eg es neh A SoG UM HS Weer ere nig DO wy ie GAC ised WNSOECS SR 3 _ Gj: GK rane 5 3 C CKE CCE CLO 7 K SS eee eC CEG CCE oe C cs mn 1 3G -< as C sf ‘oy GIIDIGIOING Wd ANd DORSOS SI, A eC C Eq x ¢ < WISY : / Ad | WW Wogtyges C2 Io: Ren S oom E eesti, —- 2 \ ee eee peg AS GN RAPA SS eRe, CC Cae C @ COL CG & TE CWE. Co CE C Cal C 5 & Es S S Cae “CG is wv CIS IG GIG ees a w PIAA» Bee a wig DF 42 SOOO Sat Avis SOUS poner vY LCs th Nine) Di OG OLD ‘ YA A OR co LG BIY NA A Sa Hh Nog ies 4 iv oe y dee DY AE 8g i! ~ - pe Le Fare) pod DIS vd dnd ce 4 Abe 5 OR | ame Naan Ae a Fe 4k oN 2 Ni nn i Bs G y) 25 e UNIVERSITY OF MISSOURI STUDIES EDITED BY W. G. BROWN Professor of Chemistry VOLUME II SCIENCE SERIES PUBLISHED BY THE UNIVERSITY OF MISSOURI IgII a2\oe¥ CONTENTS NUMBER PAGE 1. An Introduction to the Mechanics of the Inner Ear, by Max Meyrr, Pu. D., Professor of Ex- perimental Psychology... 0... c cc ec vec c cc cccees 2. The Flora of Boulder, Colorado, and Vicinity, by Francis Porter Daniets, Professor of the Ro- mance Languages, Wabash College. Formerly Assistant in the University of Missourt.......... 149 VoLuME I]. SCIENCE SERIES ~ NuMBER I THE UNIVERSITY OF MISSOURI | STUDIES EDITED BY - W. G, BROWN Professor of Chemistry AN INTRODUCTION TO THE MECHANICS OF THE INNER EAR BY MAX MEYER, Ph. D. Professor of Experimental Psychology PUBLISHED BY THE (onal Museure! UNIVERSITY OF MISSOURI } December, 1907 PRICE, $1.00 Tie AN INTRODUCTION TO THE MECHANICS OF THE INNER EAR VoLumME II SCIENCE SERIES NUMBER I THE UNIVERSITY OF MISSOURI SI UIDIVES EDITED BY W. G. BROWN Professor of Chemistry AN INTRODUCTION TO THE MECHANICS OF THE INNER EAR BY MAX MEYER, Ph. D. Professor of Experimental Psychology PUBLISHED BY THE UNIVERSITY OF MISSOURI December, 1907 Copyright, 1907, by THE UNIVERSITY OF MISSOURI COLUMBIA, MO.: E. W. STEPHENS PUBLISHING COMPANY, 1907 PREFACE About two thirds of this study has been published at different times in various German scientific periodicals, chiefly in the Zeit- schrift fiir Psychologie und Physiologie der Sinnesorgane. The author has long hesitated to present in book form the results of his labor in this remote corner of scientific investigation because the interest in these problems seems to be neither intense nor general. This lack of interest on the part of the scientific public, however, is not due to the unimpor- tance of the subject, but rather to a wide-spread conviction that all the problems ‘pertaining to it were solved half a cen- tury ago and that therefore nothing problematic is left. For years during which—since his student days—these pro- blems have been in the mind of the writer, he has belonged to an exceedingly small minority of scientific men, who have not permitted themselves to become captives of this convic- tion. But since this minority is gradually increasing in num- ber, and since professional friends have encouraged the writer he has decided to lay before the public the results of his in- vestigations in a continuous exposition of his theory as far as it goes at present. It is natural that he has preferred to do this in the English language, since nearly all his previous publications concerning it are in German. The author does not pretend to present in this book a complete, perfect, and final solution of the problem concern- ing the mechanics of the inner ear. His farthest reaching hopes will be fulfilled if he succeeds in impressing upon the reader’s mind the fact that there are here still problems left for solution and in giving these problems such a clear and definite formulation that the interest of others will be turned towards them. There is little hope for a final solution of these problems except by the co-operation of many investi- \7 gators. The contents of this book are arranged from a peda- gogical rather than from a logical point of view. The author does not intend to present a systematic representation of his own ideas for comparison with the ideas of others, but rather a series of lectures as he would deliver them before a class of college students, not presupposing any knowledge or any in- terest but what a somewhat advanced college student might be expected to possess. A reader who should prefer to make himself acquainted with the contents of this book from an- other point of view, will be able to do this by the aid of the index added. The author has attempted to omit as much as possible everything of a polemic nature. His criticism of the views of other investigators may be found in his previous publica- tions. In this book he does not propose to record the views of other scientists, but the conclusions which he has reached himself after more than a decade of thought concerning these problems. For the reader who might be interested in the development of the author’s thought concerning these prob- lems, he has added at the end of the book a list of those pub- lications of his own which are directly concerned with the problems here presented. The author hopes that this booklet will help to break down the barrier of dogmatism which has too long stood in the way of progress in this field of scientific inquiry, and which is still far from being a thing of the past. It is truly dogmatism to profess that the application of so simple a theorem as that of Fourier can do justice-to an attempt at comprehending the mechanical processes underlying the won- derfully complicated and unfortunately only superficially known phenomena of audition. vi THE MECHANICS OF THE INNER EAR Everyone knows that the part of our body which in ordi- nary life we call the ear and which anatomists call the pinna, is not the organ of hearing but a mere ap- The external ear pendage to the organ. Its chief utility consists in the fact that it aids us in dis- tinguishing sounds coming from a source in front of us from sounds in our rear. We know how much more difficult it is to understand the words of a speaker behind us than the words of one who stands before us. We can reverse this con- dition by forming of our hands leaves similar to the external ears, but naturally larger and placing them opposite the ears, that is in front of the opening, the auditory passage. Then, sounds from the rear can enter the passage and reach the tympanum with a much greater force than sounds coming from the front. Animals, being able to move their external ears, can use them, of course, to greater advantage than hu- man beings. The organ of hearing—in the narrower sense of the word—that is, the anatomical structure within which the ends of the auditory nerve fibres receive The tube con- their peripheral excitations, is to be taining the sense found stretched out along the central Geesuis) long line of a tube which is very narrow rel- and narrow ative to its length. This tube is called by the anatomists the cochlea, because it is not built in the form of a straight line, but coiled up like the tube of a snail shell. The advantage of its being coiled up in this way is obviously not to be sought in its mechanic—or rather hydrodynamic—function. At least, no (1) 2 UNIVERSITY OF MISSOURI STUDIES one, to the writer’s knowledge, has ever expressed himseli as inclined to look for it there. For its hydrodynamic func- tion it is clearly of no great importance whether the tube is curved or straight, and we shall speak of it in the following for the most part as if it were straight, in order to simplify the discussion. The real advantage of this shape of the tube is doubtless a mere anatomical one, it being possible thus to find a better place for it in the base of the skull. We must, in order to understand the function of this tube, be aware of the fact that it is filled with a watery fluid, lymph, and that its walls consist of hard The contents of Unyielding bone. Now, when we go the tube, a fluid, through the literature of the subject, we is incompressible often see writers speak of waves in the fluid which are said to pass along the tube as air waves move in a tube filled with air. Views of this kind cannot, of course, contribute towards an un- derstanding of the process of stimulation of the periph- eral nerve ends. They are not rational considerations of the facts before us, but theoretical dreams, forgetting the physical conditions of the case. Let us regard the velocity of the sound in such a fluid as that of the inner ear as about fourteen hundred meters, let us remember that the whole length of the tube is only a couple of centimeters, let us understand, then, that even with rather high tones of short wave lengths— beyond the musical range—the total length of the tube is only a small part of the spatial length of the waves said to travel up and down the tube; and we shall admit at once that to speak of tone waves travelling in the lymph up and down the tube is like speaking of a horse race which is to take place within a dog kennel. We have to follow the custom of the physicists who in such cases neglect the compressibility and elasticity of the small volume of fluid altogether. We must, therefore, regard the fluid in the cochlea as being of identical MECHANICS OF THE INNER EAR 3 density throughout at any given time, that is practically, as unelastic, incompressible. il li Fig.1. The external and the middle ear The walls of the tube consist of hard, unyielding bone, except in two places where the bone is broken through and the openings closed by flexible mem- The authe Tee branes. These two places are common- two windows to ly called the oval and the round windows. communicate with (The fact that the tube communicates the middle ear with the semicircular canals and the oth- er parts‘of the labyrinth can here be neg- lected, since all these communicating cavities are also enclos- ed in bone, not possessing any windows.) On the other side of these windows there is the air of the middle ear. Let us now consider at once what could happen to the fluid in the tube if rhythmical changes of pressure in the external air (a “tone”) caused, through the tympanum, like changes (of condensation and rarefaction) in the air of the middle ear. Let us at present, however, consider this under the imaginary assumption of no chain of ossicles existing in the middle ear. What was said about waves in the fluid of the tube holds good to some extent also for the air in the middle ear. That which occurs there is the same as that which occurs, say, in a bicycle 4 UNIVERSITY OF MISSOURI STUDIES pump, that is, an alternate condensation and rarefaction of all the particles of air almost simultaneously. This condensation and rarefaction always acts in the same _ sense (positive or negative) on both windows of the tube. According to the laws of hydrodynamics no motion inthe fluid of the tube can result from the difference in size of the two windows. It is hardly comprehensible, therefore, why we find in literature lengthy discussions of the question whether it is the round or the oval window through which “the tone waves’ enter the inner ear. They do not enter through either window since they do not occur in the middle ear, the volume of this cavity being too small to contain whole tone waves. Only after complete destruction of the tympanum would the ques- tion as to the manner in which an air wave strikes the two windows attain practical importance. Under normal condi- tions we must regard all the air particles in the middle ear as being, at any time, of identical density, and, thus, as unable to produce any movement in the inner ear. If there were no ossicles, the fluid in the tube would remain practically motionless. But to the membrane of the oval window is attached the plate of the Disturbances stirrup which has a somewhat rigid con- within the tube — nection with the tympanum. The result are caused by motion of the stirrup is that every movement of the tympanum is accompanied by a movement of the stirrup in the same (positive or negative) direction. Whenever the tympanum moves inwards, the air in the middle ear is, of course, somewhat condensed. But this condensation or rarefaction has no relevant influence on the fluid in the tube, as before mentioned. The alternate condensation and rarefaction of the air in the middle ear, re- sulting from like processes in the external auditory passage, is an unavoidable, but functionally negligible by-product of the mechanical process in question, bearing no direct rela- MECHANICS OF THE INNER EAR 5 tion to the function of the tube. It is the movement of the stirrup which causes the disturbances in the fluid of the tube which we have soon to study in detail. And this motion of the stirrup is made possible only through the mediation of solid bodies, the auditory ossicles. The bony connection between the stirrup and the tym- panum would serve its purpose of causing movements in the fluid of the tube whatever might be The auditory the special structure of this connecting ossicles are a link. As a matter of fact, it is arranged system oflevers in such a particular manner that it acts as a lever (or system of levers), the large arm, so to speak, being attached to the tympanum, the small arm to the stirrup. This effect, however, is produced in dif- ferent animals in different ways. In birds, for example, (Fig. 2) there is no chain of three little bones, but only a single bone, a rod bearing an oval plate. The leverage of this sim- ple connection is explained by the fact that the tympanum and the window plate are not in parallel planes. The far » plate Fig. 2. Schematic representation of the leverage in birds more complicated connection by means of three links of a chain of bones in most of the mammals has been theoretically studied by various investigators and found to result in a sim- ilar, but probably more delicately adjustable leverage than the simpler arrangement in birds. The advantage of the lev- 6 UNIVERSITY OF MISSOURI STUDIES erage is easily understood. To cause a fluid to move along a narrow tube requires a considerable force because of the friction resulting from the narrowness of the passage. The :extent of movement, on the other hand, may be of any minuteness, the nerve ends certainly being sensitive to the very slightest curving of their tufts of hairs of which we shall have to speak again. It is of advantage, therefore, to gain force at the expense of magnitude of displacement. Someone might here raise the question: Why are there two windows when only one of them has a solid connection with the tympanum? The answer to this Why would not question is very simple. If there were one window not a second window, the stirrup could be sufficient? not move at all. Imagine a bottle filled with water up to the stopper and the stopper fitting the neck most accurately. Would it be possi- ble to drive the stopper farther in? The water being incom- pressible, it would not be possible for a moderate force to drive a perfectly fitting stopper in any more than to pull it out. The second window, closed by a flexible membrane, is therefore necessary if the movements of the stirrup and of the fluid in the tube are to take place. If it were not for movements of the fluid, the round window would be super- fluous. It is, however, not an essential condition that the sec- ond window should open on the middle ear and not perhaps directly on the external air space; for instance, on the exter- nal auditory passage, or anywhere on the skull. But it is an essential condition that the one window containing the stirrup plate open on a drum and that the plate be rigidly connected with the external membrane of this drum. Thus every condensation or rarefaction of the air outside the drum must result through movements of the tympanum in like condensations or rarefactions inside the drum; the movements of the tympanum must result in move- MECHANICS OF THE INNER EAR 7 ments of the stirrup, and consequently in movements of the fluid in the tube. If the tympanum is destroyed to such an extent that the middle ear can no longer act even imperfectly as a drum, movements of the fluid in the tube must be dif- ficult to produce. The organ is then deprived of its normal manner of functioning—a defect which does not necessarily involve total deafness, yet certainly a great impairment of the sense of hearing. We naturally do not wonder at the fact that the round window is arranged in the simplest way possible, that is, opening on the middle ear not far from the oval window. Let us now attempt to determine what movements would occur in the tube, caused by movements of the stirrup, if this tube were a perfectly plain tube, con- ineovement taining nothing whatever but an incom- of the fluid in pressible fluid. It is a decided advantage a plain tube to study first a case as simple as can be imagined. We are sure that, thus, the elementary foundations of our thought will be clear and not confused by the influence of a complexity of conditions and a sum of powerful prejudices which almost inevitably ac- i a Fig. 3. Movement of fluid in a plain tube company a complexity of conditions. Let us try to keep clear of such influences. In figure 3 we see the anatomical facts of our imaginary case diagrammatically represented: a long and narrow tube, two windows at one end, one of these win- dows containing the stirrup, the other end of the tube closed. 8 UNIVERSITY OF MISSOURI STUDIES The question is this: What will happen to the particles of fluid in the tube when the stirrup moves slightly inwards or out- wards? This is a problem which can be answered either on the basis of our general knowledge of similar processes or by means of a special experiment. Let us first try the former way. When the stirrup is pushed inwards and the round window outwards, the liquid near the windows must certainly move in the direction indicated by the arrows in the figure. Of course, the direction of the movement would be the opposite if the movement of the stirrup changes its sign and pulls instead of pushes. But what would happen in the fluid at the other end of the tube? At x or even at y? The answer to the question is simple: Nothing would happen. No movement of any kind could possibly occur there, since there is no sufficient cause why any movement should occur. The friction of the fluid against the walls of the tube, which is quite considerable in a narrow tube, must prevent any spread- ing of the disturbance beyond a very near limit. That is, when- ever the stirrup moves back and forth, those particles of the fluid which are in the nearest path leading from the oval to the round window must move accordingly. All the rest of the fluid remains motionless. In order to demonstrate the facts just mentioned to those finding difficulty in understanding that from the general laws of hydromechanics nothing else could re- A simple sult in the case in question but what we experiment have just described, we may perform the following experiment. A box containing white clay in a plastic condition has two circular openings on one side, not far from each other, as shown by figure 4 in cross-section. We now press, by means of a piston, into one of the openings, A, a small quantity of colored clay, then a small quantity of white clay, and again colored clay until the latter becomes visible on the outside of the box MECHANICS OF THE INNER EAR 9 at the other opening, B. In our figure we see at a and b the colored clay pressed in first. The part protruding be- yond the outside of the box is cut away. At c we see the white clay pressed in afterwards, and at f the advance guard, so to speak, of the colored clay pressed in last. What has happened within the box is obviously this. The colored clay pressed in first, collects inside the box near A’ in the direc- tion of B. A corresponding amount of the white clay with Fig. 4. An experiment with plastic clay which the box was filled has been pushed out through the opening B. The white clay pressed in next forces up the colored clay somewhat as a mass of glass is blown up in a glass factory to form a bottle. This white clay is forced up in turn by the succeeding colored clay, the “bottle” of colored clay increasing its dimensions at the same time. During this whole time and afterwards the total mass moves in the di- rection of B. However, the particles of clay to the left, pie) UNIVERSITY OF MISSOURI STUDIES nearer the openings, move much more quickly than those farther to the right. This is seen from the fact that the left wall d of the white “bottle” has been separated entirely from the opening A and is just getting ready to disappear altogether through the opening B, whereas the right wall e is merely beginning to sever its connection with A. We have here a simple experimental proof for the statement of the preceding paragraph that friction prevents the spreading of the motion beyond narrow limits, causing it to occur as near the two openings as possible. Although the experiment in this form does not show it, the reader hardly doubts that somewhat farther to the right, say six inches from the open- ings, no motion whatsoever has occurred during the whole time. The quickest motion, of course, is in this particular case not found at the extreme left, at g, but about a fourth of an inch to the right, since the friction at g is too great. Without entering into a detailed study of the hydrodynamic problem which confronts us here, in which friction against the walls, internal friction in the fluid, and the momentum of the fluid play their roles, let it be sufficient to say here that the motion is practically limited to the portion of the tube near the windows in accordance with the general law of nature that whatever occurs, occurs with the least pos- sible expenditure of energy. Some clay is pressed in at A. The same quantity has to pass out at B. This can be made possible by many kinds of displacement of the particles with- in the box. But only one form of displacement becomes actual, the one that requires the smallest amount of work to be done by the piston at A. And this form of displacement consists in the displacement being confined to the neighbor- hood of the openings. MECHANICS OF THE INNER EAR Il Let us now consider another imaginary case which will contribute towards a better understanding of the processes actually occurring in the ear. Suppose Mhelehecwore a part of the tube, near the windows, to rigid partition be divided by an inflexible partition, as within the tube shown in figure 5. It is self-evident that in this case every movement of the stir- rup would cause the particles of fluid in the upper and lower division of the tube to move in the directions of the arrows, parallel to the partition; and the particles at y, at the end of the partition, to move up or down. But the fluid farther on in the undivided tube would remain motionless, as in the former case, since there is no sufficient cause why it should move. If the partition extended farther, the only change re- Fig. 5. A rigid partition in the tube sulting would be a diminution of the length of that part of the tube where the fluid remains permanently motionless. If the partition extended to x (Fig. 5), leaving only a small opening of communication between the upper and lower division, all the fluid within the tube would have to move whenever the stirrup moves. If the partition extended throughout the tube, leaving no communication whatever between the two divisions, no movement of the fluid could then take place, of course; but no piston-like movement of the stirrup could then take place either. 12 UNIVERSITY OF MISSOURI STUDIES Let us now imagine a third case. Suppose a partition to divide the tube lengthwise into two divisions, leaving, however, a small opening of communica- Mheletectiol a tion between the divisions at x. Suppose flexible, but inelas- further this partition to be neither per- tic partition with- fectly rigid like a wall of hard bone nor in the tube as readily yielding and in turn contract- ing as a thin rubber membrane, but to be of the physical nature of a soft leather strap somewhat loosely stretched out between the opposite sides of the tube to which it is assumed to be well attached. To have something definite in mind, let the reader think, for compar- ison of its function, of a leathcr-seated chair. If you press from below, the seat yields and bulges upwards; but soon it stops in spite of your effort. If now you sit down on the chair, the seat bulges downwards; but again, it soon stops—how could it otherwise be used for the support of your weight? But what is particularly important to note here, is the fact that the leather seat, after it has bulged either way, may continue to remain thus until some ex- ternal force acts upon it again from the other side. Now let us consider the movements which would occur in the fluid of a tube, divided into two divisions by a partition of the nature just described. If the partition could yield indefinitely, the case would obviously be practically the same as the first one we studied—without any partition. That is, the fluid would move near the two windows and the part of the partition suspended between moving masses of fluid would move with the fluid. Farther on where the fluid re- mains motionless the partition would remain motionless too. But we made the assumption that the partition, like the seat of a leather-seated chair, can move only within certain narrow limits up and down. Now, the result of this condi- tion will be this. When the stirrup begins moving inwards, MECHAN:CS OF THE INNER EAR 13 the part of the partition next to the windows must follow the movement of the fluid and move downwards. But soon it has reached its lower limit. Consequently it acts now as an unyielding partition, the effect of which we studied in our second case above. The fluid just above and below this temporarily unyielding part can now move only horizontally, but the particles of fluid next to the end of this now motionless piece move down and push the underlying piece of the par- tition down until it has reached its lower limit. And so, gradually, further and further pieces of the partition come Fig. 6. The partition moves within an upper and a lower limit down until the stirrup stops moving inwards. Figure 6 shows a number of successive stages of the position of the partition during this process. The vertical scale in this rep- resentation is, of course, enormously exaggerated relative to the horizontal scale. But at once after stopping, the stirrup begins to move in the opposite direction. At once the par- ticles of fluid next to the windows (not those which have moved down last) move upwards and take the corresponding part of the partition with them until it has reached its upper limit. Now the following parts come up, and so on in exactly the same way as before, except that we have now an upward instead of a downward movement, — until the stirrup stops moving in this direction. Let us remember by all 14 UNIVERSITY OF MISSOURI STUDIES means, because a mistake made here in our comprehension of the process would result in serious errors later, that the bulging of the partition, whether up or down, begins in- evitably as near the two windows as possible, and that fur- ther pieces can bulge in either direction only under the condition that all the pieces nearer the windows have already reached their limit in that same direction. We made at the beginning of the last paragraph the assumption that there was a small opening between the two divisions at the extreme end of the tube. A safety valve Let us see what purpose such an opening could serve. What would be the result of an extraordinarily large movement of the stirrup, so large that the whole length of the partition would reach its—upper or lower—limit of position before the stirrup ceased to move in the same direction? The result would be either an enforc- ed stop of the movement of the stirrup or, if the external force acting on the tympanum and stirrup was too violent, a bursting of the partition. The latter disastrous result, how- ever, can to a considerable extent be guarded against by the opening in question. As soon as the total length of the par- tition has bulged the fluid will begin to flow through this opening from one division of the tube into the other, until the stirrup stops moving in the same direction. Such an opening therefore can serve as a kind of safety valve for the protection of the partition. After having studied the hydromechanical function of several imaginary tubes with divers interior equipments, let us now turn to a careful survey of the The anatomy and facts which the anatomists have discover- physiology of ed for us concerning the structure of the the inner ear inner ear. Figure 7 shows us in a cross- section all the important details which have been found there by the anatomists. Hard bone pro- 15) MECHANICS OF THE INNER EAR auoje uo WA1ed oy} Jo UOT}eS peyluseU s10W B UMOYS SI MOl[ag ‘uolj1q1ed 94} PUL SUOISIAIP OM} 3}I YIM f9qgn} 9y3 YsNorIY} UOL}OS B UMOYS SI VAOGE }J2] 94} OT, ‘L31g 16 UNIVERSITY OF MISSOURI STUDIES trudes from diametrically opposite sides of the bony wall of the tube, on the left side more than on the right. But the bone does not protrude far enough to actually cut off the lower part of the tube from the upper. While, therefore, we do not find a hard, inflexible partition, we find indeed some kind of a partition since the space between the bony protru- sions is filled with a delicate structure which we shall have to study somewhat in detail. This structure, which we shall always refer to hereafter as “the partition” in the inner ear, is customarily spoken of under the name of its discoverer as the organ of Corti, The lower part of this par- tition has been shown to be a membrane, generally called the basilar membrane. This is obviously the strongest part of the partition, capable more than any of the other elements of structure to resist a pressure of the fluid above or be- low. But we must not think that this membrane is the main part of the partition considering its volume. It is rather small in bulk compared with the rest. Above the membrane we see a triangular structure, something like two pillars which have fallen towards each other. This structure is usually called the rods of Corti. Its mechanical significance becomes at once clear to us when we see at its sides the delicate end organs of the auditory nerve fibres. These end organs would obviously be crushed by the push of the fluid which occurs now from above, now from below, as we have seen, if they were not braced by this arch. No better protection could be devised than this triangular structure which effectually pre- serves the natural form of the soft tissues as the skeleton does in the total animal body, without interfering with a slight bending or compression of the tissues of the partition. On the upper side of the partition, opposite the basilar mem- brane, we notice another membrane, but much more delicate in structure, easily torn to pieces when sections are made for the miscroscope. This membrane touches the tufts of hairs MECHANICS OF THE INNER EAR 17 which are the extreme peripheral parts of the sensory organs. This membrane, however, is firmly attached to the left side of the partition only. Its right end is free or seems to be almost free. The kind of action exerted by this mem- brane upon the hair tufts can only be guessed. The real con- nections between, and the physical properties of, these tissues are not well enough known. We may perhaps make this action a little clearer by assuming that the upper membrane, when the partition bulges upwards, pulls the hairs slight- ly, and that a bulging of the partition downwards means merely a relief from this pull. It is hardly worth while, how- ever, to enter into details of a function which cannot be more than hypothetical since there are no data upon which to base any more definite theory. But there is little doubt, that the points between the tufts of hairs and the membrane in question are to be regarded as in the strictest sense the per- iphery of the sensory apparatus of hearing. And we shall scarcely make a grave mistake in assuming that a double bulging, back and forth in the vertical direction, of the partition causes a single shock in all those nerve fibres whose termini are located in this part of the partition, and that somewhere in the neurons a new process, perhaps a kind of chemical process, is set up if more than one of such shocks are received in quick succession, that the special character of this new process is dependent on the frequency with which these shocks follow each other, and that thus we perceive a definite tone, occupying—according to the frequency of shocks received—a definite point in the total series of sensations of hearing. 18 UNIVERSITY OF MISSOURI STUDIES In the preceding paragraph we studied briefly the ana- tomical elements of the partition in their mutual relations. We now have to get a definite idea of the The physical physical properties of the partition as a properties of whole in its relation to the surrounding the partition fluid. These properties depend, of course, as a whole on the properties of its elements. The partition as a whole can certainly not be regarded as perfectly rigid and unyielding to pressure. It con- sists of tissues too soft to be unyielding. On the other hand, we cannot possibly assume that under the influence of pres- sure the partition could bulge to any large extent, for this would be disastrous to the delicate end organs of the nerve fibres. We could hardly make a mistake, then, in as- suming that the partition can yield, but only withm very nar- row limits up as well as down, even if we did not know anything about the physical properties of the anatomical elements. We know, however, that the basilar membrane is a comparatively tough structure, probably capable of consid- erable resistance. We are justified, then, in our conviction that the whole partition bulges in response to pressure but resists such pressure as soon as a certain rather narrow limit of displacement is reached. Here, however, arises another question of the greatest importance, which, unfortunately, cannot be answered with anything approaching accuracy. This is the question as to the elasticity of the partition. Of course, all the elasticity the partition can possibly have must be the elasticity of the basilar membrane. The basilar membrane is the only one of the anatomical elements of the partition which might have a tendency to restore spontaneously the whole partition to its original position after the pressure causing the displace- ment has ceased and before any pressure in the opposite direction has had time to act towards this result. MECHANICS OF THE INNER EAR 19 There is only one way of deciding for our present pur- pose the question as to the elasticity of the basilar mem- brane. We must recall our knowledge Is the basilar of the elastic properties of similar mem- membrane elastic? branous tissues which are found in divers parts of the human body and elsewhere in the organic world. Now, we know that there are plenty of membranes in the body which, when stretched within certain limits, show a tendency to return to the original shape. But they never remain in a stretched condition, that is, under tension, for any length of time. Indeed, they would become permanently lengthened if they remained thus. This is the consequence of a universal biological law. We may, for instance, bend a sapling and expect it to straighten itself as soon as we let it go, because of the elasticity of the stretched tissues of the convex side and the compressed tis- sues of the concave side. But if we tie it in this bent po- sition to another tree and return after a year and cut the tie, we find that it has adjusted itself to the position we gave it. This biological fact does away at once with cer- tain theories found quite frequently in physical and other textbooks, which speak of the basilar membrane as con- sisting of a great number of stretched strings, comparable to the strings in a piano. These theories assert, after having introduced, in opposition to the laws of biology, the idea of a permanent, constant tension of the basilar membrane, that these different strings—as in a piano—are under different tension and differently weighted and that they serve accord- ingly as resonators, responding sympathetically to the va- rious sounds of the external world. However pretty this theory of “the piano in the ear” may appear, authors who expect their readers to accept it as the truth should first of all try to convince them of the possibility of living animal tissues retaining their tension for any length of time instead of ad- zO UNIVERSITY OF MISSOURI STUDIES justing themselves to the permanent stretching and thus los- ing their tension, as all living tissues do. We shall not, of course, entertain for a moment this idea of the basilar mem- brane being under constant tension, since our alm is not unreality, but reality. We need not, therefore, discuss any further the assumption of the presence of resonators in the inner ear, which falls with the above rejected, preposterous assumption of a permanent tension. That the membrane is capable of resistance, as it probably is, means something very different from the assertion that it is under constant tension, which is biologically impossible. The actual question before us is evidently the question as to the elasticity of the partition as a whole. Now, we have seen that the only element of it Is the partition which, according to its structure, may be as a whole regarded as elastic, is the basilar mem- elastic? brane. This membrane, however, we have found to be quite a small part of the bulk - of the partition. If the partition is displaced by an external force and, this force having ceased, is caused to return to its original place by the tension which the basilar membrane has just suffered, such a spontaneous return movement must be greatly retarded by the bulk of inelastic tissues of the partition which the membranous part of it has to drag or shove along with itself. A spontaneous return of the par- tition to its normal position must be therefore very slow when compared with the velocity of a displacement caused by a rather powerful external influence from the stirrup. Let us, then, keep in mind that with respect to the elastic properties of the partition there are only two alternatives: Either the basilar membrane is practically inelastic; then the partition as a whole is inelastic and cannot sponta- neously return to its original position after having been displaced. Or the basilar membrane is elastic; then the par- MECHANICS OF THE INNER EAR 21 tition can spontaneously return after having been displaced, but with a velocity that is only very small compared with the velocity of its displacement. Of the two alternatives the latter seems to be the more probable. We saw on a previous page, in our second imaginary case of a partition, that the fluid moves along the unyielding partition, causing friction on the sur- faces of the partition. The same friction Protection of the must be suffered by any part of the real surfaces of the partition from partition as soon as it has reached its the friction upper or lower limit and as long as the of the fluid stirrup continues to move in the same direction, pushing the fluid on over the initial parts of the partition. If we had to design an ap- paratus to function thus, would we not see that the sur- faces of the partition were sufficiently protected so that the rush of the fluid over them could not injure them? It is interesting to raise this question of protection with respect to the actual partition in the tube. If we look above at fig- ure 7, representing a cross-section of the partition, we notice that the lower surface of the partition is well protected from injury by friction of the fluid by a part of its own structure, the tough basilar membrane. The upper sur- face, however, with its delicate sensory cells would be ex- posed to injuries by friction were it not for the membrane of Reissner which we see stretching across the upper division of the tube. The space between this membrane and the partition does not communicate with the rest of the upper division or with the lower division. It would therefore be really more nearly correct, in speaking of a partition divid- ing the tube into two divisions which communicate through an opening at the extreme end, to call the total body between the membrane of Reissner and the basilar membrane the partition. No movements perpendicular to the plane of the 22 UNIVERSITY OF MISSOURI STUDIES drawing can occur in the fluid below the Reissner membrane. The fluid here can only move up and down, pushing or pull- ing the organ of Corti into its limit of displacement. No fric- tion of the kind above referred to, which might do injury to the delicate tissues of the organ of Corti, can therefore take place, and the problem of protection from friction is thus solved. We shall, however, in order to make our language as simple as possible, restrict the term partition to the organ of Corti, neglecting the membrane of Reissner, since this mem- brane, aside from the important protection which it offers to the tissues below, does not seem to possess any function whatever. We saw on a previous page that an imaginary partition which is able to yield to the pressure of the fluid only within certain limits would be exposed to the dan- The safety valve ger of breaking whenever an extraordina- rily powerful external force tended to cause a movement of the stirrup which would displace more fluid than the yielding partition could make room for, and that this danger might be avoided or at least greatly lessened by an opening of communication between the two divisions at the end of the tube. It is interesting to learn from the re- searches of the anatomists that such an opening—a safety valve, as we may call it—actually exists at the extremity of the tube of the cochlea. We may now, after making ourselves familiar with the structural elements of the inner ear and their physical prop- erties, enter into a discussion of the actual function of the organ. MECHANICS OF THE INNER EAR 23 We have thus far taken into consideration only a single movement of the stirrup, in either direction. We must now study the result of a rhythmical movement of the stirrup, back and forth, a number of Stimulations of times during a certain length of time. In the brain resulting from a given order to have a definite case before our rhythmical mind we will suppose the stirrup to move movement of back and forth in such a way that it will the stirrup describe a sine curve on a board moving parallel to the plane of the paper. In fig- ure 8 is represented a single period of such a curve in a hor- izontal position. It is not necessary, however, to imagine this definite curve. What we shall have to say will apply equally to any simple periodic movement, whether of the form of a sinusoid or of a combination of straight lines or of any other Fig. 8. A curve representing stirrup movement curve connecting each maximum with the preceding and the following minimum. The question arises then by what means —computation, simple description in words, or otherwise—we can obtain a clear and sufficiently detailed view of the move- ments of the partition. What we want to know is the form of motion for each point of the partition, and the temporal 24 UNIVERSITY OF MISSOURI STUDIES relations existing between all the several movements. Only thus can we obtain a definite view concerning the nervous stimulations received by the brain as the result of a given rhythmical movement of the stirrup. In order to find the movements of the partition in every detail we might try com- putation since this is the method which yields, although not always the clearest, yet in general the most accurate results. Our chief task, then, would be, stated again as definitely as possible, to find out for each point of the partition which moves at all the exact time which elapses Computation of | {tom a jerk down to a jerk up and from the form of a jerk up to a jerk down. Figure 9 may motion of the help us to understand the conditions of partition computing the time interval in question. Let us call x the distance of any point of the partition from the point of +, nearest the windows. The length of the part of the partition which moves in response to the motion of the stirrup depends, of course, on the ampli- tude of the movement of the stirrup. This length alone is represented in the figure. What is farther to the right re- mains motionless. The dotted lines above and below rep- resent the upper and lower limit of each moving point of Fig. 9. The partition in the tube and its limits of movement the partition. In our curve, figure 8, the minimum, at A, rep- resents the position of the stirrup most to the left, the max- imum, at the time B, the position of the stirrup most to the right. The horizontal line represents, of course, the time. To the position of the stirrup at A corresponds the position of the partition (in figure 9) in its upper limit; to the position of MECHANICS OF THE INNER EAR 25 the stirrup at B the position of the partition in its lower limit. Let us now find out when any arbitrary point +, is jerked up and when it is jerked down, measuring the time from A. It is obvious that the amount of fluid for which room is made by the piece of the partition from x, to +, moving from its upper to its lower limit is equal to the amount of fluid dis- placed by the stirrup moving inwards through the distance measured by y. (For convenience we place the zero point of the system of coordinates in a minimum point of the curve.) It would be very easy, therefore, to find the equation of inter- dependence of x and y, if the following conditions were ful- filled : 1. Ifthe quantity of fluid displaced were proportional to the horizontal movement of the stirrup. a. If the partition were perfectly in- sit elastic; that is, not offering any resistance provisionally : Hits tae made; not as to a displacement until either of the limits hypotheses, but is reached, and then offering absolute re- for the sake of a_ sistance. gradual compre- 3. If the distance between the upper hension and lower limits were the same at any point of the partition. 4. If the width of the partition at any point near the windows were the same as at any point far away from them. Let us temporarily regard these conditions as fulfilled. If they are fulfilled, + is proportional to y. That is, a unit of movement of the stirrup always pushes Four assumptions Attempt at down (or raises, as the case may be) a computation unit of the partition lengthwise. Or, ex- continued pressed in a formula: (1) y= Cr where C is a constant dependent on the physical properties of the organ. 26 UNIVERSITY OF MISSOURI STUDIES The equation of the curve in figure 8 is: (11) y = c(1— cos 2unt) ; that is, while ¢ changes from zero to _1_, y changes from 2 zero through c, 2c, and again c, back to zero. We now sub- stitute Cx for y: c (1—cos 2ant) = Cx, consequently : G (111) cos 2ant = 1 — ert This formula permits us to calculate ¢, that is, the exact time when any point of the partition is jerked down. But it holds good only for the time from A to B, that is, while the stirrup moves in one direction. As soon as the stirrup reverses its movement a new formula has to be applied, since the move- ment of the partition is of a kind which is mathematically called a discontinuous function. The moment when the stir- rup reverses its movement and the farthest point of the par- tition has been jerked down, the function jumps, so to speak, from this point to the beginning of the partition and the first point, nearest the windows, is jerked up. The formula to be used from B to C is to be derived by substituting (2c—y) for y in (1), since + would now be proportional to (2c—vy). We then have the following new equations: (IV) 2c— y= Cx. (11) y =c (1—cos 2nnt), consequently : (V) cos 2ant = HE ISS c This {crmula is valid from B to C, that is for values of t varying from = to 1, while the partition is being nN n jerked upwards. We notice that the only difference between the right side of (III)i and the right side of (V) is the sign, For the same + we obtain the same absolute value of cos 2rnt, but in the one case it is positive, in the other negative. Now, it is easy to see what this means for the time interval between a downward and an upward jerk of any point of the partition. MECHANICS OF THE INNER EAR 27 Remembering that (III) is valid for jerking down, (V) for jerking up, we notice that the arc of cos 2nt runs through the first and second quadrant while the partition is being jerked down, through the third and fourth quadrant while the partition is being jerked up. Therefore, since we found that the time of jerking down of a definite point x, and the time of jerking up of the same point are subject to the con- dition that cos 2mnt yields the same absolute value, but differ- ing in sign, the time of jerking up must be found in a quad- rant opposite to the quadrant wherein the time of jerking down occurred, never in an adjoining quadrant; that is, if the former time is to be found in the arc 2zmt, the latter must be found in the arc 2an(t + a), since the addition of 7 =a to ¢ means the addition of two quadrants. The differ- 7 ence of time, therefore, is always ak. In other words, the an time interval from a jerk down to a jerk up and from a jerk up to a jerk down of any definite point is with this particular curve always the same, being exactly one half of the whole period. We have thus found by computation the exact move- ment of the partition in case the movement of the stirrup is of the form of a sinusoid. We have seen then that, provided a certain set of condi- tions (our four provisional assumptions) is fulfilled, and pro- vided the movement of the stirrup is of the Summary of form of a simple sine (or cosine, as this the foregoing means the same) curve, computation of discussion the movement of the partition is possible. But computation is neither particularly clear—at least those who are not professional mathemati- cians will think so—nor is it universally applicable, but only in a few cases of stirrup movement, the above, the case of straight lines connecting the maxima and minima, and a very small number of others. 28 UNIVERSITY OF MISSOURI STUDIES To prove that computation is not universally applicable let the movement of the stirrup be represented by the function y = c(2— cos 2ermt — cos 2rnt) 4 and let m be equal to 4 and m equal to Computation 5 (the simple case of a major third, abandoned : : i d musically speaking). Even in a case like this, by no means far fetched, rather the contrary, computation is impossible since it would involve, as the mathematical reader may easily convince himself, the solution of an equation of the fifth degree in order to find the mutually corresponding values of y and ¢ for the maxima and minima of the curve. Without these values for the maxima and minima, which are the points of discontinuity of the func- tion representing the movement of the partition, we could not proceed at all. It is out of the question, therefore, to ex- pect that computation pure and simple, even under the four assumptions provisionally made, will ever give us a satisfac- tory comprehension of the function of the inner ear. We must look for other means in order to obtain our end, an insight into the details of movement of the partition. Let us, then, try to represent the movement of the par- tition in the above case as well as in others graphically. I shall offer to the reader two methods of i h Graphic ieee graphic representation. The first of these of determining the exact is more accurate in some respects than the movement of second, but a little more difficult of ap- the partition plication. The vertical axis of our system of coordinates in figure 10 may represent the succession of points of the partition, be- ginning from next to the windows. The First graphic horizontal axis may represent the time. I method must warn the reader against thinking that the figures resulting on the paper are pictures of something that exists in the ear or elsewhere. The MECHANICS OF THE INNER EAR 29 figures are not pictures of existing things but merely symbols of a function, that is, of the time when any point of the par- tition is jerked up or down. The construction of the figure is based on the following considerations. Let us mark on the paper the points indicating the time when any given point of the partition is jerked. When we shall have marked a sufficient number of such points, we shall draw a curve through them. But how do we find the points? The move- ment of the stirrup is represented in figure 8. When the stir- rup has its extreme position to the left (according to Fig. x Fig. to. Graph of the times when each point of the partition is jerked down (curves of odd numbers) and up (curves of even numbers). Compare figure 8 9) and just begins to move inwards, we mark the time as zero and the point of the partition which is jerked down also as zero, since the point which is jerked is the point nearest the windows. In figure 10 we find this point near a. As the time advances (Fig. 8) the stirrup moves farther and farther inwards, with gradually increasing and later again decreas- ing velocity. A further point, say b, in figure 10 must be located somewhat to the right of a and above a, since a more distant point of the partition is represented by a higher position of the mark in our system of coordinates, and the 30 UNIVERSITY OF MISSOURI STUDIES fact that it is jerked later is represented by a position farther to the right. Now, since the velocity of the stirrup increases as shown by figure 8, the following marks have to be placed higher than proportionate to their advance to the right. That is, points marked off by equal steps on the partition are now jerked successively in briefer time intervals than before. Later approaching the time B in figure 8, the stirrup moves again more slowly, and the marks in figure 10 advance there- fore more rapidly towards the right, as seen in f and g. If we now draw a complete curve through the marks a, b, c, d, e, f, g, we convince ourselves readily that the new curve is the same curve as the one in figure 8 from A to B. Of course, if we have not chosen the same vertical and horizontal scales in both figures, the new curve must appear more or less steep than the old one. But the selection of a scale for a graphic representation is entirely a matter of convenience. Choosing identical scales, we simply have to transplant the first half of the curve in figure 8 from A to B into the new figure. But now the stirrup begins to move in the opposite di- rection, causing the partition to be jerked upwards gradually. The point of the partition nearest the windows is jerked up first, the others later in regular order. Now, it can be easily seen where we have to place the further marks in our new fig- ure, namely k, 1, 7, k, 1, m, n. We find them, or rather immed- iately the complete curve of which they are points, by simply turning the second half (B to C) of the curve in figure 8 up- side down, without, however, making any change between right and left. In this way we go on, simply transplanting the parts of the stirrup curve, leaving the rising ones in the same position, but turning the falling parts upside down. If we now desire to find out for any point of the parti- tion, for example, for x, the exact time when it is jerked down and when it is jerked up, all we have to do is to pass on from this point (Fig. 10) to the right (along the dotted MECHANICS OF THE INNER EAR 31 line), since this direction, according to definition, represents the time. Our first crossing of a curve (in e¢) means a jerk down; the next crossing (in /) a jerk up; and so forth. That is, the odd crossings mean each a jerk down, the even crossings each a jerk up. The time intervals can then be measured with a rule. We find in this special case that the intervals are all equal. We have thus graphically represented the exact movement of the partition in a case where the movement of the stirrup is of the form of a sinusoid. The same graphic tepresentation is applicable to any given curve, however com- plicated it may appear. This method has universal validity. We shall soon convince ourselves of its importance for the analysis of a complicated curve. We can easily learn from the graphic representation be- fore us that under the assumptions provisionally made the stimulation of each nerve ending can RU Be rise eanent Rardly be insitienced by the ‘ona of the of the stirrup stirrup curve, that is, whether this curve produces the is a sinusoid, or made up of straight lines sensation of a connecting the maxima and minima, or of single tone (free any other shape, provided the maxima and from overtones)? minima remain unaltered. Let us sup- pose that each “down” means a shock to the nerve end and that the “ups” are indifferent as to ner- vous excitation. We see immediately (Fig. 10) that the time interval between two shocks at any point of the partition must be exactly the same, since each down curve would be exactly like any other down curve, whatever the shape of the up curve. (This result would be the same if the “ups” meant excitation of the nerve end and the “downs” were in- different.) That is, the particular shape of the curve rep- resenting the movement of the stirrup, has no significance for the question whether a single tone will be heard or not. If all the down curves are identical, a single tone only is 32 UNIVERSITY OF MISSOURI STUDIES audible. I remind the reader, however, that we are deriving this conclusion on the basis of our provisional assumptions, and further, that we are speaking here of movements of the stirrup, not of rhythmical pressure changes of the air in the external ear or of movements of a tuning fork or any other vibrating body. In discussing later the effect of the latter conditions upon the stirrup, we shall see that their form is not necessarily identical with the form of the stirrup move- ment. As yet, we have studied only very simple movements of the stirrup. Before we take up the problem of how the inner ear analyzes more complicated move- The physiological ments of the stirrup, we ought to remem- condition of ber that we have not yet discussed the tone intensity physiological condition of tone intensity. We have spoken only of the frequency with which shocks are received by the nerve ends. But the frequency of the shocks determines only the attributes of pitch and quality, not the attribute of intensity of a tone sen- sation. Let us look to another sense organ, the olfactory organ, for a suggestion. On what physiological condition does the intensity of an odor depend? Although we have no definite knowledge here any more than in the sense of hear- ing, we have reason to believe that the intensity of an odor depends, or may depend, on two conditions: 1. The num- ber of nerve ends stimulated; and 2. the concentration of the substance which stimulates each of these nerve ends. Ac- cepting this suggestion we have to see what conditions might determine tone intensity. Only these two can come up for consideration, so far as I can see: 1. The number of nerve ends which receive shocks in a definite frequency; and 2. the suddenness, the impetuosity with which each nerve end is shaken when the point of the partition in which it is lo- cated is jerked down. Now, the second of these two conditions MECHANICS OF THE INNER EAR 33 is theoretically almost beyond our reach. We cannot, in the present state of our knowledge, obtain a very clear idea of differences in the suddenness with which the nerve ends might be shaken in different cases. It will be best, therefore, to omit this factor in the discussion of intensity altogether, or at least for the present, rather than burden our theory with arbitrary hypotheses the usefulness of which is no more probable than their uselessness. At present we shall limit our discussion to the first condition, the number of those nerve ends which are stimulated with equal frequency. It is clear that the number of nerve ends stimulated de- pends in some way on the length of that part of the partition which is jerked up and down in a certain A difficulty in frequency. But here we are confronted by the hesretical this difficulty. We do not know whether determination of the nerve fibres are equally distributed tone intensity. along the partition. It might be the case Fifth provisional that on a certain length of the partition assumption near the windows a greater number of nerve ends were found than on an equal length farther away from the windows; or the reverse. In our present state of knowledge this difficulty cannot be over- come. In order to go on with our theory, we have to make an assumption. We shall make, of course, the simplest, the least arbitrary assumption. We assume, provisionally, that equal parts of the partition lengthwise contain equal num- bers of nerve ends. If it should be found that the theory agrees with the facts of auditory observation more closely un- der another assumption, we would have to substitute this for the one now made. Of course a definite answer given to the problem by the anatomists would be more satisfactory. 