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 SECTION FIRST-SUMMARIES OF EVIDENCE.

IMPORTATION; SPREAD; INCREASE; CHECKS, INTRODUCTION OF THE SPARROW.

The English Sparrow was first brought to this country, so far as authentic information has reached the Department, in the fall of 1850, when the Hon. Nicolas Pike and other directors of the Brooklyn Institute imported eight pairs into Brooklyn, N. Y.

As this first importation of Sparrows is of much interest, we give in full Mr. Pike's account of it and of the following importation a year or two later. He says:

"It was not till 1850 that the first eight pairs were brought from England to the Brooklyn Institute, of which I was then a director. We built a large cage for them, and cared for them during the winter months. Early in the spring of 1851 they were liberated, but they did not thrive.

"In 1853 a committee of members of the Institute was chosen for the re-introduction of these birds, of which I was chairman.

"Over $200 was subscribed for expenses. I went to Bngland in 1852, on my way to the consul-generalship of Portugal. On my arrival in Liverpool I gave the order for a large lot of Sparrows and song birds to be purchased at once. They were shipped on board the steam-ship Europa, if I am not mistaken, in charge of an officer of the ship. Fifty Sparrows were let loose at the Narrows, according to instructions, and the rest on arrival were placed in the tower of Greenwood Cemetery chapel. They did not do well, so were removed to the house of Mr. John Hooper, one of the committee, who offered to take care of them during the winter.

"In the spring of 1853 they were all let loose in the grounds of Greenwood Cemetery, and a man hired to watch them. They did well and multiplied, and I have original notes taken from time to time of their increase and colonization over our great country." 8404—Bull. 1—2 17

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298 knew, nor could any discover; for the next day he was found in the great hall raving mad, and the people said that Helene's curse was a potent one, that already it had wreaked vengeance on the one who had wronged her most.

"From that day, the château was called Rougemont. The d'Harcourts were all dead and the place fell into other hands. Then there grew up the rumor that the château was haunted, that the fair Helene roamed through its halls, cut off from her lover, and doomed to stay within these walls by Black George's curse."

silent, Wrexler and I looked at the portrait. My own feelings were in a turmoil. It had been a ghost's lips that had touched me last night; yet surely no ghosts could have been so beautiful or seemed so real.

Wrexler turned to me, "It would be the curse that has always been upon me that when I fell in love it would be with a ghost!" His eyes were vivid, shining brightly in his pale face. "I knew when I saw her on the stairway that I loved her."

"There is a rumor," said de Lacy, "that the man who sees the fair Helene will meet with some misadventure, unless she gives him a kiss. Then he is protected from her wrath."

I started. Wrexler smiled, "She kissed me with her eyes. I am not afraid."

"The fair Helene makes men suffer to make up for the wrong Black George did her. For years she has not been seen at Rougemont. Last night when you described her, I was afraid. My lord," de Lacy turned to me, "send your friend away. If she only looked at him and smiled, there is a grave and deadly danger for him, more deadly because it may be unexplainable. Men upon whom the fair Helene has smiled have met strange deaths."

As Wrexler looked up at the portrait, an inward light illumined his countenance. "I am not afraid," he repeated.

"There are many deaths. There is the death of the spirit as well as that of the body. I beg you to go while there is time, friend of my lord." There was real feeling in de Lacy's voice.

I too felt afraid for Wrexler. The strange, unworldly feeling he had always had, the pulling toward something he knew not what, made me doubly fearful. Had the fair Helene been calling him all this time, across the world? For myself I had no fear. She had kissed me, and besides, even death at her hands would have been preferable to never seeing her again. In these last few minutes I had realized that I too was in love with Helene, that I could hardly wait for the night, in hopes that she might visit me again.

Resolutely I put my own feelings in the background, for at the moment Wrexler was of paramount importance. If there was anything in de Lacy's story—and from my own experience I was sure there was—Wrexler was in danger. I turned to him. "If anything happened to you, I could never forgive myself. Perhaps you'd better go. I could arrange a trip for you, and later—meet you."

Somehow de Lacy seemed one of us. I had no hesitancy in speaking before him. He seemed a part of my new life. With the strange suddenness that comes on rare occasions, we were already friends.

Wrexler looked at me, then back at the portrait. Helene d'Harcourt, her red hair gleaming, smiled down upon us. Before he spoke, I knew what he would say, because in his place I would have said the same, "Unless you kick me out, I want to stay."

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302 been induced to show herself agreeable. So it was with the cherries in her childhood and with the stem of camelias in her later years; the exotic feature is an illusion to a muchtravelled naturalist, who sought to win her favour by means of a drawing of a flower. Another female patient creates a middle element out of bath-houses at a bathing resort, rural outside water-closets, and the garrets of our city dwellings. The reference to human nakedness and exposure is common to the two first elements; and we may infer from their connection with the third element that (in her childhood) the garret was likewise the scene of exposure. A dreamer of the male sex makes a composite locality out of two places in which "treatment" is given—my office and the public hall in which he first became acquainted with his wife. Another female patient, after her elder brother has promised to regale her with caviare, dreams that his legs are covered thick with black caviare pearls. The two elements, "contagion" in a moral sense and the recollection of a cutaneous eruption in childhood which made her legs look as though studded over with red dots instead of black ones, have here been united with the caviare pearls to form a new idea—the idea of "what she has inherited from her brother." In this dream parts of the human body are treated as objects, as is usually the case in dreams. In one of the dreams reported by Ferenczi there occurred a composition made up of the person of a physician and a horse, over which was spread a nightshirt. The common feature in these three components was shown in the analysis after the nightshirt had been recognised as an allusion to the father of the dreamer in an infantile scene. In each of the three cases there was some object of her sexual inquisitiveness. As a child she had often been taken by her nurse to the military breeding station, where she had the amplest opportunity to satisfy her curiosity, which was at that time uninhibited.

I have already asserted that the dream has no means for expressing the relation of contradiction, of contrast, of negation. I am about to contradict this assertion for the first time. A part of the cases, which may be summed up under the word "contrast," finds representation, as we have seen, simply by means of identification—that is, when an interchange or


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Rh Yet from the occasional statements thus made, and from various reliable published records, we have been able to make a list of more than a hundred places in the United States and Canada to which Sparrows have been taken, either by direct importation from the Old World or by transportation from place to place after their arrival in America. From the casual manner in which these data have been obtained it may be considered certain that they represent but a very small fraction of the number of points at which the Sparrow has been introduced; but the early dates of many of the importations, as well as the great distances separating many of the places, are very significant as affording a partial explanation for the unparalleled rapidity with which this bird has overspread the inhabited part of the continent. The following lists explain themselves :

Table I. — Places where English Sparrows have been introduced directly from Europe.

 * About.

Table II.—Places, not included in Table I, where Enijlish Sparrows have l)ecn introduced.

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 250 DIFFEB.h]NTi`;AIx Game 1 rw _ then the equation of the asymptote is found by subetitu i Q    ; ing values a arrl b in the equation Z Z = a + I2 1' If only one of these limits exists, but I limit (%> = M, then we have one intercept and the slope given, so that the equation of the asymptote is y=m:r+b, or z=;Z+a. Itnusrnnxve Exnmna 1. Find the asymptotes to the hyperbole Z; - g: = 1. . dl/ biz b 1 limit (dll) il _ f = 7 = _ -l d = _ = _ . Solution dz asv i a az 1 an m Z = w dx 3; a "5 2 Also z;= LL and yi:-Z; hence these intercepts are zero when a:=y=co. 33 I/ Therefore the asymptotes pass through the origin (see figure on p. 240) and their equations are 0 4; (z Ox), or ay/ ibm This method is frequently too complicated to be of practical use. The most convenient method of determining the asymptotes to algo braic curves is given in the next section 152. Method of determining asymptotes to algebraic curves. Given the algebraic equation in two variables, (A) f(1~ 9) = 0 If this equation when cleared of fractions and radicals is of degree n, then it may be arranged according to descending powers of one of the variables, say y, in tl\e form (B) a_y"+(b:c+c)y"'l+(dx”+e:c+f)y”"+-~-= ."‘ For a given value of rc this equation determines in general n values of y. from Algebra: Given an algebraic equation of degree n, Ay»\+ By"-1 + Oy”-2+Dy--8+ When A approaches zero, one root (value of V) approaches oo When A and B approach zero, two roots approach an When A, B, and C approach zero, three roots approach ao, em me 4 ' f/f`i0SOff ® 71- = Q -- = ,Ana a 0 <--==0.
 * For use in this section the attention of the student is culled to the following theorem


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The American Cyclopædia (1879)/Nebula

NEBULA (Lat., mist, vapor), an aggregation of stars or stellar matter having the appearance, through an ordinary telescope, of a small, cloud-like patch of light. An enlargement of telescopic power usually converts this appearance into a cluster of innumerable stars, besides bringing to light other nebulæ before invisible. These in turn yield to augmented magnifying power; and thus every increase in the capacity of the telescope adds to the number of clusters resolved from nebulae, and of nebulae invisible to lower powers.

Nebulæ proper, or those which have not been definitely resolved, are found in nearly every quarter of the firmament, though abounding especially near those regions which have fewest stars. Scarcely any are found near the milky way, and the great mass of them lie in the two opposite spaces furthest removed from this circle. Their forms are very various, and often undergo strange and unexpected changes as the power of the telescope with which they are viewed is increased, so as not to be recognizable in some cases as the same objects. The spiral nebulae are an example of this transformation. This class was recognized by Lord Rosse through the use of his six-foot reflector. Many of them had been long known as nebulæ, but their characteristic spiral form had never been suspected. They have the appearance of a maelstrom of stellar matter, and are among the most interesting objects in the heavens.

