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.