34 UNIVERSITY OF MISSOURI STUDIES We can measure the length of that part of the partition which is jerked up and down, only by the aid of our knowledge (if we have any) of the movement of the Another difficulty stirrup. Now, the reader will recall among in the theoretical Our provisional assumptions the one that determination of the width of the partition at any point near tone intensity the windows is the same as at any point far away from them. But the anatomists tell us that this assumption is incorrect; that the partition is about twelve (or more) times as wide at the end as near the windows. Nevertheless we shall provisionally make the assumption of proportionality between any length of the partition being jerked up and down and the extent of the movement of the stirrup which causes the movement of this piece of the partition, in order to under- stand first a simpler, though imaginary, case and to proceed gradually to a comprehension of the actual, rather compli- cated function of the partition. Let us be aware, however, that, having thus simplified the actual conditions, we cannot expect to find a perfect, but only an approximate harmony between the results of a theoretical analysis and the direct observations of an actual sound analysis by the ear. We may find, indeed, with respect to tone intensity, rather se- rious disagreements between the facts and the theory. But these disagreements will disappear as soon as the theory takes account of what, for simplicity’s sake, we provisionally neg- lect. Making the two provisional assumptions just mentioned, we can theoretically measure the intensity of a tone sensa- tion by the total length of that part of the Tone intensity partition the nerve ends of which are ex- in our graphic cited with one definite frequency. In our representation graphic representation (Fig. 10) the inten- sity can then be measured by the vertical distance between the horizontal coordinate and the top of the curves which represent the down and up jerks. MECHANICS OF THE INNER EAR 35 We discussed above the result of a simple back and forth movement of the stirrup. Let us now do the same with a more complicated movement. Figure 11 Analysis of the represents the new stirrup movement combination which we are going to study. This curve 2 and 3 is approximately the one represented by the equation y = (1—cos 2r2t) + (1 — cos 2x8t) ; which justifies us in saying that it represents physically the sum of two tones of the vibration ratio 2:3. Let us apply Fig. 11. ‘(he combination 2 and 3. First characteristic phase the same graphic method to this case. We have first to trans- plant the part of the curve from the first minimum to the fol- lowing maximum, A to B, into figure 12. Now, when the stirrup reverses its motion, the parts of the partition near the windows begin to be jerked up. Therefore, the curve from the maximum B to the next minimum C has to be turned upside down and then transplanted. The following part of the curve, from C to D, must be transplanted in its original upright position, but placed on the 36 UNIVERSITY OF MISSOURI STUDIES horizontal coordinate of the new figure, whatever its elevation in the original curve may be, since every reversal of the movement of the stirrup causes at once a movement of the parts of the parti- tion next to the windows and only later a movement of the follow- ing parts. So we continue transplanting each section of the curve, alternately upright and upside down. This figure (Fig. 12) X3 Tone 2 Figure 12. The combination 2 and 3. First characteristic phase. (A is identical with G.) Compare figure 11 is to be interpreted in the same way as figure 10. The distances from 4, toz,, z, to x, and x, to 4, represent three pieces of the partition, +, being next to the windows. During the unit of time, which is here the period from A to G, all the nerve ends located between +, and # receive, as is easily seen, three shocks, counting the number of shocks received by the number of downs (or ups, since this distinction between the physiologically effective and ineffective direction of jerk- ing is arbitrary, for want of better knowledge as to the man- ner of excitation of the nerve ends). All the nerve ends be- tween +, and +, receive, as the figure shows, counting from left to right, two shocks in the unit of time. And all the MECHANICS OF THE INNER EAR Bi nerve ends between +, and x, receive one shock. The nerve ends located farther towards the apex of the cochlea do not receive any stimulation and do not, therefore, concern us. How many tones should we expect then to hear in this case? The answer is as easy as simple: Three different tones, since shocks of three different frequencies are received by the several nerve ends. And the musical relationship, the pitch, as we say, of these tones is determined by the relative frequencies found, which are 3 and 2 and 1. The relative intensity of these tones is to be measured, in accordance with our remarks in the pre- ceding paragraph, by the relative lengths 42,2, 4,%, and Lp ee A movement of the stirrup, not probably exactly like, but similar to the one just discussed could be produced by sounding simultaneously with approxi- , mately equal intensities two tuning forks Two important ahs bi 8 See | Seuindl representing the ratio of vibration rates analysis and 3:2. It is well known that we hear in such production of a case three different tones, 3 and 2, which subjective we may call “objective” or primary tones, difference tones ang 1, which we may call a “subjective” or difference tone. Some further facts con- cerning such subjective or difference tones will be mentioned subsequently for those readers who are not familiar with the conditions under which they make their appearance. The appropriateness of calling the subjective tones in question “difference tones” will then become apparent. The fact that our theory of the function of the inner ear and actual obser- vation in this case agree so nicely, is highly satisfactory to us and ought to encourage us to proceed further in applying the theory to other special cases of movements of the stirrup. Let us keep in mind that our theory thus far has explained in a special case two most fundamental observations: 1. That our organ of hearing is capable of analyzing a compound 38 UNIVERSITY OF MISSOURI STUDIES acoustic process; and 2. that it has the power of producing on its own account subjective tones which no study of mere external conditions could ever have revealed to us as a natural consequence of the physical processes we call tones. We saw in the preceding paragraph that all the nerve ends between +, and +, received three shocks in the unit of time. A measurement of the distances in A problem for the figure, however, shows that the time future solution intervals between these three shocks, al- though approximately the same, are not’ exactly alike (and, moreover, there are differences in this re- spect between the several nerve ends all of which receive three stimulations). Now, it is probable that the particular nervous excitation set up in each ganglion cell by these three stimula- tions of its terminal fibre and thence carried farther to the brain, may be just the same in either case, whether the shocks are received in an exactly regular rhythm or in a slightly irreg- ular succession. It will be one of the problems of the future to decide what is the limit of irregularity which must not be overstepped if the sensation produced is to be the same as that of a regular series of shocks of the same frequency. At pres- ent we have hardly any certain data upon which to found a decision. We must leave this problem open for the present. It would be well, however, to remember that the above graphic representation of the movement of the partition—for simplic- ity’s sake—is based on a number of assumptions, and that the actual movement of the partition is doubtless somewhat different from the one which is here under discussion, and which contains probably only the essential features of the actual movement, not all its minor details. It is entirely pos- sible, under these circumstances, that the irregularity in ques- tion is in reality much less considerable than it appears to us now, and what seems to be an important problem, may turn out to be no problem at all. The reason we have for believ- MECHANICS OF THE INNER EAR 39 ing that the actual irregularity might be less than the one found here, is that in the graphic representation we have as- sumed a movement made up of absolutely sudden, unpre- pared jerks, with intervals of perfect rest between them. The real movement is probably a more gradual change from rest to motion and back to rest; and the result of this might very well be an equalization of the time intervals preceding the shocks received by the nerve ends. This, however, is not offered as a solution of the problem, but merely as a sugges- tion for the future investigator of this subject. Let us try another method of graphically representing the movement of the partition under the provisional as- sumptions made. This method has a cer- Second method tain disadvantage as compared with the of graphic method used above, in being less accurate representation of with regard to the time intervals, but, on the movement of the other hand, the advantage of a greater the partition simplicity for the constructor as well as for the reader. The extension of the par- tition from the windows towards the apex of the cochlea is here represented, not—as before—by the vertical, but by the hori- zontal extension of the figure, from left to right. Figure 13 shows the method as applied to the same curve (Fig. 11) which we have just discussed. The first thing we have to do is to draw in the given curve (Fig. 11) at equal distances so many lines parallel to the horizontal coordinate that each of the maxima and minima can be regarded as lying on one of these parallels. If this is not easily done, then any arbitrary number of parallels may be drawn. But the drawing as well as the interpretation of the new figure requires a little more atten- tion in this case, because we have to consider fractions. In this figure there are thirty equidistant lines drawn parallel to the horizontal coordinate. A greater accuracy than this would be entirely out of place, since our representation in any case 40 UNIVERSITY OF MISSOURI STUDIES is merely an approximate representation of the actual move- ment of the partition. These horizontal parallels are auxiliary lines, serving the purpose of a measuring scale. The second thing we have to do is to draw a second, independent, system of auxiliary lines enclosing a corresponding number of spaces. These lines are the thirty-one vertical parallels in figure 13. The horizontal lines here indicate for the times A, B, C, and so forth, the positions of the different points of the parti- tion at the upper or lower limit of movement. The vertical Fig. 13. Successive positions of the partition. The combination 2 and 3. First characteristic phase. Compare figure 11 auxiliaries serve the purpose of cutting off the partition a number of equal sections corresponding to the number of parts into which we divided the total amplitude of the given curve representing the movement of the stirrup. To the right of these sections which move are to be imagined the parts of the partition nearer the apex which do not move at all in this spe- cial case and which do not, for this reason, concern us here. At the time A, all the moving parts of the partition are at their upper limits, since the stirrup has at this time its extreme outward position. From A to B, the stirrup moves through MECHANICS OF THE INNER EAR 41 thirty units inwards, pushing down successively all the thirty sections of the initial part of the partition. We find, therefore, in figure 13 at B all the thirty sections at their lower limits. From B to C, the stirrup makes an outward movement through nineteen spaces. The result is an upward movement of an equal number of sections of the partition. We find, therefore, at C the first nineteen sections of the partition at their upper limits. All the following parts of the partition remain ex- actly in the positions at which they were at the time B, since— according to the assumptions under which we are working— no force whatsover has acted upon them. That is, the sec- tions twenty to thirty are still at the lower limits, and the further parts of the partition in their normal positions. From C to D the stirrup moves inward through six spaces, as seen in figure 11. It causes therefore the first six sections of the partition to be jerked down. In this position we find them in figure 13 at D. All the rest of the partition remains exactly as it was at C. That is, the next thirteen sections are still at the upper limits and the following eleven still at the lower limits where we found them at B. From D to E, the stirrup makes an outward movement through six spaces, causing an equal number of the initial sections of the partition to be jerked up. We therefore find in the figure at E the first nineteen sec- tions of the partition at the upper limits, the following eleven at the lower limits. From E to F, the stirrup moves inward again through nineteen spaces, causing nineteen sections of the partition to be jerked down. We find, therefore, in the figure at F all the thirty moving sections of the partition at the lower limits. From F to G, the stirrup moves outward through thirty spaces, as seen in figure 11. This causes thirty sections of the partition to be jerked up. So we find in figure 13 at G the whole initial piece of the partition which moves and therefore alone concerns us, at the upper limit. The stir- tup has now reached the very position from which it started 42 UNIVERSITY OF MISSOURI STUDIES at A; and the partition has the same position which it had then. We have thus graphically represented the characteristic positions through which the partition passes during a com- plete period of the movement in question. The graphic representation, of course, is only a means to an end.. We have to read off from this representation how many shocks are received during the Elowitalreadvotk period by the nerve ends on each section the tones heard of the partition. This is easily done. Let and their us again, for want of definite knowledge, intensities make the assumption that a jerk down of the partition means a stimulation of the nerve ends, and that a jerk up is irrelevant. We then sim- ply have to go down in the figure from the top to the bottom and count the number of times each section is jerked down. The first section is down at B, up again at C, down for a sec- ond time at D, up again at E, down for a third time at F, and up again at G. The nerve ends on this section, there- fore, receive three shocks during the period. We find the same number of stimulations on the following five sections. Let us now inspect the seventh section. It is down at B, up at C and still up at D and E. It is down for a second time at F and up again at G. That is, the nerve ends on this sec- tion receive two shocks during the period. The same is true for the following twelve sections. Let us now look at the twentieth section of the partition. It is down at B, still down at C, D, E, and F; up again at G. That is, the nerve ends here receive only one shock during the period. The same holds for the following ten sections. We see, then, that three tones must be simultaneously heard, which we may call, according to the relative frequency of stimulation, the tones 3, 2, and 1. The relative intensities of these tones may be re- garded—under the provisional assumption of a uniform dis- tribution of nerve ends lengthwise over the partition—as six, MECHANICS OF THE INNER EAR 43 thirteen, and eleven, according to the number of sections which receive the greater or smaller number of shocks. Let us now appiy the second graphic method to another given movement of the stirrup, which will make clear to us another interesting property of the ear with Difference OF respect to the AQIS in which this or- phase. Charac- am analyzes an objective sound. The curve teristic curves of the stirrup (Fig. 14) is made up of of a tone combi- two component curves, very similar to the nation curves composing the last curve discussed. That is, each of the two components is ap- proximately a sinusoid, one of a period equal to two thirds of the other’s period, both of approximately the same amplitude. The resultant curve is constructed here as before by measuring and adding together the ordinate values of the components in the drawing. The difference between the present case and the last case discussed is a difference of phase. If the reader should not know what this means, it can be easily understood by the aid of figure 14. We find there two sinusoids, one with two and one with three maxima within the same period, which accordingly may be called curve two and curve three. Now imagine curve two moved slightly to the right until the minima at the extreme right and also the minima at the ex- treme left coincide. We then have exactly the case discussed above; that is, the addition of the two curves would result in a compound curve as represented by figure 11. The curves of figure 11 and of figure 14 may be called the characteristic curves of the ratio 2:3, because they are the two extreme forms between which the compound curve changes as the result of a change of phase, that is, of a lateral movement of curve two, while curve three remains stationary. Let us convince our- selves here that there are no more than two characteristic compound curves. If we move curve two again slightly to the tight, the same distance as before, that is, one twelfth of the 44 UNIVERSITY OF MISSOURI STUDIES period, we obtain a compound curve as shown in figure 16, which is exactly like figure 14 when read from the right to the left. And if we change the phase again in the same manner, that is, move curve two again one-twelfth of the period to the right, we obtain a compound curve as shown in figure 18, which is exactly like figure 11 only turned upside down. We shall demonstrate in the succeeding paragraphs that it is entirely irrelevant with respect Fig. 14. The combination 2 and 3. Second characteristic phase to our theory whether we read a curve from the left or from the right, in its first position or turned upside down. We shall demonstrate thus that there are in- deed only two compound curves, no more, which are character- istic of a combination of two sinusoids. This is an important fact because it makes much simpler and easier our task of comprehending the function of the inner ear. MECHANICS OF THE INNER EAR 45 Let us apply, then, the second graphic method to this second characteristic curve of the combination 2 and 3. We locate, in figure 14, the horizontal coordi- Theory applied nate so that the absolute minima of the to second charac- Compound curve are to be found thereon. teristic curve of We then draw a number of equidistant combination lines, say thirty, parallel to the horizontal 2 and 3 coordinate. To avoid making the figure obscure I have indicated of these parallels only those which pass approximately through the maxima and minima of the curve. We further draw a system of thirty-one equidistant vertical parallels enclosing a series of thirty equal spaces which represent succeeding pieces of the partition. In this system of auxiliaries we represent the positions of the par- tition at the time A, B, C, and so forth. At A in figure 15 we find all the moving sections of the partition at their upper lim- its, since the stirrup has at this time, as figure 14 shows, the most outward position, the external air pressure and accord- ingly the density of the air in the middle ear being lowest. At B we find all the thirty initial sections of the partition down, sree Fig. 15. Compare figure 14 46 UNIVERSITY OF MISSOURI STUDIES since from A to B the stirrup has moved through thirty units of space inwards. At C we find the twenty-four initial sections raised again since the stirrup has moved outward through twenty-four spaces. At D the eleven initial sections of the par- tition are at their lower limits since from C to D the stirrup has moved through eleven spaces in an inward direction. From D to E the stirrup moves outwards through three spaces. Ac- cordingly we find at E the first three sections of the partition raised to their upper limits. From E to F the stirrup moves inwards through eleven spaces. Accordingly eleven sections of the partition must be. pushed down to their lower limits. We find the first three down at F. The following sections up to the twelfth were already down at E. In order to represent eleven sections of the partition as just pushed down we have to place at F the twelfth and the following, including the nine- teenth, sections of the partition at their lower limits. Then the first three and the latter eight make up the total number of eleven sections pushed down. From F to G the stirrup moves outwards through twenty-four spaces. Accordingly all sec- tions of the partition are raised to their upper limits except those from the nineteenth to the twenty-fifth which were already at their upper limits at F and therefore simply stay there. So we find the partition at the time G in exactly the same position in which it was at A; and we must find it again in the same position since now another period of stirrup move- ment begins, exactly like the period just discussed. We now have to read off the tones heard and their intensities in the same manner as we did this before. The result is that we must expect to hear the three tones 3, 2, and 1 in the relative inten- sities three, sixteen, and eleven. MECHANICS OF THE INNER EAR 47 Comparing our analysis of the curve in figure 14 with the former result obtained from figure 11, we observe that in spite of the remarkable difference of ap- Practical pearance of these curves to the eye, the irrelevance tones which we expect to hear are the of phase same. This is, of course, of the greatest importance in musical practice. Imagine the unsurmountable difficulties if the director of an orchestra were responsible for the phase in which the several tones pro- duced by the members of the orchestra acted upon the audi- tory organs of each hearer in the concert hall. But, as it is, each hearer perceives the same tones whatever the phases of the objective processes in the air. Now those who believe in the existence of a system of strings like “a piano in the ear,” have laid much stress on this fact of the practical irrel- evance of phase, and some have even gone so far as to say that it compels us to assume sympathetic resonance to be the me- chanical power of the auditory organ. I need not persuade the reader, however, that such a compulsion does not exist. Some have gone still farther and asserted that phase differ- ence has never and under no circumstances any influence whatsoever upon the auditory perception. Their theory of the mechanics of the inner ear may lead to such a consequence, to an absolute irrelevance of phase. Experiment, however, has not yet proved that phase difference of the sinusoidal compon- ents of stirrup movement has never any influence of any kind upon the perception. Our theory has shown us the practical ir- relevance of phase differences and, at the same time, left a pos- sibility for slight influences of this kind upon the perception, resulting in a change of the relative intensities of the sev- eral tones heard. The intensities of the three tones for one phase we found to be six, thirteen, and eleven; for the other phase three, sixteen, and eleven. That is to say, we would hear in the second case the same tones, but their relative 48 UNIVERSITY OF MISSOURI STUDIES intensities would not be exactly the same as those in the first case. That is, difference of phase may be irrelevant, but it need not be so. Let us recall, however, that our representa- tion is only a rather remote approximation to the actual movements of the partition, so that actually the influence of phase upon the perception may be other than it here appears to be. What is important is our insight into the possibility of a slight influence of this kind. Fig, 16. Compare figure 14 I promised to demonstrate that the application of our the- ory yields the same result if we read the curve of stirrup move- ment from the right to the left, or turn it Theoretic irrel. UPSide down. The former case is illus- evance of the trated by figure 16, which is exactly like sign of the co- figure 14 when read from the right to the ordinates left. Figure 17% shows the successive posi- tions of the partition. At B the twenty- four initial sections are down. At C the first eleven of them MECHANICS OF THE INNER EAR 49 are up again. At D three are down again. From D to E the stirrup moves through eleven units of space outwards. Fig. 17. Compare figure 16 Therefore at E the first nineteen sections are up, eight of them being up already at D. From E to F the stirrup moves in- Fig. 18. Compare figure 11 wards through a little more than twenty-four units of space. Therefore at F thirty sections are down, five of them being 5° UNIVERSITY OF MISSOURI STUDIES down already at E. At G (equal to A) all the thirty sections are up again. The tones to be heard, which the reader after all the previous practice in this task can easily read off, are 3, 2, and 1 with the relative intensities three, sixteen, and eleven. Fig. 19. Compare figure 18 As expected, this result agrees perfectly with our analysis of the curve in figure 14. Let us now demonstrate that turning the curve upside down has no influence on the theoretic result. Figure 18 is exactly like figure 11, only turned upside down. In figure 19 we see Fig. 20. The combination 24 and 25 MECHANICS OF THE INNER EAR 51 Fig. 21. The combination 24 and 25. Compare figure 20 52 UNIVERSITY OF MISSOURI STUDIES the successive positions of the partition corresponding to this curve. The interpretation of the figure is so simple that the reader will easily read off, without any aid, what tones are to be heard; namely the tones.3, 2, and 1 with the relative intensi- ties six, thirteen, and eleven. This is exactly the same result as that of our analysis of the curve in figure 11. The interval studied above is in musical terminology that of a fifth. Let us now study an interval which is even small- er than a semitone. The compound curve in figure 20 is made up of twenty-four The tone com- vibrations originating from one source and bination 24 : and 25 twenty-five from another. Figure 21 shows the successive positions of the parti- tion corresponding thereto. The initial section of the partition moves up and down twenty-five times during the period. We may, therefore, conclude that the nerve ends located here will transmit to the brain a process resulting in the sensation of the tone 25. In order to discuss this matter with more accuracy, I have not relied only upon the draftsman’s skill in con- structing the compound curve, but computed the ordinate values of some of the maxima and minima. Such a compu- tation is exceedingly tiresome work, since for each pair of val- ues in the table it is necessary to compute twenty or more values in order to select from them what appears as the maxi- mum or minimum. But the accuracy of this method can be carried to any decimal desired. We learn from the table of these values that the relative intensity (when determined in the same way as above) of the tone 25 would be nine (that is, 200—191). MECHANICS OF THE INNER EAR 53 INTERVAL 24:25, EQuAL AMPLITUDES Abscissa | Ordinate Ree Point arena Min. {o} fo} 73 fo} 400 Max. 73 400 73 I 400 Min 147 2 74 2 388 Max 1540 246 — 21 — Min 1620 167 80 22 79 Max 1685 221 65 23 54 Min 1755 191 70 24 30 Max 1800 200 45 25 9 Min 1845 191 45 26 9 Max 1915 221 70 27 30 Min 1980 167 65 28 54 Max 2060 246 80 29 79 Min.| 3453 2 = 48 -— Max.) 3527 400 74 49 388 Min 3600 {o} 73 50 400 If we regard—quite arbitrarily—the time from one stimu- lation to the next as measurable by the abscissa differences of the succeeding maxima, we observe that Do we hear this difference is about one hundred and the tone 25? forty-seven at the beginning of the period, that it decreases very slowly and is about one hundred and forty-five at the maximum twenty-three, about one hundred and fifteen at the maximum twenty-five, the same at the maximum twenty-seven, and that it increases gradually till the end of the period. One twenty-fifth of the whole period is one hundred and forty-four. This is the average abscissa difference, on which the pitch of the tone heard depends, since the abscissa difference is inversely proportional to the fre- quency of stimulation. But the actual abscissa differences, as we 54 UNIVERSITY OF MISSOURI STUDIES have just seen, deviate from the average, particularly in the middle of the period. Now, some one might prefer to conclude that we ought not to hear the tone 25 all the time, but at first a tone somewhat lower than this, gradually rising slightly and falling again in pitch towards the end of the period. Whether we should draw this conclusion I will not attempt to decide. Neither do I care to express a definite opinion as to what we actually hear. Let the reader who wants to know this find it out by an experiment of his own. What I must point out, however, is the fact that the time inter- val between two maxima is not necessarily the time between two stimulations. In a provisional way, the interval be- tween two maxima or between two minima or between two points of inflection or between two points of any other name and definition may be used thus, but let us always remember that this is only a provisional, an artificially simplified method, which can scarcely yield more than a rough approximation of what actually happens. Another section of the partition moves up and down twen- ty-four times during the period. The length of this section, which determines the relative intensity of Do we hear the tone heard, is derived from the table the tone 24? as being twenty-one (221 — 200). If we look at the time interval between the successive maxima, we find this to be at the beginning of the period: one hundred and forty-seven, to decrease gradually to one hundred and forty-five at the maximum twenty-three, tc be two hundred and thirty from maximum twenty-three to maximum twenty-seven (maximum twenty-five has disappeared, as seen in figure 21), and to fall again to one hundred and forty-five. Here again, I will not attempt to decide what we ought to expect theoretically, because we have no right to deduce anything definite from a theory in a direction in which this theory is as yet professedly indefinite, in which it obvious- MECHANICS OF THE INNER EAR 55 ly lacks as yet all details, owing to the deficiency of the requisite experimental data. I can only repeat here what I said in the preceding paragraph. Before we continue this attempt at an interpretation of figure 21, let us consider an imaginary case the application of which to our figure will soon make Notindicenimi: itself clear. Imagine that during half a nate counting of Second a nerve end receives in regular in- stimuli allowed tervals fifty stimulations, but during the following half-second no stimulations at all; then again for half a second fifty stimulations in regular intervals, and again for half a second none; and so on. What could we hear in such a case, but a tone for half a second, nothing for half a second, a tone again for half a second, noth- ing again for half a second, and.so on. And what tone would it be? Plainly the tone which we ordinarily call 100, because the frequency with which fifty stimuli are received in half a second is the same as that with which one hundred are received'in one second. I need not waste any effort in trying to prove what is self evident, namely that it would be absurd to count in a case like this simply the number of stimuli during any whole second and to expect, these being fifty, that we should hear the tone 50. Amd yet this way of counting has been actually proposed. But this proposition may well be ignored. Now let us return to the interpretation of figure 21. The third section of the partition, the length of which is twenty- four (191 — 167), receives stimulations in What beats approximately equal intervals until about the do we hear? miximum twenty-three when there is no stimulus at all until about the maximum twenty-nine. With the rough approximation here possible we may say that there is no stimulus during about one-tenth of the period. From our discussion in the preceding paragraph it fol- lows that during about nine-tenths of the period we should 56 UNIVERSITY OF MISSOURI STUDIES hear a tone and during one-tenth of the period we should hear nothing so far as the nerve ends of this section are con- cerned. The pitch of the tone we must expect to lie between the tones 24 and 25, acording to the probable frequency with which the stimulations are received during that part of the period during which they are received. It is plain that the fourth, fifth and following sections of the partition must move up and down very much the same as the third section does, with this difference only, The “mean” tone that for each further section the pause when no stimulations at all are received becomes longer and longer. The total sensation, then, which is derived from the sum of the nerve ends of the third and the following sections must be a tone of a certain intensity at a certain time when all these sections mediate the sensation, but becoming weaker and weaker as one after another of the sections stops moving until for a moment it ceases alto- gether, then appearing again and increasing up to its former intensity. And so on again and again. That is to say, we hear this tone “beating.” And since its pitch lies probably somewhere between 24 and 25, between the “primary” tones (perhaps its pitch is not quite constant but may vary slightly during each period), I propose to call it the “mean tone” (German: Zwischenton). The question whether we hear such a mean tone I do not care to answer here, this discussion being devoted to theory, not to experi- mental research. Let the reader who desires make observa- tions of this kind himself. The farthest section of the partition set in motion by this movement of the stirrup moves up and down only once dur- ing the period. The nerve ends located The difference here receive one shock during each period tone and convey therefore the sensation of the tone 1, the difference tone of this case. The intensity of the difference tone, corresponding to the length of this section of the partition, is two. MECHANICS OF THE INNER EAR 57 It is not impossible, however, it is even probable, also that a few of the sections just preceding this last convey the sensation of this difference tone, instead of that of the mean tone. The last section which may convey the sensation of the mean tone moves only twice up and down during the period, in quick succession. This double move- ment is followed by a long pause during which no movement occurs. Now, experimental research of recent years has prov- ed that two shocks received by the auditory nerve ends may be sufficient to give the sensation of the tone corresponding to the frequency with which the two shocks are received— but only within the middle region of the tonal series. To- wards either end of this series four, six, and even more shocks are found to be necessary for the sensation of the tone cor- responding to the frequency of the shocks. What, then, will be the consequence of choosing the tones 24 and 25 somewhat higher? The section of the partition which makes the two up and down movements in quick succession can no longer convey the sensation of a short mean tone. If there is only one period of movement, no sensation at all will then result. But if many periods succeed, it is much more likely that the double movement of the partition section will have the effect of a single shock than no effect at all; and the repetition of this shock in each succeeding period must result in the sen- sation of the tone 1, the difference tone. If the tones 24 and 25 are chosen still higher, it becomes improbable that even three shocks received by the nerve ends in quick succession between two long pauses can give the sensation of a short mean tone. In this case it is highly prob- able also that the second section before the last conveys the sensation of the difference tone. And so a few more of those more distant sections may convey the sensation of the dif- ference tone instead of the mean tone. 58 UNIVERSITY OF MISSOURI STUDIES If the difference tone results exclusively from the func- tion of the nerve ends located on the last moving section of the partition, its relative intensity is two, according to the above table. But if the difference tone results from the func- tion of the nerve ends of further sections, its relative inten- sity must be higher and the maximum intensity of the mean tone correspondingly lower. That is, the phenomenon of a beating mean tone must be the less pronounced the more audible the difference tone; and the difference tone of a small interval like the one in question must be the more audible the higher the pair of primary tones in the tonal series. Summarizing now our interpretations of figure 21, we must say that so far as the meager data reach from which we can draw theoretical conclusions, the fol- The combination /owing seems likely to be the total -im- 24 and 25; pression (listening with one ear, having summary the other ear plugged): 1. A tone 25 of the constant, but comparatively weak intensity nine; 2. a tone 24 of the constant, but compar- atively weak intensity twenty-one; 3. a mean tone (perhaps slightly varying in pitch during each period) of an intensity which varies once during each period from zero to a definite maximum intensity and back to zero. This maximum inten- sity may be (under the most favorable conditions) as high as (relatively) three hundred and sixty-eight, but must be much less if the primary tones are above the middle region of the tonal series. Its being less means that the “beats” are less pronounced; 4. a difference tone the relative inten- sity of which may be (under the most unfavorable condi- tions) as low as two. Its intensity, however, may be greatly increased, at the expense of the maximum intensity of the beating mean tone, in case the pitch of the primary tones is raised. MECHANICS OF THE INNER EAR 59 Before we take up the theoretical discussion of further tone combinations, the reader ought to obtain some informa- tion concerning the difference tones which awsvot we hear in addition to the “objective” difference tones in the several combinations. To tones give such information of this kind as is indispensable, I shall state here the laws of these phenomena in as clear and comprehensible a manner as possible. These laws given below do not pretend to tell all the difference tones which we might possibly hear in every possible combination of objective tones. Neither do they tell the relative intensities of the difference tones, although this is a matter of no small importance. Laws of difference tones of this scientific perfection are as yet not known and may never be known. The laws below merely tell those differ- ence tones which one is most likely to hear in those combi- nations which correspond to relatively simple ratios of the vibration rates and are therefore (musically and otherwise) particularly interesting. These laws are the following four: In case the ratio of the vibration rates does not differ much from 1:1, let us say 11:12, or 9911: 9989, a single dif- ference tone is audible, whose pitch corre First law of sponds to the pitch of a tuning fork the difference tones vibration rate of which is equal to the difference of the vibration rates of our case. In addition to the difference tone, however, beats are usually clearly audible, and a mean tone may be audible too which lies between the two primary tones. If the interval is quite small, this mean tone is usually more pronounced than either of the primary tones, particularly when we hear with one ear only, having the other ear plugged. The beats just mentioned seem to be the fluctuations of the intensity of the mean tone rather than of the primary tones, if we use one ear only. 60 UNIVERSITY OF MISSOURI STUDIES A second class of ratios which is of particular interest, is that of the ratios whose numbers differ by one. In each of these cases the difference tone 1! is audi- Second law of ble, but often quite a number of additional difference tones difference tones can be perceived. If the numbers of the ratio are rather small, as in the case of 5:4, all the tones from the highest, that is, 5, down to 1 are without any great difficulty noticeable. As we study ratios of increasing numbers, the tones following directly upon 1 (in a rising direction) seem to have a tendency to drop out. And if we go on in the same Objective tones Difference tones easily audible Fy ie - By 2 I 4, 3 2,92 Bp) a 3, 2) 25 6, 5 4, 3, % 2 7, 6 5) 4 ? 1 8, 6 5, % 1 9, 8 7 (6. 5) By 2 10, 9 By. Ty way, we soon find only one difference tone left, the tone 1. We have then simply reached a case in which the difference tone is determined by the first law above. The accompanying table represents this class of ratios with their difference tones. A third class of ratios are the ratios made up of com- paratively small numbers, representing intervals less than an MECHANICS OF THE INNER EAR 61 octave. In these cases three difference Third law of tones are often easily noticeable, one cor- difference tones responding to the direct difference of the vibration rates (4 —/) ; one correspond- ing to the difference between the lat- ter number (A—/) and the vibration rate? of the lower primary tone, that is, (2/—-h); and one corresponding to the difference between the just mentioned differences (4 —/) and (2/—/), that is (2h—31). It is to be noticed, however, that a difference tone is rarely audible which corresponds to a difference larger than the subtrahend; for example, the primary tones 9 and 5 produce the difference tones 4 and 1, but not 3 = 41, or at least not an easily noticeable tone 3, three being larger than one. The following table contains a few ex- amples of this class: Objective tones Difference tones easily audible Sh 5 By By SB |S Ap Tt Op. 5 4, 1 7 4 op Ti, fly By 1 The fourth class are the ratios made up of comparatively small numbers, representing intervals larger than an octave. The first fact to be noticed here is the lack of an easily observable difference tone corresponding to the direct difference of the two vibration rates. Such a tone, if audible, would lie between the primary tones. As a rule, only one difference tone is easily noticeable in these cases, which can be found according to the following Fourth law of difference tones 62 UNIVERSITY OF MISSOURI STUDIES tule: Find the smallest difference between the larger num- ber of the ratio and any multiple of the smaller number. The table contains a few instances of this class: Objective tones Difference tones easily audible Il, 4 I=3x4—I1 12, 5 2—=12—2 x5 9, 4 Ome, II, 3 I=4x3—I1 Gy 2 I=5—2x2 8, 3 1=3x3—8 Let me repeat that the above rules do not pretend to represent scientific laws in the strict sense of the word. They are stated here chiefly for a practical pur- The use of pose. If the reader who is unfamiliar with such laws difference tones will use the above “laws” as directions for observation and obtain a first hand knowledge of the phenomena of difference tones, he will be more interested in the theoretical discussions which are to follow, and able to decide for himself in what di- rections the mechanical theory is yet most undeveloped and most wanting in details. Let us apply our theory now to the combination of two sinusoids of the relative periods nine and four, that is, of the relative frequencies 4 and 9. The com- The combination pound curve, representing the function 4 and 9 f(+) = 1.99 + sindy + sin9x is shown in figure 22. The period is made to begin and to end with the lowest ordinate value of the function, zero, because this has certain technical advantages. MECHANICS OF THE INNER EAR 63 It is, of course, in a periodical function, entirely irrelevant for the mechanical theory what point we regard as the beginning of the period. The accompanying table contains the pairs of corresponding coordinate values of all the maxima and min- ima of the curve. These values are found by computing a large number of pairs of values and selecting from them INTERVAL 4:9, EQUAL AMPLITUDES Ordinate | Abscissa | Ordinate | pordinat Max.| + 169 119 368 | P 338 Min.| — 16 318 | 183 Q 185 Max. + 75 aos | Ais R 91 Min.| — 199 696 | oO A 274 Max.| -+ 110 929 309 B 309 Min.| — 2 1094 197 C 112 Max.| + 142 1275 341 D 144 Min.| — 189 1512 10 E 331 Max.| + 42 1724 241 1 231 Min | — 42 1876 157 G 84 Max.! + 189 2088 388 H 231 Min.| — 142 2325 57 I 331 Max. | =). 2 2506 201 J 144 Min. — 110 2671 89 K 112 Max.| + 199 2904 398 L 309 Min.|} — 75 3129 124 M 274 Max.| + 16 3282 215 N gI a — 169 3481 30 O 185 Max. + 169 3719 368 P 338 those which have the highest and lowest ordinate values. This computation is a very slow process, but has no limit of accuracy. Figure 23 shows the positions of the partition be- longing to the maxima and minima of figure 22. We see that at A the initial forty sections of the partition are in their 64 UNIVERSITY OF MISSOURI STUDIES upper positions. At B, the first thirty-one of them are at their lower limits. At C, the stirrup has caused eleven sections to assume their upper limits. From C to D, the stirrup moves inwards through fourteen units of space, pushing down the eleven sections which were up at C, leaving the following twenty unmoved since they are down already, and pushing down three more, so that now the first thirty-four Fig. 22. The combination 4 and 9 sections of the partition are down, six further sections are up, and all the following ones are in their normal positions. From D to E the stirrup makes an outward movement through thirty-three units of space, moving up the first thirty-three sections of the partition. From E to F, the stirrup moves inwards through twenty-three units of space; and so on. At S, we find the partition in the same position as at A, our starting point; then, a new period begins. Let us now try to interpret the figure. We can easily see that the first eight sections move down and up again nine times during the period. This would mean Do we hear 9? that the nerve ends located on this section convey to our mind the sensation of the tone 9 of the relative intensity eight. The ninth section of the partition moves down and up only eight times during the period; but after our discussion about the omission of stimuli MECHANICS OF THE INNER EAR 65 it is clear that we should not be justified in concluding that we must hear the tone 8. This tone would be audible only if the frequency with which the stimuli occur on the ninth section was less than the frequency on the first eight sections. However, there is no reason why we should regard the ire- aD = Ft 2 ee lf | | o_O 9 8° 6? 4 e | Fig. 23. The combination 4 and 9. Compare figure 22 quency as different. It seems most probable, then, that the nerve ends of the ninth section convey to us the sensation of the tone 9, but with a short pause (or possibly, because of the after-sensation, a diminution of intensity only) at the moment about G, when no stimulation takes place. Our total impression of the tone 9 is, of course, the sum of the sensa- tions conveyed by all the nine initial sections. This means that the tone intensity perceived would, on the whole, be nine; but that for one moment in each period this intensity of the tone might suddenly be slightly decreased. It does not 66 UNIVERSITY OF MISSOURI STUDIES seem improbable—so far as our theoretical data permit us to draw a conclusion—that such a sudden, but weak decrease in intensity might become noticeable as a kind of just per- ceptible “beat.” I leave it to the reader to decide experi- mentally whether the tone 9 in this combination appears slightly “rough” or perfectly ‘“smooth.” The tenth and eleventh sections of the partition move down and up six times during the period. But we must remember here from our previous discus- Do we hear @? sion that—in order to conclude as to the tones to be heard—no indiscriminate count- ing is permissible. Mere counting of stimuli would indicate the tone heard only in case it seems probable that these stimuli occur in equal or approximately equal intervals. Now, a survey of figure 23 does not make it appear probable that the stimuli on the two sections in question occur in even approx- imately equal intervals. The partition moves down at F and remains in the lower position until it moves up at I. It moves down at J and immediately, at K, up again. Down at L and up at M. In this upper position it remains until P, when it moves down. At Q it is up again, to stay in the upper position until B, when it moves down. At C it is up again. At D it moves down, at E up, and at F down again. Are we justified in concluding that the nerve ends located on these two sections of the partition must convey to our mind the sensation of the tone 6 of the intensity two; or any other definite sensation? I do not know how to answer this ques- tion. If we knew the time intervals between the successive stimuli exactly, we might attempt to decide whether one or the other sensation would be more or less probable in this case. But we know that figure 23 is only an approximate, not an exact representation of the actual movement of the partition. It is a certain comfort in this dilemma that the prac- MECHANICS OF THE INNER EAR 67 tical importance of a decision in this case is rather small, for the reason that, whatever sensation these two sections might produce, it would be a sensation of the relative intensity two only, a rather weak sensation compared with the tones which appear theoretically certain. The twelfth, thirteenth, and fourteenth sections of the partition move down at B, a second time at F, a third time at J, and a fourth time at P. These sec- Do we hear 4? tions, therefore, move down and up four times during the period in approximately equal intervals. The five following sections of the partition move down at B, a second time at F, a third time at L, and a fourth time at P. These sections, therefore, move down and up four times during the period in approximately equal intervals. The four sections from the twentieth to the twenty- third move down at B, a second time at F, a third time at L, and a fourth time at P. These sections, therefore, move down and up four times during the period in approximately equal intervals. The following four sections move down at B, a second time at H, a third time at L, and a fourth time at P; that is, four times during the period in approximately equal intervals. The four sections from the twenty-eighth to the thirty-first move down at B, a second time at H, a third time at L, and a fourth time at P; again, four times during the period in approximately equal intervals. The thirty-second and thirty-third sections move down at D, a second time at H, a third time at L, and a fourth time at P. These sections, therefore, move down and up four times during the period in approximately equal intervals. It follows that according to our theory we must expect to hear the tone 4 of a relative in- tensity twenty-two, since it is produced by all the sections from the twelfth to the thirty-third. 