I. Studies on bacteriophage DNA's and minicircular DNA's in M. lysodeikticus and E. coli 15. II. Flow dichroism of DNA solutions

Part I

Chapter 1.....A physicochemical study of the DNA molecules from the three bacteriophages, N1, N5, and N6, which infect the bacterium, M. lysodeikticus, has been made. The molecular weights, as measured by both electron microscopy and sedimentation velocity, are 23 x 10⁶ for N5 DNA and 31 x 10⁶ for N1 and N6 DNA's. All three DNA's are capable of thermally reversible cyclization. N1 and N6 DNA's have identical or very similar base sequences as judged by membrane filter hybridization and by electron microscope heteroduplex studies. They have identical or similar cohesive ends. These results are in accord with the close biological relation between N1 and N6 phages. N5 DNA is not closely related to N1 or N6 DNA. The denaturation T_m of all three DNA's is the same and corresponds to a (GC) content of 70%. However, the buoyant densities in CsCl of Nl and N6 DNA's are lower than expected, corresponding to predicted GC contents of 64 and 67%. The buoyant densities in Cs₂SO₄ are also somewhat anomalous. The buoyant density anomalies are probably due to the presence of odd bases. However, direct base composition analysis of N1 DNA by anion exchange chromatography confirms a GC content of 70%, and, in the elution system used, no peaks due to odd bases are present.

Chapter 2.....A covalently closed circular DNA form has been observed as an intracellular form during both productive and abortive infection processes in M. lysodeikticus. This species has been isolated by the method of CsC1-ethidium bromide centrifugation and examined with an electron microscope.

Chapter 3.....A minute circular DNA has been discovered as a homogeneous population in M. lysodeikticus. Its length and molecular weight as determined by electron microscopy are 0.445 μ and 0.88 x 10⁶ daltons respectively. There is about one minicircle per bacterium.

Chapter 4.....Several strains of E. coli 15 harbor a prophage. Viral growth can be induced by exposing the host to mitomycin C or to uv irradiation. The coliphage 15 particles from E. coli 15 and E, coli 15 T^- appear as normal phage with head and tail structure; the particles from E. coli 15 TAU are tailless. The complete particles exert a colicinogenic activity on E.coli 15 and 15 T^-, the tailless particles do not. No host for a productive viral infection has been found and the phage may be defective. The properties of the DNA of the virus have been studied, mainly by electron microscopy. After induction but before lysis, a closed circular DNA with a contour length of about 11.9 μ is found in the bacterium; the mature phage DNA is a linear duplex and 7.5% longer than the intracellular circular form. This suggests the hypothesis that the mature phage DNA is terminally repetitious and circularly permuted. The hypothesis was confirmed by observing that denaturation and renaturation of the mature phage DNA produce circular duplexes with two single-stranded branches corresponding to the terminal repetition. The contour length of the mature phage DNA was measured relative to φX RFII DNA and λ DNA; the calculated molecular weight is 27 x 10⁶. The length of the single-stranded terminal repetition was compared to the length of φX 174 DNA under conditions where single-stranded DNA is seen in an extended form in electron micrographs. The length of the terminal repetition is found to be 7.4% of the length of the nonrepetitious part of the coliphage 15 DNA. The number of base pairs in the terminal repetition is variable in different molecules, with a fractional standard deviation of 0.18 of the average number in the terminal repetition. A new phenomenon termed "branch migration" has been discovered in renatured circular molecules; it results in forked branches, with two emerging single strands, at the position of the terminal repetition. The distribution of branch separations between the two terminal repetitions in the population of renatured circular molecules was studied. The observed distribution suggests that there is an excluded volume effect in the renaturation of a population of circularly permuted molecules such that strands with close beginning points preferentially renature with each other. This selective renaturation and the phenomenon of branch migration both affect the distribution of branch separations; the observed distribution does not contradict the hypothesis of a random distribution of beginning points around the chromosome.

Chapter 5....Some physicochemical studies on the minicircular DNA species in E. coli 15 (0.670 μ, 1.47 x 10⁶ daltons) have been made. Electron microscopic observations showed multimeric forms of the minicircle which amount to 5% of total DNA species and also showed presumably replicating forms of the minicircle. A renaturation kinetic study showed that the minicircle is a unique DNA species in its size and base sequence. A study on the minicircle replication has been made under condition in which host DNA synthesis is synchronized. Despite experimental uncertainties involved, it seems that the minicircle replication is random and the number of the minicircles increases continuously throughout a generation of the host, regardless of host DNA synchronization.

