356 LEADING AMERICAN MEN OF SCIENCE 



many different ways. But the cause of these remarkable changes 

 and the conditions by which they were produced were not under- 

 stood until the application of the Phase Rule to the subject of the 

 iron carbides, and many disasters have occurred from unexpected 

 weaknesses in structural iron which in the future we shall be better 

 able to avoid. The igneous rocks, such as granite, basalt and 

 porphyry, which form the principal part of the earth so far as we 

 know it, are composed of mixed silicates which were too numerous 

 for the mineralogist to name and too complex for the chemist to 

 classify. Now, however, they are being studied very successfully, 

 and the geologist, being given by the use of the Phase Rule, the 

 conditions of heat and pressure under which they were formed, will 

 be able to explain more satisfactorily the building of the world. 



I have devoted so much space to this paper of Gibbs as an 

 example of the effect of theory upon scientific research that it will 

 be necessary to dismiss briefly his later, and, in part, equally impor- 

 tant work. Between 1881 and 1884, Professor Gibbs developed 

 and taught his system of Vector Analysis, a new algebraic method 

 of treatment of physical quantities, like force, momentum and 

 velocity, which have direction as well as magnitude and can there- 

 fore be represented by lines. This work is in many respects an 

 improvement on the Quaternions of Sir William Hamilton, which 

 has never been a favorite method of analysis with physicists. It 

 was printed in 188184 for private circulation among mathema- 

 ticians by Professor Gibbs, but was published in more complete 

 form by his pupil, Dr. E. B. Wilson, only in 1901. 



In 1886, Professor Gibbs as Vice-President of the Section of 

 Mathematics and Astronomy of the American Association for the 

 Advancement of Science, gave an address on "Multiple Algebra," 

 a development of the methods of Grassman. An astronomical 

 paper on a new method for the determination by the employ- 

 ment of Vector Analysis of elliptic orbits from three complete ob- 

 servations was published by the National Academy of Science 

 three years later; reprinted by Buchholz; translated into German 

 and incorporated in the last edition of Klinkerfues's Theoretische 

 Astronomie. 