68 UNIVERSITY OF MISSOURI STUDIES The thirty-fourth section of the partition moves down at D, and up again at O'; down at P, and up again at S. That is, the nerve ends of this section receive Do we hear any _two stimuli during the period. We may difference tones? expect to hear, therefore, the tone 2 of the relative intensity one. The three follow- ing sections of the partition move down at H and up again at O. The nerve ends on these sections receive, therefore, one stimulus during the period. The next two sections move down at H and up again at S. The nerve ends here receive one stimulus during the period. The fortieth section moves down at L and up again at S. The nerve ends here receive one stimulus during the period. We must hear, then, the tone 1 of the relative intensity six. The tones 2 (weak) and 1 (strong) are the only difference tones in this case which we can derive from our theory with some degree of certainty. Summarizing now the results derived from our represen- tation of the movements of the partition in the case of the ratio 4:9, we find that we must expect to The relative hear the tones 9, 4, 2 and 1, with the rel- intensities ative intensities nine, twenty-two, one and compared six; leaving out of discussion the doubt- ful sensation of the intensity two which may be conveyed to our mind by the tenth and eleventh sec- tions. Now, it is quite natural to ask the question whether we hear these tones with just these relative intensities. Un- fortunately, no exact answer to this question is possible, because this matter, owing to technical difficulties and other circumstances, has never been experimentally subjected to accurate measurement. It is known, however—what also ap- pears in the above statement of our results—that in a com- bination of two tones the higher one loses in intensity, com- pared with the lower one. Yet it is doubtful if this loss in intensity is so great as the number nine indicates, compared MECHANICS OF THE INNER EAR 69 with twenty-two. The present writer at least is inclined to doubt this. He believes that the theory, representing only an approximation to what actually happens in the organ of hear- ing, exaggerates the degree of this loss of intensity on the part of the higher tone. He is also inclined to believe that the theory exaggerates the relative intensity of the difference tone 1, which was found to be six. In reality, this tone seems to be somewhat weaker than is indicated by this number. Let us remember, now, the provisional assumptions which we made in order to render the graphic representation of the movement of the partition as sim- The third and ple as possible. We may raise this ques- fourth provisional tion: Is not, perhaps, the above disagree- assumptions ment between theory and experimental ob- recalled servation a result of one or more of these provisional assumptions? I shall demon- strate that this is indeed the case. Or, more exactly, I shall demonstrate that, if we omit one of these assumptions and take into account in its stead the actual anatomical conditions so far as these are known, we change the results of the theory in such a direction as to diminish the exaggerated loss of intensity of the higher primary tone and also the exaggerated intensity of the difference tone. The partition was provisionally assumed to be of equal width all along the tube. As a matter of fact, its width near the windows is only one-twelfth or one- The partition is tenth (measurements differ somewhat) of narrower near what it is at the far end of the tube. And the windows further, it is to be noted that the width of the partition does not increase uniformly along the tube, like the area between the dotted lines of figure 24, but that it increases first rather rapidly, later more slowly, like the area between the curved lines. The figure, however, does not represent the true relation between the width and 79° UNIVERSITY OF MISSOURI STUDIES the length of the partition. The partition as a whole is much Narrower in comparison to its length than appears in the fig- ure. Let us try, then, to get a clear conception of the func- tional significance of these facts. It is of no particular im- portance, in this connection, whether the measurements upon Fig. 24. Shape of the partition which the following considerations are based are more or less incorrect, as they probably are; for our intention is merely to get an idea of the general direction in which the actual shape of the partition changes the results of a theory having pro- visionally assumed that the partition is everywhere of equal width. When the partition yields in either direction, up or down, its former place is taken by the fluid of the tube. Let us call the quantity of fluid which has taken po- A unit of stirrup sitions formerly occupied by the partition movement equals “the displaced fluid.” Now, it is plain that a unit of dis- the quantity of displaced fluid must al- placed fluid ways be approximately proportional to the distance through which the stirrup has moved since its last reversal of movement. If the partition were equally wide everywhere, then any section of equal length, far from or near the windows, would make room, in moving from one limit to the other, to the same quantity of displaced fluid as any other section. And then, plainly, the length of that part of the partition which is caused to move from one limit to the other would always be proportional to that part of the stirrup movement which caused it to move. MECHANICS OF THE INNER EAR 71 This is the effect of our provisional assumption. But if the partition tapers as it does, a unit of displaced fluid (corre- sponding to a unit of stirrup movement) is made room for by sections of the partition of very unequal length according as the displaced fluid unit is located nearer or farther from the windows. Where the partition is narrow, a longer section would have to move in order to make room for a unit of dis- placed fluid. Where the partition is wider, a shorter section would make room for the same quantity of fluid. Since, then, tone intensity depends on the length of the partition section which is jerked up and down, and since this length is not proportional to the given The computation value of the stirrup movement, it is use- of a table ful to have a table showing the partition lengths corresponding to various stirrup movements in order to get a clear idea of the influence of the tapering of the partition upon the relative tone intensities. To simplify the computation of such a table, it is well to restrict it to a short distance from the windows, so that we Fig. 25. The partition widens may approximately assume the partition to increase uni- formly in width within this distance. Let us call w the smallest width of the partition, near the windows; let us assume that a distance from the windows equal to 50w the width of the partition is 6w, and let us assume a uniform in- crease of width. Let us call y the width at any point of the partition and x» the distance of this point from the beginning 72 UNIVERSITY OF MISSOURI STUDIES near the windows. We then know (Fig. 25) that the ratio 6w—w 507 Y~® is equal to the ratio of a Len OID) Ba Ee WO) low--x 10 x By, Uses The area described by the cross-section of the partition in being jerked from one limit to the other may be called a at the point where the width of the partition is smallest, g at any arbitrary point of the The area Ha described by a partition. These areas, let us assume, are cross-section of geometrically similar. This assumption the partition possesses a higher degree of probability than what would follow for the areas from the third provisional assumption made above for the sake of simplicity. It then follows that the ratio of the areas is equal to the ratio of the squares of the widths of the partition at the same points. a S BG a 2 ar For y we substitute its value found above and have then the equation: el a(1ow-+-+)? 10720" The left side of this equation is a measure of the area described by the cross-section of the partition at the point x, in being jerked from one limit to the other. The right side of the equation contains the variable +, the distance of any point of the partition from its beginning near the windows, MECHANICS OF THE INNER EAR 73 and the two constants a and w. The former of these con- stants is the area described by the initial point of the partition in moving from one limit to the other, of whatever form this area may actually be found to be. The latter is the width of the partition at the initial point. The mathematical reader immediately sees that that quan- tity F of displaced fluid for which room is made by a move- The quantity of ment of any given section of the partition fluid for which is determined by the following equation, room is made which can be easily integrated. a, i i aadx 4, In order to integrate this equation we have to express g as a function of x. This has been done above under the tem- porary assumption of a uniform increase of width. The re- sult is stated in the equation just preceding the last. We then have 1007” 4% a raf? (1ow+2)'d*z—= — Sant | (row-+1,) — (100+) 5 where +,is the farther, , the nearer of the two points enclosing whatever section of the partition is in question. If the section in question is an initial section of the par- tition, then x, is equal to zero, and the quantity of displaced fluid is imal | = I 4,)°—(10w)3) - Let us regard the partition as consisting of sections each of the length of w. We can find, then, the quantities of dis- placed fluid for which room is made by the first section, the first two, the first three, the first four, and so forth, sections 74 UNIVERSITY OF MISSOURI STUDIES by making +, successively equal to w, to 2w, to 3w, to 4w, and so forth. If + —=xnw, we have AD . ole aCor: (eee) —(10w) i = al as aes [core — 10'|. 7, Let us arbitrarily regard ae as the unit of displaced fluid. We could then easily compute a table which contains the number of fluid units displaced by the Two tables number » of partition units. If the num- possible ber of partition units is, for example, three, the quantity of displaced fluid is (13"—10°) units and so on. More useful, however, is a table which progresses in a regular series of units of fluid and tells us—in decimals—the lengths of the initial sections which make room for these quan- tities of fluid; for our representation of the movement of the partition tells us the quantities of displaced fluid, and the cor- responding section lengths are to be found in order to obtain a more correct idea of the relative tone intensities. In order to compute such a table it is advantageous to use a larger fluid unit than the above. Let us determine the total quan- tity of fluid for which room is made by the partition section from += 0 to + = 50w, that is, the whole part of the partition near the windows for which we have assumed a uniform taper- ing or change of width; and let us—arbitrarily—regard one- fiftieth of this quantity as the fluid unit. wl BN dN moe uae) 103 em __ 215000 a w fa 300 MECHANICS OF THE INNER EAR 15 The fluid unit, defined as one-fiftieth of the above quantity, is therefore 4300 a w 300 Any number m of such fluid units is then 4300 a wm 300 We derived above the following equation between fluid quantities and partition lengths = =o ae ( 1ow-+4,)>—( row)" In this equation we have to substitute for F the above expression of fluid quantity and then to solve the equation LOL ACNE DEB) BI 300 ~ 3002? | (1ow + +#,)? — (10%) (10w-+#,)? = 10°23 4300703 1ow+24, = wV 1000--4300m x, = (V1000-++4300m — 10)w The following table contains the corresponding values of m and «#,, measured in the unit of length w. 76 UNIVERSITY OF MISSOURI STUDIES Let us see, now, how we must use the table of fluid quantities and partition lengths. We recall that any unit of stirrup movement causes the displacement The use of of a unit of fluid. What we have the table called above “the relative intensities of the tones heard” refers directly to relative numbers of units of stirrup movement; indirectly also to rela- tive numbers of units of displaced fluid, since it is highly prob- able that the quantity of displaced fluid is approximately pro- portional to the extent of a stirrup movement. What we want TABLE OF THE RELATIONS BETWEEN FLUID DISPLACEMENT AND PARTITION LENGTH m nN m x m x m x m x I 7.43 II | 26.42 21 | 35-03 31 | 41.22 41 | 46.18 2 | 11.25 12 | 27.47 22 | 35.73 32 | 41.75 42 | 46.62 14.04 13 | 28 46 23 | 36.40 33 | 42.28 43 | 47.07 3 4 | 16.30 || 14 | 29.41 || 24 | 37-05 || 34 | 42-80 || 44 | 47.50 5 | 18.23 15 | 30-31 25 | 37-70 35 | 43-31 45 | 47.94 6 | 19.92 16 | 31.17 26 | 38.32 36 | 43.81 46 | 48.36 7 | 21-45 || 17 | 32.00 || 27 | 38.92 || 37 | 44-30 || 47 | 48.78 10 | 25.30 20 | 34.31 30 | 40.65 40 | 45.72 50 | 50.00 to know now, is the length of the several sections of the par- tition of which—in the last case of tone combination, 4 and 9—the first or initial one moves up and down nine times and produces the tone 9, the second produces no definite tone with MECHANICS OF THE INNER EAR 9/7) certainty, the third produces the tone 4, the fourth the tone 2, and the fifth the tone 1. The fluid quantity for the tone 9 is measured, as we found above, by the relative number nine. Now, let us, for exam- ple, assume that this means an equal number of fluid units in our table. We then read off the corresponding par- tition length as being 24.11 units. The fluid quantity for the uncertain tone was measured as two units. But now, we can- not simply read off from the table the number of partition units corresponding to two; for the partition section making TONE INTENSITIES IN THE COMBINATION 4 AND 9 Tones |Uniform width| Tapering 9 22.5% 52.7% Uncertain 5.0% 5.0% 4 55-0% 34.8% 2 2.5% L.1% I 15.0% 6.4% room for these two fluid units is not an initial section. We must read off, therefore, the value corresponding to eleven fluid units (26.42) and subtract from this the value correspond- ing to nine fluid units (24.11). We thus see that the length of the partition section about the tone of which we could not come to a decision is 2.31 units. The fluid quantity for the tone 4 was measured as twenty-two. But here again we can- not simply read off the length of the partition section pro- ducing this tone, because this section is not an initial section. We must read off the values for 9--2+-22—33 and for 9+2=11 and subtract the latter from the former. These values are 42.28 and 26.42. The length of that section of the partition 48 UNIVERSITY OF MISSOURI STUDIES which moves up and down four times is therefore 15.86 units. The intensity of the tone 2 is one fluid unit. The length of the partition section corresponding to this fluid unit is 42.80— 42.28—.52. The fluid quantity for the tone 1 is six fluid units. We have to read off from the table the values corresponding to 9+24+22+1+6=—40 and to 9+2+22+1—34 fluid units. These values are 45.72 and 42.80. The length of that section of the partition which produces the tone 1 is therefore 2.92 units of the partition. The relative intensities of the four tones 9, 4, 2, and 1, would then be, not as nine to twenty-two to one to six, but as 24.1 to 15.9 to .5 to 2.9; and the tone about Thevrelative which we could not reach a definite con- intensities of the clusion would have the relative intensity tones 9, 4, 2, 2.3 instead of two. For the sake of better and 1 . comparison let us express the relative in- tensities in percentages. The table shows in one column the tone intensities in case we regard the par- tition as of uniform width and in another column the intensi- ties in case we regard the partition as tapering and possess- ing those properties upon which the present computation is based. We must not, of course, regard the result found in the second column of intensities as any more final than that in the first column. We have assumed that This result the initial section of the partition tapers not final uniformly so that, the initial width being w, its width is 6w at a distance of 50w. But we do not know that it tapers just this way. We have further assumed that the areas described by cross-sections of the par- tition in moving from one limit of position to the other, are geometrically similar. But we do not know whether they are or not. We have further assumed that the total movement of the partition in this case extends just to the distance of 45.72w. MECHANICS OF THE INNER EAR 79 But this is an arbitrary assumption, and the results of the ta- ble, as is shown farther below, would look different if the total movement did not extend just so far, but farther or less far. We must not, then, regard this result as final, but simply ob- serve if it tends to change the relative intensities in such a direction as might correct the intensities which seemed some- what objectionable. Now, we objected, first, to the fact that the higher of the primary tones had such a slight intensity com- pared with the lower one, 22.5 per cent compared with 55.0 per cent. Now we see that taking into account the tapering of the partition raises the intensity of the tone 9 to 52.7 per cent and lowers that of the tone 4 to 34.8 per cent. As stated before, these particular figures must not be regarded as a final result. It is irrelevant that now the lower tone is weaker than the higher. What is important is the fact that the influence in question is in the direction in which it must be in order to correct the objectionable features of the former computation. A further result of this influence is the reduction of the former intensity of the difference tone 1, which we regarded as rather high, from 15.0 per cent to 6.4 per cent—again a change in the desired direction. We can obtain here a more special insight in addition to the general insight into the fact that tapering of the par- tition tends to increase the intensities of the Tihs Pee tones piocuced by tne initial sections, to tensities not inde- decrease the intensities of the tones pro- pendent of the duced by more distant sections of the par- absolute intensity tition. More especially, we shall observe of the compound that the amount of this increasing or de- sound creasing influence varies according as the total length of the partition section set in motion varies, that is, as the total intensity of the compound sound heard varies. Imagine, for example, three tones, which we call A, B, and C, being produced by successive sections of 80 UNIVERSITY OF MISSOURI STUDIES the partition. Imagine further that the quantity of displaced fluid for the tone A’ is 20 per cent of the total amount of fluid displaced by the compound sound wave, that the quantity for B is 50 per cent, and the quantity for C 30 per cent. This is a percentage which might easily be found in an actual case. The pitch of the tones A, B, and C is irrelevant. The table below contains all the values which are of interest to us, for two cases. In the first case the actual fluid quantities are two, five, and three, by assumption; in the second case they are ten, twenty-five, and fifteen. That is, the stirrup move- ment in the second case is of the same form, but exactly five times as large as in the first. Quantities of dis- Length of sections Length of sections placed fluid (absolute values) (percentages) A B C A B Cc a A B C 2 5 3 | 11.3 | 10.2 | 3.8 | 25.3 | 44.7% | 40.3% | 15.0% 18.0] 6.7 | 50.0] 50.6% | 36.0% | 13.4% Lal ° is) n 4 wn iS) on iS) The table shows that the tone intensities do not increase proportionally to the increase in the amplitude of stirrup move- ment. The amplitude in the second case is five times that of the first case; but the total intensity (3) of the audible sound in the second case is less than twice that of the first case (50.0 compared with 25.3). The table shows further that the inten- sity of the tone A is in the first case 44.7 per cent, in the second case 50.6 per cent. That is the increase in the intensity of the whole sound is favorable to the relative intensity of the tone produced by the initial section of the partition. The percentage intensity of this tone, A, is increased at the cost of the tones B and C, the percentages of both of which are diminished. MECHANICS OF THE INNER EAR 81 Thus far we have studied the effect upon the relative tone intensities of initial and more distant sections which would result from a uniform increase in width of Increase in width the partition as compared with a uniform of partition width. But we know that the partition not uniform does not increase uniformly, but rapid- ly at first, near the windows, and more slowly the farther we go from the windows (Fig. 24). To understand the theoretical result of this manner of increase, it is not necessary to compute a new table. It is plain that, if a more distant section increases less than we assumed in computing the preceding table, showing the corresponding values of m and x, this would cause a longer piece of this dis- tant part of the partition to move in order to make room for a certain quantity of displaced fluid. That is, the decrease in the broadening of the partition would counteract the effect last discussed. We saw in the preceding paragraph that an increase in the intensity of the whole sound does not leave the relative intensities of the partial tones unaltered, but favors the intensities of the tones on the initial sections, reduces those on the distant sections. But now, if we increase the in- tensity of the whole sound, we throw the tones of the more distant sections on still more distant sections, that is, on sec- tions where the broadening of the partition is much less than that assumed in the table. Consequently, the tones of distant sections cannot lose in percentage as much as a derivation from the table would indicate, but might even gain somewhat in percentage of intensity through an increase of the total in- tensity of the sound. 82 UNIVERSITY OF MISSOURI STUDIES The preceding paragraphs must impress us with the per- plexity of our situation. We want to comprehend the facts of audition as depending on the structure THe necd Of a and function of the sense organ. But every more accurate endeavor to enter into the details of the and detailed function of the organ is thwarted by the anatomical poverty and inaccuracy of our anatomical knowledge knowledge. We cannot obtain a definite idea of the intensities of the various physi- ological processes resulting from a compound aerial wave un- less we know exactly the manner of increase in width of the partition. It is not sufficient to know that it increases first tapidly, then slowly. We need a very exact measurement of the width of succeeding cross-sections of the partition and of the distance of each of them from the beginning of the par- tition near the windows. On the other hand, we need also a much more detailed and accurate comparison of the relative intensities of the components of stronger and weaker com- The nesdiok a pound sounds, based on psychological ex- more accurate perimentation and observation. Thus far, observation of the practically nothing in this regard is known psychological with exactness. It is to be hoped that, in facts of hearing spite of the extraordinary technical diffi- culties and the costliness of the apparatus required for such investigations, an accurate knowledge of these psychological facts will be obtained. We _ need this knowledge because some of the constants contained in the mechanical theory may never become directly measurable, for example, the elastic properties of the partition, and, therefore, will have to be inferred from their psychological conse- quences. MECHANICS OF THE INNER EAR 83 ‘ Two consequences of the particular shape of the partition which we have just discussed in as much detail as anatomical knowledge permits should be emphasized. The first of these is of the greatest biolog- Two important 5 SiN x g ical significance. It is certainly important consequences of the partition’s for the animal to be very sensitive to shape. sound, that is, to be able to hear sounds Sensitiveness which are very weak and cause only a of the ear minute movement of the stirrup. Now, the initial part of the partition being ex- ceedingly narrow, even the minutest quantity of fluid dis- placed by the stirrup must spread considerably lengthwise over the partition and thus stimulate quite a number of nerve ends. But it would not be advantageous to have the partition equally narrow all along. In that case comparatively weak objective sounds would cause the whole partition to move up and down and the displaced fluid for which no room can be made by the partition, to flow back and forth through the “safety valve.” Strong objective sounds would then make the same impression upon the animal as sounds of medium physical intensity. This disadvantage is overcome by the partition’s tapering, by its being narrow at the beginning, but wide farther on, so that even sounds of considerable strength do not involve the whole partition. But again, there would be a disadvantage if the partition’s width increased uni- formly : for then the relative intensities of simultaneous tones —as we have seen—would not be even approximately inde- pendent of the absolute intensity of the total sound. This disadvantage might be avoided by the width increasing first rapidly, then more and more slowly. If it is thus avoided, either partially or totally, we do not exactly know because of lack of exact anatomical data. $4 UNIVERSITY OF MISSOURI STUDIES The second of the consequences to be emphasized is probably of little biological significance, but possibly of some importance to the student observing differ- Conditions more °¢e tones in a psychological iaboratory. or less favorable It is quite possible that, as a result of the to the observation tapering not being uniform but decreasing of difference as the windows are left behind, the rela- tones tive intensity of difference tones, which are obviously produced by the more distant sections of the partition, is somewhat greater when the abso- lute intensity of the whole sound is rather great. If this is so, it would be advisable to use for the observation of dif- ference tones fairly strong primary tones rather than weak ones. Whether this conclusion is borne out by experience, I must leave to the reader to decide. The above discussion of tone intensities naturally leads us to take up the theoretical aspects of the fact frequently ob- served by experimenters that in a combina- The dis- tion of a lower and a higher tone the latter appearance of is sometimes entirely inaudible, provided, a higher tone of course, that it is physically much weaker than the former. The reverse, however, that is, the disappearance of a physically weak low tone when sounded together with a strong higher tone, has hardly been observed. The phenomenon in question can, perhaps, be most easily observed with such ratios at 1:2, 2:3, or 1:3. Let us study, then, one of these ratios, say 1:2, from the theoretical point of view. G-A Fig. 26. The combination r and 2, unequal amplitudes MECHANICS OF THE INNER EAR 85 Let us combine two sinusoids according to the following equation : f(#) = 2sina-+sin2dsv. The combination hat is, the amplitude of the sinusoid of 1 and 2, when 2 ‘the shorter period is one-half of the am- is comparatively plitude of the sinusoid of the longer pe- weak riod. Figure 26 shows the curve represent- ing the stirrup movement, and the accom- panying table shows the exact numerical values of those points of the curve which, as we shall see, are of particular import- ance to us, that is, the maxima and minima, and the points of inflection. These values are easily found in this particular case. To find the maxima and minima, we have to set the first derivative of the above function equal to zero and solve the equation for +; for the maxima and minima are those points where the tangential angle or differential coefficient is zero. f' (4) = 2cosx + 2cos2y = 0. To find the points of inflection, we have to set the second derivative equal to zero and solve the equation for x; for the points of inflection are those points of the curve where the tangential angle neither increases nor decreases. f’ (#) = — 2sinex — 4sin2« = 0. The purely arithmetical work I do not care to perform here. The table shows its results. It is plain that, if we rep- resent the successive positions of the partition according to the same rules as formerly employed, we find that only one tone can become audible, the tone 1. The tone 2 has disap- peared because its addition does not increase the number of the maxima and minima of the compound curve (Fig. 26), but merely influences its shape. However interesting this in- sight may be into the fact that a weak higher tone added to a strong lower tone may be entirely inaudible, the present theoretic result is not quite satisfactory. It is somewhat un- 86 UNIVERSITY OF MISSOURI STUDIES satisfactory because it seems improbable that the higher octave should become inaudible as soon as its amplitude is decreased to one-half of the amplitude of the lower tone. It seems, judg- ing from experimental experience, that the higher octave must be weakened by far more, in order to become entirely inaudi- INTERVAL 1:2, AMPLITUDES 2:1 Ordinate | Abscissa | Ordinate Orne, Inf. fo) fo) 2598 B 2598 Max.| + 2598 600 5196 Cc 2598 Inf. | + 1125 1045 3723 D 1473 Inf. fo) 1800 2598 E 1125 Inf. — 1125 2555 1473 F 1125 Min.| — 2598 3000 fo) GVA 1473 Inf. fo) 3600 2598 B 1473 ble. Now, to correct the above theoretic result, we cannot make use of the previous considerations concerning the in- fluence of the tapering of the partition. As long as there is an initial section, however short, jerked down and up twice during the period, the result of tapering may be the length- ening of this section and a corresponding increase of the rel- ative intensity of the higher tone. But when there is no initial section at all which moves twice, no tapering of the par- tition can create one. Let us, therefore, recall the other pro- visional assumptions. MECHANICS OF THE INNER EAR 87 The second of our provisional assumptions is that the partition is perfectly inelastic, that is, not offering any re- sistance to a displacement until either of Hel secontd the limits is reached, and then offering ab- provisional solute resistance. Now, does our anatom- assumption ical knowledge warrant such an assump- recalled tion? The most striking fact derived from an anatomical study of the organ is the absence of any solid body which might serve to interfere sud- denly, abruptly, with a yielding movement of the partition in either direction. Even the analogy with the leather seat of a chair is hardly admissible if we mean thereby a flabby, wrinkled piece of leather. The analogy probably holds good only if we imagine the leather in such a condition as we find it in a new, unused chair, occupying a perfect plane, being practically free, however, from any stresses as long as no weight is resting upon it, yielding to a certain extent if a certain weight is placed upon it, but not yielding in proportion to the weight if the weight is increased. It is probably in a similar manner that the partition resists pressure. What determines the limit of yielding must be the partition’s own elasticity. But let us always remember that there is no elastic force—no stress—in the partition while in its normal position, that its elastic force is the result of a displacement in either direction, that this elastic force increases much more rapidly than the displacement, and that therefore a constant increase of press- ure on any point of the partition does not cause a constant movement of this point, but a movement first rapid, then quickly decreasing in velocity. Figure 27 is a graphic repre- sentation of such a function under the arbitrary assumption— which, perhaps, may be regarded as a rough approximation to the actual conditions—that the elastic force of the partition increases proportionally to the tangent of its displacement. The abscisse represent the increasing pressure, the ordinates 88 UNIVERSITY OF MISSOURI STUDIES the corresponding displacements of the partition. We notice, then, that there is a practical limit of yielding, that an increase of pressure beyond a certain point is practically ineffective, does not cause any further displacement to speak of. There can be no doubt that the assumption of a relation existing between the displacement of the partition and the pressure, similar to the relation between an angle and its tangent—however rough the approximation to the facts—is ee ine | HH , ce GyeniSi Sir Ciaigine, Fig. 27. The probable relation between pressure and displacement of the partition much better adapted to the anatomical facts than the second provisional assumption. Of course, the second provisional as- sumption simplifies greatly the graphic representation of the successive positions of the partition, but at the cost of ail accuracy. Wherever the approximation thus possible is suffi- cient for our purposes, we shall, of course, continue to work under that simpler assumption. But let us now apply the latter assumption to our problem of representing the succes- sive positions of the partition which correspond to the stirrup MECHANICS OF THE INNER EAR 89 movement of the curve in figure 26. Let us disregard, how- ever, the varying width of the partition, in order to avoid too much complication. We shall again assume the partition to be of uniform width, without, however, forgetting the fact that this is an arbitrary simplification of the conditions. Imagine that the whole partition is in its normal posi- tion, free of any stress, and that the stirrup begins an outward movement of the form of the curve from E The significance to G in figure 26. We see from the curve of a point of that the stirrup moves at first very slowly, inflection then gradually more and more quickly un- til at F, the point of inflection, it moves with the greatest velocity. Now, a simple consideration will make it plain to us that the pressure acting upon the initial part of the partition must be dependent on, probably be propor- tional to the velocity of the stirrup. If the velocity of the stir- rup movement were extremely small, no point of the partition would move more readily than any other, and consequently none of them would move to a considerable extent; but the fluid would every time and all the time flow through the opening at the end of the tube which we called the safety valve, because there would then be practically no friction at any point within the tube, and an infinitesimal elastic force of displacement could keep the partition in place. On the other hand, if the velocity of the stirrup movement is not very small, the points of the partition near the windows receive the greatest push from the fluid, farther points only a slighter push, very quickly diminishing with increasing distance, and at some distance away the push could be regarded as practi- cally infinitesimal; all this as the result of the friction of the fluid in the narrow tube, the total influence of which is the greater the longer the column of fluid in question, measuring this column from the windows. go UNIVERSITY OF MISSOURI STUDIES As the stirrup moves away from H, the initial part of the partition yields upwards, as shown in figure 28 at I. By I, II, and so forth, are meant successive moments between E and G in figure 26. The increasing velocity of the stirrup re- sults at II in an increased pressure at all the points of the partition which had yielded at I. Therefore, at II in figure 28 these points are somewhat farther displaced than they were at I, but not proportional to the increase of the velocity of the stirrup but much less, according to figure 27. At the same Fig, 28. Seven successive positions of the partition, three preceding and three following an inflection point (F) time we notice that the part of the partition which has now yielded extends much farther to the right at II than at I; for the stirrup has displaced much more fluid at II than at the earlier moment I, and the slight increase in the displacement of those parts of the partition which were already displaced at I, can not nearly make room for all this fluid. Therefore the MECHANICS OF THE INNER EAR gI spreading of the displacement lengthwise over the partition. At III the velocity of the stirrup is still greater than at II. Therefore we notice again a slight increase in the displace- ment of the initial part of the partition. But as the stirrup approaches F, this increase of displacement of the initial parts must become less; for the velocity of the stirrup is now nearly constant, its increase very slight, and the increase of displace- ment is in any case much less than proportional to the increase of velocity, according to figure 27. As soon as the stirrup passes F, its velocity begins to decrease. Immediately the press- ure on the whole piece of the partition which has yielded de- creases; and this whole piece, therefore begins to move slowly back by its elasticity in the direction of its normal position. It is clear, however, from figure 27 that even a considerable decrease of the velocity of the stirrup causes only a slight decrease of the displacement until the stirrup ap- proaches G, when its velocity approaches zero and the part of the partition in question can move more rapidly by its elasticity since it has no longer to overcome much pressure caused by the stirrup. It does not follow, however, that any point of the partition has returned to its normal position by the time the stirrup reaches G. The initial sections have merely moved in the direction of their normal position. And meanwhile, new points of the partition to the right must have yielded upwards to make room for the fluid being dis- placed all the time by the stirrup in moving towards G. Three positions of the partition between F and G are shown in figure 28 at IV, V, and VI. g2 UNIVERSITY OF MISSOURI STUDIES One of the consequences of the decrease of pressure on the partition at the point of inflection between a maximum and a preceding or following minimum of the Thearetiocons curve consists in the fact that the partition sequences of does not move up and down so suddenly the inflection as it appeared from our previous graphic of the curve representations. We had to point out this fact before in mentioning the irregular- ity with which stimuli often seem to be received by the nerve ends according to our simplified graphic representation. The exact time when a stimulus—a shock, as we called it—is re- ceived we now find to be dependent also on the location of each inflection point, not merely on the temporal location of the maxima and minima. Unfortunately, however, we can not determine the time of each shock with certainty even now, taking into account the inflection point. This important ques- tion of theoretical detail must be left open for future investi- gation. Another consequence of the decrease of pressure on the partition marked by any point of inflection consists in the fact that a double movement—up and down—of the partition may result, not only from an alternation of maxima and mini- ma of a curve, but also from an alternation of inflection points marking an increasing and decreasing velocity of the stirrup. This means that the number of shocks received by the nerve ends during one period of the curve may exceed the total num- ber of maxima (or minima) in case any part of the curve from a maximum to a minimum or from a minimum to a max- imum contains more than a single point of inflection. An example will be given at once. MECHANICS OF THE INNER EAR 93 Let us return to the theoretical analysis of the whole curve in figure 26. From A to C the stirrup moves inwards, pushing down a certain length of the parti- mie sueceadive tion. The initial part of this length, how- positions of the ever, begins a slow upward movement as partition corres- soon as the velocity of the stirrup begins ponding to to decrease, at B. The same part moves figure 26 up more quickly when, at C, the stirrup reverses its movement and begins to pull it upward. We therefore see at B in figure 29 the initial two sections in an extreme downward position. At C, we see them Fig. 29. The combination 1 and 2. Compare figure 26 only in a medium downward position, and at the same time we find the following two sections of the partition in a similar downward position since the stirrup has continued, from B to C, to move inwards. It is plain that to take into account, in our graphic representation, only two kinds of displacements in either direction, an extreme and a medium one, is again an ar- tificial simplification, introduced merely to suit our momentary needs, in spite of the fact that thus we lose sight of some of the details of the movement. Actually, the movement probably occurs rather in the form of figure 28. But the simplification used in figure 29 not only renders the drawing of the figure 94 UNIVERSITY OF MISSOURI STUDIES easier, but also contributes towards a readier comprehension of the significance of the graphic representation, towards a quicker reading off of the tones to be heard. At D we see the first section in an extreme upward position since the stirrup has moved outwards and has reached a max- imum velocity. At E, the first section has returned to a me- dium displacement since the velocity of the stirrup has reached a minimum. At the same time the second section of the par- tition has moved upwards as a result of the continued outward movement of the stirrup. At F we find the initial three sec- tions of the partition in an extreme upward position; for the stirrup has continued to move outwards and has also reached a maximum of velocity. At G all four initial sections of the partition are in an upward position since the stirrup has con- tinued to move outwards. But they are only in a medium displacement since the velocity of the stirrup has again reach- ed a minimum. Looking now over the four columns in figure 29, we notice that the first shows an extreme upward position of this section of the partition at F, a medium upward De we hear position at G=A, an extreme downward both tones position at B, a medium downward posi- 2 and 1? tion at C, an extreme upward position at D, a medium upward position at E, an ex- treme upward position again at F. This section of the parti- tion, therefore, has moved up and down twice during the pe- riod, the second upward movement occurring between E and F. It is quite probable, then, that the nerve ends located on this section receive two shocks during the period. The second section of the partition has an extreme upward position at F, a medium upward position at G=A, an extreme downward position at B, a medium downward position at C and D, and a medium upward position at E. It follows that this section moves up and down only once during the pe- MECHANICS OF THE INNER EAR 95 riod, and that the nerve ends located there recefve only one shock during the period. The third section has an extreme upward position at F, a medium upward position at G=A and also at B, a medium downward position at C, D, and E, The nerve ends of this section receive therefore one shock during the period. The fourth section has a medium upward position at G=A and at B, a medium downward position at C, D, E, and F. The nerve ends of this section receive therefore one shock during the period. It is plain, then, that from our theory we must expect to hear the tone 2 as well as the tone 1, the former conveyed by the first, the latter by the three following sec- tions of the partition. To determine the relative intensities of the tones heard, we have to compare the length of the initial section of the par- tition with the total length of the three Sixth provision- following sections when added together. al assumption For simplicity’s sake, let us make this comparison again under the third and fourth provisional assumptions, and also under a new assump- tion, namely, that the fluid for which room is made or whose room is taken by a move of the partition from a medium to an extreme (or the reverse) displacement on the same side (eith- er above or below the normal position) is a negligible quanti- ty. That this assumption simplifies our representation of the successive positions of the several sections of the partition is clear, since we may thus take the length of each section pro- portional to the ordinate difference of the corresponding points of the curve. For instance, the third and fourth sections in figure 29, which move down at C, would be longer than pro- portional to the ordinate difference of the points B and C in figure 26 if the fluid displaced by the first and second sections in moving from an extreme position at B to a medium displace- ment at C were not a negligible quantity. In the latter case, the fluid displaced by the first and second sections during the 96 UNIVERSITY OF MISSOURI STUDIES time from B to C would have to be made room for by the third and fourth sections, which, then, by necessity would extend farther to the right than in proportion to the stirrup movement from B to C. To take this into account would extraordinarily complicate the graphic representation without offering, at present, a correspondingly great advantage. This additional extension of the third and fourth sections to the right could be but slight since the amount of fluid in question would be but slight. This becomes clear from a glance at figure 27. We have learnt from this figure that some pressure added to a given pressure does not cause a proportional, but a much smaller increment to be added to the previous displacement of the partition; and thus the amount of fluid in question may be entirely neglected without depriving us of the right to regard our representation as an approximation to the actual positions of the partition sections. We may, then, under the third, fourth, and sixth pro- visional assumptions, regard the relative intensities of the tones as proportional to the ordinate dif- Theurclative ferences in the table belonging to figure intensities of 26. We find in the table the value 1473: as 2 and 1 expressing the ordinate difference of C and D, the value 1125 of D and E, 1125 of E and F, and 1473 of F and G, the sum of these last three being 3728. Therefore, under the above simplifying assumptions, the relative intensity of the tone 2 compared with 1 is about as fifteen to thirty-seven. Let us now apply our theory to the ratio of the vibration rates 5:8. The curve in figure 30 represents the function f(#) = sindx + sin8x. The table below contains all the abscissa and ordinate : values of the maxima and minima as well The combina- ( E : oninndle as of the inflection points of the curve. Equal ampli- The inflection points are computed as the tudes of stirrup maxima and minima of the first derivative movement curve, represented by the function MECHANICS OF THE INNER EAR 97 f' (#) = 5cos5w ++ 8cos8xr. It is impossible, in this case, to apply the simple method of K W, Fig. 36 Fig. 38 The combination 5 and 8 with different amplitude ratios 98 UNIVERSITY OF MISSOURI STUDIES finding the corresponding ordinate and abscissa values of the maxima and minima of these two functions by making their derivatives equal to zero and solving the resultant equations INTERVAL 5:8, EQUAL AMPLITUDES Ordinate | Abscissa | Ordinate Cee Inf. fo) fo) 199 Vv 188 Max.| + 188 131 387 WwW 188 Inf. + 24 249 223 x 164 Min.| — Ioo 385 99 Y 124 Inf. | — 51 474 148 Z 49 Max.| + 3 576 202 Dye 54 Inf. — 29 661 170 Da} 32 Min.|; — 61 740 138 € 32 Inf. + 59 8472 258 D 120 Max.| + 167 983 366 & 108 Inf. | — 18 I116 181 S 185 Min.| — 199 1244 fo) A 181 Inf. | — 36 1367 163 B 163 Max.| + 137 1504. 336 Cc 173 Inf. + 61 1603 260 D 76 Min — 26 1725 173 E 87 Inf fo) 1800 199 F 26 Max.| + 26 1875 225 G 26 Inf. | — 61 1997 138 H 87 Min.| — 137 2096 62 I 76 Inf. | + 36 2233 235 J 173 Max.| + 199 2356 398 K 163 Inf. + 18 2484 217 L 181 Min.| — 167 2617 32 M 185 Inf — 59 2728 140 N 108 Max.| + 61 2860 260 Oo 120 Inf + 29 2939 228 P 32 Min.| — 3 3024 196 Q 32 Inf + 51 3126 250 R 54 Max.} -++ 100 3215 299 S 49 Inf — 24 3351 175 T 124 Min.| — 188 3469 II U 164 Inf fo) 3600 199 Vv 188 MECHANICS OF THE INNER EAR 99 for +. This is impossible because the equations to be solved would be of the eighth degree. We have to use, therefore, the only method left, however great our sacrifice of time, and to calculate directly a sufficiently large number of values from which we then select the largest and smallest. In this way the values of the table have been obtained. By adding 199 to each of the values of the first column we get the third column, which offers the advantage of containing only positive ordi- nates. This procedure is equivalent to selecting a different horizontal coordinate, which is always dependent on our choice. The ordinate value zero, thus obtained, is the one which belongs to point A in figure 30. The successive positions of the partition corresponding, under the sixth provisional as- sumption, to all the maxima, minima, and inflection points of the curve are shown in figure 31. Let us at once examine the movements of the three sec- tions, the fiftieth, the fifty-first, and the fifty-second.* At A, we find these sections occupying a medium up- What tones do ward position. From A to B they move down. we hear? The From B to C they begin to move up. tone 8 From C to D they continue to move up. From D to E they begin to move down and continue to move down until G. From G to H they move up, completing thus the second down and up movement. From H to J they move down, and from J to L up, complet- ing the third down and up movement. From L to N they move down, and from N to Q up, completing the fourth down and up movement. From Q to R they move down, and from R to T up, completing the fifth down and up movement. From T to V they move down, and from V to X up, completing the sixth * For a perfect understanding of the details, the reader will have to draw figure 31 (and the similar figures following) for himself on a larger scale, and to inscribe the exact values as derived from each corresponding table. 100 UNIVERSITY OF MISSOURI STUDIES fo} 50 100 % 8 & 8 & 8 _ a a (Se) ise) + Fig. 31. Compare figure 30 MECHANICS OF THE INNER EAR 101 dowm and up movement. From X to 9% they move down, and from % to © up, completing the seventh down and up movement. From © to D they move down, and from D to § up, completing the eighth down and up movement. From % to ®©=A they begin to move down and continue to .move down aiter A, as we have seen. The movements of the forty-nine initial sections are so sim+ ilar to those of the three sections just discussed that we convince ourselves easily that the nerve ends located there receive the same number of shocks during the period. The fifty-third and fifty-fourth sections move down from % to B, and up from B to D. Down from D to G, and up from G to H. Down from H to J, and up from J to L. Down from Lto N, and up from N toQ. Down from Q to R, and up from R to T. Down from T to V, and up from V to X. Down from X to %, and up from 2% to ©. Down from € to 9, and up from D to %. The nerve ends located on these sections therefore receive eight shocks during the period. The ten sections from the fifty-fifth to the sixty-fourth move down from % to B, and up from B to D. Down from D to G, and up from Gto H. Down from H to J, and up from J to L. Down from L to N, and up from N' to Q. Down from Q to S, and up from S to T. Down from T to V, and up from V to X. Down from X to Y%, and up from % to ©. Down from € to ©, and up from 9 to %. The nerve ends located on these sections therefore receive eight shocks during the period. The twelve sections from the sixty-fifth to the seventy-sixth move down from % to B, and up from B to D. Down from D to G, and up from Gto H, Down from H The tone 6 to J, and up from J to L. Down from L to N, and up from N to T. Down from T to V, and up from V to X. Down from X to 9, and up from ® to %. The nerve ends located on these sections therefore re- ceive six shocks during the period. The twenty seven sections from the seventy-seventh to the 102 UNIVERSITY OF MISSOURI STUDIES hundred and third move down from % to C, and up from C to H. Down from H to J, and up from J to The tone 5 L. Down from L to N, and up from N to T. Down from T to V, and up from V to X. Down from X to 9, and up from D to %. The nerve ends located on these sections therefore receive five shocks during the period. The five sections from the hundred and fourth to the hun- dred and eighth move down from % to C, and up from C to H. Down from H to J, and up from J to L. Down from L to N, and up from N to T. Down from T to V, and up from V to X. Down from X to 9, and up from 9 to 3. The nerve ends located on these sections therefore receive five shocks during the period. All the following sections to the two hundred and sixty- seventh move down and up five times during the period. Let us study in detail only the movements of the last few of this group. The sections from the two hundred and twenty-eighth to the two hundred and sixty-seventh move down from A to C, and up from C to I. Down from I to K, and up from K to M. Down from M to S, and up from S to U. Down from U to W, and up from W to Y. Down from Y to ©, and up from & to G=A. The nerve ends located on these sections there- fore receive five shocks during the period. The seven sections from the two hundred and sixty-eighth to the two hundred and seventy-fourth move down from Y to C, and up from C to I. Down from I The tone 3 to K, and up from K to M. Down from M to W, and up from Wi to Y. The nerve- ends located on these sections therefore receive three shocks during the period. The fourteen sections from the two hundred and seventy- fifth to the two hundred and eighty-eighth move down from Y to C, and up from C to M. Down The tone 2 from M to W, and up from W to Y. The sections from the two hundred and eighty- ninth to the three hundred and thirty-sixth move down from MECHANICS OF THE INNER EAR 103 A to C, and up from C to M. Down from M to W, and up from W to @=A. The sections from the three hundred and thirty-seventh to the three hundred and sixty-sixth move down from A to K, and up from K to M. Down from M to W, and up from W to G@=A. The sections from the three hundred and sixty-seventh to the three hun- dred and seventy-sixth move down from A to K, and up from K to U. Down from U to W, and up from Wi to ®@=A. All these sections therefore receive two shocks during the period. The sections from the three hundred and seventy-seventh to the three hundred and eighty-seventh move down from U to K, and up from K to U. The sections The tone 1 from the three hundred and eighty-eighth to the three hundred and ninety-eighth move down from A to K, and up from K to G@=A. All these sections therefore receive one shock during the period. The relative intensities of the several tones, if we accept the third, fourth, and sixth provisional assumptions for this case, are shown in the following table, The relative which contains the number of partition intensities sections conveying each tone in absolute numbers as well as in percentages. Tones 8 6 5 3 2 I Intensities} 64 I2 {191 7 {102 22 Percent- 16.1 3.0 | 48.0 | 1.8] 25.6] 5.5 ages Let us now apply our theory to the same ratio of the vibration rates, but with different amplitudes of the two sin- usoids. The curve in figure 32 represents The combination the function 5 and 8. The f(#) = 2sind% + sin8x. amplitude of This signifies that the stirrup movement 8 is decreased eight has an amplitude which is only one- half of the amplitude of the stirrup move- ment five. The table below contains all the abscissa and 104 UNIVERSITY OF MISSOURI STUDIES ordinate values of the maxima and minima and of the inflec- tion points of the curve. INTERVAL 5:8, AMPLITUDES 2:1 Ordinate | Abscissa | Ordinate idinae Inf. fo) fo) 298 Vv 281 Max.} + 281 142 579 Ww 281 Inf + 87 268 385 xX 194 Min — 143 436 I55 AY4 230 Inf — 118 512 180 Z 25 Max. ») I Inf. | — 82 636 216 B 36 Min ity Inf. + 110 846 408 D 192 Max.| + 248 962 546 E 138 Inf. — 34 III 264 o 282 Min.| — 298 1247 fo} A 264 Inf. | — 62 1379 236 B 236 Max.| -++ 200 1535 498 Cc 262 Inf. + 120 1638 418 D 80 Min E Inf. fe) 1800 298 F 120 Max G Inf. | — 120 1962 178 H 120 Min.}| — 200 2065 98 I 80 Inf. + 62 2221 360 J 262 Max.) -+ 298 2353 596 K 236 Inf. + 34 2489 332 L 264 Min.