Considerable difficulty was found with the nitrous oxide, as it changed slightly after it had been experimented upon, especially at the higher electric forces Z. But by using fresh quantities of gas in the apparatus consistent results were obtained. Two methods of preparation of the gas were

used, and identical results were obtained. In the first section of Table III. the agreement of k and W is good for the same values of the ratio Z/p, but in the second section there are a great many ions in the stream, probably due to the decomposition of the gas under these conditions.

5. The values of the mean free path of the electrons in centimetres, the effective radius o of the molecules of the gas in centimetres, and the proportion λ of the energy lost in collision with a molecule are given by Tables IV. and V. for carbon monoxide and nitric oxide.

The quantities, at the top of the tables are the values of the radii obtained by the viscosity method *.

In the values of λ for the carbon monoxide there is a maximum when k is equal to 5.5. Also in the carbon dioxide there was a similar maximum when k was equal to 20.

*Jeans, 'Dynamical Theory of Gases,' p. 327 (1921).

The energy of agitation of the electrons is proportional to k, and may be expressed in terms of the potential required to impart an equal quantity of energy to a particle having an atomic charge. This potential in volts is k/27. Thus

electrons lose a large proportion of their energy when they collide with molecules of carbon monoxide with velocities corresponding to 2 volt, and of carbon dioxide with velocities of 74 volt.

*

Note. In a previous paper by Prof. Townsend and? Mr. Bailey some cases were mentioned where there is a comparatively large loss of energy when electrons collide with molecules, and it was implied that in all such cases. there are ions in the gas-for example, in carbon dioxide.. The statement was based upon the fact that k was found to be small in some of the earlier experiments with this gas, and. the value of for ions must be approximately unity. Large values of k can only be obtained with electrons, but the recent experiments with carbon dioxide †, where both k and W were measured, show that k may be very small for a stream of electrons. In this gas the velocity W is very large, even when Z/p is small, due to the fact that the electrons lose a large proportion of their energy in collision, but do not form ions.

Phil. Mag. vol. xlii. Dec. 1921, p. 891.

†M. F. Skinker, Phil. Mag. vol. xliv. Nov. 1922.

LXX. On Types of Crystal Symmetry in which no finite symmetrical crystal unit having the complete symmetry of the crystal is to be found. By WILLIAM BARLOW, F.R.S.

THE tional indices as exemplified by the

HE geometrical study of crystal structure is based on

variety of forms of crystal symmetry presented in nature. Some 30 years ago, 230 distinct types of homogeneous structure were discriminated according to one or other of which alone the parts of a given individual homogeneous crystal must be regarded as arranged †.

Every similar unsymmetrical space-unit of the spacefilling uniform partitioning of a given individual crystal is by every coincidence operation characteristic of the particular type of the 230 concerned transferred to an entirely distinct position; the original and derived positions show no overlapping whatever.

For the purpose of visualizing this condition of things for some of the more regular types of the 230, the writer constructed models in which similar dolls' hands were placed in an open framework in relative positions located by the characteristic coincidence operations of one or other of these types ‡.

In order to derive some partitioning of space appropriate to an individual case of any given type, every doll's hand in the appropriate artificial structure can be supposed to grow similarly, and to cease growing wherever and so soon as the moving boundaries come in contact with one another. Space is in this way conceived to be partitioned without leaving interstices into similar grotesque cells presenting in nearly all cases more than one orientation. All of these cells are capable of being brought to coincidence one with another by some appropriate coincidence movement or mirror-image operation characteristic of the type of the 230 in question. In cases of types presenting a mirror-image relationship of some kind, two sets of dolls' hands are employed, rights and lefts equally numerous and similarly distributed.

It is obvious that the space-unit of this conception is destitute of symmetry.

Communicated by the Author.

66

Groth's Zeitschr. für Kryst. xxiii. p. 1, xxv. p. 86. Report on the Structure of Crystals," Brit. Assoc. Glasgow, 1901.

He exhibited these models at a Royal Society soirée and elsewhere in this country; also on the Continent. They are now in the Natural History Museum at South Kensington.