There is another class of nebulæ which bear a close resemblance to planetary disks, and are hence called planetary nebulæ. They are very rare. Some of them present remarkable peculiarities of color. Sir John Herschel has described a beautiful example of this class, situated in the southern cross. But in telescopes of the highest power some of the so-called planetary nebulæ assume a totally different appearance; and many of them are singularly complicated in structure, instead of being

simple globes of nebulous matter, as was formerly supposed. There are several which have perfectly the appearance of a ring, and are called annular nebulæ. A conspicuous and beautiful example is situated in Lyra. Some appear to be physically connected in pairs like double stars. Most of the small nebulæ have the general appearance of a bright central nucleus enveloped in a nebulous veil. This nucleus is sometimes concentrated as a star and sometimes diffused. The enveloping veil is sometimes circular and sometimes elliptical, with every degree of eccentricity between a circle and a straight line. There are some which, with a general disposition to symmetry of form, have great branching arms or filaments with more or less precision of outline. An example of this is Lord Rosse's Crab nebula. Another remarkable object is the nebula in Andromeda, which is visible with the naked eye, and is the only one which was discovered before the invention of the telescope. Simon Marius (1612) describes its appearance as that of a candle shining through horn.

Besides the above, which have comparatively regular forms, there are others more diffused, and devoid of symmetry of shape. A remarkable example is the great nebula in Orion, discovered by Huygens in 1656. This nebula and that in Andromeda have been admirably delineated by the professors Bond of Harvard observatory. (See “Memoirs of the American Academy of Arts and Sciences,” new series, vol. iii.) The great nebula in Argo, which Sir John Herschel has charted with exquisite care and elaborateness in his “Cape Observations,” is another example of this class. In the southern firmament there are two extensive nebulous tracts known as the Magellanic clouds; the greater called Nubecula Major, and occupying an area of 42 square degrees; the smaller called Nubecula Minor, and covering about 10 square degrees. In these tracts are found multitudes of small nebulæ and clusters. The number of these

wonderful objects which have been recognized in all the heavens is upward of 5,000. Of these fewer than 150 were known prior to the time of Sir William Herschel. In 1786 he communicated to the royal society a catalogue of 1,000 new nebulæ and clusters; in 1789 a second catalogue of the same number of new objects; and in 1802 a third which included 500 more. In 1833 Sir John Herschel communicated to the royal society a catalogue of 2,306 nebulæ and clusters in the northern hemisphere observed by him, 500 of which were new. In 1847 appeared his “Cape Observations,” which contained catalogues of 1,708 nebulæ and clusters in the southern heavens. —

The application of spectroscopic analysis to these objects, by Huggins, Secchi, Vogel, and others, has resulted in the noteworthy discovery that while some among the nebulæ are really clusters of stars, others consist in the main of gaseous matter. The former give spectra resembling in their general characteristics the spectra of stars; the latter give a spectrum of three bright lines (occasionally four), one line corresponding in position to a line in the spectrum of hydrogen, another corresponding to a line in the spectrum of nitrogen. The resolvable nebulæ mostly give spectra of the former class, while the bright-line spectrum is given by all the irregular nebulæ hitherto examined, and by the planetary nebulæ. Of about 70 nebulæ examined by Huggins, nearly one third gave the spectrum indicative of gaseity, the rest giving a stellar spectrum. — As to the nature of nebulæ, two chief theories have been advanced. It was first suggested by Wright of Durham, and afterward maintained by Kant and Lambert, that the nebulæ are stellar galaxies similar to our own star system. Sir W. Herschel, at the beginning of his researches into the constitution of the universe, adopted this view as respects certain nebulæ which he regarded as external, while holding

(contrary to the usual statement in our text books of astronomy) that many nebulæ form parts of our own star system. At a later stage of his labors he advanced the hypothesis commonly known as Herschel's nebular hypothesis, which however related only to certain orders of nebulæ. At this stage Herschel for the first time indicated his ideas respecting the arrangement of all orders of stellar aggregations and nebulous matter. At the lower extremity of the scale he placed widely spread luminosity, such as he had first described in 1802. He passed from this irregularly spread luminosity, through all the orders of gaseous nebulæ (irregular nebulæ, planetary nebulæ, nebulous stars) formed by the gradual condensation of the gaseous matter, until the star itself is formed; then he entered on the part of the series he had before recognized, passing on to the various orders of stellar aggregation, diffused clusters, ordinary stellar nebulæ, and more and more condensed groups of stars, up to the richest star clusters. At this period (1814) we no longer find him speaking of external nebulæ; not, it is to be presumed, that he no longer recognized the probability that other stellar galaxies besides our own exist, but that he no longer found it possible to discriminate those nebulæ which are external from the far greater number which unquestionably form component parts of our own sidereal system. The researches of the present writer into the subject dispose him to believe that our sidereal system extends far beyond the limits which have ordinarily been assigned to it, and that there are no nebulæ which can be regarded as external to it.

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 _-v _ L 252 DIFFERENTIAL CALCULUS Ir.Lus'r1u'rxvs Exnnns l. Find the ssympwtm of the curve nfs: = plz -ef V Solution. Arranging the terms according I/o powers of an, .- y/zz-(2a1/+a.9)z+a2y=0. Y Equating to zero the coeillcient of the high- est power of z, we get y = 0 as the asyinptote parallel to OX. In fact, the asymptote win- cides with the axis of 1. Arranging the terms according to the powers of y, (a:-a)21/-a“z = 0. E Placing the ooefiicient of 7/ equal to zero, 0 A X we get as = u. twice, showing that AB is a double asymptote parallel to OY. If this curve is examined for asymptotes oblique to the axes by the method explained below, it will be seen that there are none. Hence 7/ = 0 and an = a. are the only asyinpwtes of the given curve. CASE II. To determine ssymptotes oblique to the coordinate axes. Given the algebraic equation (F) f(1'1 .7/) = 0' Consider the straight line (G) y = mx + lc. It is required to determine ni and lc so that the line (G) shall be an ssymptote to the curve (F). Since an asymptote is the limiting position of a secsnt as two points of intersection on the same branch of the curve move oif to an infinite distance, if we eliminate y between (F) and (G), the resulting equa- tion in z, namely, (H)  rrwv+1c)=0, must have two infinite roots. But this requires that the coeilicients of the two highest powers of ar shall vanish. Equating these coeffi- cients to zero, we get two equations from which the required values of rn and lc may be determined.. Substituting these values in (GQ gives the equation of an asymptote. Hence the following rule for Ending asymptotes oblique to the ciiiniinate axes: Fmsr Sree. Replace 3/ by mz+ lc in the _qivem eqfuaiion and expand. Siscorrn STEP. Arrange the terms according to descending powers qfzv. Truim STEP. Eqz/,ate to zero the coqgicien/ts qf tlw two higlwst powers* of 1, and solve for 'IIL and lc. s lf nie term involving nf- -1 is missing, or ir the value nr ni nbuiinnd by planing uni first meilicient equal to zero causes the seoond eoeflicient to vanish, then hy placing the maili- ek-nts of ze and x'--2 equal to zero we obtain two equations from which the values of m and lc may be found. ln this msc we shall, in geneml, obtain two Ic's for each m, that is, pairs of parallel oblique asymptotes. Similarly, if the term in in*-2 is also missing, each mine of in iurnishes three parallel oblique asyinptotes, and no nn. hi/ '1»7mrosoi'i


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 ASYMPTOTES FOURTH STEP. Substitute these values of m and k in y = mx -f~ k. This gives the required asymptotes. ILLUSTRATIVE EXAMPLE 2. Examine y 3 = 2 ax 2 x 3 for asymptotes. Solution. Since none of the terms involve both A y x and y, it is evident that there are no asymptotes parallel to the coordinate axes. To find the oblique asymptotes, eliminate y between the given equation and y = mx + k. This gives (mx + k) 3 = 2 ax 2 x 3 ; and arranging the terms in powers of x, (1 + m 3 ) x 3 + (3 m"k - 2 a) x 2 + 3 k 2 mx + k 3 = 0. Placing the first two coefficients equal to zero, + m 3 = and 3 m?k 2a = Q. Solving, we get m 1, k = Substituting in y = mx + fc, we have y = x +  3 the equation of asymptote AB. EXAMPLES Examine the first eight curves for asymptotes by the method of 150, and the remaining ones by the method of 151 : . y = e?. Ans. y = 0. 2. y e-**. Ans. y = Q. . y = logx. Ans. x = 0. x y = e, x= 1. n being any odd integer, x = x = 0, y 0. y = x + 2. . y = tanx. i . ?/ = e*-l. . y 3 = . Show that the parabola has no asymptotes. . y 3 = a 3 - x 3 . . The cissoid y 2 = . y*a = y z x + x 3 . . y 2 (x 2 a) = x 3 a 3 . . x 2 ?/ 2 = a 2 (x 2 + y 2 )- . y(i . The folium x 3 + y 3 - 3 axy = 0. . The witch x 2 y = 4 a 2 (2 a - y). . xy 2 + x 2 y = a 3 . 20. y + x = 0. x = 2r. x = a. . y=x. x = 2a, y -(x + a). x =, y = a. x = 6, x-26, y + 3a y = c, X = b. y + x + a = 0. x = 0, y = 0, x + y = 0. L, x--2y = 0, x + y = 1, x y 1.


