It will be noticed, then, that the two causes tending to bring about deviations from Boyle’s law act in contrary directions. In the greater number of gases the effect due to cohesion at ordinary pressure is greater than the effect due to the actual space occupied by the molecules. In the case of hydrogen at ordinary temperature the contrary is the case; if, however, hydrogen is strongly cooled, it shows variations similar to those exhibited by other gases at ordinary temperatures. By heating these gases the effect due to cohesion—to the mutual attraction of the molecules—becomes less and less; in such circumstances these gases show departures from theory in the same sense that hydrogen does at ordinary temperatures. The effect of mutual attraction among the molecules is to make the volume of the gas less than the theoretical value; the cohesive force may therefore be regarded as equal in effect to a certain additional pressure; that is, (P + A) V = constant, in which A is the measure of the force of cohesion. A, of course, must have relation to the number of molecules mutually attracted: _A is proportional to the square of the number of the molecules_. But the number of the molecules in the unit volume is proportional to the density of the gas, and in a given mass of gas the density is inversely proportional to the volume. Hence A is inversely proportional to the square of the volume—A = _a_/V2, hence (P + _a_/V2) V = constant. Now let us trace the effect of the second cause of variation from the mathematical exactitude of Boyle’s law. The fact that the molecules are not mathematical points means that V in the foregoing expression is not identical with the space in which the molecules move. That space is V - _b_, in which _b_ is the measure of the aggregate volume of the molecules. Hence the true expression becomes (P + _a_/V2) (V - _b_) = constant. The law of Dalton (Charles) also receives its simplest explanation by the kinetic theory of gases; and, moreover, the departures from the mathematical truth of the statement follow as a necessary consequence of the facts that the molecules have sensible magnitudes and are mutually attracted. We can measure the effect of heat upon a gas in two ways. We can either keep the pressure of the gas constant, and measure the increase in volume; or we can prevent the gas from expanding, and measure the elastic force or pressure it exerts. If the law of Dalton were mathematically true, it would follow that, _if the volume of the gas were maintained constant during the heating, its pressure would increase in the same proportion as the volume would have increased if the gas had been allowed to expand, but maintained at a constant pressure_. In other words, the expansion-coefficient and the pressure-coefficient should be the same. Experiment shows, however, that they are not identical. The following table gives the results of a number of measurements by Regnault: