as they seem to be involved in the nebular knots and, with the exception of the centre, are decidedly blue. Fourteen points are probably nebular, being seemingly involved in nebulosity but not decidedly blue, or blue but not so clearly involved in the nebula. For 20 points it is quite uncertain whether or not they form part of the nebula.

Internal motions in the spiral nebula Messier 33. The dotted- and full-line arrows show the motions of points in the nebula derived from each of two pairs of photographs. The comparison stars are enclosed in small squares and circles.

For each set of plates the proper motions & and us were derived for all the points measured with respect to the 24 and 23 comparison stars used. These motions for the points belonging to the nebula are presumably due partly to a translation of the nebula as a whole, and partly to internal motion. By a method analogous to that followed for Messier 101 the motion of translation of the nebula was found to be

The results found by subtracting these values from the motions of the nebular points are assumed to represent internal motions. In plate I those for the 30 points of the 25-foot focus plates are indicated by arrows with full lines and for the 22 very probable nebular points measured on the 80-foot focus plates by arrows with broken lines; the comparison stars of the first pair are enclosed in small squares, those of the second pair in circles.

A first inspection of the plate leaves us again in doubt as to whether we are dealing with a rotation of the nebula as a whole or with a motion along the arms of the spiral; upon further examination the latter motion seems to be more clearly indicated.

Resolving the motions into components perpendicular to and along the radius, we find the following results:

Classifying the points according as they have a component of motion. outward or inward along the arms of the spiral, we have the following results:

Before discussing the possibility of an increase or decrease of motion with distance from the centre it will be necessary to measure a large number of additional points in the nebula, which is deferred for the present. The principal conclusion to be drawn from the present material is that here again we find motions analogous to those occurring in Messier 101, 81 and 51. In general they seem to be outward along the arms of the spiral.

In 1916 Pease published values for the radial velocity of the centre of Messier 33 and for the bright knot 10' nf the nucleus. The two values differ by about 200 km./sec. Taking into account the probable inclination of the nebula with respect to the tangential plane, we can gain some

idea of the order of the parallax of the nebula by comparing Pease's results with those obtained from the present investigation; the corresponding parallax is about 0".0005. The diameter of the nebula would be about 100 light-years and the individual points of the nebula would have absolute magnitudes of +1 and fainter.

If on the other hand we suppose the dimensions of Messier 33 to be comparable with those of the galactic system, its distance would be several million light-years; the motions indicated by the photographs would then represent velocities of the order of 150,000 to 300,000 km./sec., which, obviously, are extremely improbable. The internal motions in the spirals seem now to be well founded, and if time justifies this belief, they will accordingly afford a most important argument against the view that these nebulae are systems comparable with our galaxy.

1 van Maanen, A., Mt. Wilson Contr., No. 118, 1916; Astrophys. J., Chicago, Ill., 44, 1916 (210-228).

2 Amer. Astron. Soc. Publ., 3, 1918 (206-207). Monthly Notices, Lond., 77, 1917 (233-234). Observatory, Lond., 43, 1920 (255-260).

THE ATTACHMENT OF ELECTRONS TO NEUTRAL MOLECULES IN AIR*

BY LEONARD B. LOEB

RYERSON PHYsical LaboratORY, UNIVERSITY OF CHICAGO

Communicated by R. A. Millikan, December 4, 1920

It is well known that the process of ionization in gases consists of the detachment of an electron from the molecules or atoms ionized. It has further been proved that in air at atmospheric pressure the carriers of negative electricity are neutral molecules5.6 of the gas carrying an additional electron. These are called the normal ions. Now it is of interest to determine in what manner the electron liberated by the ionizing process attaches itself to a molecule to form an ion. For it is possible that an understanding of this process may help us to gain a picture of the surfaces of the molecules.

In air at atmospheric pressure the normal negative ions move with a velocity of 2 cm./sec. in unit electric field while the electrons have a mobility of about 200 cm./sec. 37 under the same conditions. Such a marked difference in the two types of carriers accordingly furnishes us an excellent means of investigating the above question as the ensuing analysis will show.