| — 248 2638 50 M 282 Inf. — 110 2754 188 N 138 Max O Inf. + 82 2964 380 1p 192 Min Q Inf + 118 3088 416 R 36 Max.| + 143 3164 441 Ss 25 Inf. — 87 3332 211 T 230 Min.| — 281 3458 17 U 194 Inf. fo) 3600 298 Vv 281 MECHANICS OF THE INNER EAR 105 These values have been computed in the same manner as in the case immediately preceding. The successive po- sitions of the partition corresponding, under the sixth pro- visional assumption, to the maxima, minima, and inflection points of the curve are shown in figure 33, ° je) ° ° ° ° je} {2} fo} Lal a ise) + 8 600 Fig. 33. The combination 5 and 8. Compare figure 32 106 UNIVERSITY OF MISSOURI STUDIES Let us examine the movements of the twenty-five initial sections. From % to B they move down, and from B to D up. From D to F down, that is, from an ex- The tone 8 treme upward position to a medium up- ward position; and from F to H_ they move up again, that is, from a medium upward position to an extreme upward position. From H to J they move down, and from J to L up, completing thus the third down and up move- ment. From L to N they move down and from N to P up, completing thus the fourth down and up movement. From P to R they move down, and from R to T up, completing thus the fifth down and up movement. From T to V down, and from V to X up, completing thus the sixth down and up movement. From X to Z down, and from Z to 8 up, com- pleting thus the seventh down and up movement. From 6 to ® down and from D to § up again. The nerve ends lo cated on these twenty-five sections therefore receive eight shocks during the period, and accordingly, convey the sen- sation of the tone 8. The thirty-six sections from the twenty-sixth to the sixty- first move down from % to B, and up from B to D. Down from D to F, and up from F to H. Down from H to J, and up from J to L. Down from L to N, and up from Ni to P. Down from P to R, and up from R to T. Down from T to V, and up from V to X. Down from X to 9, and up from D to %. The nerve ends located on these sections therefore receive seven shocks during the period. But, in accordance with previous considerations, it is highly impfobable that they could convey the sensation of the tone 7. When seven shocks are received in time intervals identical with those of the tone 8, and when the eighth shock, at the moment Z, chances to be omitted, it is rather to be expected that the tone 8 is heard, only with a little pause or, perhaps, merely a diminu- tion of intensity at the moment Z. The sensation conveyed MECHANICS OF THE INNER EAR 107 by these nerve ends, then, is probably the tone 8 slightly beating, that is, being characterized by a slight roughness. The nineteen sections from the sixty-second to the eight- ieth move down from % to B, and up from B to D. Down from D to F, and up from F to H. Down from H to J, and up from J to L. Down from L to N, and up from N to P. Down from P to R, and up from R to T. Down from T to V, and up from V to X. Down from X to 9, and up from ® to %. The nerve ends located on these sections therefore receive seven shocks during the period; but, here as above, it is highly improbable that they could convey, merely be- cause of the omission of the stimulus at Z, the sensation of the tone 7 instead of 8. Most probably the tone heard is 8 with a slight roughness. The fifty-eight sections from the eighty-first to the one hundred and thirty-eighth move down from § to B, and up from B to H. Down from H to J, and up The tone 6 from J to L. Down from L to N, and up from N to P. Down from P to R, and up fon R to T. Down from T to V, and up from V to X. Down from X to 9, and up from D to %. The nerve ends located on these sections therefore receive six shocks during the period. The fifty-six sections from the one hundred and thirty- ninth to the one hundred and ninety-fourth move down from @ to B, and up from B to H. Down from The tone 5 H to J, and up from J to L. Down from L to R, and up from R to T. Down from T to V, and up from V to X. Down from X to 9, and up from D to §. The nerve ends located on these sections there- fore receive five shocks during the period. All the following sections to the three hundred and ninety- first move down and up five times during the period. Let ‘us examine only the last twenty-five of this group. They move 108 UNIVERSITY OF MISSOURI STUDIES down from A to C and up from C to I. Down from I to K, and up from K to M. Down from M to S, and up from S to U. Down from U to W, and up from W to Y, Down from Y to G, and up from € to G6=A. The nine sections from the three hundred and ninety- second to the four hundredth move down from Y to C, and up from C to I. Down from I to K, and The tone 3 up from K to M. Down from M to W, and up from W to Y. The nerve ends lo- cated on these sections therefore receive three shocks during the period. The sections from the four hundred and first to the four hundred and twenty-fourth move down from Y to C, and up from C to M. Down from M to W, and The tone 2 up from W to Y. The sections from the four hundred and twenty-fifth to the four hundred and ninety-eighth move down from A to C, and up from C to M. Down from M to Wi, and up from W to G@=A. The sections from the four hundred and ninety-ninth to the five hundred and forty-sixth move down from A to K, and up from K to M. Down from M to W, and up from W to @=A. The sections from the five hundred and forty-seventh to the five hundred and sixty-second move down from A to K, and up from K to U. Down from U to W, and up from W to @=A. The nerve ends located on these sections of the partition therefore receive two shocks during the period. The sections from the five hundred and sixty-third to the five hundred and seventy-ninth move down from U to K, and up from K to U. The sections from the The tone 1 five hundred and eightieth to the five hun- dred and ninety-sixth move down from A to K, and up from K to G=A. The nerve ends located on these sections therefore receive one shock during the period. The relative intensities of the several tones, if we accept MECHANICS OF THE INNER EAR 109 the third, fourth, and sixth provisional assumptions, are shown in the following table, which contains the The relative number of partition sections conveying intensities each tone in absolute numbers as well as in percentages. Tones /|8, smooth} 8, rough 6 5 3 2 it Intensities} 25 55 58 253 9 162 34 Percent- 4.2 g.2 Caf || C@oH || wo |) Bes WW He¥/ ages Since in the case just studied the higher of the two primary tones, though weak, is yet audible, let us still further change the relative intensities of the objective tones in favor of the lower one. The curve in figure 34 represents the function f(#) = 3sindx + sin8x, This signifies that the stirrup move- Thevcombinas ment eight has an amplitude which is only tion 5 and 8. one-third of the amplitude of the stirrup Amplitude of 8 movement five. The table below contains still less all the abscissa and ordinate values of the maxima and minima and of the inflection points of the curve. 1@ te) Inf. Max. Inf. Min. Inf. Max. Inf. Min. Inf. Max. Inf. Min. Inf. Max. Inf. Min. Inf. Max. Inf. Min. Inf. Max. Inf. Min. Inf. Max. Inf. Min. Inf. Max. Inf. Min. Inf. UNIVERSITY OF MISSOURI STUDIES INTERVAL 5:8, AMPLITUDES 3:1 Ordinate oO + 376 + 114 — 219 + 140 + 336 7 SY +++ S Abscissa | Ordinate 820 949 1106 1250 1389 1558 1800 2042 2211 2350 2494 2651 2780 3117 3317 3451 3600 397 773 51I 178 397 116 474 794 438 61 257 616 283 21 397 SGHY*ANHVOFZRZHPAAWKMTODBAHASCAWDPRROeRSRENKK Zs Ordinate Difference 376 376 262 333 359 196 377 356 320 358 281 281 358 320 356 377 196 359 333 262 376 MECHANICS OF THE INNER EAR III The successive positions of the partition corresponding, under the sixth provisional assumption, to the maxima, minima, and inflection points of the curve are shown in figure 35. FB 88, BUN SNC seg » ive) Fig. 35. The combination 5 and 8. Compare figure 34 The five hundred and fifty-five initial sections of the par- tition move down and up five times during the period. Let us here closely examine only the one hun- The tone 5 dred and ninety-six initial sections and the one hundred and seventy-eight most distant sections of this group. The initial sections move I12 UNIVERSITY OF MISSOURI STUDIES down from % to B, and up from B to F. Down from F to J, and up from J' to L. Down from L to N, and up from N to T. Down from T to V, and up from V to X. Down from X to 9, and up from ® to %. The sections from the three hun- dred and seventy-eighth to the five hundred and fifty-fifth move down from A' to C, and up from C to I. Down from I to K, and up from K to M. Down from M to S, and up from S to U. Down from U to W, and up from W to Y. Down from Y to € and up from © to G@=A. The nerve ends of all these sections therefore receive five shocks during the period. The seven sections from the five hundred and fifty-sixth to the five hundred and sixty-second move down from Y to C, and up from C to I. Down from I to The tone 3 K, and up from K to M. Down from M to W, and up from W to Y. The nerve ends located on these sections therefore receive three shocks during the period. The sections of the partition from the five hundred and sixty-third to the five hundred and seventy-second move down and up twice during the period. Let us The tone 2 here examine only the sections from the five hundred and sixty-third to the five hundred and ninety-fifth. They move down from Y to C, and up from C to M. Down from M to W, and up from W to Y. The nerve ends located on these sections therefore receive two shocks during the period. The partition sections from the seven hundred and fifty- third to the seven hundred and seventy-third move down from U to K, and up from K to U. The sec- The tone 1 tions from the seven hundred and seventy- fourth to the seven hundred and ninety- fourth move down from A to K, and up from K to @=A. MECHANICS OF THE INNER EAR 113 All the nerve ends on these sections therefore receive one shock during the period. The relative intensities of the several The relative tones under the third, fourth, and sixth pro- intensities visional assumptions are shown in the fol- lowing table. Tones 5 3 2 I Intensities] 555 7 190 | 42 Percent- | 69.9 AONEZ3COn MSS ages Having studied the effect of changing the relative intensities of the objective tones in favor of the lower one, we shall now in- vestigate the effect of increasing the intensity of the higher objec- tive tone. The curve in figure 36 represents the function f (+) = sindx + 2sin8x. The stirrup movement eight has an am- The combination Plitude which is twice the amplitude of 5 and 8. The the stirrup movement five. The table be- amplitude of 8is low contains the abscissa and ordinate greaterthanof5 yalues of the maxima, minima, and inflec- tion points. 114 Eee eee UNIVERSITY OF MISSOURI STUDIES Ordinate | Abscissa INTERVAL 5:8, AMPLITUDES 1:2 ++ Orainate| |, 0sfinate 298 Vv 286 584 WwW 286 353 x 231 108 Y 245 249 Z 141 400 2 151 272 B 128 146 Cc 126 358 D> 212 560 & 202 278 AY 282 fo) A 278 258 B 258 527 Cc 269 358 D 169 178 E 180 298 F 120 418 G 120 238 H 180 69 I 169 338 J 269 596 K 258 318 L 278 36 M 282 238 N 202 450 O 212 324 P 126 196 Q 128 347 R 151 488 Ss 141 243 T 245 12 U 231 298 Vv 286 MECHANICS OF THE INNER EAR I 15 The successive positions of the partition corresponding, under the sixth provisional assumption, to the maxima, min- ima, and inflection points of the curve are shown in figure 37. The two hundred and forty initial sections move down and up 8 times during the period. Let us here examine only the nine most distant sections of this The tone 8 group, from the two hundred and thirty- second to the two hundred and fortieth. They move down from A to B, and up from B to E. Down from E to G, and up from G to I. Down from I to J, and up from J to L. Down from L to O, and up from O' to Q. Down from QO to S, and up from S to T. Down from T to V, and up from V to Y. Down from Y to 2%, and up from % to ©. Down from © to ©, and up from © to G=A. The nerve ends lo- cated on these sections therefore receive eight shocks during the period. The fourteen sections from the two hundred and forty- first to the two hundred and fifty-fourth do not move down from E to G. The nerve ends located on these sections do not, therefore, receive a shock between E and I, but receive the other seven shocks in the same manner as the two hundred and forty initial sections. For the same reasons as in the similar cases with which we have met before, it is not probable that these nerve ends convey the tone 7, but rather the tone 8 with a slight beat occurring once during the period, producing a slightly rough tone 8. The sections of the partition from the two hundred and fifty-fifth to the four hundred and fifty-second move down and up five times during the period. Let us The tone 5 examine those from the two hundred and fifty-fifth to the two hundred and fifty- eighth. They move down from A to B, and up from B to E. Down from E to J, and up from J to L. Down from L to O, and up from O to U. Down from U to V, and up from V. 116 100 Fig. 37. UNIVERSITY OF MISSOURI STUDIES 400 500 je} ° fe} jo} a ior) The combination 5 and 8. Compare figure 36 600 MECHANICS OF THE INNER EAR I 17 to Y. Down from Y to %, and up from 2% to G=A. The nerve ends located on these sections therefore receive five shocks during the period. The sections from the four hundred and fifty-third to the four hundred and fifty-eighth move down from Y to C, and up from C to I. Down from I to K, The tone 3 and up from K to M. Down from M to W, and up from W to Y. The nerve ends located on these sections therefore receive three shocks dur- ing the period. The sections of the partition from the four hundred and fifty-ninth to the five hundred and seventy-second move down and up twice during the period. Let us The tone 2 examine, for example, the four hundred and fifty-ninth and the four hundred and sixtieth. They move down from Y to C, and up from C to M. Down from M to W, and up from W to Y. The nerve ends located on these sections therefore receive two shocks during the period. The sections of the partition from the five hundred and seventy-third to the five hundred and eighty-fourth move down from U to K, and up from K to U, The The tone 1 sections from the five hundred and eighty- fifth to the five hundred and ninety-sixth move down from Ai to K, and up from K to A. The nerve ends located on these sections therefore receive one shock during the period. The relative intensities of the several The relative tones under the third, fourth, and sixth pro- intensities visional assumptions are shown in the fol- lowing table. Tones |8smooth| 8 rough 5 3 2 I Intensities} 240 14 198 6 114 | 24 Percent- ages. .. 40.3 Af || BeoW I 18 UNiVERSITY OF MISSOURI STUDIES The curve in figure 38 represents the function f(#) = sinds’ + 3sin8x. THe ota binetion The stirrup movement eight has an ampli- Band S)) the tude three times as great as that of five. amplitude of 8 The table below contains the:abscissa and is three times ordinate values of the maxima, minima, that of 5 and inflection points. The successive positions of the partition corresponding, under the sixth provisional assumption, to the maxima, min- ima, and inflection points of the curve are shown in figure 39. The four hundred and thirty-eight initial sections of the partition move down and up eight times during the period. Let us examine those from the three hun- The tone 8 dred and eighty-sixth to the four hundred and thirty-eighth. They move down from A to C and up from C to E. Down from E to G, and up from G tol. Down from I to K and up from K to M. Down from M to O, and up from O to Q. Down from Q to S, and up from S to U. Down from U to W, and up from W to Y. Down from Y to Y, and up from 2 to ©. Down from € to G, and up from © to G@=A. The nerve ends located on these sec- tions therefore receive eight shocks during the period. The sections from the four hundred and thirty-ninth to the four hundred and fifty-first move down and up only seven times, since they do not make a double movement between EK and I. In accordance with our former considerations, how- ever, in similar cases, it does not seem probable that the nerve ends located on these sections should convey any other tone than the tone 8 of a slight roughness. The sections of the partition from the four hundred and fifty-second to the six hundred and forty-seventh move down five times during the period. Let The tone 5 us examine those from the four hundred and fifty-second to the four hundred and eighty-ninth. They move down from A to C, and up from MECHANICS OF THE INNER EAR INTERVAL 5:8, AMPLITUDES 1:3 Inf. Max. Inf. Min. Inf. Max. Inf. Min. Inf. Max. Inf. Min. Inf. Max. Inf. Min. Inf. Max. Inf. Min. Inf. Max. Inf. Min. Int. Max. Inf. Min. Inf. Max. Inf. Min. Inf. Ordinate | Abscissa | Ordinate eae ° © 398 W 385 ‘+ 385 120 783 Ww 385 ar Be 233 454 x 329 Tm 353 111 Y 343 — 46 457 352 Z 241 + 202 566 600 yt 248 Ties 671 373 Da) 2247 an ene 774 149 ity 224 ar BF 890 456 Dd 307 + 360 IOOI 758 & 302 — 18 1121 380 % 378 = 3 eee QIAN 380 = | Ge 1356 356 B 356 + 326 1477 724, (o 368 ap Be 1584 456 D 268 Ta oe 1697 179 E 277 i 1800 398 ie 219 + 219 1903 617 G BO — 58 2016 340 H 207 G2.) SHE ip od 268 + 42 2244 440 J 368 + 398 2360 796 K 356 ap te 2479 416 0, 380 = g60 2599 38 M 378 aes 27/20 340 N 302 + 249 2826 647 O 307 7 8) 2929 423 P 224 EI 3034 196 Q 227 ar | he 3143 444 R 248 + 287 3247 685 Ss 241 TSS 3367 342 aly 343 Sa 385) 3480 13 U 329 o 3600 398 Vv 385 119 120 UNIVERSITY OF MISSOURI STUDIES Fig. 39. The combination 5 and 8. Compare figure 38 MECHANICS OF THE INNER EAR 121 C to E. Down from E to K, and up from to K to M. Down from M to O, and up from O to U. Down from U to W, and up from W to Y. Down from Y to 2%, and up from YF to @G=A. The nerve ends located on these sections therefore teceive five shocks during the period. The five sections from the six hundred and forty-eighth to the six hundred and fifty-second move down from Y to C, and up from C to I. Down from I to K, The tone 3 and up from K to M. Down from M to W, and up from W to Y. The nerve ends lo- cated on these sections therefore receive three shocks during the period. The sections of the partition from the six hundred and fifty-third to the seven hundred and seventieth move down and up twice during the period. Let us The tone 2 examine those from the six hundred and fifty-third to the six hundred and seventy- second. They move down from Y to C, and up from C to M. Down from M to W, and up from W to Y. The nerve ends located on these sections therefore receive two shocks during the period. The sections from the seven hundred and seventy-first to the seven hundred and eighty-third move down from U to K, and up from K to U. The sections The tone 1 from the seven hundred and eighty-fourth to the seven hundred and ninety-sixth move down from Ato K,and up from K to @©=A. The nerve ends located on these sections therefore receive one shock during the period. The relative intensities of the several The relative tones under the third, fourth, and sixth pro- intensities visional assumptions are shown in the fol- lowing table: 122 UNIVERSITY OF MISSOURI STUDIES Tones |8smooth| 8 rough 3 2 Intensities} 438 13 196 5 118 Percent- 55.0 1.6 | 24.6 .6 | 14.8 ages 3:3 It is interesting to compare the intensities of the several tones in the last five cases, all representing the combination 8 plus 5 of stirrup movement, but differing in the relative amplitudes of 8 and 5. The table con- tains the percentages of the five preceding ta- Comparison of the last five cases bles. The first two columns show the ra- tio of the amplitudes of the stirrup movements of 8 and 5 For example, in the first case this ratio is as 3:1 or seventy- five to twenty-five; in the fifth case as 1:3 or twenty-five to seventy-five. The columns to the right contain the relative intensities of the several tones calculated under the provisional assumptions. Amplitudes of stirrup Subjective (theoretic) intensity movement 8 5 8 6 5 3 2 I 75 25 | 56.6 | —— | 24.6 SONeT4mou|le sis 67 33 | 42.7 | —— | 33-2 |] 1.0] 19.1] 4.0 50 50 16.1 | 3.0 | 48.0 1.8 {25.6} 5.5 33. | 67 | 13-4] 9-7] 42-5] 1-5] 27-2] 5.7 A OS Wi las Ce) -9 | 23-9] 5.3 We notice that the tone 8 decreases in intensity from 56.6 to 42.7, to 16.1, to 13.4, and finally disappears entirely. This latter case, however, does not mean that now the tone 5 is MECHANICS OF THE INNER EAR 123 alone audible. We see from the table that even now, in ad- dition to 5, the very weak difference tone 3 and the fairly strong difference tones 2 and 1 are to be expected by the ob- server. As to the several difference tones, the most favorable con- dition for 6 seems to be, to have the component 5 of the com- pound stirrup movement somewhat more pronounced than 8. It appears, however, that in no case will this difference tone become very conspicuous. The most favorable condition for the difference tone 3 seems to be, to have the component 8 of stirrup movement about as strong as 5. The difference tones 2 and 1, on the other hand, appear with a maximum of in- tensity when the component 5 of stirrup movement is some- what greater than 8. But their intensities are but little less in case the amplitudes of the two stirrup movements 8 and 5 are equal. With respect to all the difference tones taken to- gether, it appears that these tones are very unfavorably influ- enced by a considerable difference in the amplitudes of the component stirrup movements, for no difference tone has a maximum intensity in either the first or the fifth case. And 1Although this booklet is devoted to theory and not to experimental methods of research, I cannot refrain from mentioning a way of testing the theoretical results just spoken of, because it is so easy for any one who possesses a skillful hand and a trained ear, and the observation to be made is so pretty. No instruments are required but two good tuning forks on resonance boxes, accurately tuned in the ratio of 5:8, and a bass bow. The fork 5 must be sounded first, as strongly as possible, and it is necessary to have a fork which continues to sound strongly for quite a while. Then the bow is applied with the most delicate touch to the fork 8. It is neces- sary for the success of the experiment that the intensity of the higher tone vibration be increased from zero very slowly and uniformly. If these con- ditions are fulfilled, one suddenly hears the low difference tones 1 and 2 being added distinctly to the tone 5, whereas of 8 no trace is yet audible. If now the fork 8 is left to itself, and the fork 5 is stopped by firmly touch- ing it with a finger, the tone 5 together with the difference tones disap- pears, but immediately one hears with surprising clearness the tone 8, which a moment ago was entirely inaudible. No similar observation can be made with a strongly sounding fork 8 and a weakly sounding fork 5. Ac- cording to our theoretic deduction the lower tone does not become inaudible when the amplitude of 8 is three times that of 5, but still has a respectable intensity. 124 UNIVERSITY OF MISSOURI STUDIES a prevailing intensity of 8 seems to be even less favorable to the difference tones than a prevailing intensity of 5. All these con- clusions have, of course, only a relative value, since taking into account the various provisional assumptions changes the result considerably. Let us study one more combination of sinusoidal stirrup movements. We have had only one interval greater than an octave, the combination 4 and 9. But The combination We did not, then, take into account the in- 3 and 8. The flection points of the curve. Let us do amplitude of 3 this with the combination 3 and 8, taking twice that of 8 the amplitude of 3 twice as great as that of 8. This ratio of the amplitudes is arbi- trarily chosen. But the selection of equal amplitudes would be no less arbitrary. The curve in figure 40. represents the function f(+) = 2sin3v + sin8x. The table below contains the abscissa and ordinate values of the maxima, minima, and inflection points of the curve. Fig. 40. The combination 3 and 8 The successive positions of the partition corresponding to the maxima, minima, and inflection points are shown in figure 41. The thirteen initial sections of the partition move down from % to B, and up from B to D. Down from D to F, and MECHANICS OF THE INNER EAR Ordinate INTERVAL 3:8, AMPLITUDES 2:1 Abscissa | Ordinate 297 525 461 392 428 462 237 24 126 242 224 207 410 594 449 BEAU ME ONHUOMRMSYGERNXKE Tan onENO Z| Ordinate Difference 228 228 64 69 36 34 225 213 102 116 18 17 203 184 145 165 13 13 165 145 184 203 17 18 116 102 213 225 34 36 69 64 228 125 126 UNIVERSITY OF MISSOURI STUDIES up from F to H. Down from H to J, and up from J to L. Down from L to N, and up from N to P. The tone 8 Down from P to R, and up from R to T. Down from T to V, and up from V to X. Down from X to Z, and up from Z to $8. Down from 8 to D, and up from D to %. The nerve ends located on these sections therefore receive eight shocks during the pe- riod. Let us examine the sections from the sixty-fifth to the sixty-ninth. They move down from § to B, and up from B to E. Down from E to F, and up from F to H. Down from H to K, and up from K to L. Down from L to N, and up from N to Q. Down from Q to S, and up from S to T. Down from T to V, and up from V to Y. Down fom Y to Z, and up from Z to 8. Down from % to ©, and up from © to %. The nerve ends located on these sections therefore receive eight shocks during the period. The seventieth section moves down from § to B, and up from B to E. Down from E to F, and up from F to H. Down from H to K, and up from K to M. Down from M to N, and up from N to Q. Down from Q to S, and up from S to T. Down from T to V, and up from V to Y. Down from Y to Z, and up from Z to 8. Down from % to ©, and up from € to §. The nerve ends located on this section therefore receive eight shocks during the period. The sections of the partition from the seventy-first to the one hundred and second move down from % to B, and up from B to E. Down from E to F, and up from The tone 6 F to H. Down from H to N, and up from N to T. Down from T to V, and up from V to Y. Down from Y to Z, and up from Z to 8. Down from % to ©, and up from & to %. The nerve ends located on these sections therefore receive six shocks during the period. The sections from the one hundred and third to the one MECHANICS OF THE INNER EAR 127 500 600 je} ° fo) fe} je) fe) a Se) + Io0o Fig. 41. The combination 3 and $8. Compare figure 40 128 UNIVERSITY OF MISSOURI STUDIES hundred and forty-fifth move down from % to B, and up from B to E. Down from E to F, and up from The tone 5 Eto H. Down from H to N, and up from N to T. Down from T to Z, and up from Z to 8. Down from $ to ©, and up from € to %. The nerve ends located on these sections therefore receive five shocks during the period. The sections from the one hundred and forty-sixth to the one hundred and eighty-fourth move down from % to B, and up from B to E. Down from E to F, and The tone 4 up from F to H. Down from H to N, and up from N to T. Down from T to Z, and up from Z to %. The nerve ends located on these sections therefore receive four shocks during the period. The sections from the one hundred and eighty-fifth to the four hundred and fifty-sixth move down and up three times dur- ing the period. Let us examine those from The tone 3 the one hundred and eighty-fifth to the two hundred and thirteenth. They move down from % to F, and up from F to H. Down from H to N, and up from N to T. Down from T to Z, and up from Z to %. The nerve ends located on these sections therefore receive three shocks during the period. The sections from the four hundred and fifty-seventh to the four hundred and sixty-eighth move down from A to F, and up from F to M. Down from M to %f, and The tone 2 up from % to G=A. The sections from the four hundred and sixty-ninth to the five hundred and first move down from A to G, and up from Gto M. Down from M to %, and up from 1 to G=A. The sections from the five hundred and second to the five hundred and forty-sixth move down from A to G, and up from G to U. Down from U to % and up from 9% to G=A. The nerve ends located on these sections therefore receive two shocks during the period. MECHANICS OF THE INNER EAR 1329 The sections of the partition from the five hundred and forty-seventh to the five hundred and seventieth move down from A to G, and up from G to ®@=A. The The tone 1 sections from the five hundred and seventy- first to the five hundred and ninety-fourth move down from A‘ to %, and up from 2% to G=A. The nerve ends located on these sections therefore receive one shock during the period. The relative intensities of the several The relative tones under the third, fourth, and sixth pro- intensities visional assumptions are shown in the fol- lowing table: Tones 8 6 | 5 4 3 2 I Intensities] 70 32 43 39— «272 go 48 Percent. THES |] Gozt |l) 4fo2 6.6 | 45.8 | 15.1 8.1 ages We notice that the tone 3 is theoretically by far the ‘strongest, as is to be expected. Of the difference tones, the tones 2, 1, and 5 appear to be somewhat more pronounced than 4 and 6. Under different assumptions concerning the physical properties of the partition these results would, of course, be somewhat different. Throughout our previous discussions we have never taken into account the possibility of the tone intensities being further modified by a more central nervous Weber’s law condition like the one usually referred to in audition as Weber’s law. All our various approxi- mations towards the intensities of the ner- vous processes take into consideration only conditions in the peripheral organ. Whether the intensities thus found are modified more centrally in accordance with Weber’s law or 130 UNIVERSITY OF MISSOURI STUDIES not, is a question which at present must be left entirely open, like so many others, because of lack of experimental data. Whenever we have spoken of “amplitudes” we have meant exclusively the amplitudes of stirrup movement. In order to make use of our theory in experi- Sounding bodies mental investigations we must remember and stirrup the fact that the stirrup movements result movement from movements of the tympanum, trans- mitted by a rather complicated system of levers, the auditory ossicles. It is quite probable that the vibratory movements of the stirrup—even when these move- ments are highly complex—are approximately like those re- ceived by the hammer, the ossicle attached to the tympanum. But no one knows as yet how close or remote this approxima- tion is. We certainly have no right to regard this approxima- tion as infinitely close, save by way of a provisional assump- tion. The movements of the tympanum result from rhythmical changes of the density of the external air. These density changes, in experimental investigations, are sometimes pro- duced by the vibrations of gaseous bodies, as in labial organ pipes; more frequently, however, by the vibrations of solid bodies, par- ticularly of tuning forks on resonance boxes. Now, we must not think that by graphically recording—which is a comparatively easy method—the vibrations of a tuning fork, we obtain a record of the exact form of the resulting air waves. It has been experimentally and mathematically proved that the form of the resulting air waves must be more or less different from the form of the vibratory movement of the fork or other solid body. The cause of this alteration of the form is to be found in the fact that the layer of air which adjoins the solid body and therefore directly receives the impulses from that body, is unsymmetric with respect to its elastic properties, because MECHANICS OF THE INNER EAR 131 it is in contact on one side with a practically unyielding body, on the opposite side with the easily yielding air. It is of the utmost importance, therefore, if we wish to develop the theory by experimental investigation, to keep free from the delusion that any of the above theoretic results, say, in the case of the combination 5 and 8 with equal ampli- tudes, applies to what we hear in case two tuning forks of the vibration ratio 5:8, standing at an arbitrary distance from our ears and from the reflecting walls of our laboratory, vi- brate with equal amplitudes. It is only by way of approxima- tion that we can derive any theoretic conclusion from such an experiment. The starting point of our theory is the form of movement of the stirrup, not of external sounding bodies. Under ordinary conditions, it is a great advantage that we possess two organs of hearing, some distance apart. In ex- perimental investigations, however, for the The duality of development of a theory of audition, this our auditory fact is often a serious obstacle. Since we organ cannot make experiments on audition while soaring like an eagle, any source of sound is likely to surround our body with standing waves, resulting from reflection. Let us regard the velocity of sound as three hundred and thirty meters, the distance between our ears as about fifteen centimeters. A tone of five hundred and fifty complete vibrations, that is, a tone representing the ordi- nary human voice quite well, has therefore a wave length of about sixty centimeters. The distance between a nodal point, where the rhythmic density changes of the air occur with full intensity, and a point of maximum vibratory movement, where there are practically no density changes affecting the tympa- num, is then about fifteen centimeters. That is, it might happen with standing waves—if the head was kept perfectly still_that the amplitude of one of the components of stirrup. movement would be almost zero in one ear, but very large in 132 UNIVERSITY OF MISSOURI STUDIES the other, and every movement of the head would greatly alter these conditions; while the resulting consciousness would be, of course, the sum total of the tones heard by each ear. It is unnecessary to point out in further detail how this fact of hearing with two ears complicates the comparison of experi- mental results with the theoretical deductions of the present study, which refer only to one stirrup and one inner ear, and to an unalterable form of the components of stirrup movement in a given case. The fact that we have two ears would be irrelevant only with exceedingly high tones, whose wave lengths in air would be so small as to be negligible quantities in comparison with the distance between our ears, as the wave lengths of light are negligible quantities in comparison with the distance be- tween our eyes and even with the sensory elements of each eye. Every one is familiar with the comparative clearness with which the ticking of a watch or the sound of a tuning fork is perceived if the vibrating body is firmly Hearing without pressed on the head or against the teeth. the ear drum Some believe that the physiological func- tion of the ear in such a case is not essen- tially different from hearing under ordinary conditions; that the sound waves, the rhythmic changes of molecular density, which pass through the head, naturally pass also through the cavities of the head, of which one, the middle ear, particularly concerns us here. As soon as rhythmic changes of density occur in the air of the middle ear, the tympanum adjusts itself to them by rhythmically moving back and forth. The stirrup cannot help following the tympanum, and so on. The only difference between this case and a case of ordinary hearing consists in the fact that the changes of density of the air affecting the tympanum originate on the inside of the tympanum in- MECHANICS OF THE INNER EAR - 133 stead of on the outside, and that they must, on the whole, be much weaker in the former case. There can be little doubt that the process just spoken of actually occurs. Some have insisted also on the possibility of hearing when the middle ear is destroyed and no movements of the stirrup occur. There is no reason why we should a priori deny the possibility of a shock being received by the nerve ends whenever a rhythmical change of molecular den- sity takes its path directly through them. Such a molecular wave might originate from a vibrating solid body being pressed against skull or teeth, or from sound waves in the air strik- ing the head and passing through it. We must not overlook the fact, however, that even when the tympanum is totally destroyed, if sounds are perceived, the perception need not be the result of the sound waves simply passing through the nerves. Even in such a case stirrup movements are not excluded. If we blow over the mouth of a bottle, we cause rhythmical changes of density within the bottle, and, as a natural consequence, the air in the neck of the bottle rushes back and forth. These move- ments may often be observed with the naked eye when a fiber adherent to the inside of the neck of a bottle is forced by friction to follow the movements of the air. Now, when rhythmic changes of density occur in a middle ear whose tympanum is destroyed, there must naturally occur a back and forth move- ment of the air in the air passage, just as in the neck of a bottle. These back and forth movements of the air may cause by friction corresponding movements of the hammer and anvil and thus of the stirrup. No doubt, stirrup move- ments which are caused in this way must be of small magni- tude. But no one who knows the surprisingly small amount of mechanical energy which is sufficient to call forth a response of the auditory organ will deny that they might result in an auditory sensation. 134 UNIVERSITY OF MISSOURI STUDIES If not only a part or the whole of the tympanum is de- stroyed, but the chain of ossicles is also lost, the mechanical processes in the inner ear could be brought about by pressure differences on the two windows. An air wave, coming in through the external passage and the open middle ear, would at any given moment affect the two windows with a slightly different phase, arriving at one window a little earlier than at the other. This difference of phase means, of course, a difference of air pressure on the windows, and a difference of air pressure on the windows, according to the laws of mechanics, results in a movement of the internal fluid from the point of higher to that of lower pressure. It is plain, however, that this difference of phase, owing to the small distance between the two windows, must be very slight; and hearing which results in this way must be rather weak. But its possibility cannot be doubted. Few cases, therefore, will be found where a sound is heard and we have to have recourse to the rather improbable assumption that the mere passing of molecular waves of density changes through the head and, thus, through the audi- tory nerve ends directly results in some weak response of the nerves. Nevertheless at least we may admit this assumption as possible. To admit it as possible would not cause any diffi- culty in comprehending the ordinary phenomena of audition, which might thus seem to become more complicated because such density waves must, of course, pass through the head whenever anybody hears anything. But such effects on the nerve ends, granted that they always exist, must ordinarily be overpowered by the incomparably stronger stimulations simultaneously received by the nerve ends by way of the stirrup movement. Having studied the function of the human ear, it is in- MECHANICS OF THE INNER EAR 135 teresting to compare this with the organ of hearing of the lower vertebrates. Figure 42 indicates the Comparative manner of evolution of the cochlea. An anatomy of the original pit (Fig. 42 a) as found in a frog is auditory organ gradually lengthened and assumes in the birds a banana-like shape (Fig. 42 b), showing a distinct tendency to coil. In mammals the process of lengthening and coiling has proceeded so far that the organ (Fig. 42 c), if it were transparent, would appear as a spiral. It is clear that the coiling can have little influence,on the mechanical function of the organ. The lengthening of the organ, however, is of the utmost functional importance. The original pit does not differ materially from the other cavities which we find within Fig. 42. Evolution of the auditory organ the labyrinth, communicating with the semicircular canals. In this pit movements of the fluid caused by movements of the stirrup—or rather columella plate, since the lower verte- brates have a much simpler connection of tympanum and oval window—produce, probably by mere friction, stimulation of the endings of the auditory nerve. The organ of the birds must function more nearly like the human organ, excepting the difference of function resulting from the fact that the endings of the auditory nerve are spread out over a small linear extent, whereas in the mammals they are distributed over a long distance. 136 UNIVERSITY OF MISSOURI STUDIES In birds one can hardly speak of some nerve ends being farther away from the windows than others. It is of some interest, in this connection, to note that ani- mals with a short tube, as the birds, do not possess in the par- tition of the tube the pillars of Corti. They can get along without these pillars. And naturally. The longer the tube, the greater is the maximum pressure which may act upon the partition near the windows, in case the bulging of the partition is forced to proceed far towards the end of the tube. The greater the possible pressure, the greater is, of course, the need of a skeleton-like support in order to protect the sensitive cells from collapsing. Thus the mammals need the pillars because of the greater length of the tube. What must be the difference of sound perception resulting from these anatomical differences in various species of ani- mals? We saw that the human ear can perceive several tones at the same time be- Comparative / ‘ ; psychology of cause the linear extension of the auditory the sense of organ permits the compound mechanical : gan p p hearing processes, transmitted from the stirrup to the fluid of the cochlea, to be analyzed into much simpler mechanical processes taking place in successive sections of the partition. It is plain, then, that in the auditory pit of a frog no analysis is possible. The result must be that the frog’s ear can perceive only one tone at any moment; and this tone is most probably, as a rule, the highest of the sev- eral tones heard simultaneously under the same circumstances by the human ear. The bird’s ear, as we have seen, is intermediate between the frog’s ear and the human ear. But it does not seem very probable that even birds can perceive very many tones simulta- neously. The fact that birds sing is no indication to the con- trary, since their song does not consist—like orchestral music —of simultaneous, but only of successive tones. Of more sig- nificance, in this respect, is the fact that some birds, for ex- MECHANICS OF THE INNER EAR 137 ample, parrots, are able to imitate human speech sounds. Speech sounds are characterized, according to the present state of phonetics, by particular groupings of tones in both simul- taneity and succession. It is not certain that the rough imi- tation of human speech sounds by parrots is more than an imitation of the successive groupings of tones. Granted even that the birds possess the ability to perceive more than one tone simultaneously, the anatomical facts would make it prob- able that this ability is very limited in comparison with the human ear which perceives the most varied combinations of tones in speech sounds and in harmonic music. Let us now briefly look back upon what we have done. We have regarded the organ of hearing as a long and narrow tube, filled with a practically incompress- hheineedios ible fluid and divided lengthwise by an im- experimental perfectly elastic partition which is the seat data of the auditory nerve ends. We have found that the problem of determining exactly, for each given form of stirrup movement, the mechanical pro- cesses taking place in the tube is from the mathematical side an almost hepelessly complex one, made still more difficult by the lack of data concerning the mere facts of hearing as well as the elastic and other physical properties of the parti- tion. In order to overcome the intrinsic and accidental diffi- culties standing in our way, we have introduced six simpli- fying provisional assumptions; not using all six in every case, but now some of them, now others, according as the purpose of the moment seems to warrant. We have thus obtained a superficial, but for a beginning satisfactory, insight into the wonderful machinery by which we analyze the complicated sound waves with a result which—for example, with respect to the hearing of difference tones—is most surprizing to one who knows nothing of the mechanics of the inner ear. 138 UNIVERSITY OF MISSOURI STUDIES The theory thus developed does not pretend to be the ultimate solution of the problems attacked. We do not pos- sess the data upon which to found a final theory. But we shall scarcely obtain these The necessity data without the guidance of a the- ae ory. Experimental research must be systematic, must start from a theory, how- ever imperfect this may be, in order to lead to scientific advancement. If the theory here offered succeeds in stimulating experimental research in a field somewhat neg- lected for many years, the author’s hope will be realized. APPENDIX A list of former publications by the same author concerning the me- chanics of the inner ear: Uber Kombinationsténe und einige hierzu in Beziehung stehende akustische Erscheinungen. Zeitschrift fiir Psychol- ogie und Physiologie der Sinnesorgane 11, 177-229. 1896. Zur Theorie der Differenzténe und der Gehdrsempfin- dungen tiberhaupt. Ibid. 16, 1-34. 1898. Uber die Intensitét der Einzeltdne zusammengesetzter Klange. Ibid. 17, 1-14. 1898. Uber die Funktion des Gehérorgans. Verhandlungen der Physikalischen Gesellschaft zu Berlin 17 (5), 49-55. 1898. Zur Theorie des Horens. Archiv fiir die Gesammte Physi- ologie 78, 346-362. 1899. Karl L. Schafer’s “Neue Erklarung der subjectiven Com- binationstone.” Ibid. 81, 49-60. 1900. E. ter Kuile’s Theorie des Horens. Ibid. 81, 61-75. 1900. Zur Theorie der Gerduschempfindungen. Zeitschrift fiir Psychologie und Physiologie der Sinnesorgane 31, 233-247. 1903. Uber Kombinations-und Asymmetrietone. Annalen der Physik (Vierte Folge) 12, 889-892. 1903. The significance of wave-form for our comprehension of audition. American journal of psychology 18, 170-176. 1907. 139 INDEX Analysis, 37. Anatomy of the inner ear, 14, 69, 81, 87. Beats, 55, 58, 66, 107, 115, 118. Birds, 5, 136. Brain, 23. Clay experiment, 8. Cochlea, 1. Comparative anatomy, 135. Comparative psychology, 136. Computation, 24, 28. Corti’s organ, 16, 22, 136. Difference tones, 37, 59, 68, 84, 123. Disappearance of higher tone, 84, 122. Duality of the organ, 131. Ear, 1, 14. Elasticity, 12, 18, 20, 87. External ear, 1. Fluid displacement, 76, 90, 95. Graphic methods, 28, 39. Inflection points, 85, 89, 92. Inner ear, 14. Intensity, 32, 34, 42, 68, 77, 79, 96, 122; 129. Labyrinth, 3. Leather seated chair, 12. Leverage of the ossicles, 5, Mean tone, 56, 58. Middle ear, 3. Ossicles, 5. Overtones, 31. Partition, 11. Pathology, 132ff. Phase, 35, 44, 47ff. Pillars of Corti, 16, 136. Pinna, 1. Pressure on partition, 88. Provisional assumptions, 25, 33, 69, 87, 95. Reissner’s membrane, 21. Resonators, 19. Psychological observation, 82, 137. Safety valve, 14, 22. Sensitiveness of the ear, 83. Snail, 1. Sounding bodies, 32, 130. Stirrup, 4. Subjective tones, 37, 59. Tension, 19. Tone combinations: 2and 3; 35, 44, 48, 49. 24 and 25; 50, 58. 4 and 9; 62, 77. land 2; 85, 93. 5 and 8; 96, 103, 109, 113, 118, 122. 3 and 8; 124. Tone intensity, 32, 34, 42, 68, 77, 79, 96, 122, 129. Tympanum, 4. Weber’s law, 129. Windows, 3, 6. UNIVERSITY OF MISSOURI STUDIES SCIENCE SERIES VOLUME I . Topography of the Thorax and Abdomen, by PETER Por- TER, M. A., M. 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The Spermatogenesis of ‘Anax Junius, by CaRouine Mc- | GILL. pPpe Vili, 15. 1904. 75 cents. Out of print. 11 FLORA OF BOULDER, COLORADO = pase Saat ax He Gay Hayy a hy VoutumeE II SCIENCE SERIES NUMBER 2 THE UNIVERSITY OF MISSOURI STUDIES EDITED BY W. G. BROWN Professor of Industrial Chemistry THE FLORA OF BOULDER, COLORADO, AND VICINITY BY FRANCIS POTTER DANIELS Professor of the Romance Languages, Wabash College Formerly Assistant in the University of Missouri PUBLISHED BY THE UNIVERSITY OF MISSOURI October, 1911 500 Copyright, 1911, by THE UNIVERSITY OF MISSOURI COLUMBIA MO.: E. W. STEPHENS PUBLISHING COMPANY, IQII a) PROFESSOR T. D. A. COCKERELL THIS STUDY IS RESPECTFULLY DEDICATED PREFACE During the summer of 1906 I was employed by the Depart- ment of Botany of the University of Missouri to collect plants in Colorado for the Herbarium of the University. I spent, therefore, a period of two months and a half in this work. I arrived at Boulder, Colorado, June eighteenth, and departed thence September third. All the collecting was done in Boul- der County, and the greater part of it within a radius of five miles from the city of Boulder. I collected altogether about 1,036 species of flowering plants and ferns. The vernal plants, of course, had blossomed before my arrival, but except for these the flora of Boulder is fairly well shown in the collection. In the list of plants here given there have been included all that are known to occur in Boulder County; but inasmuch as the boundary between Grand and Boulder Counties lies along the summits of the main range of mountains it is impos- sible often to tell in what county a given plant has been col- lected. Similarly Long’s Peak lies partly in Larimer County and partly in Boulder County. In all cases in which plants have been cited from a mountain lying partly in Boulder Coun- ty, these have been included in the list, unless a definite locali- ty in the other county is given. Plants admitted to the list because of the citations given in Rydberg’s Flora of Colorado al xii PREFACE are ascribed to Rydberg; it is of course understood that this ascription does not imply that these plants were collected by Rydberg in the localities named, but merely that by examina- tion of the plants or otherwise he is satisfied that they occur in those places. In the case of plants collected by myself I have added the collection number, so that these can be identi- fied at any time. I may add that besides the set of Boulder plants in the Herbarium of the University of Missouri, there is a duplicate set in the Herbarium of the Michigan Agricul- tural College; there is also a set in my own possession. The Herbarium of the Missouri Botanical Garden has an incom- plete set. As the numbers are the same for all plants of the same species, the identification of any of these plants can be made out from the number given in the list. In the introduction I have sought to present what knowl- edge I have of the distribution of plants in Boulder County. I have tried to present them in their natural plant-societies. I saw, however, too little of the montane, subalpine, and the alpine floras to be able to give a comprehensive account of these, and it must be remembered that I did not see the vernal facies of any portion of the vegetation. As to nomenclature I have followed, except where plainly deficient in the light of later investigation, that of Rydberg’s Flora of Colorado. While I feel that in the case of both genera and species there has been an over-multiplication—as for instance the splitting up of such a natural group as the pines into several genera, yet at the time of the preparation of this Flora the only convenient guide was Rydberg’s work. It is to Professor T. D. A. Cockerell of the University of Colorado to whom I am most indebted for assistance in this work. Remote both from the vegetation itself and from an PREFACE Xiil adequate library, I could not have carried on the work at all without his cheerful codperation. He has examined every page of the manuscript, and I owe much to his apt suggestions and kindly criticism. My thanks are also due to Professor Francis Ramaley for his kindness in examining the proof- sheets, and to Professor J. Henderson who has perused the article on the physiography. Both have given me notes of much value. ERRATA Page 15, line 13, for Chrysopogon, read Sorghastrum. Page 18, line 3 from bottom of page, for C. umbellata bre- virostris, read C. umbellata brachyrhina. Page 26, line 4, for Cogswellia Grayi read Cogswellia orientalis. Page 27, line 22, for F. confinis, read F. Kingii. Line 12 for Agropyron Vaseyi, read Agropyron spicatum inerme. Page 31, line 2 from bottom of page, for Trisetum subspicatum, read Trisetum spicatum. Page 33, line 14, same correction. Page 39, line 8 from bottom of page, for Pseudocymopterus tenuifolius, read Pseudocymopterus multifidus. Page 41, line 9, for Trisetum subspicatum, read Trisetum spicatum. Page 42, line 6 from bottom of page, for Polemonium scopu- linum, read Polemonium pulcherrimum. XIV INTRODUCTION I. PHYSIOGRAPHY Boulder, Colorado, lies nestling close to the Rocky Moun- tains just north of the 4oth parallel. There the foot- hills are strikingly beautiful and high, and only twenty miles away Arapahoe Peak, clasping to its bosom the best glacier of the southern Rockies, gleams whitely in full view, while twenty-four miles to the northwest towers jaggedly Long’s Peak, 14,271 ft. high, the highest point in Boulder County, and one of the highest peaks of the Rocky Mountains. Away to the eastward the plain stretches unbrokenly, save for an oc- casional butte, till lost to vision. There is then room for a great diversity of vegetation, ranging from the semi-desert plants of the arid plains to the arctic plants that grow at the wasting edge of the perpetual snow. The Continental Divide, which, due west of Boulder, touches its easternmost point in North America, is only from twenty to twenty-four miles away. It rises as a vast snow- covered wall of rock to an average height of from 11,000 to 12,000 feet; the highest points in the Divide in this region are Long’s Peak, 14,271 ft., Mt. Audubon, 13,173 ft., Mt. Baldy, 11,470 ft., Arapahoe Peak, 13,520 ft., and James’ Peak, 13,283 ft. Due west of Boulder Arapahoe Pass crosses the Divide at an altitude of 12,000 feet. It will be seen, therefore, that there is an almost impassable barrier between the vegetation of the Pacific slope and that of 149] I 2 UNIVERSITY OF MISSOURI STUDIES [150 the Atlantic. Since this barrier is almost everywhere above timberline, only a few Pacific species are found on the Atlantic side of the slope within the region about Boulder. Perhaps the most interesting exception is the occurrence of one of the orchids, Piperia Unalaschensis (Spreng.) Rydb., a few indi- viduals of which I found in the foot-hills near Boulder, and which is not known to occur elsewhere east of the mountains of Utah, it having its main range from Alaska to California. All the streams of Boulder County flow ultimately into the South Fork of the Platte river, and thence into the Missouri and the Mississippi. Boulder creek, the chief stream of the region, and one of the headwaters of the Platte, is fed from the snows ‘of the Divide, especially between Arapahoe and James’ Peaks. Just over the other side of the Divide are some of the headwaters of Grand river, which flows into the Colorado, and thence into the Gulf of California. All the matn streams in Boulder County have their sources in the wasting snows of the Main Range. These have cut gor- ges, in most cases over a thousand feet deep, into the elevated plateau between the main range and the foot-hills proper, and by means of these deep valleys have transformed this plateau into what are now really mountain masses, having an average altitude of about 8,000 feet, the eastern and western slopes of which are long longitudinal valleys, and the northern and southern ones the precipitous gorges cut by the streams. Be- tween Boulder and the Main Range there are about four of these mountain ridges, the first, or that of the foot-hills proper, rising to a height of from 7,000 to 8,600 feet, the others slightly lower, having an altitude of about 7,500 to 8,000 feet. Among these Sugarloaf Mountain stands out prominently as an isolated peak a thousand feet higher, it being a por- 151 | FLORA OF BOULDER, COLORADO 3 phyry dike, and thus weathering more slowly than the granitic peaks. This whole elevated plateau, cut by streams into what now appear as definite mountain ridges, we shall call the foot-hills, although the foot-hills proper are the ridges of sandstone at the edge of this granite plateau. The flora, however, is the same, save for a few ferns and other rock-plants which are confined to cer- tain kinds of rocks, some to the limestones, others to the sand- stones, still others to the granite. The main range of mountains as well as the high plateau at its base is composed of granite, granite-porphyry, and granite-gneiss, gray or reddish in color. Dikes are frequent, either of pegmatite or of felsitic porphyry. When the uplift or uplifts occurred, which made the Rocky Mountains, the sedimentary rocks resting upon the basement of granite, were tilted until they stood nearly on end. The jagged crags of the foot-hills proper are, then, the ends of these sedimentary layers. Thus it happens, too, that the oldest beds lie next the granite, while the younger underlie the plains. The oldest and lowest, that is, the one lying directly upon, or rather against the granite, is a layer of quartzite 550 feet thick, and of Algonkin age. This, however, is absent in front of Boulder and occurs in but two places in the county. The next, and of Pennsylvanian (Carboniferous) age, is the red Fountain sandstone, 500 to 1,500 feet thick. In the immediate vicinity of Boulder it lies directly upon the granite. On the east slope of Green Moun- tain it hangs in five triangular blocks of about 500 feet in thickness at an angle of about 52°. These, called the Flat-irons, are each about 1,000 feet high and about 1,500 feet wide; the third Flat-iron, however, rises to an altitude of nearly 8,000 feet, or about 2,000 feet above the mesa. At 4 UNIVERSITY OF MISSOURI STUDIES [152 Boulder Cafion the red sandstone walls are vertical. These perpendicular sandstone crags are the most striking feature of the scenery of the foot-hills. Lying next to the Fountain sandstone, and also of Pennsyl- vanian age, is the creamy Lyons sandstone, which is quarried in large amounts. It has a maximum thickness of almost 300 feet. Next in order, and still of Pennsylvanian age, is the Lykins formation, about 800 feet thick and consisting of sandstones, sandy shales, and a little limestone. It is easily weathered and is consequently thickly covered with waste. The Morrison formation occurs next, and consists of sand- stone, clays, and limestone, and is a little less than 600 feet thick. It is of Jurassic age. Then come various Cretaceous beds, the first of which, the“‘Dakota,” is a firm sandstone of about 350 feet in thickness. Its resistance to weathering causes the characteristic hogback of the foot-hills, consisting of one, two, or even three distinct combs, or crags. Then follow in succession the Benton shales, 500 feet thick; the Niobrara shales and limestones, 400 feet thick; the Pierre shales, 5,000 feet thick; the Fox Hills shales, 1,300 feet thick ; and the Laramie beds, which’are coal-bearing and about 115 feet thick. Lastly are the Quaternary deposits of allu- vium and terrace gravels. The various shales have weathered and eroded rapidly and underlie the plain, while the more resistant beds next the granite persist as crags, while the high mesas at the base of the foot-hills are shale outliers left by stream-erosion and are really stream terraces. The soil of the region, outside of the alluvium and ter- race gravels, is granitic in the mountains, while in the foot- hills it is apt to be brick-red from the detritus of the red 153] FLORA OF BOULDER, COLORADO 5 sandstones. The soft Lykins formation yields a very red soil. The Jurassic and Cretaceous rocks have layers of sand and clay. II, CLIMATE AND RAINFALL* The climate of Boulder, however enjoyable it may be to human beings, can hardly be said to be highly favorable to plant-life. At least this is true of the foot-hills, the mesas, and the plains. The Main Range, however, is well watered, but here the high elevation and the low temperature repress plant-life. The montane and subalpine slopes have a dense vege- tation, and yet even here the shallow soil and the rapid run-off of the water cause portions of them to have the aspect of deserts. A subalpine meadow has an opulent luxuriance; an adjoining slope may be gray with sage brush. In part the ap- parent thinness of vegetation in the mountains may be due to the superabundance of naked rock. In many portions of the Rockies the greater part of the surface has no soil whatever, and only a cranny-and-crevice vegetation is possible. The Rocky Mountains are new; their rocks are sharp and jagged; even lichens are rare on their surfaces. About Eldora and Arapahoe Peak, however, the rocks are beautifully rounded by glacial action. In the summer of 1906 there were rains almost daily, many of them soaking rains, but their distribution was uneven and capricious. In general the rainfall decreases as the distance from the snowy range increases. The alpine and subalpine *For the climatology of the region, consult the article by Professor Ramaley on the Climatology of the Mesas near Boulder, Univ. of Colo, Studies, 6, 19-35, also, the paper by Ramaley and Robbins on Redrock lake near Ward, Univ. of Colo. Studies, 6, 138-147. 