Part II

The flow dichroism of dilute DNA solutions (A₂₆₀≈0.1) has been studied in a Couette-type apparatus with the outer cylinder rotating and with the light path parallel to the cylinder axis. Shear gradients in the range of 5-160 sec.^-1 were studied. The DNA samples were whole, "half," and "quarter" molecules of T4 bacteriophage DNA, and linear and circular λb₂b₅c DNA. For the linear molecules, the fractional flow dichroism is a linear function of molecular weight. The dichroism for linear A DNA is about 1.8 that of the circular molecule. For a given DNA, the dichroism is an approximately linear function of shear gradient, but with a slight upward curvature at low values of G, and some trend toward saturation at larger values of G. The fractional dichroism increases as the supporting electrolyte concentration decreases.

Paranormal operator on a Hilbert space

In this thesis an extensive study is made of the set P of all paranormal operators in B(H), the set of all bounded endomorphisms on the complex Hilbert space H. T ϵ B(H) is paranormal if for each z contained in the resolvent set of T, d(z, σ(T))//(T-zI)^-1 = 1 where d(z, σ(T)) is the distance from z to σ(T), the spectrum of T. P contains the set N of normal operators and P contains the set of hyponormal operators. However, P is contained in L, the set of all T ϵ B(H) such that the convex hull of the spectrum of T is equal to the closure of the numerical range of T. Thus, N≤P≤L.

If the uniform operator (norm) topology is placed on B(H), then the relative topological properties of N, P, L can be discussed. In Section IV, it is shown that: 1) N P and L are arc-wise connected and closed, 2) N, P, and L are nowhere dense subsets of B(H) when dim H ≥ 2, 3) N = P when dimH ˂ ∞ , 4) N is a nowhere dense subset of P when dimH ˂ ∞ , 5) P is not a nowhere dense subset of L when dimH ˂ ∞ , and 6) it is not known if P is a nowhere dense subset of L when dimH ˂ ∞.

The spectral properties of paranormal operators are of current interest in the literature. Putnam [22, 23] has shown that certain points on the boundary of the spectrum of a paranormal operator are either normal eigenvalues or normal approximate eigenvalues. Stampfli [26] has shown that a hyponormal operator with countable spectrum is normal. However, in Theorem 3.3, it is shown that a paranormal operator T with countable spectrum can be written as the direct sum, N ⊕ A, of a normal operator N with σ(N) = σ(T) and of an operator A with σ(A) a subset of the derived set of σ(T). It is then shown that A need not be normal. If we restrict the countable spectrum of T ϵ P to lie on a C²-smooth rectifiable Jordan curve G_o, then T must be normal [see Theorem 3.5 and its Corollary]. If T is a scalar paranormal operator with countable spectrum, then in order to conclude that T is normal the condition of σ(T) ≤ G_o can be relaxed [see Theorem 3.6]. In Theorem 3.7 it is then shown that the above result is not true when T is not assumed to be scalar. It was then conjectured that if T ϵ P with σ(T) ≤ G_o, then T is normal. The proof of Theorem 3.5 relies heavily on the assumption that T has countable spectrum and cannot be generalized. However, the corollary to Theorem 3.9 states that if T ϵ P with σ(T) ≤ G_o, then T has a non-trivial lattice of invariant subspaces. After the completion of most of the work on this thesis, Stampfli [30, 31] published a proof that a paranormal operator T with σ(T) ≤ G_o is normal. His proof uses some rather deep results concerning numerical ranges whereas the proof of Theorem 3.5 uses relatively elementary methods.

Organization and function of the phage Lambda chromosome

The process of prophage integration by phage λ and the function and structure of the chromosomal elements required for λ integration have been studied with the use of λ deletion mutants. Since att^φ, the substrate of the integration enzymes, is not essential for λ growth, and since att^φ resides in a portion of the λ chromosome which is not necessary for vegetative growth, viable λ deletion mutants were isolated and examined to dissect the structure of att^φ.

Deletion mutants were selected from wild type populations by treating the phage under conditions where phage are inactivated at a rate dependent on the DNA content of the particles. A number of deletion mutants were obtained in this way, and many of these mutants proved to have defects in integration. These defects were defined by analyzing the properties of Int-promoted recombination in these att mutants.

The types of mutants found and their properties indicated that att^φ has three components: a cross-over point which is bordered on either side by recognition elements whose sequence is specifically required for normal integration. The interactions of the recognition elements in Int-promoted recombination between att mutants was examined and proved to be quite complex. In general, however, it appears that the λ integration system can function with a diverse array of mutant att sites.

The structure of att^φ was examined by comparing the genetic properties of various att mutants with their location in the λ chromosome. To map these mutants, the techniques of heteroduplex DNA formation and electron microscopy were employed. It was found that integration cross-overs occur at only one point in att^φ and that the recognition sequences that direct the integration enzymes to their site of action are quite small, less than 2000 nucleotides each. Furthermore, no base pair homology was detected between att^φ and its bacterial analog, att^B. This result clearly demonstrates that λ integration can occur between chromosomes which have little, if any, homology. In this respect, λ integration is unique as a system of recombination since most forms of generalized recombination require extensive base pair homology.

An additional study on the genetic and physical distances in the left arm of the λ genome was described. Here, a large number of conditional lethal nonsense mutants were isolated and mapped, and a genetic map of the entire left arm, comprising a total of 18 genes, was constructed. Four of these genes were discovered in this study. A series of λdg transducing phages was mapped by heteroduplex electron microscopy and the relationship between physical and genetic distances in the left arm was determined. The results indicate that recombination frequency in the left arm is an accurate reflection of physical distances, and moreover, there do not appear to be any undiscovered genes in this segment of the genome.

Part I: The abortive infection of bacteriophage øx174 at low temperatures. Part II: The early stages in the process of infection by bacteriophage øx174

Part I

The infection of E. coli by ΦX174 at 15°C is abortive; the cells are killed by the infection but neither mature phage nor SS (single-stranded) DNA are synthesized. Parental RF (replicative form) is formed and subsequently replicated at 15°C. The RF made at 15°C shows normal infectivity and full competence to act as precursor to progeny SS DNA after an increase in temperature to 37°C. The investigations suggest that all of the proteins required for SS DNA synthesis and phage maturation are present in the abortive infection at 15°C.

Three possible causes are suggested for the abortive infection at 15°C: (a) A virus-coded protein whose role is essential to the infection is made at 15°C and assumes its native conformation, but its rate of activity is too low at this temperature to sustain the infection process. (b) Virus maturation may involve the formation of a DNA-protein complex and conformational changes which have an energy threshold infrequently reached at 15°C. (c) A host-coded protein present in uninfected cells, and whose activity is essential to the infection at all temperatures, but not to the host at 15°C, is inactive at 15°C. An hypothesis of this type is offered which proposes that the temperature-limiting factor in SS DNA synthesis in vivo may reflect a temperature-dependent property of the host DNA polymerase.

Part II

Three distinct stages are demonstrated in the process whereby ΦX174 invades its host: (1) Attachment: The phage attach to the cell in a manner that does not irreversibly alter the phage particle and which exhibits "single-hit" kinetics. The total charge on the phage particle is demonstrated to be important in determining the rate at which stable attachment is effected. The proteins specified by ΦX cistrons II, III and VII play roles, which may be indirect, in the attachment reaction. (2) Eclipse: 'The attached phage undergo a conformational change. Some of the altered phage particles spontaneously detach from the cell (in a non-infective form) while the remainder are more tightly bound to the cell. The altered phage particles detached (spontaneously or chemically) from such complexes have at least 40% of their DNA extruded from the phage coat. It is proposed that this particle is, or derives from, a direct intermediate in the penetration of the viral DNA.

The kinetics for the eclipse of attached phage particles are first-order with respect to phage concentration and biphasic; about 85% of the phage eclipse at one rate (k = 0.86 min^-1) and the remainder do so at a distinctly lesser rate (k = 0.21 min^-1).

The eclipse event is very temperature-dependent and has the relatively high Arrhenius activation energy of 36.6 kcal/mole, indicating the cooperative nature of the process. The temperature threshold for eclipse is 17 to 18°C.

At present no specific ΦX cistron is identified as affecting the eclipse process. (3) DNA penetration: A fraction of the attached, eclipsed phage particles corresponding in number to the plaque-forming units complete DNA penetration. The penetrated DNA is found in the cell as RF, and the empty phage protein coat remains firmly attached to the exterior of the cell. This step is inhibited by prior irradiation of the phage with relatively high doses of UV light and is insensitive to the presence of KCN and NaN₃. Temporally excluded superinfecting phages do not achieve DNA penetration.

Both eclipsed phage particles and empty phage protein coats may be dissociated from infected cells; some of their properties are described.

A Direct Approach to Robustness Optimization

This dissertation reformulates and streamlines the core tools of robustness analysis for linear time invariant systems using now-standard methods in convex optimization. In particular, robust performance analysis can be formulated as a primal convex optimization in the form of a semidefinite program using a semidefinite representation of a set of Gramians. The same approach with semidefinite programming duality is applied to develop a linear matrix inequality test for well-connectedness analysis, and many existing results such as the Kalman-Yakubovich--Popov lemma and various scaled small gain tests are derived in an elegant fashion. More importantly, unlike the classical approach, a decision variable in this novel optimization framework contains all inner products of signals in a system, and an algorithm for constructing an input and state pair of a system corresponding to the optimal solution of robustness optimization is presented based on this information. This insight may open up new research directions, and as one such example, this dissertation proposes a semidefinite programming relaxation of a cardinality constrained variant of the H ∞ norm, which we term sparse H ∞ analysis, where an adversarial disturbance can use only a limited number of channels. Finally, sparse H ∞ analysis is applied to the linearized swing dynamics in order to detect potential vulnerable spots in power networks.

I. The crystal structure of a new dimer of triphenylfluorocyclobutadiene. II. A low temperature refinement of the cyanuric triazide structure

I. THE CRYSTAL STRUCTURE OF A NEW DIMER OF TRIPHENYLFLUOROCYCLOBUTADIENE

The crystal structure of thermal isomer of the “head-to-head” dimer of triphenylfluorocyclobutadiene was determined by the direct method. The Σ₂ relationship involving the low angle reflections with the largest E’s were found and solved for the signs by the symbolic method of Zachariasen. The structure was seen in the electron density map and the E-map, and was refined antisotropically by the method of least squares. The residual R was 0.065.

The structure is a gem-difluorohexaphenyldihydropentalene. All of the phenyl groups are planar as it is the cyclopentadiene ring of the dihydropentalene skeleton. Overcrowding at the position of the flourines causes some deviations from the normal bond angles in the cyclopentene ring.

The list of observed and calculated structure factors on pages 32-34 will not be legible on the microfilm. Photographic copies may be obtained from the California Institute of Technology.

II. A LOW TEMPERATURE REFINEMENT OF THE CYANURIC TRIAZIDE STRUCTURE

The structure of cyanuric triazide was refined anisotropically by the method of least squares. Three-dimensional intensity data, which has been collected photographically with MoK_α radiation at -110˚C, were used in the refinement. The residual R was reduced to 0.081.

The structure is completely planar, and there is no significant bond alternation in the cyanuric ring. The packing of the molecules causes the azide groups to deviate from linearity by 8 degrees.

An investigation of a method of underwater propulsion by direct gas injection

This report presents the results of an investigation of a method of underwater propulsion. The propelling system utilizes the energy of a small mass of expanding gas to accelerate the flow of a large mass of water through an open ended duct of proper shape and dimensions to obtain a resultant thrust. The investigation was limited to making a large number of runs on a hydroduct of arbitrary design, varying between wide limits the water flow and gas flow through the device, and measuring the net thrust caused by the introduction and expansion of the gas.

In comparison with the effective exhaust velocity of about 6,000 feet per second observed in rocket motors, this hydroduct model attained a maximum effective exhaust velocity of more than 27,000 feet per second, using nitrogen gas. Using hydrogen gas, effective exhaust velocities of 146,000 feet per second were obtained. Further investigation should prove this method of propulsion not only to be practical but very efficient.

This investigation was conducted at Project No. 1, Guggenheim Aeronautical Laboratory, California Institute of Technology, Pasadena, California.

