Search

The significance of indeterminate screening antibody test for human immunodeficiency virus (HIV) serology is still difficult to evaluate, especially in low-risk populations. One hundred twenty-seven blood donors with an initially reactive screening test for HIV antibodies were enrolled in this study. The sera of 95 of these blood donors were reactive on repetition of the test, and none had detectable circulating p24 antigen. Western blot (WB) analysis of the repeatedly reactive sera was as follows: 9 positive, 31 indeterminate, and 55 negative. One of the blood donors with indeterminate WB later presented a seroconversion. On subsequent control 3 to 12 months later, the sera from donors with indeterminate or negative WB did not present any parameters that may indicate a seroconversion. DNA was purified from citrated blood collected from the 127 blood donors at the time of the initial antibody screening. Five micrograms of each DNA sample corresponding to 7 x 10(5) nucleated white blood cells was amplified by polymerase chain reaction (PCR) in the presence of oligonucleotides (primers) corresponding to a highly conserved segment of the pol gene. The detection of amplified DNA was achieved by dot blot and Southern blot using appropriate 32P-labeled oligonucleotides. Ten DNA samples were positive, 9 corresponded to blood donors with a positive HIV serology, and 1 to the blood donor who later presented a seroconversion. These results confirm the sensitivity of the PCR for the diagnosis of HIV infection; they also suggest that repetition of the serology at 3- to 12-month intervals is a valuable procedure for the control of HIV infection status in blood donors.

A prospective study was begun in our haemodialysis unit after four previously negative patients were found to be anti-HCV positive. A dedicated area and dedicated dialysis equipment (but not a separate room) were assigned to anti-HCV-positive patients and testing for HCV antibodies was performed every 3 months. A total of 131 patients were treated during the study period of 18 months. Of these, 50 patients were dialysed during the entire 18 months, and 21 were available to be tested six or more months after having left the centre. During the first 6 weeks after implementing the precautions two more anti-HCV-positive patients were detected. However, during the rest of the study period no further newly infected patients were found. It is concluded that the spread of HCV infection in a haemodialysis environment can be prevented by limited isolation procedures.

The sera of patients with hemophilia and von Willebrand factor deficiency, collected during clinical trials with virus-inactivated coagulation factor preparations, were retrospectively screened for the presence of antibodies against hepatitis C virus (HCV). Using the anti-HCV c100-3 assay, 10 out of 35 study patients had no HCV antibodies when entering the studies. The samples originally negative for anti-HCV were retested with a second-generation assay: all negative samples except two were positive on retesting. We conclude that the HCV seroprevalence in Swiss hemophiliacs must be of the order of90%. These results confirm that the first-generation assay for HCV antibodies is not sensitive enough; to obtain more accurate information on the seroprevalence of hemophiliacs, second-generation tests should be used.

Since 1986 the factor VIII and IX concentrates of the Central Laboratory, Swiss Red Cross Blood Transfusion Service have been virus inactivated with tri-(n-butyl) phosphate and Tween 80. Clinical studies had shown that both preparations were well tolerated and hemostatically effective; no HIV infection was transmitted. However, safety from transmission of non-A/non-B hepatitis could not be shown since the study included no previously untreated patients. In the meantime, a laboratory test has become available which allows retrospective testing for anti-hepatitis C antibodies in frozen sera of the study patients. 5 of the 26 patients, observed during a 2-year follow-up study, had no HCV antibodies before entering the long-term trial. During this trial, each of these 5 patients substituted an average quantity of 40,200 coagulation factor units (7500-69,000) from 45 production lots. None of these 5 patients developed anti-HCV antibodies, nor did any of them show clinical signs of infection with hepatitis. This suggests that virus inactivation using solvent/detergent treatment reduces the risk of transmission of HCV.

Im Rahmen der Evaluation eines neuen Testsystems zur Bestimmung von Antikorpern gegen Hepatitis C-Virus (HCV) (Ortho HCV Antibody ELISA Test) wurden 26 Hamophile, die vor 1986 mit nicht-vireninaktivierten Gerinnungspraparaten behandelt worden waren, untersucht.