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 h e ‘ mmm or  251 CASE I. To determine the asymptotes to the curve (B) which are parallel to the coiirdinate axes. Let us first investigate for asymptotes parallel to 01/I The equation of any such asymptote is of the form (0) @=/C, and it must have t\vo points of intersection with (B) having infinite ordinates. First. Suppose a is not zero in (B), that is, the term in y” is present. Then for any finite value of r, (B) gives n values of y, all fnite. llence all such lines as (C) will intersect (B) in points having finite orclinates, and there are no asymptotes parallel to OK Second. Next suppose a= 0, but I2 and c are not zero. Then we know from Algebra that one root (=_1/) of (B) is infinite for every finite value of ac; that is, any arbitrary line (C) intersects (B) at only one point having an infinite ordinate, If now, in addition, l>z+c=0, or (D) ¢=-g, then the first two terms in (12) will drop out, and hence two of its roots are infinite. That is, (D) and (B) intersect in t\vo points having infinite ordinates, and therefore (D) is the equation of an asymptote to (B) which is parallel to Oli Third. lf a = b = c = 0, there are two values of at that make _y in (B) infinite, namely, those satisfying the equation (E) ` dr” + ez +f= 0. Solving (E) for ac, we get two asymptotes parallel to OK and so on in general. In the same way, by arranging _/`(:c, y) according to descending powers of rc, we may find the asymptotes parallel to OX Hence the following nxle for finding the nsymptotes parallel to the coordinate axis: Fmsr STEP. Eguate to zero the coeficient of the highest power of z in the equation. This gives all asyrnptotes parallel to OX SECOND STEP. Equate to zero the coqfcient of the hrllrhest power of y in the equation. This _#UGS all asymptotes parallel to OK Nou; Qf course if one or both qf these coqfcients do not involve z (or gy), they cannot be zero, and there will be no corresponding asymptote. -


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Rh native place, or through distrust of the kind of Sparrow already imported, which, unfortunately, was widely known from the first as the English Sparrow. We can never know how many separate importations were thus made, nor how many thousands of individuals were introduced, but it is certain that the number of places thus supplied with birds is much greater than has been supposed, and considering this fact and the rapid rate at which the Sparrow breeds, we ought not to wonder that it has so completely overrun the country.

METHOD OF DIFFUSION OP THE SPARROW.

In the ninth edition of the EncyclopediaEncyclopædia [sic] Britannica the distinguished ornithologist, Prof. Alfred Newton, makes the following statement:

This statement of the Sparrow's relations to man is unquestionably true wherever the bird is known, and hence in America we should not expect to find it except in settled portions of the country. The manner, however, in which it overruns a new country to which it is introduced differs somewhat from the way in which it extends its range in older countries as the area of cultivation is extended. In America, the method by which the Sparrows spread without the direct aid of man is peculiar. They first invade the larger cities, then the smaller cities and towns, then the villages and hamlets, and finally the populous farming districts.

The cities and towns first invaded by the Sparrow (of course excluding those where they are actually carried by men) are in most cases railroad towns; and especially in the West there is no doubt that the great railways along which vast quantities of grain are transported have been so many great highways along which the Sparrows have traveled slowly from place to place. More or less scattered grain is always to

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Rh I put my hand on Wrexler's shoulder. "So be it. Come along, let's see the library, then we'll know all of Rougemont. We've seen everything else."

Wrenching his eyes away from the portrait, Wrexler followed us.

The library was beautiful, with paneled walls that had rows and rows of books sunk in their depths. There was a long, oaken table, and on the center of it stood a carved, gilded box, the casket which held my father's letter. I wished then that I could read it at once. I wish now that I could have, but perhaps it is better that I did not; at least things moved as the fates ordained, and the responsibility for what occurred was not mine.

next three days were quiet, happy ones. Nothing occurred. I had no ghostly visitant and Wrexler saw nothing of Helene. Under de Lacy's expert guidance, we rode over the estate, hunted with falcons, a pleasing sport which we both took to our hearts; mingled with my court, found the people charming and highly cultivated. We took lessons in the old dances, visited the manor houses. It was all very gay and amusing, and I had no longing for the outside world. I did not even go down to the lodge for news.

There were many details of the estate management that I had to go into with de Lacy. We spent several hours each morning going over the affairs of Rougemont. It was virtually a small kingdom, and everything was referred to me.

Necessarily, the time I spent with de Lacy on such matters, Wrexler was alone. He had changed a great deal since we had come to Rougemont. He had come alive, and he threw himself into everything with a curious intensity. He was like a person who has been very ill, who suddenly finding himself better and fearing it is only temporary, clutches life with both hands. He devoted long hours to reading the records of the d'Harcourts, until he knew the family history as well as his own.

I did not mention Helene, although there was seldom a moment when she was out of my thoughts. I found myself watching for her day and night, and I caught the same tension in Wrexler's eyes as he searched the shadows.

The third night she came again, not to me, but to Wrexler; and although he was my friend, I almost hated him because he had seen her and I had not. He told me next morning as we walked along the lake shore.

"Jim," he said suddenly, "I saw her last night. She came to my room. She drew aside the curtains of the bed, and leaned over me. I can't describe my sensations. It was almost as though life were suspended in space—like a bridge over a timeless sea."

I had nothing to say. I knew so well how he felt.

"She leaned closer and closer to me," Wrexler went on; "then she smiled, and before I could find my breath to speak, she was gone. This is the second time she has smiled at me. I felt a nameless fear, as though there was a threatening quality in those red lips. She looked at me as though I might have been Black George himself."

In that moment, all my envy was swept away by anxiety for my friend. Indeed, I wished she had kissed him, for then he would have been safe, I started to speak, to beg Wrexler to leave Rougemont, but before the words could leave my mouth, I saw her. She was standing in the path some distance away, directly in line with my eyes, and she was shaking her head impressively.

I knew instantly what she meant. I was not to send Wrexler away, He


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 254 DIFFERENTIAL CALCULUS . Asymptotes in polar coordinates. Let/(/3, 0)= be the equa- tion of the curve PQ having the asymptote CD. As the asymptote must pass within a finite distance (as OE} of the origin, and the point of contact is at an infinite distance, it is evident that the radius vector OF drawn to the point of contact is parallel to the asymptote, and the subtangent OE is perpendicular to it. Or, more precisely, the distance of the asymptote from the origin is the limiting value of the polar subtangent as the point of contact moves off an infinite distance. To determine the asymptotes to a polar curve, proceed as follows :. FIRST STEP. Find from the equation of the curve the values of 6 which make p = oo.* These values of 6 give the directions of the asymptotes. SECOND STEP. Find the limit of the polar subtangent de dp' by (7), p. 86 as 6 approaches each such value, remembering that p approaches oo at the same time. THIRD STEP. If the limiting value of the polar subtangent is finite, there is a corresponding asymptote at that distance from the origin and parallel to the radius vector drawn to the point of contact. When this limit is pos- itive the asymptote is to the right of the origin, and when negative, to the left, looking in the direction of the infinite radius vector. EXAMPLES . Examine the hyperbolic spiral p = - f or asymptotes. Solution. When 0=0, p = oo. Also -!- = ; hence" dd u subtangent = p ^ = ^.- - = - a . It happens in this case that the subtangent is the same for all values of 0. The curve has therefore an asymptote BC parallel to the initial line OA and at a dis- tance a above it. equating to zero the coefficient of the highest power of />,
 * If the equation can be written as a polynomial in p, these values of may be found by


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 SINGULAR POINTS Examine the following curves for asymptotes : . p cos = a cos 2 0. Ans. There is an asymptote perpendicular to the initial line at a distance a to the left of the origin. . p = a tan 6. Ans. There are two asymptotes perpendicular to the initial line and at a dis- tance a from the origin, on either side of it. . The lituus p6% = a. Ans. The initial line. . p = a sec 20. Ans. There are four asymptotes at the same distance - from the origin, and inclined 45 to the initial line. . (p - a) sin = b. Ans. There is an asymptote parallel to the initial line at the distance b above it. . p = a (sec 2 + tan 2 0}. Ans. Two asymptotes parallel to, at distance a on each side of origin. . Show that the initial line is an asymptote to two branches of the curve p 2 sin B = a 2 cos 2 6. . Parabola p = costf 154. Singular points. Given a curve whose equation is Ans. There is no asymptote. Any point on the curve for which = and ^ = dx dy is called a singular point of the curve. All other points are called ordinary points of the curve. Since by (57 a), p. 199, we have . dy dx it is evident that at a singular point the direction of the curve (or tangent) is indeterminate, for the slope takes the form In the noxt section it will be shown how tangents at such points may be found. . Determination of the tangent to an algebraic curve at a given point by inspection. If we transform the given equation to a new set of parallel coordinate axes having as origin the point in question on the curve, we know that the new equation will have no constant term. Hence it may be written in the form f(x, y) = ax + ly + (ex* + dxy + ey 2 )


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24 be found along: these railways, and the Sparrows naturally follow wherever food is found. To a lesser degree carriage roads have served the same purpose, the food furnished in the latter case being mainly the partially digested grain in horse droppings.

This gradual spread may take place at any season of the year, but probably is most pronounced in late summer and autumn, for reasons which will at once appear. It has been repeatedly remarked that when Sparrows are first introduced to a new region it is impossible, without actual confinement, to keep them on a farm near a town or city. They soon abandon the country for the city, and, except at harvest time, seldom return to the farm where they were introduced until the city becomes crowded. This may mean until there is no longer an ample supply of food for all the Sparrows, or, more commonly, it means until there are no longer enough convenient breeding places for all. In most cases it is the young which are thus crowded out, and consequently in midsummer and early autumn flocks of young birds may be met with far out in the country, wherever food is abundant, and when this food fails, or the ground becomes covered with snow, they retreat to the nearest towns, villages, or even farmhouses, often at considerable distances from the places where they were reared. But, in most cities, a time arrives at last when more Sparrows collect in winter than can possibly find nesting places in spring. Then, when all desirable places have been occupied, the remaining birds are forced to go to other towns or villages, or to nest in the country.

In this way the country for miles about large cities becomes fairly crowded with Sparrows, if the food conditions are favorable, and then the Sparrow shows his great power of adaptation by constructing nests for himself in trees. Twenty years ago there were few places in this country where any such Sparrow nests could be found, but to day they are common almost everywhere, and frequently they are used as places of shelter and retreat in severe winter weather, as well as for breeding places in summer. At first, evergreen trees are preferred, and a bulky nest, hardly more than a large, irregular heap of straw and rubbish, is built; but as such trees become crowded, or as the Sparrows gain skill in building, other trees are used, and often the nests are smaller and more symmetrical. The nests of native birds also are often utilized as foundations, the rightful owners being driven off first. In places where Sparrows find abundance of food and congenial surroundings, they increase to such an extent that these nests seriously disfigure the shade trees, and by their filth even injure them. Mr. Ridgway, of the Smithsonian Institution, says:

The English Sparrow has been in Wheatland, Ind., since 1877, and is now very abundant. I recently counted twenty-one of its large nests on one oak tree by the roadside, a little distance outside of the village. (Washington, D. C., February 11, 1888.)

It may seem superfluous to many readers to introduce any evidence showing that the Sparrow is not confined to cities, but so many persons

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 256 DIFFERENTIAL CALCULUS The equation of a tangent to the curve at the given point (now the origin) will be (B) * = 1& By (1), p. 76 Let y = mx be the equation of a line through the origin and a second point P on the locus of (^4). If then P approaches along the curve, we have, from f<7) limit m = -- dx Let be an ordinary point. Then, by 155, a and b do not both vanish, since at (0, 0), from (X), p. 255,, . dx dy Replace y in (^4) by mx, divide out the factor x, and let x approach zero as a limit. Then (^4) will become * a -f- bm 0. Hence we have, from (1?) and ((7), ax + by = 0, the equation of the tangent. The left-hand member is seen to consist of the terms of the first degree in (^4). When is not an ordinary point we have a = b = 0. Assume that c, d, e do not all vanish. Then, proceeding as before (except that we divide out the factor z 2 ), we find, after letting x approach the limit zero, that (A) becomes c + dm + em*= 0, or, from ((7), Substituting from (.#), we see that (JO ex 2 + dxy + e^ = Q is the equation of the pair of tangents at the origin. The left-hand member is seen to consist of the terms of the second degree in (^4). Such a singular point of the curve is called a double point from the fact that there are two tangents to the curve at that point. of x. If now x approaches zero as a limit, the theorem holds that one root of this equation in m will approach the limit - a-r- 6.
 * After dividing by x an algebraic equation in m remains whose coefficients are functions


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 SINGULAR POINTS Since at (0, 0), from (^4), dx 2 dxdy = Xe, it is evident that (D) may be written in the form (*> dxdydx In the same manner, if there is a triple point at the origin, the equation of the three tangents bein g fz* + gx*y + hxy* + iy* = 0, and so on in general. If we wish to investigate the appearance of a curve at a given point, it is of fundamental importance to solve the tangent problem for that point. The above results indicate that this can be done by simple inspection after we have transformed the origin to that point. Hence we have the following rule for finding the tangents at a given point. FIRST STEP. Transform the origin to the point in question. SECOND STEP. Arrange the terms of the resulting equation according to ascending powers of x and y. THIRD STEP. Set the group of terms of lowest degree equal to zero, This gives the equation of the tangents at the point (origin). ILLUSTRATIVE EXAMPLE 1. Find the equation of the tangent to the ellipse x 2 + 5y 2 + 2xy-12x-12y = at the origin. Solution. Placing the terms of lowest (first) degree equal to zero, we get x 12y = 0, or x + y = 0, which is then the equation of the tangent P Tat the origin. ILLUSTRATIVE EXAMPLE 2. Examine the curve 3 x 2 xy 2-y* + x 3 8 y 3 = for tangents at the origin. Solution. Placing the terms of lowest (second) degree equal to zero, x 2 - xy - 2 y 2 = 0, or (x-y)(3x + 2y) = 0, x y = being the equation of the tangent AB, and 3x + 2y = the equation of the tangent CD. The origin is, then, a double point of the curve.


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 258 DIFFERENTIAL CALCULUS Since the roots of the quadratic equation (^), p. 257, namely, may be real and unequal, real and equal, or imaginary, there are three cases of double points to be considered, according as (ff), (S)- is positive, zero, or negative (see 3, p. 1). . Nodes. ( | :L_Z>o. dxdy / dx z dy z In this case there are two real and unequal values of the slope found from (^), so that we have two distinct real tangents dx/ to the curve at the singular point in question. This means that the curve passes through the point in two different directions, or, in other words, two branches of the curve cross at this point. Such a singular point we call a real double point of the curve, or a node. Hence the conditions to be satisfied at a node are dx dy dxdy / dx* dy* ILLUSTRATIVE EXAMPLE 1. Examine the lemniscate y z = x 2 x 4 for singular points. Solution. Here /(, y) = y* x 2 + x 4 = 0. ^/ Q ^J dx ' dy The point (0, 0) is a singular point, since its coordinates satisfy the above three equations. We have at (0, 0) y = 0. = 2. x**^*^ dxdy /a 2 / 2 a 2 /g 2 / =1 dxdy) c)x*dy 2 ' and the origin is a double point (node) through which two branches of the curve pass in different directions. By placing the terms of the lowest (second) degree equal to zero we get y 9 * x z 0, or y = x and y = x, the equations of the two tangents AB and CD at the singular point or node (0, 0).


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 SINGULAR POINTS . Cusps. dxdy dx dy 2 In this case there are two real and equal values of the slope found from (jP 1 ); hence there are two coincident tangents. This means that the two branches of the curve which pass through the point are tangent. When the curve recedes from the tangent in both directions from the point of tangency, the singular point is called a point of osculation ; if it recedes from the point of tangency in one direction only, it is called a cusp. There are two kinds of cusps. First kind. When the two branches lie on opposite sides of the common tangent. Second kind. When the two branches lie on the same side of the common tangent.* The following examples illustrate how we may determine the nature of singular points coming under this head. ILLUSTRATIVE EXAMPLE 1. Examine a*y 2 = a 2 x* x 6 for singular points. Solution. Here f(x, y) = a*y 2 - a 2 x 4 + x 6 = 0, =- 4 a 2 x 3 + 6x 5 = 0, = 2 a*y = 0, dx dy and (0, 0) is a singular point, since it satisfies the above three equations. Also, at (0, 0) we have = 0, ax 2 dxdy dxdy dx 2 dy 2 and since the curve is symmetrical with respect to OF, the origin is a point of osculation. Placing the terms of lowest (second) degree equal to zero, we get y 2 = 0, showing that the two common tangents coincide with OX. ILLUSTRATIVE EXAMPLE 2. Examine y 2 = X s for singular points. Solution. Here /(x, y) = y 2 - x 3 = 0, ax, dy showing that (0, 0) is a singular point. Also, at (0, 0) we have a 2 / a 2 / a 2 / / a 2 / 2 a 2 / a 2 / _ ft ax 2 = ' dxdy = ' dy 2 ~ 2 ' ' dxdy) dx?~dy 2 ~ This is not a point of osculation, however, for if we solve the given equation for ', we get y= Vx 3 ,
 * Meaning in the neighborhood of the singular point.


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 Integral Calculus - Granville - Revised.djvu/284]] 260 DIFFEEENTIAL CALCULUS which shows that the curve extends to the right only of OF, for negative values of x make y imaginary. The origin is therefore a cusp, and since the branches lie on oppo- site sides of the common tangent, it is a cusp of the first kind. Placing the terms of lowest (second) degree equal to zero, we get y 2 = 0, showing that the two common tangents coincide with OX. ILLUSTRATIVE EXAMPLE 3. Examine (y x 2 ) 2 = x 5 for singular points. Solution. Proceeding as in the last example, we find a cusp at (0, 0), the common tangents to the two branches coinciding with OX. Solving for y, If we let x take on any value between and 1, y takes on two different positive values, showing that in the vicinity of the origin both branches lie above the common tangent. Hence the singular point (0, 0) is a cusp of the second kind. . Conjugate or isolated points. ( *- ) --L-L<Q. dxdy / dx z dy 2 In this case the values of the slope found are imaginary. Hence there are no real tangents ; the singular point is the real intersection of imaginary branches of the curve, and the coordinates of no other real point in the immediate vicinity satisfy the equation of the curve. Such an isolated point is called a conjugate point. ILLUSTRATIVE EXAMPLE 1. Examine the curve y 2 =x s x 2 for singular points. Solution. Here (0, 0) is found to be a singular point of the curve at which = V 1. Hence the origin is a conjugate point. Solving the dx equation for ?/, y=xVx 1. This shows clearly that the origin is an isolated point of the curve, for no values of x between and 1 give real values of y. . Transcendental singularities. A curve whose equation involves transcendental functions is called a transcendental curve. Such a curve may have an end point at which it terminates abruptly, caused by a discontinuity in the function ; or a salient point at which two branches of the curve terminate without having a common tan- gent, caused by a discontinuity in the derivative. ILLUSTRATIVE EXAMPLE 1. Show that y = x logx has an end point at the origin. Solution, x cannot be negative, since negative numbers have no logarithms; hence the curve extends only to the right of OF. When x = 0, y = 0. Thera being only one value of y for each positive value of x, the curve consists of a single branch terminating at the origin, which is therefore an end point.


