye? The eye is held at rest at their centre of equilibrium. Where is that centre ? In order to answer this question, we must bring the values into a scale-relationship upon a common ground-tone, otherwise we have no means of measuring their respective contrasts, or the forces of attraction which depend upon their contrasts. Make a scale of seventeen values, exclusive of white and black, in seventeen circles of half an inch radius, in a straight line, half an inch apart, and upon a ground-tone of the middle value. Be sure that the values are at etjual intervals of equal contrasts. In order to get them into the perfect scale-relation which this implies, establish the ex- tremes first, then the mean between the extremes, tlien intermediates, until the scale is complete. The interval or contrast between value and value may be great or small; the scale may be central in pitch, high in pitch, or low. It is central in pitch when its middle value is at the half-point between white and black. Considering the scale of values which you have produced, you observe what you have observed before, that each value is a force of attraction, that this force, other things being equal, depends upon the contrast with the ground-tone. The only value which has no force of attraction is the central one of the scale, the value which coincides with the ffround-tone and cannot be distinguished from it. Lookinor at the scale again, pick out the values which have the same force of attraction. They will be those at equal distances from the half-tone, which is the ground-tone, making equal contrasts with it. In order to distinguish the different values of the scale, we will call the middle value zero (0). The values above the middle value we will call 1, 2, 3, etc., above. The values below the middle we will call 1, 2, 3, etc., below. The values above can be written thus: X, 2, 3, etc.; the values below thus: T, 2, 3, etc. The values having the same force of attraction are, then, those 12 3 havinof the same numbers: ,i -r> o' etc. The numbers are the measures ° i 2 o of the contrasts, and of the forces of attraction depending upon the con- trasts. If now we scatter our seventeen values over the ground-tone of the middle value we shall be able to discover the centre of equilibrium of their forces, that is to say, the point where the eye is held by them. AVe have simply to remember the familiar principle of balance ; that equal attractions balance at equal distances on a line connecting their centres; ROSS. — DESIGN AS A SCIENCE. 361 while unequal attractions balance in the same way, but at distances which are inversely proportional to them, as attractions. Measures, shapes, and colors being equal, values alone differing, values 4 and 1^ balance on value 0, at distances 1 and 4 respectively. If the ground-tone were 2 instead of 0, 4 and I would balance on 2, at distances 1 and 2 respectively. In this explanation of the balance of values we find the principle upon which the designer proceeds when he wishes to create such a balance. He may prefer to depend upon his visual feeling, but his feeling must be guided by the law of balance whether he thinks of the law or not. The scale of values is not merely a scale of visual attractions to be bal- anced, it is also a rhythmic movement of values. The scale-relationship is not, properly speaking, a relationship of opposition or antithesis ; it is one of association or joint action. The values of the scale combine to lead the eye in a movement from light to dark, or from dark to light, and this movement is easy in proportion to the perfection of the scale. If the scale is imperfect, if the intervals are not equal intervals of equal contrasts, we have the same discomfort that we have in walking on the irregularly placed sleepers of a railway track. We all know how tire- some it is to do that. Not only is the eye led in the scale of values from dark to light and from light to dark, but if the values be squeezed together the eye is led quickly or abruptly ; if they are pulled apart the movement is comparatively slow or gradual. By changing the direction or the shape of the scale of values the eye may be led in different direc- tions, and its movement may take a variety of shapes. A few simple dia- grams would show the rhythmic character of the scale of values in these several aspects. Values are in harmony when they are in the same scale, and when the relations of the scale can be felt, visually. Tiie least contrast of the scale is a factor of the greatest, and when this relation is distinctly felt we have a perception of harmony. The most perfect har- mony is that of corresponding values. Tone, as we have seen, means two things: value and color. We have been considering the element of value. We will now consider the other element, color. In order to do that satisfactorily we must eliminate all differences of value. Producing as many differences of color as we can, all in the same value (the half-tone between white and black), and all in the same measure and shape (the circle of half an inch radius), we shall find that we can produce perhaps twelve differences of color, and in each color a certain number, perhaps eight differences of intensity. In order to study color without being confused with the differences of intensity, let us put nil the colors not only in the same value, but in the same degree 3G2 PROCEEDINGS OF THE AMERICAN ACADEMY, of intensity, the greatest intensity possible to the pigments on our pal- ette. This being done, we shall observe, at once, that the colors have a natural order or connection with one another. Red passes into green through yellow; yellow passes into blue through green; and blue passes into red through violet. There is, in other words, a natui-al relationship for all the colors we can produce in the same value and intensity. There is a natural scale of colors, as there was a natural scale of values. This scale of colors is, of course, the scale of the spectrum. The spectrum which I have followed in this investigation, is the normal spectrum, the spectrum of the grating, not the spectrum of the prism. The difference is explained by Rood, by Lommel, and by other writers. Reading the spectrum from the red end towards the violet end, the colors follow one another, approximately at equal inter- vals of equal contrasts, as follows : red, suggesting Chinese vermilion ; yellow, suggesting aureolin ; green, suggesting emerald green ; blue, sug- gesting cobalt with a little emerald green in it; violet, suggesting ultra- marine with a little rose madder in it. Beyond the violet end of the spectrum we may observe the color which we call purple. It suggests rose madder with a little ultramarine in it. This color does not belong in the spectrum series. It is due to the overlapping of the red and violet ends of the spectrum. It is, however, a color wliich we must use, and if the primary or important colors of the spectrum are red, green, and violet, purple exists for us as an intermediate between red and violet, just as yellow is intermediate between red and green, and blue between green and violet. Between the six colors, red, yellow, green, blue, violet, and purple, come intermediates and the intermediates of intermediates up to the limit of visual discrimination. Setting the nor- mal spectrum upon the circumference of a circle, with purple as a con- necting link between the ends, the interval between any two colors can be described as an interval of so many degrees. We have an interval of 60°, the interval separating red from yellow, yellow from green, green from blue, blue from violet, violet from purple, adjaceuts in the scale of six colors. We have the interval of 120° between the adjacents of a scale of three colors, — red, green, and violet, for example ; and we have the interval of 180° between the adjacents in the scale of two colors, — red and blue, for example. This is the greatest possible interval. It is the interval between colors opposite one another in the circle, the colors which we call complementaries. In order to study the various intervals of the scale of colors with certain conclusions, we must eliminate all differences of value and all differences of intensity. We can then see ROSS. DESIGN AS A SCIENCE. 3G3 wlii(;h intervals give the greatest satisfaction to the sense of vision. The attempt to reach cotichisions on the question of color-contrast, by comparing colors in different values and of different intensities, is per- fectly futile. The greatest possible interval in the color scale is, as I have said, the interval of 180°, the interval between opposite colors of the circle. These colors are known as complementaries. In the scale of six colors there are three pairs of complementaries: red and blue, purple and green, yellow and violet. For the sake of brevity we will indicate the colors by their initial letters : R for red ; Y for yellow ; G for green ; V for violet ; B for blue ; P for purple ; N for neutral. For the scale of neutral values we have already a terminology. Complementary colors, when tones of the same value and intensity are mixed together, neutralize one another, approximately. The relation of the complemen- tary colors may, therefore, be stated in this form : — Y — N — V R — N- B P — N — -G Observe that the complementaries balance, one against the other, on the intermediate neutral, when of the same value and intensity. The degree of intensity may be represented by the distance or space between the sign of the color and the sign of the neutral which separates it from its complementary. The greater this distance the greater the intensity. Ill the statement which follows, yellow and violet and purple and green are all equally intense, but the red and the blue are twice as intense : — Y ■N — V N B N — G The complementaries balance on the intermediate neutral, other things being equal, at equal distances from one another on the straight line connecting their centres. But in the arrangement ]{ — N the neutral being the ground-tone, the red being only half as intense as the blue, it will have to be moved to twice the distance, unless its 364 PROCEEDINGS OF THE AMERICAN ACADEMY. measure or quantity is doubled. I shall, presently, speak of measure as an element of balance. When it comes to the consideration of color intervals we have to think not only of the interval between one color and another in the spectrum scale, but, also, of the interval between each color and the neu- tral in which it disappears and is lost to vision. Take red, for example, in its greatest possible intensity, an intensity limited by the pigment material which we possess. This red is contrasted not only with its neighbors in the scale of colors, purple on the one hand and yellow on the other, but it is contrasted with itself in various degrees of neutraliza- tion. Establishing the greatest possible intensity of red on the one hand and a perfect neutrality on the other, both in the same value, and using for measure and for shape the circle of half an inch radius, make a scale of nine tones of red, the extremes of intensity and neutrality being included in the scale. What has been said of the other scales may be said of this one ; a repetition is unnecessary. We have considered the scale of values and the scale of colors sepa- rately. Now let us put the two scales together. The values being neutrals in every case, we can set complementary scales of colors on the right and left of the scale of values. That will give us two scales of colors, and between them the scale of values, as follows : — Light n White 1 G 8 p Y 7 V E 6 B P 5 G V 4 Y B O O R G 2 P Y 1 V R 0 B r 1 G V 2 Y B 3 R G 4 P Y 5 V R 6 B P 7 G V 8 Y Black Darkness Following this diagram, put in the place of the value numbers values of neutral color, moving from the central neutral up towards light (white) ROSS. — DESIGN AS A SCIENCE. 365 and down towards darkness (black). Then, on a ground-tone of the central neutral, alongside of the values and in the values, set the colors in spots of puint, all in the same intensity : if you can. You will imme- diately discover that you cannot do this. The colors in the light values are inevitably neutralized by white, and colors in the dark values are inevitably neutralized by black or some equivalent dark neutral. It is oidy towards the centre of the scale of values that you can get to any considerable intensity of color. If you consider the matter you will understand that this neutralization of the coloi-s in light and in darkness is as it should be. It is exactly what happens to the colors in nature as they occur between light and darkness. Color is observed in its greatest intensity at the half-point between the light, whatever it is, and the darkness, whatever that is. It is evident that the form in which I have described the relation of the color and value scales needs to be modified. The colors as they approach the half-point between light and darkness must become more and more intense, the greatest possible inten- sity being reached at the half-point, exactly. We have seen how the measure of intensity can be indicated, diagramatically, by increasing or diminishing the space between the complementary colors in any value and the intermediate neutral ; so all we have to do in order to describe the law of increasing and decreasing intensities is to pull the color scales apart at the half-point between the extremes of light and of darkness. This has been done in the diai^ram which follows : — Light Wliite Y7 V RGB P 5 G V 4 Y B 3 R G 2 P I„.o„si,y nl 0 \ C-tSf-' V 2 Y B 3 R G 4 P Y 5 V R 6 B P7 G 8 Black Darkness 366 PROCEEDINGS OF THE AMERICAN ACADEMY. It will be fouud that this system works just as well if we turn it upside down. In doing this the relation of the color scales to the value scale is reversed, as in the following diagram : — Light White 8 P7 G KGB Y 5 V G 4 P B 3 R V 2 Y Intensity R^ 0 ^B Complementary ■^ y J Y Intensity G 2 P B 3 R V 4 Y P 5 G R C) B Y 7 V 8 Black Darkness The diagrams which have been given show systems in which the colors red and blue are the dominant colors, having the greatest intensity. Predominance might be given to yellow and violet, or to purple and green, or we might bring the point of intensity between two pairs of comple- mentaries. In that case we should have four colors as dominants, all equally intense. Every change of the dominants means, of course, a change of the whole system. The system inay be changed in other ways. We can raise or lower its pitch within the extremes of white and black, thus : — ROSS, — DESIGN AS A SCIENCE. 367 White \/ Black White <> Black White /\ \/ Black We can extend or contract the scale of values, thus : — White /\ \/ Black White 0 Black White Black We can increase or diminish the degree of intensity, thus : — White White White O A \/ Black Black Black By these various modifications an infinite number of specific forms of the system can be developed, all consistent with the system in its abstract idea. If necessary, a system of half lights, half darks, and half intensities 368 PROCEEDINGS OP THE AMERICAN ACADEMY. of color can be used in connection with the one described, in the manner shown in the following diagram : — Light White 8 Y7 V R 6 B P 5 G V 4 Y B B 8 R R G G 2 P P Intensity Y Y 1 V V R R 0 B B P PIG G V V 2 Y Y B B 3 R R G 4 P Y 5 V ROB P 7 G 8 Black Diukiit'SS Complementary Intensity As we increase the number and variety of tones to be kept all at equal intervals of equal contrasts, all in perfect rhythm and balance, the problem of consistency, which is the problem of art, becomes more and more difficult. There is a possible objection to the system of color-values or tones which I have described. In the spectrum the colors are all equally intense. They differ only in value or luminosity. In the system just described this equality of intensity is ignored, and as to the luminosities, if they are observed on the hot side of the spectrum, they are ignored on the cold side, and if they are observed on the cold side they are ignored on the hot side. A different arrangement of values and colors is pos- sible. If we distribute our range of light into five registers, — a register of half-tones, a register of lights, a register of darks, a register of high lights, and a register of extreme darks, — we can consider each one of these five registers as a potential spectrum, and we can arrange the colors in each register according to their several values or luminosities and have them all equally intense. The increase or diminution of intensities is not, then, from color to color but from register to register. In the scale of five registers, the middle one will be the register of greatest intensities. Tiie registers above it and below it will be registers of less and of least intensity. This system is described in the following diagram : — ROSS. DESIGN AS A SCIENCE. 369 Litjlit White yN G High ^^Ng L ights P V Y N Register of G R N B P Lights Y N V Regi ster of Half-T ones G R N B P Intensities Y N Register of G V R N B P Darks N Y G V E xtreme N ^ Darks P N^ Black Darl^ness This system would seem to be a particularly natural and proper arrange- ment of the values and the colors, for, if you throw the spectrum on white paper in sunlight the colors are seen all pale in the white light, ecpially intense so far as you can see them, but with the differences of value or luminosity which are indicated in the diagram. If you throw the spectrum on white paper in shadow (half light), you see the colors in equal intensity and in the greatest intensity, with the same dififcu'ences of luminosity. If you throw the spectrum on black paper in shadow, you will observe the same eijual intensity of colors, so far as you can see them, and the same differences of luminosity, but the whole spectrum is disappearing in neutral darkness. This system of color-values or tones VOL. XXXVI. — 24 370 PROCEEDINGS OF THE AMERICAN ACADEMY. in which we have a spectrum to a register, in which the colors in each register are all equally intense, but in values representing their several natural luminosities, cannot, of course, be turned upside down, because that would reverse the luminosities ; but the system admits of the other changes which I have described, — the changes of pitch, the extension or contraction of the value scale, and the extension or contraction of the intensities. When it seems desirable, the middle register of greatest intensities may be left out of the system. The register of lights and the register of darks can then be brought close together, just above and just below the central neutral. Then the lights and the darks are all equally in- tense, and the first diminution of intensity is found in the register of high lights and in the register of extreme darks. This arrangement may be used both in Pure Design and in Representation. It is a system which ought to give great satisfaction to the colorist because of the number and variety of the colors, all equally intense, which it allows him to use. If you take your palette and, following any of the diagrams which I have given, work out an illustration of the system, taking the central neutral as ground-tone, and putting the tones in circles of half an inch radius, you will observe that you have in the relationship of the tones a relation of balance, of rhythm, and of harmony. The system, whichever system it is and whatever form of the system is followed, is an illustra- tion of Pure Design. Again, I am tempted to quote a passage of Plato in his Symposium (§ 187), in which the physician Eryximachus says that " harmony is composed of differing notes of higher or lower pitch which disagreed once but are now reconciled by art." In these various systems of color-values or tones, we have a reconciliation of many differ- ing elements harmonized by the art of design. Observe how the rhythms of the different scales are so disposed that they balance in a perfect equilibrium, and how by the principle of equal intervals of equal con- trasts the many elements of each system are all perfectly related. Now we must take up and consider the second element of the spot of paint, — measure. In order to do this without confusion, take one tone, black on white paper, and one shape, the square. Thus eliminating all differences of tone and of shape, you can vary the measure and study it in all possible variations. Take some white paper and draw on it five black squares of different sizes. Observe that you have harmony of tones because the squares are all black, and you have harmony of shapes be- cause the shapes are all square, but you have no harmony of measure. There is no connection between your measures, unless you have made ROSS DESIGN AS A SCIENCE. 371 one, intentionally. It would not happen by accident. Now draw five scjuares in a scale, so that they shall be as 1 to 2, to 4, to 8, to 16, to 32, in the proportions of their measures. This is easily done by drawing the second on the diagonal of the first, the third on the diagonal of the sec- ond, and so on. Observe the difference between the five related and the five unrelated measures ; the harmony of the related measures. Arrange the related measures in a row at equal intervals apart, the smallest first and the largest last, and observe how you have in your arrangement not only a harmony of measures which the scale-relationship gives, but you have, also, in the connection of the measures, a rhythmic relationship. The eye is led from measure to measure, just as it was led in the scale of values from value to value. By rearranging the rhythm of the measures, the movement can be made to change its direction and also its shape. By bringing the squares close together the movement becomes abrupt. Separating the squares by a larger interval, you can make the move- ment more gradual. There is another point of view from which the measure must be con- sidered. Every measure is a force of attraction, and the amount of this attraction is determined (other things being equal) by the measure itself. A large measure attracts more attention than a small one. The measure of two attracts twice as much attention as the measure of one. We have in our scale of measures, therefore, a scale of visual attractions proportioned as 1 to 2, to 4, to 8, to 16, to 32. Break up the scale and scatter the squares over your paper and observe that the eye is no longer led in a rhythm, but is held at rest by the opposition of attractions at the point which is their centre of equilibrium. When the problem is, to find this point, we must remember the law of balance : that equal attractions (measures in this case) balance at equal distances on a straight line con- necting their centres, and that unequal attractions balance in the same way but at distances inversely proportional to them. In balancing tones we considered the element of contrast, measures being equal. In balanc- ing measures we consider what they amount to respectively. The centre of equilibrium may be indicated by a point, or more satisfactorily by a symmetrical outline enclosing all the balanced measures and having with them a common centre. When the measures are accidental and unrelated, as they were before we brought them into scale-relationship, they are nevertheless attractions which hold the eye at their centre, and the centre can be found, approximately, by means of a small unit of measurement taken as a common divisor. The centre can be approxi- mately ascertained by visual feeling, but we are talking about a scientific 372 PROCEEDINGS OP THE AMERICAN ACADEMY. basis for design, to be a verification or correction of visual feeling. The part which visual feeling plays in design is well enough understood. The third element of the spot of paint, the one which we have not yet considered, is shape. To study shape alone we avoid all differences of tone and measure. For tone we may take black on white paper, and for measure the square of an inch. Then we must vary the shape in every possible way without varying either the tone or the measure. It is a little difficult to vary the shape without varying the measure, but we can do it, approximately, with the help of an underlay of small squares put under a tracing paper upon which we draw. The power of estimating the measure of the shape, no matter how irregular it is, is a power which every drauglitsman, every paintei-, every designer must have. Make as many different shapes as you can; all black on white paper, and all in the measure of the square of an inch. Observe that some of the shapes are rhythmical, suggesting a joint action or movement of parts, that others are symmetrical, suggesting opposition or contradiction of parts, while others show both rhythmic and symmetric elements. Shapes are in harmony when they have the same or a similar character. Straiglit lines go together in harmony. Curved lines have in common their curvature, and fall into classes, circles, spirals, etc. Square spots harmonize as squares, and round spots as rounds. Angles go together in scale-rela- tions based upon degrees. Observe, however, in this connection as in others, that a little difference is more disturbing than a large difference, when there is no sufficient reason for any difference at all, when the repetition of the same shape- character would be as satisfactory. Most perfect harmony exists, of course, between shapes which have one and the same character, so in design we prefer a repetition of similar elements to any composition of insignificant differences. We are, however, apt to have differences of character given to us in the terms or conditions of our problem. AVhat we have to do is to make the best of these conditions. In such cases we can make up for any lack of harmony in shapes by harmony in other than shape-relations. Shapes are in harmony when they have the same meas- ure (harmony of measure). They are in harmony when they have the same tone (harmony of tone). Tliey may have the same value without havino- the same color, and the same color without bavins: the same value. They may have the same color without having the same intensity, so that there are many ways of achieving harmony when there is no harmony of the shapes themselves. Shapes having the same measure are in balance when they are reversed EOSS. — DESIGN AS A SCIENCE. 373 and set side by side so as to contradict one another. A perfect balance or aiititliesis of shapes is what we call symmetry. Symmetry is, accordingly, a specific form of balance. It is shape-balance, and as such it must be dis- tinouished from tone-balance and measure-balance. The only perfect balance of shapes is the balance of similar shapes set in reverse, one against the other, and having the same measure ; but we may have a partial balance in the reversion and opposition of similar shapes when they have different measures. ^j When two or more shapes are arranged so as to suggest a joint action or movement, we have what may be called a rhythm of shapes. This rhythm may be straight or curved in its character, or it may combine both curvature and straightness. As the eye moves more rapidly upon a straight line than upon any other, a rhythm showing many straight lines, all having the same direction, will give to the eye the sense of rapid move- ment, and this sense of rapid movement is lost in a rhythm which shows many curves or angles upon which the eye moves more intricately and therefore more slowly. There is another element to be considered in connection with the rhythmic composition of shapes ; that is the sugges- tion of a possible resistance. The idea of resistance does not lie in the shape of the spot of paint, in the shape itself, but in a mental association. If we wish to produce the sense of rapid motion we must be sure not to suggest any opposition or resistance. Rliythms set in contrary motion tend to balance one another, and in the measure in which they balance one another they bring the eye to the rest of equilibrium. T have now described the spot of paint in its three elements, tone, measure, and shape, and I have shown, or tried to show, how each of these elements may follow the principles of balance, of rhythm, and of harmony, which, as we have seen, are principles of order and of beauty. In the practice of Pure Design, which is the composition of spots of paint
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IK'rol lilli;r In our ii iiIiiiiiM lie ]|i|i|ii| |'i t|(|l|lil I y , i il' III, IuiinI, ill Ivvd |i'li iiMiliilii 1,1) (riilllliiliM wil.li tli<; liiilk III lliM I'lilciiitii, mill llin hitiiikI In diiiiiliiHli tin' nuliiliilily ul' lliM liiMl, tiiirni. 'i'lii't |iliiii vviiM lulldwi'il ill lliM roljiiwiii;/ umK, AiKil.liiT |iiiiiil, wiiK im yiil, iiii. 0,'//% •2'A 1, II •'1 li-iiiii. 0 jlilll 1 o,:;;i% 2H II II " V'. ImiiiM 11 li'idV 1 <)V.'1% •M tl II " m liiiiirM U l,.l 1 1 1 (10% AlMMIIIll 111 I'lllril! nXill mikI i^ I ) i|i |iii; ili .| (,l'iii'cells forming a slender, bluntly pointed, well-defined free projection. Stalk-cell of the appendage sub-triangular, somewhat prominent below the basal cell, which nearly equals it in length, sterile ; the fertile cells above it nearly equal, bearing rather large, apparently single, antheridia, with stout, straight necks, the series ending in a terminal spiniferous antheridium. Receptacle hyaline, the two cells nearly equal in length, the lower tapering below, the upper broader inflated, its diameter greater than the base of the perithecium and stalk-cell combined, so that the latter region appears to be con- stricted. Spores 2S X 2 fj.. Perithecium : venter 50-55 X 33-40 /x • neck 40-43 /A. Appendage 50 /a, the stalk-cell 18 ^u. Receptacle 55-65 X 20-22^. Total length to tip of perithecium 150-185 yit. On the superior surface of the abdomen, sometimes on the legs of HydrelUa sp. Kittery Point, Maine. Occurring in scattered groups. Stigmatomyces purpureas nov. sp. Becoming wholly suifused with purple. Venter of the perithecium inflated toward the base, ta[>ering distally ; the four wall-cells separated by a corresponding number of prominent longitudinal ridges, rounded in section, which run spirally, making in well-developed individuals a whole half turn about the venter, and becoming sometmies lobulated through the presence of successive constrictions and enlargements ; neck not abruptly distinguished, except by the abrupt elevations which form the terminations of the longitudinal ridges of the venter, rather slender, an abrupt posterior subterminal elevation preceded by a slight constriction, the tip distally quite hyaline ; the aj^ex becoming furcate through the presence of an anterior (shorter) and a posterior projection. Stalk-cell of the appendage relatively small, but slightly prominent below the basal cell, which is nearly as long, sterile, and, as a rule, followed by three cells bearing antheridia singly or in pairs, the terminal one spiniferous. Receptacle usually straight, the cells nearly equal or the upper larger. Spores 35 X 3 /x. Perithecium : venter 80-100 X 45-50 /x ; neck SO- 83 |U. Appendage 55 u, the stalk-cell 18 /x. Receptacle 100-120 /x. Total length to tip of perithecium 200-325 ^u. THAXTER. — NEW LABOULBENTACEAE. 405 On all parts of Scatella stagnalis Fallen. Kittery Point, Maine, and vicinity of Cambridge, Mass., September. Fully developed individuals with the typical structure are uncommon, a majority of the numerous specimens examined having the color dull or paler purplish, the ridges less well defined, without lobulations and with less than a half twist ; the neck and apex hardly, if at all, modified. The same host is infested by an amber-brown form which may prove a mere variety of that above described, being scarcely distinguishable structurally from the less well- marked individuals of this species, the type form of which is, from its remarkable color and the structure of its perithecium, one of the most peculiar members of the genus. Stigmatomyces spiralis nov. sp. Venter of the perithecium relatively long and slender, flask shaped, or more often but slightly if at all inflated, the granular wall-cells distin- guished by a corresponding number of abrupt, narrow, longitudinal prom- inent ridges, which become minutely roughened, and are spirally twisted so as to describe a full half turn ; the neck concolorous, distinguished by the abruptly elevated and abruptly broadened terminations of the longi- tudinal ridges of the venter, as long as or slightly shorter than the venter, slightly curved or sometimes straight, nearly cylindrical or slightly taper- ing ; the tip slightly but abruptly narrower, relatively short, somewhat asymmetrical ; the apex nearly symmetiical, four papillae being arranged about a somewhat more prominent central projection. Appendage rather short and stout, distinctly broadened in the middle, the stalk-cell stout, the basal cell half as large, or less, and fertile ; the series of six to eight fertile cells above it surmounted by a single antheridium, and distin- guished by slight successive constrictions, broad and much flattened, each bearing a single antheridium, the fifth furnished with a very sharp spine; the antheridia forming a usually lateral series, their necks becoming strongly curved. Receptacle elongate, slender, becoming brownish or yellowish, the upper cell often more than twice as long as the basal. Spores 22 X 2.5^. Perithecium: venter 90-165 X 35-47 yu ; neck 90- 160 X 17 /i (the tip 25-30^). Appendage 40-50 ^, the stalk-cell 15 p.. Receptacle 100-250 x 15yw.. Total length to tip of perithecium 350- 600 /x (average 500-550 /a). On Hydrina sp., Kittery Point, Maine. Usually on the upper sur- face of the thorax, less often on the legs and elsewhere. 406 PROCEEDINGS OF THE AMERICAN ACADEMY. Stigmatomyces Limosinae nov. sp. Perithecium amber brown, the venter slightly inflated, the neck not abruptly distinguished, tapering slightly ; the tip usually abruptly nar- rower, the posterior lip-cells forming an inconspicuous irregular truncate or rounded bilobed projection somewhat more prominent than a similar projection formed by the anterior lip-cells ; basal cells relatively very large, forming a short, well-defined stalk, hyaline or colored above, often carrying the base of the perithecium beyond the tip of the appendage, and consisting of an inner cell next the appendage and two superposed outer ones, the lower of which (secondary stalk-cell) is smaller ; the stalk- cell below these wholly united to the stalk-cell of the appendage, rather stout and short, separated from the cells above it by a horizontal septum, which may be slightly oblique or (as in the California variety) strongly oblique, in which case the secondary stalk-cell extends downward beside the stalk-cell so that only the lower third or quarter of the latter is free externally. Stalk-cell of the appendage relatively large, as long as or often longer than that of the perithecium and about half as broad, usually bulging externally, its outer margin usually curved symmetrically from its base to the base of the basal cell ; the latter relatively small, deep amber brown, half as long as broad, pointed distally between the antheridium which arises from its inner side and the base of the first fertile cell above it, which, with the other fertile cells, are large and prominent, thick walled, much flattened, and obliquely superposed, distinguished by rather deep constrictions, seven to ten in all, or rarely more (seven to fourteen in the Californian form), the original number being increased by the terminal proliferation of the appendage ; the antheridia borne on the inner side of the appendage, their very long but not abruptly differentiated necks ex- tending obliquely upward, appressed in a double series ; the upper anthe- ridia often infertile, becoming septate and irregularly swollen. Receptacle relatively short, the two cells nearly equal. Spores 28 X 3 /a. Peri- thecium: venter 50-90 X 40-54 /a; neck 90-125 X 15-18^ ; stalk (basal cells only) 72-100 X 25-35 (i. Appendage 60-100 /x, stalk-cell 30-45 ^. Receptacle 70-75 X 22 fi. Total length to tip of perithecium 250-360 /x. Specimens on legs often much smaller. On Limosina fontinalis Fallen. Kittery Point, Maine, vicinity of Cambridge, Mass., Berkeley, California. Usually in a dense tuft on the side or near the tip (inferior) of the abdomen and near the base of the posterior pair of legs. The Californian material, from two specimens of the host, differs constantly from the abundant New England material as THAXTER. NEW LABOULBENIACEAE. 407 noted in the description, as well as from the fact that the venter of the peritheeium is longer and less distinctly inflated, while its apex shows no perceptible modification of the lip-cells. Stigmatomyces Papuanus no v. sp. Venter of the peritheeium dark amber brown, relatively small, and rather prominently inflated, oval to elliptical ; usually not abruptly dis- tinguished distally from the hyaline or yellowish neck, which in well- developed specimens is very elongate, tapering very gradually, in others shorter and stouter ; the tip clearly distinguished (abruptly so in the shorter forms), subconical, the posterior lip-cells forming a narrow, sub- truncate, slightly recurved apical projection beyond the two laterally placed, papillate, slightly divergent projections of the anterior lip-cells ; the basal cells forming a short, stout stalk, separated from the stalk-cell by an oblique septum. Appendage relatively small, resembling that of the aS'. Limosinae in general form, the fertile cells not more than five or six in number, the upper ones separated by constrictions which may be obsolete between the lower ones. Receptacle relatively short, the cells subequal, yellowish. Spores about 20 X 2 ju. Peritheeium : venter 50- 55 X 40 ^ ; the neck 90-290 X 20 ja ; the stalk 35-45 x 33-36 /a. Appendage, 35-45 fx, the stalk-cell 22-30 X 14-17 jx. Receptacle 55- 72 f^i. Total length to tip of peritheeium 400-485 ^t. A few specimens on the legs much smaller. On three small flies of different species allied to Limosina. Ralum, New Pomerauia. Perhaps a variety of S. Limosinae. Arthrorhynchus Cyclopodiae nov. sp. Becoming tinged with brownish yellow except tiie hyaline stalk-cell of the peritheeium. Peritheeium nearly straight and symmetrical, slightly inflated, usually distinctly constricted in the region of its very small basal cells just above the very large hyaline stalk-cell, which may nearly equal it in length and diameter and is often somewhat enlarged distally : the venter comprising the lower two-thirds, not clearly distinguishable from the neck, which tapers slightly and almost symmetrically, the ti}) fairly well distinguished above a more or less distinct enlargement, from which it is separated by a slight constriction ; the apex consisting of a crown of four nearly symmetrical, distinctly tridentate, erect, or very slightly divergent projections, which are subtended by a correspoiuling number of slight elevations, the middle lobe of each projection more promiueut thuu 408 PROCEEDINGS OF THE AMERICAN ACADEMY. the lateral aud like them bluntly rounded. Receptacle consisting of two small cells, the lower twice as large as the upper, which gives rise distally to the stalk-cell and bears the free appendage laterally; the foot an unmodified cell which penetrates the host, dividing below into a very copiously branched system of slender, sinuous, rhizoidal hyphae. Ap- pendage consisting of a dumbbell-shaped, free stalk-cell, the basal half- rounded or flattened, brownish, somewhat larger than the distal portion, which is deeper brown, flattened and inflated, connected by a narrow liyaline isthmus (the lumen of which may become almost obliterated) with the lower half, and mostly broader than the base of the basal cell of the appendage, which is infertile, subrectangular, or somewhat inflated, slightly longer than broad, the lower half of the walls becoming conspicuously modified by a progressive thickening from above downward, the thick- ened portion deeper brown ; the remaining cells of the appendage three to four in number, brownish, successively smaller from below upward, giving the organ a characteristically tapering habit ; the two lowest of these cells usually relatively shorter, and bearing each three to four antheridia side by side, distally and externally ; those above relatively longer aud narrower and producing fewer antheridia, the terminal one spiniferous. Antheridia with slender curved necks. Spores 60-65 X 4.5 //. Perithecium : venter 325-350 X 70-90 yu, ; the stalk-cell 220- 250 X 75-80 /x. Appendage, 100-1 10 /x, the stalk-cell 35-40 X 30-35 /a (the upper half X 28-30 /x). Receptacle 55-75 X 45-50 ^. On the abdomen of Oyclopodia macrura Speiser. New Pomerania. Berlin Museum, No. 854. The original name given to this genus in 1857 by Kolenati is here retained in preference to the much later one applied to it by Peyritsch in 1873 ; since however absurd aud scientifically worthless the original zoological descriptions of these forms may be, there has never been the slightest question as to the generic identity of the organisms studied by these two authors. Neither the descriptions nor the figures given by Kolenati and Diesing are, however, sufficient to render a specific deter- mination possible, so that the name given by Peyritsch to the European species of the genus, although it is undoubtedly a synonym of A. D'le- singii Kol. or A. Westrimibii Kol., or more probably of both, may properly be retained. The new forms here described are very closely allied, diifering chiefly in the details of structure in the appendage and the tip of the perithecium, but are very different from Arthrorhynchus Nycteribeae. Material in my possession obtained from species of Nyc- teribia, from Europe, must, I think, be referred without (question to the THAXTER. — NEW LABOULBENIACEAE. 409 last named species ; although the conformation of the tip of the perithe- cium has apparently been incorrectly reproduced in Peyritsch's plate. Artlirorhynchus Eucampsipodae nov. sp. Hyaline throughout. Perithecium straight or distally slightly curved, tapering gradually from the middle, or lower, to the broad tip ; the apex consisting of a slight median projection surrounded by a crown consisting of four slightly shorter, broad, blunt, distinctly divergent projections, which show indistinct marks of lobing and are symmetrically placed ; the stalk- cell about one half as long as the perithecium or less. The basal cell of the appendage constricted in the middle as in the preceding species, the lower half irregularly rounded and four or five times as large as the upper half, which is very small, colorless, and less than half as wide as the cell above it ; the fertile cells three in number, the lower bearing four or (?) five antheridia, the upper three in addition to the terminal one, which is furnished with a short hyaline basal spine ; the necks of the antheridia large, tapering, divergent. Receptacle as in the preceding species. Spores about 45-50 X 4 /x. Perithecium : venter 250-325 X 65-75 ^ ; the stalk-cell 110-150 X 55 /n. Appendage, 75-90^, the stalk-cell 35 X 25 (the upper half X 10^). On the abdomen of Eucampsipoda Hyrtli Kol., Egypt. Berlin Museum, No. 855. Rhizomyces gibbosus nov. sp. General habit more or less sigmoid. Perithecium amber brown, con- colorous, with its relatively large basal cells, from which it is hardly dis- tinguished, asymmetrically inflated, bent, and tapering somewhat distally ; a subterminal abruptly rounded eidargement, beyond which the short asymmetrical tip is clearly distinguished, bearing a large two-celled out- growth posteriorly, the lip-cells being otherwise unmodified : stalk-cell hyaline, variably, sometimes greatly elongated, separated from the basal cells by a more or less distinct constriction. Appendage nearly hyaline, except the small deep brown sterile basal cell, the remaining cells, three to seven in number, bearing short one- to two-celled branches distally and laterally on which the free flask-shaped antheridia are borne singly or several together. Receptacle short and stout, the upper cell several times as large as the basal cell, which appears to penetrate the host di- rectly by means of a rhizoidal apparatus. Spores about 35 X 3 m. Peri- thecium, including basal cells, 85-108 X 30-36/a; the stalk 60-160 X 18-20//,. Appendage G5-110|U. Total length to tip of perithecium 180-325^. 