If 0 and 4) be the angles through which the selected beam of rays is bent by passing through fields of strength X and H then 0 and 4) v = LHe/m where 1,L are the lengths of the paths of the rays in the fields. From these equations it can easily be shown that if the magnetic deflection is greater than double the electric deflection all rays of constant mass, or more precisely of constant m/e, will come to a real focus F, and that the locus of the foci so generated will lie along the line GF passing through Z and parallel to the line = 2 0. If a photographic plate is placed at GF a spectrum depending on mass alone will be obtained. On account of its analogy to optical apparatus the instrument has been called a mass-spectrograph and the spectrum it produces a mass-spectrum.
The use of slits instead of a fine circular tube, combined with the enhanced intensity obtained by means of the focussing prin ciple, enables a very much higher resolving power to be used than was possible with the parabola method. Hence, although the photographs obtained do not afford so wide a range of general information upon the rays, the limit of accuracy in comparison of mass is notably increased. The first mass-spectrograph was set up in Cambridge in 1919 and used continually till 1925. In it 6 the angle of electric deflection was one twelfth of a radian. It had a resolving power of about i in 130 and an accuracy of about I in 1,000. By its means over 5o elements were analysed and the "whole number rule" established. (See ISOTOPES.) For details of its construction and technique the reader is referred to the works quoted at the end of this article.
Plate, fig. 4 shows a number of mass-spectra obtained by its means. Each dark line represents the image of the slits corres ponding to a particular mass. The number above the line indi cates the mass it corresponds to on the ordinary chemical scale 0 =16. The whole spectrum represents a range of mass of about 3 to 1, and the position of any line on the spectrum can be altered at will by changing the strength of the deflecting fields as shown by the positions of the chlorine group 35,36,37,38 in spectra II., III., IV. It will be noticed that the displacement to the right with increasing mass is roughly linear, a fortunate occurrence of great assistance in making the necessary calibrations. The measure ments of mass are not absolute, but relative to certain reference lines which correspond to known masses. Such lines, due to hydro gen, carbon, oxygen and their compounds, are generally present as impurities or purposely added for the smooth working of the dis charge tube. The two principal groups of these reference lines are the group, due to or 0(16), and the group (24 to 30) containing the very strong line (28) due to CO and other bodies. The latter group and part of the former are well shown in spectrum I., where between them may be seen the lines due to the isotopes of neon 20 and 2 2. These two groups form with CO2(44) a good scale of reference. The remarks already made about parabolas due to multiply charged rays apply to the lines obtained by this form of analysis. Lines due to par
ticles carrying one, two, three, or more charges are called lines of the first, second, third or higher order, thus in spectrum II. the faint lines at 17.5 and 18.5 are chlorine lines of the second order. In spectrum V. taken with argon the third order line of its prin cipal isotope (40) is clearly shown at IA among the group of reference lines. Spectrum VIII. shows the six isotopes of krypton; on the left their second order lines can be seen close to the first order line of argon 40.
The remarkable property possessed by the atoms of mercury, of carrying multiple charges is well exhibited in mass-spectra. Mercury is a complex element and the characteristic closely packed group of lines due to its isotopes can be seen, progressively weaker in intensity up to the sixth order. Some of these groups appearing as unresolved blurrs may be recognized in the plate. The lines of mercury have now been satisfactorily resolved and its constituent isotopes determined by a mass-spectrograph of higher power. (See ISOTOPES.) Method of "Bracketing."—The method of determining masses by the position of lines with regard to known reference lines cannot be conveniently applied to the elements hydrogen and helium as these are too remote from the scale of reference. Their masses were first compared by the following principle which in volves change in the deflecting fields. It is not practicable to deter mine the absolute values of the magnetic field but it can be kept constant without much difficulty. On the other hand, it is easy to apply electric fields whose ratios are known with certainty. From the equations already given it can be shown that for a given position on the spectrum and my GcH. Therefore if H is constant mcc If, therefore, after taking a spectrum we take another with the same magnetic field and, say, exactly double the electric field, the position due to a mass m on the first will be occupied by a line due to a mass 2m on the second. Hence if V is the original potential on the plates and v a suitable small voltage, and we take three spectra on the top of each other, one with a po tential V, one with 2V+v, and a third with 2V—v, the magnetic field being identically the same for all, a line due to a mass in will appear bracketed on each side by lines due to gym. If the two to one relation between the masses is an exact one the bracket will be symmetrical as in the case of the hydrogen atom and molecule spectrum VII. c. If the bracket is not symmetrical the ratio of the masses is not 2 as in the case of the hydrogen molecule and helium atom spectrum VII. b and d. In this way it was first proved that the hydrogen atom had a mass consider ably greater than a whole number on the oxygen scale, the value agreeing with 1.008, that deduced by chemical methods. This result, which has since been amply confirmed, is of great theoret ical importance.