It may be pointed out here that, while modern civilization differs from ancient civilization in many ways, it differs more in complexity than in any other one way. Some of the factors of ancient civilization were as good as those of today; such things, for instance as temples and pyramids and stationary objects in general. But the ancients did not understand motion clearly, especially irregular motion; and they had no fast vehicles of any kind. Their knowledge of statics must have been fairly complete, or they could not have built their temples and pyramids; but their records show little understanding of dynamics.

Now the basis of dynamics is mathematics. Dynamics is the result of the application of mathematics to the observed effects of force on bodies, in producing motion. Dynamics is a branch of the science of mechanics, and a most difficult branch. It is built on the observations, calculations and conclusions of Newton and a host of experimenters and mathematicians of lesser mentality, and it could not have come into being without them.

But dynamics has not been the only physical science involved in making the machine of civilization. All the physical sciences have taken part; and each one has taken a part which was essential to the final result, and without which the final result could not have been attained. The science of light made possible the solution of our problems of illumination and the development of inventions for producing it; the science of acoustics made possible the solution of our problems of sound, including music, and the invention of acoustic and musical instruments; the science of heat made possible the invention of all the complex and powerful steam and gas engines that have revolutionized society; the science of electricity (including magnetism) has made possible the invention of those electric and electro-magnetic machines that have supplemented the work of the steam engine; and the science of pneumatics has made possible the invention of those "flying machines" of many kinds, that promise to complicate civilization further still.

But let us realize clearly that no one of these sciences by itself has been able to perform any of the feats just mentioned. Each one was virtually dependent on every other one; and all were dependent on mathematics. In order to make the steam engine work efficiently, it was not enough that heat should expand water into steam: the mathematical laws which showed how much water was needed to secure a certain amount of steam, for instance, and how a certain desired pressure of steam could be secured, had first to be comprehended and then to be followed. In order to have boilers and engines so designed as to prevent disastrous explosions, the laws governing the strength of materials had to be known and followed. In order that a projectile could be so fired from a gun as to reach a certain predetermined spot, the laws of heat, pneumatics, chemistry and dynamics had all to be understood and followed with exactness.

But it was not only the machines and instruments that needed the assistance of those sciences, it was the sciences themselves; because it was only after eliminating phenomena caused by one agency from those caused by another, that accuracy in any conclusions whatever could be secured; and in order that the phenomena caused by one agency could be kept separate from the phenomena caused by another agency, the laws underlying both had to be understood. The science of light could not be developed until the action of heat was fairly well understood; dynamics had to wait on statics; Newton could not have contributed what he did to astronomy, unless the science of light (including optics) was sufficiently understood; and the laws of pneumatics could not have been developed, unless the laws of heat had been developed, etc. And not one of the physical sciences could have gone beyond the state of infancy, if the science of mathematics had not been invented and made into a workable machine.

The paragraph above may be put into a different form, and made to state that all the physical sciences have been brought up to their present stage, by subjecting the phenomena studied by each science to quantitative investigation. It was by making these quantitative investigations that Newton and the others were able to ascertain the exact facts from which to start in their endeavor to discover the laws of nature; and it was from the laws of nature thus induced that later investigators were able to start on still further expeditions of discovery into the unknown. As the common basis of all quantitative work is mathematics, the common basis of all the physical sciences is mathematics. This makes all the physical sciences interdependent, despite the fact that each is independent of the others. Each one of the physical sciences has contributed its part to building the machine of civilization; the part that each has specially contributed can be clearly specified; and yet, since the machine is the result of the combination of what all have contributed, their contributions are interdependent. This remark applies to the various parts of all machines. The piston of a steam engine, for instance, and the valve that admits steam to the cylinder are entirely separate from each other; but from the mere fact that they both work together, each one must be designed and operated with reference to the other; so that both in their construction and their operation, they are interdependent.

Francis Bacon, in the sixteenth century, may be said to have inaugurated the system on which the whole of modern progress has been based, and Newton in the seventeenth century to have taken up Bacon's work and carried it further on. Following Newton, only a few great investigators can be seen in the seventeenth century; but in the eighteenth, began that intense and brilliant movement of investigation, discovery and invention, that has been adding more and more to the machine of civilization—and still is adding more.

One of the earliest and most important contributions was an apparatus for measuring time accurately. Who was the inventor is not precisely known. It seems fairly well established, however, that Galileo was the first to call attention to the fact that the vibrations of a pendulum were nearly isochronous, and could be used to measure the lapse of time; and that Galileo's son (as well as Dr. Hooke, Huygens and a London mechanic named Harris, in the early part of the seventeenth century) made clocks based on that principle. It is fairly well established also that Huygens was the first one to make a mathematical investigation of the properties of the pendulum, and to enumerate the laws since utilized for making accurate clocks and watches.

Most of the investigators of the eighteenth century occupied themselves with studies indirectly or directly caused by the invention of the steam engine, that is with studies relating to heat and light; but, by reason of the interdependence of all the physical sciences, their investigations led them automatically into the allied fields of acoustics and electricity. Their investigations led even further; they led to the establishment, on the ruins of the illusions of alchemy, of a wholly new and supremely important science, chemistry.

One of the most important inventions of a purely scientific character made during the period was one that has never been known by any other name than "Atwood's machine." It is an interesting illustration of the addition of invention to investigation, in that its end was—merely investigation; and it reminds us of a fact that many people are prone to forget, that invention may be applied to almost any purpose whatever, and that even a "machine" may be devoted to a purpose not utilitarian.