Development of sensitization in rats monoassocialed with Actinomyces viscosus Ny 1 was estimated by titrating serum agglutinins and by measuring the anamnestic, in vitro response of spleen T lymphocytes to two antigen fractions. These parameters of the immune response were compared with the development of alveolar bone loss using germfree rats as controls. At 46 days of age, 19 days after monoassociation, we observed (i) a mean serum antibody litre of (log2) 3.6, (ii) considerable antigen-dependent T-cell proliferation, and (iii) statistically significant amounts of alveolar bone loss. Thereafter, sensitization to A. viscosus and total bone loss increased cuncomitantly until the end of the experiment at 88 days of age. However, the rate of bone loss decreased with time at some sites, suggesting that negative feedback mechanisms by suppressor cells enable bone remodeling. These results demonstrate that, in experimental periodontal disease elicited by A. viscosus. the immune response to dental plaque bacteria and bone loss occur simultaneously.

The T-cell triggered effector systems have been emphasized as the most important agents mediating periodontal disease in recent years. It was therefore tempting to investigate whether T-cell suppression with cyclosporin A (CS-A) had an effect on the establishment and progression of the disease in rats monoassociated with Actinomyces viscosus Ny 1. The experiment was carried out with two treatments (16 rats each) in two isolators. In one of the isolators CS-A was added to the high sucrose diet 2000 aiming at a dosage of 15 mg per day and kg bodyweight. In the second isolator (control) the same diet without CS-A was fed. At day 25, 38, 52 and 65 four animals from each treatment were removed from the isolators. Dental plaque and alveolar bone loss were evaluated. The cellular composition of blood and histological changes of periodontal lesions on a light and electron microscopic level were monitored. In addition antibody titers and the T-cell suppressing effect of individual serum samples of all animals were determined. Despite clearcut treatment differences in antibody titers as well as an interference by the sera of CS-A treated animals with the Con A dependent lymphocyte activation, bone loss was observed in both groups. Haematological and histological investigation revealed only minor differences between the two treatments. It is concluded that periodontal disease in monoinfected rats seems to be the result of a multitude of pathomechanisms and not to be strictly correlated with T-cell dependent hypersensitivity.

We describe a surface determinant shared by human monocytes and cells of the megakaryocytic axis that has been identified using a mouse monoclonal antibody. This monocyte-platelet antigen (MPA) is expressed on all (greater than 99%) of peripheral blood monocytes, platelets, and megakaryocytes. It is also expressed weakly on the monocytic cell line U937 and the promyelocytic line HL60 and is present on cells from 3 of 4 AML patients examined. It is absent from polymorphonuclear leukocytes, T and B lymphocytes, erythrocytes, and a panel of hematopoietic cell lines. MPA is stripped from monocyte membranes with pronase and is reexpressed overnight. The determinant is carried on a noncovalently linked biomolecular complex with molecular weights of 93,000 and 135,000.

Peripheral T lymphocytes from RIC-Sprague-Dawley rats primed in vivo several months earlier with Actinomyces viscosus Ny 1 reacted with a strong proliferative response upon antigenic challenge in vitro. Two different antigen preparations from A. viscosus Ny 1, a broken cell supernatant (BCS) and an extracellular fraction (EXC) gave maximum responses as measured by the uptake of [3H]thymidine at a concentration of 10 microgram at day 4 of culture. Phytohaemagglutinin (PHA) used as a control provoked a maximum proliferation in the same order of magnitude. T lymphocytes from unprimed, germfree and conventional animals showed a similar stimulation to PHA, but only a marginal reaction to BCS, and were not at all activated by EXC. Evidence is thus presented for efficient removal of cells responding non-specifically to B-cell mitogens.

We describe a surface determinant shared by human monocytes and cells of the megakaryocytic axis that has been identified using a mouse monoclonal antibody. This monocyte-platelet antigen (MPA) is expressed on all (greater than 99%) of peripheral blood monocytes, platelets, and megakaryocytes. It is also expressed weakly on the monocytic cell line U937 and the promyelocytic line HL60 and is present on cells from 3 of 4 AML patients examined. It is absent from polymorphonuclear leukocytes, T and B lymphocytes, erythrocytes, and a panel of hematopoietic cell lines. MPA is stripped from monocyte membranes with pronase and is reexpressed overnight. The determinant is carried on a noncovalently linked biomolecular complex with molecular weights of 93,000 and 135,000.

Als Erganzung zu „Der Briefwechsel von E. S. von Fedorow und A. Schoenflies", dieses Archive for History of Exact Sciences Volume 7, Number 2, 1971, p. 91-141 [Briefe F.-Sch.] konnen wir dank der Ueberlassung von Photokopien der Originalbriefe aus der ,,Oeff entlichen Bibliothek genannt nach M. E. SaltykovShchedrin" in Leningrad und der „Niedersachsischen Staatsund Universitatsbibliothek" in Gottingen den Briefwechsel zwischen E. S. von Fedorow (1853-1919) und Felix Klein (1849-1925) veroffentlichen. Wir danken den genannten Stellen fur ihre Bemuhungen und die Erlaubnis zur Publikation. In den Briefen von F. Klein haben wir die Rechtschreibung und die Interpunktion den heutigen Regeln angepast, in denjenigen von Fedorow wurden auserdem leichte sprachliche Verbesserungen angebracht. Wiederum haben wir bei den Briefen die Nummern angegeben, die sie im Verzeichnis 1. 1. Schafranowski und N. M. Raskin, Handschriftliches Material von E. S. Fedorow im Archiv der Wissenschaften SSSR (russisch), Akademia Nauk, Trudi Archiva, Heft 14, Moskau-Leningrad 1957, 217 Seiten, tragen. Dabei ist die dort auf Seite 52 angegebene Postkarte Nr. I96 in Gottingen nicht vorhanden und der Entwurf des Briefes Nr. 197 gehort wohl nicht zu einem der erhaltenen Briefe. Zu den Briefen vom 20. Januar und vom I9./3I. Marz sowie zur Postkarte vom 20. Marz 1893 ist kein Entwurf erwahnt, wahrend der Entwurf Nr. 198 im wesentlichen mit dem Brief vom 9. April 1893 ubereinstimmt. Dieser Entwurf eines Briefes von Fedorow an Klein ist daselbst in russischer Uebersetzung auf den Seiten I38139 veroffentlicht, ebenso in russischer Uebersetzung der Brief Nr. 442 von Klein an Fedorow auf den Seiten 146-147.

Wir bezeichnen sie im folgenden mit (I) und (II). (I) ist eine Ephemeride fiber ein ganzes Jahr, je fuir den i., 6., II., i6., 2I. und 26. Tag eines Monates berechnet, wahrend (II) fiber etwa anderthalb Monate die taglichen Stellungen gibt. Die Jahresbestimmung wurde von den Herausgebern auf Grund der astronomischen Angaben vorgenommen; mittels moderner Tafeln wurde das Ergebnis verifiziert. Wir stellen uns die Aufgabe nachzupruifen, ob diese Ephemeriden mit Hilfe der ,,Handlichen Tafeln" berechnet sein k6nnen. Wir beziehen uns dabei auf die vorangehende Arbeit ,,Die Handlichen Tafeln des Ptolemaios von B. L. van der Waerden", die wir kurz mit (W) und Angabe des Paragraphen und Abschnittes zitieren.