6 UNIVERSITY OF MISSOURI STUDIES [154 regions receive most; the foot-hills less; the mesas receive some from every shower; the plains for five or six miles get a portion of the larger showers; but beyond that for several hundred miles good rains are very few. The summer of 1906 was exceptional,* for even the plains about Boulder seemed to receive more water than do many parts of the eastern United States in midsummer. When I left Boulder the third of September, the native vegetation for five or six miles out on the plain was as green as a prevailingly gray vegetation well can be; there was no sign of drouth, while when I reached Missouri and Iowa, the pastures were parched. In fact what I shall remember most about Colorado is its exuberance of water. It courses down all the mountain cafions, roaring and bubbling and dashing into foam. Springs are frequent and of a pureness and coolness that make them perfect. On the plains everywhere that one goes, a ditch full to the brim runs beside one. From the top of Green Mountain a hundred lakes may be seen gleaming on the plain. It is plainly a land of abundant rain and water. And yet why this feverish haste to irrigate the fields, why these ditches, these sluices, these storage-reservoirs? Why is land with a water-right worth several hundred dollars an acre, and land without one but five dollars? And why, to ask a still deeper question, why does nearly every kind of native plant have some means of conserving water, or some contriv- ance for preventing too rapid transpiration? Why do desert plants meet one at every hand: cacti, yuccae, sages, and xerophytic grasses? No, this region cannot be a land of abundant rain and water, in spite of the fact that I have never *In 1906 the greatest rainfall was recorded (26.17 inches), while 1901 was the driest year (13.67 inches). 155] FLORA OF BOULDER, COLORADO 7 seen so much anywhere else, nor anywhere else have had such drenchings to the skin. It is a semi-arid land, parched and thirsty. And the farmer, whom I saw flooding his land the morning after an all night’s pouring rain, knew from long experience that there could not be too much water. The rapid drainage, the light dry air, the fierce light of the high elevation, the hot sun, the soil unfitted for the retention of water, all these things parch and wither our cultural plants, for while the native vegetation has organs for storing water and for diminishing transpiration, the cultivated plants have none of these. Nevertheless for the native vegetation in 1906 there was ample water-supply; it grew with an almost incredible luxuriance, so much so that I found the measure- ments given in the manuals were often valueless for my pur- pose, as many of my plants were taller and larger than the books say that they grow. I was told that after the first of July there would be no botanizing as everything on the plains and foot-hills would dry up; but I remained till September first and the plants did not dry up, and I was able to collect over a thousand species in about two months and a half. The following table, which I use by the kind permission of Professor Ramaley, will furnish the data requisite to an under- standing of the temperature and rainfall of the region. The data holds true only for the city of Boulder. 8 UNIVERSITY OF MISSOURI STUDIES [156 TABLE COMPILED BY DR. FRANCIS RAMALEY Summary of data on temperature and rainfall at Boulder, Colorado, for eleven years, ending August, 1908. & & | Warmest Coldest =| Greatest R rs E,| mean on | mean on ‘S| rainfall on eee mevatel MonvH < 3 record. record. |E"g| record. Os! LO E E [ear Degs | Year |Degs 2 : Year/Inc’s Year Inc’s January arene iar 34... 1|1906/39.0,1905|29.3/0.4 |18gg/0.87 1903 |0.08 February. ....... 32.9|1907/42 .8|1899|18 0/0. 66/1903]1 . 52 1908 0.09 March..... .-++ |39.4|1907|48.1]1906|30.2/1.6 |1899]2.79] 1908 |0.23 EN MK Goard 660000 47 -7|1908)52. 5;1900/45.6/3.58|1900/9.18] 1908 1.71 May........-- -.|56.4/1898]60. 5}1907)51 -0|3 -02/1904|5 . 35 1899 0.55 June........ ... |64.6/1902|66.8/1907|/62.1]1.53/1897|3.71/ 1908 0.29 WMbosAdosscicocnes 70.1}1901|75.3|1906|67. 2/1. '72/1906/3.81 Ig0r_ |0.46 August. ........ |71.0]1898]73.2/1906/68.0|1.3 |1897!3.3 |1900&1905]/0. 22 September....... 64.0/1897|66.8}1900)61 . 5)1. 55|1902|2.7 I90I 0.10 October -is 53 -0|1900|57.2]1905|48. 5|1.47|1903/3.43| I900 0.13 November....... .|43.0]1904]48. 3]1898/38. 1/0. 59|1906|1 .87/1899&1901/0.00 December........ 37.0|1906|41 .0]1898|29.0|0. 68] 1902/0. 54/1905 &1g06|0.00 Annual........ 51.0 18.0 Highest recorded temperature is 97 degrees, July 15, 1902. Lowest recorded temperature is —20 degrees, January 8, 1902, and again February 20, 1905. Greatest rainfall recorded, 26.17 inches, 1906. Smallest rainfall recorded, 13.67 inches, Igor. III ZONES OF VEGETATION* There are six great zones of vegetation about Boulder, which, proceeding from east to west, are: A. The Zone of *These zones of vegetation are practically those of Robbins (Cli- matology and Vegetation in Colorado, Bot. Gaz., 49, 256-280), who rec- ognized (1) plains, (2) eastern lower foothills and mesas, (3) eastern upper foothills, 6,000 to 8,000 feet, (4) montane zone, (5) subalpine zone, (6) alpine zone. Professor Ramaley, however, would unite the mesas and foothills into one zone (Univ. of Colo. Studies, 5, 50-51). 157] FLORA OF BOULDER, COLORADO 9 the Plains, CAMPESTRES; B. The Zone of the Mesas, MENSALES; C. The Zone of the Foot-hills and Mountain Plateau, SUBMONTANABE; fourth, The Zone of the Lower Mountain Slopes, MONTANAE; fifth, The Zone of the Sub- alpine Mountain Slopes, SUBALPESTRES; sixth, The Zone of the Alpine Summits, ALPESTRES. Of these the Plains Flora, the Foot-hill Flora, the Montane Flora, the Sub- alpine Flora, and the Alpine Flora are primary, while that of the Mesas is a transition from the Flora of the Plains to the Flora of the Foot-hills. The Alpine corresponds to the Arctic Circumpolar vegetation, the Subalpine to the Hudsonian, the Montane to the Canadian, the Foot-hill and the Mesa to the Upper Transition, and that of the Plains to the Lower Transi- tion with some Upper Sonoran forms. A. CAMPESTRES The plains are not so arid about Boulder as they are far- ther east. In fact after riding for hundreds of miles through a desert of dried up grass, it is with a feeling of inutterable joy that one sees this narrow ribbon of green from six to twelve miles wide at the foot of the mountains. This green- ness and freshness is due mainly to two causes: First, this strip receives more rain than does the rest of the Great Plains. The clouds do not quite rain out before reaching the plains. These rains are, however, capricious. The clouds are narrow. The southern part of Boulder may receive a thorough drench- ing, the northern part may not have a drop. One Sunday there was a cloud-burst in Sunshine Cafion, farms and bridges were washed away ; from three to five feet of water came dash- ing through the main street of Boulder, while it scarcely sprinkled where I was a half mile to the south. The second cause is the abundant irrigation. 10 UNIVERSITY OF MISSOURI STUDIES [158 The Plains Flora falls into five main societies: The Aquatic (Aquatiles); The Palustrous (Palustres); The Ri- parian (Ripariae); The Prairie Meadow, the plains flora proper, (Campanales); and the Alkali Flat (Alkalinae). a. Aquatiles, The Aquatic Flora is found in lakes and streams. It consists of submerged or floating aquatics—pond- weeds, duckweeds, water-milfoils, hornworts, water starworts, besides various algae. It is seen best in Owen’s lake and Boulder lake, which while about twenty feet deep, are very brackish. The slower streams also have aquatic plants, as do likewise the aqueous nuclei of swamps and swales. The fol- lowing is a list of typical species: Potamogeton lonchites L. minor P. heterophyllus Ceratophyllum demersum P. foliosus Callitriche palustris P. pectinatus C. bifida P. Spirillus Myriophyllum spicatum Zanichellia palustris Limosella aquatica Lemna gibba All the above species occur in the eastern United States. b. Palustres. The Palustrous, or Swamp Flora is found in bogs, in swales, along ditches, and about the miry margins of ponds and lakes and streams. It consists of rushes, bul- rushes, sedges, swamp grasses, sweet flags, cat-tails, stick- tights, swamp asters, water peppers, and various other plants. I have included here the whole subaquatic flora, since the for- mation is so slight that it is best treated as a whole without separation into amphibious, limose, paludose, and uliginose societies. The following are characteristic species: Equisetum arvense Typha latifolia E. laevigatum Alisma Plantago 159] FLORA OF BOULDER, COLORADO II Sagittaria arifolia Homalocenchrus oryzoides Phalaris arundinacea Muhlenbergia racemosa Alopecurus aristulatus Spartina cynosurioides Poa triflora Panicularia nervata P. Americana P. borealis Cyperus inflexus Scirpus Americanus S. lacustris S. atrovirens pallidus Eleocharis palustris E. glaucescens E. acicularis E. acuminata Carex vulpinoidea C. stipata C. stricta C. lanuginosa Acorus Calamus Heteranthera limosa Juncus Balticus montanus J. longistylis J. nodosus J. Torreyi J. marginatus Iris Missouriensis Rumex occidentalis R. salicifolius Persicaria lapathifolia P. emersa. P. punctata Crunocallis Chamissoi Ranunculus sceleratus eremogenes R. Macounii Halerpestes Cymbalaria Nasturtium Nasturtium-aquaticum Radicula calycina R. hispida Hypericum majus Lythrum alatum Epilobium adenocaulon Cicuta occidentalis Berula erecta Verbena hastata Phyla cuneifolia Teucrium occidentale Scutellaria galericulata Prunella vulgaris Stachys scopulorum Lycopus lucidus L. Americanus Mentha spicata M. Penardi Mimulus Geyeri M. floribundus Gratiola Virginiana 12 UNIVERSITY OF Lobelia syphilitica Ludoviciana Iva xanthifolia I. axillaris Ambrosia trifida Xanthium commune Aster caerulescens It will be noted that all MISSOURI STUDIES [ 160 A. Osterhoutii Bidens vulgata B. glaucescens Helenium montanum Lactuca pulchella L. spicata but a very few of the above species are common palustrous species of the eastern United States. c. Ripariae. The Riparian Flora occurs along the banks of streams. It consists of trees, shrubs, and herbs. There are no trees nor shrubs proper on the Great Plains, except those that grow along the streams. tonwoods, box-elders, and willows. Here occur various cot- The herbs are partly marsh herbs and partly plants from the plains, especially grasses. Equisetum laevigatum Eatonia robusta Agropyron riparium Elymus Canadensis E. robustus Populus Sargentii P. acuminata P. angustifolia Salix amygdalioides S. exigua S. luteosericea The following are typical riparian species: Betula fontinalis (only near the foot-hills) Urtica gracilis Cardamine vallicola Rulac Negundo R. Texanum Vitis vulpina Pesedera vitacea Solidago Pitcheri S. Canadensis d. Campanales. The Prairie Flora is that which is proper to the greater part of the plains region. In aspect it is a vast meadow, above which now and then a yucca rises with 161] FLORA OF BOULDER, COLORADO 13 its bayonet-like leaves and its large cluster of flowers. But this aspect changes according to the season of the year, nor is it uniform at any season. As various plants come into bloom, so is it tinged red or purple, white or yellow; here it is an upland meadow of broom-grasses with purplish leaves; there it is dark green with meadow-grasses ; yonder it is white and hoar with sages. In early summer it is red, or purple, or blue with loco-weeds, beard-tongues, and thistles, yellow with golden asters, orange with cone-flowers and gaillardias, or white with Mexican poppies. In midsummer the psoraleas are numerous; here and there are large clumps of lupines; the tall porcupine grasses abound, and sunflowers rear their heads of gold. In late summer it is yellow with gumweeds of all kinds, with golden-rods and rabbit-brushes, or purple with blazing-stars and turkey-foot grasses. In autumn the gray sages put forth their inconspicuous flowers, the late composites ripen their achenes and whiten the landscape with their pappus. But the chief plants of this formation are those not seen— the little buffalo and mesquite grasses only a few inches high, but forming the turf of these vast plains. There are no shrubs proper in this flora. At most there are a few undershrubs and suffrutescent plants, such as roses, yuccas, and the like. It should be added that the vegetation of the moister por- tions of the plains differs, especially in aspect and also some- what in species, from that of the drier portions; but while it is possible to distinguish these two elements of the flora in the extreme cases of moistness and dryness, yet in the greater part of the area the two vegetations mingle inextricably. I shall, however, arrange the plants typical of the Great Plains into two classes, Humidae and Aridae, although the two classes occur quite commonly together: 14 is UNIVERSITY OF MISSOURI STUDIES Humidae. Andropogon furcatus Panicum virgatum Agrostis alba A. asperifolia Bouteloua olgostachya Bulbilis dactyloides Koeleria cristata Poa pratensis P. triflora P. interior P. pseudopratensis Festuca elatior Bromus marginatus latior B. Pumpellianus Agropyron pseudorepens A. occidentale Hordeum jubatum Elymus Macounii Carex marcida C. scoparia C. athrostachya C. pratensis C. festucacea Juncus interior J. Arizonicus J. confusus J. Dudleyi Sisyrinchium angustifolium Argemone intermedia A. hispida Sophia intermedia Potentilla Hippiana Drymocallis arguta Rosa pratincola Lupinus decumbens L. decumbens argentatus Astragalus goniatus Homalobus Salidae Aragallus Lambertii A. patens Psoralea tenuiflora P. argophylla Petalostemon oligophyllus P. purpureus P. pubescens Poinsettia dentata Malvastrum dissectum Oenothera strigosa Anogra rhizomata A. coronopifolia Gaura parviflora G. coccinea G. glabra Asclepias speciosa Lithospermum canescens Onosmodium occidentale ' Verbena bracteosa V. ambrosifolia Salvia lanceolata Physalis lanceolata [162 163] ii, FLORA OF BOULDER, COLORADO P. Virginiana Androcera rostrata Pentstemon unilateralis Gerardia Besseyana Grindelia serrulata G. perennis Oligoneuron canescens Aster commutatus Erigeron divergens Aridae. Schizachyrium scoparium Andropogon chrysocomus Chrysopogon nutans Aristida fasciculata A. longiseta Stipa comata S. viridula S. Nelsonii Muhlenbergia cuspidata Sporobolus airoides S. cryptandrus S. heterolepis S. asperifolius Agrostis hiemalis Merathrepta spicata Bouteloua hirsuta B. oligostachya Munroa squarrosa Eragrostis pectinacea Poa crocata P. juncifolia E. flagellaris Ratibida columnaris Helianthus lenticularis H. grosseserratus Gaillardia aristata Artemisia gnaphalodes Cirsium megacephalum C. ochrocentrum Agoseris glauca P. confusa Festuca octoflora Agropyron molle Hordeum pusillum Sitanion longifolium S. brevifolium Elymus brachystachys Carex Douglasii C. siccata C. straminea Yucca glauca Eriogonum effusum Paronychia Jamesii Allionia linearis Delphinium Penardii Stanleya glauca Xylophacos Shortianus Amorpha nana Psoralea tenuiflora Linum Lewisii 15 16 UNIVERSITY OF MISSOURI STUDIES Chamaesyce Fendleri C. serpyllifolia Tithymalus Arkansanus Acerates viridiflora A. angustifolia Asclepias pumila Evolvulus Nuttallianus Lappula occidentalis L. cupulata Cryptanthe crassisepala Lithospermum breviflorum Monarda pectinata Hedeoma hispida Physalis rotundata Quincula lobata Pentstemon secundiflorus P. gracilis P. humilis Orthocarpus luteus Plantago Purshii Ambrosia psilostachya Gaertneria tomentosa Kuhnia Hitchcockii K. glutinosa Laciniaria punctata e. Alkalinae. Gutierrezia longifolia G. scoparia Chrysopsis villosa C. hispida [164 Chrysothamnus pulcherrimus Sideranthus annuus ' S. spinulosus Solidago glaberrima S. nana Townsendia exscapa Aster exiguus A. crassulus A. polycephalus Erigeron ramosus Wyomingia cana Helianthus petiolaris H. pumilus Thelesperma gracile Boebera papposa Artemisia dracunculoides A. Brittonnii Senecio Riddellii S. multicapitatus S. spartioides Cirsium undulatum The best examples of the Flora of the Alkali Flats occur in the vicinity of Owen’s lake and Boulder lake, where large tracts are white as snow with alkali. The plants are mainly succulent chenopods, but a few other plants also occur. The following species are characteristic: Distichlis stricta Puccinellia airoides Polygonum buxiforme Chenopodium rubrum 165] FLORA OF BOULDER, COLORADO 17 Monolepis Nuttalliana Iva axillaris Atriplex carnosa Chrysothamnus graveolens A. argentea C. pulcherrimus Dondia depressa Solidago gilvocanescens Sophora sericea B. MENSALES* The Flora of the Mesas is a transitional flora; the mesas have most of the plants of the plains and in addition many of the plants of the foot-hills. There are, however, a considerable number of species, which are peculiar to the mesas. These mesas are flat tablelands rising abruptly a hundred feet or so above the plains in successive terraces. The altitude of the plains in Boulder County is from 5,000 to 5,500 feet. The lowest mesa, at an altitude of about 5,600 feet, has the flora of the plains, but at the next mesa, at an altitude of 5,700 feet, the flora begins to change, and from then on to the foot of the crags, 6,000 feet, the plains plants gradually tend to disappear and the foot-hill flora to come in. The highest mesas are so filled with waste from landslips from the crags, that they may be said to be an integral part of the foot-hills. And so, too, the streams have made deep cafions through the mesas, the flora of which is not so very unlike that of the cafions of the foot-hills. West of Marshall there is a high bog on the mesa, but as its plants differ in no wise from the bog plants of the plains, it will be dismissed with this notice. Six plant-societies are to be found upon the mesas: a. The meadow (Pratenses), which differs little from the plains meadow, although certain mountain species, such as the Mari- *For a detailed account of the vegetation of the mesas, see the pa- pers by Dodds, Ramaley, and Robbins, Univ. of Colo. Studies, 6, 11-49. 18 UNIVERSITY OF MISSOURI STUDIES | 166 posa lily, the painted cups, and the wool-joints are present. b. The cactus mesa (Spinosae). c. The Yucca mesa (Ensi- formes). d. The wooded mesa (Sylvestres). e. The brush mesa (Arbustales). f. The mesa cafion (Vallicolae). a. Pratenses. The flora of the mesa meadow is com- posed of an admixture of plants both from the plains and the foot-hills. Typical plants are: Sorghastrum nutans Stipa comata S. viridula Bouteloua hirsuta B. oligostachya Atheropogon curtipendulus Koeleria cristata Poa triflora P. interior P. pseudopratensis P. juncifolia P. confusa Festuca octoflora Agropyron tenerum A. pseudorepens Elymus brachystachys E. villiflorus Carex marcida pratensis straminea . straminiformis @E@=@- Gro) . umbellata brevirostris Tradescantia Universitatis Yucca glauca Calochortus Gunnisonii Comandra pallida Eriogonum alatum E. flavum E. umbellatum Polygonum Douglasii Silene antirrhina Lychnis Drummondii Delphinium Penardii D. camporum D. Nelsonii Anemone cylindrica Pulsatilla hirsutissima Argemone intermedia Potentilla effusa Drymoceallis fissa Lupinus Plattensis L. decumbens Geoprumnon succulentum Astragalus nitidus A. goniatus . Pennsylvanica vespertina Tium Drummondii Aragallus Lambertii A. sericeus Psoralea tenuiflora 167] FLORA OF BOULDER, COLORADO P. argophylla Geranium Fremontii Linum Lewisii Tithymalus philorus Nuttallia multiflora N. stricta Epilobium paniculatum Gayophytum intermedium Meriolix serrulata Gaura parviflora Gilia candida G. pinnatifida G. sinuata Collomia linearis Phacelia heterophylla Oreocarya virgata Mertensia linearis M. lanceolata Pentstemon unilateralis P. secundiflorus b. Spinosae. 19 P. gracilis P. humilis Castilleja linariaefolia Campanula petiolata Gutierrezia longifolia G. scoparia Chrysopsis resinolens Solidago pallida Townsendia grandiflora Rudbeckia flava Ratibida columnaris Helianthus subrhomboideus Gaillardia aristata Artemisia dracunculoides A. Forwoodii A. frigida A. Brittonii Senecio Plattensis S. Nelsonii S. Fendleri The vegetation of the cactus mesa con- sists of a few species of cacti, of the prickly Ceanothus Fend- leri, and a few other xerophytic plants and undershrubs. The principal cacti are: Echinocereus viridiflorus Opuntia mesacantha O. rhodantha c. Ensiformes. O. polyacantha O. fragilis O. Greenei The best example of the Yucca mesa occurs near the entrance of Bear Cafion. There the ground is practically denuded, and only sparse clumps of Yuccas and 20 UNIVERSITY OF MISSOURI STUDIES [168 bunch-grasses occupy the ground. The two species of im- portance are Yucca glauca and Eriocoma cuspidata. d. Sylvestres. A good example of the wooded mesa lies immediately back of the Chautauqua grounds. There the bull pine has descended from the foot-hills and taken posses- sion of the mesa. Besides the bull pine, Pinus scopulorum, the low juniper, Juniperus Sibirica, is of rare occurrence. Of herbs the most noteworthy is Arnica pedunculata, which is frequent under the pines. I found also only there Centun- culus minimus, perhaps the only known station of this plant in Colorado, since it is not included in Rydberg’s Flora of Colo- rado. It is growing with Linaria Canadensis, which is like- wise an eastern plant. e. Arbustales. The brush mesa assumes various forms. Ordinarily some cne species is in control. Occasionally it con- sists of various haws, as at the entrance of Gregory Cafion, or of a thicket of juneberries, wax-currants, and skunk-bushes. South of Bluebell Cafion is a mesa covered with the peculiar mountain mahogany. Wild cherries and plums are frequent, and the hackberry occasional in these shrubby thickets. The principal species are: Celtis reticulata C. erythropoda Ribes pumilum Prunus Americana R. longifolium P. melanocarpa Oreobatus deliciosus Toxicodendron Rydbergii Batidaea laetissima Schmaltzia trilobata Cercocarpus parvifolium Ceanothus Fendleri Rosa Sayi C. mollissimus Amelanchier oreophila C. subsericeus Crataegus occidentalis Symphoricarpos occidentalis C. Coloradensis 169] FLORA OF BOULDER, COLORADO aI Of herbs the vetches and vetchlings are the most im- portant: Vicia sparsifolia V. producta V. dissitifolia Lathyrus leucanthus V. oregana f. Vallicolae. The mesa cafion has a bewildering di- versity of floral elements, now consisting of thickets of haws with extremely vicious thorns, wild briers, the long-beaked hazel, and dwarf maples, now with a fontinal vegetation strikingly like our own Carolinian. One little gulch at the base of Flagstaff Hill has a vegetation composed quite wholly of eastern plants. Here occur Phragmites Phragmites, Sani- cula Marilandica, Steironema ciliatum, Veronica Americana, Eupatorium maculatum, and a form of Apios Apios, the last of which was not known to occur west of eastern Kansas previous to this collection. Since the streams have cut deeply into the surface, the cafion of the mesa resembles greatly the cafion of the foot-hills. There are riparian, rupestrine, clivose, and fontinal elements compressed within the space of a few feet. Mountain forms follow these streams often for some distance into the plain. And yet the facies of the flora is dis- tinctly eastern. Here are haws, hazels, maples, grapes, wild cherries, willows, cottonwoods, dogwoods, nine-barks. The herbs, too, have an eastern look—sweet cicelies, false Solo- mon’s seals, water-leafs, fragile ferns, avens, bog-orchids. It is true that a closer examination reveals the fact that many of these plants belong to species which are strictly western, yet the fact remains that there is little in the vegetation that impresses as strange, one who is familiar only with the eastern flora, while all about him in plain, mesa, foot-hill, and mountain are utterly unfamiliar types of vegetation. So in this narrow 22 UNIVERSITY OF MISSOURI STUDIES [170 zone of gulches and cafions is alone to be found the exact analogue of the Carolinian flora. The following are the im- portant species: Filix fragilis Phragmites Phragmites Carex festiva Allium Nuttallii A. Geyeri A. reticulatum Vagnera stellata Nemexia lasioneuron Limnorchis viridiflora L. laxiflora Corallorrhiza Corallorrhiza Populus Sargentii P. acuminata P. angustifolia Corylus rostrata Parietaria Pennsylvanica 12), Humulus lupulus Neo- obtusa Mexicanus Cerastium occidentale Ranunculus abortivus Thalictrum purpurascens Sedum stenopetalum Heuchera parvifolia Ribes pumilum R. longifolium Opulaster intermedius O. Ramaleyi Oreobatus deliciosus Potentilla Pennsylvanica strigosa Geum scopulorum Rosa Sayi Amelanchier oreophila Crataegus Coloradensis C. occidentalis C. erythropoda C. Doddsii C. Coloradoides Prunus Americana P. Pennsylvanica P. melanocarpa Thermopsis divaricarpa Amorpha fruticosa Vicia oregana V. producta Apios Apios Boulderensis Geranium Parryi Toxicodendron Rydbergii Acer glabrum Rulac Negundo R. Texanum Vitis vulpina Pesedera vitacea Calceolaria linearis Circaea alpina 171] FLORA OF BOULDER, COLORADO 23 Aralia nudicaulis Mertensia lanceolata Svida stolonifera Dracocephalum parviflorum Sanicula Marilandica Mimulus Halli Osmorrhiza longistylis Veronica Americana O. obtusa Galium Vaillantii Ligusticum Porteri G. boreale Heracleum lanatum G. flaviflorum Steironema ciliatum Viburnum Lentago Collomia linearis Ambrosia trifida Hydrophyllum Fendleri Eupatorium maculatum Macrocalyx Nyctelea Cc. SUBMONTANAE The Foot-hill Flora covers not only the true foot-hills of the sandstone crags, but also the lower part of the mountain plateau. The flora is rich but monotonous. In most places the vegetation is thin; it is mainly a forest, but the trees are strewn but sparsely over the steep slopes. The amount of naked rock is very great. The altitude ranges from 5,800 to 8,600 feet. Some of the main streams, such as Boulder creek, have cut down to about 5,500 feet. Directly west of Boulder, and lying between Boulder and Gregory Cajfions, is Flagstaff Hill with an altitude of about 6,500 feet. Southwest of Boulder is Green Mountain, lying between Gregory and Bear Cafions and having an altitude of 8,100 feet. South of Green Moun- tain is Bear Mountain, which attains a height of 8,600 feet, and is the loftiest peak in the first range of foot-hills in the vicinity of Boulder. The Foot-hill Flora merges rather abruptly into that of the mesas at the foot of the crags, and melts insensibly into the Subalpine Flora as it approaches the Main Range. It reaches its maximum development between an altitude of 6,500 and 24 UNIVERSITY OF MISSOURI STUDIES [172 7,000 feet. Below 6,500 feet there occur still many species be- longing to the Great Plains; above 7,000 feet there is a rapid thinning out of species, and subalpine species become occas- ional, although it is not rare for such species in cold situations to go down to the 6,000 foot level. Yet at the summit of Green Mountain (8,100 feet) I found the flora still consisting in the main of the genuine foot-hill species. The Foot-hill Flora may be gathered into four main societies: a. The wooded slope (Sylvestres). b. The foot-hill meadow (Pratenses). c. The foot-hill cafion (Vallicolae). d. The crevice and cranny vegetation of the rocks (Rimosae). a. Sylvestres.* The wooded slope society consists quite purely of bull pine and Douglas spruce, with now and then a few trees of other species of pine, and spruce, and fir. The trees stand usually at wide intervals, oftenest in rows, where some fault in the rock enables them to get a secure foothold. Occasionally on the north slopes, which are moister than any other, the trees stand in such close formation that it is almost impossible to make one’s way through them. Ordinarily it is the Douglas spruce that behaves in this way, since the bull pine prefers a more open formation. Often two rather dis- *Young (Bot. Gaz. 44, 321-352) finds the following forest associa- tions about Boulder: 1. Populus occidentalis—Salix fluviatilis, riparian upon the plains, but extending somewhat up the cafions. 2. Populus angustifolia—Salix Nuttallii, riparian in the foothills. 3. Pinus scop u lorum, sylvan on the dry slopes of the foothills. 4. Pinus Murrayana, sylvan on the dry mountain sides. 5. Apinus flexilis, dry mountain slopes up to timber line. 6. Pseudotsuga—Picea Engelmanni, lower cafions (submontane and montane). 7. Picea Engelmanni—-Abies lasiocarpa, upper cafions (high montane and subalpine to timber line). 8. Aspen society, throughout (north slopes at low altitudes, all slopes higher altitudes). 173] FLORA OF BOULDER, COLORADO 25 tinct forms of forest are discernible, the one of bull pine, the other of Douglas spruce; at other times the two are mixed. The Douglas spruce is at its best in moist ravines, and ascends to timber-line on the mountains, while the bull pine seldom gets above 9,000 feet. The following are characteristic species: Botrychium Virginianum Pteridium aquilinum pubescens Pinus scopulorum P. Murrayana (rare) Apinus flexilis (rare) Picea Parryana Pseudotsuga mucronata Oryzopsis micrantha Muhlenbergia gracilis Melica bella Carex Deweyana Toxicoscordion falcatum Vagnera racemosa V. amplexicaulis Piperia Unalaschensis Peramium ophioides Populus tremuloides Betula papyrifera Andrewsii Chenopodium Fremontii Blitum capitatum Actaea arguta A. arguta eburnea Aquilegia coerulea (rare) Anemone globosa Atragene occidentalis Ranunculus abortivus R. micrantha Cyrtorrhyncha ranunculina Odostemon repens Erysimum Cockerellianum Bosseckia parviflora Oreobatus deliciosus Batidaea laetissima Potentilla Hippiana Amelanchier oreophila Sorbus scopulina (rare) Thermopsis divaricarpa T. pinetorum Tium alpinum Homalobus tenella H. decumbens Lathyrus leucanthus Xanthoxalis stricta Ceanothus velutinus Viola vallicola V. Canadensis Rydbergit Lepargyraea Canadensis Chamaenerion angustifolium Harbouria trachypleura UNIVERSITY OF MISSOURI STUDIES Aletes obovata A. acaulis Ligusticum Porteri Cogswellia Grayi Pterospora Andromedea Chimaphila umbellata Pyrola secunda P. uliginosa Arctostaphylos Uva-ursi Frasera stenosepala Apocynum scopulorum Phlox depressa Lappula floribunda L. angustata Scutellaria Brittoni Dracocephalum parviflorum Prunella vulgaris Monarda menthaefolia M. mollis Scrophularia occidentalis Pentstemon oreophilus P. alpinus P. humilis Castilleja linariaefolia C. cognata C. integra C. confusa Galium boreale G. triflorum Sambucus microbotrys Linnaea Americana Campanula petiolata Specularia perfoliata Laciniaria ligulistylis Oreochrysum Parryi Solidago oreophila S. viscidula S. radulina S. trinervata Eucephalus glaucus Aster polycephalus A. laevis A. Porteri Machaeranthera Bigelovii M. aspera Erigeron salicinus E. macranthus Antennaria oxyphylla Anaphalis subalpina Gnaphalium Wrightii Rudbeckia flava Achillaea lanulosa Arnica cordifolia Senecio salicinus S. Nelsonii S. Fendleri Cirsium Americanum C. erosum Crepis petiolata C. angustata Hieracium albiflorum H. Fendleri Symphoricarpos occidentalis Agoseris rostrata [174 175] FLORA OF BOULDER, COLORADO 27 b. Pratenses. The foot-hill meadow is not very unlike the mesa meadow; the species are in part the same, but there is no sharp line between the flora of the foot-hill forest and the foot-hill meadow, on account of the openness of the former. Only where the forest is dense enough to have a truly sylvan floor, are the light-loving plants absent. The foot-hill meadow society includes various grasses and certain herbs, such as painted-cups, fleabanes, Mariposa lilies, anemones, gaillardias, and the like. The following are the characteristic grasses and sedges: Stipa comata B. Pumpellianus S. viridula Agropyron Vaseyi S. Nelsonii A. Richardsoni S. Scribneri A. violaceum Calamagrostis purpurascens A. pseudorepens Koeleria cristata Elymus ambiguus Poa platyphylla E. strigosus P. crocata E. villiflorus P. longiligula Carex marcida P. longipedunculata C. Douglasii Festuca brachyphylla C. festiva F. confinis C. petasata Bromus lanatipes C. pratensis B. Richardsonii C. siccata c. WVallicolae. The foot-hill cafion society consists of dense thickets of hazel, dwarf birch, willows, dogwoods, al- ders, and the like. About springs and along small rills is found a brief fontinal vegetation, the most delicate of all the plant-groups—mosses, liverworts, ferns, tway-blades, adder’s- mouths, twisted-stalks, mountain lilies, shooting stars, cresses, sedges, and bog-orchids. The foot-hill cafion flora differs from 28 UNIVERSITY OF MISSOURI STUDIES [176 the mesa cafion principally in the absence of the chaparral ele- ment, the haws and wild plums being absent. Most of the re- maining shrubs and arborescent plants are identical—the dwarf maple, the birch, the dogwood, the beaked hazel, the wild cherries, and the cottonwoods. The following are the chief species: Equisetum laevigatum Cinna latifolia Avena striata Eatonia Pennsylvanica Poa triflora Panicularia nervata P. Holmii Carex tenella C. Hoodii C. festiva C. aurea Juncus Balticus montanus Juncoides parviflorum Allium Geyeri A. reticulatum Lilium Philadelphicum montanum Vagnera stellata Streptopus amplexifolius Disporum majus Limnorchis viridiflora L. laxiflora Ibidium Romanzoffanum strictum Ophrys borealis Acroanthes monophylla Populus Sargentii P. angustifolia Salix caudata S. perrostrata S. Bebbiana Betula fontinalis Alnus tenuifolia Corylus rostrata Crunocallis Chamissoi Clematis ligusticifolia Ranunculus reptans R. abortivus Thalictrum Fendleri Thlaspi Nuttallii T. Coloradense Draba streptocarpa Ribes Purpusi Opulaster intermedius O. Ramaleyi O. glabratus O. monogynus Rubus triflorus Fragaria bracteata Geum strictum G. Oregonense Rosa Macounii 177] FLORA OF BOULDER, COLORADO 29 R. Fendleri Mertensia punctata R. aciculata M. viridula R. Maximiliani M. lanceolata Prunus Pennsylvanica Collinsia tenella P. melanocarpa Mimulus floribundus Geranium Richardsonii Veronica Americana Acer glabrum Distegia involucrata Epilobium adenocaulon Adoxa Moschatellina Circaea alpina Solidago Pitcheri Aralia nudicaulis S. polyphylla Svida stolonifera Gymnolomia multiflora Heracleum lanatum Rudbeckia laciniata Angelica ampla Bahia dissecta Dodecatheon radicatum Senecio hydrophyllus D. sinuatum S. perplexus Amarella scopulorum d. Rimosae. The crevice and cranny vegetation of the rocks consists of lichens, rupestrine ferns, alum roots, orpines, selaginellas, and many shrubs, such as the Jamesia, the wax- currant, juneberries, flowering raspberries, salmonberries, roses, and gooseberries. The Rocky Mountain red cedar stands often in grotesquely gnarled and twisted forms at the verges of the crags. It mav be remarked that this flora is of prime importance, since so large a portion of the region ‘consists of naked rock. In fact the foot-hill flora in general is more or less rupestrine in character. There is gathered here only the strictly rock-loving vegetation. These are typical species : Polypodium hesperium W. oregana Dryopteris Filix-mas Filix fragilis Woodsia scopulina Cryptogramma acrostichoides 30 UNIVERSITY OF MISSOURI STUDIES Cheilanthes Féei ~ C. Fendleri Asplenium Trichomanes A. Andrewsii Belvisia septentrionalis Selaginella Underwoodii Sabina scopulorum Parietaria Pennsylvanica Talinum parviflorum Physaria didymocarpa P. floribunda Sedum stenopetalum Heuchera bracteata Micranthes rhomboidea [178 Edwinia Americana Ribes Purpusi R. pumilum Oreobatus deliciosus Rosa melina Amelanchier oreophila Xylophacos Parryi Androsace puberulenta A. pinetorum Coleosanthus minor C. albicaulis Chrysopsis caudata Senecio Nelsonii S. longipetiolatus D. MONTANAE The Montane Flora begins at about the 8,000 foot level, though, as we have seen, on the isolated peaks of the first range of foot-hills the Foot-hill Flora still largely persists even The Montane Flora extends upward to the approximate altitude of 10,000 feet. to the summits, or some 600 feet higher. It is for the most part a forest of lodgepole pine. The zone includes the slopes of the main range below 10,000 feet, and also the higher portions of the adjacent mountain plateau. Some of its characteristic species, indeed, tend to spread throughout the mountain plateau, and in cold valleys may even go as low as 6,000 feet. The montane as also the subalpine slopes have abundant rainfall, showers occur- ring nearly every afternoon. At least this was true of the sum- mer of 1906. The ground is often boggy and springy, and cold with snow water. On north and east slopes the snow remains in the higher and deeper valleys till midsummer ; 179] FLORA OF BOULDER, COLORADO 31 hence the flowering season is short. In a period of about six weeks, from the middle of July to the first of September, the main part of the vegetation in these cool valleys is brought to perfection. Species, which on the mesas had bloomed before my arrival on the eighteenth of June, I found just in blossom at Eldora on the mountainsides August thirty-first. I saw too little of the Montane Flora, since I spent only six days in collections, where it occurs, to be able to separate it definitely into plant-societies. But the chief types as I saw it at Ward, Eldora, and Glacier lake, will be briefly described. In the Montane Subzone there are, perhaps, six tolerably distinct types of vegetation-association: a. The montane forest (Sylvales). b. The montane bog (Paludosae). c. The montane lake (Lacustres). d. The arid brush slope (Arbustales). e. The montane meadow (Pratenses). f. The montane stream (Amnicolae). a. Sylvales. The montane sylva consists of a close for- est of lodgepole pine interspersed with some bull pine and Rocky Mountain white pine, as well as with the various spruces and firs. The spruces and firs occur principally in the valleys, while on the barren ridges, the pines assume a scrub- like form. On these ridges occur many peculiar species of dwarf herbs—golden rods, asters, fleabanes, cat’s-feet, actin- ellas, groundsels. A few of the more characteristic species of the montane sylva are the following: Pinus scopulorum Pseudotsuga mucronata P. Murrayana Abies lasiocarpa Apinus flexilis Calamagrostis purpurascens Picea Engelmanni Trisetum subspicatum — P. Parryana Avena striata 32 Poa longipedunculata Agropyron Arizonicum A. andinum A. violaceum Carex Geyeri Cytherea bulbosa Populus tremuloides Aquilegia coerulea Delphinium occidentalis Erysimum Cockerellianum Draba streptocarpa D. aurea Ribes lentum Potentilla concinna Fragaria glauca Thermopsis divaricarpa Tium alpinum Atelophragma elegans Aragallus deflexus Conioselinum scopulorum Eutoca sericea Pentstemon oreophilus P. alpinus Castilleja integra C. confusa C. lauta C. lancifolia C. sulphurea Pedicularis racemosa P. Grayi UNIVERSITY OF MISSOURI STUDIES [180 Symphoricarpos oreophilus Chrysopsis Bakeri Oreochrysum Parryi Solidago decurnbens S. oreophila Eucephalus Engelmannii Aster Underwoodii A. Porteri A. Andrewsi1 Erigeron multifidus . trifidus . glandulosus . superbus . macranthus . speciosus . subtrinervis esi coMes Ie eoIeo ime) . eximius Antennaria concinna A. parvifolia A. aprica Anaphalis subalpina Tetraneuris lanigera Artemisia silvicola Senecio pudicus S. lanatifolius S. ambrosioides Cirsium Coloradense Hieracium albiflorum Agoseris Leontodon A. humilis b. Paludosae. The montane bog is characterized by the presence of the quaking aspen and other Hudsonian plants. 181] FLORA OF BOULDER, COLORADO 33 The aspen, however, is not confined to the bogs, but forms groves in slight depressions throughout the mountains, and oc- curs on Green Mountain not much, if any, above 6,000 feet. The aspen occurs in the drier portions of the bogs along with other uliginose plants. The bog vegetation is very rich in species. A fine specimen of the montane bog is found just west of Eldora at an elevation of 8,600 feet. The following are characteristic species : Muhlenbergia simplex M. filiformis Phleum alpinum Cinna latifolia Trisetum montanum T. subspicatum Merathrepta intermedia Poa reflexa P. Vaseyana Carex canescens C. occidentalis C. ebenea C. Goodenovii C. utriculata Juncus Saximontanus Juncoides parviflorum Limnorchis stricta L. borealis Ibidium strictum Populus tremuloides Salix Scouleriana S. brachycarpa S. glaucops S. chlorophylla Betula glandulosa Rumex densiflorus Polygonum confertiflorum Alsine longifolia Aconitum Columbianum A. insigne A. ochroleucum Ranunculus cardiophyllus R. inamoenus R. micropetalus R. pedatifidus Pectianthia pentandra Micranthes arguta Parnassia fimbriata Dasiphora fruticosa Sidalcea candida Viola palustris V. pallens Epilobium adenocaulon E. rubescens E. anagallidifolium Oxypolis Fendleri Dodecatheon philoscia Anthopogon barbellatus 34 UNIVERSITY OF MISSOURI STUDIES [182 Amarella plebeja E. jucundus Pleurogyne fontana Gnaphalium palustre Allocarya scopulorum Artemisia biennis Mimulus puberulus Senecio triangularis Veronica Wormskjoldii S. admirabilis — Elephantella Groenlandica S. cymbalarioides Erigeron minor Crepis denticulata E. lonchophyllus c. Lacustres.* The montane lacustrine and marginal, vegetation I saw only at Glacier lake. Besides some aquatic grasses, notably Deschampsia caespitosa, there occur the float- ing bur-reed, Sparganium angustifolium, the white water- crowfoot, Batrachium flaccidum, and the aquatic mudwort, Limosella aquatica. The yellow pond-lily, Nymphaea poly- sepala, grows also in some of these high lakes. d. Arbustales. The arid brush slope vegetation consists quite wholly of the true sage-brush, Artemisia tridentata. This community is rare in the region, and I have seen it only be- tween Glacier lake and Eldora near Bluebird mine. e. Pratenses. The montane meadow is truly a paradise of flowers. It is not uncommon to see acre upon acre of meadow glorious with purple and blue and red and yellow and white and scarlet. Never have I seen flowers anywhere else in such profusion nor with such gorgeous hues—monkshoods, larkspurs, louseworts, milk-vetches, locoweeds, squawweeds, death-camasses, grasses, rushes, sedges, and blue-eyed grasses. The following species are typical: *For a detailed account of the vegetation of these high Jakes, con- sult the paper by Ramaley and Robbins on Redrock lake near Ward (Univ. of Colo. Studies, 6, 133-168). 183] FLORA OF BOULDER, COLORADO Muhlenbergia Richardsonis Anemone globosa M. simplex Phleum alpinum Agrostis asperifolia Deschampsia caespitosa Poa pratensis P. reflexa P. leptocoma P. interior P. Vaseyana Festuca rubra Carex occidentalis Hoodii festiva ebenea petasata AAP asa lanuginosa Anticlea Coloradensis Juncus longistylis J. parous J. Saximontanus Sisyrinchium alpestre S. angustifolium Delphinium occidentale Aconitum porrectum A. Columbianum A. insigne A. ochroleucum There is, of course, Rupestres, able to give an adequate account of it. a montane Clementsia rhodantha Potentilla pulcherrima P. Hippiana P. propinqua Dasiphora fruticosa Geum Oregonense Erythrocoma ciliata Tium alpinum Homalobus tenellus Aragallus Lambertii A. patens A. Richardsonii Geranium Richardsonii Sidalcea candida Dodecatheon radicatum Castilleja sulphurea Elephantella Groenlandica Pedicularis Grayi Valeriana ceratophylla Erigeron Smithi Arnica subplumosa Senecio scopulinus S. chloranthus S. pseudaureus Agoseris parviflora A. laciniata A. humilis rupestrine 35 society, but I am too little acquainted with it to be I, however, noted the 36 UNIVERSITY OF MISSOURI STUDIES [184 austromontane saxifrage, Leptasea austromontana, and the glandular phacelia, Phacelia glandulosa. There is also a brief ‘campestrian vegetation about Eldora, reproducing, in other species, the facies of the Great Plains, Campestres; I may instance as species: Grindelia subalpina, G. Eldorae, Chrysothamnus Parryi, and C. elegans. f. Amnicolae. The montane stream vegetation is seen at its best about small rills. Along the larger streams it as- sumes a typical riparian aspect, much like that of the canon society of the foot-hills along the large streams. Since the water in these streams is very cold inasmuch as they are fed from the wasting snows of the alpine valleys, the montane vegetation can scarcely be distinguished from the true sub- alpine vegetation of the streams. The list of species will, therefore, be deferred until the subalpine stream vegetation is reached. E. SUBALPESTRES The Subalpine zone extends from about the 10000 foot level to timberline, and hence coincides with the upper slopes of the Main Range. It is in the main a forest of Engelmann spruce, with occasional high meadows and bogs. Lakes, too, are numerous. I have personal knowledge of only two formations: a. The subalpine forest (Sylvales). b. The subalpine stream (Amnicolae). a. Ses.lval. The subalpine forest consists mainly of Engelmann spruce, Picea Engelmanni, and balsam fir,Abies lasiocarpa. I have but a very slight knowledge of the herbs characterizing this formation, but I noticed along the Arapahoe Trail the following species, which I had not seen in the mon- 185 | FLORA OF BOULDER, COLORADO 37 tane forest: Eriogonum subalpinum, Arnica Parryt, and Sene- cio atratus. A large number of the montane sylvan species were observed. b. Amnicolae. The subalpine stream vegetation is very luxuriant. It has on the one hand a very close affinity with the montane stream vegetation, and on the other with that of the wet alpine tundra. Not only does the snow linger late in these high valleys, the water of the streams is also very cold. In the list that follows the montane species are included as well: Poa platyphylla P. alpina Carex Goodenovii Populus balsamifera P. angustifolia Salix caudata S. Scouleriana Betula fontinalis Alnus tenuifolia Bistorta bistortioides Alsine Baicalensis Caltha leptosepala Trollius albiflorus Anemone Canadensis Ranunculus reptans R. inamoenus R. micropetalus Cardamine cordifolia C. incana Clementsia rhodantha Pectianthia pentandra Micranthes arguta Parnassia fimbriata Sidalcea candida Oxypolis Fendleri Primula Parryi Swertia palustris Polemonium robustum Mertensia polyphylla Mimulus Langsdorfii M. puberulus Helianthella quinquenervis Senecio triangularis I am almost wholly unacquainted with the remaining sub- alpine formations, such as the lacustrine, palustrous, rupes- trine, the subalpine summit and high ridge floras. I saw a 38 UNIVERSITY OF MISSOURI STUDIES [186 little of these at Ward and on the high slopes'above Bloomer- ville, and on Arapahoe Peak just below timberline, but I am unable to give any clear account of the vegetation.* F. ALPESTRES}+ Between 11,000 and 12,000 feet tree-growth ceases ab- ruptly. The spruces and firs bend and hug the ground. The willows branch and fork underground and rise to the height of but a few inches. The precise altitude of the timberline depends somewhat on the exposure, and differs, therefore, from peak to peak, but 11,500 feet is, perhaps, on an average the lower limit of the alpine zone. I am acquainted with this zone only on Arapahoe Peak, where I spent one day, Septem- ber first, and collected some 110 species, most of them above timberline. The total number of species known to reach an altitude of 12,000 feet, or above, in Colorado is 386.4 The alpine flora may be conveniently gathered into two societies: a. The wet alpine tundra (Tundrales). b. The dry rock-desert (Alpinae) of the summits. a. Tundrales. The wet tundra occupies the region of cold water-soaked soil. The water from the wasting snows collects in depressions, streams are formed, and along these the *T refer the reader to the excellent paper on Redrock lake near Ward, by Ramaley and Robbins (Univ. of Colo. Studies, 6, 133-168). +Consult for the Alpine Flora Cooper’s Alpine vegetation in the vi- cinity of Long’s Peak, Colorado (Bot. Gaz., 45, 319-337). He recog- nizes three plant formations: 1. The dry meadow. 2. The wet mead- ow. 3. The Krummbholtz. The latter, while striking enough, is rather but the upper level of the spruce forest, striving to persist in Alpine con- ditions. {For a list of these see the article by Cockerell on the Alpine Flora of Colorado (Am, Nat., 40, 86-873). 