er Teel Bay heey ae :- BAGS | | Pps 5 . sspiagpiycaagactoe ili | Fare Saale tear eprmcere ala oe aU gg ae a gS SS C MN MISCELLANEOUS COLLECTIONS. VOre X a — of ANTHROPOLOGICAL SOCIETY. bt its ultimate outgrowth results in the organization of aristocracies in various grades, with subordinate classes, as serfs and slaves. Again it appears in the organization of guilds. This form of organization was well represented not many generations ago in England, and relics of it still exist among the English people. It appears again in another form in India by the differentiation of people into castes, each caste having a distinct calling or group of callings. In my studies of sociology it has often been a matter of surprise to me that the state has not oftener and to a larger extent been based upon an organization dependent upon callings, trades, or occupations—that is, that the state has not oftener been organized upon an operative or industrial basis, But when we accumulate the facts of history relating to castes, classes, guilds, &c., it appears that the method has been tried in many ways and it has never suc- ceeded in securing justice to that extent as to commend its adoption. A caste may be briefly described as a body of men constituting a unit or integral part in the state, and such a body of men are or- ganized upon the basis of the industries or callings which they pur- sue. Around this organization are centered many other institutional characteristics. Marriage within the group is prescribed, marriage without the group prohibited; and many religious sanctions grow up around these institutions, and many social barriers to prevent escape from the body and entrance into another. Much has been written about these castes of India, sometimes from the standpoint of religion, sometimes from the standpoint of conquest, and sometimes from the standpoint of McClennan, erro- neous theories relating to exogamy and endogamy, names which he gave to correlative parts of the marriage institution found among most of the tribes of the world who are organized upon a kinship basis. It is true that the institution of caste exhibited in India may be profitably studied from each of these standpoints, but the essential characteristic of caste organization is this: That the people are thereby organized upon an operative basis, about which religious and social sanctions are gradually accumulated ;_ that such an or- ganization is in part the result of internal agencies arising from the differentiation of industries, or division of labor, as it is called in political economy, and in part by conquest, as the conquerors usually engage in those vocations deemed most honorable, and compel the conquered to engage in those considered least honorable. By such methods, 2. ¢., the division of labor through the inherit- 12 TRANSACTIONS OF THE ance of callings from family to family, and through the further di- vision, through the selection of callings of conquerors and the im- position of others upon the conquered, castes are primarily estab- lished. In the process of this establishment, and subsequently, moral and social sanctions gather about these institutions, and castes are firmly established only to be overthrown by great social convul- sions, or, and chiefly, by the march of civilization and the concom- itant establishment of justice and those institutions designed to se- cure justice. All light thrown upon the institution of caste in India must be wel- comed by every scientific student of sociology, and this census of Bengal, as set forth by Mr. Blodgett, is a valuable contribution to this subject. Dr. JOHNSON inquired as to the effects of these early marriages upon the offspring; whether the children were well developed or deformed; the effects upon health of the crowding of many indi- viduals ; whether syphilis prevailed and its general effects. Mr. BLopcetr replied that the census officials were extremely careful not to push questions that might stir into opposition the prejudices of the people. Great difficulty arose as to the question of early cohabitation from the delicacy of the question and the great variance of English and other European customs ; but as the legal ceremony took place at betrothal, betrothal became the point at which to count marriage. Cohabitation was probably at an earlier average than among western nations, but statistics do not, in this census, help us beyond the general knowledge obtained by observant individuals. There seems to be a high vitality up to advanced maturity ; but after, say, forty-five years of age, the vitality seems to be in favor of the European. No statistics are recorded on syphilis. ‘The vital statistics have considerable value, however, indicating the predominance of pes- tilential diseases in districts badly drained, overcrowded, or with other adverse sanitary conditions, and special inquiry was made as to leprosy. As to guilds and castes, a trace of such tendency may be seen in the perpetuation as a civil corporation in the city of London of more than one society originally founded on the occupation of its members, and now retaining privileges then granted, although no Pheer NS. ioe | | \ i ANTHROPOLOGICAL SOCIETY. 138 longer constituted of persons following the employment for which they were founded. Dr. FLETCHER said he inferred from Mr, Blodgett’s remarks that cohabitation does not follow betrothal, and added that it is con- sidered a disgrace if a child is not betrothed when she arrives at menstruation. Prof. Mason referred to similar kinds of legislation in this country, prohibiting marriage, especially the laws, in many states, against miscegenation. He also said that caste originated at a time when _ the conquering Aryans were ina great minority, and to preserve the _ purity of their stock they made stringent laws against intermarriages. - The laws of Menu prohibit intermarriages. The PRESIDENT informed the members that the 2d volume of the _ Transactions was now ready for distribution, and copies could be obtained by calling upon the Secretary, at the May Building, 7th and E streets N. W. SEVENTY-FIFTH REGULAR MEETING, December 19, 1883. President Col. Garrick MALLErRy in the Chair. _ The Council reported, through its Secretary, the election of Mr. Perry B. Pierce, of the U. S. Patent Office, as an active member. The Secretary of the Council read a letter from Mr. Wilson, U. S. Consul at Nantes, France, relating to his antiquarian researches ie in that country. Prof. Cyrus Tuomas then read a paper entitled ‘‘ THE Houses or _ THE Mounp-BuiLpers,’’* illustrated by diagrams and specimens of _ clay plastering. ABSTRACT. Prof. THomas commenced by saying that while the ruins in Cen- tral America furnished abundant materials for judging the architect- ural skill of the ancient people of that region, no such opportunity _-was offered in regard to the mound-builders, all their buildings having crumbled to dust. Still we are not left wholly in the dark in regard to them. He then went on to show that they must have * Published in Magazine of Am, History, 1884, 110-116. 14 TRANSACTIONS OF THE been of perishable materials, and that the little circular depressions from fifteen to fifty feet in diameter surrounded by earthen rings are the sites of ancient dwellings. From the fact that the hearth is found in the center he inferred that they were much like the conical wigwams of the modern Indians. Remains of this kind are common in middle and west Tennessee and in southeastern Missouri. Farther south, during the explorations carried on under the Bureau of Ethnology, there have been found in many of the mounds layers of burnt clay broken up into fragments. From numerous facts ascertained 1n regard to these remains, which cannot be given in this abstract, and the descriptions given by early explorers of the houses of the Indians of this section, he argued that these were the remains of the houses of the mound-builders. DISCUSSION. Mr. Jas. H. BLopcett said: I hope Prof. Thomas will heed the suggestion of Mr, Carr, whose recent work was referred to, and not suppress part of his own work because Mr.Carr has anticipated him in his statements. The public has become so thoroughly trained into the idea of a mysterious lost race of mound-builders that it will be necessary for every one who knows of facts indicating the contrary to state them on all proper occasions, Lately seeing a reference to the mysterious lost mound-builders in the manuscript of a prominent writer, I suggested to him that it might expose him to criticism, and referred him to one or two eminent names that endorsed the view that our red Indians were competent to do like work. My suggestion was the first information received in this author’s office that any such view was seriously held and I was re- ferred to an article in a standard Cyclopezedia some years‘old to in- form myself as to the true view. I trust Dr. Thomas will add his testimony in its due place. Prof. Mason said he had always wished to see this subject dis- cussed by gentlemen who had had as much experience in the matter as Major Powell and Prof. Thomas. It seems that doubts are thickening more rapidly than the proofs are forthcoming. In his own mind he had no doubts upon the subject, but took this antago- nistic stand for the purpose of drawing out such facts to enlighten others who were adherents of the belief that the mound-builders ANTHROPOLOGICAL SOCIETY. 15 were a distinct race, and one of greater antiquity than is now known to be the case. Major PowELt said the paper by Prof. Thomas is a valuable con- tribution to our knowledge of the North American Indians. It opportunely falls in with the present lines of research in two dis- tinct ways: First, as identifying the mound-builders with various tribes found on the discovery of this country ; second, as an addi- tion to our knowledge of the dwellings of the ancient inhabitants of this country. At our last meeting we had an interesting paper from Mr. Holmes, who, from his studies, concluded that the mound-builders were no other than the Indians inhabiting the country. Last year we had a paper from Mr. Henshaw arriving at the same conclusion from the facts discovered in another field of research. And now Prof. Thomas finds that some of the earth-works of this country are domiciliary mounds, as suggested long ago by Lewis H. Morgan, who was the great pioneer of anthropologic research in America ; and, further, that the houses found in ruins on the mounds are such as were built by the Indians, as recorded in the early history of the settlement of this country. Thus it is that from every hand we reach the conclusion that the Indians of North America, discovered at the advent of the white man to this continent, were mound-builders, and gradually the exag- gerated accounts of the state of arts represented by the relics dis- covered in these mounds are being dissipated, and the ancient civilization which has hitherto been supposed to be represented by the mounds is disappearing in the light of modern investigation. But Professor Thomas’ paper is valuable from the fact that it gives us a clearer insight into the character of the habitations of these people. The Indians of North America made their dwellings in various forms and of various materials. The rudest dwellings found in the country are those made by some of the Indians of Utah and Nevada of the great Shoshonian family. These are simple shelters made of banks of brush and bark, especially the bark of the cedar, piled up so as to include a circular space, but open toward a fire. Boughs near the summit of the bark project over a portion of this space, and bark and boughs are piled indis- criminately on all. Such a shelter is good protection against wind, and, to some degree, against snow and rain. But these same people occasionally build larger habitations with small posts and cross- 16 TRANSACTIONS OF THE pieces, upon which wattles of willow withes are made, and the whole is covered with willows. JI have known such a communal house to be built large enough to accommodate from seventy-five to one hundred and twenty-five persons—all the members of a little tribe— while at other times the same tribes have been found occupying the rude dwellings above mentioned. Nor have I been able to discover their reasons for changing from one to the other. This has been observed: that the communal houses are but rarely used. Many of the Indians of California build houses made of wind- riven slabs and poles inclined against a central ridge-pole and banked with earth, sometimes but part way up the sides of the inclined pole, sometimes quite over the top. At one end of such a dwelling an aperture is left for the escape of smoke. The Navajos often build similar lodges, except that they are conical ‘in shape and have a peculiar entrance—a kind of booth like a forte cochére. In the eastern portion of the United States, as among the Iroquois, large oblong house were made of poles and slabs. Many of these houses were communal. Around Pyramid Lake, and in many other por- tions of the country their dwellings were made of reeds, called in the West z/es. Sometimes these houses were made somewhat symmetrically of poles, into which the tules were woven as a kind of wattle. At other times they made fascines of the reeds and used them in the construction of their houses, and I have had described to me houses made of fascines and wattled tules on the shores of Pyramid Lake and other lakes of the West, and ofttimes built out over the water. In a large portion of the United States the climate is arid, and naked sandstone rocks appear in great abundance, while forests are very rare. In all of these regions the Indians built of stone. Sometimes they walled up the front of a cave, or built a house under an overhanging cliff, using the wall of rock behind as a part of the dwelling. Sometimes, where rocks were friable, they excavated chambers in the sides of the cliffs. The cliff dwellings and cavate dwellings are found in great abundance in New Mexico, Arizona, and some portions of Utah. Other dwellings have been discovered in certain hills of Arizona that are natural truncated cones. In such a case the summit of the hill is a volcanic breccia, exceedingly friable, through which shafts were sunk into a more friable breccia below. In this more friable rock extensive cham- bers were excavated, and the entrance to these chambers was through a shaft from above by means of a ladder. With the ees = wen sa Ni lal ie ANTHROPOLOGICAL SOCIETY. he extensive pueblos of that region you are all quite familar. To a very large extent it is observed that the arrangement of dwellings ina village is significant. In very many cases they are arranged by clans and phratries. When such an arrangement does not exist there is usually some other device taking its place. For example, among Muskokis, or Creeks, near the centre of the village, there is a square laid out in a very systematic manner with seats, or rather spaces for sitting, on the ground reiegated in a particular manner to phratries and clans, so that the tribe was arranged, in the coun- cil held from time to time in the square, in a systematic order. Usually over these sitting places booths were erected, and the posts that upheld the booths marked in a more specific way the seats of the officers of the village. In connection with these council squares a very interesting council lodge has been discovered. The booths of the square did not furnish ample protection at all seasons of the year, and in order to meet their wants on such occasions a huge conical lodge was constructed of the tall trees of that country. Slender trees 50 or 60 feet in height were cut down, trimmed, and inclined against a central, standing tree. Thus a huge conical lodge, 50 feet or more in height, was constructed, under which the whole village could take shelter. Under this they gathered in in- clement weather to conduct their dances. And just here it should be remarked that the Creek Indians have yet a tradition of a time when they built their houses with wattled walls, the interiors of which were plastered—exactly such houses as have been described by Prof. Thomas. The subject of house-building among the North American Indians is one of very great interest, as the various tribes exhibited much skill in utilizing the materials at hand, whatever they might be— bark, poles, slabs, tules, skins of animals, stone, etc. Prof. Mason further stated that he had handled thousands of Indian weapons, utensils, &c., and found that many objects occurred in the mounds for which no particular use could be now assigned. Major PowELt replied that it was very doubtful, at this time, if anything existed that could not be explained through the survival of similar articles now in use among some of the more isolated tribes of Indians. Prof. SCUDDER referred to and reviewed some of Prof. Putnam’s investigations and discoveries at Madisonville, and referred specially 2 ) 18 TRANSACTIONS OF THE to the exhumation of figurines, pearls, metecric iron, and rude plating of hammered silver. Prof. Tuomas, in reply to Prof. Scudder’s statement of what had recently been found by Prof. Putnam in certain Ohio mounds, stated that all of the types mentioned, except one, had been obtained by the assistants of the Bureau of Ethnology. Major Powe. said: The discussion this evening has brought out many interesting facts relating to the early inhabitants of this country, especially to the dwellings which they occupied and to the antiquity of the ruins which have been discovered. In 1856 or ’7 I was making exploration of mounds on the shore of Peoria Lake, in Illinois, and I discovered in a mound a copper plate—a thin sheet of copper, cut in the form to represent an eagle. At the time I supposed it gave evidence of the superior civilization of the mound-builders. Some months after, in more carefully ex- amining this thin copper plate, I discovered that it had been rolled and cut by machinery, and this led me to believe that it was not the manufacture of Indians, but that it was probably manufactured by white men. If the supposition were true it is manifest that the mound had been erected subsequent to the association of these In- dians with white people. This was the first suggestion to my mind that the age of the mounds had been misinterpreted, and that the general conclusion that the mound-builders were not tribes found in this country on its discovery was erroneous. Since that time one line of evidence after another has led to the same conclusion. Some years ago I published this conclusion in general terms, and every year it is strengthened, and it may be fairly said at the present time that it rests on a sound inductive basis. But this conclusion does not overthrow the belief that many of the mounds are of great antiquity. Domiciliary mounds, burial mounds, and mounds for many other purposes are discovered everywhere throughout North America in vast numbers, and doubtless the in- ception of mound-building dates far back in remote’antiquity. The numbers of the mounds themselves testify to this conclusion, and the conditions under which many of them are found lead to the same opinion. To account for the great numbers of the mounds it is not necessary, but is in fact illogical, to assume a dense population. Length of time will give the same result ; and I think it has been clearly shown that the number of Indians inhabiting the country at the time of its discovery by Europeans has been by many writers ANTHROPOLOGICAL SOCIETY. 19 enormously exaggerated. It is probable that at the present time the number of Indians in the country does not equal that of the time of the landing of Columbus. On the other hand, the disparity between the numbers of the two periods is not great. But here I must be permitted to remark that ofttimes the evidence adduced to prove the antiquity of the ancient works discovered ‘throughout the country is unsound. ‘There is abundant evidence of antiquity—good geologic evidence. Stone implements are found in geologic formations to such an extent as to leave no doubt that this continent was inhabited by man in early quaternary time; but sound evidence must be clearly discriminated from much of the evidence which is adduced. ‘Travelers and scholars sometimes talk very loosely on this subject. Let me illustrate this. In the southwestern portion of the United States we discover in vast numbers the ruins of ancient stone villages. Often these ruins are found at sites where water is not now accessible, and hence it has been averred again and again that all this arid portion of the United States was at some early period densely inhabited, and that the country has been depopulated by increasing aridity. And this secular change of climate has been adduced as evidence of the great antiquity of these works. In 1870 I discovered ruins on the Kanab Creek in Utah and some of its tributaries elsewhere in Utah and Arizona, away from the neighborhood of water, and, like many other travelers, it at first seemed to me that I had discovered evidence of change of climate. But my work in that region was that of the geologist rather than of the anthropologist, and I early discovered that such evidence is valueless. In that arid country years—perhaps tens or scores of years—will pass without great rains. During such times the larger valleys are filled with the materials brought down by the wash of rains and minor streams, and such accumulation in the valleys of this arid region is very often found. But there come at greater or less intervals storms of such magnitude, precipitating waters in such volume that the valleys themselves are cleared of the accumulated sands. When this is done streams flow through them for miles or scores of miles where they did not run before, and the few springs along the water courses are unmasked and yield a constant supply. And I have in my mind at the present time a ruin which I supposed to be far away from water, and which was far away from known water ten years ago, but at the foot of which to-day a beau- 20 TRANSACTIONS OF THE tiful stream is running, this valley having been cleared of its débris not more than eighteen months ago. Abundant instances of this kind can be brought up. Savage people abandon their homes for reasons not fully or easily appreciated by civilized men. Some disease carries off a great man or a number of persons in a tribe, and panic seizes the people and they leave their homes, perhaps burn them, under the belief that evil beings or evil influences have taken possession thereof. And this occurs very often. I have myself more than once witnessed the effect on a tribe of an epidemic or the mysterious death of a noted personage. For this reason the sites of Indian villages, even though dwellings may be erected of stone, are not very permanent; they are constantly changing. In the southwestern portion of the United States there are other causes for change, namely, those mentioned above—physical causes. asta ee += "= is Ts + tse ~~ Q Woe. oe Pov es tw oe SOO ee Se fF oS Ew oa Se : c theme 5 {es mecen a eneee oe SS ee Fic. 1.—Section showing two periods of occupation. section, and are so arranged as to show beyond a doubt, that they accumulated with the soil and are not subsequent intrusions. This is apparent, not only from their deposition in more or less contin- uous horizontal layers, as shown in the section, but from the identi- cal character of fragments occurring at corresponding depths. The prevailing type of ware, throughout the lower part of the section, is very archaic and is to all appearences quite distinct from the handsome pottery characteristic of the upper half of the section. It was simple in form and rude in finish and little superior in any respect to the rudest products of the wild Indians of North America. At the base the fragments are small and much decayed ; higher, they ANTHROPOLOGICAL SOCIETY. 71 are larger and better preserved, although I was unable to secure a complete, unbroken vessel. The only form that came to my notice, although thousands of pieces were examined, is a kind of deep cup or bowl, not unlike our common flower pot, and having a flattish bottom and an ex- tremely uneven and ragged rim. In all cases the exterior surface is covered with impressions of coarse woven fabrics, the single indi- cation of advance toward better finish being a slight polishing of the interior surface, which was accomphshed with a smooth imple- ment, such as a pebble or shell. Where well preserved, the paste is generally hard and fine grained, but shows in all cases a rather rough granular fracture. ‘The character of the tempering material cannot be made out, but, in a number of cases, the texture indicates the former presence of fibrous particles like finely pulverized grass, leaves, or straw. The surface is of a pale, yellowish red or terra cotta color, the result of the baking, while the interior of the mass is generally a dark gray. In Fig. 2, I present an example of this pottery which is restored from fragments. These did not come from the wall of the section, but from a pit, a short distance away, where the pieces were larger SSE Pa ty age maby ay Wa pa ‘ai lea 4 ha “a ise a ‘e 4 Fic. 2.-—Vessel of the most primitive style. and better preserved. In this example the rim is thick and slightly enlarged as if squeezed over the edge of a basket used asa mold. In most cases no attempt has been made to render the edge even or smooth, and the finger marks and the irregular partings of the mar- gin, which came from squeezing the clay into or over molds and expanding the edges to secure greater size, are all visible. It is difficult to find a well preserved and clearly defined impres- seer ea =, } mn o f ‘te TRANSACTIONS OF THE sion of the fabric employed in the manufacture of these vessels. The clay was probably not of a character to take a clear impression and the cloth was apparently of a ragged, irregular kind. The mesh was open and the thread coarse and slightly twisted. The finer specimens show about eight intersections to the inch and the coarser probably six. In some cases one series of threads seem to have been large and the other small. These fabrics were applied to the entire exterior surface of the vessel, but not with much regu- larity. They may have served to facilitate the handling of the ware while in a plastic state. This pottery is distributed in horizontal layers throughout a ver- tical series more than six feet in thickness, and represents an early epoch of the art of Anahuac. In the upper portion of the lower group of beds we encounter two other varieties of ware. These may have been developed from the rude form in the natural course of progress but there are few indications of this growth here. They are much more nearly allied to the later than to the earlier stages of the art of the section. The transition is very abrupt. As a matter of course I can only present this order of occurrence as characteristic of this locality and of this section. ‘There may be very different combinations in other places, but the order of sequence here indicated is, in the light of history, very suggestive. If the Aztecs, as tradition has it, were the first to settle on this margin of the swampy shore of the lake, then this cord-marked ware is the product of their eazliest or savage period, and the finer wares occur- ing at first so sparingly indicate trade with the more advanced peoples of neighboring settlements. The variety of ware second to appear in the ascending scale is represented by fragments of large, round-bodied, symmetrical pots or casks, with gently constricted necks and thick rounded recurving rims. The paste is generally reddish upon the surface and gray in the mass, and there is a large percentage of silicious tempering material. The surface, exterior and interior, is painted a dark brownish red and has been evenly polished. Average specimens have been, perhaps, ten inches in diameter and a foot or more in height. The walls are always very thick. Fig. 3, is drawn from fragments sufficiently large to indicate the whole shape clearly. Pottery like this is found imbedded in the adobe bricks of the pyra- 4 i | Os Sacre te aS ae a de ANTHROPOLOGICAL SOCIETY. 73 mid of Cholula, and is common in the ancient graves of Costa Rica and New Granada. Large vases recently brought from the province of Chiriqui are identical with these in every respect. Fic. 3.—Earthern vessel from the lower series of deposits. Associated with this ware and beginning apparently a little higher in the section, we find the remains of the third variety. The ves- sels are mostly cup-shaped. They are well made, are simple in treatment, and exhibit a fair degree of symmetry. The prevailing color is a light yellowish terra-cotta tending toward orange. The surfaces are moderately well polished but rarely show attempts at ornamentation. ‘The forms are repeated in the more elaborate wares that succeed it. ‘This ware is identical in most respects with much of that found in the adobe mass of the pyramids of San Juan Teotihuacan, Texcoco, and Cholula, and upon the slopes of the hill of Texcocingo. It is, apparently, the forerunner of some of the more elegant wares of the surface deposits of the section. In the upper part of the lower series of deposits this ware predom- inates greatly over both the heavy ware and the archaic pottery already described. By reference to the section it will be seen that the surface of the lower series of beds has been much dis- turbed by the more recent occupants of the site at the beginning of the second epoch. Excavations have been made and afterwards filled up with gradually accumulating refuse, so that a series of im- perfect stratified deposits has been spread over all, at first following the curves of the disturbed surface. There is, however, no very 74 TRANSACTIONS OF THE well defined line of separation between the older and newer forma- tions. The distinction is rendered much clearer by the contents of the soil. There are occasional layers of stone and adobe bricks, representing the foundations of houses, as seen in the section. There are great quantities of fragmentary pottery, among which I find many of the artistic shapes and rich decorations characteristic of the surface deposits of Anahuac. Included I find also fragments of the two varieties last described. There are occasional stone im- plements and great quantities of obsidian knives, hundreds of which are as perfect as when first struck from the core. These are char- acteristic of the later Aztec period. Near the surface there are fragments of glazed ware indicating Spanish influence. It is not unusual to see in the shallow ditches of the suburban villages, frag- ments of vessels of aboriginal form and decoration, covered with Spanish glaze. Indeed such vessels can be seen in use by the Indians of to-day and are exposed for sale in the modern markets. The pottery of the upper division of the section presents great variety of form and ornamentation, but in material and treatment it is extremely uniform. The paste is compact and heavy, and has a moderately even, finely granular fracture. In rare cases the fracture is smooth or conchoidal. The more common wares are lighter and more porous than those of finer finish. The whole mass is often of a pale brick-red color, the baking having been thorough; but more frequently the interior is of a dark blue gray, indicating imperfect firing. The paste is generally hard and the ware has in many cases a sonorous or metallic ring. The walls vary in thickness with the individual vessel. The tempering when distinguishable is always silicious. The method of finishing the surface is quite uniform although carried to very different degrees of perfection. Occasionally we find a piece without polish; and figurines and elaborately modeled forms are generally quite plain. Asa rule the vessels have been very carefully polished. In many examples the markings of the polishing implement are distinctly visible ; indeed this is true of the unimportant parts of the majority of vessels of the most perfect finish. ‘The polish of the finer examples is so perfect that it is diffi- cult to believe it the result of purely mechanical processes. The pol- ishing has generally been done after the application of the color and color-designs, but sometimes before. _Unpolished surfaces show impressions of the potter’s fingers. ANTHROPOLOGICAL SOCIETY. 15 ‘There are no indications of the use of a wheel. The vessels are seldom absolutely true in outline, but in a general way are remark- able for symmetry and grace. The colors employed in finishing and decorating are pleasing and often extremely rich. ‘The reds predom- inate, the whole surface of the simple forms being frequently finished with it. Upon this the designs are painted in black, white, and different tones of red. In the more common utensils the figures are _ drawn, often carelessly, upon the plain untinted surface. The brush __ has been handled with freedom and the designs are often quite elabo- rate. Occasionally we find incised figures and stamped patterns. The various shapes of vessels obtained at this locality may be classified under a few heads. First, there are many cups and bowls ranging from a few inches to a foot in diameter, and generally quite shallow. The bottoms - are usually flat and the walls expand regularly to the rim. Two examples varying from the rule are given in Figs. 4and 5. Fig. 4 I" Fic. 4.—Vessel from the upper deposits. _ shows a slightly polished, unpainted pan of dark, ochreous tint, - with upright sides and flat bottom. The base, outside, is slightly convex next the circumference and concave at the center. It is Fic. 5.—Vessel from the upper deposits. eight inches in diameter. Fig. 5 illustrates a deep cup of similar color and finish ; a painted design consisting of parallel encircling —— 76 TRANSACTIONS OF THE lines occupies the exterior surface of the rim. The form is an un- usual one in Mexico. Most of the vessels obtained from the upper stratum are neatly finished and tastefully decorated. Some are polished like a mirror over the entire surface, exterior and interior. —— ewan 80 TRANSACTIONS OF THE I have, from the pits at the railway station, a number of miscel- laneous articles in clay, bits of images of men and animals, whistles, spindle-whorls, and the like. A portion of a curious head found is duplicated in a pipe preserved in the Museum and represented in Fic. 13.—Pipe with grotesque heads on the bowl, in the Mexican National Museum. Fig. 13. The whistles are generally of a very simple kind, and the spindle-whorlsare not different from those of other parts of Anahuac, In conclusion, I may recall in a very few words some of the more striking features of this section, calling attention to the order of events suggested by them. It may be affirmed with certainty that the site of the City of Mexico was at one time occupied ‘by a people in a very primitive stage of art, the remains of which art, so far as found, include nothing but fragments of an extremely rude pottery. ‘There are‘no traces ot tools and no indications of houses. This period of occupancy wasa very long one, as it permitted the accumulation in nearly horizontal layers of at least eight feet of finely comminuted refuse. It is further seen that far along in this period of occupancy new forms of art appeared that do not look like the work of the proper occupants of the site produced by gradual improvement, but rather like intrusive products acquired by exchange or otherwise from more cultured tribes. Again, at the end of this first period there is a horizon, pretty well marked, above which primitive forms of art do not appear. Near the base of the deposits of the second period foundations of houses are discovered in which rubble, squared stones, and adobe bricks have been used. In this part of the section we find stone implements and ceramic products of a very high order of merit. With these, and especially near the surface, there is a layer abound- ing in obsidian implements. This marks the last and culminating stage of Aztec art, ending in the historic period proper. ANTHROPOLOGICAL SOCIETY. 81 Speculation upon the period of time represented by this section would be useless, and an attempt to correlate the events recorded with those shadowed forth in tradition would be equally vain. The earliest period is probably beyond the ken of tradition, and the last marks the historic period of Aztec occupation. SPECIAL SESSION, October 11, 1884. In accordance with a call of the Council, the Society met in special session at Columbian University Hall, for the purpose of listening to an address from Prof. E. B. Tytor, of Oxford University, Eng- land. Through invitation extended by-order of the council there were also present members of the Philosophical and Biological Societies, of the Cosmos Club, as well as officers, professors and students of Columbian University. The Society was called to order by President Powe, who ina few words introduced the speaker, who delivered the following ad- dress on— ‘¢ HOW THE PROBLEMS OF AMERICAN ANTHROPOLOGY PRESENT THEM- SELVES TO THE ENGLISH MIND.”’ I have seldom, ladies and gentlemen, felt myself in a more diffi- cult position than I do at this moment. Yesterday morning, when we returned from an expedition out into the far west—an expedition which your President was to have joined, but which, to our, great regret, he was obliged to give up—I heard that at this meeting of the Anthropological Society of Washington I should be called upon to make, not merely a five-minutes’ speech, but a subtantial address ; and since that time my mind has been almost entirely full of the new things that I have been seeing and hearing in the domain of anthropology in this city. I have been seeing the working of that unexampled institution, the Bureau of Ethnology, and studying the collections which, in connection with the Smithsonian Institution, have been brought in from the most distant quarters of the conti- nent ; and, after that, in odd moments, I have turned it over in my mind, what can I possibly say to the Anthropological Society when 6 EO ——_——— —————— =— eS \ ee ( 82 TRANSACTIONS OF THE I am called upon to face them at thirty-six hours’ notice? I will not apologize; I will do the best I can. I quite understand that Major Powell, who is a man who gener- ally has a good reason for everything that he does, had a good reason for desiring that an anthropologist from England should say something as to the present state of the new and growing science in England as compared with its condition in America—for believ- ing that some communication would be acceptable between the old country and the new upon a subject where the inhabitants of both have so much interest in common, and can render to one another so much service in the direction of their work. And therefore I take it that I am to say before you this evening, without elaborate oratory and without even careful language, how the problems of American anthropology present themselves to the English mind. Now, one of the things that has struck me most in America, from the anthropological point of view, is a certain element of old- fashionedness. I mean old-fashionedness in the strictest sense of ~ the word—an old-fashionedness which goes back to the time of the colonization of America. Since the Stuart time, though America, on the whole, has become a country of most rapid progress in development, as compared with other districts of the world, there has prevailed in certain parts of it a conservatism of even an intense character. In districts of the older States, away from the centres of population, things that are old-fashioned to modern Europe have held their own with a tenacity’ somewhat surprising. If I ever become possessed of a spinning-wheel, an article of furniture now scarce in England, I can hardly get a specimen better than in Pennsylvania, where ‘‘ my great-grandmother’s spining-wheel’’ is shown—standing, perhaps, in the lumber-room, perhaps in an or- namental place in the drawing-room—oftener than in any other country that I ever visitied. , In another respect Pennsylvania has shown itself to me fruitful of old-fashioned products. I was brought up among the Quakers— like so many, I dare say, who are present; for the number of times in the week, or even in the day in which it occurs that those whom one meets prove to be at least of Quaker descent, represents a pro- portion which must be highly pleasant to the Quaker mind. In the history of the Society of the Friends there has recently come . out a fact unknown, especially to the Friends themselves. Their opinion has always been that they came into existence in the neigh- ANTHROPOLOGICAL SOCIETY. 83 borhood of 1600, by spontaneous generation, in an outburst of spiritual development in England. It has now been shown, especi- ally by the researches of Robert Barclay (not the old controversialist, but a modern historian,) that the Quakers were by no means the absolutely independent creation that they and others had supposed them to be; that they were derived from earlier existing denomina- tions by a process which is strictly that of development. Their especial ancestors, so to speak, were a division of the early Dutch sect known as Mennonites. The Friends have undergone much modification as to theological doctrine; but some of their most pro- nounced characteristics, such as the objection to war an oaths, and even details of costume, and the silent grace before meals, remain as proofs of Mennonite derivation. To find the Mennonites least _ changed from their original condition is now less easy in their old - homes in Europe than in their adopted homes in the United States and Canada, whither they have migrated from time to time up till quite recently in order to avoid being compelled to serve as soldiers. They have long been a large and prosperous body back in Pennsy]- vania. I went to see them; and they are a very striking instance of permanency of institutions, where an institution ora state of society can get into prosperous conditions in a secluded place, cut off from easy access of the world. Among them are those who dis- sent from modern alteration and changes by a fixed and unalterable resolution that they will not wear buttons, but will fasten their coats with hooks and eyes, as their forefathers did. And in this way they show with what tenacity custom holds when it has become matter of scrupple and religious sanction. Others have conformed more and more to the world; and most of these whom I have seen -were gradually conforming in their dress and habits, and showing _ symptons of melting into the general population. But, in the mean time, America does offer the spectacle of a phase of religious life, _ which, though dwindling away in the old world region where it arose, is quite well preserved in this newer country, for the edifica- — tion of students of culture. These people, who show such plain traces of connection with the historical Anabaptists that they may _ be taken as their living representatives, still commemorate in their _ hymns their martyrs who fell in Switzerland for the Anabaptist faith. There was given me only a few days ago a copy of an old, scarce hymn-book, anterior to 1600, but still in use, in which is a hymn commemorative of the martyr Haslibach, beheaded for refusing to =a GAEL. - SEs LCN ES wiz ~— 84 TRANSACTIONS OF THE conform to the state religion, whose head laughed when it was cut off. Now, to find thus, in a secluded district, an old state of society resisting for a time the modifying influences which have already changed the world around, is no exceptional state of things. It shows the very processes of resisted but eventually prevailing altera- tion which anthropologists have to study over larger regions of space and time in the general development of the world. In visit- ing my Mennonite friends in Pennsylvania, I sometimes noticed that while they thought it nothing strange that I should come to study them and their history, yet when I was asked where I was going next, and confessed with some modesty that I was going with Major Powell to the far west to see the Zufiis, this confession on my part was received with a look of amazement, not quite unmingled with kindly reproof; it seemed so strange to my friends that any person travelling about of his own will should deliberately go to look at Indians. I found it hard to refrain from pointing out that, after all, there is a community of purpose between studies of the course of civilization whether carried out among the colonists of Pennsylvania or among the Indians of New Mexico. Investigation of the lower races is made more obscure and difficult through the absence of the guidance of written history, but the principle is the same, A glance at the tribes whom Professor Mosely and I have seen in the far west during the last few weeks has shown one or two results which may be worth stating; and one, merely parenthetical, I think I must take leave to mention, though it les outside the main current of my subject. Our look at North American Indians, of whom it has been my lot to write a good deal upon second-hand evidence, had, I am glad to say, a very encouraging effect; because it showed that on the whole much of the writings of old travelers and missionaries have to be criticised, yet if, when carefully compared, they agree in a statement, personal inspection will generally verify that statement. One result of our visit has been, not a diminution, but an increase of the confidence with which both of us in future will receive the statements of travelers among the Indians, allowing for their often being based upon superficial observation. So long as we confine ourselves to things which the traveler says he saw and heard, we are, I believe, upon very solid ground. To turn to our actual experiences. The things that one sees ANTHROPOLOGICAL SOCIETY. 85 among the Indian tribes who have not become so: ‘‘ white ’ as the Algonkins and the Iroquois, but who present a more genuine picture of old American life, do often, and in the most vivid way, present traces of the same phenomena with which one is so familiar in old- world life. Imagine us sitting in a house just inside California, engaged in what appeared to be a fruitless endeavor on the part of Professor Mosely to obtain a lock of hair of a Mojave to add to his collection. The man objected utterly. He shook his head. When pressed, he gesticulated and talked. No; if he gave up that bit of hair, he would become deaf, dumb, grow mad; and, when the medicine man came to drive away the malady, it would be of no use, he would have to die. Now, ali this represents a perfectly old- world group of ideas. If you tried to get a lock of hair in Italy or Spain, you might be met with precisely the same resistance; and you would find that the reason would be absolutely the same as that which the Mojave expressed,—that by means of that lock of hair one can be bewitched, the consequence being disease. And within the civilized world the old philosophy which accounts for disease in general as the intrusion of a malignant spirit still largely remains ; and the exorcising such a demon is practised by white men as a re- ligious rite, even including the act of exsufflating it, or blowing it away, which our Mojave Indian illustrated by the gesture of blow- ing away an imaginary spirit, and which is well known as forming a part of the religious rites of both the Greek and Roman church. How is it that such correspondence with old-world ceremonies should be found among a tribe like the Mojaves, apparently Mongo- lian people, though separated geographically from the Mongolians of Asia? Why does the civilization, the general state of culture, of the world, present throughout the whole range, in time and space, phenomena so wonderfully similar and uniform? ‘This question is easy to ask; but it is the question which, in a few words, presents the problem which, to all anthropologists who occupy themselves with the history of culture, is a problem full of the most extreme difficulty, upon which they will have for years to work, collect- ing and classifying facts, in the hope that at some time the lucky touch will be made which will disclose the answer. At present there is none of an absolute character. There is no day in my life when I am able to occupy myself with anthropological work, in which my mind does not swing like a pendulum between the two great possible answers to this question. Have the descendants of a en ~ ~ ~i > / 86 TRANSACTIONS OF THE small group of mankind gone on teaching their children the same set of ideas, carrying them on from generation to generation, from age to age, so that when they are found in distant regions, among tribes which have become different even in bodily formation, they represent the long-inherited traditions of a common ancestry? Or is it that all over the world, man, being substantially similar in mind, has again and again, under similar circumstances of life, developed similar groups of ideas and customs? I cannot, I think, use the opportunity of standing at this table more profitably then by in- sisting, in the strongest manner whicn I can find words to express, on the fundamental importance of directing attention to this great problem, the solution of which will alone bring the study of civili- zation into its full development as a science. Let me put before you two or three cases, from examples which have been brought under my notice within the last few days, as illustrating the ways 1n which this problem comes before us in all its difficulty. This morning, being in the museum with Major Powell, Professor Mosely, and Mr. Holmes, looking at the products of Indian life in the far west, my attention was called to certain curious instruments hanging together in a case in which musical instruments are con- tained. ‘These consisted simply of flat, oblong, or oval pieces of wood, fastened at the end to athong, so as to be whirled round and round, causing a whirring or roaring noise. The instruments in question came, one from the Ute Indians, and one from the Zufiis. Now, if an Australian, finding himself inspecting the National muse- um, happened to stand in front of the case in question, he would stop with feelings not only of surprise, but probably of horror; for this is an instrument which to him represents, more intensely than anything else, a sense of mystery attached to his own most important religious ceremonies, especially those of the initiation of youths to the privileges of manhood, where an instrument quite similar in nature is used for the purpose of warning off women and children. If this Australian was from the south, near Bass Strait, his native law is, that, if any woman sees these instruments, she ought immediately to be put to death; and the illustration which he would give is, that, in old times, Tasmania and Australia formed one continent, but that one unlucky day it so happened that certain boys found one of these instruments hidden in the bush, and showed it to their mothers, whereupon the sea burst up through the land in a deluge, a Rasy yee oe md a ANTHROPOLOGICAL SOCIETY. 87 which never entirely subsided, but still remains to separate Van Dieman’s Land from Astralia. And, even if a Caffre from South Africa were to visit the collection, his attention would be drawn to the same instruments, and he would be able to tell that in this country they were used for the purpose of making loud sounds, and warning the women from the ceremonies attending the initiation of boys. How different the races and languages of Australia and Africa! yet we have the same use cropping out in connection with the same instrument ; and to complete its history, it must be added that there are passages of Greek literature which show pretty plainly that an instrument quite similar was used in the mysteries of Bacchus. The last point is, that it isa toy well known to country-people, both in Germany and in England. Its English name is the ‘‘ bull-roarer ;”’ and, when the children play with it in the country villages, it is hardly possible (as I know by experience) to distinguish its sound from the bellowing of an angry bull. In endeavoring to ascertain whether the occurrence of the ‘ bull- roarer,’’ in so many regions is to be explained by historical con- nection, or by independent development, we have to take into con- sideration, first, that it is an apparatus so simple as possibly to have been found out many times; next, that its power of emitting a sound audible at a great distance would suggest to Australians and Caffres alike its usefulness at religious ceremonies from which it was desired to exclude certain persons. Then we are led to another argu- ment, into which I[ will not enter now, as to the question why women are excluded in the most rigid manner from certain ceremonies. But in any event, if we work it out as a mere question of probabilities, the hypothesis of repeated reinvention under like circumstances can hold its own against the hypothesis of historical connection ; but which explanation is the true one, or whether both are partly true, I have no sufficient means to decide. Such questions as these being around us in every direction, there are only two or three ways known to me in which at preeent students can attack them with any reasonable prospect of success. May I briefly try to state, not so much by precept as by example, what the working of those methods is by which it is possible, at any rate, to make some en- croachments upon the great unsolved problem of anthropology. One of the ways in which it is possible to deal with such a group of facts may be called the argument from outlandishness. When a circumstance is so uncommon as to excite surprise, and to lead 88 TRANSACTIONS OF THE one to think with wonder why it should have come into existence, and when that thing appears in two different districts, we have more ground for saying that there is a certain historical connection be- tween the two cases of its appearance than in the comparison of more commonplace matters. Only this morning a case in point was brought rather strongly under my notice; not that the facts were unknown, for we have been seeing them for days past at Zufi. The Indians of the north, and especially the Iroquois, were, as we know, apt to express their ideas by picture-writings, in the detailed study of which Col. Mallery is now engaged. One sign which habitually occurs is the picture of an animal in which a line is drawn from the throat, through the picture of the animal, termi- nating in the heart. Now, the North American Indians of the lake district have a distinct meaning attached to this peculiar heart-line, which does not attach to ordinary pictures of animals ; they mean some anima! which is living, and whose life is affected in some way “by a charm of some kind. It is expressly stated by Schoolcraft that a picture he gives of a wolf with such a heart-line means a wolf with acharmed heart. It is very remarkable to find, among the Zujfiis, representations of deer and other animals drawn in the same manner; and the natural infer- ence is, that the magic of the [Iroquois and the Zuiiis is connected, and of more or less common origin. I verified this supposition by asking Mr. Cushing, our authority on Zufii language and ideas, what idea was generally attached to this well-known symbol ; and his answer was, that it indicated a living animal on which magical influ- ence was being exerted. May we not, then, consider—leaving out of the question the point whether the Pueblo people invented the heart-line as a piece of their magic and the nomad tribes of the north picked it up from them, or whether it came down from the northern tribes and was adopted by the southern, or whether both had it from a common source—that, at any rate, there is some ground, upon the score of mere outlandishness, for supposing that such an idea could not occur without there being some educational connection between the two groups of tribes possessing it, and who could hardly have taken it by independent development. To mention an instance of the opposite kind; I bought a few days ago, amonge the Mojaves, a singular article of dress,—a na- tive woman’s girdle, with its long fringe of twisted bark. This or, rather two of these put on so as to form one complete skirt used to - Se i \ j c % 4 + + ee mes ANTHROPOLOGICAL SOCIETY. 89 be her only garment ; and it is still worn from old custom, but now covered by a petticoat of cotton, generally made of several pocket- handkerchiefs in the piece, bought from the traders. Under these circumstances, it has become useless as a garment, only serving as what I understand is called in the civilized world ‘‘adress-improver ;’’ the effect of which, indeed, the Mojave women perfectly understand, and avail themselves of in the most comic manner. Suppose, now, that we had no record of how this fantastic fashion came into use among them: It has only to be compared with the actual wearing of bark garments in Further Asia and the Pacific Islands in order to tell its own history,—that it is a remnant of the phase of culture where bark is the ordinary material for clothing. But the anthropo- logist could not be justified in arguing from this bark-wearing that the ancestors of the Mojaves had learned it from Asiatics. Inde- pendent development, acting not only where men’s minds, but their circumstances, are similar, must be credited with much of the simi- larity of customs. It is curious that the best illustrations of this do not come from customs which are alike in detail in two places, and so may be accounted for, hke the last example, by emigration from one place to another. We find it much easier to deal with practices similar enough to show corresponding workings of the human mind, but also different enough to show separate formation. Only this morning I met with an excellent instance of this. Dr. Yarrow, your authority on the subject of funeral rites, described to me a custom of the Utes of disposing of the bodies of men they feared and hated by putting them under water in streams. After much inquiry, he found that the intention of this proceeding was to prevent their coming back to molest the survivors. Now, there is a passage in an old writer on West Africa where it is related, that, when a man died, his widow would have herself ducked in the rivei in order to get rid of his ghost, which would be hanging about her, especially if she were one of his most loved wives. Having thus drowned him of, ‘she was free to marry again. Here, then, is the idea that water is impassable to spirits, worked out in different ways in Africa and America, but showing in both the same principle ; which, indeed, is manifested by so many peoples in the idea of bridges for the dead to pass real or imaginary streams, from the threads stretched across brooks in Burmah for the souls of friends to cross by, to Catlin’s slippery pine-log for the Choctaw dead to pass the dreadful river. In such correspondences of principle we | 90 TRANSACTIONS OF THE trace, more clearly than in mere repetition of a custom or belief, the community of human intellect. But I must not turn these remarks into what, under ordinary cir- cumstances, would be a lecture. I have been compelled to address myself, not so much to the statement in broad terms of general principles, as to points of detail of this kind, because it is almost impossible, in the present state of anthropology, to work by abstract terms ; and the best way of elucidating a working-principle is to discuss some actual case. ‘There are now two or three practical points on which I may be allowed to say a few words. The principle of development in civilization, which represents one side of the great problem I have been speaking of, is now be- ginning to receive especial cultivation in England. While most museums have been at work, simply collecting objects and imple- ments, the museum of Gen. Pitt-Rivers, now about to be removed from London to Oxford, is entirely devoted to the working out of the development theory on a scale hardly attempted hitherto. In this museum are collected specimens of weapons and implements, so as to ascertain by what steps they may be considered to have arisen among mankind, and to arrange them in consecutive series. Development, however, is not always progress, but may work itself out into lines of degeneration. There are certain states of society in which the going-down of arts and sciences is as inevitable a state of things as progress is in the more fortunate regions in which we live. Anthropologists will watch with the greatest interest what effect this museum of development will have upon their science. Gen. Pitt-Rivers was led into the formation of the remarkable col- lection in question in an interesting manner. He did not begin life either as an evolutionist or as an anthropologist. He wasa soldier. His business, at a particular time of his life, was to serve on a committee on small-arms, appointed to reform the armament of the British army, which at that time was to a great extent only pro- vided with the most untrustworthy of percussion-muskets. He then found that a rifle was an instrument of gradual growth; for the new rifles which it was his duty to inspect had not *come into existence at once and independently. When he came to look carefully into the history of his subject, it appeared that some one had improved - the lock, then some one the rifling, and then others had made fur- ther improvements ; and this process had gone on until at last there came into existence a gun, which, thus perfected, was able to hold ANTHROPOLOGICAL SOCIETY. 91 its own ina permanent form. He collected the intermediate stages through which a good rifle arose out of a bad one; and the idea began to cross his mind that the course of change which happened to rifles was very much what ordinarily happens with other things. So he set about collecting, and filled his house from the cellar to the attic, hanging on his walls series of all kinds of weapons and other instruments which seemed to him to form links ina great chain of development. The principle that thus became visible to him in weapon-development is not less true through the whole range of civilization ; and we shall soon be able to show to every anthro- pologist who visits Oxford the results of that attempt. And when the development theory is seen in that way, explaining the nature and origin of our actual arts and customs and ideas, and their gradual growth from ruder and earlier states of culture, then an- thropology will come before the public mind as a new means of practical instruction in life. Speaking of this aspect of anthropology leads me to say a word on another hardly less important. On my first visit to this country, nearly thirty years ago, I made a journey in Mexico with the late Henry Christy, a man who impressed his personality very deeply on the science of man. He was led into this subject by his con- nection with Dr. Hodgkin; the two being at first interested, from the philanthropist’s point of view, in the preservation of the less favored races of man, and taking part in a society for this purpose known as the Aborigines’ protection society. The observation of the indigenous tribes for philanthropic reasons brought the fact into view that such peoples of low culture were in themselves of the high- est interest as illustrating the whole problem of stages of civilization ; and this brought about the establishment of the Ethnological So- ciety in England, Henry Christy’s connection with which origin- ated his plan of forming an ethnological museum, ‘The foundations of the now celebrated Christy collection were Jaid on ovr Mexican journey; and I was witness to his extraordinary power of knowing, untaught, what it was the business of an anthropologist to collect, and what to leave uncollected: how very useless for anthropologic purposes mere curiosities are, and how priceless are every-day things. The two principles which tend most to the successful work of an- thropology—the systematic collection of the products of each stage of civilization, and the arrangement of their sequence in develop- ment—are thus the leading motives of our two great anthropological museum. oo TRANSACTIONS OF THE To my mind, one of the most remarkable things I have seen in this country is the working of the bureau of ethnology as part of the general working of the Government department to which it belongs. It is not for me, on this occasion, to describe the working of the Smithsonian Institution, with its research and publications extend- ing almost through the whole realm of science; nor to speak of the services of that eminent investigator and organizer, Prof. Spencer F. Baird. It is the department occupied with the science of man of which I have experience; and I do not think that anywhere else in the world such an official body of skilled anthropologists, each knowing his own special work, and devoted to it, can be paralleled. The bureau of ethnology is at present devoting itself especially to the working-up of the United States, and to the American conti- nent in general, but not neglecting other parts of the world. And I must say that I have seen with the utmost interest the manner in which the central organism of the bureau of ethnology is perform- ing the functions of an amasser and collector of all that is worth knowing; how Major Powell is not only a great explorer and worker himself, but has the art of infusing his energy and enthusiastic spirit through the branches of an institution which stands almost alone, being, on the one hand, an institution doing the work of ascientific society, and, on the other hand, an institution doing that work with the power and leverage of a government department. If we talked of working a government institution in England for the progress of anthropology in the way in which it is being done here we should be met with—silence, or a civil answer, but with no practical result ; and any one venturing to make the suggestion might run the risk of being classed with that large body described here as ‘‘cranks.”’ The only way in which the question can be settled, how far a gov- ernment may take up scientific research as a part of its legitimate functions, is by practical experiment; and somehow or other your president is engaged in getting that experiment tried, with an obvious success, which may have a great effect. If in future a prop- osition to ask for more government aid for anthropology is met with the reply that such ideas are fanatical, and that such schemes will produce no good results, we have a very good rejoinder in Wash- ington. The energy with which the Bureau of Ethnology works throughout its distant ramifications has been a matter of great in- terest. It is something like what one used to hear of the organiza- tion of the Jesuits, with their central authority ina room in a Roman ANTHROPOLOGICAL SOCIETY. 93 palace, whence directions were sent out which there was some agent in every country town ready to carry out with skill and zeal. For instance, it was interesting at Zuifii to follow the way in which Colonel] and Mrs. Stevenson were working the pueblo, trading for speci- mens, and bringing together all that was most valuable and inter- esting in tracing the history of that remarkable people. Both man- aged to identify themselves with the Indian life. And one thing I particularly noticed was this, that to get at the confidence of a tribe, the man of the house, though he can do a great deal, cannot do all. If his wife sympathizes with his work, and is able to do it, really half of the work of investigation seems to me to fall to her, so much is to be learned through the women of the tribe which the men will not readily disclose. The experience seemed to me a lesson to anthropologists not to sound the “bull-roarer,’’ and warn the ladies off from their proceedings, but rather to avail themselves thankfully of their help. Only one word more, and I will close. Years ago, when I first knew the position occupied by anthropology, this position was far inferior to that which it now holds. It was deemed, indeed, curious and amusing; and travelers had even, in an informal way, shown human nature as displayed among out-of-the-way tribes to be an instructive study. But one of the last things thought of in the early days of anthropology was that it should be of any practical use. The effect of a few years’ work all over the world shows that it is not only to be an interesting theoretical science, but that it is to be an agent in altering the actual state of arts and beliefs and _ institu- tions in the world. For instance: look at the arguments on com- munism in the tenure of land in the hands of a writer who thinks how good it would be if every man always had his share of the land. The ideas and mental workings of such a philosopher are quite dif- ferent from those of an anthropologist, who knows land-communism is an old and still existing institution of the world, and can see exactly how, after the experience of ages, its disadvantages have been found to outweigh its advantages, so that it tends to fall out of use. In any new legislation on land, the information thus to be given by anthropology must take its place as an important factor. Again: when long ago I began to collect materials about old customs, nothing was farther from my thoughts than the idea that they would be useful. By and by it did become visible, that to show that a custom or institution which belonged to an early state O47: TRANSACTIONS OF THE of civilization had lasted on by mere conservatism into a newer civilization, to which it is unsuited, would somehow affect the pub- lic mind as to the question whether this custom or institution should be kept up, or done away with. Nothing has for months past given me more unfeigned delight than when I saw in the Zzmes newspaper the corporation of the city of London spoken of as a “‘ survival.”’ You have institutions even here which have outlived their original place and purpose ; and indeed it is evident, that when the course of civilization is thoroughly worked out from beginning to end, the description of it from beginning to end will have a very practical effect upon the domain of practical politics. Politicians have, it is true, little idea of this as yet. But it already imposes upon bodies like this Anthropological Society a burden of responsibility which was not at first thought of. We may hope, however, that under such leaders as we have here, the science of anthropology will be worked purely for its own sake ; for, the moment that anthropolo- gists take to cultivating their science as a party-weapon in politics and religion, this will vitiate their reasonings and arguments, and spoil the scientific character of their work. I have seen in England bad results follow from a premature attempt to work anthropology on such controversial lines, and can say that such an attempt is not only in the long-run harmful to the effect of anthropology in the world, but disastrous to its immediate position. My recommenda- tion to students is to go right forward, lke a horse in blinkers, neither looking to the right hand nor to the left. Let us do our own work with a simple intention to find out what the principles and courses of events have been in the world, to collect all the facts, to work out all the inferences, to reduce the whole into a science ; and then let practical life take it and make the best it can of it. In this way the science of man, accepted as an arbiter, not by a party only, but by the public judgment, will have soonest and most per- manently its due effect on the habits and laws and thoughts of mankind. ~* I am afraid I have not used well, under such short and difficult conditions, the opportunity which you have done me the great pleasure and honor of giving me here. [have tried, as I said I would, to put in the simplest way before you some considerations which appear to me as of present importance in our science, both in the old world and in the new, and I thank you in the heartiest way possible for the opportunity you have given me to do this, ANTHROPOLOGICAL SOCIETY. 95 At the close of the address.a vote of thanks was moved by Judge Arthur McArthur, of the Supreme bench of the District of Columbia, and passed unanimously. The President announced that by direction of the Council there would be no regular meeting of the Society until the third Tuesday in November. EIGHTY-FIFTH REGULAR MEETING, November 18, 1884. Major J. W. Powe Lt, President, in the Chair. The President stated that by action of the Council a place for the future meetings of the Society had been secured at the Columbian University. . The Secretary of the Council announced the election of Mr. M. D. Kerr, of the U. S. Geological Survey, as an active member of the Society. A paper entitled ‘‘AUSTRALIAN Group RELATIONS,’ by Alfred W. Howitt of Gippsland, Australia, was then read by Col. Seely.* EIGHTY-SIXTH REGULAR MEETING, December 2, 1884. Major J. W. Powe t, President, in the Chair. The Secretary of the Council announced the election as active members of Messrs. Victor Mindeleff, Cosmos Mindeleff, Wm. M. Poindexter, and Wm. H. Babcock. _Dr. Franz Boas read a paper on ‘‘ THE Eskimo oF BAFFIN LAND.”’ Although the shores of Baffin Land have been visited by whalers for a very long time, there was still little known about the Eskimo tribes inhabiting this tract of land. The southwesternmost region, the land about King’s Cape, is called by the natives Sicosuilar, z. e., a land which has no fixed ice floe during the winter. It is inhabited by the Sicosuilarmiut, who go deer hunting in the low land farther north. They have inter- course with the natives of the north shore of Labrador, the Iglu- * Printed in the Smithsonian Report for 1883. = { er 96 TRANSACTIONS OF THE miut, z. e., the inhabitants of the other side, crossing Hudson Strait from King’s Cape to Cape Wolstenholme. The middle region of the north shore of Hudson Strait is inhab- ited by the Akudliarmiut who go deer hunting to the large lake Ag- makdgua, where they meet with the Nugumiut, the inhabitants of the peninsula between Frobisher Bay and Cumberland Sound. The shore of Davis Strait is divided into three parts :—Oko, Akudnirn, and Aggo, 7. e., the lee side, the centre, and the weather side. Oko, the land of the Cumberland Sound, is inhabited by the Okomiut who in olden times were divided into the Tellirpingmiut on the west shore of Cumberland Sound; the Kinguamiut, at the head of it; the Kignaitmiut on the high Cumberland peninsula, and finally the Saumingmiut on Davis Strait, as far as Exeter Bay and Cape Dier. As the number of the Okomiut has been greatly diminished there scarcely exists any difference between these tribes now. The inhabitants of Padh are nearer to the Akudnirmiut than to the Okomiut. The Aggomiut consist of two tribes: The Tudnu- mirmiut of Pond’s Bay, and the Tudnunirossirmiut of Admiralty Inlet. Besides there are the Iglulingmiut of Fury and Hecla Strait, with whom we have been made acquainted by Parry and Hall. I have visited the different tribes of Cumberland Sound and Davis Strait as far as Akudnirn, and no settlement in this country escaped my notice. As there are quite anumber of natives of differ- ent tribes settled among these I was able to gather a good deal of information about all the Eskimos from Sicosuilar to Tudnunirn. The most interesting tribe are the Tellirpingmiut, the inhab- itants of the west shore of Cumberland Sound, more particularly speaking, of Nettilling fiord. This is one of the few Eskimo tribes living inland. From former reports we only learned that the Kin- nepatu, the Eskimo of Chesterfield Inlet, on the west shore of Hudson Bay, live nearly all the year round on deer and musk oxen, which they hunt on the plains between Back River and Chesterfield Inlet, only coming down to the seaside during the winter. At the present time the Tellirpingmiut have the same custom. In the month of May they leave their winter settlement and travel with their dogs and sledges inland to the large lake Nettilling, (Lake Kennedy, of the old charts) and get to the place of their settlement, Tikerakdjuak, on the south shore of the lake, long before the ice breaks up. They take with them one or more bags of blubber for their lamps; but sometimes they do not even carry 4 ANTHROPOLOGICAL SOCIETY. 97 as much, as they are able to cook with the heather found in abun- dance on the vast plains of the lake, and burn deer marrow in their lamps. Now and then they secure a ¢eal in the lake, but they cannot rely on their hunt as these animals are too few in number. In the west- ern part of the lake they seem to be more plentiful; but in the east- ern portion their number has been greatly diminished. I suppose that this is principally the reason why the Tellirpingmiut do not any longer stay all the year round on the shores of the lake as many of them formerly did. ‘They seem to have spent there the greater portion of their lives, occasionally visiting the seaside to provide themselves with skins of the young and old seals. It very seldom happens now that any men winter inland, as the number of seals is too small. In the spring of the year they live on deer and the inumerable birds which are caught while molting. The Eskimos return to the entrance of Neltilling fiord about the beginning of December, when the ice in the fiords is strong and well covered with snow. The other Okomiut, who are settled in four places on the west shore, two on the east shore, and one between Cape Mercy and Cape Micklesham, never leave the coast for any length of time. Only a few go in their boats also to Lake Nettilling, as this is the best place for deer hunting. They leave after the breaking up of the ice in July and return during the first days of October. By far the most of them spend the summer at the head of the fiords whence they start deer hunting inland, returning after a few days’ absence. The old men and the women meanwhile live on salmon which are caught in abundance in the small rivers emptying into the fiords. In winter they settle on the islands nearest to the open sea. Throughout the cold months until the sun rises higher they go sealing with the harpoon, watching the seal at its breathing hole. In March, while the seal brings forth its young, all the natives are eager to secure as large a number as possible of young seal skins, which are highly valued for the under jackets and winter pants for men and women. In the fall the inhabitants of Saumia and Padli secure a great number of walruses which supply them with food and blubber until late in the winter. They only go sealing in order to enjoy them- selves, as they generally have sufficient walrus meat to last them the whole year. 7 9 A 98 TRANSACTIONS OF THE Sometimes even there is some left in summer. In spring they go bear hunting. The skins of these animals are exchanged for guns and ammunition, when the whalers visit the coast returning from their hunting grounds off Lancaster Sound. The Tudnunirmiut hunt the white whale and the narwhal whose ivory is highly valued. Though the Eskimos shift their habitations according to the sea- sons from one place to another we must not consider them a people without stationary abodes, for at certain seasons they are always found at the same places. There are some doubts about the origin of the old stone founda- tions met with in every part of Arctic America, even in countries not any longer inhabited by Eskimos, as the Parry Archipelago and the northern part of East Greenland. It was believed that the cen- tral Eskimos forgot the art of building stone houses and only lived in snow huts. In Baffin Land I found a great number of stone, turf, and sod foundations, apparently of very ancient origin. If the Eskimos come to a place where they know that stone houses exist they build these up into a comfortable home, covering the old walls with a double seal-skin roof and heather. In the settlement Anarnitung, near the head of Cumberland Sound, and at Okkiadliving, on Davis Strait, they frequently live in these houses which they call Kag- mong. I found two different styles of construction, one with a very large floor and aremarkably short bed-place ; the other with both parts of about the same size. The former the Eskimos ascribe to the Tunnit, or as they are often called, Tudnikjuak, a people playing a great part in their tales and traditions. ‘The latter are ascribed to their own ancestors, the ancient Eskimos. Indeed they do not build any stone houses now, as they always find in the places of their winter settlements the old structures which are fully sufficient for the number of men inhabiting the country now, which is very small as compared with that of former times. From different reports I conclude that Cumberland Sound about fifty years ago was inhabited by 2,500 Eskimos who are now reduced to about 300 souls. In winter time they mostly build snow houses consisting of a high dome with a few smaller vaults attached, used as entrances which keep the cold air out of the main room. The Okomiut and Akud- ANTHROPOLOGICAL SOCIETY. 99 nirmiut cover the inside of the same with seal-skins; while the Nugumiut and Akudlirmiut leave the walls bare. They cut the pieces of snow much thicker and bury the whole house in loose snow which they stamp down with their feet. In summer they live in tents made of seal-skin. The back part is formed by six poles, arranged in a semicircle and lashed together at their converging points. Two polesrun from this junction to the entrance, which is also formed of two poles. The Okomiut build the back part of the tents much less steep than the Akudnirmiut. The Aggomiut use a tent with only one pole in the center, and one for the entrance. I have been informed tha* three different styles of clothing are used in Baffin Land, two o which Ihave seen myself. The Sicosu- ilarmiut are said to use jacxets with a broad tail and a hood, which latter is not pointed. The Nugumiut and Okomiut are very well clad, having their garments neatly trimmed with skins of different color and adorned with skin straps. Their hoodsare long pointed, and the tails of the women’s jackets very narrow. The jackets of the men have either no tail whatever, or one that is very short. The women’s pants consist of two parts, the leggins being fastened by a string to the short breechlets. : The Akudnirmiut and Aggomiut use very large hooded jackets _ with asmall point at the top. Their clothing is much inferior to cack MeMSear Ae a | that of the Okomiut. I have seen scarcely any attempt to adorn it in any way. The women wear very large boots which reach up _ tothe hips. In Pond’s Bay they are sometimes kept up by whale _ bone, and they are in the habit of carrying the young children in them. There exist only very slight differences in the dialects from Akud- liak to Pond’s Bay, and those I found refer only to the vocabulary. However, in the most common phrases, the way of greeting, etc., _ every tribe has its ownstyle. Nor could I find any differences with reference to their traditions. It is possible that a number of the Oko stories are unknown in Tudnunirn, and vce versa, but I am not sufficiently acquainted with the Tudnunirmiut to positively decide the question. There are some differences between the Okomiut and the Akud- nirmuit in the arrangement of feasts, which are repeated every fall, during which some natiyes make their appearance disguised and masked as representatives of a fabulous tribe. 100 TRANSACTIONS OF THE All the Eskimos of Baffin Land are fond of music and poetry. They sing the old songs of their people, and spend the long winter nights telling traditions and singing the old monotonous tunes of their songs or composing new ones. I made the acquaintance of a few poets whose songs were known in every place I visited. All their tales and the themes of the old songs are closely con- nected with their religious ideas. - Though there is a strong resem- blance between many of their own traditions and those of the Green- landers, I found quite a number of new tales and religious ideas hitherto unknown. They are familiar with the Erkilik of the Greenlanders, whom they mostly call Adlet, and the Tudnik, who, however, do not inhabit the interior but are said to have lived formerly with the Eskimos on the same shores and in the same settlements. According to their tradition, which is only preserved in parts in Greenland, the Adlet, Kodlunarn, (white men) and Innuit are the children of one mother and her husband, a red dog, who jived at Igluling, in Fury and Hecla Strait. From there all the different tribes of Innuit are said to have spread over the country, now occupied by them. It is worth noticing that the Labrador Eskimos know the Adlat and the Tudnik too. In Erdmann’s Woérterbuch des Labrador Dialects, Adlat is explained as Indian of the Interior; Tudnik as a Greenlander. I believe, however, that these meanings were given to these words by the missionaries, while in reality they signify the same as in Baffin Land and Greenland. ‘To learn whether there are any traditions relating to the Adlat or Erkillek would be of special interest. The Eskimos of Baffin Land have no knowledge of the Supreme Being, Torngarsuk, whom the Greenlanders once considered to be superior to all the numerous lower spirits called the Torgnet. Of these there are a great many, but the most prominent ones ap- pear in the shape of a bear, a man, or a woman, inhabiting the large boulders, which are found in great numbers scattered over the country. These spirits act as genii of certain favored men who by their aid become great sorcerers. They are able to cure dieases, to de- tect offences, to give good luck in hunting, and they visit the spirits of the moon and of the stars. The Eskimos entertain a great fear of the Tupilat, the Spirits of the Dead, who kill every one daring to offend them. This is the ANTHROPOLOGICAL SOCIETY. 101 reason why they are afraid to touch the corpse of the deceased, and why they destroy every object which once belonged to a dead Eskimo. The soul of the dead Innung goes to the land Adlivum, beneath the earth of which an evil spirit, Sedna, is mistress. In olden times she was an Eskimo woman herself, married to a fulmar who used her very badly. She escaped in the boat of her father who flung her overboard to save his own life from the wrath of the bird, after having detected the loss of his wife. While Sedna clung to the edge of the boat the father cut off her fingers which were changed into seals and whales. ‘To revenge herself she caused two dogs to gnaw off her father’s feet and hands. ‘Then the earth opened and they went down to the land Adlivum. As the Eskimos kill the seals and whales that have risen from Sedna’s fingers she hates and_pur- sues them. Only those who come to an unnatural death escape her and ascend to Heaven to the land Kudlivum where innumerable deer are found, and where they are never troubled by either ice or snow. . Sedna is feared by the Eskimos even more than the Tupilat and the traditions about her have the greatest influence on their habits, manifesting itself mostly in laws about food and interdiction of labor on certain days. To compare the habits and traditions of the Eskimos of Baffin Land with those of the Smith Sound and Greenland will be of much interest, as these tribes connect the central with the eastern Eskimos. Tribes which may easily be studied, and whose customs are of prime importance are the Sicosuilarmiut and Iglumiut, and their connections with the Labrador natives. It isa matter of regret that so little is known of the inhabitants of Southampton Island and of the west shore of Hudson’s Bay, although Hall spent five winters in those regions. The researches of Mr. Turner in Ungava will fill a great gap in our knowledge of the central tribes. Another tribe of great importance are the inhabitants of Admi- ralty Inlet, who seem to be very numerous up to the present time. Even now it is possible to trace the connection between the tribes from King William’s Land to Smith Sound and Labrador. The Netchillirmiut of Boothia Felix, who are now mixed with the Ugjulir- miut of King William’s Land and Adelaide Peninsula most probably occupy part of the old country of the Ukusiksalingmiut of Back River. ‘These natives, who live principally upon musk oxen, cross a 102 TRANSACTIONS OF THE the land in visiting the shores of Wager River. The Netchillik Eskimos travel through the land of the Sinimiut of Pelly Bay to Eivillik (Repulse Bay). -The Eivillinmiut frequently have inter- course with the Igluling tribe, who formerly visited the Cumberland Sound Eskimos by the way of Majoraridjen, the country north of Lake Nettilling (Lake Kennedy). ‘Three roads are used in travel- ing from Igluling to the west shore of Baffin Bay and to Lancaster Sound, the most western through the fiord Tessiujang, near Cape Kater, to Admiralty Inlet; the other to Ikalualuin (Arctic Sound) in Eclipse Bay and the third one to Anaulereelling (Dexterity Bay). The Tudnunirossirmiut sometimes cross Lancaster Sound, and were found on the western part of North Devon, which they call Tudjan. They cross this land and Jones Sound on sledges and have intercourse with a tribe on Ellesmere Land, which they call Umingmamnuna. From Bessels’ researches we know that they cross Smith Sound, for he found amongst the Ita-Eskimos a man who had lived in former years amongst the Akudnimiut on the east coast of Baffin Land. I myself found a.native near Cape Kater, north of Home Bay, who had lived somewhere near Cape Isabella at the entrance of Smith Sound for several years. The questions which may be settled by a more thorough knowl- edge of the habits and traditions of all these and the more western tribes which have scarcely been seen by any white men, may prove of prime importance for the solution of the question relating to the origin and migrations of this people. Mr. Joun Murvocu read the following paper on ‘‘ SEAL CaTCH- ING AT Point Barrow.”’ The capture of seals is one of the most important of pursuits among the Eskimos of the two villages at Point Barrow. A failure of the seal harvest would be as disastrous to them as the failure of the potato crop to the Irish, or the rice crop in India. Not only does the flesh of the seal form the great staple of food, but its fat furnishes them with oil to light and warm their winter houses, to oil their water-proof boots and harpoon lines, and to keep the water out of their skin boats. The skin serves to make their water-proof boots and leggings, the soles of their winter boots, canteens, the covers of the kaiaks, or small skin canoes, and, rarely, their outer clothing; cut into thongs it furnishes a serviceable cord which they make into nets and harpoon lines, and employ for all the varied ANTHROPOLOGICAL SOCIETY. 103 purposes for which we use cord. In ‘former times and occasionally at present, the skin served to cover the summer tent, or #7 péh. No part of the animal is wasted. Even the entrails are saved, and dressed, and made into water-proof frocks to wear over the fur cloth- ing in rainy and snowy weather. If their were no seals at Point Barrow there could be no Eskimos, barren as the country is of fish and reindeer. The following species are pursued : First, and most important, the Ringed Seal or Nétyi (Phoca foetida). ‘This is ¢he seal par excellence, and the only one taken in any considerable numbers, by all the methods which will be described hereafter. Next in importance is the great Bearded Seal, tg’ru (E7ignathus barbatus). This is com- paratively rare, though a good many are taken much in the same manner as the walrus with the heavy harpoon and rifle from the umiak. The skins are especially valued for covering the large skin boats, and for making heavy harpoon lines. The other two species are of extremely rare occurrence. The Harbor Seal, kasigia, (Phoca vitulina) is occasionally caught in summer in the nets at Elson Bay, and the rare and beautiful Ribbon Seal (Aistriophoca fasciata), the kaixolifi, is now and then taken in the early winter. When the ice-pack comes in in the autumn, and the sea is begin- ning to close, it may be about the middle of October, the natives who are now all back from their summer wanderings and settled _for the winter, begin the pursuit of the ne’étyé. At this season there are many open holes in the pack to which the seals resort. Here they are taken by shooting them with the rifle as they show their heads above water, and securing them with the retrieving har- poon or natligi. The line and harpoon-head belonging to this are generally carried attached to the gun-case which is slung across the shoulders, and the shaft serves as a staff for walking and climb- ing about the rough ice. the walls resume their position gripping firmly the tissues which have protruded into the slips. Pulling only tightens the grip. This style of lance has not as far as the speaker was aware been any where described, though the specimens which he saw in 1868 were afterwards sent to one of the museums in Germany. Responding to a question, Mr. Datu said that he thought we were not at present in a position to adjudge whether the Eskimo were related to the cave dwellers as advocated by Dawkins, though their mode of life presents many similarities. Prof. Mason spoke of the richness of information now at our command in Washington, Greenland being represented by Dr. Bes- sels; Cumberband Gulf by Dr. Boas; Ungava Bay by Lucien M. Turner; Point Barrow by Mr. Murdock; and the Western Eskimos by Mr. Dall. He also called the attention of the Society to the great amount of invention wrapped up in an Eskimo harpoon. Hitherto students had been satisfied with speaking of harpoons with- ees ened e Ng INTERES Eee iis yer ANTHROPOLOGICAL SOCIETY. 107 out specifying the variety; but Mr. Murdoch’s own collection con- tained three types: lances, darts, and harpoons. Of lances there were three kinds, the whale, the walrus, and the deer lance. Of darts there were several varieties, all carried by the throwing stick, among them the bird or pronged dart (with or without side prongs), the feather dart, the float dart, the bridle or martingale dart, and the harpoon dart. Of harpoons Mr. Murdoch could exhibit several varieties. The most interesting was the retriever. The Eskimo standing on the edge near thin ice shoots the seal in the water, and after breaking a channel with the ice-pick on one end, launches the whole implement at the animal, holding on to a line attached to the harpoon. By this means he could draw the dead body to the thick ice. Mr. MurpDocu, in answer to a question of Dr. Bessels, said the seal-nets appear to have never been made from whalebone. Nets of this material with small mesh are used for taking whitefish, &c. The seal-net is a comparatively modern invention. Nikawaalu, an intelligent middle-aged native, full of tradition, says ‘* Adrani (be- yond the memory of man now living) there were no nets and they killed seals with the spear (tna) only.’”’ No work that requires hammering or pounding on wood must be done during the whaling season, and even rapping with the knuckles on wood is bad. They asked us to leave off work on our block-house in the spring of 1882, saying it would drive off the whales. The whaling was a failure that season. Mr. Murpocu also stated the following myths : A’sélu, the mythical dog, was tied toa stake. He gnawed him- self loose, and went into the house where he found an Eskimo women, with whom he had sexual intercourse. From this woman sprang the human race. A ‘“‘doctor’’ starting on a fishing trip in the fall gave tobacco to the dead man at the cemetery, breaking off tiny bits and throwing them into the air. When he arrived at the river he also gave to- bacco in the same way to the demon 7Zwéfi-a, saying ‘‘Tutfia, Tu- ffia, I give you tobacco! Give me plenty of fish.”’ They said the aurora (kidlya) was dad, that there was danger of its striking a man in the back of the neck and killing him. Con- sequently, in coming to and fro from the village after dark in twos or threes (they never dare go alone), one carries a drawn knife or dagger to thrust at the Aurora and drive it away. Frozen dogs’ excrement thrown at the aurora will also drive it off. np cee — meen cece 108 TRANSACTIONS OF THE During a bright aurora the children especially sing to it, some- times nearly all night, performing a stamping dance, with the fists clenched. The song has many verses, with the same refrain. The first verse, as follows: *“ Kidlya ke! Kidlya ke! A yana, yana, ya! Hwi, hwi, hwi, hwi!” EIGHTY-SEVENTH REGULAR MEETING, Dec. 16, 1884. Major J. W. Powe LL, President, in the Chair. The Secretary of the Council announced the election of Admiral Thornton A. Jenkins, U. S. N., Mr. John Murdock, and Mr. Lucien M. Turner as active members of the Society. The Curator presented a report showing the receipt of seventy- three gifts, comprising books, papers, and pamphlets, as follows: GIFTS. From the Direcror.—Second Annual Report of the Bureau of Eth- nology. 1880-81. Major J. W. Powell. Washington. 1883. Pp. 487. 8°. Illustrations and plates. From Mr. Gro. F. Bracx.—British Antiquities; their present treatment and their real claim, By A. Henry Rhind. Edinburgh. 1885. Pp. 47. 8°. —— Notice of a collection of flint implements found in the neigh- borhood of Fordoun, Cincardineshire. Rev. James Brodie. Pp. 5. —— On certain beliefs and phrases of Shetland Fishermen. Arthur Laurenson. Pp. 6. —— Did the Northmen extirpate the Celtic inhabitants of the Hebrides in the 9th century? Capt. F. W. L. Thomas, R. NOS BR p:35: —— Notice of a collection of flint arrow-heads and bronze and iron relics from the site of an ancient settlement, recently discovered in the Culbin Islands, near Findhorn, Morayshire. Hercules Linton. Pp. 4. Notes respecting two bronze shields recently purchased for the museum of the Society, and other bronze shields. Wm. T. McCulloch. -Pp.4: ANTHROPOLOGICAL SOCIETY. 109 From the Director.—Notes on Medieval ‘‘ Kitchen Middens’’ recently discovered in the monastery and nunnery on the Island of Iona. John Alexander Smith. Pp. 14. Note of a fragment of a Rune-inscribed stone from Aith’s Vol. Cummingsburgh, Shetland. George Stephens. Pp. 6. Letter to the Schoolmasters of Scotland, from the Society of Antiquaries. Edinburgh. 1860. Pp. 13. — Note on a cist, with an urn, discovered at Parkhill, near Aberdeen, in Oct., 1881. Wm. Ferguson. Pp. 4. Notes on some stone implements, &c., from Shetland. John Alexander Smith. Pp. 9. — — Notice of the discovery of a massive silver chain of plain double rings or links at Hardwell, Berwickshire. By the Hon. Lord Douglas. With notes of similar silver chains found in Scotland. By John Alex. Smith. Pp. 7. Notes on the Antiquities of the Island of Tiree. J. Sand. Epes Notice of a sculptured stone, bearing on one side an inscrip- tion in runes, from Kilbar, Island of Barra. Dr. Geo. Ste- phens. Pp. 4. Notice of a Cranium found in a short cist near Silvermoor, Carstairs Ianarkshire. D. R: Rankine. Pp. 3. Notice of an underground structure recently discovered on the farm of Mickle Kinord, Aberdeenshire.. Rev. J. G. Michie. Pp. 3. Notice of shell-mounds at Lossiemouth. E. G. Duff. Pp. 2. Notice of urns in the museum that have been found with articles of use or ornament. Joseph Anderson. Pp. 16. Notice of a hoard of bronze weapons and other articles found at Monadh-Mor, Killin. Charles Stewart. Pp. 5. Notice of a flint arrow-head in the shaft, found in a moss at Fyvie, Aberdeenshire, with notes in illustration of the manu- facture of arrow shafts with flint tools. Joseph Anderson. Pp: 6: Notes on the character and contents of a large sepulchral cairn of the bronze age at Collessie, Fife, &c. Joseph Anderson. - Pp: 23. — Notes on the contents of shell-heaps recently exposed in the Island of Coll. Donald Ross. Pp. 2. Notice of ancient graves at Doudan, near Ballantrae, Ayrshire. John Carrick Moore. Pp. 3. Donations to the museum. Francis Abbott. Pp. 3. — On the presentation of national antiquities and monuments in Denmark: | J:J. A. Worsaae. Pp. 15. '/ 110 TRANSACTIONS OF THE From the Direcror.—Notes of some recent excavations in the Island of Unst, Shetland, and of the collections of stone vessels, implements, etc. ‘Thomas Edmonston. Pp. 5. —— Note of a donation of four sculptured stones from Monifieth, Forfarshire. James Neish. Pp. 8. —— Notes of the sculptured caves near Dysart, in Fife, &c. Miss C. Maclagan. Pp. 14. —— Notice of the discovery of two sculptured stones, with symbols, at Rhynie, Aberdeenshire. Miss C. Maclagan. Pp. 3. — Notice of excavations in Cannis, in Strathnaver, Sutherland- shire, &c. John Stewart. Pp. 5. From Prof. L. Srizpa.—Anthropologische Untersuchungen am Becken lebender Menschen. PaulSchréter. Dorpat. 1884. Pps 83. From the AurHor.—H. Fischer. On stone implements in Asia. Worcester, Mass. 1884. From the AurHor.—Dr. H. F. C. Ten Kate. Quelques obser- vations sur les Indiens Iroquois. Pp. 5. From Revue @’ Anthrop., de Parts. ——- Sur la synonymie ethnique et la Toponymie chez les Indiens de l’Amérique du Nord. Amsterdam. 1884. Pp. 11. [Reprinted from Trans. Roy. Acad. Sci. Amsterdam. ] —— Variétés. Notes sur l’ethnographie des Zufii. Pp. 3. — Quelques observations ethnographiques recueillies dans la presqu’ile Californienne et en Sonora. Pp. 6. Sur Quelques Cranes de l’Arizona et du Nouveau Mexique. Pik ; (Extrait de la Revue ad’ Anthropologie.) —— Matériaux pour servir a l’Anthropologie de la presqu’ile Cali- fornienne. Paris. 1884. Pp. 19. [From Bull. Soc. d’Anthrop. ] From the AurHor.—Alph. de Candolle. Hérédité de la couleur des yeux dans l’espéce humaine. Geneva. 1884. Pp. 23. [Ext. Arch. des Sciences Physiques et Naturelles. ] From the AurHor.—Baron Joseph De Baye. Sujets décoratifs au Régne Animal dans!’industrie Gauloise. Paris. 1884. Pp.8. [Ext. Mem. Nat. Soc. of Antiquaries of France. ] From the AuTHor.—Adrian de Mortillet. Premier décade palé- oethnologique. Paris. 1881. Pp. 11. Deuxiéme décade paléoethnologique. Paris. 1882. Pp. 15. ANTHROPOLOGICAL SOCIETY. Lin From the AurHor.—Heinrich Fisher. Le Précurseur de l’ Homme. 1884. (L’Homme, No. 13.) Evolution des espéces, évolution des mots. (L’ Homme, No.20.) Further remarks on Nephrite. Verhandl. Berliner Anthrop. Gesellschaft. 1884. Pp. 2. Correspondenz-Blatt. June, 1884. Containing note on a Nephrite Axe, from Brazil. From the AurHoR.—Elmer R. Reynolds. Memoir on the Pre- Columbian shell-mounds at Newburg, Md., and the aborigi- nal shell-fields of the Potomac and the Wicomico rivers. Copenhagen. 1884. Pp. 22. From Proc. Cong. Amer. Copenhagen. 1883. | From the AurHoR.—Juan Ignacio de Armas. La Tabula de los Caribs. Estudios Americanistas, I. Habana. 1884. Pp. 31. | Read to the Soc. Anthrop. Havana. ] From the AurHor.—Protass Chandra Roy. The Mahabharata. Calcutta. Parts g-11, inclusive. From the AuTHor.—A. B. Meyer. Ein Zweiter Rohnephritfund in Steiermark. Vienna. Pp. 12. —— Uber Nephrite und ahnliches Material aus Alaska. Dresden. EOG4.: (Eps 21. — Ein neuer Fundort von Nephrit in Asien. Dresden. 1883. Ep: 16. — Ueber die namen Papua, Dajak und Alfuren. Wien. 1882. Bp: 18: Bemerkungen iiber Nephrit. Breslau. Dr. H. ° Traule. EOOAES spond. From the AurHorR.—Henry Phillips. On asupposed Runic inscrip- tion at Farmouth, Nova Scotia. Philada. 1884. [From Proc. Am. Phil. Soc’y. | From the AurHor.—Heinrich Fischer. Nephritfrage und sub- marginale (sub cutane) Durchbohrung von Steingerathen. Berlin. 1884. Pp. 4. [Verhandl. Berliner Anthrop. Ges- ellschaft. | From the AutHor.—C. C. Jones. The Life and Services of ex- Governor Charles Jones Jeakins. Memorial Address. At- lanta. 1884. Pp. 56. From the AurHor.—G,. A. Colini. Osservazioni etnografiche sui Givari. Rome. 1883. Pp. 47. [From Royal Lincean Acad. | From the Instirure.—Transactions of Vassar Brothers’ Institute and its Scientific Section. Poughkeepsie, N. Y. 1883-84. Wioleoe wp. 166. From the Commisston.—Bulletino della Commissione Archzeologica Comunale di Roma. Rome. 1884. Pp. 138. 112 TRANSACTIONS OF THE From the Society.—Boletino da Sociedade de Geographia de Lis- boa. 1883. 4ser. Nos. 8, 9. | From the ComMitrEE.—Mittheilungen des Komite der Geographi- schen Gesellschaft von Bern. Oct., 1883. Pp. 8. From the Sociery.—VI. Jahresbericht der Geographischen Gesell- schaft von Bern. 1883-84. From the INstirure.—Rep. of the Am. Archeol. Institute for 1884, at Boston. Cambridge. 1884. From the Company.-—Bulletin of the Library Company of Phila- delphia, for July, 1884. From the Sociery.—Bulletins de la Société d’Anthropologie de Paris. Jan.—Mar., 1884. Proc. and Coll. Wyoming Hist. and Geol. Soc’y, Wilkes- Barré, Pa. 1858-84. — The Manuscripts of the Earl of Ashburnham. (Remarks of American Newspapers.) 1884. Pp. 23. From the Insrirure.—Bulletin of the Essex Institute. Vol. 15. Nos. 1-9, and Vol. 16, Nos. 1-6. From the Socrery.—Bull. Société de Geographie de Paris. 1, 2, 3 Trimestre. 1884. — Compte rendu of the Society. Nos. 10-13, 15-17 of 1884. / Archivio per l Anthropologia e la Etnologia. Firenze. 1884. eo — > XLV siege: Publications of the Imper. Russian Geograph. Soc. St. Peters- burg. 1884. XX, Pts. 2,-4. / Report Imper. Russ. Geograph. Soc. for 1883. St. Peters- iy burg, 1884. | Bollettino della Societa Geografica Italiana. Roma. 1884. | Pts. 1-7, 9-10, inclusive. J From the Musrum.—Sixteenth and Seventeenth Annual Report of the Peabody Museum. 1884. Vol. III. Nos. 3, 4. On motion of Prof. Warp, the thanks of the Society was voted fat for these valuable documents. Mr. W. H. Hotmes read a paper entitled ‘‘ ORIGIN AND DEVEL- nh OPMENT OF FORM AND ORNAMENT IN CERAMIC ART.”’ ABSTRACT. The material for this paper was derived chiefly from the native | ceramic art of the United States. The advantages of this field, as compared with that of the classic Orient, is apparent when it is remembered that the dawn of that art lies hidden in impenetrable ee ANTHROPOLOGICAL SOCIETY. 113 shadow, while ours is in the light of the very present. The princi- ples involved in this native art are applicable to all times and to all _ kinds of art, as they are based upon the laws of nature. Ceramic art presents two classes of phenomena of importance in the study of the evolution of esthetic culture. These relate, first, _ to form, and, second, to ornamentation. _ Form in clay vessels embraces useful shapes, which may or may not be ornamental, and zsthetic shapes, which are ornamental and may be useful; also grotesque and fanciful shapes, that may or may _ not be either useful or ornamental. The shapes first assumed by ; vessels in clay depend upon the shape of the vessels employed at the time of the introduction of the art, and ornament is subject to similar laws. Form may have three origins: First, adventition or accident; second, imitation of natural and artificial models ; third, invention. In the early stages of art the suggestions of accident are often adopted by men, and are thus fruitful sources of improvements and _ progress. By such means the use of clay was discovered and the ceramic art came into existence. The accidental indentation of a mass of clay by the foot or hand, or by a fruit or stone, while serv- ing as an auxiliary in some simple art, may have suggested the -means of making a cup, the simplest form of a vessel. In time the potter learned to copy both natural and artificial models with facility. The range of models isat first, however, very limited. The primitive artist does not proceed by methods identi- cal with our own. He does not deliberately and freely examine all departments of nature or art and select for models those things most suitable to convenience or agreeable to fancy ; neither does _he experiment with the view of inventing new forms. What he at- tempts depends almost absolutely upon what happens to be sug- gested by preceding forms, and so narrow and so natural are the processes of his mind that, knowing his resources, it would be easy to closely predict his results. _ The elements of ornamentation are derived chiefly from two -sources—from the suggestions of incidents attending manufacture, and from objects, natural and artificial, associated with the arts. The first articles used by men in their simple arts have had in “many cases decorative suggestions. Shells are exquisitely embel- lished with ribs, spines, nodes, and colors. The same is true toa somewhat limited extent of the hard cases of fruit, seeds, &c. These 8 114 TRANSACTIONS OF THE decorative features, though not essential to the vessel, are never- theless an inseparable part of it, and are cast or automatically copied by a very primitive people when similar articles are artificially pro- duced. In this way a vessel acquires ornamental characters long before the workman learns to take pleasure in such details or con- ceives a desire beyond that of simple utility. Artificial utensils have astill more decided influence upon ceramic decoration. The constructional features of textile vessels impress themselves upon the plastic clay in manufacture, and in time are repeated and copied for the pleasure they give. The simple ideas of embellishment thus acquired are constantly subject to modifica- tion. A single radical gives rise to a multitude of forms. The causes that tend to bring about these results are worthy of the closest study. They may be sought in the material, the form, and above all the constructional characters of the object decorated. Prof. Mason followed Mr. Holmes with a short résumé of Prof. Hartt’s theory of the rationale of ornament, published in the Popular Science Monthly, for January, 1884. Prof. Hartt maintains that the explanation of the shape and color of beautiful objects is to be found in the eye itself. Weare pleased with certain lines because they bring the muscles of the eye into easy and health- ful play. Prof. Mason said that there was in his mind no conflict between the methods pursued in Mr. Holmes’ paper and Hartt’s theory— a little differently stated and expanded. Mr. Holmes traces the outline of that natural movement which aboriginal potters had followed. Hartt sought to show the subjective side and how it was that the primitive artist had chosen some forms and rejected others. If we will examine our own handwriting we shall find that the same two sets of facts present themselves. On the one hand we have books, papers, correspondence, copy-books, and many other printed and written things ever before our eyes. On the other hand there is the set of bones, muscles, and sinews, called the hand, with its great variety of lengths, thicknesses, flexibilities, so compounded in each as to give rise to a really individual hand. A man’s handwriting is the movement of all these mobile parts in the lines of least resist-_ ance for each part, but always in the effort to conform to the pattern. Now the natural world, with its shells, horns, gourds, carapaces, reeds ; the mechanical world, with its shapes in hard material; the | z gy ‘ ANTHROPOLOGICAL SOCIETY. 115 curves and twists of spirals, cycloids, and circles innumerable, are all the patterns of things, the letters, the copy-book. The clay and the potters’ tools are pen, ink, and paper. The lines of least resistance are partly in the hand of the potter, indeed, as Mr. Holmes has shown; they are partly in the muscles of the eye, as Mr. Hartt has said; but further back than all this is the force of usage and inherltance. If we hang a hat intentionally on a peg eleven times, the twelfth time it will hang itself up. This is the universal and beneficent law of the passage of painful voluntariness into semi-automa- tism which follows the frequent repetition of any act whatsoever. _ We are pleased with certain muscular movements which have been oft repeated. There is no doubt, therefore, that the eye accustomed to certain outlines, the brain accustomed to certain consecutive impressions, are pleased with that which has become semi-automatic and habitual. We know that such tendencies are strengthened by inheritance, for we have here the application of a universal law i of heredity. Dr. Frank BAKER said that Hartt seemed in some respects to ig- nore certain physiological laws in discussing the movements of the _ eye, and to have too little considered inventive geniuses. The source of art must be sought for in the brain that controls the eye; in the association of nerve cells that prompt the movement of mus- cles. Taste may follow and accept suggestions from natural forms, but art is not imitative, for, having its source in invention, it gives something nature does not. , Mr. Frank H. Cusuine said that Hartt apparently did not try to ascertain what the eye might develop, but having certain forms _at hand reasoned therefrom. ‘The speaker had found in his studies _ of ceramic art in the southwest that decoration in basketry had _ long preceded that of pottery, and that the resulting forms might _ be generally attributed to adventition, and taste might have its principal source in the environment, E1GHTY-EIGHTH REGULAR MEETING, January 6, 1884. Major J. W. Powell, President, in the Chair. The Secretary of the Council made the following announcements : The election of Dr. J. H. Yarnall, as an active member of 116 TRANSACTIONS OF THE the Society ; and George H. Black, Edinboro’, Scotland, and Hermann Ten Kate, The Hague, Holland, as corresponding members. Mr. H. N. Bares read a ‘‘Memorandum concerning certain Mounds in Pontotoc county, Mississippi,’’ visited by J.. M. Pollard, Esq., of Louisiana. No abstract. Mr. O. T. Mason read a paper prepared by DANIEL G. BRINTON, ‘¢On THE PROBABLE NATIONALITY OF THE MOUND-—BUILDERS.’’ Dr. Brinton said: Further reading on the subject, and also the observations during a trip made to the principal monuments in Ohio, have confirmed me in the opinion that we need not go any farther than the Southern tribes to find the modern representatives of the mound-builders. Since I wrote the article on the mound- builders, Mr. Horatio Hale has published his suggestive paper, in which he adds strength to this position by linguistic evidence. It would probably be hasty to point to any one of the Southern » tribes as being specifically the descendants of the nation who con- structed the great works in the Scioto and Miami Valleys. The evidence is ample that nearly all the tribes of the Gulf States and Lower Mississippi were accustomed to throw up works of similar character and often greater magnitude. They were of radically diverse languages, but nearly in the same plane of culture. The Natchez, the Taensas, the Choctaws, the Creeks, the Cherokees, and others might put in equal claims. The last mentioned asserted that they once lived in the Upper Ohio Valley, and that they built . the Grave Creek and other mounds, and they are borne out in such claims by various historic data. With regard to the Shawnees, it has not been sufficiently recog- nized by writers that their name in the Algonkin dialects is not a national appellation, but a geographical term. It means simply «« Southerners,’’ and in its earliest employment bore no special ref- erence to the tribe whom we call Shawnees. It first appears in a map drawn in 1614, intended to show the Dutch colony around New Amsterdam. In this the ‘‘Sawannew’”’ are located as inhabit- ing the whole of Southern New Jersey; whereas the Shawnees, as we understand the term first came to the notice of the New York colony in 1692. On this map it simply means ‘‘ Southern rivers”’ with reference to the position of New York harbor. : | Z| i 4 e , ANTHROPOLOGICAL SOCIETY. LE? By dialect, tradition, and political affiliation the Shawnees were a northern tribe who moved south at no very remote period. Their language, according to the Moravian missionaries, was closer to the Mohegan than to the Delaware, Nanticoke, or other Southern Algon- kin dialects. By tradition they at one time were a branch of the Mohegans on the Hudson, and it was to them that they returned when driven from their towns in Carolina and on the Tennessee river. The name of their principal clan, the Pequa or Pick-e-weu, is said by Heckewelder to be the same as that of the Pequods, of Connecticut, and he relates that the Mohegans told him that the two were of the same family. | If we can depend upon this evidence, and there is no reason why it should be rejected, the ‘‘ Pre-historic Shawnees’’ are to be looked for in New York and New England. Ihave no idea whether this will correspond with Professor Thomas’ views, but I should be gratified to hear that we had reached identical conclusions from in- dependent study of the subject. The four clans of the Shawnees were assembled in Ohio, but in Pennsylvania I have not found evidence of any but the Pequas, who lived in the valley that still, bears their name in Lancaster county. Their state of culture was nowise ahead of that of the Delawares. They had®one clan named Chilicothe, and three of their settlements in Ohio bore this name, but while there they had not the slightest knowledge or tradition about the ancient earthworks, as we are as- sured by the Rev. David Jones, who went out to teach them Christian- ity in 1772, and who, I think, is the earliest writer who calls attention to the remarkable remains in Southern Ohio. Prof. Cyrus THomas read a paper entitled ‘‘ Prehistoric Shawnes, from Mound Testimony.”’ Before reading his paper, Prof. THomas said, referring to the pre- ceding paper, that he had recently written a letter with a view to procuring an exploration of Pontotoc county, Miss., without any positive knowledge that ancient remains existed there, and that the paper of Mr. Pollard was in verification of the speaker’s assumption that such remains would be found in that vicinity. Mr. C. C. Royce, at the request of the Society, read an extract from a former paper of his on the origin of the ‘‘ Shawnees.”’ President PowEtt said that the papers read before the Society during the past two years seemed to establish the fact that the FRAC BEN IE? 118 TRANSACTIONS OF THE mound-builders were Indians, and that many Indians built mounds. While small burial mounds were frequent and widely distributed, the larger mounds and earthworks with circumvallation—once probably crowned with palisades—were confined to narrower limits. The old theory that attributed these remains to an extinct high grade of civilization seemed to be well nigh abandoned. Dr. Grecory said that he had held to the old theory until he had become convinced of its error, and described a large mound, some fifty feet high, that he visited in Minnesota, which gave conclusive evidence of its comparatively recent structure. Depressions were still to be seen close about the foot of the mound, from whence material had apparently been taken to aid in forming the mound. SEVENTH ANNUAL AND E1GHTY-NINTH REGULAR MEETING, January 20, 1885. Major J. W. PowE Lt, President, in the Chair. A The Secretary of the Council announced the election of John Addison Porter and H. L. Reynolds as active members of the Society, and advised the Society of the death of Dr. Henri Martin, of Paris, France, and Dr. R. J. Farquharson, of Des Moines, Iowa, corresponding members of the Society. The Treasurer then submitted his annual report. On the motion of Col. Ma.urry, the President appointed Messrs. Bates, Baker, and Holmes a committee (composed of members out- side the Council) to audit the accounts of the Treasurer. This session being the time for the annual election of officers, the balloting for officers resulted as follows : PRESIDENT : : : : ° J. W.. POWELL. ROBERT FLETCHER. LESTER F. WARD. GARRICK MALLERY. {OTIS T. MASON. GENERAL SECRETARY : P Sy VieePROUDEEE SECRETARY TO THE COUNCIL . 2 FAS SEEBILY: VICE-PRESIDENTS | i i ANTHROPOLOGICAL SOCIETY. 119 TREASURER Pees | sO) SEN aGORE,. CURATOR . : : 3 : 3 W. J. HOFFMAN. (CYRUS THOMAS. J. O. DORSEY. ! WwW. H. HOLMES. ADDITIONAL MEMBERS OF THE COUNCIL 1H. H. BATES. | FRANK BAKER. | DAVID HUTCHESON. The President announced that the next meeting would be public, _ to which the members of the Biological and Philosophical Societies _ were specially invited for the purpose of listening to the annual address of the President. : NINETIETH REGULAR MEETING, February 3, 1885. In accordance with previous announcement the Society assembled in public session to listen to the annual address of the President, there being present on special invitation the members of the Bio- — logical and Philosophical Societies and other friends of the Society. Dr. J. C. WELLING introduced to the audience President J. W. PoweELL, who delivered an address entitled ‘‘FRom SAVAGERY To BARBARISM.’’ At the close of the address, on motion of Mr. Mason, a vote of thanks to the speaker was unanimously passed. The Secretary of the Council announced that the Saturday - course of lectures under the auspices of the Anthropological and Biological Societies had been arranged, and that programmes of the ; first part of the course were ready for distribution. 120 TRANSACTIONS OF THE NINETY-First REGULAR MEETING, February 17, 1885. Prof. Oris T. Mason, Vice President, in the Chair. A report from the Curator was then read, including a list of publications received since his last report : Bull. Library Co. Philada., No. 14. Jan., 1885. Bol. Soc. Géog. Ital. Ser. II, Vol. IX, Fac. 12. Dec. ’84, ’85. Mahabharata, Calcutta. Pt. XII, XIII. Bul. Soc. Géog. de Paris. Vol. X, Tim. 4. 1884. Compte Rendu, de la Soc. de Géog. de Paris. Nos. 18, 19. Eléments d’Anthropologie. Par. Alphonse Cels. Bruxelles, vol. I, 1884. 8vo., pp. 202. Les Habitans de Suriname. Prince Roland Bonaparte. Paris. 1884. Royal 4to , pp. 227, plt. 60. Bull. Essex Institute. July—Dec., 1884. Bull. Soc. d’Anthrop. Paris. Fasc. 2, 3. 1884. Journal of Proc. of the Victoria Institute, London. XVIII, No. 7o. 1884. Grammaire Elémentaire. Quichée, L. Aleman. Pamph. Quelques observations sur les ossements de notre musée. Mari- court et Vinet, Senlis, 1884. Ymier.. “Parts 53/05 1984. Bull. Soc. Géog. de Lyon. Sept.—Dec., 1884. On the Cuspidiform Petroglyphs, etc. Dr. D.G. Brinton. Pamph. Xinca Indians of Guatemala. fe a ce Impressions of figures on a ‘‘ Meday”’ stick. Dr. D. G. Brinton. Pamph. Memoirs Soc. Antiq. de la Morinie, St. Omer. 1 Vol. 1883. Bul. Russ. Géog. Soc. Also 2 pamphlets. Mem. Soc. d’Hist., etc. Beaune. 1883. Verein fur Erdkunde zu Halle a.S. Mittheilungen. 1884. Imp. Soc. of the Friends of Nat. Hist. Anthrop. and Eth. Muscar. 3 vols. 1884. Bull. Hungarian Geog. Soc. Budapest. Complete for 1884. On motion of Prof. THoMAs, a vote of thanks was passed to the various authors and societies from which these gifts were received. Mr Bates, from Auditing Committee, reported that the com- mittee had duly examined the accounts of the Treasurer for the past year as reported at the annual meeting January 20, and had found the same correct. ANTHROPOLOGICAL SOCIETY. 121 Prof. Warp read a paper entitled ‘‘ MoraAL AND MATERIAL PROGRESS CONTRASTED.”’ One of the most obvious and frequently observed facts that lie upon the surface of modern society is the persistence of social evils in spite of the progress of discovery and invention brought about for the purpose of relieving them. The actual removal of social evils constitutes moral progress; the discovery of principles and the invention of appliances calculated to remove them constitute material progress. It is these two forms of social progress which it is proposed to consider in this paper. As to the degree to which moral progress has taken place and is taking place in society, there are wide differences of opinion. Some sanguine minds imagine it to be very rapid, but this is generally due to a confusion of unrelated phenomena. ‘They either confound material with moral progress directly, or they confound the pre- dominance of cherished religious beliefs with that of morality, or the establishment of favorite forms of government with that of justice and liberty. Others, and this is much the larger class, deny that any moral progress has ever taken place or is now taking place, and maintain, on the contrary, that there has been moral degener- acy, and that the worid is growing constantly worse. In so far as these are merely influenced by the survival of a tradition very preva- lent among early races they may, perhaps, be left out of the account. Many of them, however, disclaim such influence and base their con- victions on the facts of history and the condition of society as it is. But such also must be set down as extremists, incapable of duly weighing the evidence from all sides of the question. A highly respectable class, embracing many of the finest minds of the present period, see no hope except in the gradual change of the constitution of the human mind, to be brought about through hereditary influences and the slow developmental laws by which man has been at length raised above the brute. They deny the power of intelligence to improve the moral condition of society, and regard the ethical faculty as entirely distinct from the intel- lectual. <‘‘It is,’? said Mr. Herbert Spencer to an American reporter, ‘‘essentially a question of character, and only in a sec- ondary degree a question of knowledge. But for the universal delusion about education as a panacea for political evils, this would 122, TRANSACTIONS OF THE have been made sufficiently clear by the evidence daily disclosed in your papers.’’ And ina private letter received after his return to England, relative to views which I had expressed, he re-asserts this doctrine, and says: ‘‘As you are probably aware, and as, in fact, I said very emphatically when in America, I regard social progress as mainly a question of character and not of knowledge or enlighten- ment.”’ In the light of all these somewhat conflicting opinions, if we were to rest the case altogether upon authority, we should at least be compelled to admit that the real moral progress of the world has been extremely slow, and that it is imperceptible even in the high- est stages of enlightenment. Such, too, seems to be the lesson of history and of observation. It is only when we contemplate long periods of history and contrast the present or the recent past with the remote past that an advance can be perceived in the moral con- dition of mankind. Yet, when such an historic parallax is once secured, the fact that moral progress actually has taken place is dis- tinctly seen. To read the history of England and compare the acts committed a few centuries ago by men of our own race, with what any one can see would be done now under like circumstances, is sufficient to demonstrate that improvement has been going on in both individual and public morals. Making every possible allow- ance for all that is bad in the present social system, no one could probably be found candidly to maintain that it is inferior, from the moral point of view, to that of the middle ages or even of the six- teenth century. Modern kings, bad as they are, no longer put their sons to death to prevent them from usurping their thrones, and the sons of kings, however profligate they may be, do not seek to dethrone their fathers. When Rome was at its zenith, it was no more than every one expected that the great armies of Cesar and Pompey, on their triumphal return from victorious fields, would turn their arms upon each other for the mastery of the empire. And I have heard those familiar with Roman history predict, at the time when the vast armies of Grant and Sherman, far outnumbering the Roman legions, were marching victoriously through different parts of the South, that the last grand struggle of the war would be between the Army of the Cumberland and that of the Potomac— forgetting that since the age of the Cesars there had been moral progress sufficient to render both the leaders and the soldiers incap- able of such an act. ANTHROPOLOGICAL SOCIETY, 128 Political opponents are no longer beheaded on the accession of a new party to power; neither are they thrust into dungeons nor exiled, as formerly. Persecution for opinion’s sake has practically ceased. Scientific men are no longer burned at the stake, like Bruno and Servetus, nor made to recant, like Galileo and Buffon. Witch- craft has dwindled into innocent palmistry, and heresy is only pun- ished in a few backward communities by a mild form of social ostracism. Imprisonment for debt has been abolished, and the Fleet and the galleys are things of the past. Primogeniture and entail have disappeared from most codes of law, and trial by jury has been instituted in the most influential states. The slave trade has been suppressed wherever European powers have acquired su- premacy, and slavery has been abolished in all the most enlight- ened countries. Vast public and private charities have been insti- tuted, and societies for the prevention of cruelty to children and to animals receive the sanction of law. And finally a great moral crusade, with a display of far more zeal than knowledge, is being preached against the admitted evils of intemperance. There has, then, been some moral progress within the historic period, but, considering the amount of moral agitation, it has been slight. It is the characteristic of moral progress that it takes place rhyth- mically. In the achievement of moral reforms there are always experienced partial and temporary failures, prolonged interruptions, serious reverses, and constantly recurring waves of reaction, so that at no time has it been possible for the candid observer to perceive that any certain advance was being made. The-ground continually being lost is never appreciably less then the ground gained, and none but the ignorant, the blinded, or the oversanguine see much cause for congratulation. In the great ocean of moral action so nearly equal are the tidal ebbs and flows that only the stoi- cal philosopher whose vision ranges back into the remotest past or forward unto the remotest future, with utter contempt for the transient present, can perceive the minute increments of secular change—much as the geologist, provided with his vast time- measures, perceives the changes that are slowly taking place on the coasts of continents washed by the tides and waves of the appar- ently changeless ocean of waters. Such is moral progress in society. With it we may now compare, or rather contrast, the other form of social progress which we have distinguished as material. i74 TRANSACTIONS OF THE Material progress results entirely from mental and manual labor laid out on invention and construction. Moral progress is a pro- duct of feeding, material progress one of thought; the action ac- companying the former is called conduct, that accompanying the latter is called Zador. Conduct is confined to the avoidance of inter- ference with liberty of action in others. Labor is directed to the production and distribution of the objects of desire. Moral action aims at the restraint or control of the forces of society, of human desires, prejudices, and passions. Invention and labor aim at the control and utilization of physical and mechanical forces, and of such vital processes as underlie pastoral and agricultural pursuits. The contrast in the essential nature of these two classes of social phenomena is thus seen to be very wide, but it is not greater than is the difference in their mode of operating. We have seen that moral progress always takes place by rhythmic action, and that its secular slowness is not due to its own inherent sluggishness, but to the fact that only the algebraic sum, of its many fluxes and refluxes can be counted. In material development nothing of the kind is found. Every step isa permanent gain. Every mechani- cal invention is an inalienable contribution to the material pros- perity of society. If the particular device first produced becomes at length obsolete, as is usually the case, it is only because from it as a basis better devices, involving additional principles and doing more efficient service, have grown up. And such, in fact, is the nature of ail inventions. But the machine is only the material embodiment of intellectual conceptions, and it is these that lie at the foundation of all material progress. Indeed, much of this progress has consisted of such conceptions without any definite materialization. Of this class is all real knowledge of nature, only part of which can be directly applied to man’s material ameiioration. Every natural truth acquired proves advantageous, and the progress of pure science, like the progress of invention, has been steady though not uniform, never intermittent nor ryhthmical. The misguided forces of feeling which underlie the fluctuating moral activities of society have often resisted the progress of science, have seriously checked it, some- times apparently arrested it during long periods, but they have never succeeded in forcing it backwards. The same is true of art, espec- ially of practical or useful art. This fact is strikingly exemplified in the interest attaching to the few alleged ‘lost arts’’, as though ANTHROPOLOGICAL SOCIETY. 125 it were next to impossible for a single art to be wholly lost. And so it is. Every age has known all that was known by the age that preceded it and has added something to this. Every age has pos- sessed all the arts of the age that preceded it, and has added some- thing to them. And this in spite of the most prolonged moral reactions, such, for example, as that of the middle ages. If we examine the arts, implements, utensils, and weapons of any of the lower tribes, as, for example, the Esquimaux of the extreme north, we shall find that they represent a high degree of skill, a large amount of inventive thought, and a considerable real knowl- edge of the laws of nature and of physical forces. A comparison of many such tribes also shows that these devices represent, like those of the most enlightened peoples, a series of steps in invention answering to our improvements, But a better implement is never abandoned for a poorer one, and here, as in the higher races, pro- gress has been constant—always forward. We may therefore safely conclude that the present high state of material advancement in scientific nations is the result of a series of intellectual conceptions materially embodied in art, stretching back into that dim past when the club embodied the highest mechanical principles known to man. Such is material progress, and such are the essential particulars in which it so widely differs in nature and method from moral pro- gress. But, great as these differences seem and are, there is a point toward which they may be made, hypothetically at least, to con- verge. This point is where the human activities are conceived as natural phenomena, and their control through the normal inventive process is contemplated as a true art. If the power to do this shall ever be attained, there is no reason why morals may not progress in the same manner and at the same rate as material civilization. The true interpreters of human history now understand that it is to material progress, z. e., to science and art, that what moral progress has actually taken place is indirectly due. It is knowledge of the universe enlarging the mental horizon that has dispelled the bigotry of pre-scientific ages and thrown the mantle of charity over indi- vidual conduct and: opinion. And it is the arts of intercommuni- cation that have really civilized the modern world, as compared with the world ‘before their introduction. But since morals, from the point of view of social science, are concerned exclusively with the welfare of men, and since material progress, both physical and intellectual, is also directed exclusively a .“ ee ma Ss -— 148 TRANSACTIONS OF THE if any, they follow; and what results, immediate and ultimate, flow from them. I conceive that these inquiries are best pursued in connection with mechanical inventions. A parallel inquiry might be pursued in respect to inventions in the broader sense. In fact the study of savage society is, to a certain extent, such an inquiry. Before proceeding to the consideration of the subject, it is im- portant to call attention to the various meanings and shades of meaning of the word ¢zvention, which we have such constant occa- sion to employ. A late writer on Patent Law* refers to this in his opening chapter as a source of much confusion, since, as he remarks, it is not uncommon to find the word used in different senses in the same paragraph, even in the same sentence. He distinguishes four meanings of the word : (x) The mental act of inventing. (2) The thing invented. (3) The fact that an invention has been made. (4) The faculty or quality of invention. It is scarcely necessary to illustrate these significations, since on a little reflection they become apparent. We may say of the sew- ing machine, ¢¢ was the invention of Howe, referring to the mental process which produced it ; we may say it zs @ great or useful tnven-— tion, meaning the machine itself; we may say the invention of tt revolutionized the manufacture of clothing, in which we mean the fact that it was made; and we may say of any particular form presented to us, there ts no invention in it over some earlier form, in which we refer to the quality of invention as distinguished alike from the mental act, the concrete product, and the historical fact. In view of all these uses of the word and not to overload it further, I shall venture to suggest a new one to designate the study of invention. This study has not yet perhaps developed itself as a true science, though it appears to possess all the elements of a science. As a study of growing interest it is worthy of a name of its own, | and, with all deference, I submit to the Society, as an appro-. priate name worthy of adoption the word Lurematics.~ This should include the study not of arts, machines, laws or insti- * Merwin. Patentability of Inventions. Boston. 1883. + E5onua, Aninvention. If the Greeks had been in the habit of philoso- phizing about inventions, they would have had an adjective, ‘evpnpadtinos, and the word would have found its place in English long ago, as has ereka. ANTHROPOLOGICAL SOCEKETY. 149 _ tutions in themselves, but of them all in respect to their methods | of growth and the means by which they have been’ developed _ and are still developing. This is a study which many are pur- _ suing with eagerness and delight; and the need of a name for it _ clearly separating it from other kindred studies is every day more ’ apparent. | It is my purpose to present in this paper a brief chapter in this science, following out and perhaps to some extent repeating some of __ the thoughts expressed in a paper presented to the Society two years ~_ago,* in which I discussed the nature of the earliest human inven- _ tions, the original germs out of which they grew, and the steps and processes by which they were evolved or elaborated. Speculative ‘as some of my suggestions may have been as to the nature of these _ primitive inventions, nevertheless the nature of the processes by _ which they were made is so inherent in all arts that it cannot be regarded as in any degree speculative. Possibly the inven- _ tions pointed out were not actually the first contrived by man, but whatever were the first, the way described is beyond doubt the way in which they were arrived at. I propose in the course of this paper to discuss the development __ of the stone hatchet in its most finished form; but before doing so it is necessary to inquire into the nature of invention and some of _ the general principles it follows. Lying absolutely at the bottom of such principles are the following postulates, the A BC of Eurematics: Given any artificial implement or product, we must assume—rst, that there was a time when tt did not exist; 20, that before it existed there must have been a creature capable of producing it; and 3d, that | such creature before producing it must have been conscious of needing it, or must have had use for tt. _ There can be no orderly discussion of the genesis of any art iF: without recognizing the truth of these postulates at every step. - Questions may arise upon resultant or collateral propositions, but, | | admitting all that can possibly be claimed for accident as an ele- ment in invention, these propositions are not to be questioned. _ They are fundamental, and no logical consequences that flow from them can be evaded. The first proposition, that before any artificial product existed * An Inquiry into the Origin of Invention. Vol. u, Trans. Anthrop. Soc., Washington. 