=104.= In the case of the α particle, no direct measurements have been made upon the variation of the ionization with the velocity of the particle, so that the law of absorption of the rays cannot be deduced directly. An indirect attack upon the question has, however, been made recently by Bragg and Kleeman[166] who have formulated a simple theory to account for the experimental results which they have obtained upon the absorption of the α rays. The α particles from each simple type of radio-active matter are supposed to be projected with the same velocity, and to pass through a definite distance a in air at atmospheric pressure and temperature before they are all absorbed. As a first approximation the ionization per unit path is supposed to be the same over the whole length traversed before absorption, and to cease fairly suddenly at a definite distance from the source of radiation. This is in agreement with the observed fact that the ionization between parallel plates increases very rapidly when it approaches nearer than a certain distance to the radiant source. The range _a_ depends upon the initial energy of motion of the α particle and will thus be different for different kinds of radio-active matter. If a thick layer of radio-active matter is employed, only the α particles from the surface have a range _a_. Those which reach the surface from a depth _d_ have their range diminished by an amount ρ_d_, where ρ is the density of the radio-active matter compared with air. This is merely an expression of the fact that the absorption of the α rays is proportional to the thickness and density of matter traversed. The rays from a thick layer of active matter will thus be complex, and will consist of particles of different velocity whose ranges have all values between 0 and _a_. Suppose that a narrow pencil of α rays is emitted from a thick layer of radio-active material, and confined by metal stops as in Fig. 39. [Illustration: Fig. 39.] The pencil of rays passes into an ionization vessel _AB_ through a fine wire gauze _A_. The amount of ionization is to be determined between _A_ and _B_ for different distances _h_ from the source of the rays _R_ to the plate _A_. All the particles coming from a depth _x_ of the material given by _h_ = _a_ − ρ_x_ will enter the ionization vessel. The number of ions produced in a depth _dh_ of the ionization vessel is equal to _nxdh_, _i.e._ to _a_ − _h_ _n_ --------- _dh_, ρ where _n_ is a constant. If the depth of the ionization vessel be _b_, the total number of ions produced in the vessel is $$ \int_h^{h+b} n \frac {a-h} {\rho} dh = \frac {nb} {\rho} (a − h - \frac {b} {2}) $$ . This supposes that the stream of particles passes completely across the vessel. If not, the expression becomes $$ \int_h^a n \frac {a − h} {\rho} dh = \frac {n (a − h)^2} {2\rho} $$ .