Nov. 13, 1879] 



NATURE 



43 



through five. In every case like this, where forces are in 

 equilibrium on a system, we can imagine a motion given, 

 every point moving according to the geometrical circum- 

 stances. Let us imagine such a motion. When two 

 forces act on a system and keep it at rest, multiply the 

 space through which the point of application of each 

 force moves, referred to the line in which the force acts, 

 by the measure of the force. When there is equilibrium 

 the resulting quantities are equal and of opposite signs. 

 The one child weighing 50 lbs. rises vertically through 

 7 inches, and we may call the product 350 inch-lbs. up- 

 wards. The 70 lbs. child moves in the same time 5 

 inches downwards, and the product, which is 350 inch- 

 lbs, downwards, is equal and opposite to the other. If 

 there is equilibrium it must always be so ; if it is so there 

 must be equilibrium. It was to Galileo that we owe this 

 most fruitful of statical principles. It can easily be ex- 

 tended to the case when any number of forces act at any 

 number of points on a body or a system, but it was not 

 till a century later that John Bernouilli could state it in all 

 its generality, or show how admirably it serves as a 

 sufficient basis for the whole theory of equilibrium. 



These laws of falling bodies and of virtual velocities 

 marked the greatest advance in mechanical science since 

 the world began. The nature of the earth's common 

 action on all bodies at its surface had, in fact, been 

 ascertained. The question that had been put directly to 

 nature had been completely answered, and the answer 

 was final. 



The Peripatetics had a singular notion of what they 

 called Inertia. According to them, a body had a natural 

 tendency to move at a given speed straight towards the 

 centre of the earth if it were heavy, and straight away 

 from it if it were light. The continuance of that natural 

 motion, in that direction, at that speed was ensured by 

 inertia. Strike the body in that or in any other direction, 

 and an immediate change takes place, but it is a change 

 which disappears if the body is moving in a vacuum. In 

 ordinary air it is kept up, because the air behind, from 

 which the body is suddenly taken away when it is 

 struck, instantly closes up, and strikes it like a spring 

 which has been let go. At every new position it leaves 

 air, and air springs after it to keep it going. As far as 

 it was then possible, Galileo worked out the consequences 

 of this theory and those of his own, which was that 

 stated in Newton's first Law of Motion — that except 

 where any external force operates, motion in any 

 direction at a certain rate will continue indefinitely 

 in that direction at the same rate. The result was 

 that the old theory was proved to be wrong. As with 

 the first law of motion, so with the second. It is 

 substantially this, that when a force acts on a particle 

 in motion, it produces the same effect in changing 

 that motion as it would if, before it began to act, 

 the body were at rest. Suppose a particle moving 

 with a speed which may be described as iofeetper second 

 northward and 8 feet per second eastward. Let a force 

 suddenly act on it, the effect of which is to change its rate 

 of going to 17 feet per second northward and 13 feet per 

 second eastward. The amount gained is an addition of 

 speed of 7 feet per second northward and 3 feet per second 

 eastward. Imagine the same force acting on a particle 

 identical with the former, but initially at rest. It will 

 make that particle begin to move from rest at the same 

 rate of 7 feet per second northward and 3 feet per second 

 eastward which it gained in the former motion. The 

 effect in changing rate has been the same as if the body 

 had been at rest, and the whole eftect on the eastward 

 direction has been the same as it would have been had 

 there been nothing to affect it in a northerly direction. 



It was through the combination of these two principles 

 that Galileo was able to solve another and more difficult 

 problem. Until they were verified by the success of 

 millions of predictions founded on them, they were not so 



mu:h principles as theories or hypotheses. A fulfilled 

 prediction of any complicated phenomenon raises the 

 hypothesis on which it has been explained to the dignity 

 of a probable truth. Let a bullet be started in an oblique 

 direction at a certain speed — we can predict, by applying 

 these two principles, the way in which it will move and 

 the course it will follow. Let us take one which is sent 

 off at a rate of speed compounded of 32 feet per second 

 vertical and 20 feet per second horizontal. At every point 

 of its path, it will keep both these rates except so far as 

 gravity changes them, and gravity will do by it as a 

 moving body just what it would do by a body starting 

 from rest. To the latter it would give a downward speed 

 of 32 feet per second in a second. In a second it will 

 give just enough downward speed, therefore, to annihilate 

 the upward speed of the bullet. After a second, it will 

 have ceased to have any upward speed, but it will go on 

 with the horizontal speed of 20 feet per second. In its 

 first second the bullet has moved away from its starting- 

 point 20 feet in a horizontal direction and 16 feet upward, 

 because a fall of 16 feet from rest is needed to generate 

 that velocity of 32 feet per second downward, which is 

 wanted to destroy the upward velocity of the amount with 

 which it started. At the end of the first second it has 

 reached its new position by a certain path. Till the bullet 

 comes to the ground again another second will suffice, 

 during which it will fall through 16 feet vertically, and 

 acquire a speed of 32 feet per second downward as it 

 started with 32 feet per second upward, and it will move 

 horizontally 20 feet further from the starting-point. When 

 the second second closes, the particle has again reached 

 the ground by a path which is the left-handed facsimile of 

 that by which it rose. 



There are thus three measurable things, all conse- 

 quences of our fundamental laws. Does the bullet rise 

 16 feet? does it strike the ground 40 feet away from, 

 where it started? does it take 2 se.onds to do it in? 

 Nature answers that all these things are so. If we take 

 some means of making the bullet record or picture its 

 path on a board or paper we shall have a still completer 

 answer to the question. Galileo's mathematics were 

 enough to show him that if these two laws were true the 

 curve described must be a parabola — except so far as it is 

 slightly modified by the resistance of the air — and the 

 parabola calculated is the parabola described. Such a 

 proof is all but conclusive. Every point in the path 

 really found has thus been predicted as the mathematical 

 consequence of these two laws, and when this prediction 

 is repeated and confirmed in every experiment, doubt 

 vanishes, the laws are securely established, and the secret 

 of nature has been found. 



( To be continued. ) 



JAMES CLERK MAXWELL, F.R.S. 



JAMES CLERK MAXWELL, whose premature death 

 on Wednesday last week, science has to deplore, was 

 born in 1831, being the only son of John Clerk Maxwell, 

 Esq., of Middlebie. His grandfather was Captain James 

 Clerk of Penicuik, whose two sons were the Right Hon. Sir 

 George Clerk, Bart., of Penicuik, and the above-mentioned, 

 John Clerk Maxwell. Captain James Clerk was a younger 

 brother of Sir John Clerk of Penicuik, and on the death, 

 of the latter Sir George Clerk succeeded to the estate of 

 Penicuik, while John succeeded to the estate of Nether 

 Corsock, part of the Middlebie estate, which had come 

 into the family through marriage in a previous generation 

 with Agnes Maxwell Along with this estate John Clerk 

 assumed the family name of Maxwell. When James 

 Clerk Maxwell was eight years old, his mother died, and 

 his father, who had been called to the Scotch Bar, but 

 never practised as an advocate, lived a retired life, 

 devoting himself to the care of his estates, and of his 