410 PROCEEDINGS OF THE AMERICAN ACADEMY. On the upper surface near the tip of the abdomen of a species of Diopsis. Berlin Museum, No. 850. Tanga, Africa. CERAIOMYCES nov. gen. Structure of peritliecium as in Laboulbenia, its stalk-cell united to the free base of the free stalk-cell of the appendage, which bears a well differ- entiated basal cell terminally, from the end of which are borne antheridial branches, the successive cells of which produce terminally either succes- sive secondary branchlets or antheridia or both, much as in Laboulbenia. Receptacle two-celled. Ceraiomyces Dahlii nov. sp. Perithecium large, blackish brown, with an olive shade, becoming opaque, usually slightly curved, tapering gradually to the slender undifferentiated tip ; the anterior lip-cells forming two appressed hyaline-tipped finger- like projections ; the base very broad, translucent, dull brownish, bulging conspicuously below the venter, especially on the left side ; the stalk-cell small, nearly isodiametric, united on its inner side to the base of the stalk- cell of the appendage. The latter free, though often in contact with the base of the perithecium, dull blackish olive, outwardly inflated, narrower terminally where it bears the characteristically differentiated basal cell of the appendage, which becomes almost opaque and is somewhat flask- or bottle-shaped with a rounded extremity, from which, typically, two diver- gent branches arise which in turn may branch one to three times sub- dichotomously ; the long slender flask-shaped antheridia borne, one to two together, distally from the successive cells. The basal cell of the recep- tacle nearly spherical, penetrating the host by a long filament which is slender except for an enlargement immediately below the integument of the host, simple at first but becoming more or less copiously branched; the upper cell very large and elongate. Spores about 30 X 3 ^u. Peri- thecium 275-310 X 55-60 ju; the base, including the stalk-cell, 68-72 X 58-68 |U. Appendage 75-85 /x (the basal cell 18 X 12 /x), the stalk-cell 40-45 X 18-22 /A. Receptacle 175-240 x 35ya (the basal cell 20-22 /x). Total length to tip of perithecium 400-675 fx, average 550 /x. On various parts of a small flower fly. Ralum, New Pomerania. Berlin Museum, Nos. 1283 and 1298. Occurring more often on the head, where it might be mistaken for a dipterous antenna. Dimeromyces coarctatus nov. sp. Male Individual. Receptacle nearly hyaline, consisting of usually three superposed cells, the upper separated by a dark-colored constriction THAXTER. — NEW LABOULBENIACEAE. 411 from a short, simple, two- to three-celled hyaline or brownish appendage. The antheridia usually two, seldom three, borue singly from the succes- sive cells of the receptacle, from which they are separated by a small basal cell ; the venter having an external depression and not abruptly distin- guished from the stout curved neck. Receptacle 35-45 X 6-7 fi. Ap- pendage 25-50 fjL. Antheridia 18 X 5 /x. Female Individual. Receptacle consisting of a large basal cell about twice as long as broad, bulging so as to form a rounded base which pushes the small brownish-black foot to a lateral or sublateral position ; the re- maining cells, usually eight or nine in number, separated by horizontal septa and superposed in a simple series ; the lower cells greatly flattened, those above somewhat less so, the series ending in a somewhat abruptly narrower terminal cell, which is more than twice as long as broad, subcy- lindrical, its extremity rounded symmetrically and bearing a short, simple, usually four-celled terminal brownish appendage, which is distinguished by a constricted dark basal septum and terminated by a somewhat inflated lighter larger cell, which becomes characteristically disorganized on one side, so that the appendage appears to end in a slender curved projection. The remaining cells of the receptacle producing single appendages or peri- thecia, except the basal and sometimes a subbasal cell. The uppermost of these secondary appendages arises from the inner side of the subconical subterminal cell of the receptacle, occupying a position in the median line between the primary appendage and the base of the first perithecium, and consists of a short subconical basal cell, from the narrow extremity of which the simple, several-celled terminal portion is distinguished by a constricted dark septum ; the remaining appendages laterally divergent on opposite sides in such a way as to appear paired, usually three on each side, each consisting of a rather long basal cell inflated along its upper side so as to appear more or less geniculate, concolorous with the recep- tacle, its narrower extremity suffused with dark brown, distinguished without constriction by a dark septum from the simple terminal portion, which is usually five-celled, more or less strongly recurved, brown, its ter- minal cell becoming inflated and undergoing gelatinous degeneration on the lower side, which causes it to appear split in two, the hook-like upper half of the cell alone persisting in some individuals. Perithecia yellow- ish, distally l)rownish, one, rarely two, in number ; the first always arising from the cell immediately below that which bears the upper secondary appendage, the second, when one is present, replacing one of the append- ages lower down ; consisting of a symmetrically inflated venter, which tapers gradually downward, passing into the short stalk ; a short neck 412 PROCEEDINGS OF THE AMERICAN ACADEMY. rather abruptly distinguished, deeper brown below, its tip inflated below four terminal projections, three or two of which are in the form of rounded papillae of unequal size, and one or two of which are pointed and much more prominent. Spores 42 X 3.5 /x. Perithecium, including the stalk, which is continuous with it, 125 X 20-35 jj.. Receptacle to base of pri- mary appendage 50-75 fi. Secondary appendages about 75 /x. Total length to ti23 of perithecium 150-180 /x. Densely crowded on the inferior surface of the abdomen or rarely on the legs of a small pale fly, remarkable for a prominent black spur-like bristle on the posterior legs. Ralum, New Pomerania. Berlin Museum, No. 1282. Dimeromyces rhizophorus nov. sp. Male Individual. Receptacle consisting of a basal cell which penetrates the host directly without a diiferentiated foot, and two to three super- posed cells above it, each of which usually bears an antheridium, the upper terminated by a short, pointed, slender cell. The antheridia rather short and stout, with short, stout necks. Receptacle about 50 X 8 fi. Appendage 12 X 3.5 /x. Antheridia 25 X 9 yu. Female Individual. More or less deeply tinged with amber brown. Receptacle amber brown, consisting of six superposed cells, the small basal cell, hardly visible above the integument, penetrates the host directly by means of a very large, abruptly furcate rhizoid, the two cells above it similar, broader than long, bearing each an appendage consist- ing of a basal cell bent toward the receptacle, darker and narrower distally, and separated by a dark septum from the three-celled terminal portion, which is straight or slightly curved, larger toward the middle, the smaller terminal cell becoming partly disorganized. The next (fourth) cell of the receptacle bears the single perithecium ; the distal terminal cell longer and narrower, and terminated by a shoi't, pointed, one- some- times two-celled primary appendage (similar to that of the male in- dividual), from which it is separated by a constriction ; the subterminal cell narrower distally, producing on its inner side an appendage similar to those below it, but straight and somewhat shorter. Perithecium with a short stout stalk rapidly expanding into the asymmetrically inflated deeper brown venter of the perithecium ; the neck very short and abruptly distinguished ; the tip relatively large, four-lobed, inflated with two lateral papillate outgrowths, above which the lips form a subconical projection. Spores about 25 X 3 ^. Perithecium including stalk 70-90 X 20- THAXTER. — NEW LABOULBENIACEAE. 413 25 fi. Receptacle about 45 X 12 /x. Primary appendage 12 |U ; second- ary appendages 35-40 fi. Penetrating rhizoidal branches 150-184 X 10-12 ft. Total length to tip of perithecium 90-110 /u. On the inferior surface of the abdomen of a small fly. Ralum, New Poraerauia. Berlin Museum, No. 1295. Dimeromyces crispatus nov. sp. Male IndividiiaL Receptacle consisting of four superposed hyaline cells, the basal one much longer than the rest combined ; the upper bear- ing distally a two-celled terminal appendage, the lower cell of which is small, the upper elongate, brownish ; the two remaining cells of the receptacle producing each a single antheridium. Antheridia superposed, tlie stalk-cell, neck, and venter well distinguished, the latter symuietri- cally and considerably inflated, the neck slightly curved. Receptacle 50 X 8 //. Antheridia 33 x 8-9 fx.. Appendage 36 /x. Female Individual. Receptacle consisting of usually five superposed cells, the basal cell very elongate, slender, and hyaline ; while of the four remaining cells the two lower are much flattened, broader than long, and separated by oblique septa, the two upper unlike and narrower. Of these four cells the second from below cives rise to the stalk-cell of the perithecium, while the others by successive proliferation produce each a branch consisting of" eight or ten obliquely superposed cells ; while each of these cells in turn produces a single simple branchlet from its upper side, originally terminal, but becoming lateral through the further pro- liferation of the cell which bears it; the branchlets distinguished by a slight constriction and a brond dark septum at the base, brown, curved, distally helicoid, slightly enlarged and paler. The primary terminal appendage thus appears as the lowest of the upper series of branchlets, from which it does not differ in structure. Perithecia one to three in number, the first lowest, and always formed from the second from below of the four distal cells of the receptacle, others sometimes arising from each of the two upper distal cells ; the stalk hyaline, long and slender, the venter small, narrow, not distinguished from the stalk, becoming brown- ish, distally slightly inflated, the neck short and well but not abruptly distinguished ; the tip well differentiated, hyaline, symmetrical or nearly so, shovel shaped or spatulate, swollen at its base, and tapering to the broad, bluntly rounded or nearly truncate apex. Spores about 30 X 3,5 /x. Perithecium : 70-75 X 18 /*. the stalk 50-12") X 15 ,«/. Reoe[)- tacle, basal cell 185-250 X 18 ^, the distal portion about 50 /x. Total 414 PROCEEDINGS OF THE AMERICAN ACADEMY. length to tip of perithecium 360-435 /x. Lateral cell series or branches about 50 fi long, their branchlets to tip of helix about 50 /x. On the legs and superior surface of the abdomen of the same host parasitized by D. coarctatus. Ralum, New Pomerania. Berlin Museum No. 1282. ' Proceedings of the American Academy of Arts and Sciences. Vol. XXXVI. No. 2i. — April, 1901. CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE MUSEU]\I OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE. E. L. MARK, DIRECTOR. — No. 119. A STUDY OF VARIATION IN THE FIDDLER CRAB GELASIMUS PU GIL AT OR Latr. By Robert M. Yerkes. CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE. E. L. MARK, DIRECTOR. — No. 119. A STUDY OF VARIATION IN THE FIDDLER CRAB GELASIMUS PUGILATOR LATR. By Robert M. Yerkes. Presented by E. L. Mark, February 13, 1901. Received March 4, 1901, Contents. Page I. Introduction 417 II. Problems •. ... 418 III. Methods and Material 419 IV. Results 423 1. Tables of Means, Modes, Standard Deviations, and CoefScients of Variability 423 2. Tables of Occurrence of Right- and Left-Handedness 425 3. Polygons of Frequency 425 4. Table of Correlation of Meropodites of Chelae 438 V. Discussion of Results 440 VI. Summary 441 Bibliography , 442 I. Introduction. This study was undertaken to get light on some minor problems of variation, and to furnish records for future reference. The matter of future reference seems to me of special importance, for it is evident that with records of the variations of a race during stated intervals available, the course and progress of evolution may be more or less accurately traced. Davenport ('99) has emphasized the need of the collection and filing of statistics of variation, especially of Place- Modes ; and it was in response to his plea for this kind of work that I undertook to determine some place-modes for one of the Fiddler Crabs (Gelasimus pugilator) of a certain region. In order to make the records of measurements together with my com- putations and interpretations available for any who may, in the future, VOL. XXXVI, — 27 418 PROCEEDINGS OF THE AMERICAN ACADEMY. desire to use them, they will be placed iu the Library of Harvard Uni- versity, subject to the order of either the librarian or the writer. Through the kindness of Mr. Alexander Agassiz and the authorities of the United States Fish Commission Station at Wood's Hole, Massa- chusetts, I was permitted to occupy, during a part of the summer of 1899, one of the tables in the Fish Commission Laboratory controlled by the Museum of Comparative Zoology. I desire to thank them for the privilege, and also Professor H. C. Bumpus, Director of the Labo- ratory, for facilities in collecting material and for many courtesies which made work pleasant. To Professor E. L. Mark I am indebted for suggestions and assistance iu the arrangement of this report ; to Pro- fessor C. B. Davenport I owe the knowledge and interest which led me to the problems, and to him I am also indebted for invaluable assistance in the prosecution of the work. II. Problems. The original purpose of this work was the determination of place- modes for Gelasimus pugilator of West Falmouth, Mass. Examination of the material for measurement and consideration of the probable value and significance of various dimensions led to the inclusion of several other problems. For it seemed advisable to select for the determina- tion of place-modes such measurements as would be likely to contribute data for problems of adult form, of development, and of function. The male Fiddlers are either right- or left-handed, one chela being enormously developed, the other small. The proportions of right- and left-handed animals will be considered later. In the females the chelae are nearly equal. One immediately asks: (1) What is the meaning of this condition in the males ? (2) What relation does the size of the chela bear to the other body measurements ? (3) What determines whether an animal shall be ricrht- or left-handed ? These are some of the problems which, it was hoped, might be at least partially solved by a quantitative study of variation ; for unquestionably this method can supplement in important ways histological and physiological studies. It was my purpose to measure equal numbers of the two species of Fiddlers, Gelasimus pugilator and G. pugnax, found in the vicinity of Wood's Hole,* selecting equal numbers of males and females fi-om each of the two species. But the task of measuring was slow, and the time then available for the work was exhausted before its completion. This * G. minax does not occur in the vicinity. YERKES. — VARIATION IN THE FIDDLER CRAB. 419 report, therefore, represents only a fragment of what was planned, and what the complete solution of the suggested problems demands. III. Methods and Material. The followintj measurements were made : — 1. Frontal Breadth, the distance between the anterior marginal points of the carapace (Figure 1, FB). B Figure 1. Dorsal aspect of carapace. BA, right marginal length. FB, frontal breadth. AJL, median length. 2. Median Length, the maximum length of the carapace in the median plane. (Figure 1, ML). 3. Right Marginal Length, the distance from the right anterior mar- ginal point of the carapace to the posterior end of the lateral ridoe, just above and between the fourth and fifth legs (F'igure 1, BA). 4. Left Marginal Length. 5. Meropodite of the Right Cliida, the distance between the articula- tions on the anterior face. The proximal point of measurement, i. e. the articulation between ischiopoditc and meropodite, is on the anterior ventral surface, and therefore does not show in Figure 2. 6. Carpopodite of the Right Chela, the distance between the anterior articulations (Figure 2, CL). 7. Propodite of the Right Chela, the distance from anterior articula- tion with carpoiiodite to articidation with dactylopodite (Figure 2, PL). 420 PROCEEDINGS OF THE AMERICAN ACADEMY. 8. Meropodite of Left Chela. 9. Carpopodite of Left Chela. 10. Propodite of Left Chela. 11. Meropodite of Second Right Leg ; points the same as for meropo- dite of chela. 12. Meropodite of Second Left Leg. 'ba''pd. dae'pd. rncr^pd. carp^pd pr^pd. Figure 2. Dorsal surface of Right Chela, dac'pd., dactylopoilite; pr'piL, pro- podite; wr/j'/)^., carpopodite ; mer'pd., meropodite; ba'pd., hasipodite; C'Z, length of carpopodite ; LP, length of propodite. The above measurements are similar to those made for Caicinus maenas by Weldou ('93), but in no case identical with his. He has, furthermore, expressed all measurements in terms of total carapace length, so comparison of our results is impossible. Dr. H. W. Rand * has repeated Weldon's measurements on C. maenas at Wood's Hole. His results, which have not as yet been published, will furnish, in con- nection with this study, interesting data for the comparison of Carcinus and Gelasimus. The measuring apparatus used consisted of a pair of spring dividers, which could be adjusted easily and accurately by means of a thumb- screw. In measuring, the end of one arm of the dividers was fixed upon the point marking one limit of the dimension to be measured and the other arm was adjusted by means of the thumb-screw until its point coin- ."ided with the other limit of the dimension. The dividers were then transferred to a steel millimeter scale, above which a pocket lens was so arranged as to give a magnification of about twelve diameteis, thus en- abling one readily to read from the scale the distance between the points of the dividers. The scale was ruled to fifths of a millimeter, and by determining whether the fine point of the arm rested in or between * Data and description of measurements, in manuscript. YERKES. VARIATION IN THE FIDDLER CRAB. 421 marks it was possible to read to tenths. Although in case of these measurements readings were made to tenths, accuracy to fifths is all that can be claimed, because of the tendency to judge in favor of the marks ou the scale. Over a thousand individuals of Gelasimus pugilator were collected, without any attempt at selection, from a large colony on the shore of West Falmouth Harbor, between July 24th and August 22d» The accompanying map of the harbor and vicinity shows the location of the colony ; two small circles mark the limits of the ground used for collecting. "Weak alcohol, about 20%, gave satis- factory results as a killing agent. Sub- stances which act very quickly, such as hot water, formol, or strong alcohol, cause autotomy. Twelve measurements were made for each of four hundred right-handed ani- mals, and for the same number of left-handed individuals. For these two groups of measurements the means, modes, standard deviations, and coeili- cients of variability have been found. To avoid the possibility of misunder- standino: as to the meanings of these Figure 3. Map of West Fal- nioutli Harbor. Material was collected from the region between the small circles. terms, I shall briefly define them.* The Mean is the sum of the products of each class into the number of individuals in the class, divided by the total number of individuals. The Mode is the class containing the greatest number of individuals. The Standard Deviation "is found by adding the products of the squared deviation-frora-the-tnean of each class multiplied by its frequency, dividing by the total number of variates, and extracting the scjuare root of the quotient."! Tlio Coefficient of Variability is one hundred times the quotient of the standard deviation divided by the mean. * The terms and methods given by Davenport ('99'). t Davenport ('99", p. 15). 422 PROCEEDINGS OF THE AMERICAN ACADEMY. H P3 O w H O o Q ^< - P Q -\ r—* CO o o o CO CO t^ <>) lO o o r3 00 a t- C5 o CO (M CO CT> LO t- LO CO s IS tM ^ >o o CO O t-H CO o •<*< O CO iC '^ CO CO a~. •^ ii B (>1 CO -t< Tti o l© I-H CO I-H I-H r^ (M P (N CO «• o (>J r^ LO or MH r- a t-^ t-^ CO CO 05 o o CO oi 00 00 cd o I-H r-» O CT> CO o CO o 1^ CO o CO o OS CO d m a Ci 05 ro ■* l~ o CO L5 •^ t^ t— t^ .2 ^ O C-1 ■^ 1-- (M CO Tt* CO o (M CO (M 2 ►S a r-l 05 t-- r-; iq CO o\ CO t>; 05 CO t-- 'P T— * a; 53 ^ CO CO CO 1—1 V.O O 0? t^ Ci CO CO "* co w a -t< a> (M o ^^ oo LO lO o LO CO 1 ^ o CO CO (M 03 o lO LO >c lO LO LO o ^ a >o Oi CO CO l^ 1-J CO LO Oi t— r— I t- W) a lO ,-H CO CO CO t~^ Ci LO <^i oi t-^ CD S I—H I-H CO r^ lO CO IM 05 CO CO CO CO LO CO m a LO Ctl CO 1—1 T-H o CO LO t~ CO CO (M (S o Ol (M t-; CO o i~ o CO o p L3 3 a o (>i CO 00 lO <>i M CO CO d> cd' t-^ r-l T-H 9 cd 0) ^ 00 -4J CO lO iM o o LO CO CO o o o t^ a C<1 -^ t< o CO I-H ■nl C£) LO CO M ja l^ (M CO >* I-^ i-H (M LO o t^ LO I-H .Sf a o o\ OD CO co' t~^ oi lO CO c4 t~^ r-^ K T— 1 I-H • • • n • • • s 5 -4^ ^ "3 s ,5 JS [S Eh 'u, "s "a! ci 'C 2 3 • C "So c3 a "So J3 o «tH "5 b£ OI *-H be -a JO 3 3 g •3 j2 H S o o "u «tH o o « ■*-> ^ ii 5 ■♦-» ■4J -4-' '5 o o '3 o O 'a o o 0) ■♦H o '3 o '3 o c o '3 1^ 2 to o 2 p-i o Ih eS o C4 2 CM o u 2 YERKES. — VARIATION IN THE FIDDLER CRAB. 423 IV. Results. 1. Tables of Means, Modes, Standard Deviations, and Coefficients of Variability. Table I. contains the results of all calculations so arranged as to facili- tate comparison of right and left-handed animals. The first of each pair of columns gives the values for the right-handed individuals, — indicated at the top by "Rights;" the second, for the left-handed, — indicated by " Lefts." It is to be noted that no identical measurements for Rights and Lefts (for sake of brevity we shall hereafter speak of the tvv^o types as Rights and Lefts instead of right-handed and left-handed) are strictly comparable, except frontal breadth and median length, for in every other case there is marked asymmetry, and the measurements for the left side of one type have to be compared with those for the right side of the other. TABLE II. Means and Coefficients of Variability arranged for Direct Comparison. Qelasimus pugilator (Males). Mean. Coefficient of Variability. Rights. Lefts. Rights. Lefts. Frontal breadth Median length Lateral margin, great chelar side . . Lateral margin, small chelar side . . Meropodite of great chela Carpopodite of great chela .... Propodite of great chela Meropodite of small chela Carpopodite of small chela .... Propodite of small chela Meropodite of 2d leg, great chelar side Meropodite of 2d leg, small chelar side mm. 15.728 12.245 8.842 8.400 8.780 7.115 9.248 5.563 3.050 2.710 7.589 7.127 mm. 15.658 12.237 8.710 8.285 8.656 6.878 9.038 5.312 2.969 7.523 6.965 mm. 7.022 7.266 8.845 8.649 9.000 10.160 10.215 8.734 9.518 8.313 8.479 8.724 mm. 7.471 7.598 8.880 9.000 9.657 10.472 10.255 9.920 11.139 8.898 9.660 9.100 424 PROCEEDINGS OF THE AMERICAN ACADEMY, Table II. gives the means and coefficients of variability which are directly comparable. In every case, with the exception of the propodite of the small chela, the means for the Rights are larger than those for the Lefts ; the coethcieuts of variability are without exception greater for the Lefts. In other words, the right-handed individuals are the larger and the less variable. TABLE III. Right- and Left-Handedness. G. pugilator. G. pugnax. Males. Females. Rights. Lefts. Lot from W. Falmouth, Aug. 18, 1899. Lot from W. Falmoutli, Aug. 22, 1899. 215 286 185 280 90 151 85 110 Totals. Per cent. 501 51.86 of males. 465 4814 of males. 241 20.00 of all 195 TABLE IV. Right- and Left-Handedness. G. pugilator. G. pugnax. Males. Females. Males. Females. Rights. Lefts. Rights. Lefts Lot from i W. Falmoutli, > .July IG, 1900. ) 431 431 195 552 578 5^ Per cent. 50 of males. 50 of males. 18.45 of all. 48.85 of males. 51.15 of males. 4.5G of all. YERKES. — VARIATION IN THE FIDDLER CRAB. 425 2. Tables of Occurrence of Rigid- and Left- Handedness. In this connection a statement of the relative frequencies of right- and left-handedness is important. Table III. offers an analysis of two lots of pugilator and pugnax from West Falmouth. Of 9GG males 51.86% were right-handed, 48.14% left-handed. During the summer of 1900 additional evidence was obtained on this subject. Over two thousand Fiddlers from the same colony were examined, with the results shown in Table IV. Comparison of these two tables (III. and IV.) indicates that the male Fiddlers are about equally divided into right- and left-handed individuals. The number of females captured was always small, prob- ably because the males remain outside to fight, while the females and immature individuals scurry into the burrows. According to Table IV. the percentage of female pugilators captured was four times as large as that of female pugnax, but for this I am unable at present to offer any explanation. 3. Polygons of Frequency. "We shall now consider the various measurements individually, and examine the Polygons (more accurately Rectangles) of Frequency. The polygons are all constructed thus. Each vertical column repre- sents a class, and each of the squares in these columns represents five individuals. Tlie classes are separated by 0.4 mm.* In polygon No. 1 R, for example, the first class is 13.15 mm. and contains one individual ; the second class is 13.55 mm. and contains four individuals. 1. Frontal breadth. This is the largest and least variable dimension of the twelve under consideration. Polygon No. 1 R represents the distribution, among the various classes, of the right-handed individuals, and No. 1 L that of the left-han-i Ki ^1 hi hi hi hi hi hi Co Cti C-1 l~4 52 Co C^i K4 ti Co C;» --1 hi CJ, Polygon No. IR. 10 GO CO 40 30 20 10 CO hi to Co >-1 1-1 1-1 1-1 >-1 C5 hi -I hi hi hi Oo hi Oo hi K4 Ol C-1 to Co ^1 CJ. Co Cn Ki Cn Ct Oi Co ^1 hi Polygon No. 1L. YERKES. — VARIATION IN THE FIDDLER CRAB. 42T ■were collected at three different times (75 July 24, 125 August 17, and 200 August 24), of which the first aud last were separated by over three weeks, this is not improbable. But as I have no data on ecdyi^is, it is impossible to settle this point. 2. Median length. This is the second larg- est dimension taken. It is slightly more variable than the frontal breadth. The polygons No. 2R and 2L represent simi- lar distributions, with a greater frequency, how- ever, at the mode of the Rights, as in the frontal Breadth, indicating less variability than in the Lefts. 3. Right margin. It should be remembered that No. 3R and 3L are not strictly comparable because of the asymme- try of the animals. The polygons have been placed together because they represent identical measurements. Compar- ison should also be made of No. 3R with 4L, the polygons for the margin on the side of the great chela of the Rights aud 80 70 60 50 40 30 20 10 — " to iM o 1-4 1-^ (0 V-4 03 Co 1-4 03 1-4 1-4 In ' CO ^7 to Co to 03 1-4 Polygon No. 2R. so :o GO 50 40 30 20 10 to K-4 to to 1-4 1-4 1-4 1-4 1-4 1-4 l--t <>3 1-4 <0 1-4 03 1-4 03 I~4 Oo 1-4 1-- Ik 1-4 Oi to 03 Oi 1-4 0-1 0. Oi 5i 00 Oi ^1 1-4 Oi Oi 0. o. Oo Oi -1 Oi 1~. 0.1 Polygon No. 2L. 428 PROCEEDINGS OF THE AMERICAN ACADEMY. Lefts respectively. No. 3R differs from 3L in having greater modal fre« quency and more classes ; it differs from 4L by much greater modal frequency. As compared with the left margin the right is somewhat less variable. For both Rights and Lefts the margin on the side of 100 90 SO 70 60 50 40 30 20 JO Ci ^I v» ■M Co Co 50 5= <3 k4 1-^ — ^1 t-1 Co Ct Oo t1 100 DO 80 70 60 50 40 30 20 10 Ob ^j *l •^I Oo 05 ca « la Kl o Co Ct Cl to Co C.T Polygon No. 3R. Polygon No. 3L. the small chela is 5% shorter than the other. In the case of the Rights, 8.400 (Left) ^ 8.842 (Right) = .9500, i. e. Left is 95% of Right. And for the Lefts 8.285 (Right) -f- 8.716 (Left) = .9505, i. e. Right is 95+ % of Left. All dimensions are considerably larger on the side of the great chela, a fact which will be discussed later in connection with the problem of right- and left-liandedness. YERKES. — VARIATION IN THE FIDDLER CRAB. 429 90 8D 7D CO 50 40 30 20 10 o» 05 •-J ^ ^ Oo Oo to CO I* K4 1— to k4 to "^1 1-4 g Co to. -I 90 SO 70 CO 50 40 30 20 10 ^i •^ ^* Or, Oo -< ta ti 1* Co C-1 c« to Polygon No. 4R. Polygon No. 4L. 4. Left margin. Polygons No. 4R aud 4L. Compare also No. 4R with 3L. The three dimensions thus far considered are the most valu- able for place-mode determinations because they are expressive of the form of the carapace and may be measured with ease and accuracy. As given in Table I., the modal classes of the Lefts, — in two instances, — the frontal breadth and right margin, are below those of the Rights; in both of these cases there is considerable difference in the means. 430 PROCEEDINGS OF THE AMERICAN ACADEMY. oc — . 1 1 so TO CO 50 40 30 20 10 _ - — Ci Ci ^ ^^ ^I Co Oo to to to 1-1 ' 0< t1 Oi *< to Polygon No. 5R. 90 - " SO 70 60 oO 10 30 22. 10 ■ — Ol c- -t ^I -I >> Co to to to hi I-4 hi h-4 hi to ^1 t. to Co t1 k-4 Ci to Co C1 Ct Ci Ct 5. Meropodite of great chela. I shall here consider homol- ogous organs. With the exception of the usual greater fre- quency of the modal class of the Rights, the polygons No. 5R and 5L are very sim- ilar. The difference in the coefficients of variability between the Rights and Lefts is .657 in favor of the Rights. POLTGON No 5L. YERKES. VARIATION IN THE FIDDLER CRAB. 431 110 100 ror, 90 90 so so 70 70 GO 60 50 50 40 40 30 30 20 20 10 10 - Oi C t) C5 Ci •^ ^ »J Oo Oo «! Cx Ol Ck C5 OS •<» •^l vj Oo Oo to k^ Ct ^1 5 l^ Co 1^ t1 S? to Co C.-I Polygon No. 6R. PoLYGOv No. 6L. 6. Carpopodite of great chela. Here we meet an exception in the matter of modal frequency, for the Lefts' mode contains more individuals than that of the Rights. No. GR and 6L are otherwise similar. In comparison with the meropodite the carpopodite is much more variable. Bateson ('94, p. 79), in his book on meristic variations, states that terminal members of a series are likely to be most variable. " In such cases as that of the last rib of I\Ian, and several other animals, the wis- dom teeth of Man, etc., it is (juite true that in the terminal member Variation is more noticeable than it is in the other members." But such series as those of teeth and ribs, in which there is repetition of similar organs, are so different from the linear series of joints with which wt; are dealing, as to make inferences from one to the other unwarrantable. 432 PROCEEDINGS OP THE AMERICAN ACADEMY. Bateson does mention (p. 63) substantive variation in the joints of the leg of the cockroach (Blatta americana), but only in its relation to the number of joints, no light being thrown upon our problem. In case of the series of joints of the crab leg it would seem probable that the distal would be the most variable, since they are most likely to be modified by the use of the leg. For convenience of comparation the Coefficients of Variablity of the measurements taken on the chelar joints are here repeated (see Table II.). Meropodite of great chela, Carpopodite of great chela, Propodite of great chela, Meropodite of small chela, Carpopodite of small chela, Propodite of small chela, Only for the great chela of the Rights is there a constant increase in variability from the proximal to the distal joint. In every case, how- ever, the carpopodite is much more variable than the meropodite. Rights. Lefts. 9.000 9.657 10.166 10.472 10.215 10.255 8.734 9.920 9.518 11.139 8.313 8.898 so 70 00 50 40 30 20 10 c O) OS ■^ •^ •^> oo Oo «J «o CO ^4 t~4 i-0 1-^ 1\5 ci to Li 1^1 5= Ci e1 Or C-1 Polygon No. 7R. YERKES. — VARIATION IN THE FIDDLER CRAB. 433 Among the hundreds of crabs examined not a single variation in the jiumber of joints was noticed. 80 70 60 50 40 30 20 10 ti C5 OJ ^ •^? •^ Cc Oo «3 ^ ^ Ki Co .5^ 5C Cj. C-1 «3 to Polygon No. 7L. 7. Propodite of great chela. Polygons No. 7R and 7L are more nearly symmetrical than any of those already examined; 7R has a slightly wider range of variation. VOL. XXXVI. ■28 434 PROCEEDINGS OF THE AMERICAN ACADEMY. 740 130 120 110 100 90 SO 70 60 50 40 30 20 10 *< n< Oi Cl c> Oi Q> ^J ^1 1-^ C1 t1 to o. 140 13C 120 110 100 90 SO 70 60 50 40 ■■ 30 20 10 to rfi H, Ct tn Oi C5 C5 >-< to to Polygon No. 8R. Polygon No. 8L. S. Meropodite of small chela. Polygons No. 8R and 8L. YEUKES. — VARIATION IN THE FIDDLER CRAB. 435 110 100 90 80 70 60 50 40 30 20 10 to ^D i »o >o C^ Co Co Co oo C«3 ^1 >-< to t-l ^1 IOC 00 SO 70 GO 50 40 30 20 10 to to to to 03 Co Co_, _Co_ ■■I Co Co ^t C-1 C-i k-1 Co C.T !0 Polygon No. 9R. Polygon No. 9L. 9, Carpopodite of small chela. Polygons No. 9R and 9L. The car- popodite is the most variable organ measured, the largest coefficient of variability being that of the carpopodite of the small chela of the Lefts, and the second largest, that of the carpopodite of the great chela of the Lefts. 436 PROCEEDINGS OF THE AMERICAN ACADEMY. 730 130 lie 100 ' 90 80 70 60 50 40 30 20 10 to bo to >\3 ^D Oo to to 0-> Co 120 lie 100 90 SO 70 00 00 40 30 20 10 N3 W ^3 fo t^ to to Oj to t1 1-^ to tT t-l t-T Polygon No. lOR. Polygon No. lOL. 10. Propodite of small chela. Polygons No. lOR and lOL. The propodite of the small chela of the Rights is absolutely the least variable of the measurements made on the legs, while the propodite of the great chela of the Rights (Polygon No. 7R) is the most variable of all the organs of the Rights. We have here an illustration of Darwin's law, that a part (the propodite of the great chela) developed to an extraordi- nary degree is more variable than a part (the propodite of the small chela) of ordinary size. This law of variation holds for all the measurements on the great and small chelae of the Rights. YERKES. VARIATION IN THE FIDDLER CRAB. 437 IOC 100 90 00 SO SO 70 70 60 60 oU 50 40 40 30 30 1 20 20 10 10 ti C"i Ci ^ •^1 ^ Co «c «o «= ^» C5 Ci •^1 ^i •^j Co 03 to ^1 >~4 0.1 -I t1 to tl to to ^1 >-- ti to tT to ^1 TOLVGON No. 11 li. Polygon No. IIL. 11. Meroj)odite of second kg on side of great chela. Fol3'gons No. 1 IE, and llL. 438 PROCEEDINGS OF THE AMERICAN ACADEMY. no 100 00 so TO GO 50 ■iO 30 20 10 ti t. Ci C5 M ^l •^I Co Co ^1 C1 ^1 [ — 90 SO 70 60 50 40 30 20 JO Oi CI Oi •^> ■M • <" ■-" - !»w T ^ ■ 00 o P f— < p o CO p "* 00 f— 1 o T-H o4 1 «■'■ ■"■ 1 1 1 1 1 1 + + + + + + + + o c a o o -; ■■o wJ ■JS CO Ci f— t 03 (M -* X ,-^ l^ ,_^ -t1 5S o ■■CSS Ci o I— 1 O L.O 'N 04 P (N 1* 0 o T-H 1-H CO I—t ■rr Q 1 1 1 1 1 1 + + -L- + + + + T o i-O M lO lO (N o -* CO o Ci o t- CO CO ■^ o I^ ^ 1 ■* Tt* ■^ ^ lO uO o o o lO CO CO CD CO C<1 CO •M CO -^ O o t^ CC -o (M CC CO o o •siBnpiAipuijo -0(1 1-H CO o o t~ lO C<) o^ m o 'If CD 4- CM o »-H o 1-H I-H Ol '"' 00 CO. o -M t-H 1-H I-H l- Ci •M 1-H Tji + S ^ s (M CO t^ ,_, co "M o " I* s s; (M f—t 1—1 1-H -t* r^ CO (M lO -r 1-H (M CO 1-H Ci lO ■^ r-( CO -f o O C» !M uO o CO CO o •^ 1 (M o ^ CO CO 1 '^ 1-H CD 00 i^ £3 • >;:r o Q> Sijjf^ p o o o o o o o o <-> o o o cn 0) 13 o a « 3 00 > OT a 1 1 »v. o n CO 1 C5 1 1 iffl 1 I— t »-H 1 !-■; 1 CO 1 + + P + CO + + + Ci + 00 c: 1 d 1=^ is >o 1.0 o i-O l.O o 'O >o K-O lO i-O "-0 i-O lO t-H "oj III ti CO t~ •"^ lO Oi CO r~ 'O Ci CO t^ 1-H o C<-i B! CO o t^ t~ r^ 00 CO a Oi o o o ^ 1-H O ^■i : rr.'_, „,,„^ ^^^^ 1-H f-H 1-H " o 440 PROCEEDINGS OF THE AMERICAN ACADEMY, V. Discussion of Results. Concerning the original purpose of this study, the determination of some place-modes for the Fiddler Crab, it may he said that a number of modes have been given in Table I., which it is hoped will be of value in the future as helps in the study of racial variation and of the formation of species. As before remarked, those measurements which would seem the most valuable for place-modes are : (a) the frontal breadth, (h) the median length, (c) the right marginal length, and (d) the left marginal length. It remains to be asked, What answers do the results of this study enable us to give to the group of questions centring about the Great Chela condition, with which we set out ? (1) What is the significance of right- and left-handedness ? (2) What relation does the size of the great chela bear to other dimensions ? (3) What determines right- and left-haudedness ? The chief significance of the great chela, observation leads me to con- clude, is in its value (1) as a means of defence and offence, and (2) as a means of burrowing. But granting that these are sufficient reasons for its existence, we have still to ask why it is sometimes on the right side, sometimes on the left. The fact that approximately equal numbers of Rights and Lefts are found, seems to indicate that the great chela is not determined by heredity, or, at least, not directly. For if this were the case, the probability of an equal distribution between the two types would be very slight. It is more likely, therefore, that we are dealing with what is usually called (although improperly) a chance determina- tion ; that is, there ai'e a number of variable factors, only partially known at present, whicli throw the great-chela-developing-tendency now this way, now that. Oilier instances of determination of this kind are the determination of sex and of the crossing of the optic nerves. Pro- fessor G. H. Parker, who has studied the crossing of the optic nerves of fishes, but whose results have not yet been published, has found that many symmetrical fishes are about equally divided between those bavins the risfht nerve crossing above the left and those having it cross- ing below the left. Since it is at present impossible to point out, in sucli cases, any uniform cause or group of causes for the condition, we say it is a matter of chance. In answer to the second question, — What relation does the size of the great chela bear to the other dimensions ? — it may be said, that the meas- urements which allow of comparison of the two sides of the body, namely, YERKES. — VARIATION IN THE FIDDLER CRAB. 441 the margin and the meropodite of the second leg, are larger on the side of the great chela. Expressed in percentages, the relations are as follows: JMargin on chelar side in case of Riglit^, 5% greater than on opposite side, — the same is true of the Lefts ; meropodite of second leg on chelar side in case of Rights, 6 % greater than that of the opposite side ; meropodite of second leg on chelar side in case of Lefts, 8% greater. The fact that measurements are greater on the chelar side may be taken in support of (a) the idea of chance determination, for any advantage of one side of the body over the other would be likely to aflf'ect all organs. On the other hand it may be held (b) that the development of the great chela is itself the cause of the greater development of the other organs on the same side. Or, combining these two views, it might be maintained (c) that the causes which led to the development of the great chela were operative also in case of the other organs, but that the development of the great chela was an additional cause for the unusual size of the other organs. As to the difference in size of the Rights and Lefts T can only say that It is an interesting and surprising fact, for winch I have found no expla- nation. I at first interpreted the fact that the Lefts are the smaller and the more variable as meaning that the Rights represented the stable form ; and in support of this I had, as a result of the first summer's work (see Table III.), evidence that there were more Rights than Lefts. But this conclusion was not confirmed by the additional observations made during the summer of 1900 (see Table IV.). It may be, however, that the proportion of right- and left-handed animals varies in different col- onies, and that during the interval between the collection of the animals referred to in Table III. aiid those of Table IV". migration or some otiier change had caused alteration in the relative frequency of Rights and Lefts ; but this does not seem very probable. VI. Summary. 1. The place-modes for twelve measurements on the carapace and extremities of right- and left-handed Gelasimus pugilator are given iu Table I. 2. The means of Table I. show that the right-handed animals are larger and less variable than the left-handed. 3. Right- and left-handed animals occur in approximately equal numbers. 442 PROCEEDINGS OF THE AMERICAN ACADEMY, 4. Two " Stages " appear to be represented by the iudividuals meas- ured. Many of the curves are compound, and it is probable that in these one mode represents those individuals which have recently molted, the other those which are almost ready for the process. 5. All the measurements are larger on the side of the great chela. 6. The results of this study in variation seem to indicate that right- and left-haudedness is not directly due to heredity, but is caused by certain slight variations which give one side of the body an advantage over the other. Bibliography. Bateson, "W. '94. Materials for the Study of Variation treated with special Regard to Discontinuity in the Origin of Species. Loudon and New York, Macmillan & Company. 608 pp. Davenport, C. B. '99. The Importance of Establishing Specific Place-Modes. Science, N.S., Vol. 9, No. 220, pp. 415-41G. Davenport, C. B. '99". Statistical Methods with special Reference to Biological Variation. 59 pp., 10 tables, and 28 figs. New York, John Wiley & Sons. "Weldon, W. F. R. '93. On Certain Correlated Variations in Carcinus maenas. Proc. Roy. See. London, Vol. 54, pp. 318-329. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVI. No. 25. — April, 1901. CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE, UNDER THE DIRECTION OF E. L. MARK— No. 122. THE DEVELOPMENT AND FUNCTION OF REISSNER'S FIBRE, AND ITS CELLULAR CONNECTIONS. A PRELIMINARY PAPER. By Porter Edward Sargent. With Two Plates. CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE, UNDER THE DIRECTION OF E. L. MARK. — No. 122. THE DEVELOPMENT AND FUNCTION OF REISSNER'S FIBRE AND ITS CELLULAR CONNECTIONS. A PRELIMINARY PAPER. By Porter Edward Sargent. Presented by E. L. Mark, March 13, 1901. Received March 15, 1901. In a recent number of the Anatomischer Anzeiger (Bd. XVII. pp. 33- 44) I have described the occurrence of Reissuer's fibre in the canalis centralis of vertebrates, and I there promised the early appearance of a paper on its development. My further researches on its development and cellular connections have led to the discovery of a highly specialized apparatus, of vrhich the so-called fibre forms a part. The subject has developed much larger aspects than was anticipated, and the consequent delay in the public;ition of my complete results makes necessary a fur- ther preliminary paper. As described in the previous paper, Reissner's fibre lies in the cere- bro-spinal fluid ; it extends through the whole length of the canalis centralis and the brain ventricles to the anterior portion of the optic lobes, where it passes into the brain tissues; it gives off throughout the posterior portion of its course fine branches, which enter the tissue of the spinal cord. In the present paper I hope to show briefly that there is normally in the central nervous .system of all vertebrates a highly specialized appara- tus, the cells of whicli lie in the optic lobes and send their axons into the optic ventricle and the central canal to form the so-called Reissner's fibre. I have investigated the occurrence of this apparatus in upwards of one hundred species, representing all the principal classes and sub- classes of vertebrates. The development has been studied in about twenty different species, and has been more or less completely worked out in representatives of all the chief groups of vertebrates. In this paper I shall describe the apparatus and its development in a few char- 446 PROCEEDINGS OF THE AMERICAN ACADEMY. acteristic forme, reserving the more detailed account of the investigations for a later and more extended article. In Amia, at about the time of hatching, there is in the anterior por- tion of the roof o€ the third ventricle a differentiation of the neuroblasts. Some of them have already increased in size, have become more nearly sf)herical and take the stain more deeply than the surrounding cells (Figure 1). These enlarged cells are concentrated for the most part in the median plane at the anterior end of the tectum opticum near the posterior commissure. During tlie first stage of differentiation there are from twenty to thirty of these cells, but by the development of indiffer- ent neuroblasts they increase rapidly in number, so that by the end of the fourth day after hatching there are from eighty to one hundred of them. During the first day the tectum is only one cell thick. Each cell has a large nucleus — • whose diameter is somewhat more than one half that of the cell — with a single deeply staining nucleolus. During the first and second days the axons develop from the cells as extremely fine processes, which always appear on the side of the cell nearest the ventricle, directly towards and into which they grow. Early in the third day adjacent axons, now projecting into the ventricle, come together in groups and coalesce at their tips (Figure 2), appearing as a single fibril in their further growth through the cerebro-spinal fluid. In later stages these fibrils coalesce with others similarly formed, and in their growth backwards through the fluid of the ventricles and canal form what has been known as Reissner's fibre (PI. 2, Figure 8.) During larval development the fibrils which make up Reissner's fibre coalesce more and more, until by the eighth day there are only six or eight separate divisions of the fibre in the ventricle, and later these are still further reduced in number by further coalescence. The cells also give off den- drites, which run backward through the substance of the tectum. In the later development of the tectum opticum these cells undergo an apparent migration, due to the development of intervening tissue, as a result of which their relative positions are considerably changed ; the cells become more crowded together. During these changes in position the axis of the cell may rotate through an arc as great as 180°. It is an interesting fact that the eccentric nucleus always retains its position at the side of the cell opposite that from which the axon emerges. At about the time of hatching one may find in the extreme posterior end of the canalis centralis (Figure 5) a number of small cells, three to four micra in diameter, lying in the lumen of the canal and ventriculus SARGENT. — REISSNER'S FIBRE. 447 teroiinalis. The surrounding walls of the canal are made up of a single layer of cells, actively dividing. Certain of these cells become separated from the walls and pushed into the lumen. Of these many atrophy and disintegrate. Some eight to twelve of them persist and continue to develop. These cells, at first spherical, become spindle-shaped, as they in- crease in size. These posterior canal cells (as I temporarily call them) give off peripherally a number of dendrites which penetrate the tissue of the cord (Figure 3). From the taperiug anterior end of the cell is given off the axon (Figure 4), which runs cephalad through the lumen, eveutuaJly coalescing with the axon of similar cells (Figure 5) and then continuing its growth cephalad. About the third day this system of forward-growing axons meets the system of axons from the cells of the tectum growing backward and the two systems coalesce in a way not yet clearly made out, to complete what has been called Keissner's fibre. This fibre, then, is a nerve tract, composed of axons running in opposite directions, both cephalad and caudad. The development of this apparatus as outlined for Amia is typical of all vertebrates. The condition of the apparatus in Selachii is especially interesting. In the skate Raja erinacea the cells are of great size (25 fj. to 30 /x in diameter), being the most conspicuous elements in the brain. They are three hundred to four hundred in number, and lie in two bands, one on either side of the median plane, extending the whole length of the roof of the optic lobe (PI. 2, Figure 9). At the anterior end these two bands meet, forming a large group of closely aggregated cells. The cells are multipolar, giving off" several processes in addition to the large axon, which is 2 /A to 3 ^u. in diameter. As in Amia, the nucleus is eccentric, being always at the side of the cell opposite that from which the axon emerges. The number of the capillaries in the neighborhood of these cells, supply- ing them with blood, gives evidence as to the extent of the activity of the cells. Although these cells are so conspicuous in the brain of the skate, they have attracted but little attention. They were first seen by Rohon in selachians and correspond in position to the " Dachkerne " which have been described for Amphibians and Reptiles, the function of which has not been established. The axons pass dorsad and laterad from their cells, turning either cephalad or caudad, and form two great tracts of non-medullated fibres of large size, which extend through the whole tectum opticum lateral and dorsal to the cells. The fibres running caudad can easily be traced to the posterior end of the tectum, whence they pass into the cerebellum. 448 PROCEEDINGS OP THE AMERICAN ACADEMY. and come ihto close proximity to the Purkinje cells. The fibre tract which ruus forward may be traced to the anterior end of the tectum, where the fibres converge, apparently forming Reissner's fibre, which emerges from the tectum into the ventricle at this point. Where Reiss- ner's fibre leaves the brain tissue, the membrane covering of the roof of the ventricle is continued in a cone-like projection surrounding the fibre (Figure 9). Still another process given off from these cells passes peri- pherad nearly to the outer surface of the tectum, where it comes directly in contact with the endings of the optic nerve fibres. These cells, whose axons form Reissner's fibre, are, then, in direct connection with the eye through the optic nerve, and in turn are connected with the Purkinje cells of the cerebellum, which are known to coordinate muscular move- ments. The posterior canal cells in the selachians are of relatively large size and about a dozen in number. In the Cyclostomata this apparatus is in a more primitive condition. In Petromyzon marinus it begins to develop some time after hatching, and is not fully established until the second month of larval life. In larvae thirty days after hatching the cells form a small but well-marked group lying in the roof of the rudimentary optic lobes in the median plane, and occupying the whole thickness of the tectum (Figure 7). The axons emerge directly into the optic ventricle and unite in groups to form Reissner's fibre. These axons may continue backward to the fourth ventricle in three or four separate divisions, but in later development these coalesce more and more. At this stage the posterior canal cells are already developed and are sending their axons cephalad through the canal, but they have not yet united with the axons of the tectal cells running caudad. In the adult Petromyzon Reissner's fibre passes through the canalis centralis and the fourth ventricle, from which it enters the brain tissue of the basal portion of the cerebrum and passing through this emerges into the third ventricle. Here it breaks up into several trunks and continues forward to the anterior portion of the ventricle, where after further division it enters the tectum. The passage of Reissner's fibre for a portion of its course through the nervous tissue in cyclostomes is especially interesting as throwing light on a little understood structure in Amphioxus. Of the dorsal colossal nerve cells in the anterior portion of the central nervous system of Amphioxus, the largest and most anterior, designated by Rohde as the " kolossale ganglien-zelle," is median and lies across the lumen of the canalis centralis. The cell is in direct connection with the pigment spot. SARGENT. — RETSSNER S FIBRE. 449 The axis cylinder runs caudad in the median plane just ventral to the floor of the canal. I venture the conjecture that this cell represents, in Amphioxus, the tectal cells of crauiotes, and that its giant axis cylin- der is homologous with Reissner's fibre. In the phylogeny of this appa- ratus the cyclostomes would then furnish the connecting link between Amphioxus and the gnathostomes. A number of experiments have been performed to determine the func- tions of this apparatus. The best results have been obtained with dogfish (Squalus aoanthias), and small sharks (Charcarias littoralis). In these animals Reissner's fibre is of such size (10 /x to 20 ^i in diameter) that it is possible to remove portions of it from the brain ventricles or canal for microscopical examinations. The operation of breaking the fibre cll .:^'^i ,„ tcf.opt. fbm. opt. eiopt rfx. Figure A. Diagram of the optic reflex apparatus, cbl., cerebellum ; d. can. p., posterior canal cells ; cl. opt. rfx., optic reflex cells ; d. P., Purkinje cells of cere- bellum ; fbr. n. opt., afferent optic nerve fibres ; fbr. R., Eeissner's fibre ; vnf. inn., ventriculus terminalis; tct. opt., tectum opticura. was easily performed. By an incision through the integument, and the removal of a small bit of cartilage, the tela choroideus covering the fourth ventricle was exposed. Through this a curved needle was plunged, and drawn several times transversely across the ventricle to break the fibre. The wound was then dressed ; the animal, when replaced in the water, usually recovered from the shock in from twenty to thirty minutes. Those individuals in which the operation had been performed without success in breaking the fibre, served for the control experiments. The success or failure was ascertained at the autopsy, performed at death or on the fourth or fifth day after operation. Furthermore, the cord and medulla of each individual was preserved for microscopical examina- tion. In about one third of the cases the operation had failed to VOL. xxxvi. — 29 450 PROCEEDINGS OF THE AMERICAN ACADEMY. break the fibre. These individuals showed a marked difference in be- havior from those in which the fibre had been broken. The former, after recovery from shock, were apparently normal in their reactions. Those in which the fibre had been broken showed a slowness in response to optical stimuli. For example, such an animal, in swimming about the tank in which it was confined, would bump into the sides of the cage. If any obstacle were suddenly placed in front of it while swimming, its effort to avoid the obstacle would come apparently too late to prevent collision. Those individuals in which subsequent autopsy and examina- tion showed the fibre to be intact exhibited much greater dexterity and quickness in avoiding obstacles. The behavior of the animals operated on was constantly compared with normal individuals kejjt with them in the same enclosure. These experiments could be made entirely con- clusive only by comparing the time reactions in cases where the fibre was cut with those where it remained uncut. No attempt has yet been made to do this. The apparatus which is the subject of this paper forms, I believe, a short circuit between the visual organs and the musculature, and has for its function the transmission of motor reflexes arising from optical stimuli. This view as to its function is supported by many distinct lines of evidence, which are here classified and summarized. (1) Anatomy. There is normally in all vertebrates a group of cells lying in the optic lobes which by some of their processes are in direct connection with the central terminations of the optic nerve, and by others with the Purkinje cells of the cerebellum. Their axons pass by the shortest route through the ventricles and canal to the posterior por- tion of the nervous system, where they pass into the cord and probably out through the ventral roots to the musculature. These anatomical connections make it probable that this apparatus is a direct path for the transmission of motor reflexes arising from optical stimuli. The connection with the Purkinje cells of the cerebellum, it is equally evi- dent, is for the coordination of muscular movements. (2) Experimental Physiology. When Reissner's fibre is cut or broken, the animal loses the power of responding quickly to optical stimuli. This is not due to the shock resulting from the operation, for animals on which the equivalent operation has been performed without breaking the fibre are nearly or quite normal in this respect. (3) Com-paralive Physiology, (a) In any one group, as for example the teleosts, the apparatus has its highest development in those animals which are most active. In the predatory and rapacious bluefish (Poma- SARGENT. — REISSNER'S FIBRE. 451 tomus) the apparatus is highly developed, Eeissner's fibre having a di- ameter of 10 ^. In Lophius, which is a much larger fish, but is usually sedentary and quiescent in its habits, and more dependent upon tactile than visual sensations for obtaining its food, the apparatus is degenerate and Reissner's fibre inconspicuous, {b) The corpora quad- rigemina in higher vertebrates are degenerate organs, having given up most of their functions to other parts of the brain. In mammals they are, it is generally believed, concerned only with reflex functions. As- suming this to be true, the apparatus under discussion, since it has its centre in the corpora quadrigemina, must have, in the higher vertebrates at least, a purely reflex function. (4) Embryology, (a) The apparatus does not reach full development until just before the animal attains free life. In the active fry of trout and salmon, which give reflex responses at this early age, it is fully devel- oped afe the time of hatching. In those forms in which the young are retained within the uterus of the mother until a late stage of develop- ment, as in mammals and some selachians, the apparatus is not developed until a relatively much later stage, {b) In sluggish larvjB the apparatus is not established until after the time of hatching; in Amia not until the fourth or fifth day, in Petromyzon not until the second month. This corresponds closely with the time at which these larvai begin to respond promptly to definite optical stimuli from surrounding objects, (c) In those mammals which are born blind, as the mouse and kitten, the apparatus at birth is in a very incomplete state, so that it cannot be functional. In the mouse at birth the axons are just penetrating into the ventricle, and Reissner's fibre is as yet unformed. (5) Degeneration. A study of the blind vertebrates of the cave fauna from the collections of Professor C. H. Eigenmann show that the optic reflex apparatus is reduced in direct proportion to the degeneracy of the eye. In those species which are totally blind no trace of this apparatus is to be found. Experiments are now in progress to determine the effect of artificial extirpation of the eye on this apparatus. Such a " short circuit " for the transmission of optical motor reflexes must be of great importance in saving time. If the impulse were trans- mitted from the termination of the optic nerve to the posterior muscula- ture through the cord, it would involve transmission through a chain of from two to three neurons. Now, it is well known to psychologists that the time of transmission of a nerve impulse is delayed by passing through 452 PROCEEDINGS OF THE AMERICAN ACADEMY. a cell body, aud by passing from one neuron to another. Wundt found that the delay in the spinal ganglion cell of man was 0.003 second. The delay in passing between different neurons is probably greater, say 0.005. So in man, if two cell bodies and two contacts between separ- ate neurons are to be traversed, the loss of time would be ([0.003 X 2] -[- [0.005 X 2] =) 0.016 second. In lower animals, as is well known, the time reactions are much greater. It is quite probable that in some of the lower animals this short circuit may mean the saving of a considerable fraction of a second. An animal suddenly confronted with some optical evidence of danger from which it recoils in fear, does so reflexly, calling into operation this apparatus. When we pause to consider how often in the struggle for existence the saving of a fraction of a second may be a question between life and death, we see how important a part this apparatus may have played throughout the vertebrate series in the survival of the fittest. EXPLANATION OF PLATES. Abbreviations. cbl., Cerebellum. cl. opt. rfx.y Optic reflex cells. toms. p., Posterior commissure. e'pky., Epiphysis. fbr. R., Reissner's fibre. tct. opt.. Tectum opticum. vnt. III., Third ventricle. vnt. IV., Fourth ventricle. PLATE 1. FiGUHE 1. Amia calva, 1st day. Sagittal section (anterior end at right) through roof of mid-brain. The large cells in the tectum opticum are the tectal reflex cells, a few of which are just beginning to send out their axons. Figure 2. Amia calva, 12th day. Sagittal section (anterior end at left) through anterior part of tectum opticum. The numerous fibrils entering tlie third ventricle are the axons of tectal reflex cells, a few of which are shown in the section, but the most of which are lateral to this section. Figure 3. Amia calva, 6th day. Transverse section of the spinal cord through the ventriculus terminalis ; posterior canal cell sending its dendrites through the fluid of the canal into the tissue of the cord. Figure 4. Amia calva, 1st day. Sagittal section through the posterior end of the spinal cord and ventriculus terminalis, showing a single posterior canal cell, its long process directed ceplialad. Figure 5. Amia calva, 12th day. Sagittal section of a portion of the spinal cord near its posterior end ; posterior canal cells in the ventriculus ter- minalis and canalis centralis, sending their axons forward to form Reissner's fibre. Reconstruction drawing from four successive sections. Figure 6. Squalus acanthias, embryo 2 cm. long. Longitudinal sagittal section. Posterior canal cells in the canalis centralis sending dendrites into the cord and its axon ceplialad. Figure 7. Petromyzon marinus, 30 days. Sagittal sections of the tectum opticum (anterior end to the right) ; the axons of the developing tectal reflex cells are just emerging into the third ventricle. PLATE 2. Figure 8. Amia calva, 12lh day. Sagittal section through brain, somewhat diagrammatic. Figure 9. Raja crinacea, 11 cm. long. Sagittal section of the mid-brain, dia- grammatic. SaRGENT.-Rei55NER'S FiBRE. Plate 1. 'im '\ -^ '^?>^ K!'- '•\ 9 t V A §^Bv^f## •J '•^^ V-? T 4. ""VV /^; , ^> yr- ,r-T-K /^^ ^0 /fi' .^y ,N. 6. ■-■'"-'fii' ^ ,v' Sargent-Reissner's Fibre. Plate 2. (ct.opt- •jntVL. epiit- Coins.))- c ( ( 8. 9. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVI. No. 26. — April, 1901. CONTRIBUTIONS FROM THE GRAY HERBARIUM OF HARVARD UNIVERSITY. New Series. — No. XX. By B. L. Robinson. I. Synopsis of the Genus Melampodiurn. II. Synopsis of the Genus Nocca. III. New Species and newly noted Synonymy among the Spermato- phytes of Mexico and Central America. CONTRIBUTIONS FROM THE GRAY HERBARIUM OF HARVARD UNIVERSITY, NEW SERIES, NO! XX. By B. L. Robinson. Presented March 13, 1901. Iteceived March 16, 1901. J. _ SYNOPSIS OF THE GENUS MELAMPODIUM. In the following key to Melampodium the genus is limited as by Ben- tluira and Hooker in their Genera Plantarum and by Hoffmann in Eugler & Prantl's Natiirlichen Pflanzenfamilien. It will, therefore, be unneces- sary here to reproduce the generic description or give generic synonymy. The key is based chiefly upon the material which has accumulated in the Gray Herbarium, including the recently acquired Klatt collection and some borrowed material from the U. S. National Museum. The writer has also in connection with this work been kindly permitted by Mr. Casimir de Candolle to examine and trace the types in the Prodromus Herbarium. Much difficulty has been experienced in giving the species a natural sequence, and after many efforts the hope of securing such an arrangement has been abandoned. The employment of pubescence in grouping the species of this genus is new and appears to yield more satis- factory results than an implicit reliance upon the fructiferous bracts. The latter, as is well known, often surpass the achenes, forming above them a cup or hood. This hood is often pointed dorsally at the summit and the point may be recurved or spirally coiled. Unfortunately, how- ever, these features, the hood and its appendage, show too great varia- bility in certain nearly related forms, such as M. sericevm and its varieties, to yield diagnostic characters of the first rank. However, the presence or absence of a hood can usually be determined readily, and the two sections Emnelampodium and Zarabellia may conveniently be retained. Bentham and Hooker, 1. c, estimated the species at eighteen, and Hoffmann, 1. c, accords twenty-five species to the genus. It will be seen, however, that this number can. with our present knowledge, be somewhat increased. The genus reaches its greatest development in Mexico, where, if we include Lower California and Central America, no less than thirty-one species occur. Of these species three reach the southern United States (one merely as an introduction), two are found 456 PROCEEDINGS OF THE AMERICAN ACADEMY. in the West Indies, and two or three extend to South America. There are also two species known exchisively from South America. Early in the nineteenth century a species of" Melampodium (31. diffusmn) was discovered on the island of Luzon in the Philippines. As the genus is otherwise American, the occurrence of this species in a region so remote has always been problematic, and it has been a matter of no small inter- est to find the Philippine plant closely matched by specimens recently collected by Dr. Edward Palmer, about Acapulco, Mexico. There can therefore be scarcely a doubt that the genus is in reality of New World origin, and that a single Mexican species was accidentally introdi'^^ed into the Philippines, where it attracted scientific attention before it was recog- nized in America. This seems the more likely from the circumstance that Mexico and the Philippines were under the same national control, and early connected by a certain amount of oceanic traffic. This being the case, the transference of seed from Acapulco, the most important Pacific port of Mexico, to the neighborhood of Manila, presents no inherent improbability. The writer is under obligation to M. Robert Buser of the De Candollean Herbarium for critical comparison, notes, and sketches relative to this and related species. In this paper the term, ffuit is applied to the ray-achene and the closely enveloping bract. § 1. EuMELAMPODiUM, DC. Inner (fructiferous) bracts of the invo- lucre exceeding the inclosed achene and developed at the summit into a cup or hood (this obsolete ia some forms of M. sericeum). — Prodr. v. 518 (1836). * Lower surface of the leaves sparingly pubescent to hirsute, villous, or tomentose, but not sericeous. -1- South American species : hoods scarcely or not at all appendaged. ->-»■ Herbaceous annual : rays conspicuous, 6.5 mm. long, unguiculate. 1. M. PALUDICOLA, Taubert in Engl. Jahrb. xxi. 455 (1896). — Swamps on the Paranahyba River, Prov. Goyaz, Brazil, Ule, no. 2978. Not seen by the writer. •M- t-t- Suffrutescent : rays very small, inconspicuous. 2. M. suFFRUTicosuM, Baker in Mart. Fl. Bras. iv. pt. 3, 162 (1884). On the Esmeralda plains of the upper Orinoco in S. Venezuela. A species omitted from the Index Kewensis. The achenes are crowned by a shallow cup, otherwise the plant would be placed next M. camphoratum, to which according to the original description it is presumably related. H- -(- Species of Mexico and S. United States. ** Rays short and inconspicuous : appendage of the hood elongated, recurved or coiled : heads usually (but not always) subsessile or short-peduncled. ROBINSON, — SYNOPSIS OP THE GENUS MELAMPODIUM. 457 3. M. LONGICORNU, Gray, Mem. Am. Acad. v. 321 (PI. Thurb.), 1854, where by misprint longicorne. — S. Arizona, near Ft. Huachuca, Lemmon, no. 2777 ; Sonora, Santa Cruz, Thurber, no. 937 (type) ; Chi- huahua, near the city, Pringle^ uo. 10 ; Sau Luis Potosi, Parry & Palmer, no. 4431. ++ ** Ligules longer, exceeding the involucral bracts, conspicuous : peduncles mostly long. = Soft-stemmed, strictly herbaceous and annual. a. Pubescence short, scanty : leaves oblong to linear, entire : appendage of the hood long: involucre gamophyllous about to the middle. 4. M. appendiculatum. Slender, erect, sparingly pubescent an- nual, 3 to 4 or more dm. high, branched almost from the base : leaves thin, oblong to linear, attenuate at the apex, scarcely narrowed to the sessile subauriculate base : obsoletely serrate to quite entire, the larger ones (near the middle of the stem) 5 cm. long, 1 cm. broad : pediui- cles 2 to 7 cm. long, erect, slender : involucre saucer-shaped or shal- lowly cup-shaped, gamophyllous, the limb shallowly 5-lobed; the lobes rounded or barely and very obtusely pointed, their margins scarious : pubescence of the peduncles and involucres short and sparing: rays 8 to 10, oblong, yellow, G mm. in length, 2--3-toothed at the apex; fruit tuberculate, the conspicuous appendage a linear coiled awn from an ovate-lanceolate somewhat 2-toothed base : pales scarious. — South- western Chihuahua, Dr. Edward Palmer, no. 245 (collection of 1885). Type in herb. Gray. This species has the outer involucre of M. cupulatum, Gray, and the fruit of M. longicornu, Gray, yet it is clearl}' distinct from' both, differing from the former not only in its long peduncles and well-developed ligules, but in stature and in the size of the leaves, and from the latter in the presence of a hood and appendage (both totally lacking in M. cupulatum) and in the subauriculate base of the leaves. Var. leiocarpum. Similar in all points but the fruit smooth, striate, glandular-punctate, not at all tuberculate. — Collected by Dr. Edward Palmer at Alamos, 16-30 September, 1890, no. 726. Type in herb. Gray. Var. sonorense. Involucre deeper, subcampanulate : fruit slightly roughened : otherwise like the type. — Collected by C. V. Ilartmau at Cochuto, Sonora, 2 October, 1890, no. 71. Type in herb. Gray, h. Pubescence short and stiff: leaves lanceolate, undulate : fruit hooded, but the appendage shorter or sometimes obsolete. 5. M. arenicola. Decumbent or suberect, branching from near the base; stems dark purple, covered with stiff white somewhat reflexed 458 PROCEEDINGS OF THE AMERICAN ACADEMY. hairs : leaves lanceolate from a narrowed auriculate base, undulate to sparingly and irregularly scabrous-pubescent upon both surfaces, 3 to 5 cm. long, 8 to 11 mm. broad: peduncles slender, pubescent, 3 to 7 cm, long; heads often nodding, 1.2 cm. in diameter (including narrow yellow entire or bidentate ligules) ; involucre shallow, saucer-shaped, the 5 divi- sions united nearly to the middle, broad, scarious and ciliate at the margin : fruit finely striate, punctate and slightly tuberculate, bearing a well-developed hood surmounted by a slender recurved hispidulous appendage not flanked by lateral teeth at the base. — Collected by F. H. Lamb in sandy soil on Isla Piedra, Mazatlan, Sinaloa, 31 December, 1894, no. 361a. Mr. Lamb's no. 380 also from Mazatlan differs in hav- ing no tubei'cles upon the fruit and in the obsolescent appendage, yet it is probably of the same species. Type in herb. Gray. c. Pubescence copious, soft, long, villous : leaves ovate-lanceolate to ovate : ap- pendage of the hood short : involucre gamophyllous only near the base. 6. M. LONGiPiLUM, llobinson. Involucre externally villous, its divisions acutish. — Proc. Am. Acad, xxvii. 173 (1892). — San Luis Potosi, Prinyle, nos. 3639, 4537. = = Stems tending toward lignescence : roots at least in part perennial : species of northern Mexico and southern United States. a. Heads rather small, (including the rays) about 1 to 1.2 cm. in diameter: leaves conspicuously sinuate or pinnatifid : rays thin, short. 7. M. ciNEREUM, DC. 1. c. (1836). Hood muticous. — Laredo, Texas, Berlandier, who appears to have confused this with the variety ratnosissi- mum, so that his numbers cannot be depended upon. Var. RAMOSissiMUM, Gray. Hood mucronate, — Syn. Fl. i. pt. 2, 239 (1884), in part. 3£ ramosissimum, DC. Prodr. v. 518 (1836). — Near Laredo, Berlandier, S. W. Texas and adjacent Coahuila, Palmer, nos. 556, 557, 558 (colh of 1880). Var. ARGOPHTLLU^r, Gray. Hood rauticous : leaves small, tomentose upon both surfaces, canescent above, snowy white beneath. — Gray in Wats. Proc. Am. Acad, xviii. 104 (1883 without description). — Coahuila and Nuevo Leon, Palmer, no. 2068 (coll. of 1880). 8. M. LEUCANTHUM, Torr. & Gray, FL ii. 271 (1842). — The com- monest form of our southwestern States. Kansas, Hamilton County, Hitchcock, no. 250 ; W. Texas, Lindheimer, no. 636, Peverchon, no. 1380*, Thurber, no. 128, Heller, no. 1632, Pope, Bigelow, Wislizenus ; New Mexico, Thurber, no. 1105, Wooton, no. 117; Arizona, RothrocJc, no. 327, Palmer, no. 608, Pringle, coll. of 1884; Chihuahua, Privgle. This plant has of late been generally regarded as a mere form of ROBINSON. — SYNOPSIS OP THE GENUS MELAMPODIUM. 459 M. cinereum, DC. However, it differs conspicuously in its more entire erect or ascending thickish leaves, its much larger heads (nearly or quite twice as broad) and its long thickish, firm, persistent, and veiny rays. It is a much commoner and more widely distributed plant than M. cine- reum, and may be conveniently regarded as a specific type. * * Lower surface of the leaves silky-villous, the pubescence more or less floccu- lent and tending to be deciduous. -t- Ligules shorter than or about equalling the fructiferous bracts : heads sessile or short-peduncled. 9. M. SERiCEDM, Lag. Hoods tipped by a slender recurved append- age.—" Elench. Hort. Madr. 1805," Gen. et Spec. Nov. 32 (1816) ; DC. Prodr. v. 518; not HBK. — Mexico, Mendez ; Oaxaca, Pringle, no. 6728; Durango, Rose, no. 3476; Jalisco, Rose, nos. 2819, 3561; Espe- ranza, Duges. Var. exappendiculatum. Hood destitute of a mucro or appendage, sometimes itself obsolete. — In mountains near Morales, San Luis Potosi, Schaffner, no. 271 in part; base of Iron Mountain, Durango, Dr. E. Palmer, no. 926 (coll. of 1896) ; Guanajuato, Prof. A. Duges, Pringle, no. 5309 ; Federal District, Pringle, no. 7978 (form approaching 31. hispidum, HBK). ■*- -I- Ligules conspicuous, usually much exceeding the fructiferous bracts : pedun- cles long and slender. *+ Leaves (at least in part) pinnatifid ; segments rather broad. 10. M. AMERiCANUM, L. Spec. ii. 921 (1753); Rel. Houst. 9, t. 21 ; DC. Prodr. V. 518. — Vera Cruz, Mexico, Houston. "With this clearly figured plant from Vera Cruz I have been unable to match any speci- mens from Southeastern Mexico. However, the following specimens from the western coast probably belong here : Manzanillo, Xantiis, and Colima, Palmer, no. 136 (coll. of 1897), and no. 1172 (coll. of 1891). ** ** Leaves, at least in part, deeply cleft, segments narrow, linear. = Outer bracts of the involucre pointless, surrounded by a thin yellow somewhat hyaline border. 11. M. LlNEARiLOBUM, DC. Prodr. V. 518 (1836). M. sericeum, Benth. in Oerst. Vidensk. Meddel. 1852, p. 86, not Lag. — A well-marked species represented by the following specimens : Oaxaca, Nelson, nos. 2809, 2339 (pathological) ; Chiapas, Nelson, no. 2949 ; Guerrero, hills near Iguala, Pringle, no. 9162 ; Nicaragua, Oersted; Sinaloa, Rose, no. 3183. = = Outer bracts of the involucre not membraneous-margined or colored, herbaceous to the acuminate apex. 12. M. longipes. M. sericeum, var. longipes, Gray, Proc. Am. Acad, xxii. 423 (1887). — Erect, 4 to 5 dm. high, widely branched: upper and 460 PROCEEDINGS OP THE AMERICAN ACADEMY. lower leaves entire, lance-linear, acute at both ends, 4 to 5.5 cm. lono-, 4 to 5 mm. broad, the middle cauline leaves deeply and pinnately 3-cleft into linear acute segments, finely pubescent above, flocculent-sericeous beneath : peduncles filiform, springing from the forks, 2 to 5 cm. lonw : heads 1.2 to 1.4 cm. broad (including the rather numerous well-exserted narrow bright yellow ligules) : fruit tuberculate, the hood well developed and passing gradually and without intermediate toothing into a lone slender spirally coiled appendage. — Jalisco, Mexico, on dry hillsides near Tequila, Dr. Edward Palmer, no. 391 (coll. of 1886), O. G. Pringle, no. 4598. Type in herb. Gray. This plant although in habit identical with M. hetcrnphyllum^ Lag., is strictly herbaceous and annual. This fact, together with the hooded and appendaged fruit, seems to war- rant its separation. It is certainly distinct from M. sericeum, Lag. •)-+++•»-+ Leaves undivided. 13. M. KuNTHiANUM, DC.Prodr. V. 519 (1836). 31. serlceum,B.BK. Nov. Gen. & Spec. iv. 272, t. 398 (1820), not Lag. — Of this species I have seen only a single and imperfect specimen in the De Candollean Herbarium. The leaves are linear, or nearly so, and entire ; the fruit is provided with a well -developed hood but no appendage. This species also exhibits a suspicious resemblance to 31. heterophyllum, Lag., and it may represent Lagasca's var. ft. 14. M. DiFFUSUM, Cass. Diet. lix. 238 (1829). 31. manillense, Less. Linnaea, vi. 155 (1831). After examining authentic material of this species in the Prodromus herbarium I can confidently refer to it Dr. Palmer's nos. 3 and 281 from Acapulco, Mexico (coll. of 1895). The species has been hitherto recorded only from the Island of Luzon. As the genus as a whole is American, and as this species is now found to be also an American plant, its occurrence in the Philippines may very likely be due to introduction. At all events it seems from the distribution of the other species more likely that this plant has been carried from Mexico to the Philippines, than the reverse. Var. lanceolatmn. 3L lanceolatum, DC. Prodr. v. 519 (1836). — Fruit with a short hood but no appendage ; otherwise closely like the typical form. — Collected by Nee, but the locality unknown. Nee visited both Acapulco, Mexico, and the Philippine Islands. § 2. Zarabellia, DC. Fructiferous bracts not exceeding the in- closed achenes, nor developed into a cup, hood, or appendage at the summit. — Prodr. v. 519 (1836). Zai-abellla, Cass. Diet. lix. 240. * Peduncles long and slender : ligules well exserted, conspicuous, ■t- Leaves sericeous beneath. ROBINSON. — SYNOPSIS OF THE GENUS MELAMPODIUM. 461 •tH- Leaves of diverse forms, partly entire, partly cleft : Mexican. = Peduncles long : ra3's conspicuously exserted : sterile flowers numerous : pales yellow-tipped. 15. M. HETEROPHYLLUM, Lag. Gcu. et Spec. Nov. 33 (181G) ; DC. I.e. — Tantoyuca, Huasteca, Berlandier, nos. 741, 2161, Ervendberg, no. 80; between San Luis Potosi and Tampico, Palmer, no. 1103 (coll. of 1879). = = Peduncles short or none : rays 3 to 4, minute : sterile flowers 1 to 3: pales purple-tipped. 16. M. Pringlei. Root perpendicular, long, with fibrous branches, probably annual ; stem copiously branched from the base ; the branches terete, purple, hirsute : leaves chiefly undivided, narrowly elliptic-lan- ceolate, 2 to 3 cm. long, 3 to 6 mm. broad, acutish, finely subappressed- pubescent above, snowy-sericeous beneath : lower heads short-peduucled from the forks, the upper subsessile, lateral and terminal, all small and few-flowered ; outer bracts of the involucre 5, lance-linear and acute or somewhat spatulate, 3.5 mm. long, so narrow as to disclose the young fruit at an early stage in its development : ray-flowers 3 to 4 ; ligules very small, oval or sub-orbicular, entire or slightly 2-toothed: pales pur- ple tipped ; disk-flowers 1 to 3, mostly reduced to a clavate rudiment : fruit of the ray-flowers obovoid, strongly tuberculate, destitute of hood, cup, or appendage. — Collected by C. G. Pringle, at Las Sedas, Oaxaca, altitude 1,850 m., 15 September, 1894, no. 5722. Type in herb. Gray. ++ ++ Leaves all undivided, linear : South American. 17. M. ANGUSTiFOLiUM, DC. 1. c. (1836). — Peru, Haenke. ■*- -t- Leaves not sericeous beneath. ++ Slightly lignescent perennial : Lower California. 18. M. siNUATU.M, Brandegee, Proc. Calif. Acad. Sci, ser. 2, iii. 144 (1891). — San Jose del Cabo, Brandegee, no. 302. •w- *+ Mexican and S. American species: annuals except M. montanum. = Leaves cordate- or auriculate-clasping at the base. 19. M. Rosei. Erect annual, 3 to 4 dm. high ; stem purplish, copi- ously branched almost from the base, covered with short white retrorse hairs : leaves oblong-lanceolate, attenuate, sinuately toothed, slightly narrowed to auriculate-clasping somewhat connate bases, sparsely pubes- cent upon both surfaces, scabrous on the margin, scarcely paler beneath, the larger about 7 cm. long, 2.5 cm. broad : peduncles in the forks of the stem, 7 cm. long, filiform, retrorsely pubescent ; outer involucre 5-parted, the divisions broadly ovate or suborbicular, rounded or barely pointed at the apex, pubescent upon the back : ray -flowers 8 to 10, ligules oblong, 462 PROCEEDINGS OF THE AMERICAN ACADEMY. golden yellow, 2-toothed at the tip, about 4 mm. long ; fructiferous bracts (without hood or appendage) marked with 3 rows of tubercles upon each lateral surface. — Collected by Dr. J. N. Rose between Rosario and Concepcion, Sinaloa, no. 3271. Type in herb. U. S. Nat. Museum. Var. subintegrum. Leaves clasping at the base but their margins unlobed, obsoletely crenate-serrate. — Collected by Dr. J. N. Rose at Rosario, Sinaloa, 7 July, 1897, no. 1568. 20. M. mimulifolium. Dichotomously branched herb ; stems pur- plish-streaked, loosely villous and finely pubescent along a longitudinal line : leaves lanceolate, acuminate, entire or obsoletely serrulate, 5 to 7 cm. long, 1.2 to 2 cm. broad, appressed-pubescent upon both surfaces, some- what narrowed to an auriculate amplexicaul base : peduncles in the forks of the stem, 4 cm. long, filiform, covered with a fine s|)readiug pubescence : outer involucre 5-parted ; segments ovate-lanceolate, acute, somewhat accrescent, appressed-villous : ligules about 8, short-oblong, 2-3-toothed : fruit short, broad, somewhat quadrate, without hood or appendage, compressed, thin, depressed upon the lateral faces, finely tuberculate dorsally. — Collected by E. W. Nelson in the vicinity of Totontopec, Oaxaca, altitude 1700 to 2150 m., 15 July, 1894, no. 740. Tj'pe in herb. U. S. Nat. Museum. The foliage recalls that of Mimulus ringens. = = Leaves neither cordate nor auriculate-clasping (except obscurely so in j\[. gracile). a. Divisions of the outer involucre 3, ovate to ovate-lanceolate, acute or acuminate. 21. M. PANiCDLATDM, Gardn. in Hook. Lond. Jour. Bot. vii. 287 (1848). — Eastern and Central Brazil. 22. M. GRACILE, Less. Leaves rhombic, unlobed or panduriform, more or less narrowed to an obscurely auriculate or at least obtuse base. — ■ Linnaea, vi. 407 (1831). — Papantla, Schiede & Deppe ; Tantoyuca, Huasteca, Ervendherg, no. 92; Jalapa, C. L. Smith, no. 1605. 23. M. OBLONGiFOLiUM, DC. Leaves oblong to oblong-lanceolate, acute to attenuate at the base, never lobed. — Prodr. v. 519 (1836). — Vera Cruz, near Orizaba, Botteri, no. 809, Sealon, no. 461, Cordova, Bourgeau, no. 1628, near Tantoyuca, Berlandler, no. 733; Oaxaca, at San Felipe, Conzatti & Gonzalez, no. 560 ; Michoacan, Pringle, no. 4322 ; Morelos, Pringle, no. 7321 ; Costa Rica, Plttier, no. 6963. h. Divisions of the outer invohiere 5, obliquely acuminate. 24. M. MiCROCEPHALUM, Less. Linnaea, ix. 268 (1834). — This species is known to me only from Lessing's characterization and from an excellent tracing, prepared from the type at Berlin by Mr. J. M. Green- ROBINSON. — SYNOPSIS OF THE GENUS MELAMPODIUxM. 463 man. It is evidently close to M. paludosum in habit and foliage, differ- ing chiefly, as Lessing himself notes, in its obliquely acamiuate instead of rounded or obtuse involucral bracts. c. Divisions of the outer involucre obovate, rounded or obtuse. 1. Decumbent perennial with elliptical discolorous leaves and pale j-ellow rays (often tinged with purple). 25. M. MONTANUM, Benth. PI. Hartw. 64 (1840). M. Liehman- nii, Sch. Bip. in Klatt, Leopoldina, xxiii. 89 (18S7). — Oaxaca, Graham, PringIe,i\o. 4666; Chiapas, Ghieshreght, nos. 174, 564; Sau Luis Potosi, Prinyle, no. 3818 ; Cumbre de Estepa and Yavesia, Liebmann, no. 232. 2. Erect annuals. 26. M. TEXELLUM, Hook. & Arn. Bot. Beech. 299 (1840). — Aca- pulco, Sinclair. 27. M. CUPULATU5I, Gray, Proc. Am. Acad. viii. 291 (1870). — Sonora, jPa/wer, no. 20 ; Mazatlan, W. G. Wright, no. 1213; Alamos, Palmer, no. 726 (coll. of 1890). This species may possibly prove iden- tical with the preceding. Both are distinguished from the following by their narrow lance-linear or oblong-linear leaves. 