1883. ae a, 150 TRANSACTIONS OF THE there was a time when it did not exist, is not startling, and may be passed over for the second: before it existed there was a creature capable of producing it. This is as much as saying that no product of art came into existence simultaneously with its producer, and seems to be no more startling a proposition than the first ; and yet, if I rightly interpret the ideas of most writers, they have failed to grasp even so common-place a truth. The third proposition, that the producer must have been conscious of needing the product, or must have had use for it before producing it, is not at first sight so obvious. In fact I believe the failure to grasp this truth is a great source of error and misconception among many writers. No one, however, who has given any thought to the nature of invention, has failed to observe that every step in the mechanic arts has grown out of a pre-existing want. Not neces- sarily out of a pressing need. Invention now-a-days does not wait for the call to be so urgent that waiting can be no longer. Long before this stage necessities are anticipated, and the means by which they are overcome often do not become indispensable till the very habits they engender make them so. Illustrations of this are all around us. ‘The sewing machine, the reaper, the telephone—what could we do without them? And yet in our own generation we have done without them all. They have themselves created the conditions which have made them indispensable. But none of them came by accident. They have been, every one, the fruit of years of toil and thought and anxiety on the part of those who saw, what few clearly comprehended, the imperfection of the means employed to do the daily work of mankind, and studied to produce better means. This is the history of steam, of electricity, of railroads, of metal working, of pottery, of every art that has a recorded his- tory. Prevision and calculation are so truly elements in the growth of all known arts that in asserting their universality we incur no more risk than did Newton in asserting the law of gravitation. What then, it may be asked; is the place due to accident in inven- tion? Notwithstanding a popular belief that many if not most of the great inventions have been the fruit of accident, it may be asserted that the contrary is true. Fortuitous circumstances, trifling unforeseen incidents, have in many cases doubtless suggested expe- dients which have led to the consummation of great inventions. It was an accident—the result of his poverty—which led Senefelder to write on a stone slab his family wash-bill, and so led to the inven- ANTHROPOLOGICAL SOCIETY. Let tion of the lithographic process; but the accident did not occur, and could not, till long and persevering pursuit of a method of printing cheap music had brought together the polished stone, the ink, the acid,—all the materials necessary to accomplish the result. Possibly it was an accident which led Goodyear to the use of sulphur for the vulcanization of India rubber; but the accident, if such it were, did not occur till years of expense and toil and experiment with a great variety of materials had led the way to it. And the rubber and the sulphur and all the appliances necessary for the ex- periment were ready to his hand, all accumulated in the pursuit of his lifelong purpose. Such experiences are common, and familiar illustrations of them are found, as for instance, in the lives of Pal- issy, the Huguenot potter, and William Lee, the inventor of the stocking loom. In these the element of accident enters in some degree into the consummation of the invention; but in every case it is such accident as might have occurred a thousand times over with- out result to other men whose minds were not intent upon the inven- tion. Lamps had swung for centuries in the Italian cathedrals, and men had idly counted their oscillations as they kept time to the tedious delivery of generations of dull sermons ; but the isochronism of their swing, if observed at all, was not regarded till Galileo came. ; The true and only field that philosophy can concede to accident in invention is that it supplements and sometimes abridges the labor, calculation, and time of the inventor. To a man filled with a steadfast purpose, all his senses alert to every means chance or calculation may present to accomplish it, the most trifling incident may furnish the clue, which has fled from him like an zgas fatuus. To another the same chances may come and go continually without result. And while it cannot be said that accident has no place in invention, it must be conceded that its place is completely subordi- nate to other elements. Great inventions have been the fruit of accident in the same sense and to the same degree that a ripened peach is the fruit of the rude blast that shakes it from the bough. It is important in a discussion like this to keep clearly in mind the difference between invention proper and discovery. ‘The function of the latter is to bring to light the material facts, and the natural laws, which the former applies to useful purposes ; and in respect to discovery, the element of chance, of accident, is im- 152 TRANSACTIONS OF THE portant. The progress of scientific discovery is marked at every milestone by the revelations of accidents, which the thoughtful mind of the inventor did not apply to practical ends till long after- wards, when the need had arisen. If it was an accident that led Galileo to the discovery of the isochronous oscillation of the pen- dulum, it was not till fifty years afterwards that this discovery was applied to regulate the movement of a clock. ‘The phenomena of electricity that accident may have revealed to Galvani and Volta, are the basis of inventions that the most active minds of this decade are expending their best energies upon. It cannot be denied that in discovery accident has played an important part; but the more this fact is considered, and the more we consider the true function of discovery, the more strongly do we find the proposition con- firmed that improvements in the arts are not the result of chance but of intelligent efforts to supply conscious needs. Hence I shall regard this proposition as conceded, and I pass to another. . (4) Lvery human invention has sprung from some prior invention or from some prior known expedient. Inventions do not, like their protectress, Pallas Athéne, spring forth full grown from the heads of their authors. This suggestion needs no argument when made re- garding any of the modern inventions. Every one of them is seen by the most superficial observer to be built upon or elaborated out of inventions and expedients previously in‘use. It is only when we go back of these and study the expedients and appliances out of which they have grown, and whose history is unrecorded, that the proposition I contend for is not obvious. And yet there is not a single one of them which does not when studied exhibit in itself the evidences of a similar substructure. In the process of elimina- tion we go back and back, and find no resting place till we reach the rude set of expedients, the original endowment of men and brutes alike. This is a truth which study more and more confirms, and from it the proposition stated may be deduced as one of the laws of invention. It may be deduced as a corollary to this proposition, but at the same time a fact determinable by independent observation, that the generation of one invention from another is not immediate but always through one or more intermediate steps. The effect of every invention fundamental in its character is first to generate wants be- fore unknown or unfelt. The effort to supply these wants. leads to ee ANTHROPOLOGICAL SOCIETY. 153 new inventions.* These may be quite distinct in their character _ from the original invention to which they indirectly owe their origin. They are related to it only as means to supply some want to which it has given birth. I shall not pursue this branch of the subject. Illustrations will occur to all. There is hardly a branch of industry that has not felt the effect of inventions based upon wants created by the introduction of petroleum, or the general use of the tele- phone. Wood-working, mining, transportation by land and sea all the avocations of men—have felt their influence, have found wants engendered by their use, and improvements have been made to meet these wants. The wants of primitive man were limited, _ and his inventions were accordingly few. As wants increased in number and intensity, inventions multiplied, and the numberless wants of modern civilized life are only paralleled by its numberless arts and expedients. I set it down as a fifth proposition: /yventions always generate wants, and these wants generate other inventions. A sixth proposition is that the ¢xvention of tools and implements pro- ceeds by specialization. ‘This is true to a certain extent of all arts, though perhaps not a universal truth regarding all invention. It results, as will be apparent on reflection, from the last proposition. A single tool may have a great variety of uses, but, if there is a suffi- cient requirement, men will not long be contented with one tool for those uses for which it is least convenient. It will be reserved for that to which it is best adapted, and other forms will be devised better suited for special uses; possibly the parent type may be found inferior for all uses to some of its modified forms, and it may, on the principle of the survival of the fittest, become obsolete. Look‘ at the variety of tools on a joiner’s bench, chisels, planes, saws, each especially adapted for its particular work, but all pointing back to a time when there was but one form of chisel, or plane, or saw. The ‘jack-plane’’ and ‘‘long-jointer’’ may each be made to perform the work of the other, but they do it very imperfectly. The primitive bench plane was like neither, but was the type of a = = Se —————— ——— a ——————=> * A curious instance of this is brought to my attention while writing this paper. In consequence of the expiration of the earlier patents on roller-skates, a great impetus has been given to their manufacture, the result being the exhaustion of the world’s stock of boxwood of certain sizes used for rollers. And to supply the want so created hundreds of people are trying to invent a suitable and cheap substitute for boxwood for this purpose. 154 TRANSACTIONS OF THE both. There is nothing more striking than the variety of cutlery on a well-furnished table. The time is not remote when one knife worn at the belt served the purpose of all these, so far as these pur- poses existed, and of many others; when the table knife was not differentiated from the dagger of the soldier or the tool of the artisan. A man then used one knife to cut out a leather sole, to shape his arrow, to carve his food, and to stab his enemy. Changes in modes of living have led first to the broader specializations ; fashion, caprice, and increasing refinement to others ; till one scarcely dares attempt to enumerate the various forms of carvers and table knives of various sorts differing in form and material, each adapted by some feature for its particular use, and each the result of some degree of invention, with which the tables of Europe and America are furnished. Undoubtedly this process has gone on ever since man became an inventor, and might be illustrated as perfectly, though not so profusely, in the implements and weapons of the savage as in those of civilized men. All study of invention must take account of it. As soon as men began to adapt sticks to their use by artificially pointing them they began to find in them various degrees of hardness, weight, length, and rigidity, qualities fitting them for diverse uses, and as skill and experience were acquired they fashioned them accordingly. Likewise when man had begun to employ flint flakes, and before he had learned to fashion them to his will, he selected from the splinters made by accident or by his own unskilled blows those which served best such diversified uses as he had found out. My seventh proposition, and final one so far as this paper is con- cerned, is that zo art makes progress alone. I venture to assert the universality of this truth from what is seen in the recorded history of all inventions. In the development of the mechanic arts, two or more arts distinct in their nature but having close interdependence make advance pari passu. If one lags the other is necessarily retarded. If one makes rapid progress the other springs forward with quickened impulses. An improved utensil or article of manufacture may be the result of or may lead to improved processes and tools and machines for producing it, or to improved means for its employ- ment. The progress of the steam-engine was long retarded by the imperfection of iron-working machines, since perfect cylinders could not be produced. The progress of electrical invention has neces- sitated the invention of new machines and processes for insulating i i - a A | ( a o | % | : ‘ és x ae Py ois _ ANTHROPOLOGICAL SOCIETY. 155 wire. The introduction of illuminating gas has created a demand for metal tubing, and machines for its rapid and perfect manufac- ture. And so every step in every art is marked by one or more corresponding steps in other arts. These general principles, imperfectly stated as they are, by no means exhaust the study of invention. , They only lie at its thresh- hold. They are among the more obvious laws which inventions follow as they are every day presented to the mind of those who deal with them: so obvious, that I have found myself hesitating as to the value of their presentation in this form; a hesitation which is removed by observing that, so far as writers upon early inventions are con- cerned, they are unnoticed and apparently unknown. Further chap- ters in Eurematics might be devoted to the elucidation of other truths equally generic and universal, but more intricate and therefore less obvious. I might cite for instance the tendency of civilization to convert luxuries into necessaries, true not only of absolute civiliza- tion but of every stage of it or every step towards it. The effect of this tendency upon inventions is marked and positive. I might cite the fact that invention is stimulated by rewards and retarded _ by opposition, which history abundantly illustrates,—eminently the histories of France in the middle ages, of The Netherlands, of Great . Britain, and of our own country. Another proposition might be that the truth regarding biologic evolution—that the type of any species which is to predominate is at its first appearance uncon- spicuous—applies equally to the evolution of arts. Many such propo- sitions more or less recondite might be stated, the adequate discus- sion of which would require a volume; but I can afford to pass them by, as I have not set out upon an exhaustive study. The few propositions considered are enough for the present purpose. I shall now discuss the progress of invention ina single direction, partly as a study in itself, partly by way of illustration of the doc- trines I have enunciated. I have selected the stone hatchet for this purpose because in some of its ruder forms it represents the earliest human workmanship of which any knowledge has come to us, and also because in its rudest form it presents the evidences of being the fruit of long antecedent growth. Further than this I - observe that primitive as it indeed is, and in its highest develop- ment rude and ineffective in comparison with the finished imple- ment of this age of steel, the thoughtful student of invention sees in it the culmination for the time being of human art rather than 156 TRANSACTIONS OF THE the beginning. For the purposes of this paper I regard nothing less than the hafted celt as the finished implement whose genesis I shall attempt to indicate. I assume as the starting point the conclusion reached in my paper before referred to,* that the earliest mechanical process employed by man was the art of working wood by abrasion. This cannot be regarded as proven ; absolutely proven it can never be; but it comes in as a link connecting what must have been in the history of primitive man with what is revealed to us regarding the man of the earliest stone age. This art, or something closely similar to it, appears as the immediate derivative of the original mechanical expedients of man in a state of nature, and of the wants engendered by his human characteristics. Tracing back the art of wood work- ing we find no resting place till we come to the art in this condition. In short the more the subject is contemplated, and from whatever point of view, the stronger appear the probabilities, so strong that to my own mind they are convincing. Starting from this basis, what was the process, what the result sought, what the methods employed to produce it? ; The object sought for was a pike, a strong, rigid, sharp-pointed stick or shaft adapted for use as an offensive and defensive weapon, a want early felt and hitherto imperfectly supplied by chance and nature. The means employed was a rough rock, a coarse sand- stone or mill-stone-grit upon whose exposed surface the wood was rubbed or drawn back and forth until reduced as desired. A tedious — process, but not more so than many of those employed to this day in the arts of savage life. We can imagine men coming from great distances to the inventor of this art with poles on their shoulders to be prepared in the new style. It would not at once be perceived that no special properties attached to this particular rock, that rocks having similar properties and perhaps better suited to the purpose were every where. The mind was dull in grasping the essential fact of the art, and perhaps for ages superstition and fetichism may have been engendered by this very improvement. It is easy to see, however, that it had created a new want, or perhaps intensified the old one. Pikes were liable to be broken, were subject to natural decay. They must be replaced, and new ones were always in de- mand, Their artificial production had increased the number of their * An Inquiry into the Origin of Invention. Vol. II. Trans. Anthrop. Soc. Washington. 1883. ANTHROPOLOGICAL SOCIETY. Loy possessors, and the want of a ready means for the replacement was more widely felt. ‘To the majority it wasa new want. Hence among people widely scattered, more convenient and accessible means were sought for supplying the demand ; and in answer to this want came the discovery, perhaps the result of similar experiences and obser- vations, that gritty rocks every where would yield the same results to similar manipulation by the hands of any one. And a further discovery followed close on the heels of this, that the jagged edges of flints and other hard rocks would by a manipulation but little varied perform the work better and faster than the gritty surface of the sand stones. A stick drawn forcibly over such a sharp edge has its surface scraped from it in thin shavings instead of being merely abraded as heretofore. This important step from abrasion to scraping, which is in fact cutting, was therefore reached before -any cutting or abrading tool had been devised. Reached by slow steps, in answer to a felt want, but a want in no way pointing to it, it was actually the invention of another and quite distinct mechani- cal process. It wasa better process, gave better results, and the weapon and the art of wood working made progress together. We have advanced one step, man now has the notion of the cut- ting edge and its use. But it is part of an immovable bowlder or ledge, not always accessible, and the want of a convenient means always at hand is but partially supplied. The long pilgrimages which had to be taken to the primitive pointer of pikes were at an end, but the journeys though shorter still have to be made. How was the next step, resulting in the production of a portable cut- ting implement, to be accomplished ? It will be seen at once that in the use for a considerable period of the edge of a rock for cutting purposes it will become dulled. Other parts of the rock having exposed edges will be sought, and these will become dull in turn. This dulling process proceeds more or less rapidly according to the material applied to it; and as the harder woods were found to be in all respects more serviceable they were more generally used. We may conceive that at some time by the violent application of a hard piece of timber to an edge some- what thinner tan ordinary, the edge itself instead of being merely dulled is broken off, and to the pleasant surprise of the operator a new edge, sharp and clear, and better than the half-dulled one he had been using, makes its appearance. And he eventually learns that he can at any time produce a new edge by shivering off a piece ; J 158 TRANSACTIONS OF THE of the rock with blows. He is not long in learning that the part broken off has similar edges. If it be large enough to lie firmly he can employ it as he does the parent rock. If smaller, he may hold it firmly with his feet while he manipulates the wood upon it with his hands. Perhaps he can carry it away and use it at the place most convenient to him; when dulled he can shiver it by a blow or two and it is sharp again. And then at last by slow degrees, requiring ages perhaps, one can hardly tell how, but by the continuance of this process, he observes that these splinters struck from the fragment, these fragments of fragments, possess the same cutting edges as the original rock, and in a bit of stone not larger than his hand or his finger he possesses an instrumentality capable of doing all that he and his ancestors have been laboriously doing on the parent rock or clumsy fragment. He learns also that instead of dragging the wood over the edge, he can, with a totally different manipulation, . hold the wood firmly and operate on it with the stone splinter, and the tool is invented.* When I think of man in his primitive condition, as the logical necessities of this subject have compelled me to think of him, help- less, miserable, the prey of beasts, without tools, withouc means of defense except such as he shared with the beasts, and then think of him in the condition to which he is brought in this outline of his inventions, I find it impossible to adequately express my sense of the progress he has made. One effective weapon, its structure im- proved, and skill in its use acquired by generations of experience, and one cutting tool, even in the rudimentary form of an unfash- ioned flake, have separated him incalculably from the condition of his ancestors. His knife or hatchet, as we may henceforth call it, contained within it all the possibilities of the future, but for the present—his present—its capabilities were learned by constant les- sons and with every new occasion. He had no want to which it did not minister. It not only served its first purpose to prepare his weapon, but it became itseifa weapon. It served him to procure and prepare his food, both animal and vegetable, his shelter, his raiment, if he had reached the stage of wanting raiment. Its *It is only by a loose construction of language that this can be called the inven- tion of atool. The tool, a mere flake of stone, had already long existed. The actual invention was an art or process quite distinct from any heretofore employed. The brief and more popular form of expression may be employed with this explanation. See Te a ~ os aioe eH SRE ANTHROPOLOGICAL SOCIETY. 159 acquisition was the greatest step he had taken in invention; and when we regard what has grown out of it, the infinite variety of _ cutting tools, implements, and machines, whose origin we remotely trace to it, and the unnumbered needs they supply, we cannot hesitate to ascribe to it the highest place among all the inventions of all time. If the hafted celt was for the time the culmination of art, this is not less true, of its time, of the flint knife. As in man’s rudest estate he used the expedients with which nature endowed him, _ selecting those best adapted to his immediate purpose, so now out of the diverse forms assumed by flakes and chips, he selects those _ best adapted for particular purposes. He is repeating what occurred in his earliest period, but with new and diversified wants, wider intelligence, and a greater range of material out of which to select. He finds blunt edges give satisfactory results in the old process of scraping wood, but he finds that thinner and sharper edges pene- trate the wood deeper, and remove the superfluous material faster. He finds he can work more deftly, more conveniently, can put a finer point on his weapon, can apply the new tool to all parts of it, can reduce and trim the shaft as well as the point, can even sever _ the growing saplings to obtain his material. He finds that some forms can be made to penetrate and divide the tough skins of beasts, _and carve their flesh. In fact, in whatever direction his necessities _ or inclinations lead him, he finds his knife in some form contribut- ing to his comfort, his protection, and the supply of his wants. The possession of the tool has wrought out his mastery over nature. This culmination in invention is but momentary. It is a mile- _ stone, a breathing place in the history of arts. But the march still goes on, and we find man still searching among fragments for forms adapted to his particular uses, but gradually learning by experience that by well-directed blows he can sometimes produce chips having special forms, and so fitted for special uses. But these are chips and flakes only. There is no attempt as yet at dressing or shaping stone. The rude forms they bear when shivered from the rock, are all that man has yet conceived in the structure of a stone implement. These rude forms seldom appear in our museums. _ They are the scoff of archeologists. They are not distinguish- able from the work of the elements. In fact, the splinters thrown off by frost or fire may have been as readily selected for use as _ those formed by human agency. And as writers have agreed upon 160 TRANSACTIONS OF THE the name faleolthic to indicate the age marked by the first traces of human workmanship in stone implements, we must recog- nize the protolithic age, in which stone fragments showing no trace of such workmanship were the common implements of man- kind. ‘The earliest age of wrought implements could never have come but for such a precursor. ‘The rudest wrought forms did not appear till something of the same nature and used for the same pur- poses, but imperfectly adapted for their performance, had created the need of them and led up to the means for its supply, and the one thing which bore these relations to the earliest recognizable forms of dressed-stone implements was the unformed flake. What were the steps from this form of flint knife, or scraper, or hatchet, to the hafted celt ? I formerly reached the conclusion that the original endowment of man could include no less than the stick and stone for striking and hurling, and the string or withe for tying or binding. In the course of this paper I have traced the synchronous development of the art of dressing wood, and of stone appliances for the purpose. With the advancement of these it is not to be supposed any former art or expedient was lost. On the contrary it is to be presumed that progress in them had been made corresponding to that we have been following. The club was better fashioned ; approved forms of hurling-sticks may have been discovered and come into use. Greater skill may have been acquired in the use of the hammer-stone, and judgment in the selection of suitable forms either for crushing, or for splitting, and with more convenient hand-grasp. The flexi- ble vines and strips of bark, with which primitive man lashed his frail shelter, his successor may have improved by rudely twisting the fibres or strands, or have supplemented by other materials, notably, after he had acquired the use of the flint knife, by strips of skin and animal tendons. ‘The inventory of his possessions then would embrace the club and pike, each clearly specialized, the hammer- stone, not formed by art but selected, the stone knife, and strings of various materials. The pike, the hammer stone and knife may have been of many forms. Now it will be seen that these elements may be brought together in various ways so as to accomplish a variety of results, the elements in every case being a stick, a stone, and a string to bind them together, and the difference in result de- pending on the particular form of stick and stone. For instance the heavy end of a club is made heavier by lashing to it a hammer stone—result the mace. ‘The pike is improved by securing to it a ANTHROPOLOGICAL SOCIETY. 161 _ pointed flake of flint. A flint flake too small for the hand is made } effective by fixing it to a piece of wood, making a knife or dagger. _ A heavier sharp-edged fragment secured to a handle adapting it for striking, becomes the axe or hatchet. What immediate incidents or needs led to any of these combinations, I do not propose to guess. It is enough to have shown that at a period when man was as yet unlearned in respect to any dressing of stone beyond knock- ing off rude splinters from a rock, he may have had in his posses- sion the means to produce, and was fully capable of producing, such implements and weapons as I have named. This being true, the same wants which might at any period of his history have led to their production may without violence be presumed to have done so _ then. ‘They are in the line of his acquired arts, and the necessary links between these and the arts he is yet to acquire. Whether these various combinations were made prior to actual _ working of flint it would be idle tospeculate. It is more likely that _ neither preceded the other. While man was finding out how to use his possessions by bringing them together in new combinations, he was naturally improving them all. Having found the flint and other rocks of similar texture so far obedient to his power that they could be shattered, and new and useful forms produced, having ac- - quired uses for these forms, having learned the purposes to which a sharp edge could be applied, and that a fresh one could be pro- duced by knocking off the dulled one—it followed in due course, from experience, to form the new edge with less violent blows, with more judgment and dexterity, and, as the advantage of special forms _ became apparent, with a view to bringing it as close as possible to such forms. And all this time the old art of reducing by abrasion had not been lost; applying it now to the stone as finer and finer chipping suggested and provoked the desire for a smoother edge, the celt appeared, polished at first on its edge only, afterwards on its entire surface. There was no dividing line between the palee- - olithic and neolithic ages. If separated at all, it is by a broad zone through which the implements of both are found side by side. _ Neither was there any step from the finished celt to the hafted im- plement. The essential step, that of securing a stone in some form _ toa handle, had been taken long ago. Lest it might be suggested that in order to sustain a theory regard- _ ing the developement of the arts, I have myself been led to invent _ Steps in art that were never known to man, it is worth while to remark II SSS SSeS Sa al x ye) . oI ———————————— a a ee ae = —— ee 162 TRANSACTIONS OF THE that none of the steps I have set forth are imaginary. All of them are in existence and in use yet, in their appropriate places, often amidst the completest appliances of modern mechanic arts. If the primitive man sharpened a stick by rubbing it over a rough grit, he used the same means an artist employs to-day to produce a fine point on his pencil, and the same by which we sharpen all cutting tools. The scraping tool is one of the ordinary provisions of a joiner’s outfit; but the use of a bit of broken glass is more comnion still. As the edge becomes dulled by use, the glass is simply broken and two fresh edges are formed. ‘This is universal in civilized life, and a curious instance of it in savage life has just been brought to — light by the Rev. Lorimer Fison, in his pamphlet on the Nanga or Sacred Stone Inclosure of Fiji, in which he relates often having | seen ‘a mother shaving her child’s head with a bit of glass, and biting a new edge on the instrument when it became dull.’” These original arts have never been lost. Probably it is a general truth © regarding mechanic arts that no one of them once commonly acz _ quired is ever again lost. It may be laid aside for a time or sus- pended, but it revives in some form; and I venture to think that much of the eloquence that has been expended upon the ‘‘ The Lost Arts’’ has resulted from a very imperfect acquaintance with those that exist. It is apparent that every step in the progress that has been recited | resulted in an improvement in man’scondition. ‘The first improved weapon, club or pike or missile, was equivalent to.so much greater — strength of arm or length of reach. It augmented man’s superior- ity over the brutes; it made his life less precarious; it put the means of securing food, shelter, and covering more fully within his power. His environment, to which he had in his primitive con- dition been completely subject, he now could to a certain extent control, could subject to himself. The first improved means of fabricating a weapon, the first tool or mechanical process, accom- plished these results in an increased ratio. The step that made the cutting tool the possible possession of every man, which made the knife even in its clumsiest form a common tool, did for the whole race what the earliest steps did for a limited number, and made this amelioration general. The increased number of forms and varieties of tools and weapons, growing out of the diverse and manifold — wants they were adapted to supply, were each steps in the better- ment of his material condition, each an indication of progress; man’s advance towards civilization, slow as it must have been, was ANTHROPOLOGICAL SOCIETY. 163 marked off step by step by the advances he made in his mechanic arts. The more he became independent of nature and capable of forcing her into his service the more time and inclination he found for the perfecting of his implements; and the more he perfected his implements the more capable he became of subduing nature. _ And this interaction has never ceased, it goes on to-day. But the ' achievements of to-day are not the conquest of savage beasts, nor the solution of the problems of food and shelter and warmth. We are overcoming time and distance; we are conquering the barriers | of sea and mountain; we are finding out the more hidden forces of nature, and subjecting them. ‘The fruit of our inventions is not seen | in rough flakes of stone lashed by sinew to rude hafts, but in the / mighty movement of the railway train thundering across the conti- / nent, or the click of the telegraph as London talks with Calcutta. | And every step in progress has been a step in the improvement of _man’s condition from the first to the last. And so it shall be in the future. Artists depict the genius of invention as a voluptuous female [ figure, in various stages of imperfect attire, attended by innocent | boys in their primitive nudity, and with gear wheels and anvils and other rough equipments of the artisan in ill-assorted proximity. | This is a feeble conception. The genius of invention is not a crea- “ture of delicate mould, but one of brawn and sinew. His voice is no gentle song of lullaby, but comes to us in the deafening clatter ' of Lowell looms and the roar of Pittsburgh forges. Mighty and _ beneficent and responsive to human wants—this is the kind of song _he sings in his rugged rhythm: i “IT am monarch of all the forges: I have solved the riddle of fire; The amen of Nature to cry of man Answers at my desire. I grasp with the subtle soul of flame The heart of the rocky earth; And hot from my anvils the prophecies Of the miracie years leap forth. I am swart with the soot of my furnace, I drip with the sweat of toil; My fingers throttle the savage waste, I tear the curse from the soil; I fling the bridges across the gulfs That hold us from the To-Be; And build the roads for the bannered march Of crowned humanity.” i % be Pe * ie | | —— 164 TRANSACTIONS OF THE DISCUSSION. Mr. P. B. Pierce, discussing the paper, referred to some of the curi- | osities or phenomena of invention; for this science of eurematics, like every science, has its attendant phenomena. Indeed, that invention is a science is demonstrated by its attendant phenamena. | Invention is not creation; the first deals with matter direct; the latter supplies that with which invention deals. The student of eurematics, giving heed to what the history of his science has to teach, soon discovers the principles of the great law of evolution. Let him inspect the almost humanized giant that bears its load of living freight daily from Washington to New York in less than six hours, and what does he find, except that since the days of Watt the process of selection or differentiation has been intelligently going on! The clumsy, the crude, the ruder elements have been — rejected; the harmonious, the simple, the efficient, and stronger have been utilized. Increment by increment complexity has given | way to simplicity, until the perfected machine stands forth as we know it ; that is to say, the machine we are pleased to call perfect, the selected excellence, the swmmum bonum, of all that experience and long use have taught to be best of those that have preceded it. Each inventor has contributed his mite, and lo! the grand result! _ And its maker, man, is he not perfecting himself along with that_ dull matter upon which he works and in which he achieves! Is he | not, as described by the poet, The heir of all the ages in the foremost files of time ? Is not matter reflex? Is Frankenstein in reality the monster his author protrayed him to be? Will not the science of eurematics, when once fairly beset by the persistent inquisition of scientific study and investigation, open wide the door of the temple that is even now ajar, and permit its disciples to enter and make intelligent conquest, under a full knowledge of its laws, where until now they have only been permitted to make occasional, random captures from the vestibulum, as it were? The thousand forces of nature lie hidden within grasping distance ; but for lack of systematic study they elude our clutch, escaping from our wiliest approaches as the thistle down upon a puff of air. This may not always remain so. The Lilliputians bound Gulliver with straws; let us ply Nature with pitiless interrogation till she yields ANTHROPOLOGICAL SOCIETY. 165 us the fullest knowledge of all her laws. For this is eurematics in ' its broadest significance ; it is encompassing the laws of nature with _ material form and compelling matter to do the bidding of psychi- cal energy. But evolution does not account for all. There is in invention a synchromism that is almost mysterious. The present is the grand harvest time of all the seed that has been planted by the generations that have preceded us; but why the thoughts of inventive minds appear to move in batallions, all aiming at some common objective, seems at first view almost inexplicable. A given function is demon- _strably demanded; a hundred minds set themselves at once, in all parts of the world, to produce the means for its satisfaction. With the almost universal diffusion of information that has come about - with the art of printing, even in all languages and tongues, aided _ by the telegraph and the telephone, who fails to know in all the _ broad earth to-morrow morning what the chiefest want of to-day has been? Within one month’s time from the great flour-dust explosion in the mills of Minneapolis, in May, 1878, there were over thirty inventions made for preventing the recurrence of such an accident, and all practically effective. Many of them were almost if not quite identical, although made by men _ having _ no knowledge even of each others’ existence, and in all parts of _ the world! So quickly, when a pressing want is known, is the ib means supplied for staying the same. When the-science of inven- tion has been perfected, and every want has been given a means for its satisfaction, will not the highest type of invention then be the . discovery of a new want, latent in the human soul, but never before _ developed? _ Another feature of invention noticeable to an attentive observer 1s the isolation in which an important discovery is often times set. The evolution of the automatic grain binder of this day, from the | sickle of Egypt and the Orient, is plain and familiar. ‘To one who _ has witnessed the devouring knives of this latest type of human genius, hungrily levelling the yellow harvests of the great northwest and tossing the bundled sheaves backward in serried rows upon the stubble, and contrasts its action with that of the reaper in the time of Boaz, how far apart they seem separated! Aad so they are, wide centuries apart. But the quick mind of invention anticipated the _ want almost in:the earliest day of the reaper. In the year 1854 two | men invented, perfected, reduced to practice, and patented the rn abn ee =e 166 TRANSACTIONS OF THE completed machine whose opportunity for use did not come until twenty-five years later. Like lonely islands arising out of the reced- ing waters of an ocean, such inventions, though they may after- wards be the highest lands of great and fundamental enterprise, are lost for want of use. Although pioneers their inventors are without remuneration because they are too far in front of the needs of the | world. The world itself is ever unready; the lines of necessity are conservative and strenuously refuse to make room for the new appli- cant for favor, even though full of promise. Mr. Wn. H. Bascock said no one, on glancing over our patents, can fail to observe how many of the inventions covered by them are obviously outgrowths of those already in existence rather than contrivances adapted to meet any real want. A man sees a partic- ular machine, or a description of one, and forthwith proceeds to devise a similar but slightly different construction. Thus there are, — for example, more than three thousand patents on car couplers, most of them varying from others in a trivial degree, very few of them being actually in use. Se. Mr. Murpocu read a paper on the ‘‘ SINEW-BACKED Bow OF THE EskiMo.”’ All the branches of the widely-distributed Eskimo race now live in regions which are either treeless or else deprived of the ash and other elastic woods fit for making bows. ‘The fact that the bow was / in general use among the Eskimo previous to the introduction of firearms is one of the arguments that they have not always lived in j the regions which they now inhabit, but have moved on from places where wood suitable for the purpose was to be obtained. As they gradually became settled in their new homes, probably before the f different branches were so widely separated from the original stock . as they are now, and as the simple bows which they had brought with them from their old country became worn out and had to be ; replaced, it was necessary to find some means of giving the needful elasticity to the brittle spruce and fir, frequently rendered still more brittle by a long drift on river and sea, followed by exposure . tosun and rain on the sea-beach. In some places even driftwood is so scarce that bows were made of no better inaterial than dry antler. The elastic sinews of several animals, especially of the rein- deer, furnished the means desired of making an efficient weapon out of these poor materials. This is not employed in the way used by the Indians of the plains, who- glue a broad strip of sinew along the { ANTHROPOLOGICAL SOCIETY. 169 back of the bow, but is braided or twisted into a cord the size of stout whip-cord, which is laid on in acontinuous piece so that there are numerous strands of the elastic cord. running along the back of the bow so as to be stretched when the bow isdrawn. The simplest or, so to speak, ancestral pattern of sinew-backed bow from which the types now in use are evidently derived is one in which there are a dozen or twenty of such plain strands along the back, running around the ‘“‘nocks’’ and held down by knotting the end of the cord round the handle. Bows of this form, slightly modified by having the cords somewhat twisted from the middle, so as to increase their tension, are still to be found in Baffin Land, where many of the arts seem in a lower state of development than among the Greenlanders, on the one hand, or the Western Eskimos, on the other. Let us now consider how in course of time the different branches of the Eskimo race have improved upon this simple invention. Along the well-wooded shores of southern Alaska, from the island of Kadiak nearly to the mouth of the Yukon, where there is plenty of fresh, living spruce, they have chiefly increased the efficiency of the bow by lengthening and broadening it, and have paid but little atten- tion to the sinew backing, contenting themselves with slightly in- creasing the number of strands, wrapping them round with a spiral seizing, which prevents them from spreading, and occasionally add- ing a few more strands which only extend part way to the tips, being secured by hitches round the bow. This makes the bow a little stiffer in the middle than at the ends, where less strength is required. On the other hand, the people who live along the tree- | @less shores of the Arctic Ocean, from the Mackenzie river to Ber- ing Strait, can obtain no wood better than the dead and weathered spruce which the sea casts upon the beach. Consequently, all im- provements in the weapon were of necessity confined to the sinew backing, which has developed into a marvel of cemplication and perfection, while the bow itself is rather short and not especially stout. Starting as before with a loop at one end of the cord strands are laid on from nock to nock until there are enough of them to give sufficient stiffness to the ends of the bow. ‘Then the cord goes only to within 6 or 8 inches of the tip and is secured round the bow by hitches, sometimes a very complicated lashing of as many as a dozen half hitches alternately in opposite directions, and returns to a corresponding place at the other end, where it is similarly hitched. In this way strand after strand is laid on, each pair shorter ret Ne ~~ — ~ fi a 170 TRANSACTIONS OF THE than the preceding, and the backing constantly thickening towards the middle of the bow. When sufficient strands are laid on they are separated into two parcels, and with a pair of very ingenious little bone or ivory levers are twisted from the middle into two tight cables, so that the twist of the cords adds to the resistance to be overcome in drawing the bow. ‘These are prevented from un- twisting by a lashing at the middle which runs through the cable and round the bow in a sort of figure of 8. The end of the cord then makes a tight spiral seizing round the bow which not only keeps the backing from slipping, but serves to distribute the strain — evenly and keep the bow from breaking. ‘This pattern is probably the ultimate development of the sinew-backed bow. Not only is it difficult to imagine making a more perfect weapon from the mate- rial, but attention will no longer be paid to possible improvements ina weapon which is rapidly falling into disuse. As would naturally be supposed the region about Norton Sound, where the tribes of the Arctic coast meet those of Bering Sea, is a debatable ground, where bows of the two types described are found side by side, along with others partaking of the characteristics of both. If now we cross to St. Lawrence Island, we find Eskimos depending solely on drift- wood, who employ another and most pecular modification of the original type. They have lengthened the ends of the bow so that the original simple backing hardly reaches within a foot of either end, while these ends are bent up as in the Tartar bow, and separate backings are stretched across these bends. The Eskimos of the mainland of Siberia, who have long main- tained direct intercourse with the St. Lawrence Islanders and with the Eskimos of the Arctic coast by way of the Diomedes, show the evidence of this intercourse in the pattern of their bows, using either the peculiar St. Lawrence tpye, or purely American bows of the Arctic pattern, or weapons which curiously combine characteristic features of both. DISCUSSION. Mr. Bares said that the little blocks which are tied into the concave outer limb of several of Mr. Murdoch’s bows are some- thing more than a mere stiffener of the wooden portion. It is a truly mechanical expedient, to give efficiency to the tension mem- ber of the combination, which is the sinew. It not only acts as a strut to increase the leverage of the tension member, which is the ANTHROPOLOGICAL SOCIETY. Lt function of the strut in all combination trusses, but it shortens and straightens the line of the sinew, thus bringing its rigidity and elasticity into full play. In this, as in so many other instances of merely experimental evolution, the best results of abstract theory are arrived at. NINETY-SEVENTH REGULAR MEETING, May 19, 1885. Vice-President Dr. RoBerT FLETCHER in the Chair. The Chair announced the death of Count Giovanni Battiste Erco- lani, of Bologna, Italy, a corr€sponding member, after which a memoir was read by Dr. E. R. Reynolds, who, in the course of his remarks, presented to the Society an embroidered Italian flag and a number of scarfs and mourning wreaths contributed by various scientific societies of Italy, of which Count Ercolani was a member. The Chair remarked that Count Ercolani would probably be remem- bered principally for his discovery that the circulation of the blood was known and promulgated prior to Harvey. Dr. Matruews then read a paper upon ‘‘ THE CUBATURE OF THE SKULL,’’ which was followed by some inquiries by Dr. Frank Baker and Mr. Bates, leading to further remarks by Dr. Matthews. ABSTRACT. The lecturer discussed briefly the various methods which have been employed in the volumetric measurement of the cranial con- tents and pointed out their various defects. He then described a method which he had recently devised and employed in the Army Medical Museum at Washington, After recording the weight of the skull it is varnished inside with thin shellac varnish, applied by means of a reversible spray apparatus. Artificial or accidental orifices are closed with India- rubber adhesive plaster. ‘The foramena and fossz are filled with putty. The skull is wrapped in a coating of putty an inch or more in thickness, which renders it water-tight. It is filled with water by means of a special apparatus in forty-five seconds and emptied: in flfteen seconds. The rapidity of this manipulation in conjunction with the varnishing prevents soaking into the sinuses and the undue measurement of water which does not pertain to the a LZ TRANSACTIONS OF THE cranial cavity. The water is poured into a measuring glass of 2,000 Cc. c. capacity, and lycopodium is scattered on the water to define the true surface. The putty is taken from the skull; the latter is cleansed and placed in a dry, warm apartment until by slow evaporation it is reduced to its former weight and consequently to its former capacity. Then it is measured a second time to verify the results of the former measurement. Hitherto anthropologists have chiefly employed solid particles, such as shot or seeds, in the cubature of skulls. Water had been tried by former experimenters without success, and abandoned—the objections to its use being considered insuperable. The lecturer, however, considered that by his method he had overcome the chief difficulties. Although the method new and still susceptible of improvement, it is thought that the results—an average of one cubic centimetre difference between the first and second measurements— have not been excelled. One of the bronze skulls of Professor J. Ranke, of Munich, was exhibited, and the claims of the inventor, as published in ‘‘ Cor- respondenz-Blatt der Deutschen Gesellschaft fiir Anthropologie Ethnologie und Urgeschichte,’’ September, 1884, were quoted. The lecturer had found one difficulty in using the artificial skull which Prof. Rauke had not suggested. The cavity varied greatly in capacity with changes of temperature. For a perfect conformity of measurements not only was it necessary that the water used should be certain specified heat, but the bronze skull, the various vessels used, and the atmosphere of the apartment in which the experiments were made should be of a corresponding temperature. At 4° centigrade the lecturer obtained for the bronze skull, estimating both by weight and measure, a capacity of 1,220. ¢., while at 14° centigrade he obtained 1,240c.c. In no case did he get a result as high as that engraved on the skull, wz: 1,255.6c.c. The skull was presented by Prof. Rauke to the Army Medical Museum. A paper followed from Dr. Baker upon ‘‘ THE PRINCIPLES OF INTERPRETATION OF BRAIN, Mass, AND Form.’’ This paper was illustrated by numerous charts. ANTHROPOLOGICAL SOCIETY. 173 FROM SAVAGERY TO BARBARISM. ANNUAL ADDRESS OF THE PRESIDENT, j-aW. POweLe, Delivered February 3, 1885. It is a long way from savagery to civilization. In the attempt to delineate the progress of mankind through this long way, it would be a convenience if it could be divided into clearly defined stages. The course of culture, which may be defined as the development of mankind from savagery to civilization, is the evolution of the humanities—the five great classes of activities denominated arts, institutions, languages, opinions, and intellections. Now if this course of culture is to be divided into stages, the several stages should be represented in every one of the classes of activities. If there are three stages of culture there should be three stages of arts, three stages of institutions, three stages of language, three stages of opinions, and three stages of inteilections. Three such culture stages have been recognized by anthropologists, denominated Savagery, Barbarism, and Civilization. But they have been vaguely characterized and demarcated. Savagery has been considered a low stage of culture, barbarism a middle stage of culture, and civilization a high stage of culture. Ina brief address it is not practicable to set forth the essential characteristics of the whole course of culture ; and it is intended on this occasion simply to characterize Savagery and Barbarism, and to define the epoch of transition. To this end it will be necessary to set forth the charac- teristics of savage art as distinct from barbaric art, and the nature of the change; to explain savage institutions and barbaric institu- tions, and how the lower class developed into the higher; to set forth briefly the characteristics of savage language and barbaric language, and the origin of the change; to show the nature of the opinions held by savages and the opinions held by barbarians, and to explain the reason of the change from one to the other; and finally to explain savage and barbaric intellections, and to show ”—— ———2s 174 TRANSACTIONS OF THE how savage methods of reasoning were transformed into barbaric methods of reasoning. The most noteworthy attempt hitherto made to distinguish and de- fine culture-stages is that of Lewis H. Morgan, in his great work enti- tled ‘‘ Ancient Society.’’ In it these’ three grand periods appear — Savagery, Barbarism, and Civilization—each with sub-divisions. Morgan recognized the importance of arts as the foundation of cult- ure, and his ‘‘ ethnic periods,’’ as he calls them, are based on art development. With him, Savagery embraces all that stage of human progress extending from the beginning of the history of man, as dis- tinguished from the lower animals, to the invention of pottery. Barbarism then succeeds and extends to the invention of the alpha- bet. He adds that among some peoples hieroglyphic writing takes the place of phonetic writing, and civilization begins at this time. He then divides each of these periods into epochs which need not here be considered. In some of Morgan’s works he connects the evolution of institutions with the development of arts, but to an imperfect degree, and without explaining their interdependence. He also, at different times, hints at the relation of linguistic devel- opment to arts; but he considers mythology to be too vague to afford valuable data for this purpose. The scheme here presented differs from Morgan’s in placing the epoch of demarcation between Savagery and Barbarism later on in the course of human culture; and it is proposed to characterize the stages, not by arts alone, but by all the fundamental activities of man. The next most noteworthy attempt to define culture-periods is that by Lester F. Ward, one of the Vice-Presidents of this Society. In hisscheme there are four stages of social progress, or social aggre- gation, viz: ‘¢rst. The solitary, or autarchic stage ; 2d. The constrained aggregate, or anarchic stage ; 3d. The national, or politarchic stage; and, 4th. The cosmopolitan, or pantarchic stage,”’ Ward seeks to establish these as veritable stages on the basis of institutionsalone. They are treated as stages of social aggregation, and not as culture-stages. The first, second, and fourth are purely hypothetic. I have elsewhere stated my reasons for not accepting the first and second stages; but, whether real or imaginary, they antedate all possible objective knowledge of the condition of man- porebieem inn Ate oy alte AY, He a ro eS + ore ANTHROPOLOGICAL SOCIETY. iS kind. The fourth stage is a prophecy, and though I believe that his prophetic vision is clear and that he sees a true picture of the future, it need not be considered here. His politarchic stage em- _ braces all the course of human culture with which science may at present deal on a basis of observed fact, and it is this stage which is here divided into three parts—Savagery, Barbarism, and Civili- zation. ; EK. B. Tylor, also, has classified the stages of culture as Savage, -Barbaric, and Civilized. The lowest or savage stage he defines ‘as that in which man subsists on wild plants and animals, neither till- ing the soil nor domesticating creatures for his food.’’ He considers that men arrive at the barbaric stage when “they take to agricult- ure,’’ and pass from the barbaric to the civilized stage by acquiring the art of writing. In relation to the epoch which separates Savagery from Barbar- ism, Tylor does not greatly disagree with Morgan. Morgan uses as a criterion of Barbarism as distinguished from Savagery the acquisition of the art of making pottery; Tylor, the acquisition of agriculture. But usually the two arts have been acquired at about the same time, and it seems probable that the conditions of life brought about by agriculture were necessary properly to develop ceramic art. If this is true, agriculture is the more fundamental. If stages of culture are to be established on conditions of art ‘development alone, the invention of agriculture should doubtless be accepted as the plane of demarcation between the two lower stages ; but if the culture-stages are to be based upon characteristics derived from all the classes of human activities, the separation between Savagery and Barbarism must be placed somewhat later on. Such a plane of demarcation has been adopted by me for a number of years, both in my publications.and in the discussions and exposi- _ tions informally presented to this Society from time to time; and it is my purpose to make a somewhat fuller exposition of my method. All the grand classes of human activities are inter-related in such a manner that one presupposes another, and no one can exist with- out all the others. Arts are impossible without institutions, lan- guages, opinions, and reasoning; and in like manner every one is developed by aid of the others. If, then, all of the grand classes of human activities are interdependent, any great change in one must © _ effect corresponding changes in the others. The five classes of activi- 176 TRANSACTIONS OF THE ties must progress together. Art-stages must have corresponding institutional, linguistic, philosophic, and psychic stages. Stages of progress common to all the five grand classes of human activities may properly be denominated Culture-Stages, and such culture-stages should be defined by characterizing all these activi- ties in each stage. This I shall attempt to do, but in a brief way- ARTS OF SAVAGERY. The very early history of mankind is covered by obscurity, through which conjecture peers at undefined forms; but when that portion of human history which rests upon a solid basis of known facts is reached, a succession of arts is discovered, each of which challenges attention and admiration. In the lowest stage of culture which comes within human knowledge, men understand the use of fire, and we may pretty fairly guess how they have learned of its utility. This early man also uses tools and implements of stone, bone, horn, wood, and clay, and by them adds skill to his hands. It is the genius of savage intellect that makes the hand more than a paw, that makes it an organ for the fashioning and the use of tools and implements. At this earlier stage man also knows how to protect himself from winds and storms and the cruel changes of the seasons by providing him- self with clothing and shelter. He has also explored and experi- mented upon the whole realm of the vegetal world, and discov- ered in a more or less crude way the properties of plants, so that he knows those which are useful for food, the woods that are useful for fire, and the fibres that are useful for woven fabrics. In the same period of culture man has learned that the animals of the land and the waters are useful for food, and has discovered crude methods by which to kill and ensnare them, and has invented many simple instruments for hunting and fishing. Such is the state of the , industrial arts in that stage of culture which we call Savagery. INSTITUTIONS GF SAVAGERY. Institutions relate to the constitution of bodies politic, to forms of government, and to principles of law; and in describing Savag- ery we must characterize the constitutions of savage tribes, the forms of savage government, and the principles of savage law. In Savagery the tribe is always a body of kindred —actual kindred in the main; but, to a limited extent, artificial kinship obtains by RIOR OC Ae ape Sage js ee CS x Say ANTHROPOLOGICAL SOCIETY. Lae methods of adoption. In this stage of society no method is con- ceived in the human mind by which a number of men can be held together in one common body except the bond of kinship—the ties of consanguinity and affinity. The savage thinks and says, ‘* My kindred are my friends, and he who is not my kin is my enemy,”’ and upon this theory he acts. The tribal state, therefore, is organized upon the basis of kinship. It is literally a bond of blood entwined in a bond of conjugal love, and the family organization thoroughly permeates the constitution of the tribal state. In this stage of culture the family, as under- stood in the civilized world, is unknown. The marriage of one man to the woman of his choice, and of one woman to the man of her choice, is unknown. ‘The right of the father to his own children, is unknown. The husband does not take the wife to his own home; the husband is but the guest of his wife, who re- mains with her own kindred; and the children of the union belong to her, and over her the husband has no authority. The tribe is always divided into kinship clans. Each clan of this character is a group of people related to one another through the female line, and children belong to the clan of the mother, and submit them- selves to the authority of the mother’s brother or the mother’s uncle. The husband of a woman is selected, not by herself but by her clan, to be the guest of the clan and the father of additional members of the clan. In this form of soeiety, then, a clan is a body of consanguineal kindred in the female line governed by some male member of the clan, usually the elder man. ‘The clans con- stituting the tribe are bound together by ties of affinity. The methods by which they are thus bound vary from time to time and from tribe to tribe. In the simplest possible case a tribe is com- posed of two clans, each furnishing the other with husbands and fathers, and in such a case the men of the one clan are the guests of the other, are the husbands of the women and the fathers of the children of the other clan. In such a case the common gov- ernment is a council of the elder men of both clans, or of chosen or hereditary representatives of both clans, and the council chooses the tribal chief. Such is the simplest possible form of tribal society. This plan of the tribal state and form of government becomes very highly developed; there may be three, four, twenty, or fifty clans, with many curious ties of affinity, with many curious re- lations arising from marriage laws. The clan A may furnish 12 whe a Se Hi! 178 TRANSACTIONS OF THE husbands to clan B, and clan B to clan C, and clan C to clan D, and clan D to clan A. It will be impossible to explain all the forms of kinship society in Savagery; but it is sufficient to say that everywhere the tribal state is organized on a kinship basis. If two tribes form an alliance for offensive and defensive purposes, an artificial kinship is always established. Under such circum- stances the tribes entering into the alliance make an agreement with one another what their relationship shall be. If two tribes are thus joined they may call each other brothers; then one will be the elder- brother tribe, the other the younger-brother tribe. Or they may assume the relationship of parent and child to each other, and the men of one tribe call the men of the other ‘ fathers’’ and the women ‘*mothers,’’ &c. But all clan relations and all tribal relations are really or theoretically kinship relations. In all such bodies poli- tic there is a perpetual conflict between tribal and clan prerogatives, and it is settled by different methods in different tribes and at dif- ferent times; but, in general, crimes are of two classes in this respect: those over which the tribe has jurisdiction, and those over which the clan has jurisdiction. Sometimes the clan assumes almost supreme jurisdiction ; at other times the tribe assumes almost supreme jurisdiction. All petty crimes, as they are considered in savage society, fall under the jurisdiction of the clan. It may be asked how a state of social organization so strange to us ever became estab- lished, and yet it may be easily seen that, anterior to the develop- ment of modern ideas and methods of government, it was the simplest way of settling difficulties, establishing peace, and con- solidating peoples into bodies-politic that could occur to a people. In the 34th chapter of Genesis there is recorded a proposition to organize a barbaric tribe: «“And Hamor the father of Shechem went out unto Jacob to commune with him. % * * * % x * x «And Hamor communed with them, saying, The soul of my son Shechem longeth for your daughter: I pray you give her him to wife. «And make ye marriages with us, and give your daughters unto us, and take our daughters unto you. “And ye shall dwell with us: and the land shall be before you; dwell and trade ye therein, and get you possessions therein.”’ In all stages of society, laws regulate conduct in those particu- lars about which men disagree. Wherever there is universal agree- ment there is no need for law, and when men disagree about the ANTHROPOLOGICAL SOCIETY. 179 actions of life, their actions must be regulated. Now, in early _ stages of society, the chief things about which men disagree are the relations of the sexes, personal authority, possession of property, -and conduct relating to mythical beings. Their laws therefore relate, first, to marriage: and they avoid controversies in this re- spect by establishing the law that individuals themselves shall have no personal choice in the selection of mates, but that husbands shall be furnished to wives by legal appointment through the officers or ‘rulers of the clan. Second, property rights are established by laws which make certain classes of the property belong to the tribes, other classes to the clans, and a very small part to individuals ; and the property held by individuals cannot descend to other persons; and to prevent controversy in relation to personal property, it is _ established by law that every man’s personal property shall be placed with him in his grave. ‘Third, personal authority is established on seniority. The elder always has authority over the younger; and as _ the people in this stage of society have not yet developed arithmetic _ and records to such an extent that the ages of individuals are known, -acurious linguistic device is established by which relative age is always known. Every man, woman, and child addresses every other _ man, woman, and child by a kinship term which always indicates rela- tive age: thus, there is no term for brother, but a man in speaking to his brother always uses a term which signifies that he is an elder brother or a younger brother, as the case may be ; and thus, through the entire system of kinship terms in tribal society no man can speak to another without addressing him by a term which, in its very ‘nature, claims or yields authority. The younger must always be obedient to the elder. Fourth, laws involving conduct relating to mythic beings are very diverse and multifarious, and cannot be fully characterized. But one of the most essential of those laws concerns behavior in relation to the tutelar deity. Each clan has its tutelar deity and defends its honor, and punishes all impious acts or words “against its tutelar god. And in savage society no man may speak disrespectfully of his neighbor’s god, but may praise or defame his ‘own, as that god is propitious or angry. ; The general principle running through all these laws is this: ‘That in order that men may live together in peace and render each other mutual assistance, controversy must be avoided ; and in con- nection with this first principle, a second arises and runs through savage law, viz, when controversy has begun it must be terminated. i Wil =e —_ ~ Mea ee Se a > ee — ~ 180 TRANSACTIONS OF THE The methods of terminating such controversy are various, and may not here be entered upon. But, in Savagery, the struggle is for peace, and peace is secured by preventing and terminating contro- versy. Such are the institutions of Savagery. THE LANGUAGE OF SAVAGERY. It is not easy to characterize savage languages in such a manner that the subject may be clearly understood by scholars who are not specialists in philology. ‘This is due to the fact that a false stand- ard of linguistic excellence has been set up through the worship of Greek and Latin. These languages, at the time when they were taken as classical models, were very highly specialized, but not highly developed as compared with the languages of modern civilization. But having been taken as the models of excellence and the stand- ards of comparison, erroneous ideas of the course of linguistic growth and of the value or excellence of linguistic methods have obtained currency. In order to understand clearly what savage, barbaric, and civilized languages are, and how they rank, | it becomes necessary to eradicate these preconceived ideas, and this cannot be attempted in a short address. It can only be stated in a general way, and without hope that the statement will be fully understood, that savage languages have the parts of speech very imperfectly differentiated, that the grammatic processes and methods are heterogeneous and inconsistent, and that the body of thought which they are competent to express is greatly limited. But there is one linguistic characteristic of Savagery that may be made very clear; it is this: That. simple picture-writing is found among savage peoples as a linguistic art, and that in such picture- writing conventional characters are rarely used. Hieroglyphs are never found among savage peoples, and of course alphabets are un- known. THE PHILOSOPHY OF SAVAGERY. It seems probable that, in the lowest stage of Savagery, all change, motion, or activity —1in fact, all phenomena—are attributed to life supposed to exist in the objects exhibiting the phenomena. Thus, all things, animate and inanimate, are supposed to have life and to exercise will. But gradually, in the development of savagery it- self, the animate and the inanimate are distinguished ; and finally these ideas are usually woven into the grammatic structure of savage ANTHROPOLOGICAL SOCIETY. 