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 260 DIFFEEENTIAL CALCULUS which shows that the curve extends to the right only of OF, for negative values of x make y imaginary. The origin is therefore a cusp, and since the branches lie on oppo- site sides of the common tangent, it is a cusp of the first kind. Placing the terms of lowest (second) degree equal to zero, we get y 2 = 0, showing that the two common tangents coincide with OX. ILLUSTRATIVE EXAMPLE 3. Examine (y x 2 ) 2 = x 5 for singular points. Solution. Proceeding as in the last example, we find a cusp at (0, 0), the common tangents to the two branches coinciding with OX. Solving for y, If we let x take on any value between and 1, y takes on two different positive values, showing that in the vicinity of the origin both branches lie above the common tangent. Hence the singular point (0, 0) is a cusp of the second kind. . Conjugate or isolated points. ( *- ) --L-L<Q. dxdy / dx z dy 2 In this case the values of the slope found are imaginary. Hence there are no real tangents ; the singular point is the real intersection of imaginary branches of the curve, and the coordinates of no other real point in the immediate vicinity satisfy the equation of the curve. Such an isolated point is called a conjugate point. ILLUSTRATIVE EXAMPLE 1. Examine the curve y 2 =x s x 2 for singular points. Solution. Here (0, 0) is found to be a singular point of the curve at which = V 1. Hence the origin is a conjugate point. Solving the dx equation for ?/, y=xVx 1. This shows clearly that the origin is an isolated point of the curve, for no values of x between and 1 give real values of y. . Transcendental singularities. A curve whose equation involves transcendental functions is called a transcendental curve. Such a curve may have an end point at which it terminates abruptly, caused by a discontinuity in the function ; or a salient point at which two branches of the curve terminate without having a common tan- gent, caused by a discontinuity in the derivative. ILLUSTRATIVE EXAMPLE 1. Show that y = x logx has an end point at the origin. Solution, x cannot be negative, since negative numbers have no logarithms; hence the curve extends only to the right of OF. When x = 0, y = 0. Thera being only one value of y for each positive value of x, the curve consists of a single branch terminating at the origin, which is therefore an end point.


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The American Cyclopædia (1879)/Nebular Hypothesis

NEBULAR HYPOTHESIS, the celebrated speculation of Sir William Herschel, adopted and developed by Laplace, assigning the genesis of the heavenly bodies to the gradual aggregation and condensation of a highly attenuated self-luminous substance diffused through space. (See “Philosophical Transactions,” 1802 and 1811.) To this hypothesis Herschel was led by his conclusion that there were nebulosities not composed of stars. The Rosse telescope having decomposed nebulæ hitherto considered to be irresolvable, and exhibited symptoms of resolvability in others still more intractable, it was assumed that all nebulæ are stellar, their nebulosity being solely a question of distance; and thus, the basis of Herschel's reasoning failing, the fabric of his hypothesis was thought to be demolished. Mr. Herbert Spencer came to its support in the “Westminster Review,” No. cxxxvii. (July, 1858). The argument in its favor is substantially as follows. The assumption that all nebulæ are remote galaxies does not invalidate the indications furnished by the structure of the solar system, which still points to a nebular origin just as significantly as before. But the assumption is inadmissible. The mode of distribution of the nebulæ furnishes evidence of a physical connection with our stellar system; and this

evidence is confirmed by the fact of their resolvability with telescopic power which fails to make individually visible the most distant stars of our own milky way. If they are remote galaxies, it may be assumed that, speaking generally, the largest are the nearest, and therefore the most resolvable. But the fact is, the smallest are the most resolvable. Another difficulty is presented by the Magellanic clouds. (See .) Sir John Herschel, considering the structure of the larger of these clouds, concludes that “it must be taken as a demonstrated fact that stars of the seventh or eighth magnitude, and irresolvable nebula, may coexist within limits of distance not differing in proportion more than as 9 to 10.” (“Outlines of Astronomy,” London, 1851, p. 615.) This clearly supplies a reductio ad absurdum of the popular doctrine. Assuming, for the sake of the argument, a rare, homogeneous, nebulous matter, widely diffused through space, the following successive changes will, on physical principles, take place in it: 1, mutual gravitation of its atoms; 2, atomic repulsion; 3, evolution of heat, by overcoming this repulsion; 4, molecular combination, at a certain stage of condensation, followed by, 5, sudden and great disengagement of heat; 6, lowering of temperature by radiation and consequent precipitation of binary atoms, aggregating into irregular flocculi and floating in the rarer medium, just as water when precipitated from air collects into clouds; 7, each flocculus will move toward the common centre of gravity of all; but being an irregular mass in a resisting medium, this motion will be out of the rectilinear, that is to say, not directly toward the common centre of gravity, but toward one or other side of it; and thus, 8, a spiral movement will ensue, which will be communicated to the rarer medium through which the flocculus is moving; and, 9, a preponderating momentum and rotation of the whole mass in some one direction, converging in spirals toward the common centre of gravity. Certain subordinate actions are to be noticed also. Mutual attraction will tend to produce groups of flocculi concentrating around local centres of gravity, and acquiring a subordinate vertical movement. These conclusions are shown to be in entire harmony with the observed phenomena. In this genetic process, when the precipitated matter is aggregating into flocculi, there will be found here and there detached portions, like shreds of cloud in a summer sky, which will not coalesce with the larger internal masses, but will slowly follow without overtaking them. These fragments will assume characteristics of motion strikingly correspondent to those of the comets, whose physical constitution and distribution are seen to be completely accordant with the hypothesis. — The physical characters resulting from the hypothesis are found totally with the facts. In a rotating spheroid of aëriform matter in the latter stages of

concentration, but before it has begun to take a liquid or solid form, the following actions will go on: 1, more and more rapid aggregation of its atoms into a smaller and denser mass, as the common centre of gravity is approached; 2, development of oblateness; 3, evolution of heat, greatest at the central parts; and, as a consequence, 4, circulation — currents setting from the centre toward the poles and thence to the equator, and counter currents from the equator to the centre. In the course of this round there will be, 5, an oscillation of temperature: first, from the centre outward — expansion by diminished pressure and other causes, and consequent lowering of temperature; secondly, from the equator inward — rise in temperature for converse reasons. 6. As a corollary to 4 and 5, external condensation will occur according to the laws of precipitation from gases, resulting in a belt of vapor about the equator, gradually widening and condensing into a fluid; 7, this fluid film will gradually extend itself till it eventually closes over at the poles, thus forming a thin hollow spheroid filled with gaseous matter; 8, at length the liquid shell will become very thick, the outer surface will experience a fall of temperature and begin to harden into a solid crust. This hypothesis explains the relative specific gravities of the planetary bodies, the formation of the asteroids, the earth's sup- posed interior structure, indications of past or present high temperature throughout the solar system, and the sun's incandescence. — These considerations relate chiefly to the physical changes undergone by a forming system. Laplace's nebular hypothesis deals with the changes of arrangement in the distribution of matter forming into a system under the action of dynamical laws. He takes as the basis of his theory certain features of our solar system which are not explained by the theory of gravitation. Gravity accounts for Kepler's laws, which are shown to be among its necessary consequences. No system could circulate in any manner around a centre, for instance, without the law holding that the numbers representing the cubes of the mean distances would be proportional to the numbers representing the squares of the periodic times. But a system could exist under gravity in which the planets would travel in widely eccentric orbits or in planes largely inclined to each other. Nor has it been proved that the planets might not safely circulate in different directions. Assuredly, if revolution in different directions, or in planes largely inclined to each other, or in very eccentric paths, might in the long run result in collisions and therefore in the destruction of the system as such, there is yet no reason to believe that all the axial rotations need take place in the same direction as the motions of revolution. But, to say the truth, none of those laws of harmony in our solar system, except the laws depending directly on gravity, can be regarded as essential

to the well being of the system; nor, as will presently appear, would the difficulty of regarding the system as other than a product of evolution be appreciably diminished by supposing that without those laws the destruction of the system must inevitably have occurred in the course of time. For it would be manifestly unreasonable to regard our system as one in which the original arrangements were fortuitously so happy that it has continued to exist as a system, if we find that the probability of these arrangements so existing by mere coincidence is exceedingly minute. Now, how small this probability is may be inferred by considering only the motion of the planets in one common direction. There are known at the present time 8 major planets and 137 minor planets (the number of these is increasing year by year). Thus there are 145 known planets. Taking the earth's direction of revolution as a standard direction, the chance that any one of the remaining 144 planets would have this direction as a result of mere chance is of course one half, since a planet must revolve in one of two ways. Therefore, by the laws of probability, the chance that all the 144 other planets would revolve in that direction is represented by a fraction whose numerator is unity and its denominator 2 raised to the 144th power. Now 144 times the logarithm of 2, (or .3010300) = 43.3483200, showing that the above mentioned denominator is a number of 44 digits, beginning 2230077 with 37 digits to follow. This inconceivably enormous num- ber represents the odds to 1 against the observed arrangement being the result of chance, even considering only one relation out of several mentioned above, all of which present the same order of antecedent improbability. Thus Laplace was led to his conception of a vast rotating nebulous disk, from the gradual contraction of which, and the consequent throwing off of rings, breaking up into globes, all revolving and rotating in one common direction and nearly in the same level, the solar system was formed. This hypothesis, however, does not explain the distribution of the masses of the solar system; one planet (Jupiter), for example, containing nearly 5/7 of all the matter outside the sun, and Saturn and Jupiter together containing about 11/12 of all that matter. Accordingly, the present writer has suggested a modification of it, in which, starting from some such primary condition as that assumed by Herbert Spencer, the various parts of the solar system were formed by processes of aggregation such as are still going on (though now with extreme slowness). For the motions of the flocculi of Spencer (or of the parts, whatever their nature, from which the system was to be formed) would be more and more rapid with proximity to the central aggregation, according to well known dynamical laws. Accordingly, subordinate aggregations would form with difficulty close by the sun; and hence we can understand the smallness of the