Die Entdeckung der 23 0 Raumgruppen (auch Bewegungsgruppen oder regelmasige Systeme genannt) am Ende des 19. Jahrhunderts ist in mehrfacher Hinsicht eine bedeutende Leistung. Einerseits ist sie ein Ergebnis rein mathematischer Forschung, wobei sowohl die Geometrie wie auch die Gruppentheorie zum Erfolg mitgeholfen haben. Andererseits drangte die Erforschung des molekularen Aufbaues der Materie zur Diskussion aller moglichen Raumformen, wodurch der enge Zusammenhang physikalisch-chemischer und mathematischer Forschung hergestellt wurde. Man darf die genannte Entdeckung aber nicht nur als einen Abschlus verschiedener Forschungsrichtungen ansehen. Sie ist ebensosehr Grundlage und Ausgangspunkt von neuen Betrachtungen in unserem Jahrhundert geworden. Sowohl die Mathematik wie auch die Kristallographie, die Mineralogie und die Festkorperphysik haben von ihr fruchtbare Anregung erhalten. Diese kurzen Bemerkungen mogen dazu dienen, die vorliegende Veroffentlichung des Briefwechsels der beiden Entdecker der Raumgruppen zu rechtfertigen. Wir sehen bei der Lekture dieser Schriften in die Werkstatt zweier Forscher hinein, die, vollig unabhangig voneinander und mit verschiedenen Methoden, an der Losung desselben Problems arbeiten. Im gegenseitigen Austausch ihrer Ansichten werden die letzten Schwierigkeiten behoben, die sich einer endgultigen Formulierung der Ergebnisse entgegenstellen. Neben seiner wissenschaftlichen Bedeutung stellt der Briefwechsel ein Zeugnis edelster geistiger Gelehrtenkultur des vergangenen Jahrhunderts dar und ist damit ein Dokument, das auch diejenigen ansprechen wird, denen zunachst die Lehre von den Bewegungsgruppen ferner steht. Die Originalbriefe von Schoenflies an Fedorow befinden sich im „FedorowInstitut der Kristallographie, Mineralogie und der Fundorte der nutzlichen Gesteine" an der Leningrader Bergakademie. Leider ist es uns trotz umfangreichen Suchens in Deutschland, bei dem wir in dankenswerter Weise von vielen Bekannten unterstutzt wurden, nicht gelungen, die Originalbriefe von Fedorow zu finden. Was wir veroffentlichen, sind die deutsch verfasten Entwurfe zu diesen Briefen, die ebenfalls im genannten Institut in Leningrad aufbewahrt werden.

Numerous pathomechanisms have been proposed as relevant in periodontal disease (1). The T-cell triggered effector systems have been especially emphasized as the most important mediators of this particular chronic inflammation (2–4). It was therefore tempting to investigate whether T-cell suppression by a suitable antilymphocytic agent had a major influence on the establishment and progression of the disease.

Partially purified glucosyltransferases (GTF) isolated from Streptococcus mutans OMZ 176 and respective rabbit antisera were used to study enzyme-antibody interactions. A comparison between sensitive serological techniques and a functional inhibition test based on a radioenzyme assay demonstrated that the latter test system was the only one that discriminated between different antisera. Positive reactions in high dilutions in the former test systems were explained by the involvement of non-GTF contaminants and/or antibodies against enzyme regions distant to the catalytic site. The minute cross-reactions between two enzyme fractions and the respective antisera in the functional inhibition test indicated that the two immunogens contained mainly GTF that differed in the structure of their catalytic region. Control rabbit sera, rat oral fluid, and insoluble and soluble glucans considerably activated the GTF eluted with a 0.5 M phosphate buffer from hydroxapatite. It is suggested that these enzymes had additional binding sites for macromolecules inherent to rabbit sera and rat oral fluid, respectively, and that the observed increase in enzyme activity was due to a more stable enzyme conformation. Possibly the stimulation of GTF by the soluble glucan fraction was caused by a primer and/or acceptor function; however, this was not the case of the insoluble glucan. A stable complex was formed in the absence of the enzyme substrate, sucrose, the activity of which was not readily enhanced. It is concluded that the GTF of strain OMZ 176 are composed of multiple, multi-reactive molecules that enable these enzymes to act as cross-linking agents.

Cell-mediated cytotoxicity against syngeneic fetal rat fibroblasts that require in vitro exposure of effector cells to Actinomyces viscosus Ny1 fractions was investigated by measuring the uptake of radioactivity by fibroblasts during a 2-h pulse with [14C]aminoisobutyric acid after 1 to 3 days of coculture with splenic effector cells. By using splenocytes from inbred RIC-Sprague-Dawley rats as effector cells and syngeneic embryonic rat fibroblasts as target cells, strong cell-mediated cytotoxicity dependent on the in vitro exposure to an A. viscosus Ny1 fraction was observed, but only within a small range of effector-to-target cell ratios (3:1 to 10:1). Concanavalin A and lipopolysaccharide from Escherichia coli induced a comparable cytotoxicity, indicating that the effect might be connected with the mitogenic activity of the A. viscosus NY1 fraction. Splenocytes from rats immunized with A. viscosus Ny1 and from control rats induced similar levels of cytotoxicity in 72-h cytotoxicity assays. In shorter assays (24 h), however, splenocytes from immune animals induced low cytotoxicity, which was, however, significantly higher than that induced by splenocytes from control animals. We conclude that both antigen- and mitogen-dependent cell mediated effector mechanisms are operative in this system and that the two normally overlapping effects can be experimentally separated. This new system describes a fibroblast impairment in the presence of splenocytes and bacterial components and may provide a useful model for studying pathogenic mechanisms operative in periodontal disease.