28. M. PALUDOSUM, HBK. Nov. Gen. & Spec. iv. 273 (1820). M. divaricatum, DC. Prodr. v. 520 (1836). M. pumilum, Benth. PI. Hartw. 64 (1840), described from starved specimens. M. copiosiim and 31. panamense, Klatt in Enul. Jahrb. viii. 41, 42 (1887), founded upon tri- fling foliar variations without accompanying floral distinctions. Dyso- dium divaricatum, Rich, in Pers. Syn. ii. 489 (1807). D. radiatum, Desf. Cat. Hort. Paris, 1829, p. 182. Alcijia ovalifolia, Lag. ''Elench. Hort. Madr. 1805," Gen. et Spec. Nov. 32 (1816). A. ovatifolia, Jacq. f. Eclog. i. 115, t. 78 (1815?). A. minor, Cass. Diet. lix. 243. Wedelia ovatifolia, Willd. Suppl. 61 (1813). W. minor, Hornem. Hort. Hafn. 855 (1813). — A common weed throughout Mexico, Central America, and also occurring in the West Indies. Highly variable in leaf contour, length of ligules, etc., thus passing into many very diverse yet seemingly unstable forms. * * Rays short, inconspicuous, exceeded by the involucre : peduncles short or none. H- Leaves ovate4anceolate, rounded at the subsessile base : Panama to Brazil. 29. M. CAMPHORATU.M [Benth. & Hook. f. Gen. ii. 349 (1873)], Baker in Mart. Fl. Bras. vi. pt. 3, 161 (1884). M. digynum, Benth. & Hook. f. 1. c. ace. to Hook. f. & Jacks. Ind. Kevv. ii. 188. Unxia cam- phorata, L. f. Suppl. 368 (1781). U. digyna, Steetz in Seem. Bot. Herald, 154, t. 30 (1852-1857). — Panama, Seemann, and Llanos de 464 PROCEEDINGS OP THE AMERICAN ACADEMY. Cumaral, Colombia, Andre, no. 1120, to British Guiana and tropical Brazil, where apparently common. +- ■*- Leaves narrowed to a petiole or an exauriculate base : stems solitary. -w Leaves rhombic to elliptic-oblong, obscurely toothed, undivided. 30. M. FLACCiDUM, Benth. Vidensk. Meddel. 1852, 8G. M. tenellum, var. jiaccidum, Benth. Bot. Sulph. 115 (1844). — Nicaragua near Granada, Oersted; Costa Rica, San Francisco de Guadalupe, Tonduz, nos. 7187, 8498; Tepic, Mexico, Hinds, Palmer, no. 1814 (starved specimens). •w- -i-t- Leaves narrow, linear-oblong and imlobed or deeply cleft into narrowly oblong segments. 31. M. HispiDUM, HBK. Nov. Gen. & Spec. iv. 273, t. 399 (1820). M. coronopifuUum, Sch. Bip. in Hemsl. Biol, Cent.-Am. Bot. ii. 145 (1881), without character. — Arizona, Apache Pass, and near Ft. Hua- chuca, Lemmon, nos. 331, 2795, Santa Uha Mountains, Pringle ; Sonora, JVrifjhi, no. 1205; Chihuahua, Pringle, no. 297; Durango, Palmer, no. 486 (coll. of 1896) ; San Luis Potosi, Parry & Palmer, no. 4441 ; Jalisco, Palmer, no. 260 (coll. of 1886), in part; Tacubaya, Bilimek, no. 593, Schaffner, no. 195. — Except in the nature of the pubescence this species closely simulates 31. sericeum, Lag. •^ -1- -^ Leaves obovate, narrowed to an exauriculate base : stems several from the very base. 32. M. arvense. Prostrate spreading annual; root fibrous; stems several, 1 to 2 dm. long, more or less branched, purplish, covered all around with short weak white hairs : leaves obovate, entire or obsoletely crenate, rounded at the apex, 3-nerved above the acuminate and slightly connate base, bright green and glabrous or nearly so upon the upper surface, distinctly paler aud hispidulous upon the nerves beneath, 1.2 to 2.5 cm. long, 1 to 1.6 cm. broad: heads very small, surrounded by small ovate to orbicular foliaceous bracts and borne close in the forks of the stem and also upon such short lateral cymes as to appear axillary; outer bracts of the involucre 2, ovate, distinct at the base, obtusely pointed : ray flowers 1 to 3, disk flowers about equally numerous: fruits semi- obovate, strongly compressed, reticulated upon the sides, more or less tuberculate dorsally. — Collected by C. G. Pringle in the Valley of Mexico, Federal District, 19 October, 1896, no. 7327 (type, in herb. Gray), and in fields near Toluca, 26 September, 1892, no. 5257, also at an earlier date by Schaffner in mountains near Santa Angela. Nearest M. bihrarf.eatum., Wats., but differing markedly in the contour and cuneate base of the leaves as well as in its prostrate several-stemmed habit. ROBINSON. — SYNOPSIS OF THE GENUS MELAMPODIUM. 465 ••- 4- -4- -I- Leaves rhombic to oblong, narrowed to a sessile auriculate base. t-f Leaves oblong, relatively narrow. = Outer Involucral bracts 2, not accrescent, or scarcely so. 33. M. BiBRACTEATUM, Watsou, Proc. Am. Acad. xxvi. 140 (1891). Fields, Del Rio, State of Mexico, Pringle^ no. 3230. = = Outer bracts 4 to 5, obtuse, united at the base into a cup. 34. M. GLABRUM, Watson. Proc. Am. Acad. xxvi. 139 (1891). — Guanajuato in valley near Irapuato, Pr ingle., no. 2821, and Jalisco near La Barca, Pringle., no. 3863. ++ ++ Leaves broad, mostly obovate or rhombic : outer involucral bracts 5, con- spicuously accrescent. = Outer bracts of the involucre lance-oblong, acute, distinct nearly or quite to the base. 35. M. LONGiFOLiuM, Cerv. ace. to Cav. Anal. Cien. Nat. vi. 303 (1803). 31. rhomboideum, DC. Prodr. v. 520 (1836). — San Luis Potosi, Parry & Palmer^ no. 444 ; Valley of Mexico, Pourgeaii^ no. 868, Pringle, no. 6455, Harshberger, no. 176, = = Outer bracts of the involucre ovate, obtuse or obtusish, connatp toward the base. 36. M. PERFOLiATUM, HBK. Nov. Gen. & Spec. iv. 274 (1820).— A common and well-marked weed throughout Mexico, also established in S. California at Los Angeles, Parish Brothers. Synonyms and Doubtful or Excluded Species. M. achillaeoides, Hemsl. Biol. Cent.-Am. Bot. ii. 145 (1881) =Vil- lanova achillaeoides, Less. M. australe, Loefl. It. Hisp. 268 (1758) = Acanthospermum brasilum, Schrank, ace. to Hook. f. & Jacks. Ind. Kew. ii. 188. M. Bar-angiiillae, Spreug. Syst. iii. 619 (1826) [3f. Baranquillae, DC. V vodiV. V. b2\'\=^ Sclerocarpus africanus, Jacq., ace. to DC. Prodr. v. 521. M.Berterianum, Spreng. 1. c. An unrecognized and poorly described West Indian plant, very likely not of this genus. M. hracJiyglossiim, J. D. Smith, Bot. Gaz. xiii. 74 (1888) =^Jaegeria hirta, Less. 31. copiosum, Klatt in Engl. Jahrb. viii. 41 (1887) = M. paludosian, HBK. M. coronopifolium, Sch. Bip. in Hemsl. 1. c. = 31. hispidum, II BK. 31. digynum, Benth. & Hook. f. Gen. ii. 349 (1873), ace. to Hook. f. & Jacks. 1. c. = 31. camphoratum, Benth. & Hook. f. 31. divaricatum, DC. 1. c. = 3L paludosum, HBK. VOL. XXXVI. — 30 466 PROCEEDINGS OF THE AMERICAN ACADEMY. M. Domheyanum, DC. 1. c. 521, is a still doubtful species from Peru. M. Hildalgoa, DC. 1. c. == HildaUjoa ternata, Llav. &> Lex. M. hirsutum, Benth. & Hook. f. 1. c. ace. to Hook. f. & Jacks. 1. c. = M. camphoratum, Benth. & Hook. f. M. humile, Sw. Prodr. Veg. lud. Occ. 114 {17 SS) = Acanthosper mum /nc/nile, DC. 3r. lanceolahim, DC. Prodr. v. 519 (1836) = M. diffusum, var. lanceolatum. 31. Liebinannii, Sch. Bip. in Klatt, Leopoldina, xxiii. 89 (1887) = M. montanum, Benth. M. longifolium, Brouss. ex Willd. Euum. Hort. Berol. 934 (1809) = (?) M. longifolium, Cerv. M. manillense, Less. Linnaea, vi. 155, t. 2 (1831) = M. diffusum, Cass. 31. ovatifoliiim, Reicheub. Ic. Exot. t. 42 (1827) = 31. paludosum, HBK. 31. panamense, Klatt, 1. c. 42 = 3f. paludosum, HBK. 3[. pumilum, Benth. PI. Hartw. 64 (1840) = starved 3f. paludosum, HBK. 31. ramosissimum, DC. Prodr. v. 518 (1836) = 3f. cinereum, var. ramosissimum. Gray. 31. rhomhoideum, DC. 1. c. 520 (1836) = 31. longifolium, Cerv. 31. ruderale, Sw. Fl. Ind. Occ. iii. 1372 (1806) = EUutheranthera ovata, Poit., ace. to Hook. f. & Jacks. 1. c. 31. sericeum, Benth. in Oerst. Vidensk. Meddel. 1852, p. 86, not Lag. = ikf. Imearilobum, DC. 3f. sericeum, var. hrevipes, Gray, Proc. Am. Acad. xsii. 423 (1887) = typical M. se7'iceum, Lag. 31. sericeum, var. longipes, Gray, Proc. Am. Acad. xxii. 423 (1887) = 31. longipes, Robinson. 31. ternatum, DC. ace. to Hook. f. & Jacks. lud. Kew. ii. 188, = Hidalgoa ternata, Llav. & Lex. It must be frankly confessed that among the species here kept up the following are to the writer still doubtful : — 31. americanum, L., which, although the type of the genus, cannot be matched by any specimen from near the original station. 31. microcephalum, Less. Not as yet satisfactorily represented in the herbaria examined. 31. paludicola, Taub., the description of which suggests a Sclerocarpus. M. paniculatum, Gardn., which from descrijDtion is not clearly sepa- rable from 31. oblong i folium, DC. KOBINSON. — SYNOPSIS OF THE GENUS NOCCA. 467 II. — SYNOPSIS OF THE GENUS NOCCA. NOCCA, Cav. Icon. iii. 12, t. 224 (1795) ; Pers. Syn. ii. 498 (1807) ; La Llave & Lex. Nov. Veg. i. 31 (1824) ; Spach, Hist. x. 40 (1841). Noccaea, Willd. Spec. iii. 2393 (1804) ; Jacq. Frag. 58, t. 85 (1805); Sprang. Auleit. ii. 548 (1818) ; Less. Linnaea, vi. G95 (1831), & Syn. 151 (1832) ; not Moench. Lagasca, Cav. Ann. Cien. Nat. vi. 331 (1803). Lagascea, Willd. Enum. Hort. Berol. 941 (1809); Spreng. 1. c. 549 (1818) ; HBK. Nov. Geu. & Spec. iv. 24 (1820) ; DC. Prodr. V. 91 (1836); Benth. & Hook. f. Gen. PI. ii. 342; Hoffmann in Engl. & Prantl, Nat. Pflanzenf. iv. Ab. 5, 212. — Heads 1- to rarely 2-flowered, aggregated in dense campanulate or subglobose capitate glomerules ; these subtended by ovate to linear more or less specialized herbaceous bracts ; proper involucre calyx-like, tubular, gamophyllous, 5-toothed. Flowers alike, perfect, fertile. Corolla with narrow proper tube, en- larged cylindric throat, and 5-toothed limb, yellow to white or reddish purple, well exserted from the surrounding involucre. Style-branches long, attenuate ; achenes columnar or attenuate toward the base ; pap- pus of 2 to several short scales or rudimentary. — Annual herbs or more often shrubs, probably all natives of tropical America, a single annual species now widely distributed in the tropics. Leaves chiefly opposite. The name Nocca (given by Cavanilles in 1795 in honor of Dominico Nucca, professor of botany at Padua) is clearly the one to be employed for this genus by those who wish to apply consistently the generally conservative Berlin Rules. From the definite characterization and ex- cellent figure given by Cavanilles there can be no doubt as to the iden- tity of his genus Nocca, and the fact that the name was taken up in the same sense within fifty years by Persoon, Jacquin, La Llave, and Sweet, should establish its validity. The form Noccnea, adopted by various botanists from Cassini to Kuntze, may be regarded as a different spelling of the same name. Althouirh substantive in form it has no advantage over Nocca commensurate with the indefiniteness which succeeds any modification of a name as originally published, and it is preferable tliere- fore to take the name in its earliest form. While always reluctant to change any current generic name like Lagascea, I hesitate the less in this instance from the fact that this genus has attained no importance in horticulture or pharmacy, and its nomenclature has accordingly little or no significance outside technical systematic botany. 468 PROCEEDINGS OF THE AMERICAN ACADEMY. * Involucres 2-flowered. 1. N. BiFLORA, 0. Kuntze, Rev. Gen. i. 354 (1891), as Noccaea. Lagascea bijlora^ Hemsl. Diag. PI. Nov. 33 (1879), & Biol. Cent.-Am. Bot. ii. 139, t. 44 (1881). — Mexico, without locality, Parkinson, Salina Cruz, C. C. Deam. * * Involucres 1-flowered. -t- Shrubs or perennial herbs : Mexican. ++ Flowers large: glomerules sessile or scarcely peduncled, even in age more or less campanulate, the subtending bracts ovate to lanceolate, large and conspic- uous : central and southern Mexico. = Leaves cordate-clasping at the sessile base. 2. N. HELiANTHiFOLiA, Cass. Stem pilose : leaves scabrous above, scabro-hirtellous beneath. — Diet. Sci. Nat. xxv. 104 (1822), as I^oc- caea. Lagascea helianthifolia, HBK. Nov. Gen. & Spec. iv. 25 (1820). L. 7nacrophylla, Zucc. ace. to Stead. Nomen. ed. 2, ii. 4 (1841). Noccaea macrojjhijlla, Zucc. ace. to DC. Prodr. v, 92 (1836). Acapulco, Mexico, Humboldt & Bonpland ; Jalisco, Rio Blanco, Palmer, no. 664 (coll. of 1886) ; Guadalajara, Pringle, no. 1824, in part. Var. levior. Stem pulverulent-puberulent, destitute of the long spreading pilosity characteristic of the typical form : leaves scabrous above, scabrous-hirtellous beneath. — Colima, Mexico, Dr. Edw. Palmer, no. 1148 (coll. of 1891) ; Zopelote, Tepic, altitude 615 to 924 m.. Lamb, no. 561. Var. suaveolens. Stem pilose ; leaves soft-pubescent beneath. — Lagascea suaveolens, HBK. 1. c. (1820). Noccaea suaveolens, Cass. 1. c. 105 (1822). Nocca latifoUa, Cerv. in La Llav. & Lex. Nov. Veg. i. 31 (1824). Lagascea latifolia, DC. Prodr. v. 92 (1836). — Tamau- lipas, Santa Barbara, Berlandier, nos. 753, 2173 ; Guanajuato, Duges (a form resembling the type) ; Oaxaca, Nelson, no. 1804, L. C. Smith, no. 964; Conzatti & Gonzalez, no. 558, Holway, no. 3724; Puebla, Conzatti, no. 861 ; Vera Cruz, Mirador, Liehmann, no. Ill ; Orizaba, Schaffner, Bourgeau, no. 3342, Botteri, no. 499, Gray, Tantoyuca, Ervendberg, no. 317; Chiapas, Ghiesbreght, nos. 146, 571 (form with leaves exceptionally pubescent almost lanate beneath) ; Guatemala, J. D. Smith's nos. 2410, 4227. = = Leaves short-petioled, ovate, 2 or .3 times as long as broad : flowers red or purple. a. Indumentum of the stem spreading, dense, imiform in length, partially glandu- lar : leaves elliptic, obtusish, remotely denticulate. 3. N. N. sp. [?]. Branches lignescent, covered throughout by a fine dense spreading pubescence, a part of the hairs glandular, others of ROBINSON. — SYNOPSIS OF THE GENUS NOCCA. 469 equal length without glandular tip, not rubescent: leaves elliptical-ob- tusish or very shortly acuminate, grayish-pubescent beneath, somewhat scabrous upon both surfaces, shortly but manifestly petiolate, the upper leaves much reduced, oblanceolate, acuminate, remotely denticulate, much shorter than the rather elongated interuodes; secondary nerves 2 or 3, oriirinatinw some distance above the base : bracts linear, acute, exceeding the flowers. — Lagascea Moginniana, DC. Prodr. v. 92 (1836) as to pi. of Haenke not of Mociiio. — Mexico without locality, Haenke, in herb. De Candolle. For an excellent sketch of this plant and informa- tion concernina: it I am indebted to the kindness of Mr. Robert Buser. h. Indumentum unknown : leaves ovate, acute, green upon botli surfaces, finely serrulate with approximate purple-glandular teeth (about 10 to the centimeter). 4. N. MogiNNiANA, O. Kuntze, 1. c. (1891), as Noccaea 3Togi)iiana. Lagascea Moginniana, DC. Prodr. v. 92 (1836) as to pi. of Mociiio. — Mexico without locality, Mocifio. c. Indumentum of tlie stem widely spreading, composite, consisting of a dense sliort gray subglandular puberulence and a long white horizontally spreadhig villosity : leaves ovate, serrate, tlie margins neither purple nor glandular ; both surfaces grayish-piibescent. 5. N. Pringlei. Stems slightly lignescent, 1 to 2 m. high, brown, in dried state striate, covered with a fine spreading gray puberulence and long spreading white villosity : leaves ovate, somewhat rio-id, 5.5 to 6.5 cm. long, 3 to 4 cm. broad, serrate with about 2 teeth to the centimeter, 3-nerved from much above the base and pinnately veined, gray-tomen- tose upon both surfaces, especially so beneath, obtuse or acntish at the apex, rounded at the base ; petiole 3 to 4 mm. long : branches of the inflorescence rigid, divergent, with long internodes and spatulate bracts ; glomerules rather loose, not many-flowered : involucres 1-flowered, cylin- drical, upwardly canescent-villous, 1 cm. long, cleft nearly to the middle into o erect very unequal teeth: corolla 1.2 cm. long, purple, covered on the outside with a fine gray tomentura ; the tube very short, slender; the throat cylindrical, 4 to 5 mm. in length ; teeth 5, ovate, scarcely acute : mature achene not seen. — Collected by C. G. Pringle on lime- stone ledges above Iguala, Guerrero, Mexico, 10 October, 1900, no. 8400. Type in herb. Gray. d. Indumentum of the stem fine, appressed: leaves elliptic-ovate, finely or more coarsely serrate, but not noticeably purple-glandular on the margin. 1. Leaves green, lucid, and scabrous-pubescent upon both surfaces. 6. N. RiGiDA, Cav. Ic. iii. 12, t. 224 (1795) ; Sweet, Brit. FI. Gard. ser. 2, t. 26. Noccaea rubra, Cass. 1. c. 104 (1822). Lagascea rubra, IIBK. 1. c. 24, t. 311 (1820). — Mexico, Cordillera of Guihilaque, 470 PROCEEDINGS OF THE AMERICAN ACADEMY. Berlandier, no. 1018; State of Mexico, Bourgeau, no. 1235, Schaffner, no. 293, Pringle, nos. 3500, 3896, 9098 ; Cuernavaca, Bourgeca no. 1205. 2. Leaves green above, niveous-sericeous beneath. 7. N. Heteropappds, 0. Kuntze, I.e. (1891) as Noccaea. Lagascea Heteropappus, Hemsl. Diag. PI. Nov. 33 (1879). — Mexico, Parkinson, without locality ; hillsides near Morelia, Michoacan, Pringle, no. 4541. e. Indumentum of the stem spreading, compound, the sliort glandular hairs much exceeded by a long non-glandular villosity ; leaves ovate-oblong, attenuate, dull and gray-pubescent upon both surfaces, even the upper ones exceeding the internodes. 8. N. tomentosa. Lagascea tomentosa, Rob. & Greenm. Proc. Am. Acad, xxxii. 43 (1896). — Guerrero, Mexico, between Ayusinapa and Petatlau, B. W. Nelson, no. 2121. = = = Leaves oblong-oblanceolate, 4 to 5 times as long as broad, narrowed at the base to a distinct petiole. 9. N. ANGUSTiPOLiA, O. Kuntze, 1. c. (1891) as Noccaea. Lagascea angiistifolia, DC. Prodr. v. 92 (1836). — N. W. Mexico, Seemann ; Duraugo, Palmer, no. 853 (1896) ; Jalisco, Palmer, no. 643 (1886), Pringle, no. 1784. ++ t-* Glomerules slendor-peduncled, usually raised much above the foliar leaves, at length subglobose, the subtending bracts mostly small and narrow. = Teeth of the gamophyllous involucre relatively long and narrow, lance-linear to subulate. a. Involucres soft-villous. 10. N. DECiPiENS, O. Kuntze, 1. c. (1891) as Noccaea. Lagascea decipiens, Hemsl. Diag. PI. Nov. 33 (1879), & Biol. Cent.-Am. Bot. ii. 140, t. 44, f. 1-4 (1881). — North Mexico in the Sierra Madre, See- mann, DO. 2056; Southwestern Chihuahua, Palmer, no. 145 (coll. of 1885); Sonora, at Guaymas, Pa/»2er, no. 256 (coll. of 1887), Alamos, Palmer, no. 401 (1890), La Tinaya, Hartmann, no. 249. b. Involucre hirsute. 11. N. glandulosa. Lagascea glandulosa, Fernald, Bot. Gaz. xx. 534 (1895). — W. Mexico, head of Mazatlan River, W. G. Wright, no. 1305; Rosario, Sinaloa, Lamh, no. 483. = = Teeth of the involucre very short (1 to \\ mm. in length), ovate to deltoid- lanceolate. a. Stem and floral branches pubescent to tomentulose. 12. N. Liebmannii. Lagascea Liehmannii, Sch. Bip. in Klatt, Leo- poldina, xx. 91 (1884). — Leaves soft-pubescent beneath: involucre ROBINSON. — SYNOPSIS OP THE GENUS NOCCA. 471 finely villous, 6 to 7 mm. long : corolla 7 mm. long, puberulent, the teeth ovate. — Pochutla, Oaxaca, Liehmann, no. 250 (type in herb. Bot. Gard. Copenhagen ; fragment and good sketch in herb. Gray). h. Stem and floral branches glabrous. 13. N. Palmeri. Slender-stemmed shrub, with terete divaricate da- brous branches ; internodes long, in dried state finely ribbed : leaves ovate, acute, scabrous both above and beneath with enlarged and indur- ated bases of trichomes (in the manner of many Borraginaceae) , nearly or quite entire, 1.5 to 2.5 cm. long, abruptly narrowed at the base to a very short petiole : floral branches opposite ; peduncles slender, 2 to 4 cm. long ; glomerules 2.5 cm. in diameter, subglol)ose, about 25-headed; subtending bracts ovate-oblong to narrowly oblong, 6 to 8 mm. in length, their pubescence similar to that of the leaves ; involucres tei'ete, 10-nerved, 1 cm. long, sparingly villous; segments deltoid-lanceolate, minutely ciliated : corolla 1 cjn. long, essentially glabrous; its teeth ellip- tic-oblong, 3 mm. in length, 2-nerved : pappus a finely fringed campanulate cup. — Collected by Dr. Edward Palmer, at Colima, Mexico, 27 to 28 February, 1891, no. 1320. H- -t- Annual: tropics of both hemispheres. 14. N. MOLLIS, Jacq. Frag. 58, t. 85 (1809). Lagasca mollis, Cav. Ann. Cien. Nat. vi. 333, t. 44 (1803). Isfoccaea mollis, Cass. 1. c. 103 (1822). Lagascen Kunthiana campestris, Gard. in Hook. Lond. Journ. Bot. V. 238 (1846). Lagasca parvifolia, Klatt, Ann. k. k. Nat. Hofmus. Wien, ix. 360 (1894). — Western and southern Mexico, tropical South America, West Indies, also Bengal, etc. III. — NEW SPECIES AND NEWLY NOTED SYNONYMY AMONG THE SPERMATOPHYTES OF MEXICO AND CENTRAL AMERICA. Dioscorea platycolpota, E. B. Uline in litt. " Glabrous throutrhout: stem stout, dextrorsely twisted ; leaves membranaceous, orbicular-cordate, 9 to 11-nerved; $ racemes short, solitary, densely flower-bearing nearly to the base; flowers pedicellate, disposed in 3 to 5-flowered cymules, which in turn are closely arranged on the pendant rachis ; perianth greenish yellow, campanulate, equalling or surpassing the slender pedicel; stamens three, rising divaricately from the somewhat fleshy receptacle, a little shorter than the ovate segments of the perianth ; anthers extrorse. Pistillate spikes short, solitary; perianth very shortly stipitate ; style 472 PROCEEDINGS OF THE AMERICAN ACADEMY. column slender, its slender, divaricate branches bifurcate at the ajiex ; capsules small and crowded, obovate, leathery in texture ; seed small, corrugated, with peripheral wing. — Collected by C. G. Pringle on lime- stone mountains near Iguala, State of Guerrero, Mexico, altitude 1,230 m., 15 September, 1900, no. 9224. This plant exhibits close affinities for D. Pt'lnglei, Rob., the essential floral characters being identical ; but the striking difference displayed in its much larger and densely crowded flowers serves to give it an entirely distinct aspect, and seems to justify a specific description. Leaves 8 to 9 cm. in diameter. Racemes 12 cm. long, with rather stout rachis. Perianth o mm. wide ; segments 4 mm. long. Capsules 7 to 8 mm. wide." Calocliortus Pringlei. Bulb ovoid, 3.5 cm. long, covered by more or less thickened somewhat reticulated fibres, and surmounted by a cylin- drical mass of long linear fuscous scales, from the midst of which rises the stem; this 4 dm. high, terete, glabrous, simple or branched, 3-5- leaved : leaves flat, linear, attenuate, the basal 3 dm. long, the cauline gradually shorter ; bracts of the spathe 2, opposite, subequal, 2 to 3 cm. long, lanceolate, acuminate; pedicels glabrous, 2 to 7 cm. long; flowers 3 cm. in diameter, dark purple or almost black; sepals narrowly obovate, bluntly pointed or retuse, glabrous except at a small roundish area a little below the middle on the inner surface : petals broadly obovate, cuneate, 1.4 cm. long, two-thirds as broad, obtusely pointed, externally glabrous, internally covered on all parts except the narrowed base by rather coarse violet or yellow hairs : filaments 5 lines long, glabrous ; anthers 3.5 lines long, apiculate : ovary glabrous; capsule acute at each end, 2.5 cm. long, 8 mm. in diameter. — Collected by C. G. Pringle in thin soil of the top of knobs of the Sierra de Tepoxtlan, State of Morelos, Mexico, altitude 2,300 m., 15 September, 1900, no. 8435. Type in herb. Gray. Evidently related to C. jiavus, Schultes, f. but differing in its dark colored flowers, short and broad fruit, etc. Mimosa ACANTHOCARrA, Benth., var. desmanthocarpa. Habit, foliage, and thorns of the typical form : pods unarmed, the valves mi- nutely fulvous-tomentose. — Collected by E. W. Nelson between San Cristobal and Teopisca, Chiapas, Mexico, altitude 2,0G0 to 2,620 m., 4 December, 1895, no. 3428. Type in herb. U. S. Nat. Museum; frag- ment in herb. Gray. Mimosa eurycarpoides. Branches glabrous, soft-woody, with rather large pith, terete or subaugular, armed by a few small scattered spines: leaves large, (including the petiole) 1.2 to 2dm. long; pinnae 7 to 12 pairs, 3.5 to 5 cm. long, puberulent upon the rachis; leaflets 20 ROBINSON. — SPERMATOPHYTES OF MEXICO. 473 to 30 pairs linear-oblong, 5 to 8 mm. long, 1.6 mm. wide, acutish, oblique at the base, finely appressed-pubesceut upon both sides : flowers capitate, heads globose, 1.3 cm. in diameter; peduncles filiform, 1.5 cm. long, borne b}' twos and threes in the axils of the upper leaves : calyx turbinate- campanulate, scarious, slightly cuspidate-toothed, 0.8 mm. long: corolla 2.3 mm. long, glabrous, not conspicuously ribbed : stamens 8 or 10 : pod 4.5 cm. long, 1.2 era. broad, unarmed, glabrous, dark colored, ob- lanceolate, acute, thickisb ; valves not segmented. — Collected by Dr. J. N. Rose in the foothills of the Sierra Madre, near Colomas, State of Sinaloa, Mexico, 21 July, 1897, no. 1805. Type in herb. U. S. Nat. Museum ; fragment in lierb. Gray. To this species I should refer also Dr. Rose's no. 3157, collected on a road between Acaponeta and Rosario. While it is more copiously armed it shares all important char- acteristics with the plant from Colomas. The species is readily distin- guished by its smooth unjointed fruit and axillary inflorescence. Mimosa ionema. Shrub or small tree 3 to 5 m. high ; branches unarmed, terete or nearly so, puberulent ; branchlets green, angled and costate, tomentulose : stipules filiform, 8 mm. long, tomentulose under a lens ; petioles angled, straight, puberulent-tomentulose, 4 to 6 cm. long, equalled by the foliar rachis; pinnae 4 to G subremote pairs, 5 cm. long, the lower ones commonly alternate ; stipels 1 mm. long ; leaflets about 15 pairs, oblong, obtuse, green and nearly or quite glabrous upon both surfaces, slightly paler beneath, oblique at the base, excentrically 1-nerved, pinnately veined, 1 cm. long, 3 to 4 mm. broad : flowers loosely spicate, spreading or somewhat deflexed ; spikes fascicled by 3's and 4's in the axils of the upper leaves, ascending, 6 cm. long, on penduneles 2 to 3 cm. in length: corolla white or pale yellow, 2.5 mm. long, cleft to below the middle, without conspicuous nerves or ribs, glabrous ; segments 4 to 5, lance-oblong, acutish: stamens 8 to 10; filaments violet-tinged: fruit (immature) narrowly oblong, acute at both ends, thin, glabrous, 5 cm. long, 7 mm. broad, about 8-seeded. — Collected by C. G. Prin"-le in the valley below Cuernavaca, Mexico, altitude 1,230 m., 17 October, 1900, no. 8377. Type in herb. Gray. Mimosa Watsoni. Fruticose and probably scandent : stems sub- terete, tomentulose chiefly along six longitudinal lines, these bearino- minute approximate subequal very short recurved spines : branchlets grayish-tomentose : petioles (including the rachis) 5 cm. long, rigid, angled, armed laterally and ventrally by 2 or 3 lines of recurved spines, tomentulose especially along the armed angles ; pinnae 2 pairs ; the lower bearing 1 or 2 pairs of leaflets, the upper with 2 or 3 pairs ; 474 PROCEEDINGS OF THE AMERICAN ACADEMY. leaflets rhombic-ovate or obovate, lucid and finely pubescent above, to- mentulose beneath, destitute of setae and ciliatioii, pinnately veined ; the lateral 1.5 to 2.5 cm. long, subsymmetrical, the terminal twice as large, oblique and with excentric midnerve : globular heads (7 mm. in diameter) white, racemosely disposed on the long spreading unarmed grayish lo- mentose branches of a loose panicle ; pedicels slender, 1 cm. long : corolla 4-parted to the middle, its lobes short-oblong, rounded at the apex : stamens 8: pods 5 cm. long, 7 to 10 mm. broad, glabrous and lucid upon the disarticulating valves but finely papillose under a strong lens, dark brown, unarmed except for a few scattered minute recurved spines upon the tomentulose replum; rectangular segments thin, broader than long. — Collected by the late Dr. Sereno Watson in the eastern portions of Vera Paz and Chiquimula, Guatemala, in 1885, nos. 323 in fruit and 185 in flower. Types in herb. Gray. This species of the sub- genus Habhasla is closely related to the South American M. Spruceana, Beuth. From this it differs, however, in the much less dense and less rufescent pubescence of the stem, more strongly armed petioles, less numer- ous leaflets of different venation and finally in its much smaller fruit, which is at full maturity less than half as broad as in the Brazilian plant. Russelia Deamii. Stems becoming 1,6 m. long, 4-angled below, 6-angled toward the ends, copiously branched, glabrous except on the smaller branchlets, with slender ribs at the angles: leaves 1.5 to 2 cm. long, two thirds as wide, ovate, acute, incisely serrate except near the cuneate base, green, loosely pubescent and sparingly punctate above, slightly paler and strongly white-villous beneath especially about the larger nerves and near the base: cymes numerous, 3-flovvered ; peduncles slender, 4 mm. long, pubescent as are also the filiform slightly longer pedicels ; bractlets linear : lobes of the villous calj'x lance-acuminate from an ovate base: corolla scarlet, 1.6 to 2 cm. long, the nearly equal lobes suborbicular : fruit not seen. — Collected at Cuernavaca, Mexico, 7 July, 1900, by Charles C. Deam, no. 30. This species differs from R. sarmentosn^ Jacq., in its villous more incisely toothed leaves and G-angled branches, from R. jaliscensis, Rob., in the form of its calyx- lobes, from R. polyedra, Zucc, in its larger flowers and glabrous less strongly ribbed stems as well as in the form and sharp dentation of the leaves. Russelia trachypleura. Stems 6-angled; angles prominent, rib- like, pale, roughened by small scattered callosities ; areas between the ribs flat, green, glabrous or (especially near the nodes) somewhat hairy ; branches usually 4-ang1ed : leaves ternate on the stem, opposite on the ROBINSON. — SPERMATOPHYTES OP MEXICO. 475 branches, elliptic-ovate, acute or acutish at each end, short-petioled, sharply serrate, green, resinous-dotted, and pubescent on the upper sur- face, slightly paler and pubescent upon the pinnately arranged veins beneath : tlowers in short few-flowered axillary cymes : calyx-lobes ovate, caudate-acuminate, externally pubescent toward the sharp tip, 4 mm. long: corolla bright scarlet, 1.2 cm. long, with cylindrical tube and 4 short rounded subequal lobes, the upper one broader and emarginate. — Collected by C. G. Pringle on the Sierra de Tepoxtlan, State of Morelos, Mexico, altitude 2,300 m., 11 September, 1900, no. 9445. Readily distinguished from all the other species by the callosities on the rib-like angles of its stems, Piqueria pyramidalis. Stem terete, 2 to 2.5 m. high, puberulent, green but maculate with elongated dark brown or purplish dots : leaves alternate (at least the upper ones), petiolate, broadly ovate, shallowly about 7-lobed, coarsely crenate, 3-nerved from the rounded to strongly cordate base, green and scabrous-puberulent above, paler and tomentulose beneath, the larger 1.7 dm. long and about as broad; petioles subterete, tomentulose: small and very numerous heads in pedicellate racemose glomerules ; these forming a large leafy -bracted pyramidal panicle : in- volucral scales oblong, green, about 2-seriate, 2.5 to 3 mm. long, puberu- lent and covered with minu'e amber-colored particles upon the outer surface: corolla white, 3 mm. long, with short proper tube and relatively large throat, also bearing a few amber-colored particles : styles much exserted, clavate, purplish or brown ; achenes dark-colored, glabrous, lucid, 2.5 mm. long. — Collected by C. G. Pringle in shade of cliffs on mountains above Iguala, altitude 1,230 m., 10 October, 1900, no. 8389. Type in herb. Gray. This species, although possessing all the technical characters of the genus, differs considerably in habit from the other Mex- ican species, being in fact nearer some of the South American, Ageratum lucidum. Shrub with buff cortex and opposite spread- ing curved-ascending terete finely striate glandular-puberulent branches : leaves opposite, ovate, acutish, serrate from below the middle, thin, veiny, glabrous or early and completely glabrate upon both surfaces and lucid especially above, 4 cm. long, half as broad, ciliolate upon the margin, 3-nerved from somewhat above the abruptly acuminate shortly petiolate base, minutely white-dotted beneath and also covered with globular resinous or glandular atoms : corymbs long-peduncled (often irregularly compound), 2-6-headed and subtended by reduced opposite lance-oblonw to linear sessile bracts; pedicels 1 to 2.4 cm. long, curved-a,scendinff, 1-headed with or without 1 or more filiform bractlets; heads campanu- 476 PROCEEDINGS OF THE AMERICAN ACADEMY. late, 70-100-flowered, nearly 1 cm. in diameter; outer involucral scales linear-filiform, ciliated, the inner lance-oblong, acuminate, rigidulous, the subscarious margins erose : acheiies black, 2 lines long, sharply angled, glabrous, very finely and transversely striate ; pappus a shallow un- toothed cup without awns. — Collected by C. G. Pringle, on mossy sides of conglomerate knobs of the Sierra de Tepoxtlan, near Cueruavaca, State of Morelos, Mexico, altitude 2,310 m., 31 October, 1900, no. 8362, and previously 15 March, 1899, no, 7851. Well marked. Type in herb. Gray. Ageratum rhytidophyllum. Shrub with opposite terete dark red branches covered with a fine crisped cinereous puberulence : leaves op- posite, subsessile, lance-oblong, 4 to 7 cm. long, 1.2 to 2 cm. broad, entire or obscurely serrate, revolute at the margin, acute at both ends, tliickish, grayish green, scabrous-pubescent and strongly rugose above ; veins much reticulated and prominulous beneath where covered by a dense spreading white pubescence ; interstices covered by aureous par- ticles : inflorescence of compound corymbs terminal upon the branches ; bracts linear ; heads rather small, 5 mm. in diameter, nodding on short glandular-puberulent pedicels, about 25-flowered ; involucral scales un- equal, pluriseriate, lance-linear, acute, pungent, green, striate, finely and sparingly pubescent; pales similar but narrower, rather rigid: corolla 3 mm. long, glabrous but covered with aureous particles ; the jDroper tube greenish, about equalling tlie combined length of the whitish throat and lavender colored limb : achenes glabrous ; pappus a short obscurely toothed cup. — Collected by C. G. Pringle on the Sierra de San Felipe, Oaxaca, Mexico, altitude 2,150 m., 5 October, 1894, no. 5675. Type in herb. Gray. Also secured in an immature state somewhat earlier (20 September, 1894) in the valley of Oaxaca by E. W. Nelson, no. 1446, and a little later (4 November, 1894) in the mountains of San Juan del Estado by Rev. L. C. Smith, no. 277. Ageratum stachyofolium. Erect perennial with long tough filiform white roots ; stem 5 to 6 dm. tall, terete, finely striate, purplish, densely covered with fine crisped white hairs : leaves elliptical, sessile or nearly so, mostly alternate, crenate, obtuse, pubescent upon both sur- faces, 3-nerved, deep green above, paler green and veiny beneath, 3 cm. long, half as broad: corymbs terminal, simple, regular, 7-10-headed; bractlets filiforra-spatulate ; pedicels 2 to 2. 5 cm. long, canescent-tomen- tulose ; heads large for the genus, 1.2 cm. in diameter, about 100-flow- ered ; scales of the involucre linear, acute, strongly striate, hirsute: achenes glabrous, sharply angled, dark browu^ somewhat tapering toward ROBINSON. — SPERMATOPHYTES OF MEXICO. 477 the base, 2 mm. long; pappus a short scarious untoothed cup without awns. — Collected bj E. W. Nelson in the vicinity of La Parada, Oaxaca, altitude 2,310 to 2,620 m., 19 August, 1894, no. 991. Types in herb. Gray and herb. U. S. Nat. Museum. Eupatoriiim anisopodum. Plerbaceous perennial : stems terete, decumbent, flexuous, irregularly branched, puberulent especially near the nodes and under a strong lens, green or purplish tinged, 3 to 5 dm. high : leaves ovate or rhombic-ovate, opposite, 2 to 2.5 cm. long, 1.2 to 1.7 cm. broad, thickish, not punctate, crenate-serrate from the broadest portion to the acutish apes, covered above with fine short curved hairs, slightly paler beneath and appressed-pubescent upon the veins, 3-5-nerved, sub- cuneate at the base to a short petiole (5 mm. in length) : bracts ovate- lanceolate, acute, 3 to 7 mm. long, the lower petiolate the upper sessile ; heads small, 25-30-flowered, 5 to 7 mm. in diameter, not numerous, in-egu- larly corymbose on pedicels of very unequal length ; scales of the turbi- nate-campauulate involucre pluriseriate, very unequal, the outer short, ovate, acuminate, herbaceous, pubescent ; the inner oblong, acute, pale, 2-3-nerved, ciliolate, sparingly pubescent or glabrous: corolla 2.2 mm. long, probably white, glabrous except at the limb where under a strong lens puberulent, the proper tube short, considerably exceeded by the subcylindric scarcely ampliate throat: achenes columnar, at length black, hispidulous on and between the five nerve-like angles, 1.5 mm. long; pappns-bristles 15 to 20, bright white, about equalling the corolla. — JE. pyoiocephalum, Coult. iu J. Donuell Smith, Enum. PI. Guat. ii. 9-4 (1891), not Less. — Collected by H. von Tiirckheim at Santa Rosa, Department Baja Vera Paz, Guatemala, altitude 1,540 m., April, 1887, no. 1177 of Mr. J. Donnell Smith's Guatemalan set. Type iu herb. Gray. While possessing something the habit of E. pycnocepkalam, Less., this plant is readily distinguished by its very different pluriseriate involucre. EuPATORiuji ARALIA.EFOLIUM, Less. Linnaea, vi. 403 (1831). Add syn. E. heterolepis, Robinson, Proc. Am. Acad. xxxv. 335 (1900). EuPATORiUM BiGELOVii, Gray, Bot. Mex. Bound. 75 (1859). Add syn. E. madrense, Wats. Proc. Am. Acad. xxvi. 137 (1891). EuPATORiUM coNSPicuuM, Kunth & Bouche, Ind. Sem. Hort. Berol. 1847, p. 13. Of this, E. grandifoUum, Regel, Gartenflora, i. 102, t. 12 (1852), is certainly a synonym. Eupatorium Coulteri. Stem slender, straight, terete, densely fus- cous-puberulent : leaves opposite, deltoid-ovate, acute or subcaudate, somewhat hastate-lobed at the almost truncate base, shallowly dentate, 478 PROCEEDINGS OF THE AMERICAN ACADEMY. thiu, harsh and slightly scabrous upon both surfaces, 4 to 5 cm. long, half as broad, minutely punctate, slightly pubescent upon the nerves ; slender fuscous-pubescent petioles 1 cm. long : heads in rounded axillary and terminal thyrsoid panicles ; pedicels filiform, flexuous, covered with fine spreading purple pubescence ; bracts and bractlets subulate, minute ; involucre turbinate, the lower much reduced scales somewhat decurrent upon the pedicels, the inner scales oblanceolate-oblong, acuminate, arose, puberulent or granular dorsally, thiu, striate, often purplish-tinged ; flowers about 8 : corolla tubular, slightly and gradually narrowed from the summit to the base, essentially glabrous, slightly exceeding the bar- bellate pappus: achenes dark-colored, upwardly hispid upon the prominent angles. — E. ageratifolium, var. purpureum, Coulter, Bot. Gaz. xvi. 98 (1891). — Collected by H. von Tiirckheim in Coban, Depart. Alta Vera Paz, Guatemala, altitude 1,415 m., March, 1887, no. 52 of Mr. John Donnell Smith's sets. This plant differs from E. ageratifoUum, DC, so greatly in pubescence, leaf-texture, involucre, and inflorescence that iutergradation does not appear likely. EuPATORiUM DAsrCARPUM, Gray, Proc. Am. Acad. xxii. 420 (1886). Add syn. Stevia rapimculoides, DC. Prodr. v. 124 (1836). Eupatorium dryophilum. Perennial from a thickish branched caudex ; stems several, erect, 5 to 7 dm. high, terete, finely striate, puberulent or tomentulose, slightly scabrous, not glandular, reddish brown, branched at the summit : leaves opposite or ternate, sessile, ovate or oval, the lowest obtuse, the upper acute, all 3-nerved, shallowly few- toothed, thickish, reticulate-veiny, very scabrous upon both surfaces, entirely destitute of glands or resinous particles: heads large, 1.4 cm. in diameter, slender-pedicelled, erect ; involucral scales thin, green, oval to oblong, rounded at the apex, 4-5-seriate, striate, glabrous, mealy not viscid: corollas purple, glabrous except at the short-toothed limb: pappus- bristles sordid, barbellate, very unequal; achenes dark olive, 4 mm. long, granular. — Collected by Dr. Edward Palmer, ou the Rio Blanco, Jalisco, October, 1886, no. 651, and by C. G. Pringle with oaks and pines on roicky hills near Guadalajara, nos. 2171, 2323. This species is near E. pleianthum, Robinson, but differs from it in the absence of resin- ous globules upon the leaves and the presence of mealiness upon the involucre which is not viscid, also in its shorter darker achenes with fine transverse striation. Eupatorium htssopinum, Gray, Proc. Am. Acad. xv. 28 (1880). Add syu. E. koelUaefolium, Greene, Pittouia, iii. 31 (1896). Identity exact. ROBINSON. — SPERMATOPHYTES OF MEXICO, 479 EuPATORiUM Lemmoni, RobinsoD, Proc. Am. Acad, xxvii. 171 (Ls02). Add syu. E. euoivjmifuliuin, Greeue, Pittonia, iii. 31 (1896), founded upon a co-type. Eupatorium Gonzalezii. Apparently herbaceous and to the unas- sisted vision glabrous throughout ; stems terete, green, finely striate, lucid, purple at the nodes, slender ; the younger parts microscopically puberuleut : leaves opposite, long-petioled, deltoid-ovate, obtuse, coarsely crenate-dentate, 3-nerved from the entire abruptly acuminate base, thin, bright green and glabrous upon both surfaces, 4.5 to 7 cm. long, 4 to 4.0 cm. broad ; petioles slender, 3 cm. long ; the uppermost leaves ovate- lanceolate, entire, shorter-petioled : heads numerous, about 18-fiowered, small, in compound axillary and terminal cymes ; peduncles and pedicels ascending, obscurely puberulent ; bracts spatulate and mucronate to linear and acute, small ; involucral scales green, striate, narrow, linear, obtuse at the scarious erose and often crumpled apex, a few of the outer considerably shorter, ovate, acuminate, ciliolate : corollas white, glabrous throughout, the greenish white proper tube somewhat exceeded by the pure white throat aud spreading limb : achene dark, 1.3 mm. long, up- wardly hispid on the angles ; pappus pure white, sparse ; the bristles essentially equal, nearly as long as the corolla, slightly connate into a minute cup at the base. — Collected by Professors C. Conzatti aud V. Gonzalez at El Fortin, Oaxaca, altitude 1,600 m., March, 1807, no. 387. Eupatorium leonense. Stem 4 mm. in diameter, slightly lignes- cent, pithy, yellowish brown, glabrate ; branches opposite, curved-as- cending, striate, tomentulose, finely pubescent : leaves o^iposite, ovate to deltoid-ovate, long-petioled, thin, coarsely and rather bluntly few-toothed, acutish, abruptly contracted at the entire base to an acuminate attach- ment to the long petiole, finely pubescent when young, nearly or quite glabrate at maturity, 3 to 5 cm. long, nearly as broad, 3-nerved from a little above the base; petioles 3 to 4 cm. long, pubescent: jxjdicels slender, flexuous, green, puberulent ; bracts minute, subulate ; heads rather few in a small round-topped panicle, medium-sized, 8 ram. long, about r2-flowered ; involucre campanulate, loosely imbricated, lance- linear, attenuate, very acute, green, striate, thin, sparingly white-pubes- cent, the outer much shorter : corolla narrowly cylindrical, of essentially uniform diameter throughout its length and without clearly marked throat or proper tube, glabrous : style-branches strongly clavate, yellow ; achenes black, glabrous, lucid, 2 ram. long with conspicuous yellow cal- losity at the base ; pappus white, equalling the corolla. — Collected by 480 PROCEEDINGS OP THE AMERICAN ACADEMY. C. G. Pringle on the Sierra Madre near Monterey, Nuevo Leon, Mexico, 16 June, 1887, no. 2277. Eapatorium Liebmannii^ Sch. Bip. in Klatt, Leopoldina, xx. 75 (1884). From the characters given and from an excellent drawing (in herb. Klatt) prepared from the original material I cannot avoid the conclu- sion that this is identical with the earlier E. hirsutum, DC, the type of which I have recently examined in the Prodromus Herbarium. The species is represented by Mr. Pringle's no. 6046 from the foothills of the Sierra de San Felipe, Oaxaca. Eupatorium longifolium. Suffrutescent, 1 m. high : stems virgate, terete, finely striate, covered by a fine spreading purplish and probably viscid pubescence : leaves opposite, short-petioled, ovate-lanceolate, cre- nate-serrate, 3-nervetl, thin, dark green and strigillose (under a lens) above, paler and tomentulose especially upon the veins and veinlets beneath, 1 to 1.2 dm. long, 4 to 5 cm. broad, attenuate to a caudate apex, rounded and deeply cordate at the base, the sinus narrow : inflor- escences rounded-corymbose, together forming a large leafy oval or sub- pyramidal j5anicle ; its branchlets, slender pedicels, and filiform bracts 'brown-pubescent; heads very numerous, 4 to 5 mm. long, about 10- flowered ; involucral scales linear, attenuate, subequal, 3 mm. long, covered with jointed purple hairs and resinous lucid atoms : corolla scarcely 2 mm. long, gradually contracted toward the base, nearly equalled by the simple white pappus: achene dark, minutely pubescent, 1.5 mm. long. — Collected by C. G. Pringle in Taraasopo Canon, San Luis Potosi, Mexico, 28 November, 1890, no. 3372. This number was distributed as E. Pahneri^ Gray, to which it is obviously related. It differs, however, both in the nature of its indument and the form of the leaves. The latter are rounded at the base in E. Palmeri while in E. longifolium they are deeply cordate. E. Jilicaule, Sch. Bip., is also a nearly related species, but its heads are conspicuously racemose, which is not the case here. Eupatorium luciduji, Ort. Hort. Matr. Dec. 35 (1797). An ex- amination of authentic material of this briefly characterized species shows that it is just the plant to which I have recently assigned the name E. capnoresbium, Proc. Am. Acad. xxxv. 331, a name which must accordingly sink into synonymy. Eupatorium. Luxii. Apparently shrubby : branches subterete, stri- ate, covered with a fine spreading and very dark pubescence : leaves opposite, elliptic-ovate (the upper ovate-lanceolate), acute to acuminate at each end, pinnately nerved, 6 to 13 cm. long, half as broad, serrate, ROBINSON. — SPERMATOPHYTES OP MEXICO. 