members of the interior family of planets, comprising Mercury, Venus, the earth, and Mars. Again, with extreme distance from the centre, the gravity of available material whence aggregations could form would be so far reduced, that for that reason the planets so formed would be smaller. Hence we can understand why Uranus and Neptune are so far inferior to Jupiter and Saturn. These two giant orbs are thus seen to occupy the space where the conditions were most favorable to the rapid development of subordinate aggregations. In this intermediate region there was abundance of material while yet the motions were not so rapid that a subordinate aggregation could not readily master, so to speak, the matter rushing past toward the aphelion of its orbital motion round the sun. The theory also explains well the existence of a zone of discrete bodies next within the path of Jupiter, that is, in a region disturbed at once by his attraction and that of the sun. — It is not improbable, as remarked in the article, that the study of cometic and meteoric astronomy may before long throw considerable light on the interesting question of the evolution of our solar system, and may enable us to form a nebular hypothesis on safer grounds than those on which the theories now in vogue have been based.


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RICHMOND, VA.:

Secretary Southern Historical Society.


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Rh replacement can be connected with the contrast. We have given repeated examples of this. Another part of the contrasts in the dream thoughts, which perhaps falls into the category "turned into the opposite," is represented in the dream in the following remarkable manner, which may almost be designated as witty. The "inversion" does not itself get into the dream content, but manifests its presence there by means of the fact that a part of the already formed dream content which lies at hand for other reasons, is—as it were subsequently—inverted. It is easier to illustrate this process than to describe it. In the beautiful "Up and Down" dream (p. 267) the representation of ascending is an inversion of a prototype in the dream thoughts, that is to say, of the introductory scene of Daudet's Sappho; in the dream climbing is difficult at first, and easy later on, while in the actual scene it is easy at first, and later becomes more and more difficult. Likewise "above" and "below" in relation to the dreamer's brother are inverted in the dream. This points to a relation of contraries or contrasts as obtaining between two parts of the subject-matter of the dream thoughts and the relation we have found in the fact that in the childish fancy of the dreamer he is carried by his nurse, while in the novel, on the contrary, the hero carries his beloved. My dream about Goethe's attack upon Mr. M. (p. 345) also contains an "inversion" of this sort, which must first be set right before the interpretation of the dream can be accomplished. In the dream Goethe attacks a young man, Mr. M.; in reality, according to the dream thoughts, an eminent man, my friend, has been attacked by an unknown young author. In the dream I reckon time from the date of Goethe's death; in reality the reckoning was made from the year in which the paralytic was born. The thought determining the dream material is shown to be an objection to the treatment of Goethe as a lunatic. "The other way around," says the dream; "if you cannot understand the book, it is you who are dull-witted, not the author." Furthermore, all these dreams of inversion seem to contain a reference to the contemptuous phrase, "to turn one's back upon a person" (German: "einen die Kehrseite zeigen"; cf. the inversion in respect to the dreamer's brother in the Sappho dream). It is also remarkable how


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Encyclopædia Britannica, Ninth Edition/Jay

JAY (French, Géai), a well-known and very beautiful European bird, the Corvus glandarius of Linnæus, the Garrulus glandarius of modern ornithologists. To this species are more or less closely allied numerous birds in habiting the Palæarctic and Indian Regions, as well as the greater part of America, but not occurring in the Antilles, in the southern portion of the Neotropical Region, or in the Ethiopian or Australian. All these birds are commonly called Jays, and form a group of the Crows or Corvidæ, which may fairly be considered a Subfamily, Garrulinæ. Indeed there are, or have been, systematists who would elevate the Jays to the rank of a Family, Garrulidæ — a proceeding which seems unnecessary. Some of them have an unquestionable resemblance to the Pies, if the group now known by that name can be satisfactorily severed from the true Corvinæ. In structure the Jays are not readily differentiated from the Pies; but in habit, so far as is known of them, they are much more arboreal, delighting in thick coverts, seldom appearing in the open, and seeking their food on or under trees. They seem also never to walk or run when on the ground, but always to hop. The body-feathers are commonly loose and soft; and, gaily coloured as are most of the species, in few of them has the plumage the metallic glossiness it generally presents in the Pies, while the proverbial beauty of the “Jay's wing” is due to the vivid tints of blue — turquoise and cobalt, heightened by bars of jet-black, an indication of the same style of ornament being observable in the greater number of the other forms of the group, and in some predominat ing over nearly the whole surface. Of the many genera that have been proposed by ornithologists, perhaps about nine may be deemed sufficiently well established.

The ordinary European Jay, Garrulus glandarius (fig. 1), has of late years suffered so much persecution in the British Islands as to have become in many districts a rare bird. In Ireland it seems now to be indigenous to the southern half of the island only; in England generally, it is far less numerous than formerly; and Mr Lumsden (Scottish Naturalist, iii. pp. 230-240) has shewn that in Scotland its numbers have decreased with still greater rapidity. There is little doubt that it would have been exterminated by this time but for its stock being supplied in autumn by immigration, and for its shy and wary behaviour, especially at the breeding-season, when it becomes almost wholly mute, and thereby often escapes detection. No truthful man, however much he may love the bird, will gainsay the depredations on fruit and eggs that it at times commits; but ths gardeners and gamekeepers of Britain fall into the usual

error of persons imperfectly acquainted with the ways of Nature, and, instead of taking a few simple steps to guard their charge from injury, or at most of punishing the individual birds from which they suffer, deliberately adopt methods of wholesale destruction — methods that in the case of this species are only too easy and too effectual — by proffering temptation to trespass which it is not in Jay-nature to resist, and accordingly the bird runs great chance of total extirpation. Notwithstanding the war carried on against the Jay, its varied cries and active gesticulations shew it to be a sprightly bird, and at a distance that renders its beauty-spots invisible, it is yet rendered conspicuous by its cinnamon-coloured body and pure white tail-coverts, which contrast with the deep black and rich chestnut that otherwise mark its plumage, and even the young at once assume a dress closely resembling that of the adult. The nest, generally concealed in a leafy tree or bush, is carefully built, with a lining formed of fine roots neatly interwoven. Herein from four to seven eggs, of a greenish-white closely freckled, so as to seem suffused with light olive, are laid in March or April, and the young on quitting it accompany their parents for some weeks.

Though the common Jay of Europe inhabits nearly the whole of this quarter of the globe south of 64° N. lat., its territory in the east of Russia is also occupied by G. brandti, a kindred form, which replaces it on the other side of the Ural, and ranges thence across Siberia to Japan; and again on the Lower Danube and thence to Constantinople the nearly-allied G. krynicki (which alone is found in southern Russia, Caucasia, and Asia Minor) shares its haunts with it. It also crosses the Mediterranean to Algeria and Morocco; but there, as in southern Spain, it is probably but a winter immigrant. The three forms just named have the widest range of any of the genus. Next to them come G. atricapillus, reaching from Syria to Beloochistan, G. japonicus, the ordinary Jay of southern Japan, and G. sinensis, the Chinese bird. Other forms have a much more

limited area, as G. cervicalis, the local and resident Jay of Algeria, G. hyrcanus, found on the southern shores of the Caspian Sea, and G. taevanus confined to the island of Formosa. The most aberrant of the true Jays is G. lidthi, a very rare species, which seems to come from some part of Japan (vide Salvadori, Atti Accad. Torino, vii. p. 474), though its exact locality is not known.

Leaving the true Jays of the genus Garrulus, it is expedient next to consider those of a group named, in 1831, Perisoreus by Bonaparte (Saggio, &c., Anim. Vertebrati, p. 43) and Dysornithia by Swainson (F. B.-Americana, ii. p. 495).

This group contains two species — one the Lanius infaustas of Linnæus and the Siberian Jay of English writers, which ranges throughout the pine-forests of the north of Europe and Asia, and the second the Corvus canadensis of the same author, or Canada Jay, occupying a similar station in America. The so-called Siberian Jay is one of the most entertaining birds in the world. Its versatile cries and actions, as seen and heard by those who penetrate the solitude of the northern forests it inhabits, can never be forgotten by one who has had experience of them, any more than the pleasing sight of its rust-coloured tail, which an occasional gleam of sun shine will light up into a brilliancy quite unexpected by those who have only surveyed the bird's otherwise gloomy appearance in the glass-case of a museum. It seems scarcely to know fear, obtruding itself on the notice of any passenger who invades its haunts, and, should he halt, making itself at once a denizen of his bivouac. In confinement it speedily becomes friendly, but suitable food for it is not easily found. Linnæus seems to have been under a misapprehension when he applied to it the trivial epithet it bears; for by none of his countrymen is it deemed an unlucky bird, but rather the reverse. In fact, no one can listen to the cheery sound of its ordinary calls with any but a hopeful feeling. The Canada Jay, or “Whiskey-Jack” (the corruption probably of a Cree name), seems to be of a similar nature, but it presents a still more sombre coloration, its nestling plumage, indeed, being thoroughly Corvine in appearance and suggestive of its being a pristine form.