187] FLORA OF BOULDER, COLORADO 39 vegetation clings. Often the streams flow concealed under the dwarf spruces and firs, their existence there being known only by their roaring underneath. Parry’s primrose, saxi- frages, globeflowers, white cowslips, gentians, red elephants, several sedges, grasses, and rushes are examples of the wet tundra vegetation. The Krummboltz of spruce and fir at the timberline consists chiefly of Engelmann spruce, Picea Engel- manm, and balsam fir, Abies lasiocarpa. The wet tundra con- tinues down to the lower edge of the alpine zone, whence it de- scends and coalesces with the subalpine stream vegetation. The following are characteristic species: Lycopodium annetinum Picea Engelmanni Abies lasiocarpa Alopecurus occidentalis Trisetum majus Poa reflexa P. leptocoma P. alpicola P. alpina Carex festiva C. ebenea C. bella Juncus Drummondii Juncoides spicatum Salix glaucops S. chlorophylla Bistorta bistortioides B. vivipara Alsine Baicalensis Caltha leptosepala Trollius albiflorus Ranunculus pedatifidus R. alpeophilus Thlaspi Coloradense Draba Fladnizensis Clementsia rhodantha Pectianthia pentandra Saxifraga debilis Micranthes arguta Viola Canadensis Neo- Mexicani Angelica Grayi Pseudocymopterus tenuifolius Kalmia microphylla Primula Parryi Androsace subumbellata A. diffusa Anthopogon elegans A. barbellatus 40 UNIVERSITY OF MISSOURI STUDIES [188 Amarella monantha Erigeron jucundus A. plebeja Holmii E. salsuginosus Swertia palustris E. superbus Mertensia polyphylla Senecio carthamoides Veronica Wormskjoldia S. blitoides Castilleja Arapahoensis S. pseudaureus Elephantella Groenlandica Hieracium gracile Pedicularis Parryi b. Alpinae. The dry rock-desert lies mingled with or above the wet tundra and extends to the summit, wherever there is soil not covered with snow. The vegetation suffers from ex- treme exposure, and grows close to the ground, seldom, unless sheltered by rocks, rising more than an inch or two in height. In sheltered places under rocks, even at this extreme altitude, I found several beautiful clusters of the blue columbine, the state flower of Colorado, with stems twelve to eighteen inches high, and with blossoms two inches across. The wooly-headed thistle, too, was found of the same height. But in general the vegetation is much dwarfed. Next to the wet tundra the Krummholtz of spruce and fir still persists, under which I detected some fine specimens of club-moss; but farther up there is no shrubby vegetation except the underground wil- lows. The vegetation grows in little rounded tussocks, and consists of the alpine catch-fly, rock-primrose scarcely half an inch high, sibbaldia, dryas, alpine clovers, dwarf sedges, grasses, and rushes, and, last of all, the little yellow saxi- frages and the snowflowers, which are often blossoming at the snow-line. Now and then on the high exposed ridges the beautiful rydbergia rises five or six inches above the mountain turf, its stems and leaves and large yellow flowers swathed in dense wool. For what must be the tribulations of this 189 | alpine vegetation at the line of perpetual snow, with the alter- FLORA OF BOULDER, COLORADO 41 nate freezing by night and thawing by day, with the keen light, And yet It shares the fascina- and bleak winds, and the fierce fury of the storms? the alpine flora is exquisitely beautiful. tion of its sublime mountain home, to which it lends the only touch of delicate grace. I append a list of alpine summit species, most of which I found on Arapahoe Peak or are known to grow there: \ Trisetum subspicatum Poa crocata P. rupicola P. Pattersonii P. longipedunculata Festuca brachyphylla F. minutiflora Agropyron violaceum Carex incurva . atrata . chalciolepis . rigida C C Cc C. chimaphila C. nigricans C. Pyrenaica C. rupestris C. obtusata C. capillaris Juncus triglumis J. castaneus Allium Pikeanum Erythronium parviflorum Lloydia serotina Salix pseudolapponicum S. petrophila S. Saximontana Monolepis Nuttalliana Oxyria digyna Paronychia pulvinata Claytonia megarrhiza Oreobroma pygmaea Arenaria Tweedyi A. Fendleri Alsinopsis propinqua A. obtusiloba Silene acaulis Aquilegia coerulea Ranunculus adoneus Thlaspi Nuttallii T. purpurascens Erysimum nivale E. Cockerellianum Draba crassifolia D. cana D. streptocarpa D. luteola UNIVERSITY OF MISSOURI STUDIES D. aureiformis D. aurea D. decumbens Sedum stenopetalum Heuchera Hallii H. parvifolia Micranthes rhomboidea Leptasea chrysantha L. austromontana L. flagellaris Potentilla dissecta Sibbaldia procumbens Erythrocoma ciliata Acomastylis turbinata A. Arapahoensis Dryas octopetala Amelanchier polycarpa Trifolium lividum T. dasyphyllum Epilobium anagallidifolium Vaccinium scoparium Primula angustifolia P. Parryi Dasystephana Romanzovii D. Parryi Polemonium scopulinum P. delicatum P. Brandegeet: Eutoca sericea Mertensia alpina M. perplexa Pentstemon glaucus stenosepalus Chionophila Jamesii Besseya alpina Castilleja occidentalis Pedicularis scopulorum Campanula uniflora Tonestus pygmaeus Solidago decumbens Erigeron pinnatisectus E. multifidus E. melanocephalus E. simplex E. leucotrichus Antennaria media . umbrinella . imbricata . corymbosa aprica > > > > > . anaphaloides Tetraneuris lanigera Rydbergia grandiflora Artemisia spithamea Arnica platyphylla A. Parryi Senecio crassulus S. atratus S. crocatus Cirsium scopulorum C. griseum Crepis alpicola 191 | FLORA OF BOULDER, COLORADO 43 IV. SPECIAL CLASSES OF PLANTS Independent of the five great zones of vegetation are two special classes of plants: A. The saprophytic and parasi- tic plants (SAPROPHYTICALES ET PARASITI- CALES). B. The plants which largely owe their presence to human agency (ANTHROPOPHYTICALES). These consist of the various cultural plants, of weeds, and of es- capes. A. SAPROPHYTICALES ET PARASITICALES Besides the saprophytic and parasitic fungi there are a few phanerogams, which are destitute of chlorophyl and are true saprophytes or parasites. The following are known to occur in the region: Corallorrhiza Corallorrhiza (saprophytic in rich soil) C. multiflora (saprophytic in rich soil ) Razoumofskya Americana (parasitic on lodgepole pine) R. cryptopoda (parasitic on bull pine) Pterospora Andromedea (parasitic on the roots of bull pine) Cuscuta curta (parasitic on Iva xanthifolia and other coarse herbs) C. indecora (parasitic on Thermopsis pinetorum and other legumes ) Thalesia fasciculata (parasitic on Artemisia frigida and other Composites ) There are also a few root-parasites with green foliage, notably Comandra pallida, Gerardia Besseyana, and the Cas- tillejas. B. ANTHROPOPHYTICALES Only three kinds of anthropophytic plants need concern us here: a. Forage plants (Faenales), which have become 44 UNIVERSITY OF MISSOURI STUDIES [192 thoroughly naturalized. b. Weeds (Ruderales). c. Cul- tural and ornamental plants that have escaped (Fugitivae). a. Faenales. Most of the common forage grasses and clovers have become thoroughly established about Boulder. I have noted the following: Phleum pratense Festuca elatior Agrostis alba Lolium Italicum Dactylis glomerata Trifolium pratense T. repens T. hybridum Medica sativa Poa pratensis P. compressa P. trivialis b. Ruderales. In the appended list of weeds only those that have been introduced from elsewhere, or, if native, are also common weeds in many parts of the United States, have been included. However, many native species, such as the various gum-weeds and spurges, must often be bad weeds in cultivated grounds. But to do justice to the ruderal aspects of the native flora would require much special study, such as one is unable to make in the course of a few weeks, and es- pecially one who is unfamiliar with agriculture as carried on in Colorado. I noted the following weeds: Syntherisma sanguinale B. secalinus Panicum capillare Echinochloa Crus-galli Chaetochloa glauca C. viridis Cenchrus Carolinianus Avena fatua Eragrostis major Poa annua Bromus brizaeformis B. hordeaceus B. tectorum Rumex Acetosella R. crispus R. obtusifolius Polygonum erectum P. aviculare Persicaria Persicaria Tiniaria Convolvulus | FLORA OF BOULDER, COLORADO Chenopodium leptophyllum Mentha spicata C. album C. hybridum C. Botrys Salsola Tragus Amaranthus retroflexus A. blitoides A. graecizens Mollugo verticillata Portulaca oleracea P. retusa Alsine media Silene antirrhina S. noctiflora Vaccaria Vaccaria Thlaspi arvense Bursa Bursa-pastoris Sisymbrium officinale Brassica juncea B. nigra Camelina sativa Tridophyllum Monspeliensis Medicago Lupulina Melilotus alba M. officinale Erodium cicutarium Malva rotundifolia Pastinaca sativa Convolvulus arvensis Nepeta Cataria Glecoma hederacea Leonurus Cardiaca Physalis Virginiana P. heterophylla Datura Stramonium D. Tatula Verbascum Thapsus V. Blattaria Veronica serpyllifolia V. Byzantina Plantago major P. lanceolata Micrampelis lobata Iva xanthifolia I. axillaris Ambrosia trifida A. artemisifolia A. psilostachya Xanthium commune Erigeron ramosus Leptilon Canadense Helianthus petiolaris Bidens vulgata Boebera papposa Anthemis Cotula Tragopogon pratensis T. porrifolius Cichorium Intybus Taraxacum Taraxacum Lactuca integrata Sonchus arvense S. asper 45 UNIVERSITY OF MISSOURI STUDIES [194 c. Fugitivae. I noted the following escapes: Chaetochloa Italica Avena sativa Triticum vulgare Hordeum sativum hexastichon Asparagus officinale Atriplex hortensis Saponaria officinalis Delphinium Ajacis Papaver Argemone Armoracia Armoracia Brassica campestris Koniga maritima Raphanus sativus Ribes vulgare Althaea rosea Carum Carvi Pharbitis purpurea Lycopsis arvensis Lycium vulgare Lycopersicon Lycopersicon V. BIBLIOGRAPHY. Allison, Edith M. Bibliography and history of Colorado botany. Univ. of Colo. Studies, 6, 51-76, 1908. Clements, Frederic E. Formation and succession herbaria. Univ. of Neb. Studies, 4, 329-355. Cockerell, T. D. A. The alpine flora of Colorado. Am. Nat., 40, 861-873. Cooper, William S. Alpine vegetation in the vicinity of Long’s Peak, Colorado. Bot. Gaz., 45, 319-337. Dodds, Gideon S. Students of mesa and foothill vegetation, I. 1. Geology and physiography of the mesas. Univ. of Colo. Studies, 6, 11-19. Ramaley, Francis. Botanical opportunity in Colorado. Univ. of Colo. Studies, 6, 5-10. Ramaley, Francis. Botany of northeastern Larimer County, Colo. Univ. of Colo. Studies, 5, 119-131. Ramaley, Francis. Plants of the Florissant region in Colorado. Univ. of Colo. Studies, 3, 177-185. Ramaley, Francis. Remarks on some Northern Colorado plant communities with special reference to Boulder Park (Tolland, Col- orado). Univ. of Colo. Studies, 7, 223-236. Ramaley, Francis. The silva of Colorado, I. Trees of the Pine family in Colorado. Univ. of Colo. Studies, 4, 109-122. Ramaley, Francis. The silva of Colorado, IJ. The poplars, aspens, and cottonwoods. Univ. of Colo. Studies, 4, 187-197. Ramaley, Francis. The silva of Colorado, 888. Woody plants of Boulder County. Univ. of Colo. Studies, 5, 47-63. Ramaley, Francis. Studies of mesa and foothill vegetation, I. 2. Climatology of the mesas near Boulder. Univ. of Colo. Stud- ies, 6, 19-31. Ramaley, Francis. The University of Colorado mountain lab- oratory. Univ. of Colo. Studies, 7, 91-95. 195] 47 48 BIBLIOGRAPHY [196 Ramaley, Francis, and Robbins, W. W. Ecological notes from North-Central Colorado. Univ. of Colo. Studies, 5, 111-117. Ramaley, Fancis, and Robbins, W. W. Studies in lake and streamside vegetation, I. Redrock lake near Ward, Colorado. Univ. of Colo. Studies, 6, 133-168. Robbins, W. W. Climatology and vegetation in Colorado. Bot. Gaz., 49, 256-280. Robbins, W. W. Studies in mesa and foothill vegetation, I. 4. Distribution of deciduous trees and shrubs on the mesas. Univ. of Colo. Studies, 6, 36-49. Robbins, W. W., and Dodds, G. S. Studies in mesna and foot- hill vegitation, I. 38. Distribution of conifers os the mesas. Univ. of Colo. Studies, 6, 31-36. Shantz, H. L. A biological study of the lakes of the Pike’s Peak region. Trans. Am. Micro. Soc., 27, 75-98. Shantz, H. L. A study of the vegetation of the mesa region east of Pike’s Peak. Bot. Gaz, 42, 16-47; 179-207. Young, R. T. Forest formations of Boulder County, Colorado. Bot. Gaz. 44, 321-352. FLORA OF BOULDER, COLORADO, AND VICINITY Subkingdom I. PTERIDOPHYTA, Fern-worts. Order 1. OPHIOGLOSSALES. Family 1. OPHIOGLOSSACEAE Presl. Adder’s-tongue family. 1. BOTRYCHIUM Swartz. Moonwort. 1. B, Virginianum (L.) Swartz. VIRGINIA GRAPE-FERN. Forested slopes of Green Mt., above 7000 ft.; very scarce, only two or three plants discovered (Daniels, 606).* Laprapor to British Cotumpia; FLroripA to TExas and WASHINGTON. Order 2. FILICALES. Family 2. POLYPODIACEAE R. Br. Polypody family. 2. POLYPODIUM L. Potyropy. 2. P. hesperlum Maxon. WESTERN POLYPODY. On a single rock in a cafion on the north slope of Green Mt., 7500 ft. (Daniels, 605). Montana to British CoLumBiA and WASHINGTON; COoLo- RADO to ARIZONA. 3. DRYOPTERIS Adans. SHIELD-FERN. 3. D. Filix-mas (L.) Schott [Aspidiwm Filix-mas (L.) Swartz]. MALE-FERN. Summit of South Boulder Peak; Bear Cafion; high cafions of Green Mt.; Boulder Cafion near Falls; apparently quite * See preface for explanation of numbers. 197] 49 50 UNIVERSITY OF MISSOURI STUDIES [198 evenly, but not abundantly distributed throughout in moist rocky cafions, 6000-8600 ft. (Daniels, 555). Nova Scotia and Micuicgan to ALaskA; NEw Mexico and CoLoRADo to CALIFORNIA. 4, WOODSIA R. Br. 4. W. scopulina D. C. Eaton. Ciirr Woopsta. The most abundant fern of the foot-hills and lower moun- tainsides, occurring wherever rocks are exposed to the sur- face, 5700-8100 ft. (Daniels, 156). Micuican to British CcLumBpia; COLORADO and ARIZONA to CALIFORNIA. 5. W. Oregana D. C. Eaton. Mountain Woopsta. With the preceding, but much scarcer, and ranging to the timberline or above, 5600-11000 ft. (Daniels, 361). Long’s Peak (Coulter in Wabash College Herb.). Micuican to British Cotumpia; CoLorApo and ARIZONA to CALIFORNIA. 5. FIIX Adans. BLADDER-FERN. 6. F. fragilis (L.) Underw. [Cystopteris fragilis Bernh.]. FRAGILE-FERN. Throughout on the moister rocks; apparently the only fern of the plains region, 5100-13000 ft. (Daniels, 23). Almost cosmopolitan. 6. PTERIDIUM Scop. BRACKEN. 7. P. aquilinum pubescens Underw. Hairy BRAKE. Cafions of Green Mt., and gulches at the foot of the Flat- irons; Bear Cafion; local, but abundant where found, 5800- 10000 ft. (Daniels, 277). Monrana and Cortorapo to ArIzoNA and CALIFORNIA. 7. CRYPTOGRAMMA R. Br. PARSLEY-FERN. 8. C. acrostichoides R. Br. Rock PARSLEY-FERN. High ridges of rock, descending on Green Mt. to about 6500 ft., thence to above 11000 ft. (Daniels, 271). Micuican to ALASKA; COLORADO to CALIFORNIA. 199] FLORA OF BOULDER, COLORADO 51 8. CHEILANTHES Swartz. Lip-FERN. g. C. Féei Moore [C. gracilis Mett.; C. lanuginosa Nutt.]. WOOLLY LIP-FERN. Growing with Asplenium Andrewsit A. Nelson on the south face of a white sandstone (alkaline) cliff extending along Boulder creek for a mile or more (Andrews, in Nelson, Proc. of the Biol. Soc. of Wash., 17, 175). InLrnois and Minnesota to BririsH CotumBia; Missouri to Texas and ARIzONA. 10. C. Fendleri Hook. FENDLER’S LIP-FERN. Dry rocks, Boulder, 5900-8500 ft. (Rydberg). CoLorapo and TrExas to CALIFORNIA. 9, ASPLENIUM L. Sprreenwort. 11. A. Trichomanes L. MaIpDEN-HAIR SPLEENWORT. Limestone rocks, South Boulder Canon, 5400-7000 it. (Rydberg). NortH AMERICA: Europe: AsIA: SOUTH AFRICA: PACIFIC ISLANDS. 12. A. Andrewsii A. Nelson. ANDREWS’S SPLEENWORT. Growing abundantly in crevices with Cheilanthes Féci Moore (Andrews, in Nelson, loc. cit. pp. 174-175). Known only from the type locality as above. 10. BELVISIA Mirb. Grass-FERN. 13. B. septentrionalis (L.) Mirb. [Asplemum septentrio- nalis (L.) Hoffm.] NorTHERN GRASS-FERN. Bald ridges of Green Mt.; south slope of Bear Mt.; South Boulder Cafion, 6000-7000 ft. (Daniels, 358). Soutu Daxora to Monrana; New MExico to ARIZONA. 52 UNIVERSITY OF MISSOURI STUDIES [200 Order 3. EQUISETALES. Family 3. EQUISETACEAE Michx. Horsetail family. 11. EQUISETUM L. MHorserait. 14. E. arvense L. FIELD HORSETAIL. Swales and shores of streams; sandy moist meadows, 5100- 10000 ft. (Daniels, 260). NortH AMERICA: Europe: ASIA. 15. E. laevigatum A. Br. SMOOTH SCOURING RUSH. Along streams and railway embankments in the plains and on the mountains, 5100-12500 ft. (Daniels, 392). New Jersey to British Co_umpia; NorTH CAROLINA to Mexico and CaLrFornia. Order 4. LYCOPODIALES. Family 4. LYCOPODIACEAE Michx. Clubmoss family. 12. LYCOPODIUM L. Ciusmoss. 16. L. annotinum L. StirF CLUBMOSS. Under dwarf and procumbent shrubs, hidden almost com- pletely from view, Arapahoe Peak, above timberline, 11000- 11500 ft. (Daniels, 370). LaBRADOR to ALASKA; WEST VIRGINIA to COLORADO and WASHINGTON: EUROPE: ASIA. Family 5. SELAGINELLACEAE Underw. Selaginella family. 18. SELAGINELLA Beauv. LItTtLe cLUBMoss. 17. §. densa Rybd.[S. Engelmanni Hieron.] DENSE SELA- GINELLA. Forests, Redrock lake, 10100 ft. (Ramaley & Robbins). Soutu Daxora to Montana; NesRaAsKaA to COLORADO. 174%. §. Underwoodii Hieron. [S. rupestris Fendlert Un- derw.]. UNDERWOOD’S SELAGINELLA. Common on exposed rocks, 6000-8100 ft. (Daniels, 151). Redrock lake 10100 ft. (Ramaley and Robbins). CoLorabo to New Mexico. 201 | FLORA OF BOULDER, COLORADO 53 Subkingdom II, SPERMATOPHYTA. Seed plants. Class1. GYMNOSPERMAE. Order 5. PINALES. Family 6. PINACEAE Lind]. Pine family. 14, PINUS L. Prne. 18. P. scopulorum (Engelm.) Lemmon [P. ponderosa scopu- lorum Engelm.]. BULL PINE. Common on the higher mesas, foothills, and mountains, 5700-10000 ft. (Daniels, 97). South Daxkota and Nersraska to Montana; Trexas to ARIZONA. 19. P. contorta Murrayana (Oreg. Com.) Engelm. Lopce POLE PINE. Mountains about Ward, and between Sugarloaf Mt. and Glacier Lake, 7000-10000 ft. (Daniels, 302). Montana to ALASKA; COLORADO to CALIFORNIA. 15. APINUS Necker. CEMBRA PINE. 20. A. flexilis (James) Rydb. [Pinus flexils James]. Rocky MOUNTAIN WHITE PINE. Rare on high ridges of Green Mt.; also at Ward, 7300- 11000 ft. (Daniels, 771). ALBERTA to TEXAS and CALIFORNIA. 16. PICEA Link. Spruce. 21. P. Engelmanni (Parry) Engelm. ENGELMANN SPRUCE. Bear Cafion; Boulder Cafion near Falls; common upon the main range of the mountains, 7000 (Bear Caiion) -11000 ft. (Daniels, 294). ALBERTA to British Cotumpia; NEw Mexico to ARIZONA. 22. P. Parryana (Andrée) Sarg. [P. pungens Engelm.]. BLUE SPRUCE. Common in cafions throughout, 6500-10000 ft. (Cockerell); Fourth of July Mine; South Boulder Cafion (Ramaley). Wyomine and New Mexico to Uran. 54 UNIVERSITY OF MISSOURI STUDIES [202 17. PSEUDOTSUGA Carr. Rep Fir. 23. BP. mucronata (Raf.) Sudw. [P. Douglasti Carr.]. DOUGLAS SPRUCE. Abundant on the foothills and mountains; some trees have green foliage, others glaucous blue, 6000-10000 ft. (Daniels, 142). ALBERTA to BritisH CoLumpia; Texas to Mexico and CALIFORNIA. 18. ABIES Miller. Batsam Fir. 24. AA, lasiocarpa (Hook.) Nutt. WESTERN BALSAM FIR. North slope of Green Mt.; Bear Cafion; Boulder Cafion near Falls and above them; common on the main mountain range, 7000 (Bear Cafion) -11000 ft. (Daniels, 303). ALBERTA to ALaskA; NEw Mexico to ARIZONA. Family 7. JUNIPERACEAE Horan. Juniper family. 19. JUNIPERUS L. Juniper. 25. J. Sibirica Burgsd. MouUNTAIN JUNIPER. Mesa at the foot of the Flat-irons, 5700-6000 ft. (Daniels, 182). Mountains between Sunshine and Ward (Rydberg). Laprapor to ALasKka; MassacHusETts and MuicuHicGan to Utau: Europe: ASIA. 20. SABINA Haller. Savin. 26. §. scopulorum (Sarg.) Rydb. [Juniperus scopulorum Sarg.]. Rocky MOUNTAIN RED CEDAR. High mesas and mountain crags; some trees have green foliage, others glaucous blue, 5700-8500 (Daniels, 217). ALBERTA to British CoLumBra; Texas to ARIZONA and OREGON. 203] FLORA OF BOULDER, COLORADO 55 Class II. ANGIOSPERMAE. Subclass 1. MONOCOTYLEDONES, Order 6. PANDANALES. Family 8. TYPHACEAE Jo Sito Lehi, Cattail family. Pal, UM aeo Ib) (Amerie, 27. 1. latifolia L. Broap-LEAVED CATTAIL. Swales and bogs in. the plains, common, 5100-5600 ft. (Daniels, 408). Nortu AMERICA, except the far north: EUROPE: AsIA. Family 9. SPARGANIACEAE Agard. Bur-reed family. 22. SPARGANIUM L. Bur-reep. 28. 8S. angustifolium Michx. [S. simplex angustifolium (Michx.) Engelm.]. NARROW-LEAVED BUR-REED. Floating in a pond at Glacier Lake, gooo ft. (Daniels, 620). Also Redrock lake, 1o100 ft. (Ramaley and Robbins). NEWFOUNDLAND to OREGON; NEw York to CALIFORNIA. Order 7. NAIADALES. Family 10. ZANICHELLIACEAE Dumort. Zanichellia family. 23. POTAMOGETON L. Ponpweep. 29. P.lonchites Tuckerm. [P. fluitans Roth.] Lonc-LEAvED PONDWEED. Owen’s lake; Boulder lake, 5300 ft. (Daniels, 683). NEw Brunswick to WASHINGTON; FLORIDA to CALIFORNIA. 29%. P.alpinus Balbis [P. rufescens Schrad.]. ALPINE POND- WEED. Redrock lake, 10100 ft. (Ramaley and Robbins.). Nova Scotra to ALasKA; New Jersey to CALIFORNIA. 56 UNIVERSITY OF MISSOURI STUDIES [204 30. P. heterophyllus Schreb. VARIOUS-LEAVED PONDWEED. Near Boulder, 5100-6000 ft. (Rydberg). NortH AMERICA, except extreme north: Europe. 31. P. foliosus Raf. [P. pauciflorus Pursh]. Lrary PoNp- WEED. Streams and ditches east of Boulder, 5100-5500 ft. (Dan- iels, 736). New Brunswick to BritisH CoLumBiA; FLoripa to CaL- IFORNIA, 32. P. Spirillus Tuckerm. SprraAL PONDWEED. Swales along railroad between Boulder and Marshall, 5400 ft. (Daniels, 486). Not included in Rydberg’s Flora of Colorado. Nova Scotia to MINNESOTA; VIRGINIA to COLORADO. 33. P. pectinatus L. FENNEL-LEAVED PONDWEED. Owen’s lake; Boulder lake, 5300 ft. (Daniels, 681). Nort AMERICA: EUROPE. 24. ZANICHELLIA L. 34. Z. palustris L. Marsa ZANICHELLIA. Owen’s lake; Boulder lake, 5300 ft. (Daniels, 682). Red- rock lake, 1o100 ft. (Ramaley & Robbins). NortH TEMPERATE ZONE. Order 8. ALISMALES. Family 11. ALISMACEAE DC. Water-plantain family. 25. ALISMA L. WatTER-PLANTAIN. 35. A. Plantago L. ComMoN WATER-PLANTAIN. Bogs west of Marshall; swales, ditches, streams, and ponds east of Boulder, 5100-6000 ft. (Daniels, 424). NorTHERN HEMISPHERE. 26. SAGITTARIA L. ARROWHEAD. 36. S. arifolia J. G. Smith. ARUM-LEAVED ARROWHEAD. With the preceding, 5100-6000 ft. (Daniels, 441). QuEBEC to BriTisH CoLtumBiA; MAINE and MIcHIGAN to New Mexico and CaLtFornia. 205] FLORA OF BOULDER, COLORADO 57 Order 9. POALES. Family 12. POACEAE R. Br. Meadowgrass family. 27. SCHIZACHYRIUM Nees. BuNcH-GRASS. 37. §. scoparium (Michx.) Nash [Andropogon scoparius Michx.]. BRroom-Grass. Common in dry plains and mesas; occasional in the lower foothills, 5100-6300 ft. (Daniels, 478). NEw Brunswick to SASKATCHEWAN; FLORIDA to TEXAS. 28. ANDROPOGON L. Berarp-crass. 38. A. fureatus Muhl. TuRKEY-FOOT GRASS. Common on the plains, mesas and foothills, 5100-8000 ft. (Daniels, 512). Marne to SASKATCHEWAN; FLorIDA to TExas and CoLo- RADO. 39. A. chrysocomus Nash. GOLDEN BEARD-GRASS, Common on the plains and mesas, 5100-6000 ft. (Daniels, 486). NEBRASKA to COLORADO; Kansas to TEXAS. 29. SORGHASTRUM Nash. INDIAN Grass. 4o. §. nutans (L.) Nash [Chrysopogon nutans (L.) Benth.]. NoppincG INDIAN GRASS. Frequent on the plains and mesas, 5100-6000 ft. (Daniels, 655). ONTARIO to MANITOBA; FLORIDA to ARIZONA. 30. SYNTHERISMA Walt. Crap GrAss. 41. §. sanguinale (L.) Dulac. [Panicum sanguinale L.]. FINGER GRASS. Along roadsides, and in yards and fields, still uncommon, 5300-5700 ft. (Daniels). Op Wor Lp, thence to the NEw. 31. PANICUM L. Panic-crAss. 42. P. capillare L. WutTcH GRASS. Along roads and railroads, and in yards and fields, appear- ing as if introduced, 5100-6500 ft. (Daniels, 586). 58 UNIVERSITY OF MISSOURI STUDIES [206 A form, undoubtedly native, with somewhat narrower leaves, slenderer stems, which are branched from the root, the sheaths less hairy and less prominently papillose, the spikelets acute and greenish, or the uppermost purplish, occurs in swales in the plains region, 5100-5500 ft. (Daniels, 985). An analogous, or perhaps identical form, gathered by P. A. Rydberg in the sand-hills of Nebraska, is referred by him (somewhat doubtfully) to P. capillare agreste Gatt. with the remark that the form is named var. occidentale in the National Herbarium with no published description (Rydberg U. S. Nat. Herb. Cont. 3, 186). Throughout SouTHERN CANADA and the Unirep States. 43. P.virgatum L. Tat switcH GRAss. Frequent on the plains and mesas, 5100-6000 ft. (Daniels, 397). Marne to AssINIBoIA; FLORIDA to ARIZONA. 43%. BP. Tennesseense Ashe. TENNESSEE PANIC-GRASS. Collected by Jones at South Boulder (Hitchcock and Chase). Marne to Mrnnesora and UTAH; GeorciA to ARIZONA. 44. P. Scribnerianum Nash [P. scoparium Auct., not Lam.]. SCRIBNER’S PANIC-GRASS. Common among rocks on the foot-hills, but occurring oc- casionally on the mesas and plains, 5400-7000 ft. (Daniels, gg). Maine to BritisH CoLumBIA; VIRGINIA to ARIZONA and OREGON. 32. ECHINOCHLOA Beauv. BARNYARD GRASS. 45. E. Crus-galli (L.) Beauv. [Panicum Crus-galli L.]. COCKSPUR GRASS. Common in waste places and along irrigation ditches, 5100-6000 ft. (Daniels, 741). Europe, thence to NortH AMERICA. 45a. HE. Crus-galli mutica (Vasey) Rydb. With the type (Daniels, 997). Range of the type. 207] FLORA OF BOULDER, COLORADO 59 33. CHAETOCHLOA Scribn. Foxratt. 46. C. glauca (L.) Scribn. [Setaria glauca (L.) Beauv.]. YELLOW FOXTAIL. Along streets and waste places, 5100-5700 ft. (Daniels, 773): Europe, thence to NortH AMERICA. 47. (. viridis (L.) Scribn. [S. viridis (L.) Beauv.]. GREEN FOXTAIL. With the preceding, but far more common, 5100-6000 ft. (Daniels, 507). Europe, thence to NortH AMERICA. 48. C. Italica (L.) Scribn. [S. Italica (L.) Kunth.]. Irartan MILLET. Escaped to roads and waste places, 5100-5700 ft. (Daniels): The OLp Wor Lp, thence to the New. 34. CENCHRUS L. Bur-crass. 49. C€. Carolinianus Walt. [C. tribuloides Auct., not L.]. SAND-BUR. Along railroads and on the sandy shores of streams, 5 100- 6500 ft. (Daniels, 776). Marne to MInnESoTA; FLorIDA to TEXAS and CoLoRApbo. 35. HOMALOCENCHRUS Mieg. CatTcH-FLY GRASS. 50. H. oryzoides (L.) Poll. [Leersia oryzoides (L.) Sw.]. RICE CUT-GRASS. Swales, streams, and irrigation ditches, 5100-6000 ft. (Dan- iels, 786). Nova Scotia to WasHINGTON; FLORIDA to CALIFORNIA: Europe: ASIA. 36. PHALARIS L. CANARY-GRASS. 51. P. arundinacea L. RreeD CANARY-GRASS. Swales and wet meadows near Boulder lake, 5300 ft. (Daniels, 732). Temperate NortH AMERICA: Europe: ASIA. 60 UNIVERSITY OF MISSOURI STUDIES [208 3614. HIEROCHLOE Gmel. Hoty crass. 51%. H. odorata (L.) R. and S. [Savastana odorata (L.) Scribn; H. borealis R. and S.] SWEET HOLY GRASS. Redrock lake, to100 ft. (Ramaley & Robbins). Laprapor to ALASKA; NEw JeERSEY to ARIZONA; EUROPE: ASIA. 3¢. ARISTIDA L. TripLe-AWNED GRASS. 52. A. fasciculata Torr. BusHy POVERTY-GRASS. In the plains, scarce, 5100-5700 ft. (Daniels, 777). Kansas to CatirorniA; Texas to MExico. 53. A. longiseta Steud. LoNnc-AWNED POVERTY-GRASS. Abundant on the plains, mesas and foothills, 5100-8500 ft. (Daniels, 300). Also on the mountains between Sunshine and Ward (Rydberg). ILLtnoIs to WASHINGTON; TExAs to MExIco. 38. STIPA L. Porcupine GRASS. 54. §S. comata Trin. & Rupr. WESTERN PORCUPINE GRASS. Common on the plains and foothills, 5100-8500 ft. (Dan- iels, 197). ALBERTA to ALaskA; NEw MExico to CaLiFornia. 55. 8. viridula Trin. [S. parviflora Americana Schultes]. GREENISH PORCUPINE GRASS. Common on the plains, mesas, and foothills, 5100-8500 ft. (Daniels, 301). Also at Gato (Rydberg). SASKATCHEWAN to Montana; Kansas to Uran. 56. SS. Nelsonii Scribn. NELSON’S PORCUPINE GRASS. On the mesas, foothills, and mountain sides, 5700-10000 ft. (Daniels, 365). AssInrpo1A to IDAHO and CoLorapbo. 57. 8. Scribneri Vasey. SCRIBNER’S PORCUPINE GRASS. On the plains, mesas, foothills and mountainsides, 5100- g500 ft. (Daniels, 749). CoLorapo to New Mexico. 209] FLORA OF BOULDER, COLORADO 61 58. S. Lettermannii Vasey. LrTTERMANN’S PORCUPINE GRASS. Barren hilltops east of the Flat-irons, 5800 ft. (Daniels, 184). Wyominec to IpaHo; CoLorapo to UTAH. 39. ORYZOPSIS Michx. MounrTaAIN RICE. 59. 0. micrantha (Trin. & Rupr.) Thurber. SMatLi-FLow- ERED MOUNTAIN RICE. ; Rocky soil on the mesas and foothills, 5700-8500 ft. (Dan- iels, 260). ASSINIBOIA to Montana; NEBRASKA to ARIZONA. 40. ERIOCOMA Nutt. 60. E. cuspidata Nutt. [Oryzopsis cuspidata (Nutt.) Benth.]. SILKY MOUNTAIN RICE. Barren mesa near entrance to Bear Cafion, 5800-6000 ft. (Daniels, 765). SASKATCHEWAN to WASHINGTON; TExas and Mexico to CALIFORNIA. 41. MUHLENBERGIA Schreb. Drop-sEED GRASS. 61. M. racemosa (Michx.) B. S. P. [M. glomerata Trin.]. MARSH DROP-SEED GRASS. Cafion on Green Mt.; subalpine meadows at Eldora, 6000-10000 ft. (Daniels, 526). NEWFOUNDLAND to British CoLumBia; NEw JERSEY to New Mexico. 62. M. cuspidata (Torr.) Rydb. [Sporobolus cuspidatus (Torr.) Woods]. PRAIRIE RUSH-GRASS. Dry ledges, Gregory Cafion, 6000 ft. (Daniels, 371). Manirospa to ALBERTA; Missouri to COLORADO. 63. M. Richardsoni (Trin.) Rydb. [Vilfa Richardsomi Trin.; Sporobolus depauperatus Coulter in part]. Ricu- ARDSON’S RUSH-GRASS. Subalpine meadows and open bogs, Eldora, 8600 ft. (Dan- iels, 840). Anticosti to British CoLtumpia; NEw Mexico to Catti- FORNIA. 62 UNIVERSITY OF MISSOURI STUDIES [210 64. M. simplex (Scribn.) Rydb. [Sporobolus simplex Scribn.]}. SIMPLE RUSH-GRASS. In shallow water, aspen bogs about Glacier Lake, gooo ft. (Daniels, 708). Also mountains between Sunshine and Ward, (Rydberg). NEBRASKA to WyominG and New Mexico. 65. M. filiformis (Thurber) Rydb. [Vilfa depauperata fili- formis Thurber]. FILiFORM RUSH-GRASS. Subalpine bogs, Eldora, 8600 ft. (Daniels, 366). Wyominc to OREGON; COLORADO to CALIFORNIA. 66. M. gracilis Trin. SLENDER DROP-SEED. Summits of crags on the foot-hills, thence to subalpine mountain-ridges, the most characteristic grass of such places, 6000-10000 ft. (Daniels, 208). CoLoRAbDO to CALIFORNIA; TExas to MExico. 42. LYCURUS H. B. K. 67. UL. phleoides H. B. K. Fatse tTImMotHy. Meadow Park, 6500 ft. (Rydberg). Cotorapo and TrExas to ARIZONA and Mexico. 43. PHLEUM L. Timorny. 68. P. pratense L. CoMMON TIMOTHY. Throughout the area of cultivation, but has penetrat- ed distant cafions, 5100-11000 ft. (Daniels, 504). Temperate OLp Wor Lp, thence to all temperate lands. 69. P. alpinum L. Mountain TIMOTHY. Subalpine meadows from Glacier Lake to Eldora; above timber-line, Arapahoe Peak, 8500-12000 ft. (Daniels, 632). Circumboreal and alpine, Europe: Asta: NortH AMERICA. 44, ALOPECURUS L. Foxrait. 70. A. aristulatus Michx. [d. fulvus J. E. Smith]. Swamr FOXTAIL. Along irrigation ditches and at the margins of ponds and puddles, 5100-5600 ft. (Daniels, 246). MaINneE to ALASKA; PENNSYLVANIA to CALIFORNIA. 2it]| FLORA OF BOULDER, COLORADO 63 7i. A. oceidentalis Scribn. [A. alpinus Coulter, not L.]. WESTERN FOXTAIL. Above timber-line, Arapahoe Peak, 11000-11500 ft. (Dan- iels, 942). i ALBERTA to BriTIsH CoLumsBia; CoLorapo to Uran. 45. SPOROBOLUS R. Br. Dropserep. 72, §. airoides Torr. HArr-GRASS DROPSEED. Alkaline flats about Boulder lake, scarce, 5300 ft. (Dan- iels, 731). NEBRASKA and TExas to CALIFORNIA. 73. SS. cryptandrus (Torr.) Gray. SAND DROPSEED. Common on the plains, mesas, and grassy slopes of the foothills, 5100-8000 ft. (Daniels, 513). MASSACHUSETTS to WASHINGTON; PENNSYLVANIA to ARIZONA and Mexico. 74. §. heterolepis Gray. NORTHERN DROPSEED. Common along the railroad between Boulder and Mar- shall, 5400 ft. (Daniels, 518). QUEBEC to SASKATCHEWAN; PENNSYLVANIA to COLORADO. 75. . asperifolius (Nees & Meyen) Thurber. RoucH prop- SEED. Common on the plains, 5100-5600 ft. (Daniels, 493). ASSINIBOIA to BriTISH CoLumBiA; Missouri and TExAs to CALIFORNIA. 46. POLYPOGON Desf. BEARD-GRASS. 76. BP. Monspeliensis (L.) Desf. DitcH FOXTAIL. Common along irrigation ditches east of Boulder, 5100- 5500 ft. (Daniels, 676). Europe and Asia, thence to NoRTH AMERICA. 47. CINNA L. Woop REED-GRASS. 77. C. latifolia (Trev.) Griseb. [C. pendula Trin.]. SLENDER WOOD REED-GRASS. Deep cafions in shade, frequent; in aspen bogs at Glacier lake and Eldora, 5700-8600 ft. (Daniels, 987). 64 UNIVERSITY OF MISSOURI STUDIES [212 NEWFOUNDLAND to British CoLtumspiA; NoRTH CAROLINA to Urau: Europe, 48. AGROSTIS L. Bernt-crass. 78. A.alba L. WHITE BENT-GRASS. REeED-TOP. Common about ditches and swales throughout the culti- vated area, and already penetrating remote cafions, where the smaller forms are quite possibly native. The larger cultivated form is A. alba vulgaris (With.) Thurber, 5100- 8600 ft. (Daniels, 689). Mostly naturalized from Europe, and now in all temper- ate lands; there are indigenous boreal and alpine forms in NortH AMERICA. 79. A. asperifolia Trin. [A. exarata Coult. in part, not Trin.]. HARSH BENT-GRASS. Moist meadows throughout, 5100-10500 ft. (Daniels, 376) Manirospa and New Mexico to CALiFoRNIA. 791%. A. Rossae Vasey [A. varians Trin.]. Miss Ross’s BenT- GRASS. Long’s Peak (Holm). BritisH CotumBiIA to CoLorapo and CALIFORNIA. 80. A. hyemalis (Walt.) B. S. P. [A. scabra Willd.]. Hatr- GRASS. Common throughout in both dry and moist soil, 5100- t1000 ft. (Daniels, 374). Also on the mountains between Sunshine and Ward (Rydberg). NortH AMERICA, except the extreme north. 80%. A. tenuiculmis Nash [A. ¢enwzs Vasey]. THIN BENT- GRASS. Redrock lake, roroo ft. (Ramaley and Robbins). Montana to WASHINGTON; COLORADO to CALIFORNIA. 49. CALAMAGROSTIS Adans. ReEeEp-cRAsS. 8r. C. purpurascens R. Br.- [Deyeuxria sylvatica Vasey, not DC.]. PURPLE BLUE-JOINT. Barren ridges in the foothills and mountains, common, 6000-12500 ft. (Daniels, 700). Long’s Peak (Holm). GREENLAND to ALASKA; COLORADO to CALIFORNIA. 213] FLORA OF BOULDER, COLORADO 65 82. C. Canadensis (Michx.) Beauv. [Deyeuxia Canadensis (Michx.) Munro]. CANADA BLUE-JOINT. Along streams in the plains; also in deep cafions and aspen bogs in the foothills and mountains, 5100-11000 ft. (Daniels, 649). Lasprapor to British CoLumpra; NorTH CAROLINA to ‘ CALIFORNIA. 50. DESCHAMPSIA Beauv. Hair-crass. 83. D. caespitosa (L.) Beauv. TUurrepD HAIR-GRASS. Wet margins of Glacier lake, often in water of some depth, 9000 ft. (Daniels, 617). Redrock lake, ro100 ft. (Ram- aley and Robbins). NEWFOUNDLAND to ALASKA; NEW JERSEY to CALIFORNIA. 51. TRISETUM Pers. Fatser oat. 84. T. spicatum (L.) Richter [7. subspicatum molle Gray]. NARROW FALSE OAT. Mountainsides at Ward, Bloomerville, Glacier Lake, and Eldora, 8600-13000 ft. (Daniels, 330). GREENLAND to ALaska; NEw HAmpsHIRE to COLORADO and CaLiFORNIA: EuROopE: ASIA. 85. T.majus (Vasey) Rydb. [Z. subspicatwin majus Vasey |. LARGER FALSE OAT. Arapahoe Peak above timberline, 11000-12000 ft. (Daniels, 988). Montana to British CoLumBIA; COLORADO to UTau. 86. T. montanum Vasey. MouNTAIN FALSE OAT. Deep cafions and aspen bogs, local, 7000 (Bear Cafion) -10000 ft. (Daniels, 631). Wyominc to New Mexico. 52. AVENAL. Oar. 87. A. striata Michx. PURPLE OAT. Rare in deep canons and aspen bogs, usually with the preceding; Bear Caton; Eldora, 7000-11000 ft. (Daniels, 665). New Brunswick to British CoLuMBIA; PENNSYLVANIA to COLORADO. 66 UNIVERSITY OF MISSOURI STUDIES [214 88. A. fatua L. WIzp oat. Common along streets and waste places in the city of Boulder, 5300-5700 ft. (Daniels, 387). Europe: Asia, thence to NorTH AMERICA. 89. A. sativa L. Common oat. Adventitious along railroads, 5300-5400 ft. (Daniels, 479). Op WorLD, thence universal in cultivation. 53. MERATHREPTA Raf. WHI OAT-GRASS. go. M. Californica (Bolander) Piper [Danthonia Calfornica Bolander]. CALIFORNIA WILD OAT-GRASS. Arapahoe Pass, 12000 ft. (Rydberg). Montana to BritisH CoLUMBIA ; COLORADO to CALIFORNIA. gt. M. intermedia (Vasey) Piper [Danthonia intermedia Vasey]. INTERMEDIATE WILD OAT-GRASS. Aspen bogs at Glacier Lake and Eldora, 8600-11500 ft. (Daniels, 621). ALBERTA to BRITISH COLUMBIA; COLORADO to CALIFORNIA. 92. M. spicata (L) Raf. [Danthonia spicata (L) Beauv.]. COMMON WILD OAT-GRASS. Common on dry slopes in the foothills, 6000-8000 ft. (Dan- iels, 370). Also mesas at foot of the Flat-irons. NEWFOUNDLAND to British CoLtumBpia; NortTH CaroLina to Louisiana and CALIFORNIA. 54. SPARTINA Schreb. Corp-Gcrass. 93. S. cynosuroides (L.) Willd. Tati MARSH GRASS. FRESH- WATER CORD-GRASS. Swales and bogs in the plains, infrequent, 5100-5500 ft. (Daniels, 522). Nova Scotia to Mackenzie; NEw JERSEY to TExas and COLORADO. 55. SCHEDONNARDUS Steud. Crazs-crass. 94. S. paniculatus (Nutt.) Trelease [S. Texanus Steud.]. WILD CRAB-GRASS. Frequent on the plains and mesas, 5100-6000 ft. (Daniels, 175). 215] FLORA OF BOULDER, COLORADO 67 Manitopa to AssInipoiA; ILLINoIs to TExas and NEw Mexico. 56. BOUTELOUA Lag. Grama-crass. MESQUIT-GRASS. g5. B. hirsuta Lag. Harry MEsQuirt. Dry plains and mesas, less common than the next, 5100- 6000 ft. (Daniels, 956). Also at Meadow Park, 6500 ft. (Rydberg). ILLiInoIs to SourH Daxora; Texas to ARIZONA. 96. B. oligostachya (Nutt.) Torr. ComMoN GRAMA-GRASS, Or MESQUIT-GRASS. Common on the plains and mesas; occasional on the foot- hills, 5100-8000 ft. (Daniels, 220). One of the most charac- teristic grasses of the Great Plains. Wisconsin to ASSINIBOIA; Mississippr1 to ARIZONA and MEXxIco. 57. ATHEROPOGON Muhl. Tati mesourr. 97. A. curtipendulus (Michx.) Fourn [Boutelowa racemosa Lag.]. PRAIRIE GRAMA-GRASS. Frequent on the plains, mesas and foothills, 5100-7000 ft. (Daniels, 299). Meadow Park (Rydberg). Onrario and Micuican to Manirosa; NEw JERSEY to TEx- AS, ARIZONA, and Mexico. 58. BULBILIS Raf. Burrato crass. 98. B. dactyloides (Nutt.) Raf. [Buchloe dactyloides (Nutt.) Eng.]. COMMON BUFFALO GRASS. Abundant on the plains and mesas, 5100-6000 ft. (Daniels, 198). Minnesota to NortH Daxota; ArKANSAS to NEw Mexico and Mexico. 59. PHRAGMITES Trin. Reep. 99. P. Phragmites (L.) Karst. [P. communis Trin.]. Com- MON REED. About a spring at foot of Flagstaff Hill, only three or four plants, 6000 ft. (Daniels, 834). Europe: ASIA: temperate NorTH AMERICA. 68 UNIVERSITY OF MISSOURI STUDIES [216 60. MUNROA Torr. FALSE BUFFALO GRASS. too. M. squarrosa (Nutt.) Torr. Muwnro’s crass. Dry plains and mesas, 5100-6000 ft. (Daniels, 359). Also at Lafayette (Rydberg). Nort Dakota to ASSINIBOIA; TEXAS to ARIZONA. 61. KOELERIA Pers. 1o1. Koeleria cristata (L.) Pers. [K. mitida Nutt., as to some of the forms]. PRAIRIE-GRASS. Throughout below 10000 ft., but especially common on the foothills, 5100-10000 ft. (Daniels, 133). Ontario to British CoLtuMBIA; PENNSYLVANIA to CALI- FORNIA. 62. ERAGROSTIS Beauv. STINK-GRASS. io2. E.major Host. SKUNK GRASS. Waste places and along railroads, 5100-6000 ft. (Daniels, 588). Also at Longmont (Rydberg). Europe, thence to NORTH AMERICA. 103. E. pectinacea (Michx.) Steud. PURPLE STINK-GRASS. Meadow Park, 6500 ft. (Rydberg). MassacHusetrs to SourH Dakota: FLoripA to TExAs and CoLoRADo. 68. EATONIA Raf. Eaton Grass. 104. E. robusta (Vasey) Rydb. [E. obtusata robusta Vasey]. Stout EATON GRASS. Along streams and springy cafions, 5100-7000 ft. (Daniels, 416). NEBRASKA to WasHINGTON; NEw Mexico to ARIZONA. 105. E. cbtusata (Michx.) Gray. BLunt-scatep EATON GRASS. About Boulder, 5100-6000 ft. (Rydberg). MassACHUSETTS to MONTANA; FLORIDA to ARIZONA. 106. E. Pennsylvanica (DC.) Gray. PENNSyLvVANIA EATON GRASS. Deep mountain cafions, 5600-7000 ft. (Daniels, 718). 217] FLORA OF BOULDER, COLORADO 69 New Brunswick to British CoLuMBIA; GEORGIA to CoLo- RADO. 64. MELICA L. Metic-crass. 107. M. bella Piper [M. bulbosa Geyer]. BuLsBous MELIc- GRASS. North slopes of Flagstaff Hill along Boulder Cafion, 6000-7000 ft. (Daniels, 144). Spikelets often monstrous. Monrana to WASHINGTON; CoLoRADO and UraH to OREGON. 65. DACTYLIS L. OrcHARD GRASS. 108. D. glomerata L. CoMMON ORCHARD GRASS. Throughout the whole cultivated district and penetrating into shady cafions; 5100-go00 ft. (Daniels, 235). Europe, thence to NorTH AMERICA. 66. DISTICHLIS Raf. Satt-crass. 1og. D. stricta (Torr.) Rydb. [D. maritima stricta (Torr.) Thurber]. Mars SPIKE-GRASS. Alkali flats about Boulder lake, 5300 ft. (Daniels, 728). SASKATCHEWAN to WasHincton; Missouri to TExas and CALIFORNIA. 67. POA L. Merapow-ecrass. 110. P. annua L. Low SPEAR-GRASS. Roadsides and at the entrance to Gregory Cafion, 5100- 6000 ft. (Daniels, 250). Europe and Asia, thence to NortTH AMERICA. 111. P. pratensis L. KrNTUCKY BLUE-GRASS. Meadows throughout, 5100-11500 ft. (Daniels, 558). Prob- ably naturalized in the irrigated district. Europe: Asta: NortH America, but only the boreal and alpine forms native. 112. P. trivialis L. RouGH MEADOW-GRASS. About ponds and ditches, 5400-5500 ft. (Daniels, 245). Not in Rydberg’s Flora. Europe, thence naturalized in many places in the UniTED STATES. 70 UNIVERSITY OF MISSOURI STUDIES [218 112%. P. cenisia All. [P. flexuosa Wahl.]. FLEexuous MEADOW-GRASS. Long’s Peak (Holm). GREENLAND to ALASKA; COLORADO. 113. P. callichroa Rydb. FAIR-HUED MEADOW-GRASS. Mountain-sides at Eldora, 8600-11500 ft. (Daniels, 647). CoLoRAbo. 114. P. reflexa V.& S. REFLEXED MEADOW-GRASS. In mountain meadows descending to the slopes of the foothills, 6400 (Flagstaff Hill) -13000 ft. (Daniels, 952). Montana to New Mexico and OrEGoNn. 115. P. leptocoma Trin. SMooTH-GLUMED MEADOW-GRASS. In mountain meadows with the preceding, 6300 (Flagstaff Hill) -12500 ft. (Daniels, 225). Monrana to ALASKA; COLORADO to CALIFORNIA. 116. P. alpicola Nash [P. Jara Thurber]. Mountain MEADOW-GRASS. Above timberline, Arapahoe Peak, 11500-13000 ft. (Daniels, 941). Also on Long’s Peak (Rydberg). CoLorAbDOo to UTAH; CALIFORNIA. 117. P. platyphylla Nash & Rydb. [P. occidentalis Vasey]. WESTERN MEADOW-GRASS. Along mountain streams, 5600 (Boulder Cafion) -10500 ft. (Daniels, 150). Cortorapo to NEw Mexico. 118. P. compressa L. ENGLISH BLUE-GRASS. Common throughout the irrigated district, but not noticed in the mountains, 5100-6000 ft. (Daniels, 242). Europe, thence to NortH AMERICA. 119. P. triflora Gilib. [P. serotina Ehr.]. Fowt MEADOW- GRASS. Common in swales and wet meadows, 5100-8600 (Eldora) ft. (Daniels, 482). NEWFOUNDLAND to BririsH CoLumBia; NEw JERSEY to CALIFORNIA: EUROPE. 2 19] FLORA OF BOULDER, COLORADO 7 i 120. P. interior Rydb. INLAND MEADOW-GRASS. Along streams and in wet meadows, 5100-10000 ft. (Dan- iels, 28). MACKENZIE to WasHINGTON and NEw Mexico. 121. P. crocata. Michx. [P. caesia strictior Gray]. Woop MEADOW-GRASS. High mesas, dry slopes of the foothills, and mountain ridges, 6000-13000 ft. (Daniels, 154). Mountains between Sunshine and Ward (Rydberg). LABRADOR to ALASKA; MassACHUSETTS to MINNESOTA and ARIZONA. 122. P. rupicola Nash [P. rupestris Vasey]. CRAG MEAD- OW-GRASS. Dry tundras above timberline, Arapahoe Peak, 11500- 13000 ft. (Daniels, 1010). Montana to OREGON; COLORADO to UTAH. 123. P. Pattersonii Vasey. PATTERSON’S MEADOW-GRASS. Above timberline, Arapahoe Peak, 11000-13000 ft. (Dan- iels, 895). CoLoRADO to ARIZONA. 124. P. alpina L. ALPINE MEADOW-GRASS. Above timberline, Arapahoe Peak, 11000-13000 ft. (Dan- iels, 935). Long’s Peak (Holm). GREENLAND to ALASKA; QUEBEC to UTAH. 124%. P. Wheeleri Vasey. [P. cuspidata Vasey]. WHEEL- ER’S MEADOW-GRASS. Redrock lake, 10100 ft. (Ramaley and Robbins). Montana to IDAHO; CoLorRADO to OREGON. 125. P. Vaseyana Scribn. VASEY’S MEADOW-GRASS. Subalpine meadows at Eldora, 8600-10000 ft. (Daniels, 868). COLORADO. 72 UNIVERSITY OF MISSOURI STUDIES [220 120. P. longiligula Scribn. & Will. LOoNnG-LIGULATE MEAD- OW-GRASS. Boulder (E. Bethel), determined by P. L. Ricker of U.S. Dept. of Agric., and recorded (as host of a fungus) by Ar- thur in Journal of Mycology, Jan. 1908, p. 13. SoutH DaxoTa to OrEGoN; New Mexico to CALIFornia. 127. P. pseudopratensis Scribn. & Rydb. Fatse Kentucky BLUE-GRASS. About swales and streams in tne plains and mesas, 5100- 6000 ft. (Daniels, 953). SoutH Dakota to NEBRASKA and CoLoRADO. 128. P. longipedunculata Scribn. LoNG-PEDUNCULATE MEAD- OW-GRASS. Plains and mountain-cafions, 5100-12500 ft. (Daniels, 503). Wyominc to New Mexico. 129. P. juncifolia Scribn. RUSH-LEAVED MEADOW-GRASS. Common on the plains and mesas, 5100-6000 ft. (Daniels, 905). WyomiInG to CoLorapbo and Urau. 130. P. confusa Rydb. BUNCH MEADOW-GRASS. Dry plains, mesas, and mountainsides, 5100-10000 ft. (Daniels, 924). NEBRASKA to Montana and CoLorapo. 131. P. pratericola Rydb. & Nash [P. andina Nutt.]. Pratrie MEADOW-GRASS. Near Long’s Peak (Porter & Coulter). NEBRASKA to WyomInG and CoLorapbo. 68. PANICULARIA Fabr. MANNA-GRASS. 132. P. nervata (Willd.) Kuntze [Glyceria nervata ( Willd.) Trin.]. NERVED MANNA-GRASS. About streams and ditches, in swales and at the margins of lakes and ponds, 5100-9000 ft. (Daniels, 264). LaBprRADoR to British CoLumpBia; FLoripa to Mexico and CALIFORNIA. 221] FLORA OF BOULDER, COLORADO 8 133. P. Americana (Torr.) Mac M. [Glyceria grandis Wats.]. REED MEADOW-GRASS. In swales and along streams, less common than the pre- ceding, 5100-8600 ft. (Daniels, 969). New Brunswick to ALASKA; TENNESSEE to NEVADA. 134. P. Holmii Beal. Hotm’s MANNA-GRASS. Deep cafions on north slope of Green Mountain, 7000- 8100 ft. (Daniels, 464). Lamb’s Ranch, Long’s Peak, g100 ft. (Beal). COLORADO. 135. 2. borealis Nash. NorTHERN FLOATING MANNA. In irrigation ditches about Boulder; also floating in Glacier lake, 5100-9000 ft. (Daniels, 739). MaInE to ALASKA; NEw York to CALIFORNIA. 69. PUCCINELLIA Parl. SALT MEADOW-GRASS. 136. P. airoides (Nutt.) Wats. & Coult. SLENDER SALT MEADOW-GRASS. Along water-courses in the mesas, and in alkaline soil on the plains, 5100-6000 ft. (Daniels, 383). Also at Longmont (Rydberg). Maniropa to MACKENZIE and British CoLtumpia; Kansas to NEVADA. 70. FESTUCA L. FeEscue-crass. 137. F. octoflora Walt. [F. tenella Willd.]. SLENDER FESCUE- GRASS. Abundant on the plains and arid open mountain slopes, 5100-goo0 ft. (Daniels, 181). QUEBEC to BritisH CoLumpra; FLoRIDA to CALIFORNIA. 138. F. elatior L. [F. elatior pratensis (Huds.) Gray]. MEADOW FESCUE. Common throughout the irrigated area, especially along ditches, 5100-6000 ft. (Daniels, 785). Europe, thence to temperate NortH AMERICA. 74 UNIVERSITY OF MISSOURI STUDIES [222 139. F. rubra L. RED FESCUE. Subalpine meadows at Glacier Lake, gooo ft. (Daniels, 699). LaBRApDoR to ALasKA; NORTH CAROLINA to CALIFORNIA: Europe: ASIA. 140. F. brachyphylla Schultes [F. ovina brevifolia S. Wat- son]. SHORT-LEAVED FESCUE. Bald ridges in the mountain region, 7000 (Green Mt.) -14500 ft. (Daniels, 364). GREENLAND to ALASKA; VERMONT to CALIFORNIA. 141. F. minutiflora Rydb. SMALL-FLOWERED FESCUE. Mountainsides at Eldora, and on Arapahoe Peak above timberline, 8600-12000 ft. (Daniels, 1oor). COLORADO to CALIFORNIA. 141%. F.ovinaL. SHEEP FESCUE. Redrock lake, 10100 it. (Ramaley and Robbins). Long’s Peak (Holm). NortH AMERICA: EUROPE. 141%a. F. ovina supina (Schur). Hack. Prostrate FESCUE. Long’s Peak (Holm). GREENLAND and British CotumeB1a to NEw HAMPSHIRE, ARIZONA, and CALIFORNIA. 142. F. ingrata nudata (Vasey) Rydb. [F. ovina nudata Vasey]. NAKED-STEMMED FESCUE, BLUE BUNCH-GRASS. Common throughout the mountain region and the mesas, 5700-12000 ft. (Daniels, 174). The type doubtless occurs, but all the material preserved belongs to the variety. Montana to BritisH CoLumBiA; CoLorapo to Urau. 143. F. Kingii (S. Watson) Scribn. [F. confinis Vasey]. KINnG’s FESCUE. Boulder Cafion, 6500-10000 ft. (Rydberg); Boulder (E. Bethel). Montana to COLORADO and CALIFORNIA. 71. BROMUS L. Brome-crass. 144. B. marginatus latior Shear. LARGE MARGINATE BROME. Vicinity of Boulder, 5100-6000 ft. (Rydberg). ALBERTA to BRITISH CoLUMBIA; COLORADO to CALIFORNIA. 223] FLORA OF BOULDER, COLORADO 75 145. 3B. brizaeformis F. & M. QUAKE-GRASS BROME. The commonest ruderal grass about Boulder, and fast spreading throughout the plains district, 5100-6000 ft. (Daniels, 257). Europe and Asta, thence to the UNITED STATES. 146. B. secalinus L. ComMMON CHESS, or CHEAT. In fields and waste places, 5100-6000 ft. (Daniels, 388). Europe and Asta, thence to all temperate lands. 147. B. hordeaceus L. [B. mollis L.]. Sort cHEss. Along the railroad between Boulder and Marshall, 5400 ft. (Daniels, 524). Europe, thence to the UNITED STATEs. 148. B. lanatipes (Shear) Rydb. [B. Porteri lanatipes Shear]. LanaTE BROME. Common on the mesas, foothills, and mountain slopes, less frequent in the plains, 5100-goo00 ft. (Daniels, 346). Also at Lafayette (Rydberg). COLORADO. 149. B. Richardsonii Link. RIcHARDSON’S BROME. Common on the mesas, foothills, and mountains, 6000- 11000 ft. (Daniels, 454). SASKATCHEWAN to BritisH CoLumBIA; COLORADO to ARIZO- NA and OREGON. 150. B. Pumpellianus Scribn. PUMPELLY’S BROME. Frequent throughout, 5100-10000 ft. (Daniels, 382). SASKATCHEWAN to ALASKA and NEw Mexico. 151. B. tectorum L. THatcH CHEAT. Waste places about Boulder, 5100-6000 ft. (Daniels, 496). Also at Longmont (Rydberg). Europe, thence to the UNITED STATES. 72. LOLIUM L. Darnet. 152. LL. Italicum A. Br. ITALIAN RYE GRASS. About irrigation ditches in the city of Boulder, 5300- 5600 ft. (Daniels, $39). Not in Rydberg’s Flora. Europe, thence to the UNITED SraTEs. 76 UNIVERSITY OF MISSOURI STUDIES [224 78. AGROPYRON Gaertn. WHEAT GRASS. 153. A. Scribneri Vasey. ScRIBNER’S WHEAT GRASS. Long’s Peak (Holm). Montana to CoLorapo and ARIZONA. 15344. A.spicatum inerme (Scribn. & Sm.) Heller [4, Vaseyi S.&S.]. VaAsEy’s WHEAT GRASS. Frequent on the mesas and foothills, 5700-7000 ft. (Daniels, 171). MontTaANA to OREGON; COLORADO to UTAH. 154. A. Arizonicum S. & S. ARIZONA WHEAT GRASS. Mountains between Sunshine and Ward, 8000-11000 ft. (Rydberg). CoLorapo to ARIZONA and Mexico. 155. A. Richardsonii (Trin.) Schrad. [A. unilaterale Cas- sidy]. R1cHARDSON’S WHEAT GRASS. Mountain meadows, rather local, 7000 (Bear Cafion)-10000 ft. (Daniels, 830). Minnesora to BritisH CoLumspia; Iowa to COLORADO. 156. A. andinum (S. & S.) Rydb. [4. violaceum andinum S. & S.J. Mounrarn WHEAT GRASS. Mountainsides at Eldora 8600-9000 ft. (Daniels, 640). Montana to COLORADO. 157. A. violaceum (Hornem.) Vasey. VIOLET WHEAT GRASS. Common on the foothills and mountains, 6300 (GreenMt.) —12000 ft. (Daniels, 362). GREENLAND to ALAaskKA; NEw HampsuireE to UTAH. 158. A. tenerum Vasey. SLENDER WHEAT GRASS. Common on the plains, foothills, and lower mountain slopes, 5100-7500 ft. (Daniels, 395). LaBRADOR to ALASKA; NEW HAMPSHIRE to COLORADO. 159. A. pseudorepens S. & S. FALSE QUACK GRASS. Common on the plains and in mountain meadows, 5100- 10000 ft. (Daniels, 511). Iowa to ALBERTA; NEw Mexico to UTauH. 225] FLORA OF BOULDER, COLORADO Wai 160. A. riparium S. & S. RIPARIAN WHEAT GRASS. About ditches in the plains, 5400-5700 ft. (Daniels, 398). Montana to CoLorapo. 161. A. occidentale Scribn. WESTERN WHEAT GRASS. On the plains, where it is very abundant; also sparingly in mountain meadows, 5100-9500 ft. (Daniels, 402). Also at Longmont (Rydberg). MANITOBA to SASKATCHEWAN and OreEGon; Missouri to ARIZONA. 162. A.molle (S.&S.) Rydb. Sorr WHEAT GRASS. On the plains, where it is especially characteristic of alkaline flats, and in the drier mountain valleys, 5100- gooo ft. (Daniels, 978). SASKATCHEWAN to WASHINGTON and NEw Mexico. 74. TRITICUM L. Wueat. 163. T. sativum vulgare (Vill.) Hack. [T. vulgare Vill.]. WHEAT. Adventitious along the railroad between Boulder and Marshall, 5400 ft. (Daniels, 514). Op Wor Lp, thence to the NEw. 75. HORDEUM L. Bar tey. 164. H. jubatum L. SQUIRREL-TAIL GRASS. Common on the plains and in mountain cafions; a fre- quent weed in waste places, 5100-11000 ft. (Daniels, 380). Ontario to Araska; Missourr to CaLtrorniA, thence naturalized eastward. 165. H. pusillum Nutt. LirrLe BARLEY. Abundant on the plains and mesas, and following the roads into the mountain district, 5100-7000 ft. (Daniels, 203). Ontario to British CoLuMBIA; FLORIDA to CALIFORNIA. 166. H. sativum hexastichon (L.) Hack. SIx-ROWED BARLEY. Adventitious along the railroad between Boulder and Mrshall, 5400 ft. (Daniels, 480). OxLp WorLD, thence to the NEw. 78 UNIVERSITY OF MISSOURI STUDIES [226 76. SITANION Raf. BristLe GRASS. 167. S. longifolium J. G. Smith. LONG-LEAVED BRISTLE GRASS. Common on the foothills and mountain slopes, 6000-9000 ft. (Daniels, 363). NEBRASKA to NEvApDA; TExas to ARIZONA, 168. §S. brevifolium J. G. Smith. SHORT-LEAVED BRISTLE GRASS. Abundant on the plains, and frequent on open mountain slopes, 5100-10000 ft. (Daniels, 202). Also on the mountains between Sunshine and Ward (Rydberg). Wyomine to UTAH; CoLorapo to ARIZONA. 77. ELYMUS L. Lyme erass. 169. E. Canadensis L. CANADIAN WILD RYE. Common along ditches and streams both in and out of shade, 5100-7000 ft. (Daniels, 357). Nova Scotia to WASHINGTON; GEORGIA to NEw Mexico. 170. E.robustus S.& S. Srour wip RYE. In swales along railroads and on stream-banks, 5100-6000 ft. (Daniels, 489). SoutH Daxota to IpaHo; Missourt to COLORADO. 171. E. brachystachys Scribn. & Ball. SLENDER WILD RYE. Plains south of Boulder, 5400-5700 ft. (Daniels, 396). Micuican to Sour Dakota; Texas to Uran and Mexico. 172. EH. Macounii Vasey. Macoun’s WILD RYE. On the plains and in meadows on the foot-hills, 5100-7000 ft. (Daniels, 417). MAniTopa and SASKATCHEWAN to ALBERTA; NEw Mexico to UrauH. 173. E. condensatus Presl SmooTH LYME GRASS. Dry meadows throughout, 5100-10000 ft. (Daniels, 961). ALBERTA to BritisH CoLumpia; New Mexico to CAti- FORNIA. 227| FLORA OF BOULDER, COLORADO 79 174.. E. ambiguus Vasey & Scribn. AMBIGUOUS LYME GRASS. Common on the foothills and mountainsides, 5900-9000 ft. (Daniels, 158). COLORADO. 175. 4K. strigosus Rydb. STRIGOSE LYME GRASS. Common on the foothills and mountain ridges, 6000-8600 ft. (Daniels, 962). Boulder is the type locality. WyominG to CoLorabo. 176. E. villiflorus Rydb. ViLLous LYME Grass. Common on the foothills; occasional on the plains and mesas, 5100-8000 ft. (Daniels, 963). Boulder is the type locality. SoutH Daxora and the Canapran ROCKIES to COLORADO. Family 13. CYPERACEAE J. St. Hil. Galingale family. 78. CYPERUS L. GaALINGALE. 177. C. inflexus Muhl. [C. aristatus Boeckl.]. AWNED cy- PER GRASS. Scarce on the plains and foothills in moist sands, 5100- 6500 ft. (Daniels, 253). VERMONT to BritisH CoLuMBIA; FLORIDA to CALIFORNIA and Mexico. 178. C. Bushii Britt. Busu’s CYPER GRASS. In sandy soil at Meadow Park, 6500 ft. (Rydberg). WISCONSIN to OREGON; Kansas to COLORADO. 79. SCIRPUS L. BuLrusuH. 179. §. Americanus Pers. [S. pungens Vahl.]. THREE SQUARE. In swales, along ditches and streams, and at the margins of ponds and lakes, but apparently not following the streams very far into the foothills, 5100-6500 ft. (Daniels, 668). NortH AMERICA: CHILI: EUROPE. 80 UNIVERSITY OF MISSOURI STUDIES [228 180. S. lacustris L. GREAT BULRUSH. With the preceding but often in water of greater depth, and penetrating farther back into the mountains, 5100-8600 ft. (Daniels, 414). Throughout the NortH TEMPERATE ZONE. 181. §. atrovirens pallidus Britton. PALE BULRUSH. Swales, ditches and streams in the plains and mesas, and ascending but slightly into the foot-hills, 5100-6000 ft. (Daniels, 490). Minnesota to the NoRTHWEST TERRITORY and COLORADO- 80. ELEOCHARIS R. Br. Spike RUSH. 182. KE. palustris (L.) R.& S. Swamp SPIKE RUSH. Common in swamps, swales, and stagnant pools through- out, 5100-10000 ft. (Daniels, 492). Nortu AMERICA: Europe: Asta. 183. EH. glaucescens (Willd.) Schultes [E. palustris glauces- cens (Willd.) Gray]. PALE SWAMP SPIKE RUSH. Common with the above, but in shallower water, 5100-go00 (Glacier Lake, Eldora) ft. (Daniels, 733). Onrario and the UNITED STATES. 184. EK. acicularis (L.) R.& S. NEEDLE RUSH. Common in limose places throughout, 5100-i0000 ft. (Daniels, 254). Europe: Asra: NortH AMERICA: CENTRAL AMERICA. 1844. E. tenuis (Willd.) Schult. SLENDER SPIKE RUSH. Redrock lake, ro10o ft. (Ramaley and Robbins). NEWFOUNDLAND to MANITOBA; FLorIDA to CoLoRapo. 185. E. acuminata (Muhl.) Nees. FLat-steEMMED SPIKE RUSH. Ditches and swales in the plains, 5100-5600 ft. (Daniels, 734): ANTICOSTI to ALBERTA; GEORGIA to Louisiana and COLORADO. 229 | FLORA OF BOULDER, COLORADO 81 81. CAREX L. SeEncE. 186. C. canescens L. SILVERY SEDGE. Subalpine bogs at Eldora, 8500-11500 ft. (Daniels, 852). Redrock lake, 1o1co ft. (Ramaley and Robbins). NEWFOUNDLAND to BRITISH COLUMBIA; VIRGINIA to COLO- RADO and OREGON: EUROPE and Astra. 187. ©. tenella Schkuhr. Sorr-LEAVED SEDGE. Local in deep mountain cafions in shade, 6000-11500 ft. (Daniels, 610). NEWFOUNDLAND to BritisH CoLtumBia; NEW JERSEY to CALIFORNIA: EUROPE. 188. C. Deweyana Schwein. DEWEyY’s SEDGE. Only detected in Bear Cafion, where it is very rare, 6000- 7000 ft. (Daniels, 762). Nova Scotia to ManiToBA and OREGON; PENNSYLVANIA to New Mexico and Uran. 189. Carex stipata Muhl. AWtL-FRUITED SEDGE. Irrigation ditches, 5100-5600 ft. (Daniels, 237). Not in Rydberg’s Flora. NEWFOUNDLAND to British CoLumBIA; FLoripA to CaLi- FORNIA. 190. C. vulpinoidea Michx. Fox SEDGE. Irrigation ditches, 5100-5600 ft. (Daniels, 745). New Brunswick to Maniropa; FLoripa to Trxas and COLORADO. 191. C. occidentalis Bailey [C. muricata Americana Bailey]. WESTERN SEDGE. - Low meadows at Eldora, 8600-11000 ft. (Daniels, 611). CoxLorapo to New Mexico and Arizona. 192. ©. Hoodii Boott [C. muricata confixa Bailey]. Hoop’s SEDGE. Grassy meadows, Bluebell cafion, thence to the subalpine zone, 5800-10000 ft. (Daniels, 497). Montana to British CoLumBiIA; COLORADO to CALIFORNIA, 82 UNIVERSITY OF MISSOURI STUDIES [230 193. ©. marcida Boott. CLUSTERED FIELD SEDGE. Abundant in dry meadows, 5100-8600 ft. (Daniels, gs). ManitTospa to British CoLumBia; Kansas to New Mexico and Nrvapa. 194. C. Sartwellii Dewey. SaRTWELL’S SEDGE. Swales along railroads in the plains, 5100-6000 ft. (Dan- iels, 971). OnTaArIo to BritisH CoLumBiA; NEw York to Ura. 195. ©. Douglasii Boott. Doucias’ SEDGE. Common in dry soil throughout, 5100-11000 ft. (Daniels, 317). Also near Long’s Peak (Rydberg; Coulter in Wabash College Herb.). Manitospa to British CoLumpia; NEBRASKA to New MeEx- 1cO and CALIFORNIA. 196. (C. scoparia Schkuhr. Broom sEDGE. Wet meadows about ditches and streams, 5100-7000 ft. (Daniels, 266). Nova Scotra to ManiToBa; FLORIDA to CoLoRADO. 197. C. athrostachya Olney. BRACTED SEDGE. Shores of a pond south of Boulder, thence to timberline, 5500-11000 ft. (Daniels, 258). ASSINIBOIA to BRITISH COLUMBIA; COLORADO to CALIFORNIA. 198. C. festiva Dewey. PRETTY SEDGE. Abundant throughout the foothills and mountains in cafions and humid meadows, 6000-13000 ft. (Daniels, 103). ASSINIBOIA and BritisH CoLtumBia to Mexico. 199. O©.ebenea Rydb. [C. festiva Haydemana Bailey]. Esony SEDGE. In frozen ground, alpine valley near snow, above Bloom- erville, go00-10000 ft. (Daniels, 324). Also on Long’s Peak (Rydberg). ALBERTA to BRITISH CoLumBIA; COLORADO to UTAH. 200. C. petasata Dewey. WESTERN’S HARE’S-FOOT SEDGE. Deep cafions, north slope of Green Mt., 7000 ft. (Daniels, 469). ALBERTA to ALASKA; COLORADO to OREGON. 231 | FLORA OF BOULDER, COLORADO 83 2o1. C. pratensis Drej. MEADOW SEDGE. Gregory Cafion, 6000-6500 ft. (Daniels, 688). Also on Long’s Peak (Rydberg). Ontario to ALASKA; MicuiGAn to COLORADO. 202. C. siccata Dewey. DRry-SPIKED SEDGE. Common in dry meadows throughout, 5100-10000 ft. (Daniels, 972). Also near Long’s Peak (Rydberg). Ontario to British CotumBia; NEw YorK to CALIFORNIA. 203. C.straminea Willd. Srraw SEDGE. Common along watercourses and grassy meadows in the plains, mesas, and foothills, 5100-6500 ft. (Daniels, 372). New Brunswick to Manirosa; NortH CaROLina to OKLA- HOMA and COLORADO. 204. C.straminiformis Bailey. FALSE STRAW SEDGE. Dry torrents, high mesas at the foot of the Flat-irons, 5700-6000 ft. (Daniels, 381). CoLorabDo to WASHINGTON and CALIFORNIA. 205. C. festucacea Schkuhr. FESCUE SEDGE. Meadows and swales, frequent in the plains and mesas, and in meadows on the lower foothills, 5100-6400 (Flagstaff Hill) ft. (Daniels, 185). New Brunswick to MINNESOTA; FLORIDA to COLORADO. 206. (C. stenophylla Wahl. NArROW-LEAVED SEDGE. Dry mesas between Marshall and South Boulder Peak, 5700-6000 ft. (Daniels, 438). Maniroga to British Cotumsia; Iowa to CoLoRApDo. 207. C. incurva Lightf. CURVED SEDGE. Arapahoe Peak above timberline, 11000-12000 ft. (Daniels, 916). GREENLAND to ALASKA; CoLoRApO to BriTISH COLUMBIA. 208. C. alpina Stevenii Holm. STEVEN’S ALPINE SEDGE. Lamb’s ranch, near Long’s Peak, gioo ft. (Rydberg). COLORADO. 84 UNIVERSITY OF MISSOURI STUDIES [232 209. C. atrata L. BLAcK SEDGE. Long’s Peak, 11500-13000 ft. (Rydberg). LABRADOR to ALASKA; QUEBEC to CoLorapo and Catt- FORNIA. 