482 SCIENCE PROGRESS 



complete solution of any mechanical system which can be completely specified 

 in terms of co-ordinates. And these co-ordinates need not be of the simple 

 character previously referred to, but may be any measurable quantities of any 

 nature, provided their number is sufficient to determine the system, e.g. in 

 the case of a system of material particles, three times the number of particles 

 requiring distinct consideration. But in many modern problems relating to 

 molecular and electrical phenomena the number of co-ordinates involved is 

 practically infinite, e.%. in the case of the molecules in a gas. If, however, such 

 systems remain, during the period considered, in a steady state, i.e. free from 

 changes in constitution, closely approximate solutions may be obtained in terms of 

 a limited number of co-ordinates obtained by a process of averaging. That is to 

 say, the system must be one which can be treated as capable of being brought 

 back to any previous state by purely mechanical means, such as reversing the 

 sensible velocities. The Lagrangian equations can be most easily obtained by Sir 

 William Rowan Hamilton's principle of least action, which is applicable to all such 

 systems. The potential energy, IV, of such a system can be expressed in terms of 

 the co-ordinates only, and the kinetic energy, T, in terms of the co-ordinates and 

 their first derivatives with respect to the time. The action determining the motion 

 is taken as the difference, T — IV; and the principle asserts that when the system 

 passes from its state at one instant to its state at any other, the path followed— i.e. 

 the sequence of changes through which the system passes — will be such that the 

 average value of this difference, during the interval of time occupied by the passage, 

 will be smaller far the actual path than for any other possible closely adjacent 

 path. The principle is expressed mathematically by the equation — 



hfaT- W)dt = o, 



where t and t\ are the initial and final values of the time. 



Hilbert succeeded, in 191 5, in generalising Hamilton's principle into a form 

 suitable for application to Minkowski's four-dimensional manifold, and in the same 

 year Einstein obtained a set of equations representing the generalised law of 

 gravitation as viewed from Minkowski's standpoint, and succeeded by their aid in 

 arriving at a practically exact solution of a problem which had baffled astronomers 

 for several generations — the considerable discrepancy between the observed 

 motion of the perihelion of the planet Mercury, and the value predicted by 

 Newton's law of gravitation. 



These results appear to warrant Lorentz's conclusion that the relativity theory 

 may now be said to have taken a definite form, and I propose in another article, to 

 which the present one may be regarded as preliminary, to deal with what I think 

 ' I am justified in calling the general theory of relativity. 



THE ELECTRIFICATION OF SEEDS (Charles Mercier,M.D.,F.R.C.P.) 



This process has now reached a stage of practical success that requires some 

 notice in Science Progress. Begun with experiments in a few pots, it has 

 advanced year by year to larger and larger plots of ground, until at the present 

 time electrified seed is being grown on more than 2,000 acres. These 2,000 acres 

 are now ripe for harvest, and in many cases are being harvested, so that a decisive 

 judgment on the merits of the process can now be formed, and it may be said at 

 once that the judgment of competent experts who have visited the farms and 