Protein-coated silica, a macrophage toxin, was used to assess the requirement for accessory cells in the induction of an in vitro proliferative response to (i) antigens from Actinomyces viscosus and (ii) the mitogens conconavalin A (Con A) and phytohaemagglutinin (PHA). T cells were obtained from RIC-Sprague-Dawley rats primed in vivo with A. viscosus Nyl by splenectomy and filtering the spleen cell suspensions through Degalan Ig-anti-IgG columns. In the presence of 100 microgram silica/ml during 4 days of culture, the proliferative response of T lymphocytes was not diminished. In contrast, when the T cells were precultured with silica for 24 h, washed, and subsequently cultured with the antigen fractions, antigen-induced proliferation was abolished. This procedure, however, had no influence on mitogen-induced proliferation was abolished. This procedure, however, had no influence on mitogen-induced T-cell activation. It is therefore concluded that the antigen-dependent anamnestic in vitro response (but not activation by mitogens) of rat T lymphocytes needs help from silica-sensitive macrophages.

Euler hat gezeigt, das jede gegebene Ortsveranderung eines starren Korpers um einen festen Punkt durch eine einfache Drehung um eine feste Achse dargestellt werden kann, wenn nur der Anfangs- und Endzustand, aber nicht die Zwischenzeit in Betracht kommen. Nimmt man den festen Punkt als Ursprung eines orthogonalen Achsensystems an, dem im Anfang die identische Substitution entsprechen moge, so wird die gegebene Ortsveranderung durch eine orthogonale Substitution dargestellt. Diese hat nun ein einziges invariantes Element den Winkel der Drehung um jene feste Achse, der den eigentlichen Betrag der gegebenen Ortsveranderung ausdruckt, frei von der Zufalligkeit der Wahl der Achsen des Korpers.

Im Gebiete von n Variablen x, y,..., z heise jede Gruppe von Werten derselben ein Punkt, und die einzelnen Werte seien die Koordinaten dieses Punktes. Wenn uberdies das Quadrat der Distanz zweier Punkte durch die Summe der Quadrate der Unterschiede gleichnamiger Koordinaten beider Punkte definiert ist, mogen die Koordinaten rechtwinklige heisen, wenn durch eine andere homogene Funktion zweiten Grades, schiefwinklige. Ich setze die Eigenschaften einer orthogonalen Transformation, das heist einer solchen linearen Transformation der Koordinaten, welche jene erste Form des Ausdrucks der Distanz nicht andert, als bekannt voraus. Ein Punkt, dessen Koordinaten x 1, y 1, ..., z 1 den Zeiger 1 tragen, werde mit diesem Zeiger 1 bezeichnet. Die Gesamtheit aller Punkte, welche der in rechtwinkligen Koordinaten ausgedruckten Gleichung x 2+ y 2+ ... + z 2=1 genugen, heise n-Sphare; der Punkt, dessen Koordinaten alle Null sind, heise das Zentrum O derselben ; 1 ist ihr Radius ; von einem Punkte, der jener Gesamtheit angehort, sage ich, er liege auf der n-Sphare. Die n Punkte 1, 2, 3, ..., n seien nun nach Belieben auf der n-Sphare gegeben, doch so, das die Determinante $$\sqrt \Delta = \left( {\begin{array}{*{20}{c}}{x{\kern 1pt} y...z}{1{\kern 1pt} 2...n} \\\end{array} } \right)$$ nicht verschwindet; ferner ordne man entweder die Koordinaten oder die Punkte so, das diese Determinante positiv wird. Der Minor \(\left( {\begin{array}{*{20}{c}}{y...z} \\{2...n} \\\end{array} } \right) \) Dieser Determinante zum Beispiel werde mit \(\left( {\begin{array}{*{20}{c}}x \\1 \\\end{array} } \right)\) bezeichnet usw.

