Let us now suppose that V has this peculiar value: that is, if we look on this value V as known, we must suppose that β is given by the second of the above formulæ. The other condition allows P and S to be put in the forms P = -β_v_/λV^2, S = β/λ, where V′ = λV. Thus we have the bundle of formulæ β^2 = 1/(1 - _v_^2/V^2), T = β{_t_ - _vx_/V^2}/λ, V′ = λV. The value which we give to λ is purely a matter for the adjustment of units. If we want A and B to agree in their judgments of the magnitude of this peculiar muzzle-velocity, we put λ = 1. We then get the formulæ usually adopted, namely β^2 = 1/(1 - _v_^2/V^2), } T = β{_t_ - _vx_/V^2}, } (II) V′ = V. } But if we prefer that A and B should reckon (according to A's judgment) in the same units of time, we put λ = β, and obtain β^2 = 1/(1 - _v_^2/V^2), T = (_t_ - _vx_)/V^2, V′ = βV. But A and B are in any case in such hopeless difficulties over their comparisons of time-judgments that the detail of using the same units does not help them much. Accordingly the formulæ marked (II) are those used. Thus A and B agree in their judgments as to the magnitude of one special velocity V, whatever may be the direction in which the entity possessing it is moving. In order to reach this measure of agreement, they have to disagree as to their space judgments and their time judgments. The root cause of their disagreement is their diverse judgment as to which axis system is to be taken at rest for the purpose of measuring velocities. Before discussing the nature of the disagreement disclosed in formula (II), let us ask why we should bring these difficulties on our heads by supposing that two people in relative motion, who both (for the purpose of measuring velocities) assume that they are at rest, should agree in their judgments in respect to this special velocity V. Such an agreement has no counterpart in any of our obvious judgments made from railway carriages. Surely we can wait till the contingency occurs before discussing the confusion which it creates. But the contingency has occurred. It occurs when we consider the velocity of light. Perhaps I may venture to remind a philosophical society that light moves so very quickly that it is difficult to consider its velocity at all. So we need not be surprised that this peculiar fact concerning its velocity is not more obvious. Now V being the velocity of light, unless _v_ is large, _v_/V (and still more _v_^2/V^2) will be quite inappreciable. The only velocity ready to hand which is big enough to give _v_/V an appreciable value is the velocity of the earth in its orbit.