Current dependence of the energy gap in superconductors : a direct measurement

From the tunneling characteristics of a tin-tin oxide-lead junction, a direct measurement has been made of the energy-gap variation for a superconductor carrying a current in a compensated geometry. Throughout the region investigated – several temperatures near T_c and down to a reduced temperature t = 0.8 –the observed current dependence agrees quite well with predictions based on the Ginzburg-Landau-Gor’kov theory. Near T_c the predicted temperature dependence is also well verified, though deviations are observed at lower temperatures; even for the latter, the data are internally consistent with the temperature dependence of the experimental critical current. At the lowest temperature investigated, t = 0.8, a small “Josephson” tunneling current allowed further a direct measurement of the electron drift velocity at low current densities. From this, a preliminary experimental value of the critical velocity, believed to be the first reported, can be inferred in the basis of Ginzburg-Landau theory. For tin at t = 0.8, we find v_c = 87 m/sec. This value does not appear fully consistent with those predicted by recent theories for superconductors with short electronic mean-free-paths.

Ecological effects of trial pumpings in the Upper Lambourn: Stage 1 group pumping test Upper Lambourn group, September - November 1975

This report to the Thames Water Authority and Central Water Planning Unit is on research carried out in conjunction with the Stage 1 Group Pumping Test of five boreholes in the upper Lambourn Group for a period of three months in September, October and November 1975. The aim of the study was to assess the ecological effects of the pumpin g of five bore-holes in the upper Lambourn. That is, to determine how the seasonal sequence of ecological events in the river differed from what would hav e occurred had no pumping taken place. Since this 'experiment' has no control it is not possible to make a direct assessment. Nevertheless, by careful monitoring of ecological events before, during and after the pumping it is possible to document changes in th e river and by reference to the data already available for the Rive r Lambourn, normal seasonal changes in the flora and fauna can be separated from changes which may be attributable to the pumping and subsequent events.

Morfologia dentofacial e características oclusais dos índios Arara: revisitando o papel da hereditariedade e da dieta na etiologia da má oclusão

A influência da dieta e da hereditariedade nas características dentofaciais foi avaliada através do exame de duas populações indígenas amazônicas divididas por um processo de fissão linear. Os indígenas que constituem a aldeia Arara-Iriri são descendentes de um único casal expulso da aldeia Arara-Laranjal. O crescimento da aldeia Iriri ocorreu pelo acasalamento de parentes próximos, ratificado por um alto coeficiente de consanguinidade (F=0,25, p<0,001). A epidemiologia da má oclusão e das características da face foi analisada nos indivíduos entre dois e 22 anos, das aldeias Iriri (n=46) e Laranjal (n=130). A biometria da dentição e da face foi obtida em 55 indígenas em dentição permanente sem perdas dentárias, através da fotogrametria facial e dos modelos de gesso. O desgaste dentário foi examinado em 126 indivíduos através da análise de regressão múltipla. Os resultados revelaram uma determinação significativa da idade no desgaste dos dentes (R2=87,6, p<0,0001), que se mostrou semelhante entre as aldeias (R2=0,027, p=0,0935). Por outro lado, diferenças marcantes foram observadas nas características dentofaciais. Revelou-se uma face mais vertical (dolicofacial) entre os índios Iriri e o predomínio do tipo braquifacial nos indígenas da aldeia original, corroborado pela fotogrametria. Uma face sagitalmente normal foi observada em 97,7% da aldeia Laranjal, enquanto faces convexas (26,1%, RR-16,96) e côncavas (15,2%, RR=19,78) eram mais prevalentes na aldeia Iriri (p<0,001). A biprotrusão, com consequente redução do ângulo nasolabial, era uma característica comum entre os Arara, porém com maior prevalência no grupo Iriri (RP=1,52, p=0,0002). A prevalência da má oclusão foi significativamente mais alta na aldeia Iriri (RP= 1,75, p=0,0007). A maioria da população da aldeia original (83,8%) apresentou uma relação normal entre os arcos dentários, contudo, na aldeia resultante (Iriri), 34,6% dos indivíduos era Classe III (RP=6,01, p<0,001) e 21,7% era Classe II (RP=2,02, p=0,05). Enquanto nenhum caso de apinhamento e de sobremordida foi observado na aldeia Iriri, a razão da prevalência era 2,64 vezes maior para a mordida aberta anterior (p=0,003), 2,83 vezes (p<0,001) para a mordida cruzada anterior, 3,93 (p=0,03) para a sobressaliência aumentada, e de 4,71 (p=0,02) para a mordida cruzada posterior. Observou-se uma alta prevalência das perdas dentárias, sem diferença entre as aldeias (RP=1,46, p=0,11). O exame dos modelos revelou uma tendência de incisivos maiores e pré-molares e caninos menores na aldeia Iriri, delineando uma semelhança na massa dentária total entre as aldeias, que, aliada a arcadas dentárias maiores, justificaram o menor índice de irregularidade dos incisivos entre esses indígenas. Esses resultados minimizam a influência do desgaste dentário, uma evidência direta de como um indivíduo se alimentou no passado, no desenvolvimento dentofacial e enfatizam o predomínio da hereditariedade, através da endogamia, na etiologia da variação anormal da oclusão dentária e da morfologia da face.