As though to make amends for the dull plumage of the species last mentioned, North America offers some of the most brilliantly coloured of the Subfamily, and the common

Blue Jay of Canada and the Eastern States of the Union, Cyanurus cristatus (fig. 2), is one of the most conspicuous birds of the transatlantic woods. The account of its habits by Alexander Wilson is known to every student of ornithology, and Wilson's followers have had little to do but supplement his history with unimportant details. In this bird and its many allied forms, coloration, though almost confined to various tints of blue, seems to reach its climax, but want of space forbids more particular notice of them, or of the members of the other genera Cyanocitta, Cyanocorax, Xanthura, Psilorhinus, and more, which inhabit various parts of the Western continent. It remains, however, to mention the genus Cissa, including many beautiful forms belonging to the Indian Region, and among them the G. speciosa and C. sinensis, so often represented in Oriental drawings, though doubts may be expressed whether these birds are not more nearly related to the Pies than to the Jays. (A. N.)


text: 1911 Encyclopædia Britannica/Jay

title: 1911 Encyclopædia Britannica/Jay


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304 frequently inversion becomes necessary in dreams which are inspired by repressed homosexual feelings.

Moreover, inversion or transformation into an opposite is one of the favourite methods of representation, and one of the methods most capable of varied application which the dream activity possesses. Its first function is to create the fulfilment of a wish with reference to a definite element of the dream-thoughts. "If it were only just the other way!" is often the best expression of the relation of the ego to a disagreeable recollection. But inversion becomes extraordinarily useful for the purposes of the censor, for it brings about in the material represented a degree of disfiguration which all but paralyses our understanding of the dream. For this reason it is always permissible, in cases where the dream stubbornly refuses to yield its meaning, to try the inversion of definite portions of its manifest content, whereupon not infrequently everything becomes clear.

Besides this inversion, the subject-matter inversion in temporal relation is not to be overlooked. A frequent device of dream disfigurement consists in presenting the final issue of an occurrence or the conclusion of an argument at the beginning of the dream, or in supplying the premises of a conclusion or the causes of an effect at the end of it. Anyone who has not considered this technical method of dream disfigurement stands helpless before the problem of dream interpretation.

Indeed in some cases we can obtain the sense of the dream only by subjecting the dream content to manifold inversion in different directions. For example, in the dream of a young patient suffering from a compulsion neurosis, the memory of an infantile death-wish against a dreaded father was hidden behind


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Rh the following words: His father upbraids him because he arrives so late. But the context in the psychoanalytic treatment and the thoughts of the dreamer alike go to show that the sentence must read as follows: He is angry at his father, and, further, that his father is always coming home too early (i.e. too soon). He would have preferred that his father should not come home at all, which is identical with the wish (see page 219) that his father should die. As a little boy the dreamer was guilty of sexual aggression against another person while his father was away, and he was threatened with punishment in the words: "Just wait until father comes home."

If we attempt to trace the relations between dream content and dream thoughts further, we shall do this best by making the dream itself our starting-point and by asking ourselves the question: What do certain formal characteristics of dream representation signify with reference to the dream thoughts? The formal characteristics which must attract our attention in the dream primarily include variations in the distinctness of individual parts of the dream or of whole dreams in relation to one another. The variations in the intensity of individual dream images include a whole scale of degrees ranging from a distinctness of depiction which one is inclined to rate as higher—without warrant, to be sure—than that of reality, to a provoking indistinctness which is declared to be characteristic of the dream, because it cannot altogether be compared to any degree of indistinctness which we ever see in real objects. Moreover, we usually designate the impression which we get from an indistinct object in the dream as "fleeting," while we think of the more distinct dream images as remaining intact for a longer period of perception. We must now ask ourselves by what conditions in the dream material these differences in the vividness of the different parts of the dream content are brought about.

There are certain expectations which will inevitably arise at this point and which must be met. Owing to the fact that real sensations during sleep may form part of the material of the dream, it will probably be assumed that these sensations or the dream elements resulting from them are emphasized by peculiar intensity, or conversely, that what turns out to be U


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306 particularly vivid in the dream is probably traceable to such real sensations during sleep. My experience has never confirmed this. It is incorrect to say that those elements of the dream which are the derivatives of impressions occurring in sleep (nervous excitements) are distinguished by their vividness from others which are based on recollections. The factor of reality is of no account in determining the intensity of dream images.

Furthermore, the expectation will be cherished that the sensory intensity (vividness) of individual dream images has a relation to the psychic intensity of the elements corresponding to them in the dream-thoughts. In the latter intensity is identical with psychic value; the most intense elements are in fact the most significant, and these are the central point of the dream. We know, however, that it is just these elements which are usually not accepted in the dream content owing to the censor. But still it might be possible that the elements immediately following these and representing them might show a higher degree of intensity, without, however, for that reason constituting the centre of the dream representation. This expectation is also destroyed by a comparison of the dream and the dream material. The intensity of the elements in the one has nothing to do with the intensity of the elements in the other; a complete "transvaluation of all psychic values" takes place between the dream-material and the dream. The very element which is transient and hazy and which is pushed into the background by more vigorous images is often the single and only element in which may be traced any direct derivative from the subject which entirely dominated the dream-thoughts.

The intensity of the elements of the dream shows itself to be determined in a different manner—that is, by two factors which are independent of each other. It is easy to see at the outset that those elements by means of which the wishfulfilment is expressed are most distinctly represented. But then analysis also teaches us that from the most vivid elements of the dream, the greatest number of trains of thought start, and that the most vivid are at the same time those which are best determined. No change of sense is involved if we express the latter empirical thesis in the following form: the greatest


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Rh intensity is shown by those elements of the dream for which the most abundant condensation activity was required. We may therefore expect that this condition and the others imposed by the wish-fulfilment can be expressed in a single formula.

The problem which I have just been considering—the causes of greater or less intensity or distinctness of individual elements of the dream—is one which I should like to guard against being confused with another problem, which has to do with the varying distinctness of whole dreams or sections of dreams. In the first case, the opposite of distinctness is blurredness; in the second, confusion. It is of course unmistakable that the intensities rise and fall in the two scales in unison. A portion of the dream which seems clear to us usually contains vivid elements; an obscure dream is composed of less intense elements. But the problem with which we are confronted by the scale, ranging from the apparently clear to the indistinct or confused, is far more complicated than that formed by variations in the vividness of the dream elements; indeed the former will be dropped from the discussion for reasons which will be given later. In isolated cases we are astonished to find that the impression of clearness or indistinctness produced by the dream is altogether without significance for its structure, and that it originates in the dream material as one of its constituents. Thus I remember a dream which seemed particularly well constructed, flawless, and clear, so that I made up my mind, while I was still in the somnolent state, to recognise a new class of dreams—those which had not been subject to the mechanism of condensation and displacement, and which might thus be designated "Fancies while asleep." A closer examination proved that this rare dream had the same breaches and flaws in its construction as every other; for this reason I abandoned the category of dream fancies. The content of the dream, reduced to its lowest terms, was that I was reciting to a friend a difficult and long-sought theory of bisexuality, and the wishfulfilling power of the dream was responsible for the fact that this theory (which, by the way, was not stated in the dream) appeared so clear and flawless. What I considered a judgment upon the finished dream was thus a part of the


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308 dream content, and the essential one at that. The dream activity had extended its operations, as it were, into waking thought, and had presented to me in the form of a judgment that part of the dream material which it had not succeeded in reproducing with exactness. The exact opposite of this once came to my attention in the case of a female patient who was at first altogether unwilling to tell a dream which was necessary for the analysis, "because it was so obscure and confused," and who declared, after repeatedly denying the accuracy of her description, that several persons, herself, her husband, and her father, had occurred in the dream, and that it seemed as though she did not know whether her husband was her father, or who her father was anyway, or something of that sort. Upon considering this dream in connection with the ideas that occurred to the dreamer in the course of the sitting, it was found unquestionably to be concerned with the story of a servant girl who had to confess that she was expecting a child, and who was now confronted with doubts as to "who was really the father." The obscurity manifested by the dream, therefore, is again in this case a portion of the material which excited it. A part of this material was represented in the form of the dream. The form of the dream or of dreaming is used with astonishing frequency to represent the concealed content.

Comments on the dream and seemingly harmless observations about it often serve in the most subtle manner to conceal—although they usually betray—a part of what is dreamed. Thus, for example, when the dreamer says: Here the dream is vague, and the analysis gives an infantile reminiscence of listening to a person cleaning himself after defecation. Another example deserves to be recorded in detail. A young man has a very distinct dream which recalls to him phantasies from his infancy which have remained conscious to him: he was in a summer hotel one evening, he mistook the number of his room, and entered a room in which an elderly lady and her two daughters were undressing to go to bed. He continues: "Then there are some gaps in the dream; then something is missing; and at the end there was a man in the


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Rh room who wished to throw me out with whom I had to wrestle." He endeavoured in vain to recall the content and purpose of the boyish fancy to which the dream apparently alludes. But we finally become aware that the required content had already been given in his utterances concerning the indistinct part of the dream. The "gaps" were the openings in the genitals of the women who were retiring: "Here something is missing" described the chief character of the female genitals. In those early years he burned with curiosity to see a female genital, and was still inclined to adhere to the infantile sexual theory which attributes a male genital to the woman.

