PRESIDENTS ADDRESS—-SECTION A. 39 
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Repeating the process for the line integral of electromotive force 
round the perpendicular face of the cube by the corresponding 
theorem, that this is equal to the decrease of magnetic induction 
through the face, we obtain E = » VH. Multiplying these 
values for E and H together, and dividing out by E H, we get 
l= pK V? or V = 1/7 »p K. The energy cannot be propa- 
gated faster than at this rate, which is its maximum velocity. 
When the intensities are perpendicular to each other, as they 
must be in a homogeneous isotropic non-magnetisable medium, if 
light is an electro-magnetic disturbance this then must be its 
velocity. Consequently, if we know the values of » and K, and 
not their nominal values only, we can calculate the velocity of 
light. The matter is perhaps best approached indirectly. Sup- 
pose we adopt the electrostatic system of measurement, then if 
the medium is air we have K = | and p = 1/v?, where v is the 
ratio of the units, so that the velocity of light will, if the 
hypothesis be correct, be equal to the number of electrostatic 
units of electricity in one electro-magnetic unit. Without ex- 
plaining in detail why » should = 1/v? one may get an idea very 
simply. We have already seen that on the electrostatic system 
the quantity of electrification chosen as unity depends on the 
value of K. Again, in a precisely analagous manner we can 
show that the same quantity on the electro-magnetic system will 
depend on the quantity ». We should require merely to start 
with lines of magnetic instead of lines of electric force. Since 
the electro-magnetic unity of quantity is derived from the unit of 
current, and this again defined from its action on a unit magnetic 
pole, it is clear that the magnitude of the unit will depend on p 
since the force does so. But the force will be greater the greater 
the value of p, and hence the magnitude of the quantity of 
electricity making up the unit will be inversely as p. If we 
measure the same quantity of electricity electrostatically and 
electro-magnetically, it is clear that the ratio of the two numbers 
expressing the result of the measurement in terms of the respec- 
tive units will involve » and K as product. Moreover, if the 
dimensions of K and yp are ignored, as is done by Maxwell, the 
resulting ratio will not be merely numerical, but will have the 
dimensions of length” x Time” or, in other words, of some 
power of a velocity or slowness according to the nature of the 
quantity we select for comparison. In any case, if we measure 
any electrical quantity, be it really quantity, capacity, current, 
electromotive force or resistance, both electrostatically and mag- 
netically, and compare the numerical values, we shall have a 
number from which which we can calculate the ratio of the units. 
This has been done by many observers, and it is found that the 
number is really the same as it ought to be if the electro-magnetic 
1G or H = KVE the function of the time being zero. 