I. The attenuation and dispersion of sound in a condensing medium. II. The flow of a gas-particle mixture downstream of a normal shock in a nozzle

I. The attenuation of sound due to particles suspended in a gas was first calculated by Sewell and later by Epstein in their classical works on the propagation of sound in a two-phase medium. In their work, and in more recent works which include calculations of sound dispersion, the calculations were made for systems in which there was no mass transfer between the two phases. In the present work, mass transfer between phases is included in the calculations.

The attenuation and dispersion of sound in a two-phase condensing medium are calculated as functions of frequency. The medium in which the sound propagates consists of a gaseous phase, a mixture of inert gas and condensable vapor, which contains condensable liquid droplets. The droplets, which interact with the gaseous phase through the interchange of momentum, energy, and mass (through evaporation and condensation), are treated from the continuum viewpoint. Limiting cases, for flow either frozen or in equilibrium with respect to the various exchange processes, help demonstrate the effects of mass transfer between phases. Included in the calculation is the effect of thermal relaxation within droplets. Pressure relaxation between the two phases is examined, but is not included as a contributing factor because it is of interest only at much higher frequencies than the other relaxation processes. The results for a system typical of sodium droplets in sodium vapor are compared to calculations in which there is no mass exchange between phases. It is found that the maximum attenuation is about 25 per cent greater and occurs at about one-half the frequency for the case which includes mass transfer, and that the dispersion at low frequencies is about 35 per cent greater. Results for different values of latent heat are compared.

II. In the flow of a gas-particle mixture through a nozzle, a normal shock may exist in the diverging section of the nozzle. In Marble’s calculation for a shock in a constant area duct, the shock was described as a usual gas-dynamic shock followed by a relaxation zone in which the gas and particles return to equilibrium. The thickness of this zone, which is the total shock thickness in the gas-particle mixture, is of the order of the relaxation distance for a particle in the gas. In a nozzle, the area may change significantly over this relaxation zone so that the solution for a constant area duct is no longer adequate to describe the flow. In the present work, an asymptotic solution, which accounts for the area change, is obtained for the flow of a gas-particle mixture downstream of the shock in a nozzle, under the assumption of small slip between the particles and gas. This amounts to the assumption that the shock thickness is small compared with the length of the nozzle. The shock solution, valid in the region near the shock, is matched to the well known small-slip solution, which is valid in the flow downstream of the shock, to obtain a composite solution valid for the entire flow region. The solution is applied to a conical nozzle. A discussion of methods of finding the location of a shock in a nozzle is included.

Normal structures and automorphism groups of t-designs

Combinatorial configurations known as t-designs are studied. These are pairs ˂B, ∏˃, where each element of B is a k-subset of ∏, and each t-design occurs in exactly λ elements of B, for some fixed integers k and λ. A theory of internal structure of t-designs is developed, and it is shown that any t-design can be decomposed in a natural fashion into a sequence of “simple” subdesigns. The theory is quite similar to the analysis of a group with respect to its normal subgroups, quotient groups, and homomorphisms. The analogous concepts of normal subdesigns, quotient designs, and design homomorphisms are all defined and used.

This structure theory is then applied to the class of t-designs whose automorphism groups are transitive on sets of t points. It is shown that if G is a permutation group transitive on sets of t letters and ф is any set of letters, then images of ф under G form a t-design whose parameters may be calculated from the group G. Such groups are discussed, especially for the case t = 2, and the normal structure of such designs is considered. Theorem 2.2.12 gives necessary and sufficient conditions for a t-design to be simple, purely in terms of the automorphism group of the design. Some constructions are given.

Finally, 2-designs with k = 3 and λ = 2 are considered in detail. These designs are first considered in general, with examples illustrating some of the configurations which can arise. Then an attempt is made to classify all such designs with an automorphism group transitive on pairs of points. Many cases are eliminated of reduced to combinations of Steiner triple systems. In the remaining cases, the simple designs are determined to consist of one infinite class and one exceptional case.