481 sparingly pubescent when young, quite glabrate except on the nerves and somewliat lucid in age, nigrescent iu drying, the teeth salient, mu- crunulate ; petioles 1.8 to 3 cm. long : heads medium-sized, about 25- flowered, 8 to 10 mm. long, in an opposite-branched corymbose panicle ; involucral scales 3-4-seriate, ovate to lanceolate, acuminate, closely im- bricated externally, nigrescent at the tip, pale at the base, ciliolate, silvery and lucid on the smooth inner surface : corolla-tube 5 to 6 mm. long, glabrous, gradually narrowed from the summit to the base, the teeth vt^ry short, sparingly pubescent : achenes 2 mm. long, dark, glab- rous, lucid, the angles very prominent ; pappus rather copious, white, nearly equalling the corolla. — Collected by Heyde and Lux at Nebaj, Depart. Quiche, Guatemala, altitude 2,150 m., April, 1892, being no. 3387 of Mr. John Dounell Smith's sets of Central American plants, and having been distributed as E. Tuerckheimii^ Khitt, a species with much narrower leaves and linear-oblong involucral scales, gUibrous stem, etc., well shown by no. 77 of Mr. John Donnell Smith's sets. Eupatorium lyratum. Coulter, Bot. Gaz, xvi. 96 (1891), is Conyza lyrata, HBK. Eupatorium Mariarum. Herbaceous ; stems terete, weak, pithy, obscurely pulverulent-puberulent and also covered with scattered spread- ing white trichomes ; branches ascending: leaves opposite, long- petioled, deltoid, acute, coarsely crenate except at the abruptly contracted base, thin, deep green and bearing a few scattered white trichomes above, somewhat paler and essentially glabrous beneath, 3-nerved from the slightly acuminate point of attachment, 5 to 7 cm. long, 4 to 5 cm. broad ; petioles weak, flexuous, 3 to 5 cm. long, with a double pubes- cence as on the stem : heads about 25-ilowered, in small axillary and terminal corymbs, pedicellate ; bractlets acute, lance-linear to filiform ; involucral scales linear-oblong, acute, subequal, thin, mostly 2-nerved, green, 3 mm. long: corolla (probably white) ghxbrous, with a slender proper tube exceeding a much broader well-marked throat and spreading limb: achenes dark-brown, slightly spindle-formed, hispidulous toward the summit. — Collected by E. W. Nelson on Maria Madre Island of the Tres Marias Group, May, 1897, no. 4244. At first taken for E. pnzcuarense^ IIRK., but clearly distinct by its long petioles, different leaf-contour and dentation, also in its pubescence. Eupatorium pachypodum. Caudex thickish, lignescent, branched; stems annual, one to several, erect, simple to the inflorescence, 3 to 4 dm. high, terete, cinereous-tomentulose : leaves opposite, small, much ex- ceeded by the internodes, ovate to suborbicular, acute, rounded at the VOL. xxxvi. — 31 482 PROCEEDINGS OP THE AMERICAN ACADEMY. essentially sessile base, serrate, 1.3 to 1.8 cm. long, nearly as broad green and sparingly pubescent above, covered beneath by a short soft ashy more or less deciduous pubescence, and bearing upon both surfaces golden resinous particles: panicle flat-topped, its slender ascending branches and pedicels (7 to 9 mm. long) grayish-tomentulose; bractlets linear to filiform; heads about 12-flowered, 7 mm. long; involucral scales subequal, oblong, soft-pubescent and pale green upon the outer surface, 3 to 4 mm. long, obtuse : corollas vifhite or at least pale, 4 mm, long, with slender tube somewhat exceeded by the gradually ampliated throat, glabrous : achenes 2 lines long, hispid on the angles, pappus white, equalling the corolla. — Collected by C. G. Pringle on rocky hills near Guadalajara, Jalisco, 26 May, 1891, no. 3718. Distributed as E. scordonioides ? a species with shrubby perennial stems, deltoid- peltate leaves, etc. Eupatorium pansamalense. Stem glabrous, rather strongly angled, striate, pithy : leaves opposite or ternate, slender-petioled, rhombic-ovate, caudate-acuminate, acute at the base, mucronate-serrate, thin, pinnately nerved, deep green and nearly glabrous except on the miduerve above, paler and puberulent or tomentulose upon the nerves and veins beneath, 1 to 1.3 dm. long, half as broad ; petioles 2 to 3 cm. long : branches of the inflorescence and filiform pedicels fuscous-tomen- tulose ; heads about 35-flowered, very numerous in a round corymbose panicle ; scales of the involucre in about 3 series, narrowly oblong, acute to acutish, in a dried state stramineous except a central dark brown streak, the more or less narrowed tips thin, erose : corollas slender, without definitely marked throat, glabrous except near the limb : pappus white, equalling the corolla; achenes very small, scarcely 1.4 mm. long, gla- brous. — ■ E. Tuerckheimii^ Coulter, But. Gaz. xvi. 97 and in J. D. Smith, Enum. PL Guat. ii. 95, as to no. 1342, not Klatt. — Collected by H. von Tiirckheim at Pansamala, Depart. Alta Vera Paz, Guatemala, altitude 1,170 m., April, 1888, no. 1342 of Mr. John Donnell Smith's sets. E. Tiierchbeimii^ Klatt, difi'ers in having much narrower oblong- lanceolate subcoriaceous short-petioled leaves which are quite glabrous upon both sides, paler beneath, and marked by a fine transverse venulation. Eupatorium pinabetense. Shrub with angled and striate glabrous branches : leaves opposite, lance-oblong, acuminate at each end, mucron- ulate-serrate, smooth, green and glabrous upon both surfaces, 1 to 1.5 dm. long, 2 to 3 cm. broad, pinnately veined from a strong mid- nerve : smaller branches of the rather dense thyrsoid panicle fuscous- ROBINSON. — SPERMATOPHYTES OF MEXICO. - 483 tomeiitulose under a lens; heads numerous, crowded, small, about 10- flowered, short-pedicelled ; scales of the involucre very few, unequal, elliptical, rounded at the apex, glabrous but erose-ciliolate, in a dried state brown : corolla glabrous or nearly so even at the limb, without clearly marked throat, equalled by the white pappus : achenes (young) pale, glabrous, 1.8 mm. long. — Collected by E'. W. Nelson near Piua- bete, Chiapas, Mexico, 8 February, 189G, no. 3785. This species is near but clearly distinct from E. daleoides, Hemsl. and E. tepicanum, Hemsl. Eupatorium pleianthum. Doubtless perennial : stem slender, terete, scabrous-puberulent, finely striate, reddish brown, loosely few- branched above : leaves opposite, ovate, essentially sessile, thickish, reticulate-veiny, coarsely few-toothed, acute, cordate, 3-nerved, 2.5 to 3.5 cm. long, two-thirds as broad, slightly scabrous upon both surfaces, covered below by bright resinous globules : heads large, 2 cm. in diame- ter, slender-pedicelled, erect ; involucral scales imbricated in 3 or 4 rows, oval to oblong, rounded at the apex, thin, glabrous and glutinous, striate, pale green, scarcely herbaceous : corollas 6 mm. long, gradually nar- rowed from the summit to the base, about equalled by the copious stiffish tawny pappus : styles very long and conspicuous, clavate ; achenes 5 to 6 mm. in length tapering toward the base, reddish brown, covered with resinous globules, not tranversely striate. — E. adenospermnm, var. pleianthian, Gray, Proc. Am. Acad. xv. 26. — Collected by Dr. Ber- thold Seemann, \Yestern Mexico. Type in herb. Gray. While sharing many characters with E. adenospermum, Sch. Bip., this plant differs so markedly in its opposite (not alternate), shorter, ovate not oblong leaves of differing dentation that intergradation seems very unlikely. Eupatorium prionobium. Branches ascending, terete, green, striate, pul)erulent : leaves opposite, petiolate, deltoid, ovate to ovate- oblong, cordate witli open sinus and hastate tendency, acutish to rounded at the apex, crenate or crenate-serrate, thickish, bright green but covered with short scattered white hairs upon both surfaces, scarcely paler be- neath, 2 to 4 cm. long, 1.7 to 2.5 cm. broad ; petiole puberulent, 6 mm. long, sulcate upon the upper side : heads small, about 20-flovvered, in round-topped sessile cinereous-puberulent corymbs; pedicels 3 to 5 mm. long; bractlets subulate; involucre green, the scales lance-oblong, acute, subeqiial, loosely imbricated, 2.5 mm. long, scarcely half the length of the flowers : corolla in dried specimen white, 8 mm. long, with a rela- tively long throat narrowed into a shorter tube, glabrous, e(iualled l)y the bristles of the pappus; these somewhat unequal, barbellate, white 484 PROCEEDINGS OF THE AMERICAN ACADEMY. but the barbules upon the lower half tipped ^Yith deep purple or violet : achenes 1 .8 mm. long, upwardly hispid ou the angles. — Collected by E. W. Nelson on the Sierra Madre, State of Chihuahua, Mexico, 29 September, 1899, no. 6499. Type in herb. Gray and herb. U. S. Nat. Museum. Related to E. ageratifoUum, DC, and E. occidentale, Hook. Eupatorium prionophyllura. Tree ; appearing glabrous to the unassisted vision, but covered upon the branchlets, petioles, veins of the leaves, and pedicels by traces of a short close fuscous tomentum ; branches curved ; cortex gray : leaves opposite, slender-petioled, broadly ovate, conspicuously acuminate, usually obtuse at the base, incisely and often somewhat doubly serrate-dentate nearly from the base to the apex, thin, green on both surfaces, pinnately veined, 7.5 to 9 cm. long, two- thirds as broad ; the teeth acuminate, incurved ; petioles 1 to 4 cm. long : heads 2o-30-flowered, in terminal opposite-branched rounded at first thyrsoid at length more open panicles ; bractlets filiform ; scales of the involucre imbricated in about 3 series, the outer short and ovate, acute, mucronate with a glandular tip, the inner oblong, obtusish, all striate, fimbriate-ciliolate, externally stramineous becoming purplish or fuscous in age especially near the tip, silvery and lucid within : corolla glabrous, gradually narrowed from the summit to the base : pappus white, barbellate, moderately copious, nearly equalling the corolla : achenes at maturity dark brown, glabrous, lucid. — E. ixiocladon^ Klatt, Bull. Soc. Bot. Belg. xxxi. 190, not Benth. — Collected by Prof. H. Pittier ou the banks of the river Poros, no. 1705 (type in herb. Gray) and near the Rancho Flores, no. 1900, Costa Rica. This sjiecies has no close affinity with E. ixiocladon, Benth., a plant well shown by Mr. J. D. Smith's no. 7501. Eupatorium quadrangulare, DC. Prodr. v. 150 (1836). Of this, E. thyrsoideam, Moc, notwithstanding its supposed terete stems, is cer- tainly a synonym. Nothing beyond the younger branchlets of E. thyr- soideum appears to be known, while even in the square-stemmed E quadrangulare these younger branches are often subterete. Eupatorium viscidipes. Stem slender, terete, dark-purple, mi- nutely glandular and very viscid ; bi'anches opposite, spreading, curved upward : leaves opposite, deltoid-ovate, caudate-acuminate, crenate-serrate in the middle, 3-uerved from the obtuse or subtruncate base, 2.2 to 3.5 cm. long, 1.3 to 2.5 cm. broad, minutely puberulent above, slightly paler and punctate beneath with translucent dots ; petioles 1.2 to 1.7 cm. long : heads rather numerous, small, 6 mm. iu diameter, about 18-flowered, borne in a large loose corymbose leafy-bracted panicle ; pedicels filiform, 3 to ROBINSON. — SPERMATOPHYTES OF MEXICO. 485 13 mm. long, glandular and very viscid, covered with extraneous particles ; involucre turbinate-campanulate ; the scales very unequal, much imbri- cated, pluriseriate, the outer ovate-oblong, the inner oblong, subscarious, striate, all obtuse or rounded at the apex, glabrous or slightly glandular, viscid : corolla glabrous, white, 2.3 mm. long ; the proper tube short, much exceeded by the scarcely enlarged cylindric throat : achenes nearly black, columnar, hispidulous on and between the angles ; pappus bright white, a little shorter than the corolla. — E. pycnocephalum^ Coult. in J. Don- nell Smith, Enum. PI. Guat. iv. 75 (1895), as to no. 3397, not Less. — Collected by Heyde & Lux at Chicaman, Department Quiche, Guate- mala, altitude 1,230 m., April, 1892, no. 3397 of Mr. J. Dounell Smith's Guatemalan sets. Type in herb. Gray. To be distinguished from E. pycnocephalum, Less, by its viscidity, quite different and much more imbricated involucre, etc., and from E. anisopodutu, described above, by its viscidity, different leaf-form, rounded instead of acute or acuminate involucral scales, etc. Brickellia amblyolepis. Stem large, fistulose, 2 to 2.5 m, high, glabrous, purple mottled with green : leaves whorled .below, opposite above, alternate in the upper parts of the open inflorescence, ovate, acu- minate, 3-ribbed from the cuneate entire base, coarsely serrate from below the middle to the acuminate apex, green and glabrous above, paler and finely pubescent upon the veins beneath, 7 to 13 cm. long, half as broad; petioles 1.3 to 3.4 cm. long: heads rather large, broader than high, nodding in an open leafy panicle ; pedicels bearing a few linear to spatuUite bractlets ; scales of the involucre in 3 to 4 series, spatulate- oblong, rounded at the apex, green and nearly glabrous except upon the deep purple tomentulose margin : corollas greenish, 5 mm. long, glabrous, nearly equalled by the rather copious purple-tinged pappus : achenes (immature) 5 mm. long, minutely pubescent ; styles strongly clavate, bright orange turning to brown. — Collected by C. G. Priiigle on moun- tains above Iguala, Guerrero, Mexico, 4 October, 1900, no. 8415. A stately species 2 to 3 metres high, not very closely related to any hitherto described. Type in herb. Gray. Brickellia cardiophylla. Herbaceous ; stem terete, glandular- pubescent; branches opposite, widely spreading: leaves ovate-triangular, acute or obtusish, entire or nearly so, broadly cordate at the base, mem- branaceous, 3-uerved, minutely glandular-puberulent, green upon both surfaces, scarcely paler beneath, 5 to 6 cm. long, nearly as broad ; peti- oles slender, 2 to 3 cm. long : heads subumbellate near the ends of the branches, campanulate, 1 to 1.5 cm. in diameter; pedicels filiform, gland- 486 PROCEEDINGS OF THE AMERICAN ACADEMY. ular-puberulent, 2 to 3 cm. long, naked or bearing a single minute lance- olate bract; involucral scales appressed, imbricated in about 5 series, from ovate to linear obtusish, striate, the outer herbaceous-tipped, the inner often purplish ; achenes columnar, 2.5 mm. long, minutely rough- ened or hispid ; pappus bright white, not copious, 7 mm. in length : corollas in a dried state cream-colored. — Collected by C. G. Pringle in a barranca near Guadalajara, Jalisco, 1 May, 1894, no. 5885a. Type in herb. Gray. Near B. Jloribunda, Gray, but heads fewer and consid- erably larger : leaves subentire and of different contour. Brickellia hebecarpoides. Erect herb, seemingly perennial but root not seen ; stem straight, terete, striate, glandular-pubescent, copiously branched above : leaves opposite (the upper with a slight tendency to be alternate), ovate to ovate-oblong, acute or obtuse, membranaceous, finely and regularly serrate (the rameal entire or nearly so), rounded or ab- ruptly acuminate at the 3-5-uerved often oblique base to the slender petiole, puberulent above, glandular-puberulent beneath, both surfaces green, the lower scarcel}^ paler ; branches slender, spreading, leafy : peduncles solitary in or usually a little above the forks of the branches, 1 to 2.5 cm. long, filiform, ascending or erect, glandular-pubes- cent, bractless ; involucre 1.2 cm. long, campanulate, its outer bracts lance-oblong, acute, glandular-puberulent, herbaceous or at least herba- ceous-tipped, half to two thirds the length of the lance-linear attenuate striate often purplish inner bracts ; flowers about 30: corolla 1.3 cm. long, slender, glabrous, purple-tinged at least near the limb : achenes short, only 2 mm. in length, minutely pubescent ; style-branches orange, strongly clavate. — Collected by C. G. Pringle in a barranca near Cuernavaca, State of Morelos, Mexico, altitude 1,540 m., 24 June, 1896, no. 7332. Type in herb. Gray. This species is related to B. Itebecarpa, Gray, but differs in its scarcely pubescent achenes and much longer outer involucral scales, as well as in other ways. Brickellia petrophila. Compact shrub, 3 to 6 dm. high ; stems branched from near tlie base ; branches curved-ascending, becoming erect, gray or lightish brown, covered with a fine spreading pubescence consisting of minute gland-tipped hairs and longer non-glandular hairs, the latter readily distinguishable to the unassisted vision : leaves oppo- site, small, reniform, ovate, crenate, obtuse, broadly and shallowly cordate at the base, 7 to 10 (rarely 28) mm. long, 1 to 3 cm. broad, somewhat rugose above, finely pubescent or even tomentulose upon both surfaces, but scarcely or not at all canescent : heads subsessile, terminal on short or more elongated branchlets either forming a cylindric racemiform or a ROBINSON. — SPERMATOPHTTES OF MEXICO. 487 broader and more pyramidal inflorescence, the two forms occurring upon the same individual ; involucre cjliudric or in a dried state narrowly campauulate, the scales stramineous, striate, imbricated in about four very unequal series, the outer ovate, obtuse, pubescent or at least ciliate, the inner oblong-linear, acute, abo.ut 8 mm. long ; flowers about 20 : achenes columnar, 3 mm. long, olive brown, slightly hispid on the ribs. — Collected by C. G. Pringle on rocky hills near the city of Chihuahua, 13 October, 1885, no. GIO (type, in herb. Gray). To this species I would refer the following specimens : from Sun Luis Potosi, Schaffiier, no. ^&b, Parry «fe Palmer, no. 351 ; from Guanajuato, Duges, no. 449; from Zacatecas, Beam, no. 140; from Durango, Palmer, no. 753. This species is nearly related to and has been generally confused with the more southern B. veronicaefolia, Gray, a species which is readily distin- guishable by the extremely fine canescent non -glandular pubescence of its branchlets, in which the individual hairs cannot be seen without the use of a strong lens. The involucral scales of B. veronicaefolia are more closely imbricated and in more numeroUvS rows. Var. umbratilis^ Heads larger, 1.5 cm. in diameter, terminal upon more elongated branches. — Collected by Dr. Edward Palmer in a shady ravine at Parras, Coahuila, October, 1898, no. 438, and also a solitary individual in a ravine at Mapimi, Durango, no. 521. Brickellia vernicosa. Shrub with striate buff or at length gray cortex and erect scabrous-puberulent branches: leaves alternate, ovate, serrate, acutish, bright green, coriaceous, veiny, subsessile, minutely his- pidulous, glandular-punctate beneath, often vernicose, 1 to 1.7 cm. long: inflorescences cylindric thyrses 1 to 1.5 dm. long; bracts leaf-like but very small; heads subsessile, 1.2 cm. long, on short branches; involu- cral scales about 4-seriate, varying from ovate to linear-oblong, obtuse, minutely granular, striate : slender corollas 7 to 8 mm. long, the upper half violet: achenes slender, columnar, light-colored, 4 mm. long, upwardly hispid; pappus copious, G mm. long; styles yellow, only moderately clavate. -—Collected by Dr. Edward Palmer at Santiago Papasquiaro, Durango, "April and August," 1896, no. 57. Related to B. baccharidea, Gray, but readily distinguished by its much longer achenes, etc. MoNTANOA ARBORKSCENS, Sch. Bip. {Montagnaea arborescens, DC. Prodr. v. 505). An examination of the type shows that the tips of the pales are recurved as in most of the other species of this genus and not inflexed as unfortunately described in the original characterization. The leaves are oblong-lanceolate, attenuate at each end, rather sharply 488 PROCEEDINGS OP THE AMERICAN ACADEMY. and regularly serrate near the middle and relatively narrower than in the nearly related M. frutescens, Hemsl. I am unable to find M. arhor- escens represented in any of the many recent Mexican collections. Galea Pringlei. Stems terete, 6 to 9 dm. high, in dried state striate, dull brown, covered with a fine spreading or slightly reflexed tomentum of sordid color, and on young parts somewhat glandular ; branches op- posite : leaves broadly ovate to nearly orbicular, sessile, acute, coarsely dentate (1 to li- teeth to the centimeter), rugose and scabrous-puberulent above, paler green, reticulate veiny, and covered with a fine white crisped pubescence beneath : heads 8 mm. long, 3 mm. in diameter, about 10- flowered, borne on pedicels 2 to 5 mm. long in opposite-branched com- pound umbelliform cymes ; scales of the cylindrical involucre pale yellow, striate, very unequal, rounded at the tip, the outer sparingly jjubescent, small, not foliaceous nor even herbaceous ; pales erose, nearly or quite glabrous : corolla nearly glabrous but covered with transparent globules, the proper tube slender and somewhat contracted to the summit where it suddenly expands into the very short throat and deeply cleft limb of five linear segments : achenes slender, somewhat attenuate toward the base, dark-colored with a violet tinge, appressed-pubescent ; pappus scales about 1 mm. long, also purple-tinged. — Collected by C. G. Pringle on mountains above Iguala, Guerrero, Mexico, altitude 1,230 m., 24 October, 1900, no. 8373. Type in herb. Gray. Galea ZACATECHicni, Schlecht., var. calyculata. Involucre sub- tended at the base by 2 or 3 herbaceous-tipped bracts ; these usually shorter than but sometimes exceeding tlie inner scarious scales. — Mexico, Nuevo Leon in the Sierre Madre near Monterey, C. G. Pringle, no. 2224, 16 July, 1888; also in the same locality, C & E. Selei^ no. 1080, 12 October, 1895. Proceedings of the American Academy of Arts and Sciences. Vol. XXXVI. No. 27. — April, 1901. CONTRIBUTIONS FROM THE GRAY HERBARIUM OF HARVARD UNIVERSITY. New Series. — No. XXI. SOME NEW SPERMATOPHYTES FROM MEXICO AND CENTRAL AMERICA. By M. L. Ferxald. CONTRIBUTIONS FROM THE GRAY HERBARIUM OF HARVARD UNIVERSITY, NEW SERIES, No. XXI. SOME NEW SPERMATOPHYTES FROM MEXICO AND CENTRAL AMERICA. By M. L. Fernald. Presented March 13, 1901. Received March 20, 1901. Fimbristylis melanospora. Glaucous, tufted from a hard base: leaves firm, smooth, strongly nerved, 1 to 1.5 mm. wide, tending to become involute, the longest barely 1 cm. long, vpith a short deltoid cartilaginous tip : culms compressed, with thin edges, 2 dm. or less high : umbel decompound, with very short rays, forming a dense inflores- cence I to 2 cm. broad ; involucre of 2 or 3 very unequal leaves, the longest not equalling the mature umbel ; spikelets ovoid-oblong, 3.5 to 4.0 mm. long, 2 to 2.5 mm. thick : scales ovate, blunt, slightly carinate, pale brown with broad white scarious margins : style slender, terete, smooth, with 2 pubescent branches ; achenes lenticular, obovoid, broadly rounded above, 1 mm. long, brownish black, minutely muriculate. — Vera Cruz, low grounds, Vera Cruz, April 23, 1894 (C G. Pringle, no. 5773). Superficially resembling some forms of F. polymorpha, Boeckl., but differing in the paler and smoother leaves, the broader white margins of the scales, the very different blackish achene, and the slender (not compressed) smooth style. F. alamosana. Low tufted annual, about 1 dm. high : leaves flat, smooth, mostly much shorter than the slender flexuous culms, rarely longer; the sheaths densely ciliate : umbels decompound, with 3 to 7 slender lax unequal rays, the longest 2 or 3 cm. long, the spikelets mostly long-pedicelled ; involucre of 2 or 3 unequal leaves, the longest equalling or exceeding the rays; spikelets pale straw-colored or whitish, ovoid-oblong, acutish, 2.5 to 3.5 mm. long, 1 to 1.75 mm. thick: scales ovate, acutish, or the lowest mucronate, slightly carinate: style com- pressed, pubescent, with 2 branches; achene barely 1 mm. long, broadly cuneate-obovoid, with 10 or 12 obscure longitudinal bands, white, pearly and finely muriculate all over. — Sonora, Alamos, Sept., 1890 {Edw. 492 PROCEEDINGS OF THE AMERICAN ACADEMY. Palmer^ uo. G99). Differing from F. laxa, Vahl, in its paler smaller spikelets and smaller white and glossy achenes. F. Holwayana, Culms slender, 1 to 3 dm. high, much overtopping the pale green narrow (0.75 mm. wide) ciliate leaves : umbel simple, with 2 (rarely 1) to 4 ovoid-oblong spikelets 6 to 8 mm. long, 2.5 to 3.5 mm. thick, the middle (or rarely solitary) one sessile, the others on slender ascending rays 0.5 to 2 cm. long; involucre of 2 or 3 ciliate leaves, the longest one usually much exceeding the rays: scales from orbicular to ovate, blunt, castaneous and shining, the green midrib in the outer somewhat prolonged into a short awn, in the others barely into a cusp: achene short-stipitate, pearly, broadly obovoid, subtruncate above, half as long as the scale, 1.25 mm. long, nearly as thick, with about 16 lon- gitudinal ribs, and many linear transverse markings; style flat, fimbriate, exserted. — Jalisco, Chapala, Sept. 18, 1899 {E. W. D. Holway^ no. 3443). Closely related to F. pentastachya^ Boeckeler, but differing ia its narrower spikelets and broader scales, and in the achenes which are smooth or with one or two tubercles at the very summit, not tuberculate- roughened throughout as in F. pentastachya. F. obscura. Glaucous, loosely tufted from slender branching caudex : leaves flat, 2 or 3 mm. wide, the longest 1.5 dm. long, smooth, or the margins ciliolate-scabrous except at the acutish cartilaginous tip: culms compressed, with thin edges, 4 dm. or less high : umbel decompound, with 2 to 4 rays 2 or 3 cm. long and several shorter ones; involucre of 2 leaves much shorter than the umbel; spikelets mostly pedicelled, or rarely 2 or 3 fascicled and sessile, lanceolate, acute, 5 to 8 mm. long, 1.5 to 2 mm. thick : scales dark brown, ovate-oblong, strongly carinate and mucronate: style slender, terete, smooth, with 3 pubescent branches; achenes trigonous with obtusish angles, obovoid, barely 1 mm. long, whitish, with extremely obscure longitudinal markings (seen only under strong magnification). — DuRA-NGO, alkaline bottoms near Durango, June, 189G (Eiio. Pihner, no. 186) : San Luis Potosi, in the moun- tains, San Miguelito, 1876 {Schaffner, no. 558). Resembling F. autumnalis. R. & S., but clearly differing in its caespitose perennial habit, and its larger, paler, and duller achenes. Glyphosperma Palmeri, Watson, Proc, Am. Acad, xviii. 164. Mr. Pringle calls attention to the fact that this plant, which in Mexico appears like an introduced species, is identical with the Old World Asphodelus jistulosus^ L. Cologania Deamii. Stems slender, 1.5 to 2 dm. long, from a slen- der creeping rootstock, ascending and branched, the tips flexuous but FERNALD. — SOME NEW SPEKMATOPHYTES. 493 slightly twining, covered with fuscous retrorse-hispid pubescence : stip- ules ovate to lanceolate, 4 to 6 mm. long: petioles retrorse-hispid, 1.5 to 2.5 cm. long ; leaflets oblong-ovate to obovate, mucronate, slightly strigose above, pale and hispidulous beneath, 2 to 4 cm. long, the terminal on a petiolule (0.5 cm.) thrice as long as those of the lateral leaflets : umbels 3-6-flowered, the principal peduncles 4 to 6 cm. long, retrorse-hispid, those on the flexuous branches shorter ; pedicels 1 to 1.75 cm. long : calyx 1 to 1.2 cm. long, hispid: corolla violet, 2 to 2.5 cm. long. — MoRELOS, Cuernavaca, July 7, 1900 (C C. Dcam^ no. 40). Unique in its long peduncles. Platanus glabrata. Leaves from broad-cuneate to subcordate, unequally 5-9-lobed, the middle lobe and the upper pair of lateral ones long-acuminate, the lower ones short-acuminate ; the margin entire ; at first closely cinereous-tomentose beneath, soon becoming glabrate : pedun- cles 0.5 to 1 dm. long, bearing 1 or 2 heads 1.5 to 2 cm. in diameter. — P. Lindeniana, Wats. Proc. Am. Acad, xviii. 155, not ]Mart. & Gal. — CoAHDiLA, Monclova, Aug., 1890 {Edw. Palmer, no. 1269); Saltillo, April 5, 1887 (C. S. Sargent); by streams near Diaz, alt. 216 m., April 24, 1900 (C. G. Pringle, no. 8319). Differing much from P. Lindenia7ia of southern Mexico, which has the less lobed leaves perma- nently cinereous beneath, and the heads more numerous. Croton Palmeri, Watson, var. ovalis. Leaves oval, 1.5 to 3 cm. broad, not lanceolate, rounded at base : clusters many-flowered. — NuEvo Leo\, Monterey, Oct. 11, 1895 (C & E. Seler, no. 1047). Alcoceria, nov. gen. of Eiiphorbiaceae (^Hippomaneai^). Monoecious. Staminate flowers in a terminal ament; the individual flowers slightly imbedded at base by close dens6 pubescence. Calyx of staminate flower with 2 broad fleshy valvate sepals and a third narrow inconspicuous one. Stamen solitary ; filament thick, columnar ; anther 2-celled, longitudinally dehiscent, dorsally aflixed toward the sheathing tip of the filament. Calyx of pistillate flower with three deltoid-subulate teeth and few or no intermediate small glands. Ovary depressed-globose, suhtrigonous, the three 1-ovulate cells alternating with the calyx-teeth. Style cylindric, erect, equalling the three recurved branches. Fruit a 3-locular capsule. Seed pisiform, scarcely carunculate. — Dedicated to Gabriel Alcocer, acute observer, teacher in the Escuela Preparatoria, and botanist at the Museo Nacional and the Instituto Medico Nacional of Mexico. A. Pringlei. Slender shrub, 3 to 5 ra. high, the sprawling branches herbaceous, striate, the lower nodes remote : leaves pilose or glabrate beneath, reniform, acuminate, varying from 0.4 to 1.3 dm. long, and from 49-i PROCEEDINGS OF THE AMERICAN ACADEMY. entire to more or less palmately 3-7-lobecI, palmately 5-nerved, the nerves conspicuous beneath ; petioles 1.5 to 4 cm. long, pubescent at tip : inflorescence axillary or terminal ; the staminate ament linear-oblong, 2 cm. long, long-peduncled, with few strongly reflexed pistillate flowers at base ; pedicel of pistillate flower glandular at base, thick-clavate, 1 to 2 cm. long : capsule about 1 cm. broad. — Guerrero, limestone moun- tains above Iguala, alt. 1,230 m., Sept. 26, 1900 (C. G. Pringle, no. 8433). Related to Dalembertia, Baillon, which differs in the single bract (instead of a 3-lobed calyx) at tlie base of the anther. Also approaching Tetraplandra, 'B-a.iU.OQ, and Maprounea^ Aublet, but the former is distin- guished by its four terminal anthers, and the latter by its sbort staminate sjDike and two more or less connate stamens. Euphorbia (Anisophyllum) puberula.^ Branching from the base, the branches subligneous, ascending, 2.5 dm. or less high, puberu- lent, the tips cauescent and tomentulose : leaves rhomboidal, 1 to 2 cm. long, 0.5 to 1 cm. broad, very oblique, glaucous beneath, blunt, crenate- serrate, sparingly pilose ; stipules setaceous : cymes dense, 1 or 2 cm, broad, terminating the leafy branches : involucre white-pilose, turbinate- campanulate, 1.5 to 2 mm. long, with deltoid hairy lobes; glands 4, short-stipitate, with or without narrow appendages ; false gland absent from the broad shallow sinus : capsule appressed-pilose, subacutely lobed, 1.5 mm. long: seed pulverulent, 1 mm. long, oblong or ovoid-oblong, quadrangular, with somewhat broken ridges between the angles. — Mexico without locality (^Coulter, no. 1438 in part): Guanajuato, hills of Guanajuato, 1895 {A. Buges): Morelos, Puente de Ixtla, July 3, 1900 (Charles C. Beam, no. 26) ; Huerta de la Hacienda de Miacatlan, Distr. Tetecala, Dec. 28, 1887 (C. & K Seler, no. 341): Oaxaca, near Mitla, Distr. Tlacolula, June, 1888 ; Tecomavaca, Nov. 15, 1895 ; Tomellin, Distr. Cuicatlan, Nov. 15, 1895 (C. & B. Seler, nos. 31, 1360, 1376) ; mountains of Oaxaca, alt. 1,750 m., July-Aug., 1900 (C. Gonzatti &, V. Gonzalez, no. 1042): Chiapas, Ocozuquaulitla, Distr. Tuxtla, Feb. 19, 1896 (C. & E. Seler, no. 1952). Nearest related to £J. pilulifera, L., and E. lineata, Watson, differing from the former in its terminal cymes and blunter leaves, from the latter in its rather stouter habit and more rhomboidal leaves, and from both in its cinereous puberulence. 1 In the preparation of the descriptions of these Euphorbias the writer has been greatly assisted by Professor C. F. Millspaugh, who has generously examined tlie specimens, and who has already pointed out (Bot. Gaz. xxv. 13) the impor- tance of the involucral appendages in differentiating the species of this genus. FERNALD. — SOME NEW SPERMATOPHYTES. 495 E. (Anisophyllum) potosina. Ascending annual, branching from the base : steins glabrous, or the younger parts minutely pilose, 2 dm. high: leaves 1 to 1.75 cm. long, oblong, oblique, rounded or subtruucate at base, bluiitish at tip. glabrous, pale green above, glaucous beneath, the margin coarsely appressed-crenulate ; stipules deltoid-acuminate, lacini- ate: flowers few in small mostly terminal clusters: involucre pyri form, glabrous ; the lobes elongate-triangular, entire or nearly so, the 2 flank- ing the broad rounded sinus much larger and lacerate ; glands 4, long- stipitate ; appendages very narrow or wanting ; false gland aristate, rising from the base of the sinus: capsule glabrous, ellipsoidal, 2.5 to 3 mm. broad, barely 2 mm. high, the three lobes rounded: seed short- oblong, subquadrate, 1.5 to 1.75 mm. long, the dorsal angle prominent, the ventral suppressed, blackish, pulverulent, the angles and the margins of the unequal honeycomb-pits paler. — San Luis Potosi and adjacent Tamaulipas. San Luis Potosi, without locality, 1876 (/. G. Schaffner, no. 856, in part) ; region of San Luis Potosi, alt. 1,850 to 2,460 m., 1878 {Parry & Palmer^ no. 814, in part) : Tamaulipas, near Tula, Sept. 21, 1898 {E. W. D. Holway, no. 3200). — Related to E. hyperici- folia, L., E. Preslli, Guss., and E. brasiliensis, Lam., but differing in its fewer flowers, larger capsule, and much larger ditfer&utly marked seed. E. (Anisophyllum) interaxillaris. Perennial, with slightly woody base : stems prostrate or slightly ascending, 1 dm. or so long, pilose with more or less spreading hairs : leaves short-petioled, oblong or obovate- oblong, oblique, rounded at each end, 0.5 to 1 cm. long, 4 to 7 mm. wide, minutely crenulate, mostly purple-tinged or blotched, sparingly pilose on the margins when young, soon glabrate ; stipules narrowly triangular, fimbriate : flowers solitary, a single one accompan3'ing each pair of leaves, on slender pedicels 2 or 3 mm. long: involucre campanulate, 1.5 mm. long, glabrous outside ; the lobes triangular, about equal, hairy within ; glands 3 or 4, brownish, mostly with suborbicular white appendages 1 mm. in diameter ; the 5th gland replaced by an elongated false-lobe at the base of the shallcjor triangular sinus : ovary glabrous. — Morelos, Puente de Ixtla, July 3, 1900 {Charles C. Deam, no. 25). Related to E. stictospora, Engelm., but less pubescent and with solitary flowers. E. (Zygophyllidium) muscicola. Caudex tuberiform, globose or oblong, 3 to 5 cm. long, narrowed above to a cylindric neck ; stem very slender, branching from near the base, the slender flexuous subsimple or slightly forked branches 2 or 3 dm. long, glabrous : lower leaves subor- bicular to ovate, rounded or blunt; the upper elliptic-lanceolate, 0.5 to 40G PROCEEDINGS OF THE AMERICAN ACADEMY. 1.5 cm. long, mucronate, entire or appressed-serrulate, glabrous or sparingly pilose-setulose ; the lower equalling the capillary petioles, the upper short-petioled : flowers few, terminal and axillary, on joedicels 2 cm. or less in length: involucre short-campanulate, 2 mm. long, ap- pressed-setulose, the deltoid-oblong truncate erose lobes incurved ; glands 4, dark, with pale oblong-lanceolate blunt appendages 1 to 1.5 mm. long; false gland similar : capsule rugulose, 4 mm. high : seed oblong-ovoid, minutely puncticulate, gray or gray-green, mottled with olive or brown. — MoRELOS, on mossy ledges of Sierra de Tepo-xtlan, alt. 2,310 m., Sept. 12, 1900 (C. G. Primjle, no. 8443). E. (Cyttarosperraum) calcicola. Annual, freely branching, 5 or 6 dm. high, the slender stem and branches viscid-setulose with long pale hairs : leaves broad-ovate, rounded or bluntish at tip, truncate or sub- cuneate at base, the lower 2 cm. long, the upper much smaller, setulose on both faces, dark above, pale beneath, about equalling the capillary petioles: flowers axillary on capillary pedicels 1 to 1.5 cm. long: in- volucre broad-campanulate, green and yellow, 1 mm. long, the short in- curved cuneate lobes lacerate ; glands 4 with 3 finger-like appendages ; the false gland slightly larger, with 4 appendages : ovary glabrous. — Guerrero, limestone mountains above Iguala, alt. 1,230 m., Oct. 5, 1900 (C. G. Pringle, no. 8398). Closely related to E. astroites, F. & M., but the stem conspicuously setulose. and the pedicels much longer, E. LAXCiFOLiA, Schl., var. villicaulis. Stems more or less villous with crisp jointed hairs: leaves rhombic-ovate, acutish, green and lucid above, pale and more or less villous beneath : involucre campanulate, pilose or glabrate, 3 or 4 mm. long; lobes truncate, serrate ; glands 1 or 2 associate, hoof-shaped ; false glands 3, columnar, truncate, one-third longer than the lobes : capsule (young) pilose, 5 mm. long, with rounded lobes : seed (young) short-oblong, 2 or 2.5 mm. long, pale brown. — Chiapas, mountain-slope above Ococingo, March 13, 1896 (C. & E. Seler, no. 2214). Distinguished from the species by its pubescence, in- volucral lobes, and false glands. In E. lancifoUa the iuvolucral lobes are fimbriate, equalling or slightly exceeding the subalate false glands. Pernettya ovata. Branches pale brown, minutely puberulent or glabrate : leaves ovate, sliort-petioled, 1 to 1.5 cm. long, pale and mi- nutely canescent-tomentulose toward the rounded base ; margins finely appressed-serrate, the youngest glandular-ciliate, as are the lower faces of the young leaves : infloi'escences axillary, subsessile, all the parts glabrous, the deciduous bracts sometimes with erose margins : flower- ing calyx 3 mm. long, cleft half-way to the base into deltoid smooth- FERNALD. — SOME NEW SPERMATOPHYTES. 497 edged lobes: corolla ovate-campanulate, 6 or 7 mm. loug. — Chiapas, mountain woods between San Cristobal Las Casas and Huitztan, March 10, 1896 {G. & E. Seler, no. 21 20'^. Growing with P. ciUaris, Don, but nearer related to P. coriacea, Klotzsch, from which it differs in its pale and minutely puberulent branchlets, paler leaves and glandless calyx. Arctostaphylos Conzattii. Shrub with smooth reddish bark easily peeling from the brandies : leaves oblong-oblanceolate, acute, 2 to 4 cm. long, 0.75 to 1.0 cm. wide, entire and subeuneate below to a short petiole, sharply serrate above the middle, smooth and sublucid above, sparingly sordid-pilose beneath : racemes terminal, panicled, 1 dm. or less long ; the rachis, pedicels and short ovate-lanceolate bracts puberulent ; pedicels 1-3-bracted, 1 cm. long : calyx puberulent, with ovate bluntish lobes : corolla urceolate, glabrous, 5 or 6 mm. long. — Oaxaca, Sierra de Saa Felipe, alt. 3,000 m., April 7 and 8, 1898 (C. Conzatti, no. 691). In its inflorescence resembling A. rupestris, Robinson & Seaton, but differing in its much smaller but more coarsely toothed leaves. A. glabrata. Shrub with smoothish gray-brown bark; the young branches reddish-brown : leaves narrowly elliptic-oblong, acute or blunt, 2 to 4 cm. long, about 1 cm. wide, tapering to short thick petioles 3 or 4 mm. long, entire or sharply serrate with short mucronate teeth, bright green above, paler beneath, ferrugineous-tomentulose when young, becoming glabrate : racemes simple, terminal or axillary, 2 or 3 cm. long; the rachis, the lance-acuminate bracts, and the short (3 to 5 mm. long) pedicels ferrugineous-tomentose, rarely a little glandular : calyx slightly tomentulose, the lobes broadly deltoid : corolla urceolate, glabrate, 4 or 5 mm. long : berries dark, 6 or 7 mm. in diameter. — Oaxaca, ledges at the .summit of Sierra de San Felipe, alt. 3,500 m., Sept. 25, 1894 (C. G. Pringle, no. 5712), Aug. 15,1897 (C. Conzatti & V. Gonzalez in Exsicc. Conzatti, no. 409) ; mountains about Yalalag, alt. 1,850 m., Aug. 1. 