181 languages. Still, in this stage of culture, the animate is supposed to act on the inanimate ; so that while life is not attributed to all things, all attion is attributed to life—that is, unseen beings are supposed to actuate all nature and to produce all the phenomena of existence. Thus it is that the stars have spirits, the mountains have spirits, and all inanimate and vegetal nature, to a greater or less extent, is the abode of invisible beings. Superimposed on this is found an exalted conception of the wisdom, skill, and powers of the lower animals. In savagery the animals are considered to be the equals of man, and in some cases even his superiors. There is also a general belief that the form in which men and animals ap- pear is but transitory and that these forms may be changed. They believe not so much in ¢vansmigration as in transformation. Then, through the principle of Ancientism, by which the remote past is exalted —in Savagery, Barbarism, and among the ignorant in Civili- zation alike—the ancients of the star, mountain, and river spirits, the ancients of the birds and beasts, are deified and worshiped. The most important characteristic of savage philosophy, then, is the exaltation of the lower animals, the worshiping of these animal gods, and the belief that they are the chief actors in the creation and his- tory of the universe. Savage philosophy is best characterized by —Zoétheism. PSYCHIC OPERATIONS OF SAVAGERY. Sensation is the recognition of external action upon the apparatus _ of the mind. When the olfactory nerves take cognizance of an odor, a sensation is received; but when the mind associates that odor with previous sensations of odor, and recognizes it as of some quality, or as belonging to some known object, it performs an act of inductive reasoning, and pronounces judgment that the odor is sweet, or that it emanates from some pleasant substance. When, therefore, we say that the odor of the rose is perceived, we fairly affirm that in that perception a train of reasoning has been pursued and a judgment formed thereon. By long exercise of the individual in the cultivation of the faculties of inductive reasoning, and by the inheritance of such faculties from ‘ancestors, trains of reasoning of this character gradually come to be so spontaneous and so appar- ently instantaneous that the course of inductive reasoning is not recognized. The judgment is instantly formed, and the inductive reasoning is unconscious induction upon the data of sensation. Induction is the composition of data. > ae = eo a a a, 182 TRANSACTIONS OF THE Again: asound falls upon the ear; that is, many waves of sound beat upon the nervous receptacle which groups the sensations we call sound; the mind recognizes qualities in the sounds, and at the same time compares them with the memories of other sounds having the same quality, and the ear thus recognizes the voice of a friend. But there may be something more recognized, such as characteristics that express joy or sorrow, and the mind recognizes not only the voice of the friend but the state of hisemotions. Now this process is wholly inductive, both in the perception of a known voice and in the perception of aknownemotion. It is all a complex course of in- ductive reasoning, but that reasoning is so instantaneous that the facts which lie at the basis of induction, and the methods of induction, are not discerned, and the unconscious induction is called perception. When the eye is turned to look upon a horse it is affected by certain conditions of light, transformed by reflection from the object upon which the eye is directed. ‘The different rays of light coming to the eye are of a multiplicity of kinds, exhibiting different degrees of light and shade and different degrees in the analysis of light into its con- stituent colors; thus, chiaroscuro and color strike upon the eye, the vast multiplicity of minute effects upon the eye are composed in the mind by an inductive process, and the inductive process goes beyond the composition of these facts to infer others. Perhaps the left side of the horse is turned to the eye, and the mind infers that there is a right side, that the hither side of the ear has a farther side, that beyond there is a right ear, and a right side throughout, so that the conclusion is reached that the object is characterized by ‘ bilateral symmetry. Still more than that, through that profound principle known as the correlation of parts, internal organs are in- ferred; it is concluded that the animal has a backbone, a heart, and other parts. All these facts, observed and inferred, are combined into a general conclusion by the mind that the object seen is a horse, and we say that a horse is perceived. Now this process of -perception differs in no wise from any long and patient course of reasoning except in one characteristic, namely, that the process of reasoning is so instantaneous that the steps and methods do not arise in consciousness. ‘The individual facts upon which the reason- ing is based do not appear in severalty, but as forming integral parts of the whole; and the steps by which these observed facts are combined with previous knowledge, and reasoned upon from the basis of the principle of the correlation of parts, are unobserved. ANTHROPOLOGICAL SOCIETY. 183 The mind is unconscious of the facts upon which reason is based, and of the process of reasoning, but instantaneously reaches a con- clusion. ‘Thus perception is unconscious induction. This may be further illustrated by facts familiar to all. The untrained arithmetician. ]abors with a simple problem in addition; he steps slowly from one number to another with his eye and his _ mind’s eye as he ascends the column; but an expert accountant _ glances his eye up and down the column and instantaneously states the sum; and that which was a slow inductive problem in arith- metic for the child and the ordinary adult is performed as an instan- _ taneous process by the expert accountant; and that which was - conscious induction in the one was perception in the other. In _ many ways and on all hands this fact may be illustrated, that per- ception and induction (or reflection, as it is usually called) are one and the same process in kind, but differ only in degree. Perception 2s unconsctous tnduction. It was necessary to explain this fundamental principle in psychol- _ ogy in order that we may properly characterize the psychic operations of Savagery. The psychic condition of a people can only be fully explained by setting forth fully the whole system of intellections, embracing perceptions, inductions, and inventions (or imagination, _ as the process of invention is more usually denominated in psychol- ogy), and also characterizing the emotions, the desires, and the purposes, so frequently denominated the ‘‘will.’’? But it will be suf- ficient for our purposes here if we characterize the perceptions and inductions of Savagery; and it may be safely inferred that the _ imaginings, the emotions, the desires, and the purposes will corre- spond thereto. : Now the perceptions of Savagery are of a very rudimentary char- acter and are greatly restricted. This can be shown in many ways, but two particulars will suffice for present purposes. The first is _ this, that the savage is unable to perceive a conventional meaning. He can perceive a horse, and he can even perceive the picture of a . horse if its outlines are fairly drawn, but he cannot perceive a horse in a conventional character, like a hieroglyph or a written word. Again: the savage can perceive numbers but toa very limited extent, but cannot perceive the relations of numbers; for example, | he cannot add groups of numbers, as 3 to 5; but wishing to add 3 to 5, he first- counts off carefully 5, and then adds the 3, one at a _ time—that is, he counts his addition. To subtract 3 from 8, he 6S oe a. =e 184 TRANSACTIONS OF THE subtracts one ata time until 3 are taken away, and subsequently counts the remainder to discover the 5. In like manner he cannot multiply, that is, add like groups to each other. Nor can he divide, that is, separate into like groups, but must in each case go through the process, not by considering abstract numbers, but by consider- ing individual things, one at a time. Thus it is that in Savagery a very large field is included in conscious induction which belongs to perception in a higher stage of culture. There are many other mental characteristics of Savagery, but those given are sufficient for present purposes. Savagery has been thus described with all the minuteness possible on such an occasion, and perhaps with sufficient thoroughness for present purposes. The savage has invented rude arts by which he obtains food, clothing, and shelter. He has invented a rude system of kinship society, with descent in the female line. He has spoken language, gesture-speech, and picture-writing, but is without hieroglyphic, syllabic, or alphabetic writing. He has a philosophy which informs conspicuous and important inanimate objects with spirit life, and which deifies the brute; and a mind whose percep- tions are so slightly developed that conventional characters do not convey to him ideas, and his arithmetic is yet ‘‘counting.’’ Such, in general, are the characteristics of all savage peoples that have been carefully studied by anthropologists. _ Now the question arises, how was this Savagery transformed into Barbarism; and what is that Barbarism ? In the lower stages of culture all progress rests upon the arts of life. To discover any great change in the condition of mankind we must look for the art-invention which was the efficient agency in producing the change. If the early course of human progress be surveyed for the purpose of discovering the most important art-epochs, it will be safe to re- gard those of the greatest importance the effects of which are most clearly exhibited 1y the concomitant activities —that is, institutions, languages, opinions, and psychic operations. If an invention has but slight influence on these correlative activities, its importance may be questioned. But if an art-invention is discovered to have worked radical changes in all other activital departments, such art must be of the highest importance. . There are two arts intimately associated the invention of which causes a radical change in all of the departments of humanity, ANTHROPOLOGICAL SOCIETY. 185 viz, agriculture and the domestication of animals. Agriculture began in Savagery. Many savage tribes cultivate little patches of ground and thereby provide themselves with a part of their subsistence. This petty agriculture does not of itself result in any radical change; but when the art has developed to such an extent that the people obtain their chief subsistence therefrom, and especially when it is connected with the domestication of animals, so that these are reared for food and used as beasts of burden, the _ change for which we seek is wrought. It seems that extensive agri- culture was first practiced in arid lands by means of artificial irriga- tion. In more humid lands the supply of food is more abundant, and the incentive to agriculture is less. On the other hand, agri- culture is more difficult in humid lands than in arid lands. The savage is provided with rude tools, and with them he can more ~ easily train water upon desert soils than he can repress the growth of valueless plants as they compete for life with those which furnish food. ‘The desert soil has no sod to be destroyed, no chapparal to be eradicated, no trees to be cut down, with their great stumps to be extracted from theearth. The soil is ready for the seed. Throw upon that soil a handful of seed and then sprinkle it with a few cal- abashes of water once or twice through the season, and the crop is raised; or train upon a larger garden patch the water of a stream and let it flood the surface once or twice a year, and a harvest may be reaped. Petty agriculture, such as I have described as belonging properly to Savagery, has been widely practiced in the four quarters of the globe among savage peoples, quite as much in humid as in arid regions; but the art seems not to have indigenously extended beyond that stage in any but arid regions. The earliest real agri- culture known to man was in the Valley of the Nile, an almost rain- less land; but the floods of the Nile were used to fertilize the soil. Again, in the land of Babylon, along the Tigris and the Euphrates, extensive agriculture grew up, but it was dependent upon artificial irrigation. Still farther to the southeast, in the Punjab, another system of indigenous agriculture was developed by utilizing the waters of the five great rivers. " Still farther to the east an indige- nous agriculture was developed on an extensive scale, all dependent upon artificial irrigation, as the Chinese use the waters of the Ho- ang-ho and the Yang-tse-Kiang. In South America the first system of agriculture was developed in Peru, all dependent upon artificial pe eee i —_ —_, 186° TRANSACTIONS OF THE irrigation ; and finally, to the north of the Isthmus of Panama, in Central America and Mexico, agricultural arts were highly devel- oped, and here also they were dependent upon artificial irrigation. From these six examples of high agricultural art, all the agricult- ure of the world has been developed; from these centers it has spread. ‘The petty agriculture of humid lands never went beyond the utilization of little patches of ground in the forest glades until it was borrowed in a higher state from arid lands. Everywhere with the development of agriculture in the arid lands, the art of domes- ticating animals was associated, and everywhere such animals were raised for food, and to a large extent they were used as beasts of burden. Now, it is to be noted that the animal industry eventually devel- oped beyond the vegetal industry, and spread more widely, and many tribal peoples became herdsmen and nomads before they came to be agriculturists. -The art of domesticating animals was more ~ easily borrowed, especially in humid regions, than was the art of | agriculture. : These industries enabled mankind to obtain a far more generous © subsistence and more thorough protection from unfriendly nature. They thus caused a great increase in population. They also con- stituted the first great agency for the accumulation of wealth, by creating it in giving value to land, by creating it in flocks and herds, and by storing it through the discovery of methods by which the wants of the future could be met. By planting fields the wants of to-morrow and all the days of the year to come are served; and when the young of animals are reared, provision for future years is made, and thereby men learn to accumulate. This change in the arts of life, and the increase of population resulting therefrom, entirely changed the constitution of society. In savage society, when mother-right prevails, a tribe is a group of classes or clans living together in a village that is easily moved from time to time. If a colony departs from a tribe, a segment of two or more clans goes away and starts a new village, and the clans again live as a village community upon the same plan as the parent tribe. Now, let us suppose that a tribe separates by clans, so that each goes off by itself; a curious condition arises therefrom: first, it results in the divorce of all marriages, because husband and wife are always of different clans; and for the same reason the father is ANTHROPOLOGICAL SOCIETY. 187 separated from his children. In such communities there is often a partial separation by clans of this nature: in savage society the ‘men of a clan often go off together on a hunting or fishing excur- sion. Sometimes these excursions or travels are prolonged for weeks or months. In such cases the men often take their wives with them, and under these circumstances the women are separated from their clan and kindred and are not under the control of clan authority, but fall under the temporary control of their husbands and fathers. Now, if we could suppose a state of affairs where his separation of women and children from kindred and clan authority becomes permanent, it is manifest that the power of clan authority would wane, and the authority of the husband and father would grow. Such a condition of affairs results from ex- tensive agriculture by irrigation and the care of extensive flocks. It must be remembered that in this stage of society property is communal; that is, property in the main belongs to the clan. A flock of sheep, a herd of cattle, a band of horses; is the property of the men of aclan. When such property becomes so large that it will occupy for its sustentation a large valley, the men to whom it belongs will necessarily be occupied all the time with its care and protection, and they must have their wives and children with them in order that domestic life may be possible. Under such circumstances it results that women and children are gradually taken from the control of those persons who had previously been supposed to be their natural protectors, their clan kindred, and fall under the control of their husbands and fathers, who are members of other lans. The same result has always been produced by the segrega- tion of the male members of the clan from the tribe through agri- culture by irrigation. The circumstances are these: In this early agriculture the agricultural implements are very crude, and great hydraulic works cannot be undertaken. It is thus necessary to attempt the control of only the small streams, and the men of each clan will therefore select some small stream and occupy the little alley through which it runs and upon which its waters are trained ; the men of one clan, with their wives and children, occupy a dis- tinct valley, the male members of another clan another valley, and the tribe is thus segregated into groups, the male members of each group belonging to the same clan and having with them their wives and children. The women and children being thus severed from clan authority, fall under the authority of their husbands, and mother- in, Soo, a 188 TRANSACTIONS OF THE right, or descent in the female line, is changed into father-right, or _ descent in the male line; and thus is established the patriarchy, a _ form of society with which we are all familiar, as it is very clearly _ set forth in the post-Noachian history of the Bible. Under this form of society kinship bonds are still preserved, but they are of a different nature. First, descent is transferred to the — male line—that is, children belong to the clan of the father, and are controlled by him instead of by the mother’s brother, or the — mother’s uncle; second, the husband is no longer the guest of the — wife and herclan. At first the wife is the guest of the husband and his clan, but gradually this relationship of guest and host is changed to the relationship of master and owner, and the husband becomes the owner of his wife, and finally the owner of his children. They are considered to be his property; they are responsible to no one but himself—that is, the tribe does not hold the wife and children responsible for their acts, but holds the husband responsible for them. (It is impossible in an evening’s address to characterize fully — the causes and the consequences of the change from enatic to ag- | natic descent, but the statement here given is perhaps sufficient for present purposes. ) Another great change is effected, the increase of wealth which has been described multiplies the relations between men arising from the possession of property. And these are relations about which men disagree, and therefore they must be regulated by law. The state, therefore, comes to be organized in part on a property basis; hitherto it has been organized wholly upon a kinship basis. — The plan of the structure of the state is thus changed. The laws, too, are enlarged to regulate the relations that arise out-of owner- ship. . And yet another change is effected. Some clans prosper and — increase in wealth; other clans fall into poverty. With this increase — of wealth and desire for wealth, labor becomes of value, because it | can be converted into wealth, and the poor are employed by the rich, and the relations of the employer and the employed are estab- lished. Out of this grows the relationship of master and slave, and ranks or grades are established in society. With this grows ambi- tion for wealth and power, and tribe wars on tribe to drive away its herds and to take possession of its accumulated property, and cap- tured peoples become slaves, and the chiefs of conquering tribes extend their authority over conquered tribes, and gradually great ANTHROPOLOGICAL outa 189 _ them, giving to them protection from Sanur and claiming in - compensation for the same fealty, tribute, and service under arms. Such is a brief outline of the characteristics of tribal society in | barbarism, brought about through the cultivation of the soil and _ the domestication of animals. THE CHANGE IN LANGUAGE. The great changes wrought in arts and institutions which have _ been described doubtless had their influence on languages, as the new ideas required new means of expression. While in the present _ state of knowledge it is perhaps not possible to’set forth clearly the _ resultant sematic and structural effects upon any language, in lin- guistic arts important effects are discovered. In the lower status of culture, here denominated savagery, picture- writing was highly developed ; but in the transition to barbarism, _ picture-writing was transformed into ideographic writing. In the earlier stage a slight tendency to conventionalism is discovered ; but in ideographic writing the original pictorial signs are conven- _ tionalized to such a degree that it becomes an important linguistic art, by which ideas may be recorded and transmitted from person to person and from generation to generation. It must be under- stood that the evolution of picture-writing had all along been in _ the direction of ideographic writing, but a great impulse is given to this tendency by the enlargement of human activities in the arts _ of life and the institutions of society. This is discovered in many directions, the chief of which may be here enumerated. The increase of property demands increase in the methods of identifying property and of substantiating ownership. 2d. The separation of clans and the distribution of cognate peoples over large areas of territory demand means of intercom- munication other than that of direct oral conversation ; and 3d. Nomadism, which is the direct result of the domestication of animals, makes men travelers, and so enlarges their horizon of _ observation that some method for the record of events becomes necessary. Under such stimulus, picture-writing speedily develops into ideographic writing. . THE CHANGE IN PHILOSOPHY. In savagery, mythology develops into a high form of zodtheism. ° i SS 190 TRANSACTIONS OF THE The beasts are not gods, but many of the gods are beasts—the ancients of beasts, the prototypes or progenitors of the living animals. The rudiments of physitheism also exist in the worship of the heavenly bodies, the winds, and other natural phenomena personified. When animals become beasts of burden they are degraded ; they are discovered to be inferior beings, and the mysteries of animal life are largely dispelled; and by the development of agriculture man becomes more dependent upon the sun, the seasons, and the weather. The heavenly bodies and meteorologic powers and phenomena grow in importance and become more and more the subject of interest and speculation, until the personifications of natural objects in the heavens and natural phenomena in the seasons and the weather are deified, and the tribal worship presided over by medicine-men and prophets becomes a religion based upon physitheism. The occult lore of the people is composed of stories of the sun, moon, and stars; of thunder, hghtning, and the rain- bow: of the storms, clouds, and winds, and of dawn and gloaming. There is another important development in the religion of bar- baric peoples. With the establishment of the patriarchy the patri- arch comes gradually to be the great power, and worship of a clan tutelar deity is changed into ancestral worship—the worship of the ancient chiefs or patriarchs; ancestor gods and ancestral worship replace tutelar gods and tutelar worship.. Barbarism, then, is prop- erly characterized by domestic ancestor worship and tribal nature worship. THE PSYCHIC CHANGE. The enlarged plane of human activities already outlined causes an important development in psychic activities. First, percep- tion is enlarged. This is seen in the fact that people at this stage are able to read hieroglyphs; they can perceive meanings in conventional characters. Again, stimulated by the accumu- lation of wealth, arithmetic is developed beyond the counting stage, and man can add a number of units to a number of units, and can subtract numbers from numbers, and divide numbers by numbers. In savagery, men learn to count; in barbarism, men learn arithmetic, and can at once perceive the simpler relations of numbers. ‘The entire field of human thought is greatly enlarged, and with this enlargement there may be observed a nicer discrimi- ls oe patel! eee ee ee iss Son Satna ME alin tt ANTHROPOLOGICAL SOCIETY. 191 nation of phenomena, and a grouping of phenomena on a new _ system of analogies, . From the foregoing brief characterization it will be seen that bar- _baric culture implies a somewhat high state of agriculture and the _ domestication of animals, one or both. It implies that patri- _archal institutions have been organized, that descent is in the male line, that ranks in society have been established, and that new Jaws regulating property have been enacted. It implies that the _ people use hieroglyphs. It implies that domestic worship is ances- tral worship, that tribal worship is based on physitheism, and ; that the phenomena of the universe are attributed to nature gods. And finally. it implies that men can perceive meanings in conven- _ tional signs, and that arithmetic has been invented. The statement I have hitherto made rests on the postulate that _ the progress of culture has been essentially along the same line in all times and places. The facts accumulated by the researches of modern anthropologists fairly establish this. It is true there has been much variation in the order and steps of culture, but this variation has been confined within certain limits. The chief variation lies in the fact that all races have not made progress to _,the same extent. Some tribes are yet savages; other tribes are yet barbarians; and some peoples have attained civilization. The common origin of mankind, otherwise denominated the unity of the human race, is a conclusion to which the modern science of anthropology gives abundant evidence. Although the diversity among men is so great that no two are alike, yet this di- versity is restricted to narrow limits. The units of the mass of humanity are discovered to be homogeneous in essential endow- ments to such an extent as almost to startle the student who studies man in all lands and at all times. Primitive men had a common origin, but early in their history they differentiated into biotic varieties, characterized by the con- formation of the skull, the proportions of the skeleton, the color of the skin, the structure of the hair, the attitude of the eyes, and other biotic peculiarities. Had this tendency to differentiate con- tinued through the entire course of human culture, species would have been established, but early in the period of human history the tendency to differentiation was checked and a return to homogene- ity initiated. henceforth the progress of mankind has been by methods radically differing from the methods of biotic evolution as exhibited among plants and animals. 192 TRANSACTIONS OF THE This return to biotic homogeneity is due to the development of human activities, which make men depend one ‘upon another in such a manner that the welfare of one involves the welfare of others, so that no man may claim the right to live for himself, but every man lives and labors for the good of his kind. The fundamental prin- ciple of animality is supreme selfishness ; the fundamental principle of humanity is mutual assistance. As man is an animal, in systematic biology he may be grouped with other animals as determined by morphologic characteristics. He has a head, body, and limbs ; he has organs which perform the functions of biotic life; and when we consider man in this aspect — the study is a part of biology. Man is more than animal by reason of his activities; man is man by reason of his humanities; and when we study him in this aspect the subject is anthropology. Henceforward human evolution differs radically from biotic evo- lution as exhibited among plants and animals. Animal evolution has been accomplished by the survival of the fittest in the struggle for existence. By this method animals were adapted to environ- ment, and in the course of this adaptation they differentiated into a multitude of species, genera, families, and orders. Animal evolu- tion, then, has these three characteristics: first, the agency of evolu-. tion was the survival of the fittest in the struggle for existence, brought about by over-population ; second, the fittest that survived were adapted to environment; and third, progress resulted in im- measurable variety, carried to the utmost degree. In all of these characteristics human evolution differs radically from animal evolu- tion. First, man has not progressed by the survival of the fittest in the struggle for existence. Man does not, to any important extent, compete with plants and the lower animals, but he utilizes them, developing such as he will in directions that best subserve his inter- ests, and gradually destroying others from the face of the .earth. Nor does man progress by reason of competition within the species. When the highwayman and the traveler meet, the robber is not always killed ; and when races battle with each other, the strongest and the best go-to die. In the course of human history, in a few localities and at a few times population has been overcrowded, but in the grand aggregate the world has never been fully peopled, and man has not crowded upon man for existence. While man has not progressed by the struggle for existence, he ANTHROPOLOGICAL SOCIEFY. 193 has progressed by his endeavor to secure happiness ; and in this en- deavor he has invented arts, institutions, languages, opinions, and methods of reasoning — that is, he has progressed by the development of five great classes of human activities. In the establishment of these activities, he transfers the struggle for existence from himself to his activities, from the subject, man, to the objects which he creates. Arts compete with one another, and progress in art is by the survival of the fittest in the struggle for existence. In like manner, institutions compete with institutions, languages with lan- guages, opinions with opinions, and reasoning with reasoning ; and in each case we have the survival of the fittest in the struggle for existence. Man by his invention has transferred the brutal strug- gle for existence from himself to the works of his hand. Again, man has not been adapted to environment. There is no aquatic variety of man, no aérial variety, no tropical variety, no boreal variety, no herbivorous or carnivorous variety. On the other hand, man has adapted the environment to himself—that is, he has created for himself an artificial environment by means of his arts. He can sail upon the sea and live on the products of the sea, and he utilizes the denizens of the air and the plants and animals of the _Jand. He protects himself from great heat and great cold and in a multitude of ways creates an artificial environment. And this he has done to such an extent that were he suddenly to lose his control over the environment gained through his arts, he would speedily perish from the earth. Again, among the lower plants and animals the course of adap- tation to environment led progressively to the differentiation of species, until a multiplicity of biotic forms covered the earth. The method of human evolution by endeavor to secure happiness through human activities, which resulted in the creation of an artificial en- vironment, checked the tendency of the animal man to differentiate into distinct species, and the interdependence and solidarity that were established through these activities tend more and more to restore the units of mankind to pristine homogeneity. This is accomplished biotically by a constant interfusion of streams of blood, as men are commingled and intermarried throughout the world. When races of higher culture spread civilization over infe- rior races, the admixture goes on at an increased rate. ‘The blood of the American Indian is to a large extent mixed with the blood of the European, and especially is this true where Latin peoples rs 194 TRANSACTIONS OF THE have established themselves. The African tribes transplanted in America are rapidly bleached by the synthetic chemistry of social life. When three generations more have passed, it may not be possible to find a drop of pure Indian or negro blood on this con- tinent. Civilization overwhelms Savagery, not so much by spilling blood as by mixing blood, but whether spilled or mixed, a greater homogeneity is secured. This return to homogeneity is accomplished by the spread of arts from their centers of invention to the circumference of their util- ities. As an art is expressed in material form, it is an object-lesson readily learned. It may be that the tongue of the inventor can be understood by no people but those of his own tribe, but his handi- work needs no interpreter; and so arts are spread from land to land, and those who engage in common arts are trained by homo- geneous methods. This return to homogeneity is accomplished by the spread of institutions from tribe to tribe and from nation to nation, for waves of conquest have rolled again and again over all lands, and when civilization is reached institutions and institutional devices are trans- planted, for civilized men are ever engaged in comparison and ever striving to select the best. This tendency to homogeneity is accomphshed by linguistic com- munication, for with the progress of culture men come to speak more and more in synonyms, and dominant languages are spread far beyond the boundaries of their native lands; and thus there is a tendency to homogeneity of tongue. This return to homogeneity is accomplished by the spread of opin- ions, for the opinions that influence the highest of the race come ultimately to influence all; and scientific philosophy is rapidly spreading to the uttermost parts of the earth. And finally this homogeneity is accomplished by the spread of the same methods of reasoning, the same psychic operations. Hom- ologic methods of reasoning, by which the truth is reached, are steadily replacing analogic methods, by which myths only are in- vented ; and as gradually the same facts are brought to the hight. of all mankind, and the same processes of reasoning are pursued, men are gradually becoming occupied in the same mental activities. Thus it is that if we consider man biologically, or man in relation to his activities, expressed in arts, institutions, languages, opinions, and reasoning, we discover that the tendency to the differentiation ANTHROPOLOGICAL SOCIETY. 195° of species has been checked, and that a tendency to homogeneity has been established. To recapitulate: Human evolution has none of the characteristics _ of animal evolution. It is not ‘‘ by the survival of the fittest’’ in the struggle for existence, but it is by human endeavor to secure happi- ness; and in this endeavor man has transferred the struggle for existence from himself to the works of his hand and mind. It is not by adaptation to environment, but by the creation of an artifi- cial environment. It does not secure differentiation into varieties and species, but establishes a tendency toward homogeneity. By the division of labor men have become interdependent, so that every man works for some other man. To the extent that culture has progressed beyond the plane occupied by the brute, man has ceased to worked directly for himself and come to work directly for others and indirectly for himself. He struggles directly to benefit others, that he may indirectly but ultimately benefit himself. This principle of political economy is so thoroughly established that it needs no explication here; but it must be fully appreciated before we can thoroughly understand the vast extent to which interdepend- ence has been established. For the glasses which I wear, mines were worked in California, and railroads constructed across the con- tinent to transport the product of those mines to the manufactories in the East. For the bits of steel on the bow, mines were worked in Michigan, smelting works were erected in Chicago, manufac- tories built in New Jersey, and railroads constructed to transport the material from one point to the other. Merchant-houses and banking-houses were rendered necessary. Many men were employed in producing and bringing that little instrument to me. As I sit in my library to read a book, I open the pages with a paper-cutter, the ivory of which was obtained through the employment of a tribe of African elephant-hunters. The paper on which my book is printed was made of the rags saved by the beggars of Italy. A watchman stands on guard in Hoosac Tunnel that I may some time ride through it in safety. If all the men who have worked for me, directly and indirectly, for the past ten years, and who are now scattered through the four quarters of the earth, were marshaled on the plain outside of the city, organized and equipped for war, I could march to the proudest capital of the world and the armies of Europe could not withstand me. Iam the master of all the world. But during all my life I have worked for other men, and thus I am 196 TRANSACTIONS OF ANTHROPOLOGICAL SOCIETY. every man’s servant; so are we all—servants to many masters and masters of manyservants. It is thus that men are gradually becom- ing organized into one vast body-politic, every one striving to serve his fellow man and all working for the common welfare. Thus the enmity of man to man is appeased, and men live and labor for one another; individualism is transmuted into socialism, egoism into altruism, and man 1s lifted above the brute to an immeasurable height. Man inherited the body, instincts, and passions-of the brute; the nature thus inherited has survived in his constitution and is exhibited along all the course of his history. Injustice, fraud, and cruelty stain the pathway of culture from the earliest to the latest days. But man has not risen in culture by reason of his brutal nature. His method of evolution has not been the same as that of the lower animals; the evolution of man has been through the evolution of the humanities, the evolution of those things which distinguish him from the brute. The doctrines of evolution which biologists have clearly shown to apply to animals do not apply to man. Man has evolved because he has been emancipated from the cruel laws of brutality. The evolution of man is the evolution of the humanities, by which he has become the master of the powers of the universe, by which he has made life beautiful with zesthetic art, by which he has established justice, by which he has invented means of communi- cation, so that mind speaks to mind even across the seas ; by which his philosophy is the truth of the universe. Man is man because of the humanities. Abandonment of homes by savages........... Abbott, C. C., elected a corresponding BMBF TIUVGI ce nacrunscclinccsecacccrestecesscecedssnesseste 50 Aborigines Protection Society... 91 PAPEL VAL ATISTNV.ETIULON .....ccc0e.cc0ccc-escoecesces "150, 167 dams, ©. N., Election of, to membership. 141 Adams, Henry B., elected a corresponding PEPSAUS Teen nene tenessrssaacersvancasetsansscocees 50 MEISICEICCNINSUIA:.....::.-2.sscceeccccesesesceesess 101 Pee tecindicabterc en stestevenncs cewncsitcteesvesvssnad 100 BRITA GU PET Chi. .conc oc'sctesetev-sosiccccsescesessccsase 96 BAX GUTS: Of PACES... 2cc.0c...sccesesecccssescesesss 193 Adyance towards civilization marked by BeestepS in Mechanic arts:....../.......0...--+- 162 Bsthetic taste as a sociologie force............ 62 96 96 96 griculture began in savagery ........... 185 Akudliarmiut... 96 ikudnirmiut 96° MRICS) ss ccccevausissapseswcevecsscteveses 96 \ltruistic motives explained.................:66 37 Amendment to the Constitution................ 21 American aborigines, Circular architect- ARCO Me cenenen ene codts sceeksneeacosecccreesacc 116 | Clothing, The desire for, a social force...... Bull-roarer, Analogue of the, among say- Cohabitation and child-marriages.............. AE OibTIDES. ve csuesessscevecneco teens Pecthhevectess 87 | Collett, John, Election of, to membership.. Bureau of Ethnology, Researches and col- Colored race in the United States, Compa- VECHONS Of, cascctas coveeescteroseeccaceecnecce -acces 8, 24, 42 rative frequency of certain eye dis- — — —, importance of its work..............0 92 Cases: Of OHEl..c.., sec. Sostaseasear Burnett, Swan M., Paper read by...........000 67 | Columbian University, icons: of ie Burnt clay in mounds Srcdusacthectesasesecieseases a6 14 Society to be held at thes.....0...s..cssesuene Communism a primitive institution.......... California Indians, houses Of...........:seeeeeees 16 Companionship, Desire for, the social in- Camp Verde, Arizona, Yumaceremoniesat 143 StINn‘Gt PLOPers.cs2..<..baccsasseceeaossesse eee CAPO DIST. cosca ccacrasseedecasecesenss Wsdshaesessuseses 96 Competition in human society.............cc00 . = MSAD SI Os.. hessciencecesseectwccctoesessdsceeas aes 102: | for, happiness! ss. tescoescsecstess-ee-tees aeeeeeeee SS IGA GOL i seasensvccdenessse cosssccesscesacseseyeseaeseseaes VOR) OF ‘ALES. .o. cosccessdvcseesaosescos sastetesseseecsscameeee wm ICT COW: ins: actaescse.scacuwananecees oassduedensseescscees °7 | —— institutions and opinions.................. — Micklesham........... Renee eetes ct seater srececeteses 97 | Conant, A. J., elected a corresponding —=AWiOIStEMMO]ING.....<,0ssedecseecssvececatnsssseveceses 96 MEMBDEMs..... 2252 ives gevsiees eva snastaceueesee cere Carl, Anton, Election of, to membership.... 22 Consciousness as a source of knowledge... Garr, UCien, GUuOted......1.2..-s--scss0nwerene 2, 7, 14, 24 Conservatism in America... ssh ennc-sccesesess — elected a corresponding member.......... 51 Conventional character not perceived by Caste in India and elsewhere.......... the Savages. ....2.0hl Gece eee aeteees Casts of mound-builders’ textiles.............. Co-ordinations of natural forces in the Catlin POLtLAltS ts a5. .cseaecsesessee sess alucsssvsesaseees 44 Ikingdoms Of Matures....cc.s-cecesereceoesnses Cave-dwellers, Relation of the Eskimo to.. 106 Copper as a preservative of mound relics.. Cave-dwellings of France, Antiquities — plate In MOUNAS.........5.. -innsccssrecsescsecerec he ceeees Spencer, Herbert, on the conditions to MMOTSAL PNOPLOSS:-sccssessacceen cutee caeacnee 121, 122 —, Opinion of, on tribal society.. 28 = QUOLO I, sc ceveveors ce cauctescartaeee eo eae PEE ODS Statical and dynamic methods in sociol- OL Yincsanaccsancacecdavecsdccenetececenrctntieateneanacenee 64 Stejneger, L. M., Collections of, from Beh- ring, Islands ciccccsonee een eee 43 Stevenson, James, Paper read by.............. 143 —,and Mrs., work of, among the Pueblos... 3 Stone carvings in the mounds...............00 18 — graves in West Virginia and the Missis- SIPPIW all Oye a esesscclabemcestusesesesrestesees 1-4 — hatchet, the culmination for the time OMAN Socareccusecccstsetsons orccsercctecosvactenerarre 155 Study of invention, Postulates in the.......... 149 Survival of the fittest does not obtain in MUMANSVOMMELON secesesse-c se ceee secenoessees aces 192 — — —— in human society... 35 —, The term, becoming popularly under- STOO rece cre tacttencrcoccconsscenets cotncmencacreres 94 Swan, James G., Explorations of................ 45 Synechronism of invention...............s....---++ 166 Synonomy of tribes of North America...... 65 Taensas as mound-builders...............cseeeeee 116 Tagore, Surindro Mohun, Rajah, Donation of musical instruments by............cceee 44 Tamenents Indian in West Virginia.......... 1 Tellirpingmiut 96 ‘Temporary home Of SaVages......-.e...-seeeceeee 20 Ten Kate, Hermann, elected a correspond- TN PMC MID EN: sececeseaceaseaseusvecsenctareessacentss 116 Teotihuacan, Pyramid of... 73 Tessiujang Fiord.............. 102 Texcocingo, Pottery from 73 MexCOCOs VLANs Ofersnscesessencesseteccaakecenest 73 Textile fabrics of mound-builders............ 6 — section in National Museum.................. 41 (PHiITSh as) & SOCIA TOLCC ...-...c.wecsesssnnnsvewenes 60 ‘Thomas, Cyrus, Papers read by............ 13, 24, 117 — QUOTE .........seereeeecsessnereccenserencecseeseareeees 7 —— SEMA IZS! DYjersessnesscsneeecsase 18, 32, 53, 57, 117, 1380 Thompson, A. pores Election of to mem- bership... seme lad Thompson, tan fas eae es on eree 56 Thompson, Gilbert, ones PY sezceecescncens 140 TikkerakGjUak..........cc.sccoccsessssecenscsencseee rears 96 Tools, Invention Of,.......22..-seesccceeerseesesenene 158 Tradition, Cherokee, respecting tribal PYIOTILY ........0..ccescenecssercccseseeescesersesecene 25 Travelers, Degree of confidence to be placed in the statements Of..........:sse0 84 Tribal conductrelating tomythical beings 179 — laws regarding marriage — — — property......... ReReeaenenaneese — — — personal authority..........seeereereeeee 17 204 INDEX. Page. Triballaws to prevent andendcontroversy 179 — peoples, herdsmen and nomads.............. 186 =< PLIOMI Vs. dec esesctasasssicccssccteavéserseigessssctesstes 25 — State; Nature iof:the:::......icsccovsecseseesenseese 177 — states; OrganizationsOf. 0. ..sccteccssevesoccssees 10 Tripod dishes from Mexico (figured)......... 76, Tv AITO De waestescee sass: sectsaccacseec che cacetee sea vesceaecsses 102 Mv mikey alk .2c5sssvesscssereascecececess 98 Tudnumirmiut 96 Tudnunirossirmiut 96 AISI TAGs sh ccss sdiess. Sot cestaustecsecasateceeuttasevetoete 98 MAP CKe.2 ove sasscecccewsserseneeteascencdeaucssrestascteestes 103 Turner, Lucien M., Collection of, from UWNGRV A. “BAY. ccocesciccesererecsstvenscesescneseres 44 —, Election of, to membership............cc0008 108 —, Researches of, in Ungava...............s000+ 101 TNC CLOS:.sreiecocddanoecscoutveccssot oreateanccevecess-teesers 65 TWO" CrOWSiscctascedsscarscscaseseovectccatsbesevececeseces 148 Dylor, H.2Biy AGGress:Of ...21ecssssteevessotessevees 81 —, his scheme of culture stages............... 81 Werria.a ey taterphal ents tesa henna etaeene 103 Ukusiksalingmiut 101 OMNIS MIA MANU Ai. stsecsesss cots c0tscasveess-ceesi ses 102 Unearned increase of land, John Stuart Mill’s proposition to prevent, by taxa- GLOW T. ctaw ccs ees dassasssecass Cove ereostaceseses cess ace 135 Ungava, Turner’s researches iN...........ss006 101 Unity of the human race, Evidence of an- thropology: UPON er ovesevcesescsvecsscaseeress 191 Vendéme, Collection of antiquities from... 67 Vice-presidents’ sections assigned............ 31 Vuleanization of India rubber, Origin of... 151 WIA PSI RIVEIie: ctccesoscccescsuccecnscdeescesle-cceresecos 102 Wankel, Dr. Heinrich, Gifts from.............. 23 Wants generated by inventions............00 152 —=; Vital, aS ’SoCial fOrGeSi.. 2. -c.ccececccecocassece 60, 61 Ward, Lester F., Papers read by............31, 120 —, Mind defined by...............see00 sesscsorse LOZ ==, Remarks iDy....1ssessssceseeseet 29, 53, 64, 130, 136 Page. Ward, Lester F., his scheme of culture SLAZOS cs cecsves.ccceescesevsascessunesoensccesestateeres Warfare the expression of public and pri- VALOTCOMPCUIUION: <5.c00ccusacn0sssccaesceesereree — the enemy Of progress..........ccceccccsssseeees Warren, Charles, Election of, to member- SUP \c.Fensccceee vesveccesbolsetavathes tescesnsee coer reee Waste Of Competitionss..cccs..secccccocseceosseeeeere Water impassable to spirits..............::0es0008 —supply of arid regions...............:s.-s0sseus Wealth, Possibility of greatly increased PLOGUCTION OL... ..cc-.cccetaccecstececeasesoneaceets Welling, J. C., Remarks by............ 32, 53, 130, I West Virginia, Mounds and graves in........ White goose, Mystic use of down of.......... 1 Whittlesey, Charles, elected a correspond- IN MEMDEM =. ==L]™>==ESESESESESS DATE. AUTHOR. REMARKS. REFERENCES. 1887 -2\ Hany Sts<2=o see Color reaction ~_.----- C. R., cv, 1074. Ber., 1887, 24. Abs. J. Chem. Soe., 1887, 304. 18872)| DEMAROAY ==. 225 Action of carbon te-|C. R., ctv, 111. trachloride upon ni- | Abs. J. Chem. Soc., 1887, 529. obic anhydride. 188/72 2|Kinop= 2 fs sss 2. Crystallization niobic | Zeitschr. Kryst. Min., x11, 610. anhydride. ‘MINERALS. DATE. AUTHOR. REMARKS. _ REFERENCES. 1801.2) HAtCHEDT <2-2.=.2 Colum bite: .2=2--.2-2— Phil. Trans. Roy. Soc., xctt, 49. Chem. J., Crell, 1, 197. Ann. der Phys., Gren., x, 500; xr, 120: Nicholson’s J., Jan., 1802, 82. 180524) VALENTINE. -~ = Columbite <--== -22=22 Magazine Encyclop., Dec., 1805, 388. Ann. der Phys., Gren., xxiv, 120. 154122) GILBERTS = se 23 Uolumbite, 2-2-3 =- Ann. der Phys., Gren., xX XVII, 105. 1897 223)| donvey 2-522 os a Aeschynite -22-22=_=- Phil. Mag., 1, 27. , 1828-2) HART WALL —-22 Fergusoniteandaeschy-| K. Vet. Acad. Handl., 1828, 167. — nite. Berzelius’ Jsb., 1830, rx, 195. Ann. der Phys., Pogg., xv11, 483. TSO en unVv s eeeeee Aceschynite: 22-2. === Phil., Magy) xplsi 183122) BROOKE =2-2c22c-- Aeschynite, 225 eos Ann. der Phys., Pogg., XXIII, 361. 1886__| THOMSON ---.----- Columbite 222-2. ==. Records of General Science, Iv, 407. 1844 _._| HERMANN -_-~---- Aeschynite: ---=2 ===: J. prakt. Chem., x11, 221. J. prakt. Chem., xxx1, 89. Berzelius’ Jsb., xxv, 371. 1346--| AROSE 22-2. ac Researches on miner-| Ann. der Phys., Pogg., LxIx, als. 115. Berzelius’ Jsb., 1846, xxv, 158. 1846__| HERMANN -_------ Researches on miner-| J. prakt. Chem., xxxviit, 91. als. 184822) SCHERRER <..2—-=| Wohleritess__--- 2252 Ann. der Phys., Pogg., LXxII, 565. Jsb. Chem., 1848, 1203. Minerslog. Forsch., Kenn, 1849, 197. 1848__| SCHEERER ---~---- | Euxenite and poly-| Ann. der Phys., Pogg., 1, 149; crase. LXXII, 256, 568. Berzelius’ Jsb., Xx1, 179; XXVI, 3874. Jsb. Chem., 1848, 1206. 9 eee INDEX TO THE LITERATURE OF COLUMBIUM. AUTHOR. REMARKS. PER WING osc =-._- Specific gravity and composition of American colum- bite. ROMEIS 4 —~ == 5=__ Composition of Sibe- rian columbite. 7548__| HERMANN -.-.-_-- Composition of colum- - bite from Middle- ! town, Conn. mp4s__| DAMOUR ~-__~.____ Composition of colum- bite from Bavaria. Bese i. ROSE 255-2. — Columbite {2-2-2 _1848_ HERMANN —_..-.-- Samarskite.2+.-.__. +2 fiieas__|G. Rose _-__----- Samarskite__________ PERN oe Yttroilmenite and sa- marskite. HRRMANN 2U=° --.- Pyrochlore and colum- bite. HERMANN -_------ Aeschynite, columbite, polyerase, pyro- chlore, ete. MU BR == S522 Columibites === 2e—2 == EDSON pe eee re Columbite and samer- skite. Fores and DaHLi| Bragite, Fergusonite, and euxonite. HOUNGOTT 22-2 ADytite ee goo aoe DESCLOIZEAUX -_--_| Crystallization of co- lumbite. CHANDLER-------- Samarskite and colum- bite. REFERENCES. Ann. der Phys., Pogg., xx, 572. Ber. d. Chem. Ges., 1847, 86. J. prakt. Chem., xr, 219; xuu1, 451. Jsb. Chem., 1848, 1207. CoAR., Xv, 670: ae der Phys.,, Fore.) Gxxt, 57. Ramm. Handw., 3d supp., 118. Jsb. Chem., 1848, 1207. J. prakt. Chem., xiv, 207. Jsb. Chem., 1848, 1207. Ann. des Minn, [4], x111, 387; [4], xiv, 423. Jsb. Chem., 1848, 1208. J. prakt. Chem., xxxvitr, 91, 119. Ann. der Phys., Pogg., XLv1tit, 555. Reise n. d. Ural, 11, 72. Jsb. Chem., 1848, 1209. Ann. der Phys., Pogg., LXXI, 157. Ber. d. Chem. Ges., 1847, 141. Rammels. Handw., 3d supp., 105, 129. Jsb. Chem., 1848, 1209. J. prakt. Chem., xz, 475; X11, 129) xutv, 216. Jsb. Chem., 1848, 1210. J. prakt. Chem., 3, 164-172, 185-192. Jsb. Chem., 1850, 748. Correspondenz-blatt des zoolog- isch-mineralogischen Vereins zu Regensburg, 1852, No. 3, 73. J. prakt. Chem., 1853, Lxvit1, 183. Jahrb. Min., 1853, 367. Am. J. Sci. [2], x1v, 340. Pharm. Centrbl., 1853, 341. Nyt. Mag. fir Naturvidensk, VIL, 3, 218. Jsb. Chem., 1855, 962. J. prakt. Chem., uxvi, 444, 446. Phil. Mag., 1855, 62. Pharm. Centrbl., 1855, 114. Ann. der Phys., Pogg., xcvit, 622. Ann. Min. [5], vir, 398. Mise. Chem. Researches, Disser- tation Gottingen, 1859. Ann. der Phys., Pogg., CLXXx1, V5 fis) CLS 460 selenite 449. er Sr === | | 10 INDEX TO THE DATE. AUTHOR. 1858__| BREITHAUPT =----- 1858__| Huco MULLER -__-| 1860__| NoRDENSKIOLD ---| 186022) BERZEDIUS=--—--— 1860__| DESCLOIZEAUX ---- 1860__| KoKSCHAROW ----- 1860-_| JEL, ROSE —=----2--- 1860__| Devitie and Da- MOUR. 1861__| HERMANN __------ 1861-4) SCHRAUS —.2-—_=22 1862__| H. Ros ___--_-_-- 1862__| KoxscHAROW -_--_-- 1868-2 El eRosmae See 1863 __ 1863_- 1863 _ - LETTSON..—~_--___- MICHAELSON _----- NoRDENSKIOLD __- REMARKS. Crystallization of co- lumbite. Composition of colum- bite. NTINeTe Sse Mineral from Ytterby - W ohlerite-_-_-------- Weschynite = --=.2-= Colunbite, samarskite, euxenite, Ferguson- ite, tyrite. Columbite, euxenite-_- Columbite, samarskite— Columbite Coluinbite, samarskite_ Specific gravity of aes- chynite. Columbite, samarskite, Fergusonite, tvrite. ® Crystalline form of co- lum bite. Bragite, tyrite --._-_-- LITERATURE OF COLUMBIUM. REFERENCES. Berg- und Zeitung, XVII. Am. J. Sci. [2], xxvi, 349. Q. J. Chem. Soc., x1, 248. Oefversigt af. Konig] Vetenseap | Akademiens Forhandl., 1860, — No. 1. Ann. der Phys., Pogg., cx1, 278. J. prakt. Chem., LXxx1, 193. Jahrb. Min., 1861, 329. Chem. Centrbl,, 1860, 969. Rep. chim. pure., m1, 181. Jsb. Chem., 1860, 778. Afhand. i Fisik, Kemi, och Miner., Iv, 281. Jsb. Chem., 1860, 780. Ann. Min. [5], Xvi, 229. Jsb. Chem., 1860, 780. Materialien zur Miner., Russe lands, 111, 384. Jsb. Chem., 1860, 781. Ber., 1860, 296. J. prakt. Chem., Lxxx1, 212. Chem. Centrl., 1860, 738. Rep. chim. pure., 111, 115. Ann. der Phys., Pogg., ex11, 468, 482, 549. Jsb. Chem., 1860, 146, 152. Instit., 1861, 152. Jsb. Chem., 1860. Note, page 152. J. prakt. Chem., Lxxxtit, 106, 317. Rep. chim. pure., Iv, 50. Jsb. Chem., 1861, 209. Wien. Akad. Ber., xutv, 2d Abth., 445. Jahrb. Min., 1862, 284 Ber., 1862, 138, 166. Chem. Centrbl., 1862, 262. J. prakt. Chem., rxxxv, 438. Rep. chim. pure., Iv, 456. Am. J. Sei. [2], xxxv, 427. Jsb. chem., 1862, 753. Materialien zur Min. Russ., Iv, DD. Ann. der Phys., Pogg., CXVIII, 339, 406, 497. Bull. Soe. Chim., v, 491. Jsb. Chem., 1868, 827. Phil. Mag. [2], xxv, 41. Jabr. Min., 1863, 594. J. prakt. Chem., xc, 108. Jahrb. Min., 1864, 236. Oefversigt af. K. Vetenseaps Academien Verh., 1863, 4338. Hiittenmanisehen INDEX TO THE LITERATURE OF COLUMBIUM. dL REFERENCES. AUTHOR. REMARKS. INORDENSKIOnD: | Colmmbites. == = CHYDENTUSs --_~--_| Analysis of pyrochlore_ FINKENERand Ste-| Composition of samar- PHENS. skite. GIBBS Action of hydrofluoric acid on columbite. 1864__| BLomsTRAND--_-~~- Columibites =-2-5 2s! 1865__| HERMANN ------—- Aeschynite, samar- r skite, Hergusonite, pyrochlore, Wohler- ite. BUSG5—_|| MARIGNAC -_=.--=- Polumbitev=2=*=s=—-5- MS66="| SHEPARD ..-.--_.- Specific gravity of co- lumbite. 1866__| Bromsrranp-__._- Analysis of columbite_ | : : (ee l866__| HERMANN -__-~_---- Analysis of columbite > and aeschynite. | 1866_.| CHYDENIUS ______- Analysis of euxenite __ ‘b f501-2.| HERMANN -_----=- Ilmenorutile, analysis - piS6/_.| MARIGNAC ________ Analysis and specific gravity of aeschy- nite, euxenite. iso. —| PMTPSON 2-2 -2_- Coluntbites=2===e= are 1869__| RAMMELLSBERG __-_| Yttrotantalite, pyro- chlore, euxenite. 1869__| HERMANN ____--_- Fergusonite, tyrite, ' bragite. Ann. der Phys., 604. Juhrb. Min., 1865, 86. J. prakt. Chem., xcv, 119. Jsb. Chem., 1864, 856. Jsb. Chem., 1863, 831. Verhandi. Min., St. Pet., 1863, 13. Aim. J. Sci, [2], Sxxvin, 35. Chem. News, x, 87, 49. Zeitschr. Chem., 1865, 16. J. prakt. Chem., xctv, 121. Chem, Centrbl., 1864, 990. Zeit. Anal. Chem., 111, 899. Jsb. Chem., 1864, 685. Oefversigt af. Akad. Foérh., 1864, xXI, 541. J. prakt Chem., xcvir, 46. J. prakt. Chem., xcv, 1038, 108, 128, 128. Jahrb. Min., 1866, 89. Jsb. Chem., 1865, 898. IN. Arehi phe nite, xxv. 124. Am. J. Sci. [2], xx11, 248. Jahrb. Miner., 1867, 198. Jsb. Chem., 1866, 944. Om tantalmetalliana, 1866. J. prakt. Chem., xcrx, 40. N. Arch. ph. nat., xxv1, 337. Jsb. Chem., 1866, 944. J. prakt. Chem., xcvit, 350. Jsb. Chem., 1866, 945. Bull. Soe. Chim. [2], v1, 433. Zeitschr. Chem., 1867, 94. Chem. Centrbl., 1867, 751. Jsb. Chem., 1866, 946. J. prakt. Chem., c, 100. Bull Soe. Chim. [2], virr, 42. Jsb. Chem., 1867, 997. INSFAT Chi plie Mtit., XOIXe 282: Bull. Soe. Chim., vitr, 178. Jsb. Chem., 1867, 998. Cains, Lava 419} J. prakt. Chem., cri, 448. Chem. Centrbl., 1868, 896. Bull. Soe. Chim. [2], vi11, 333. Chem. News, xvi, 160. Jsb. Chem., 1867, 998. Bern 7224" 1, 87, 26s Zeitschr. Chem., x11, 442. Zeitschr. d. deutsch. geoiog. Ges., XXI, 555. Jsb. Chem., 1869, 1229. J. prakt. Chem., cvir, 129. Bull. de la soc. imp. des, Natur- ulistes de Moscow, 1869, 141. Chem. News, xx, 119. Poge fo.) CXKIT, Lund., 12 DATE. 1869__ 1869__ 1869__ 1870_- 1870-5 1870_- 1870_- 1S 7le= dSilee 1S ie 1872__ 187225 1873__ 1873__ 1873__ 1876__ 18/622 V876.- Wi ies sii = 1877_- INDEX TO THE LITERATURE OF COLUMBIUM. AUTHOR. HERMANN ________ HERMANN ____-_-- FTE RMANN 222 se 225 HERMANN -__---__- SHEPARD 22222. 24 RAMMELLSBERG __-_ RAMMELLSBERG __-_ RAMMELLSBERG ~___ RAMMELLSBERG ~__-_ NORDENSKIOLD .___ STELZNER ___--_-- JEREMEJEW-___--~-- GroTrH and ARz- RUNI. SHEPARD 22 55e2 oe. H=RMANN -___.___- Hos OANA 2s eee J. L. SmMitH___--.- ALLEN see es RAMMELLSBERG _-_- REMARKS. Fergusonite, tyrite, bragite. Samarskite -..-..=---- Aeschynite, euxenite, polycrase. Samarskite, columbite_ Columbite_____-..____ Fergusonite and tyrite_ Eijelmite====.—=—— ee Minerals _______ sae PyrochloréS2ns-s2ao—= Ruxenite: 222 = as Aeschynite and samar- skite. INGhiite 22) =e Occurrence of minerals in granite. Crystalline form of co- lumbite. Crystalline form of co- lum bite. Hermannolite ________ Analysis of Hermann- olite. Crystalline form of sa- marskite. Minerals, columbite, samarskite, euxenite, Hatchettolite, Rog- ersite, Fergusonite. REFERENCES. Jahrb. Min., 1870, 629. Jsb. Chem., 1869, 1230. J. prakt. Chem., cvir, 139. J. prakt. Chem., cvi1, 158. Chem. News, xx, 119. Jsb, Chem., 1869, 1230. J. prakt. Chem. [2], 11, 128. Chem. Centrbl., 1870, 551. Amer. Chemist [2], 1, 236. Jsb. Chem., 1870, 1811. Am. J. Sci. [2], L, 90. Chem. Centrbl., 1870, 708. Jsb. Chem., 1870, 1312. Ber., 1870, 947. Ber., 1870, 926. Chem. Centrbl., 1870, 828. Jsb. Chem., 1870, 1813. Ber., 1871, 157, 406, 584, 874. Instit., 1872, 58, 302. Ann. der Phys., cxiiv, 56, 191. J. Chem. Soc., xxv, 189. Chem. Centrbl., 1871, 511. Zeitschr. Geolog. Ges., xx11l, Ji 656. Jahrb. Min., 1872, 534. Jsb. Chem., 1872, 1166. Jenau Dissertation in Jahrb. Min., 1872, 319. Ann. der Phys., Pogg., cxttv, |§ 595. Ber., 1872, 17. Jsb. Chem., 1872, 1128. Jahrb. Min., 1872, 535. Min. Mittheil., 1873, 224. Jahrb. Min., 1874, 305. Jahrb. Min., 1873, 421. Ann. der Phys., Pogg., cxLIXg® 235. Am. J. Sei. [3], x1, 140: Instit., 1876, 188. Jsb. Chem., 1876, 1257. J. prakt. Chem. [2], x11r, 386. Jahrb. Min., 1876, 662. Am. J. Sci. [3], x1, 201. Am. J. Sci. [8], x111, 359; xiv, 128. Ann. chim. phys. [5], x11, 255. Zeitschr. Kryst., 1, 499. | Jahrb. Min., 1877, 728. Analysis of Hatchett- olite and samarskite. Analysis of samarskite and aeschynite. C. R., txxxrv,, 10386. Abs. J. Chem. Soc., xxx1t, 576 Zeitschr. Kryst., 1, 502. Jsb. Chem., 1877, 1343. Ann. Phys. [2], 11, 658. Ber., 1877, 656. INDEX TO THE LITERATURE OF COLUMBIUM. 13 REFERENCES. Zeitschr. 815. Jahrb. Min., 1878, 529. Jsb. Chem., 1877, 1844. IN. Arch, phi nat. pxix, 176; Am. J. Sci. [8], x11, 390. Zeitschr. Kryst., 1, 503. Jsb. Chem., 1877, 1846. Geolog. Ges., XXIXx, Analysis of minerals __| Zeitschr. Kryst., 1, 503. Analysis of samarskite_| N. Petersb. Acad. Bull., Dare. AUTHOR. REMARKS. 1877__| RAMMELLSBERG ___| Analysis of samarskite and aeschynite. 1877__| DELAFONTAINE___-_| Hermannolite ....---- 1877__| NORDENSKIOLD--_-. ’ i= — | DAMOUR,--2-——==- get) Konop. 2.2. L 2. Dy sanalitersssas = =a Seg =| MALLET -.--.--.- Sipy lites 226 <3 Jy '1877__| DELAFONTAINE____| Samarskite __..._______ mis7S__| DELAFONTAINE.__-| Sipylite______-______- Sic 79__| BROGGER-__-..---- Ateschynifemeaa= ase —s m3 ;9__| SCHARIZER___--~-- Columbite== 1 m380__| Comstock _________ Columbites2s: 22s sss mies0__| JANOVSKY __----_- INTO bite =e tr -1880__ BLOMSTRAND ~-____ iPOly.craseron sae ee aa ms80__| SHEPARD ________- Nittrotamtalite) sss. Ree (e | ETD D RN 2 — S058 Hereusomite) 2222222 === mcs0__| SHEPARD ________- Ruthertordites.-——.. = “1881__ ETD Ne eens See Nesey mite === ee Biss. FAT HOCK Sessa © Columbite= aaa “1881__ MCA eee ee 2 Bk Sipylite S22 oe 1881 __ DUNNINGTON______ Microlitent.220 2 ae. ETD DENG Se Se Columbite:. === “1882__ G. C. Horrmann __| Samarskite _-_---_-___ = SEAMON) S25 22a 8 Herausomitem= =o ‘80. ROSCORM == oe asee Samanskite==se= = =see Ma ape Sanaars a epee /1Ss4__ DonaLp Jsb. Chem., 1877, 1346. XXIDI, 463. Zeitschr. Kryst., 1, 284. Jahrb. Min., 1877, 647. Am. J. Sci. [3], x1v, 397. Zeitschr. Kryst., 11, 192. Jahrb. Min., 1878, 208. Chem. News, xxxvi, 158. Abs. J. Chem. Soe., xx x11, 8538. N: Arch. ph. nat., LxIx, 176: C..K., LXSxxvi, 983. Jsb. Chem., 1878, 261. Zeitschrift Kryst., 111, 481. Jsb. Chem., 1879, 12388. Verhand. Geol. Reichs aust., 1879, 243. Zeitschr. Kryst., 1v, 633. Chem. News, x11, 244. Amn ed). SClep |e |p, SER, Lal. Zeitschr. Kryst., 1v, 616. Wien. Acad. Ber., Lxxx, 34. Zeitschr. Kryst., v, 400. Bers excT el 39! Min. Petr. Mitth. [2], 111, 94. Zeitschr. Kryst., rv, 524. Jsb. Chem., 1878. Ami JS Sei. [is i|,oex, 56: Am. J. Sci. [3], xx, 57. PASTS te) fem Clan [|p PREKS ON Us Am. J. Sci. [3], xx11, 23. Jsb. Chem., 1881, 1409. Am. J. Sci. [3], xxz, 412. Zeitschr. Kryst., vr, 208. Am." J. Sei, X11, 52: Zeitschr. Kryst., v1, 208. Am. Chem. J., 111, 180. Zeitschr. Kryst., vr, 112. Am. J. Sci. [3], xxiv, 372. Jsb. Chem., 1882, 1573. Am. J. Sci. [3], xxrv, 475. Jsb. Chem., 1882, 1573. Chem. News, xLv1, 205. Abs. J. Chem. Soc., xutv, 32. Monit. Scientif. [3], x1r1, 246. Jsb. Chem.; 1883, 361. Chem. News, xLrix, 259. Jsb. Chem., 1884, 1994. 14 INDEX TO THE LITERATURE OF COLUMBIUM. DATE. 1884__ 1884__ 1886_- 1887__ 1887 __ 1887 __ AUTHOR. BGAKH yes setae SCHAEFFER ______- DANA 22. 25 1s COSSIAY 2 2s 2 2S IPTCOOENT: 22 2 ee ABADDON. -o+2 68 REMARKS. Columbite, occurrence_ Columbite, analysis —_- Columbitezs.2-25. =.=" Columbite from Gra- veggia. Mineral associated with columbite. Columbite from Colo- rado. REFERENCES. Am. J. Sci. [8], xxv111, 340. Am. J, Sci. [8], xxvii, 340. Zeitschr. Kryst., x11, 266-274. Abs. J. Chem. Soe., 1887, 20. Gazzetta, XVII, 31-387. Abs. J. Chem. Soc., 1887, 645. @ Zeitschr. Kryst. Min., x111, 302. Abs. J. Chem. Soc., 1887, 1085. | Zeitschr. Kryst. Min., x11, 513.8 Abs. J. Chem. Soc., 1887, 847. — 1 SANEA Seep tens.) | ALPHABET The numbers refer to the years, the part 18 being dropped. ICAL INDEX OF AUTHORS. When preceded by M it refers to minerals. AUTHOR. SUBJECT. DATE. PAG IH IHN GME Meee cc ee ws Analysis Hatchettolite and samarskite ________ MET IBMR REMUS aoe eee Mam eraileirompsyitter bigest ee ey ees M., ’60 SPANK pe ee Occurrencelofycolumibitess = sae eee M., 784 IBTOMSTRAND) 2-2 5 Calor idle syern cls ci cls y= eeeeerem = aa eee See ee 64 DO MEM ka peta (6 oy earn ts ea eee ee 2 M.,’64 OMAN pee ea 2 Am sulysisycolum|bltege=== en oe ee OG Do. eerste Saas ONVCTAS CRUE = ame ee tus ee ee eee ee M.,’80 BOISBAUDRAN —=4--~2——- == Separation trom) calliumiss 2 22 =e ee 783 Ey CN Gee eee eee ae NIOERO GYAN ein eae = seat oN eR Eee. 78 SRE URMAUP Tone 2S ee Oxystallizationof columbite-==== =. 2255-2 M.,’58 IIR OCG Ree) See ee PACS CIV MITC ee ee ot eet A en M.,779 ISR OMNIS Sse -se een So ale Composition Siberian columbite______________ M.,’48 ROOK ye ey Sue ee Le NeSChy Mitel == soe coe ee ed 2k oe M., 789 IWINGHING = ote ee Ee IN gwon) EROUO MN = ee ee ee GE CUATRO, 3S & ey aie neg ss Ni obreacird ping ting one yess eae ee eee 65 WAN DINER: =o ose oS Sumearsiaterandscolumibites sss 222) ee ee M., ’56 AOYGMHNIUS 2 hte es JAIME ARIE! oniaeaved Kine ee AE es M., 63 ID) Oa eee eae ke Amallysisxeuxenite== === ee Bee atten ey we M., 66 RGMISPO CK cy WOR TO a Columaljitegee sss ewe eer 2 eee a Le M.,’80 BeneNI ee oe at ae INC) oes as he a ee ee 54 ==2242 =.=. __| M58 cei se" 2 Min Grail sie 8 2 See pe bee Lae bots Fee 2 ae Me 60) eee eee INTODI CAC CE See ee Mee eatin el he Bel ae hai, Ee 61 ares Seal Bin e @ohamibitews2 2 2Ne ee ee ed Se eae = oe in oes I MGS SEN Denes 2 INGo nile ees es eerie see ie kee Ria. SED Serer: Feels PRAY SIS TUM OTH IS aes eae tone nik wan = tees 2 MR Tig peewee oe Nee GSC nehes Sea eente wus ab a oe a 756 Penn Sees See eae RESCH RCT OS ieee meer sete ee el We iy tel DO Rete fe ts 58 ae eee LS = LON 3 Quantitativevestimationy= *==422--ss25 555 258 85 Eta EE SE Niobic, pelopic, and ilmenic acids _-_____-____ 48 BEEMUPSON) 225282 eee Coline ities sae oes Ce aed Deis a ae as M., 67 PeNCCINT =.= Ee eect eet i Mineral associated with columbite________ ___ M., ’87 RAMMELLSBERG_-____..-__-_- Compounds, atomic weight —_-___ SNE Ss 16 Ne 2 69 ID orem ameeN kn) k= Nba tere Yttrotantalite, pyrochlore, and euxenite —_____ M., ’69 ER ee oe EC lmnnie Bess sare Pe alse ee eta FO M.,’70 le) gt es ee HOO USOMIte VIG vel te eer eee meee ce M.,’70 Soh ee eee te Composition of natural niobates and separation vie of metallic acids. Sane ee Mic ert [sense ee oar nee in eke Wales Seeinal | rs cate teh Me A SE RAR eos EPs ACS VMILO rae SAIMATSIILer sy 2s at vas AP MOTD awa meena iS Analysis samarskite and aeschynite-__-_______] M.,’77 See pee em Ri Pa Dudrasleiers ost ac oe nem Stns Behe ae Seale Ie 4S NS ee eo Soe Samer tenet. see eee esta ene es |, MAS Baerga. Pee ve a INGSCATCH Es ets as eke er re a a 2 40 Ey ele eee eT See er NEBEATC OS) Jae he 8 as ern es Sat ee ee 744 ee er Se ees FROSCOTGH GS 235 es ies i ae SU eS ge ee Nt 46 SIMU em 3 or) ee Mice ral sae 2s So eee ee ea Se el teh MA AG err Cen ee SR Acidssmycolum bites == ses ees ee 247 Dre Seah ee eee ee Effect of temperature on specific weight of 48 compounds. eerie 10 Ley Niobic, ilmenic, and pelopic acids_____-_______ 48 Beet pe ead Identity of ilmenium and niobium __________-_ 48 Se ee eee Properties of metal and oxides _-_____-_=_____ 748 ea eee OGM a Se pee Ot ee oh a ce RNS *48 RES ee eels eae Columibipe Lae oe cae alk) So. LM Pas pee eee eS Researches, identification, compounds, etc. ____ 53 eS re oe ea Niobic and niobous acids, metal, chlorides, ete._ 58 Seta Se eee Compounds se oo see ewe OE Pe ce to 58 DESO RE ESS Sepa ees Ul pile ee eee eee Re ee dye 758 SE ee er aL ed Mivorides,and.ehtorides 2 2.2210 7 Le ses 58 i ee ee INipribe Hs tee hE Pale ee De Sn 2 lcs 759 OE 18 ALPHABETICAL INDEX OF AUTHORS. AUTHOR. SUBJECT. Date. ROSH wes see nee ee ee INlobIC acidi-=2ae==. 224 eee 59. 1D) Os Ar ae ee eee Daltga lw = Fae bo bee 759 Dows | 22e2eset soe eee Compounds!:--5-562- =. 5 =¢ SS eee 609) Do estes eee Niobousjicid.2-= 220.224... 20) ee 60 DO ly ee Se INitraie 224 2. 3 =22 2 on ees 60 LD PS ee ee Columbite and samarskite ---_----------+---- M., 62 Dovey Ale: Se ee ee ae Columbite, samarskite, euxenite, Fergusonite, | M., 63 tyrite. | SANDESSON coos os) ee Hydrates, niobates, and fluoniobates -_.-.--___- 75 SCHADEP ER S22 os seen Analysis columbite 222. <=-2252- 25 ees M., ’84 | SCHARIZER 2222= sess Colum biter = 2.2. 22.0252 oe ee M.,’79 SCHERRER =#22. = 2 me Metallic acids in minerals -=_! -20 == 2s ses8 48 TO: OL he ee ee ee Wohlerite, euxenite, and polycrase ___---_--__ M.,’48 SCHRAUR Mae see a eos Columbites.2 22. = a3 ee ee M., ’61 SEAMON 2222-52 ce5 22- eeo Analysisvol a Mio bate-=-=)) = ese 83 DO) Os ee ae eee Analysis of columbite= =.) == 32252 === aes M., 82 SHEDARD 22s o. .aeoee Specific gravity columbite -..- ..2c.-22-fso a5 M., 66 1) Of Peer a ee ia Columbite 22> oes ie So ee M.,’70 AT) Ce pantera Hermannolite -22-a= 2 S22 ees 22g ae es M., 769 OM eta sa ae sans o Rutherfordite and yttrotantalite-__._________- M., ’80 SMUD, Gl. live a-2- 2-2 ee Researches 2... he s- Sane eee Uh Os Senne eee rw a Nameic a2 So 22 es | ee ee Tn DOM 0) ) seeetou tee es Columbite, samarskite, euxenite, Hatchettolite, | M.,’77 Rogersite, and Fergusonite. Dow wee beers Researches, Mosandrium) 2-22-25 =2222 256 —==o= 78 1) One an ees ee eee Method: of analysisi< ==> se eae °83 SUPLANMR, == 22225 2-222 se Occurrence of minerals in granite_____--_-_-_- M203 IHOMSON =222-c2-----a-e Columbite- 2-242 = 53 eee M., 36 Troost. See Deville and : Troost. VER ENDINE 2 ee Columbitess2c2nc 52 oes ee ee eee M.; 05 VoagEL. See Leonhard and : Vogel. WON KOsELL o2--2 2-2-2" Dianium and dianic acid === == =seesa=sea= 60 DOS eee tee ae Dianivin: <= 88s 2 ee eee ee 61 DD Ove Dene = eee Dianic-acid’ «i227. = Soe ae eee oe eee 65 WV ELE. eens eae Action of hydrogen peroxide on oxides ~__-_-- 82 WOHGER Seneca secs Properties, of oxidel us? 2022 ee eee 39 WOLLASTON —_ =. 5--4 2222 Identity of columbium and tantalum ____-_~~_ 09 Worst) pee ee ee Hlement 2228.2 See. 2 ee eee 11 INDEX OF SUBJECTS. MINERALS. MINERAL. AUTHOR. DaTE. Brasth yiNit@s. 22-2) 5. = (4 == ase ce see seses=a-==- TMV Mise eres eee Noll CM Ree eK oe Ma ie Se ee BROOKN a2 2See =| Me? 3 Pee niet lee eS Wal ede et eo Ee En RMAEN IN Re ee M., ’44 Rp ee er eee es PLR. Mts see eek le oe pg es ene re M., 50 cM adits eg woe NY My Bd as ie ee ee LE es KoxkscHAROW ------ M.,’60 et Specitucionravity 22. == 2-2-2 ee Ce halite ere M., ’62 COMO aRN Es SERIA) ue Re HERMANN _____---- M.,’65 a Amaillysis aie sue StS See ee Une at (ERE eEN ee M., ’66 uo (s Jand specific sravity—--—-.--..2-=- NEARIGNAC Hee tLe. 22 M., ’67 Mee Dry kota, IN OE CEERI FES a eh ERR MUAUNEN]) Sees ee M.,’69 aN i peat oe ea Mela ee As he a oe RAMMELLSBERG -_-_-.| M., 72 “ Amialyaise Ghee s lee Sleek cose eS oe ‘a eae age aie CM aig dice pa Ot fe eS ns at oe lS ee BROGGER) 2225s 225c= M.,’79 CM teh ey iant me ER MAY 2 eee ELD DNs M.,’81 mornvars: Columbite a2 292-2425. 22- ---=-=4----- GREWINCK=—s.+-=-= M., 748 a Siberia oluin thes se a ene eee BROMEISE2 “2 S2snee M., ’48 ce Columbite from Middletown, Conn. -_------ ER MeACN Nig M., 48 us Columbitentrom: Bavaria oe=---=—--— = — = DANO UR M., ’48 ee ce a CC eaten Se Se ose Se ee «US Mitgnn Re Ses Sebel M.,’58 ee ee cc OL OC es ae ies es BLOMSTRAND--~--_- M.,’66 ue Columbite and Aeschynite ....2_/.----.