Part 10

Another very large class of problems in crystallography is based on the relation of faces in a zone; that is, of faces which are all parallel to one line called the zone axis, and whose mutual intersections, therefore, are all parallel to each other. If, now, _h_ _k_ _l_ and _p_ _q_ _r_ are the indices of any two planes of a zone (not parallel to each other), any other plane in the same zone must fulfill the condition expressed by the simple equation

u·_u_ + v·_v_ + w·_w_ = _o_,

where _u_ _v_ and _w_ are the indices of the third plane, and u v w have the values

u = _k_·_r_ - _l_·_q_ v = _l_·_p_ - _h_·_r_ w = _h_·_q_ - _k_·_p_.

Since _h_ _k_ _l_ and _p_ _q_ _r_ are whole numbers, it is evident that u v w must also be whole numbers, and these quantities are called the indices of the zone. The three whole numbers which are the indices of a plane when written in succession serve as a very convenient symbol of that plane, and represent to the crystallographer all its relations; and in like manner Miller used the indices of a zone inclosed in brackets as the symbol of that zone. Thus 123, 531, 010 are symbols of planes, and [111], [213], [001] symbols of zones.

An additional theorem enables us to calculate the symbols of a fourth plane in a zone when the angular distances between the four planes and the symbols of three of them are known, but this problem can not be made intelligible with a few words.

The few propositions to which we have referred involve all that is essential and peculiar to the system of Professor Miller. These given, and the rest could be at once developed by any scholar who was familiar with the facts of crystallography; and the circumstance that its essential features can be so briefly stated is sufficient to show how exceedingly simple the system is. At the same time, it is wonderfully comprehensive, and the student who has mastered it feels that it presents to him in one grand view the entire scheme of crystal forms, and that it greatly helps him to comprehend the scheme as a whole, and not simply as the sum of certain distinct parts. So felt Professor Miller himself; and, while he regarded the six systems of crystals of the German crystallographers as natural divisions of the field, he considered that they were bounded by artificial lines which have no deeper significance than the boundary lines on a map. How great the unfolding of the science from Haüy to Miller, and yet now we can see the great fundamental ideas shining through the obscurity from the first! What we now call the parameters of a crystal were to Haüy the fundamental dimensions of his "integrant molecules," our indices were his "decrements," and our conceptions of symmetry his "fundamental forms." There has been nothing peculiar, however, in the growth of crystallography. This growth has followed the usual order of science, and here as elsewhere the early, gross, material conceptions have been the stepping-stones by which men rose to higher things. In sciences like chemistry, which are obviously still in the earlier stages of their development, it would be well if students would bear in mind this truth of history, and not attach undue importance to structural formulæ and similar mechanical devices, which, although useful for aiding the memory, are simply hindrances to progress as soon as the necessity of such assistance is passed. And, when the life of a great master of science has ended, it is well to look back over the road he has traveled, and, while we take courage in his success, consider well the lesson which his experience has to teach; and, as progress in this world's knowledge has ever been from the gross to the spiritual, may we not rejoice as those who have a great hope?

Although the exceeding merit of the "Treatise on Crystallography" casts into the shade all that was subordinate, we must not omit to mention that Professor Miller published an early work on hydrostatics, and numerous shorter papers on mineralogy and physics, which were all valuable, and constantly contained important additions to knowledge. Moreover, the "New Edition of Phillips's Mineralogy," which he published in 1852 in connection with H. J. Brooke, owed its chief value to a mass of crystallographic observations which he had made with his usual accuracy and patience during many years, and there tabulated in his concise manner. As has been said by one of his associates in the Royal Society, "it is a monument to Miller's name, although he almost expunged that name from it."[I] It is due to Professor Miller's memory that his works should be collated, and especially that by a suitable commentary his "Tract on Crystallography" should be made accessible to the great body of the students of physical science, who have not, as a rule, the ability or training which enables them to apprehend a generalization when solely expressed in mathematical terms. The very merits of Professor Miller's book as a scientific work render it very difficult to the average student, although it only involves the simplest forms of algebra and trigonometry.

[I] "Obituary Notices from the Proceedings of the Royal Society," No. 206, 1880, to which the writer has been indebted for several biographical details.

Independence, breadth, accuracy, simplicity, humility, courtesy, are luminous words which express the character of Professor Miller. In his genial presence the young student felt encouraged to express his immature thoughts, which were sure to be treated with consideration, while from a wealth of knowledge the great master made the error evident by making the truth resplendent. It was the greatest satisfaction to the inexperienced investigator when his observations had been confirmed by Professor Miller, and he was never made to feel discouraged when his mistakes were corrected. The writer of this notice regards it as one of the great privileges of his youth, and one of the most important elements of his education, to have been the recipient of the courtesies and counsel of three great English men of science, who have always been "his own ideal knights," and these noble knights were Faraday, Graham, and Miller.