All the dreams which have been dreamed in the same night belong to the same whole when considered with respect to their content; their separation into several portions, their grouping and number, all these details are full of meaning, and may be considered as information coming from the latent dream content. In the interpretation of dreams consisting of many principal sections, or of dreams belonging to the same night, one must not fail to think of the possibility that these different and succeeding dreams bring to expression the same feelings in different material. The one that comes first in time of these homologous dreams is usually the most disfigured and most bashful, while the succeeding is bolder and more distinct.

Even Pharaoh's dream in the Bible of the ears and the kine, which Joseph interpreted, was of this kind. It is reported by Josephus (Antiquities of the Jews, bk. ii. chap, iii.) in greater detail than in the Bible. After relating the first dream, the King said: "When I had seen this vision I awaked out of my sleep, and being in disorder, and considering with myself what this appearance should be, I fell asleep again, and saw another dream much more wonderful than the first, which did still more affright and disturb me." After listening to the report of the dream, Joseph said, "This dream, King, although seen under two forms, signifies one and the same issue of things."

Jung, who, in his Beitrag zur Psychologie des Gerüchtes relates how the veiled erotic dream of a school-girl was understood by her friends without interpretation and continued by them with variations, remarks in connection with reports


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310 of this dream, "that the last of a long series of dream pictures contained precisely the same thought whose representation had been attempted in the first picture of the series. The censor pushed the complex out of the way as long as possible, through constantly renewed symbolic concealments, displacements, deviations into the harmless, &c." (l.c. p. 87). Scherner was well acquainted with the peculiarities of dream disfigurement and describes them at the end of his theory of organic stimulation as a special law, p. 166: "But, finally, the phantasy observes the general law in all nerve stimuli emanating from symbolic dream formations, by representing at the beginning of the dream only the remotest and freest allusions to the stimulating object; but towards the end, when the power of representation becomes exhausted, it presents the stimulus or its concerned organ or its function in unconcealed form, and in the way this dream designates its organic motive and reaches its end."

A new confirmation of Scherner's law has been furnished by Otto Rank in his work, A Self Interpretation Dream. This dream of a girl reported by him consisted of two dreams, separated in time of the same night, the second of which ended with pollution. This pollution dream could be interpreted in all its details by disregarding a great many of the ideas contributed by the dreamer, and the profuse relations between the two dream contents indicated that the first dream expressed in bashful language the same thing as the second, so that the latter—the pollution dream—helped to a full explanation of the former. From this example, Rank, with perfect justice, draws conclusions concerning the significance of pollution dreams in general.

But in my experience it is only in rare cases that one is in a position to interpret clearness or confusion in the dream as certainty or doubt in the dream material. Later I shall try to discover the factor in the formation of dreams upon whose influence this scale of qualities essentially depends.

In some dreams, which adhere for a time to a certain situation and scenery, there occur interruptions dsecribed in the following words: "But then it seemed as though it were at the same time another place, and there such and such a thing happened." What thus interrupts the main trend


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Rh of the dream, which after a while may be continued again, turns out to be a subordinate idea, an interpolated thought in the dream material. A conditional relation in the dream-thoughts is represented by simultaneousness in the dream (wenn—wann; if—when).

What is signified by the sensation of impeded movement, which so often occurs in the dream, and which is so closely allied to anxiety? One wants to move, and is unable to stir from the spot; or one wants to accomplish something, and meets one obstacle after another. The train is about to start, and one cannot reach it; one's hand is raised to avenge an insult, and its strength fails, &c. We have already encountered this sensation in exhibition dreams, but have as yet made no serious attempt to interpret it. It is convenient, but inadequate, to answer that there is motor paralysis in sleep, which manifests itself by means of the sensation alluded to. We may ask: "Why is it, then, that we do not dream continually of these impeded motions?" And we are justified in supposing that this sensation, constantly appearing in sleep, serves some purpose or other in representation, and is brought about by a need occurring in the dream material for this sort of representation.

Failure to accomplish does not always appear in the dream as a sensation, but also simply as a part of the dream content. I believe that a case of this sort is particularly well suited to enlighten us about the significance of this characteristic of the dream. I shall give an abridged report of a dream in which I seem to be accused of dishonesty. ''The scene is a mixture, consisting of a private sanatorium and several other buildings. A lackey appears to call me to an examination. I know in the dream that something has been missed, and that the examination is taking place because I am suspected of having appropriated the lost article. Analysis shows that examination is to be taken in two senses, and also means medical examination. Being conscious of my innocence, and of the fact that I have been called in for consultation, I calmly follow the lackey. We are received at the door by another lackey, who says, pointing to me, "Is that the person whom you have brought? Why, he is a respectable man." Thereupon, without any lackey, I enter a great hall in which machines are standing, and which reminds me''


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312 ''of an Inferno with its hellish modes of punishment. I see a colleague strapped on to one apparatus who has every reason to be concerned about me; but he takes no notice of me. Then I am given to understand that I may now go. Then I cannot find my hat, and cannot go after all.''

The wish which the dream fulfils is obviously that I may be acknowledged to be an honest man, and may go; all kinds of subject-matter containing a contradiction of this idea must therefore be present in the dream-thoughts. The fact that I may go is the sign of my absolution; if, then, the dream furnishes at its close an event which prevents me from going, we may readily conclude that the suppressed subject-matter of the contradiction asserts itself in this feature. The circumstance that I cannot find my hat therefore means: "You are not an honest man after all." Failure to accomplish in the dream is the expression of a contradiction, a "No"; and therefore the earlier assertion, to the effect that the dream is not capable of expressing a negation, must be revised accordingly.

In other dreams which involve failure to accomplish a thing not only as a situation but also as a sensation, the same contradiction is more emphatically expressed in the form of a volition, to which a counter volition opposes itself. Thus the sensation of impeded motion represents a conflict of will. We shall hear later that this very motor paralysis belongs to the fundamental conditions of the psychic process in dreaming. Now the impulse which is transferred to motor channels is nothing else than the will, and the fact that we are sure to find this impulse impeded in the dream makes the whole process extraordinarily well suited to represent volition and the "No" which opposes itself thereto. From my explanation of anxiety,


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Rh it is easy to understand, why the sensation of thwarted will is so closely allied to anxiety, and why it is so often connected with it in the dream. Anxiety is a libidinous impulse which emanates from the unconscious, and is inhibited by the fore-conscious. Therefore, when a sensation of inhibition in the dream is accompanied by anxiety, there must also be present a volition which has at one time been capable of arousing a libido; there must be a sexual impulse.

What significance and what psychic force is to be ascribed to such manifestations of judgment as "For that is only a dream," which frequently comes to the surface in dreams, I shall discuss in another place (vide infra, p. 390). For the present I shall merely say that they serve to depreciate the value of the thing dreamed. An interesting problem allied to this, namely, the meaning of the fact that sometimes a certain content is designated in the dream itself as "dreamed"—the riddle of the "dream within the dream"—has been solved in a similar sense by W. Stekel through the analysis of some convincing examples. The part of the dream "dreamed" is again to be depreciated in value and robbed of its reality; that which the dreamer continues to dream after awakening from the dream within the dream, is what the dream-wish desires to put in place of the extinguished reality. It may therefore be assumed that the part "dreamed" contains the representation of the reality and the real reminiscence, while, on the other hand, the continued dream contains the representation of what the dreamer wished. The inclusion of a certain content in a "dream within the dream" is therefore equivalent to the wish that what has just been designated as a dream should not have occurred. The dream-work utilises the dream itself as a form of deflection.

(d) Regard for Presentability

So far we have been attempting to ascertain how the dream represents the relations among the dream-thoughts, but we have several times extended our consideration to the further question of what alterations the dream material undergoes for the purposes of dream formation. We now know that the dream material, after being stripped of the greater parts


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314 of its relations, is subjected to compression, while at the same time displacements of intensity among its elements force a psychic revaluation of this material. The displacements which we have considered were shown to be substitutions of one idea for another, the substitute being in some way connected with the original by associations, and the displacements were put to the service of condensation by virtue of the fact that in this manner a common mean between two elements took the place of these two elements in the formation of the dream. We have not yet mentioned any other kind of displacement. But we learn from the analyses that another exists, and that it manifests itself in a change of the verbal expression employed for the thought in question. In both cases we have displacement following a chain of associations, but the same process takes place in different psychic spheres, and the result of this displacement in the one case is that one element is substituted for another, while in the other case an element exchanges its verbal expression for another.

This second kind of displacement occurring in dream formation not only possesses great theoretical interest, but is also peculiarly well fitted to explain the semblance of phantastic absurdity in which the dream disguises itself. Displacement usually occurs in such a way that a colourless and abstract expression in the dream-thought is exchanged for one that is visual and concrete. The advantage, and consequently the purpose, of this substitution is obvious. Whatever is visual is capable of representation in the dream, and can be wrought into situations where the abstract expression would confront dream representation with difficulties similar to those which would arise if a political editorial were to be represented in an illustrated journal. But not only the possibility of representation, but also the interests of condensation and of the censor, can be furthered by this change. If the abstractly expressed and unwieldy dream-thought is recast into figurative language, this new expression and the rest of the dream material are more easily furnished with those identities and cross references, which are essential to the dream activity and which it creates whenever they are not at hand, for the reason that in every language concrete terms, owing to their evolution, are more abundant in