Page:Popular Science Monthly Volume 27.djvu/431

Rh paper, giving the results of his observations, and the more valuable, as it is a comparative study of the health-merits of the two localities; the marked advantages being in favor of the Yellowstone Park over the celebrated Swiss valley. The article is most instructive, and the subject one of interest and moment to our people.



was applied to in 1871 to prepare a volume for the "International Scientific Series." He was asked if he would undertake a book to be entitled "Mathematics for the Non-Mathematical," the object of which should be to find out how far it is possible to go in explaining mathematical ideas to persons of intelligence who have had none of the higher mathematical training. This idea had been before proposed to several mathematicians, who agreed that nothing could be made of it; but it was suggested that if anything could be done with it Clifford's was the genius to do it. Professor Clifford was struck with the idea as novel and interesting, and said he would make a study of it and see what it promised. The result was so favorable that he decided to undertake the book and give such attention to it as his slender health and various pre-engagements would allow. There was but little doubt that the project was eminently suited to the peculiar characteristics of Clifford's mind; and that the subject was certain to be handled by him with originality and result in a valuable contribution to mathematical literature. But it soon became apparent that there was a serious question about the possibility of his accomplishing the task at all, on account of his declining health. He, however, did considerable work on it, but left it in an unfinished and fragmentary condition at his death in 1879.

In arranging the plan of the work it was Professor Clifford's intention to treat the fundamental conceptions of mathematics in six parts or chapters under the heads of Number, Space, Quantity, Position, Motion, and Mass. Of these six subjects he dealt with but four, dictating the chapters on Number and Space completely, the first portion of the chapter on Quantity, and nearly the entire chapter on Motion. Shortly before his death he expressed a wish that the book should only be published after very careful revision; that the title, The First Principles of the Mathematical Sciences explained to the Non-Mathematical, should be abandoned, and that the volume should be entitled The Common Sense of the Exact Sciences.

It was not easy to find a mathematician who would undertake to finish Professor Clifford's work. Upon his death, Professor Rowe, of University College, engaged to do it; but he also died before accomplishing the task, so that the final revision had to be made by still another hand. There are parts of this work contributed by Professor Clifford which answer finely to the original idea of it, and show what might have been done if he had lived and adhered to the first conception. A mistake was made by the subsequent editors in seeking to finish the work as they thought Clifford would have done it, rather than as in their judgment it might seem best. As it is, the work will probably be found more attractive to mathematicians than to non-mathematicians.

the earliest record we have of astronomical observation is the catalogue of 1 ,028 fixed stars in the "Almagest" of Ptolemy, the epoch of which is a 138. The chief value of this catalogue consists in its classification of the stars into six magnitudes, which classification, so far as those stars which are visible to the naked eye are concerned, has been continued to the present day. Since that time many other astronomers have made systematic observations on the relative brightness of the stars, the