Let us assume that the electrons liberated from the plate P, figure 1, by ultraviolet light unite with gas molecules on their first impacts to form ions. Now let a second plate, E, connected to an electrometer be placed

parallel to P and d em. above it. On applying an alternating potential difference of half period 7 between P and E the ions starting from P will alternately be driven from, and drawn back to P, for periods of T seconds. If u is the velocity of the ion in unit field, then for given values of T and d there will be no current to E until V reaches a value V. such

Fia I

P

=

that uTV./d d. At V. then a current to E will become manifest which will increase with increasing V to a saturation value. On plotting the current i as ordinate against the voltage V as abscissa we will get a curve of the type of curve I, figure II. Such a curve will be termed a mobility curve for if the value of the intercept V. of such an experimental curve be substituted in the equation

the mobility u of the carrier is at once obtained if d and T are known. When the pressures are reduced the curves remain the same but the value of the mobility u of the ion is found to increase inversely as the pressure. In other words up/760 independent of pressure.

K, where K, the mobility constant of the ions, is

Now let us assume with J. J. Thomson' that an electron does not attach to form an ion on its first encounter with a gas molecule, but that the attachment is a chance phenomenon occurring on the average in one out of n impacts with molecules. Let us further assume that for air n is large, say, about 250,000. Under ordinary conditions the velocity of thermal agitation of the electron is great compared with its velocity acquired in the electric field. The electron, therefore, covers a zigzag path drifting slowly all the while in the direction of the electric field. Consequently while making the 250,000 impacts necessary for attachment the majority of the electrons will move a distance, A, in the field, which may be estimated. Since A is covered by the electron in 1/100 of the time that an ion would take, one may practically assume that the majority of the ions start at a point distant A em from P instead of from P. For appreciable values of A the values of V required to drive the majority of the carriers to E may become notably lower than they are for ions starting at P. The values of u and hence of K obtained from experiments where A becomes significant will then be high. In air at atmospheric pressure the time taken for an electron to make 250,000 impacts is about 1.2 × 10−6 In a field of 40 volts with d 15 mm. the electron would cover a distance of 6.3 × 10−2 mm. towards E in this time. This small value of

sec.

-2

=

the distance A covered as an electron would produce no measurable effect on V. and the values of K would be normal. Now let the pressure be reduced to 152 mm. The mobility of the electrons will be increased fivefold. Furthermore as the density of the gas is reduced to one-fifth the electrons will take five times as long to make the 250,000 impacts required to attach. The distance A will, therefore, become 1.5 mm. which is an appreciable fraction of the 15.0 mm. between the plates. The intercept V. as determined from the portion of the curve corresponding to the majority of the carriers will, therefore, be but 0.9 of the V. required for ions, and the value of K will be about 10% higher than for normal ions. In other words assuming the Thomson mode of attachment the mobility constant of the ions will appear to increase with decreasing pressures below about 152 mm.2 Since the number of impacts required to form an attachment is a chance phenomenon there will be an appreciable number of ions reaching E that have traversed distances greater than A before attaching. These will reach E at values of V. below those for the majority of carriers. As a result the otherwise sharp intercepts of mobility curves with the voltage axis observed for ions will be masked by asymptotic feet of exponential form rising at values of V well below the V. required for the majority of the ions. These will become rapidly more pronounced

0 10 20

30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100

as the pressures decrease. Such curves are seen in the experimental curves II, III, IV, V and VI, figure II, obtained in air under conditions. indicated in the legend. To estimate the hybrid mobilities of such carriers the asymptotic feet must naturally be ignored, as has been done by previous observers. 28

With the method of analysis outlined above it would be possible to pursue the evolution of the mobility curves as a function of p and T in a qualitative manner indefinitely. Fortunately a much simpler and more accurate study of the theory is made possible by the application of the mathematical analysis of Thomson. On the basis of his theory Thomson has shown that out of Q. electrons starting from P the number that can travel x cm. through the air without combining to form ions is given by e-(Wx)/(nK'LV/d)

=

(2)