--- IFLR CARN Nie eee M., ’66 ee JMG Teheran ee ee ee Cy DENTUS See =a == M.,’66 et Mmanonntilete west sa eee eee EUR RMEANING S23 oa M., 67 ug Aeschynite and: Huxenite _.-..=----------- MARIGNAC __=_----- Mie Ore ue [Eltermamino lite eae ee eee eee ee ee EURRMANN: = 2522 22—4 M.,’76 ce Hatchettolite and Samarskite---.---_-_---- ATIGEN) Sees Soe Me ihe, ub Aeschynite and Samarskite__--_----------- RAMMELLSBERG .---| M.,’77 ce IMiimerals) Sema eee oo Tee eS NoRDENSKIOLD -_--| M.,’77 ge STS a) yeaa see Se ee ASM ONR Re eee MEG ce Golumbitem ao sare Fe ee ee ees SCHAEFFER -_------ M.,’84 Hvar Columbite from. = = S222 DAMOUR ==2sae === M., 48 apiert eeeee a See ree MICHAELSON ____--- M., 63 CM pe eke ls Scat i A A Po Se ees ERAN ee a M., 69 Wolorsdon Columbia == essa ee ee FEAD DONS ae M., 87 MONT COs ee en a ee ees ae eet VAUD GESRIED eee M., ’01 Nee tagcat sk A Sto ON Ee pit Se Seto ess SVP ACITHNERIENU EL sey ee oe M., ’05 Lape mem earn eed) SECT Tat UAE as oes ee GaitBERTS22ses2—52 M., 711 CN pine ceisrank neste SA Ve a Eye ete iRTOMSONG@==—=—=———= M., ’36 a Specific gravity and composition. American | GREWINCK~-_------- M., ’48 specimen. BC Sibentansaeste a 32s oo ae ee eS IBROMMIS = eae M., 48 ub Wonnecticnt ate a es eS Soest ISR MANN Nie ee M., ’48 ue Baverig=s 224 ee fs on See tehs IDAROUR Eo ee M., 748 COR rte ee REL EE 9 Fe ep No ee 1Bly 10 chy ag M., 748 as Santa a enV pg Pelt 28 Loerie Ma Eh es EB tae (EUR AUN Niet M., 748 Tay ie Stacie RR ENS IAS ME a et Nace d tO ies ao M., ’50 (19) = 20 INDEX OF SUBJECTS. MINERAL. AUTHOR. Date. Colum bites ase 2 ears eo Se een eee ee ee NUniHRe2 Sees M., ’52 Uaae eo Dror Be eee en Lee AUNT 22223 ee, CM af Crystallization 2 == =9 =. = Se = ee DESCLOIZEAUX -_~-- M., 56 BE ON eed ee ep ed eee CHANDLER 2 = 02222 M., ’56 ef Crystallization eo 5 oe fo BREITHAUPT 2-2" M., 58 vt Composiiiome sem cen 22 coo ssh oe es MULLER... =-2_2=2 2], Meog OC gtitae te ee ee eee ee eee HL Rosh, 2.22 M.,’60 “ Sa ee ANY fre re tee eed DEVILLE and Da-| M.,’60 MOUR. AC teense ee MSMR eel ns ee HERMANN __._---__| M., 60 ec eee Se eer es ee SCHRAUN 22-2 aeee M.,’60 ET a 7 Se ee Be a i eg He Rosh] se M262 Ce ee ee ee ee ee ite. ae M., ’63 at Crystallization: Busia ee he DEUTSON 2 eee M., ’63 CCSy ay 1 = eee eee Oe Pe ee ey eee NoRDENSKIOLD____- M.,.’63 & Action Hydrofluoric acid on ___----------- GIBBS -2e-ses seems M., '64 ey Oe: ree Ze Oe aah ES ae ee eee BLOMSTRAND_______ M., 64 SO en ee ees 2 geen ne 2 Oy a es Bares MARIGNAC -_=-._2.- M., ’65 6 peciie eravibyes. = 2-22 = 4 ee SHEPARD .2___.___.| M.} 766 a Taye ees CAS wh Seen cota BLOMSTRAND--_~-_-~- M., ’66 a eg ee a ee ee ee HERMANN ___-__-_- M., 66 OS gh ee eee a ee ee PERI SONG == ae MM... 164 COR Pe ne ta Geet eee HERMANN —_3.c___- M.,’70 OW ie aeons 8 syne ger ee ee SHEPARD 2202 ols lee M7740 “ Cnystalliziition =a saa 26 22 een ne eee ee JEREMEJEW —_____- M., ’73 ce c Bh ae) eee eee GrRoTH»nd ARZRUNT] M.,’73 OT am, ns ee Me Ne SE eee nn ee SMUD S22 le See MES ein CC ee ene Oe ne Ae A ee ek ta ee SCHARIZ BRN ssa- ese M.,’79 LOM Ce = Oe eC a ee ot ee COMSTOCK (22.4;2- 44 M.,’80 a ee eee Se SOP See een le HALLOCK . 2. = 3 | Mae ei CME Mey Se once Seer) ot. eee le eee HIDDEN 22 ae ae oe M.,’82 ue OCGUINENCOsNs Sea 5S. Sane. Fee BN As ee ee M., ’84 a PATIGI SIS ee ane ee ReneS Aa eee SCHAEWHER) 42522 2= M., ’84 EOD ee eee ee ence et, Net Lee ee ID ANA Ee 5 eee M., ’86 SO ee ee ee ere ee et. oe tt COSSA, 2isle08 2 = Me Si gee a See Mee Oe 8 ET HAD DEN === M., ’87 Composition. See Analysis. Crystallization, ‘Colirmbite <.2.--- 2522.22. -. Secs DESCLOIZEAUX __.-- M., ’56 “ fC ar ees oo Se PS ee BREITHAUPD 222592. M., 58 ce FD goer eo ee. ee es: LE®TSON S22 ses2-—" M., 63 “ Sa en ee ee ee ee JEREMEJEW _______ Mig 23 “ ee pote epee een e--=- 2 -----| GROTMAnG ARZRUNE| MENS tt Samarsicite: 25+. _------.25.-=.-.---- DANA, Soe a ae M.,°76 Dysandtee 6 -o e ae a e e aee eeeee JKiNOP 2. eee Mei iuxenite, Amal VSisi 52a eee ee ee CHYDENTUS. 53. s==5 M., 66 a EO ee ee ee ee ee eee MARIGNAC =_ 22 2225 M.,’67 CO ae eas Ab ee epee ee es a ee ok ee SCHRER ER) 95-5 so5== M., 48 OO gs cae ee Oe fe ee Ee Ae ee .-| Forses and Dauxi_}| M.,’55 ot se Hs Se ROT) SS Rea a = nee Hi. Rost) 222 2-seeee M., ’60 CS ange te Bs eee ee a ee ee ee ee DEVILLE and Da-| M.,’60 MOUR. Ly Pies eet ene Bele ere ns Re ys eee ee RAMMELLSBERG -__-| M., ’69 CO gs Sete a tol A oe ee tae eee HERMANN 2222 -te== Mie 269 Oop pee. an eee oN oe POO Oe ee eee ee JBN. 2 aes Me, a RCE Sha) ec) eae. Pir de Et Pe eee eae eet SMITH 26225 === Me 27 7 « ppechicvwrayvitys G23. eee Se eee MaARIGNac._____._- M ,’67 Mergusonite: 2.262 Ses ek a HARTWALL 6-2. 22-4] Mes OR Oe oo ae eee ee eee oe co ee Forbes and Dauii_| M., 55 INDEX OF SUBJECTS. MINERAL. AUTHOR. DATE. Brerousonitess.s42 90 i sy hs 8 Eee OST pees nee eee NE G0) CCMEN ry pean 5 PN ME RUA E EL Ser eth ot te tn Tee A ere eae Ouch M., 63 COMMER aya Riera hae EU ALSO att wl te ek ee AIBRMANN: 252522 02 M., ’65 CRT Se Serer AE EN MORE St Sa Ak ol ee CRE ceeds OU aes M., ’69 Cag Nees est LOS EIR By Oo Gen RI OANe RL 2 RAMMELLSBERG ____| M.,’70 ca ATE Oa SIE EINE AUTH PPT SN hae Oe ee! ELED DN) ee eee M., ’80 | COR enters Oke La Se le DEAMON) See sans M.,’82 meoravesoia,,Columbite_--/_.--_-____-.--------.--_-- COS SA way feat ae M., ’87 meelatchettolite; Analysis_02-—-_____-------- -___=- -_-- AC IEGN Ne Sse SN a eS Mead i. CMMs ARAL IPSS tee oe) Sa hk ae SMI eeef ste Mal merormennolite, Analysis... —-___------------.--- FER MAGNEN ts ee IME 7G Be A MN TIMES) SRST EE 8 Co a SHEPARD ps ee M.,’76 CUE AUR hme) el pm be aie #r 28 LP wh Tha Se DELAFONTAINE ____-| M.,777 Sijelmite._.—_.- ane Mae ES | Rasp ERe 2 | NL ZO Hydrofluorie Acid, Action on Columbite ---~-------- GIBBS eo eee M., ’64 SPINE TNO TUG mae keen ak Fh EP hn ee Sa Se EAGER MivAsNYNo MES Gin PNM HO tei see ee aS Vi el ees DUNNINGTON---.--~~- M.,’81 BPRS col An cous semen mrt Ad ek ti TN 2 ee He Rosh aes M., 46 UMAR Str Aemieeeune agg sta) Saye oe FFE MEAN f= M., ’46 COMER RNps Pee Set RYERSS Ae oe ee See NorDENSKIOLD ____| M., 60 CORMAN eye se i ea Lea RAMMELLSBERG ___-| M.,’71 . SE a bf oe ea A See 2 NoRDENSKIOLD -__-| M.,’77 Niobite. See Columbite. BPE eee Ie EMRE ol 1 Ue ee 66 pores Ni ao Be iccurnances: ©olumbite==s2 22 222. 2 ee [Bai Alek eee eee M., ’84 ub Minerals imiGranite ss = =2— 22 ee we STPREZNMR] ss. see M., 773 BeEBWaE cee ern ene tes be tae ee ERR RIMANING ees M.,’50 , CO AniyWn Repetto t e CCT Mp sac) te eel gerne M. 269 7 PERS Be Ea a a CHYDENIUS -_------ M., 63 - CEREPE E tarp ee fag, ee ene Ne ie Su eee || ERMAN Nee eee M.,’48 a eae Nera ih wer eae ere Sy ir bg Ot A La I Ge rai) Mis a ek a Pt M ; 750 Sues wade een teed ee be So Pe ek oe a SO re Rate 2 M=. 165 meena tip Sune) pages eee so eee NOSIS eae he RAMMELLSBERG ___-| M., 69 CORR Ueto w eft) PUA AO Lh eee SE ren etl ee KN OPS sos ae ee Ie ae mes Ped ees age Red ads OS Fh ee pik eee uaa BLOMSTRAND-_----- M.,’80 Servesearches:on i Miimeralss= 2s bi Se. ea ere ee Se HeRosm aes 222s M., ’46 ue CO aie a a te a aes oe Ma = HERMANN —.------- M., 46 SUG as ee ee a ee ee ee ee SMI ae oes Mee tin ETE eETORGiiC meee ee tl eeu See Bee SHEPARD aes ee Mew S80) Bein CoKiLe s Amolypigys 8 lie Uo hoe AST AEEIN Se oe eee eae VES a oe CUMIN pt See ye ee Se Wee ee ee DAMOUR === 2-5-2 === Mei re CRNA cart Reo Ribena eS RAMMELLSBERG -_--| M.,’77 ge Se a a ee FINKENER and STe- | M.,’63 PHENS. Ca eC eal ss CRA eR Pra pS SPE ee LS ae Joe ELLER MAN NGS eon oS M., 48 ORM ree kim (see a yk dena A BY a ee te Ga Rosnssees 2223 Me VAs eae twee APM ute SS ee ea SS PR NZ Ee M.,’48 (8, 9s gh eS SSRI MET ag Ee ee tO, IB Nee ee eee Miz, 262 men amp rs eter Wise 40s 5 8 oe ee Ae teh oe SE CHANDLER__--__-.-| M.,.’56 SPA ia po Sern SNPS WL ON Da eee a es Ne FDRRMCANNE SSS. 2 oe = Me 6 pn ene ine i RSE eS eS Sk ELS ROS ee ee ME 62 Abas wore beter the 4 be NN A le Wii Meee tat Ek M.,’68 Hae pa pece sn ey CP ee TS NT ee ee HERMANN -_-___--- M., 65 Cea nen tere ee US oe ie Bee ie ee CT wise 3st M., 69 SON A eee es eS Rae eae on bee ae io ete os 23 3M su O BEM PA Py ccrnn ny Meee ee AIS oe es oe SE RAMMELLSBERG ____| M., 772 ee Crystalline formi=8 2. = see ss eS SIS UAEN Ava ee Aa M.,’76 OT ict te ee SS Le Ae ee eed SMUT Hs 6 oe ee eM Td 22 INDEX OF SUBJECTS. MINERAL. AUTHOR. DaTE. DAMATSkite= = 2. <2 a ae ee ee eee DELAFONTAINE_-_-__- M., i On ala seh A cry OS 2 ee ee ee HoFFMANN--------- M7282 WOE gS oe Sas at Se ee ee ee eee Roscons== = M., ’83 OO Myers Su as a Oe En eee eee DONALD 2222 = eee M., 845 SOW UG = ee ee ae ae eee ee eee ee NALD ET S225. 20 oe Man RS yee Se eee ee Le oe a meee tances DELAFONTAINE ___-| M., Cae ee ee ea el Ae age Be ee MATL Unit Se awe. M.,, Siti Speciiic cravity Aesehynite> KoxkscHAROW --~---- M., ‘ a ut (So a okaek ne | ACARI AG ee eran M.,’67 4 “ cc) = Columbite:! top 2e——) ee ee GREWINCK_____---- M.,’48 ae a Uy Ree Pee kT are omen Ee SHUPARD 222 eee M., 66 Ye 7 GAKeniteeee alo. 2) Pee ee MARIGNAC ______--- M2670 i Mgt ae eee eee eee eee eee KENNGOTP © 2coose-4 M., ’55 CO ome ar Se eA cre el Nie g Pep Viens ee See et His ROSH 2222 ssoeeee M., 60 0 let A Se tt eee ey UP OG OP 55 a tee M., 7638 OS 8 Fee mam eete Sse oe a ee ee, MICHAELSON -_--__- M., 63 CON a tS ot hee Sts elk See ee ee ee IMR MANN 222252 es M., ’69 GS ee ne on ee er RAMMELLSBERG ._--| M.,’70 Wiohletite: 2: s...4 2223 ea Ce eee SCHEBRER ¢o--2-2-= M,, 489 Sie oe ee ee ee DESCLOIZEAUX 2 22- M., ’60 ee oe Seen ee ee | CER RAN oe ee M.,’65 eYsLLTOMIMeN ite == a=) See eee ee ee PEREDZ 0222s M., ’48 Ltterby, mineral from —=-=)- Sooo Sees BERZELIUS..22225-4 M., 60 RVGtbrotantaliter 2s ees eee es ee ee ee RAMMELLSBERG -_--| M., OME) El pre cle ese Ee A oe eee ee eee es SHEPARD 22S M., GENERAL INDEX. SUBJECT. AUTHOR. DATE. Ncrdseme COlumMDiteme eee aa ee ee ROSIE ecg ee "AT Acid, Ilmenic, in Columbite ..------. --------------- HERMANN (2-5 "48 “© -Niobic, in Wohlerite___----------------------- SCHERRER === 48 CCIE) [1G ent ee ee eee LER MA NING == eee 48 ce Cine ant aliCrAC dessa sean ae Sirah Nees lp ta Pa "48 cc CO nan LEK TA © ene ee SCHERRER cis. 2 oe "48 Acids, ‘ Ilmenic and Pelopic------------------- OSH, Eco = emt ee 48 cc cc 6c ch (CMMs) gee bearer ete PERETZ NL ee AS ae ‘« Tlmenie, in Pyrochlore and Columbite---| HERMANN ------~~- 48 Acid, “'* Crystals of __-----------___.---____---- NBELMANIS==-255—22" 251 Acids, ‘ and Tantalic, separation of ------------- ELBR MANN 25028 28 58 Weide) o and Niobous, = =-=—--_2==__- == _- ROS wh Pigs yf te 5S Acid, Pelopic ---------~--------------------------- FL ER MANNING 2222 = 58 06.” TRIG Oa 5 = Ae ae Se ee ae ROS la ee ee ee 59 00. IDAs oe ee ee WON KOBEIIy === 60 ERB NATTY OLS nee ee eee ROSH ne lees = seen ae 60 PoE NG OC eee een See See ee NORDENSKIOLD ___-| ’61 PNT cee en ee ee ee a ne BLOMSTRAND_-~- ~~ ~- 64 Acid, Niobic, in tin ore -__------------------------- (OLN ON eee ee 65 Ne eee ee IMEARIG NING eee wees 65 eid, limenic=—= == eS __--___ CCT tpbone th ia 2) 65 CREM) ey Cpe ee eee ee ee ee Vion KoOBELig===—= 65 PN eC ee eee eee ER NCANING ee = 65 (a OS pe ee Be ee eee Cee TW, ete et 2). 768 Geer Separations snes = | RAMMELLSBERG ==—-) -*71 Cn een eee a a ose ae JOLY 2 oes ec "76 Action of Hydrofluorie Acid on Columbite ---~------ GIBBS) 22220 es 64 me «¢ Hydrogen Peroxide on oxides ------------- WWinbimr oS: 82 Ge “« Carbon Tetrachloride on Niobiec Anhydride_| DEMARGAY-_-__-__- 87 i he ee DonatH and May-| 783 ERHOFER. Analysis of a Niobate..____------------------------- SIRMMON) 2s 83 aC Wietnoilg, Wor ee Se a ee SMiIcGH = aes eee eae 83 oS De ata Oss ee ee ee HERMANN 225-25 _2 58 “ IPISHIMIAT ION 2 ee Soe es ee Soto VIUAUR GEN GAG en ee 67 a SOPUTAiON.= =e eae ee ee ERMAN Ne eee 70 & uC GLMtetaliliewANcide== = eee see Se RAMMELLSBERG ----| ‘71 6 ue frrco rane Grell NCU gee eee see ere BoIsBAUDRAN -~~--- 185 & ee IMG CROSCOpIC==e set aaa ae HAUSHOREReE=2-= === 184 “ Quantitative determination ___--_------__-- OSEORNHE= =e =e 85 oe Colormedcilone et ee een ee LR ysyeo 2 es Sees 87 ee IMleraney. 2 WG pi see ee ee eee BiUiINSE Neo oe ee 66 Anhydride, Niobic, action of Carbon Tetrachloride | DEMARGAY -_------ 87 upon. 6 Niobic, crystallization of ___. ----------- KeNop ==. so 87 J xterm \WWONGIN@) a A eee DonatH and May-| 783 ERHOFER. Ee Sel ey re re eee re we ee RAMMELLSBERG -.--| 769 Cadmium Fluoniobate -_-.-------- Rr Cee ee Ek SANGINSS ON ae "15 Calcium peel eer ee SOE A ek (Oe ngs esa se Sine ed i ido 24 GENERAL INDEX. SUBJECT. AUTHOR. Gobaltehiuoniobates 22212 s2 =) 2a eee DANTESSON 222 sees Copper 60 eee beh ele seo8 = bes Secs ee Us @alcinumeNiobite sr sere see eee ee JOLY. see @arbideSc2 ss2522- 55-2 82 So ae oe ee SO SAM Foy 8 Ale 3 Carbon Tetrachloride, action on Niobic Anhydride __-| DEMaRgcaY-____-_-- @imordes? 2 2. ul oe ee ee ee Ross, Ha. oe ce Be gd Mean denne ceocee © eae Eee Geiie..,) “atin ak ee sea ae a ce tare tS BLOMSTRAND______- ee eS acme Be ste wey ieee A tls ee ee NOSCOM 22222222 ae Wiapon Wensit ygOt eae ese eg eee DeEvVILLEand Troost Columbite, “Acidsiin: 42 2 ee ee eee ROSH, Hie. we Ste rents ee HERMANN _--__-__- j “ Action of Hydrofluoric Acid upon___~---- GIBES Reese eee Wolormred ChiOm Sa ee ce a LEV Yea COMMPOUNIGS ee eee tet eerste ae ee ee ROSE ES === ae oe oe ee Constitution of 202220 2 52s eee ELGG RATAN: =25 See oe Constitution, of mimerals=_ 2 = 2.2. = 2 es tt eee Composition, of natural Niobatee....<_--. 2. 22ease RAMMELLSBERG --__- Constitution of minerals 222.2. 2 2 = eee 3 Se Crystallization of niobic anhydride_.___=.____.-___—_ KN ORs: a) fee eee MD iamiceA Cid Sh esis een se eee EB eee eee Von KoBEnL:=£22-— ac Ce rs Ae re ag REN oe re oe ne ks © Ey Be! ob Ne eee OTANI 2 eae An ok ee ae eee ee Oe renee RN EO Re Oa ee ee HERMANN --__---_- i. MCR Pe 9c fee A aR kg OR) a Me PG ot ee Von Koprrnt 33822 Determination, Quantitative-______-___-.--_____=-- OSBORNH22S= 52222342 | Discovery ol element==- == aae=— 2 ae a eee ee EVAT CEU see ee ‘ Effect of temperature on specific weight -----.____-_- Rosnhe t= Stim tlOMe = 2- a a tae eR ey a MARIG@NAC__--_---- | Huxenite, Niobieacid i Se2 222) 28 ee SCHEEBRER =) 3222 Merroevanide st: . 122 228 eked oe ee en BONG 2320. See A IVES CA CEO Ma ee ee ee ee ee eee ee BUNSEN; 2e2chse2e8 Wluorides¢ = ee se== saeco eee 2 ea, Ne Se EEN IROSE, dels So eee Hinomlobates © = 25 = fake. S25 ee ee SANTESSON = eos Granite; occurence in 2280 25355. ae eee STREZNE Ros. ee Gallium, separation tromeio = =. = as eee BoIsBAUDRAN-_-__~-- Hydrofluoric Acid, Action on Columbite ~_--_-_--___- GIBBS*= 5222 3o= eee Elvdrates 4-222". 2 2 oo ea Ae ee MARIGNS Cleese Peas ie serene By ee te kee ae DAN TESSON- == ee Hydrogen peroxide, Action on oxides___-________-=_- WELLER 25222. 2s— Identity of Columbium and Tantalum______-___.__-- \WoOLEASTON: =e ears . a6 sc LC = kh ES pn pe LEONHARD and Vo- f GEL. a Tinienivinvand Niobium= 222 et ROSE VE aon Se aeeee Tdentitie ation: 2 22 tae el Rae et Sere Oe ni ceo 35 eee imenicw Acids 2s. ae Oe ee eee HIRBRMANN 2222 2eee us CO Sere oa See A Nees, ee ROSH ELS 2-32 eae Le ae ee a ee ee ee ee {PURI N7j= =" = eee oT *¢ in Pyrochlore and Columbite-__._.-_-- MER MANNG 2 oe SED) GALCIG: Sate, eats mo are ie eee eee ener ee ee MARIGNAC =e same Pimenivum, 22) 2 Sas eae sik ee, oe ve eee PRE RMANING. = seen Ee dentityewitht Niobiimigs2 22s = ea ee Rosi; Hgts 22 eee ec Researches Su A a eee ee ee 3. (HERMAN Nes?! eos ce BORLA ii uke ten WL ce peel AAO iid he, Sn Set we Ces 20 ee ee ee ee a) ° “6 CORN ease (Ne 2 aie tne eden ath Wt cnet ee ws ce 2 ce Oe Oe ee Nae eee Ae tee Se es AO i.) eae GENERAL INDEX. 25 SUBJECT. Seeeetrguiiiim researches = 22 2 22 oo Le. ; “ce cb os Separation from Niobium-_-------------- mineinesc-luoniopabe 286-2) +s 7--2 22 sees ue niobate Mercury fluoniobate Emraodcrotranalivsis.~ SO Relat see eek ek Sk Metal “ce BerisCopleranuly sis 2a a) a oe ee ee MERCED sa CONStIbUtIONe eee es a a ee ce ce Mosandrium Name ce Niobie acid in Wohlerite__- “ ce in Tantalic Acid Euxenite and Polycrase “ ce ce ce rag ce (a4 ee ce oe Crystals Separation from Tantalic Acid ce ce ce ce ae ce ce ec ce ce ce “eo Eieebie anhydride erystallization...---~~-.-..-.-..+- a Action of carbon tetrachloride upon_ ce ce oe Niobium, Discovery pa eat Je a ee Identity with Tantalum Tid entit ya walt he Uline urine se Propertios: 4 Sass sl ase ea oases ee Researches ce ce Atomic weight Separation from Ilmenium___-_.-----_..-_- Researches eo AUTHOR. MIARTGNAGQ LoS.) 222. ee HERMANN SANPESSON Efe 2b JOLY ce Roscor EAC SHORMRE ==) see HERMANN RAMMELLSBERG ___- SMITH CoNNELL SMITH ScHEERER HERMANN ce SCHEERER 20SE, H. STIS TU Teves Nexen HERMANN RosE, H. ae NORDENSKIOLD ___-_ BLOMSTRAND=____—- 1D) VAN CAG ere HERMANN Ross, H. JOLY SAINTIESSON = 222 22 aun Roser, H. ce LEONHARD GEL. Rost, H. and Vo- Rose, H. IMPASRTG:NVAG eee ee a9 -| DEVILLE RAMMELLSBERG ___-_ HERMANN ce SMITH RoscoE BoIsBAUDRAN ______ DATE. "67 68 70 ies ie 75 83 48 58 78 84 69 aD, "78 54 rite 48 7938 65 48 68 70 zie ata 78 83 26 GENERAL INDEX. ; SUBJECT. | AUTHOR. Date. Niobium, Atomic volume and affinity. ~--__--------- DonatH and May- 783. ERIOFER. “ Wicroscopic. analysis-.--_ ae eee HAUSHOFER == _=2 "84 “ Quantitative determination ~-------------- OSBORNE s2— 2222 85- “ Color Tenctionm 2.2 ee eee tye ST te Mame teach onese! 2. == ae een nee BUNSEN ___~~---_-- 66 Nickel fluoniobite se n= a ne ee SANTESSON ________- 715 INitrate, 2 a ee ae ee ee ee Ros, H.-2 2222) 2as2 59 CO ie es ee eles ee eee ee Co) ae eee "60 ENGET 1 Cl Operate ee ee ee JOLY) oe 2s eee "76 Ne pUUNO I 2228 aa ee ee es See HERMANN ___.__=_- 77 Occurrencein erate =e se ee | STELZNER.-o 2522255 73 Osyiliorides 22522. eas ee ae See eee foae:| aL ae eee ee 75. Oxides 25-2. see rent ba ee eee ea aaa sone WOHRLER?.2_22- 2 | 7389: WE a eee ee eee RR es ee ee ee Fit aANIN =e oe "46 CC in SEE SE el Ti Spo as ee ee et: KOSn, He 2s = ses eae 48 CCD I este ag ey eee en ee ee oe eee DELAFONTAINE ____| ’66. CT) ee ee ne ee eee HERMANN __=__-.-- 66. - Action of hydrogen peroxide upon —...------.| WELLER.___~___<_- 182 Pelopie Qe a.seSse2 on ee ees SCHEBRER,.9).2—52= 48. te pe dies ast ee See ee eee HERMANN ________- 48 “ the | eR ee 8 ele ot a Ao Ot 48 “ Ce ee enone ener er ee ee eee ee IPERERZ.* 222-2 48 ee Oo ce a eye ee eee ee ee ees HERMANN ____.____ 58 Pelopium: =. .2422-+ 22-55-5262 52s Rosn) Hy eeoa2 ee 48 Peroxide of hydrogen, Action on oxides -___--------. Wil tir ence eee 82 Properties of oxide ~.-----1---------------------_-- WOHLER 222225 2on= 39: ce ‘ and metal 22 ee ee tee HERMANN _____-___ 48 Polyorase, Acids 1250-2302. Sees Pe ee SCHEEBRER —.=--2- 22 48 Pyrochlore; Acids 1n__._--2-- == S22 ss HERMANN ]22e2es3 48 Quantitative determination_--__.-—--_-- -=---..35==_- OSBORNE. 2 == oe 85, RBACUION, AUOlON toe teen ae ee ee GR Vee 225 eee 87 “ MlamGe =< .282 225. 2See ee Sb eee BUNSEN. 66 Remarks on. Pelopic) Acide == 2222-52 a ee ae HERMANN -___-____ 5S Researches: s-- So. st ee ae ee ee eee ROSE El. 22a 40) ys SS eke ee eee eee ee cy" See 44 av Te ee ee ee ot On ee ane eee (¢) Gitte ae 46 BE re ee Oe ee ee Cp Serres 53 CG Os eNO te Rana he ee ee HERMANN, 22222222 155 cy 9 Aen BAR core, iS en ee eee OuSTEN. =e eee 56 ep 4’ __. e f ee ee eeee Wb Oe te eaten 158. ES a Wb el en a ee HERMANN -____-__- a7 LE Se eee 8 ene re, ee eee SMUT 25a ee 17 tif iit ee Pee ee ee eee eee ee ELERMANN 29s mT Ce ee ee re ree eee eee ie eee SS MIDE 2 See 1a SOUL ES eee ee eee oat De eS Oe eee nee eee IROSm< dH. Se ee 59) CS ee Oe ee ee ae ee ee eee MARIGNAG___.-.._= 8 165 Ws 2 oe Ee See ee eee JOLY if Lee m5 Separation niobic and tantalie acids _._-----------~-- HERMANN __-.-..--] 758 J Niobium from I]menium ,____-_---------- * 5 ete 70 “ IMetalheiacrds==3-. 2s eee See RAMMELLSBERG-__.-} ’71 “ from, Gallina Se BoISBAUDRAN-______ 183 Sodiumimiobate: 2-2 s = > ae ee eee DSANTESSON oes "15 Specific weight, effect of temperature upon____~-~~~-- Rosh; H.-S ae 48 Sulphides _____. ---_--- --=----~-- ---=---=----=-~-=- (CS |e 58 CC Fee en ae A! oe a ee CUS 2 eee 59 Tantalum, Identity, with Niobium --.-.-----—_-____- WOLLASTON._-.-._- 09 GENERAL INDEX. ure SUBJECT. AUTHOR. | DATE. Tantalum, Identity with Niobium —_ -._.____-_____-- LEONHARD and Vo-| 717 GEL. Temperature, effect of, upon specific weight_________- NOS NET oe 2 pe 2 4G MiMaOLewMIODINM Meee ae A eee Pek eee eee CRO Nee ete 65 Seamordensity of chloride. -—- --2-.--4-_--+--=-- DEVILLEandTROostT| 765 Buen aLOMG == eee || Donare and May-| 783 ERHOFER. eee ALOU Grane oe SE Se Se Se FER MANNGS 222 Soe 65 Weight, specific, effect of temperature upon_____~___- Rosme ire a2 22. 48 DWGHLEnitew IN LOG Acid, im) 222 = 2 ole Fe SC HAH FO eee "48 PianmUNnnTO Dates ae ts ee ee JiOmy: Se eee eS 75 PmcenuOmiQnate.- =. OMe 2 a5. 2k Selb Stee ace SANTESSON_-_______- "75 SMITHSONIAN MISCELLANEOUS COLLECTIONS. GO4 BIBLIOGRAPHY or oe iy ONG) NEY: FOR THE YEAR 1887 BY WILLIAM C. WINLOCK, ASSISTANT ASTRONOMER, UNITED STATES NAVAL OBSERVATORY. WASHINGTON: PUBLISHED BY THE SMITHSONIAN INSTITUTION. 1888. PRINTED AND STEREOTYPED BY JUDD & DETWEILER, ° a Zz a o a Be n & B ee < BIBLIOGRAPHY OF ASTRONOMY: 1887. BY WILLIAM C. WINLOCK. The following subject-index of astronomy for 1887 was originally compiled as an appendix to a general review of the progress of astronomy during that year, and though not exhaustive, it may, perhaps, be found a useful reference list. Important contributions to astronomy published during 1887 in scientific journals and trans- actions of societies, as well as all more elaborate publications that have come to the ~ compiler’s notice, have been included—a few titles being taken from reviews, or book- 4 catalogues. Observations of asteroids and comets, except those of the comets of 1887, have generally been omitted. The prices quoted are usually from Friedlander’s Nature Novitates, in German ““marks’’ (1 Mark = 100 Pfennige = 1 franc 25 centimes = 25 cents, nearly.) The abbreviated titles will probably be readily understood by those familiar with scientific periodicals without special explanation, beyond the following list of less obvious contractions. Abstr. = Abstract. Lfg. = Lieferung. pt. = part. Am. = American. M. = marks, Tr. = reale. Bd. = Band. n. d. = no date. Rev. = review. d. = die, der, del, etc.| mn. p. = no page. S. = series. ed. = edition. n. F. = neue Folge. sc. = science, scien- Hft. = Heft. Nn. Ss. = new series. tific. hrsg. = herausgegeben. not. = notices. sh. = shilling, il. = illustrated. obsns. = observations. sup. = supplement. j., jour. = journal. Obsry. = Observatory. v., vol. = volume. k. k. = kaiserlich konig- p- = page. lich. | pl. = plates. In the references to journal articles the volume and page are simply separated by a colon, thus: ‘“ Bull. astron., 4 : 94-98,’’ indicates volume 4, pages 94 to 98. Aberration. Micwetson (A. A.) & Moriey (E. W.) Relative motion of the earth and the luminiferous ether. il. Am. j. sc., 1384: 333-345. THEWIs (—.) Sur la théorie de l’aberration de M. Seeliger. Bull. astron., 4: 94-98. _ Aberration (Constant of). Comstock (G.C.) New mode of determining the constants of refraction and aberration. Sid. mess., 6: 310-317. (Abstract of Loewy’s method.) Note on the determination of the constant of aberration. Astron. jour., food. (3) 4 BIBLIOGRAPHY OF ASTRONOMY: 1887. Aberration (Constant of )— Continued. Hovzeav (J. C.) Note sur une méthode pour déterminer la constante de l’aber- i ration. @p. 8vo. Bruxelles, 1887. i Bull. de l’acad. roy. de Belg., 3. s. 13, no. 2. 104: 278. ; Note additionelle sur la mesure de l’aberration. Jdid., 563. Loewy (M.) Nouvelle méthode pour la détermination de la constante de I’aber- ration. Compt. Rend., 104: 18-26, 396. Détermination de la constante de aberration. Premier procédé d’obser- i vation. Ibid., 455-461. e Same. Premier et seconde procédé d’observation. Ibid., 538-544. ——— Same. Conclusions. Jbid., 615-621. Réponse a la Note additionelle de M. Houzeau. Jbid., 727. Méthode générale pour la détermination de la eonstante de ]’aberration. ' 1bid., 1207-1214, 1398-1405. : Same. Calcul de l’azimut de la direction horizontale du mouvement ter- i restre. Ibid., 1650-1656. 4 Same. Procédé particulier pour rendre la recherche indépendante du - Av tour de vis, et conclusions. Jbid., 105: 11-17. Bh Nouvelles méthodes pour la détermination de la constante de V’aberration. 57 p. il. 4to. Paris, 1887. (Repr. from: Compt. Rend., 104, 105.) Lorwy’s method of determining the constant of aberration. il. Se. Am. sup., 9651. Tréprep (C.) Sur /’application de la photographie aux nouvelles méthodes de M. Loewy pour la détermination des éléments de la réfraction et de l’aberra- tion. Compt. Rend., 104: 414-417. Almanacs. See Ephemerides and almanacs. Almucantar. CHANDLER (S.C.) jr. The almucantar: an investigation made at the observatory [of Harvard college] in 1884 and 1885. 9+ 222p.,1 pl. 4to. Cambridge, 1887. [Results of latitude work.] Sid. mess., 6: 87. American astronomical society. Papers... no.2. 55p. 8vo. Brooklyn, 1887. American ephemeris. American ephemeris and nautical almanac for .. . 1890. led. 6+ 521+8 p. | 4to. Washington, 1887. ($1.00: ae Astronomical papers ... Vol. 2, pts. 3 and 4. Velocity of light in air and refracting media. 152 p.,8pl. 4to. Washington, 1885. Rev. by Wagner (A.) Vrtljschr. d. astron. Gesellsch., 22: 236-247. Report of the superintendent of the nautical almanac for the year ending June 30, 1887. 7p. 8vo. Washington, 1887. BIBLIOGRAPHY OF ASTRONOMY: 1887. 5 Armagh observatory. Dreyer (J. L. E.) Electric illumination of the Armagh refractor. Month. not., 47: 117. [Report for 1886.] Jbid., 151. Asteroid 5. GALLE (A.) Uber die im September, 1888, stattfindende Annaherung der Plan- eten (5) Astraea und (8) Flora. Astron. Nachr., 118: 78. Asteroid 17. CuaARLIER (C. V. L.) Untersuchung uber die allgemeinen Jupiter-Stérungen des Planeten Thetis. 98p. 4to. Kongl. svenska Vetens-Akad. handl. 22, no. 2. Asteroid 69. [Kreutz (H.)] Neuer Planet Luther vermuthlich identisch mit (69) Hesperia. Astron. Nachr., 116: 335, 365. Detected by Luther 1887, Apr. 11, and by Coggia 1887, Apr. 16, and announced as a new asteroid. Asteroid 80. Rogerts (I.) Photographic search for the minor planet Sappho. Month. not., 47: 265. Asteroid 181. DE Bat (L.) Recherches sur l’orbit de la planéte (181) Eucharis. 44 p. 4to. Bruxelles, 1887. (M. 2.50.) Asteroid 240. Sarnt-BiancatT (D.) [Elements from observations 1884-1886.] Bull. astron., 4: 198. Asteroid 264. MILLosEvicH (E.) [Elements from normals 1886, Dec. 20;. 1887, Jan. 22, and observation of Feb. 24.] Atti d. r. accad. d. Lincei, s. 4, Rend., 3: 476-480. Asteroid 265. Anna. Discovered by J. Palisa at Vienna, 1887, Feb. 25. Circ. Berl. astron. Jahrb., 292. Also: Astron. Nachr., 116: 223. Kwnopr (O.) [Elements from obsns. 1887, Feb. 25, Mar. 25, Apr. 17.] Cire. Berl. astron. Jahrb., 296. Lance (H.) [Elements from obsns. 1887, Feb. 25, Mar. 11, 25.] Ibid., 294. MILLOSEVICH (E.) Sul pianetino (265). Attid.r. accad. d. Lincei,s. 4, Rend., 3: 266. Asteroid 266. Aline. Discovered by J. Palisa at Vienna, 1887, May 17. Circ. Berl. astron. Jahrb., 298. Also: Astron. Nachr., 117: 47. Lance (H.) [Elements from obsns. 1887, May 17, 29, June 11.] Circ. Berl. astron. Jahrb., 299. Asteroid 267. Tirza. Discovered by A. Charlois at Nice, 1887, May 27. Circ. Berl. astron. Jahrb., 298. Also: Astron. Nachr., 117: 68. Also: Bull. astron., 4: 260. 6 BIBLIOGRAPHY OF ASTRONOMY: 1887. Asteroid 267. Tirza—Continued. Cuartors (A.) [Elements from obsns. 1887, May 27, June 9, 22.] Cire, Berl. astron. Jahrb., 301. Also: Compt. Rend., 105: 53. [Elements from obsns. 1887, May 27, June 25, July 23.) Circ. Berl. i astron. Jahrb., 303. Asteroid 268. Adorea. Discovered by A. Borrelly at Marseilles, 1887, June 9. Cire. Berl. astron. Jahrb., 299. Also: Astron. Nachr., 117: 103. Lance (H.) [Elements from obsns. 1887, June 9, 28, July 13.] Circ. Berl. astron. Jahrb., 301. : Asteroid 269. Discovered by J. Palisa at Vienna, 1887, Sept. 21. Circ. Berl. astron. Jahrb., 305. Also: Astron. Nachr., 117: 359. BERBERICH (A.) [Elements from normals 1887, Sept. 28, Oct. 13, and observa- tion Nov. 12.] Cire. Berl. astron. Jahrb., 308. Asteroid 270. Anahita. Discovered by C. H. F. Peters at Clinton, 1887, Oct. 8. Circ. Berl. astron. Jahrb., 806. Also: Astron. Nachr., 117: 15. Lance (H.) [Elements from obsns. 1887, Oct. 11, 26, Nov. 15.] Cire. Berl. astron. Jahrb., 308. VIENNET (E.) [Elements from obsns. 1887, Oct. 11, 18, 26.] Compt. Rend., 105: 1002. [Elements from normals 1887, Oct. 12, 27, Nov. 16.] Jbid., 1254. Asteroid 271. Penthesilea. Discovered by V. Knorre at Berlin, 1887, Oct. 18. Cire. Berl. astron. Jahrb., 306. Also: Astron. Nachr., 118: 31. Knorr (O.) [Elements from obsns. 1887, Oct. 18, 25, Nov. 18.] Cire. Berl. astron. Jahrb., 308. Asteroids. [Asteroids discovered in 1886.] Month. not., 47: 172. Also: Bull. astron., 4: 15. GLAUSER (—.) Lage der Asteroiden-Bahnebenen. Astron. Nachr., 117: 153- 162. KrrKxwoop (D.) The asteroids or minor planets between Mars and Jupiter. 60 p. 12mo. Philadelphia, 1887. (30.75.) Distribution of the minor planets. Sid. mess., 6: 116. Eccentricities and inclinations of the asteroidal orbits. Ibid., 169. LEHMANN (P.) Zusammenstellung der Planeten-Entdeckungen im Jahre 1886. Vrtljschx d. astron. Gesellsch., 22: 9-14. Parkuurst (H. M.) Photometric observations of asteroids. Sid. mess., 6: 353. Astronomische Gesellschaft. Bericht tiber die Versammlung . . . zu Kiel, 1887, Aug. 29 bis 31. Vrtljschr. d. astron. Gesellsch., 22: 264-284. BIBLIOGRAPHY OF ASTRONOMY: 1887. 7 Astronomische Gesellschaft— Continued. Berichte tiber die Beobachtung der Sterne bis zur neunten Grosse am nérdlichen Himmel. Ibid., 350-358. Berichte betreffend die Vorbereitungen der Zonen-Beobachtungen zwischen — 2° und — 23° 10’. [bid., 358-361. Kriicer (A.) Zwélfte Versammlung der astronomischen Gesellschaft . . Kiel, 1887, Aug. 29-31. Astron. Nachr., 117: 199, 297-306, 391. See, also, Ibid., 116: 383. Also: Obsry., 10: 387-339. [Report of Kiel meeting, 1887, Aug. 29-31.] Obsry., 10: 337-339. Vierteljuhrsschrift der astronomischen Gesellschaft. Hrsg. von E. Schoenfeld und H.Seeliger 22. Jahrg., 1887. 417p.,pl.,por. 8vo. Leipzig, 1887. (M.8.) Astronomy. McFaruianp (R. W.) Astronomy and the ice-age. Sid. mess., 6: 117. Monk (W.H.S8.) Astronomy and the ice-age. Jbid., 57, 194. Astronomy (Bibliography of). Hovzrau (J. C.) & Lancaster (A.) Bibliographie générale de l’astronomie. Tome premier. Ouvrages imprimés et manuscrits. Premiére partie. 7 + 858 p. 4to. Bruxelles, 1887. (M. 25.) Rev. by Houzeau (J. C.) & Lancaster (A.), Ciel et terre, 8: 153-161, 187-193; Faye (H.), Compt. Rend., 105: 923; Liagre (J.), Ciel et terre, 8: 321; Maunder (E. W.), Obsry., 10: 421-423. See, also, L’Astron., 6: 480-484. Also: Bull. astron., 4: 468. Astronomy (Descriptive). Bau (R. 8.) The story of the heavens. 2ed.,il. 8vo. London, 1887. (M. 32.50.) Forster (W.) Sammlung von Vortrigen und Abhandlungen. 2 ed. 350 p. 8vo. Berlin, 1887. (M. 6.) JOCHMANN (—) & Hermes (—.) Grundriss der Experimentalphysik und Ele- mente der Astronomie und mathematischen Geographie. 10.ed. 16-+ 444 p. 8vo. Berlin, 1887. (M. 5.80.) Luevers (F. G. J.) Memorial to the representatives of physical astronomy 12 p. 8vo. Madison, 1887. Parkes (8S. H.) Unfinished worlds: a study in astronomy. il. 8vo. London, 1887. (M. 5.20.) Proctor (R. A.) Half hours with thestars. Newed. 12pl. 4to. New York, 1887. Other suns than ours: series of essays on suns, old, young, and dead. 428 p. 8vo. London, 1887. (M. 7.80.) Lancuey (8S. P.) The newastronomy. Thestars. il. Century, 33: 586-598. 1887, Jan. Same. Comets and meteors. il. Jbid., 339-355. 1887, Feb. Thenewastronomy. 12+4260p. il. 8vo. Boston, 1888[1887]. ($4.00.) LiaGreE (J.) Cosmographie stellaire. 278 p.,4maps. 12mo. Bruxelles, 1887. (M. 3.) Lynn (W. T.) Celestial motions: Landy book of astronomy. 5 ed. 12mo. London, 1887. (M. 2.20.) 8 BIBLIOGRAPHY OF ASTRONOMY: 1887. Astronomy (Descriptive)—Cbontinued. Meyer (M. W.) Die Lebensgeschichte der Gestirne: eine populare Astron- omie der Fixsterne. 8 + 294 p- il. 8vo. Jena, 1887. (M. 4.) NIEsTEN (L.) Le ciel, son aspect, ses curiosités: atlas élémentaire . . . uvec © texte explicative ... 4to. Bruxelles, 1887. (fr. 5.) Von SEEFELD (F.S.) Astronomische Aufsitze eines Amateurs der Naturwis- senschaft. Hft.1. 54p. 8vo. Gratz, 1887. (M. 0.80.) SERVIss (G. P.) Astronomy with an opera glass. il. Pop. se. month., 30: 743; Ibid., 81: 187, 478; Ibid., 82: 53. VALENTINER(W.) Der gestirnte Himmel: eine gemeinverstandliche Astron- omie. 7+ 3827p. il. 8vo. Stuttgart, 1887. (M. 6.) Astronomy (History of). See, also, Astronomy (Progress of). Bonnut (J. F.) Etude sur Vhistoire de l’astronomie: la découverte du double mouvement de laterre. 208 p. 8vo. Tours, 1887. CLERKE (A. M.) History of astronomy during the 19th century. 2 ed., enl. 16+ 502 p. il. 8vo. Edinburgh, 1887. (M. 18 ) Homeric astronomy. Nature, 35: 585, 607. Loorr (F. W.) Die Himmelskunde in ihrer geschichtlichen Entwicklung und nach ihrem gegenwirtigen Standpunkte. 8 -+- 182 p., 2 pl. 8vo. Langen- salza, 1887. (Mo25) Astronomy (Progress of). 4 ALLEN (Grant.) Progress of science from 1836 to 1886. Pop. se. month., 31: 505, 513-515. Kern (H. J.) Fortschritte der Astronomie. Nr. 12, 1886. 112 p. Leipzig, 1887. Repr. from: Rev. d. Naturwissensch., Nr. 71. Swirt (L.) Astronomical progress and phenomena [1886]. eycl., 1886. 24 (n. s. 11): 48-59, Astronomy (Spherical and practical). gation, ete. 12mo. Appleton’s ann. See, also, Azimuth; Illumination; Navi- Goopwin (H.B.) Problems in navigation and nautical as tronomy. 86 p. 8vo. London, 1887. (M. 5.30.) Herr (J. P.) & Tinter (W.) Lehrbuch der spharischen Astronomie in ihrer Anwendung auf geographische Ortsbestimmung. 644 p. il. 8vo. Wien, 1887. (M. 16.) Jeans (H. W.) Problems in astronomy, surveying and navigation... Part 1. 244 p. 8vo. London, 1887. (M. 2.70.) OLIveR (J. A. W.) & others. Astronomy for amateurs: practical manual of telescopic research . . . adapted to moderate . . . instruments. 7+ 316 p. il. 12mo. London, 1888 [1887]. (M. 7 80.) Astronomy (Theoretical). See, also, Lunar theory; Mechanics (Celestial); Orbits. IsrarL-Ho.tzwart (K.) Supplement zu den Elementen der theoretischen As- tronomie. Insbesondere, analytische Theorie der Anziehung von konstanter und verinderlicher Dichtigkeit. 100 p. 8vo. 1887. der Sphiroide Wiesbaden, (M. 1.60.) BIBLIOGRAPHY OF ASTRONOMY: 1887. 9 Auerbach (Carl Heinrich August) [1813-1886]. WEINEK (L.) [ Biographical sketch.] Vrtljschr. d. astron. Gesellsch., 22: 6-9. Aurora. CuLERKE (A. M.) The aurora borealis. Nature, 35: 433-436. LaGRANGE (E.) Aurores boréales, comates et étoiles filantes. Cicl et terre, fits: 494-500. RENDALL (R.) Noises accompanying aurorv. Obsry., 10: 303. Wesser (H. J.) Noises accompanying aurore. Tbid., 10: 161. Azimuth. Crate (J. E.) Azimuth: a treatise on this subject, with a study of the astro- nomical triangle, and of the effect of errors in the data. 4-4 107 p. +- 4to. New York, 1887. Bamberg observatory. Harrwie (E.) Uber die Bamberger Sternwarte. il. Vrtljschr. d. astron. Ge- sellsch., 22: 329-385. See, also, Obsry., 10: 279. Basel observatory. [Report for 1886. ] Vrtljschr. d. astron. Gesellsch., 22: 75. Baxendell (Joseph) [1815-1887]. Esprn (T. E.) [Biographical notice. ] Astron. Nachr., 118: 175. Stewart (B.) [Biographical notice.j Nature, 36: 585. Berlin observatory. Forster (W.) [Report for 1886.] Vrtljschr. d. astron. Gesellsch., 22: 75-85. JESSE (0.) Tiber die Biegung des Rohres und des Kreises des kleineren Merid- ian-Instrumentes der Berliner Sternwarte, sowie liber die Biegung der bei dieser Bestimmung benutzten Collimatoren. Astron. Nachr., 117: 33- £0, 185. Bermerside observatory. [Report for 1886. ] Month. not., 47: 160. Bethlehem (Star of). Exuis (J. T.) [Hypotheses in regard to the star of Bethlehem.] Sid. mess., 6: 360. Payne (W. W.) Star of Bethlehem. Sid. mess., 6: 265-269. [Venus mistaken for] the star of Bethlehem. Nature, 37: 169; Obsry., jhle Wa6 Eng. mec., 46+ 388, 390. Birr castle observatory. [Report for 1886.] Month. not., 47: 160. Bonn observatory. ScHONFELD (E.) [Report for 1886.] Vrtljschr. d. astron. Gesellsch., 22: 89-92. - Bordeaux observatory. | Annales de ’observatoire de Bordeaux, publifes par G. Rayet. Tome 2. 159+- 306 p. 4to. Paris, 1887. a oe ” ATS : 10 BIBLIOGRAPHY OF ASTRONOMY: 1887. di Brera observatory. Pubblicazioni . . . No. 31. Azimut assoluto del segnale trigonometrico del monte Palanzone sull’ orizzonte di Milano, determinato nell 1882 da M. Rajna. 125p. 4to. Milano, 1887. Pubblicazioni . . . No. 32. Nuova triangolazione della citta di Milano eseguita | da F. Borletti. 15 p.,4 pl. 4to. Milano, 1887. Breslau observatory. GALLE (J. G.) [Report for 1886.] Vrtljschr. d. astron. Gesellsch., 22: 92. Brussels observatory. Fourie (F.) [Report for 1885 and 1886.] Vrtljschr. d. astron. Gesellsch., 22: 93-99. [Removal to Uccle.] Nature, 36: 41. Calendar. ABETTI (A.) Nozioni sul calendario dei Cofti e degli Abissini cristiani. 9 p. 4to. Roma, 1887. (M. 1.) Repr. from: Atti d.r. acead. d. Lincei, s. 4, Rendic., 3: 396-404. GéERIGNY (P.) Reforme du calendrier: rapport sur les projets présentés au con- cours. L’Astron., 6: 212, 260, 298, 339, 384. Poncer (G.) Pourquoi l’année commence-t-elle le 1* Janvier? L’Astron., 6: 378-382. Cambridge [Eng.] observatory. [Report for 1886.] Month. not., 47: 151. Cambridge [U. S.] observatory. See Harvard college observatory. Cape of Good Hope observatory. [ Report for 1886.] Month. not., 47: 164. Carleton college observatory. [Payne (W. W.) Description of the Repsold meridian circle, ete.] il. Sid. mess., 6: 802-306, 319. Chromosphere. See, also, Prominences (Solar). Perry (S. J.) [Observations of] the chromosphere in 1886. Obsry., 10: 129. Chronodeik. Verbesserung des Chronodeik. Sirius, 20: 108-112. Chronographs. BucKNEY (—) & others. [Remarks on chronograph of Melbourne observa- tory.] Obsry., 10: 49. Herz (N.) Streifen-Ableseapparat. Astron. Nachr., 117: 263. von Respeur-Pascuwirz (E.) Registrirapparat mit Centrifugal-Regulirung. il: Ztschrs f. Instrmiknds, 7: 7a Chronometers. CELLfrier (G.) Etude numérique des concours de compensation des chronu- métres faits 4 l’observatoire de Genéve en 1884 et 1886. 45 p. 4to. Genéve, 1887. (Mém. soc. phys. et d’hist. nat. Geneve, 29, no. 6.) Every (R. L. J.) [Break-cireuit chronometer devised and used in Australia in 1860.] Obsry., 10: 427. BPS pcs BIBLIOGRAPHY OF ASTRONOMY: 1887. 11 Chronometers— Continued. GAUTIER (E.) Rapport sur le concours pour Je réglage des chronométres, 1886. \ fit] p: Svo. fn: p:, 1887. ] Hirscuw (A.) Rapport du directeur de l’observatoire cantonal de Neuchatel . sur le concours des chronométres observés pendant l’année 1886. 28-+12p. 12mo. Locle, 1887. Perers (C. F. W.) Hinfluss der Luftfeuchtigkeit auf den Gang der Chronome- ter. Vrtljschr. d. astron. Gesellsch., 22: 284-292. Rates of chronometers on trial . . . at the Royal observatory, Greenwich. 7p. 4to. [London, 1887.] In: Greenw. obsns. 1885. Recherches sur les chronomeétres et les instruments nautiques. 123 p. 8vo. Paris, 1887. (M. 1.50.) Youne (C. A.) [First use of] break-circuit chronometers. Obsry., 10: 140, 334. Cincinnati observatory. Publications of the Cincinnati observatory, 9. Zone catalogue of 4,050 stars for the epoch 1885... by J. G. Porter. 104p. 8vo. Cincinnati, 1887. Circle-divisions. Repsoitp (A.) Schreib-Apparat fur Theilungs-Beyifferung il. Ztschr. f. In- strmknd., 7: 396. Clark (Alvan) [1804-1887]. For Biography, see Am. j.sc., 184: 322, Also: Eng. mec., 45: 603. Also: Na- tion, 45: 149. Also: Nature, 36: 476. Also: Science, 10: 96. Also: Se. Amer., 57: 145, 218. Also: Sid. mess., 6: 250-253. Also: Sirius, 20: 241. For Portrait, see Science, 10: 96. Also: Se. Amer., 57: 198. Clocks. AppeEL (D.) Freie Schwerkraft-Hemmung der Normal-Stern-Uhr zu Princeton. Ztschr. f. Instrmknd., 7: 29. Buckney (T.) _ Note on the performance of the Westminster clock. Month. not., 47: 519. CurisTiE (W. H. M.) Method of regulating clocks. Obsry., 10: 326. Cornu (A.) Synchronisation des horloges de précision et la distribution de Vheure. Compt. Rend., 105: 1106-1112, 1209. Fouiz (F.) Sur l’enregistrement par microphone des battements d’une pendule. Bull. de l’acad. roy. de Belg. [1887?] Notice: Bull. astron., 4: 291. GarDNER (H. D.) Fifty years’ progress in clocks and watches. il. Nature, 36: 484. Wotr (C.) Comparaison des divers systémes de synchronisation électrique des. horloges astronomiques. Compt. Rend., 105: 1155-1159, 1211. Colored stars. BackHovuseE (T. W.) Proposed nomenclature for star-colors. Obsry., 10: 254. CHAMBERS (G. F.) [Color of Achernar.] Obsry., 10, 3C1. Franks (W. 8S.) Proposed nomenclature for star-colors. Obsry., 10: 275. Also: Month. not., 47: 269-272. a? BIBLIOGRAPHY OF ASTRONOMY: 1887. Colored stars—Continued. Franks (W.S.) Report from colored star section. J. Liverp. astron. soc., 5: 297 oil. von Kéves.ticeTHy (R.) Neue Methode der Farbenbestimmung der Sterne. Sirius, 20: 219, 271. Also, Reprint. (M. 0.40.) Monk (W. H.S.) Colors of the stars and solar heat. Obsry., 10: 164. WiuitaMs (A.S.) Color of Achernar. Obsry., 10: 272, 334. ‘Comet Olbers = Comet 1887 V (/). Detected by Brooks at Phelps, N. Y., 1887, Aug. 24. Astron. jour., 7: 127. Also: Astron. Naehr., 117: 279. Also: Sc. Amer., 47: 181, 192. Also: Sid. mess., 6: 289. Comet Olbers (Elements of). EGBERT (H. V.) [From obsns. 1887, Aug. 26, 28, 30.] Astron. jour., 7: 128. Also: Se. obsr. circ., 79. See, also, Sid. mess., 6: 294. —-— [Correcting Ginzel’s elements by obsns. 1887, Aug. 27 to Sept. 23.] As- tron. jour., 7: 135. Franz (J.) [From obsns. 1887, Aug. 27, 28, 29.] Astron. Nachr., 117: 295. GinzzeL (F. K.) [Elements corrected by obsns. 1887, Aug. 27, Sept. 6, 14.] Astron. Nachr., 117: 390. Gruzy (L. J.) [From obsns. 1887, Aug. 27, 30, Sept. 2.] Astron. Nachr., 117: 348. Krticer (A.) [Ginzel’s elements corrected by obsns. 1887, Aug. 27.] Astron. Nachr., 117: 309. LEBEvF (A.) [From obsns. 1887, Aug. 27, 380, Sept. 2.] Astron. Nachr., 117: 843. Also: Bull. astron., 4: 427. RamBaupD (A. A.) & Sy (—.) [From obsns. 1887, Aug. 29, 31, Sept. 2.] Compt. Rend., 105: 487. TzTens (O.) [Ginzel’s elements corrected by obsns. to Sept. 20.] Astron. Nachr., 117: 358. ‘Comet Olbers (Observations of position of). Albany, Aug. 26-30; Astron. journ., 7: 128. Sept. 23; Ibid., 186. Sept. 15, Nov. 1; Jbid., 152. Algiers, Aug. 29, 31, Sept. 2; Astron. Nachr., 117: 325. Aug. 29, 31; Compt. Rend., 105: 480. Sept. 10, 12, 18, 14, 16; Zdid., 511. Sept. 17, 19, 21, 22; Bull. astron., 4: 466. Besancon, Aug. 29, 30, Sept. 1; Astron. Nachr., 117: 341. Also: Compt. Rend., 105: 431. Sept. 14-17, 21, 22, 26, 30, Oct. 1; Compt. Rend., 105: 609. Bordeaux, Sept. 8, 9, 10; Compt. Rend., 105: 456. Sept. 8, 9, 10, 15, 18, 19, 21, 23, 24, 25; Ibid., 1001. Also: Astron. Nachr., 118: 109. Bothkamp, Sept. 18, 20, 21, 23, 24; Astron. Nachr., 117: 387. Oct. 21, 26; Ibid., 118: 105. Geneva, Aug. 29; Astron. Nachr., 117: 293. Sept. 6; Jdid., 3807. Oct. 1, 17, 25, 27, Nov. 4; Ibid., 118: 109. Hamburg, Sept. 20; Astron. Nachr., 117: 355. Sept. 23, 24; Idid., 387. et a ne at ee | eee en BIBLIOGRAPHY OF ASTRONOMY: 1887. Nes Comet Olbers (Observations of position of )—Continued. Kiel, Sept. 14; Astron. Nachr., 117: 827. Sept. 15, 18; Jbid., 341. Sept. 20; Tbid., 355. Konigsberg, Aug. 27, 28, 29; Astron. Nachr., 117: 295. Aug. 27, 28, 29, Sept. 10, 12; Ibid., 341. Sept. 21, 27; Ibid., 887. Oct. 8,12, 14; Ibid., 118: 42. Oct. 26, 27, Nov. 11; Ibid., 118: 94. Kremsminster, Aug. 28; Astron. Nachr., 117: 293. Aug. 28, 30, Sept. 6, 10, Wiimote WS LOT. Lyons, Aug. 30; Compt. Rend., 105: 482. Sept. 9, 10; Ibid., 487. Sept. 13, BL 22, Loid., 612. Marseilles, Aug. 27, 29; Bull. astron., 4: 462. Aug. 29, 30, 31, Sept. 13, 15, 16, 18, 20, 22, 23, 26; Ibid., 464. Milan, Aug. 80, 31; Astron. Nachr., 117: 307. Nashville, Aug. 27, 28; Astron. jour., 7: 127. Also: Astron. Nachr., 117: 327, 391. Nice, Aug. 29-Sept. 2; Compt. Rend., 105: 456. Also: Bull. astron., 4: 467. Sept. 5, 6; Bull. astron., 4: 467. Padua, Sept. 18, 14, 15, 24; Astron. Nachr., 117: 390. Plonsk, Sept. 6; Lbid., 327, 391. Pulkowa, Sept. 25, Oct. 10, 15, 22, Nov. 18, 15; Ibid., 118: 109 Rome, Aug. 27; Astron. Nachr., 117: 293. Strassburg, Aug. 27; Ibid., 298. Aug. 27, Sept. 14; Ibid., 341. “Turin, Aug. 29; Ibid., 298. Aug. 29, 31; Ibid., 327. Sept. 10, 18, 15, 16, 17, AWOL eS cpeto: Vienna, Aug. 27; Ibid., 117: 294. Oct. 21; Ibid., 118: 42. Washington, Aug. 29, 30, 31, Sept. 16,19; Astron. jour., 7: 134 Comet Olbers (Orbit of). See, also, Comet Olbers (Elements of ). Krticer (A.) Wiederkehr des Olbers’schen Cometen. Astron. Nachr., 117: 310. SEARLE (G. M.) Recent approach of the Olbers comet to Mars. Astron. jour., 7: 184. Comet Temple. See Comets and Meteors. Comet Winnecke. von Hirprt (E.) Bestatigen die neuesten Beobachtungen das Resultat Prof. von Oppolzer’s: dass auch bei dem periodischen Cometen Winnecke, Encke’s Hypothese des Widerstand leistenden Mediums Geltung zu haben scheine ? Vrtlijschr. d. astron. Gesellsch., 22: 313-319. Comet 890 and Comet 1075. GinzeEL (F. K.) [Apparition of two historical comets, 890, May 23, and 1075, July-Aug.] Astron. Nachr., 118: 47. Comet 1457 I. ScHuLuor (L.) Orbites des cométes 14571 et 18181. Bull. astron., 4: 51-54. Comet 1672. BERBERICH (A.) Der Comet des Jahres 1672. Astron. Nachr., 118: 50-72. 14 BIBLIOGRAPHY OF ASTRONOMY: 1887. Comet 1690. Lynn (W. T.) Comet of 1680 and its supposed previous appearances. Obsry , 10: 318. Comet 1780 II. Lynn (W.T.) The comet discovered by Montaigne and Olbers in 1780. Obsry., 10: 355. Comet 1818 I. Sce Comet 1457 I. Comet 1825 IV. Lynn (W. T.) [Erratum in Carl’s Repertorium.] Obsry., 10: 232. Comet 1840 I. Gauze (J. G.) Berichtigung zu den Angaben uber die Zeit des Periheldurch- ganges ... Astron. Nachr., 117: 167. Comet 1846 IV. von HeprEeRGER (J.) Bahnbestimmung des Cometen 1846 1V. 42 p. 8vo. Wien, 1887. (M. 0.70.) Abstr.: Astron. Nachr., 117: 246. Comet 1846 VI. Berperica (A.) Bahn des Cometen 1846 VI, Peters. Astron. Nachr., 117: 249. Comet 1848 I. Brpscnor (F.) Bestimmung der Bahn des Cometen 1848 I. 17 p. 8vo. Wien, 1887. (Abstr.: Astron. Nachr., 117: 247.) (M. 0.40.) Comet 1863 IV. Svepstrup (A.) Definitive Bahnbestimmung des Cometen 1863 1V. Astron. Nachr., 117: 222-242. Comet 1865 I. Korser(F.) UberdenCometen 18651. 58p. 8vo. Breslau, 1887. (M. 1.50.) Trpputt (J.) Note onthe tail... Astron. Nachr., 117: 385. Comet 1877 VI. Larssén (R.) Bahn des Kometen 1877 VI. 24p. 8vo. Stockholm, 1887. Bihang. till k. svenska vet. akad. Handlingen. Bd.12. Afd.I, No. 8. Comet 1882 I. von ReBEUR-PascHwiTz (E.) Uber die Bahn des Cometen 1882 I. Astron. Nachr., 117: 281-287. Rev.: Bull. astron., 4: 448. Rev.: Bull. astron., 4: 448. Comet 1883 IT. Bryant (R.) [Elliptic elements from normals 1884, Jan. 19, Jan. 25, Feb. 2.] Month. not., 47: 484. Tennant (J. F.) [Note on the orbit.] Jbid., 520. Comet 1884 III. BersBericH (A.) Elemente... aus den Strassburger Beobachtungen .. . Astron. Nachr., 117: 251. THRAEN (A.) Definitive Bahnbestimmung des Cometen 1884 III, Wolf. As- tron. Nachr., 117: 65-98. BIBLIOGRAPHY OF ASTRONOMY: 1887. Le Comet 1886 I. Morrison (J.) [Hyperbolic elements from obsns. 1885, Dec. 7, to 1886, June 6.] Month. not., 47: 437. Comet 1886 III. CxLoria (G.) [Elements from normals 1886, May 4, 10, 22.] Astron. Nachr., Lees: Comet 1886 V. Witson (H. C.) Thecomets of De Vico, 1844 I, and Finlay, 1886 V. il. Sid. mess., 6: 121-126. Comet 1886 VII. Boss (L.) Orbit of the periodic comet 1886, e, Finlay. Astron. jour., 7: 23, 43. See, also, Astron. jour., 7: 7. Fintay (W.H.) [Elements from normals 1886, Sept. 28, Dec. 15, and observa- tions Oct. 21, Nov. 13, Dec. 27. Month. not., 47: 302. HoLetTscHEK (J.) [Elements from obsns. 1886, Sept. 26, Oct. 14, Oct. 29, Nov. 28.] Astron. Nachr., 116: 47. Krtcer (A.) [Elements from obsns. to 1887, Feb. 23.] Ibid., 335. See, also, Astron. Nachr., 116: 77, 127. Moncx (W. H.S.) [Resemblance of elements to those of comet of 1585.] Sid. mess., 6: 222. OPPENHEIM (H.) Elements from obsns. 1886, Oct. 1, Nov. i, 7, 27.] Astron. Nachr., 116: 45. SEARLE (G. M.) [Elements from obsns. 1886, Sept. 26, Oct. 16, Nov. 4.] As- tron. jour., 7: 15. [Elements from obsns. 1886, Sept. 26, Nov. 4, Dec. 14.] Jbid., 52. Comet 1886 VIII — Comet 1887 c. Discovered by Barnard at Nashville, 1887, Jan. 23. Astron. jour.,7: 56. Also: Astron. Nachr., 116, 143. Also: Sid. mess., 6: 114. - Comet 1886 VIII (Elements of ). CuHartois (A.) [Elements from obsns. 1887, Jan. 26, 29, Feb. 1.] Bull. astron., 4: 58. Easert (H. V.) [Elements from obsns. 1887, Jan. 23, 24, 26.] Astron. jour., Mie tO4: [Elements from obsns. 1887, Jan. 23, 26, 30.] Jdid., 71. [Elements from obsns. 1887, Jan. 24, Feb. 18, Mar. 20.] Jbid., 87. OprENHEIM (H.) [Elements from obsns. 1887, Jan. 24, 29, Feb. 3.] | Astron. Nachr., 116: 175. Also: Obsry., 10: 144. Weiss (E.) [Elements from obsns. 1887, Jan. 24, 26, 29.] Astron. Nachr., Di6:) 159: {Elements from two normals 1887, Jan. 24-30, and observation Feb. 3.] Tbid., 191. Comet 1886 IX. ALLEN (W. H.) [Elements from normals 1886, Oct. 8, Nov. 8, Dec. 2, Dec. 10.] Astron. jour., 7: 55. fe “5 - 16 BIBLIOGRAPHY OF ASTRONOMY: 1887. Comet 1886 IX— Continued. BREDICHIN (T.) [Discussion of observations of the tail.] 7 p., 1 pl. 8vo. Moscou, 1887. Morrison (J.) [Elements from obsns. 1886, Oct. 7-Dec. 2.] Month. not., 47: 438. . Svepstrup (A.) [Elements from normals 1886, Oct. 8, 28, Nov. 18.] Astron. Nachr., 116: 15. WENDELL (O. C.) [Elements from obsns. 1886, Oct. 7, Nov. 6, Dec. 10.] Jbid., LUT od. Comet 1887 I — 1887 a. Discovered by Thome at Cordoba, 1887, Jan. 18. Astron. jour., 7: 55. Also: Astron. Nachr., 116: 148. Also: Obsry., 10: 112. See, also (independent discovery near Cape Town), Month. not., 47: 303. Comet 1887 I ‘Elements and Orbit of ). CHANDLER (S. C.) jr. [Elements from obsns. 1887, Jan. 20-29.] Astron. jour., limo: — [Elements from Cape and Adelaide obsns. combined into normals, 1887, Jan. 22, 25, 27.] Jozd., 100. Fintay (W. H.) [Elements from obsns. 1887, Jan. 22, 25, 28.] Month. not., 47: 304. OprenuEeIM (H.) Uber die Bahn des grossen Stidcometen 1887 I. Astron. Nachriy 117 > 13: R. (A. W.) The present southern comet. Nature, 35: 438. Comet 1887 I (Observations of position of). 1887. Adelaide, Jan. 21, 22, 25, 26, 27; Month. not., 47: 305. Cape of Good Hope, Jan. 22-25, 27, 28; Ibid., 303. Cordoba, Jan. 21, 22, 24, 25, 27; Astron. jour., 7: 91. Also: Astron. Nachr., Tis 259. Motony (E. J.) [Observations with sextant Jan. 21, 22, 25.] Month. not., 47: 432. Comet 1887 I (Physical appearance of ). Biags (A. B.) [General description.] Eng. mec., 45: 174. F[LamMMARION] (C.) La grande cométe australe de 1887. il. L’Astron., 6: 201-205. [Rio Janeiro observations, with sketch.] Rev. d. obsrio., 2: 17. Tessurt (J.) [Description of a large southern comet.] Obsry., 10: 166. , TuHomeE (J. M.) O grande cometa austral. Rev. d. obsrio., 2: 35. Comet 1887 II — Comet 1887 6. Discovered by Brooks at Phelps, N. Y., 1887, Jan. 22. Astron. jour., 7: 55. Also; Astron. Nachr., 116: 148. Also: Sid. mess., 6: 118. Comet 1887 II (Elements of). BerBericH (A.) [From obsns. 1887, Jan. 25, 26, 28.] Astron. Nachr., 116: 109. Boss (L.) [From obsns. 1887, Jan. 24, 26, 29.] Ibid., 116: 160. BIBLIOGRAPHY OF ASTRONOMY: 1887. Lz ‘ Comet 1887 II (Elements of )—Continued. Boss (L.) [From obsns. 1887, Jan. 24, 29, Feb. 9.] Astron. jour., 7: 63. [From obsns. 1887, Jan. 24, Feb. 15 (4 obsns.), Mar. 12.] bid., 85. OrrENHEIM (H.) [From obsns. 1887, Jan. 25, 27, 29.] Astron. Nachr., 116: 174. Also: Obsry., 10: 145. [From obsns. 1887, Jan. 95, 27, 29, Feb. 11;] Astron. Nachr., 116: 221. [From obsns. 1887, Jan. 25, Feb. 11, Mar. 11, 28.] Ibid., 317. SprraLer (R.) [From obsns. 1887, Jan. 25, 27, 29.] Ibid., 173. [From obsns. 1887, Jan. 25, 26, Feb. 12.] Jbid., 206. [From normals 1887, Jan. 24, Feb. 11, and an observation Feb. 25.] Tbid., 253. Comet 1887 II (Observations of position of). 1887. ; Albany, Jan. 24, 26, 27, 29, Feb. 9; Astron. jour.,7: 56,61. Mar. 12; Jbid., 85. Algiers, Jan. 27, 28; Compt. Rend., 104: 348. Jan. 27, 28, Feb. 19, 21, 23, 26, Mar. 14; Bull. astron., 4: 1386. Mar. 18, 21-25, Apr. 13, 14; Tbid., 423. Berlin, Feb. 11; Astron. Nachr., 116: 189. Besangon, Feb. 24, 26, 28, Mar. 1, 2, 18, 29, Apr. 10, 18, 20; Compt. Rend., 105: 738. Bethlehem, Feb. 9, 18, 19; Astron. jour., 7: 80. Bordeaux, Jan. 29; Astron. Nachr., 116: 157. Also: Compt. Rend., 104: 277. Jan. 30, Feb. 4, 5, 7, 9, 10, 11; Compt. Rend., 104; 417. Jan. 29, 30, Feb. 4, 5, 7, 9, 10, 11, 18, 15, 16, 17, 24, 26, 27, Mar. 2, 3, 4, 7, 16, 17, 18, 25, 28, 380; Astron. Nachr., 117: 99. Bothkamp, Mar. 19, 20; Astron. Nachr., 118: 105. Cambridge (Harv. coll. obsry.), Jan. 24, 27; Ibid., 116: 191. Copenhagen, Feb. 13, Mar. 16; Jbid., 118: 73. . Dresden, Feb. 15; Astron. Nachr., 116: 203. Feb. 19; Ibdid., 249. Mar. 11; Ibid., 267. Mar. 24; Ibid., 317, 327. Geneva, Feb. 10, 11, 12, 14, 17, 18, 21-24, 26, 28, Mar. 18, 29-31; Astron. Nachr., 116: 333. Apr. 18, 20; Ibid., 117: 55. Gottingen, Feb. 15; Astron. Nachr., 116: 203. Feb. 14, 17, 24; Ibid., 249. Mar. 11, 15; Ibid., 116: 267. Feb. 14-18, 24, 28, Mar. 1, 11, 15; Tdid., 117: 149. Greenwich, Feb. 27, 28; Month. not., 47: 275. Mar. 13, 16, 18, 23, 24, 27; Ibid., 392. Hamburg, Feb. 13, 15; Astron. Nachr., 116: 203. Kiel, Jan. 27; Ibid., 157. Feb. 10, 11; Ibid., 189. Feb. 15; Ibid., 203. Kremsminster, Jan. 24-30; Astron. Nachr., 117: 149. Feb. 12, 14, 15-18, 24, Mar. 1, 2,4, 21; Jbzd., 118: 105. Milan, Jan. 27; Ibid., 116: 178. Nashville, Jan. 23; Astron. jour., 7: 63. Also: Astron. Nachr., 116: 203 Nice, Jan. 27-29; Bull. astron., 4: 135. Orwell Park, Feb. 12, 13, 15, 16, 17, 21, 24-28, Mar. 1, 2, 6, 10, 11, 12, 14, 16, 18, 23, 25, 27, 28, 30, Apr. 10, 11, 15, 16, 17, 20, 23; Month. not., 48: 58. 2BA 18 BIBLIOGRAPHY OF ASTRONOMY: 1887. Comet 1887 II (Observations of position of). 1887—Continued. Padua, Jan. 27-30; Astron. Nachr., 116: 171. Palermo, Jan. 29-31; Ibid., 219. Feb. 15, 24; Ibid., 265. Paris, Jan. 27; Astron. Nachr., 116: 173. Jan. 27, 28,29; Compt. Rend., 104: 276. Plonsk, Feb. 11, 14, 17, 20, 25; Astron. Nachr., 117: 305. Strassburg, Jan. 25-28; Ibid., 116: 148, 157. Feb. 11; Ibid., 203. Toulouse, Jan. 27-31, Feb. 4; Compt. Rend., 104: 487. Vienna, Jan. 28, 29; Astron. Nachr., 116: 173. Feb. 12; Jdid., 205. Feb. 18: Ibid., 208. Washington, Jan. 24, 25; Astron. jour., 7: 62. Feb. 12, 16, 18; Idid., 78. Mar: 11512) “fbzd.. 86: Comet 1887 III = Comet 1887 d. Discovered by Barnard at Nashville, 1887, Feb. 16. Astron. jour.,7: 72. Also: Astron. Nachr., 116: 207, 251. See, also, Sid. mess., 6: 161. Comet 1887 III (Elements of). BARNARD (E. E.) [From obsns. 1887, Feb. 16, 18, 22.] Sid. mess., 6: 161. [From obsns. 1887, Feb. 16, 28, Mar. 8.] Astron. jour., 7: 95. [From obsns. 1887, Feb. 16, 28, Mar. 12.] | Astron. Nachr., 117: 59. Boss (L.) [From obsns. 1887, Feb. 16, 18, 20.] Astron. Nachr., 116: 207. Also: Obsry., 10: 144. [From obsns. 1887, Feb. 16, 19, 22.] Astron. jour., 7: 72. Also: As- tron. Nachr., 116: 228. OPPENHEIM (H.) [From obsns. 1887, Feb. 17, 23, 26.] Astron. Nachr., 116: 255. [From obsns. 1887, Feb. 17, 28, Mar. 11.] Jbid., 271. Pauisa (J.) [From obsns. 1887, Feb. 17, 23, 28.] Ibid., 256. WENDELL (O. C.) [From obsns. 1887, Feb, 22, 25, 28.] Ibid., 317. Comet 1887 III (Observations of position of). 1887. Albany, Feb. 19, 22, 25; Astron. jour., 7: 84. Algiers, Feb. 24, 26; Compt. Rend., 104: 671. Feb. 24, 26, Mar. 12, 18, 14; Bull. astron., 4: 187. Mar. 21-25; Ibid., 424. Berlin, Feb. 28; Astron. Nachr., 116: 251. Cambridge (Harv. coll. obsry.), Feb. 17, 19, 25, 28; Astron. jour., 7: 72, 79. Also: Astron. Nachr., 116: 267. Copenhagen, Mar. 16; Astron. Nachr., 118: 73. Dresden, Feb. 24; Jbid., 116: 221. Mar. 11; Ibid., 267. Mar. 24; Ibid., 317. Geneva, Feb. 24, 26; Ibid., 116: 251. Mar. 18; Ibid., 315. Gottingen, Feb. 24; Ibid., 116: 221. Greenwich, Feb. 28; Month. not., 47: 275. Hambnrg, Feb. 26; Astron. Nachr., 116: 221. Kremsmiinster, Feb. 24, 25; Ibid., 117: 149. Nashville, Feb. 16, 18, 22; Astron. jour., 7: 79. Also: Astron. Nachr., 116: 251. BIBLIOGRAPHY OF ASTRONOMY: 1887. 19 Comet 1887 III (Observations of position of). 1887—Continued. Nice, Feb. 28, Mar. 1; Bull. astron., 4: 194, Orwell Park, Feb. 28, Mar. 13, 14, 16,18, 19, 23, 27, Apr. 10; Month. not., 48: 61. Palermo, Feb. 27; Astron. Nachr., 116: 267. Paris, Feb. 17; Astron. Nachr., 116: 207. Feb. 17, 24,27; Compt. Rend., 104: 559. Rome, Feb. 24; Astron. Nachr., 116: 251. Feb. 25; Idid., 117: 270. Strassburg, Feb. 23; Jdid., 116: 221. Mar. 14; Ibid., 267. Vienna, Feb. 24; Ibdid., 221. Feb. 28; Ibid., 251. Washington, Feb. 24; Astron. jour., 7: 78. Comet 1887 IV — Comet 1887 e. Discovered by Barnard at Nashville, 1887, May 12. Astron. jour.,7: 96. Also: Astron. Nachr., 117: 31. Also: Sid. mess., 6: 220. Comet 1887 IV (Elements of). ABETTI (A.) [From obsns. 1887, May 14, 18, 21.] Astron. Nachr., 117: 102. BieELow (F. H.) [Three normals from obsns. 1887, June 12-22.] Sid. mess., 6: 321. Boss (L.) [From obsns, 1887, May 12, 14, 15.] Astron. jour., 7: 96. CHANDLER (S. C.) jr. [From normals 1887, May 14, 19, 24, 20.] Astron. jour , 7: 104. [From normals 1887, May 14, 30, June 12, July 12.] Jbid., 121. [Elliptic elements from normals 1887, May 14, June 12, July 12.] Jbid., 122) Lamp (E.) [From obsns. 1887, May 12, 14, 16.] Astron. Nachr., 117: 31. OPPENHEIM (H.) [From obsns. 1887, May 12, 15, 17.] Jbid., 46. [From normals 1887, May 14, 19, and an observation May 23.] Jbid., 61. [From obsns. 1887, May 14, 19, 28, June 16.] Jbid., 119. OPPENHEIM (S.) [From obsns. 1887, May 12, 14, 15, 17.] Astron. Nachr., Wie: —— [From obsns. 1887, May 12, 17, 22, 29.] Jbid., 62. ——— [From normals 1887, May 15, 22, 29, June 24.] Ibid., 165. WENDELL (O. C.) [From obsns. 1887, May 13, 19, 25.] Jbid., 119. Comet 1887 IV (Observations of position of). 1887. Albany, May 18, 15, 18, 23; Astron. jour., 7: 103. Algiers, May 16, 18-21, 23, 24; Astron. Nachr., 117: 57. Also: Compt. Rend., 104: 1493.. May 25, 26, 28, June 9, 10, 15, 16, 20, 22, 23; Bull. astron., 4: 424. Aug. 8,9; Bull. astron., 4: 465. Berlin, May 23; Astron. Nachr., 117: 48. June 16, 24, 26; Jbid., 117: 385. Besancon, June 13, 14, 16, 17, 18, 20-24, July 8, 12, 16, 23; Compt. Rend., 105: 518. 20 BIBLIOGRAPHY OF ASTRONOMY: 1887. Comet 1887 IV (Observations of position of ). 1887—Continued. Bordeaux, May 22, 26, 27, June 8-18, 21, 22; Astron. Nachr., 117: 151. Also: Compt. Rend., 104: 1822. June 28-July 2, 6, 7, 11, 12, 18, 19, 22, 23, 24, 27, 29, Aug. 6, 8, 10; Astron. Nachr., 117: 307. Also: Compt. Rend., 105: 403. Bothkamp, June 15, 16, 24; Astron. Nachr., 117: 133. June 28, July 25; Ibid., 215. Cambridge (Chandler), May 30, July 12; Astron. jour., 7: 152. Cambridge (Harv. coll. obsry.), May 18, 14, 19, 25, 30; Astron. jour., 7: 111. Also: Astron. Nachr., 117: 243. June 7, 8, 18, 14, 15, 25; Astron. jour., 7: 119. Also: Astron. Nachr., 117: 248. Cape of Good Hope, May 19, 21, 28, 24, 27, June 8, 9, 11, 18, 14, 16, 17; Astron. Nachr., 117: 339. Dresden, May 19; Jbid., 43. May 22; Ibdid., 59. June 13; Ibid., 133. July 16; Ibid., 215. Geneva, May 19; Ibid., 43. Gohlis, June 13, 14, 16-19, 22, 25; Astron. Nachr., 117: 214. Gottingen, June 15-17, 22; Tbid., 183. Greenwich, June 12, 18, 19; Idid., 215. Hamburg, June 16, 17, 19; Iid., 119, 133. Harrow, June 12, 15, 17, 19, 22. Month. not., 47: 550. Kiel, May 14; Astron. Nachr., 117: 31. May 16, 21; Jéid., 43. Kremsminster, May 15, 26, June 13, 15, 18, 19, 28, 24, 25, 27, July 12; Ibid., 118: 107. Marseilles, May 14, 18, 22, 23, 24, 27, June 8-18, 15, 16, 17, 22,28; Bull. astron., 4: 462. Nashville, May 12, 18,14; Astron jour., 7: 99. Also: Astron. Nachr., 117: 57. May 12, 13, 14, 18, 24, 25, 26, 28, June 9, 10, 11, 16, 17, 18, 20, 23; Astron. jour., 7: 111. Also: Astron. Nachr., 117: 243. July 8, 9, 11, 13-16, 19, 20, 26, Aug. 10,11; Astron. jour., 7: 126. Also: Astron. Nachr., 117: 385. Nice, May 14; Astron. Nachr., 117: 43. May 14, 17, 18, 20-23; Bull. astron., 4: 225. May 27, July 7, 11, 18, 23; Jdzd., 380. Nicolaief, May 14, 15, 17, 18, 21; Astron. Nachr., 117: 55. Orwell Park, June 9, 10, 12, 13, 15, 17, 18, 20, 22, July 11, 12, 13, 14, 18-21, 24, 27, 28; Month. not., 48: 61. Padua, May 14; Astron. Nachr., 117: 43. May 18, 21; Jdid., 101. Palermo, May 15, 21; Ibid., 31, 59. May 28, 30, 31; Ibid., 101. Paris, May 14; Astron. Nachr., 117: 43. Also: Compt. Rend., 104: 1360. Prague, May 27; Astron. Nachr., 117: 59. Rome, May 14, 15; Astron. Nachr., 117: 43. May 17, 19, 27, 30, June 7, 15, 18; Tbid., 270. May 14, 15, 17, 19, 27, 80, June 7; Atti. d. r. accad. d. Lincei, s. 4. Rendic., 3: 481. July 8, 10-17, 21, 22, 24, Aug. 6, 7; Astron. Nachr., MTR e2u: Scarborough, May 20, 21, 29; Month. not., 47: 498. o BIBLIOGRAPHY OF ASTRONOMY: 1887. 21 Comet 1887 IV (Observations of position of). 1887—Continued. Strassburg, May 15; Astron. Nachr., 117: 31. Vienna, May 15, 17; Ibid., 43. Washington, May 14, 19, 21; Astron. jour., 7: 101. Comet 1887 V = Comet 1887 f. See Comet Olbers. Comets. See, also, Comets and meteors; Comets (Orbits of). BeRBERICH (A.) Methode sonnennahe Cometen bei Tage aufzufinden. Astron. Wachr:, 118): 71. CLEVINGER (S. V.) Optical appearances of comets. Sid. mess., 6: 89-95, 120. DeLauNneEY (J.) Sur les distances des planétes au soleil, et sur les distances des cométes periodiques. Adbstr.: Compt. Rend., 105: 515. GUILLEMIN (A.) Les cométes. 12+ 287 p. il. 8vo. Paris, 1887. (M. 1.20.) Ho.etscHexk (J.) Uber die Frage nach der existenz von Cometensystemen. Anzeiger der Wiener Akad. 1887, Nr. 15. Rev.: Astron. Nachr., 117: 359. Kirkwoop (D.) Note on the origin of comets, Am. j. sc., 133: 60. Also: Sid. mess., 6: 77. Moncxk (W.H.S8.) [Connection of comets and asteroids.] Obsry., 10: 230. UNTERWEGER (J.) Zur Kometen-statistik. [Comets and the periodicity of sun- spots.] K. Akad, d. Wissensch. in Wien, sitzng. d. math.-naturwissen. Cl. 21 Julie 1887. ‘Also: Mem. soc. spettrosep. ital., 16: 99-101. Also, abstr.: Sirius, 20: 227. Wiruiams (G. O.) [Cometary phenomena reproduced by reflections from spher- ical surfaces.] il. Sc. Am. sup., 9782. Comets and meteors. BuszczynskI (B.) Eine wahrscheinliche Periodicitét von hellen Meteoren und ihr wahrscheinlicher Zusammenhang mit dem periodischen Cometen Tempel. Astron. Nachr., 115: 268, 309. See, also, Ibid., 116: 101. Hrirscu (A.) Les météores de Biela, 27 nov., 1885. Bull. soc. sce. nat. de Neu- chatel, 15: 186-189. Kirxwoop (D.) Biela’s comet and the large meteors of Nov. 27-30. Proe. Am. phil. soc., 24: 242. Note on the possible existence cf fireballs and meteorites in the stream of Bielids. Jbid., 436. LAGRANGE (E.) Aurores boréales, cométes et étoiles filantes. Ciel et terre, 7: 494-500. Meteoros de 18-14 de Novembro. il. Rev. d. obsrio., 2: 168. von Nizsst (G.) Uber die grossen Meteore im Juni und ihre vermuthete Bezie- hung zum periodischen Cometen Tempel. Astron. Nachr., 116: 97-102. Proctor (R. A.) Origin of comets and meteors. Knowl., 10: 64,135. Also: Pop. sc. month., 31: 50-60. WENDELL (0. C.) [Radiants of the comets of 1886.] Astron. Nachr., 118: 175. Also: Sid. mess., 6: 359. Comets of 1886. B[1courRDAN] (G.) Cométes et planétes de 1886. Bull. astron., 4: 15. 22 BIBLIOGRAPHY OF ASTRONOMY: 1887. Comets of 1886—Continued. Kreutz (H.) Zusammenstellung der Cometen-Erscheinungen des Jahres 1886. Vrtljschr. d. astron. Gesellsch., 22: 14-23. Also, transl.: Sid. mess., 6: 201- 210. Also, Reprint. P. (W. E.) Comets of 1886. Month. not., 47: 172. WInLock (W. C.) [List of the] comets of 1886. Sid. mess., 6: 112. Comets (Orbits of). See, also, Orbits. Evans (W.C.) Motion of a comet when perturbed and resisted. Obsry., 10: 130-134. Harkness (W.) Representation of comets’ orbits by models. il. Sid. mess., 6: 329-349. HotetscHEK (J.) Richtungen der grossen Achsen der Kometbahnen. 29 p. 8°. Wien, 1887. (M. 0.60.) Hoover (W.) Cometary perturbations. 18 p. 8vo. Wooster, Ohio, 1887. Krevurz (H.) Bericht tber Cometen. Vrtljschr. d. astron. Gesellsch., 22: 361- 365. e Monck (W.H.S.) Inclinations of cometary orbits. Month. not., 47: 433. Orbits of comets. Obsry., 10: 324. SEARLE (G. M.) Method of computing an orbit from three observations. As- tron. jour., 7: 140-144, 153-155. Constellations. Lynn (W.T.) [Babylonian origin of the constellations.] Obsry., 10: 162. Copenhagen observatory. THIELE (T. N.) Bestimmung der Liangen-Differenz zwischen Lund und Kopen- hagen. 56 p. 4to. Lund, 1886. (M. 2.) Cordoba observatory. Goutp (B. A.) Corrections to the Uranometria Argentina and the Cordoba catalogues. Astron. Nachr., 116: 379. Resultados del observatorio nacional Argentino en Cordoba bajo la direccion del B. A. Gould. J. M. Thome, director. Vol. 5. Observaciones del av 1874. 180 + 559 p. 4to. Buenos Aires, 1886. (M. 80.) Same. Vol. 6. Observaciones del afio 1875. 44+ 649 p. 4to. Buenos Aires, 1887. Same. Vol. 9. Observaciones del afio 1876. . 22+ 261 p. 4to. Buenos Aires, 1887. Corona (Solar). Ennis (J.) Colors in the solar corona. Sid. mess., 6: 273-281. Westey (W.H.) The solar corona as shown in photographs taken during total eclipses. Month. not., 47: 499-510. Discussed: Obsry., 10: 251. Cosmogony. See, also, Nebular hypothesis. Brawn (C.) Uber Cosmogonie vom Standpunkt christlicher Wissenschaft, mit einer Theorie der Spnne. 167 p. 8vo. Munster, 1887. Rev. by Clerke (A. M.\) Nature, 36: 321, 341. See, also, Bull. astron., 4: 141-143. Also: Obsry., 10: 201. BIBLIOGRAPHY OF ASTRONOMY: 1887. 23 Cosmogony—Oontinued. FLAMMARION (C.) L’univers antérieur. L’Astron., 6: 41-48. GanseR (A.) Die Entstehung der Bewegung: eine Kosmogonie. 15 p. 8vo. Graz, 1887. (M. 1.) LaGRanceE (C.) Une réflexion au sujet de la conception purement mécanique de univers. Ciel et terre, 8: 345-353. ZENGER (C. V.) L’évolution sidérale. Compt. Rend., 105: 1289. Dearborn observatory. [Proposed transfer of instruments, etc.] Sid. mess., 6: 81, 324. Reports (Annual) of the board of directors of the Chicago astronomical society, together with the report of the director of the Dearborn observatory for 1885 and 1886. 50p. il. 8vo. Chicago, 1887. Domes. Topp (D. P.) Best device for revolving a dome. il. Month. not., 47: 272- 274. Discussed: Obsry., 10: 90. Dorna (Alessandro) :[1825-1886]. Sracci (F.) Alessandro Dorna. Commemorazioni e catalogo delle sue pubbli- cazioni. 8p. 8vo. Torino, 1887. Dorpat observatory. Beobachtungen der kaiserlichen Universitats-Sternwarte Dorpat. 17. Bd. Redu- cirte Beobachtungen am Meridiankreise von Zonensternen und mittlere Orter derselben fur 1875-6, . . . von L. Schwarz. 39-+151 + 47 p- 4to. Dorpat, 1887. Double stars. Franks (W.S.) Magnitudes of double stars. J. Liverp. astron. soc., 5: 44-47. Gore (J. E.) Masses and distances of the binary stars. Jbid., 47. Hau (A.) Nomenclature of double stars. Astron. jour., 7: 120. Linou (B.) Moyen facile d’observer les étoiles doubles avec une grande ap- proximation sans équatorial ni micrométre. L’Astron., 6: 187-191. Macue (J.) Nachtrag zu dem Artikel, ‘‘ Die Auflésbarkeit der Doppelsterne in Fernrohren von verschiedener Grésse.’’ Sirius, 20: 38-44. Moncx (W.H.S.) Brightness and masses of binary stars. Obsry., 10: 96. Further notes on binary stars. Obsry., 10: 184. [Prize of the royal Danish academy.] Bull. astron., 4: 164. TIsSERAND (F.) Sur la force qui produit les mouvements des étoiles doubles. Bull. astron., 4: 5-15. Double stars (Measures of ). DempowsKI (E.) Misure micrometriche . . . 2v. Roma, 1883, 1884. Rev. by Schur (W.) Vrtljschr. d. astron. Gesellsch., 22: 209-236. von ENGELHARDT (B.) Mikrometrische Beobachtungen von ¢ Cancri. Astron. Nachr., 117: 278. Mikrometrische Messungen von Struve’schen weiten Doppelsternen. Ibid., 1-6. 24 BIBLIOGRAPHY OF ASTRONOMY: 1887. Double stars (Measures of )—Continued. ENGELMANN (R.) Doppelsternmessungen. Jbid., 17-80. Hovau (G. W.) Catalogue of 209 new double stars discovered with the 184-inch refractor of the Dearborn observatory. Astron. Nachr., 116: 273-804. Also, Reprint. JEDRZEJEWICZ (J.) Mesures micrométriques d’étoiles doubles, [1882-86.] As- tron. Nachr., 116: 177-186. Lamp (E.) Uber systematische Beobachtungsfehler bei der Bestimmung der Parallaxe der schwacheren Componente des Doppelsterns ¥ 2898. Vrtljschr. d. astron. Gesellsch., 22: 342-345. LEAVENWoRTH (F. P.) [Proper motion of Lal. 4219.] Sid. mess., 6: 80. LEAVENWORTH (F. P.) & MuLuer (F.) New double stars discovered at the Leander McCormick observatory. Astron. jour., 7: 95. RussELL (H. C.) Measures of southern double stars made at the observatory, Sydney, N.S. W. Month. not., 47: 473-477. Tarrant (K.J.) Micrometrical measures of 25 double stars. J. Liverp. astron. soc., 5: 41, 166, 201, 229. Double stars (Orbits of). CELoriA (G.) Nuova determinazione dell’orbita della stella doppia Y 3121. Astron..Nachr., 117: 3879. VON GLASENAPP (S.) Bahn des Doppelsterns 6 Equulei. Jdid., 116: 169. GorE (J. E.) Orbit of 12 Lyncis (¥ 948). J6id., 117: 290. Orbit of 14 (z) Orionis (O. Struve, 98). Month. not., 47: 266. Orbit of Y1757. Ibid., 478. Orbit of p Eridani. Jbid., 48: 26. Marru (A.) Formule for correcting approximate elements of the orbits of binary stars. Jbid., 47: 480-494. Also, Reprint. Dresden observatory (Engelhardt’s). von ENGELHARDT (B.) [Report for 1886.] Vrtljschr. d. astron. Gesellsch., 22: 99. Dresden observatory (K. math. Salon). DrecusLer (A.) [Report for 1886.] Jbid., 100. Dunecht observatory. [Report for 1886.] Month. not., 47: 158. Dunsink observatory. Astronomical observations and researches... Pt. 6. 99 p. 4to. Dublin, 1887. (M. 10.) [Report for 1886.] Month. not., 47: 153. Dusseldorf observatory. Luter (R.) [Report for 1886.] Vrtljschr. d. astron. Gesellsch., 22: 102. Baling observatory (Common’s). [Report for 1886.] Month. not., 47: 158. ae eS BIBLIOGRAPHY OF ASTRONOMY: 1887. 25 Earth. Axsngy (W. de W.) Transmission of sunlight through the earth’s atmosphere. 33 p. 4to. London, 1887. (M. 1.30.) AnpeErRson (A. A.) Terra: on a hitherto unsuspected second axial rotition of ourearth. 8vo. London, 1887. (M. 6.30.) Lockyer (J. N.) The movements of the earth. 130 p. 12mo. New York, 1887. ($0.60. ) Parkuurst (H. M.) The earth’s temperature. Papers Am. astron. soc., 1: 49-52. ScHWAHN (P.) Anderungen der Lage der Figur-und der Rotations-Axe der Erde sowie einige mit dem’ Rotationsproblem in Beziehung stehende geo- physiche Probleme. 51 p. 4to. Berlin, 1887. (M. 2.) Witsine (J.) Mittheilung uber die Resultate von Pendelbeobachtungen zur Bestimmung der mittleren Dichtigkeit der Erde. Sitzungsb. d. k. preuss. Akad. d. Wissensch. zu Berlin, 1887: 327-834. Also, Reprint. (Gui ale) Garthquakes. ALBRECHT (T.) Uber eine durch Erdbeben veranlasste Niveaustérung. Astron. Nachr., 116: 129-1384. Easter. LAKENMACHER (E.) Osterformeln, Astron. Nachr., 116:°325-328; 117: 185. Scumipt (R.) Noch einige Bemerkungen zu den Lakenmacher’schen Oster- formeln. Jbid., 117: 51. Scuram (R.) Bemerkungen zu Herrn Lakenmacher’s Osterformeln. Jbid., 116: 378-378. Eclipse of the moon 1887, Aug. 3. BAUSCHINGER (J.) [Obsn. at Munich.] Astron. Nachr., 118: 122. C. (M.) [Obsns. at La Tour de Peilz.] Nature, 36: 413. H. (H.) [Peculiar distortion of earth’s shadow observed.] Nature, 36: 367. Jounson (S. J.) Color of eclipsed moon. Obsry., 10: 325. KueEIn (H. J.) [Obsns. at Cologne.] Sirius, 20: 193. von Konxoty (N.) [Obsns. at O’Gyalla.] Ibid., 235. LeEescaRBAULT (E.) KEelipse . . . visible 4 Orgéres. Compt. Rend., 105: 370. Mater (H. P.) [Obsns. at Killin.] Nature, 36: 413. Rayret (G.) [Obsns. at Bordeaux.] Compt. Rend., 105: 305. [Resumé of observations.] il. L’Astron., 6: 348-351. Scour (W.) [Obsns. at Géttingen.] Astron. Nachr., 117: 383. WEINEK (L.) [Obsns. at Prague.] Astron. Nachr., 117: 381. Eclipse of the sun 1884, Oct. 4. Kistner (F.) Bestimmung der Orter der vom Monde wahrend der totalen Fin- sterniss 1884, Oct. 4, bedeckten Sterne am grossen Meridiankreise zu Berlin. Astron. Nachr., 116: 225-240. t Eclipse of the sun 1886, Aug. 28-29. Jounson (S. J.) [Photographs of partial phase at sea.] Obsry., 10: 224. 