1894 {E. W. Nelson, no. 973). Related to A. arguta, Zucc, but differing in its shorter leaves, and shorter simple essentially glandless raceme. Parathesis chiapensis. Branches stout, gray and smoothish, the younger parts closely tomentose with short stellate ferrugineous hairs : leaves elliptic, 1.5 to 2 dm. long, narrowed above to a short slender acumen and below to a thick cinereo-ferrugineous petiole 0.5 to 1 cm. long ; margin closely and finely crenate-dentate ; upper surface smooth and dull, the lower ferrugineous-tomentose when young, becoming gla- brate: panicle terminal, leafy below, in anthesis 1.5 dm. high, pyram- idal, the spreading branches 3 to 6 cm. long, bearing many-flowered VOL. XXXVI. — 32 498 PROCEEDINGS OF THE AMERICAN ACADEMY. corymbs, rusty tomentose and finely linear-maculate throughout ; bracts lanceolate, 5 mm. long ; pedicels thickish, somewhat clavate, becoming 1 to 1.5 cm. long: calyx in an thesis 3 or 4 mm. long, deeply cleft into 5 linear lobes : corolla-lobes lanceolate, 6 mm. long, strongly recurved, tomentulose within : filaments broad at base, 2 mm. long ; anthers oblong- lanceolate, 3 mm. long. — Chiapas, in mountain-woods between San Martin and Ococingo, March 13, 1896 {G. &, E. Seler, no. 2226). Ec- lated to P. sessilifolia, Donnell Smith, but differing in its crenate dull leaves, closer shorter pubescence and larger flowers. Evolvulus Seleriana. Perennial: stems prostrate or slightly ascending, 1 to 2 dm. long, slightly branched, silky pilose, the older becoming glabrate : leaves obcordate, obovate or obovate-oblong, short- petioled, 5 to 12 mm. long, above appressed long-sericeous or glabrate, beneath permanently sericeous : flowers axillarj', the filiform arcuate sericeous peduncles bractless, 9 to 13 mm. long: calyx very pubescent, 4 mm. long, with lanceolate lobes : corolla pale (apparently white) some- what silky without, 8 to 9 mm. high. — Chiapas, Tuxtla, Feb. 19, 1896 (C & E. Seler, no. 1926). Nearest related to E. nummularius, L., but with different pubescence, obcordate leaves, longer peduncles, and larger flowers. Ipomoea caudata. Slender glabrous vine : leaves on slender petioles 3 to 5 cm. long; blade 1 dm. or less long, narrowly ovate, prolonged into a caudate-acuminate tip, the base rounded-sagittate, the basal lobes varying from blunt to acuminate, dark green above, glaucous beneath, palmately 7-nerved at base: jDcduucles slender, 1 to 1.5 dm. long, simple or once forked at the tip ; pedicels 2 to 4 cm. long : calyx narrowly oblong, 1 cm. long, the unequal oblong blunt lobes mottled : corolla rose-purple, 0.5 dm. long, the cylindric tube 4 cm. long, the short spreading limb 2 cm. broad: style filiform, glabrous. — Morelos, on mossy faces of the knobs of the Sierra de Tepoxtlan, alt. 2,310 m,, Sept. 5, 1900 (C. G. Pringle, no. 8448). Habitally resembling I. simu- lans, Hanbury, but with longer peduncles and calyx, and more slender corolla. Cordia (Sebestenoides) Seleriana. Branches straggling, cov- ered with brown verrucose bark : leaves ovate or suborbicular, 1 to 2 cm. long, pulverulent and hispidulous ; petioles slender, hispid, 3 or 4 mm. long : corymbs few-flowered, the parts very hispid ; peduncles 2.5 cm. or less in length : calyx oblong-carapanulate, 1 cm. long, with short rounded lobes : corolla 3 cm. long, somewhat hispidulous below, the thin ovate- oblong round-tipped creuulate lobes 1 to 1.5 cm. long. — Oaxaca, dry FERNALD. — SOME NEW SPERMATOPHYTES. 499 woods, Huilotepec, Teliuantepec, Jan. 20, 189G (C. & E. Seler, no. 1779). Salvia (Micranthae) ageratifolia. Tall branching annual, the sharply quadrangular herbaceous stems long-setulose, with somewhat shorter gland-tipped hairs intermixed : leaves cordate, ovate or deltoid- ovate, 2 to 4 cm. long, coarsely crenate, bluntish, dark green and minutely pilose or glabrate above, glaucous and puberulent beneath ; petioles slender, 1 to 3 cm. long, more or less setulose : racemes simple, elon- gated, becoming 2 dm. long; verticels 2-4-flowered, the lower 1.5 to 2 cm. apart ; bracts persistent, ovate-acuminate, 2 mm. long ; pedicels becoming 3 mm. long : calyx at first narrowly later broadly campanulate, in anthesis 5 or 6 mm. long, 2 or 3 ram. broad, in fruit 8 or 9 mm. long, 4 or 5 mm. broad, setulose, the entire mucronate upper lip slightly shorter than the narrower acuminate lower lobes : corolla 7 or 8 mm. long, blue, the tube included, the pilose galea shorter than the lip. — ■ Oaxaca, mountains near Oaxaca, alt. 1,750 ra., July, Aug., 1900 (C. Conzatti &, V. Gonzalez^ no. 1049). Closely related to S. micrantha^ Vahl, & *S'. setosa, Fernald (nos. 8 & 9 of the writer's Synopsis ^). From the former quickly separated by its loose elongated raceme and setulose stem ; from the latter by its cordate leaves, setulose stem, and scarcely secuud racemes. S. TiLiAEFOLiA, Vahl, var. rhyacophila. Stem (especially above), petioles, and calyces densely villous :, leaves more pubescent than in the species. — Morelos, lava-fields below Cuernavaca, alt. 1,230 m., Oct. 17, 1900 (C. G. Pringle, no. 8381). S. (Angustifoliae) setulosa. Tall (about 1 m. high) and erect shrub with stiff ascending branches ; stem and especially the young branches setulose with long white hairs : leaves rhombic-oblonsf to del- toid, blunt, cuneate at base into slender petioles, 2 to 4.5 cm. long, 1 to 2.5 cm. broad, dark green and sparingly pilose above, pale and more or less pilose beneath, the margin finely crenate-serrate: peduncles 1 to 1.5 dm. long, sparingly setulose or glabrate: racemes becoming 2 dm. long; the ovate long-acuminate puberulent bracts 1 to 1.5 cm. long, long-ciliate on the margins, tardily deciduous: verticels G-10-flowered, becominor remote, the lowest 3 or 4 cm. apart ; pedicels 2 to 4 mm, long, canescent with appressed pubescence: calyx in anthesis 7 mm. long, hirsute espe- cially on the tubO; the ovate-lanceolate long-subulate lobes about equal- ling the tube, the upper lip usually tridentate : corolla deep blue, 18 1 Proc. Am. Acad., xxxv. 489-556. 500 PROCEEDINGS OF THE AMERICAN ACADEMY. to 20 mm. long, the scarcely ampliate tube twice exceeding the calyx ; the pilose lips subequal : style densely bearded. — Morelos, mountains above Cuernavaca, alt. 2,460 to 2,620 m., Oct. 13, 1900 {C. G. Pringle, no. 8403), Sept. 1, 1900 (C. G. Pringle, no. 9204). Closely related to S. prunelloides, HBK. (no. 40 of the writer's synopsis), but differing from that and the other members of the group in its tall erect stem. S. (Vulgares) igualensis. Tall (1 m. or more high), the strongly grooved quadrangular stem canescent with close pubescence : leaves broad-ovate, the lower suborbicular, short-acuminate, rounded at base, 5 to 7 cm. long, 4 to 5.5 cm. broad, coarsely crenate-serate, minutely puberulent or glabrate on both faces, pale beneath, on slender canescent petioles 1 cm. or less in length: racemes long and slender, becoming 1.5 to 2 dm. long ; verticels 10-20-flowered, mostly approximate, the lower 1.5 cm. apart ; bracts lanceolate, caducous ; pedicels becoming 2 mm. long : calyx in anthesis about 3 mm. long, short-pilose-hispid on the nerves, with short deltoid teeth; corolla blue, pilose, 1 cm. long; the slightly ventricose tube twice exceeding the calyx ; galea and lip sub- equal : style bearded. — Guerrero, limestone mountains above Iguala, alt. 1,230 m., Sept. 26, 1900 (C. G. Pringle, no. 8418). Related to S. brachyodonta, Briq. (no. 59 of the writer's Synopsis) and S. Ghies- hreghtii, Fernald (no. 60). From the former distinguished by its coarser habit, cinereous stem, short petioles and appressed teeth of the leaves, and shorter pedicels ; from the latter by its coarser habit, and broader glabrate leaves without the characteristic lanate pubescence of S. Ghiesbreglitii. S. (Scorodoniae) Dugesii. Shrub, the branches canescent with closely matted simple hairs : leaves oblong or oblong-ovate, 2 to 4 cm. long, rounded at base, acute or bluntish at tip, strongly rugose, green above, canescent beneath with close simple hairs ; petioles slender, 1.5 cm. or less long : racemes becoming 1 dm. or so long, simple ; verticels 8-12-flowered, the lowest 1 to 1.5 cm. apart ; pedicels at most 1 mm. long: calyx cuneate-campanulate, canescent with short mostly simple appressed hairs, in anthesis 7 ram. long, with short flaring blunt or merely short-subulate lobes: corolla 1.5 cm. long, pubescent with short gland-tipped hairs. — Guanajuato, Aug., Sept., 1900 {A. Duges). This plaut, known as '■'■Chia cimarona,'' is nearest related to S. lasiantha, Benth. (no. 104 of the writer's Synopsis), but is distinguished by its narrow leaves, shorter pubescence throughout, larger calyx, and by the pubescence of the corolla, which in S. lasiantha is pilose and essentially glandless. FERNALD. — SOME NEW SPERMATOPHYTES. 501 S. LEUCANTHA, Cav., forma iobaphes. Calyx and corolla both deep violet. — MoRELOS, ou ledges of the Sierra de Tepoxtlan, alt. 2,310 m., Oct. U, 1900 (C. G. Pringk, no. 8402). S. (Macrostachyae) albicans. Shrub 3 to 5 m. high, the branches cinereous-piiberulent : leaves elliptic-ovate, acuminate, rounded or sub- cuneate at base, 4 or 5 cm. long, 2 to 2.5 cm. wide, rugulose, minutely canescent-puberulent, becoming glabrate ; the margin finely appressed- serrate ; petiole slender, cauescent, 1 cm. or less long : racemes 3 to 10 cm. long, the verticels about 10-flowered, mostly crowded, the lower becoming 1.5 cm. apart; bracts thick and firm, densely cinereous-tomen- tose, ovate, acuminate, 1 to 1.5 cm. long, semi-persistent, the earliest finally deciduous : calyx cuneate-campauulate, densely white tomentose, ill anthesis 8 mm. long, the short broad lobes slightly unequal, the longer upper one acute, the lower blunt: corolla 14 mm. long, canescent with- out ; the narrow galea and the tube whitish, the broad lip deep blue : style densely bearded. — Guerrero, limestone mountains above Iguala, alt. 1,230 m., Sept. 14, 1900 {C. G. Pnngle, no. 8430). Nearly related to S. Shannoni, Donnell Smith (no. 128 of the writer's Synopsis), but the smaller thinner leaves, not tomentose beneath, and the inflorescence more canescent. S. Sessei, Beuth. Mr. Pringle's nos. 7065 and 7080, from Cuerna- vaca, cited under S. puhescens, Benth., are not that species, but are better placed with ^S*. Sessei. Mr. Pringle's no. 8378 is also referable to the latter species. Monarda. Pringlei. Simple, about 1 m. high, the stem obtusely angled, minutely and sparingly puberulent above: leaves thin, lanceo- late, 7 to 9 cm. long, 1.5 to 2.5 cm. wide, subtruncate at base, the lower half rather coarsely appressed-serrate, the elongate-acuminate upper half entire, minutely puberulent on both faces, slightly paler beneath ; peti- ole slender, puberulent, 0.5 cm. long: the glomerule terminal, 12-15- flowered ; bracts like the foliage-leaves, but smaller and entire; bractlets filiform, often e of Class II. George H. Parker, ) James B. Ames, ^ William Everett, > of Class III. A. Lawrence Lowell, J Member of the Committee of Finance. Augustus Lowell. Rumford Committee. Erasmus D. Leavitt, Amos E. Dolbear, Edward C. Pickering, Arthur G. Webster, Charles R. Cross, Theodore W. Richards, Thomas C. Mendenhall. C. M. Warren Committee. Charles L. Jackson, Leonard P. Kinnicutt, Samuel Cabot, Arthur M. Comey, Henry B. Hill, Robert H. Richards, Henry P. Talbot. The following gentlemen were elected members of the Academ)'- : — Jay Backus Woodworth, of Cambridge, as Resident Fellow in Class II., Section 1 (Geology, Mineralogy, and Physics of the Globe.) Merritt Lyndon Fernald, of Cambridge, as Resident Fellow in Class II., Section 2 (Botany). William Ernest Castle, of Cambridge, as Resident Fellow in Class II., Section 3 (Zoology and Physiology). George Mercer Dawson, of Ottawa, as Associate Fellow in Class II., Section 1 (Geology, Mineralogy, and Physics of the Globe), in place of the late Sir John William Dawson. 532 PROCEEDINGS OF THE AMERICAN ACADEMY Melville Weston Fuller, of Washington, as Associate Fellow in Class III., Section 1 (Philosophy and Jurisprudence). Rufus Byam Richardson, of Atliens, as Associate Fellow in Class III., Section 2 (Philology and Archaeology). Tliomas Day Seymour, of New Haven, as Associate Fellow in Class III., Section 2. Henry Morse Stephens, of Ithaca, as Associate Fellow in Class HI., Section 3 (Political Economy and History). William Cawthorne Unwin, of London, as Foreign Honorary member in Class I., Section 4 (Technology and Engineering). Sir Archibald Geikie, of London, as Foreign Honorary Mem- ber in Class II., Section 1 (Geology, Mineralogy, and Physics of the Globe), in place of the late Carl Friedrich Rammelsberg. Sir John Murray, of Edinburgh, as Foreign Honorary Mem- ber in Class II., Section 1, in place of the late Alfred Louis Olivier Legrand Des Cloizeaux. Arthur G. Webster called attention to the bill before the House of Representatives for the establishment of a National Standardizing Bureau, and on his motion, it was Voted, That the Academ}^ approves this project. On the motion of W. M. Davis, it was Voted, That the committee appointed at the meeting of April 11, 1900, to consider the propriety of amending the finst chapter of the Statutes be instructed to correct certain clerical errors in the Statutes. Clarence J. Blake made some remarks on the scientific researches of his father, the late John H. Blake, which he intended to describe more full}^ in a forthcoming biographical notice. John Trowbridge described some results obtained with a storage battery of twenty thousand cells and exhibited the bat- tery in operation. Experiments on the passage of powerful discharges through minute orifices were described, and proofs of the oscillatory nature of sparks six feet long were given. Since these sparks closely represent tlie main features of lightning, it is probable that most lightning discharges are also oscillatory. Tlie battery with tlie aid of large condensers furnishes OF ARTS AND SCIENCES. 533 powerful quantity discharges which are more interesting from a scien- tific point of view than discharges of high electromotive force ; for a new field appears to be opened in spectrum analysis. Photographs of the spectra of gases can be obtained with one or two discharges with a nar- row slit. Perhaps the most interesting results obtained with the battery were from the methods of exciting the X-rays. Photographs of the usual subjects treated by these rays can be taken, and they exhibit great con- trasts ; moreover, there are traces of ligaments and muscles as well as bones. The members of the Academy visited the battery room and saw a hydrogen tube excited by the discharge from three hundred Leyden jars, and the lighting of an X-ray tube. The following papers were presented by title : — Paleontological Notes V. A New Fossil Crab from the Mio- cene Greensand Bed of Gay Head, Martha's Vineyard, with Remarks on the Phylogeny of the Genus Cancer. By Alpheus S. Packard. On the Thermal Diffiisivities of Different Kinds of Marble. By B. O. Peirce and R. W. Willson. Paleontological Notes VI. On Supposed Merostomatons and Other Paleozoic Arthropod Trails, with Notes on those of Limulus. By Alpheus S. Packard. On the Continuity of Groups generated by Infinitesimal Transformations. By S. E. Slocum. Presented by Henry Taber. On the Thermal and the Electrical Conductivity of Soft Iron. By Edwin H. Hall. An Apparatus for Recording Alternating Current Waves. By Frank A. Laws. The Dinitro Compounds of Paradibrombenzol. By C. Loring Jackson and D. F. Calhane. On Certain Derivatives of Orthobenzoquinoue. By C. Lor- ing Jackson and Waldemar Koch. Geometry on Ruled Quartic Surfaces. By F. B. Williams. Presented by W. E. Slory. On the Action of Sodic Sulphite on Tribromdinitrobenzol and Tribromtrinitrobenzol. By C. Loring Jackson and Richard B. Earle. 534 PROCEEDINGS OF THE AMERICAN ACADEMY Nine Iiunclred aud eighteentli meeting. June 13, 1900. — Adjourned Annual Meeting. A quorum was not present and the Academy was not called to order. Nine hundred and eigliteentli Meeting. October 10,1900. — Stated Meeting. The Corresponding Secretary in the chair. The following letter was read : — 843 Exchange Buildixg, Boston, September 5, 1900. Francis Blake, Esq., Treasurer of the American Academy of Arts and Sciences. Dear Sir, — By a letter enclosed in his will, my Father, Mr. Augustus Lowell, requested his sons to pay "to the American Academy of Arts and Sciences $10,000." It gives me great pleasure to enclose to you, in accordance with this request, a check for the amount named. Very truly yours, A. Lawrence Lowell. The Corresponding Secretary also read letters from W. E. Castle, M. L. Fernald, Jeremiah Smith, and J. B. Wood worth, accepting Fellowship ; from George M. Dawson, M. W. Fuller, T. D. Seymour, and H. M. Stephens, accepting Associate Fel- lowship; and from Sir Archibald Geikie, F. Kohlrausch, Sir John Murray, and W. C. Unwin, acknowledging election as Foreign Honorary Members. Announcement was received of the death of D. T. Day, formerly President of the Buffalo Society of Natural Sciences. The following deatlis were announced : — Augustus Lowell, Vice-President for Class III. ; John Elbridge Hudson, of Class TIL, Section 1., Sylvester R. Koehler, of Class IIL, Section 4, Resident Fellows ; James Edward Keeler, of Class I., Section 1, Jacob Mandes DaCosta, and Alfred Stills, of Class II., Section 4, William Mitchell, of Class III., Section 1, Associate Fellows; Willy Kiihne, of Class II., Section 4, Charles Russell, Baron Russell of Killowen, and Henry Sidg- wick, of Class III., Section 1, Foreign Honorary Members. OF ARTS AND SCIENCES. 535 The Chair appointed the following standing committees : — Committee of Publication. Samuel H. Scuddee, Seth C. Chandler, Ckawford H. Toy. Committee on the Library. A. Lawrence Rotch, Henry W. Haynes, Samuel Henshaw. Auditing Committee. Henry G. Denny, William L. Richardson. The Chair appointed from the next retiring Councillors Theodore W. Richards, of Class I, William T. Councilman, of Class II., James B. Ames, of Class III., a committee to nominate candidates for the ofiQces made vacant by the death of Augustus Lowell. Thomas Messenger Drown, of South Bethlehem, was elected an Associate Fellow in Class I., Section 3 (Chemistr}^). J. H. Wright gave an account of " Recent Excavations in Crete," by Miss Helen S. Boyd, of the American School at Athens. Barrett Wendell read an essay on the " Literary History of America." W. M. Davis presented some " Geographical Notes on Brit- tany and Devonshii-e." The following paper was presented by title by W. C. Sabine: — False spectra from the Rowland Concave Grating. By Theo- dore Lyman. Nine hundred and nineteenth Meeting. November 14, 1900. The Corresponding Secretary in the chair. The Corresponding Secretary read a letter from the Ameri- can Chemical Society transmitting resolutions relative to the establishment of a National Standards Bureau in connection 536 PROCEEDINGS OF THE AMERICAN ACADEMY with the United States Office of Standard Weiohts and Meas- ures and requesting cooperation in its efforts to secure the establishment of such bureau. On the motion of Arthur G. Webster, it was Voted, That this matter be referred to a committee to be appointed by the Chair. The committee was constituted as follows : — James M. Crafts, Chairman, Arthur G. Webster, Theodore W. Richards, Edwin H. Hall. On the motion of Barrett Wendell, the following resolution was adopted : — Whereas, The Academy has received the sum of ten thou- sand dollars paid by tlie sons of the late Augustus Lowell at the request of tlieir father, therefore be it Resolved, That the Academy accepts this gift with grateful appreciation of the generosity of its late honored Vice-Presi- dent, and that the Corresponding Secretary notify this action to Mr. Lowell's sons. The following papers were presented by title : — On the Composition of California Petroleum. By Charles F. Mabery and Edward J. Hudson. On the Chlorine Derivatives of the Hydrocarbons in Cali- fornia Petroleum. By Charles F. Mabery and Otto J. Sieplein. On the Composition of Japanese Petroleum. By Charles F. Mabery and Shinichi Takano. James Ford Rhodes read an account of " Sherman's March to the Sea," of which the following is an abstract : — After the capture of Atlanta, the question in Sherman's mind was how he should still further proceed on the offensive. Hood gave him trouble by severing his communications, but he could not be brought to a battle, nor could he be caught in a pursuit. Sherman resolved to leave Ten- nessee in the care of Thomas and march through Georgia to the sea. He severed his communications with the North, November 12, 1864, and from that day to December 14 no direct intelligence from him OF ARTS AND SCIENCES. 537 reached the North. There was little fighting, but the suf)ply of 62,000 troops in the enemy's country called for foresight and system on the part of the general ; to prevent the host from degenerating into a law- less mob required the enforcement of discipline l)y the general and his' officers. The army foraged liberally on the country in an orderly man- ner. While there were some abuses, some wanton destruction of prop- erty, and some pillage, there were no cases of murder or rape. On the whole the army behaved as well as could have been expected. Sher- man estimated the damage done to the State of Georgia at $100,000,000. On the night of December 20, 1864, the Confederates evacuated Savan- nah, Sherman took possession of the city, and sent his celebrated Christ- mas-gift despatch to President Lincoln. H. Helm Clayton read a paper entitled: "The Eclipse C}-- clone and the Diurnal C3'clone : Results of Meteorological Observations during the Solar Eclipse of May 28, 1900." Nine hundred and twentieth Meeting. December 12, 1900. The Academy met at the house of William W. Jacques. The President in the chair. The death of Thomas Gaffield, Resident Fellow in Chiss I., Section 3, was announced. On the motion of the Corresponding Secretary, it was Voted, That a committee be appointed to make revision of certain passages in the Statutes and report thereon to the Academy. This committee was constituted as follows: — The President, The Corresponding Secretary, C. Loring Jackson. Wallace C. Sabine spoke on "The Influence of Architecture on Melody and the Development of the Musical Scale." John E. Wolff described the celebration of the two-hundredth anniversary of the foundation of the Royal Academy of Sciences, at Berlin, on the 19th and 20th of March last, which John W. White and himself attended as delegates from the American Academy. 538 PROCEEDINGS OP THE AMERICAN ACADEMY William Everett gave an account of the life and works of the late Henry Sidgwick, referring particularly to his eminent abilitj^ and estimable character. The following paper was read by title : — "Symmetrical Triiodbenzol." By C. Loring Jackson and G. E. Behr. Nine Iiundred. and twenty-first Meeting. January 9, 1901. — Stated Meeting. ViGE-PnESiDENT Hyatt in the chair. On the motion of C. L. Jackson, it was Voted, To defer action on the proposed amendments of the Statutes. looted, That the Academy send a message of congratulation to Vladimir Markovnikoff, of Moscow, on the occasion of the 40th anniversary of his work on chemistry. The vacancies occasioned by the death of Augustus Lowell were filled by the election of James B. Thayer, Vice-President for Class III. Eliot C. Clauke, 3Iember of the Cornmittee of Finance. Denman W. Ross read a paper entitled, " Design as a Science." S. C. Chandler gave an account of his "New Discovery con- cerninsf the Motion of the Earth's Pole." The following papers were presented by title : — " Suggestion concerning the Nomenclature of Heat Capacity." By T. W. Richards. " A Study of Growing Crystals by Instantaneous Photomicro- graphy." By T. W. Richards and E. H. Archibald. Nine hundred and twenty-second Meeting. February 13, 1901. The Corresponding Secretary in the chair. The Chair announced the death of Charles Hermite, Foreisfu Honorary Member in Class I., Section 1. An invitation to the Ninth Jubilee Celebration of the Uni- versity of Glasgow was read. On the motion of the Recording Secretary, it was OP ARTS AND SCIENCES. 539 Voted, That the Academy send delegates to this celebration. A circular inviting attendance at the Fifth International Congress of Phj^siologists was read ; also, a letter from James B. Thayer, acknowledging his election as Vice-President for Class III. The following paper was read by title : — " A Study of Variation in the Fiddler Crab (Gelasimus pugi- lator Latr.) " By Robert M.Yerkes. A Contribution from the Zoological Laboratory of the Museum of Comparative Zoology at Harvard College. Presented by E. L. Mark. Nine hundred and twenty-third Meeting. March 13, 1901. — Stated Meeting. Vice-President Hyatt in the chair. The following deaths were announced : — Charles Carroll Everett, Resident Fellow in Class III., Sec- tion 1. George Mercer Dawson, Associate Fellow in Class II., Sec- tion 1. The following gentlemen were elected members of the Academy : — Alexander Wilmer Duff, of Worcester, as Resident Fellow in Class I., Section 2 (Physics). Theodore Lyman, of Brookline, as Resident Fellow in Class I., Section 2. Lewis Jerome Johnson, of Cambridge, as Resident Fellow in Class I., Section 4 (Technology and Engineering). Henry Lloyd Smyth, of Cambridge, as Resident Fellow in Class I., Section 4. Frank Shipley Collins, of Maiden, as Resident Fellow in Class II., Section 2 (Botany). Ephraim Emerton, of Cambridge, as Resident Fellow in Class III., Section 3 (Political Economy and History). Frank William Taussig, of Cambridge, as Resident Fellow in Class III., Section 3. Eliakim Hastings Moore, of Chicago, as Associate Fellow in Class I., Section 1 (Mathematics and Astronomy). 540 PROCEEDINGS OF THE AMERICAN ACADEMY George Elleiy Hale, of Williams Bay, as Associate Fellow in Class I., Section 2 (Physics). Edward Leamington Nichols, of Ithaca, as Associate Fellow in Class I., Section 2, in place of the late William Augustus Rogers. Cyrus Guernsey Pringle, of Charlotte, Vermont, as Associate Fellow in Class II., Section 2 (Botany), in place of the late George Clinton Swallow. Franklin Paine Mall, of Baltimore, as Associate Fellow in Class II., Section 3 (Zoology and Physiology), in place of the late Alfred Stille. Henry Fairfield Osborn, of New York, as Associate Fellow in Class II., Section 3, in place of the late Otimiel Charles Marsh. Charles Otis Whitman, of Chicago, as Associate Fellow in Class II., Section 3. William Stewart Halsted, of Baltimore, as Associate Fellow in Class II., Section 4 (Medicine and Surgery), in place of the late William Alexander Hammond, William Williams Keen, of Philadelphia, as Associate Fellow in Class II., Section 4, in place of the late Jacob Maudes Da- Costa. Jules Henri Poincare, of Paris, as Foreign Honorary Member in Class I., Section 1 (Mathematics and Astronomy), in place of the late Francesco Brioschi. Heinrich Miiller-Breslau, of Berlin, as Foreign Honorary Member in Class I., Section 4 (Technology and Engineering), Hugo Kronecker, of Bern, as Foreign Honorary Member in Class II., Section 3 (Zoology and Physiology), in place of the late Willy Kiihne. Sir Thomas Lauder Brunton, of London, as Foreign Honorary Member in Class II., Section 4 (Medicine and Surgery), in place of the late Sir James Paget, Bart. Robert Koch, of Berlin, as Foreign Honorary Member in Class TL, Section 4, in place of the late Louis Pasteur. Albert Venn Dicey, of Oxford, as Foreign Honorary Member in Class IH,, Section 1 (Philosophy and Jurisprudence), William Edward Hearn, of Melbourne, as Foreign Honorary OP ARTS AND SCIENCES. 541 Member in Class III., Section 1, in place of the late Charles Russell, Baron Russell of Killowen. Henry Jackson, of Cambridge, as Foreign Honorary Member in Class HI., Section 2 (Philology and Archaeology), in place of the late Henry Sidgwick. Edmondo de Amicis, of Florence, as Foreign Honorary Mem- ber in Class HI., Section 4 (Literature and the Fine Arts), in place of the late John Ruskin. On the motion of the Corresponding Secretary, it was Voted, To meet, on adjournment, on the 10th of April next. B. L. Robinson gave an account of " Recent Advances in the General Classification of the Flowering Plants." R. T. Jackson spoke on " Resorption as a Factor in Growth." The following papers were presented by title : — The Occlusion of Magnesic Oxalate by Calcic Oxalate, and the Solubility of Calcic Oxalate. By Theodore W. Richards, Charles F. McCaffrey, and Harold Bisbee. Contributions from the Cryptogamic Laborator}^ of Harvard University, XLVI. Preliminary Diagnoses of New Species of Laboulbeniaceae, IH. By Roland Thaxter. The Development and Function of Reissner's Fibre and its Cellular Connections. By Porter E. Sargent. Presented by E. L. Mark. The Solubility of Manganous Sulphate. By Theodore W. Richards and F. R. Fraprie. Contributions from the Gray Herbarium of Harvard Uni- versity. New Series, No. XX. I. Synopsis of the genus Melampodium. II. Synopsis of the genus Nocca. HI. New Species and Newly Noted Synonymy among the Spermato- phytes of Mexico and Central America. By B. L. Robinson. Contributions from the Gray Herbarium of Harvard Univer- sity. New Series, No, XXI. By M. L. Fernald. Some New Sperraatophytes from Mexico and Central America. 542 PROCEEDINGS OF THE AMERICAN ACADEMY Nine hundred and twenty-fourth Meeting. April 10, 1901. — Adjourned Stated Meeting. Vice-President Trowbridge in the chair. The Corresponding Secretary read letters from L. J. Jolinson, Theodore Lyman, H. L. Smyth, and F. W. Taussig, accepting Fellowship ; and from W. S. Halsted, W. W. Keen, Franklin P. Mall, E. H. Moore, Edw. L. Nichols, and Henry F. Osborn, acknowledging election as Associate Fellows. The chair announced the following deaths: — Edward Elbridge Salisbury, of New Haven, Associate Fellow in Class III., Section 2. Jacob Georg Agardh, of Lund, Foreign Honorary Member in Class n., Section 2. On the recommendation of the Rumford Committee, presented by A. G. Webster, it was Voted, To appropriate from the income of the Rumford Fund the sura of five hundred dollars (t|500) to T. W. Richards in aid of a research on the Joule-Thomson experiment on free expansion. Edwin H. Hall presented " An Exposition of the Theory of Electrons, the Electrical Fragments of Atoms." The following paper was presented by title : — The Law of Physico-chemical Change. By Gilbert Newton Lewis. Presented by T. W. Richards. Dr. W. G. Farlow was appointed Delegate of the Academy to tlie celebration of the ninth jubilee of the foundation of the University of Glasgow and was charged with the presentation of the address on the following page, signed by the Vice-President of Class HL and the Corresponding Secretary. OF ARTS AND SCIENCES. 543 ViRO Illustrissimo Cancellario Curiae Senatuique Universitatis Glasguensis AcADEMiA Artiuji et Scientiarum Americana Quae est Bostoniae Nov.-Anglorum. S. P. D. Vix dici potest quanto guadio audiverimus vos in mente habere istam diem celebrare qua Universitas vestra annum quadringentesimum exple- verit, ex quo Pontifex ille benevolus nomen ac jura Universitatis con- cesserit; quis enim ignorat longam illam annorum seriem orbi terrarum perpetuis illuxisse virorum operibus, in omui arte atque in omni scientia praestantissimorum, nomen semper illustre Caledoniae vel ad majus fasti- gium efferentibus ? Quorum ut neque tempus neque charta sufRceret nominibus tantum percurrendis, nostro officio satisfiat si gratias praecipuas ageutes quod ad sollemnia celebranda amicissime invitastis socium nostrum virum ornatissi- mum Gulielmum Gilson Farlow legaverimus qui istis caeremoniis inter- futurus nostram erga vos benevolentiam pro virili parte libentissime praestabit. Ilium ergo, viri illustrissimi, prccamur ut benigne excipiatis ut qui amicitiae vincula inter Scotiam Americamque arctiora dignissime b'gave- rit. Dabamus Bostoniae Nov.-Anglorum A. D. Non : Maias anno sal- utis MCMI, atque Rerumpublicarum Foederatarum libertatis vindicatae cxxv. 544 PROCEEDINGS OF THE AMERICAN ACADEMY A TABLE OF ATOiVlIC WEIGHTS OF Seventy-seven Elements. Compiled in April, 1901,_//o?« the most Recent Data. By Theodore William Richards. Name. Symbol. Atomic AVeiglit. Name. Symbol. Atomic Weight. Aluminium . . Al 27.1 Molybdenum . . Mo 96.0 Antimony . Sb 120.0 Neodymium . . Nd 143.6 Argon . . A 39.92 Neon .... Ne 19.94 Arsenic . . As 75.0 Nickel .... Ni 58.70 Barium . . , Ba 137.48 Niobium . . . Nb = Cb 94. Beryllium . Be = Gl 9.1 Nitrogen . . . N 14.04 Bismuth Bi 208. Osmium . . . Os 190.8 Boron . . B 11.0 Oxygen (standard) 0 16.000 Bromine . Br 79.955 Palladium . . . Pd 106.5 Cadmium . Cd 112.3 Phosphorus . . P 31.0 Caesium Cs 132.9 Platinum . . . Pt 195.2 Calcium Ca 40.1 Potassium . . . K .39.14 Carbon . . C 12.001 Praseodymium . Pr 140.5 Cerium . . Ce 140. Rhodium . . . Rh 103.0 Chlorine . CI 35.455 Rubidium . . . Rb 85.44 Chromium Cr 52.14 Ruthenium . . Ru 101.7 Cobalt . . Co 59.00 Samarium ? . . Sm 150. Columbium Cb = Nb 94. Scandium . . . Sc 44. Copper . . Cu 63.604 Selenium . . . Se 79.2 " Didymium " Nd + Pr 142± Silicon .... Si 28.4 Erbium. . Er 166. Silver .... Ag 107.93 Fluorine . F 19.05 Sodium .... Na 23.05 Gadolinium Gd 156. 1 Strontium . . . Sr 87.68 Gallium Ga 70.0 Sulphur . . . S 32.065 Germanium Ge 72.5 Tantalum . . . Ta 183. Glucinum . Gl=Be 9.1 Tellurium . . . Te 127.5 ? Gold . . . Au 197.3 Terbium ? . . . Tb 160. Helium . . He 3.96 Thallium . . . Tl 204.15 Hydrogen . H 1.0075 Thorium . . . Th 233. Indium . . In 114. Thulium ? . . . Tu 171.? Iodine . . . I 126.85 Tin Sn 119.0 Iridium . . Ir 193.0 Titanium . . . Ti 48.17 Iron . . . Fe 55.9 Tungsten . . . W 184. Krypton Kr 81.7 Uranium . . . U 238.5 Lanthanum La 138.5 Vanadium . . . V 51.4 Lead . . Pb 206.92 Xenon .... X 128. Lithium Li 7.03 Ytterbium . . . Yb 173. Magnesium Mg 24.36 Yttrium . . . Yt 89.0 Manganese Mn 55.02 Zinc Zn 65.40 Mercury . Hg 200.0 Zirconium . . . Zr 90.6 OP ARTS AND SCIENCES. 545 NOTE COXCERXIXG THE TABLE OF ATOMIC WEIGHTS. Three new elements are included in the table, namely, Neon, Krypton, and Xenon, discovered by Ramsay in the atmosphere. Their molecular weights cannot be considered as wholly settled, but approximate values are given in the list. There is a possibility that each of these values, as well as those given for Argon and Helium, should be halved in order to obtain the atomic weights ; but for the present it seems safest to assume a monatomic molecule in each case. Radium, the singular substance discovered by Madame Curie, is not included on account of the great uncertainty concerning its atomic weight. It is possible that some of the work upon thorium and uranium is vitiated by radium, and that the presence of this impui-ity may account for the inconsistencies of the data. The value given for uranium depends primarily on recent work by Richards and Merigold, as yet unpublished; but the matter cannot be considered as settled. Attention is called to the low atomic weight of iron,* which was included without comment last year. Investigation upon this important constant is still in progress. * Richards and Baxter, These Proceedings, 35, 253. (1900.) VOL. XX XVI. — 85 AMERICAN ACADEMY OF ARTS AND SCIENCES. Report of the Council. — Presented Mat 8, 1901. BIOGRAPHICAL NOTICES. Charles Carroll Everett Ephraim Emerton. Xathaniel Holmes Jeremiah Smith. Silas Wiiitcomb Holman Charles R. Cross. Sylvester R. Koehler Charles G. Lorixg. John Elbridge Hudson James B. Thayer. John Harrison Blake Clarence John Blake. Charles Franklin Dunbar .... Frank William Taussig. REPORT OF THE COUNCIL. The Academy has lost twenty-one members by death since the annual meeting of May 9, 1900, as follows : Six Resi- dent Fellows, — Thomas Gaffield, C. C. Everett, N. Holmes, J. E. Hudson, A. Lowell, and S. R. Koehler ; Seven Associate Fellows, — J. E. Keeler, H. A. Rowland, G. M. Dawson, J. M. DaCosta, A. Stills, Wm. Mitchell, and E. E. Salisbury ; Seven Foreign Honorary Members, — C. Hermite, J. G. Agardh, W. Kiihne, Baron Russell of Killowen, H. Sidgwick, M. MUller, Due de Broglie, and the Bishop of Oxford. CHARLES CARROLL EVERETT. Charles Carroll Everett, D.D., LL.D., Bussey Professor of Theology and Dean of the Faculty of Divinity in Harvard University, died at Cambridge, October 16, 1900, in the seventy-second year of his age. Dr, Everett was, through his ancestry on both sides, identified with the community in and about Boston. His father's family bad long been settled in Dorchester, and that of his mother in Beverly. His father, a graduate of Harvard College in 1806, removed to Brunswick, Marine, soon after his marriage, and entered there upon the practice of the law, which he carried on with distinction throughout his life. Dr. Everett was graduated from Bowdoin College in 1850, and seems to have been drawn first to the study of medicine. He was entered during four years as a student of the Bowdoin Medical Colleee, and studied also with a neighboring practitioner, as was the custom of the time. His literary tastes, however, as well as his somewhat delicate health, led him in the years 1851 and 1852 to spend some time in Europe, cliiefly in the study of modern languages and literature, and on his return, wliile still regis- tered in the ]\Icdical School, he was appointed to be Instructor in Mod- ern Languages at Bowdoin. All accounts agree that his service in this 550 CHARLES CARROLL EVERETT. capacity was admirable and duly appreciated, but Bowdoin was at the time going through a financial crisis, which caused its governing board to be more than ordinarily anxious as to a strict interpretation of their trusts. A large endowment had recently been secured upon distinct declarations that Bowdoin was " of the Orthodox Conaresational denom- ination." Dr. Everett had been brought up in the orthodox faith of his mother, but his father was already known as an avowed Unitarian, and his own views were inclining more and more in that direction. On this ground his appointment as Professor, twice made by the Trustees, was rejected by the Overseers, and thus his bent towards theological study definitely determined. He entered the Harvard Divinity School, was graduated there in 18o9, and at once entered upon his first and only pastorate at Bangor, Maine. Ten years later, in 18G9, he was called to be a professor at Cambridge, and in 1878 was made Dean of the Faculty of Divinity. On the 14th of February, 1871, he was elected a Fellow of the American Academy. These are the brief outlines of a life singularly filled with varied activities, yet passed within the narrow limits of a remote parish and an academic position. As a pastor. Dr. Everett left upon his parish- ioners an equal impression as preacher and as man. His first passion was scholarship, but his was a scholarship that did not cut off its votary from human sympathy. His preaching, cast always in philosophic form, was yet in a high degree " practical." It addressed itself to the highest instincts, and sought to direct these by a principle of reason. In the trying times of the Civil War his voice gave no uncertain sound, and he was sought by his fellow-citizens as their orator on many an occasion of civic discussion or commemoration. The removal to Cambridge gave to Dr. Everett full scope for the literary and speculative tastes which had been developing in Bangor. The "Science of Thought," first published in 1869, was his introduction to the world of technical scholarship. It was a fresh and individual attempt to present, on the lines of the new Hegelian thought, the funda- mental processes of the human reason. It attracted wide attention, and became for many their first inspiration to clear and rational thinking. At Cambridge, Dr. Everett's activity was largely absorbed in his regular duties of teaching and administration. His instruction took naturally the form suggested by the nature of his mind. Never, probably, was there any teaching of theology less conventional or, in the narrow sense, less "academic" than his. Theology was to him not a system fixed in forms that could be handed on from master to pupil ; it was the inter- CHARLES CARROLL EVERETT. 551 pretation, on broad philosophic principles, of that which Christianity has to contribute to the solution i)f the universal religious problem. Chris- tianity could be accepted only as it commended itself to the fundamental needs of the human soul. First, then, it must be shown what these needs are, and this Dr. Everett undertook to do in his introductory lec- tures on the Psychological Basis of Religious Faith. Upon this basis he then developed his presentation of Christian ideas as rationally cor- responding to a universal and fundamental demand. These lectures were his real life-work. They furnished the intellectual nucleus about which he gathered the results of his ever ripening thouglit and his ever wider readincr. It is they that have given him his peculiar hold upon a full gen- eration of students, and it is they that will form, if their substance can be restored from the scattered material available, the most complete recoi'd of his intellectual life. Dr. Everett was not a voluminous writer. His best work was done in response to some outward occasion which roused him to formulate his thought upon some given problem. Probably the book most likely to be remembered outside of strictly academic circles is the volume of essays on Poetry, Comedy, and Duty, published in 1891, in which his profound reflection, his wide learning, and his playful fancy found equal scope. His " Gospel of Paul," in 1893, was an altogether original treat- ment of the Pauline theology, and was, perhaps, the work of his later years which appealed most strongly to himself. Plis contributions to the " New World." of which he was one of the responsible editors, were numerous and important. In losing him the University and the world of scholarship have lost a unique figure, an interpreter of truth in a transition age, a guide to all those who were seeking light in the confusion of faiths and in the temptations of doubt. His value as a scholar is to be measured only by his singular quality as a man. After all it was his personality that impressed, and charmed, and made the way clear for the truth he had to convey. He satisfied the inquirer, not by the cheap method of com- promise, but by a subtle gift of leading men away from the unessentials to the realities of faith. His mind had that element of greatness which consists in the ability to see tlirough the mists of the unimportant and the transient down to the permanent and the essential in the religious life, and not only to see this but to make it clear to others. One of his greatest aids in exposition was his ever-present sense of humor. If, as he has taught us, the essence of the comic is to be found in the sense of incongruity, it should follow that the truly humorous mind is keen also 552 NATHANIKL HOLMES. to discern the congruities of things. In the midst of the most serious development of an idea, it was often a flash of wit that lit up the obscure point so that it remained clear forever. Quite in harmony with his wide human interest was also his love of outward Nature, and the use he made of it in his writing. All experience contributed with him to the interpretation of that religious instinct which in turn gave to experience its meaning and its purpose. Ephraim Emerton. NATHANIEL HOLMES. Nathaniel Holmes was born at Peterborough, N. H., July 2, 1814. His paternal gi'andfather was an emigrant from Antrim County, Ireland ; afterwards a soldier in the Revolution and a Deacon in the Presbyterian Church. His mother was a daughter of a Presbyterian clergyman, Rev. David Annan, a native of Fifeshire, Scotland. As a boy he worked in a machine shop and on his father's farm. From 1831 to 1833 he was a student in Phillips-Exeter Academy ; and he graduated at Harvard in 1837. After spending a year in Maryland as a private tutor, he studied law at the Harvard Law School and in the office of Henry H, Fuller, Esq., in Boston. In 1839 he began practice at St. Louis, Mo. In 18G5 he was appointed one of the Judges of the Supreme Court of Missouri, serving until 1868. His judicial opinions are contained in Volumes 36 to 42 (inclusive) of the INIissouri Reports. In 1868 he gave up his position on the bench to accept the Royall Professorship of Law in the Harvard Law School. In 1872 he resigned the professorship and re- turned to the practice of law in St. Louis, where he remained eleven years. In 1883 he returned to Cambridge, and made his home there until his death, on February 26, 1901. Outside the legal profession, Judge Holmes is best known by his book entitled " The Authorship of Shakespeare," a work designed to prove that the plays attributed to Shakespeare were written by Bacon. This book was first published in 1866, and went through three editions. One of the ablest opponents of the view taken by Judge Holmes has recently said of the latter's book: " This contains the fullest and strongest presentation of the argument in favor of Bacon's authorship which has yet appeared, and it is also marked for its fairness and candor." (Notes on the Bacon-Shakespeare Question, by Hon. Charles Allen, pp. 1 and 2.) Judge Holmes also published, after his return to Cambridge, a work SILAS WHITCOMB HOLMAN. 