tion was made by Kaufmann when he measured the ratio ()

in the case of the negative carriers (i. e., the B-rays) from radium. These rays have a higher average speed than cathode rays and in Kaufmann's experiments rays of different speeds were measured. The ratio (varied from (1.31 to 0.63) × 107 according to the speed of the corpuscles.

Now Thomson, in his "Recent Researches," develops a formula for the electrical momentum of a charged body without any limitation to the speed:

in which is the velocity of aether wave-motion-i. e., that of

light.

2 e2 This easily reduces to v, the value obtained before, 3 a when is small compared with V; while if V, I becomes infinite.

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Referring now to Kaufmann's experimental results mentioned above, attention is directed to the following table:

Column I gives five speed values actually measured of Brays from radium. Column II gives the corresponding e/m for each experiment. Column III gives the five respective values calculated from the results of experiment, of the ratio of the mass of radium corpuscles to that of cathode ray corpuscles. For these latter particles ()=1.95 × 107, the speed being

less, the charges being of course the same. In column IV are found the ratios of the same masses calculated from the theoretical formula by substituting the different values of v given in column I. Attention is called to the very close agreement between columns III and IV, and also to the very weighty evidence thereby offered that the total mass of a moving corpuscle. is electrical. It is surely worthy of note, too, that the agreement is closer for the higher speeds; which farther strengthens one's belief in the theory that all mass is electrical.

Consider now the effect of such impact of these particles or corpuscles as occurs in a Crookes tube. According to our theory each corpuscle is accompanied by lines of force having inertia. Because of this inertia the parts of lines at a distance from the corpuscles do not participate at once in the effect of the impact, since this effect has to travel along each line outward from each particle with the speed of aether wave-motion. The conclusion is that these radiating pulses constitute the Roentgen rays, and the results of some recent researches of Blondlot for the purpose of measuring the speed of propagation of these rays are consistent with this view. Blondlot seems to have shown by experiment that the Roentgen rays travel with the speed of light.

Since it has been proved by experiment almost beyond question that the corpuscular carriers of negative electricity are always of the same mass from whatever source derived, the idea is at once suggested that these bodies may be the units from which all kinds of atoms are formed, this unit of building material being the same in all substances. The following crude illustration may help to make this idea conceivable: For example, a whole city (a molecule) or group of cities (a mass) might be composed of separate buildings (the atoms), either all alike (an element) or of many shapes and sizes (a compound), while every building might be made of bricks (the corpuscules) exactly alike in every respect. This notion that' all matter in its simplest state is of only a single kind is, of

course, not new, though the very forcible experimental evidence indicating such a state of affairs has been offered within a comparatively few months. While it may be urged that another step has indeed been taken but only deeper into the mystery, yet assuming the truth of the above conclusion, we find ourselves now face to face with a single problem instead of many, the solution of which would open wide the door to a comprehensive knowledge of many things now unknown and formerly unknowable.

If we assume that a volume of the jelly-like aether-very large compared to a corpuscle is surrounding a group of corpuscles, the latter filling this space with lines of force mutually repellent, but all gripping the aether, we shall have a structure behaving dynamically just like a uniform sphere of positive electricity, throughout which are scattered particles of negative electricity or corpuscles. The spherical positive body will exert a force on each negative electron directed towards the center of the space and in magnitude proportional to the distance from the center directly; while each pair of negative bodies will mutually repel with a force inversely proportional to the square of the distance between them.

Because of these two kinds of action, it occurs to one at once that combinations differing both in number and in configuration must also be unlike in their stability of permanent identity. Suppose we consider the conditions of equilibrium for different numbers of corpuscles. If the number be small enough the problem can be solved easily; e. g., in the case of three, the arrangement will be in the form of an equilateral triangle; of four, in a square or a regular tatrahedron. For larger numbers the forms that result can best be determined and studied by experiment. As a suggestion of how this might be possible, suppose a number of magnets floating vertically in a liquid, similar poles up. Above this system with an opposite pole directed downward, station another magnet; the following plane figures will be formed by the floating poles depending on the number:

1.

3

10

23

Etc.

As the number increases it appears that the arrangement developes into a series of concentric symmetrical forms, the innermost one developing from a single unit. For example, the triangular formation occurs first with three units; next with ten; then again with twenty-three, two rows encompassing the three-part center, and so on for larger numbers.

This is suggestive of the recurrence of definite chemical properties periodically when the elements are arranged in the sequence of their atomic mass values, since it would be most reasonable that the properties of a substance should depend, in part at least, on the configuration as well as on the number of its atomic units. This theory also indicates a possible relation and its cause, between the different spectrum lines of an element, as well as that between the spectra of allied elements.

Consider the vibrations in the case of a simple form, e. g., the triangular arrangement. As each corpuscle has three degrees of freedom of motion there could be as many as nine periods of vibration, though probably not so many would actually occur, as they would not likely all be different; so the spectrum might consist of a number of lines up to nine as a maximum. Again, 'in the next occurrence of the trio, there will be ten corpuscles in all, seven around the triangle. By influence of the seven, the periods of the inner three would be somewhat changed, and those that were equal when the grouping consisted of the triangle alone must now be slightly different because of the dynamical asymmetry of the system, giving rise therefore to double or triple groups of lines. A higher complexity of the structure, which implies a greater atomic mass, would result in more complex spectrum groups-as, for example, greater and different spaces between the components of different lines.

Any theory suggesting a satisfactory view of the sub-atomic structure of matter must account for the individual stability of the atom. If we consider the necessary expenditure of energy for atomic disintegration, it is evident that in some way it must depend on the number of corpuscles, and on the value of their corresponding charges, as well as on the mean radius of the whole system. That is:

atomic energy = ¢ (n)

in which e is the charge on each of n corpuscles assembled into a group of average radius a. If r be taken as the radius of one neutral unit composed of a negative corpuscle embeded in its complementary positive electricity, then nr3-a3, and the above energy formula becomes:

atomic energy = $ (n) ns r

Now the obvious condition that this atom shall not split up into two is that:

in which, and 1, would be the number of units in each part, n,+n, being equal to n. If (n) is proportional to a power of n less than the three-fourths power, this unequality will not be satisfied for any value of n, and an atom coming into that dynamic state from any cause, would be unstable and break up, the neutral units redistributing themselves according to the new conditions, so that the dependence of energy on the number of units would be according to a power of n large enough to have the above condition satisfied. Again, it is possible that for higher values of n the test of stability would indicate the existance of an atom to be impossible; where for values of n near the limit the atoms would be on the verge of being unstable.

Just in this connection attention is called to the fact that radio-active substances, such as radium, thorium, uranium, have the greatest atomic masses known, i. e., they are on the