VII.

WILLIAM BARTON ROGERS.

William Barton Rogers was born at Philadelphia, on the 7th of December, 1804. His father, Patrick Kerr Rogers, was a native of Newton Stewart, in the north of Ireland; but while a student at Trinity College, Dublin, becoming an object of suspicion on account of his sympathy with the Rebellion of 1798, he emigrated to this country, and finished his education in the University of Pennsylvania, at Philadelphia, where he received the degree of Doctor of Medicine.

Here he married Hannah Blythe, a Scotch lady--who was at the time living with her aunt, Mrs. Ramsay--and settled himself in his profession in a house on Ninth Street, opposite to the University; and in this house William B. Rogers was born. He was the second of four sons--James, William, Henry, and Robert--all of whom became distinguished as men of science.

Patrick Kerr Rogers, finding that his prospects of medical practice in Philadelphia had been lessened in consequence of a protracted absence in Ireland, made necessary by the death of his father, removed to Baltimore; but soon afterward accepted the Professorship of Chemistry and Physics in William and Mary College, Virginia, made vacant by the resignation of the late Robert Hare; and it is a fact worthy of notice that, while he succeeded Dr. Hare at William and Mary College, his eldest son, James, succeeded Dr. Hare at the University of Pennsylvania. At William and Mary College the four brothers Rogers were educated; and on the death of the father, at Ellicott Mills, in 1828, William B. Rogers succeeded to the professorship thus made vacant.

He had already earned a reputation as a teacher by a course of lectures before the Maryland Institute in Baltimore during the previous year, and after his appointment at once entered on his career as a scientific investigator. At this period he published a paper on "Dew," and, in connection with his brother Henry, another paper on the "Voltaic Battery"--both subjects directly connected with his professorship. But his attention was early directed to questions of chemical geology; and he wrote, while at William and Mary College, a series of articles for the "Farmer's Register" on the "Green Sands and Marls of Eastern Virginia," and their value as fertilizers. Next we find the young professor going before the Legislature of Virginia, and, while modestly presenting his own discoveries, making them the occasion for urging upon that body the importance of a systematic geological survey for developing the resources of the State. So great was the scientific reputation that Professor Rogers early acquired by such services, that in 1835 he was called to fill the important Professorship of Natural Philosophy and Geology in the University of Virginia; and during the same year he was appointed State Geologist of Virginia, and began those important investigations which will always associate his name with American geology.

Professor Rogers remained at the head of the Geological Survey of Virginia until it was discontinued, in 1842, and published a series of very valuable annual reports. As was anticipated, the survey led to a large accumulation of material, and to numerous discoveries of great local importance. As this was one of the earliest geological surveys undertaken in the United States, its directors had in great measure to devise the methods and lay out the plans of investigation which have since become general. This is not the place, however, for such details; but there are four or five general results of Professor Rogers's geological work at this period which have exerted a permanent influence on geological science, and which should therefore be briefly noticed. Some of these results were first published in the "American Journal of Science"; others were originally presented to the Association of American Geologists and Naturalists, and published in its "Transactions." Professor Rogers took a great interest in the organization of this association in 1840, presided over its meeting in 1845, and again, two years later, when it was expanded into the American Association for the Advancement of Science.

In connection with his brother Robert, Professor William B. Rogers was the first to investigate the solvent action of water--especially when charged with carbonic acid--on various minerals and rocks; and by showing the extent of this action in nature, and its influence in the formation of mineral deposits of various kinds, he was one of the first to observe and interpret the important class of facts which are the basis of chemical geology.

Another important result of Professor Rogers's geological work was to show that the condition of any coal-bed stands in a close genetic relation to the amount of disturbance to which the enclosing strata have been submitted, the coal becoming harder and containing less volatile matter as the evidence of disturbance increases. This generalization, which seems to us now almost self-evident--understanding, as we do, more of the history of the formation of coal--was with Professor Rogers an induction from a great mass of observed facts.