On a reduit depuis longtemps l’integrale multiple $$\int {{}^{^n}dx\;dy\;dz\;...,\quad \quad \left( {{x^2} + {y^2} + {z^2} + \cdot \cdot \cdot < 1} \right)} $$ c’est-a-dire l’integrale \(\int {{}^{^n}dx\;dy\;dz\;...} \) prise pour toutes les valeurs positives ou negatives de x, y, z,... remplissant la condition $${x^2} + {y^2} + {z^2} + \cdot \cdot \cdot < 1$$ , a l’expression \(\frac{{{\pi ^{n/2}}}} {{\Gamma \left( {\frac{n} {2} + 1} \right)}}\) qui, pour n = 2, represente l’aire du cercle, et, pour n = 3, le volume de la sphere de rayon 1. Mais si l’on demande que l’integrale proposee represente, pour n = 2, un secteur de cercle, ou, pour n = 3, une pyramide spherique triangulaire, il faut ajouter encore des limites lineaires et homogenes par rapport a toutes les variables, comme ax + b y +...> 0; et l’on a besoin au moins de n inegalites partielles, si l’on veut que la formule proposee ne se reduise pas des le premier abord a un nombre moindre d’integrations. Lorsque, au contraire, le nombre des polynomes-limites lineaires surpasse n, on peut toujours partager l’integrale multiple en plusieurs autres, ou ce nombre est precisement n. C’est donc le cas de n limites lineaires qui excite surtout notre attention; et comme il ne m’est pas connu que l’on ait deja traite cette integrale ainsi limitee, j’en signalerai quelques proprietes remarquables dans ce memoire.

Im 19. Band dieses Journals1) steht eine Abhandlung von Herrn C. G. J. Jacobi, in welcher die Fruchtbarkeit einer verallgemeinerten Betrachtung der konfokalen Flachen zweiten Grades fur die Theorie der Abelschen Integrale, zugleich mit der Bestimmung der geodatischen Linie auf dem Ellipsoid, gezeigt wird. Da nun dort nur kurz erwahnt ist, das auch diese letztere Aufgabe, der geodatischen Linie, der Ausdehnung auf eine beliebige Zahl von Variablen fahig sei, so sei es mir vergonnt, dieselbe hier zu behandeln, wobei ich mich moglichst der geometrischen Einfachheit zu nahern trachten werde.

When we displace a rigid system of n orthogonal axes, represented in its primitive state by the identical substitution $$\left| \begin{gathered} 1,\quad 0,\quad 0,\quad ... \hfill \\ 0,\quad 1,\quad 0,\quad ... \hfill \\ \hfill \\ \end{gathered} \right|$$ about its origin to an infinitely small extent, the substitution representing its altered state in relation to the primitive axes cannot but assume the form $$\left| \begin{gathered} 1,\quad a,\quad b,\quad c,\quad ... \hfill \\ - a,\quad 1,\quad f,\quad g,\quad ... \hfill \\ - b,\quad - f,\quad 1,\quad h,\quad ... \hfill \\ \hfill \\ \end{gathered} \right|$$ where a,b, ... denote infinitesimals of the first order, and squares and products of them are neglected ; for else the new system could not fulfil the orthogonal conditions. By erasing the units on the diagonal we should obtain the coefficients for the representation of the projections of the displacement of any point of the rigid system; should we then demand their vanishing in order to find resting points, a skew symmetrical determinant ought to vanish. But this is only then generally possible when n is odd; and as in this case the first minors do not vanish, there is consequently an axis, all points of which rest immovable during the displacement. Since such axis may be taken as a primitive one, and the corresponding dimension dropped, the question reduces to an even number of dimensions.