553 in two volumes, " Realistic Idealism in Philosophy Itself," and another work entitled ''Philosophy of the Universe." In 1889 he delivered the address at the loOth anniversary of the settlement of Peterborough. The life of Judge Holmes in Cambridge for the last eighteen years was a very retired one, but it was neither solitary nor unhapi^y. He was a bachelor, but always had some relatives in his household, and never failed to find adequate companionship in his books. A great reader on a great variety of subjects, with a tenacious memory, lie was full of knowledge of all sorts, and was a very interesting talker. Judge Holmes was a man of great candor and of remarkable equanimity. He had had successes and disappointments, but he was neither unduly elated by the one nor depressed by the other. Judge Holmes was elected Fellow of the Academy May 24, 1870. Having removed from the State, he was elected Associate Fellow May 30, 1876. Having returned to Cambridge, his name was restored to the list of Resident Fellows November 30, 1889. Jeremiah Smith. SILAS WHITCOMB HOLMAN. Silas Whitcomb Holman was born at Harvard, Massachusetts, January 20, 1856, and graduated from the Massachusetts Institute of Technology in 1876, having made a specialty of the study of physics throughout his course. He was thereupon appointed to a position as assistant in the physical laboratory of that institution, but on account of illness did not enter upon his duties until a year later. Continuing in the service of the Institute, he was promoted to more advanced positions, and was made Professor of Physics in 1893. Even at this date his health, never firm, had become much impaired, and a few years later it became necessary for him to relinquish active work. In 1897 he was made Emeritus Professor of Physics. He died April 1, 1900. Professor Holman was elected to membership in this Academy March 14, 1883. His original contributions to science were of high merit, and give evidence both of great skill in manipulation and of remarkably clear insight into the choice of methods for conducting a difficult investigation. The most important of his researches are those upon the viscosity of air and carbonic acid as affected by temperature, which were published in the Proceedings of this Academy in 1870 and 1885 ; the first of which was based upon his graduating thesis at the Institute of Technology. These contain by far the most complete study of this difficult subject which 554 SILAS WHITCOMB HOLMAN. had been made up to their date, and the results are still of standard value. Indeed within tlie |)ast few years they have played an important part in the advancement of the kinetic theory of gases. In tlie Proceedings for 1888 is found a further noteworthy paper written in conjunction with one of his pupils, upon the determination of fixed reference points for thermometric measurements at high tempera- tures, in which several such points are established. A number of years later, in 1895, appeared another groi>p of papers, the last published by him, relating to the thermo-electric measurement of high temperatui'es, and a single paper upon calorimetry, which subjects had occupied much of his attention for some time previously. Of these, the one entitled " Thermo-electric Interpolation Formulse " is particularly valuable for its critique of the various methods of interpolation which have been employed in dealing with the results of high temperature observa- tions, and that upon the "Melting Points of Aluminium, Silver, Gold, Copper, and Platinum," published in colhiboration with his pupils, Law- rence and Barr, contains wliat are undoubtedly the best measurements of the points of fusion of these metals that had been obtained at the time of their publication. A third paper contains a description of a novel method of calibrating the Le Chatelier thermo-electric pyrometer, and the fourth a new method of applying the cooling correction in measurements of the heat of combustion. The papers of Professor Hoi man thus far referred to have all been published in the Proceedings of this Academy. Several others of minor importance have appeared in different scientific journals. An extended critique upon thermometry of precision presented at the Boston meeting of the American Association of the Advancement of Science in 1880 unfortunately was never printed. Besides his published researches, Professor Holman was the author of several valuable scientific works. The two volumes of " Physical Labora- tory Notes," prepared for the use of his pupils in the Massachusetts Institute of Technology, embody the results of many years of successful experience in teaching and form an important contribution to the litera- ture of that subject. They contain much original matter and exhibit a rare discrimination in the selection and comparison of the methods of measurement which are discussed. This is particularly the case with the volume relating to electrical measurement and testing. In 1892 he published a treatise upon " The Discussion of the Precision of Measurements," the basis of which consisted of the notes of lectures given to his classes. This volume, which is quite unique in its contents, SILAS WHITCOMB HOLMAN. 655 contains in convenient form a very compendious and lucid consideration of the application of the principles of least squares to the theory of obser- vations, the calculation of their precision and the choice of proportions in designing physical apparatus to be used for measurement. Its value as a text-book has been verv great. The collection of four and five place logarithmic tables prepared in 1896 embodies several features of marked originality, and is prefaced by a brief but exceedingly useful discussion of the fundamental principles of computation which contains many useful suggestions for the economizing of labor. The last work written by Professor Holman, entitled " Matter, Energy, Force, and Work," appeared in 1898, and is of a character widely differ- ent from any of those which preceded it. It is a philosophical study of the fundamental concepts of modern physics in which the subject is approached from the point of view that matter and energy rather than matter and force are the primary entities with which physics has to deal, and that matter itself may be dependent upon energy for its own existence. While not technical in its character, and intended especially for the help of teachers not wholly familiar with modern views, it is distingui.slied throuo'liout by great clearness, and is a remarkable presentation of the newer modes of viewing the subjects which it considers. Valuable as are his scientific publications, however, Professor Holman 's great work was that of a teacher of young men in the laboratory. From the beginning of his service as an assistant in the Rogers Laboratory of Physics, his influence was marked, and by his patient labors, extending through years, he brought the work which was under his charge to a high state of development. He possessed great skill in the planning of apparatus and methods, and rare judgment as to the processes best suited either for purposes of instruction or for the securing of accurate scientific results. To the development of the Laboratory of Electrical Measurements in the Massachusetts Institute of Technology, he gave for years his best endeavors, and to him is due the success of its work. He was also placed in charge of the newly-instituted Laboratory of Heat Measurements, and though prevented by failing health from developing this as he would have chosen, he laid a solid foundation for those coming after him. Professor Holman was born a teacher, and never grew weary in his profession. His personal relations with his pupils were very intimate. By that example which is better than the wisest |)recept, he impressed upon them the pre-eminent necessity of thoroughness, accuracy, and 556 SYLVESTER R, KOEHLER. honesty in all work which they might be called upon to perform either as students or in professional life. He is remembered by them with the most affectionate regard. Reference has already been made to the interference of ill-health with the prosecution of the labors of Professor Holman. In fact, after reach- ing manhood he was never in good health, and during almost the whole of his active life as a teacher he struggled with a painful chronic disease, which gradually, though with some intermissions, sapped his strength. His cheerful disposition and persistence in carrying on his work were such tliat none but those who knew him well were aware of the fact that it was only his indomitable courage which prevented him from yielding to his malady for some years before it finally overcame him. In the spring of 1890 he was obliged to discontinue work for a time. He spent the following year abroad, and came home much improved in healtli, but the relief was only temporary. In 1895 he finally gave up his work of instruction. For some years after this, however, though confined to his chair, and at last even deprived of sight, he continued to labor diligently, and published the tables of logarithms and the work on Matter and Energy mentioned above. His mind was clear to the last, and his cheerfulness never forsook him. His latest years were his best ones, and his whole life was a fine illustration of the manner in which a noble spirit may rise superior to circumstances and produce the best results under conditions to which an ordinary mind would utterly succumb. Chas. R. Cross. SYLVESTER R. KOEHLER. Sylvester R. Koehler was born in Leipsic in 1837. He came to America at the age of twelve years. Son of an artist, grandson of a miusician, he was destined by inheritance to an artistic career. Its bent was determined by his moving to Boston in 1868 and entering the estab- lishment of L. Prang & Co. as technical manager. This position, after ten years, was given up, that he might devote himself exclusively to his art studies. With Charles C. Perkins and William C. Prime as asso- ciate editors, he launched the " Art Review," the most dignified and scholarly periodical devoted to art that has been published in the United States. It was aimed, to quote the preface, " to dwell upon the larger, more robust, more serious features of modern art," but it was in advance of its time, — the circle to which it appealed was small, and when after SILVESTER R. KOEHLER. 557 two years its publication ceased, its projector modestly claimed that it had " quickened somewhat the forces at work iu the healthy development of art in the United States." Contributions without number flowed from his pen to magazines and journals iu America, to the " Zeitschrift ftir bildende Kunst" and other periodicals in Germany, and to a few of the London publications. For a while he held the appointment of Curator of the Section of Graphic Arts in the United States National Museum at Washington. When, in 1888, the Trustees of the Museum of Fine Arts, Boston, found themselves under the necessity of appointing a Curator of the Department of Prints, Koehler was the expert to whom they turned without hesitation. His appointment to this curatorship gave him the position for which his previous career had fitted him. To the years passed in the Prang establishment he owed a mastery of every detail of the technical processes used in the Graphic Arts. This technical knowl- edge was supplemented by an artistic temperament, which showed itself also in his fondness for music, in his love of verse, and his skill, though a moderate one, with the pencil. Years of study, too, had given him an intimate acquaintance with the history of his art, and confirmed his judgment. He was an admirable critic of work, both creative and tech- nical. These were rare qualifications for the post offered. In it he not only became the ultimate authority in the land of his adoption, but his knowledge and judgment were held in great esteem in the art centres of Europe. A man of strong individuality, of critical mind, interested in all prob- lems of life and religion, a bold thinker on questions of social reform, a sharp critic of pul)lic abuses, bitterly conscious of the injustices of the world as compared with the ideal life he pictured iu verse, he was a radical in his views of bettering human institutions. Yet he was a sym- pathetic friend, sociable, of quaint humor, and in the conduct of his department distinguished for unfailing, unwearied courtesy to all seekers for information. At the Museum his career was one of ceaseless activity. Numerous exhibitions were held, the catalogues of which offered the opportunity to impart his knowledge in the introductions and in the copious notes, descriptive, explanatory, and critical, of the etched work of Rembrandt, of Albert Diirer, of Blake, Mcryon, Seymour-Haden, the Cheneys, and on various other occasions. Notable amonc; these was that for an exhibi- tion in 1892, "Illustrating the Technical Methods of the Reproductive Arts from thei XV. Century," " with special reference to the photo- 558 JOHN ELBRIDGE HUDSON. mechanical processes," for which there was a steady demand from museums and collectors in Europe lung after the edition was exhausted. His most important work, " Etching," a sumptuous volume with thirty plates by old and modern etchers, and numerous reproductions, was pub- lished in New York in 1885, before his appointment at the Museum. In 1893 he delivered a course of nine lectures before the Lowell Insti- tute, subsequently repeated in Washington, on " Old and Modern Methods of Engraving." At other times he lectured before the Art Club, the Society of Arts, and on various occasions to private classes. In 1892 Harvard conferred the honorary degree of A. M. He was elected Resident Fellow of the Academy May 10, 1893. The recent transfer to Harvard of the collections deposited with the Museum, and the sudden acquisition by purchase and bequest of great numbers of prints a year or two before his death, was a source of anxiety to him in his feeble health. The end came suddenly, unexpectedly, but painlessly, following within a year that of his wife. For his reputation one can but regret that his untimely death prevented the completion of a " History of the Art of Color-printing," for which he had accumulated a large amount of material, — a difficult task, for which no one was so well fitted as he to sift the facts and refute jirevalent errors. The large and valuable library which he had accumulated he gave, with many prints, to the Museum of Fine Arts. A list of his publica- tions is given in the twenty-fifth annual report of that Museum. Chas. G. Loring. JOHN ELBRIDGE HUDSON. Thk duty has been assigned to me of communicating to the Academy some account of our late associate, John Elbridge Hudson, who was elected a Fellow on June 15, 1892, and was a member of the Council from May 8, 1896, to May 10, 1899. It is a grateful duty, for I had known Mr. Hudson long and well, and had for him a very great regard. He was a student at Harvard College when 1 first saw him, — a shy, studious, thoughtful boy, at the head of his class. A few years later he walked into the office of the law firm with which I was connected and asked to be received as a student. From that time to the moment of his death — for half of my life and more than half of his — I saw much of him. With few men could he have talked more confidentially of what most concerned him than he did with me, and certainly with few men did I hold a more intimate friendship. JOHN ELBRIDGE HUDSON. 559 At the time of his death, — on the first day of October last, suddenly, at the railroad station in Beverly, five minutes before he was to take his train for his daily tasks in Boston, — he was a little over sixty-one years of age, having been born in Lynn August 3, 1839. He was a man of a very handsome and impressive presence, tall, large, with a massive head, and an expression in his face of quiet dignity, strength, and composure which truly reported the quality of the inward man, and attracted a re- spect and confidence that were never disappointed. Hudson's ancestry runs back to the very early days of the Massachu- setts Colony. At his own birthplace of Lynn, the earliest immigrant of his family had settled, — Thomas Hudson, — about 1630. It is said that the first iron works in the country were established on his land, at the head of navigation, below the ford, on the Saugus River. Nine years a^o our associate presented to his native city an iron kettle, the first casting made at these works, just two hundred and fifty years before. His father was John Hudson, of Lynn, and his mother Elizabeth Chase Hall Hilliard, of Cornish, New Hampshire. Through her Mr. Hudson was descended from two clergymen, her great-grandfather and her grand- father, — one the Rev. Dr. David Hall, a graduate of Harvard in 1724, and for sixty years minister of the First Church in Sutton, Massachusetts, and the other the Rev. Samuel Hilliard, "a pioneer in Universalism, and a soldier of the Revolution, serving at Bunker Hill and Bennington." * Mr. Hudson himself was brought up as a Unitarian, and although not a regular attendant upon any church, was a member of the Unitarian Club of Boston. Educated at the public schools of Lynn, Hudson provided himself with whatever other special fitting for college was needed. He entered Har- vard in 1858, being a little older than the average of his class; took distinguished rank as a scholar and graduated in 1862 at the head of his class; became at once a tutor in Harvard College, where for three years he taught Greek, Latin, and Ancient History; and for two years of the same period was a member of the Harvard Law School, where he gradu- ated in 1865. His work as a tutor gave great satisfiiction, and he would have been welcomed as a permanent member of the teaching force at the College. But, with a sound instinct as to the character and reach of his own powers, he chose the world of affairs. As a scholar and a teacher he would, un- * Memoir by George V. Leverett ; The New-England Historical and Genealogi- cal Register, LV. 136. 560 JOHN ELBRIDGE HUDSON. doubtedly, have been distinguished, but he had a very great and unusual capacity for business, for shaping large affairs and for influencing men, a faculty that would have largely missed its opportunity in the quiet life of a college officer. He entered the office of Messrs. Chandler, Shattuck and Thayer, as a student, in Boston, in 1865 or 1866. Admitted to the Suffiilk Bar in October, 1866, he soon became managing clerk in the office of the firm just mentioned on terms which indicated a high appreciation of his ability ; and in February, 1870, on the retirement from the firm of Mr. George 0. Shattuck, he became its junior member. Here he continued, during some changes in the firm, until its dissolution in 1878. In the interval between this and the year 1880, when that connection with the telephone business began which was to last for the remaining twenty years of his life, he practised law alone, and added some editorial work upon the tenth volume of the United States Digest. That was a task which it was quite possible to carry through in a seemingly respectable and yet entirely perfunctory fashion. But Mr. Hudson took it up as he took up every- thing, and planned a volume of distinguished merit. On entering the service of the telephone company he had to leave the completion of the book to another ; but he had begun by making a new analysis and classi- fication of the titles of the law employed in the Digest, — one which was so much valued that it forms to-day the model of a recent great under- taking by a Western publishing house, known as the Century Digest, now in general use among lawyers. Mr. Hudson was thus an active member of the bar for fourteen years. His preference was for office work ; vei-y seldom could he be induced to try a case, or to argue a point of law before a court. During the nine years that we were connected with the same firm, before I went to the Law School, in 1874, 1 can speak of his work from an intimate knowledge of it. He had the oversight of our accounts, and took charge of a great part of tlie office work, such as the drawing of contracts and wills, and the preparation of pleadings and court papers. In all this, his work was admirably well done. The character of it, at a little later period, attracted the attention of the Chief Justice of the Supreme Court, who sent for him and expressed a wish that he would take the place of Clerk of that court. I recall also the great satisfaction expressed by a client, a very able business man in the China trade, who had had occasion to consult liim about some tangled affairs. "I have not seen," he said, "such a head for complicated accounts since my early experience with John M. Forbes." JOHN ELBRIDGE HUDSON. 561 As I have said, there was another department of work in which it was practically impossible to interest Hudson, that is to say, work in court. You could hardly drive him to take hold of that. He took no pleasure in it and showed little capacity for it. He was always a shy person, little inclined to put himself forward, and absolutely unwilling to appear in public, if he could avoid it ; and for that reason the breadth and versa- tility of his extraordinary powers were sometimes 'overlooked. Indeed many of those who knew him well and bes^t appreciated his remarkable qualities were surprised at the developments of later years. Early in 1880, Colonel William H. Forbes, the President of what was soon to become the American Bell Telephone Company, who had known Mr. Hudson in college and also as a lawyer, invited him to become the Solicitor of the Company. The invitation was accepted, and Hudson entered at once upon his new duties. Five years later he was asked to become the General Manager. To accept such a place as that was a serious step. So far he had not left the law, but this new proposition would plunge him into a career of business, and business of a very engross- ing sort. He came to talk it over with me ; and I had many misgivings. He knew, the Company knew, all his friends knew, what he could do in the law. But this was a new venture. What if all this tremendous, novel, swiftly developing business should not suit him, or should prove too much for him? Was he sure that he could handle it? I was greatly impressed by his answer. Oh, yes, indeed ; as to that he had no doubt whatever; he could handle it well enough. As Solicitor he had got a good insight into the nature of it all, and he had no fears on that head. This confidence in his own powers of dealing with the men and the affairs of so great a concern, a confidence fully justified by the event, opened my eyes to a new side of Hudson's capacity. He took the office, without relinquishing the place of Solicitor, filled it to the entire approval of the Company, added to it the next year that of Vice- President, and in 1887 that of President of the American Telephone and Telegraph Company, then known as The Long Distance Company, and two years later became President also of the main organization, the American Bell Telephone Company. These last two offices he held with great success and distinction up to the time of his death ; for the final steps in the absorption of the last named company in the first were not then, and I believe are not yet, completed. Of the ability which ]\[r. Hudson showed in guiding and shaping the development of this new and complex industry of the telephone, others VOL. XXXVI. — 36 562 JOHN ELBRIDGE HUDSON. who were associated with him have already spoken. Mr. Francis Blake, one of the directors of the Telephone Company, has said that wliile Mr. Hudson was Manager and President the number of miles of telephone increased more than tenfold, to over a million miles in 1899, and the number of exchange connections more than sixfold, reaching nearly seventeen hundred millions in the same year ; and he adds: " Moreover, during this period there was conceived and developed a system of long- distance service which brought more than half the population of the United States within the limits of telephonic speech. These statistics," he adds, "emphasize the broad statement that the growth of Mr. Hudson's busi- ness capacity not only kept pace with, but kept in advance of the ever increasing needs of the companies under his control." * Added to great intellectual capacity, to a remarkable strength, grasp, and tenacity of mind, Mr. Hudson had another source of power, — his sound moral quality. He made no parade of his integrity, but he was thoroughly honest and honorable, and all who dealt with him saw it. In one of the Company's great law-suits an antagonist thought fit to charge it with indirection in a particular matter. The counsel of the Company, the late William G. Russell, met the charge with a statement by Mr. Hudson. " And I need not say to the court," he added, "that on a question of fact within his knowledge, the word of John E. Hudson imports absolute verity." To a specific reliance upon these personal qualities of the Presi- dent of the Telephone Company, upon his great intellectual gifts, his forecasting and shaping power, his sound judgment, cautious and yet bold in advancing to meet the great emergencies which he foresaw, upon his absolute integrity and his power over men, in a word, to personal confidence in him, may be traced the investment of millions of dollars in that great corporation. Undoubtedly Mr. Hudson sacrificed his life to the enormous and ever- growing requirements of the office which he held. It was his habit to rest by going abroad for a month or two in the summer, and to pass the remainder of that season at the seashore within easy reach of his office. It is said, and probably with truth, that he lacked somewhat in one of the qualities of a great administrator, namely, in the power to turn over work to subordinates. He could not bear to see work imperfectly done, when he himself could do it so thoroughly well. His friends had Ion? urged him to withdraw from these heavy cares, and a few years ago he had * Memoir by Francis Blake; Proceedings of the American Antiquarian Society, October 24, 1900. JOHN ELBRIDGE HUDSON. 563 ■well-nigh done it. But he was persuaded to remain, arranging at that time to withdraw in the year 1900. Doubtless, like all strong men, he enjoyed the exercise of his strength. Moreover, the development of the business and increasing complications seemed to demand his personal attention just a little longer, — and so the end came as it did. He seemed, for the most part, to bear it all easily enough, but the strain was immense, incessant, increasing ; and before he knew, it was too late. A word or two more should be said as to Mr. Hudson's mental habits, and his methods of working ; and a word or two also as to the personal qualities that made him much beloved. At home Mr Hudson used to have by the side of his plate, as he sat at table, a pencil and paper, for he knew the worth of a memorandum taken at the moment. In his business he was in the habit of causino- to be taken and preserved such memoranda of all that took place at each stage of any particular affair. This full record, perfectly arranged and indexed, was of the utmost service to him in handling his great business. He had only to turn to his books to find a record of everything. Often, indeed, he had no need to turn to his books, unless to convince his inter- locutor ; for he had an extraordinary capacity of remembering facts, of visualizing them, and holding them all mapped and co-ordinated in his mind. In his private studies he was apt to begin by preparing a chart of the subject, with names and dates and the order and place of leading facts and events, all set forth with extraordinary neatness, open to inspection, and speaking volumes to a glance of the eye. These things, thus quickly visible, passed over into his mind and stood there fixed permanently in a rational order. It was so with places. London and Paris and all their streets he saw. He had explored the maps so that he hardly needed them longer. His mind held the maps. This faculty gave an extraordinary interest to his conversation. Last summer I passed several days with him at his house, and he, later, a week with me at mine. He had been reading Plutarch, and everything about him that he could lay hands on. He was trying to place him and his thought in their true relation to the men and the ideas of the time just past and just to come. He had been reading also of Alexander, and reading with equal ease in the Greek and Latin authors as in those in our own tongue. It was a pleasure of the highest sort to listen to his talk. The precision and extent of his knowledge, the way in which it lay in his mind, co-ordinated with whatever related things tlnew light 564 JOHN ELBRTDGE HUDSON, upon it, these and the breadth and ilhiminating good sense of his own reflections were equally instructive and delightful. Alexander and Plu- tarch stood out before you in their trne place in history, and in their true relations to the men, the dates, and the events of their time. No one could see Hudson vrithout guessing at the strength and force of his character; and no one who knew him well could fail to see that under his gentle demeanor there lay qualities of energy and passion that were not to be trifled with when once the}' were aroused. But he was an affectionate and charming friend, and one that women and little chil- dren and those who were dependent upon him loved. Mr. Hudson married in 1871 Miss Eunice Wells Healey, of Hamp- ton Falls, New Hampshire, who survives him, to bear a most heavy loss. He left no children. One sister also survives him, the wife of Samuel J. HoUis of Lynn. He went little into society and but little to the larger clubs.* He was happiest at home, and there he gave himself up to the refined and simple pleasures in which he always had his chief enjoyment. He had a large library, of great range and variety, to which he was forever adding. Most of all he seemed to like, at the end of the day, to sit down among his books and explore his old friends the Greek and Roman classics, — reading them, as he did, with entire ease in the original. When it came to the matter of his real tastes and likings, as his associate Mr. Leverett has happily said, " He was, above all, a scholar, fond of his home." James B, Thayer. * Mr. Hurlson was a member of many societies and clubs. In the Memoir for the Historic Genealogical Society, already quoted, Mr. Leverett says : " Mr. Hudson was at tlie time of his death a vice-president of this Society. He was also a fellow of the American Academy of Arts and Sciences, a member of the Corpo- ration of the Massachusetts Institute of Technology, a member of the American Antiquarian Society, the American Association for the Advancement of Science, the British Association for the Advancement of Science, American Geographical Society, National Geographic Society, the Colonial Society of Massachusetts, the American Institute of Electrical Engineers, the Virginia Historical Society, the Association for the Preservation of Virginia Antiquities, the Bostonian Society, Selden Society, Hakluyt Society, Lynn Historical Society, the Bar Association of the City of Boston, and also of the Algonquin, Boston Art, Exchange, National Arts, St. Botolph, Union, UniA'ersity, and other social clubs." It may be added that he took much pleasure in one or two social clubs made up of college friends or contemporaries. JOHN HARRISON BLAKE. 665 JOHN HARRISON BLAKE. In reviewing the printed matter, letters, completed manuscripts, and note-books which furnish the material for a personal memoir of my father, I have been impressed by the paucity of record of the achievements of an active life extending over the greater part of a century. The reason for this is to be found in the character of the life itself, looking rather to accomplishment than to recognition, and seeking to ex- press the sense of an obligation for the privilege of living by doing the work at hand simply and well. Of published papers there are but few, — the Transactions of this Acad- emy, of which he was elected a member May 30, 1843, contain none, other journals in the library of the Academy but five, and the records of the Boston Society of Civil Engineers, of which he was one of the founders and its first Secretary, an equally small number. Of letters, especially family letters, there are many, all clearly written, containing information as to his travels and treating of the subjects in the study of which he was most interested. Of the manuscripts, the majority, in the form of essays, were written after his retirement from active life with the evident purpose of continu- ing a companionship which has, to his son, the value both of a precious memory and a continued inspiration ; the persistency with which this purpose was pursued, under conditions of failing strength and sight, is shown especially in one of them, begun in ink, continued in black and then in blue pencil when the blue mark alone was visible to him, and concluded by sense of touch. These essays cover a wide range of scientific subjects and bear witness to an intellectual activity persisting to within the last three years of a life which ended, as gently and as graciously as it had been lived, at the age of ninety 3'ears. Through this life there had run one dominant pur- pose, — that of usefulness; in it there had always been one keen pleasure, — that of scientific research. The note-books, containing many valuable records and memoranda, are the transcripts of a variously active profes- sional life, — one series covers very nearly the whole of the early experi- mental and constructive history of the manufacture of illuminating gas in this country, another is a record of researches in the chemistry of arts and manufacture, and another is devoted to mining, metallurgy, and civil engineering. John H. Blake, the youngest son of Thomas and Mary Lowell Bar- nard Blake, was born December 5, 1808, in the house still standing on 566 JOHN HARRISON BLAKE. Washington Street, corner of Union Park Street ; he died in his home on Marlborough Street, Boston, July 5, 1899, in his ninety-first year. Mr. Blake was educated in private schools and in the English High School, which he entered in 1821 as a member of its first class. Later he became a pupil of the Rev. James Blake Howe, then rector of the West Parish Church in Claremont, N. H., whose daughter, a second cousin, he mar- ried on his return from his explorations in South America. While his studies with Mr. Howe were mainly classical and he was fitted to enter Harvard, his interest in chemistry and in anatomy was such as to lead him to prefer these studies to those of a collegiate course prin- cipally literary and mathematical. It was in pursuit of his chosen subjects that, after a period of study in a chemical manufacturing estab- lishment, he became assistant to, and pupil of, Dr. Webster, from whom he received valuable instruction, whicli enabled him in the year 1827, when only nineteen years of age, to establish, with money advanced by his father, the Norfolk Laboratory, for the manufacture of pure drugs and chemicals. This laboratory was situated in Jamaica Plain near Forest Hills, upon the Dedham Turnpike. One of its products was pure sulphuric ether, and it was in the larger laboratory of later construction that the ether used in the first demonstration of the value of ether anaes- thesia was made under Mr. Blake's personal supervision. In addition to the commercial work of the laboratory Mr. Blake carried on a series of investigations into the physiological effects of poisons, the composition of precious stones, and the production of alloys applicable to the mechanic arts. At the end of three years of successful operation the buildings were destroyed by a fire, resulting from the explosion of a carboy of ether, but were immediately rebuilt on a larger scale ; a joint stock company was formed, arrangements were made with the Rothschilds for the importation of quicksilver, and with a house in Tuscany controlling what was then the world's principal supply of boric acid ; and Mr. Maximilian Isnard, who introduced the manufacture of beet-root sugar into France, became an associate. At that time but little was known of the sources of supply of nitrate of soda, of which large quantities were used in the works, beyond the names of the small ports on the coast of Peru from which it was shipped. Ignorance on the subject, the value of the article, and the novelty of entering and exploring an unknown region were sufficient incentives to turn Mr. Blake's thoughts in this direction rather than along the beaten lines of travel in search of tlie rest and recreation which he needed after eight years of anxious labor. Books gave very little information concern- JOHN HARRISON BLAKE. 567 ing the country between the Pacific Oceau and the Andes, constituting the extreme southern part of Peru, the western part of Bolivia, and the northern part of Chili, and all the knowledge that could be obtained was that it was, for the most part, uninhabited and uninhabitable, destitute of vegetation, and known as the Desert of Atacama ; it was on the shores of the northern part of this desert that the shipment ports referred to were situated. The winter of 1835 and 1836 was very cold. New York harbor was frozen over, and it was not until the lOth of February, 183G, nearly a month after the time proposed for her departure, that the ship " Factor," in which Mr. Blake was a passenger, made her way through a channel cut in the ice and sailed for Valparaiso, where she arrived June 9, sailing again on the 9th of July for Arica and Tacna, whence Mr. Blake proceeded by land to Pisaqua and Iquique, arriving at the latter place on the Gth of August. The next three months were devoted to surveys in the province of Tarapaca, and on the 7th of November Mr. Blake left Iquique with a pack train, two Indians, and dogs to make the first re- corded exploration of the Desert of Atacama from north to south, arriving at Valparaiso on the 10th of March, having occupied four months and three days in a trying passage over an arid and waterless region, in which all of the animals were lost and the men nearly perished from thirst. On March 15 Mr. Blake left Valparaiso for Buenos Ayres by San- tiago, the pass of Uspalato and Mendoza, crossing the Andes and the Pampas de la Plata, arriving on the ■28th of April and making prepara- tions for immediate departure for the United States.* At this time Rosas, the then Dictator of the Argentine Republic, was engaged in strengthening his position by military activity and the pro- jected subjection of the Indian tribes to the westward. Mr. Blake was detained as consulting engineer on fortifications, and was not released until the autumn of 1837,f when he returned to the United States to find * Tlie only record of this interesting and perilous journey is to be found in family letters, in the collection of mummies and other objects of arcliaioloj^ical value now in the Peabody Museum, Cambridge, and in the description of tliis collection published from Mr. Blake's notes in the reports of the IMuseum. The carefully kept notebook, containing not only the daily incidents of travel, but especially the memoranda of geologic observations, of barometric measurements and surveys, was stolen after Mr. Blake's return to this country, and never recovered. t Information to be derived from a traveller who had just crossed the continent was of value, and Mr. Blake received a courteous note, saying that a house adjoin- ing that of the British Embassy had been placed at his disposal, and requesting him 568 JOHN HARRISON BLAKE. a condition of general financial disaster, in which tlie Norfolk Laboratory had shared and which made it impossible to take up the grants for the mining and exportation of nitre secured from the Peruvian government. Under these conditions he accepted the management of the Fernandez copper mines in Santa Clara, Cuba, married, and took up his residence there, where, in addition to the work in hand, he made observations on the character and climate of the country. In 1847 he assisted in the geo- logic survey of Isle Royale, Lake Superior,* and in 1848 entered into partnership with Franklin Darracott as a civil engineer, to which work he added that of a consulting chemist and geologist. It was his custom to make no charge for consultation to individuals seeking to develop new industries, regarding this as his contribution to the general welfare. Among many to whom he gave valuable advice were Goodyear and Babbitt. The business of the firm of Blake and Darracott had largely to do with gas engineering and the construction of gas works, and Mr. Blake organ- ized and was at one time president of five gas companies, his executive ability and power of control over men making such work a pleasure. In addition he was interested in iron and gold mining, carrying on the ore beds and blast furnaces and car wheel works at Brandon, Vermont, and organizing and operating the Yahoola River Hydraulic Mining Company, of which he was president, in the Dahlonega belt, Georgia. After the dissolution of the firm of Blake and Darracott he became interested in street railways, building the Middlesex Road and being the President of the Metropolitan Road during the period of the Civil War : subsequently he was President of the Connecticut Arms Manufacturing Company, and organized and was the first President of the Chapman Valve Manufac- turing Company. One of Mr. Blake's latest contributions to manufactures was the so- called antique glass. Wishing to carry out previous experiments on molecular movement in solids at protracted high temperatures, he con- structed a crucible furnace in South Boston, and in order to make it pay its expenses manufactured glass upon the basis of his earlier analyses of precious stones, the result being a glass of great brilliancy and vivid color. to remain as the guest of the Dictator. The invitation was declined, but was re- peated in an equally courteous note brought by a file of soldiers, the note further stating that the Dictator trusted that the invitation would be accepted, as it would pain him to be obliged to provide any narrower accommodation. * The promontory at the northeasterly extremity of the island is called Blake Point. CHARLES FRANKLIN DUNBAR. 