By far, however, the most memorable contribution of Professor Rogers to geology was that made in connection with Henry D. Rogers, in a paper entitled "The Laws of Structure of the more Disturbed Zones of the Earth's Crust," presented by the two brothers at the meeting of the Association of American Geologists and Naturalists, held at Boston in 1842. This paper was the first presentation of what may be called in brief the "Wave Theory of Mountain Chains." This theory was deduced by the brothers Rogers from an extended study of the Appalachian Chain in Pennsylvania and Virginia, and was supported by numerous geological sections and by a great mass of facts. The hypothesis which they offered as an explanation of the origin of the great mountain waves may not be generally received; but the general fact, that the structure of mountain chains is alike in all the essential features which the brothers Rogers first pointed out, has been confirmed by the observations of Murchison in the Ural, of Darwin in the Andes, and of the Swiss geologists in the Alps. "In the Appalachians the wave structure is very simple, and the same is true in all corrugated districts where the crust movements have been simple, and have acted in one direction only. But where the elevating forces have acted in different directions at different times, causing interference of waves like a chopped sea, as in the Swiss Alps and the mountains of Wales or Cumberland, the undulations are disguised, and are with extreme difficulty made out." The wave theory of mountain chains was the first important contribution to dynamical and structural geology which had been brought forward in this country. It excited at the time great interest, as well from the novelty of the views as from the eloquence with which they were set forth; and to-day it is still regarded as one of the most important advances in orographic geology.

A marked feature of mountain regions is that rupturing of the strata called faults; and another of the striking geological generalizations of the brothers Rogers is what may be called the law of the distribution of faults. They showed that faults do not occur on gentle waves, but in the most compressed flexures of the mountain chains, which in the act of moving have snapped or given way at the summit where the bend is sharpest, the less inclined side being shoved up on the plane of the fault, this plane being generally parallel to, if it does not coincide with, the axis plane; and, further, that "the direction of these faults generally follows the run of the line of elevation of the mountains, the length and vertical displacement depending on the strength of the disturbing force."

The last of the general geological results to which we referred above was published under the name of William B. Rogers only. It was based on the observed positions of more than fifty thermal springs in the Appalachian belt, occurring in an area of about fifteen thousand square miles, which were shown to issue from anticlinal axes and faults, or from points very near such lines; and in connection with these springs it was further shown that there was a great preponderance of nitrogen in the gases which the waters held in solution.

It must be remembered that, during the time when this geological work was accomplished, Professor Rogers was an active teacher in the University of Virginia, giving through a large part of the year almost daily lectures either on physics or geology. Those who met him in his after-life in various relations in Boston, and were often charmed by his wonderful power of scientific exposition, can readily understand the effect he must have produced, when in the prime of manhood, upon the enthusiastic youths who were brought under his influence. His lecture-room was always thronged. As one of his former students writes, "All the aisles would be filled, and even the windows crowded from the outside. In one instance I remember the crowd had assembled long before the hour named for the lecture, and so filled the hall that the professor could only gain admittance through a side entrance leading from the rear of the hall through the apparatus-room. These facts show how he was regarded by the students of the University of Virginia. His manner of presenting the commonest subject in science--clothing his thoughts, as he always did, with a marvelous fluency and clearness of expression and beauty of diction--caused the warmest admiration, and often aroused the excitable nature of Southern youths to the exhibition of enthusiastic demonstrations of approbation. Throughout Virginia, and indeed the entire South, his former students are scattered, who even now regard it as one of the highest privileges of their lives to have attended his lectures."

Such was the impression which Professor Rogers left at the University of Virginia, that, when he returned, thirty-five years later, to aid in the celebration of the semi-centennial, he was met with a perfect ovation. Although the memories of the civil war, which had intervened, and Professor Rogers's known sympathies with the Northern cause, might well have damped enthusiasm, yet the presence of the highly honored teacher was sufficient to rekindle the former admiration; and, in the language of a contemporary Virginia newspaper, "the old students beheld before them the same William B. Rogers who thirty-five years before had held them spellbound in his class of natural philosophy; and, as the great orator warmed up, these men forgot their age; they were again young, and showed their enthusiasm as wildly as when, in days of yore, enraptured by his eloquence, they made the lecture-room of the University ring with their applause."

Besides his geological papers, Professor Rogers published, while at the University of Virginia, a number of important chemical contributions, relating chiefly to new and improved methods in chemical analysis and research. These papers were published in connection with his youngest brother, Robert E. Rogers, now become his colleague as Professor of Chemistry and Materia Medica in the University; and such were the singularly intimate relations between the brothers that it is often impossible to dissociate their scientific work. Among these were papers "On a New Process for obtaining Pure Chlorine"; "A New Process for obtaining Formic Acid, Aldehyde, etc."; "On the Oxidation of the Diamond in the Liquid Way"; "On New Instruments and Processes for the Analysis of the Carbonates"; "On the Absorption of Carbonic Acid by Liquids"; besides the extended investigation "On the Decomposition of Minerals and Rocks by Carbonated and Meteoric Waters," to which we have referred above. There was also at this time a large amount of chemical work constantly on hand in connection with the Geological Survey, such as analyses of mineral waters, ores, and the like. Moreover, while at the University of Virginia, Professor Rogers published a short treatise on "The Strength of Materials," and a volume on "The Elements of Mechanics,"--books which, though long out of print, were very useful text-books in their day, and are marked by the clearness of style and felicity of explanation for which the author was so distinguished.