210. ©. chalciolepis Holm. BroNzE-sCcALED SEDGE. Long’s Peak, 8500-13000 ft. (Rydberg). COLORADO. 211. ©. bella Bailey. BrautTIFUL SEDGE. Above timberline, Arapahoe Peak, 11000-12000 ft. (Dan- iels, 940). CoLorapo to UraH and Arizona, 212. €. rhomboidea Holm. RuHompBIc SEDGE. In swamps near Long’s Peak, 8500-9500 ft. (Rydberg). COLORADO. 213. ©. Goodenovii J. Gay [C. vulgaris Fries]. Common SEDGE. Subalpine bogs, Eldora, 8600-10000 ft. (Daniels, 851). NEWFOUNDLAND to ALASKA; PENNSYLVANIA to COLORADO: EUROPE. 214. C. rigida Good. [C. vulgaris alpina Booth]. Stirr SEDGE. Arapahoe Peak above timberline, 11000-12000 ft. (Dan- iels, 907). ALASKA to COLORADO. 215. ©. chimaphila Holm. WHINTER-LOVING SEDGE. Above timberline, Arapahoe Peak, 11000-12000 ft. (Dan- iels, 923). Also on Long’s Peak (Rydberg). COLORADO. 216. C. acutina Bailey. ACUTISH SEDGE. Boulder Cafion (5400-7000 ft. (Daniels, 556). Also Lamb’s ranch, near Long’s Peak, g100 ft. (Rydberg). MacKENZIE to ALASKA; COLORADO to OREGON. 217. C. stricta Lam. EREcT SEDGE. Swales along railroad between Boulder and Marshall, 5400 ft. (Daniels, 418). Not in Rydberg’s Flora. 233) FLORA OF BOULDER, COLORADO 85 Eastern UNITED States and Canapa to COLORADO and TEXAS. 21744. C. variabilis Bailey. VARIABLE SEDGE. Redrock lake, toroo ft. (Ramaley and Robbins). Montana to CoLorapo. 218. C. aurea Nutt. GOLDEN SEDGE. About springs in deep cafions, 6700-11000 ft. (Daniels, 354). NEWFOUNDLAND to BritTIsH COLUMBIA; PENNSYLVANIA to UraH and WASHINGTON. 219. C. Geyeri Boott. GEYER’S SEDGE. At edge of snow in alpine valley above Bloomerville,. gooo-10000 ft. (Daniels, 311). Montana to British CoLumpiA; COLORADO to OREGON. 220. OC. nigricans C. A. Mey. BLACKISH SEDGE. Above timberline, Arapahoe Peak, 11000-13000 ft. (Dan- iels, 926). Also Thompson’s Cafion, Long’s Peak (Rydberg). ALBERTA to ALASKA; COLORADO to CALIFORNIA: ASIA. 221. C. Pyrenaica Wahl. PyRENAIC SEDGE. Above timberline, Arapahoe Peak, 11000-14000 ft. (Dan- iels, 925). Also on Long’s Peak (Rydberg). ALBERTA to ALASKA; COLORADO to OREGON: EUROPE. 222. (C. rupestris All. CRAG SEDGE. Above timberline, Arapahoe Peak, 11000-13000 ft. (Dan- iels, 930). Also on Long’s Peak (Rydberg). GREENLAND to ALASKA and CoLoraADo: Europe: ASIA. 223. C. obtusata Lilj. OxsrusisH SEDGE. Above timberline on Arapahoe Peak, 11000-12000. ft. (Daniels, 931). Also on Long’s Peak (Rydberg). NEWFOUNDLAND to BritisH CoLumBi1a and COLORADO. 224. C. oreocharis Holm. MouNTAIN-GRACE SEDGE. Lamb’s ranch, near Long’s Peak, g100 ft. (Rydberg). CoLoRabo. 86 UNIVERSITY OF MISSOURI STUDIES [234 225. C. Pennsylvanica vespertina Bailey [C. vespertina (Bai- ley) Howell]. Western PENNSYLVANIA SEDGE. Common on the plains and foothills, 5100-8500 ft. (Dan- iels, II). CoLoRADO to OREGON and British CoLumBia. 226. C. umbellata brachyrhina Piper [C. wmbellata breviros- tris Boott]. SHORT-BEAKED UMBELLATE SEDGE. Dry rocky mesa fronting Flagstaff Hill, 5700-6000 ft. (Daniels, 125). Marne to British CoLtumBia; NEw Mexico to CALiFoRNIA. 227. C. Beckii Boott [C. durifolia Bailey]. Brck’s SEDGE. Cafion at base of Flagstaff Hill, 5700-6000 ft. (Daniels, 463). Ontario to Manitrosa; New York to CoLorapo. 228. C. capillaris L. Harr sEpGe. Above timberline, Arapahoe Peak, 11000-12000 ft. (Dan- iels, 915). Also Thompson’s Cafion on Long’s Peak (Ryd- berg). GREENLAND to ALAsKA; NEw Hampsuire to Uran: Europe: ASIA. 229. OC. utriculata Boott. BotTLe SEDGE. Swales and limose banks of streams, local (Boulder creek half way to Falls; subalpine bogs at Eldora, etc.), 5100-10000 ft. (Daniels, 563). LaBRADOR to BRITISH COLUMBIA; DELAWARE to CALIFORNIA. 229%. C. saxatilis L. [C. pulla Gooden.]. Rock sEpGE. Redrock lake, 10100 ft. (Ramaley & Robbins). GREENLAND and ALASKA to CoLoranpo. 230. C. lanuginosa Michx. Woorty sepcE. Subalpine bogs at Eldora, 8600 ft. (Daniels, 652). Nova Scotia to British Cotumpia; NEw JERSEY to CALIFORNIA. 235 | FLORA OF BOULDER, COLORADO 87 Order 10. ARALES. Family 14. ARACEAE Neck. Arum family. 82. ACORUS L. CarLamus. 231. A.Calamus L. Sweet FLac. Swales along railroad in the city of Boulder, 5300-5400 ft. (Daniels). Nova Scotia to MinngEsota; FLormpa to Trxas and CoLoRADO: EuROPE: ASIA. Family 15. LEMNACEAE Dumort. Duckweed family. 83. LEMNA L. Duckweep. 232. L. gibba L. Gippous DUCKWEED. Ponds near Boulder, 5100-6000 ft. (Rydberg). NEBRASKA to CALIFORNIA; TEXAS to Mexico: OLD WorLD and AUSTRALIA. 233. L. minor L. LrsseR DUCKWEED. Springy swales in the city of Boulder, 5400 ft. (Daniels 748). Cosmopolitan. Order 11. XYRIDALES. Family 16. COMMELINACEAE Reichenb. Dayflower family. 84. TRADESCANTIA L. SprpERwort. 234. T. Universitatis Cockerell [T. occidentalis Rydb., not Britton]. UNIVERSITY SPIDERWORT. Common on the plains, mesas, and foothills, and follow- ing the deeper cafions several miles into the mountain re- gion, 5100-7000 ft. (Daniels, 44). The vicinity about Bould- er is the type locality. Both 7. scopulorum Rose and T. oc- cidentalis Britton, according to Rydberg’s Flora, occur about Boulder, but the former is a New Mexico plant, while the latter is from Wisconsin. CoLoRabo. 88 UNIVERSITY OF MISSOURI STUDIES [236 Family 17. PONTEDERIACEAE Dumort. Pickerel-w eed family. 85. HETERANTHERA Willd. Mup pLanTain. 235. H. limosa (Sw.) Willd. Limose Mup PLANTAIN. Between Longmont and Loveland, 5100-5500 ft. (Ryd- berg), in shallow water or mud. Vircinia to NEBRASKA and COLORADO; FLoRIpA to MExI- co, the West INpI&s, and CENTRAL AMERICA. Orden n2.) ee PAS: Family 18. MELANTHACEAE R.Br. SBunch-flower family. 86. ANTICLEA Kunth. ZycGapENus. 23514. A. elegans (Pursh) Rydb. [Zygadenus elegans Pursh]. SHOWy ZYGADENUS. Redrock lake, 10100 ft. (Ramaley). SASKATCHEWAN to ALASKA; COLORADO to NEVADA. 230. A. Coloradensis Rydb. CoLoraDo zYGADENUS. In canons and subalpine meadows, locally abundant, 7000 (Bear Cafion) -12000 ft. (Daniels, 651). CoLorapo and New Mexico to Urau. 87. TOXICOSCORDION Rydb. Poison camass. 237. T.gramineum Rydb. DEATH CAMASS. Mesas and foothills; blossoming in June, 5800-7000 ft. (Daniels, 106). SASKATCHEWAN to IDAHO and COLORADO. 238. T. faleatum Rydb. FaLcaTE POISON CAMASS. Spruce forests along Bear Cafion, 6000-7500 ft. (Daniels 759). COLORADO. Family 19. JUNCACEA® Vent. Rush family. 88. JUNCUS L. Rusu. 239. J. Balticus montanus Engelm. Mountain Battic RUSH. Along ditches and in swales and wet meadows, 5100-11000 ft. (Daniels, 3709). LABRADOR to WASHINGTON, CoLoRabo, and Urau. 237] FLORA OF BOULDER, COLORADO 89 240. J. Drummondii Mey. DrumMonn’s RUSH. Above timberline, Arapahoe Peak, 11000-13000 ft. (Dan- iels, 922). Montana to ALASKA; COLORADO to CALIFORNIA. 241. J. interior Wiegand. INLAND RUSH. Common in swales and meadows on the plains, mesas, and foothills, and following the main streams some distance into the mountains, 5100-6500 ft. (Daniels, 152). ILLinors to Wyomrine; Missouri to COLORADO. y 242. J. Arizonicus Wiegand. ARIZONA RUSH. Cry beds of torrents, mesas at foot of the Flat-irons 5700-6000 ft. (Daniels, 964). Texas to CoLorapo and ARIZONA. 243. J. confusus Coville. CoNFUSED RUSH. Swales along the railroad between Boulder and Marshall, 5400 ft. (Daniels, 421). Montana to WASHINGTON and CoLorapo. 244. J. Dudleyi Wiegand. DupLeEy’s RUSH. Swales, meadows, and mountain cafions, 5100-8600 ft. (Daniels, 965). Replaces /. znterzor Wiegand in the moun- tain region. Maine to Wasuincton; New York to Mexico. 245. J. bufonius L. Toap rusH. Wet sandy soil throughout except at the higher eleva- tions, 5100-9000 ft. (Daniels, 251). Cosmopolitan. 246. J. marginatus Rostk. GRASS-LEAVED RUSH. Irrigation ditches along the Arapahoe Road, 5300 ft. (Daniels, 740). Not in Rydberg’s Flora. MaINneE to ONTARIO; FLORIDA to COLORADO. 247. J. longistylis Torr. LoNG-sTYLED RUSH. Common in swales, about ditches and ponds, and in wet meadows throughout, 5100-10000 ft. (Daniels, 240). ALBERTA to IpaHo; NEBRASKA to Mexico and CALIFORNIA. go UNIVERSITY OF MISSOURI STUDIES [238 248. J. trigumis L. THREE-FLOWERED RUSH. Above timberline, Arapahoe Peak, t1000-12000 ft. (Dan- iels, 1007). LasBrapor to ALasKA; NEw YORK to COLORADO. 249. J. /castaneus Smith. CHESTNUT RUSH. Above timberline, Arapahoe Peak, 11000-12500 ft. (Dan- iels, 639). GREENLAND to ALASKA and CoLorapo. 250. J. nodosus L. KNOTTED RUSH. In swales and along ditches and streams, 5100-6500 ft. (Daniels, 735). Nova Scotia to MacKENZzIE and BritisH CoLumBia: VIR- Ginta to NEVADA. 251. J. Torreyi Coville. Torrey’s RUSH. With the preceding, but more abundant, 5100-6500 ft. (Daniels, 495). New York to Montana; Texas to ARIZONA. 25144. J. Mertensianus Bong. MERTENS’ RUSH. Redrock lake, rotoo ft. (Ramaley and Robbins). Montana to ALASKA; COLORADO to CALIFORNIA. 252. J. parous Rydb. REDDISH BROWN RUSH. Dry beds of torrents, mesas fronting the Flat-irons, 5700- 6000 ft. (Daniels, 373). CoLorapo to New Mexico. 253. J. Saximontanus A. Nelson [J. xiphioides montanus Engelm.]. Rocky MouNTAIN RUSH. Aspen bogs at Glacier Lake and Eldora; also a dwarf form on Arapahoe Peak above timberline, 8500-12000 ft. (Dan- iels, 703). 89. JUNCOIDES Adans. Woop RUsH. 254. J. parviflorum melanocarpum (Michx.) Cockerell. Nov. comb. [Luzula melanocarpus Michx.]. SMALL-FLOWERED WOOD RUSH. Cafions on the north slope of Green Mt., 7000-8100 ft. 239] FLORA OF BOULDER, COLORADO QI (Daniels, 332). A similar form was gathered above Bloom- erville, go00-10000 ft. Also at Caribou (Rydberg). GREENLAND to ALASKA; COLORADO to CALIFORNIA: EUROPE: ASIA. 2s4a. J. parviflorum subcongestum (S. Wats.) Daniels. Nov. comb. [Luzula spadicea subcongesta S. Wats.]. DENSE- CYMED WOOD RUSH. Alpine valley near edge of snow, Bloomerville, 8500- 11500 ft. (Daniels, 328). CoLoRADO to CALIFORNIA. 255. J: spicatum (L.) Kuntze [Luzula spicata (L.) Desv.]. SPIKED WOOD RUSH. Above timberline, Arapahoe Peak, 11000-13000 ft. (Dan- iels, 896). GREENLAND to British CoLumpiA; NEw HAMPSHIRE to CALIFORNIA. Family 20. ALLIACEAE Batch. Onion family. 90. ALLIUM L. Onton. 256. A. recurvatum Rydb. [4. cernuwm obtusum Cocker- ell]. RECURVED WILD ONION. Common throughout the mesas, foothills and the moun- tain plateau, 5700-8600 ft. (Daniels, 452). Also in the mountains between Sunshine and Ward (Rydberg). South Daxora to British CoLumBia and New Mexico. 257. A. Nuttallii S. Wats. NutraLi’s WILD ONION. Aspen bog at Glacier Lake, gooo ft. (Daniels, 336). Also southwest of Ward (Rydberg). SourH Daxora to WyominG; Kansas to COLORADO. 258. A. Geyeri S. Wats. [A. dictyotum Greene; A. reticula- tum deserticola Jones|. GEYER’S WILD ONION. Common throughout in both dry and moist soils, 5100- 11500 ft. (Daniels, 54). NortuH Dakota to WasHINGTON and New Mexico. 92 UNIVERSITY OF MISSOURI STUDIES [240 259. A. reticulatum Fraser. FRASER’S WILD ONION. Springy cafions in the foothills and the mountain plateau, 6000-8500 ft. (Daniels, 292). SASKATCHEWAN to IpAHO; SouTH DaKoTa to ARIZONA. 200. A. Pikeanum Rydb. Prke’s PEAK WILD ONION. Above timberline, Arapahoe Peak, 11000-13000 ft. (Dan- iels, T002). CoLoRADO. Family 21. LILIACEAE Adans. Lily family. 91. LEUCOCRINUM Nutt. Sawnp tity. 261. L.montanum Nutt. MouNnTAIN SAND LILY. Along the railroad between Boulder and Marshall, 5400 ft. (Daniels). Very abundant at Boulder (Cockerell). SoutH Daxora to Montana and CoLorapo. 92. LILIUM L. Luiry. 262. L. Philadelphicum montanum (A. Nelson) Cocker- ell. Nov. comb. Mounratn tity. Springy cafion on north slope of Green Mt., 6500-8000 ft. (Daniels, 355). Occasionally bearing two or more flowers. Montana to CoLorapo. 93. ERYTHRONIUM L. Avper’s-roncur. Doc-TooTtH VIOLET. 263. E. parviflorum (S. Wats.) Goodding [E. grandiflorum parviftorum S. Wats.]. SMALL-FLOWERED ADDER’S TONGUE. Above timberline, Arapahoe Peak, 11000-11500 ft. (Dan- lels, 888). WyomineG to CoLorapo and Urau. 94. LLOYDIA Salisb. 264. LL. serotina (L.) Sweet. Late Lioypta. Arapahoe Peak, 10000-14000 ft. (Rydberg). Monrana to ALASKA and COLORADO. 241] FLORA OF BOULDER, COLORADO 93 Family 22. CONVALLARIACEAE Link. Lily-of-the-valley family. 95. VAGNERA Adans. Fatse SoLOMON’S SEAL. 265. V. racemosa (L.) Morong [Smilacina racemosa (L.) Desf.]. WILD SPIKENARD. Boulder Cafion, 6500-8500 ft. (Rydberg). Nova Scotia to WASHINGTON; GEORGIA to CALIFORNIA. 266. V. amplexicaulis (Nutt.) Greene [Smilacina amplex- tcaulis Nutt.] CLASPING-LEAVED FALSE SOLOMON’S SEAL. Common in shady cafions throughout; at the edge of the wasting snows in a high alpine valley above Bloomerville July 7, 1906, 5700-10000 ft. (Daniels, 143). Montana to British CoLuMBIA; COLORADO to CALIFORNIA. 267. V. stellata (L.) Morong [Smuilacina stellata (L.) Desf.] STARRY FALSE SOLOMON’S SEAL. Common throughout; along ditches and streams in the plains, and in cafions and wooded valleys in the mesas and mountains, 5100-12000 ft. (Daniels, 111). St. Vrain creek (Coulter in Wabash College Herb.). NEWFOUNDLAND to SASKATCHEWAN and MonrtTaANA; VIRGINIA to COLORADO. 96. STREPTOPUS Michx. TwisTED STALK. 268. 8S. amplexifolius (L.) DC. CLASPING-LEAVED TWISTED STALK. Local in deep cafions in the foothills and mountains, 6500-10000 ft. (Daniels, 456). GREENLAND to ALasKA; NorTH CAROLINA to COLORADO and OREGON. 97. DISPORUM Salisb. 269. D. majus (Hook.) Britton [D. trachycarpum (S. Wats.) B. & H.; Prosartes trachycarpa S. Wats.]. Roucu- FRUITED DISPORUM. Local in company with the preceeding, 6500 (Green Mt.; Bear Cafion) -11000 it. (Daniels, 455). Also at Eldora (Rydberg). MAnitopa to British CoLumpia; NEBRASKA to ARIZONA. Q4 UNIVERSITY OF MISSOURI STUDIES [242 98. ASPARAGUS L. 270. AA. officinalis L. CoMMON ASPARAGUS. A common escape throughout the cultivated district, 5100-6000 ft. (Daniels, 114). Europe, thence to NortH AMERICA. Family 23. DRACAENACEAE Link. Dragon-tree family. 99. YUCCA L. SPANISH BAYONET. 271. Y. glauca Nutt. [Y. angustifolia Pursh]. Narrow- LEAVED SPANISH BAYONET. Common in the plains, mesas, and foothills; just north of the entrance to Bear Cafion it forms the main facies of the vegetation, 5100-6500 (Green Mt.) ft. (Even higher I think on the first line of hills). (Daniels, 39). NEBRASKA to Montana; Missouri to Texas and ARIZONA. Family 24. CALOCHORTACEAE Rydb. Mariposa lily family. 100. CALOCHORTUS Pursh. Mariposa LIty. 272. C. Gunnisonii S. Wats. GUNNISON’S MARIPOSA LILY. Common in the mesas and mountain meadows, 5600- 10000 ft. (Daniels, 53). At Ward occurs the forma zmma- culatus Cockerell (Cockerell). Montana to COLORADO and ARIZONA. Family 25. SMILACEAE Vent. Greenbrier family. 101. NEMEXIA Raf. Carrion FLOWER. 273. N. lasioneuron (Hook.) Rydb. [Smilax lasioneuron Hook.; WV. herbacea melica A. Nelson]. WESTERN CAR- RION FLOWER. Cafions in the mesas and foothills; especially frequent in gulches on the east slope of Flagstaff Hill, 5700-7000 ft. (Daniels, 224). The type locality of VV. herbacea melica A- Nelson. SASKATCHEWAN to NEBRASKA and CoLorapo. 243] FLORA OF BOULDER, COLORADO 95 Order 13. AMARYLLIDALES. Family 26. IXIACEAE Ecklon. Ixia family. 102. SISYRINCHIUM L. BLvueE-EvYeED GRASS. 274. §. alpestre Bickn. ALPINE BLUE-EYED GRASS. Mountain meadows at Eldora, 8600 ft. (Daniels, 648). CoLoRabo. 275. S. angustifolium Miller. NARROW-LEAVED BLUE-EYED GRASS. Common in meadows and about streams throughout ex- cept at the higher elevations, 5100-9000 ft. (Daniels, 72). Also at North Boulder Peak (Rydberg). NEWFOUNDLAND to MackENzIE and British COLUMBIA; VIRGINIA to COLORADO. 108. IRIS L. FLeur-peE-.ts. 276. I. Missouriensis Nutt. Missouri BLUE FLAG. 2 In swales and wet meadows about Boulder, 5100-6000 ft. (Daniels). Common at 8000-9000 ft. at Eldora, Hesse, Mil- ler’s Ranch (Ramaley). Near Long’s Peak (Coulter in Wa- bash College Herb.) Nortu Dakota to IDAHO; COLORADO to CALIFORNIA. Order 14. ORCHIDALES. Family 27. ORCHIDACEAE Lindl. Orchis family. 104. LIMNORCHIS Rydb. Boc orcuis. 277. UL. stricta (Lindl.) Rydb. NArrRowW-SPIKED BOG ORCHIS. Subalpine bogs and springy mountainsides at Eldora, 8600-10000 ft. (Daniels, 993). Montana to ALASKA; COLORADO to WASHINGTON, 278. L. viridiflora (Cham.) Rydb. GREEN-FLOWERED BOG OR- CHIS. Common in deep cafions and about springs throughout the mesas, foothills, and mountains, 5800-10000 ft. (Daniels, 69). ALBERTA to ALASKA and CoLoRADO, 96 UNIVERSITY OF MISSOURI STUDIES [244 279. lL. borealis (Cham.) Rydb. NorrHERN BOG ORCHIS. Springs on mountainside at Eldora, 8600-10000 ft. (Dan- iels, 842). Montana to ALASKA; COLORADO to WASHINGTON. 280. L. laxiflora Rydb. Loosr-FLOWERED BOG ORCHIS. Common in deep mountain cafions, 6500-10000 ft. (Dan- iels, 602). OREGON to CoLorADOo and UTAH. 105. PIPERIA Rydb. Piper’s orcHts. 281. P. Unalaschensis (Spreng.) Rydb. [Habenaria Una- laschensis S. Wats.| ALASKAN PIPER’S ORCHIS. Under pines on north slope of Green Mt., very rare, 6000- 8100 ft. (Daniels, 470). Also on South Boulder Peak, 8500 ft. (Rydberg). Montana to ALASKA; COLORADO to CALIFORNIA. 106. IBIDIUM Salisb. LaptEs’ TRESSES. 282. I. Romanzoffianum strictum (Rydb.) Daniels. Nov. comb. [Gyrostachys stricta Rydb.| Narrow - SPIKED LADIES’ TRESSES. One plant in a deep cafion on the north slope of Green Mt.; common in springy bogs at Eldora, 7000-10000 ft. (Daniels, 769). NEWFOUNDLAND to ALASKA; PENNSYLVANIA to COLORADO. 107. OPHRYS (Tourn.) L. Tways ape. 283. 0. borealis (Morong) Rydb. [Listera borealis Morong]. NORTHERN TWAYBLADE. Deep cafions on north slope of Green Mt., very rare, 6500- 8100 ft (Daniels, 607). Hupson Bay to MackENzIE; COLORADO to MONTANA. 283%. 0. nephrophylla Rydb. [Listera nephrophylla Rydb.] KIDNEY-LEAVED TWAYBLADE. Redrock lake 1oroo ft. (Ramaley and Robbins). ALASKA to CoLorADO and OREGON. 245] FLORA OF BOULDER, COLORADO 97 108. PERAMIUM Salisb. RATTLESNAKE PLANTAIN. 284. P. ophioides (Fernald) Rydb. SNAKE-MOUTH RATTLE- SNAKE PLANTAIN. Densely wooded cafions on north slope of Green Mt., very rare, 7000-8100 ft. (Daniels, 827). PRINCE Epwarp’s IsLanp to SoutH Daxota; NortH Car- OLINA to COLORADO. 109. ACROANTHES Raf. ApprER’s MOUTH. 285. A. monophylla (L.) Greene [Microstylis monophylla (L.) Lindl.]. ONE-LEAVED ADDER’S MOUTH. Deep cafions on north slope of Green Mt., very scarce, 6500-8100 ft. (Daniels, 342). QueEBEc to MINNESOTA; PENNSYLVANIA to COLORADO. 110. CYTHEREA Salisb. Catypso. 286. C. bulbosa (L.) House. [Calypso borealis Salisb.]. NORTHERN CALYPSO. Nederland, Boulder County, 8263 ft. (Miss Zora Phillips). LABRADOR to ALASKA; MAINE to CALIFORNIA: EUROPE. 111. CORALLORHIZA R. Br. Coratroor. 28044. C. ochroleuca Rydb. YELLOW CORALROOT. Redrock lake, 10100 ft. (Ramaley and Robbins). NEBRASKA to COLORADO. 287. ©. Corallorhiza (L.). Karst. [C. innata R. Br.]. Earty CORALROOT. Cafion in mesa at foot of Flagstaff Hill, only two plants, 5700-5800 ft. (Daniels, 122). Also at Caribou, 10000 ft. (Rydberg). Nova Scotia to Ataska; GkEORGIA to CoLorapo and WASHINGTON. 288. C. multiflora Nutt. LARGE CoRALROOT. A solitary cluster of plants under conifers at the Royal Arch at base of the Flat-irons, 6200 ft. (Daniels, 229). Also on North Boulder Peak (Rydberg). Nova Scotia to ALASKA; FLORIDA to CALIFORNIA. 98 UNIVERSITY OF MISSOURI STUDIES [246 Sub-class 2. DICOTYLEDONES. Series t. CHORIPETALAE. Order 14-)) SALICALE'S: Family 28. SALICACEAE Lindl. Willow family. 112. POPULUS L. Poprar. Aspen. Corronwoop. 289. P. tremuloides aurea (Tidestrom) Daniels, Nov. comb.* AMERICAN ASPEN. Throughout the foothills and mountain region except at the higher elevations, 5800-10000 ft. (Daniels, 314). NEWFOUNDLAND to Hupson Bay and Ataska; NEw JERSEY and TENNESSEE to Mexico and LOWER CALIFORNIA. 290. P. Sargentii Dode. [P. occidentalis (Rydb.) Britton; P. deltoides occidentalis Rydb.]. WESTERN COTTONWOOD. Common along streams, ascending Boulder creek as far as Eldora, 5100-8600 ft. (Daniels, 820). Also at Lyons (Rydberg). SASKATCHEWAN to Montana; Kansas to ARIZONA. 291. P. acuminata Rydb. BLack corronwoop. A solitary tree near a stream about half way between Boulder and Marshall, 5400 ft. (Daniels, 819). Common in all gulches ; there are large trees in Sunshine Cafion, 6500 ft. (Ramaley). SoutH Daxora to Ipano; NEw Mexico to Nevapa. 292. P. angustifolia James. NARROW-LEAVED COTTONWOOD. Along streams and in cafions on the mesas and in the foothills and mountains, 5400-9000 ft. (Daniels, 52). Nortu Dakota to WasHinecton; New Mexico to Cattr- FORNIA. 293. P. balsamifera L. Batsam POPLAR, Fourth of July mine; Eldora; Allenspark, 8000-10000 ft. (Ramaley). Laprapor to ALASKA; New ENGLAND to COLORADO. *See Appendix A. 247 | FLORA OF BOULDER, COLORADO 99 113. SALIX L. WILtLow. 294. §. amygdaloides Anders. PEACH WILLOW. Common along streams; the only willow, except the next, of tree size about Boulder, 5100-7000 ft. (Daniels, 90). Quesec to WasuHincton; New York to Mrssourr and ARIZONA. 295. S. caudata (Nutt.) Piper [S. Fendleriana Anders. ; S. pentandra caudata Nutt.; S. lasiandra Fendleriana Bebb]. FENDLER’S WILLOW. Along streams in mountain cafions, 5500 (Boulder creek)- 10000 ft. (Daniels, 807). ALBERTA to British Cotumpia; NEw Mexico to Cati- FORNIA. 296. §. exigua Nutt. NarrRoWLEAF WILLOW. Marshall; Valmont; Boulder; South Boulder Cafion; near junction of Fourmile and Boulder creeks, 5000-9000 ft. (Ramaley). MACKENZIE to WASHINGTON; COLORADO to CALIFORNIA. 297. S. luteosericea Rydb. SILKY SANDBAR WILLOW. Sandy stream flats in the plains and mesas, 5100-7000 ft. (Daniels, 134). Nesraska to IDAHO and CoLoRabo. 297%. S. lutea Nutt. YELLOW wiILiow. Redrock lake, roroo ft. (Ramaley and Robbins). CaNnapA to CoLorapo and CALIFORNIA. 298. S. Wolfii Bebb. WotLrF’s wILLow. Eldora to Baltimore, 8000-10000 ft. (Rydberg). Wyominc to COLORADO. 299. S. irrorata Anders. BLOOM-BRANCHED WILLOW. Gregory Cafion (E. Bethel). Cotorapo to NEw Mexico. 300. S. perrostrata Rydb. LonG-BEAKED WILLOW. Common in mountain cafions, 5500-8600 ft. (Daniels, 811). Hupson Bay to ALAsKA and CoLoRADO. 100 UNIVERSITY OF MISSOURI STUDIES [248 301. §. Bebbiana Sarg. [S. rostrata Richardson]. Brss’s WILLOW. Cafions and mountain valleys, frequent, 5700-10000 ft. (Daniels, 824). St.Vrain Cafion (Coulter in Wabash College Herb.). Anticosti to ALASKA; New JerSEy to CALIFORNIA. 302. §. Scouleriana Barratt [S. Nuttall Sarg.; S. flavescens Nutt.]. NUurTraLi’s wILLow. High alpine valley next to snow, above Bloomerville, Boulder Cafion, 5700-10000 ft. (Daniels, 321). Also from Eldora to Baltimore (Rydberg). Asstnigo1a to British Cotumsia; New Mexico to CAtt- FORNIA. 303. 8. brachycarpa Nutt. Dwarr wiLtow. Silver lake, 7000-11000 ft. (Ramaley). QueEsec to ALBERTA and COLORADO. 304. §. pseudolapponicum Seem. FaLts—E LAPLAND WILLOW. Above timberline, Arapahoe Peak, 11000-13000 ft. (Dan- iels, 883). Also between Eldora and Baltimore (Rydberg). COLORADO. 305. 8. glaucops Anderson. GLAUCOUS WILLOW. Above timberline, Arapahoe Peak, 11000-13000 ft. (Dan- iels, 937). Also mountains south of Ward, and between Sunshine and Ward, (Rydberg). ALBERTA to YUKON; COLORADO to CALIFORNIA. 306. §. chlorophylla Anders. GREEN-LEAF WILLOW. Near Fourth of July mine, (Ramaley). LasBrapor and New Hampsurre to ALASKA and CoLorabo. 307. §. petrophila Rydb. [S. arctica petraea Anderson]. ROCK-LOVING WILLOW. Above timberline, Arapahoe Peak, 11000-14000 ft. (Dan- iels, 951). New HampsHtreE to British CoLtumpia; CoLoRApO to UTAH. 249 | FLORA OF BOULDER, COLORADO IOI 308. §. Saximontana Rydb. Rocky MounraIn wIiLLow. Above timberline, Arapahoe Peak, 11000-14000 ft. (Dan- iels, gOI). WyominG and CoLorapo to WASHINGTON and CALIFORNIA. Order 16. FAGALES. Family 29. BETULACEAE Agardh. Birch family. 114. BETULA L. Brrcu. 309. B. papyrifera Andrewsii (A. Nels.) Daniels [B. Andrews A. Nels.] ANDREWS’S CANOE BIRCH. A few patches in valleys on the north slope of Green Mountain (Daniels, 1018). The type locality. COLORADO, as above. 310. B. fontinalis Sarg. [B. occidentalis S. Wats.]. Foun- TAIN BIRCH. WESTERN RED BIRCH. Everywhere along streams except at high altitudes, where the next takes its place, 5100-9000 ft. (Daniels, 149). Also Eldora to Baltimore (Rydberg). Near Long’s Peak (Couiter in Wabash College Herb.). ALBERTA to YuKoN; SoutH Dakota to New Mexico and OREGON. 311. B. glandulosa Michx. GLANDULAR BIRCH. SCRUB BIRCH. In bogs, Eldora to Baltimore, gooo-11000 ft. (Rydberg): Ward (Cockerell). GREENLAND to ALASKA; Maine to CoLorADO and OREGON: ASIA. 115. ALNUS Gaertn. ALprer. 312. A. tenuifolia Nutt. [A. imeana virescens S. Wats.]. THIN-LEAVED ALDER. Along streams throughout, 5400 (Boulder creek) -10000 ft. (Daniels, 571). Also mountains between Sunshine and Ward (Rydberg). Montana to ALaskA; NEw Mexico to CALIFORNIA. 102 UNIVERSITY OF MISSOURI STUDIES [250 Family 30. CORYLACEAE Mirbel. Hazel family. 116. CORYLUS L. Haze. 313. C. rostrata Ait. BEAKED HAZEL NUT. Abundant in cafons in the mesas, foothills, and the moun- tain plateau, 5600-8000 ft. (Daniels, 116). Nova Scotia to NortH Dakota; GEorGIA to COLORADO. Order 17. URTICALES. Family 31. URTICACEAE Reichenb. Nettle family. 117. URTICA L. Nertte. 314. U. gracilis Ait. SLENDER NETTLE. Common in stream-flats both in and out of shade, 5100- gooo ft. (Daniels, 583). Also mountains between Sunshine and Ward (Rydberg). Nova Scotia to ALasKA; NorTH CAROLINA to NEw Mexico 118. PARIETARIA L. PEL.irory. 315. P. Pennsylvanica Muhl. PENNSYLVANIA PELLITORY. Moist places under rocks and in cafions and on shady banks of streams, 5100-7000 ft. (Daniels, 498). Ontario to British CoLumBiIA; FLoripa to MExtco. 316. P. obtusa Rydb. OBTUSE-LEAVED PELLITORY. Sunset Cafion, 6000 ft. (Rydberg). CoLorapbo to UTAH; TEXAS to CALIFORNIA. Family 32. CANNABINACEAE Lindl. Hemp family. 119. HUMULUS L. Hop. 317. H. Lupulus Neo-Mexicanus A. Nels. & Cockerell. NEw MEXICO HOP. Rocky banks of cafions and along streams and in waste places as along fences, 5100-8000 ft. (Daniels, 573). Wyominc to UTan; NEw Mexico to ARIZONA. 251] FLORA OF BOULDER, COLORADO 103 Family 33. ULMACEAE Mirbel. Elm family. 120. ULMUS L. Exo. 318. U. Americana L. AMERICAN ELM. A tree of considerable size occurs in a wild place near the entrance to Boulder Cafion, doubtless self-sown from trees planted for shade, 5500 ft. (Daniels). NEWFOUNDLAND to Manitopa; FLoripa to TEXas. 121. CELTIS L. Hackperry. 319. OC. reticulata Torr. VEtNY-LEAVED HACKBERRY. Rocky ridges on the mesas and foothills, scarce, 5700- 6500 ft. (Daniels, 796). Texas to COLORADO and ARIZONA. Order 184 SAIN APA Ae BS) Family 34. LORANTHACEAE D. Don. Mistletoe family. 122. RAZOUMOFSKYA Hofim. SMALL MISTLETOE. 320. R. Americana (Nutt.) Kuntze [Arceuthobium Ameri- canum Nutt.]. AMERICAN SMALL MISTLETOE. On Pinus contorta Murrayana (Oreg. Com.) Engelm. at Sunset, 7700 it. (Rydberg). British CoLumpia to COLORADO and OREGON. 321. R. eryptopoda (Engelm.) Coville [Arceuthobium cryp- topodum Engelm; A. robustum Engelm]|. HipDEN-FOOTED SMALL MISTLETOE. On Pinus scopulorum (Engelm.) Lemmon upon high ridge well toward eastern summit of Green Mt., 7500-8000 ft. (Daniels, 770). Also between Sunshine and Ward (Rydberg). Texas and CoLorapo to Arizona and Mexico. Family 35. SANTALACEAE R. Br. Sandalwood family. 123. COMANDRA Nutt. Bastarp TOAD-FLAX. 322. €. pallida A. DC. Pate BASTARD TOAD-FLAX. Frequent on the plains, mesas, and foothills, 5100-8000 ft. (Daniels, 49). St. Vrain Cafion (Coulter in Wabash Col- lege Herb.). Manitopa to BritisH CoLumBia; TEXAS to CALIFORNIA. 104 UNIVERSITY OF MISSOURI STUDIES [252 Order 19. POLYGONALES. Family 36. POLYGONACEAE Lind]. Knotweed family. 124. ERIOGONUM Michx. Woot-joInt. . 323. KE. alatum Torr. WINGED WOOL-JOINT. Common on the plains, mesas, foothills, and open moun- tainsides, 5100-10000 ft. (Daniels, 170). NEBRASKA to WyomINnG; TEXAS to ARIZONA. 324. E. vegetius (T. & G.) A. Nels. [E. flavum vegetius T. & G.; E. Jamesu flavescens S. Wats.; E. Bakeri Greene]. BAKER’S WOOL-JOINT. Mountains between Sunshine and Ward, and at Meadow Park, 9000-10000 ft. (Rydberg). Wyominc to Uran; NEw Mexico to ARIZONA. 325. E. flavum Nutt. [E. crassifolium Dougl.]. YELLow WOOL-JOINT. Common in open places throughout, 5100-12000 ft. (Dan- iels, 368). SASKATCHEWAN to ALBERTA; NEBRASKA to COLORADO. 326. KE. umbellatum Torr. UMBELLATE WOOL-JOINT. Very abundant in open places throughout, 5100-12000 ft. (Daniels, 55). Wyominc to IpaHo; Cotorapo to UTAH. 327. E. subalpinum Greene. SUBALPINE WOOL-JOINT. Along the Arapahoe Trail from Eldora to Arapahoe Peak and ascending to the timberline, but not above it, 8600- 11000 ft. (Daniels, 950). ALBERTA to British CoLtumBiIA; CoLorapo to NEVADA. 328. KE. effusum Nutt. Errusr wooL-yornt. Plains and mesas between Marshall and South Boulder Peaks, and along the railroad between Boulder and Marshall, 5 400-6000 ft. (Daniels, 439). NEBRASKA to MonTANA and CoLorapo. 253] FLORA OF BOULDER, COLORADO 105 125. RUMEX L. Dock. 329. R. Acetosella L. SHEEP SORREL. Along railroads and roadsides, and in fields and waste places, in 1906 still somewhat scarce, 5100-6000 ft. (Daniels, 589). Very common now (1910), along railways up to gooo ft. and higher (Ramaley). Europe: Asta, thence to NortH AMERICA. 330. R. occidentalis S. Wats. WESTERN DOCK. In Bear Cafion, 6000-7000 ft. (Daniels, 710). LABRADOR to ALASKA; TEXAS to CALIFORNIA. 331. R. densiflorus Osterh. [R. Bakeri Greene]. DENSE- FLOWERED DOCK. Subalpine bogs at Eldora, 8600-10000 ft. (Daniels, 908). WYoMING to COLORADO. 332. R. crispus L. Curty DOcK. Fields and waste places and becoming common in ditches and swales, 5100-5700 ft. (Daniels, 491). Europe and Asta, thence to NortH AMERICA. 333. R. salicifolius Weinm. WAILLOW-LEAVED DOCK. Common in ditches, shallow streams, and in swales and low meadows, 5100-10000 ft. (Daniels, 234). Laprapor to ALASKA; TEXAS to LOWER CALIFORNIA: Evu- ROPE. 334. R. obtusifolius L. Bitrer Dock. Waste places and fields, 5100-6000 ft. (Daniels). Europe and Asta, thence to NortH AMERICA. 126. OXYRIA Hill. 335. 0. digyna (L.) Hill. Mounrarn sorre-. Creek-banks at Eldora; above timberline, Arapahoe Peak, 8600-12000 ft. (Daniels, 844). GREENLAND to ALASKA; New HAmpsHire to ARIZONA and CALIFORNIA: Europe: Asta. 106 UNIVERSITY OF MISSOURI STUDIES [254 127. POLYGONUM L. KwNorweep. 336. P. erectum L. Erect KNOTWEED. Along the railroad in Boulder Cafion, 5500 ft. (Daniels, 580). Marne to ALBERTA; GEorGIA to ARKANSAS and CoLoRADO. 337. P. buxiforme Small. Box-LIkE KNOTWEED. Bear Cafion, and all waste places, 5100-10000 ft. (Daniels, 698). ONTARIO to WASHINGTON ; VIRGINIA to TEXAS and NEvADA. 338. P. aviculare L. Doorweep. Common about houses, along railroads, and in all waste places, 5100-8000 ft. (Daniels, 582). Asta: Europe: NortH AMERICA. 339. P. ramosissimum Michx. Bushy KNOTWEED. Common along railroads and roads, and in low weedy - grounds, 5100-10000 ft. (Daniels, 519). MinNEsora to WASHINGTON ; ILLINOIS to NEw Mexico and Nevapa; Marne to New Jersey along the coast. 340. P. Sawatchense Small. SAaGUACHE KNOTWEED. High mesas at foot of the Flat-irons, 5700-6000 ft. (Dan- iels, 178). SoutH Daxora to WASHINGTON; COLORADO to ARIZONA and CALIFORNIA. 341. P. confertiflorum Nuttall [P. Watsonit Small]. War- SON’S KNOTWEED. About the quarries at foot of the Flat-irons, 5700-6000 ft. (Daniels, 660). Montana to WASHINGTON ; COLORADO to CALIFORNIA. 342. P. unifolium Small. ONE-LEAVED KNOTWEED. Aspen bogs at Glacier Lake, gooo ft (Daniels, 672). Montana to CoLorabo. 343. P. Engelmannii Greene [P. tenue microspermum Engelm.]. ENGELMANN’S ENOTWEED. Sandy stream-flats, especially common along the railroad in Boulder Cafion, 5100-10000 ft. (Daniels, 568). Montana and CoLorapo to British CoLuMBIA. 255] FLORA OF BOULDER, COLORADO 107 344. P. Douglasii Greene. DouGLas’s KNOTWEED. Common in open, especially sandy places throughout, 5100- 10000 ft. (Daniels, 958). VeRMONT to BritisH CotumpiA; NEw York to New Mex- Ico and CALIFORNIA. 344a. P. Douglasii consimile (Greene) Small [P. consimile Greene]. BRANCHED DOUGLAS'S KNOTWEED. Gregory Cafion, 6000-6300 ft. (Daniels, 546). Lower Boul- der Canon (Rydberg). Range of the type? 128. PERSICARIA Adans. SMaArTWEED. Lapy’s THUMB. 345. P. emersa (Michx.) Cockerell. Nov. comb. [Polygonum Muhlenbergu S. Wats; Polygonum emersum (Michx.) Britton]. MUHLENBERG’S LADY’S THUMB. Along ditches and in swales in the plains, 5100-6000 ft. (Dan- jels). Marne to BritisH CoLUMBIA; VIRGINIA to CALIFORNIA and MExIco. 346. P. lapathifolia (L.) S. F. Gray [Polygonum lapathifo- lium L.|. Dock-LEAVED LADY’S THUMB. Swales and ditches in the plains, 5100-6000 ft. (Daniels, 506). ; Europe: Asta: NortH AMERICA. 347. P. Persicaria (L.) Small. [Polygonum Persicaria L.]- COMMON LADY'S THUMB. Common in waste places, and along ditches and in swales, 5100-6000 ft. (Daniels, 517). Europe, thence to NortH AMERICA. 348. P. punctata (Ell.) Small [Polygonum punctatum ELL. ; Polygonum acre H. B. K.].. WATER SMARTWEED. DOTTED WATER PEPPER. Margins of ponds, in swales and springy grounds, 5100-6000 ft. (Daniels, 798). NortH AMERICA: CENTRAL AMERICA: SOUTH AMERICA. 108 UNIVERSITY OF MISSOURI STUDIES [256 129. BISTORTA Tourn. Brsrorr. 349. B. bistortoides (Pursh) Small [Polygonum Bistorta ob- longifolium Meisn.]. OBLONG-LEAVED BISTORT. Along Arapahoe Trail and above timberline on Arapahoe Peak, 8600-13000 ft. (Daniels, 890). Montana to WasHIncTon; NEw Mexico to CALIFORNIA. 350. B. vivipara (L.) S. F. Gray [Polygonum viviparum L.]. ALPINE BISTORT. Above timberline, Arapahoe Peak, 11000-12000 ft. (Daniels, 894). Also Eldora to Baltimore (Rydberg). Redrock lake, 1o1oo ft. (Ramaley & Robbins). GREENLAND to ALASKA; New Hampsuire to CoLorapo: Ev- ROPE: ASIA. 130. TINIARIA Reichenb. Fatse BucKWHEAT. 351. T. Convolvulus (L.) Webb. & Mog. [Polygonum Con- volvulus L.].. BLACK BINDWEED. COMMON FALSE BUCK- WHEAT. Along railroads and roads; throughout the cultivated area as a weed in fields, 5100-go00 ft. (Daniels, 484). Europe and Asta, thence to Nort AMERICA. Order 20. CHENOPODIALES. Family 37. CHENOPODIACEAE Dumort. Goosefoot family. 131. CHENOPODIUM L. Goosrroor. Lamp’s QuAR- TERS. PIGWEED. 352. C. leptophyllum Nutt. NARROW-LEAVED GOOSEFOOT. Common in the plains, mesas, and gullies of the foothills and mountains, 5100-8000 ft. (Daniels, 604). NEBRASKA to Montana; Missourt to ARIZONA. 353. C. oblongifolium (S. Wats.) Rydb. [C. leptophyllum ob- longifolium S. Wats.]. OBLONG-LEAVED GOOSEFOOT. Common in dry places on the plains and mesas, 5100-7000 ft. (Daniels, 994). NortH Daxora to Wyominc; Missourt and Texas to ArRI- ZONA. 257]| FLORA OF BOULDER, COLORADO 109 354. C. incanum (S. Wats.) Heller [C. Fremonti imcanum S. Wats.]. Hoary GOOSEFOOT. Frequent on the plains and in waste places, 5100-6000 ft. (Daniels, 411). NEBRASKA to Cotorapo; NEw Mexico to NEvapa. 355. C. Fremontii S. Wats. FREMONT’S GOOSEFOOT. Bear Cafion in shade, 6000-7000 ft. (Daniels, 829). Soutu Daxota to Montana; New Mexico to Arizona and Mexico. 356. ©. album L. WHuite GoosEeroor. COMMON PIGWEED. Common in fields, yards, and waste places, 5100-8600 ft. (Daniels, 806). Europe and Asia, thence a cosmopolitan weed. 357. C. hybridum L. MapLr-LEAVED GOOSEFOOT. Common in shady cafions, and as a weed in gardens and waste places, 5100-8600 ft. (Daniels, 6or). Temperate NortH AMERICA: EUROPE. 358. C. rubrum L. [Blitum rubrum (L.) Reichenb.]. Rep GOOSEFOOT. Along Boulder Cafion near Falls, 6500-8000 ft. (Daniels, 549). NEWFOUNDLAND to BritisH CotumBIA; NEW JERSEY to CoL- ORADO: Europe: Asia. 359. C. Botrys L. FEATHER GERANIUM. JERUSALEM OAK. Common in waste places and along railroads in coal ashes. 5100-8000 ft. (Daniels, 598). Europe and Asta, thence to NorrH AMERICA. 132. BLITUML. B.itre. 360. B. capitatum L. STRAWBERRY BLITE. Frequent in cafions and along mountain roads, 6000-10000 ft. (Daniels, 545). Also mountains between Sunshine and Ward (Rydberg). Nova Scotia to ALAsKA; New JERSEY to CALIFORNIA: Eu- ROPE. 110 UNIVERSITY OF MISSOURI STUDIES [258 133. CYCLOLOMA Mog. 361. ©. atriplicifolium (Spreng.) Coult. [C. platyphyllum Mogq.] WINGED PIGWEED. Along the railroad between Boulder and Marshall ; also along the railroad in Sunset Cafion, 5400-7700 ft. (Daniels, 485). Marshall (W. W. Robbins). Ontario to Montana; ARKANSAS to ARIZONA. 134. MONOLEPIS Schrad. 302. M. Nuttalliana (R. & S.) Greene [M. chenopodioides Mog.].. Nurraty’s Mono.erts. Above timberline, Arapahoe Peak, the only ruderal observed there, 11000-15000 ft. (Daniels, 918). MINNESOTA to WASHINGTON; TEXAS to CALIFORNIA. 135. ATRIPLEX L. Oracue. 363. A. carnosa A. Nels. FLESHY ORACHE. Alkaline flats at Boulder lake, 5300 ft. (Daniels, 729). NEBRASKA to MontANA; KANSAS to COLORADO. 364. A. argentea Nutt. SILVERY ORACHE. Alkaline flats at Boulder lake, 5300 ft. (Daniels, 730). NortH Dakota to British CoLtumBiaA; Kansas to CoLo- RADO. 365. A. occidentalis Torr & Fremont. WESTERN ORACHE. Dry mesas at Boulder (Rydberg). CoLorapo to UTAH; TExAs to ARIZONA. 366. A. hortensis L. GaRDEN ORACHE. Along railroads and in yards, 5100-7000 ft. (Daniels, 679). Evurorpr, thence to NortH AMERICA. 136. EUROTIA Adans. WHITE SAGE. 367. E. lanata (Pursh) Mog. WooLLy WHITE SAGE. Plains at Boulder (Rydberg). SourH DaKoTa to WASHINGTON; KANSAS to CALIFORNIA. 137. CORISPERMUM L. Bucseep. 368. C. marginale Rydb. MaARrGINAL-FRUITED BUGSEED. Valleys near Boulder (Rydberg). Wyominc to CoLoRADO. 259] FLORA OF BOULDBR, COLORADO ITT 138. DONDIA Adans. SEA BLITE. 369. D. depressa (Pursh) Britton [Suaeda depressa S. Wats. ]. Low SEA BLITE. About the shores of Boulder lake, and other brackish lakes and pools, 5100-6000 ft. (Daniels, 778). Near Boulder (W. W. Robbins ). SASKATCHEWAN to MontTANA;-CoLorApo to NEVADA. 369%. D. erecta (S. Wats.) A. Nels. [Suaeda depressa erecta S. Wats.]. ERECT SEA BLIT# Calkins lake (W. W. Robbins). NorrH Dakota to MontTANA; CoLorApo to NEVADA. 139. SALSOLA L. Sattrworr. SEA KALE. 370. §. Tragus L. RussIAN THISTLE. Very common in waste places and along railroads, 5100- 7ooo ft. (Daniels, 419). Europe and AsrA, thence to NorrH AMERICA. Family 38. AMARANTHACEAE J. St. Hil. Amaranth family. 140. AMARANTHUS L. AmarantH. PIGWEED. 371. A. Powellii S. Wats. POWELL’s PIGWEED. Sandy valleys at Boulder (Rydberg). Texas to CoLoraApo and CALIFORNIA. 372. A. retroflexus L. RoUGH PIGWEED. Abounding in fields and waste places, 5100-7000 (clearings in Bear Canon, perhaps even higher in the mountains) ft. (Daniels, 812). TropicAL AMERICA, thence a cosmopolitan weed. 373. AA. blitoides S. Wats. PRosTRATE PIGWEED. Along thoroughfares, and in fields, waste places, and creek- sands throughout, very common, 5100-10000 ft. (Daniels, 814). CoLorapo to Uran and Mexico, thence to the rest of the Unitep States and SOUTHERN CANADA. II2 UNIVERSITY OF MISSOURI STUDIES [260 374. A. graecizans L. [A. albus L.]. WHITE PIGwEED. TUM- BLE WEED. Common in waste places, especially on the plains, 5100-6000 ft. (Daniels, 813). TropicaAL America, thence throughout NortH AMERICA. 141. FROELICHIA Moench. 375. F. gracilis Moq. SLENDER FROELICHIA. Along the railroad between Boulder and Marshall; also along the railroad in Boulder Cafion, 5400-6000 ft. (Daniels, 476). NEBRASKA to CoLorADo; ARKANSAS to TEXAS. Family 39. CORRIGIOLACEAE Reichenb. Corrigiola family. 142. PARONYCHIA Adans. WuitrLowwort. 376. P. pulvinata Gray. PULVINATE WHITLOWWORT. Massif de Il’ Arapahoe, 1100-13500 ft. (Rydberg). Wyominc and Cotorapo to UTAH. 377. P.Jamesii T.& G. JAMES’S WHITLOW-woRT. Common in open situations throughout, 5100-10000 ft. (Dan- iels, 136). Also mountains between Sunshine and Wee, and at Meadow Park and Lyons (Rydberg). NEBRASKA to WYOMING; TEXAS to NEw Mexico and MeEx- ICO. Family 40. ALLIONIACEAE Reichenb. Umbrella-wort family. 143. ABRONIA Juss. 378. A. fragrans Nutt. FRAGRANT ABRONIA. Near Boulder (Tweedy). Valmont Butte, not getting to Boulder (Ramaley). SoutH Daxora to IpaAHo; Kansas to New MExIco. 144, ALLIONIA Loeffl. Umpretia-worr. 379. A. nyctaginea Michx. [Oxybaphus nyctagineus Sweet]. HEART-LEAVED UMBRELLA-WORT. Plains and mesas, especially about streams, 5100-6000 ft. (Daniels, 113). ILLInoIs to SASKATCHEWAN ; Missourt to COLORADO. 261 | FLORA OF BOULDER, COLORADO 113 380. A. hirsuta Pursh. HaAtRY UMBRELLA-WORT. Common on the plains, mesas, and foothills, 5100-7000 ft. (Daniels, 353). WIsconsiIn and Minnesota to SourH Daxota; Missouri to COLORADO. 381. A. diffusa Heller. Dirrus— UMBRELLA-WoORT. On the plains and mesas and rich mountain slopes, 5100- gooo ft. (Daniels, 167). Nortu Daxora to WyomMIncG; Kansas to ARIZONA. 382. A. lanceolata Rydb. LANCE-LEAVED UMBRELLA-WORT. Between Sunshine and Ward (Tweedy). Minnesota to Wyominc; TENNESSEE to TExAs and CoLo- RADO. 383. A. linearis Pursh [Oxybaphus angustifolius Sweet]. NARROW-LEAVED UMBRELLA-WORT. On the plains, 5100-6000 ft. (Daniels, 960). Minnesota to Montana; LoursiANna to Arizona and MEx- ICO. Family 41. TETRAGONIACEAE Reichenb. New Zealand spinach family. 145. MOLLUGO L. Carpet-weEeEb. 384. M. verticillata L. CoMMON CARPET-WEED. Common on shales with thin soil between Marshall and South Boulder Peaks, 5400-6000 ft. (Daniels, 427). Not in Rydberg’s Flora. TroprcaAL AmerIcA, thence to NortH AMERICA. Family 42. PORTULACACEAE Reichenb. Purslane family. 146. TALINUM Adans. FAME-FLOWER. 385. TT. parviflorum Nutt. SMALL-FLOWERED FAME-FLOWER. Common on shales with thin soil between Marshall and South Boulder Peaks; also on rocks in Gregory Cafion, 5400- 7000 ft. (Daniels, 437). Minnesota to SoutH Daxkota; Texas to ArRIzonA and Mexico. 114 UNIVERSITY OF MISSOURI STUDIES [262 147. CLAYTONIA L. Sprinc Beauty. 386. C. rosea Rydb. Rosy spRiNG BEAUTY. Common at Boulder (Cockerell). SASKATCHEWAN to BritisH CoLuMBIA; CoLorapo to CALT- FORNIA. 387. C. megarrhiza Parry. LARGE-ROOTED SPRING BEAUTY. Arapakoe Peak, towards summit, 12000-13500 ft. (Daniels, 889, collected by Mrs. T. D. A. Cockerell). Montana and Cotorapo to Uran. 148. CRUNOCALLIS Rydb. WATER SPRING BEAUTY. 388. C. Chamissoi (Ledeb.) Cockerell. Nov. comb. [Claytonia Chamissonis Esch.]. CHAMISSO’S WATER SPRING BEAUTY. Along ditches in the plains, and in deep cafions in the foot- hills and mountains ; along streams at Ward and Bloomerville; in subalpine bogs at Eldora; and in wet tundras on Arapahoe Peak, 5100-11000 ft. (Daniels, 239). Arapahoe Pass (Ryd- berg). Minnesota to British Cotumsia; New Mexico to Cati- FORNIA. 149. OREOBROMA Howell. Burrrer root. 389. 0. pygmaea (Gray) Howell. [Calandrinia pygmaca Gray; Lewisia pygmaea (Gray) Robinson]. PyGmy sit- TER ROOT. Arapahoe Peak, 12000 ft. (Rydberg). Redrock lake, 10100 ft. (Ramaley & Robbins). Montana and CoLorapo to CALIFORNIA. 150. PORTULACA L. Purstane. PussLey. 390. P. oleracea L. CoMMON PURSLANE. Campus of the University of Colorado at Boulder (Cock- erell). TROPICAL AMERICA, now cosmopolitan. 391. P. retusa Engelm. RETUSE-LEAVED PURSLANE. Along the railroad in Sunset Cafion, 5700-7700 ft. (Daniels, V2.2). ARKANSAS to NEvADA; TExas to New Mexico. 263] FLORA OF BOULDER, COLORADO IIc Family 43. ALSINACEAE Wahl. Chickweed Family. 151. ALSINE L. CuickweEep. STARWORT. 392. A. media L. [Stellaria media (L.) Cyr.]. COMMON CHICK- WEED. Streets in the city of Boulder, 5300-5600 ft. (Daniels, 803). Europe and Ast, thence a cosmopolitan weed. 393. A. Baicalensis Coville [Stellaria umbellata Turcz.]. LAKE BAICAL STARWORT. Arapahoe Peak above timberline in wet tundras, 11000- 13500 ft. (Daniels, 929). Also along mountain streams from Eldora to Baltimore (Rydberg). Montana to OrEGON; CoLorADO to CALIFORNIA: SIBERIA. 394. A. longifolia (Muhl.) Britton [Stellaria longifolia Muhl.]. LoNncG-LEAVED STITCHWORT. In high alpine valley near snow above Bloomerville, gooo- t1000 ft. (Daniels, 326). NEWFOUNDLAND to ALASKA; MARYLAND to CoLtorapo: Eu- ROPE: ASIA. 395. A. longipes (Goldie) Coville [Stellaria longipes Goldie]. LONG-PEDICELLED STITCH WORT. Wet meadows at Caribou, 8000-10000 ft. (Rydberg). LABRADOR to ALASKA and COLORADO: SIBERIA. 395a. A. longipes stricta (Richardson) Rydb. [Stellaria stricta Richardson]. STRICT LONG-PEDICELLED STITCHWORT. Eldora to Baltimore, 8000-11000 ft. (Rydberg). Range of the type, but extending to CALIFORNIA. 396. A. Jamesiana (Torr.) Heller [Stellaria Jamesiana Vorr.]. JAMES’S STARWORT. Along a stream in the mesa fronting Flagstaff Hill, 5700- 6000 ft. (Daniels, 26). The plants have fimbriate petals! Wyominc to NEw Mexico and CALtrornta. 152 CERASTIUM L. Mousr-Ear CHICKWEED. 397. C. occidentale Greene. WESTERN MOUSE-EAR CHICKWEED. Common on the mesas, foothills, and mountainsides in 116 UNIVERSITY OF MISSOURI STUDIES [264 sheltered places and about streams and springs, 5700 (stream in mesa fronting Flagstaff Hill)—12000 ft. (Daniels, 24). St. Vrain Cafion, 7000 ft. (Coulter in Wabash College Herb.). Montana to CoLorapo and Uran. 153. ARENARIA L. SAnpwort. 398. A. Tweedyi Rydb. Twerepy’s sANDWoRT. Above timberline, Arapahoe Peak, 11000-12000 ft. (Dan- iels, 1003). Wyominc to New Mexico and Arizona. 399. A. Fendleri Gray. FENDLER’S SANDWORT. High mesas between Marshall and South Boulder Peaks, thence throughout the mountain region, 5700-12000 ft. (Dan- iels, 425). Also mountains between Sunshine and Ward, and at Caribou (Rydberg). Wvyominc to New Mexico and Arizona. 399a. A. Fendleri diffusa Porter & Coulter. Dirrusr FENnp- LER’S SANDWORT. Plains and mesas about Boulder and Marshall, and in the foothills and mountains, 5100-10000 ft. (Daniels, 423). CoLoRADo. 154. ALSINOPSIS Small. 4oo. A. propinqua (Richardson) Rydb. [Arenaria propinqua Richardson; A. verna aequicaulis A. Nels.]. GLANDULAR SANDWORT. Arapahoe Peak in dry tundras, 11000-13000 ft. (Daniels, 754). Also Eldora to Baltimore (Rydberg). Hupson Bay to British CotumBraA; CoLtorapo to UTAH. 4o1. A. obtusiloba Rydb. [Arenaria obtusa Torr.]. OBTusE- LEAVED SANDWORT. Very common in dry tundras, forming often the main part of the turf, Arapahoe Peak, 11000-13500 ft. (Daniels, 913). Also at Caribou, 10000 ft. (Rydberg). Redrock lake, 10100 ft. (Ramaley & Robbins). ALBERTA to British CoLumBia; NEw Mexico to UTAH. 265 | FLORA OF BOULDER, COLORADO 117 Family 44. CARYOPHYLLACEAE Reichenb. Pink family. 155. SILENE L. Campion. CATCHFLY. 4o2. S. antirrhina L. SLEEPY CATCHFLY. Common on the plains and mesas, and in deep cafions for some distance in the mountains, 5100-6500 (Boulder Cafion), ft. (Daniels, 477). NEWFOUNDLAND to BritisH CoLuMBIA; FLortpa to CALI- FORNIA and Mexico. 4o2a. §. antirrhina depauperata Rydb. DrEPAUPERATE SLEEPY CATCHFLY. Bear Cafion, 7000 ft. (Daniels, 974). SASKATCHEWAN to BritisH CoLumpBiA; CoLorapo to ARI- ZONA. 403. S. noctiflora L. NiGHT-BLOOMING CATCHELY. Along streets and in waste places in the city of Boulder, 5300-5600 ft. (Daniels, 815). Campus of the University of Colorado (Cockerell). Europe, thence to NorrH AMERICA. 4o4. §. acaulis L. Moss cAmpPion. Dry tundras, Arapahoe Peak, where it is abundant and char- acteristic, I1000-13500 ft. (Daniels, 902). GREENLAND to ALASKA; NEw HAMPSHIRE to ARIZONA: arc- tic-alpine in the OLD Wor tp. 156. LYCHNIS L. 405. L. Drummondii (Hook.) S. Wats. DrumMoNnp’s PINK. Common in open places throughout, 5100-10000 ft. (Daniels, 173). Also mountains between Sunshine and Ward (Ryd- berg). Manirtora to British Cotumpia; New Mexico to ARIzoNna. 157. WACCARIA Medic. 406. V. Vaccaria (L.) Britton [V. vulgaris Host; Saponaria Vaccaria L.]. Cow HERB. Common in waste places about Boulder, 5300-5700 ft. (Dan- iels, 135). Europe, thence to NortH AMERICA. 118 UNIVERSITY OF MISSOURI STUDIES [266 158. SAPONARIA L. Soapwort. 407. S. officinalis L. Bouncine Ber. Roadsides and along railroads, 5300-5600 ft. (Daniels, 725). Not in Rydberg’s Flora. Europe, thence to NortH AMERICA. Order 21. RANALES. Family 45. CERATOPHYLLACEAE Gray. Hornwort family. 159. CERATOPHYLLUM L. Hornwort. 408. €.demersum L. COMMON HORNWORT. Owen’s lake; Boulder lake, 5200-5300 ft. (Daniels, 614). NortH AMERICA: Europe: Astra. Family 46. RANUNCULACEAE Juss. Crowfoot family. 160. CALTHA L. MarsH MARIGOLD. 409. C. leptosepala DC. [C. rotundifolia (Huth) Greene; C. chionophila Greene]. \WHITE MARSH MARIGOLD. Along brooks crossing the Arapahoe Trail from Eldora to Arapahoe Peak, where in the wet tundras it ascends above timberline, 8600-12000 ft. (Daniels, 880). Long’s Peak (Coul- ter in Wabash College Herb.). MackKeENzIE to YuKON and ALAsKA; CoLtorapo to NEVADA and OREGON. 161. TROLLIUS L. GLope FLOWER. 4to. T. albiflorus (Gray) Rydb. [T. laxus albiflorus Gray]. WHITE GLOBE FLOWER. Along brooks crossing the Arapahoe Trail from Eldora to Arapahoe Peak, where in the wet tundras it ascends above timberline, g000-12000 ft. (Daniels, 919). Long’s Peak (Coul- ter in Wabash College Herb.). Montana to WASHINGTON; CoLorApo to Uran. 267 | FLORA OF BOULDER, COLORADO - 119 162. ACTAEA L. BANEBERRY. 4ut. A. arguta Nutt. WESTERN RED BANEBERRY. Frequent in deep cafions throughout, 6000 (Bear Cafion at entrance )—10000 ft. (Daniels, 970). Montana to ALtAska ; NEw Mexico to Cattrornia: Nortu- ERN ASIA. 4tta. s sooo bo aacoos eco 218] WOVva gern cuss nasa kites eorenls [183] ROGtEMSs paca sicko sens etree [183] Lower Transition vegetation. . 9 MG UGERN ES wares vie seee sp eeteatenie sete [154] Bungwortercc sce rice een (202) allpines ye Ne eye eye [202] STEEMISM LAs pes sre isaevons cierto [202] airy see al hed hetobey ova cate teeter spa [203] lance-leavied nei arse en [202] linear-leaved.............. [202] DEGDIexi noe et ten eet [203] Dleasantameterceynce ieee rs [202] small-flowerede.. se -6-)ee [203] Pupils ines aaa tae ec ere 13, [153] Alpine yee ne hears eee erect [153] decumbentss. en eer [153] SUVERYcS odcinek [154] 1 et Soe eieantereraniicin a aeciatccotrns [153] red-stemmed.............. [153] small-flowered............. [153] ILW PMN s5 o scocccaccb coco sollilSsill AEs cooosaoocouoda {153] 201 alsophilus.. 53) argenteus decumbens.. [153] decumbens, defecssas eens 14, 18, [153] argentatus. | 5... 14, [154] Leplostachs) Smears [153] DAV OR Semen etter [153] Plattensismecrraarecie 18, [153] MUllyaKeRIEGo bo oooaca cence [153] Luzula melanocarpus........- [90] spadicea subcongesta........ [91] SPUCCLG ai rsisy etaye oe sh susterersy eae [91] Wy Chisels grees sae semen tee (117] Drummondii 18, [117] Ey ciuan ey ae cio ve sensei eee [210] WLS Aes eile clades sees 46, [210] Lycopersicum, see Lycopersicon LEyCGOpPErsiCOnner waite [21 Lycopersicum ....... 46, [210] EVCORODIAGCEAES Eee [52] ILMCORODWNUDS sod uelocgo ec ne [52] ILAAOO OGM o obncoo obese a. IS AMON, condagousc 39, [52] TSVCOPSISy Ua cleiiie sxe nents eee [204] AGVENSIS Satara eo 46, [204] ey COPUS Meir ete sails sete [208 Americanusse secs 11, [208] Europeus sinuatus.........{208] Lucidtisn aaa ter 11, [208] SULUGIUS A HAS Lo ee [208] WAU Ss gocooneooadvaccos ce All phleoideswasneee eee eer [62] Eyvcodesmitase aerate [256] PACH, cove esono0c ear [256] juncea.. . [256] Lygodesmia, large- flowered... .. [256] rush-like. . Moiiointctoanion [256] Lyimegrasss yada ieee [78] AM DIS11O USHA eee [79] SMOOUCHS 3 fi etnd sane eee eae [79] SUFIZOSCs5 0 8 Se Ute ee [79] VALGUS vers susan Aichossy Saw toere tenes [79] LYTHRACEAE [176] Lythrum fan sed nee tert [176] alabums eyo erences 11, [176] Machaeranthera............. [235 aS Dera dina asrertasionienet 26, [235] Bicclovienenmneee rere OFlZo5)| Coronopitoliasen sneer aeZo5) PAtteLsOni seer eee eee Zoo) Varian ssi fcc 3s Webs abacheluavarhens [235] Macrocaly.x-an nee ene ooo) INwvcteleatiiascnaueieeins 23, [199] Macronema pygmaeum....... [230] MADDER FAMILY............ [220] Miadwortinacanadcce nace [132] Mahogany, mountain........ 147] IMMATIACE AE NS Rona eod seeker te [150] INDEX References to the Flora are in brackets [ 1 2092 Malle-ferneey ss easier as [49] IMatlloweeeseiicice er eee Ol) Fallse eevee MN aaa at arte ee [170] scanletenyiis sie hae ({170] round-leaved ace [170] WESEE RI Ae a yi en eal whanau {170} Whites wisn etree {170] MALLOW FAMILY............. {170] Mallia ian ciceiNte Meee ile gay nea 170 rotundifolia............ 45, [170] MUNN PNGDINONOS SSG Hn Sie abaldod [170] INVAD VATS ery epslorstebietaier oyna [170] Miallyais taut tein ernst 170 dissectumen ys enie ae 14, [170] Manna=orassa inner eine [72] floating, northern.......... [73] lo limis aa asia at ie pa Maco e [73] MET VEC HA ohne te Naa [72] Miaples siya cnaianl Myr Shean ..21, [167] dwar ee BUSS Uns aie ian 1 STOO EMMA Mercenaries aa [167] three-leaved............... {167] MAPLE PAMILY..............[167] Messe unsere [244] fetid.. pinata [246] FEV aS He RUAN en oa [118] Mariposa lily.......17, 18,27, [94] Cunnisonyss panera [94] MARIPOSA LILY FAMILY....... [94] Marsh cress, blunt-leaved.... .[129] curved-podded............ [129] aI Tey ee hermit sy alanine ened {129] Miarsh=elderi)js sys inca cee [224] Bur weeds Ayaan niece [224] small-flowered............. [224] Marshvgrasssitallpa sean ne [66] Marshwmarigoldtee mre aie: [118] WHILE EIS chews Mee [118] Mary, little blue-eyed........[211] Matrimony vine............. [210] COMMON A Saat [210] Miaryweedeii eye bsiuarssi unr ae lin [246] COMMING Graocdododeoosue 246] Meadow-grass.. 13, [69] Alpines isteley cia eleee pean anal es {71] JoXeeVe NINH H BIO Ia ee hi ete Oe [72] (Oeabee Mitt ee el aie eligi orien cic: G (71] fair=huedaeei se seer nears [70] MexOUS ee EAR eevee aes [70] Ho) EA Sena eb tum ae Oh [70] AMlan ds ya ON Aue enl rip (71] long-ligulate.............. [72] long-pedunculate.......... [72] MOMMA NG soolsoob so aso ooM [70] Rattersonisp iar an sepes ae (71] PLairie ie OR ANE ca heen [72] Keflexed yA Neh eS a Mana [70] fel ex0 CA Naas epee Hana MATS \ I [73] TOUS eleva sack eR ea [69] RUSH leavieduni eet ree [72] Salley eA ett ee [72] smooth-glumed............ [70] Vialseyis ly sien iA asa [e719] WeStEEMsa elton nies [70] Wiheelerist occa merece [71] WOOG Ay Hace WLU ta {71] Mieadow-rues peer [125] BendlernisheyQusn ann san in (125] pPUuTplisher yy were eee [125] Meadowsweet............... ([147] ushy...... (147] Medi cya Ue AAD [155] 1aX0) ODS eat sem HATA GH) [155] Medica ei ai ha ae UASu eae [154] SAtiVvaan en ehe sees 44, [154] Miedicag ov asn aise hate ei aoe [155] lupulina Rea etary SCA 215, Lars) RYT MOA MA et a tata te [154] MELANTHACEAE............. [88] Mielicaia, } 25 So eeu UR Saad [69] bella py ncoeise cee ane an ean 25, [69] DULDOSa RE Se Ee [69] Melic-grassaee ene [69] IUNTXONOSS J 6sabcatoardcness [69] Mello tai iie rary UE oe [155] NINO eal iguacatacneta a ally ereuareca i (155] Melilotusheenenee ron ne (155] all Dar Rye A au 45, [155] Oficinaliskeese ee eee 45, [155] MENSALES Hees nlne seer 9, [17] Mentha ee ia Ae [208] arvensis Penardy ........ [208] Renardithwrava seri ente 1, [208] spicata.. iersan testa nig [208] ULTLA TS oteser ene EN AA a [208] Mentzelia albicaulis . oe Al albicaulis integrifolia....... [174] decapetalas nen ee [173] AUS Pensa ree aay ue (174] MULT LOZ eae [173] CU TENCHRALEANS emi nsaryes uae aN aia [173] ODay Oe dighiodia big oe [173], [174] SPECLOS Gina) etna nel Ain Can [173] Mentzeliaseene nna eet Lis] broad-leavedsa see [174] entire-leaved.............. (174] white-stemmed............ ({174] Mierathrepta reece [66] Californicaseaee eee ene [66] intermedia............. 33, [66] Spicarta) je Mehaes eames 15, [66] Meniolixtvenanyacstace earns [180] Sernulatase ee eee eee OM ool Mertensiay i eee aes [202] 441] INDEX. References to the Flora are in brackets [ ] Alli, can coocas sacos 0! | ZO EMianYoycha¥ ect ous) ONE aacts Boe (202] lanceolata... ..-- 23, 29, Be lateriflorav a ais 2ecler actise [202] MINE ATISNa ea cae 19, [202] MICLantharyepryer ene seats [203] perplexainn sa eislscheie 42, [203] polyphylla..........37, 42, [202] Punctatar meyers cine 29, [202] Secundoqumpeee seen eee [203] Wate GDI ELS oo cis bente nig aus a eis 29, [202] Miesanflorar/s 22s 18.08 SAGAR 9, [17] Mesa cafion society... ...18, oie [28] Mesa meadow society... : Ae {18] Mesquit-grass............ 1 aat [67] COMMO Tete ray aie [67] hairy.. [67] Cal DW erettvak st citiayissci sia eee eet [67] Mexican) poppy-s-4J- skies ee 13 Mitcramipelisseerinmen eae (222] LOD altaya ptescrsnpe seat ase 45, [222] IMircranthessery arenes eran ae [137[ AL Utaee OO OM OOM LSS] rhomboidea......... 39, 42, Heel INiicrOStenismenec ates [196] VGA MEIB gocccebecanccs oe 196] Microsteris, small-flowered.. . .[196] Wihibionl, Werc6 5 doc Foe oec 10, [181] Milk vetch.. 34, [155] ADIN er pasciere he eeu since chars [156] Hauspie seve steccussy nl ve Were [156] Canadas gas eisreyesinistolek (155] decumbent-sere ere 157] Drummondisss-e yee [156] HeExiles aunts a cmaaee et [157] MOMMA ee [155] IBArryase nay vate cit eye aye {157] DIAINSEM LR Ee ae ee [157] FMAM rerio non amie e tO crororole [156] DUTP learcaletoes phew shaveeny Savona [156] Salidasrer-ettepet atari {158] Shamim Seyeyae oper eee sees [156] Shortissyasccsace rae {157] slend en aediisicce cae (157] Gul N Ro sookcoucoecanco solllS@| three-fingered.............