495one employed in these experiments. The number of ions produced by a single a-particle under the special conditions of the experiment is easily found from the curve given in fig. 3. The determination of the ionisation current in the bulb then gives at once the total number of a-particles. Care has to be taken to obtain saturation and to avoid ionisation by collision, which occurs when too large a voltage is applied. I wish to acknowledge the assistance which Mr. E. Marsden has given me in some of these observations.In conclusion, I desire to express my gratitude to Prof. Rutherford for his valuable suggestions and his kind interest in the experiments.On a Diffuse Reflection o f the a.-Particles. When /3-particles fall on a plate, a strong radiation emerges from the same side of the plate as that on which the /3-particles fall. This radiation is regarded by many observers as a secondary radiation, but more recent experi ments seem to show that it consists mainly of primary ^-particles, which have 'been scattered inside the material to such an extent that they emerge again at the same side of the plate* For a-particles a similar effect has not previously been observed, and is perhaps not to be expected on account of the relatively small scattering which a-particles suffer in penetrating matter.f On a Diffuse Reflection of theIn the following experiments, however, conclusive evidence was found of the existence of a diffuse reflection of the a-particles. A. small fraction of the a-particles falling upon a metal plate have their directions changed to such an extent that they emerge again at the side of incidence. To form an idea of the way in which this effect takes place, the following three points were investigated:-

But whatever value is attached to the numerical evidence by those competent to judge, the broad conclusion from the direction of the changes is unaffected. I should llke also to reply to one criticism which has been made. It is not necessary to the hypothesis that the atomic free frequency should be absolutely invariable throughout all chemical changes. If it were the case that a slight change (say 1 per cent.) in the atomic free frequency would account for all the observed changes of refractivity and dispersion, the criticism would have force. But any one who examines the figures in lhe table for (e. g.) hydrogen, nitrogen, and ammonia, will see that no slight change in a frequency can possibly account for the observed changes. For hydrogen no2X 10-~r=12409, for nitrogen 17095. For ammonia the nmnber which expresses its average value is 8135, an enormous drop. At the same time the refractivity has gone up only 3} per cent. But if the number of vibrators had remained constant while the average free frequency decreased, the increase of the refractivity must have been much greater than this. Hence, to account for the observed changes, one must also assume that the number of vibrators (? electrons) has fallen off in about the same proportion as the frequency. These two hypotheses seem much more improbable than that which is here put forward. LXI. The Laws of .Deflexion of a Particles through Large Angles*.

We have measured the spatial distribution of motile Escherichia coli inside spherical water droplets emulsified in oil. At low cell concentrations, the cell density peaks at the water-oil interface; at increasing concentration, the bulk of each droplet fills up uniformly while the surface peak remains. Simulations and theory show that the bulk density results from a 'traffic' of cells leaving the surface layer, increasingly due to cell-cell scattering as the surface coverage rises above ∼ 10%. Our findings show similarities with the physics of a rarefied gas in a spherical cavity with attractive walls. PACS numbers: Valid PACS appear hereThe physics of self-propelled particles [1] -natural or synthetic 'swimmers' -is an active area of current condensed matter and statistical physics, where understanding non-equilibrium effects poses a 'grand challenge'. Swimmers are intrinsically out of equilibrium even without external driving. There is as yet no general recipe for predicting their collective behavior.Confinement is of significant interest in diverse areas of physics. In this context, it is fascinating to note that selfpropelled particles can confine themselves spontaneously. Motile Escherichia coli and other bacteria encountering a surface continue to swim along it, giving rise to selforganised confinement to a 2D layer. Experimentally, the number density of motile E. coli between two parallel glass slides peaks strongly at the slides [2, 3]. However, in this geometry, the cell density between the walls remains low and there is little 3D confinement, because the 'wall-hugging' swimmers can escape essentially to infinity along the wall. Even the 2D confinement is weak: surface swimmers spread out to minimise interaction, and singlebody physics suffices to explain 'wall hugging' [2][3][4][5].The interesting question now arises: what would happen if there is confinement in all spatial dimensions? Biologically, motile bacteria in nature are sometimes confined in this way, e.g. in raindrops [6] or infected host cells [7], possibly leading to motility loss [8]. In physics, the collective behavior of confined swimmers has attracted recent interest. At high density, motile Bacillus subtilis in a cylindrical drop develop stable vortices [9, 10], while simulations of swimmers in a 2D box suggest novel forms of phase separation near close packing in the absence of hydrodynamic interactions [11]. In this work, we perform experiments starting from the opposite limit, and probe the way in which interaction effects emerge amongst motile bacteria confined within spherical emulsion droplets as the average swimmer density, ρ 0 , increases from a small value.As expected, at ρ 0 → 0, we observe motile cells 'hugging' the inner surface in a layer [2, 3]. As ρ 0 increases, we find that the drop fills up in an unexpected way: the bulk density increases uniformly while the surface peak remains. We present simulations and theory that reproduce essential features of our observations, and which suggest that the physics is reminiscent o...

We present a simulation study of pattern formation in an ensemble of chemotactic run-and-tumble bacteria, focussing on the effect of spatial confinement, either within traps or inside a maze. These geometries are inspired by previous experiments probing pattern formation in chemotactic strains of E. coli under these conditions. Our main result is that a microscopic model of chemotactic run-and-tumble particles which themselves secrete a chemoattractant is able to reproduce the main experimental observations, namely the formation of bacterial aggregates within traps and in dead ends of a maze. Our simulations also demonstrate that stochasticity plays a key role and leads to a hysteretic response when the chemotactic sensitivity is varied. We compare the results of run-and-tumble particles with simulations performed with a simplified version of the model where the active particles are smooth swimmers which respond to chemotactic gradients by rotating towards the source of chemoattractant. This class of models leads again to aggregation, but with quantitative and qualitative differences in, for instance, the size and shape of clusters.

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