The year 1853 formed a turning-point in Professor Rogers's life. Four years previously he had married Miss Emma Savage, daughter of Hon. James Savage, of Boston, the well-known author of the "New England Genealogical Dictionary," and President of the Massachusetts Historical Society. This connection proved to be the crowning blessing of his life. Mrs. Rogers, by her energy, her intelligence, her cheerful equanimity, her unfailing sympathy, became the promoter of his labors, the ornament and solace of his middle life, and the devoted companion and support of his declining years. Immediately after his marriage, June 20, 1849, he visited Europe with his wife, and was present at the meeting of the British Association for the Advancement of Science, held that year at Birmingham, where he was received with great warmth, and made a most marked impression. Returning home in the autumn, Professor Rogers resumed his work at the University of Virginia; but the new family relations which had been established led in 1853 to the transfer of his residence to Boston, where a quite different, but even a more important, sphere of usefulness surrounded him. His wide scientific reputation, as well as his family connection, assured him a warm welcome in the most cultivated circles of Boston society, where his strength of character, his power of imparting knowledge, and his genial manners, soon commanded universal respect and admiration. He at once took an active part in the various scientific interests of the city. From 1845 he had been a Fellow of this Academy;[J] and after taking up his residence among us he was a frequent attendant at our meetings, often took part in our proceedings, became a member of our Council, and from 1863 to 1869 acted as our Corresponding Secretary. He took a similar interest in the Boston Society of Natural History. He was a member, and for many years the President, of the Thursday Evening Scientific Club, to which he imparted new life and vigor, and which was rendered by him an important field of influence. The members who were associated with him in that club will never forget those masterly expositions of recent advances in physical science; and will remember that, while he made clear their technical importance to the wealthy business men around him, he never failed to impress his auditors with the worth and dignity of scientific culture.

[J] This notice is reprinted from the Proceedings of the American Academy of Arts and Sciences, vol. xviii, 1882-'83.

During the earlier years of his residence in Boston, Professor Rogers occupied himself with a number of scientific problems, chiefly physical. He studied the variations of ozone (or of what was then regarded as ozone) in the atmosphere at the time when this subject was exciting great attention. He was greatly interested in the improvements of the Ruhmkorff Coil made by Mr. E. S. Ritchie; and in this connection published a paper on the "Actinism of the Electric Discharge in Vacuum Tubes." A study of the phenomena of binocular vision led to a paper entitled "Experiments disproving by the Binocular Combination of Visual Spectra Brewster's Theory of Successive Combinations of Corresponding Points." A paper discussing the phenomena of smoke rings and rotating rings in liquids appeared in the "American Journal of Science" for 1858, with the description of a very simple but effective apparatus by which the phenomena would be readily reproduced. In this paper Professor Rogers anticipated some of the later results of Helmholtz and Sir William Thomson. In the same year an ingenious illustration of the properties of sonorous flames was exhibited to the Thursday Evening Club above mentioned, in which Professor Rogers anticipated Count Schafgottsch in the invention of a beautiful optical proof of the discontinuity of the singing hydrogen flame.

In 1861 Professor Rogers accepted from Governor Andrew the office of Inspector of Gas and Gas-Meters for the State of Massachusetts, and organized a system of inspection in which he aimed to apply the latest scientific knowledge to this work; and in a visit he again made to Europe in 1864 he presented, at the meeting of the British Association at Bath, a paper entitled "An Account of Apparatus and Processes for Chemical and Photometrical Testing of Illuminating Gas."

During this period he gave several courses of lectures before the Lowell Institute of Boston, which were listened to with the greatest enthusiasm, and served very greatly to extend Professor Rogers's reputation in this community. Night after night, crowded audiences, consisting chiefly of teachers and working-people, were spellbound by his wonderful power of exposition and illustration. There was a great deal more in Professor Rogers's presentation of a subject than felicity of expression, beauty of language, choice of epithets, or significance of gesture. He had a power of marshaling facts, and bringing them all to bear on the point he desired to illustrate, which rendered the relations of his subject as clear as day. In listening to this powerful oratory, one only felt that it might have had, if not a more useful, still a more ambitious aim; for less power has moved senates and determined the destinies of empires.