[158] Malkweedie cava vorecsyetsieos ees [194] Ghigid oid noemeeo ee mee nos [194] PTEEMSy4 yc epse rane [194] short-crowned [194] SHO Wiyicpretorderatoy aes tee eee tate [194] SWa1l Dace ricer {194] MILKWEED FAMILY........... (194] NMilletwitalian eerie [59] IMM. bes bobbie bodase oes 213] HOLDING USee eee eee 11, 29, [214] Geyerige es Ga see 11, , [213] 293 ISIN TIE G ng, croveebre aicteeentrl sic 23, [213] NOGLOS Bac.3 10 60.6 100 6066 BGI04 3 [213] Wangsdoriineeeea ee OMe 2 Lol] AMET OG ees spar ai stiaea alstisenionse (213] NUN OVATE Ao [213] puberulus........... 34, 37, ae IMEI NESS Spscavetaieie aecei el asshole (20 Renardists eave eee Bae Mistletoe) smallies essen: [103] MISTLETOE FAMILY.......... [103] Mitella pentandra............ [136] SPRATT Sos coeedoos oe se {137] IMGT OO) ese pis-ouoc odne be as [137] narrow-petalled............[137] Mollugo....... sp Mae aika (ube ny paees {113] werticillatan sme eee 45, [113] Mionardas sane is eee [207] menthaefolia..........- 26, [207] MO] TSH meas oa 26, [207] INCE 60.06 66:60 9.6 02.0-4 80 [207] pectinataseamet aor 16, [207] Ramaleyi-eaycrsa nese [207] SELIG Ay Vee eee eae (207] Moneses sii etyatve anaes [185] uniflora sae le eee [185] Monkey-flower............-. [213] Geyen'sire aia jee ee [213] ase ans ee a Seer aera [213] angsdorfs seer (213] Small Vek a esesiee eee ee [213] many-flowered............ [214] puberulentseeeerie eee [213] Monkshoodeneeninaeieneee 34, [120] Colimbiaeeee eee [120] ochroleucous.+-.5--.2.-4.- [120] POrrect= 245 Ho aoe eee {120] SHOW yserseuceh otf eee [120] MONOCOTYLEDONES.......... [55] IMonolepisse see eee LO chenopodioides............. {110] INtttallianaseee nce [110] Monolepis, Nuttall’s......... [110] MONOTROPACEAE.. sao eal lilS]] MONTANAE.. se acoesy (SO) Montane bog association . .31, [32] Montane flora.......... 9, 30, [31] Montane forest........ 31, 36, [37] Montane lake association. .31, [34] Montane marginal vegetation. [34] Montane meadow.........31, [34] Montane rupestrine society.... [35] Montane stream ass’n..... 31, [36] Montane subzone...........- {31] Montane sylva........... 31, [37] Moonworte- eee eee [49] Moxningiglonyeceiei ree [195] COMMON. 3 ee w= INDEX References to the Flora are in brackets [ } 204 MORNING GLORY FAMILY...... [195] MoschatelQannnennicne rie [222] MOSCHATEL FAMILY.......... [222] Miossesiinit yah tiie) aaa a 27 Motherwort...... (206] COMMON Ae ee [206] Mountamntashseeee eee eee (151) Rocky Mountain.......... {151] Mountain avens.............[145] PUEple eRe Re ee [145] three-flowered............. (145] cunbinatey Mey nee ee [146] WES a ete RT AUS Shahn aa [147] VITO WEEE HAM Pa ent Aaa Su [146] Arapahoewa anna e nie [146] Mountain caraway...........[182] obovate-leaved............ [182] Stemlessenee eee ae [183] Mountainidaisyserenenennne [239] NOaTy aij valerian eee [239] Mountain forget-me-not ....[201] Silvery ye etclavee yee eae (201] Mountaingoldl) Soe) es [230] Barry eS st Nant cee p aps [230] Mountain mahogany. ....20, [147] smalll-leaved see entenee {147] Mountaintnute eee eee (201] NAMES KSA ai AAS Ne [201] Pulvinatese eae eee [201] VIR gate avi N anew) [201] Mountainirices pee ene [61] SI Rey Bin HN ai cee [61] small-flowered............. [61] Mountain sorrel............. [105] Mouse-ear chickweed.........[115] WEAMse beadooessove nba ols] Mouseytallae eee an [122] Dealkedd is Oey Ne a Sie tsa {122] Mudiplantainey ane Sol HimosesAy sence [88] Mudworteeneenonee eee [214] EGIMENRISS So acacudbu sabe 34, [214] Miugwortipe ee eee [246] al pin ee Sen a eas [247] PEAT Cae Ae wee lesa [246] Miuhlenbergialeee eerie [61] cuspidata seen 15, [61] filitOrM See ee ee 33, [62] glomeratas eee [61] Sracilissmy sano Les 25, [62] TaceMmosawuee eee 11, [61] Richardsoni soe Koall] simplex) hyo aus 33,35, [62] Mallen ea yan iniaht pees 211] COMMON eee ees (211] paeCold eg inimenaemrare muainey ariel rity 2 [211] Min roantsiicieninnpiin aan these tehrmn [68] squarrosa..............15, [68] Miunnrolsigrassy eerie een [68] IMUTSUNEOM ccoooocodadodce os cos divaricatum. eee ee LOS Musineon, leafy............. [183] Miuskroothnisskice ie eee [222] Musquash root, western...... [182] Mustard seen eye ene {131] latches Ree ho ny a [131] hed ey) yeaa ons ana [130] Lindiaini eyes rn aera ae a [131] LENG NAsclaa Pale nea se Gaicis uate b [130] treacley Aa ie ieee eee [130] MUSTARD FAMILY. .......... [127] Myagrum sativum. ......... [128] Miyalonunpeniany pena ae (128] IMGYORUWIAEEhes gods bop obSobobec [122] apetallusi cepaecie nie acts paar [122] GAVOMSsos00c80q00000800¢ [122] Myriophyllumaa-eeeaeeeene {181] SpICAGUIMN Eee 10, [181] IMEI RIND 5 55.06 oad ooo o0 {176] Nannyberry............:.... (221] INEASENTMIINS Cobo gobo bob Uo DOE [128] AVAWOMEHO> fo 3500600450010) GUBIEDEPacc59 05 00b00Db005 {129} [BSDWIOS 09-6. 6'9'9 5.6.0 010.0 0G oe {129] Nasturtium-aquaticum...11, [128] ObLUSUTIRA Rae cee [129] OQUPCHHM2.5 Joico sehoocsodeese [128] RUED Bo soocosobecediocco [129] Negundo aceroides. ......... [168] NCB s.0000 6006505000 colll@S| INGmexda a2 bith: ses ee [94] henbacea) melicanmccaaeeeee [94] lasioneuron............ 22, [94] INE peta eae ak ates (206} Cataria... [206] Glechomanene ene eee ee [206] Nettle ene ae a neae {102] (a L320 |e rre l aeraneg ee ene [205] hedge... . [206] Slen'densvaeh ie eerily ae [102] INR IVAN ica ool oo oo co GO [102] INettleispurgessncn seen [164] branchin gene ecioeeeecines [164] New Jersey tea.............. [168], Kendlerishie aussie [168] hainyeeer {168] Silkishye nag eis ea eee [168] varnished....... NEw ZEALAND SPINACH FAMILY[113] INicotianasne see eee ALO} attenuata rer rnneneie (210] Nightshade seems heretics [209] burycommons ieee [209] enchanternSiacomnoee eee [180]. 443] INDEX 295 References to the Flora are in brackets [ ] inland a.4 it ee atseuereite [210] borealiseet ene ee eee coool three-flowered.. .......... [209] mephropliyllaseseeeeeee eee [96] WillOuSs) ancien nsec PO RO pulastersaseeceee tere [140] NIGHTSHADE FAMILY.........[208] WPODABT BS scdobdodscadcsass [140] INimesbanicsSan semen reriere 21, [140] glabratusteeeen ec . 28, [140] glabrousis. issm aac rioe {140] intermedius......... Oy, 28, {140} AMtCLMedIAtes see eee [140] Missouriensis....... . [140] Ramaleysshecas sence sere LLL Ol MONO Gy S eerie 28, {140] POrrey/Sios cece some ees [140] Ramaleyitenes sere 20, 28, [140] Nodding violet.. 22.5. .s460- 26 hO puntiageeem see eee 175] narrow-leaved. ...........[172] fragilistysteascrsse sae 19, [175] INothocalaiswanaeaees eee [257] Gréeneleeehist sos oe 19, [175] GUSPIGataryscicuslncis oe see [257] (PAE TSOS J iciecaoo0808 085% {175] Nuphar polysepalum......... [125] MLeSAcanth asm eee 19, [175] INUttallia ye saey estes ae oe ete [173] Greenet nen sone [175] decapetalay ss caine ses oees [173] polyacanthaserin- sae 19, [175] AULA OLa ae seye oie ee [173] ROS MESCUI AN eee eres iio) SNGEIS" S Sio tone oI eine cme [173] Ghodanthasnne ee eeprom iS) SIMUMAtAs) eres se acacia stharaleve | |) QHURMWNDE 5 ooloocoosuuasoe [173] SPECIOSAls nats trom Aeiecat eee (dS ROracheta nae sere eee [110] SEMIC tana cyst eis edi cee [173] Mesh yeti oracer eee: [110] INvcteleaiasaccics Acad vc eeeeas [199] Pardeninsvea aes seiacun one [110] INiy ti Ae ale iliac) a de ye ve cise [195] PRolemoniumlsee eee [198] Brandegeei............. 42, [199] COMPETE ene [199] VILELLOLUTI eee ttn eee [198] delicatumeyeaaee eee [198] meliittumibee arn eee [198] TILO LT Ore Ae se NAME UP ae [198] pulcherrimum..............[198] TODUStUIME neon LOS SCOpUlinUTm mre eee 4 ROLEvGONAGCESE See eeineooe (104] POLYGONALES...............[104] Polygonuimebnee icici [106] CHAO AA a SIT aelne.clsis) ca: ale {107] aviculanelen Hence nitiae 44, [106] Bistorta oblongifolium.......{108] buxitonmes semen 16, [106] confertiflorum.......... 33, [106] CONSINIIIER eee een {107] GColvolouluisse saree ae een [108] Douglasiteranimceecet 18, [107] Consimilesneee ee eece [107] COLES LIT eect aN [107] Engelmanniine je iceaeerier [106] Grable sasosaoouoooas 44, [106] lapathifoliums. 4) 14-0): [107] Muhlenberg... ......-.-: [107] IRAP FUGOs 6 bb 0 U'd ob8.e!9.9\6 [107] DUNCEALU UNE Coli sieenns (107] ramosissimum, ........... [106] 447] i INDEX References to the Flora are in brackets [ ] Sawatchense ............. [106] tenue microspermum........ [106] io MNS doo opaneous so colllOol DGHNOLY Oro ad dead pavace ao [108] WAGES ON. 5 ose atsiee eens eee [106] IROLYPODIAGEAES: seer koe [49] Rolypoditimtenn eae [49] eS peniume eee eee 29, [49] THE FBA AOS Gana od Osta Bion [49] Roly podiy itis are Sepepatsy sive caine [49] WEStEEMYs ee dnlaie eich ees ener La Roly pogoneeree eee eerie [63] Monspeliensis............. [63] Ronmmelblanchesserias ee [160] Pond lily, yellow......... 34, [125] Rondweedtnrimntarrira aie 10, [55] Cuber a dle cieiota ci oct oicua abe [55] fennel-leaved.............. [56] long-leaviedenenrinnricni tt [55] Meer tiygerieteoryeieorte nso geyG) EAI tue [56] Spinal vragen s ev vetocsshie eens [56 various-leaved............. [56] PONDWEED FAMILY........... [55] PONTEDERIACEAE............ [88] IBoplaiiianrscitadieesewereener set [98] av Sarrnwlomshrct ANA aie ib Abe ie 98 IBODDYA Ae eee eke nlc [126] IMiexicain ieee sataitenevle mats 13 Dahyocooudoooobeesemnio [126] | rough-fruited..............[126] IRORPWARAMIE Ny arlcieteiatielciiete [126 FOUN o hoc aa noEooe bene oe [98] AUCUIMIAT Atay elteeneel el: 12,22, [98] angustifolia.12, 22, 24, 28, 37 [98] QUT EO say des at anat chee ter 98 Dalsamiteraseee eee 37, [98 deltoides occidentalis........ [98] GMC TAS 3300.0 a. 000 9000 a6 [98] Sareentiineee ane 12, 22,28, [98] tremuloides...... 25, 32, 33, [98] AUNCAse cused erie tee 98] Porcupine grass.......... 13, [60] HAS MINGso op cede yanoo [60] Wettermannys cee eer {61] INIGIBOHVERG IS cian von abesocode [60] Scribmenissacriacicn ae ee [60] WESECRI es tices esse ee hoeneed ens [60] POEs ooacaoodudopadagn [114] oleracea sa cieruy reine 45, [114] TECUSAL. 4) siesta cieneyerets 45, [114] PORTULACAGCEAE epee see els Potamosetoneee eee eee lool Vi IME Jbovasaccaddsuanos [55] ELBE Sac 3.6. b.00'9.018.90000 0926 [55] FOLOSUSH Ae ent oracle 10, [55] heterophyllus.......... 10, [56] lonchitessss- semen: 10, [55] 299 OUCULONSHA Ere eee [56] pectinatusseeeee eer 10, [56] (PUYIGTTALOS dob o0dcddoaoo sc [56 Spintllusteeeeeeeeeeeee 10, [56] Rotentillaseneeerin eee [142] UEKI. oc oo adeeddcdaseeac [144] COncinnayee eae ere 32, [142] dissecta. . PRN RAD LAD glaucophylla. Re raetetateved Noseee [142] diversifoliaeeeeeoce eee (142] MUSA a Peete sie minmeiaeste 18, [143] MPSS Ose te Msi} eae re eee ate {145] IP MULELCOS Gey fraps avey eet en sneha ody [144] glaucophyllasesaene ears [142] Huppianayeeeae 14, 25, 35, tre GUUS OF Re Oats Reba [PUTPAOXE eoodosobvvigsacue Ha UMAAPOO Saoaclogassso0¥0 [142] 2D EDABARXD 65 604.456 ovo cin 0 ¢ (142] MPM NGO ca ggaobdoomoo¢ {143] Monspeliensis.............[142] Norvegica hirsuta.......... [142] POTHLOAO 6 66°30 406 bo 06 dacs [141] . Pennsylvanica arachnoidea. [143] StI ZOSae Renee 22, [143] PLOpinguare ae eeee roe 35, [143] pulcherriman ssi 35, [143] Poverty-grass, bushy......... [60] long-awned err asee eee [60] Prainieicloveneeri-eiiae ines [160] slender whites-en aoe [160] VIOlets ine ois ake a [160] hagryes tera ee ea [160] Prairie flora.. 12 Brairie-orass ay asa eee [68] PRATENSES 17,18,24, 27,31, 34 Bricklyicereus see eee eee ee [174] green-flowered............. (174] Bricklyspeate. eee eee {175] brittless oe c\lia neat eloere eens [175] Greene's:i oye ae ee {175] Many-Sidedsiys nce ae [175] TFed—tloweredssaa eer [175] WESEEDIMS syne ncvsieherore ne epee {175] Brcklyspoppyaseeneneeeeeee [126] BIT 23 tea AC eee [126] WD TEC TA .\ siete Deane iter ae [126] Prim nose tis eta eR rae [187] Evening ea Vea cone [178] Delaivaxe.s ee aoe (179[ SCAPOSENy seein erepa) see [179] tooth-leaved ...........[180] Wi LLO seperate as eRe pee [178] narrow-leaved. ........... {187] Parry) Simin cerns alten ees 39, [187] rock... PRIMROSE. FAMILY... Wea As INDEX References to the Flora are in brackets [ ] 300 IBshiile ys bs So aols gid sido ciao wie {187] angustifolia. . .42, [187 Parryi.. Wai 39, 42’ ee PRIMUUACHAE Lia Moa aminanis {18 PRIMULATES ashe e tiie Her Prosartes trachycarpa......... [93] Prunella ua sees nia ae a [206] Viulgarish ee an ian 11, 26, [206] IPTUNUSHAe ee teen [151] Americana.......... 20, 22, [151] Bessey ae eieideitustieneiaieket [152] melanocarpa..... 23, 29, 30, [152] Pennsylvanica....... 22, 29, [152] Prunella ee Renee ane {151] NWViAESOnIgNe a Renee [152] Pseudocymopterus...........[185] montanus multifidus........ [185] footihanschiGe 6 gmoulco cl oo o0 86 [185] Sylvaticussy sree ioe ciee [185] TENUOUS HA eee oD Pseudotsugannaontcaeieiiere 24, [54] DOMAOSBG Sobbodo4o0edgb eos [54] mucronata.......... 25,31, [54] Psoraleara sein a [160] argophylla.......... 14, 18, [160] tenuiflora........ 14, 15, 18, [160] Psoralea eens ANN ie subdues 13 Ptericiumee eee eee (50] aquilinum pubescens....25, [50] PTERIDOPHYTA.............. [49] PUTO DOM odboedooseasaade [185] Andromedea........ 26, 43, [185] Ptiloniaeee tee eee Zool paucihonra eee eee eee 255] HAMLOSA ee Arh te) arereueM steer: [255] Ptiloria, branching...........[255] few-flowered.............. [255] Puccinelliaseee ae Ee [73] AIGOI eS Seen ee 16, [73] PUCCOON EE eos [203] HoOaTyiaey a Ae aReu ate [203] narrow-leaved [203] short-flowered............. 203 IFAM ERNIE Wig ho adiod wold ooo 4 6 121 hirsutissimare sick ee 18, [121] TOSCA Aart AUC eLeEat nets {121] Purple false foxglove......... [215] Bessey’s. . Bis ord aie gil PAaes) Purple ground cherry BS CMa [209 LO Ded ee een a eae [209] Purshia tridentata............[147 Purshia.. WESC CONGR Bn LAST three- toothed Ba An ra tbe ea [147] Purslanencenrac einen [114] common. Ne aN NSS {114] retuse- leaved.. POR SaRaTAtenat one {114] PURSLANE FAMILY........... {113] Pussleyaaea ea selene {114] Pyro lace iets Mi Ata bil vena [186] rotundtfolia uliginosa....... [186] SECU AME MCSE Enie 26, [186] Wliginosaeyenja once aes 26, [186] UNULONG err tel eee [185] PY, ROUAGEAE wae ae eee [185] Ry rrocoma seer cine [229] CLOGEA ie iailiare ere saree [229] Pyrrocoma, yellow...........[229] Quack grass, false............ [76] Oirhvetlkys seonasecaqsacacgion 209] lobata eyes ay leven rey 16, [209] Rabbit-brush 13, [229] fairest eS ee aS [229] fasciculatess eae [229] handsome:eae ener [229] heavy-scented............. [229] [EE NO AACN ioIatE eee Gioia diglad [229] Radi culls niece elated tah ts {129] cally cinabenemaeeinin 11, [129] GUEVADES )s5seisave amoeisalones [129] Hispidaneen erste or 11, [129] Ob tulsa see Cee eae [129] SINUAtA ee aeons [129] Readishu pyciiGee hyena, Cor ain le (131] Gard emyite ise se seckeve eons {131] Ragweed secu yen any paniue Huan (224] COMMON ee [224] entire-leaved..............[224] PTE Aten kOe Ue Ue [224] WEStELM state i penelienaten eat p as (224] RAGWEED FAMILY... ........ [224] Rainfall ea Tevet a a aia 5- 8 RVANALES Hes hee ne aera sect dono) RANUNCULACEAE............[118] Ranunculusmeci eee [122] abortiviuls: eee eee 22, 28, [124] AGOWMEAWISS 6 oo oaddoan od oe 41, [123] OPN US eae RU ON Learn ems [123] cardiophyllus............[123] micropetalus.............[123] alpeophilusase eeeien car 39, [123] cardiophyllus........... 33, [123] Cymbalarnca syle asic (124 ellipticu seen aeani kena [123] eremogeneS...... {124| Flammula reptans.. . [122] inamoenus. A 33) Bin [123] Macounii..... . SER SIC IAS pects [124] MUcranthuUSH ee eer [124] micropetalus. . Op Sd, a INOHOUG.6 coobe dbacoss coos {12 pedatifidus.. 31h GOO [123 Teptans eee eee 28, 37, [122]. sceleratus eremogenes. ..11, Hea IREVOMAMING 5 gugcooldoabosoe on {131] 449] INDEX References to the Flora are in brackets [ | SACIVIUS SS coi ererern earn 46, [131] Raspberry, dwarf............ [141] HOWELIN GME 29, [141] hor Gorancnno DEE Aaa [141] inthe s ons MbloO Matonto ca clot o [141] Vist olererona ata cteioucstotoneeclone sc (141] Rati id acne yendieessryrace te era [242] columinarise isi 15, 19, [242] pulchercima. pee [242] Rattlesnake plantain......... [97] snake-mouwchy sen sie cael {97] Razonmots kaya sera rere [103] PNIMELICATIA shy alae ere 43, [103] CEypLopodan sesame ce 43, [103] Red cedar, Rocky Mount’n 29, [54] Red cherry, wild.. ae [52] Redtelephamtssuemoreeeceie 39 DEEL vane Ya Heats cay ata [218] RG Ai iraepaeuc ie sy Lisa ate cena ierctens [54] Rederaspbernysee see sacle [141] seve cepts a LA i Ee a cr re a [141] INEC=tO persicae tol een [64] Ree dere ay sos arc oate raises sie leieas te [67] [DRED eS erietatnond RERanerOIN eR ntnars Bia [55] COMMON ele nuc hes [67] Reed=orassisc ene teeatiee sae oe [64] WOO Cistrerereucen tact peaie nue aia sacle IRFANMINAT ESS: ees) ejeieieenes es ae LOS] RHINANTHACEAE............. (211] Rihodiolakieeyen incite eu. [136] MEERA as oaadoe acwooe [136] IC b cia oto Sie CEC OIE CERO CNC {167] CUSIMONLO RO En ee eae [167] glabra cismontana.........[167] TRAN Tse Nols the pie He epee {167] THOUS J bac ccogonged eon [167] RUDE se oes cisieon sc oisea ba ie lnee [139] CUTEUTU SN Pe onsets seis [140] CONC UITINUIN aes Street feyet actich Asan ([140] lacustre molle Soeie ae nL 39] ral efOb Gipsy gneteenicn cheat ech eakenes [139 longiflorum......... 20, 22, [140] PERV W ons no padopagaaned [139] pumilum........ 20, 22, 30, [140] IPL 6 o's a0 bolo ale 28, 30, [130] Wallicolaraecs eaten eis liete [139] WALL Caeser penis tetas ials 46, [140] Rub erassaasieat cee erste ets [219] RIGeCut=erassse ees aoe [59] RTM O SAB ais seus sense Z4, 29 RIPARIAE...... sO, ly Riparian flora. .. “il, 12, 21, 36 IROGK=Gresst is eiscieacsaes es [134] divergently podded........ [135] Bemdlerssws cise ee tty very earths [134] 301 sharp-leavedee meric aeriariae {134] snow-loving...............[134] Rock desert formation..... 38, 40 Rock primrose.............40, [188] diffuse ake nee aero [188] DINEMOLeES EME eae rie acelin [188] WIMNAA Sito cscowskoouaaes [188] subumbellate.............. [188] Roripa Armoracia............ {130] COLIN CANO ee oe {129] GUNULDES veins) \eictsesepercie hits {129] RUS PLd Ge Sires Pia ey Ere elles g {129] IMPORT boo boo oe oh odes {128] OOLUS Ais eae ss eee tere eee [129] StMUALD Wee acne ey sae eio evens [129] RO Sas is ara acter et atin Geng [148] aciculatanmrmem neni rs 29, [149] blanda aciculatare.. ae: [149] Engelmannii......... ian [149] Rendlent heen eaiee oe 2o no) Maicounnite ieee: | De, [149] Maximiliani............29, [150] MEIN AAV ante 30, [149] Nutkanay i Oue tire aa [149] Pratincolaeey sere 14, [148] angustianiimnae ee ene [148] SCtUlOSAs shipeyen eee eae [148] AYA hae eae eee 20, 22, ae suffulta.. Wieoalsts So éscabedcbouus ase ROSAGCBAB ee yaiely Mine ener gee [140] ROSAEES 334/25. dis been mate [136] Rose. . ee .13, 29, Nice ashen. TENURE A cAI fa ts Sy et [14 Castle Rock.. Te StS ee Engelmann’s.. NODS UG AO EN lee [149] rendler sins eee eee [149] Macounts}-.-e eee hone [149] MaximilianiSseeeeeeeeeiee [150] PLAITIe A Dee eee IEE (148] pricklys che tie ore elements [149] Say. Stace cave Meee be eae [149] ROSE HAMIL Y.s-ce eee ee ai LO) INOS€=rOOts. sc eRe eae [136] entire-leaved..............{136] Rubacer parviflorus........... {141] RUBIACHAER rian ook [220] IRUBIATES Us shesseeiepe stereos [220] Rubus Ase see ate ({141] Americantiseeenienice etn lean GeliCiOsuUs eee eee ete [141] NA RANUSy eet: {141] UgOrUsseniee eee 28, [141] Rud beckian seta eieri-wer reeds ete [242] flava acc! a sisueye caine 19, 26, [242] laciniata.. bit 29, On RUDERALES Melee in uals INDEX References to the Flora are in brackets [ ] 302 PROS A in ab a ong olaale [168] Negundosee)-n- or 12, 22, [168] Texanum...........12) 22, [168] FRAME XA een nace el nananeta the [105 Acetosella............- 44, [105] BORETE Me RAP ele sete aE an [105] CHISPUSHU Aa Rie Naess 44, [105] GenisimlOTUSM wie oilseed ete [105] obtusifolius .......... 44, [105] occidentalis ......... 11, [105] Saliciholiusyiienieylstener: 11, [105] RUPESDRESE yo oeeenee 35 Bupestine | ior Wo pea AO ANS Se Rush. .10, 34, 39, 40, [88] TER arava a OMA ae [89] Baltic, mountain.......... [88] Chestnut seca eters [90] Confused See eee [89] Druimmondyssy i eeien er ({89] IDyGlENASY deo oclgedicoo0.50'Go [89] grass-leaved [89] ted eivoa yeh a eib is a Bisse ore /o0'0\0'8 [89] KO EEEGIS eel creineen tatdeaerens [90] long-styled.. ............ [89] IMertenys eeomiaecrnie [90] reddishybrowily heise eiee [90] Rocky Mountain.......... [90] SCOUTIN SA Pk eer tat: [52] Spilcevnys span aerate ava [80] MOnKe VES ey Ato eaee: [90] three-flowered [90] LOA a NT Adda [89] WOOC Ea SMT aun Ene ahage [90] RUSH RAMETS sry sleiel tet snyar ale [88] Rush-grass, filiform. ....... [62] PUALLS A sania atte R Maltw EN [61] Rucharcdsonvssyeeianieee tee [61] Sasha) SO aaio mala Wistolsigiaidiaty's [62] RutavBalgasyaann iiss [132] Rydbergia................--[245] granditlorascyaaeiierie vein 42, [245] Ry dibergiane sae renin tiene O large-flowered.............[245] Rye vy iwal dayne ce naisioey ae [78] Rye-grass, Italian............ (75] Sabina. Ris (54) scopulorum.. WSS eMac 30, [54] SECO RIM TA SIGN GING) ABS A eIH G 13, [207] barrens:eae eee wy ee es LAAT Brictonysy ease kee [247] cudweed.. (247] diverse-leaved............ [247] orwood!siat sais) aes [246] lance-leaved...............[207] OC HSI ULE MARE Seas [247] Rocky Mountain..........[247] Scoulenis ye iene ieee [246] sylvan acre bees [246] sw nabele ee a ae dicen ae 110] Salige-brushin nian ane 5, 34, [246] COMMON aye me hea ea [246] SHENG sun d's BAG os amo xo MSO AudbOVem wabaimaias ou eae pls 11, [56] SEI OhNSwonthawes eee [171] Canadian, larger...........[171] handsomeseee seen {171] ST. JOHNSWORT FAMILY.......[171] SVNGIOUNGIINO SN big Gog aalorone Bis [98] SATTC@ATERS uaa Unni Aa een [98] Sallie nye a eT SENG [99] amygdaloides.......... 12, [99] COMED, JABAL 010 6 Boo'd 60 [100] Bebbianasan aaneeer ete 28, [100] brachycarpasanenccece 33, [100] catidaitala eens 28,37, [99] chlorophylla........... 39, [100] exigua.. Bias .12, [99] Fendleriana. rohan A RULE [99] Haviescensseance ieee [100] WENBENMES ols b dodo clo od Oe e 24 glaucops..07.04)..0-)- 33, 39, [100] WHOM aos Cele hb oaooboo bo So [99] lasiandra Fendleriana.. [99] INTEC SraNA MR rah SaaS a te [99] luteosericea............ 12, [99] INERT Gob s:o'e ois ovo d oc 24, [100] pentandra caudata.......... [99] DELLOStLata-saane ena 28, [99] petrophilaneey seine 41, [100] pseudolapponicum...... 41, [100] TOSIT GLA a Le {100] Saximontanace)) sonia ena Ona Scouleriana......... 33, 36, [100] AVON Gite AN areca eRe [99] Salmon-berry............ 29, [141] INutkalSoundscrmciee eine {141] Sallsutyi eyes Meni vein ca a [255] Sallsolayie ese vans enh eer {111] Mra Suse eran aeons 45, [111] Salltconasssaa eee eee [69] Salt meadow-grass........... [73] slender ic eee [73] Saleworteene 20 ean penta ena {111] Sall via Seige nee eea gg ie ein tees [207] lanceolatan nner oer La 2 Od Sam bDUCUS Mee aee eo (220] melanocanpavciy tse ae 22H Microbotrys.s.s ses ZO n220) SANDALWOOD FAMILY.........[103] Sand-bur.. ‘ Ae See aU S Ol] Sand cherry, Bessey’: Bole so oa USAT Saindililysecimaaw arse dati [92] MOUNCtAIN PaO ee eee [92] Sandworteaceort tore ocroon {116] 451] INDEX. 303 References to the Flora are in brackets [ 1] Rendlenis eters smet trace rer [116] Americanus st). =!) oe) 11, [79] GMs dodos bho code o alktH()| atrovirens pallidus...... 10, [80] HEMCWEB eS Bio coso oe be ae 6 [116] HEV 6 ind osieoogocdo 10, [80] obtuse-leaved............- [116] DUNZENS Meshal aianieestrc eee {79] ANSGCCOY Soasaonmaeenina doles {116] | Scouring rush, smooth........ [52] Samicle. Me eisscisiesce Sl oesieciets WSiisieScrophulaniaseaeeee see: (211] IMarylandeenerr ere erreer {181] nodosa occidentalis......... [211] Samicilaranccmct tates cree eens {181] Occidentalisa-ne aie 26, [211] Mam EMEhe poo on cool, AK [Sill || SomaBleisesccoadsocencbsoges [205] SARMALACIADD Sisp con boos cos [103] Britlontieaee eee ee 26, [205] SIANNDAT ES Sen epyanice sceneries [103] ULL SU OO eae [205] SAPTINDIAT BS sea aerer) salieri [167] galericulatar-eneeaeee 11, [205] Saponanian eee toi [118] TESINOSAL nahin) emleiseys ata [205] Oficinalis=eee eee eee eos uts)] WHA po osdoonaocoon te [205] WiGecarta sickened (ULE Seat birtera a ae Uatuny sy ical apy tas 111] Sapro phy teste alert sere ct 43 EHECEAM aes weather {111] Saprophytic plants........... 43 LOW) SEAN at A TO ea URED Te EE {111] SARPROPHYTICALES We) Wau Wa onlisearkalenee nese anu wae {111] Sarsaparillary waldeia tet ita [181] | Sedge....... 10, 27, 34, 39,40, [81] Savastana odorata............ [60] EVs Ho esi et bis oly anhete [84] Se rihak sll es Wel eet aya eset RSNA [54] Bindeirwieedlso does edesbedebe (81] Saxifma sane sor ncreesieiry a seus [137] eater Peer rs eee [84] AG CULER erage stole) ehciisyaveleialalsvopeo siete [138] Beck Sy aa enna S Ol austromontana............- [138] Lee ees Nee see ny ck RO ee [84] DLOMCHLGLES inne ee eee [138] pla ckish aan fees ars wo peei aia [85] NTU Sa caoosadenedae {138] (efoyciel (aarti OR Cre ae ee alte [86] Gebiliss ests Seisuieuaey 39, [137] bracted cue aes eine [82] GENE OLO a Eee [138] bronze-scaled ae anaes [84] UGS sa gag Ob COB A) [138] broom eae aa re ie [82] LAr CULUS AT Noe ee orks [138] Glustere dene eee [82] MWA sed eos kbuouiceoenes {137] COMO G5 chobbdsasdouns [84] DUNGLOLOM RNR seit rN cone: [138] CEA cae te ea aa [85] rhomboidea...........----- [137] Ciaene sere coenesewas [83] SASINRAGACE ARE eran aan: [136] Deweyis nnn ne ee eee [81] Samitrag en niermicta aioe 39, [137] Douglass eee eee [82] EMT CLT O eve ERA RA OEE RE ee [138] Ciyespiked eee eerie [83] austromontane...........- 36 EDONVE ee eT ete [82] acellate arent rier [138] Chaz BAP GIS ey brotci eaalauaaalaNsiers [84] FOlMEeMsse emis ere eel seats [138] FESClie eRe eee [83] rhomboid-leaved...........[137] oy SRM alba eddy atcia [$1] STOOL aE Ce Eon [138] Geyer sie) ae eee. (85] Titazl lon sls meatal au (137] Polder ee eee an mceeeaytts [85] western mountain.......... [138] ara Sa EA IR SN sai [86] Veo Was ecient eees Samer 40 hare’s-foot, western........ [82] SAXIFRAGE FAMILY...........[136] Elood’Sh et eee ane oie [81] Scapose evening primrose. ....[179] meadow Rae (8S Fairey sto) panne titres eter [179] mountain-grace........-..- [85] large-throated............. [179] narrow-leaved............. [83] MOUtATR Ee eee nice {179] ODLUSISH EEE Eee eee ee [85] Schedonnanrduss- inner ener [66] Pennsylvania, western...... (86] PRMVCHIERHS. seccedcos5Genc [66] DEELEY eee eee un SZ EOL OIVUS US Pee ee oake [66] Ry renaice erties rel [85] Schizachyxiume eee ier (57] THOMDIC EEOC ee [84] SCOPAn UME eeet eit 15, [57] TOC Ke eee eee bake ease eh oo Ma [86] Schimaltziasee ere ete eee [167] Sartwellistaurres seu sceaare [82] IO MB pdossapodoencds 20, [167] SIhiaaiaseisinih cid @ cation pie (81] SOiMNSs osaacasebsoosooegde [79] SOftleaved epee ee eee nl oul 304 INDEX [452 References to the Flora are in brackets [ 1 Stevens Given inane hie [83] SC Like sy Meas UDA Ae Pa ote [84] SENAWio corals stem nereioile [83] falseny sinh SMa Se Mee nae [83 short-beaked.............. [86] Variable sae yeitataa iain es [85] WESEE RM nie) toniey Nansen ee einer (81] winter-loving.............. [84] WOO] ymcri cea ene Reins [86] SEDGERPAMIUL Ven seer an eniae [79] Sedume eeu eecin arouses eae [136] ACU DIKIT AS 5 Ob oo od peloo Ae 136] stenopetalum... ..22, 30, 42, ite! rubrolineatum.......-... [136] Seediplantssemee meine [53] Selaginellaeaneeiaises hice (52] GETS a A eA AE RIS [52] EN Gel Mannie nae oe [52] rupestris Fendlert.......... [52] Underwoodii........... 30, [52] Selaiginellaneeeeeariac eater mne®) GEMS pe enue a ST [52] Winderwoodistisanier cee [52] SELAGINELLA FAMILY......... [52] SELAGINELLACEAE........... [52] Selfcheal anaes ee eee 206) COMMON eee ee 206 Senecio neem eer 19, 26, 30, [249] adiminalbilisw. J.) sl ices 34, [250] ambrosioides........... 32, [252] ALLALCUS iene Nera evan 37, 42: [251] aurelluseee eynenueeise isi [252] aureus Balsamitae...........[252] ORECITS Ree Te aMa [252] Croceus Halli... a2 202) Balsamitaese eae eee [252] Bigelout Halli... .....-.-: [249] blitoidesaeeecen ae ee ee ON(249)] carthamoides...........40, [249] chiloranthushes sea 35, [249] GColumbianusanaesreeeee [250] crassulusia sion aeons 42, [250] crocatus. aa eretyiey ecereiae CA eS Yl| cymbalarioides. ENON MeSH 34, [252] dior hep iis, MINUS I are [252] Fendleri. . wee O26" pet Lanatusseee eee nee [252] fililfolius Fremontit.........[253] PLAVOUIZEN Sse Ze WLAVULUS SAS Hotes [252] Mar bouriite eee ene eee [251] heterodoxus... Seicio o's SolASAl| Hookerih yay sea [250] hydrophilus............ 29, [250] lanatifoliusys eee 32, [252] lapathifoliamanns aoe [250] longipetiolatus......... 30, [252] lugens foliosus..............[251] RAMEN IG elac eyotne eh era eek [250] multicapitatus.......... 16, [253] MUtabilisyeraaeeieee eee (252] Nelsonii......... 19, 26, 30, [251] Perplexuseeeaeeee ee 29, [250] IPlattensis serene neenon 19, [251] pseudaureus.. .35, 40, [252] DUGICUS ARR 32, [249] Ipurshiants eee eee [251] PANES. soadbdacdcasoous [250] Riddellissnaeeee eee 16, [253] FOSUIAtUSH THe eee (251] Sallicitus:2).c05 ceil eee 251 Scopulinusseys sien aeelee 35, [249] , Spantioides.e 4 ce een 16, [253] triangularis. . 34, 37, [249] SHE HOYER co seooes bases [59] Wt GHiCa sae ee [59] DLUL AUS Neenah [59] Shadbushte ane nereee ere {150] alder-leaved............... [150] THOME NN, cuolsooodudduces [150] Sheepberry ese ser eee [221] Sheeprsonrel eee eee eee [105] Shepherdia Canadensis........{175] Shepherd’s purse............ {128] COMMONS ene [128] Shield-ferne se erieimeeee ie [49] Shinleaty esos ua see re [186] bog.. ied Ansa Nanay al Leo) Gnersidede ey yet AM [186] Shootingistansaneree eee 27, [189] few-flowered.............. [189] many-flowered............ [189] shade-loving.............. [189] wavy-leaved.............. [189] Sibbaldiasaaeeeeeeeeeearree [144] procumbens............ 42, [144] Sibbaldiatea eee ere 40 PLOcumMbent waar eee [144] Sidalcean scan nev anye wea [170] candida aeninnae 33, 35, 37, [170] Sideranthusssee eee eee nee 29] ANNUUSH Eee 16, [229] Spinulosustenee eee 16, [229] Silene sane Ra Aa Ane {117] acaulis san envs Pye 41, [117] antirrhina.......... 18, 45, [117] depauperata............ ({117] MOCLIDOTA Se Reee eee 45, [117] SILVERBERRY FAMILY.........[175] Singlejdelightsaaeemmuearcies [185] Sisyanbritum eee: [130] ANGUSU IM. Seminar RTE [130] officinale miacismrionee 45, [130] Sisyrinchiwumyne eee [95] 453] INDEX References to the Flora are in brackets [ 1] alpestre. 8.4 ssuef claire 35, [95] angustifolium.......14,35, [95] Sitamionee Sars wine eosin tee [78] brevatolimm=sneeeeeniee 15, [78] longifolium(e):)). eet 15, [78] Skullcap sentry in see ween [205] Brieconyspee nore ae [205] hooded se esissciwecs Seen se [205] Wan dali kespeyqsiry tetera crore [205] Skumk=bush emcee error 20 Skunk=prasseaseie as cecacn ee [68] Small mistletoe.............. [103] AIMETICANs tides aioe [103] hidden) footedepean asses ee [103] Smartweedsenen wuts sa calenen [107] WENN 4 to NCOO CSI ERES SRE oie [107] SMIDAGHAIE ae ania tie esr 94] Smilacina amplexicaulis...... [93] MECEMOS Oa eee [93] SLELLOEC ry Nosh rere nevanmoes ear al eter [93] Smilax lasioneuron........... [94] Snakerootyblacks-.jeaenneae [181] DUtEOTIE cr arkoomierece sues [226] Sneezeweed oes.) s6 secs eee [245] MMOLIMEVI osoadapoaumod ue [245] Snowhernynece neuer [221] WESEELM sete rae nue ett aie bees (221) SNOWHOWELSEcmmcaac ce 40, [213] ia@MeES (Sens mest cses creer see [213] Snow-on-the-mountain....... [165] Bowlderaaeiceisic tects oie scree [165] Soapwonttescs seca cence es ({118] SOLARINGIING Sd saloouaounada06 [208] Solanutmencny aise aya aeereser [209] LMEERIU SH coeyeneved even sheer areiaie ts [210] WEN GOPELSUCILIN eee [210] nigrum villosum...........- [210] HOSTUM Boocgoasco0nee5006 [209] CriAOGUMMs cue ose ate [209] Solidagolttmucsmpeceane eee [230] Ganadensishaaeseeeee ee 12, [231] gilvocanescens............ [231] COncinnas.ceee eee ene [231] decumbens..........32, 42, [230] MINWESCENS HEE ee eee Zool dilatatare ecw eee [230] gilvocanescens.......... 17, [231] Slaberrima-reneree eer Onlzoul PIAS (Li Bososnaosdaoo00 [230] Pathersonttaeene ache [230] Missouriensts extraria......[231] MOLISE chy eco iSroee lente [232] MEMES cadciy ond aon Oc 16, [232] nemoralis incand.........-. 232] oreophilayeee eae 26, 32, [230] pallidakrercey-semece er 19, [231] PONTE 5 Gacog0d000 12, 29, [231] 3095 poly phyllavewrerartee 29, [231] pulchernma ear ae [232] Ladulinayepee ee aeteie 26, [232] TUT WUMAS os ee ee el [232] speciosa pallida............ [231] trinenvatanrre tree 26, [231] VISCICU aera 26, [231] Solomon’s seal, false...... 21, [93] Sonchussjecnsey eee [259] ALVENSIS iia nse eis eee 45, [259] ASPENS eines Teese tte 45, [259] Sophiattiew acre {130] andrenaniineeeeri eee eis [130] hash CRIBS Aiba ni ae Bice cay Mots [130] IN cenMedia-e eee eee 14, [130] leptophiyllamemeiaarieen en [130] Sophoraictyec ote seem ae cee [152] SELICCA sy ects 7 ISA 2 Sophoranisilkysseeere ene [152] Sorbus se Ee a [151] SOOM Ed socodaceooo 25, [151] SOMA co asoaccovasd call OY TUtan sae reer 18, [57] SOLLelsaMountain=ae eee [105] SHEED ieee ene ao ee [105] WOOK si iied my eats vemaetne [163] Vellowe ee Ane eee ie [163] Sowithistles. asc [259] Held a sein A ae cee eae [259] Harsha) os sce aerney ete: [259] Spanish bayonet............. [94] narrow-leaved............. [94] Spanish needles, western...... [244] SPARGANIACEAE............. [55] Sparganitine eee eter nr [55] ‘angustifolium.......... 34, [55] simplex angustifolium....... [55] Spartina.) [66] cynosuroides .......... 11, [66] Spatter dock, western........[125] Spearmint. aceon [208] Special classes of plants...... 43 Speculiariaeaeeeeiee eerie (223] leptocarpa- eee eee [223] perfoliata... a. assess ene 26, [223] Speedwellis- eaten veel eee [214] Byzantines eee eee [215] field. AP or eon eee [215] thyme-leaved............. (214] Wornmskjoldes eens: [214] Kallapaisslosenien seca eee [214] SPERMATOPHYTA............. [53] Spiderworteeeeecrneoecnen Loal Wniversityanere meee [87] Spiesia Lamberti.............{159] Lamberti sertcea........... [159] Spike-grass, marsh........... 306 INDEX [454 References to the Flora are in brackets [ ] Spike srushyo eae estan reel oy flat-stemmed.............. [79] bot stata KOM Sel A uMiA ag RENT atiee ie {79] Slendersisa aii os lucida arenes [79] SWAT Py a eC IE nana atniels [79] Dale ree via yay Mia WA a [79] SPINOSAB ao eeeeieysue 18, 19 Spiraea dumosay iis eile eee [147] Spleenwortaaice eee [51] ATI Ge WSIS CNM ee iaetel ate (51] maiden-haireqaws aces [51] SPRONDEAGEAE ea a eee noe [167] Sporobolus see eae eieee eee [63] AITOLdeESeaaEae ee 15, [63] asperifolius............ 15, [63] cnyptandruse eco. Lon 103) CUSPLdGtUS iar jer [61] depauperatus.............- {61] heterolepis............. 15, [63] SUNUDIC CMG Epa un ara EAS [62] Springybeautyaseeee alee {114] large-rooted............... {114] THOS nee Ue ses tueana {114] SW) DE TAIN A AN Mu Sn ae Eero {114] C@hamissojsse seein {114] Spruce ssc 24, 31, 38, 39,40, [53] Bree ae OTe ae aN [53] Douglas eee seen 242 5a [OS Engelmann.........36,39, [53] SPULZO Tee eee aan 44, [164] Arkansas tenements [165] Benders anni sen raion [164] MOUNTS Ay ob plasisie alee 60 [165] FOSRELeI CHAU MIRA ARS MUA nt ate [164] ridge-seeded............... {164] rugulose-seeded............[164] SEO UCASE MAPA testers Se Earn [165] thyme-leaved............. [164] reoYaye eYetoliy een eta Maal ey ana [166] SEMTUNZ nid Genie RNB oulol slates [166] white-flowered............. [164] SPURGE RAMIEY einen Nene {163] Squaiwiwe edie cabin enue 34 Squirrel-tail grass............ [77] SHV DVA uid a bus olald gine asarcidlallp b [206] scopulorum............ 11, [206] Stanley aaisiua avarice seus [135] lau Caaanminmetencueyiis 15, [135] Stanley’s cress, glaucous...... [135] Star-lowervee ne aeons (229] ann alan see e Ce SI ae ee (229 Sspinulose cya eee alae [229] Stanithistle sy wan eee [255] Stanwonre seen eee {115], [233] NJAATIES YS! EOIN LAB Aen {115] alkeyBaicalleyaetsyan plete {115] State flower of Colorado.... Steijoneman nana [ eliatiumaeee aan 21, 23, [188] Stellaria Jamesiana.......... [115] UO EON 5 3'5 Calais be bla\ 6 60 (115] LOGE IOS Six dato dloicia'a a. casld, 66 (1135] GAUGING Raa aI EA Si {115] SETECED so star dneyainrd Cen evap {115] UMUC GLE eee ee [115] Stephanomeria runcinata...... [255] Stickseedinicni is mine eae [200] Cupulatesaern see eeent ior: [200] large-flowered.............[200] narrow-leaved............. [200] western ?ccn anita een amie [200] Sticktightsssaeme aceon 1 COMMONER eee eee [244] Stiff golden rod, hoary........ Stinks crass en eerie ota [68] UI OMEbecd do nsoeedod ba noose [68] S fi pan cance eG I Mi aaa [60] Gomatasaee ene 15,18,27, [60] Wettermannit.s24. 96 eee [61] Nelsonii............15,27, [60] parviflora Americana....... [60] Sceribnerigncs saeco ene 27, [60] ViriClulaepeeee ser 15, 18,27, [60] Stitchwort, long-leaved.......[115] long-pedicelled...... ..[115] Gide leona Rta aa ast to emi At uAate ({115] SOME Vas sicosdsaas saeoloc [136] Stornksbill Peas erGe eer LOSI hemlock wenn ee eee a LOS) Stra wbernyeen cc ccior ace [143] LMONKIMEUNSS bo agocudh ov woes [143] bracted.. 4 {143] PIAUCOUS Ae amie eset {144 PrLOliNGs wey sees Cee ae [144] small-flowered.............[144] Streptopussqama ascii [93] amplexifolius............28, [93] Stylosanthus laciniatus........[238] Suaeda depressa............. {111] depressaenectane a yen ats {111] SUBALPESTRES............9, 36 Subalpine flora............9, 23, 36 Subalpine forest formation..... 36 Subalpine stream formation 36, 37 Subalpine summit flora....... 37 Subalpineizoneten eee ik 36 Subaquaticiloraseewinee rer 10 SUBMONTANAE...........9, 23 Sumachoriantiacccacen teenie. [167] CiSMOntaneae see eee [167] fragranteee inert ieee (167] three-lobed............. {167] SUNMOW Ene eee eos 13, [242] 455] INDEX References to the Flora are in brackets [ ] coarsely toothed........... [243] COMMON eee see (242] GWArh wees eu ysis.cteon suvenetsean: [243] false, five-ribbed...........[243] petioledins eyicnis mys cee [243] red-streaked..............[242] Subrhomboid-anee ees [243] Wat ere eed abt cabal’ [243] Sis EV ates ae Men Eee er eet Oict oe [181] stolonifera..........23, 29, [181] Swampitloraseenerier eee 10 Swamp laurel, small leaved.. . . [186] Sweet ciceley...... obtuse-frurtedse jie eae ack [182] STOO UI Re ir cee ie eae ata [182] Sweeticloverznivse sea alae [155] WIRTEE LAT Pare) acne lola neces earpiece {155] Sweet coltsfoot...............[248] Boro Enealogacns cs asacox [248] Sweetihaee eats ryeeacue eee i0, 87 SS ACIATE I on ser pee ig ote Alcea emenoet ey lt Ke)74T| COMBE Ho ecard bie sclalc [192] Palustristeiseeeee 34, 40, [192] SHIGE SG a sinte onteeeerei teri cart oer [192] dense-flowered..... [192] TENE NES Neeliaia WHat Geka elena lebeecte [192] Swicehyorassecall eee ere [58] SIVA VAIE Sees cereale: Bil) BO SYLVESTRES..........18, 20, 24 SPADE NID AD Meee Gite Bini 8G [185] Syiphoricanpose.4 ee. [221] -20, 26, [221] 13-5 2, (22M occidentalis........ oreophilussee ees: WACSMOC~E OG sa goocbe be oe [221] SiyAlelenismeasey sapere ae (57] TAMMIE 55 46 50cG done 44, [57] Synthyris alpina.............[215] Syuthyrissalpines see. [215] Atal kiaiiirlsa a aiololoras Hecliacme cle [113] Eagvillonumeree nee e305 lS (tansyemilustanrd eae eee [130] Gut-leaved Barre eis cia ois [130] iene -leavied eye shen oh elas ya the [130] noaiys earn elie miaay NA de At {130] WESEORM Sa spaepen i Mehiaerene. cs {130] MaraxacumlmenyAckoecaeetec! [258] PHO MAM G 65 co oo boaueHoS [258] OPC Bow 6 odiecod de enos 5 olOSs}} (liaraxacumnner ae see 45, [258] Temperature and rainfall...... 88 MEDRAGONTACBAR. 64)... 525. 2) [113] Metranetinissee eee eee eZa5 HOURS SAG Gino oie rOenete rome Veo lanigeraeye eco 32,42, [245] UGUCHITIR ob Bo oars easdeaceos| AOS ccecidentalesaaeenrcicee 11, [205] pH alesiaw remeron wen ies. ccisy nose [219] 307 fasciculatassaeeeeee ee 43, [219] lutea a sis saan wean [219] (chalictrum-eeer eee rete (125] Mendlertsocc ee) settee 28, [125] purpurascens........... 22, [125] (hielespermasaae eee eee ee er [244] race eae ye Naan 16, [244] Thelesperma, slender.........[244] ihhely podiums eee ieee [135] paniculacimeree eee ee [135] SOZULLCLU TI Cee [135] LoGulosume eee eee [135] Thelypodium, panicled....... [135] (Rhermopsisuneeoree re eee [152] ATEN OSaé a Ae Ay eae [153] divaricarpa...... PY BS. S(t S3SHI pinetorum.......... 25, 43, [152] Thermopsis, divaricate-podded[153] pinelandseeer eee (152] SET Aes ae) NAD eth ea [153] Myhistlen eae : 13, [253] Colorado see eee eee eee [254] (ol ge =a SPA me Rta ee I rou [253] erose-bracted...:.......... [254] STAY, Lei ie ea aeasaye Vaan [253] Knaip weeds aca ceeeee [254] large-headed.............. [254] Parryys: a yevisnieeiceneeerlae [253] Platters uy ave ae eey ey, [254] Russian? eee See eee [111] SOWG Mdina eee OSG eas [259] Stars she hind aon sieve os kepeeons [255] woolly-headed............. yellow-spined............. [255] PDAISTE ES AMIL Verrier ieee) (22,5) Thlaspiss ices eee eae eines (127] Barbecue sdococav soso AM Coloradense.........28, 39, [127] INimt¢allivees eee 2 les tes [eral] purpurascens........... 41, [127] (ihorn=applese see eee eee [210] PUNPlE=5 he:< sie A cictiseneeieiek: [210] (Rioroughwortieeeee ieee (225] Mhreevsquaneyie ice [79] (DAVMELTATES yey ieee ee [175] Dimothy. esto ckeyeee atte etek [62] COMIN ON See een aan [62] failses 0 NYS SER Aer aaa [62] MLOUNtAIM eee r heer rere [62] Miniarias acted sie eer nee [108] Conwolvulusteeee cece 44, [108] Pbithyamalushes eee ets [165] Arkansanusue-j ieee cel On liLooll MAL CUMMALUSaee seer LLOO| LetLamMerus ayer dares [165] philorussyienn Geseeee 19, [165] dichotomalanenarereerricr [165] 308 INDEX [456 References to the Flora are in brackets [ ] TODUSCUSS ee eee LOS) MOTUS Ae ee OORT ARDS cole iaha aati eMusic [156] COURS Seo snicliodeed sous o, KOSI] all pinuimeeeeee PR CH Sop (MOGI || Atanas so de soe cook noeey (77] Drummondii........... 8, [156] sativum vulgare 77] foald= fan ayy nema ltenacttete [211] UULCAT Ee eA eye eae 46, [77] bastardy ey ae aie anrd ata (MOR) Asolo Soc bobo bvoo bo does [118] Gaintald aye gael sea Ba (211] albiflorus...........37, 39, [118] HAG) oF Korero ais Menerorcciaiaie ous ota bic [210] laxus albiflorus............ [118] night-blooming............ [210] | Troxtmon cuspidaium.........[157] Pomatopaiwis ane oe [210] PIGUCU NDA Cee ene [258] commons eee ene [210] PATUULORILTU RAR eee [258] Monestush eee eee [230] | Troximon, cuspidate.........[257] DYSMAcUs eee 42, [230] | Tumble weed............... (112] Touterea decapetala........... {174] | Tundra, wet sone be 38, 39, 40 TEU OME en ey ie [173] TUNDRALES . idly ile lacs oxo) UGC err AUN seein eee [173] | Turkey-foot grass BAA lata 13, [57] SENUALE PIAA a este vars Roe MAS) |) Uva Goss dodbooes 27, [96] SPECLOS Dla deri nea ers e [173] kidney-leaved............. [96] Mownsendiasnaaiec nee [232] MOMMA daogobooobuod oo [OO EXSCapaleseeiu tei LOn (25.5) u menwainl Hl OWers ee ae ei eee [221] grandiflora eee 19, [232] IAMeGI CON eee [221] SELECE Os SrA Lae ei [233)]5\ @iwasted-stalkeas woe aeee 27, [93] Townsendia, large-flowered. . .[232] clasping-leaved............ [93] Silleya yay ER OE Sapa Gene ZS) UMO oS ossslodeddocosaboce [55] Toxicodendron.............. [167] latifoliay tiara see anne 10, [55] Riyidibergirssyeieceiee XD MAA |) | IaaUNCVND, OO Goes bo oa oo} oe ([55] MOxiCOSCOLdione eee [88] | Uliginose society............. 10 falcatuimeyy eae aan Pe (RSEU| Ih) WGRUNCIDYNID OS So 5 66 05.0 65 06 [103] SrAMINe ume yas ineice (RSU i Obron Bisbee iy cubediond tanaio Maro o {103] Mradescantiayy noni qe [87] PNeagiceGlog go asabenboodeo [103] occidentalis aia einer ES |) Wavirimnr NUDES bodes boda ss {181] Scopulonumeyne eerie [87] | Umbrella-wort.............. [112] Universitatis........... 18, [87] bboy agin etna yea Bete BiNG 8 [113] nL ESeeeaies), Li ata ee eat eee eR [164] TEIN BE Rie are ao hietainlarctas 6 ({113] LAMIOSA Van ars onset aeree [164] heart-leaved.............. {112] ‘ra copogsoneee Meets [255] lance-leaved............... ({113] PoTnloliusseseeee eee 45, [255] narrow-leaved............. (113] porrifolius X pratensis...... [255] | UMBRELLA-WoRT FAMILY......[112] Pratensisemewws eerie 45, [255] | Upper Sonoran vegetation.... 9 Dreacleymustard:))) 4 -s9- 2 oe [130] | Upper Transition vegetation... 9 Mridophy lume udeeaeeeoe. (ZEUS Gy eng ooo on cow cce so OB lateriflorum............... [142] gracilishc ce eee Nae 12, [102] leucocarpum.............. Re NUR YNGNDG Gh! ou bo dood ooo [102] Monspeliense........... ANS AZ) MURRICAT ES efter eee eae [102] paradoxum-cqes sae ees PANE Urticulaniayees eaten [219] sbritolitnm sane oe [154] Wall Sari siies ie panieusse pat pene [219] dasyphyllum........... 42, [154] | Uva-ursi procumbens......... {186] hybridum..............44, [154] (CLV OL RRM E a G BAG eb Elo sO [186] Lividiuimbaacaecie sea OP Sa) Wee bicoccco vega dio obicd duos {117] pratenses yn Avy aes 44, [154] Vaccariasa-peene eae 45, [117] FEPENS are Psa eiee 44, [154] DULIATUS HAC eae {117] Triple-awned grass........... [60] | Vaccinium.................. [187] ARTISEE UIE LC eee [65] caespitosum............... [187] MAUS ae eee 39, [65] CPrVENNOCOCCUME:. 02 sie oioiels ai [187] montanum............. 33, [65] Myrtillus microphyllum.... .{187] SPIca tums avail aie [65] oreophilum............... [187] SUDSPICALUM Anse eisetelr 31,32, 41 SCOPATIUIMe Eee eee 42, [187]. 457] INDEX References to the Flora are in brackets [ | WAGCGCINTACEAE:. so 42 oe elo Vagnera......... Rare aye TeASeet [93] amplexicaulis........... 25, [93] KACCIMMOSAK ie) ceheislvenere cle 25, [93] stellataynercr cence 22,28, [93] Wallerian ecrtischscccaceon miners 223] edible. . [223] Greek ae aceeenval terns [198] VALERIAN FAMILY............ [223] Walenianaselsciccis acelin 223] ceratophylla........... 35, [223] COTS Saeed o tors o Teter Dati [223] VALERIANACEAE............. [223] WATE RTANALES sie cicieiet (223] VALLICOLAE........18, 21, 24, 27 Venus’s looking-glass. ata . [223] COMMON sno Oeil [223] WESTER th amiaccysererses cheats [223] Werbascum*:scererielcereiei [221] Blattariay cose e cies aie 45, [211] aphapsusia)spcvacvecvsicnnels 45, [211] Wien benal-\ryaly sate neiehe eas 204 ambrosifolia............ 14, [204] AlcDLetia at ayetie ominstoisiekenete a Dracteosaseeeeaen eee 204] albiflora emcee [204] Canadensisheceeea ease [205] hastata ioe eicitys\s a etetiel- 11, [204] Verbena, common wild.......[205] IWERBENA GEAR ere eietereley ie) feet: [204] Wernbesinast rca. saci css aces we [243] encelioides exauriculata[243], [244] exaunculatareereer oor: [243 Weronicam eis ysrciacieac cals [214] AQLEStIS rote hee) . [215] Americana....... on Ag, 29, pial IBUSUCUIIE eee (215 ByZantinaee ernie 45, [215] PEKERTINA sen tee aarciiens (214] Senpyllitolianssee ea 45, [214] Wormskjoldii....... 34, 40, [214] J ueXalapensisiaa-yraceraciscrie [214] WOnichiiamanaoioddameiciimorae > [204] Wey sisi rotenone eee ioe ns [204] large-bracteditei))-.)-12 mis [204] white-flowered........... [204] ragweed-leaved............ [204] VERVAIN FAMILY.............[204] Wetcht itamgiesasr serene 21, [161] tN) per neta iero crt o aaa 34, [155] mop uMEvt es So anaoeadoadodC {161] narrow-leaved............. [161] remote-leaved..............[161] small-flowered............. {161] Wetchlling sa aicrectancr il: 21, [161] white-flowered.............[161] WA XBEM, oo cboaddoddoga aC (221] 309 Bentagoteniccvesssc vse 23, [221] PANG OLUMISst leer eee [221] Miciaiis lars Aoio sie didislaiocuarekote 161] Gissitifolianeerereeee eee 21, [161] UGTA Sandon as oane ne tee eae 161 Oneganayisiteeioe 21, 22, [161] PLOdLuctareee eee: 21, 22, [161] Sparsitolianeerreeeaoee 21, [161] Vilfa depauperata filiformis... (o7] Ruchardsonteseeree nacre (61 Viola dU eS ae aa eee (171] bellidifoliaseeyaceic ste crek [172] biflorasie hese s see [172] Canadensis- Neo-Mexicanus 39, [172] Ryd bergieeerrenine cn 23, [172] Cognatay wwe ww notes ae [171] Neo-Mexicana............. [172] Nuttalllitey (uae ceoaciasie (172] pallens nee cae 33, [171] Dalustriswa ener 33, [171] DIY SCLOCESS Reenter cate {172] ene: HIDE Greer nae [172] vallicola.. 25, [172] VIOLACEAE.. SR Ghote oes {171] Violetin nce Maier ven teil {171] blue, western..............[171] Gereeleeniaelos sodboncccade {172] dog=tootheeeericneee error: [92] marsh iayicikr uneasy: [171] New) Mexicosscemsasec eee: {172] noddingiNncaarcnysceeto: {172] Nuttallisy eye [171] Delbaere riding cicinio coin ana {171] Rydbergishs Seance: [172] two-flowered.............. {172] Valleys s-vita eee on: [172] WIGEWAN INS Soacecooocdds (172] VIOLET RAMI Yaseen eee Lal Wiornaye a,c ac sista enero rae nae {121] erlophoraeac-mieeeiorecie (122] NOnests ema cacobdecdabmes [121] Virginia creeper............. [169] Vinelike\.Sactseiennee eas [169] Wir ginisiboweletneee eet {121] WESLELD vais aveisvetcyesse seitence ia: {121] VITACHAE en yacuiiaer var treae [169] Witistxc eee tiarher eee as [169] ATIZOMICAs eerie ae LOO Boulderensisiece seein ee [169] palmatasysieierrerrm tortie [169] FLPOVAD said wispe 0s ts)'s a apa haa [169] Tyee cgos oo dooee 12, 22, [169] Wolwiiluss.ceiarcg aceite [195] ANLOLIOMepsbetonetekstrctete te tehatrete [195] Wallflower, Cockerell’s....... {131] INDEX References to the Flora are in brackets [ ] 310 STOW MEN EIS ene tedsete [131] WeESLELM ese einai aite [130] Washingtonia longistylis...... [182] CDIUSA MES Maurie) coe aelster ees [182] Weer Crees cose edoadod soe [128] Water crowfoot.............. (122 White muy cae serene 34, [122] flaccid-leaved........... (122] Water dropwort.............. [183] endlersshanreneicieericiniitcr [183] Water hemlock.............. [182] Water hoarhound............ [208] ENINANCEIGY ob adoopidagboooK [208] WESLETM ss iierleperesetsieneheteteiele [208 Wraterleateaciaaier tle oo] Rendler/s ayy ones [199] WATER-LILY FAMILY.......... [125] Water milfoil.............10, [181] Spiked AEM aate [181] Water parsnip............... [183] Gut-leavedsaenmmmiirnacevatcl [183] Water pepper............... 10 Water-plantain.............. COMMON eae [56] WATER-PLANTAIN FAMILY..... [56] Water spring bee [114] Chamisso’s. (114] Water starwort........... 10, [166] AIKEN be 5 )4'g'd6 go Go clauiae.s [166] MATS Hes ae ee eer years 166] WATER STARWORT FAMILY [166] Wiax-cunrantanenineneeehicn 20, 29 Sra ee Pe ile aap aaa [140] Wieed Sure Naya yA RUE ae Western mallow............. [170] WATER vn eee aya paar [170] Westernlistare oreo: [173] many-flowered............ [173] nakedwer ae are eee Ludo SHOW Eset csi ciel eno tinier [173] StrIiCE Se etnine np au nh enn hunreioe {173] ten-petalled............... {174] wavy-leaved.............. [173] Wihea ea ica ine natn itratora [77] Wiheatioralssmmemecianiri-iets [76] ANGVANIES os ola gesododagood00 [76] WHOMINEMINSG Gig gbeesodoaucos [76] Ruchardsonvs eae eeeeeee [76] Lipanane verter Keio [77] Scnibnerissseeueiince ace [76] Slender (eiepaiicrewstaye/aaisherhoinvs [76] SOLE RU a LN rade Sat rela [77] Vasey’s [76] VIOLE EN ROCHA Vt NOR eee ar naa [76] WESTER! siirean ie cr om a Vann [77] White evening primrose....... [178] cut-leaved nye ateliaraior [179] INUttallis heise saan ers [179] rhizomatous............... [179] white-stemmed............ [178] White sage.................. [110] woolly.syhaieee sua ee ee [110] Whitlow-grass............... [132] artic) whitess casero ae [133] Baker’se.i7. ee eS 3] Goloradone ae eee [132] hoary jessy Nese idee milo cesses [133] thick=leaved-eeysemeneenee ts [132] twisted-podded............ [133] wihitefancticun ee eee [133] iC Bab StoES HLS Gididia wuoldraiorokn [132] Wihitlowworteeeeseeinee ane (112] decumbentso555), sheen [133] fexo) (a Keron Iu Bid eh Atala lai [133] James sii ane aaa Ne tage {112] pUlVvinate.se eee {112] vellowisheer cece ne [133] Waldibrientiarien sec ince 21 Wild cherry ponee bCWS Mile 2X) black- fated western....... [152] Wild oat-grass............... [66] (Camtigaws) Gucb igs cabooo 0% [66] COMO Nooisccceddacss aa [66] intermediate.............. [66] Waldiliquonicesse nyse lent [159] SCaly eat ei httene oceans [159] Wild onion, Fraser’s......... [92] Geyer Gee snes ee aes yale [91] Nuttall lise eee ea Ss [91] Pike's) Peak.cs-32))2 20-5. 4. [92] GHECURVER rp iae ee bieeene [92] Waldéplummaraeniie steric 20, 28 Almerican ere enoeeeemeree {151] Wild rye, Canadian.......... [78] Macounys ieee [78] slendere nae oe ene [78] StOUEN: Agen Een ona [78] Wildsarsaparilla............. [181] COMMMONG daiscosegesoooaos 181 Willow. . 12, 21,27, 38, [99] Bebbis se uuice see yee 00] bloom-branched........... [99] Gwar k eee ca eae ear ae eeom [100] falseyWaplandeeeeeeeeeeers [100] Hendlerisceriiciiuas sured [99] clacous nn nee eee [100] green-leates einen ieee [100] aplandtifalsesseemaaeeceee [100] long-beaked............... [99] Narrow-leatye eee [99] Nuttall lice ie ant eae siete [100] Peachy eee MMO Se [99] rock-lovingesee semen [100] Rocky Mountain.......... [101] 459] INDEX References to the Flora are in brackets [ ] Wolf starr aruercraristeetce sy ctcrerets Yellows ee CIO ere STA Easy fore secs tere neree srekete Nortehernvaceve reese eee paniclediwrnsa cc seimchktee ee glandulanacceee ieee Plmperne leslie TEA dishes wapeje sere eesetaiels rae western.. Pra ele WILLow- HERB PAMIDY Jone IDOa socnmic adios eed GoMlnsidD creeping... PAL ed CU KN eae Gnestlowerede animale one-sidedmanseie cea oae i WINTERGREEN FAMILY........ Witchvonasseniniyeine yikes Wood reed-grass............. SIS ET esi sere cmcailsbateuetebers Wicoal ®iGitcssscdbogomecdsans dense-cymed.............. small-flowered............. Sprecher te velerter ition WooD SORREL FAMILY........ Wooded mesa formation...... Oreganan eo silos woe 29, SCOpULInaas eee tei 29, WioodsiaNiclittivnisererr rica MOMMMEAV Ga concadonuoaaae Wiool-jomltenmr eerie 18, Bakerisiisemisiicesmia ioctl ares SUbal pines -tereyetceasieaeieret: umbellate BAH Sais marcia crolatrok WOlOiocdodccosacunovesce Bur bienniallvin racine omcheatssmens (247] Wiyethialy arises Oye ions read [242] amplexicaulissn. cis.) [242] Wyethia, clasping-leaved..... [242] \WarowiieAs Gboobubecocapasc [239] (6a FIG, Gate el SU nm Ents ian 16, [239] DERI, doodosicoocacebonS [225] Commune eee 12, 45, [225] MantEhOxalisueryeieva seer {163] stricta einem 25, [163] Ximenesia exauriculata....... [244] Xylophacoswae yee aes [157] ISEWe wid boone aio consi Ceteasc 30, [157] Shortianuss see 15, [157] EXGVIRIDAT ESS alsin yecd evar aera [87] AERO Wirsaactsuallensenyeie eteuattncra tke [246] WOOL Lys ey a wat testa ele [246] Nellowicressee eee eee {129] Spreadinccnew cy tae rrr ne {129] warty-podded:2......../.- [129] Yellow mountain avens.......[146] Arapahoehnancneraaiicncceit [146] Yellow pond lily.......... 24, [125] many-sepalled.. 5c ol ASI) Yellow wood sorrel.. [163] tikoyated raced oldiama Arico e3 [163[ h Alcor Banter dich caacicca waco n [94] ONMSUSTUROLLO Aeterna [94] glaucarepaeroer 15,18, 20, [94] Yucca nae ats aR 19 Yucca mesa formation.. aouliyy te) Zanichellia. . RARE Dodie tieen SO] palustriss-ceee cee ene 10, [56] Zanichellia, marsh........... [56] ZANICHELLIACEAE.... [55] Zones of vegetation.......... 8 alpine summits............ 9 foothills and mountain pla- EAU Laer Matte 9 lower mountain slopes Beat 9 mesas. babe 9 plains... : 9 subalpine mountain slopes... 9 Zygadenus elegans...........- [88] ESPEN MCD Cb aoa sooo KO Od [88] Coloradowepeterarrya-Precrer [83] SHOW shisloseision gl seatsien selee aieeke [88] (Ss) UNIVERSITY OF MISSOURI STUDIES Edited by W.“G, Brown) ' SCIENCE SERIES VOLUME I Topography of the Thorax and Abdomen, by PETER Por- TER, M. A., M,,.D., Associate Professor of Anatomy, St. Louis University. pp. vii, 142. 1905. $1.75. Qut of print. The Flora of Columbia and Vicinity, by Francis Pot- TER DANIELS, Ph, D. pp. x, 319. 1907- $1:25. VOLUME II An Introduction to the Mechanics of the Inner Har, by Max Meyer, Ph. D., Professor of Experimental By chology. pp. viii, 140. 1907. | $1.00. The Flora of Boulder, Colorado, and Vicinity, by Fran- cis Porrer DANIELS, Ph. D., Professor in Wabash Col- lege, Indiana. Formerly Assistant in the’ University of Missouri. pp. Vili, 311. 1911.» $1.50. ‘LITERARY AND LINGUISTIC SERIES VOLUMEL — Chevalerie Vivien, Facsimile Phototypes, with an intro- duction and notes, by RAyMoND WEEKS, Ph. D., Profes- sor of the Romance Languages and Literatures, Columbia University, New York. pp. 12 with XXIV plates. 1910. $1.25. VOLUME II “The Cyclic Relations of the Chanson de Willame, by THEODORE ELy Hamitton, A. M., Ph. D., Assistant Pro- fessor of Romance Languages in Ohio State University. Formerly Instructor in Romance Languages in the Uni- versity of Missouri, pp. ix, 301. 1911. $1.50. . Balted by We G Bow By pony ey a A RIAN Aes VOLUME Ly ‘i ‘ The Clothing Industry, in New ion by Fett E. PorR, Ph. 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