26 BIBLIOGRAPHY OF ASTRONOMY: 1887. Eclipse of the sun 1886, Aug. 28-29—Obntinued. Perry (S. J.) Report of the observation ... at Carriacou. Proc. roy. soc., 47: 316. Proxertna (W. H.) [Account of his observations.] Science, 10: 9. Also, abstr.: Obsry., 10: 306. Also, abstr.; Bull. astron., 4: 408. [ScnusteR(A.) Preliminary account of observations.] Abstr.: Obsry., 10: 203. SrocKwELt. (J. N.) [Obsn. of last contact.] Astron. jour., 7: 3. T[urNER] (H. H.) [Results of the English expedition to Granada.] Month. not., 47: 175. Eclipse of the sun 1887, Aug. 18. AupBreEcutT (T.) Die totale Sonnenfinsterniss am 19. August, 1887, nebst Uber-' siche tiber die hervorragendsten Sonnenfinsternisse innerhalb Deutschlands im 19. u. 20. Jahrh. 3832p. 8vo. Berlin, 1887. (M. 0.50.) Darstellung der totalen Sonnenfinsterniss . . . auf carton mit verschiebbarer Mondscheibe. Berlin, 1887. (M. 0.50.) Ennis (J.) The total solar eclipse of August next. Sid. mess., 6: 105-109. FLAMMARION (C.) L’éclipse totale de soleil du 19 aott 1887. il. L’Astron., 6: 241-252. GARNIER (P.) L’éclipse de soleil du 19 aotit 1887. il. Ibid., 306. {List of stations and observers.] Obsry., 10: 207. NixsTEN (L.) ([Circumstances, path, etc., of the eclipse.] Ciel et terre, 8: 177. Scuuria (R.) Karte der grossen Sonnenfinsterniss am Morgen des 19. Aug., 1887. fol. Leipzig, 1887. (M. 0.40.) Topp (D. P.) On observations of the eclipse of 1887, Aug. 18, in connection with the electric telegraph. Am. j. sc., 183: 226. Woerkor (A.) [List of stations in Russia desirable for meteorological observa- tions.] Nature, 36; 77. ZENKER (W.) Sichtbarkeit und Verlauf der totalen Sonnenfinsterniss in Deutsch- land. 29p.,1pl. 8vo. Berlin, 1887. (M. 1.20.) Eclipse of the sun 1887, Aug. 18. (Observations of.) ABETTI (A.) at Padua. Astron. Nachr., 117: 279. ALBRECHT (T.) at Goldap. Jbid., 280. BrLopotsky (A.) at Jurjewetz. Ibid., 118: 45. DE BoHDANOVITHZ (G.) at Irkoutsk. L’Astron., 6: 425. CopELAND (R.) & Perry (S. J.) near Kineshma. Month. not., 48: 48-54. Dunér (N. C.) at Lund. Astron. Nachr., 118: 26. GALLE (J. G.) [Report of observations at Breslau; also, at Frankfort by Lach- mann, and at Kolmar by Korber.] Astron. Nachr., 117: 311. GARNIER (P.) at Wilna. L’Astron., 6: 354. GourpeT (P.) L’éclipse et le tremblement de terre en Russie. il. Ibid., 388. Herz (N.) at Wien-Ottakring. Astron. Nachr., 118: 26. JANSSEN (J.) Note sur l’éclipse du 19 aout dernier. Compt. Rend., 105: 365. KononowItscu (A.) at Petrowsk. Astron. Nachr., 118: 24. BIBLIOGRAPHY OF ASTRONOMY: 1887. a7 Eclipse of the sun 1887, Aug. 18. (Observations of )—Continued. von Kovesticetuy (R.) at Bromberg. Ibid., 117: 295, Krteur (A.) at Kiel. Ibid., 268. Ktstner (F.) at Berlin. Ibid., 263. Lamp (E.) at Goldap. Jdid., 263. LascHoBeERr (F.) at Pola. Jbid., 118: 23. NizEsten (L.) at Jurjewetz. Ciel et terre, 8: 297, 839. Also: L’Astron., 6: 861-864. Also, transl.: Sid. mess., 6: 262-265. Ostr (H.) Die Sonnenfinsterniss am 19. Aug. beobachtet in Upsala. Photo- graphische Aufnahsne in 6 verschiedenen Momenten. 1 sheet, 2.5 x 15.5cm. Upsala, 1887. (M. 1.) PARSEHIAN (J.) at Constantinople. L’Astron., 6: 391. Porro (F.) at Turin. Astron. Nachr., 117: 279. [Preliminary reports from various stations.] Nature, 36: 398, 430, 452, 455. Report of the solar eclipse of 19th August, 1887. Naval observatory in the hy- drographic office, Tokio. No. 11. 388p.,2pl. 4to. Tokio, 1887. Japanese characters. VON SPIESSEN (—) near Berlin. Astron. Nachr., 117: 295. SuaiyamMa (M.) Photographs taken at Yomeiji-vama, Echigo, Japan. 1 p. 4to. Tokio [1887]. Summary of observations at various stations.] Sirius, 20: 207, 229, 258. Topp (D. P.) [Account of the expedition to Japan.] Obsry., 10: 871-376. Topp (M.L.) The eclipse expedition to Japan. Nation, 45: 157, 169, 229, 554. Urecu (J.) at Elpatievo Narischkine. L’Astron., 6: 353. Weber (L.) Photometrische Beobachtungen wahrend der Sonnenfinsterniss 1877, Aug. 18-19 [Breslau]. Astron. Nachr., 118: 17-22. Eclipses. Eclipses (Les) du dix-neuviéme siécle. il. L’Astron., 6: 252-260. Ginzet (F. K.) Uber einige von persischen und arabischen Schriftstellen er- wahnte Sonnen-und Mondfinsternisse. Sitzungsb. d. k. preuss. Akad. d. Wissensch., 1887. Also, Reprint. (M. 0.50.) JoHnson (S. J.) Notes ona manuscript eclipse volume. Month. not., 47: 430. Eclipses in England A. D. 538—A. D. 2500. Remarks on the ‘‘ Canon der Finsternisse.’’ Obsry., 10: 302. Eclipses of the sun. Exner (K.) Uber die bei totalen Sonnenfinsternissen auftretenden Erschein- ungen der ‘fliegenden Schatten ’’ und der “ Baily’s beads’”’ (Perlenreihe). Astron. Nachr., 116: 321. GinzeL (F. K.) Uher die geringsten Phase welche bei der Beobachtung von Sonnenfinsternissen mit freiem Auge noch gesehen werden kann. Astron. Nachr., 118: 119. Uber einige historische besonders in altspanischen Gesichtsquellen er- wahnte Sonnenfinsternisse. Sitzungsb. d. k. preuss. Akad. d. Wissensch. zu Berlin, 1886: 963-980, 2 pl. Also, Reprint. (M. 1.50.) 28 BIBLIOGRAPHY OF ASTRONOMY: 1887. Eclipses of the sun—Continued. Mauter (E.) Eine in einer syrischen Grabinschrift erwahnte Sonnenfinsterniss. | 8p. 8vo. Wien, 1887. (M. 0.20.) Edinburgh observatory. [Report for 1886.] Month. not., 47: 153 Ephemerides and almanacs. Almanaque nautico para el aio 1889... 11+ 559p. 4to. Madrid, 1887. American ephemeris and nautical almanac for . . . 1890. led. 6+ 52148 p. | 4to. Washington, 1887. ($1.00.) } Annuaire de l’observatoire royal de Bruxelles. Année 55. 1888. 16mo. [Brux-|} elles, 1887. ] Annuaire pour l’an 1888, publié par le bureau des longitudes. 19+ 808 p. 16mo, [Paris, 1887.] (1 fr. 50 ©.) Annuario del observatorio de La Plata para el ano 1887. 424 p. 8vo. Buenos Aires. (M. 8.) 8 Annuario publicado pelo imperial observatorio do Rio de Janeiro para o anno | | 1888, 12mo. Rio Janeiro, 1887. Anuario del observatorio astronédmico nacional de Tacubaya para el afio 1888 Afio 8. 299 p. 16mo. México, 1887. 5 Astronomisch-nautische Ephemeriden fur das Jahr 1888. Hrsg. von astronomisch- meteorologischen Observatorium der. k. k. Handels und nautischen Akad- emie in Triest unter Redaction von F. Anton. Jahrg.1. 38 + 256 p. 8vo. Triest, 1887. (M. 2.70.) Berliner astronomisches Jahrbuch fiir 1889. 8 + 495+ 36+ 25p. 8vo. Berlin, 1887. (M. 12.)) CHARRIER (A.) Effemerdi del sole, della luna et dei principali pianetini per anno 1888. 29p. 8vo. Torino, 1887. Repr. from: Attid. r. accad. d. se. d. Torino, 22. Companion (Annual) to the Observatory. 55 p. 8vo. London, 1887. (1s. a”) Repr. from: Obsry.,11: 1-55. 1888. { Con des temps pour l’an 1888, publiée par le bureau des longitudes. 5 + 829+ 126 p. 8vo. Paris, 1887. Same. Extrait 4 l’usage des écoles d’hydrographie et des marins du com-- merce. 100 p. 8vo. Paris, 1887. et D6LLEN (W.) Stern-Ephemeriden auf das Jahr 1888 zur Bestimmung von Zeit } und Azimut mittelst des tragbaren Durchgangsinstruments im Verticale ie Polarsterns. 24+ 27 p. 4to. St. Petersburg, 1887. Dusots (E.) Ephémérides astronomiques et annuaire des marées pour 1888. oe Paris, 1887. (M. 12.) Ephemerides astronomicas calculadas paro o meridiano do observatorio da unio sidade de Coimbra . . . para o anno de 1888. 12+ 304416 p. 8vo. Coimbra, 1887. ¥ FLAMMARION (C.) Annuaire astronomique pour 1887. L’Astron., 6: 1-21. Loewy (M.) Ephémérides des étoiles de culmination lunaire et de longitude pour 1888. 41 p. 4to. Paris, 1887. 9 BIBLIOGRAPHY OF ASTRONOMY: 1887. 29 iphemerides and almanacs— Continued. Nautical (The) almanae and astronomical ephemeris for the year 1891. 10 + 514+.16 p. 8vo. London, 1887. 2s. 6d.) Nautisches Jahrbuch oder Ephemeriden und Tafeln ftir das Jahr 1890 zur Bes- timmung der Zeit, Lange und Breite zur See nach astronomischen Beobach- tungen. Hrsg. von Reichsamt des Innern. Berlin, 1887. (M: 1.50.) Equatorial. See, a/so, Illumination. Wotr (M.) Hinfache Methode den Gang eines Triebwerks zu priifen. Astron. Nachr., 116: 117. Grrors. See Observations (Errors of ). Eudozus. _ Ars astronomica, qualis in charta egyptica superest. Denuo edita a F. Blass. a 25 p. 4to. Kiliac, 1887. (M.. 1.) Pacule, cee, also, Sun (Statistics of facule, prominences, spots, ete., for 1886). Mascari (A.) Latitudine eliografiche e frequenza dei gruppi di facole brillanti durante il sessennio 1881-1886. Mem. soc. spettrscp. ital., 16: 80-85. Measures of positions and areas of spots and facule ... on photographs taken . at Greenwich, in India, and in the Mauritius. Greenw. spectrscp. obsns. 1885: 34-104. TaccHINI (P.) Facole solari osservate al regio osservatorio del collegio Romano nel 1886. Mem. soc. spettrsep. ital., 16: 4~7. Observations solaires du deuxiéme semestre 1886. Compt. Rend., 104: 216. Osservazioni di macchie e facole solari. [4° trimestre, 1886.] Atti d. r. acead. d. Lincei, s. 4. Rendic., 3: 14. Same. 1° trimestre, 1887. Jdrd., 265. Observations solaires faites 4 Rome pendant le premier trimestre de l’année 1887. Compt. Rend., 104: 1082; 105: 210. Same. 2° trimestre. Jdid., 105: 211. Same. 3®trimestre. Jdid., 1002. Z Macchie e facole solari osservate al regio osservatorio del collegio Romano nel 1° trimestre del 1887. Mem. soc. spettrscp. ital., 16: 33-36, 54-57. Same. 2®trimestre. IJbid., 87-90. Same. 3°trimestre. Jdzd., 118. Feil (Charles). For Obituary, see L’Astron., 6: 392. Also: Nature, 35: 306 Fellocker (Sieginund) [1816?-1887]. WaGnNER (—) Todes-Anzeige. Astron. Nachr., 117: 391. Flexure. SCHAEBERLE (J. M.) Horizontal flexure of vertical circles. Astron. Nachr., 118: 147-152. Method for measuring the astronomical flexure in zenith distance for all positions of the instrument. Ibdid., 147. Fraunhofer (Joseph) [1787-1826]. _ BAvERNFEIND (C. M.) Gediachtnissrede auf J. von Fraunhofer zur Feier seines 100 Geburtstages. 30p. 4to. Munchen, 1887. (M. 0.80.) ’ Bee As > — _—_e a al 30 BIBLIOGRAPHY OF ASTRONOMY: 1887. Fraunhofer (Joseph) [1787-1826 ]— Continued. \ 5 Festbericht uber die Gedenkfeier zur hundertjahrigen Wiederkehr des Geburt-— stages Josef Fraunhofer’s am 6. Marz, 1887,im Berliner Rathhause. Ztschr. 3 f. Instrmknd., 7: 114-128. [Portrait.] wt Voir (—) [Biographical notice.] 20 p., portr. 8vo. Munchen, 1887. 7; (M. 1.50. q See, also, Obsry.; 10: 239, Also: Sirius, 20: 49-54, 113. Geneva observatory. GauTIER (E.) [Report for 1886,.] Vrtljschr. d. astron. Gesellsch., 22: Rapport sur le concours pour le réglage des chronométres pendant l’année ee .. par E.Gautier. [11] p.- 8vo.. [n. p,, 1887.] Fr Glass (Optical). See, also, Objectives. | DaLLINGER (W. H.) Value of the new apochromatic lenses. Adst7.; Nature, 35: 467. i Gitt (D.) [Remarks on the new optical glass,] Obsry., 10: 214. Also, abstr.: 4 Bull. astron., 4: 301. NIELSEN (V.) Schott and Abbé’s new optical glass. Eng. mec., 44: 564. Sec, also, Ibid., 563. Tornow (E.) Relative Preise der Rohglasplatten fiir Fernrohr-objective nebstillt einem Vorschlage zu deren systematischer Normirung. il. Ztschr. f. In- | strmknd., 7: 247. Gotha observatory. BecKER (E.) [Report for 1886.] Vrtljschr. d. astron. Gesellsch., 22: 110. ae a Gottingen observatory. Scuur (W.) Festlegung des stidlichen Endpunktes der Gauss’schen Gradmess | sung auf der Sternwarte in Gottingen. Astron. Nachr., 118: 94. [ Report for 1886.] Vrtljschr. d. astron. Gesellsch., 09 : 104-109. Gravitation. See, also, Mechanics (Celestial); Planets. ReTHWIscH (E.) Die Bewegung im Weltenraum. Kritik der Schwerkraft und — Analyse der Axendrehung. 146 p. 8vo. Berlin, 1887. (M. 4.50.) — SrerNneck (R.) Untersuchungen tiber die Schwere im Innern der Erde. Mit- theil. d. k. k. militar-geogr. Inst. Wien, 1886. = | | | Rev.: Bull. astron., 4: 234. | Greenwich observatory. Astronomical and magnetical and meteorological observations made at the royal observatory, Greenwich, in the year 1885, under the direction of W. H. M. Christie. [965] p. 4to. London, 1887. (M. 22.) [Report for 1886.] Month. not., 47: 148-151, Report of the astronomer royal... 4to. [London, 1887.] Turner (H. H.) Variations of level and azimuth of the transit circle. Month. — not., 47 : 325-333. ; Grignon observatory. Lamry (F.M.) [Report for 1886.] Vrtljschr. d. astron. Gesellsch., 22: 111-_ 115. ji , BIBLIOGRAPHY OF ASTRONOMY: 1887. 3l Harrow observatory (Tupman’s). [Report for 1886.] Month. not., 47: 161. Harvard college observatory. Annals... vol. 17. Thealmucantar: an investigation made at the observatory in 1884 and 1885, by S. C. Chandler, jr. 9 + 222 p.,1 pi. 4to. Cambridge, 1887. (M. 18.) Annals . . . vol. 18, [nos. land 2.] 27 p. 4to. [Cambridge, 1887.] No.1: Magnitudes of stars employed in various nautical almanacs. No. 2: Disecus- sion of the Uranometria Oxoniensis. Boyden fund [circular no. 1]. 3p. 4to. [Cambridge, 1887.] Same. No. 2. Meteorological observations. 6 p. 4to. [Cambridge, 1887. ] Boyden fund and preliminary experiments in Colorado. Se. Am. sup., 9715. [Description of the instruments and of the methods of astronomical photography at Harvard college observatory.] il. Se. Am., 57: 2389, 278. Draper (Henry) memorial. First annual report of the photographic study of stellar spectra .,. . [by] E. C. Pickering. 10 p.,1 pl. Cambridge, 1887. Also: Mem. soc. spetirsep. ital., 16: 93-98. Also, Rev.: Obsry.,10: 231. Also: Nature, 36: 31, 41. Report (42d Annual) of the director... E. C. Pickering .. . Dec. 2, 1887. 12 p. 8vo. Cambridge, 1887. Helsingfors observatory. Donner (A.) [Report for 1886.] Vrtljschr. d. astron. Gesellsch., 22: 115-117 Herény observatory. von GoTHARD (E.) [Report for 1886.] Jbid., 118-120. Herschel (Sir William) [1738-1822]. CHAMBERS (G. F.) [Note concerning his life at Bath.] Obsry., 10: 166. Hong Kong observatory. [Report for 1886.] Month. not., 47: 171. Illumination. Dreyer (J. L. E.) Electric illumination of the Armagh refractor. Month. not., 47: 117. Stone (O.) Telescopic illumination. [Electric.] Sid. mess., 6: 73. Instruments. See Chronometers; Clocks; Circle-divisions; Equatorial; [llumina- tion ; Objectives. Interpolation. Rapavu (R.) Surun probléme d’interpolation. Bull. astron., 4: 515-519. THIELE (T. N.) Ausgleichung und Interpolation von Zeitbestimmung. Vrtljschr. d. astron. Gesellsch., 22: 302-3138. Weyer (G. D. E.) Interpolation bei periodischen Functionen. Jbid., 292. Interpolation fir die Mitte bei periodischen Functionen. Astron. Nachr., 117: 313-322. Iowa college observatory. [New observatory at Grinnell, Iowa.] Sid. mess., 6: 322. 32 BIBLIOGRAPHY OF ASTRONOMY: 1887. Journals (Astronomical). Astronomical (The) journal. Edited by B. A. Gould, Cambridge, Mass. [Semi- monthly.] v.7. 4to. Boston. ($5.00. ) L’Astronomie. Revue d’astronomie populaire . . . publiée par C. Flammarion. [Monthly.] 6. Année, 1887. 488 p. 4to. Paris, 1886. (14 fr.) Astronomische Nachrichten. Hrsg von A. Kriiger. Bd. 116 [Nr. 2761-2784]. 7+ 402 p. 4to. Kiel, 1887. (M. 15.) Same. Bd. 117 [Nr. 2785-2808]. 7+ 407 p. 4to. Kiel, 1887. (M. 15.) Bulletin astronomique, publiée sous les auspices de l’observatoire de Paris par F. Tisserand [and others]. [Monthly.] Tome 4, 1887. 557p. 8vo. Paris, 1887. Bulletin des sciences mathématiques et astronomiques. Rédigée par Darboux, Houel, et Tannery. Année 1887. Serie 2. Tome 11. 8vo. Paris, 1887. (M. 18.) Ciel et terre. Revue populaire d’astronomie de météorologie et de physique du globe. [Semi-monthly.] 2. serie, 2. année (7. année de la collection). 8vo. Bruxelles, 1887. Memorie della societa degli spettroscopisti italiani, raccolte et pubblicate . . . P. Tacchini. 6+ 220p. 4to. Roma, 1888. Monthly notices of the royal astronomical society . . . Nov., 1886, to Nov., 1887. Vol. 47. 8vo. London, 1887. Observatory (The); a monthly review of astronomy. Edited by E. W. Maun- der, A. M. W. Downing, and T. Lewis. Vol. 10. 7+ 440 p. 8vo. Lon- don, 1887. (14s.) Revista do observatorio. Publicagao mensal do imperial observatorio do Rio de Janeiro, Anno 2,1887. Red. L. Cruls [and others]. 8+ 198p. 4to. Rio de Janeiro, 1887. Sidereal (The) messenger; a monthly review of astronomy. Conducted by W. W. Payne. Vol. 6. 368p. 8vo. Northfield, 1887. ($2.00.) Sirius. Zeitschrift fir populare Astronomie . . . Hrsg. von H. J. Klein. [Monthly.] 20 Bd. odern. F.15 Bd. 288p. 8vo. Leipzig, 1887. (M. 10.) Vierteljahrsschrift der astronomischen Gesellschaft. Hrsg. von . . . E. Schon- feld und H.Seeliger. 22. Jahrgang. 7+ 417 p.,2pl., portrs. 8vo. Leip- zig, 1887. (M. 8.) Wochenschrift fur Astronomie, Meteorologie und Geographie. Hrsg. von H. J. Klein. Jahrgang 30. 8vo. Halle, 1887. (M. 10.) Jupiter. Denninc (W. F.) La tache rougeatre de Jupiter. il. L’Astron., 6: 330, Motion of Jupiter’s red spot. Obsry., 10: 229. Lamey (F. M.) Périodicité moyenne des taches de Jupiter. Compt. Rend., 104; 279. See, also, Ibid., 613. Lynn (W.T.) [Rotation time.] Obsry., 10: 431. MartuH (A.) Ephemeris for physical observations of Jupiter, 1888. Month. not., 48: 68-76. Also, Reprint. Noxsie (W.) Engraving (An old) of Jupiter. Month. not., 47: 515. BIBLIOGRAPHY OF ASTRONOMY: 1887. 30 Jupiter— Continued. TarRANT (K. J.) and others. [Observations of Jupiter, 1885-86.] J. Liverp. astron. soc., 5: 63-66. Tepsurt (J.) [Near approach to Lal. 25797, 1887, Apr. 21.] | Obsry., 10: 278. TerBy (F.) Tache rouge de Jupiter. Obsry., 10: 107. [Obsn. of red spot, 1887, May 10.] Jid., 231. Witiiams (A. 8.) [Obsn. of red spot, 1886, Dec. 20.] Jbid., 71. [Motion of red spot from obsns. 1886, Dec. 20, to 1887, Apr. 21.| Jdid., 193. Jupiter (Satellites of). BacKLuND (O.) Sur la théorie des satellites de Jupiter. Bull. astron., 4: 321- 339. Batu (R. 8.) Notes on Laplace’s analytical theory of the perturbations of Jupiter's satellites. Proc. roy. Irish acad., 2s., 4: 557-567. 1886. Sov1LLart (—) Théorie analytique des mouvements des satellites de Jupiter. Partie 2. Réduction des formules en nombres. 200 p. 4to. Paris, 1887. (M. 12.) Spirra (E. J.) Appearances presented by the satellites of Jupiter during transit, with a photometric estimation of their relative albedos, and of the amount of light reflected from the different portions of an unpolished sphere. Month. not., 48: 32-48. Trouvetor (E. L.) Duplicité de i’ombre du premier satellite... il. L’As- tron., 6: 414. Juvisy observatory. [Description of the observatory and instruments.] il. L’Astron., 6: 321-330, Kew observatory. [Report for 1886.] Month. not., 47: 154. Kiel observatory. Kritiaer (A.) [Report for 1886.] Vrtljschr. d. astron. Gesellsch., 22: 120-122. Kirchhoff (Gustav Robert) [1824-1887]. Tait (P.G.) [Biographical sketch.] Nature, 36: 606. VogEL (H.C.) Todes-Anzeige. Astron. Nachr., 118: 47. Kis Kartal observatory. von KivesticerHy (R.) Sternwarte des Baron Geiza von Podmaniczky in Kis Kartal, Ungarn. il. Sirius, 20: 146. Kremsmunster observatory. WaGner (C.) [Report for 1886.] Vrtljschr. d. astron. Gesellsch., 22: 122. Latitude. Friint (A. 8.) Most probable value of the latitude, and its theoretical weight from entangled observations occurring in the use of Talcott’s method. Ann. math., 3: 172-185. Also, Reprint. Least squares. See, also, Latitude; Observations (Errors of ). Gauss (C. F.) Abhandlungen zur Methode der kleinsten Quadrate. In deutscher Sprache hrsg. von A. Borsch und P. Simon. Berlin, 1887. BUA 34 BIBLIOGRAPHY OF ASTRONOMY: 1887. Leipzig observatory. Bruns (H.) [Report for 1886.] Vrtljschr. d. astron. Gesellsch., 22: 123. Leipzig observatory (Engelmann’s). ENGELMANN (R.) [Report for 1886.] Ibid., 124. Lenses. See Glass (Optical); Photography (Astronomical); Spherometer. Lick observatory. AppxEL (D.) Der grosse Refraktor der Lick-Sternwarte. Sirius, 20: 54. [Description of instruments, progress of work, etc.] Eng. mec., 44: 149, 474, 519; 46: 321. Also: Nation, 44: 233; 45: 506. Also: Obsry., 10: 110, 168. Also: Sc. Am., 57: 330. Also: Sid. mess., 6: 86, 87, 157, 295. Also: Sirius, 20. 285. KEELER (J. E.) Time service of the Lick observatory. 16p. 8vo. [Northfield, 1887. ] Repr. from: Sid. mess., 6: 233-248. Proctor (R. A.) The great Lick telescope. Knowl., 10: 205, 209. Publications of the Lick observatory of the university of California... by E. S. Holden. Vol. 1, 1887. 3+312p. il. 4to. Sacramento, 1887. Topp (D. P.) [Lecture on] the Lick observatory. Sc. Am., 56: 73. Liége observatory (Ougrée). DE BALL (L.) [Report for 1886.] Vrtljschr. d. astron. Gesellsch., 22: 125. Light. See, also, Earth; Sky-glows; Spectrum analysis. Bett (L.) Absolute wave-length of light. Am. j. sc., 133: 167-182. Micuetson (A. A.) Velocity of light in air and refracting media. Sc. Am. sup. 9331. MicuHetson (A. A.) & Mortey (E. W.) Relative motion of the earth and the luminiferous ether. Am. j. sc., 134: 333-345. Method of making the wave-length of sodium light the actual and prac- tical standard of length. Jbid., 427-480. Liverpool observatory. [Report for 1886.] Month. not., 47: 155. Louvain observatory (Terby’s). PauwELs (C.) L’observatoire particulier de M. F. Terby 4 Louvain. Ciel et terre, 8: 13-16. Lunar theory. Airy (G. B.) Numericallunartheory. 10+178p. 4to. London, 1886. (15s.) Rev. by R[adau] (R.) Bull. astron., 4: 275-286. Also: Obsry., 10: 339,377. See, also, Obsry., 10: 175. CoLBeRT (E.) Motion of the lunar apsides. Sid. mess., 6: 49, 82. GLAISHER (J. W. L.) Address . . . on presenting the gold medal of the [royal astronomical] society to G. W. Hill. Month. not., 47: 203, 220. Hatt (A.) Note on Mr. Stockwell’s ‘Analytical determination of the inequali- ties in the motion of the moon arising from the oblateness of the earth.” Astron. jour., 7: 41. Netson (E.) On G. W. Hill’s paper on Delaunay’s method. Month. not., 47: 517. BIBLIOGRAPHY OF ASTRONOMY: 1887. 35 Lunar theory— Continued. Rapau(R.) Remarques complémentaires relatives 4 la théorie dela lune. Bull. | astron., 4: 385. SrocKWELL (J. N.) Inequalities in the moon’s motion produced by the oblate- ness of the earth. Astron, jour., 7: 4, 17, 25, 35. Certain inequalities in the moon’s motion arising from the action of the | planets. IJbid., 105, 118. | Inequalities of long period in the moon’s motion arising from the action of Venus. IJbid., 145-150. Stone (E. J.) Observations of the moon made at the Radcliffe observatory, 1886, and comparison of the results with the tabular places from Hansen’s lunar tables. Month. not., 47: 79-85. Lund observatory. {Report for 1886.] Vrtljschr. d. astron. Gesellsch., 22: 127. Luther (Eduard) [1816-1887]. Franz (J.) Todes-Anzeige. Astron. Nachr., 118: 31. Lyme Regis observatory (Peek’s). [Report for 1886.] Month. not., 47: 160. McCormick observatory. Report of the director . . . for the year ending June 1, 1887. 4p. 4to. [n. p., n. d.] Maresfield observatory (Noble’s). Nosie (W.) Latitude and longitude of Maresfield observatory. Month. not., 48: 67. Mars. Louse (J. G.) [Observations 1886, Apr. 23, 26.] Month. not., 47: 496. Marr (A.) Ephemeris for physical observations of Mars. Jbid., 48: 78-83. Also, Reprint. MEUNIER (S.) Recent phenomena on the surface of Mars. il. Sc. Am. sup. 9384. Also: Pop. sc. month., 31: 532-534.- PoRETZKI (P.) Mars-opposition im Jahre 1877 beobachtet ... zu Kasan. Astron. Nachr., 116: 241-246. Same. 1879. Jdid., 369. Same. 1886. Jbid., 187. Mars (Satellites of ). _ Morrison (J.) Ephemerides of the satellites of Mars during the oppositions of 1888 and 1890. Month. not., 47: 439-442. Mechanics (Celestial). See, also, Gravitation; Lunar theory; Orbits; Perturba- tions; Planets. Bruuns (H.) Uber die integrale des Vielkorper-Problems. Ber. u. d. Ver- handl. d. k. sach. Gesellsch. d. Wissensch. zu Leipz. Math.-phys. Cl., 93: 1, 55. CALLANDREAU (Q.) Sur le calcul des integrales ... Bull. astron., 4: 192. Hatt (A.) Special case of the Laplace coefficients 69’. Ann. math., 3: 1-11. 36 BIBLIOGRAPHY OF ASTRONOMY: 1887. Mechanics (Celestial)—Continued. Hii (G. W.) Coplanar motion of two planets, one having a zero mass. Ann. math., 3: 65-78. Also, Reprint. Differential equations with periodic integrals. Ann. math., 3: 145-155. JouKovsky (N. E.) [Sur le mouvement d’un eorps solide qui a des lacunes remplies par un liquide homogéne.] 8vo. St. Pétersbourg, 1885. Rev.: Bull. astron., 4: 429. Lance (L.) Die geschichtliche Entwickelung des Bewegungsbegriffes. 10+ 141 p. 8vo. Leipzig, 1886. Rev. by Seeliger (H.) Vrtljschr. d. astron. Gesellsch., 22: 252-259. —— Uber das Beharrungsgesetz. Ber. u. d. Verhandl. d. k. siichs Gesellsch. d. Wissensch. zu Leipzig. Math.-phys. K]., 1885: 338-351. Rev. by Seeliger (H.) Vrtljschr. d. astron.Gesellsch., 22: 252-259. TisSERAND (F.) Note sur un passage de la ‘‘ Mécanique céleste.’’ Bull. astron., 4: 457-462. Melbourne observatory. Report (22nd) of the board of visitors . . . with the annual report of the govern- ment astronomer. 12p. 4to. Melbourne, [1887.] Meteors. See, also, Comets and meteors. DeEnninG (W. F.) Determination of meteor-paths and radiants. Obsry., 10: 358. [Hirn (—)] Explosion of meteorites. No, 4138. A CLINICAL STUDY OF THE SKULL. 43 In the skull of an Araucanian' a large opening is detected in the perpendicular plate at a point directly back of the nasal plate of the frontal bone. Openings elsewhere in the perpendicular plate are so common that no special mention of them need be made. The Vomer—When the vomer at the posterior nares is not at the level of the openings, but lies at its lower part a little way within the chambers, the bone may be said to be recedent. It is a reversion effect, since it is commonly seen in the skulls of carnivora and in important groups of ungulata. (See p. 31.) In a Peruvian’ skull of five years and a Bengalese*® skull of six years this recedence may be said to be present. The same pecu- liarity is seen in the aduit skull of a Narragansett Indian,‘ an Assiniboin,’ a Golgonda,® a Sioux,’ and a Blackfoot.® Recedence is so marked in a Maltese’ skull that the bone unites with the maxillary crest at the maxillo-palatal suture. There is no upward extension of the spine of the palatal bone. The exact position of the vomer at the choanz in determining the posterior projection of the inferior turbinated bone is of clinical importance. The vomer may have two grooves—one for the triangular cartillage (it may be so obliquely placed as to appear to belong to the parie- ties) anteriorly, and one for a vein placed far back on the side. Examples of the obliquely placed groove for the triangular carti- lage are seen in an Araucanian” skull and in several skulls of North American Indians. 3. The Choane. The choanee vary remarkably in form and dimensions. They may be as large as 25™" long by 13™" wide, or as smal] as 15™™ long by 6™™ wide. Usually wide and of a rectangular form inferiorly, as the borders join the transverse palatal process, they may be oval. The larger varieties include the shape first named, and the smaller one the shape last named. DINOn O34 eNom 492 ss 48 7 ole o lop4) Ol sio; 11605); 81227. 9 No. 117 (Col. of Phys.). 10 No. 651. See 44 THE TONER LECTURES. The smaller varieties exhibit relatively long palatal crests when, indeed, they occupy one-third or one-half of the septum at the choane plane. Since this arrangement is seen in the foetus at term, and the openings are oval or sub-rounded, it is fair to assume that the small oval variety is a form of arrested development. Ina case of atresize nasi seen in an adult I detected this variety of choanal shape. The small oval form is so often met with in clinical studies that the conclusion may be tentatively drawn that it aids in retain- ing mucus in the nasal chambers, and in this way an anatomical factor may materially aid in establishing a morbid state. For ex- amples in adult crania see a skull of a Miami Indian't and a Me- nominee.” In immature skulls, an Armenian,®? an Austrian,’ a Czech, a Genoese,’ a Sandwich Islander,’ a Ruthene,’ and a Nea- politan.’ . It is well to remember, as already stated, p. 29, that it is possible to have the image of the choanze, as seen by the rhinal mirror, nar- rowed by thickening of the internal pterygoid process of the sphe- noid bone. 4. The Floor of the Nasal Chamber. In many subjects the plane of the lower border of the nostril is higher than that of the floor of the chamber. The inferior turbi- nal lies a variable distance within this depression. The finger when inserted into the nostril will not, in such cases, enter the in- ferior meatus, but will pass into a space which is defined by the septum on the one hand and the upper part of the inferior turbi- nalson the other. An example of the skull showing the depressed floor is seen ina Menominee” Indian. 5. Deviations of the Septum. When it is recalled that the bony septum is composed not only of the vomer and the perpendicular plate of the ethmoid bone, but LNo. 1052. 2 No. 1222. 3 No. 58, Col. of Phys., 6 years. *No. 60, Col. of Phys., 16 years. OPCS a rc CCT me ie 6 «& 13; as cc ea (Games 148, cc « 16 Si ck 19, ce cc Tm Kt 9 ue I “cc 66 9 « 10 No. 44. A CLINICAL STUDY OF THE SKULL. 45 of the frontal bone at the region of the vestibular roof, and small portions of the maxilla and of the palatal bones, it follows that if it is possible for defects to arise from faults of union, more than a single place for such defects must be sought for ; or, if by mere dis- tortion any one of the parts may be found out of the straight line, the localities at which such deviation may occur are many. In point of fact the consideration of some of the lines of suture and plates of bone need not be regarded. Deviations at the region of the frontal spine and at the region of the palatal bone almost never occur, but in the remaining component parts they are of fre- quent occurrence and are apt to occur are as follows: The perpendicular plate of the ethmoid bone. The perpendicular plate of the ethmoid bone and the vomer acting as one factor. The vomer. The ethmoido-vomerine suture. The maxillary crest. As a rule, it may be said that deviations result from two struct- ures differ in nature uniting one with another under unfavorable conditions. The perpendicular plate of the ethmoid bone may be bent on a broad curve, while all the remaining parts are normal. This is well seen in a Chilian skull,’ in a Hindoo,’? and in an Arab.? In the skull last named the plate is bulged to the left. The perpendicular plate may be in the position described and the vomer be bent with it. No hyperostosis need exist at the suture. This is well seen in a Peruvian skull.* The perpendicular plate and the vomer may be straight, but not lie in the same vertical plane. In this way a “fault” is defined between the two. This peculiarity also is shown in a Peruvian skull? The vomer may exhibit an angulation on the side, posteriorly — i. é., at a point near the choanz—and is, therefore, best seen from 1No. 1699. 2No. 432. 3 No. 499. * No. 1465. >No. 408. 46 THE TONER LECTURES. behind. The septum may be in other respects straight. The apex of the angulated part often presents a groove which closely resem- bles the suleus found in localities marked by the course of vessels. In the skull of an Ottawa Indian’ the ethmoido-vomerine spur bears a groove which is continuous with a distinet canal posteriorly. The following specimens of skulls may be referred to, in each of which the groove is present on the left side: A Columbia River Indian,’ two Peruvians,’ and an Anglo-American.‘ In one additional skull—that of a Peruvian’—the angulation and groove are on the right side. That the chamber to which the septum inclines should be the smaller is shown by many examples.’ Deviations to the right side are seen in two Peruvians,’ an Afghan,° a Circassian,’ an Armenian,” a Finn," and a Utah Indian.” The disposition for the ethmoido-vomerine suture, as well as the maxillary crest at the triangular notch, to be hyperostosed and to present spur-like projections to the left side are such striking feat- ures in the majority of crania that no more than a recognition of their presence is here demanded.” In a skull of a Ruthene (No. 19, Col. of Phys.) from a child seven years old the perpendicular plate and the vomer slip by one another, are not united, but are simply in apposition. The apposed surfaces are 3™" long. If the degree of variation had been expressed in re- sistance at the line of normal union, it is difficult to see how deflec- tion could have been avoided. Adult skulls not infrequently show the nasal surface of the frontal bone with the nasal process retaining the long plate of bone in place of the short, compressed spine, as is usually described. Examples of this conformation are seen in three Egyptians, two Peruvians,” and one each of Circassians,” 1 No. 573. 2 No. 1363 and 1407. 3 No: 62: “NOG. >Egyptian, No. 819; Circassian, 765, 498; and a Malay, 459. 6 Nos. 412, 1407; 71333; $762; 9790; 11543; 140. 12See a paper by the writer, Amer. Journ. Med. Sci., April, 1880, 70. 13 Nos. 799, 819, 804, aged 16 years. 14 No. 432. 15) tt 1642) 1137. 16 «626, aged 12 years. A CLINICAL STUDY OF THE SKULL. A7 Hindoo,' Bengalese,” a North American Indian (Lenapé), an’ Anglo- American lunatic, and one unnamed. Fia. 8.—View within the anterior nasal aperture of an adult negro (No. Bat ye. IN. Se) . Nasal bone. . Frontal bone, forming at this place a keel instead of a spine. Perpendicular plate of the ethmoid bone. . Ascending process of the maxilla. Lateral mass of the ethmoid bone. . Inferior turbinated bone. . Alveolar process. NOoar ON ee Thus ten well-defined examples of the nasal plate of the frontal bone were met with. With reference to this conclusion it is stated I have met it in 56 out of 76 negro skulls, and it would appear that we have in the nasal plate a valuable guide to the identity of this race. These facts lead me to consider 6. The Region at which the Frontal Bone Forms Part of the Nasal Chamber. The frontal bone as it enters into the composition of the nasal chamber is usually described in forming a nasal spine.‘ I have found that in the child the nasal portion of the frontal bone is of a different form from that described, and that in the adult 2 No) 763. 2 No. 40. 3 Hoffman’s ‘‘ Lehrbuch der Anatomie des Menschen; ”’ describes the ‘ pars nasalis ’’ as yielding asharp process of variable length—the spina nasalis supe- rior-—-which extends between the nasal bones and the perpendicular plate of the ethmoid bone. This description may be accepted as representative ot those found in the text-books. 48 THE TONER LECTURES. numbers of examples may be cited which do not answer to the ac- counts given by writers. In the child, from the fourth to the eighth year the nasal portion is never furnished with a spine, but, in its place, with a plate which extends the entire length of the interval between the nasal and ethmoid bones." The plate joins the perpendicular plate of the ethmoid bone inferiorly. A shallow groove on either side of the plate defines the roof of the nasal chamber at this place. The nasal plate of the frontal bone is very rarely united to the perpendicular plate of the ethmoid bone. That there exists in the nasal chamber, in the races other than the Negro, an occasional, and in the Negro a frequent, absence of bony union between the two component parts of the septum, is an interesting fact. Good examples of such apposition without union are seen in Nos. 951, 957 (Narragansett Indians), No. 651 (Araucanian), and No. 15 (Chinese). In the Army Medical Museum at Washing- ton out of twenty Negro crania the parts above named are open in fifteen. Care should be taken not to confound a fissure of absorption in the perpendicular plate with the form of retention as above de- scribed. A defect of this kind is noted in a Peruvian skull. Among the examples in which the conversion of the nasal plate into the nasal spine takes place it is interesting to observe the great size which may be attained. In a Negro’ the spine was found to be nearly as large as the nasal bone. In two Araucanian* skulls the processes are also very large. The nasal spine is found in an Afghan® skull to form part of the periphery of the external nose where it was lodged between the nasal bones. Good examples are also seen in an Egyptian’ and in a Nubian’ skull. 1Good examples are presented in Nos. 426, 670, Chinese (A. N. S.). 2No. 1705. 3No. 914. 4Nos:, 790; 792: 5 No. 735. 6 No. 1817. 7™No. 829. A CLINICAL STUDY OF THE SKULL. 49 That deviations from the vertical plane, which so commonly occur in the nasal septum, might be connected in some way with the changes that take place in the region of the nasal plate is not im- probable. It is known that the parts at the root of the nose are exceedingly firm, and that the nasal bones vary greatly in diameter from the outer to the inner surface. It is also known that the per- pendicular plate of the ethmoid bone is of inconstant proportion, but on the whole tends to advance. Hence, the nasal plate of the frontal bone may be compressed between these opposed directions of growth; but if the naso-frontal parts are preternaturally fixed the perpendicular plate of the ethmoid bone may be deflected, or the entire septum be forced to expand in a region whose boundaries have been already fixed. The external nose during the period of transition from childhood to adult life changes greatly in shape. It is probable that at this time the substitution from the nasal plate to the nasal spine takes place, and that the deviation in some way correlates with the shape of the nasal bones in the adult. In the negroes, in whom the nasal bones are small and flattened, both at the root and the bridge (the juvenile shape), the process in question retains the plate-like form, while in other races the prominence of the root and bridge is asso- ciated with increased frequency of change of the nasal. plate to the nasal spine; but in the alteration last named the increase of sep- tal deviation is also to be noticed, and an obliteration of the har- monic apposition of the spine with the perpendicular plate of the ethmoid is likely to occur. Enough has been observed to warrant the tentative conclusion that a cause for deviation of the septum (especially in that portion of the septum into which the perpendicular plate of the ethmoid en- ters) exists at the junction of the nasal spine of the frontal bone and the ethmoid, together with the rate and character of the change in the forms of the nasal bones. While this is a conclusion which the premises in many instances validate, it is true that no one explanation suffices for the explana- tion of all deviations. (See p. 45.) ai OL Se 50 THE TONER LECTURES. 7. The Anterior Part of the Lateral Mass of the Ethmoid Bone. This region, as a rule, has a narrow border. The superior border of the middle turbinal and the base of the uncinate process here unite. Occasionally, as is seen in a Peruvian skull,’ the three structures are separated by a large globose surface, which forms the boundary of the most advanced of the ethmoid cells. The Uneinate Process—The uncinate process is flat and usually lies on the plane of the outer wall of the nose. In a low type of skull (this is well exemplified in a Hottentot,? in which it is firmly united to the inferior turbinal) the process may be found lying transverse to the long diameter of the nasal chamber, and of such dimensions as almost entirely to conceal the large middle tur- binal. ‘This disposition is seen in the left side of a skull of a Negro, and in a second from Santa Barbara, Cal. In two Peru- vian‘ skulls the uncinate process on the left side is united to the ethmoid cells. The degree to which the uncinate process extends in an antero- posterior direction is subject to considerable variation. It may be in contact anteriorly with the inferior turbinal, so that an opening on the lateral wall of the chamber alone exists between the pedicle of the uncinate and the ascending process of the superior maxilla. It may be entirely free from the inferior turbinal at this section of the chamber, so in place of a foramen a long interval is found between its antero-inferior limit and the maxilla and the inferior turbinal. The extent to which the opening into the maxillary sinus is nar- rowed is also subject to variation. The opening appears to be the smallest in the prognathic and the largest in the orthognathic form of crania. THE VERTEX. The sconce or crown constitutes in thelanguage of craniology the vertex. The main parts comprising it are so easily determined by 1No. 1482. 2No. 1107. 3 No. 964. *No. 1705, 1432. ~ A CLINICAL STUDY OF THE SKULL. ol palpation that, so far as they are concerned, the clinical and ana- tomical study can be pursued on identical lines. Respecting the details, especially such as are seen in the sutures, it is only neces- sary to say that the topography of the general surface has been based, by common consent, on the arrangement of the parts at or near the sutures, and I have concluded to give the details of such localization the first place. The names proposed for the suture-divisions, eminences, and de- pressions are easily adapted to the nomenclature of Broca. While it is acknowledged that multiplicity of terms is undesirable, I see no way out of the difficulty in presenting new names, since accu- racy of description is impossible without them. It is hoped that by their aid not only the vertex, but the scalp as well, can be mapped out for clinical purposes. The sagittal, coronal, and lambdoidal sutures show peculiarities of the several parts entering into their composition which are worthy of special description. To speak first of the sagittal suture, it is found that the portion which answers to the parietal end of the anterior fontanel and to the suture a short distance back from this opening is simpler in composition than the adjacent part of the suture.*| It measures 1 to 2 centimetres in length. It is convenient to call this the bregmal portion. The second portion of the sagittal suture is the longest and con- tains, as a rule, the largest serrations. These are either denticulate or lobate. The line answers to the region of the parietal tubera, and measures from 4 to 6 centimetres in length. In the normal cranium it represents the highest portion of the glabello-inial curve, and may receive the name of the intertuberal portion of the sagittal suture. The part of the intertuberal portion which lies back of the breg- mal for a distance of 1° to 1° 5™™ is often of a distinct type of ser- 1Out of the 66 negroes’ crania with open sutures examined 21 retained sinuate and 45 serrate bregmal portions. 52 THE TONER LECTURES. ration and may be deflected from the line of the intertuberal por- tion. It corresponds nearly to the position of a depression which is commonly symmetrical on either side of the suture as seen on the endocranial surface. When well marked it may receive the name of the post-bregmal portion. In Negroes it is commonly merged in the intertuberal. The third portion of the sagittal suture is the obelion of Broca.' The parietal foramina lie on the sides and serve as guides to this the obelial portion. | Broca describes the obelion as having a length of 2°, measuring, as it does, 1° either way from the foramina. The suture is very commonly harmonic, while it may be sinuate, serrate,’ or lobate, but rarely the last named. The vertex, as a rule, is rounded or ridged at the sides of the obelion, which thus appears to be depressed. The fourth and last portion of the sagittal suture also appears to be depressed. It extends from the obelial to the lambdoidal sut- ure. The serrations are coarse, and are often composed of denti- cles which exceed in length any seen in the foregoing divisions of the sagittal suture. In the growing subject it is often the thickest part of the suture. It measures from 1 to 2 centimetres in length and may be called the post-obelial portion. The coronal suture is constantly divided into three parts—the in- ternal or ental, which answers to the anterior fontanel; the mid- dle or mesal, and the external or ectal. The internal is simple or wavy ; the middle is denticulate and extends from the internal third to the stephanion, while the external or ectal is again simple, and lies between the stephanion and the pterion. It is covered by the tem- poral muscle. The external or ectal may remain open while the remaining portion of the suture is obliterated (No. 38, Col. of Phys.). In some subjects, notably the Negro, the middle portion 1 Instructions Craniologiques et Craniometriques, Paris, 1875, p. 24. 2 Out of the 55 crania of negroes in the collection of the Academy of Nat- ural Sciences 35 exhibited sinuate obelial portions and 20 serrate. A CLINICAL STUDY OF THE SKULL. 53 becomes simple when it runs forward parallel to the temporal ridge for a short distance before crossing it at the stephanion. In an Esquimaux skull (No. 200, A. N. 8.) the line of the tem- poral fascia crosses an almost simple coronal suture 28"™" from the bregma. The stephanion is practically unseen. Kuppfer und Bessel Hagen, in 281 skulls from East Prussia, found the coronal suture running along the temporal ridge a short dis- tance before crossing it in 5 per cent. males and 6 per cent. females. In the skulls of the insane these observers noted the disposition in 40 per cent. W. Sommer (Virchow’s Archiy., vol. 90) in a similar examination found this disposition in 17 per cent. of males and 7 per cent. of females. The lambdoidal suture,’ like the coronal, is divided also into three parts, which may be named, in a similar manner, the endal, mesal, and ectal. Of these the ectal is the simplest in composition, and the mesal the most denticulated. _Wormian bones, when present, are commonly situate in one or the other of these divisions, and not at their lines of juncture. The divisions appear to be subject to greater variation than in the cases of the sagittal and coronal su- tures.” W. Sommers (loe. cit.) found the lambdoidal suture concave for- ward in 90 per cent. of skulls of the insane, and 10 p:>r ceat. con- vex. No mention is made of the eminence which I have named meso-lambdoidal. It is fair to assume that it was present in those 1 Broca practically makes similar subdivisions of the coronal and lamb- doidal sutures in his method of studying the relations which exist between the cranium and the cerebrum. (See Revue de Anthropologie, v. 1, p. 36.) 2In No. 461, Clickitat (Columbia river) and 780 (Seminole) the lam- bdoidal suture is completely occupied by a number of Wormian bones. The divisions of the sutures, as above named, are lost, 1nd the entire re- gion presents an elliptical figure. In No. 208, Nisqually, A. N.5., the suture is nearly straight and with few serrations. Out of 60 negro crania examined the lambdoidal suture was straight, or nearly so, in 21, and arranged as described above in 39. In Esquimaux crania the outer part of the lamb- doidal is much smaller than is usually found in skulls of other races, and the meso-lambdoidal is less convex forward. + 54. THE TONER LECTURES. in which the suture was convex, inasmuch as this convexity is most marked in, if not confined to, the mesal part of the suture. (See infra.) THE EMINENCES AND DEPRESSIONS OF THE VERTEX. The eminences of the vertex which have been separately named are the frontal, the parietal or the tuberal, and the occipital. In addition, I venture to name five others, as follows: The meso-coronal. The metopic. The para-tuberal. The meso-lambdoidal. The meso-coronal eminence, lies on the frontal bone just in advance of the meso-coronal portion of the suture, about two centimetres above the stephanion. It may involve the suture itself, when the, corresponding part of the parietal bone is also elevated. It is marked in many Peruvian crania, but is often absent in the skulls of Negroes and Esquimaux. The metopie eminence is a median elevation of the frontal bone over the interfrontal suture. It is inconstant, but may amount to @ conspicuous carination which can be seen often in the living individual. The para-tuberal eminence is a rounded elevation which lies be- tween the parietal tuber at its posterior limit and the obelion. It is commonly present. Itis least developed in the Esquimaux. The meso-lambdoidal eminence lies on the parietal bone in advance of the lambdoidal suture at its middle portion, or it may cross the suture and involve the occiput. It is marked in synostotic crania of the criminal type. It is very well seen in a skull of a Krim.* In some crania it appears to be continuous with the tubera. In No. 1561, Esquimaux (A. N.8.), the vertex is marked by a large adventitious but distinct swelling (measuring 2 centimetres 1 Coll. Phys. A CLINICAL STUDY OF THE SKULL. 55 long by 1 wide), which lies between the tuber and the lambdoidal suture. In No. 1562, of the same race, an elevation extends from the tuber to the sagittal suture. It limits the inclination of the parietal bone towards the occiput. The temporo-frontel eminence.—Under this head may be men- tioned a swelling which is felt occasionally in the living subject directly to the outside of the temporal ridge as it is defined on the frontal bone. It forms a low obtuse prominence, measuring about 3 centimetres in diameter. It is best discerned in young indi- viduals, since in adults it is obscured by the massive temporal muscle. I have found the temporo-frontal eminence, so frequently in Peruvian crania that it may be included among the characters distinguishing them. In a Marquesas skull, in the Ae eNeuSs similar prominence is marked. The depressions which can be detected on the vertex are arranged as follows: In advance of the bregma; this constitutes the pre-breg- mal. At the centre of the fontanel, or embracing in a general way the region of the fontanel; this is the bregmal. At the line of the coronal suture and the part directly back of it; this is the coronal. At the broad interspace between the frontal bone and the tuhera; this is the post-coronal, and appears to be an extension of the foregoing. An apparent depression is defined at the obelion. The coronal depression has been described by Prof. J. Cleland (Philosoph. Trans., vol. clx, 1870). It can be easily defined in the living subject. Abundant means are at hand for confirmation of this statement. Children exhibit the peculiarity as well as adults. It is generally seen in short high heads, which also retain a short sagittal suture and an abrupt curve to the mid-vertex. Rolleston (British Barrows, 1877) names skulls which show this peculiarity “cut off;” it appears to be the same variety as is described by Lissauer (Archiv. f, Anthropologie, 1885, p. 9) under the name of “sagittal Kriimmung.” When the two coronal depressions are associated with large tu- 56 THE TONER LECTURES. bera and para-tubera, and the interval between them (viz., the obe- lion and the post-ebelion) is on a lower plane than the occipital angle, the variety of skull named by Prof. Cleland, “ trilobate,” is defined. Trilobate skulls have been found by Prof. Rolleston! in the barrows of England. In the College of Physicians, No. 87, Carniolian, and No. 10, Hollander, exhibit the peculiarity. I have detected one in a Peruvian, another in N. A. Indian (No. 747, A. N.S.), and a third-in a Tschutchi Indian (No.3, A.N.S.). An imperfectly developed form is seen in a Nantucket Indian child aged 12 years. W. H. Flower givesan example in Catalogue Os- teol. Collection, Col. of Phys. and Surgeons, Lond., 1879, 172. The natiform skull of congenital syphilis appears to be of the same nature as the tribolate. The post-coronal depression is often associated with the general roundness and fullness of contour of the frontal bone just in front of the coronal suture. This is well seen in No. 1492, Peruvian (A. N.S.), aged five years, and in 890, Ibid. Instead of the coronal depression being marked the bregma may be greatly depressed, the sagitta shortened, and the occiput knobbed. Such crania are frequently seen, and in the living subject make it exceedingly difficult to determine accurate measurements from the line into which the bregma enters. The subjects are apt to exhibit hyperostosis of the sutures of the hard palate, and to have small choane. Examples are seen in two Italian skulls in the College of Physicians (Nos. 110 and 115). Occasionally a depression is seen above the temporal ridge and corresponds to the curve of this elevation. It is well seen in an Esquimaux cranium (No. 677, A. N.S). The Ridges of the Vertex.—The ridges of the vertex are those at the sagittal suture, above the temporal ridge, and at the sides of the obelion and the post-obelion. The ridges of the sagittal suture constitute the carinations de- 1«The precipitous dip downward of the posterior half of the parietals which is so characteristic of brachyeephaly generally.—Ibid, p. 682. Bet ~ 4 ; ; d = : -—— A CLINICAL STUDY OF THE SKULL. od scribed by anthropologists. They may be restricted to the subdi- visions of the sagittal as above proposed. Thus the post-obelial and the intertuberal parts are often separately and distinctly eari- nated. The bregmal and post-bregmal parts may be carinated, while the rest of the sagitta is normal. The post-obelial, obelial, and the posterior half of the intertuberal parts have been found to be carinated, together with the bregmal and post-bregmal, the ante- rior part of the intertuberal alone remaining normal. The cari- nated portion of the sagitta may extend the entire length of the suture, excepting only the post-obelial. This arrangement is ad. mirably seen in the figures of a woman’s skull in Welcker’s mono- graph (infra, xiii, Figs. 1, 2, 3, 4). The ridge which conforms to the temporal ridge is relatively in- frequent. It is found in heavy male skulls as far as my observa- tions go. It should be easily felt in the head of the living subject. The enormous lateral ridges of Uintatherium are probably develop- ments of the temporal ridges, thus showing the extraordinary influ- ence muscle-traction can exert over bony surfaces. If the exact degree of influence of all the muscles having bony attachments could be measured, osteology would be placed upon a philosophical . basis. Instead of the sagittal suture at the obelion and the post-obelion being depressed it may remain unchanged. The margins of the parietal bone remain also unchanged, while a ridge-like elevation of bone passes obliquely from the sagitta, at the end of the inter- tuberal portion, backward and outward to the meso-lambdoid eminence. Such conformation is well marked in the skull of a Chinese in the College of Physicians. In a living individual retaining such a peculiarity it is highly probable that a large tri- angular depression could be felt at the posterior part of the vertex. THE STUDY OF THE INTERIOR OF THE VERTEX. The interior or endo-cranial view of the vertex confirms the pro- posed division of the sagittal suture. The several parts are as dis- 58 THE TONER LECTUEES. tinctly separated as on the exterior, and, as the interior plane of the sagittal suture tends to remain open when the exterior is closed, the evidence of the disposition is here often alone available. The side of least expansion of the parietal bones correlates with increase of thickness of the inner plate. The elevation of the inner plate of the unexpanded side is easily detected by the finger. In No, 24 of the College of Physicians the vertex-sutures are open, the bregmal, post-bregmal, obelial, and post-obelial parts are serrated, both exteriorly and interiorly, while the intertuberal (the post-bregmal portion being here counted a separate quantity) is harmonic. In No. 50, of the same collection, the interior view of skull is har- monic throughout, the bregmal being alone distinguished by its obliquity to the rest of the sagittal suture. The relations of the depressions (presumably for the Pacchionian bodies) are, if of simple form, very commonly on either side of the intertuberal portion of the suture at the post-bregmal division. In thirty examinations of normal crania I have found but five where the depression was either absent or merged with a depression placed still farther back. When the vitreous plate is thickened at the region of the former anterior fontanel and extends along the lines of the sutures so as to form a lozenge-shape figure, depressions for the Pacchionian bodies are often seen at its sides. It is rare to see depressions at the obelial or the post-obelial parts, though they may be oftener found on the frontal bones below the frontal eminences: Between the parietal tubera and the sagittal suture at the obelion an emi- nence is frequently found which almost equals the tuber in size. It is very commonly found in the skulls of Peruvians. As in all other anatomical quantities, the subdivisions of the sutures of the vertex are subject to variation. The simple statement upon which such subdivisions may be ren- dered tenable is one universally conceded, namely, that structures in their range of variation show traces of their origin and rates of A CLINICAL STUDY OF THE SKULL. 59 growth. That the bregmal and post-obelial portions of the sa gittal suture are distinct from the remaining portion is probable when it is recalled that both portions are completed after birth in the process of obliteration of the fontanels. That the post-bregmal portion may be a good subdivision is also probable, since it answers pretty nearly to the position of the Pacchionian bodies and from the fact that in the parietal bone of the young subject this portion is seen to be pectinated, while the intertuberal is nearly smooth. The intertuberal portion represents the shortest distance from the tuber to the suture. The obelial portion has an admirable raison d’ctre in being the region of the parietal foramina. The following notes in illustration of the manner in which the foregoing statements may be employed in description of crania may be found useful: The specimens are all in the College of Phy- sicians. No. 114, native of Elba: Sutures open. ; Bregmal, 1°5"™"; post-bregmal, 1°5™™"; intertuberal, 4° 5"™"; obe- lial, 2°; post-obelial, 1°. No. 30: Acrocephalic, synostotic. Bregmal and post-bregmal, 4°. Entire region elevated; not carinate; intertuberal, 4°, slightly carinate ; obelial, 2° 5™™, flat ; post-obelial, 2°, carinate. No. 92, Uskoke: Left coronal suture closed ; obelial portion lobate ; post-bregmal with markedly oblique axes to the serrations, in contrast to the transversely disposed serrations of the intertuberal portions. No. 38, Kabardine : Both coronals obliterated ; no wisdom teeth, yet the basi-cranial suture is closed; bregmal, 1° 2™™; post-bregmal, 1° 2™"; intertu- 60 THE TONER LECTURES. beral, 5° 5™"; obelial, 2°; post-obelial, 2°. The obelial is serrate ; post-bregmal depression is markedly developed. No. 34, Krim: Synostotic, forehead prominent; resembles skull of Pomeranian weaver described by B. Davis; metopic eminence conspicuous. Entire region of bregmal, post-bregmal portions, and the anterior half of the intertuberal is elevated, but broadly carinate. The posterior half of the intertuberal is smooth ; the obelial and post- obelial portions carinate. No. 98, Gypsy : Vertex remarkably “cut off” posteriorly. Entire suture-line is carinate except the post-obelial portion. Australian skull (Col. of Phys.) : Sagittal suture open; bregmal, 1°; post-bregmal, 1°; intertuberal, 6°; obelial, 2°; post-obelial, 2°. In the skulls of Esquimaux, A. N. S., the vertex is “cut off,” the intertuberal, excepting the post-bregmal part, is carinate in No. 678. The entire intertuberal is carinate in No. 279; the para-obelial eminence continuous, with a smaller ridge which ex- tends one-half the length of the intertuberal portion of the sagittal suture in No. 677. The right and left sides of the vertex are almost always asym- metrical. The left side at the forehead is commonly more project- ing than the posterior part of the parietal bone of the same:side. The reverse of these proportions is seen on the right. At the level of the occiput the left part may be projecting. Thus a circumfer- ential measurement of the left side at the level of the frontal emi- nence may show the curve exaggerated anteriorly while diminished posteriorly, and a similar measurement taken from frontal emi- nence, so as to include the occiput above the inion, will show both anterior and posterior parts exaggerated on the left side as com- pared with those on the right. A CLINICAL STUDY OF THE SKULL. 61 Linear measurements taken in the median line from the glabella to the inion will represent more nearly the curve of the left side of the calvarium than do those taken on the right. ‘The measurements last named may differ so widely from those of the left side as to throw the point given by Thrane for the fissure of Rolando on the right side as much as one-half inch out from that of the left. The vertex in the space included at the sides by the temporal ridges—at the front by the corona and at the back by the lambda—is subject to local atrophic changes. Rounded depressions measuring one or two centimetres across and one to three millime- tres in depth are scattered irregularly over the surface. There is no diseased action elsewhere in the skulls showing this peculiarity, and no evidence can be presented that the depressions themselves are of morbid origin. They have been seen always in crania show- ing early signs of advanced age, and some of them are found in dis- tinctly senile skulls. Examples are seen in several of the skulls of Arabs (A. N. 8.). A Narragansett’ and a Chinese skull? also ex- hibit the depression. In a cranium in the possession of the Academy of Natural Sci- ences the vertex has been mapped out and the localities named after the phrenological method of Gall and Spurzheim. It is interesting to note that a number of the enclosures which constitute what is ee known in the language of phrenology as the ‘“ organs” answer accurately to the eminences which I have named as above. Thus the para-tuberal eminence becomes the organ of ‘‘ ambition,” the meso-lambdoidal eminence that of “ friendship,” etc. The “organ” of “ philoprogenitiveness ” “appears to be always well developed in females, and frequently so in males. I find no reference to this association of parts in the writings of phrenology, and I am, therefore, led to infer that it is a co-incidence only that the emi- nences which I have named happened also to have attracted the attention of the phrenologist. INo. 951. 2 No. 94. 62 THE TONER LECTURES. Norr.—H. Welcker (Wachsthum und Bau des menschlichen Schadels, 1862, Fig. 7, p. 17) divides the sagittal suture into five parts. These divis- ions are the same as I suggest in the text. My attention was called to Welcker’s work by Dr. Frank Baker after I had delivered the lecture. In- stead of naming the parts separately, Welcker includes them in the numbers 1, 2, 3,4, and 5. It will be noticed that this writer retains the post-bregmal division, which I have included with some doubt. The reference of Welcker to the entire subject is very brief and is embraced in the follow- ing language: ‘For more accurate examination of the shape of these su- tures I have illustrated (Plate iii, Fig. 7) five regions, of which No. 1 is on the coronah ; No. 5 borders on the lambdoida, while No. 4, which lies be- tween the straight parts of the parietal foramina, is a trifle smaller than the other divisions.’’ Rolleston (British Barrows, 1877, 623), probably influenced by the same authority, speaks of the sagittal suture as divided into fifths. The post- obelial is the ‘ posterior fifth ’’ of this writer, and the obelial the ‘‘ penulti- mate fifth.’ REMARKS ON THE SUTURES OTHER THAN THOSE OF THE VERTEX. Sutures often indicate the manner in which the bones have grown. As already stated, the comparatively deep serrations in the middle of the sagittal and coronal sutures correspond to the most preco- cious extensions of growth-force in those directions. Premature union of two opposed portions of bone, namely, at the surfaces of greatest acceleration, may lead to a suture at such portions, being raised above the plane of the adjacent surface. The carinated por- tion of the sagittal suture is an illustration of this peculiarity. A group of instructive examples is seen in the sutures between the maxilla and the bones adjacent; thus the malo-maxiliary at its lower part, where two obtuse processes project, the process pertain. ing to the maxilla being the larger; the inequality and even rugosity of the same suture, as it aids in‘defining the lower border of the orbit ; the union of the horizontal plates of the maxillze by means of which an upward extension results, aiding in the composition of the nasal septum ; a downward extension of the same in the form of a thicken- ing and even of an exostosis, which lies upon the roof of the mouth; and also in the nasal spine, which is formed at the intermaxillary A CLINICAL STUDY OF THE SKULL. 63 suture and projects from the lower anterior margin of the nasal cham- ber. These changes on the line of union of the maxilla with the malar bone, and with its fellow of the opposite side of the body, indicate that the direction of pressure during the growth of the bone has been greater at the sides toward the malar bone and at the median line of the face than elsewhere. It has been least between the maxillze and the nasal bones and between the maxillze and the palatals, which weuld indicate that the maxilla has grown forward and from side to side earlier and more aggressively than it has grown upward and backward. In this statement it is assumed that each nasal bone lies above the ascending process of the maxilla rather than in front of it. The backward extension of the maxilla against the palatal bone in the line of the dental arch demands special consideration, since it belongs to the means of accommodation of the molar teeth. Such as it is, however, the pressure of the extending bone in this direc- tion leads to increased thickening of the palatal bone in all directions, and forms the pyramidal process. This process may be looked upon as an exemplification of an active suture-formation, which leads to hyperostosis of a part, although only one of the bones interested becomes entirely involved. The maxilla in two places shows the effects of nerves and vessels in modifying suture lines. The roof of the infra-orbital cana! is closed in a variable manner by the approximation of two portions of the maxilla at the inferior border of the orbit. Very commonly the border is thickened and an additional element of roughness and unevenness presented to that already noticed in the malo-maxillary suture. In like manner the maxilla as it joins the malar bone at the orbito-temporal septum exhibits one to three fissures in the imma- ture bone (for the accommodation of minute vessels and nerves), which by the closure determine the positions of new grooves. Now, the growth in the direction of the orbito-temporal septum is vari- able. The maxillary process may reach the sphenoid bone or it may terminate at the malar. If it attains the bone first named, the malar bone is excluded from the spheno-maxillary fissure. If it 64 THE TONER LECTURES. does not so attain, the malar enters into the composition of the fis- sure. (See p. 11.) The connection which exists between nutritive processes and grooves caused by the positions of blood vessels is considered on page 70. It becomes difficult at times to decide which is the most effective in inducing the position of sutures. For example: While the masseteric ridge answers in position to the intermalar suture, it also corresponds to the position of a vessel groove. The groove is commonly seen in the immature skull. It is, however, conspicuous in the skull of an adult idiot.’ In illustration of the fact that nutrition of bone is apt to be in- fluenced by the position of sutures the following may be mentioned: Nodules of a size of a millimetre, sessile in form and of hard con- sistence, are occasionally seen on the frontal bone near the median line. They are to be attributed to localized hyperostoses in the neighborhood of the interfrontal suture.’ The frontal bone directly in advance of the coronal suture is often the seat of a convexity only secondary in height to the frontal eminence. It is especially well developed in Peruvian crania. A second eminence, more generally distributed, is seen on the same bone in the temporal fossa, directly below the temporal ridge.* The coronal suture is deflected forward slighily as it is crossed by the temporal ridge. In 31 out of the 64 skulls of negroes ex- amined the suture extended parallel to the ridge for about two centimetres before it crossed it. In no other skull, save in a Semi- nole Indian* and a Carib,’ was a similar peculiarity noticed. Ut thus becomes a character which should be sought for in describing the cranium of the negro. (See Vertex, p. 53. The borders of muscular impressions, such as the temporal ridge is to the impression for the temporal muscle, may be said to modify 1No. 1190, German, A. N.S. 2 No. 1035, Apache; 742, Mandan; 647, and three Peruvians. 3 This is well seen in 316, a young Malay; 1029, Fiji; and 44, Menominee. 4No. 708, Academy of Natural Sciences. 5 692, ibid. A CLINICAL STUDY OF THE SKULL. 65 the bone itself, and may even lead to the separation of the bone in two parts. This is apparently the case in the instance of a double parietal bone as figured by Professor Turner in the skull of an Ad- miralty Islander." The line of origin on the inner surface of the malar bone answers to the position of the suture in two instances of double malar bone which I have studied.” In four crania’ traces of a suture were seen on the maxillary portion of the hard palate ex- tending obliquely forward and outward at or near the maxillo-pal- atal junction. They may unite with the junction last named at the median line or lie a little to the ectal side. The squamosal suture (parieto-temporal) ends posteriorly at the mastoid process somewhat abruptly. A process of the suture is apt to be directed upward and backward from the hinder part of this suture on the level of the temporal vein-groove. Although small, the process practically limits the squamosal region in this direction, since the curves which are continuous with the tuber of the parietal bone here begin. The slope from the side of the skull to the occi- put is also announced.* THE SUTURE BETWEEN THE INFRA-ORBITAL FORAMEN AND THE INTERIOR MARGIN OF THE ORBIT, INCLUD- ING VARIATIONS OF THE LATTER. An interesting region for variation is seen in the inferior border of the orbit. The border may be said to lie below a curved line which is continued across the orbit along the upper limit of the zygoma. The bones which enter into the composition of the border are the malar and the superior maxilla. The malar comprises the outer half, nearly, of the border. As a rule, the anterior limit reaches a point about 4™™ from the infra- orbital canal, but in place of this it may end over the canal, or may reach the ascending process of the maxilla. 