Limited merely by the last inequality, this integral (exhibiting for n = 2, 3 the area of a circle or the volume of a sphere with the radius 1) was, long ago, ascertained to be π n/2/Г[(n/2) + 1]1). But I do not know that the similar generalization of the integral representing a sector of a circle or a spherical sector on a triangular base has hitherto treated of. For this purpose, there must besides be given n limits of the linear and homogeneous form p > 0. For if the number of such limits were less than n, the integral can quite easily be reduced to a number of integrations equal to that of the linear limits given; and if there were more than n such limits, the integral may be resolved into several others having each only n such limits. We shall therefore here confine our attention principally to the integral with n linear limits.

Der Beweis, den Gauss (Disquisitiones arithmeticae [Lipsiae 1801], S. 352 = Werke, Bd. 1, Art. 235) dafur gibt, das die Elemente A, B, C der Form $$F = A{X^2} + 2BXY + C{Y^2}$$ welche durch die Substitution $$\begin{gathered} X = \lambda xx' + \lambda 'xy' + \lambda ''yx' + \lambda '''yy', \hfill \\ Y = \mu xx' + \mu 'xy' + \mu ''yx' + \mu '''yy' \hfill \\ \end{gathered} $$ $$\int {{}^ndx\;dy...dz} $$ in das Produkt der Formen $$\begin{gathered} f = a{x^2} + 2bxy + c{y^2}, \hfill \\ f' = a'{{x'}^2} + 2b'x'y' + c'{{y'}^2} \hfill \\ \end{gathered} $$ ubergeht, aus seinem Verfahren die Substitutionselemente λ, µ, ... zu bestimmen, als ganze Zahlen hervorgehen, schliest eine merkwurdige symbolische Formel in sich, welche verallgemeinert werden kann.

Die Besselschen Funktionen sind diejenigen, die als Funktionen eines Vielfachen des Exzentrizitatsverhaltnisses auftreten, wenn die Keplersche Aufgabe mit Anwendung der Fourierschen Reihe gelost wird. Herr Neumann nennt sie in der erwahnten Abhandlung Besselsche Funktionen erster Art, um sie von solchen zweiter Art zu unterscheiden, deren er bedarf, um arbitrare Funktionen, die gewisse Bedingungen erfullen, in Summenreihen zu entwickeln, die entweder nur nach Besselschen Funktionen der einen Art oder nach solchen beider Arten fortschreiten. Das Studium der interessanten Schrift veranlaste mich zu einigen Wahrnehmungen, die ich dem Verfasser brieflich mitteilte, und die ich nun, seiner freundlichen Aufforderung folgend, zu veroffentlichen wage.

Wenn im folgenden alle Winkel zwischen 0 und π und alle Quadratwurzeln positiv angenommen werden und man setzt $$\begin{gathered} \cos a = \frac{{\sin \alpha \cos \gamma }} {{\sqrt {{{\sin }^2}\alpha - {{\cos }^2}\beta } }}, \hfill \\ \cos b = \frac{{\cos \alpha \cos \beta \cos \gamma }} {{\sqrt {{{\sin }^2}\alpha - {{\cos }^2}\beta } \sqrt {{{\sin }^2}\gamma - {{\cos }^2}\beta } }}, \hfill \\ \cos c = \frac{{\sin \gamma \cos \alpha }} {{\sqrt {{{\sin }^2}\gamma - {{\cos }^2}\beta } }} \hfill \\ \end{gathered} $$ so wird man die drei Bedingungen dafur, das die Formel $$ad\alpha + bd\beta + cd\gamma $$ ein vollstandiges Differential sei, erfullt finden. Wir bezeichnen das Integral mit f(α, β, γ) und bestimmen seine Konstante dadurch, das wir es fur $$\sin \alpha \sin \gamma = \cos \beta $$ verschwinden lassen, weil es dann zugleich mit seinen Abgeleiteten a, b, c verschwindet. Aus dieser Definition erhellt, das die Funktion f ihren Wert nicht andert, wenn man die ausern Argumente α und γ vertauscht; das heist, es ist $$f\left( {\alpha ,\beta ,\gamma } \right) = f\left( {\lambda ,\beta ,\alpha } \right)$$ .