569 The mental activity which had stimulated bodily action beyond the usual term of working years continued to find its expression, even after he had become confined to the limits of his own home, in the manuscripts which contain those products of liis mental laboratory impossible of record in busier times ; as might be expected they give an insight into the motive power of his life and show the strength of a character which looked for- ward calmly to bodily dissolution as a part of the process of growth to greater knowledge. Through the vicissitudes of incessant and protracted work, with the usual meed of disappointment and much of physical pain, Mr. Blake held always the cheerful courage born of a simple faith, which counted life as a primary school and the suffering of his advanced years as a part of its graduating exercises ; prominent in my memory of him are his fearless- ness, his kindliness, his love of truth, and his earnest desire not to fail in doing his part of the world's work, whatever that might honestly be, and this also, that in fifty-seven years of a dear and close companionship, I cannot recall a single unkind, unjust, or impatient word. Clarence John Blake. CHAKLES FRANKLIN DUNBAR. Charles Franklin Ddnbar, Fellow of the American Academy for twenty-eight '•' years, Professor of Political Elconomy in Harvard Uni- versity for nearly thirty years, was born at Abington, Massachusetts, July 28, 1830, and died at Cambridge, Mass., January 29, 1900. Professor Dunbar's career divides itself into two very different parts ; a first, during which he was editor and guiding spirit of the Boston Daily Advertiser ; and a second, during which he lived the quiet life of the teaclier and scholar. It was not until he had reached mature manhood that he entered on his newspaper career. After graduating from Harvard College in 1851, he engaged for a short time in business ; then, health failing, spent a year in farming; then studied at the Harvard Law School and in the office of the late Justice E. R. Hoar, and was admitted to the Bar in 1858. Meanwhile, contributions from his pen had appeared in the Advertiser ; and finally, in 1859, he became permanently associated with * Elected January 31, 1872. 570 CHARLES FRANKLIN DUNBAR. that newspaper. At first associate editor, he became in 1864 sole responsible editor, and such he remained until he severed his connection with the Advertiser. The decade during which he was thus in charge of the most influential newspaper in New England was the most trying and perhaps the most important in the country's history. His position as editor brought him into contact with leading men in every sort of career in New England. Both his conduct of the paper, and his association with men, gradually gave him a position of respect and confidence in the community, rarely obtained by those in charge of ephemeral pub- lications. He wrote constantly on a great variety of subjects ; on political and military affairs as a matter of course, but with special care and with unusual judgment on the remarkable financial and eco- nomic events of the period. His editorials were marked from the outset by the grace and dignity of style which characterized everything that came from his pen. They showed, moreover, the firm and unwaver- ing spirit of the man ; never abating by a jot the conviction that in spite of defeat and disaster, in spite of foreign complications and domestic disaffection, the war must be carried on uufiinchingly until the supremacy of the Union should be restored. There is not only steadfast faith, but often inspiring eloquence, in the editorial pages of the Advertiser as Professor Dunbar conducted them ; and not seldom, after a military failure, his courageous words rang through the community like a bugle blast. The financial and economic events of this period were of the most extraordinary and varied kind. A huge national debt, a new banking sys- tem, an immense and complicated system of taxation, a high protective tariff, an excessive issue of paper money, a wearisome struggle between the advocates of paper money and specie, the turmoil of reconstruction in the South, — such were the phenomena to which the editor of the Advertiser was compelled to give daily attention. His inborn apti- tude led him to observe the course of events with keen sagacity, and gave him a fund of experience invaluable for his later career. Few economists have been so fortunate in having been brought into unremit- ting contact with the actual affairs of life. Few also have been so fortunate in securing contact with men of all classes and all opinions. Daily there came into the office of the editor of the Advertiser persons of every sort, bringing advice, exhortation, information. A characteristic trait of Professor Dunbar's showed itself in these conferences, — a remarkable capacity for silent attention. However certain of his own CHARLES FRANKLIN DUNBAR. 571 ground, he would listen without response to those whose views were different from his own, refrain from stating his objections unless the situation imperatively called for statement, and give his auditor an impression, and a true impression, of respectful and sympathetic interest ; and yet in due time would follow the course which his own judgment dictated as wise. The quality of his mind was eminently judicial. He saw all sides of a difficult question so clearly that he sympathized with those who saw perhaps only one side. In the Advertiser office he dealt with business men, statesmen, soldiers, conservatives, radicals, vision- aries ; learned something from all, dealt courteously with all, gained the respect of all, and yet never failed to maintain his own sound and independent judgment. The most active and strenuous years of Professor Dunbar's life, between the ages of twenty-nine and thirty-nine, were given to the Adv-ertiser. In his hands its editorship was distinctly a public service ; and, cool- headed and sagacious as he was, uninfluenced by any vapid sentimental- ism, he so regarded his vocation. But his strength, never very great, was seriously shaken by these ten years of severe application, and in 1869, when the Advertiser changed hands. Professor Dunbar was glad to dispose of his mterest and to retire from the paper. Shortly after, he was offered a professorship of political economy in Harvard University. This was a career he had never looked for- ward to, and he doubted his own capacity for it. Nevertheless, after some hesitation, he accepted, on condition that he should have time for restoring his strength and adding to his equipment. After two years spent in Europe in study and travel, he entered in 1871 on the duties of the professorship, to which he devoted himself for the rest of his life. Although thus launched on the career of a scholar and teacher, his abilities were such as to cause him to be enlisted soon in the work of guiding and managing the affairs of the University. On the retirement of the late Professor Gurney, in 1876, he became Dean of the Faculty of Harvard College, and retained that post until 1882. When the present Faculty of Arts and Sciences in Harvard University was organ- ized in 1890, he became its first Dean, and so acted until 1895. In addition, he served frequently on committees, and was in constant intercourse with the .President of the University, who relied greatly on his advice. Repeatedly through his academic cai-eer, he was called upon to act as judge, as mediator and pacificator, as organizer of new plans, as administrator of new systems. All these duties were discharged with remarkable judgment and success ; yet they were felt by him to be 572 CHARLES FRANKLIN DUNBAR. distractions from his chief tusk as professor in a great institution of learning. Professor Dunbar's career as editor, and his administrative work in Harvard University, need to be borne in mind when making an esti- mate of his work as scholar and man of science. To those who knew him well, nothing was more admirable in his career than the solidity of his schohirly attainments, the breadth of his interests, the maturity of his conclusions on his chosen subjects. It might have been expected that one who had been a busy newspaper editor, and who remained to the end keenly interested in current political happenings, should con- tinue to deal largely with questions of the day, and take an active part in current discussion of public issues. Professor Dunbar, however, had too clear a perception of the ideals and duties of a scholar to give him- self to newspaper and periodical writing. For many years he delved iu the literature of political economy at large, and equipped himself in the whole range of his subject. Not only the writings of contemporary economists, but those of earlier days, especially the English and French authors of the seventeenth and eighteenth centuries, and those of Ricardo's school, were thoroughly examined. It is characteristic of Professor Dunbar that notwithstanding the wide scope of his reading in the theoretic literature of political economy, he published virtually nothing on this phase of the subject ; though the maturity of the conclu- sions derived from that reading are unmistakably evident in some of his essays on the recent phases of economic theory. He regarded these researches as essential to his equipment as a University teacher, partly also as preparation for the inquiries by which he hoped eventually to contribute to the world's stock of knowledge and thought. The special subjects on which he planned to publish the results of research, and to which he gave most attention in the later years of his life, were public finance, taxation, currency, banking. It was to these that he had given most attention among the economic topics that pre- sented themselves to him as editor of the Advertiser ; it was to these that his own bent most attracted him. His range of information on them was remarkably wide. Here, again, his writings give but frag- mentary indication of the extent of his attainments. He was familiar with the financial history and fiscal experiences of England and France quite as much as with those of the United States, to which his writ- ings were chiefly devoted. And not only was he familiar with the facts ; he was singularly skilful in interpreting them. All who had the pleasure of following his courses of instruction in the University CHARLES FRANKLIN DUNBAR. 573 found before them the couclusious of a sagacious mind, furnished with ample information on every essential aspect of the situation. It was Professor Dunbar's undeviating habit to turn to the primary sources of information, — to the statutes, the official documents, the contem- porary sources of knowledge. He was never content with information at second hand, and was frequently able to point out how the conclusions of authors of repute were overthrown by a careful comparison with the sources from which their conclusions should have been derived. Professor Dunbar's writings, as already intimated, were compara- tively scanty; they were certainly scanty as compared with what he was equippetl to do. His little book on Banking, brief and unpreten- tious, is a model, and indeed well-nigh a classic, in its field. His essays on the financial history of the United States, published in the Qiiarterl}- Journal of Economies, are also models of their kind. Occa- sional comparisons, undertaken in these essays, with the financial experience of other countries, — as, for example, in the essaj' on Some Precedents followed by Alexander PlamiJton, — give indication of the wide range of his researches. Similar evidence appears in essays on some recondite and little understood phases of economic history, such as those on the Bank of Amsterdam, on the Bank of Venice, and on Early Banking Schemes. Those who had the privilege of Professor Dunbar's intimate acquaintance knew that he had pushed his way into other obscure and difficult places also. He had given much attention to the history of the Assignats in France, and to the peculiarities in the course of depreciation during that remarkable episode in monetary history. On this subject he had collected, as was his habit, a store of contemporary material, and had planned at some time to present the results of his researches in published form. He had undertaken a minute and careful study of the financial administration of Alexander Hamilton, of which the results appeared in print only to a very slight extent. He had followed with e(|ual thoroughness the history of bank- ing operations in the United States, especially from the middle of the century to the present time ; but here also failing strength and an untimely death prevented the execution of his matured plans. No small part of Professor Durd)ar's time and thought was given in the later years of his life to the Quarterly Journal of Economics. That Journal was established by Harvard University in 188G, Professor Dun- bar being appointed its editor, and remaining in charge from 1886 to 1896. It was a very different editorial post from that which he had held on the Advertiser; but its duties were performed with no less 574 CHARLES FRANKLIN DUNBAR. fidelity and sliill.- From the first a high standard was set. The Journal was to be a medium of communication for investigators, and took rank at once as one of the leading scholarly repertories on its subject. Space in it was sought by eminent writers the vvorkl over, and publication in its pages served as guarantee of a claim to the attention of the learned world. Professor Dunbar always looked back with just satisfaction on what he had here achieved, and found in it some solace for his inability to carry out his plans for independent publication. Professor Dunbar was by nature reserved ; always dignified ; in con- versation, happy in the intuitive selection of the right word ; guarded in expressing an opinion, but sure to express a just one when his conclusions had been reached. His writings, reflected these qualities. They are distinguished by a rounded stateliuess of diction more sought for a generation ago than in our own day ; dignified, yet never stilted, flowing, yet never affected. No more just and delightful tribute has been paid to a man in his own lifetime than is contained in Professor Dunbar's paper on President Eliot's Administration of Harvard Univer- sit}', published in the Harvard Graduates' Magazine (for June, 1894) at the close of the twenty-fifth year of President Eliot's administration. Equally sympathetic, and at the same time judicial and discriminating, are his memoirs, in the Proceedings of this Academy, of three men of very diflferent types, — Henry C. Carey, Francis A. Walker, and E. W. Gurney. It is a singular fact that Professor Dunbar wrote with hesitation, and often had to nerve himself anew to the task of literary composition. Notwithstanding many years of experience in rapid writing, he shrank from taking pen in hand ; yet, when the first sentence was written, the others followed apparently with ease, and certainly in logical sequence and with an immediate happy choice of phrase. The present writer has been so fortunate as to examine some of the notes, memoranda, and unfinished manuscript left by his lamented colleague ; and in the briefest and most fragmentary of these papers he has been repeatedly struck by the appositeness of the language, the instinctively systematic arrange- ment, the constant proof of clear and well ordered thought. In personal intercourse with those who enjoyed his more intimate acquaintance, Professor Dunbar's habitual dignity and reserve were often broken by flashes of humor. He enjoyed keenly a good story, and saw the mirthful side of every subject. Often in solemn meetings the twinkle of his eye, perceptible only to those who knew him well, showed his appreciation of the oddities and idiosyncrasies of his contemporaries. CHARLES FRANKLIN DUNBAR. 575 As is common with men whose sense of humor is strong, his affection was deep and lasting ; and in the domestic circle the devotion which he gave and received was touching. His character, not less than his abilities and attainments, won from associates in varied walks of life an universal feeling of esteem and admiration. F. W. Taussig. There have been no resignations during the year, but one Resident Fellow has abandoned his fellowship. One Resident Fellow, having removed from Massachusetts, has been elected to Associate Fellowship. New members elected during the year are : Resident Fellows, 7 ; Associate Fellows, 9 ; Foreign Honorary Members, 9. The roll of the Academy now includes 197 Resident Fellows, 96 Associate Fellows, and 70 Foreign Honorary Members.* * By election, May 8, 1901, the roll is 198, 98, 74, American Academy of Arts and Sciences. OFFICERS AND COMMITTEES FOR 1900-1901. president. Alexander Agassiz. Class I. John Trowbridge. VICE-PRESIDENT. Class II. Alpheus Hyatt. CORRESPONDING SECRETARY. William M. Davis. recording secretary. William Watson. treasurer. Francis Blake. librarian. A. Lawrence Rotch. Class III. James B. Thayer. Class I. Henry Taber, Theodore W. Richards, John E. Wolff, Harry M. Goodwin. George H. Parker COUNCILLORS. Class II. Class III. William T. Councilman, James B. Ames, William Everett, A. Lawrence Lowell. Alexander Agassiz, COMMITTEE OF FINANCE. Francis Blake, Eliot C. Clarke. rumford committee. Erasmus D. Leavitt, Edward C. Pickering, Charles R. Cross, Amos E. Dolbear, Arthur G. Webster, Theodore W. Richards, Thomas C. Mendenhall. Charles L. Jackson, Leonard P. Kinnicutt, C. M. WARREN COMMITTEE. Samuel Cabot, Henry B. Hill, Arthur M. Comey, Robert H. Richards, Henry P. Talbot. committee of publication. Samuel H. Scudder, Seth C. Chandler, Crawford H. Toy. COMMITTEE ON THE LIBRARY. A. Lawrence Rotch, Henry W. Haynes, Samuel Henshaw. auditing committee. Henry G. Denny, William L. Richardson. LIST OF THE FELLOWS AND FOEEIGN HONORARY MEMBERS. (Corrected to May 20, 1901.) RESIDENT FELLOWS. — 198. (Number limited to two bundreil.) Class L — Mathematical and Physical Sciences. — 80. Sectiox I. — 2L Section II. — 21. Mathematics and Astronomy Solon I. Bailey, Maxime Bocher, William E. Byerly, Seth C. Chandler, A. W. Duff, Gustavus Hay, Theodore Lyman, Henry Mitchell, William F. Osgood, James Mills Peirce, Cambridge. Cambridge. Cambridge. Cambridge. Worcester. Boston. Brookline. Nantucket. Cambridge. Cambridge. Edward C. Pickering, Cambridge. William H.Pickering, Cambridge. John Ritchie, Jr., John D. Runkle, T. II. Safford, Edwin F. Sawyer, Arthur Searle, William E. Story, Henry Taber, O. C. Wendell, P. S. Yendell, VOL. XXXVI. — 37 Boston. Cambridge. Williamstown. Brighton. Cambridge. Worcester. Worcester. Cambridge. Dorchester. Physics. A. Graham Bell, Washington, D.C. Clarence J. Blake, Francis Blake, Charles K. Cross, Amos E. Dolbear, H. M. Goodwin, Edwin H. Hall, Hammond V. Hayes, \Yilliam L. Hooper, William W. Jacques, Frank A. Laws, Henry Lefavour, T. C. IMendenhall, Benjamin O. Peirce, A. Lawrence Rotch, Wallace C. Sabine, John S. Stone, Elihu Thomson, John Trowbridge, A. G. Webster, Robert W. Willson, Boston. Weston. Brookline. Somerville. Roxbury. Cambridge. Cambridge. Somerville. Newton. Boston. AVilliamstown. "NV^orcester. Cambridge. Boston. Cambridge. Boston. Swampscott. Cambridge. Worcester. Cambridge. 578 RESIDENT FELLOWS. Section III. — 22. Chemistry. Samuel Cabot, Boston. Arthur M. Coiney, Cambridge. James M. Crafts, Boston. Charles W. Eliot, Cambridge. Henry B. Hill, Cambridge. Charles L. Jackson, Cambridge. Walter L. Jennings, AVorcester. Leonard P. Kinnicutt, Worcester. Charles F. Mabery, Cleveland, O. Arthur Michael, Boston. George D. Moore, AVorcester. Charles E. Munroe, Wash'gton, D.C. John U. Xef, Chicago, 111. Arthur A. Noyes, Boston. Robert H. Richards, Boston. Theodore W. Richards, Cambridge. Charles R. Sanger, Cambridge. Stephen P. Sharpies, Cambridge. Francis H. Storer, Boston. Henry P. Talbot, Charles H. Wing, Edward S. Wood, Newton. Ledger, N. C. Boston. Section IV. — 16. Technology and Engineering. EUot C. Clarke, Boston. Ira N. HoUis, Cambridge. L. M. Johnson, Cambridge. Gaetano Lanza, Boston. E. D. Leavitt, Cambridge. William R. Livermore, Boston. Hiram F. Mills, Lowell. Cecil H. Peabody, Boston. Alfred P. Rockwell, Manchester. Andrew H. Russell, Wash'ton, D.C. Peter Schwamb, Arlington. H. L. Smyth, Cambridge. Charles S. Storrow, Boston. George F. Swain, Boston. William Watson, Boston. Morrill Wyman, Cambridge. Class II. — Natural and Physiological Sciences. — 64. Section I. — 13. Geology, Mineralogy, and Physics of the Globe. H. H. Clayton, Algernon Coolidge, William O. Crosby, William M. Davis, Benj. K. Emerson, O. W. Huntington, Robert T. Jackson, WilHam H. Niles, John E. Pillsbury, Nathaniel S. Shaler, Robert DeC. Ward, John E. Wolff, J. B. Wood worth. Milton. Boston. Boston. Cambridge. Amherst. Newport, R. I. Cambridge. Cambridge. Boston . Cambridge. Cambridge. Cambridge. Cambridge. Section II. Botany. F. S. Collins, Geo. E. Davenport, William G. Farlow, Charles E. Faxon, Merritt L. Fernald, George L. Goodale, H. H. Hunnewell, John G. Jack, B. L. Robinson, Charles S. Sargent, Arthur B. Seymour, Roland Thaxter, -12. jMalden. ]\Iedford. Cambi'idge. Boston. Cambridge. Cambridge. Wellesley. Boston. Cambridge. Brookline. Cambridge. Cambridge. Section III. — 24. Zoology and Physiology. Alexander Agassiz, Cambridge. Robert Amory, Boston. RESIDENT FELLOWS. 579 :MiIton. Boston. Cambridge. Brookline. Cambridge. AVilliamstovvn. IJostou. James M. Barnard, Henry P. Bowditch, William Brewster, Louis Cabot, William E. Castle, Sanmel F. Clarke, W. T. Councilman, Charles B. Davenport, Chicago, 111. Harold C. Ernst, Boston. Edward G. Gardiner, Boston. Samuel Ilenshaw, Cambridge. Alpheus Hyatt, Cambridge. John S. Kingsley, Somerville. Edward L. Mark, Cambridge. Chai'les S. Minot, Boston. Edward S. Morse, Salem. George H. Parker, Cambridge. James J. Putnam, Boston. Samuel H. Scudder, Cambridge. William T. Sedgwick, Boston. James C. White, Boston. William M. Woodworth, Cambridge. Section IV. — 15. Medicine and S Samuel L. Abbot, Edward H. Bradford Arthur T. Cabot, David W. Cheever, Frank W. Draper, Thomas Dvvight, Regiirald H. Fitz, Charles F. Folsom, Frederick I. Knight, Samuel J. Mixter, W. L. Richardson, Theobald Smith, O. F. Wads worth, Henry P. AValcott, John C. Warren, urcjery. Boston. Boston. Boston. Boston. Boston. Boston. Boston. Boston. Boston. Boston. Boston. Boston. Boston. Cambridge. Boston. Class III. — Moral and Political Sciences. — 54. Section I. Philosophy and Jiir James B. Ames, Horace Gray, John C. Gray, G. Stanley Hall, Geo. F. Hoar, Francis C. Lowell, Josiah Royce, Jeremiah Smith, James B. Thayer, — 9. isprudence. Cambridge. Boston. Boston. Worcester. Worcester. Boston. Cambridge. Cambridge. Cambridge. Section II. — 21. Philology and Archceology. William S. Appleton, Boston. Charles P. Bowditch, Boston. Lucien Carr, Franklin Carter, Joseph T. Clarke, Henry G. Denny, William Everett, Cambridge. Williamstown. Boston. Boston. Quincy. J. W. Fewkes, William W. Goodwin, Henry W. Haynes, Charles R. Lanman, David G. Lyon, Bennett H. Xash, Frederick W. Putnam, Edward Robinson, F. B. Stephenson, Joseph II. Thayer, Crawford II. Toy, John W. White, Jolm n. Wright, Edward J. Young, Washington. Cambridge. Boston. Cambridge. Cambridge. Boston. Cambridge. Boston. Boston. Cambridge. Cambridge. Cambridge. Cambridge. Waltham. Section III. — 12. Political Economy and History. Charles F. Adams, Lincoln. Edward Atkinson, Andrew M. Davis, Ejihraim Kmerton, John Fiske, Boston. Cambridge. Cambridiie. Cambridge. 580 RESIDENT FELLOWS. A. C. Goodell, Salem. Henry C. Lodge, Nahant. A. Lawrence Lowell, Boston. James F. Rhodes, Boston. Denman W. Ross, Cambridge Charles C. Smith, Boston. F. W. Taussig, Cambridge Section IV. — 12. Literature and the Fine Arts. Francis Bartlett, Boston. John Bartlett, Arlo Bates, George S. Boutwell, J. Elliot Cabot, T. W. Higginson, Geoi-ge L. Kittredge, Charles G. Loring, Percival Lowell, Charles Eliot Norton, Horace E. Scudder, Barrett Wendell, Cambridge. Boston. Groton. Brookline. Cambridge. Cambridge. Boston. Boston. Cambridge. Cambridge. Boston. ASSOCIATE FELLOWS. 581 ASSOCIATE FELLOWS. — 98. (Number limited to one hundred. Elected as vacancies occur.) Class I. — Mathematical and Physical Sciences. — 37. Skction I. — 14. Mathematics and Astronomy. Edward E. Barnard, Williams Bay, S. W. Burnham, Chicago. [Wis. George Davidson, San Francisco. Fabian Franklin, Baltimore. Asaph Hall, Cambridge, Mass. George W. Hill, W. Nyack, N.Y. E. S. Holden, Washington. Emory McClintock, ^Iorristown,N.J. E. H. Moore, Simon Newcomb, Charles L. Poor, George M. Searle, J. N. Stockwell, Chas. A. Young, Chicago. Washington. Baltimore. Washington. Cleveland, O. Princeton, N. J. Section II. Physics. Carl Barus, J. Willard Gibbs, G. E. Hale, S. P. Langley, A. A. Michelson, Providence, R.I. New Haven. Williams Bay. Washington. Chicago. Ogden N. Rood, E. L. JSichols, New York. Ithaca. Section III. — 8. Chemistry. T. M. Drown, So. Bethlehem, Pa. Wolcott Gibbs, Newport, R.I. Frank A. Gooch, New Haven. S. W. Johnson, New Haven. Charlottesville, Va. Cleveland, O. New Orleans. Baltimore. J. W. Mallet, E. W. Morley, J. M. Ordway, Ira Remsen, Section IV. — 8. Technology and Engineering. Henry L. Abbot, New York. Cyrus B. Comstock, New York.[Va. W. P. Craighill, Charlestown, ^V. John Fritz, Bethlehem, Pa. F. R. Hutton, New York. George S. Morison, Chicago. William Sellers, Edgemoor, Del. Robt. S. Woodward, New York. Class II. — Natural and Physiological Sciences. — 34. Section I. — 14. Geology, Mineralogy , and Physics of the Globe. Washington. Cleveland Abbe, George J. Brush, New Haven. T. C. Chamberlin, Chicago. Edward S. Dana, New Haven. Walter G. Davis, Cordova, Arg. G. K. Gilbert, Clarence King, Joseph LcConte, J. Peter Lesley, S. L. Penfield, J. W. Powell, R. Pumpelly, A. R. C. Selwyn, Charles D. Walcott. Washington. New York. Berkeley, Cal. Milton, Mass. New Haven. Washington. Newport, R.I. Vancouver. Washington. 582 ASSOCIATE FELLOWS. Section II. — 6. Botany. L. H. Bailey, Ithaca. D. H. Campbell, Palo Alto, Cal. J. M. Coulter, Chicago. C. G. Pringle, Charlotte, Vt. John D. Smith, Baltimore. W. Trelease, St. Louis. Section III. — 8. Zoology and Physiology. Joel A. Allen, New York. W. K. Brooks, Lake Roland, Md. F. P. Mall, Baltimore. S. Weir Mitchell, Philadelphia. H. F. Osborn, New York. A. S. Packard, Providence, R.I. A. E. Verrill, New Haven. C. O. Whitman, Chicago. Section IV. — 6. Medicine and Surgery. John S. Billings, New York. W. S. Ilalsted, Baltimore. W. W. Keen, Philadelphia. William Osier, Baltimore. Wm. H. Welch, Baltimore. H. C. Wood, Philadelphia. Class III. — Moral and Political Sciences. — 27. Section I. — 6. Philosophy and Jurisprudence. James C. Carter, New York. Joseph H. Choate, New York. Melville W. Fuller, Washington. William W. Howe, New Orleans. Charles S. Peirce, Milford, Pa. T. R. Pynchon, Hartford, Conn. Section II. — 7. Philology and Archceology. Timothy Dwight, New Haven. B. L. Giklersleeve, Baltimore. D. C. Oilman, Baltimore. T. R. Lounsbury, New Haven. Rufus B. Richardson, Athens. Thomas D. Seymour, New Haven. A. D. White, Ithaca, N.Y. Section III. — 6. Political Economy and History. Henry Adams, Washington. G. P. Fisher, New Haven. H. E. von Hoist, Chicago. Henry C. Lea, Philadelphia. Henry M. Stevens, Ithaca. W. G. Sumner, New Haven. Section IV. — 8. Literature and the Fine Arts. James B. Angell, Ann Arbor, Mich. L. P. di Cesnola, New York. II. H. Furness, Wallingford, Pa. R. S. Greenough, Florence. Augustus St. Gaudens, New York. John S. Sargent, London. E. C. Stedman, Bronxville, N. W. R. Ware, New York. FOREIGN HONORARY MEMBERS. 583 FOREIGN HONORARY MEMB ERS. — 74. (Number limited to seventy-five. Elected as vacancies occur.) Class I. — Mathematical and Physical Sciences. — 24. Sectiox I. / . Mathematics and Astronomy. Berlin. Cambridge. Arthur Auwers, George H. Darwin, H. A. E. A. Faye, Paris. Sir William Huggins, London. H. Poincare, Paris. Otto Struve, Karlsruhe. H. C. Vogel, Potsdam. Section II. — 6. Phyaics Ludwig Boltzmann, A. Cornu, Oliver Heaviside, F. Kohlrausch, Lord Rayleigh, Vienna. Paris. Newton Abbot. Berlin. With am. Sir G. G. Stokes, Bart., Cambridge. Section III. — 6. Chemistry. Adolf Baeyer, Munich. ]\Larcellin Berthelot, Paris. J. H. van't Hoff, Berlin. D. Mendeleeff, St. Petersburg. Sir H. E. Roscoe, London. Julius Thomseu, Copenhagen. Section IV. — 5. Technology and Engineering. Sir Benjamin Baker, London. Lord Kelvin, Largs. ^Maurice Levy, Paris. II. ]Miiner-Breslau, Berlin. William C. Unwin, London. Class II. — Natural and Physiological Sciences. — 27. Section I. — 7. Geology, Mineralogy, and Physics of the Globe. Sir Archibald Geikie, London. Albert Heim, Zurich. Sir John Murray, Edinburgh. A. E. Nordenskicild, Stockholm. Freih. v. Richthofen, Borlin. Henry C. Sorby, ShcfTield. Heinrich Wild, Zurich. Section II. — 6. Botany. E. Bornet, Paris. A. Engler, Berlin. Sir Joseph D. Hooker, Snnningdale. W. Pfeifer, Leipsic. II. Graf zu Solms- Laubach, Stras.sburg. Eduard Strasburger, Bonn. 584 FOREIGN HONORARY MEMBERS. Section III. — 8. Zoology and Physiology. Sir Michael Foster, Cambridge. Heidelberg. Koniijsbero:. Wiirzburg. St. Petersburg. Carl Gegenbauer, Ludimar Hermann, A. von KoUiker, A. Kovalevsky, H. Kronecker, H. de Lacaze-Duthiers Elias MetschnikofE, Bern. Paris. Paris. Section IV. — 6. Medicine and Surgery. Sir T. L. Bruuton, London. A. Celli, Eome. R. Koch, Berlin. Lord Lister, London. F. V. Recklinghausen, Strassburg. Rudolph Virchow, Berlin. Class III. — 3foral and Political Sciences. — 23. Section I. — 5. Section HI .—4 Philosophy and Jurisprudence. Political Economy and History. Heinrich Brunner, Berlin. James Bryce, London. A. V. Dicey, Oxford. Herman Grimm, Berlin. W. E. Hearn, Melbourne. Theodor Mommsen, Berlin. F. W. Maitland, Cambridge. Sir G. 0. Trevelyan, Sir Frederick Pollock, Bart., London. Bart., London. Section H. — 7. Section IV .—7. Philology and Archmology. Literature and the Fine Arts. Ingram Bywater, Oxford. E. de Amicis, Florence. W. Dorpfeld, Athens. Georg Brandes, Copenhagen. Sir John Evans, Hemel Hempstead. F. Brunetiere, Paris. H. Jackson, Cambridge. Jean Le'on Ge'rome, Paris. J. W. A. Kirchhoff, Berlin. Rudyard Kii^ling, Rottingdean G. C. C. Maspero, Paris. G. Paris, Paris. Karl Weinhold, Berlin. Leslie Stephen, London. STATUTES AND STANDING YOTES. STATUTES. Adopted May 30, 1854: amended September 8, 1857, November 12, 1862, May 24, 1864, November 9, 1870, May 27, 1873, January 26, 1876, June 16, 1886, October 8, 1890, January 11 and May 10, 1893, May 9 ah*/ Ociineromyces coarctatus, 410. crispatus, -113. ihizophorus, 412. Dioscorea platycolpota, 471. Diurual Cyclones, 305. Earle, R. B. See Jackson, C. L., and Earle, R. B. Eclipse Cyclone, 305. Electrical Conductivity of Iron, 119. Eunielampodium, 456. Eupatorium anisopodum, 477. araliaefolium, 477. Bigelovii, 477. conspicuum, 477. Coulteri, 477. dasycarpum, 478. dryophiliun, 478. Gonzalezii, 479. hyssopinum, 478. Lemmoni, 479. leonense, 479. Liebniannii, 480. longifolium, 480. lucidum, 480. Luxii, 480. lyratuni, 481. Mariarum, 481. pachypodum, 481. pansamalense, 482. pinabetense, 482. pleianthum, 483. prionobium, 483. prionophyllum, 484. quadrangulare, 484. viscidipes, 484. Euphorbia calcicola. 496. interaxillaris, 495. lancifolia, var. villicaulis, 496. muscicola, 495. potosina, 495. puberula, 494. Everett, W., The Life and Works of the late Henry Sidgwick, 538. Evolvulus Seleriana, 498. Fellows, Associate, deceased, — Frederick f^dwin Church, 517. Jacob Maudes DaCosta, .534. George INIercer Dawson, 539. James Edward Keeler, 534. William Mitchell, 534. Henry Augustus Rowland, 549. Edward Elbridge Salisbury, 542. Fellows, Associate, deceased, — Alfred Stills. 534. Fellows, Associate, elected, — George Mercer Dawson, 531. Thomas Messenger Drown, 535. Melville AVeston Fuller, 532. Charles Ellery Hale, 540. William Stewart Halsted, 540. William Williams Keen, 540. Franklin Paine Mall, 540. Eliakim Hastings Moore, 539. Edward Leamington Nichols, 540. Henry Fairfield Osborn, 540. Cyrus Guernsey Pringle, 540. Rufus Byam Richardson, 532. Thomas Day Seymour, 532, Henry Morse Stevens, 532. Charles Otis Whitman, 540. Fellows, Associate, List of, 581. Fellows, Resident, deceased, — Charles Carroll Everett, 539. Thomas Gaffield, 537. Nathaniel Holmes, 549. John Elbridge Hudson, 534. Sylvester R. Koehler, 534. Augustus Lowell, 534. Fellows, Resident, elected, — William Ernest Castle, 531. Frank Shipley Collins, 539. Alexander Wilmer Duff, 539. Ephraira Emerton, 539. Merritt Lyndon Fernald, 531. Lewis Jerome Johnson, 539. Theodore Lyman, 539. Henry Lloyd Smyth, 539. Frank William Taussig, 539. Jay Backus Woodworth, 531. Fellows, Resident, List of, 577. Fernald, M. L., Some New Sper- niatophytes from Mexico and Central America, 489-506. Finibristylis alamosana, 491. Holwayaiia, 492. melanospora, 491. obscura, 492. Foreign Honorary Members, de- ceased, — Jacob Georg Azarth, 542. Due de Broglie, 549. Charles Hermite, 538. Willy Kiihne, 534. Max Midler, .549. Baron Russell of Killowen, 534. Henry Sidgwick, .534. William Stubbs. 549. INDEX. 599 Foreign Honorary Members, elected, — Edmondo de Amicis, 541. Sir Thomas Lander Brunton, 540. Albert Venn Dicey, 540. Sir Archibald Geikie, 532. William Edward Heai"n, 540. Henry Jackson, 541. Robert Koch, 540. Hugo Kronecker, 540. Heinrich IMiiller-Breslau, 540. Sir John Murray, 532. Jules Henri Poincare, 540. William Cawthorn Unwin, 532. Foreign Honorary Members, List of, 583. Fossil Crab from Gay Head, 1. Fraprie, F. R. See Richards, T. W., and Fraprie, F. R. Frost, E. B., Report of Progress to Rumford Committee, 521. Gelasimus pugilator, 415. Geometry on Ruled Quartic Sur- faces, 17. Glasgow, University of. Ninth Jubi- lee Celebration, 538, 542. Glyphosperma Palmeri, 492. Gray Herbarium of Harvard Uni- versitv, Contributions from, 453, 489. Groups, Continuity of, 83. Hale, G. E., Report of Progress to Rumford Committee, 522. Hall. E. H., On tlie Tliermal and Electrical Conductivity of Soft Iron, 119-141; Report of Pro- gress to Rumford Committee, 523 ; An Exposition of the Theory of Electrons, the Elec- trical Fragments of Atoms, 542. Hardystonite, 111. Harvard Mineralogical Museum, Contributions from, 111. Heat Capacity, Nomenclature of, 325. Heterotoma Goldinanii, 504. stenodonta, 504. Hudson, E. J. See. Mabery, C. F., and Hudson, E. J. Hydrocarbons in Petroleum, 283. Infinitesimal Transformations, S3. International Atomic Weights, 169. Ipomoea caudata, 498. Iron, Conductivity of, 119. Isopod Crustaceans, Tracks of, 67. Jackson, C. L., and Behr, G. E., Symmetrical Triiodbenzol, 331- 338. Jackson, C. L,, and Calhane, D. F., The Dinitro Compounds of Para- dibrom benzol, 533. Jackson, C. L., and Cohoe, W. P., Certain Derivatives of Metadi- bromdinitrobenzol, 73-82. Jackson, C. L., and Earle, R. B., On the Action of Sodic Sulphite on Tribromdinitrobenzol, and Tribromtrinitrobenzol, 229-238. Jackson, C. L., and Koch, AV., On Certain Derivatives of Orth- obenzoquinone, 195-228. Jackson, R. T., Resorption as a Factor in Growth, 541. Japanese Peti'oleum, 295. Koch, W. See Jackson, C. L., and Koch, W. Laboulbeniaceae, 395. Laws, F. A., An Apparatus for recording Alternating Current Waves, 319-324 ; Report of Progress to Rumford Commit- tee, 523. Lewis, G. N., A New conception of Thermal Pressure, and a Theory of Solutions, 143-1(18; The Law of Physico-chemical Change, 542. Librarian, Report of, 528. Limulus polyphemus, 64; Trails of, 61. Lobelia gruina, var. conferta, 503. Nelsonii, 503. regalis, 503. Lowell, A., Bequest of, 534, 536. Lyman, T., False Spectra from the Kowland Concave Grating, 239- 252. Mabery, C. F., Investigations on the Composition of I'etroleum, 253-304. Mabery, C. F., and Hudson, E. J., On the Composition of Cali- fornia Petroleum, 255-283. 600 INDEX. Mabery, C. F., and Sieplein, O. J., On the Chlorine Derivatives of the Hydrocarbons in California Petroleum, 283-295. Mabery, C. F., and Takano, S., On the Composition of Japanese Petroleum, 295-304. Magnesia Oxalate, 375. Mangauous Sulphate, 507. Marbles, Thermal Diffusivities of, 11. Mayer, 328. McCaffrey, C. F. See Richards, T. W., McCaffrey, C. F., and Bisbee, H. Melampodium, Synopsis of, 455. Melampodium Achillaeoides, 4G5. Americanum, 459, 466. angustifolium, 461. aj^pendiculatum, 457. appendiculatum, var. leiocar- pum, 457. appendiculatum, var. sonorense, 457. arenicola, 457. arvense, 464. australae, 465. Baranguillae, 465. Berterianum, 465. bibracteatum, 465. brachyglossnm, 465. camphoratum, 463. cinereum, 458. cinereum, var. argophyllum, 458. cinereum, var. ramosissimuni, 458. copiosum, 465. coronopifoliiim, 465. cupulatum, 463. diffusum, 460. diffusum, var. lanceolatnm, 460. digynum, 465. divaricatum, 465. Dombeyanura, 466. flaccidum, 464. glabrum, 465. gracile, 462. heterophyllum, 460. Hildalgoa, 466. hirsutnm, 466. hispidum, 464. humile, 466. Kunthiaiium, 460. lanceolatum, 466. Melampodium leucanthum, 458. hiebmannii, 466. linearilobum, 459. longicornu, 457. longifolium, 465, 466. longipes, 459. longipilum, 458. manillense, 466. microcephalum, 462, 466. mimulifolium, 462. montanum, 463. oblongifolium, 462. ovatifolium, 466. paludicola, 456, 466. paludosum, 463. panamense, 466. paniculatum, 462, 466. perfoliatum, 465. Pringlei, 461. pumilum, 466. ramosissimum, 466. rhomboideum, 466. Eosei, 4 61-. ♦ Rosei, var. subintegrum, 462. ruderale, 466. sericeum, 459, 466. sericeum, var. brevipes, 466. sericeum, var. exappendicula- tum, 459. sericeum, var. longipes, 466. sinuatum, 461. suffruticosum, 456. tenellum, 463. ternatum, 466. INIelczer, G. ^ee Wolff, J. E. Merostomatous Trails, 61. Merostomichnites beccheri, 67. narragansettensis, 70. Metadibromdinitrobenzol, 73. Meteorological Observations, 305. Mimosa acanthocarpa, var. des- manthocarpa, 472. eurycarpoides, 472. ionema, 473. Watsoni, 473. ]\rontanoa arborescens, 487. Monarda Pringlei, 501. Nichols, E. L., Report of Progress to Rumford Committee, 523. Xocca, Synopsis of, 467. Nocca angustifolia, 470, biflora, 468. decipiens, 470. glandulosa, 470. INDEX. 601 Nocca helianthifolia, 468. helianthi folia, var. levior, 408. helianthifolia, var. suaveoleus, 468. heteropappus, 470. Liebinannii, 470. Mo^iuiiiana, 469. mollis, 471. Palmeii, 471. Pringlei, 469. rigida, 469. tomentosa, 470. Nomenclature of Heat Capacity, 325. Nominating Committee, 535. Officers elected, 530, 538; List of, 576. Orthobenzoquinone, 195. Packard, A. S., A New Fossil Crab from the INIiocene Greensand Bed of Gay Head, 1-9 ; On Sup- posed INlerostomatous and Other Paleozoic Arthropod Trails, 61- 71. Parathesis chiapensis, 497. Pectis J.essingii, 506. Peiree, B. O., Report of Progress to Rumford Committee, 525. Peiree B. O., and Wilson, R. W., On the Thermal Dift'usivities of Different Kinds of Marble, 11-16. Pernettya ovata, 496. Petroleum, 2.53. Physalis puberula, 502. Physical Laboratory of the Massa- chusetts Institute of Tech- nology, Contributions from, 319. Pickering, E. C, Report of Progress to Rumford Committee, 524. Piqueria pyramidalis, 475. Plateanus glabrata, 493. Quartic Surfaces, 17. Records of Meetings, 517. Reissner's Fibre, 443. Rhizomyces gibbosus, 409. Rhodes, J. F., Sherman's March to the Sea, 536. Richards, T. W., International Atomic Weights, 169-170; Sug- gestion concerning the Nomen- clature of Heat Capacity, 325- 329 ; Report of Progress to Rumford Committee 526; A Table of Atomic Weights, 545- 546. Richards, T. W., and Archibald, E. H., A Study of Growing Crystals by Instantaneous Mi- crophotography, 339-353. Richards, T. W., and Fraprie, F. R., The Solubility of Manga- nous Sulphate, 507-514. Richards, T. W., McCaffrey, C. F., and Bisbee, II., The Occlusion of Magnesic Oxalate by Calcic Oxalate, and the Solubility of Calcic Oxalate, 375-393. Robinson, B. L., Synopsis of the genus Melampodium, 455-466; Synopis of the genus Nocca, 467-471 ; New Species and newly noted Synonymy among the Spermatophytes of Mexico and Central America, 471-488 ; Recent Advances in the General Classification of the Flowering Plants, 541. Ross, D. W., Design as a Science, 355-374. Rowland Concave Grating, 239. Ruellia cupheoides, 502. Rumford Committee, Report of, 519 ; Reports of Progress to, 521. Rumford Fund, Papers published by Aid of, 11, 119, 239, 339. Rumford Premium, 595 ; Award of, 520, 529. Russelia Deamii, 474. trachypleura, 474. Sabine, W. C, Report of Progress to Rumford Committee, 526 ; The Influence of Architecture on Melody and the Develop- ment of the Musical Scale, 537. Salvia ageratifolia, 499. albicans, 501. Dugesii, 500. igualensis, 500. lencaiitha, for. iobaphes, 501. setulosa, 499. Sessei, 501. tiliaefolia, var. rhyacophila, 499. 602 INDEX. Sargent, P. E., The Development and Function of Reissner's Fibre, and its Cellular Connec- tions, 443-452. Schefferite, 111. Sieplein, O. J. See Mabery, C. F., and Sieplein, O. J. Slocum, S. E., On the Continuity of Groups generated by Infinites- imal Transformations, 83-109. Sodic Sulphite, 229. Solanum rostratum, var. subinteg- rum, 502. Solar Eclipse of May 28, 1900, 305. Solidago Pringlei, 505. Solubility of Calcic Oxalate, 375; of Manganous Sulphate, 507. Solutions, Theory of, 143. Spectra, False, from the Rowland Concave Grating, 239. Spelerpes bilineatus, 177. Spermatophytes from Mexico and Central America, 471, 489. Statutes and Standing Votes, 585. Stigmatomyces constrictus, 401. Diopsis, 399. dubius, 402. gracilis, 403. humilis, 401. Ilydrelliae, 404. Limnophorae, 400. Limosinae, 406. Papuanus, 407. proboscideus, 403. purpureus, 404. rugosus, 398. Scaptomyzae, 400. spiralis, 405. Symmetrical Triiodbenzol, 331. Takano, S. See Mabery, C. F., and Takano, S. Thaxter, R., Preliminary Diagnoses of New Species of Laboulbenia- ceae, 395-414. Thermal Conductivity of Iron, 119. Thermal Diffusivities of Marbles, 11. Thermal Pressure, 143. Trails, Arthropod, 61. Transformations, Infinitesimal, 83. Treasurer, Report of, 517. Tribromdinitrobenzol, 229. Tribromtrinitrobenzol, 229. Triiodbenzol, 331. Trowbridge, J. Results obtained with a Storage Battery of Twenty Thousand Cells, 532. Valeriana retrorsa, 502. Variation in Fiddler Crab, 415. Warren (C. M.) Committee, Report of, 527. Warren (C. M.) Fund, Aid from, 253. Wendell, B., Literary History of America, 535. Williams, F. B., Geometry on Ruled Quartic Surfaces, 17-60. Willson, R. W. See Peirce, B. O., and Willson, R. W. Wolff, J. E., On Hardystonite and a Zinc Schefferite from Franklin Furnace, N. J. ; with a note on the Optical Constants of the Schefferite by Dr. G. Melczer, 111-118. Wright, J. H., Recent Excavations in Crete, 535. Xanthocephalum 505. megaloceplialum, Yerkes, R,M., A Study of Variation in the Fiddler Crab, Gelasimus pugilator Latr., 415-442. Zarabellia, 460. Zoological Laboratory of the Mu- seum of Comparative Zooloiry at Har\ard College, Contribu- tions from, 177, 415, 443.