1The Challenger Rep. X, 57. 21255, Ostrogoth; and 130, Chinese. 3 Nos. 20, 60, 80, 136, 139, College of Physicians. 4See 1482 (A. N. S.), Peruvian, right side 5 T = ee Ne ees ~, 66 THE TONER LECTURES. The maxillary portion is divided into the part over the infra- orbital foramen and the part answering to the base of the ascending process of the maxilla. The first of these divisions is exceedingly variable. The remains of the suture at the roof of the infra-orbital foramen, usually ending at the border, may extend to the malar.’ The entire sutural are of the orbital border may be depressed below the rest of the curve, and a minute spicule on the median side appears to indicate that fibrous tissue had bridged or occupied the interval caused by the depression. Negroes frequently exhibit the ,above-named variety. The line of the suture over the foramen is often hyperostosed, so as to assume a rounded form which may be irregularly roughened. — Such a variation is often found in large, heavy crania.? The ascending process of the maxilla entering into the composition of the border may be sharply ridged and abruptly raised above the planes of the floor of the orbit.’ In No. 1516, Malay, the infra-orbital suture does not extend to the inferior border of the orbit, but reaches the malar bone. A well-defined groove is seen on the inferior orbital border in 1450, Australian; 44, Menominee; and 739, Mandan. In the same group, with the rugose suture over the infra-orbital foramen, may be placed the rather decided ledge-like hyperostosis which marks the maxilla directly above and in front of the palatal as it lies over the spheno-palatine foramen. 11316, Malay (A. N.58.), aged eight years. ? Well illustrated in a skull of Lenapé (North American Indian), No. 40, Ae eS. 3 The suture over the infra-orbital foramen is raised or rugose in many examples of crania. In this connection see 1451, 1262, Australian ; 747, Minitari; 740, Mandan. The suture is often open. Examples are seen in Nos. 1800, 1342, Sandwich Islanders; Nos. 69, 708, 707, 733, and 726, Semi- nole; Nos. 951 and 955, Narragansett; Nos. 1227, 745, 1233, Blackfoot ; 1322, Pottawatomie; and 739, Mandan. A CLINICAL STUDY OF THE SKULL. 67 NOTES ON SOME OF THE FORAMINA OF THE SKULL. The foramina of the skull are chiefly of interest in exhibiting re- tentions of embryonic states. The most striking of these states are seen at the base of the skull, at the region of the union of the vomer with the sphenoid bone and the sphenoidal processes of the palatal bone and pterygoid process, as already seen’ (page 23). The foramina may be asymmetrical; the foramen ovale less so than the others. A second group of retention—variations is seen at the surface of the sphenoid bone, where it lies against the petrosal to form the petroso-sphenoidal suture. Along the lines of this suture are found the oval foramen, the spinous foramen, and the canalis innominata. The suture widens not infrequently at the outer end to form an opening, which may receive the name of the petroso- sphenoidal foramen. The oval, spinous, and _ petroso-sphenoidal foramina may be confluent, or the spinous and_petroso-sphenoidal may alone unite, or the oval and the spinous. The canalis innomi-- nata’ may be large or absent. In the skull up to the fourth year the spinous and petroso-sphenoidal openings are always united: I have often remarked that the spinous foramen may be entirely absent on one side.* In some lower animals, as is seen in the Vir- ginian opossum, the foramina retain throughout life the type seen in this disposition to coalescence. | The development of the tympanic bone is peculiar, for instead of uniformly extending in all its proportions a large foramen is always seen on the bone at its inferior surface. The significance of the opening is unknown. The foramen is very variable in form and position. As a rule, it recedes with age from the aperture of the meatus, so that in adult examples the retained foramen is almost always a centimetre or more from the outer free margin. Examples of the retention of the 1 For a good example see No. 924, negro. 3 The foramina ovale are at times asymmetrical. 3 No. 142, Marquesas (A. N.5S.), furnishes an example. 68 THE TONER LECTURES. foramen in adult life are by no means infrequent. In fourteen skulls of Esquimaux examined eight showed the tympanic foramen of defect. I have never seen the foramen in a Sandwich Island or Tahite cranium. Extended examinations might show variable per- centage of occurrences in the different races. That the foramina are factors in the distribution of pus in peri-meatal abscesses there can be no doubt. The oval foramina of the sphenoid bone are often unequal in size and of different shapes. The form may be so slightly changed from the circular that the term oval is scarcely applicable to it. This is often seen in Esquimaux crania. The rounded shape is frequently found associated with the short skull and the oval form with the long skull. When an asymmetry of the openings exists it is rational to entertain the opinion that the side of the skull which shows the greater elongation is also the side which will retain the most elliptical foramen. If the base of the skull were perfectly symmetrical the line of the basio-cranial suture, produced outward to the right and left, should intersect the oval foramina at a fixed point; but, in fact, the inter- section is variable. This is in part owing to the differences in the shapes of the openings, as already noted, and in part to the torsion of the anterior segment of the skull. (See page 18.) The carotid canals may be asymmetrical. The left canal, when asymmetry is present, is ordinarily the smaller." The foramen Jacerum medium may be entirely absent, as is the rule with the lower animals. The union of the apex of the petrosal element against the body of the sphenoid bone is more frequently seen in long, narrow skulls than in others, but may be seen inde- pendently of skull form. The foramina on the side of the skull are the familiar mastoid and the alisphenoid foramina. The latter are infrequently present. They are the orifices of small diploic veins which come to the sur- 1 For good examples see 1548, Swede; 914, negro (A. N.S.). A CLINICAL STUDY OF THE SKULL. 69 ‘face, probably to unite with the deep temporal veins. The spheno- palatine foramina are relatively of large size in the skull of the young subject. In an adult Tchutchi skull’ these foramina were 6™™ in diameter. The foramina of the vertex are few in number. The parietal foramina may be larger than usual, or they may disappear and abrupt openings may occur through the outer plate so as to expose the diploe along the line of the temporal ridge. They are more common on the frontal portion of the crest than elsewhere. The variations of the front of the skull pertain to the anterior lacerated foramina, the infra-orbital foramina, and the opening along the line of the frontal suture. The differences in the anterior lac- erated foramina are chiefly those of symmetry. The infra-orbital foramina vary chiefly in the manner by which the fissures of the maxilla close and the extent of the forward growth of the malar bone. Foramina occasionally appear at the median line, of the forehead, and are doubtless due to the partial failure of the two halves of the frontal bone entirely to unite. ' The foramina which transmit important structure are commonly modified from fissures, and in reversion easily assume again the stage of the fissure. Since they so originate, it is easy to account for their presence near the margins of fissures (as is seen in the for- amen ovale and foramen spinosum, near the fissure between the sphenoidal and petrosal elements). In like manner the parietal foramina appear at the side of the sagittal suture. Exceptions to this rule are seen in a small canal (occasionally present) which transmits a vein between the squamosal and parietal bones, and in a foramen in a Peruvian skull.’ 1 No. 1030, A. N.S. 2? No. 17, from San Mateo, which exhibits an opening between the frontal and parietal bones. 70 THE TONER LECTURES. THE GROOVES, OR THE INFLUENCES EXERTED BY BLOOD- VESSELS IN DETERMINING THE FORM OF THE SKULL. Inspection of the bones of the human subject shows that the sur- faces are not infrequently marked by superficial grooves which appear to be the tracks of blood-yessels. Such markings are best seen in the long bones, which exhibit the usual appearances of chronic inflammation. Assuming that the impression made upon the bones are’proportionate to the amount of increase of volume of the bone, and that the vessels remain fixed, a simple problem is presented by means of which the observer can determine the signifi- cance of blood-vessel tracks in other than in inflammatory conditions. The vessel-grooves on the periphery.—The cranium yields a num- ber of examples of these grooves. In the forehead, especially of specimens in which the forehead is rounded, numbers of deep, narrow grocves an inch or more in length are seen extending up- ward and backward from near the supra-orbital foramen or from the outer side of the frontal eminence and in line with the supra-orbital foramen or supra-orbital notch. In rare instances a simple small- groove lies near the frontal portion of the temporal ridge.’ I have seen both the above-named grooves present in a child of nine months of age. They appear earlier than the grooves described in the suc- ceeding paragraphs. Good examples of the frontal vessel-grooves have been found in skulls of all nationalities. They are not uncommon in the negro, when the narrow, convex forehead appears to favor their appear- 2 ance.” 1See No. 760, Copt, for a good example and many negro erania. 2For example see: Nos. 905, 912, negro ; No. 438, Ohio Indian; No. 1035, Apache; No. 87, Peruvian; No. 1024, Fiji; No. 1214, Hamilton, Ohio, Indian; No. 1043, Pawnee; Nos. 78, 44, 35, 1222, Menominee; Nos. 749, 650, Minitari; Nos. 744, 745, Blackfoot; No. 1057, Miami; ~Nos. 644, 742, Mandan; Nos. 39, 1333, 1233, unnamed. Lf A CLINICAL STUDY OF THE SKULL. cL It has been found in one side of the skull only, as seen in the skull of a Sandwich Islander." In a second skull of a Sandwich Islander (No. 695) the frontal grooves are absent, but a number of foramina perforating the outer plate of the bone are directed upward. It would appear that diploic veins had passed into the frontal veins, which had in their turn failed to make any impression upon the bone itself. Many crania show a vertically placed groove, which is more or less arborescent, and rather shallow as compared to the frontal, lying upon the squamosal, a short distance above the external audi- tory meatus and reaching as far as the upper limit of the bone, or even crossing the paricto-squamosal suture and describing a curve upward and forward over the parietal bone, a short distance below the temporal crest. In a few examples the track originates in the parieto-squamosal when the squamosa itself is free. The grooves are absent on surfaces from which muscles arise, as is seen on the occiput.” The squamosal groove is an apparent ex- ception to this conclusion. May it be said that the temporal muscle makes but little traction at the region of the groove? The region of the asterion is quite commonly the seat of numerous closely disposed grooves which are deep and sharply defined. It will be observed that in the above examples the grooves are deepest where the skull is thick, as on the convex frontal bone and in the massive region of the asterion, and most shallow when the bone is the thinnest, as over the squamosal; also that they may communi- cate with the diploic veins, as in the forehead, or even anastomose with an intra-cranial vein, as in the parieto-squamosal suture.’ 1 No. 572. * I have observed a branched depression of unknown significance above the nucha-mark in the skull of a Hindoo child four years of age. 3 For good examples of squamosal vessel-grooves see the following: 542, Miami; 670, Chinese; 741, Mandan; 1043, Pawnee; 1283, 1051, Hottentot ; 59, 987, 1283, 28, unnamed. te THE TONER LECTURES. Linear grooves of doubtful origin on the periphery.—A number of grooves are seen on the superior maxilla as it enters into the com- position of the outer wall of the orbit and of the boundaries of the spheno-maxillary sinus which closely resemble those caused by ves- sels. They are seen as fissures in the skull of the child and as linear depression in the skull of older subjects. Should they be accepted as vessel-grooves, the interesting question is raised: May not such irregular fissures as are here seen on the maxilla as it ex- tends upward toward the orbital wall be caused by the presence of vessels, and may not the irregular sinuate edges on the margin of a growing bone of the flat class be generally associated with such modifying causes ? The malar bone occasionally exhibits a transverse linear groove upon the middle of the inner (temporal) surface. (See page 8.) It corresponds to the division between the masseteric and the tem- poral surfaces as seen in the child at three years, and to the line of the suture which so rarely divides the malar into two parts. Vessel-grooves on the eneranial surface——Among the grooves on the endocranial surface of the parietal bone which are of undoubted influence, the form of the surrounding parts, is the conspicuously broad and deep depression which lies directly back of the coronal suture. The constriction so commonly seen in the periphery in this portion of the skull cannot be disassociated with the position of these vessels. The nutritive processes appear to be at first stim- ulated by the presence of this line of vessels, but after union with the frontal bone it remains stationary and permits the adjacent por- tion of the skull to rise above it. At the antero-inferior angle of the parietal bone the groove is converted into a canal and the inner layer of the bone notably thickened. In crania which exhibit a tendency to thickening of the vitreous plate the vessel-grooves are deep, sharply defined, and resemble the tracks made by insect-larvee in old wood and in neglected books. The diploe is often exposed at the bottom of these grooves. Doubtless the diploic vessels freely unite with the vessels. A CLINICAL STUDY OF THE SKULL. ee Vessel-grooves within the nasal chamber.—The nasal bone is often marked with a groove which extends the entire length of the sur- face within the nasal chamber and lies near the mavxilla-nasal suture. A similar groove is often found on the ascending process of the maxilla near and parallel to the same suture. The temporal ridge, as it is crossed by the coronal suture, is occa- sionally depressed, or the line of the ridge may be said to exhibit a fault at the point of section of the coronal. This arrangement is seen oftener in the skulls of negroes than those of other races.’ The temporal ridges divide the dome of the cranium (7. e., the parts included in the sides and vertex of the brain case) into the natural divisions within which the characters of the minor details are distinctive. The vertex between the ridges is almost uniformly marked by more numerous diploic openings (aperturz emissariz). The vessel-grooves are absent. In some examples the strize which radiate from the tubera medianward and backward are retained and distinguish the adult cranium.’ In narrow “ill-filled” skulls the temporal ridge may overlie the parietal tuber, as I have observed in a cranium of a convict, or greatly underlie it, as is seen in No. 77 of the College of Physicians collection. Among the processes of bone which were noticed in the course of the examination may be mentioned the following: A number of small but stout spines, each measuring a millimetre or two millimetres in length, which were appended to the frontal portion of the temporal ridge and directed downward ; the spines 1 The following are the numbers of negro crania in A. N.S. showing this peculiarity : No. 912, to a marked degree; also 975, 1102, 920, 994, 1094, 918, 907, 902, 918. The ridge is well seen in No. 1300, Sandwich Islander; 1064, German ; 207, Puget Sound; 133, Cossack; 89, Adrian; 99, Armenian (the four last named are in the College of Physicians). 2 The temporal ridges often limit the distribution of morbid processes and the changes due to old age. The diameter of the vertex measured between the two temporal ridges varies greatly in individuals. In tapeinocephalic and in all long, narrow crania the distance is smaller than in other types. 74 THE TONER LECTURES. were slightly curved. They were undoubtedly developed in the direction of the vertical fibres of the temporal muscle.’ The pneumatic process of the occipital bone was met with in six’ instances. In six of these the process was on the left side. The paroccipital process may be bent inward and flattened,’ and in one instance was found to articulate on the left side with the atlas.* Regions of great density of bone structure.—The disposition for some parts of the cranium to show dense ivory-like thickenings is very noticeable. The causes which induce the vascular cancellous tissue to assume greater density with diminution of blood-vessel supply would be interesting to trace. Four localities are named for the occurrence of this change—Ist, the petrous portion of the temporal bone; 2d, the inner or vitreous plate of the bones entering into the composition of the vertex; 3d, the margins of the jugular foramen, notably the anterior; 4th, occasionally in the interior of sinuses, as seen in the maxillary and ethmoid sinuses. The disposition to ivory-like density is often morbid (this prob- ably includes the third and fourth groups as given above), and may even be present in the vitreous plate of the vertex. Scarcely a cranium can be found in our dissecting-rooms in which solid nodules are not found in some part of the interior of the cal- varium, especially at the frontal portion on either side of the me- topic line. Many individuals exhibit dense, white, low eminences of the general internal surface at the region of the bregma. They are lozenge-shaped and measure four to six centimetres in diameter. 1See No. 1271, North American Indian; No. 742, Mandan; No. 968, negro. 2No. 1229, Upsarooka; 20, Bengalee; 78, 35, Menominee; 204, Che- nook; 707, Seminole. * See skull of Alaskan in museum of Princeton College, N. J. 4 No. 706, German. 5 This is seen to be the case to a remarkable degree in the skull of an Esquimaux (No, 1554) in the Army Medical Museum. A CLINICAL STUDY OF THE SKULL. Te The formations as they exist in the sinuses are nodular and appar- ently lead up by easy grades to the ivory-exostoses recognized by the physician as distinctly pathological.’ ON THE MANNER OF TAKING A CLINICAL NOTE OF THE CRANIUM. It will be remembered that one of the objects in view in under- taking the study which is now completed was to ascertain the degree of correlation, if any existed, which could be traced between struct- ural peculiarities in the region of the mouth, of the nasal chamber, of the naso-pharynx, and other portions of the cranium. A laryn- gologist has an opportunity of taking measurements in the mouth, throat, and adjacent parts which is withheld from the general ob- server. It goes without saying that for general craniological pur- poses it will be impossible for measurements within the nose and throat to be made. The contrast between any of these regions in patients is so great it was suggested that a series of observations might be of some importance. The following is an example of the kind of measurements which can be secured in the living subject: In a woman aged twenty-six, suffering from chronic nasal catarrh, it was found that the distance from the axis tubercle (which is very plainly seen when the velum is lifted) to the cutting edge of the right superior incisor at the median line was 8° 1™; the distance from the vault of the naso-pharynx to the lower border of the ante- rior nasal aperture, 7°7™"; the distance from the glabella to the post-remal prominence, 18°; the circumference of the head taken on the line of the parietal tubera was 54°. It will be noted in the above that the axo-incisorial measure- ment ends at the edge of the incisor. It is acknowledged that this is undesirable, since the inclination of the teeth is a variable quan- tity. Indeed, any point about the dental arches is subject to the same criticism, but does not apply with any greater force in this 1Fora general essay on hyperostosis in man and animals see Gervais Journal de Zoologie, 1875, p. 421. = 10 THE TONER LECTURES. measurement than to other craniological lines into which the teeth may enter. It is also difficult to determine the anterior limit of the line extending from the vault of the naso-pharynx to the anterior nasal aperture (pharyngo-narial line), for the reason that the depth of the soft parts covering the nasal aperture is variable; but such an ending is not more inconstant than that of the anterior nasal spine, which is relied upon generally as a point from which meas- urements may be taken. The individual who furnished these measurements had a high basi-cranial angle. Indeed, it was im- possible to inspect the vault of the pharynx of this subject with satisfaction, since the anterior position of the body of the axis con- joining with the acute angle of the vault made it difficult to depress the mirror so as to obtain a satisfactory image of the space. In addition to the above the following observations were made: The lower jaw with marked outward deflection of the left angle; the antegonial depression marked; the mentum high; the bregmal depression marked; the post-coronal depression absent; the deep depression in the region of the obelion present; the para-tuberal and meso-lambdoidal eminences well developed. It is submitted that a series of measurements made on this simple scheme might yield interesting results. The material I have col- lected is insufficient for study at this time. The study of the skull in children often throws light upon the nature of morbid processes. In this connection I have special ref- erence to minor changes, some of them, indeed, so slight as to escape notice if the standards of comparison be those which the observer is usually expected to entertain—such, for example, if the gross changes recognized as cretinic, hydrocephalic, ete., be selected as basis for study. I allude more particularly to such appearances as would follow a delayed disappearance of the anterior fontanel, the result of which is a saucer-shaped concavity at the anterior portion of the vertex. Another peculiarity is an unduly marked convexity on either side of the sagittal depression. This need not be suffi- cient to constitute the natiform skull (see page 56), but to suggest A CLINICAL STUDY OF THE SKULL. Te with this variety a common interest, namely, a disposition to pre- mature disappearance of the sagittal suture associated with retarded ossification of the parietals, as a result of which they become unduly convex. The third variety is confined to the anterior cranial segment— a. €., a phase of deformation in which all the peculiarities are in the frontal bone or in the bones of the face. The frontal eminences may be too near one another; the metopic suture may be here and there carinated; the muscular ridge at the anterior border of the temporal fossa may be unduly prominent; the inferior border of the orbit at the region of the union of the malar bone and the line over the infra-orbital canal may be roughened, etc. Many of these peculiarities are associated with errors in the shape of the mouth and the nasal chambers, and easily come within the range of ana- tomical studies which are suggested by clinical observations on catarrhal diseases of the respiratory mucous surfaces. ADDENDUM.—The number of skulls stated on 8th line from bottom page 29 refers to others than those in the collection of the Academy of National Sciences. Vn INDEX. Page. Angle, basi-cranial -.-.....--. 34 PUGOOMMLMNY We ae esa kes 12 Basiecranial angle [== — a ae 34 Bone structure, great density of. 74 Bones, processes Ofe=..===-=-_ == 73 IDMeGIM Ay eke e soe eas 51 Bregmal depression_.._._...-. 55 @hambers, nasgl_-———. ~-=--.—- 36 Wihoan eee See eee 43 Coronal depression _._..-.--_- 55 Coronalesutures== == so 22 Ses 52 Cranial segment, anterior_-__- 16 Cranium, clinical notes of_____ 75 Depression, bregmal ______ -___ 55 Depression, coronal...-__.-_-- 55 Depression, post-coronal___-___ 56 Depression, pre-bregmal______- 55 Depressions on vertex ---_..-= 55 Deviations of septum _-___--_-- 44 Eminence, meso-coronal_-____- 50 Eminence, meso-lambdoidal_-_ 54 PIMINENCe | MeLOPIC Ieee aa 54 Eminence, para-tuberal ____.._. 54 Eminences and depressions of Vierbex. ans Se eek 54 Eminence, temporo-frontal__-. 55 Miamoid. bones2= 22.2 +2. = 50 Fissure, spheno-maxillary—-__ ~~ 11 iHoraminaon skull see 67 iMrontel bones 2--- 22-2 25 47 NEMO OVER 6 Sees! oo le 70 Grooves, linear, of doubtful ori- Dm eesenes Whee: See se ae 72 Miripertuberd, <= ne) PA 57 SID Wal OWICT yao sae ke ae ail Lambdoidal suture ___---_-_-- 53 Linear grooves of doubtful ori- Ole eee See ERS Hongitudinal line)... ..-.--_. ly LGN SP SC es aes Malar b ones a= 2s Se ses owl Malo-maxillary suture____-__- 60 Meso-coronal eminence-_-.---. 50 Meso-lambdodial eminence.--_ 54 Metopic eminence -___-__-__.- Middle turbinated bone ~_____- Wasalichamiber 2 5s5-. s—=aae Nasal chamber, floor of ______- Norman basilariss. =a2-se.— eee Obeliomms oF aks Ue) Oe ee Para-tuberal eminence_______.. Perpendicular plate of ethmoid Ome ee eee pa se Sw ee ROStabrecimnara =a ae Se ee ee Post-coronal depression NRoOstenulaye. == eS ae eM Post-obelion Pre-bregmal depression -__--__., Processes Of DON CSE s= ere = Process uncinate Ridces=of vertexeee = ose sa— Sagittal suture Septum, deviation of_____-__-_- SG }oUU a )s) na cet ee eee ree Skullesforaminavot === ase Spheno-maxillary fissure-____- Spheno-turbinals Squamoso-malar series SUtUMe COLON a les aaa eee Supurelamibdoidal’===—======2 Suture, malo-maxillary -__--~-- SUEUR SOU beyl meee ee ae Temporo-frontal eminence_-__- . Mransverse linen.) 22522 a= === Turbinated bone, middle Uncinate process NWienie swe eae eee 50, Vertex, eminences and depres- SLOTS 10 tpn ee ae ee Wiertiexsrideesiofa a= = se Vessel-grooves on endocranial surface Vessel-grooves on periphery---~ Vessel - grooves within nasal chambers sess asts8— - SS Page. 54 38 36 44 15 52 54 42 67 11 32 16 2, 65 52 60 51 55 12 70 SMITHSONIAN MISCELLANEOUS COLLECTIONS. 741 INDEX TO THE LITERATURE OF THERMODYNAMICS. BY ALFRED TUCKERMAN, Pu. D. WASHINGTON: PUBLISHED BY THE SMITHSONIAN INSTITUTION. 1890. oo, PRINTED AND STEREOTYPED BY | JUDD & DETWEILER, WASHINGTON, D. C. Pee A Ci. This is similar to my Index to the Literature of the Spectroscope, published in the Miscellaneous Collections of the Smithsonian Institution, vol. xxx1I, for 1888. e All of the titles are given in full in the author-index ; but in the sub- ject-index, to save useless repetition, only the authors and the places where their works are to be found are given—except in the case of books. Applications of thermodynamics have been found, and kept, to the number of more than double the titles here given. They were omitted so as not to overload the index with matter of little or no use. But, of course, no titles have been left out which belong to the applications named in the table of contents. The work has been brought down to the middle of the year 1889. ALFRED TUCKERMAN. Newport, R. L., July, 1890. (iii) CONTENTS. Page. Page Pe SOUBILCr-(NDEX 2-252 2. 0 oe 1/1. Supsect-InpEx—Continued. PANT EAMG ees tte et a Se 1 ORCC i222 Stone ae a ee eee 72 nO yee as eee vets ede 2 riGtiones) 32226 220% ea eC G [EGTA eae 4 Gases, (Kinetic Theory of) ---. 75 General Papers in Periodicals._--___ 18 EHamilton’s:Principle.- 2-322 84 Application of thermodynamics to— Ice. (See Cold.) PAG TTT Eyes eee tare rs 22 Integral. (See Equations.) PISEPOROMIY, fees ee ee 23 Dieoht 22s PU So a oe ee 84 Aworadro’s, law 02.222 2ce 25 Raguidepee ere 2k eek en 84 Boling se oimts:o2 2.5 -2Ge SoS 26 Moariotte’silaw 22 £2. ou oe 86 -Caoutchouec. (See Rubber.) Molecules 2 a2 ale ee oe 86 Capillary Action-_--_- sate he 27 Onthowie2 seks Se TS 89 Warnot’s; Theorem 2-- 22- == == 28 EALOSS nC unee een eeye ce Si Bet Te 90 @liniate sae ee Sooke 28 PEEUOE TAU e ae 2 phe tee Sr eS Seu oe ae 92 (Woh pee as hs at RE a 28 ACTA tlOMyss tes ees ke ee 93 Chemical Combination -___---- 36 Refrigeration. (See Cold.) Wompressions=22-— 2 25225 22. 40 Rubber S29 send So ae eee 96 Concussion ==. == = 22 42 alisee 2 So0 Se Se eet eee 98 Condensation and Contraction_. 42 Saturated Vapors —-___._.- SUE a 99 Correlation of Forces_--_---__- 43 Second Proposition____-__.---- 96 RATS Ut yest ts ea cee Se Ue 43 Olid setae ei See ea 100 th St Onys aaa eee eee ee ae 46 Solutionss2.s= es eee 101 Dissipation of Energy--------- 46 Stationary Motions_____.-____- 102 Dissociation 22 222 ee Ue eo 47 Temperature: 22.5 te oe ae 102 il aStiCiby) = See a ee 50 onsionto2s hee eee as 105 CCiTiCiiy= = ee 52 apt et eERS at Meas a 106 IMOIe pa ees ek Se eee 56 Wiscosity 220s Sao. Cokes 106 IB Gines ese estes eee ee 57 Witalehorcees=——— Se eee 107 MGLO Dyke eo ae ee ee eee eee OL Volume 22i ees ltrs eeleees 109 Hquations sass se se ean 61 Wonks Site so sens eee 110 Bivaporations 22. s sce he 2.8L 62 Hero, Asolivtes oa ae ee 112 BRA ISTOM ee ee ee ee 63 arlosiiyesys sot re wuts A 67|11. AurHorR-INDEX, (with titles in aR Merveh gee aN ye 71 full).------------~---- -------- 116 (v) \ ) (1853) 47. 9; Jahresb. Rankine (W. J. M.). Phil. Mag. [4] 5 (1853) 6. Wittwer. Phil. Mag. [4] 7 (1854) 528, abs. from Comptes rendus, 29 (1854) 750. . Joule (J. P.). Phil. Mag. [4] 12 (1856) 155, 321. . Woods (T.). Phil. Trans. (1856) ; Proc. Roy. Soc. 8 (1856-7) 211. 58. Kirchhoff (G.). Ann. Phys. u. Chem. 103 (1858) 203. . Laboulaye (Ch.). Comptes rendus, 47 (1858) 824. . Marié-Davy et Troost. Ann. chim. et phys. [8] 53 (1858) 423; Comptes rendus, 46 (1858) 748, 936; Jahresb. (1858) 31. Raoult. Comptes rendus, 49 (1859) 81; Instit.(1859) 230; Jahresb. (1859) 31. Cooke (J. P., Jr.). Amer. J. Sci. April, 1860; Phil. Mag. [5] 9 (1860) 367. . Deville (H. Sainte-Claire). Comptes rendus, 50 (1860) 534, 584.— See Robin and Baudrimont, same vol. 683, 723. N. Arch. ph. nat. 8 (1860) 60; Instit. (1860) 85, 98; Jahresb. (1860) 32. Mann. Z. Math. u. Phys. (1861) 72. Clausius (R.). Ann. Phys. u. Chem. 116 (1862) 72; C.’s Abhandl. 1, 242; Compses rendus, 54 (1862) 732; Phil. Mag. [4] 24 (1862) 81, 201; Mittheil. d. naturf. Ges. in Zurich, 7 (1862) 48. . Marié-Davy. Comptes rendus, 54 (1862) 1103; Instit. (1862) 168; N. Arch. ph. nat. 14 (1862) 402. . Rankine (W. J. M.). Edinb. Proce. 4 (1857-62) 616. 38 LITERATURE OF THERMODYNAMICS. 1863. Raoult (F. M.). Comptes rendus, Sept. 14, 1863; Phil. Mag. [4] 26 (1863) 522. 1864. Schréder van der Kolk. Aun. Phys. u. Chem. 122 (1864) 439, 659; Ann. chim. et phys. [4] 4 (1864) 193, abs.; Phil. Mag. [4] 29 (1864) 269; Amer. J. Sci. [2] 39 (1864), 92, abs. 1865. Berthelot. Ann. chim. et phys. [4] 6 (1865) 290, 292, 329, 442. —. Raoult (F. M.). Ann. chim. et phys. [4] 2 (1865) 317; 4 (1865) 392.—See Favre, Ann. chim. et phys. [5] 40 (1865) 293 ; Jahresb, (1865) 101. 1866. Brodie (B. C.). Phil. Trans. 156 (1866) 781; Phil. Mag. [4] 32 (1866) 227; Proce. Roy. Soc. May 3, 1866. ——. Dupré. Comptes rendus, 62 (1866) 791. —. Gill (J.). Phil. Mag. [4] 32 (1866) 420. —. Harcourt (A. Vernon) and Esson (W.). Phil. Trans. 156 (1866) 1933 Loe (1s67) Te. 1867. Berthelot. Ann. chim. et phys. [4] 12 (1867) 122; Comptes rendus, 64 (1867) 413; J. de Pharm. 5 (1867) 336; Jahresb. (1867) 74. ——. Harbord (J. B.). Phil. Mag. [4] 34 (1867) 105. ——. Schréder van der Kolk. Ann. Phys. u. Chem. 131 (1867) 277, 408; Phil. Mag. [4] 36 (1868) 433; Z. f. Chemie (1868) 188 ; Jahresb. (1867) 74. 1868. Berthelot. Ann. chim. et phys. [4] 18 (1868) 5. 1871. . Ann. chim. et phys. [4] 22 (1871) 134; Phil. Mag. [4] 42 (1871) 152%; (Proc: Roy. Soe. April 27, 1371. 1873. Comptes rendus, 76 (1873) 1106. Comptes rendus, 77 (1873) 24. ——. Moutier (J.). Comptes rendus, 76 (1875) 365; Phil. Mag. [4] 45 (1873) 236; Jahresb. (1873) 110; Chem. Centralbl. (1873) 382 1874. Berthelot. Comptes rendus, 78 (1874) 162, 1670 ; 79 (1874) 1242. 1875. Markownikoff. Comptes rendus, 81 (1875) 668, 728 et 776. ——. Moutier (J.). Comptes rendus, 80 (1875) 40; Phil. Mag. [4] 49 (1875) 154. —. Bull. soe. philom. [6] 13 (1876) 51. 1876. 9 APPLICATIONS—CHEMICAL COMBINATION. og 1877. Berthelot. Ann. de l’Keole norm. [2] 6 (1877) 63; Ber. chem. Ges. 10 (1877) 897, 900; Comptes rendus, 84 (187/) 407, 477, 1408, 1467 ; 85 (1877) 651, 919. —. Maumené (E.). Comptes rendus, 85 (1877) 914, 1026. ——. Brodie (B. C.). Phil. Trans. 167 (1877) 35. —. Moutier (J.). Bull. Soe. philom. [7] L (1877) 39. —. Wright (C. A.). Nature, 16 (1877) 377; Rept. British Assoc. (1877) 1; Ber. chem. Ges. 11 (1878) 1218. 1878. Berthelot. Comptes rendus, 86 (1878) 628; Ber. chem. Ges. 11 (1878) 365. —. Hood VJ.). Phil. Mag. [5] 6 (1878) 371; 8 (1879) 121. ——. Moutier (J.). Bull. soe. philom. [7] 2 (1878) 60. ——. Phipson (T. L.). Comptes rendus, 86 (1878) 1196. 1879. Berthelot. Comptes rendus, 89 (1879) 1195 Do. 90 (1880) 1511; 91 (1880) 256. ——. Moutier (J.). Bull. soe. philom. [7] 3 (1879) 31. ——. Naquet (A.). Moniteur scientif. Nov. 1878, Mars et Avril, 1879; Phil. Mag. [5] 7 (1879) 418. 1880. Berthelot. Comptes rendus, 90 (1880) 1511; 91 (1880) 701. —. Beketoff (N.). Ber. chem. Ges. 13 (1880) 2404. 1881. Carnelly (T.). Phil. Mag. [5] 11 (1881) 28. 1882. Berthelot. Comptes rendus, 94 (1882) 916, 1619. ——. Helmholtz (H. v.). Ber. d. Berliner Akad. (1882) 22, 825; Jahresb. (1882) 154. ——. Schroder (H.). Ann. Phys. u. Chem. n. F. 15 (1882) 636. 1883. Berthelot. Comptes rendus. 96 (1883) 1186. —, Boltzmann (1..). Ber. d. Wiener Akad. 88 1 (1883) 861; Ann. Phys. u. Chem. [2] 22 (1884) 39; Jahresb. (1884) 151. —. Helmholtz (H.v.). Ber. d. Berliner Akad. (1883) 647; Jahresb. (1885) 108. —. Laurie (A. P.). Phil. Mag. [5] 15 (1883) 42. 1885, . Hood (J. J.). | Phil. Mag. [5] 20 (1885) 323; Ber. chem. Ges. 18 ts 1886. 1887. . Ramsay and Young. Chem. News, 56 (1887) 18; Beiblatter, 12 1888. . Pickering (S. U.). Proc. Chem. Soc. Nov. 15, 1888; Chem. News, LITERATURE OF THERMODYNAMICS. . Mackey (W. M’D.). Phil. Mag. [5] 16 (1883) 429. . Guthrie (F.). Phil. Mag. [5] 18 (1884) 499. . Hood (J. J.). Phil. Mag. [5] 17 (1884) 352. . Thomson (J. J.). Phil. Mag. [5] 18 (1884) 2 Hartley (W.N.). Phil. Mag. [5] 19 (1885) 55. (1885) R. 519, 653; Jahresb. (1885) 11 Becker (G. F.). Amer. J. Sci. [3] 31 (1886) 120; Ber. chem. Ges. 19 (1886) Ref. 195. Armstrong (H. E.). Phil. Mag. [5] 23 (1887) 73 (1888) 36, abs. . Urech (F.). Ber. chem. Ges. 20 (1887) 56. . Landero et Prieto. Comptes rendus, 105 (1886) 934; Beiblatter, 12 (1888) 7, abs. . Fitzgerald (G. F.). Proce. Roy. Soc. 42 (1887) 216; Beiblatter, 12 (1888) 33 Parker (J.). Phil. Mag. [5] 25 (1888) 406. 58 (1888) 262. COMPRESSION. . Berthollet (C. L.). Annals of Phil. n. s. 9 (1825) 184, abs. from Mem. Soc. Arcueil, 2 (1825) 42. . Rankine (W. J. M.). Edinb. Jour. 51 (1851) 128. D3. Koosen. Ann. Phys. u. Chem. 89(1853) 437 . Joule (J. P.). Proc. Roy. Soc. 8 (1857) 564; Ann. chim. et phys. ; Jahresb. (1853) 37. [3] 52 (1857) 120. 1858. 1862. 1883. 1886. 1887. APPLICATIONS—COMPRESSION. 41 Joule (J. P.). Phil. Trans. (1859) 183; Proc. Roy. Soc. 9 (1858) 496. Thomson (W.). Ann. chim. et phys. [3] 64 (1862) 504; Edinb. Trans. 20 (1862) 1. . Tschermak (G.). Ber d. Wiener Akad. 44 m (1862) 137, 141. 1863. Clausius (R.). Comptes rendus, 56 (1863) 1115.—See Dupré, same vol. 960. ——. Dupré. Comptes rendus, 56 (1863) 960.—See Clausius, same vol. 1115. ——. ——. Comptes rendus, 57 (1863) 774. 1864. Comptes rendus, 58 (1864) 539.—See Do. 59 (1864) 490, 665, 705, 768. 1872. Amagat (E. H.). Comptes rendus, 75 (1872) 479; Ann. chim. et phys. [4] 28 (1872) 274; 29 (1873) 246. . Berthelot.. Comptes rendus, 84 (1877) 477. . Heath (J. M.). Phil. Mag. [5] 4 (1877) 14. - . Amagat (E. H.). Comptes rendus, 87 (1878) 432. - Roth (F.). Ann. Phys. u. Chem. n. F. 11 (1880) 1. . Sarrau (E.). Comptes rendus, 94 (1882) 639; Phil, Mag. [5] 13 (1882) 306. Berthelot. Comptes rendus, 96 (1883) 1186. Amagat (EH. H.). Comptes rendus, 103 (1886) 429. ——. Comptes rendus, 105 (1887) 1120. . Isambert (F.). Ann. chim. et phys. [7] 11 (1887) 538. . Tait (P. G.). Edinb. Proc. Dec. 19, 1877; Nature, 36 (1887-88) 259. . Amagat (EH. H.). Comptes rendus, 107 (1888) 522. . Puschl (P.). Wiener Anzeiger, (1888) 123; Ber. d. Wiener. Akad. 96 11, (1888) 1028. 42 LITERATURE OF THERMODYNAMICS 1888. RudolifGrtibs (R.). Compressious-Kaltemaschinen. 4to. Berlin, 1888. v, 150 pp. [See also Condensation, and Pressure. ] CONCUSSION. 1869. Mayer(A.M.). Proc. American Assoc. 18 (1869) 64. [Waterfalls. ] 1870. Hagenbach (E.). Phil. Mag. [4] 40 (1870) 462, abs. from Ann. Phys. u. Chem. no. 7, 1870. 1873. Ledieu (A.). Comptes rendus, 77 (1875) 94, 165, 260, 325, 414, 455, 517; Jahresb. (1875) 51. 1874. Tresca. Nature, 10 (1874) 400. CONDENSATION AND CONTRACTION. 1827. Ivory (J.). Phil. Mag. n. s. 1 (1827) 89, 165. 1844. Joule (J. P.). Proc. Roy. Soc. 5 (1843-50), abs.; Phil. Trans. (1844) 1; Phil. Mag. [8] 25 (1844) 1; 26 (1845) 369. 1861. Clausius (R.). Ann. Phys. u. Chem. 114 (1861) 37.—See E. Edlund, Ann. Phys. u. Chem., same vol., 13. 1863. —. Comptes rendus, 56 (18635) 1115. 1879. Chappuis (P.). Ann. Phys. u. Chem. n. F. 8(1879) 1; Nachtrag, 672. 1881. Moser (J.). Ann. Phys. u. Chem. [2] 14 (1881) 62. 1882. Wiedemann (E.). Ann. Phys. u. Chem. n. F. 17 (1882) 988. 1887. Birnie (S.). Recueil des travaux chimiques des Pays-Bas, 7 (1887) 389. 1847. 1848. 1870. 1806. 1811. 1812. » 1820. 1822. 1825. 1827. 1832. APPLICATIONS—DENSITY. 43 CORRELATION OF FORCES. - Melloni. Ann. Phys. u. Chem. 37 (1836) 486, 39 (1836) 31; from Ann. chim. et phys. 59 (1836) 418. Seguin. Comptes rendus, 25 (1847) 420; Cosmos, 2 (1853) 568. Goodman (J.). Phil. Mag. [8] 382 (1848) 172; from Manchester Soc. Mem. 8 (1848) 1; Phil. Mag. [4] 2 (1851) 498; abs. from Proc. Roy. Soc. May 22, 1851; Rept. Brit. Assoc. (1848) 53.— See Tyndall, Phil. Mag. [4] 3 (1852) 127. . Thomson (W.). Edinb. J. [2] 1 (1855) 90; Comptes rendus, 40 (1855) 1197; Jahresb. (1855) 25. 08. Masson. Ann. chim. et phys. [3] 53 (1858) 257. . Seguin. Cosmos, 26 (1864) 296. Heath (J. M.). Phil. Mag. [4] 40 (1870) 51. DENSITY. Dalton (J.). Nicholson’s Jour. 13 (1806) 377; 14 (1806) 128. Gay-Lussac. Ann. de Chimie, 80 (1811) 218. Grotthuss. Ann. de. Chimie, 82 (1812 (34, from Schweigger’s Jour. f. Chemie, 3 (1812) 219; Nicholson’s J. 35 (1813) 30. Berzelius et Dulong. Ann. chim. et phys. 15 (1820) 386. Despretz ( Ce’s.). Ann. chim. et phys. 21 (1822) 143. Hallstrom (G. G.). Ann. chim. et phys. 28 (1825) 56; Annals of Phil. n. s. 9 (1825) 155, abs. from Stockholm Trans. (1823). Ivory (J.). Phil. Mag. n. s, 1 (1827) 89, 165. Dumas (J.). Ann. chim. et phys. 50 (1832) 170. 44 LITERATURE OF THERMODYNAMICS. 1833. Mitscherlich (E.). Ann. chim. et phys. 55 (1833) 5. 1838. Bineau (A.). Ann. chim. et phys. [2] 68 (1838) 416; [3] 18 (1846) 226. 1845. Regnault (V.). Ann. chim. et phys. [5] 14 (1845) 211. 1847. Southern (J.). Phil. Mag. [3] 380 (1847) 115. 1851. Waterston (J. J.). Phil. Mag. [4] 2(1851)565; Rept. Brit. Assoc. (1852) 11, 2; Phil. Trans. (1852) 83. 1853. Potter. Phil. Mag. [4] 6 (1853) 161; 23 (1862) 52. ——. Rankine (W. J. M.). Edinb. Trans. 20 (1853) 475; Phil. Mag. [4] 9 (1855) 523; Jahresb. (1855) 24. 1854. ———. Edinb. Trans. 21 (1854) 63; 24 (1857) 57; Phil. Mag. [4] 8 (1854) 409; 9 (1855) 36; Comptes rendus, 39 (1854) 529. 1856. Deville (H. Sainte-Claire). Phil. Mag. [4] 11 (1856) 144. 1859. Rankine (W. J. M.). Phil. Mag. [4] 18 (1859) 316. —. Challis. Phil. Mag. [4] 17 (1859) 401. 1860. Deville (H. Sainte-Claire) et Troost (L.). Ann. chim. et phys. [3] 58 (1860) 257; Phil. Mag. [4] 19 (1860) 207, abs. ——. Fairbairn (W.). Phil. Trans. 150 (1860) 185. — and Tate (T.). Proc. Roy. Soc. May 10, 1860; Phil. Mag. [4] 21 (1861) 230. 1861. Waterston (J. J.). Phil. Mag. [4] 21 (1861) 401. 1864. Phipson (T. L.). Phil. Trans. (1864) 1; Proc. Roy. Soc. 13 (1863-64) 240, abs. ——. Rankine (W. J. M.). Edinb. Trans. 23 (1864) 147. 1865. Edmonds (T. R.). Phil. Mag. [4] 29 (1865) 169; 380 (1865) 1. | ——. Wanklyn (A.). Phil. Mag. [4] 29 (1865) 111. 1866. Deville (H. St. Claire). Comptes rendus, 62 (1866) 1157; Phil. Mag. [4] 32 (1866) 387, abs. 1883. 1884, 1885. 1887. APPLICATIONS—DENSITY. 45 }. Cahours. Comptes rendus, 63 (1866) 16; Phil. Mag. [4] 32 (1866) 388, abs. Heath (J.M.). Phil. Mag. [4] 39 (1870) 347. . Puschl (C.). Ber. d. Wiener Akad. 69 11 (1874) 324; Jahresber (1874) 59. . Fromme (C.). Ann. Phys. u. Chem. n. F. 8 (1879) 352; Phil. Mog. [5] 8 (1879) 421. . Gibbs (J. W.). Amer. J. Sci. [3] 18 (1879) 1. . Winkelmann (A.). Ann. Phys. u. Chem. n. F. 9 (1880) 208, 358. — —. Ann. Phys. u. Chem. n. F. 11 (1880) 474. . Gerosa, Atti Accad. Lincei, [3] 10 (1880-81) 75. . Schoop (P.). Ann. Phys. u. Chem. n. F. 12 (1881) 550. . Babo (L. von) und Warburg (E.). Ann. Phys. u. Chem. n. F. 17 (1882) 390; Phil. Mag. [5] 14 (1882) 51; Ber. d. Wiener Akad. 77 11 (1882) 509. . Goldstein (E.). Ann. Phys. u. Chem. n. F. 15 (1882) 277; Phil. Mag. [5] 14 (1882) 402; Ber. d. Berliner Akad. (1881) 876. . Haga (H.). Ann. Phys. u. Chem. n. F. 15 (1832) 1. Bender (C.). Ann. Phys. u. Chem. n. F. 20 (1883) 560. Warburg (E.) und Sachs (J.). Ann. Phys. u. Chem. n. F. 22 (1884) 518. Amagat (E. H.). Comptes rendus, 100 (1885) 633. Scott (A.). Edinb. Proc. 14 (1887) 410. . Vicentini (G.) e Omodei (D.). Atti Accad. Torino, 23 (1887) 8. . Bott (W.). Jour. Chem. Soe. Dec. 6, 1888; Chem. News, 58 (1888) 288, . Fuchs (K.). Repert. a. Physik, 24 (1888) 298. 46 1840. L366. 1870. 1878. 1879. 1884. 1887. 1888. 1852. 1879. 1882. L886. LITERATURE OF THERMODYNAMICS. DIFFUSION. Melloni. Ann. Phys. u. Chem. 49 (1840) 577; 53 (1841) 47. Dupré. Comptes rendus, 62 (1866) 1072. Thomsen (J.). Ber. chem. Ges. 3 (1870) 829. Clausius (R.). Ann. Phys. u. Chem. n. F. 4 (1878) 841; Phil. Mag. [5] 6 (1878) 237.—See Preston (S. T.), Nature, 17 (1877- 78) 31, 202. Jahresb. (1878) 64. Boltzmann (L.). Ber. d. Wiener Akad. 78 t1 (1879) 733; Jahresb. (1879) 90. Kirchhoff (G.). Ann. Phys. u. Chem. n. F. 21 (1884) 563. Burbury (S. H.). Phil. Mag. [5] 24 (1887) 471; 25 (1887) 129. Gouy et Chaperon. Ann. chim. et phys. [6] 15 (1888) 120. . Obermayer (A. v.). Ber. d. Wiener Akad. 81 rm (1880) 1102; 85 11 (1883) 147; 87 11 (1884) 188; 96 rm (1888) 546. . Schlidlowsky (F.). Phil. Mag. [5] 25 (1888) 78, abs. from J. Soc. phys. chim. Russe, 1886. . Weinhold (A.). Z. f. phys. u. chem. Unterricht, 1 (1888) 262. Dilatation see Expansion. DISSIPATION OF ENERGY. Thomson (W.). Phil. Mag. [4] 4 (1852) 304; Jahresb. (1873) 114. Tait (P.G.). Phil. Mag. [5] 7 (1879) 344. Burbury (S. H.). Phil. Mag. [5] 413 (1882) 417. Becker (G. F.). Amer. J. Sci. [8] 31 (1886) 115. [See Energy below. ] 1853. 1857. 1859. 1860. 1861. 1863. 1865. APPLICATIONS—DISSOCIATION. 47 DISSOCIATION. Tilghman (R. A.). Amer. Philosoph. Soc. Trans., n. s. 10 (1858) 173. Instit. Deville (H. St. Claire). Comptes rendus, 45 (1857) 857; 3; Jahresb. (1857) 393; Ann. Chem. u. Pharm. 105 (1857) 38 (1857) 58. Boedecker. Instit. (1859) 219; Jahresb. (1859) 28. Deville (H. Sainte-Claire). N. Arch. ph. nat. 9 (1860) 51; Phil. Mag. [4] 20 (1860) 448; Jahresb. (1860) 24. Remarks by Th. Woods, Phil. Mag. [4] 21 (1861) 202. Mann. Z. f. Math. u. Phys. (1861) 72. Deville (H. St. Claire). Phil. Mag. [4] 25 (1863) 557; abs. from Comptes rendus, Feb. 2, 1865. Clausius (R.). Arch. deGenéve, Oct., 1865; Ann. Phys. u. Chem. 127 (1866) 477; Phil. Mag. [4] 31 (1866) 28.—See Phil. Mag. [4] 24 (1862) 81, and Ann. Phys. u. Chem. 116 (1862) 73. . Deville (H. Sainte-Claire). Comptes rendus, 59 (1865) 873; 60 (1865) 317; Phil. Mag. [4] 30 (1865) 252, abs.; Bull. soc. chim. [2] 3 (1865) 366; 5 (1865) 104. . Rankine (W. J. M.). Phil. Mag. [4] 80 (1865) 407. . Clausius (R.). Ann. Phys. u. Chem. 127 (1866) 477 ; 141 (1870) 427 ; Erginzbd, 6 (1874) 602. E. Budde dazu, 141 (1870) 428. . Deville (H. Sainte-Claire). Bull. soc. chim. (1866) 115. . Clausius (R.). Zamminer’s Jahresb. (1867) 40; Liebig’s Jahres). (1867) 81. . Deville (H. Sainte-Claire). Comptes rendus, 63 (1867) 19; 64 (1867) 66; Instit. (1867) 17; Jahresb. (1867) 79; Ann. Chem. u. Pharm. 141 (1867) 46.—See Schréder van der Kolk, Ann. Phys. u. Chem. 129 (1867) 495. . Debray (H.). Comptes rendus, 64 (1867) 603; Instit. (1867) 89; J. de Pharm. 5 (1867) 302; Jahresb. (1867) 85. 48 1867. 1863. 1870. . Peslin. Ann. chim. et phys. [4] 24 (1871) 208. LITERATURE OF THERMODYNAMICS. Gernez (D.). Phil. Mag. [4] 33 (1867) 479, abs. from Comptes rendus, Nov. 19, 1866. . Naumann (Alex.). Ann. Chem. u. Pharm. Suppthd. 5 (1867) 341 ; Jahresb. (1867) 84. . Pfaundler (L.). Ann. Phys. u. Chem. 131 (1867) 55; Z. f. Chem. (1867) 573; Jahresb. (1867) 81. . Schréder van der Kolk (H.). Ann. Phys. u. Chem. 129 (1867) 481; 131 (1867) 425; Arch. néerland. 1 (1866) 418; 2 (1867) ‘221; Jahresh. (1867) 80. Graham (T.). Phil. Mag. [4] 36 (1868) 63; Proc. Roy. Soc. June 11, 1868. Budde (E.). Ann. Phys. u. Chem. 141 (1870) 426; Jahresb. (1870) 113.—See Ann. Phys. u. Chem. 116 (1862) 1, and Clausius’s Abhandlungen, 1864, 1, 264. . Tichborne (C. R. C.). Rept. British Assoc. (1871) 81; Proe. Irish Acad. [2] 1 (1870-74) 169. . Berthelot et Louguinine. Comptes rendus, 75 (1872) 100. . Gladstone (J. H.) and Tribe (A.). Rept. Brit. Assoc. (1872) 75, abs. 3. Debray (H.). Comptes rendus, 77 (1873) 123; Jahresb. (1875) tile . Myers (J.). Ber. chem. Ges. 6 (1873) 11; Jahresb. (1873) 110; Chem. News, 27 (1873) 110. - Horstmann (A.). Ann. Chem. u. Pharm. 170 (1873) 192; Jahresb. (1873) 114. . Thomson (W.). Phil. Mag. [4] 4 (1873) 304; Jahresb. (1873) 114. 74. Mohr (F.). Ann. Chem. u. Pharm. 171 (1874) 361; Jahresb. (1874) 110. . Pfaundler (L.). Ann. Phys. u. Chem. Jubelbd. (1874) 182; J. prakt. Chem. [2] 10 (1874) 387; Chem. Centralbl. (1874) 248; Jahresb. (1874) 110.—See Jahresb. (1867) 81. 1877. APPLICATIONS—DISSOCIATION. 49 Berthelot. Comptes rendus, 85 (1877) 880; 96 (1883) 1186. . Hicks (W. M.). Phil. Mag. [5] 3 (1877) 401; 4 (1877) 80, 174. . Pareau (A. H.). Ann. Phys.u. Chem. n. F.1 (1877) 39; 2 (1877) 144. . Petri. Ann. Phys. u. Chem. n. F. 2 (1877) 304; Phil. Mag. [5] 4 (1877) 470, abs. . Tichborne (C.-R. C.). Proce. Irish Acad. [2] 2 (1875-77) 250. 78. Berthelot. Comptes rendus, 87 (1878) 619. . Debray (H.) et Deville (H. St.-C.). Comptes rendus, 86 (1878) 517; 87 (1878) 441; Phil. Mag. [5] 6 (1878) 394; Jahresb. (1878) 117. . Wiedemann (G.). Ann. Phys. u. Chem. n. F. 5 (1878) 45. . Lemoine (G.). Comptes rendus, 93 (1881) 265, 312; Jahresb. (1881) 1133. . Chroustchoff (P.). Comptes rendus, 95 (1882) 221. . Berthelot. Comptes rendus, 96 (1883) 1186. . Vogel (H. W.). Ber. d. Berliner Akad. (1882) 905; Phil. Mag. [5] 15 (1883) 28. . Wiedemann (E.). Ann. Phys. u. Chem. n. F. 18 (1883) 509. 5. Natanson (E. und L.). Ann. Phys. u. Chem. n. F. 24 (1885) 454. . Riidorff(F.). Ann. Phys. u. Chem. n. F. 25 (1885) 626. . Duhem (P.). Ber. chem. Ges. 19 (1886)) R. 592. . Ramsay (W.) and Young (S8.). Parts I and II, Phil. Trans. (1886) m Oe i23.) bar ebty Phil irans.) (1386) a1, lish Part LV, Trans. Chem. Soc. (1886) 790; Phil. Mag. [5] 23 (1887) 435; 24 (1887) 196. —. Phil. Mag. [5] 23 (1887) 129. . Arrhenius (Sv.). Z. phys. Chem. 1 (1887) 631. . Foussereau (J.). Ann. chim. et. phys. [7] 11 (1887) 553 G 50 LITERATURE OF THERMODYNAMICS 1887. Frowein (P. C. F.). Z. phys. Chem. 1 (1887) 5, 362. ——. Ramsay and Young. Phil. Mag. [5] 24 (1887) 196; Beiblatter, 12 (1887) 35, abs.; Z. phys. Chem. 1 (1887) 277, 433. 1888. Chatelier (H. Le). Z. phys. Chem. 2 (1888) 782. ——. Lescoeur (H.). Recherches sur la dissociation des hydrates salins et des composés analogues. Lille: L. Danel. 1888. 8vo. 158 pp. —. Ostwald (W.). Z. phys. Chem. 2 (1888) 270. ——. Planck (Max). Z. phys. Chem. 2 (1888) 343. —. Wiedemann (E.). Z. phys. Chem. 2 (1888) 241.—See Ostwald, same vol. 248. ELASTICITY. 1821. Laplace (M. de). Ann. chim. et. phys. 18 (1821) 181, 273; 21 (1822) 22. 18253. Thenard et Dulong. Ann. chim. et. phys. 24 (1825) 380. 1827. Ivory (J.). Phil. Mag. n.s. 1 (1827) 1. 1828. Prevost (P.). Ann. chim. et phys. 38 (1828) 41; Mem. de Genéve, 4 (1827) 1. 1829. Avogadro (A.). Mem. Accad. Torino, 33 (1829) 237. ——. Dulong. Ann. chim. et. phys. 45 (1830) 74, 88,110; Phil. Mag. . n. s. 7 (1830) 235; Le Globe, Dec. 9, 1829. f 1845. Wertheim (G.). Ann. chim. et phys. [5] 15 (1845) 114. 1848. Person. Comptes rendus, 27 (1848) 258. 1850. Dulong. Ann. chim. et phys. [2] 41 (1850) 113; Jahresb. (1850) 42. APPLICATIONS—ELASTICITY. Dil 1850. Rankine (W.J.M.). Phil. Mag. [4] 2 (1851) 509; Jahresb. (1851) 39; Rept. British Assoc. (1850) 1. 1851. Waterstone. Phil. Mag. [4] 2 (1851) 565; Jahresb. (1851) 44. 1852. Rankine (W. J. M.). Edinb. Trans. 20 (1852) 425. 1855. Magnus. Phil. Mag. [4] 9 (1855) 44. 1857. Joule (J. P.). Phil. Mag. [4] 14 (4857) 211. 1860. Regnault (V.). Phil. Mag. [4] 20 (1860) 275; Comptes rendus, June 11, 1860. 1861. Clausius(R.). Ann. Phys. u. Chem. 114 (1861) 57.—See E. Edlund, same vol. 15, 1862. Clebsch (A.). Theorie der Elasticitaét fester Korper. Leipzig, 1862. x1, 424 pp. gr. 8vo. 1865. Kuez. 4%. f. Math. u. Phys. (1865) 428. —. Potter. Phil. Mag. [4] 29 (1865) 98. —. Thalén (R.). Phil. Mag. [4] 80 (1865) 199; Aun. Phys. u. Chem. April, 1865. ‘ ——. Thomson (W.). Phil. Mag. [4] 30 (1865) 63; Proc. Roy. Soc. May 18, 1865. —. Rankine (W. J. M.). Phil. Mag. [4] 29 (1865) 283. 1870. Lorenz (L.). Phil. Mag. [4] 40 (1870) 390; Ann. Phys. u. Chem. no. 8, 1870. 1872. Saint-Loup (L.). Ann. chim. et phys. [4] 27 (1872) 211. 1875. Hirn (G. A.). Comptes rendus, 81 (1875) 72; 82 (1876) 52; Jahresb. (1876) 63. 1878. Roiti. Atti Accad. Lincei, [3] 2 (1877-8) 126. ——. Warburg (E.). Ann. Phys. u. Chem. n. F. 4 (1878) 232. 1882. Amagat (E. H.). Comptes rendus, 95 (1882) 281. 1886. Chree (C.). Phil. Mag. [5] 21 (1886) 81. 31. Mellom e Nobili. Ann. chim. et phys. 48 (1831) 198. LITERATURE OF THERMODYNAMICS. ELECTRICITY. See Provostaye, Ann. chim. et phys. [3] 54 (1858) 129. . Sturgeon (W.). Phil. Mag. n. s. 10 (1831) 1, 116; 3 (1833) 392. . Locke (J.). Phil. Mag. n. s. 21 (1837) 378. . Peltier. Ann. chim. et phys. 71 (1839) 225. . Joule (J. P.). Phil. Trans. (1840) 1; Proce. Roy. Soc. 4 (1837-43) 280, abs. ——. Manchester Phil. Soc. Mem. [2] 7 (1846) 87. . Kuppfer (A. F.). Bull. Acad. St. Petersburg, 7 (1849) 289; Jahresb. (1849) 53. . Joule (J. P.). Phil. Mag. [3] 23 (1851) 263, 347, 435; Ann. chim. et phys. [3] 35 (1851) 118, abs.; Jahresb. (1851) 32, abs. . Thomson (W.). Phil. Mag. [4] 2 (1851) 429, 551. . Clausius (R.). Ann. Phys. u. Chem. 86 (1852) 337; 87 (1852) 415; C’s Abhandlungen, 11, 98; Ann. chim. et phys. [3] 38 (1853) 200; Ber. d. Berliner Akad. (1852) 278; Instit. (1852) 289; Jahresb. (1852) 39. —. Ann. Phys. u. Chem. 87 (1852) 415; C.’s Abhand- lungen, 11, 164; Ann chim. et phys. [8] 42 (1854) 122. - Joule (J. P.). Ann. chim. et phys. [3] 34 (1852) 504. . Magnus. Ann. chim. et phys. [8] 34 (1852) 105. . Thomson (W.). Rept. British Assoc. (1852) 1, 16. —. Phil. Mag. [4] 3 (1852) 529; Phil. Trans. 146 (1856) 649; Ann. chim. et phys. [3] 54 (1858) 105. . Rankine (W. J. M.). Edinb. Trans. (1852) 425. 1853. Clausius (R.). Ann. Phys. u. Chem. 90 (1853) 513 ; C’s Abhand- lungen, 11, 175. . Favre (P. A.). Comptes rendus, 36 (1853) 342; 39 (1854) 1212; 45 (1857) 56. a — — i 1853. 1854. 1855. 1856. 1857. 1859. 1862. 1864. 1865. 1867. 1867. APPLICATIONS—ELECTRICITY. 53 Riess (P. T.). [Book.] Frictional Electricity. Berlin, 1853. 2 vols.—See Phil. Mag. [4] 9 (1855) 150. Thomson (W.). Phil. Mag. [4] 7 (1854) 347 ; Quar. J. Mathemat. 1 (1855) 57. Rankine (W. J. M.). Phil. Mag. [4] 10 (1855) 354, 411. Baumgartner (G.). Ber. d. Wiener Akad. 22 (1856) 513. Bosseha. Ann. Phys. u. Chem. 101 (1857) 517; 102 (1857) 487; Ann. chim. et phys. [8] 65 (1862) 367. . Clausius (R.). Aun. Phys. u. Chem. 101 (1857) 338; Ann. chim. et phys. [8] 53 (1858) 252; C.’s Abhandlungen, 1,202; Arch. de Genéve, 86 (1857) 119. . Icilius (Quintus). Ann. Phys. u. Chem. 101 (1857) 73 ; Comptes rendus, 45 (1857) 420. . Joule (J. P.). Proc. Roy. Soc. 8 (1857) 300. . Thomson (W.). Edinb. Trans. 21 (1857) 123. . Buys-Ballot. Ann. Phys. u. Chem. 103 (1858) 240. . Marié-Davy et Troost. Comptes rendus, 46 (1858) 748; Ann. * chim. et phys. [8] 53 (1858) 423. Bosscha. Ann. Phys. u. Chem. 108 (1859) 162. Marié-Davy. Comptes rendus, 54 (1862) 1103. Edlund (E.). Ann. Phys. u. Chem. 123 (1864) 193; Oefversigt af Forhandl. Stockholm, (1864) 77; Phil. Mag. [4] 31 (1866) 253. . Mauritius (M.). Ann. Phys. u. Chem. Noy. 1863; Phil. Mag. [4] 27 (1864) 398. . Raoult (F. M.). Ann. chim. et phys. [4] 2 (1864) 317; 4 (1865) 392. Lindig-(F.). Ann. Phys. u. Chem. Sept. 1864; Phil. Mag. [4] 29 (1865) 408, abs. Gerlach. Ann. Phys. u. Chem. 131 (1867) 480; Phil. Mag. [4] 34 (1867) 382. Joule (J. P.). Rept. British Assoc. (1867) 512. 1869. 1870. 1371. 1879. LITERATURE OF THERMODYNAMICS, Edlund (E.). Phil. Mag. [4] 38 (1869) 263, abs. from Oefversigt af Forhandl. Stockholm, April 14, 1869. Bleekrode (L.). Phil. Mag. [4] 40 (1870) 310, abs. from Ann. Phys. u. Chem. 138 (1870) 571; Ann. chim. et phys. April, 1870. Siemens (C. W.). Phil. Mag. [4] 42 (1871) 150; Proc. Roy. Soe. April 27, 1871. . Edlund (E.). Phil. Mag. [4] 44 1872) 81, 174; Mem. Stockholm Acad. May 10, 1871. . Branly (E.). Comptes rendes, 77 (1873) 1420. . Kohlrausch (F.). Ann. Phys. u. Chem. 149 (1875) 185.—See Réntgen, same vol. 579; and Ann. Phys. u. Chem. 136 (1869) 618, and 149 (1873) 589; also Clausius, Do. 160 (1877) 429. 76. Edlund (E.). Ann. Phys. u. Chem. 159 (1876) 420; Phil. Mag. [5] 3 (4877) 428, 501. . Lippmann (G.). Comptes rendus, 82 (1876) 1425. . Lodge (O. J.). Phil. Mag. [5] 2 (1876) 524.—See Note by Avenarius, Phil. Mag. [5] 3 1877) 156. Lodge’s reply, 349. 7. Clausius (R.). Ann. Phys. u. Chem. 160. (1877) 420. . Guignet. Comptes rendus, 84 (1877) 1084. . Helmholtz (H. v.). Phil. Mag. [5] 5 (1878) 548; Monatsber. d. Berliner. Akad. (1877) 715. . Moser (J.).. Naturforsch. Versammlung in Miinchen, Sept. 1877 ; Ber. d. Berliner Akad. 8. Nov. 1877; Ann. Phys. u. Chem. n. F. 3 (1878) 216. . Wiedemann (G.).. Ann. Phys. u. Chem. 145 (1872) 235, 364; 158 (1876) 35; Phil. Mag. [5] 3 (1877) 161. Cohn (E.). Ann. Phys. u. Chem. n. F. 6 (1879) 385. . Duter. Comptes rendus, 88 (1879) 1260. . Moutier (J.). Bull. Soe. philom. [7] 3 (1879) 88. . Righi. Comptes rendus, 88 (1879) 1262. } 3 ; A . | 1880. 1881. 1887. 1888. 1889. APPLICATIONS—-ELECTRICITY. 5D Fletcher (L. S.). Phil. Mag. [5] 10 (1880) 436. Hoorweg (J. L.). Ann. Phys. u. Chem. n. F. 12 (1881) 75. . Wright (C. A.). Phil. Mag. [5] 11 (1881) 169. . Budde (E.). Ann. Phys. u. Chem. n. F. 15 (1882) 558; n. F. 21 (1884) 277; n. F. 25 (1885) 564. | Wassmuth (A.). Ber. d. Wiener Akad. 85 11 (1882) 997; 86 11 (1882) 539; 87 1 (1883) 82. . Edlund (E.). Ann. Phys. u. Chem. n. F. 19 (1883) 287. . Jahn (H.). [Book.] Die Elektrolyse. Wien, 1883. 206 pp. . Clausius (R.). Ann. Phys. u. Chem. n. F. 21 (1884) 385. . Czapski (S.). Ann. Phys. u. Chem. n. F. 21 (1884) 209. . Duhem (P.). Comptes rendus, 99 (1884) 1113. . Lippmann (G.). Comptes rendus, 99 (1884) 895. . Fletcher (L.8.). Phil. Mag. [5] 20 (1885) 1. . Lodge (O. J.). Phil. Mag. [5] 19 (1885) 448. . Rayleigh (Lord). Phil. Mag. [5] 20 (1885) 361; Nature, 32 (1885) 556. . Case (W. E.). Proc. Roy. Soc. 40 (18386) 345. . Cross (C. R.). Proc. Amer. Acad. n. s. 13 (1885-86) 257. . Roiti (A.). Mem. Accad. Torino, [2] 87 (1886) 367. Krebs (G.). Z. phys. u. chem. Unterricht, 1 (1887) 118. Battelli (A.). Nuova Cimento, [3] 23 (1888) 64. . Duhem (P.). Théorie de l’aimentation par influence fondée sur Ja thermodynamique. Paris, 1888. 4to. 140 pp. . Gouy. Comptes rendus, 107 (1888) 329; Beiblatter, 13 (1889) 44, abs. Chroustschoff (P.). Comptes rendus, 108 (1889) 1003. 1854. 1859. 1863. Loe LITERATURE OF THERMODYNAMICS. ENERGY. . Thomson (W.). Phil. Mag. [4] 5 (1853) 102; Jahresb. (1853) 46 ; Instit. (1855) 202. Clausius (R.). Ann. Phys. u. Chem. 91 (1854) 601. Rankine (W. J. M.). Phil. Mag. [4] 17 (1859) 250, 347. Airy (G. B.). Phil. Mag. [4] 26 (1863) 329. . Kelland. Phil. Mag. [4] 26 (1863) 326. . Rankine (W. J. M.). Phil. Mag. [4] 26 (1863) 388, 436. . Tait (P.G.). Phil. Mag. [4] 25 (1863, 429; 26 (1863) 144. 1865. 1866. Bohn (Prof.). Phil. Mag. [4] 29 (1865) 215. Clausius (R.). Phil. Mag. [4] 32 (1865) 1; Z. f. Mathemat. 11 1 (1866) 31. Odling (W.). Chem. News, 23 (1871) 245, 256; Ber. chem. Ges. 4 (1871) 421, abs.; Jahresb. (1871) 61, abs. 2. Rankine (W. J. M.). Phil. Mag. [4] 43 (1872) 160. . Moon (W. R.). Phil. Mag. [4] 46 (1873) 219; 47 (1874) 291. . Rigg (A.). Chem. News, 28 (1873) 5, 15, 28, 54, 67, 78, 92, 104, 119, 139, 1538, 176, 190, 199, 223, 236, 273, 284, 309, 319, 392; 29 (1874) 3; Jahresb. (1873) 51, abs. ; Do. (1874) 59, abs. . Clausius (R.). Comptes rendus, 87 (1878) 718. . Lodge (0. J.). Phil. Mag. [5] 8 (1879) 277; Jahresb. (1879) 89. . Trowbridge (J.). Proc. Amer. Acad. n. s. 7 (1879-80) 235. . Boltzmann (L.). Ann. Phys. u. Chem. [2] 11 (1880) 529; Jahresb. (1880) 82; Phil. Mag. [5] 14 (1882) 299. . Meyer (O. E.). Ann. Phys. u.Chem. n. F. 10 (1880) 296; Jahresb. (1880) 82, abs. . Browne (W. R.). Jour. Phys. Soc. Nov. 11, 1882; Phil. Mag. [5] 15 (1883) 35.—See note by Tunzelmann, same vol. 152 Browne’s reply, same vol. 228. Tunzelmann’s answer, 299. . Burbury (S. H.). Phil. Mag. [5] 13 (1882) 417. 18853. 1886. 1887. . Helm (G.). Die Lehre von der Energie. Leipzig, 1887. 8vo. 1807. 1821. 1824. APPLICATIONS—ENGINES. 57 Abney (W. de W.) and Festing. Phil. Mag. [5] 16 (1883) 224. Siemens (W.). Phil. Mag. [5] 21 (1886) 453; Ber. d. Berliner Akad. 4. Marz, 1886. Dufet (H.). Soc. frane. de phys. (1887) 117. Beiblatter, 12 (1888) 407, abs. . Larmor (J.). Proce. Phil. Soc. Cambridge, 6 m (1887) 95. . Michelson (M. W.). J. de Phys. 6 (1887) 467; Phil. Mag. [5] 25 (1888) 425. . Tilly (J. M. de). Bull. Acad. Belg. 14 (1887) 975. . Forkas (J.). Z. phys. Chem. 2 (1888) 148. . Langley (S. P.). Amer. J. Sci. [3] 36 (1888) 359. . Michelson (W.). Phil. Mag. [5] 25 (1888) 425. . Planck (Max). Erhaltung der Energie. Leipzig, 1887. 8vo. Beiblitter, 12 (1888) 134. . Langley (S. P.). Phil. Mag. [5] 27 (1889) 1. ENGINES. (CALORIC AND OTHER.) Cayley (Sir G.). Nicholson’s Jour. 18 (1807) 260. Prosny (M. de). Ann. chim. et phys. 19 (1821) 165. Carnot. Puissance motrice du feu. Paris, 1824. 8vo. Jahresb. (1850) 37. . Séguin (B. R.). Influence des chemins de fer. Paris, 1839. 8vo. . Regnault (V.). Principales lois physiques des machines 4 vapeur. Paris, 1847. 8vo. Jahresb. (1847) 87. . Thomson (W.). Phil. Mag. [8] 387 (1850) 386. 51. Joule (J. P.). Phil. Mag. [4] 2 (1851) 150; Instit. (1852) 15. 38 1851. LITERATURE OF THERMODYNAMICS. Rankine (W. J. M.). Edinb. Trans. (1851) 235. . Reech. Machine ad air. Paris, 1851. 8vo. . Thomson (W.). Phil. Mag. [4] 1 (1851) 474. Reply by Clausius, Phil. Mag. [4] 2 (1851) 159. Thomson’s second note, same vol. 273. 2. Rankine (W. J. M.). Rept. British Assoc. (1852) m1, 128. . Thomson (W.). Phil. Trans. (1852) 78. . Vaux (De). Bull. Acad. Belg. 19 111 (1852) 296. . Aitkin. Cosmos, 2 (1853) 395. . Barnard (F. A. P.). Amer. J. Sci. [2] 16 (1853) 218, 232, 292, 351, 431; 17 (1858) 153. . Belleville. Cosmos, 2 (1855) 268. . Cazalat (Galy-). Bull. Soe. (encour, (1853) 44—See Franchot, Comptes rendus, 36 (1853) 395. . Cazavan. Cosmos, 3 (1853) 342. . Cheverton. Mech. Mag. 58 (1853) 148, 170. . Gebauer. Jahresb. d. schlesischen Ges. zu Breslau, (1853) 310. . Fréchin. Instit. (1853) 248. . Lemoine. Instit. (1855) 88, 107; Comptes rendus, 36 (1853) 263. . Liais. Comptes rendus, 36 (1853) 260; 37 (1853) 999. . Lissignol. Arch. des sci. phys. 24 (1853) 209. . Moser. Polytechn. Centralbl. (1853) 1220. . Nicklés. Amer. J. Sci. [2] 15 (1853) 418. . Norton. Amer. J. Sci. [2] 15 (1853) 393. . Poppe. Dingler’s Jour. 127 (1853) 401. . Rankine (W. J. M.). Edinb. Trans. (1853) 195, 205. . Redtenbacher. Dingler’s Jour. 128 (1853) 86. . Reech. Comptes rendus, 36 (1853) 526; Bull. Soe. encour. (1853) 204. . Sehlen. Dingler’s pol. Jour. 127 (1853) 245. APPLICATIONS—ENGINES. 59 53. Tremblay (Du). Ann. des Mines, [5] 4 (4855) 219. —. Ann. des Mines, [5] 4 (1853) 203, 281. . Wilson. Mech. Mag. 58 (1853) 564. . Barnard (F. A. P.). Amer. J. Sci. [2] 18 (1854) 161. . Ericsson. Polytechn. Centralbl. (1854) 183. . Ewbank. Mech. Mag. 61 (1854) 411; 62 (1854) 78. . Franchot. Comptes rendus, 58 (1854) 151. . Liais. Mem. Soc. Cherbourg, 2 (1854) 113. . Napier and Rankine. Repertory of Patent Inventions, [2] 23 (1854) 886. . Poole. Repertory of Patent Inventions, [2] 24 (1854) 506. . Rankine (W. J. M.). Phil. Trans. (1854) 115; Proe. Roy. Soe. 6 (1850-54) 388, abs. ———. Edinburgh Jour. [2] 1 (1854) 1. . Shaw. Mech. Mag. 61 (1854) 97. , . Wrede. Mech. Mag. 60 (1854) 65. 59. Hirn (G. A.). Cosmos, 6 (1855) 679; 7 (1855 85 ) 455; Bull. de ) ) Mulhouse, (1855) nos. 128, 129; Jahresb. (1855) 29. . Napier and Rankine. Mechanics’ Mag. no. 1628; Dingler’s Jour. 135 (1855) 241; Jahresb. (1855) 30. . Newton (A). Repertory of Patent Inventions, [2] 26 (1855) 120. . Seguin. Comptes rendus, 40 (1855) 5.—See Siemens, same vol. 309. . Cheverton. Mech. Mag. 64 (1856) 82. . Clausius (R.). Ann. Phys. u. Chem. 97 (1856) 441, 513; C.’s Abhandlungen, 1, 155; Phil. Mag. [4] 12 (1856) 241,338, 426 ; Amer. J. Sci. [2] 22 (1856) 180, 364; 23 (1856) 28.—See Joule, Phil. Mag. [4] 12 (1856) 385. C.’s reply, same vol. 463. . Ericsson. Mech. Mag. 64 (1856) 1, 487. . Joule (J. P.). Phil. Mag. [4] 12 (1856) 385. . Pascal. Mech. Mag. 64 (1856) 241. 60 LITERATURE OF THERMODYNAMICS. 1856. Ramsbottom. Mech. Mag. 64 (1856) 110. ——. Siemens. Mech. Mag. 65 (1856) 55, 79. 1857. Bourget et Burdin. Comptes rendus, 45 (1857) 742, 1069. 1859. Rankine (W.J.M.). Phil. Mag. [4] 18 (1859) 71; 19 (1860) 460; Proc. Roy. Soe. 9 (1859) 626; 10 (1859) 183; Phil. Trans. 149 (1860) 177, 748. 1864. Caligny. Imnstit. (1864) 30. ——. Cazin. Mondes, 5 (1864) 220. Paris, 1864. 8vo. ——. Rankine (W. J. M.). Phil. Mag. [4] 28 (1864) 282.—See R. in Phil. Mag. Oct. 1863, and [4] 29 (1865) 25. 1865. Zeuner. Grundziige der mechanischen Warmelehre mit Anwen- dungen auf der Maschinenlehre. Leipzig, 1865. 8vo. 1869. Combes (C.). Application de la théorie mécanique de la chaleur aux machines locomotives. Paris, 1869. 8vo. 1872. Oettingen (A. J. v.). Ann. Phys. u. Chem. Erghd. 5 (1872) 540; Jahresb. (1875) 46. 1875. Hirsch. Comptes rendus, 80 (1875) 922. ——. Ledieu (A.). Comptes rendus, 80 (1875) 1040, 1199, 1278; 81 (1875) 711, 773, 928, 1023. 1876. Bourget (J.). Ann. de l’Ecole norm. [2] 5 (1876) 111. ——. Mac Culloch (R.). Mechanical Theory of Heat and its Applica- tions to the Steam Engine. New York, 1876. 8vo. ——. Résal (H.). Comptes rendus, 82 (1876) 537, 599, 647. 1878. Ledieu (A.). Comptes rendus, 87 (1878) 905, 952, 1024, 1062. ——. Weisbach (P. J.). Manual of the Construction of Machines. New York, 1878. 8vo. 1879. Herrmann (Emil). Mechanische Warmetheorie. Berlin, 1879. 8vo. Mit besonderer Riicksicht auf der Maschinentechnik. 1881. Ledieu (A.). Comptes rendus, 93 (1881) 25. —. Etude thermodynamique expérimentale sur les ma- chines 4 vapeur. Paris, 1881. 8vo. 96 pp. 1883. Charpentier (P.). Comptes rendus, 96 (1883) 782. ; ae APPLICATIONS—EQUATIONS. 61 1883. Hirn (G. A.). Comptes rendus, 96 (1883) 561, 413. ——. Witz (A.). Comptes rendus, 96 (1883) 1310; 97 (1883) 523. 1884. Charpentier (P.). Comptes rendus, 98 (1884) 1262. 1887. Pictet (R.). Nature, 87 (1887) 167. ——. Anderson (W.). Practical Treatise on Heat Engines. London, 1887. 8vo. Beiblatter, 12 (1888) 4066. 1888. Roéntgen (R.). Principles of Thermodynamics, with special appli- cations to hot-air, gas and steam-engines. 2. edition, translated and enlarged by A. Jay Du Bois. New York, 1888. 8vo. 703 pp. ENTROPY. 1866. Clausius (R.). Z. Math. u. oe 111 (1866) 31; Phil. Mag. [4] 32 (1866) 1. EQUATIONS. 1856. Reech. Jour. des mathémat. 21 (1856) 58. 1861. Marié-Davy et Troost. Comptes rendus, 53 (1861) 904. 1862. Baumgartner (G.). Z. f. Math. u. Phys. (1862) 127. ——. Kahl. Z. f. Math. u. Phys. (1862) 127. 1863. Boole. (G.). Phil. Trans. 153 (1863) 485. —. Clausius (R.). Comptes rendus, 57 (1863) 339; Mondes, 6 (1864) 687, réponse 4 M. Dupré. 1864. Dupré. Comptes rendus, 58 (1864) 539; 59 (1864) 490, 665, 705, 768. 1865. 1856. 1869. 1875. 1874. . Ledieu (A.). Comptes rendus, 78 (1874) 221, 309; 537. 1876. 1882. 1884, 1885. 1886. LITERATURE OF THERMODYNAMICS. Clausius (R.). Ann. Phys, u. Chem. 125 (1865) 353; C.’s Abhand- lungen, 11,1; J. de Liouville, [2] 10 (1865) 361. Bauschinger (L.). Z. f. Math. u. Phys. (1866) 152, 180.—See Clausius, same vol. 455. Reech. Comptes rendus, 69 (1869) 913. Clausius (R.). Phil. Mag: [4] 42 (1871) 321. —. Comptes rendus, 78 (1874) 461. Lippmann (G.). Comptes rendus, 82 (1876) 1425. Cantoni e Gerosa. Atti Accad. Lincei, 3 (1882) 16; Ann. Phys. u. Chem. Beibliatter, 7 (1883) 242; Jahresb. (1883) 112. . Lippmann (G.). Comptes rendus, 95 (1882) 1058. 1883. Planck (Max), Ann. Phys. u. Chem. n. F. 19 (1883) 358 ; Jahresb. (1883) 111. Ledieu (A.). Comptes rendus, 98 (1884) 69. Fletcher (L. 8.). Phil. Mag. [5] 20 (1885) 1. Webb (J. B.). Proc. Amer. Assoc. 35 (1886) 107. EVAPORATION. . Moutier (J.). Instit. (1876) 76, 84, 165; Jahresb. (1876) 64; Bull. Soc. philomat. [6] 13 (1876) 5, 11, 49. . Moutier (J.). Bull. Soe. philomat. [7] 1 (1877) 17; 4 (1880) 247. . Planck (Max). Ann. Phys. u. Chem. n. F. 15 (1882) 446. . Ramsay (W.) and Young (S8.). Phil. Mag. [5] 24 (1887) 196; Beiblatter, 12 (1887) 55, abs.; Z. phys. Chem. 1 (1887) 277, 438. . Fuchs (K.). Repert. d. Physik, 24 (1888) 141. 1799. 1802. S17. . Gay-Lussac. Ann. chim. et phys. 1 (1817) 108; 2 (1817) 130. 1842. . Regnault (V.). Ann. chim. et phys. [8] 4 (1842) 5, 64; 5 (1842) 1844. 1847. 1849. APPLICATIONS—EXPANSION. 63 EXPANSION. Rittenhouse (D.). Trans. Amer. Phil. Soc. 4 (1799) 29. Gay-Lussac. Ann. de Chimie, 43 (1802) 187. Dulong et Petit. Ann. chim. et phys. 2 (1817) 240. . Gay-Lussac et Dalton. Ann. chim. et phys. 1 (1817) 110. 9. Petit. Ann. chim. et phys. 9 (1819) 196.—See Pattu, same vol. 91. . Walter, et Gay-Lussac. Ann. chim. et phys. 19 (1821) 486; Institut, 29 avril, 1822. 23. Biggs (M.). Thomson’s Annals of Phil. n. s. 6 (1823) 415; 7 (1824) 133. _ Crichton. Annals of Phil. n.s. 7 (1824) 241. . Emmett (J. B.). Annals of Phil. n. s. 8 (1824) 254. ee Phil iMag. in) &: 59829) :419: . Erman (G. A.). Ann. chim. et phys. 40 (1829) 197. . Ewart (P.). Phil. Mag. n. s. 5 (1829) 247. . Meikle (H.). Phil. Mag. n. s. 11 (1832) 243. Magnus. Ann. chim. et. phys. [3] 4 (1842) 316. 52. Joule (J. P.). Proe. Roy. Soe. 5 (1843-50) 517, abs.; Phil. Trans. (1844) 1; Phil. Mag. [8] 25.(1844) 1; 26 (1845) 369. Pierre (J. I.). Ann. chim. et phys. [3] 19 (1847) 193; 20 (1847) 5; 21 (1847) 3363 31 (1851) 118; 33 (1851) 199. Regnault (V.). Ann. chim. et phys. [5] 26 (1849) 257 ; Comptes rendus, 28 (1849) 325; Instit. (1849) 90; Ann. Phys. u. Chem. 77 (1849) 99; J. prakt. Chem. 47 (1849) 188; Jahresb. (1849) 29. . Berthelot (M.). Ann. chim. et phys. [3] 30 (1850) 232. 1857. 1853. 1860, -—— LITERATURE OF THERMODYNAMICS. . Clausius (R.). Ann. Phys. u. Chem, 82 (1851) 263; C.’s Abhand- lungen, 1, 103; Ann. chim. et phys. [3] 37 (1853) 368; Phil. Mag. [4] 1 (1851) 398; Jahresb. (1851) 26. . Smyth (C. P.). Edinburgh Jour. 51 (1851) 114. 52. Kopp (H.). Phil. Mag. [4] 3 (1852) 268, abs. from Ann. Chem. u. Pharm. 81 (1852) 1; Ann. chim. et phys. [3] 34 (1852) 338. . Koosen. Ann. Phys. u. Chem. 89 (1853) 457; Jahresb. (1853) 37. . Rankine (W. J. M.). Phil. Mag. [4] 8 (1854) 357. ——w—. Phil. Trans. (1854) 115; Proc. Roy. Soc. 6 (1850-54) 388, abs. Joule (J. P.). Proc. Roy. Soc. 9 (1857) 3. ——. Phil. Mag. [4] 16 (1858) 54. . Kirchhoff (G.). Ann. Phys. u. Chem. 104 (1858) 1. 1859. Andréeff (E. da’). Ann. chim. et phys. [3] 56 (1859) 317. . Drion (Ch.). Ann. chim. et phys. [8] 56 (1859) 5. Calvert (F. C.) and Lowe (G. C.). Phil. Mag. [4] 20 (1860) 2380; Proc. Roy. Soc. Feb. 16, 1860. . Joule (J. P.). Manchester Soc. Mem. [2] 15 (1860) 143. . Clausius (R.). Ann. Phys. u, Chem. 114 (1861) 387.—See E. Edlund, same vol. 13. . Mendelejetf, Phil. Mag. [4] 22 (1861) 520; Liebig’s Ann. July, 1861. . Fairbairn (W.). Phil. Trans. 152 (1862) 591. . Reye (Th.). Ann. Phys. u. Chem. 116 (1862) 424, 449. . Clausius (R.). Comptes rendus, 56 (1863) 1115. . Potter. Phil. Mag. [4] 26 (1863) 347. . Reech. Comptes rendus, 57 (1863) 505. Notede M. Dupré, méme vol. 589. Réponse de M. R. 634. . Waterston (J. J.). Phil. Mag. [4] 26 (1863) 116; 27 (1864) 348. 1864. ——— . Fizeau. Ann. chim. et phys. [4] 2 (1864) 143. Potter. Phil. Mag. [4] 28 (1864) 271. APPLICATIONS—EXPANSION. 65 5. Matthiessen (A.). Proc. Roy. Soc. Dec. 21, 1865, June 21, 1866 ; Phil. Mag. [4] 31 (1866) 149, 472, abs.; Phil. Trans. (1865) 231, 861. . Cazin (A.). Comptes rendus, Jan. 2, 1866; Phil. Mag. [4] 31 (1866) 163. Reply by Rankine, same vol. 197. . Fizeau (H.). Ann. chim. et phys. [4] 8 (1865) 335. . Hirn (G. A.) et Cazin(A.). Comptes rendus, Dee. 31, 1866; Phil. Mag. [4] 33 (1867) 236, abs. . Cazin (A.), Comptes rendus, June 8, 1868; Phil. Mag. [4] 36 (1868) 238. . Fizeau (H.). Phil. Mag. [4] 36 (1868) 31, transl. from Comptes rendus, 66 (1868) 1005, 1072; Ann. Phys. u. Chem. 135 (1868) 372; Jahresb. (1868) 48. . Cazin (A.). Comptes rendus, Aug. 9, 1869; Phil. Mag. [4] 38 (1869) 322. . Moutier (J.). Comptes rendus, 68 (1869) 95; Phil. Mag. [4] 38 (1869) 76, abs. . Regnault (V.). Comptes rendus, Oct. 11, 1869; Phil. Mag. [4] 39 (1870) 127. . Phillips. Comptes rendus, 71 (1870) 355; Jahresb. (1870) 111. . Marignac (C.). Arch. des Sci. ph. nat. Nov. 1870; Phil. Mag. [4] 41 (1871) 134. . Govi. Atti Accad. Torino, 6 (1870-71) 122, 1953. . Amagat (E. H.). Comptes rendus, 74 (1872) 1299. . Buff (H.). Ann. Phys. u. Chem. 145 (1872) 627; Phil. Mag. [4] 44 (1872) 544. . Dahlander (G. R.). Ann. Phys. u. Chem. 145 (1872) 147 ; Jahresb. (1872) 59. . Amagat (E. H.). Ann. chim. et phys. [4] 29 (1878) 246. . Résal (H.). Comptes rendus, 75 (1872) 1475; Phil. Mag. [4] 45 (1873) 77. . Herwig (H.). Ann. Phys. u. Chem. 147 (1873) 161; Phil. Mag. [4] 45 (1873) 401. 1874. 1875. 1876. 1878. 1879. 1880. 1881. . Volkmann (P.). Ann. Phys. u. Chem. n. F. 14 (1881) 260. 1882. . Moutier (J.). Bull. Soc. philom. [7] 4 (1882) 182. 1884. . Charpentier (P.). Comptes rendus, 98 (1884) 85, 425 LITERATURE OF THERMODYNAMICS. 3. Kurz(A.). Ann. Phys. u. Chem. Ergiinzbd.6 (1873) 314; Jahresb. (1878) 55. - Kohlrausch (F.). Ann. Phys. u. Chem. No. 8, 1873; Phil. Mag. [4] 47 (1874) 156. Recknagel (G.). Ann. Phys. u. Chem. Erginzbd. 6 (1874) 278. . Willner (A.). Ann. Phys. u. Chem. 153 (1874) 440. . Mallet (R.). Phil. Mag. [4] 49 (1875) 231; Proc. Roy. Soc. June 11, 1874. Marsh (B. V.). Proc. Amer. Phil. Soc. 14 (1874-75) 114. Clarke (F. W.). Smithsonian Miscell. Coll. 14 (1878) 58. Ledieu (A.). Comptes rendus, 82 (1876) 132 et 192. . St. Venant (M. de). Comptes rendus, 82 (1876) 33. . Thorpe (T. E.) and Riicker (A. W.). Proc. Roy. Soc. 24 (1876) 159; Phil. Trans. 166 (1876) 405. . Glatzel (P.). Ann. Phys. u. Chem. 160 (1877) 497. . Hirn (G. A.). Comptes rendus, 84 (1877) 592, 632, 680. . Winkelmann (A.). Ann. Phys. u. Chem. n. F. 1 (1877) 480; Jahresb. (1877) 58. Boltzmann (L.). Comptes rendus, 87 (1878) 593. Réponse de M. Lévy, méme vol. 649. Nouvelles remarques de M. Boltzmann, méme vol., 676, 773. Clausius, méme vol. 718; Massieu, méme vol. 731; St. Venant, Do. 713; Jahresb. (1878) 69. Pictet (R.). Comptes rendus, 88 (1879) 1315. Nichols (E. H.) and Wheeler (A. W.). Proc. Amer. Assoc. Aug. 28, 1880; Phil. Mag. [5] 11 (1881) 113. Korteweg (D. J.). Ann. Phys. u. Chem. n. F. 12 (1881) 186. . Hovenden (F.). South London Microscop. Club, Dee. 1882, p. 1. Bartoli. Atti Accad. Lincei, [3] 19 (1883-84) 577. 1797. . Lucas le jeune. Aun. de chimie, 23 (1797) 81. - Rumford (Count). Nicholson’s Jour. 1 (1797) 459, 515. = APPLICATIONS—-EXPLOSIVES. 67 . Pagliani (S.). Atti Accad. Torino, 20 (1884-85) 54. . . Wiedemann (E.) und Ludeking (Ch.). Ann. Phys. u. Chem. No. 6, 1885; Phil. Mag. [5] 20 (1885) 220. . Wroblewski (S. v.). Comptes rendus, 100 (1885) 979; Jahresb. (1885) 141. . Ayrton (W. E.) and Perry (J.). Phil. Mag. [5] 22 (1886) 325, read before the Physical Soe. March 27, 1886. . Langlois (M.). Comptes rendus, 102 (1886) 1231. . Lucas (F.). Comptes rendus, 103 (1886) 1251. . Thorpe (T. E.) and Riicker (A. W.). Phil. Mag. [5] 21 (1886) 451, read before the Physical Soc. April 10, 1886. . Andrews (Th.). Proce. Roy. Soe. 43 (1887) 299, 305, 308. . Duda (Th.). Ber. d. Gymnasium zu Brieg, 1886-87, p. 1. . Nicol (CW. W. J.). Phil. Mag. [5] 23 (1887) 385. . Vicentini (G.) e Omodei (D.). Atti Accad. Torino, 23 (1887) 8. . Antoine (Ch.). Comptes rendus, 106 (1888) 116. . Craur (C.). Electrotechn. Zeitschr. 9 (1888) 426. : . Le Chatelier (H.). Comptes rendus, 107 (1888) 862. . Puschl (C.). Wiener Anzeiger, (1888) 43. . Vicentini (G.) e Omodei (D.). Rend. Accad. Roma, 4 (1888) 805; 5 (1888) 18, 39, 75. . Pionchon. Comptes rendus, 108 (1889) 992. EXPLOSIVES. Goettling. Ann. de chimie, 23 (1797) 75. ® 68 1799." 1800. 1803. 1804. 1805. 1806. 1813. Lhe. 1819. 1847. . Draper. Phil. Mag. [3] 30 (1847) 299. . Porrett (R.) and Teschemacher (E. F.). Phil. Mag. [3] 30 (1847) LITERATURE OF THERMODYNAMICS. Brugnatelli. Ann. de chimie, 29 (1799) 327. Howard (E.). Nicholson’s Jour. 4 (1800) 173, 200, 249; Phi Trans. (1800) 204. Accum (F.). Nicholson’s Jour. 6 (1803) 1. . Robert. Ann. de chimie, 44 (1803) 521. Bartholdi. Ann. de chimie, 48 (1804) 249. . Veau de Launay. Nicholson’s Jour. 9 (1804) 203. Laugier (A.). Ann. de chimie, 55 (1805) 503; 56 (1806) 13:. Wollaston (W. H.). Nicholson’s\ Jour. 15 (1806) 3L; Phil. Trans. (1806) 1; Proce. Roy. Soc. Nov. 1805. . Guyton-Morveau et Carnot. Ann. de chimie, 71 (1809) 70; 74 (1810) 18. . Sage (B.G.). Nicholson’s Jour. 23 (1809) 279, from Jour. de phys. 65 (1809) 425. Thenard et Berthelot. Ann. de chime, 86 (1813) 37. Clarke (E. D.). Thomson’s Annals of Phil. (1817) 1; Ann. chim. et phys. 3 (1817) 39; 5 (1817) 441. Gibbs (G.). Amer. J. Sci. 1 (1819) 87; Ann. chim. et phys. 10 (1819) 332. . Comité des Poudres ete. Ann. chim. et phys. 23 (1825) 217. . Haycraft (W. T.). Annals of Phil. n. s. 8 (1824) 245. . Magnus (G.). Ann. chim. et phys. 39 (1825) 103; Annals of Phil. n. s. 12 (1826) 464, abs. . Baudrimont (A.). Ann. chim. et phys. 61 (1836) 319; 62 (1836) 907 Boa. Crum (W.). Phil. Mag. [3] 30 (1847) 426. 208, 273. ' . Schoenbein. Phil. Mag. [3] 31 (1847) 7. . Ransome (T.). Phil. Mag. [3] 30 (1847) 1. 1849. 1855. 1859. 1861. 1862. 1863. 1867. 1869. 1870. . Hagenbach (E.). Ann. Phys. u. Chem. 140 (1870) 486 ; 143 (1871) 1873. 1874. 1875. APPLICATIONS—EXPLOSIVES. ' 69 Hare. Phil. Mag. [3] 34 (1849) 227; 37 (1850) 525. Ashby (J. E.). Phil. Mag. [4] 6 (1853) 77. Thomas (L.). Phil. Mag. [4] 17 (1859) 366. Berthelot. Ann. chim. et phys. [5] 61 (1861) 468. Bianchi. Phil. Mag. [4] 24 (1862) 407, abs. from Comptes rendus, July 14, 1862. Airy (G. B.). Phil. Mag. [4] 26 (1863) 329. . Brettes (Martin de). Comptes rendus, 57 (1863) 904. . Karolyi (Ll. von). Phil. Mag. [4] 26 (1863) 266; Ann. Phys. u. Chem. April, 1863. Abel (F. A.). Phil. Mag. [4] 33 (1867) 545; Proce. Roy. Soe. April 4, 1867; Phil. Trans. 157 (1867) 181. Dufour. Phil. Mag. [4] 57 (1869) 478, abs. from Comptes rendus, Feb. 15, 1869. Abel (F. A.). Ann. chim. et phys. [4] 21 (1870) 97. 153. . Bodynski (J.). Ann. Phys. u. Chem. 141 (1870) 594; 145 (1872) 623. . Berthelot. Ann. chim. et phys. [4] 22 (1871) 1380; 23 (1871) 223. . Bleekrode (L.). Phil. Mag. [4] 41 (1871) 39. . Melsens. Ann. chim. et phys. [4] 24 (1871) 218. . Violette (H.). Ann. chim. et phys. [4] 23 (1871) 306. . Volpicelli. Comptes rendus, 73 (1872) 492; Ann. Phys. u. Chem. 146 (1872) 307. Champion et Pellet. Chronique d’Industrie, Jan. 29, 1873; Phil. Mag. [4] 46 (1873) 256. Castan (F.). Comptes rendus, 78 (1874) 1200. Gernez (D.). Phil. Mag. [4] 49 (1875) 157; Comptes rendus, 80 (1875) 44. LITERATURE OF THERMODYNAMICS. . Schtitzenberger (P.). Comptes rendus, 86 (1878) 598; Jahresb. (1878) 43. . Boutmy (H.). Comptes rendus, 89 (1879) 414. . Mallard et Le Chatellier. Comptes rendus, 91 (1880) 825. . Sarrau et Vieille. Phil. Mag. [5] 9 (1880) 455; Comptes rendus, 90 (1880) 1058. . Berthelot. Comptes rendus, 93 (1881) 18. . Mallard et Le Chatellier. Comptes rendus, 93 (1881) 145. . Sarrau et Vieille. Comptes rendus, 95 (1881) 215, 269, . Debus (H.). Phil. Trans. 173 °(1882) 525. . Deville (H. St. C.). Comptes rendus, 94 (1882) 1557; Phil. Mag. [5] 14 (1882) 152. . Pfaundler (L.). Ann. Phys. u. Chem. n. F. 17 (1882) 175. . ——— —. Ann. Phys. u. Chem. n. F. 17 (1882) 176. . Berthelot. Comptes rendus, 96 (1885) 672, 1186. Sur la foree des matiéres explosives. Paris, 1883. 2 vols. 8vo. Jahresb. (1885) 177. . Witz (A.). Comptes rendus, 96 (1885) 1510. 1884. 1885. Liveing (J. D.) and Dewar (J.). Phil. Mag. [5] 18 (1884) 161. Berthelot et Vieille. Ann. chim. et phys. [6] 4 (1885) 13; Jahresb. (1885) 177. . Wesendonck (K.). Ann. Phys. u. Chem. n. F. 26 (1885) 81. . Witz (A.). Comptes rendus, 100 (1885) 1131. 1886. Threfall (R.). Phil. Mag. [5] 21 (1886) 165. . Munroe (Charles E.). Index to the Literature of Explosives. Part I. Baltimore, 1886. [This is to be a complete list of all the hooks and papers on Explosives, especially for the use of military men, compiled by an officer of the United States Navy. What is given above is only the application of thermodynamics to explosives and explosions. | at eee SS Site ee Ne i Sao eee, 1847. 1850. 1851, 1853. 1858. 1860. 1862. 1865. 1864. 1869. 1872. 1875. APPLICATIONS—FLUIDS. ae FLUIDS. Joule (J. P.). Phil. Mag. [3] 31 (1847) 173; Comptes rendus, 25 (1847) 309. Dulong. Ann. chim. et phys. [2] 41 (1850) 113; Jahresb. (1850) 42. Joule (J. P.). Manchester Soc. Mem. [2] 9 (1851) 107; Ann. chim. et phys. [3] 50 (1857) 381. Joule and Thomson. Phil. Trans. (1853) 357. . Rankine (W. J. M.). Edinb. Trans. (1853) 535; Edinb. Proe. 3 (1854) 223. . Joule and Thomson. Phil. Trans. (1854) 321. 55. Thomson (W.). Phil. Mag. [4] 9 (1855) 523; Edinb. Trans. 20 (1853) 475; Jahresb. (1855) 24. . Joule (J. P.). Phil. Mag. [4] 14 (1857) 211, 381. . Thomson (W.). Proce. Roy. Soc. 8 (1857) 566. Joule (J. P.). Proc. Roy. Soc. 9 (1858) 496; Phil. Trans. (1859) 133. Joule and Thomson. Phil. Trans. (1860) 325. Croll (J.). Rept. Brit. Assoc. (1862) m1, 21. Joule and Thomson. Phil. Trans. (1863) 579. Dupré. Comptes rendus, 58 (1864) 1061. Massieu (F.). Comptes rendus, 69 (1869) 858; Mem. divers savants, [2] 22 (1876) 1. Thomson (W.). Phil. Mag. [4] 45 (1872) 227. Gibbs (J. W.). Trans. Connecticut Acad. 2 (1873) 309. ~I ho 1802. 1829. 1845. 1851. 1852. 1861. 1862. 1865. 1865. 1866. . Dupré. Comptes rendus, 65 (1866) 268. . Schroeder van der Kolk (H. W.). Ann. Phys. u. Chem. 13 (1867) LITERATURE, OF THERMODYNAMICS. FORCE. Dalton (J.). Manchester Soc. Men. 5 rt (1802) 585; Ann. de chimie, 44 (1803) 40, 217, 218. Avogadro (A.). Mem. Accad. Torino, 33 (1829) 237. Joule (J. P.). Phil. Mag. [3] 27 (1845) 205; 28 (1846) 205. Colding (A.). Vidensk Selsk. Skrift. Kjobenhavn, 2 (1851) 121, 167. Waterston. Rept. Brit. Assoc. (1852) u, 11; Instit. (1853) 370; Jahresb. (1852) 66. . Seydlitz. Ann. Phys. u. Chem. 99 (1856) 562. Hoppe dagegen, Do. 101 (1857) 143. . Thomson (W.). Phil. Mag. [4] 11 (1856) 447. . Fuchs. Verhandl. d. Presburg. Ver. 1 (1857) 3. . Leconte (J.). Phil. Mag. [4] 19 (1860) 133, from Amer. J. Sci. Nov. 1859. Maxwell (J. C.). Phil. Mag. [4] 21 (1861) 161, 281, 338.—See Challis, same vol. 250. Codazza. Cimento, 15 (1862) 61. Sorby (H.C.). Phil. Mag. [4] 27 (1864) 145; Proc. Roy. Soe. April 30, 1863. . Akin (C. K.). Phil. Mag. [4] 28 (1864) 470; 29 (1865) 205. . Schroeder van der Kolk (H. W.). Ann. Phys. u. Chem. 122 (1864) 439, 658; Ann. chim. et phys. [4] 4 (1865) 193; Phil. Mag. [4] 29 (1865) 269. Edmonds (T. R.). Phil. Mag. [4] 29 (1865) 169. Babinet. Comptes rendus, 63 (1866) 531, 662, 903. 277, 408; Phil. Mag. [4] 36 (1868) 433. 1884. 1887. 1798. APPLICATIONS—FRICTION. ae . Clausius (R.). Ann. Phys. u. Chem. i141 (1870) 124; Jahresb. (1870) 76; Phil. Mag. [4] 40 (1870) 122. . Rankine (W. J. M.). Phil. Mag. [4] 40 (1870) 288; Nature, 2 (1870) 440, abs. . Ledieu (A.). Comptes rendus, 78 (1874) 1182. . Purser (J.). Rept. British Assoc. (1874) 23. . Weinberg (J.). Ann. Phys. u. Chem. Ergbd. 6 (1874) 586; Jahresb. (1875) 47. . Chase (P. E.). Proc. Amer. Phil. Soc. 14 (1874-5) 651. (7. Stoney (G. J.) and Moss (R. J.). Phil. Mag. [5] 4 (1877) 67. . Fitzgerald (F.G.). Phil. Mag. [5] 7 (1879) 15. Remarks by Prof. Reynolds, same vol. 179. . Browne (W. R.). Phil. Mag. [5] 15 (1883) 35; read before the Physical Soc. Nov. 11, 1882. Note by Tunzelmann, same vol. 152. Browne’s reply, 228. Answer by Tunzelmann, 299. Czapski (S). Ann. Phys. u. Chem. n. F. 21 (1884) 209. Crookes (W.). Proc. Roy. Soc. 42 (1887) 345; Beiblatter, 12 (1888) 188. . Thore (J.). Une nouvelle force? Paris, 1887. 8vo.—See Crookes, Fitzgerald’and Stoney above. . Lindemann (F.). Nature, 38 (1888) 458, 578. . Thomson (Sir W.). Phil. Mag. [5] 25 (1888) 116. FRICTION. Rumford (Count). Phil. Trans. 88 (1798) 80, 286; Nicholson’s Jour. 2 (1798) 106. . Sherer. Ann. de chimie, 26 (1798) 113. 1810. Haldat (Dr.). Nicholson’s Jour. 26 (1810) 50; J. de phys. 65 (1810) 215. 74 LITERATURE OF THERMODYNAMICS. 1816. Thomson (Dr.). Annals of Phil. 7 ees 241. 1824. Watson (J. T.). Amer. J. Sci. 8 (1824) 2 Se ee ee 1826. Graham (T.). Annals of Phil. n. s. 12 (1826) 260. 1838. Becquerel. Comptes rendus, 7 (1838) 563 1847. Joule (J. P.). Phil. Mag. [3] 31 (1847) 173; Comptes rendus, 25 - (1847) 309. 7 ——. Pitter. Mech. Mag. 46 (1847) 492. 1855. Decher. Dingler’s Jour. 136 (1855) 415; Jahresb. (1855) 29. ——. Hirn(G.A.). Bull. Soe. Mulhouse, (1855) Nos. 128,129; Dingler’s J. 1386 (1855) 405; Jahresb. (1855) 29-50. 1859. Joule (J. P.). Rept. Brit. Assoc. (1859) 11, 12. 1862. Hirn (G. A.). Cosmos, 21 (1862) 257. 1863. Abel (F. A.). Phil. Mag. [4] 26 (1865) 355. 1866. Cooke (J. P.). Phil. Mag. [4] 31 (1866) 241; Amer. J. Sci. January, 1866. 1872. Jellett (J. H.). Theory of friction. New York, 1872. 8vo. 220 pp. Phil Mag. [4] 43 (1872) 469. 1873. Ledieu (A.). Comptes rendus, 77 (1873) 94, 163, 260, 325, 414, 455 et 517; Jahresb. (1875) 51. —. Maschke (O.). Arch. des Sci. phys. nat. 46 (1873) 271; Phil. Mag. [4] 45 (1873) 400. 1877. Puluj (J.). Ann. Phys. u. Chem. n. F. 1 (1877) 296. ‘ _— 1878. Puluj (J.). Ber. d. Wiener Akad. July 1, 1878; Phil. Mag. [5] | | 6 (1878) 157. | 1851. Koch (S.). Ann. Phys. u. Chem. n. F. 14 (1881) 1; 19 (1883) OK dol. 1884. Cantone. Atti Accad. Lincei, [3] 19 (1883-84) 253. 1887. Arrhenius (Sv.). Z. phys. Chemie. 1 (1887) 285. 1888. De Heen (P.). Bull. Acad. Belg. 15 (1888) 57, 195. or APPLICATIONS—KINETIC THEORY OF GASES. KINETIC THEORY OF GASES. 27. Ivory (J.). Phil. Mag. n. s. 1 (1827) 89, 165. 1829. Avogadro (A.). Mem. Accad. Torino, 33 (1829) 49. —. Dulong. Le Globe, Dec. 9, 1829; Phil. Mag. n. s. 7 (1830) 235, Ann. phys. et chem. 43 (1830) 74, 88, 110. 1844. Joule (J. P.). Proc. Roy. Soc. 5 (1848-50) 517; Phil. Mag. [3] 25 (1844) 1; Phil. Trans. (1844) 1. 1845. Holtzmann. Wiarme und Elasticitiit der Gase und Dimpfe. Mannheim, 1845. 8vo. Jahresb. (1851) 28. 1850. Rankine (W. J. M.). Phil. Mag. [4] 2 (1851) 509; Rept. Brit. Assoc. (1850) 1. 1851. Clausius (R.). Ann. Phys. u. Chem. 82 (1851) 274; C’s Abhand- lungen, 1, 119; Jahresb. (1851) 31; Phil. Mag. [4] 2 (1851) 488. —. Rankine(W.J. M.). Phil. Mag. [4] 2 (1851) 509; Jahresb. (1851) —, ——— — ——. Edinb. Jour. 5 (1851) 128. © ——w—. Edinb. Trans. (1851) 147; Phil. Mag. [4] 7 (1854) 1, 111; Jahresb. (1854) 36. 1953. —— — — —.. Phil. Mag. [4] 5 (1853) 483. , . Joule (J. P.) and Thomson (W.). Phil. Trans. (1853) 357; Phil. Mag. [4] 4 (1853) 357. - Koosen. Ann. Phys. u. Chem, 89 (1853) 437; Jahresb. (1853) 37. . Rankine (W. J. M.). Phil. Mag. [4] 5 (1855) 437. ———. Phil. Trans. (1854) 115; Proc. Roy. Soc. 6. (1850-54) 388, abs. . Magnus (G.). Phil. Mag. [4] 9 (1855) 44. . Seguin. Comptes rendus, 40 (1855) 5.—See Siemens same vol. 309. . Clausius (R.). Ann. Phys. u. Chem. 98 (1856) 173; Amer. J. Sci. [2] 22 (1856) 402; Jahresb. (1856) 27.—See Rankine, Phil, Mag. [4] 12 (1856) 103; Hoppe, Jahresb. (1854) 44. 76 LITERATURE OF THERMODYNAMICS. 1856. Krénig. Chem. Centralbl. (1856) 725; Ann. chim. et phys. [3] 51 (1857) 491. 1857. Bunsen (R.). Gasometry; comprising the leading physical and chemical properties of gases. Translated by H. E. Roscoe. London, 1857. 8vo. Phil. Mag. [4] 14 (1857) 146. 1858. Kirchhoff (G.). Ann. Phys. u. Chem. 104 (1858) 1; 103 (1858) 206. 1859. Baumgartner (G. v.). Ber. d. Wiener Akad. 38 11 (1859) 379. ——. Bernouilli. Ann. Phys. u. Chem. 107 (1859) 490. —. Bourget (J.). Ann. chim. et phys. [8] 56 (1859) 257. —. Jochmann. Ann. Phys. u. Chem. 108 (1859) 153; Z. f. Math. u. Phys. (1860) 24, 96. ——. Maxwell (J. C.). Phil. Mag. [4] 19 (1859) 19; 20 (1860) 21, 33. ——. Rankine (W. J. M.). Phil. Mag. [4] 18 (1859) 316. 1860. Clausius (R.). Phil. Mag. [4] 19 (1860) 454. —. Fairbairn (W.). Phil. Trans. 150 (1860) 185, the Bakerian Lec- ture. ——. Joule (J. P.). Manchester Phil. Soc. Mem. [2] 15 (1860) 143. ——. Regnault (V.). Phil. Mag. [4] 20 (1860) 275; Comptes rendus, June 11, 1860. ——. Tate (P. G.) and Fairbairn (W.). Proce. Roy. Soe. May 10, 1860, April 3, 1862; Phil. Mag. [4] 21 (1861) 230, abs.; 25 (1863) 65, ——. Stephan (J.). Ann. Phys. u. Chem. 110 (1860) 596. 1861. Kirchhoff (G.). Phil. Mag. [4] 21 (1861) 241, comm. by Roscoe. 1862. Clausius (R.). Ber. d. Wiener Akad. 46 11 (1862) 402. —. Ann. Phys. u. Chem. 115 (1862) 1,512; C.’s Abhand- lungen, 11, 277; Phil. Mag. [4] 23 (1862) 417. —. Croll (J.). Rept. British Assoc. (1862) 11, 21. APPLICATIONS—KINETIC THEORY OF GASES. 77 . Fairbairn (W.). Phil. Trans. 152 (1862) 591. . Reye (Th.). Ann. Phys. u. Chem. 116 (1862) 424, 449. . Thomson (W.). Ann. chim. et phys. [8] 64 (1862) 504; Edinb. Trans. 20 (1862) 1. . Dupré. Comptes rendus, 56 (1863) 960; 57 (1863) 774.—See Clausius, same vol. 1115. . Fairbairn (W.) and Tate (P.G.). Phil. Trans. 152 (1863) 591. . Reech. Comptes rendus, 57 (1863) 505. . Stephan (J.). Ber. d. Wiener Akad. 47 11 (1853) 81; Phil. Mag. [4] 27 (1864) 75, abs. . Zeuner (G.). Civil Ingenieur, 10 11 (1863) 1; Comptes rendus, 69 (1869) 101. . Caligny (De). Instit. (1864) 50. . Clausius (R.). ° Z. f. Math. u. Phys. (1864) 376. . Dupré. Mondes, 6 (1864) 315.—See Clausius, same vol. 423. Dupré’s reply, same vol. 477. Comptes rendus, 58 (1864) 806, 1004; 59 (1864) 905. . Rankine (W. J. M.). Edinb. Trans. 23 (1864) 147. . Edmonds (T. R.). Phil. Mag. [4] 30 (1865) 1. . Loschmidt. Z. f. Math. u. Phys. (1865) 511. . Rankine (W. J. M.). Phil. Mag. [4] 29 (1865) 283. ———. Phil. Mag. [4] 31 (1866) 199; Ann. chim. et phys. [4] 8 (1865) 378; Proce. Roy. Soc. 5 (1865) 449.—See Cazin, Comptes rendus, Jan. 2, 1866. . Bauschinger (L.). Z. f. Math. u. Phys. 12 (1866) 208. . Maxwell (J. C.). Phil. Trans. 156 (1866) 249; Phil. Mag. [4] 32 (1866) 390. ——. Phil. Trans. 157 (1867) 49; Phil. Mag. [4] 35 (1868) 129, 185. . Kirchhoff (G.). Ann. Phys. u. Chem. 134 (1868) 177. . Meyer (O. E.), Ann. Phys. u. Chem. 135 (1868) 285. 78 1868. 1869. 1873. 1874. LITERATURE OF THERMODYNAMICS. Moutier (J.). Comptes rendus, 66 (1868) 544; Jahresb. (1868) 71. Andrews (T.). Phil. Trans. 159 (1869) 575 (The Bakerian Lec- ture); Ann. chim. et phys. [4] 21 (1870) 208; Phil. Mag. [4] 59 (1870) 150; Proe. Roy. Soc. June 17, 1869, abs. . Moutier (J.). Comptes rendus, 68 (1869) 95; 69 (1869) 1157. Phil. Mag. [4] 38 (1869) 76. . Blaserna. Comptes rendus, 69 (1869) 134; Phil. Mag. [4] 38 (1869) 326. . Cazin (A.). Comptes rendus, Aug. 9, 1869; Phil. Mag. [4] 38 (1869) 322. . Kurz(A.). Ann. Phys. u. Chem. 136 (1869) 618 ; 158 (1869) 536.— See Boltzmann, Do. 140 (1870) 254; Hoppe, Do. same vol. 263 ; Kurz again, Do. 141 (1870) 159; Boltzmann again, 141 (1870) 473; and Kohlrausch, 149 (1875) 580. . Mohr (F.). Ber. chem. Ges. 4 (1871) 490. . Amagat (E. H.). Comptes rendus, 74 (1872) 1299. . Bourget (J.). Comptes rendus, 74 (1872) 1230. . Jamin et Richard. Phil. Mag. [4] 44 (1872) 241, 457; Comptes rendus, 75 (1872) 105, 455. . Moutier (J.). Comptes rendus, 74 (1872) 1095. . Oettingen (A. J. von). Ann. Phys. u. Chem. Ergbd. 5 (1872) 540; Jahresb. (1875) 46. Résal (H.). Comptes rendus, 75 (1872) 1475; Phil. Mag. [4] 45 (1873) 77. Amagat (E. H.). Ann. chim. et phys. [4] 29 (1873) 246. Moutier (J.). Bull. Soe. philomat. [7] 3 (1873) 233. —. Comptes rendus, 76, (1875) 1077. Roéntgen (W.C.). Ann. Phys. u. Chem. 148 (1873) 610. Clausius (R.). Ber. d. niederrhein. Ges. Nov. 9, 1874; Jahresb. (1874) 60. Moutier (J.). Ann. chim. et phys. [5] 1 (1874) 343. APPLICATIONS—KINETIC THEORY OF GASES. 79 . Reeknagel (G.). Ann. Phys. u. Chem. Erghd. 6 (1874) 278. . Andrews (T.). Phil. Mag. [5] 1 (1876) 78; Proc. Roy. Soc. June 17, 1875. . Antoine (Ch.). Comptes rendus, 80 (1875) 435; Do. 81 (1875) 574. . Boltzmann (L.). Ber. d. Wiener Akad. 72 ut (1875) 427; Phil. Mag. [4] 50 (1875) 495. . Lockyer (J. N.). Phil. Mag. [4] 49 (1875) 320. . Moutier (J.). Bull. Soc. philomat. [6] 12 (1875) 38. . Rayleigh (Lord). Phil. Mag. [4] 49 (1875) 311. . Andrews (T.). Phil. Trans. 166 (1876) 421 (the Bakerian Lec- ture); Phil. Mag. [5] 3 (1877) 63; Proc. Roy. Soc. April 27, 1876, abs. . Burbury (S. H.). Phil. Mag. [5] 1 (1876) 61; Jahresb. (1876) 63. . Holman (S. W.). Proc. Amer. Acad. June 14, 1876; Phil. Mag. [5] 3 (1877) 81, abs. by the Author. . Massieu (F.). Mem. par divers savants, [2] 22 (1876) 1. . Moutier (J.). Bull. Soe. philom. [6] 13 (1876) 5, 11, 49, 51, 60; [7] 1 877) 7,17; 2 (1878) 247; 3 (1878) 87; 4 (1880) 86, 247; 5 (1880) 31. . Pictet (R.). Comptes rendus, 82 (1876) 260; Aun. chim. et phys. [5] 9 (1876) 180; N. Arch. ph. nat. 55 (1876) 66; Phil. Mag. [5] 1 (1876) 477; Jahresb. (1876) 63. - Watson (O. E.). Kinetic Theory of Gases. Oxford, 1876. 8vo pamphlet. - Heath (J. M.). Phil. Mag. [5] 4 (1877) 14. . Hirn (G. A.). Comptes rendus, 84 (1877) 592, 632, 680. : “Meyer (O. E.). Kinetische Theorie der Gase. Breslau, 1877. 8vo. 2 Puluy (J.).., Ann. Phys; u. Chem. n. F.'1 (1877) 296; \ Ber. d. Wiener Akad. 1 Juli, 1878; Phil. Mag. [5] 6 (1878) 157. . Winkelmann (A.). Ann. Phys. u. Chem. n. F. 1 (1877) 430; Jahresb. (1877) 58. . Preston (S. T.). Phil. Mag. [5] 4 (1877) 206 and 364; 5 (1878) 117, 297. 1878. 1879. 1880, . Nichols (E. L.) and Wheeler (A. W.). Phil. Mag. [5] 11 (1881) LITERATURE OF THERMODYNAMICS. Ritter (A.). Ann. Phys. u. Chem. n. F. 5 (1878) 405, 543; 6 (1879) 185; 7 (1879) 157; 10 (1880) 130; 11 (1880) 382. Boltzmann (L.). Ber. d. Wiener Akad. 78 11 (1879) 733; Jahresb. (1879) 90. —. Ann. Phys. u. Chem. n. F. 8 (1879) 653; Jahresb. (1879) 89. Most’s Erwiderung, Ann. Phys. u. Chem. 10 (1880) 296; Jahbresb. (1880) 82. . Gibbs (J. W ). Amer. J. Sci. [3] 18 (1879) 1. . Maxwell (J. C.). Phil. Trans. 170 (1879) 231.—See Meyer in Ann. Phys. u. Chem. n. F. 7 (1879) 317; 8 (1879) 653. Moutier (J.). Revue scientif. 20 Oct. 1880. 133, comm. by Authors, read before the Amer. Assoc. August 28, 1880. . Obermayer (A. von). Ber. d. Wiener Akad. 81 1 (1880) 1102; 85 11 (1883) 147; 87 1 (1884) 188; 96 11'(1888) 546. . Winkelmann (A.). Ann. Phys. u. Chem. n. F. 11 (1880) 474. . Cellérier. Arch. phys. nat. [3] 6 (1881) 3537; Jahresb. (1881) 1073; Phil. Mag. [5] 13 (1882) 47. . Clausius (R.). Ann. Phys. u. Chem. n. F. 14 (1881) 279, 692; Jahres. (1881) 55; Phil. Mag. [5] 13 (1882) 132. . Lorentz (H. A.). Ann. Phys. u. Chem. n. F. 12 (1881) 127, 660. . Moser (J.). Ann. Phys. u. Chem. 14 (1881) 62. . Nipper (F. E.). Phil. Mag. [5] 14 (1882) 283, from Trans. St. Louis Acad. April 3, 1882. . Walter (A.). Ann. Phys. u. Chem. n. F. 16 (1882) 500. . Jamin et Richard. Phil. Mag. [5] 16 (1883) 71, see note by. Ramsay, 118; Comptes rendus, 95 (1883) 1448. . Planck (Max). Ann. Phys. u. Chem. n. F.19 (1883) 358 ; Jahresb. (1888) 111. . Boltzmann (L.). Ber. d. Wiener Akad. 89 1 (1884) 714; Jahresb. (1884) 152. . Kirchhoff (G.). Ann. Phys. u. Chem. n. F. 21 (1884) 563. ates = j Sine ES = eR es 1884. 1885. APPLICATIONS—KINETIC THEORY OF GASES. 81 Schumann (O.). Ann. Phys. u. Chem. n. F. 23 (1884) 353. Boltzmann (L.). Ann. Phys. u. Chem. n. F. 24 (1885) 37 ; Jahresb. (1885) 116. . Meslin. Jour. de Phys. [2] 4 (1885) 132. . Blondlot. Jour. de Phys. [2] 5 (1886) 548. . Burbury (S. H.). Phil. Mag. [5] 21 (1886) 481.—See Tait, same vol. 248. . Cailletet et Matthias. Jour. de phys. [2] 5 (1886) 549. . Duhem (P.). Le Potentiel thermodynamique. Paris, 1886. 8vo. - Holman (S. W.). Proc. Amer. Acad. n. s. 18 (1885-86) 1; Phil. Mag. [5] 21 (1886) 199. . Langlois (M.). Comptes rendus, 102 (1886) 1231. . Pirogow (A.). Jour. d. russ. phys. chem. Ges. (8) u. (9) 18 (1886), u. (1) 19 (1887); Zusatz, pp. 1-70; Beiblatter 13 (1889) 356, abs. . Schlidlowsky (F.). Jour. d. russ. phys. chem. Ges. (1886); Phil. Mag. [5] 25 (1888) 78, abs. . Siemens (W.). Phil. Mag. [5] 21 (1886) 453. . Tait (P. G.). Edinburgh Trans. 33 1 (1885-86) 65; 33 11 1886—- 87) 251. - ——— — —. Phil. Mag. [5] 21 (1886) 343; 23 (1887) 141. . Tammann. Jour. de phys. 5 (1886) 488. . Warburg. Jour. de phys. 5 (1886) 467. . Wilde. Jour. de phys. 5 (1886) 474. . Boltzmann (L.). Ber. de Wiener Akad. 94 11 (1887) 891; Beib- litter, 12 (1888) 765, abs. . Bouty. Jour. de phys. 6 (1887) 26 et 28. - Burbury (S. H.). Phil. Mag. [5] 24 (1887) 471. . Burton (C. V.). Phil. Mag. [5] 24 (1887) 166; Beiblitter, 12 (1888) 33. 1888. LITERATURE OF THERMODYNAMICS. . Cailletet et Matthias. Jour. de Phys. 6 (1887) 414. . Guglielmo (G.) e Musina(V.). Riv. Sci. industr. di Firenze, 1887. 14 pp. . Hein. Jour. de phys. [2] 6 (1887) 251. . Hoff (J. H. van’t). Z. f. physikal. Chemie, 1 (1887) 481. . Hugoniot. Jour, de phys. 6 (1887) 79. . Isambert (F.). Ann. chim. et phys. [7] 11 (1887) 538. . Kahlbaum (W. A.). Verhandl. d. naturf. Ges. zu Basel, 1887, 363, 418. . Lorentz (H. A.). Ber. d. Wiener Akad. 95 11 (1887) 115, Separat. . Miller (W.). Ber. chem. Ges. 20 (1887) 1402; Beiblitter, 12 (1888) 33, abs. . Pusch] (C.). Monatshefte f. Chemie, 8 (1887) 527, 874; Beiblatter, 12 (1888) 33, 338; Ber. d. Wiener Akad. 96 11 (1887) 61. . Ramsay (W.) and Young (S.). Phil. Mag. [5] 23 (1887) 61, 547 ; Nature, 56 (1887) 23. . Schwalbe (B.) u. Fischer. Z. f. phys. u. chem. 1 (1887) 115. . Thomson (J. J.). Phil. Mag. [5] 23 (1887) 379. Ostwald’s reply, 472. . Thomson (W.). Phil. Mag. [5] 23 (1887) 287, 459, 529; 24 (1887) 188. Amagat (E. H.). Comptes rendus, 107 (1888) 522. . Antoine (Ch.). Comptes rendus, 106 (1888) 57, 116; 107 (1888) 778, 836. . Bakker (G.). Beibliatter, 13 (1889) 371, abs. from Inaugural-Diss. Schiedam, 1888. 8vo. 91 pp. . Barus (C.). Amer. J. Sci. 35 (1888) 407. Bezold (W. v.). Ber. d. Berliner Akad. (1888) 485, 1189; Beib- latter, 13 (1839) 567, abs. . Boggio-Lera (E.). Il nuovo Cimento, [3] 23 (1888) 32, 158. Sl cl ce Se ge = 1888. . Pusch] (C.). Monatshefte f, Chemie, 9 (1888) 93; Wiener Anzeiger APPLICATIONS—KINETIC THEORY OF GASES. 83 Boltzmann (L.). Ber. d. Wiener Akad. 96 1 (1888) 891; Phil. Mag. [5] 25 (1888) 81. . Burbury (S. H.). Phil. Mag. [5] 25 (1888) 129. . Cailletet (L.). Comptes rendus, 106 (1888) 333. . Errera (G.}. Gazz. chim. Ital. 18 (1888) 225. . Hirn (G. A.). Comptes rendus, 106 (1888) 166.—See Natanson, same vol. 164. . Hodgkinson (W. R.) and Lowndes (F. K.S.). Chem. News, 58 (1888) 187, 223. . Hoff (J. H. van’t). Phil. Mag. [5] 26 (1888) 81. . Meyer (O. E.). Z. phys. Chem. 2 (1888) 340. Ostwald, 342. . Natanson (L.). Comptes rendus, 106 (1888) 164. Hirn’s remarks, 166. —. Ann. Phys. u. Chem. [2] 33 (1888) 683; 34 (1888) 970. . Ostwald (W.). Z. phys. Chem. 2 (1888) 81. . Pérot (A.). Jour. de Phys. [2] 7 (1888) 129. . Planck (Max). Z. phys. Chem. 2 (1888) 405. > (1888) 14. . Raoult (F.). Z. phys. Chem. 2 (1888) 353; Ann. chim. et phys. [7] 15 (1888) 375; Comptes rendus, 106 (1888) 442. . Richarz (F.). Z. phys. Chem. 2 (1888) 338. . Tait (P.G.). Phil. Mag. [5] 25 (1888) 38, 172. . Voley (W.). Proc. Roy. Soc. 44 (1888) 239. . Walker (J.). Z. phys. Chem. 2 (1888) 602; Beiblatter, 13 (1889) 13, abs. [See Saturated Vapors.] ——= = Sa 2 = 84 LITERATURE OF THERMODYNAMICS. HAMILTON’S PRINCIPLE. 1872. Clausius (R.). Ann. Phys, u. Chem. 146 (1872) 585; Phil. Mag. [4] 44 (1872) 365. —. Szily (C.). Phil. Mag. [4] 45 (1872) 339, comm. by Author, from the Magyar Ertekesei ; Do. 46 (1875) 426; Ann. Phys. u. Chem. 145 (1872) 295, 302; 149 (1875) 74.—See Clausius dagegen, 146 (1872) 585; Jahresb. (1872) 60. LIGHT. 1835. Ampére. Ann. chim. et phys. [2] 58 (1835) 452; Phil. Mag. 7 (1835) 342.—See Savary, Comptes rendus, 9 (1839) 557. 1843. Biot. Ann. chim. et phys. [3] 10 (1843) 5, 175, 307, 385; 11 (1844) 82. 1854. Thomson (W.). Edinb. Trans. 21 (1854) 63; 24 (1857) 57; Phil. Mag. [4] 8 (1854) 409; 9 (1855) 36 ; Comptes rendus 39 (1854) 529. 1860. Biot. Ann. chim. et phys. [3] 59 (1860) 206. 1864, Clausius (R.). Ann. Phys. u. Chem. 121 (1864) 1; C’s Abhand- lungen, I, 322. > 1865. Thomsen (J.). Phil. Mag. [4] 30 (1865) 246. LIQUIDS. 1822. Cagniard de la Tour. Ann. chim. et phys. 21 (1822) 127; 22 (1823) 410; 23 (1828) 267; Phil. Mag. n. s. 5 (1823) 290, abs. — 1828. Tredgold (T.). Phil. Mag. n. s. 3 (1828) 249. 1851. Grassi. Ann. chim. et phys. [3] 31 (1851) 487. 1851. 1858. 1881. APPLICATIONS—LIQUIDS. | 85 Rankine (W. J. M.). Edinb. Trans. 20 (1851) 191. Thomson (W.). Proc. Roy. Soc. 9 (1858) 255; Phil. Mag. [4] 17 (1859) 61. . Joule (J. P.). Phil. Mag. [4] 17 (1859) 364, abs. from Proce. Roy. Soe. Nov. 25, 1858. . Desains (E.). Ann. chim. et phys. [3] 64 (1862) 419. . Guthrie (F.). Phil. Trans. 159 (1869) 468, 637. . Duclaux (E.). Ann. chim. et. phys. [4] 21 (1870) 378. 2. Mensbrugghe (G. van der). Phil. Mag. [4] 43 (1872) 399. . Favre et Laurent. Comtes rendus, 77 (1873) 981. . Mensbrugghe (G. van der). Bull. Acad. Belg. [2] 41 (1876) nos. 4et7; Phil. Mag. [5] 2 (1876) 450; 4 (1877) 40. . Sprung (A.). Ann. Phys. u. Chem. 159 (1876) 1. . Boileau (P.). Comptes rendus, 85 (1877) 1155; Jehresb. (1877) 87. . Pictet (R.). Jour de Genéve, Dec. 23, 1877; Phil. Mag. [5] 5 (1878) 80, 158; Comptes rendus, 86 (1878) 106, 107. . Rosencranz (A.). Ann. Phys. u. Chem. n. F. 2 (1877) 387. 1878. Mensbrugghe (G. van der). Bull. Acad. Belg. [2] 46 (1878) no. 11; Phil. Mag. [5] 7 1879) 432. Onnes (H. Kamerlingh). Ann. Phys. u. Chem. Beiblatter, 5 (1881) 718-726; K. Ak. van Wetensch. Amsterdam, 45 ff.; Jahresb. (1881) 1072. . Schréder van der Kolk (H.). Ann. Phys. u. Chem. n. F. 14 (1881) 656; 16 (1882) 660. . Schmidt (Th. S.). Ann. Phys. u. Chem. n. F. 16 (1882) 633. . Schiff (R.). Atti Accad. Lincei, [3] 18 (1882-83) 449, . Slotte (K. F.). Ann. Phys. u. Chem. n. F. 20 (1883) 257. . Pagliani e Palazzo. Atti. Accad. Lincei, [3] 19 (1883-84) 273. . Réntgen (W.C.). Ann. Phys. u. Chem. n. F. 22 (1884) 510. . Pagliani e Battelli. Atti Accad. Torino, 20 (1834-85) 607, 845. 86 1886. 1887. 1588. 1869. 1887. 1860. 4 © a LITERATURE OF THERMODYNAMICS. Vautier (Th.). Comptes rendus, 103 (1886) 372. Meyer (O. E.). Jahresb. d. schlesischen Ges. (1887) 2. Konowalow (D.). Z. phys. Chem. 2 (1888) 1. . Pusch] (C.). Wiener Anzeigen, (1888) 123. . Weilenmann (A.). Vierteljahresschr. d. Zuricher Ges. 33 (1888) 37; Beiblitter, 12 (1888) 766, abs. MARIOTTE’S LAW. Amagat (E. H.). Comptes rendus, 68 (1869) 1170. Pusch] (C.). Ber. d. Wiener Akad. 96 rr (1887) 61; Monatshefte f. Chemie, 8 (1887) 527, 374; Beiblitter, 12 (1888) 33. MOLECULES. . Waterson (J. J.). Phil. Trans. (1846) 1; Proc. Roy. Soc. 5 (1843-50) 604, abs. . Rankine (W. J. M.). Edinb. Proc. 2 (1850) 275, . Tyndall (J.). Phil. Mag. [4] 6 (1853) 121. . Menabrea. Comptes rendus, 40 (1855) 1229. . Rankine (W. J. M.). Phil. Mag. [4] 10 (1855) 354, 411. 58. Clausius (R.). Ann. Phys. u. Chem. 105 (1858) 239; C’s Abhand- — lungen, 1, 260; Phil. Mag. [4] 17 (1859) 81. | Leroux. Comptes rendus, 50 (1860) 656, 729. . ! . Maxwell (J. C.). Phil. Mag. [4] 19 (1860) 19; 20 (1860) 21, 33. 9 1861. 1863. 1864. 1871. 1872. APPLICATIONS—MOLECULES. S7 Puschl (C.). Jahresb. d. Ober-Gymnas. zu Melk, Wien, (1861) 1. Subic (S.). Ber. d. Wiener Akad. 47 11 (1863) 346; Do. 48 1 (1863) 62. Kopp (H.). Ann. Chem. u. Pharm. Suppl. 3(1864) 1, 289; Proce. Roy. Soe. 13 (1864) 229. . Rankine (W. J. M.). Phil. Mag. [4] 27 (1864) 313.—See Here- path, North British Rev. . Girdlestone (A. G.). Phil. Mag. [4] 29 (1865) 108. . Colnet d’Huart. Comptes rendus, 61 (1865) 431. . Babinet. Comptes rendus, 63 (1866) 581, 662, 903. . Dupré. Comptes rendus, 62 (1866) 39, 622 ; 65 (1866) 268. . Naumann (A.). Ann. Chem. u. Pharm. Suppl. 6 (1868) 295; Jahresb. (1868) 61. —. Ann. Chem. u. Pharm. Suppl. 5 (1867) 253; Phil. Mag. [4] 34 (1867) 551, abs. . Thomson (W.). Phil. Mag. [4] 34 (1867) 15. . Dupré. Comptes rendus, 66 (1868) 141. . Herrmann (L.). Ber. d. deutsch. chem. Ges. 2 (1868) 18, 84, Chem. Centralbl. (1869) 529, 545; Z. f. Chem. (1869) 472. . Bayma (J.). Phil. Mag. [4] 87 (1869) 182, 275, 348, 431.—Reply by W. A. Norton, Phil. Mag. [4] 38 (1869) 208. . Blaserna. Comptes rendus, 69 (1869) 1384; Phil. Mag. [4] 38 (1869) 326. . Rankine (W. J.M.). Phil. Mag. [4] 38 (1869) 247; 39 (1870) 211; Edinb. Trans. 25 (1869) 557; Jahresb. (1869) 99. ———. Phil. Trans. 160 (1870) 277; Phil. Mag. [4] 39 (1870) 306 ; Proc. Roy. Soc. Dec. 19,1869. Reply to Heath, Phil. Mag. [4] 40 (1870) 103, 291; Jahresb. (1870) 75. ———. Phil. Mag. [4] 40 (1870) 288; Nature, 2 (1870) 440, abs. ———, Phil: Mag. [4] 41 (1871) 62. Croll (J.). Phil. Mag. [4] 44 (1872) 1. a, ee me = we 1880. 1881. LITERATURE OF THERMODYNAMICS. 5. Hinrichs (G.). Comptes rendus, 76 (1873) 1592. . Maxwell (J. C.). Phil. Mag. [4] 46 (1873) 453. . Lockyer (J. N.). Proc. Roy. Soc. June 11, 1874; Phil. Mag. [4] 49 (1875) 235. . Weinberg (J.). Ann. Phys. u. Chem. Erghd. 6 (1874) 586; Jahresb. (1875) 47. . Berthelot. Comptes rendus, 80 (1875) 512; Ann. chim. et phys. [5] 4 (1875) 5, 141; Jahresb. (1875) 95. . Klingel. Ann. Phys. u. Chem. 158 (1876) 160.—See H. L. Bauer, 612. . Lucas (F.). Mém. par divers savants, [2] 22 (1876) 1. . Thomsen (J.). Ber. chem. Ges. 9 (1876) 1355. 77. Boileau (P.). Comptes rendus, 85 (1877) 1135; Jahresb. (1877) 87. . Clarke (F. W.). Phil. Mag. [5] 3 (1877) 398; Amer. J. Sci. April, 1877. . Crookes (W.). Phil. Mag. [5] 7 (1879) 57; Proce. Roy. Soe. Dee. d, 1878. . Lévy (Maurice). Comptes rendus, 87 (1878) 488; Phil. Mag. [5] 6 (1878) 466. . Warburg (E.). Ann. Phys. u. Chem. n. F. 4 (1878) 232. rookes (W.). Phil. Trans. 170 (1879) 135, 641. 2 . Pictet (R.). Comptes rendus, 88 (1879) 855; Phil. Mag. [5] 7 (1879) 445. Clausiug (R.). Ann. Phys. u. Chem. n. F. 10 (1880) 92. Rrown (F. D.). Phil. Mag. [5] 12 (1881) 253. . Cellérier (C.). Arch. phys. nat. [3] 6 (1881) 337; Jahresh. (1881) 1073; Phil. Mag. [5] 13 (1882) 47. . Dorn (E.). Ann. Phil. Mag. n. F. 13 (1881) 378. 1882. . Walter (A.). Ann. Phys. u. Chem. un. F. 16 (1882) 500. Hovenden (F.). South London Microscop. Ciub. 1882, p. 1. Ss eS eee) aasesaael ae i: (Rattner 0 Lee WS Shei ao / SSIS ee eal i Se oa 1853. 1865. 1864. 1874. 1885. APPLICATIONS—OUTFLOW. 89 Lucas (F.). Mém. par divers savants, [2] 27 (1883) 1. . Nicol (W. W. J.). Phil. Mag. [5] 16 (1883) 121; 18 (1884) 179. Berthelot. Comptes rendus, 98 (1884) 952; Jahresb. (1885) 156. . Trouton (F.). Phil. Mag. [5] 18 (1884) 54. . Planck (Max). Z. phys. Chem. 1 (1887) 577. . Sutherland (W.). Phil. Mag. [5] 24 (1887) 118, 168; 22 (1886) 81; Beibliatter, 12 (1888) 321, abs. . Sandrucci (A.). Nuovo Cimento, [3] 21 (1887) 121; Beiblitter, 12 (1888) 31, abs. . Buchanan (J.). Phil. Mag. [5] 25 (1888) 165; Beiblatter, 12 (1888) 848. . Heen (P. de). Bull. Acad. Belg. 15 (1888) 165. . Kopp (H.). Ber. chem. Ges. 21 (1888) 1880. . Lehmann (O.). Molekularphysik, 1. Leipzig, 1888. 8vo. X. 852 pp. . Riicker (A. W.). Jour. chemical Soc. (1888) 222. OUTFLOW. Joule and Thomson. Phil. Trans. (1853) 357; Phil. Mag. [4] 4 (1853) 357. Baumgartner (G.). Z. Math. u. Phys. (1863) 81, 158. . Zeuner (G.). Civil Ingenieur, 10 m (1863) 1; Comptes rendus, 69 (1869) 101. Depré. Comptes rendus, 58 (1864) 1004; 59 (1864) 596. Baumgiirtner (G.). Ann. Phys. u. Chem. 153 (1874) 44.—Meyer’s Bemerkungen dazu, same vol. 619. Wilde (H.). Phil. Mag. [5] 20 (1885) 531; Manchester Soc. Mem. Oct. 20, 1885; Jour. de Phys. 5 (1886) 474. ee 4 s eS ee ra 90 1886. 1887 1804. LITERATURE OF THERMODYNAMICS. Vautier (Th.). Comptes rendus, 103 (1886) 372. . Hein. Jour. de Phys. 6 (1887) 251. . Hugoniot. J. de phys. 6 (1887) 79. . Ostwald (W.). Z. phys. Chem. 2 (1888) 81. PRESSURE. Hope (T. C.). Edinb. Trans. (1804); Nicholson’s Jour. 12 (1805) 539.—See Dalton, Do. 15 (1806) 377. . Hall (Sir J.). Nicholson’s Jour. 9 (1804) 98 ; 13 (1806) 328, 381 ; 14 (1806) 13, 113, 196, 302, 314. . Northmore (T.). Nicholson’s Jour. 12 (1805) 368. . Vauquelin et Berthelot. Ann. de chimie, 59 (1806) 170. . “Hall (Sir J.). Edinb. Trans. 6 (1812) 71. . Calladon (D.). Phil. Mag. n. s. 2 (1827) 390. . Despretz. Phil. Mag. n. s. 2 (1827) 392; Ann. chim. et phys. 37 (1828) 182. . Henwood (W. J.). Phil. Mag. 19 (1841) 60. . Aimé (G.). Ann. chim. et phys. [8] 8 (1843) 257. 51. Rankine (W. J. M.). Phil. Mag. [4] 1 (1851) 548. 7. Beequerel (Ed.). Comptes rendus, 44 (1857) 958 ; Mem.de l’Acad. des Sci. de France, 27 11 (1860) 278. . Joule (J. P.). Proc. Roy. Soc. 8 (1857) 564; Ann. chim. et phys. [3] 52 (1857) 120; Phil. Mag. [4] 15 (1858) 538, abs. . Thomson (W.). Proc. Roy. Soe. 8 (1857) 566. . Cazin (A.). Ann. chim. et phys. [4] 14 (1868) 374. . . Cailletet (L.). Phil. Mag. [4] 40 (1870) 146; Comptes rendus, May 23, 1870. APPLICATIONS—PRESSURE. 91 . Berthelot. Ann. chim. et phys. [4] 22 (1871) 184. . Mohr (F.). Ber. chem. Ges. 4 (1871) 490. . Resal (H.). Comptes rendus, 75 (1872) 1475; Phil. Mag. [4] 45 (18738) 77. . Benevides (F.). Ann. chim. et phys. [4] 28 (1873) 358. . Chase (P. E.). Proc. Amer. Phil. Soc. 14 (1874-75) 651. 77. Berthelot. Comptes rendus, 84 (1877) 477. Ann. chim. et phys. [5] 15 (1878) 149; Phil. Maz. [5] TCLS 79) 70. . Lévy (Maurice). Comptes rendus, 87 (1878) 554. - Moutier (J.). Bull. Soc. philom. [7] 3 (1878) 87. . Cailletet (L.). Phil. Mag. [5] 9 (1880) 235; Comptes rendus, 90 (1880) 210, 211. . Clausius (R.). Ann. Phys. u. Chem. n. F. 9 (1880) 337; 14 (1881) 279, 692; Jahresb. (1881) 55; Phil. Mag. [5] 18 (1882) 132. . Kundt (A.). Ann. Phys. u. Chem. n. F. 12 (1881) 538. . Kipper (F. E.). Phil. Mag. [5] 14 (1882) 233, from Trans. St. Louis Acad. April 3, 1882. . Tait (P.G.). Edinb. Proc. 11 (1880-82) 217. . Blumcke (A.). Ann. Phys. u. Chem. n. F. 23 (1884) 404. . Amagat (E. H.). Comptes rendus, 103 (1886) 429. . Main (P. T.). Rept. British Assoc. (1886) 100. . Battelli. Jour. de phys. [2] 6 (1887) 90. . Duhern. Jour. de phys. 6 (1887) 134, 397. . Hoff (J. H. van’t). Z. phys. Chem. 1 (1887) 481. . Ramsay (W.) and Young (S.). Phil. Mag. [5] 23 (1887) 61; Nature, 36 (1887) 23. O2 LITERATURE OF THERMODYNAMICS. PRIORITY. 1845. Person. Comptes rendus, 20 (1845) 1457. vs. Desains. 1848. Mayer (J. R.). Comptes rendus, 27 (1848) 385; Do. 28 (1849) 132; Do. 29 (1849) 554. vs. Joule. 1855. Seguin. Comptes rendus, 40 (1855) 5. vs. Siemens. 1856. Clausius (R.). Phil. Mag. [4] 11 (1856) 388; Jahresb. (1856) 28. vs. Thomson. 1860. Robin et Baudrimont. Comptes rendus, 50 (1860) 683, 723. vs. Deville. 1862. Joule (J. P.). Phil. Mag. [4] 24 (1862) 121, 173. For Mayer. 1863. Verdet. Phil. Mag. [4] 25 (1863) 467, from his “ Exposé de la théorie mécanique de la chaleur,” pp. 109-118. 1864. Dupré. Comptes rendus, 59 (1864) 596. 1872. 1874. 1875 . Joule (J. P.). Phil. Mag. [4] 28 (1864) 150. . Séguin. Cosmos, 26 (1864) 296. . Tait (P.G.). Phil. Mag. [4] 28 (1864) 288; 29 (1865) 55. vs. Mayer. . Tyndall (J.). Phil. Mag. [4] 28 (1864) 25. For Mayer. Clausius (R.). Ann. Phys. u. Chem. 145 (1872) 132. Tait, same vol. 496. Clausius, Do. 146 (1872) 308; Phil. Mag. [4] 43 (1872) 106, commenting on Maxwell’s book, “ Theory of Heat.” Tait, same vol. 358. Clausius again, same vol. 443. Tait, same vol. 516. Correction by Clausius, Phil. Mag. [4] 44 (1872) 117. Tait’s reply, same vol. 240. Jahresb. (1872) 60. Avenarius (A.). Ann. Phys. u. Chem. 151 (1874) 175. vs. Tait. . Berthold (G.). Heidelberg, 1875. 8vo. 1813. 1817. 1826. 1827. 1832. 1835. 1835, 1838. 1840. APPLICATIONS—RADIATION. 93 RADIATION. Delaroche (F.). Thomson’s Annals of Phil. 2 (1813) 100. Fourier. Ann. chim. et phys. 4 (1817) 128; 6 (1817) 259. . Prévost (P.). Ann. chim. et phys. 6 (1817) 412. . Fourier. Ann. chim. et phys. 27 (1824) 256. . Poisson. Ann. chim. et phys. 26 (1824) 225, 442. . Fourier. Ann. chim. et phys. 28 (1825) 357. . Powell (Baden). Phil. Trans. 115 (1825) 189. . Poisson. Ann. chim. et phys. 28 (1825) 37. Powell (Baden). Annals of Phil. n. s. 12 (1826) 13, 122.—See Ritchie, Edinb. Phil. Jour. (1826) 281. Ritchie (W.). Phil. Trans. (1827) 139; Proc. Roy. Soc. 2 (1815- 30) 310, abs. Powell (Baden). Rept. British Assoc. (1831-32) 259. Maurice. Phil. Mag. 2 (1833) 105. Hudson. Rept. British Assoc. (1835) 163. . Melloni. Comptes rendus, 1 (1835) 300; Ann. chim. et phys. 60 (1835) 402. —. Comptes rendus, 6 (1838) 801. Comptes rendus, 10 (1840) 537, 826; 11 (1840) 659, 678, 682. . Powell (Baden). Rept. British Assoc. (1840) 1. . Wrede (J.). Phil. Mag. 20 (1842) 379, from Forhandl. d. Skan- dinaviske Naturforskeres, Kjobenhayn 3-9 Juli, 1840. . Provostaye et Desains. Ann. chim. et phys. [3] 12 (1844) 129; Comptes rendus, 19 (1844) 410; 20 (1845) 1767. = “Ss — > { \ it SS Se Pati OE —————— Eee Se ee 94 1845. 1846. 1847. 1848. 1851. 1852. 1854. 1862. . Waterston (J. J.). Phil. Mag. [4] 23 (1862) 497. 1863. 1864. 1865. 1867. 1873. 1874. LITERATURE OF THERMODYNAMICS. Melloni. Comptes rendus, 20 (1845) 575. Knoblauch (H.). Instit. (1846) 22; Amer. J. Sci. [2] 1 (1845) 429. . Provostaye et Desains. Ann. chim. et phys. [3] 16 (1846) 3537 ; Comptes rendus, 22 (1846) 825, 1139. Glaisher (J.). Phil. Trans. (1847) 119. . Masson et Courtépée. Comptes rendus, 25 (1847) 936. . Provostaye et Desains. Comptes rendus, 24 (1847) 60, 684, 697; 25 (1847) 106. —— — ——. Ann. chim. et phys. [3] 22 (1848) 358. Stokes. Phil. Mag. [4] 1 (1851) 305. Provostaye et Desains. Comptes rendus, 34 (1852) 951. . Thomson (W.). Phil. Mag. [4] 4 (1852) 256. Powell (Baden). Rept. British Assoc. (1854) 337. Provostaye (F. de la). Comptes reudus, 55 (1862) 273. Provostaye (F. de la). Ann. chim. et chim. [3] 67 (1863) 5. Magnus (G.). Phil. Mag. [4] 29 (1865) 58; Ber. d. Berliner Akad. Aug. 11, 1864. ' —. Phil. Mag. [4] 30 (1865) 81; Aun. Phys. u. Chem. 124 (1865) 476. . Desains (P.). Comptes rendus, July 3, 1865; Do. Oct. 22, 1866 ; Phil. Mag. [4] 30 (1865) 136; 32 (1866) 476. Soret (J. L.). Comptes rendus, Sept. 23, 1867; Phil. Mag. [4] 34_ . (1867) 404. Crookes (W.). Proc. Roy. Soc. August, 1873; April 22, 1875; Phil. Mag. [5] 1 (1876) 245. Crookes (W.). Phil. Trans. 164 (1874) 501; 165 (1875) 519; 166 (1876) 325; 169 (1878) 245; 170 (1879) 87. 1879. 1881. APPLICATIONS—RADIATION. 95 . Poggendorff. Ann. Phys. u. Chem. Noy. 1875; Phil. Mag. [5] 1 (1876) 250. . Challis. Phil. Mag. [5] 2 (1876) 374; 1 (1876) 395. . Finkener (R.). Ann. Phys. u. Chem. 158 (1876) 572. . Stoney (G. J.). Phil. Mag. [5] 1 (1876) 177, 304. . Hankel (W.). Ann. Phys. u. Chem. n. F. 2 (1877) 627. . Zollner (F.). Ann. Phys. u. Chem. 160 (1877) 154, 296, 459. . Berger (A.). Ann. Phys. u. Chem. n. F. 3 (1878) 317. . Challis. Phil. Mag. [5] 5 (1878) 452. . Riecke (E.). Ann. Phys. u. Chem. n. F. 3 (1878) 142. Soret (J. L.). Phil. Mag. [5] 7 (1879) 145. Langley (S. P.). Proce. Amer Acad. 8 (1880-81) 342-359. . Bell (A. G.). Phil. Mag. [5] 11 (1881) 510; Proc. National Acad. April 21, 1881. . Schuster (A.). Phil. Mag. [5] 12 (1881) 261. . Violle (J.). Phil. Mag. [5] 13 (1882) ; Comptes rendus, 92 (1881) 1204. . Dufourcet (E.). Le Radiométre par absorption de M. Thore. Paris, 1882. 8vo. 8 pp. . Eddy (H. T.). Proc. Amer Acad. 31 (1882) 225. . Bauer (C.). Aun. Phys. u. Chem. n, F. 19 (1883) 12. . Pringsheim (E.). Ann. Phys. u. Chem. n. F. 18 (1883) 32; Phil. Mag. [5] 15 (1883) 101. . Schneebeli (H.). Ann. Phys. u. Chem. n. F 22 (1884) 430; Phil. Mag. [5] 18 (1884) 468. . Boltzmann (L.). Jour. de phys. [2] 4 (1885) 525. . Schleiermacher (A.). Ann. Phys. u. Chem. [2] 26 (1885) 287; Jahresb, (1885) 125. ges,” ees ei 96 1858. 1866. 1871. 1875. 1888. 1854. . Villari (E.). Ann. Phys. u. Chem. 144 (1871) 274; Phil. Mag. . Puschl (P.). Wiener Anzeigen, (1888) 125. . Kirchhoff (G.). Ber. d. Berliner Akad. Oct., Nov., 1859. \ . Hirn (G. A.). Paris, 1862. 8vo. . Achard. Arch, des sci. phys. [2] 22 (1865) 214; Comptes rendus,. — . Clausius (R.). Comptes rendus, 60 (1865) 1025. . Rankine (W. J. M.). Phil. Mag. [4] 30 (1865) 241; Rept. Brit. — LITERATURE OF THERMODYNAMICS. RUBBER. Hirn. Comptes rendus, 46 (1858) 1. Govi. Atti Accad. Sci. Torino, 2 (1866) 225, 455; 4 (1868-69) 571. Schmulewitsch (G.). N. Petersb. Bull. 14 (1871) 517; Ann. Phys. u. Chem. 144 (1871) 280; Jahresb. (1871) 23. [4] 43 (1872) 157. Kohlrausch (F.). Ann. Phys. u. Chem. 149 (1873) 577; Dingler’s Jour. 210 (1873) 444; Jahresb. (1875) 55. Gladstone (J.). Jour. Chem. Soe. (1888) 679. SECOND PROPOSITION. Clausius (R.). Ann. Phys. u. Chem. 93 (1854) 481; C.’s Abhand- lungen, 1, 127; Jour. de Liouville (1855) 63; Phil. Mag. [4] © 12 (1856) 81; Jahresb. (1854) 43; Comptes rendus, 40 (1855) — 1147. i | | 60 (1865) 1216. i Assoc. (1865) 13, abs. 4 1866. 1867. 1868. 1869. APPLICATIONS—-SECOND PROPOSITION. oF Boltzmann (L.). Ber. d. Wiener Akad. 53 11 (1866) 188, 195. Clausius (R.). Phil. Mag. [4] 35 (1868) 405, comm. by the Author from 41. Vers. deutscher Naturforscher zu Frankfurt a. M. Sept. 25, 1867. . Rankine (W. J. M.). Aun. chim. et phys. [4] 12 (1867) 258. Boltzmann (L.). Ann. Phys. u. Chem. 137 (1868) 495 ; 140 (1870) 639. Loschmidt (J.). Ber. d. Wiener Akad. 69 rr (1869) 395; Instit. (1869) 159, abs. . Most (R.). Ann. Phys. u. Chem. 136 (1869) 140.—See Boltzmann above. . Budde(E.). Ann. Phys. u. Chem. 141 (1870) 426; Jahresb. (1870) 113. Cs Abhandlungen, 1, 264. . Clausius (R.). Ann. Phys. u. Chem. 142 (1871) 433.—See Boltz- mann, Do. 143 (1871) 211. Cs Erwiderung, Do. 144 (1872) 265; 150 (1873) 106, 120. —. Phil. Mag. [4] 42 (1871) 161, from Niederrhein Ges. Nov. 7, 1870: . Horstmann (A.). Ber. chem. Ges. 4 (1871) 847. . Clausius (R.). Ann. Phys. u. Chem. 146 (1872) 585; Phil. Mag. [4] 44 (1872) 865.—See Suily below. . Mallard (E.). Comptes rendus, 75 (1872) 1479; Phil. Mag. [4] 45 (1873) 77; Jahresb. (1873) 52. . Szily (C.). Magyar Akademie Ertekesei (1872); Ann. Phys. u. Chem. 145 (1872) 295, 302; 149 (1873) 74. Clausius dagegen, 146 (1872) 585; Jahresb. (1872) 60. . Boltzmann (L. von). Ber. d. Wiener Akad. 68 11 (1873) 526,712. . Szily (C.). Ann. Phys. u. Chem. Ergbd. 7 (1875) 154; Jahresb. (1875) 46; Phil. Mag. [5] 1 (1876) 22, comm. by the Author. . Burbury (S. H.). Phil. Mag. [5] 1 (1876) 61; Jahresb. (1876) 63. . Clausius (R.). Ann. Phys. u. Chem. 159 (1876) 327; Jahresb. (1876) 62. G 3 \ ; i EES 98 _ LITERATURE OF THERMODYNAMICS. 1876. Nichols (R. C.). Phil. Mag. [5] 1 (1876) 369; Jahresb. (1876) 62.—See Szily, above. 1877. Boltzmann (L. von). Ber. d. Wiener Akad. 76 1 (1877) 373 ; Do. 78 11 (1878) 1, 733; Phil. Mag. [5] 6 (1878) 236, abs. ; Jahresb. (1878) 64, abs. 1878. Clausius (R.). Ann. Phys. u. Chem. n. F. 4 (1878) 341; Phil. Mag. [5] 6 (1878) 237, 400.—See Preston, Nature, 17 (1877-78) 31, 202; 18 (1878) 92.—See also Aitken, Nature, 17 (1877-78) 260. 1879. Boltzmann (L.). Ber. d. Wiener Akad. 78 11(1879) 733; Jahresb. (1879) 90. ——. Planck (Max). Miinchen, 1879. 8vo. 61 pp. 1881. Horstmann (A.). Ber. chem. Ges. 14(1881) 1242 ; Jahresb. (1881) 1134. 1882. Eddy (H. T.). Proc. Amer. Assoc. 31 (1882) 225, abs. 1884. Boltzmann (L.). Ann. Phys. u. Chem. [2] 22 (1884) 31; Jahresb. (1884) 166. —. Puschl (C.). Ber. d. Wiener Akad. 89 m1 (1884) 631. 1835. Bartoli (A.). Carl’s Repert. 21 (1885) 198. 1887. Pictet (R.). 60. Vers. deutscher Naturforscher zu Wiesbaden, (1887) 231; Nature, 387 (1887) 167. ——. Wald (F.). Z. phys. Chem. 1 (1887) 408; Do. 2 (1888) 523; Beiblitter, 12 (1888) 321. SALTS. 1867. Fouqué. Phil. Mag. [4] 33 (1867) 555; Comptes rendus, Jan. 21, 1867. 1873. Riidorff (Fr.). Ann. Phys. u. Chem. 148 (18738) 456, 555; J.de — phys. 2 (1873) 366; 3 (1874) 190. —. Ber. d. Berliner Akad. (1885) 355. 1855. APPLICATIONS—SATURATED VAPORS. 99 1886. Lescoeur (L.). Comptes rendus, 103 (1886) 1260. | 1887. Goodwin (W.S.). Rept. British Assoc. (1887) 48. 1888. Bremer (G.J.). Recueil des Travaux chim. des Pays-Bas, 7 (1888) 268-309; Z. phys. Chem. 3 (1889) 425. ——. Perot (M. A.). Ann. chim. et phys. [7] 12 (1888) 145. —. Roozeboom (H. W. Bakhuis). Z. phys. Chem. 2 (1888) 515. > Vignon (L.). Comptes rendus, 106 (1888) 1671. ——. Weinhold (A.). Z. phys. u. chem. Unterricht, 1 (1888) 262. 1889. Chroustschoff (P.). Comptes rendus, 108 (1889) 1003. —. Roozeboom (H. W. Bakhuis). Comptes rendus, 108 (1889) 1010 SATURATED VAPORS. 1859. Rankine (W. J. M.). Phil. Mag. [4] 18 (1859) 71; 19 (186v) 460; Proce. Roy. Soc. 9 (1859) 626 ; 10 (1859) 183; Phil. Trans. 149 (1860) 177, 745. 1863. Dupré. Comptes rendus, 57 (1863) 108, 589. 1864. Rankine (W. J. M.). Edinb. Trans. 25 (1864) 147. 1865. ———. Proc. Roy. Soc. 5 (1865) 449; Phil. Mag. [4] 31 (1866) 199; Ann. chim. et phys. [4] 8 (1865) 578. —. —— — — —. Phil. Mag. [4] 31 (1865) 285. 1866. Cazin (A.). Comptes rendus, Jan. 2, 1866; Phil. Mag. [4] 31 (1866) 163, abs. Rankine’s reply, 197. 1868. Cazin (A.). Ann. chim. et phys. [4] 14 (1868) 374; Comptes. rendus, June 8, 1868; Phil. Mag. [4] 36 (1868) 238. 1872. Gladbach (Ph.). Aun. Phys. u. Chem. 145 (1872) 318, 326. 1880. 1881. 1886. 1887. 1888. 1857. 1858. 2. Résal (H.). Comptes rendus, 75 (1872) 1475; Phil. Mag. [4] 45 . Antoine (Ch.). Comptes rendus, 80 (1875) 435; 81 (1875) 574. . Puschl (C.). Ber. d. Wiener Akad. 70 rt (1875) 571; Jahresb. . Willner (A.) und Grotrian (O.). Ann. Phys. u. Chem. n. F, 11 . Duhem (P.). Comptes rendus, 103 (1886) 1008; Ber. chem. Ges. . Lescoeur (L.). Comptes rendus, 103 (1886) 1260. . Warburg. Jour. de phys. [2] 5 (1886) 467. . Pérot (A.). Ann. chim. et phys. [7] 12 (1888) 145. LITERATURE OF THERMODYNAMICS. (1878) 77. (1875) 27. Winkelmann (A.). Ann. Phys. u. Chein. n. F. 9 (1880) 208, 358. (1880) 545 Planck (Max). Ann. Phys. u. Chem. [2] 13 (1881) 535; Jahresb. (1881) 55, Cailletet et Matthias. Jour. de phys. [2] 5 (1886) 549. 19 (1886) R. 572. Perot (A.). Thése. Paris, 1887. P.,8vo. 46 pp. Jour. de phys. [2] 7 (1888) 129. Gerber (P.). Nova Acta Leop.-Car. Ak. 52 (1888) No. 103; Beib- latter, 12 (1888) 455. SOLIDS. Joule (J. P.). Proc. Roy. Soc. 8 (1857) 355, 564; Ann. phys. u. — chem. [38] 52 (1857) 120. ——. Proc. Roy. Soc. 9 (1858) 254; Phil. Mag. [4] 17 7) (1859) 61, abs.; Phil. Trans. 149 (1860) 91. APPLICATIONS—SOLUTIONS. 101 . Edlund (E.). Phil. Mag. [4] 24 (1862) 329. —. Ann. Phys. u. Chem. 126 (1865) 572. . Fizeau (H.). Ann. chim. et phys. [4] 8 (1866) 335. —. Comptes rendus, May 25, 1868; Phil. Mag. [4] 36 (1868) 31. . Moutier (J.). Ann. chim. et phys. [4] 24 (1871) 306. . Kohlrausch (F.). Ann. Phys. u. Chem. 149 (1873) 185.—See Rontgen, same vol, 579, 580, and Do. 136 (1869) 618. . Wiebe (H. F.). Ber. chem. Ges. 12 (1879) 788. . Lévy (M.). Comptes rendus, 106 (1888) 414. SOLUTIONS. . Loschmidt (J.). Ber. d. Wiener Akad. 59 1 (1869) 263, 395 ; Instit. (1869) 159; Jahresb. (1869) 152. . Berthelot. Ann. chim. et phys. [4] 29 (1873) 94, 289, 433; 30 (1873) 145, 4338, 456. . Braun (F.). Z. phys. Chem. 1 (1887) 259. . Nicol (W. W. J.). Phil. Mag. [5] 23 (1887) 385. . Duhem (P.). Jour. de phys. [2] 7 (1888) 5. . Loeb (O.) und Nernst (W.). Z. phys. Chem. 2 (1888) 948.—See same vol. 615. . Nernst (W.). Z. phys. Chem. 2 (1888) 613. . Reyher (R.). Z. phys. Chem. 2 (1888) 744. . Chroustschoff (P.). Comptes rendus, 108 (1889) 1003. . Pickering (S. U.). Chem. News, 59 (1889) 249. ee eee —S SS SSeS =. Se eS 102 LITERATURE OF THERMODYNAMICS. STATIONARY MOTIONS. 1873. Clausius (R.). Ber. d. Niederrhein Ges. 16 Juni, 1873; Ann. Phys. u. Chem. 150 (1873) 106; Phil. Mag. [4] 46 (1873) 236, 266; Jahresb. (1873) 51. 1882. Oppenheim (S.). Ann. Phys. u. Chem. n. F. 15 (1882) 495. TEMPERATURE. 1799. Seguin. Ann. de chimie, 3 (1799) 148; 5 (1800) 191. 1823. Faraday (M.). Thomson’s Annals of Phil. n.s. 5 (1823) 74; Ann. chim. et phys. [4] 20 (1823) 329. 1825. Fresnel (A.). Ann. chim. et phys. 29 (1825) 57, 107. 1837. Mohr (Fr.). Ann. Chem. u. Pharm. 24 (1837) 1; Phil. Mag. [5] 2 (1876) 110. 1838. Mallet (R.). Rept. British Assoc. 1838) 312. 1840. Coathupe (C. T.). Phil. Mag. 17 (1840) 130. 1845. Joule (J. P.). Phil. Mag. [3] 27 (1845) 205; 28 (1846) 205. 1850. Dulong. Ann. chim. et phys. [2] 41 (1850) 113; Jahresb. (1850) 42, abs. 1851. Holtzmann. Ann. Phys. u. Chem. 82 (1851) 1. ——. Rankine (W. J. M.). Edinb. Trans. 20 rr (1851) 191; Jahresb. (1854) 36, abs. i. 1852. Apjohn (J.). Francis’s Chemical Gazette, (1852) 396. —. Proce. Irish Acad. 5 (1855) 272. —. Joule (J. P.). Phil. Mag. [4] 5 (1853) 1; Instit. (1853) 164; | Ann. Chem. u. Pharm. 88 (1853) 179; Jahresb. (1853) 47, abs. s APPLICATIONS—TEMPERATURE. “LOS 53. Koosen. Ann. Phys. u. Chem. 89 (1853) 487; Jahresb. (1853) 37, abs.. . Waterston (J.J.). Rept. British Assoc. (1853) 1, 11; Instit. (1853) 370; Jahresb. (1853) 66, abs. . Hoppe (R.). Ann. Phys. u. Chem. 97 (1856) 30; C.’s Bemer- kungen dazu, Do. 98 (1856) 173; H.’s Erwiderung, Do. 101 (1857) 146; Phil. Mag. [4] 12 (1856) 75; Amer. J. Sci. [2] 21 (1856) 409; Jahresb. (1856) 26. . Rennie. Rept. Brit. Assoc. (1856) 11, 165, . v. Seydlitz. Ann. Phys. u. Chem. 99 (1856) 562. Hoppe dagegen, 101 (1857) 148. . Clausius (R.). Ann. Phys. u. Chem. 100 (1857) 353; Phil. Mag. [4] 14 (1857) 108; Ann. chim. et phys. [38] 50 (1857) 497; C.’s Abhandlungen, 11, 229. . Joule (J. P.). Proc. Roy. Soc. 8 (1857) 564; Ann. chim. et phys. [3] 52 (1857) 120. . Thomson (W.). Proce. Roy. Soe. 8 (1857) 566. . Buys-Ballot. Ann. Phys. u. Chem. 103 (1858) 240. . Decher. Dingler’s Jour. 148 (1858) 1. . Hoppe (R.). Ann. Phys. u. Chem. 110 (1869) 598. . Sorby. Comptes rendus, 50 (1850) 999. . Tschermak (G.). Ber. Wiener Akad. 44 1 (1862) 137, 141. . Subic (S.). Ber. d. Wiener Akad. 47 1 (1863) 346; Do. 48 11 (1863) 62. . Ciausius (R.). Ann. Phys. u. Chem. 121 (1864) 1; C.’s Abhand- lungen, 1, 322; Mitt. d. nat. Ges. Zurich, 8 (1863) 1. . Croll (J.). Phil. Mag. [4] 27 (1864) 346. . Dupré. Comptes rendus, 58 (1864) 163. Comptes rendus, 60 (1865) 559, 1024. . Edlund (E.). Ann. Phys. u. Chem. 126 (1865) 539. —. Ann. chim. et phys. [4] 8 (1866) 257. . Amagat (E. H.). Comptes rendus, 63 (1869) 1170. = eae ge ke ee ee ee ee ee 104 LITERATURE OF THERMODYNAMICS. 1870. Heath (J. M.). Phil. Mag. [4] 39 (1870) 288; 40 (1870) 51. 1872. Mallard.(E.). Comptes rendus, 75 (1872) 1479; Phil. Mag. [4], 45 (1873) 77; Jahresb. (1873) 52. ——. Schenck (R.). Rept. British Assoc. (1872) 82, abs. 1874. Avenarius (M.). Ann. Phys. u. Chem. 151 (1874) 305. 1873. Favre (P. A.). Ann. chim. et phys. [5] 1 (1873) 209; Jahresb. (1873) 22, abs. 7 1876. Clausius (R.). Aun. Phys. u. Chem. 159 (1876) 527; Jahresb. (1876) 62, abs. ——. Holman (S. W.). Proc. Amer. Acad. June 14, 1876; Phil. Mag [5] 3 (1877) 81, abs. by the Author. ——. Tait (P.G.). Phil. Mag. [5] 2 (1876) 110; Jahresb. (1876) 62.— See Liebig’s Aunalen, 24 (1837) 1. 1877. Berthelot. Comptes rendus, 84 (1877) 407; 91 (1880) 256; 96 (1883) 1186. 1878. Lévy (Maurice). Comptes rendus, 87 (1878) 554. 1879. Carnelly (T.). Phil. Mag. [5] 8 (1879) 305, 368, 461. 1880. Clausius (R.). Ann. Phys. u. Chem. n. F. 9 (1880) 337. ——. Diihring (E.). Ann. Phys. u. Chem. n. F. 11 (1880) 163. A. Winkelmann’s Bemerkungen dazu, 534. 1882. Nipper (F. E.). Phil. Mag. [5] 14 (1882) 233, Traus. St. Louis Acad. April 3, 1882. 1883. Schiff (R.). Atti Accad. Lincei, [3] 18 (1882-83) 587. ——. Miller (A.). Ann. Phys. u. Chem. n. F. 20 (1883) 94. 1886. Holman (S. W.). Proc. Amer. Acad. n. s. 13 (1885-86) 1; Phil. Mag. [5] 21 (1886) 199. 1884. Berthelot. Comptes rendus, 98 (1884) 952; Jahresb. (1884) 156. 1886. Keller. Atti Accad. Lincei, [4] 1 (1885) 671; Beiblatter, 10 (1886) 333; Phil. Mag. [5] 22 (1886) 312. ——. Main (P. T.). Rept. British Assoc. (1886) 100-139. ——. Petterson. Jour. de phys. [2] 5 (1886) 48. 1887. Battelli. Jour. de phys. [2] 6 (1887) 90. ig 1857. 1858. 1859. 1864. | . Croll (J.). Phil. Mag. [4] 27 (1864) 380. 1866. 1872. 1876. 1879. . Maxwell (J. C.). Phil. Trans. 170 (1879) 231.—See Meyer, Ann. 1882. 1883. 1885. APPLICATIONS—TENSION. 105 . Antoine (Ch.). Comptes rendus, 107 (1888) 681. . Berthelot et Ricoura. Ann. chim. et phys. [7] 13 (1888) 289, 304 321. . Duhem (P.). Z. phys. Chem. 2 (1888) 568. . Gerber (P.). Nova Acta Leop. Carol. Ak. 52 (1888) No. 3, p. 103; Beiblatter, 12 (1888) 455, abs. by the Author. . Parsons (C.). Proc. Roy. Soc. 44 (1888) 320. . Weilenmann (A.). Vierteljahrsschr. d. Ziiricher naturforsch. Ges. 88 (1888) 37. TENSION. Joule (J. P.). Proc. Roy. Soc. 8 (1857) 355. Kirchhoff (G.). Ann. Phys. u. Chem. 103 (1858) 206 ; 104 (1858) 1. Maxwell (J. C.). Phil. Mag. [4] 19 (1859) 19; 20 (1860) 21, 33. Dupré. Comptes rendus, 58 (1864) 806. Maxwell (J. C.). Phil. Trans. 156 (1866) 249. Dahlander (G. R.). Ann. Phys. u. Chem. 145 (1872) 147. Pictet (R.). Comptes rendus, 82 (1876) 260; Ann. chim. et phys. [5] 9 (1876) 180; N. Arch. ph. nat. 55 (1876) 66; Phil. Mag. [5] 1 (1876) 477; Jahresb. (1876) 63. Cohn (E.). Ann. Phys. u. Chem. n. F. 6 (1879) 385. Phys. u. Chem. n. F. 7 (1879) 317; 8 (1879) 653. Tait (P.G.). Edinb. Proe. 11 (1880-82) 131. Tomlinson (H.). Phil. Trans. 174 (1883) 1. Miller (A.). Ann. Phys u. Chem. n. F. 25 (1885) 450. 106 LITERATURE OF THERMODYNAMICS. 1886. Lescoeur (L.). Comptes rendus, 103 (1886) 1260. 1888, Antoine (Ch.). Comptes rendus, 107 (1888) 681. ——. Chervet (A.). Jour. de phys. [2] 8 (1888) 485. ——. Fuchs (K.). Repert. d. Physik, 24 (1888) 298. ——. Januschke (H.). Z. d. Realschulwesen in Wien, (1888) 519, 586. ——. Planck (Max). Z. phys. Chem. 2 (1888) 405. VIRIAL. 1870. Clausius (R.). Ann. Phys. u. Chem. 141 (1870) 125,128; Ergbd. 6 (1874) 279; Comptes rendus, 78 (1874) 1351, 1731; Phil. Mag. [4] 50 (1875) 26, 101, 191, comm. by the Author from Ber. d. Niederrhein. Ges. Nov. 9, 1874. VISCOSITY. 1866. Maxwell (J. C.). Phil. Trans. 156 (1866) 249. 1876. Holman (S. W.). Proc. Amer. Acad. June 14, 1876; Phil. Mag. [5] 3 (1877) 81, abs. by Author. 1877. Puluj (J.). Ann. Phys: u. Chem. n. F. 1: (1877) 296; Ber. rd! Wiener Akad. 1 Juli, 1878; Phil. Mag. [5] 6 (1878) 157. 1882. Babo (L. von) und Warburg (E.). Ann. Phys.u. Chem.n. F.17 | (1882) 390. ——. Schmidt (Th. §.). Ann. Phys. u. Chem. n. F. 16 (1882) 633. ——. Slotte (K. F.). Ann. Phys. u. Chem. n. F. 20 (1883) 257. 1845. 1846. APPLICATIONS—VITAL FORCE. 107 . Warburg (E.) und Sachs (J.). Ann. Phys. u. Chem, n. F. 22 (1884) 518. . Pagliani (S.) e Battelli (A.). Atti Accad. Torino, 20 (1880-85) 607, 845. - Holman (S. W.). Proc. Amer. Acad. n. s. 13 (1885-86) 1; Phil. Mag. [5] 21 (1886) 199. . Arrhenius (Sv.). Z. phys. Chem. 1 (1887) 285. . Meyer (O. E.). Jahresb. d. Schlesischen Ges. (1887) 2-4. . Barns (C.). Phil. Mag. 26 (1888) 183. . Heen (P. de). Bull. de Acad. Belg. 15 (1888) 195-206. . Reyher (R.). Z. phys. Chem. 2 (1888) 744. VITAL FORCE. . Petit. Ann. chim. et phys. 8 (1818) 287. . Rive (dela). Ann. chim. et phys. 15 (1820) 103. . Chossat. Thomson’s Annals of Phil. n.s. 2 (1821) 37, abs. from Ann. chim. et phys., with additions. . Home (E.). Phil. Trans. 116 1 (1826) 60. . Becquerel et Breschet. Ann. chim. et phys. 59 (1835) 113. . Frémy. Comptes rendus, 5 (1837) 389; 6 (1838) 599. . Winn (J. M.). Phil. Mag. 14 (1839) 174. Davy (J.). Ann. chim. et phys. [5] 13 (1845) 174; Phil. Trans. (1844) 1, 57. . Mayer (J. R.). Heilbronn, 1845. 8vo. Comptes rendus, 27 (1847) 385; 32 (1851) 652. Rigg (R.). Phil. Mag. [8] 29 (1846) 407; Proc. Roy. Soc. June 18, 1846. 1858. 1859. 1860. 1862. . Lecoq. Comptes rendus, 55 (1862) 191. 1864. 1865. 1866. 1867. 1869. 1871. . Volpicelli. Comptes rendus, 75 (1871) 492. 1873. 1874. 1876. V7 Fs 1878. 1879. LITERATURE OF THERMODYNAMICS. . Thomson (W.). Phil. Mag. [4] 4 (1852) 256. . Tyndall (J.). Phil. Trans, (1853) 1; Proc. Roy. Soe. 6 (1850-54) 270, abs. Habich (G.). Proc. Amer. Assoc. 12 (1858) 266. Martin-Dacla (E.). Dela chaleur comme cause modificateur de Porganisme vivant. Paris, 1869. 8vo. 1 fr. Leconte (J.). Phil. Mag. [4] 19 (1860) 133; Amer. J. Sci. Nov., 1859. Hirn (G. A.). Cosmos, 21 (1862) 257. Heidenhain. Mechanische Leistung, Warmeentwickelung und Stoffumsatz bei der Muskelthitigkeit. Leipzig, 1864. 8vo. Berthelot. Comptes rendus, 60 (1865) 485, 527. Frankland (E.). Phil. Mag. [4] 32 (1866) 182,485; 382 (1866) 289. Chmoulewitsch. Phil. Mag. [4] 54 (1867) 403; Comptes rendus, Aug. 26, 1867. Hébert (L.). Action de la chaleur sur les composés organiques. Paris, 1869. 8vo. 2 fr. Calvert (F. Crace). Proc. Roy. Soc. 19 (1870-71) 472. Boltzmann .(L.). Ber. d. Wiener Akad. 68 1 (1873) 526, 712. Fritsch (H.). Ann. Phys. u. Chem. 153 (1874) 306. Erwiderung dazu von W. H. Fabian, Do. 156 (1875) 826. Jahresb. (1874) 59. . Weber (W.). Ann. Phys. u. Chem. Jubelband (1874) 199; Jah- resb, (1874) 59. Tyndall (J.). Proc. Roy. Soc. 25 (1876) 569. Nawalichin. Nature, 16 (1877) 451.—See Molison, same vol. 477. Fick (A.). Archiv f. Physiol. 16 (1878) 1; Nature, 17 (1877-78) 285, abs. Hirn (G. A.). Comptes rendus, 89 (1879) 687, 833. 1882. 1886. 1843. 1845. 1862. 1866. 1871. . Mohr (F.). Ber. chem. Ges. 4 (1871) 490. 1872. 1874. . Weinberg (J.). Ann. Phys. u. Chem. Erghd. 6 (1874) 586; Jah- 1875. 1876. 1880. 1881. 1882. 1886. 1887. APPLICATIONS—VOLUME. 109 Lombard (J. 8.). Proc. Roy. Soc. 33 (1881-82) 11; 34 (1882-83) 173; 40 (1886) 1. Blix. Ber. chem. Ges. 19 (1886) R. 115. VOLUME. Kopp (H.). Ann. chim. et phys. [3] 7 (1848) 389. Playfair (Lyon) and Joule (J. P.). Phil. Mag. [3] 27 (1845) 453, 489.—See Marignac, Do. 28 (1846) 527. Edlund (#.). Phil. Mag. [4] 24 (1862) 329; Ann. Phys. u. Chem. 126 (1865) 572. —. Ann. chim. et phys. [4] 8 (1866) 257. Berthelot. Ann. chim. et phys. [4] 22 (1871) 134. Résal (H.). Comptes rendus, 75 (1872) 1475; Phil. Mag. [4] 45 (1878) 77. Recknagel (G.). Ann. Phys. u. Chem. Ergbd. 6 (1874) 278. resb. (1874) 47, abs. Chase (P. E.). Proc. Amer. Phil. Soe. 14 (1874-75) 651. Puschl (C.). Ber. Wiener Akad. 73 1 (1876) 345. Clausius (R.). Ann. Phys. u. Chem. n. F.9 (1880) 337 ; 11 (1881) 279, 692; Jahresb. (1881) 55; Phil. Mag. [5] 13 (1882) 132. Paalzow (A.). Ann. Phys. u. Chem. n. F. 13 (1881) 332; 14 (1881) 176. Nipper (F. E.). Phil. Mag. [5] 14 (1882) 233. Main (P. T.). Rept. Brit. Assoc. (1886) 100-139. Braun (F.). Z. phys. Chem. 1 (1887) 259. 110 1854. 1855. 1856. 1858. 1860. 1561. 1862. LITERATURE OF THERMODYNAMICS. WORK. . Apjohn (J.). Francis’s Chemical Gazette, (1852) 396. . Clausius (R.). Ann. Phys. u. Chem. 87 (1852) 415; Clausius’s Abhandlungen, 11, 164; Ann. chim. et phys. [3] 42 (1854) 122. Apjohn (J.). Proc. Irish Acad. 5 (1853) 272. . Joule (J. P.). Phil. Mag. [4] 5 (1853) 1; Instit. (1853) 164; Ann. Chem. u. Pharm. 88 (1853) 179; Jahresb. (1853) 47, abs. Soret (L.). Arch. des Sci. phys. 26 (1854) 33; Jahresb. (1854) 47. Laboulaye. Instit. (1855) 160; Jahresb. (1855) 30. Clausius (R.). Ann. Phys. u. Chem. 98 (1856) 173; Amer. J. Sci. [2] 22 (1856) 402; Jahresb. (1856) 27.—See Rankine, Phil. Mag. [4] 12 (1856) 103, and Hoppe, Jahresb. (1854) 44, abs. ; Ann. Phys. u. Chem. 97 (1856) 80; 101 (1857) 146; Phil. Mag. [4] 12 (1856) 75; Amer. J. Sci. [2] 21 (1856) 409; Jahresb. (1856) 26. . Rankine(W. J. M.). Phil. Mag. [4] 11 (1856) 388; Do. 12 (1856) 103. . Seydlitz. Ann. Phys. u. Chem. 99 (1856) 562. Hoppe, 101 (1857) 145. Marié-Davy et Troost. Comptes rendus, 46 (1858) 748; Ann. chim. et phys. [3] 53 (1858) 423. Béclard. Comptes rendus, 50 (1860) 471. . Hoppe (R.). Ann. Phys. u. Chem. 110 (1860) 598. Mann. Z. f. Math. u. Phys. (1861) 72. Clausius (R.). Ann. Phys. u. Chem. 116 (1862) 72; C.’s Abhand- lungen, 1, 242; Comptes rendus, 54 (1862) 732; Phil. Mag. [4] 24 (1862) 81, 201; Mittheil. d. naturf. Ges. in Zurich, 7 (1862) 48. . Edlund (E.). Phil. Mag. [4] 24 (1862) 329. . Thomson (W.). Ann. chim. et phys. [8] 64 (1862) 504; Edinb. Trans. 20 (1862) 1. 1863. 1864, 1866. 1868. 1869. APPLICATIONS—WORK. LTh Subic (S.). Ber. d. Wiener Akad. 47 11 (1863) 346; 48 rr (1863) 62. Dupré. Comptes rendus, 58 (1864) 163, 539.—See Do. 59 (1864) 490, 665, 705, 768. . Edlund (£.). Ann. Phys. u. Chem. 123 (1864) 193; Oecefversigt. of Forhandl. Stockholm (1864) 77; Phil. Mag. [4] 31 (1866) 253; Ann. chim. et phys. [4] 8 (1866) 257. Dupré. Comptes rendus, 62 (1866) 791 ; 63 (1866) 268 ; 66 (1868) 141. Moutier (J.). Comptes rendus, 66 (1868) 344; Jahresb. (1868) 71, abs. Kurz (A.). Ann. Phys. u. Chem. 136 (1869) 618; 138 (1869) 336.—See Boltzmann, Do. 140 (1870) 254; Hoppe, same vol. 263. Kurz again, Do. 141 (1870) 159. Boltzmann, same vol. 473; and Kohlrausch, 136 (1869) 618, and 149 (1873) 580. . Moutier (J.). Comptes rendus, 68 (1869) 95; Phil. Mag. [4] 38 (1869) 76. . —— —. Comptes rendus, 69 (1869) 1137. . Clausius (R.). Ann. Phys. u. Chem. 141 (1870) 124; Phil. Mag. [4] 40 (1870) 122. . Rankine (W. J. M.). Phil. Trans. 160 (1870) 277; Phil. Mag. [4] 39 (1870) 306. Reply to Heath, Do. 40 (1870) 103, 291 ; Jahresb. (1870) 75, abs. . Heath (J. M.). Phil. Mag. [4] 40 (1870) 51. . Buff (H.). Ann. Phys. u. Chem. 145 (1872) 627; Phil. Mag. [4] 44 (1872) 544. . Mach. Geschichte und Wurzel des Satzes von der Erhaltung der Arbeit. Prag, 1872. 8vo. . Moutier (J.). Comptes rendus, 74 (1872) 1095. . Oettingen (A. J. von). Ann. Phys. u. Chem. Ergbd. 5 (1872) 540; Jahresb. (1875) 46. Moon (R.). Phil. Mag. [4] 46 (1873) 219; Do. 47 (1874) 291. . Moutier (J.). Bull. Soc. philomath. [7] 3 (1873) 233. 1879. . Thomson (W.). Edinb. Trans. 28 (1879) 741; Phil. Mag. [5] 7 1883. +1886. 1887. 1806. 18453. LITERATURE OF THERMODYNAMICS. . Résal (H.). Comptes rendus, 75 (1872) 1475; Phil. Mag. [4] 45 (1875) 77. . Kurz (A.). Ann, Phys. u. Chem. Ergbd. 6 (1874) 314; Jahresb. (1874) 55, abs. . Ledieu (A.). Comptes rendus, 78 (1874) 1182. 5. Moutier (J.). Comptes rendus, 80 (1875) 40; Phil. Mag. [4] 49 (1875) 154. . Rayleigh (Lord). Phil. Mag. [4] 49 (1875) 311. 77. Berthelot. Comptes rendus, 85 (1877) 880; 96 (1893) 1186. . Boileau (P.). Comptes rendus, 85 (1877) 1135; Jahresb. (1877) 87. . Guignet (M.). Comptes rendus, 84 (1877) 1084. . Aitken (J.). Nature, 17 (1877-78) 260. . Clausius (R.). Ann. Phys. u. Chem. n. F. 4 (1878) 341; Phil. Mag. [5] 6 (1878) 237.—See Preston, Nature, 17 (1877-78) 31, 202. Bainbridge (E.). Rept. British Assoc. (1879) 523. (1879) 348. Drecker (J.). Ann. Phys. u. Chem. n. F. 20 (1883) 870. Blix. Ber. chem. Ges. 19 (1886) R. 115. Krebs (G.). Z. phys. u. chem. Unterricht, 1 (1887) 118. ZERO-ABSOLUTE. Gough (J.). Nicholson’s Jour. 13 (1806) 189. Provostaye et Desains. Ann. chim. et phys. [8] 8 (1843) 5; Comptes rendus, 16 (1845) 837.—See Regnault, same vol. 977. 1862. 1871. APPLICATIONS—ZERO-ABSOLUTE. 113 Ridorff(Fr.). Phil. Mag. [4] 23 (1862) 560; Ann. Phys. u. Chem. 122 (1862) 337. Coppet. Ann. chim. et phys. [4] 23 (1871) 355; 25 (1872) 502; 26 (1872) 98. 2. Schenck (R.). Rept. Brit. Assoc. (1872) 82. . Forel (F. A.). Phil. Mag. [5] 14 (1882) 238. . Kolacek (F.). Ann. Phys. u. Chem. n. F. 15 (1882) 38. . Ayrton and Perry. Phil. Mag. [5] 2 (1886) 325. Goosens (B. J.). Phil. Mag. [5] 24 (1887) 295. . Gerber (P.). Nova Acta Leop. Car. Acad. 52 (1888) No. 3, p.103 ; Beiblitter, 12 (1888) 455, abs. . Raoult (9. M.). Z. phys. Chem. 2 (1888) 488. See Cold and Equations. II—AUTHOR INDEX. Asse. Erfahrungsmassige Begrtindung des Satzes von der Aequivalenz zwischen Wirme und mechanischer Arbeit. Inauguralschrift. Gét- tingen, 1861. 8vo. Ape. (F.A.). Some results of experimentsinstituted with lucifer matches and others ignited by friction. Phil. Mag. [4] 26 (1863) 355 (comm. by Author, read to British Assoc., August, 1863). — —. Researches on the stability of gun-cotton. Phil. Mag. [4] 33 (1867) 545, abs. from Proce. Roy. Soc. April 4, 1867; Phil. Trans. 157 (1867) 181. ——. Nouvelles études sur les propriétés des corps explosibles. Ann. chim. et phys. [4] 21 (1870) 97. Apney (W. de W.) and Festina (Lieut. Col.). An investigation into the relations between radiation, energy and temperature. Phil. Mag. [5] 16 (1885) 224. Accum (F.). The compound of sulphur and phosphorus, and the danger- ous explosions it makes when exposed to heat. Nicholson’s Jour. 6 (1803) 1. AcHARD. Exposé du second principe de la théorie mécanique de la chaleur. Arch. des sci. phys. [2] 22 (1865) 214; Comptes rendus, 60 (1865) 1216. Appams (R.). Action of cold in maintaining heat. Phil. Mag. [2] 11 (1837) 446. Apik (R.). On ground ice found in the beds of running streams. Phil. Mag. [4] 5 (1855) 540. Acassiz (L.). Observations sur le glacier de |’Aar. Ann. chim. et phys. [3] 6 (1842) 465, 469. —. Extrait d’une lettre de M. Agassiz 4 M. de Humboldt, en date du 19 Novembre 1842, et relative aux glaciers. Ann. chim. et phys. [8] 7 (18438) 125. Armeé (G.). Mémoire sur la compression des liquides. Ann. chim. et phys. [8] 8 (1843) 257. (115) 116 LITERATURE OF THERMODYNAMICS. Arry (G. B.). On the numerical expression of the destructive energy in the explosions of steam-boilers, and on its comparison with the destruc- tive energy of gunpowder. Phil. Mag. [4] 26 (1863) 329. AITKEN (J.). Ona means for converting the heat-motion possessed by matter at normal temperature into work. Nature 17 (1877-78) 260. Arrkin. Sur l’air chauffé considéré comme pouvoir moteur. Cosmos, 2 (1853) 398. Axin (C. K.). On the history of force. Phil. Mag. [4] 28 (1864) 470. ——. On tbe conservation of force. Phil. Mag. [4] 29 (1865) 205. AuLuARD. Expériences sur la température d’ébullition de quelques mé- langes binaires de liquides qui se dissolvent mutuellement en toutes proportions. Ann. chim. et phys. [4] 1 (1864) 245. AmaGAt (E. H.). De influence de la température sur les écarts de la loi de Mariotte. Comptes rendus, 68 (1869) 1170. —w—. Sur la dilatation des gaz humides. Comptes rendus, 74 (1872) 1299. —-—. Recherches sur la dilatation et la compressibilité des gaz. Ann. chim. et phys. [4] 29 (1875) 246. —-—. Sur la compressibilité de Phydrogéne et de lair 4 des températures élévées. Comptes rendus, 75 (1872) 479; Ann. chim. et , phys. [4] 28 (1873) 274. ——. Sur la compressibilité des gaz 4 des pressions élévées. Comptes rendus, 87 (1878) 482. ——. Sur Pélasticité des gaz raréfiés. Comptes rendus, 95 (1882) 281. -——. Sur la densité limite et le volume atomique des gaz, et en particulier de Poxygéne et de ’hydrogéne. Comptes rendus, 100 (1885) 633. ——. Sur la mesure des trés fortes pressions et la compressibilité des liquides. Comptes rendus, 105 (1886) 429. — —. Sur la dilatation des liquides comprimés, et en particulier sur la dilatation de l’eau. Comptes rendus, 105 (1887) 1120. ——. Compressibilité des gaz; oxygéne, hydrogéne, azote et air jusqu’d 3000 atm. Comptes rendus, 107 (1888) 522. oe AUTHOR INDEX. EL AmprrRe. Note sur lachaleur et la lumiére considérées comme provenant de mouvements vibratoires. Ann. chim. et phys. [2] 58 (1835) 452 ; Phil. Mag. [3] 7 (1835) 342.—See Savary, Comptes rendus, 9 (1839) 507. ANDERSON (W.). On the conversion of heat into work. A_ practical treatise on heat-engines. London: Whittaker. 1887. (252 pp.) Beiblatter, 12 (1888) 406. ANDREEFF (E.d’). Recherches sur le poids spécifique et la dilatation par la chaleur de quelques gaz condensées. Ann. chim. et. phys. [3] 56 (1859) 317. Anprews(T.). Note on the heat produced during metallic substitutions. Phil. Mag. [3] 25 (1844) 93. —. Law of the heat of combination. Amer. J. Sci. 46 (1844) oo co ~I —. On the heat disengaged during the combination of bodies with oxygen and chlorine. Phil. Mag. [3] 32 (1848) 321, 426. —. On the state of our knowledge of thermochemistry. Brit. Assoc. Rept. (1849) 65. —. Report on the heat of combination. Brit. Assoc. Rept. (1849) —. Note on the heat of chemical combination. Phil. Mag. [4] 4 (1852) 497.—See reply by Dr. Woods, Phil. Mag. [4] 5 (1853) 10. On the continuity of the gaseous and liquid states of matter. Phil. Trans. 159 (1869) 575. The Bakerian Lecture. Ann. chim. et phys. [4] 21 (1870) 208; Phil. Mag. [4] 39 (1870) 150; Proc. Roy. Soc. June 17, 1869, abs. —. Preliminary notice of further researches on the physical properties of matter in the liquid and gaseous states under varied con- ditions of pressure and temperature. Phil. Mag. [5] 1 (1876) 78; Proce. ~Roy. Soc. June 17, 1875. —. On the gaseous state of matter. Phil. Trans. 166 (1876) 421 ; Phil. Mag. [5] 3 (1877) 63; Proc. Roy. Soc. April 27, 1876, abs. —. Heat dilatation of metals from low temperatures. Proc. Roy. Soe. 43 (1887) 299, 305, 308. ANGELHARDT. Surla formation de la glace au fond deVeau. Ann. chim. et phys. [4] 7 (1866) 209. 118 LITERATURE OF THERMODYNAMICS. AwntornE (Ch.). Mémoire sur quelques propriétés mécaniques de la vapeur d’eau saturée. Comptes rendus, 80 (1875) 455; 81 (1875) 574. —. Sur les variations de température des gaz et des vapeurs qui conservent la méme quantité de chaleur sous des tensions différents. Comptes rendus, 106 (1888) 57. —. Variation de température d’une vapeur comprimée ou dilatée, en conseryant laméme chaleur totale. Comptes rendus, 106 (1888) 116. —. Tension des vapeurs? nouvelle relation entre les tensions et les températures. Comptes rendus, 107 (1888) 681-685. —. Calcul des tensions de diverses vapeurs. Comptes rendus, 107 (1888) 778, 836. Apgsoun (J.). Ismechanical power capable of being obtained by a given amount of caloric employed in the production of vapor independent of the nature of the liquid? Francis’s Chemical Gazette, (1852) 396. —. On the quantity of calorie necessary to produce equal volumes of the vapors of different liquids. Proc. Roy. Irish. Acad. 5 (1853) 272. ArmstronG (H.E.). On the determination of the constitution of carbon compounds from thermochemical data. Phil. Mag. [5] 23 (1887) 73. ARRHENIUS (Sv.). Ueber die innere Reibung verdtinnter wiasseriger Lésungen. Z. phys. Chemie, 1 (1887) 285, 631. —. Ueber den Gefrierpunkt verdiinnter wisseriger Losungen. Z. phys. Chemie, 2 (1888) 491-505. Asupy (J. E.). Observations on catalytic combustion. Phil. Mag. [4] 6 (1853) 77. AssMANN. Ueber Erwirmung und Erkaltung von Gazen durch plotzliche Volumianderung. Ann. Phys. u. Chem. 85 (1852) 1. Avenarius. Eine Prioritatsfrage. Ann. Phys. u. Chem. 151 (1874) 175. [in reply to Prof. Tait. ] —. Ueber innere latente Warme. Ann. Phys. u. Chem. 151 (1874) 303. AvoGcapro (A.). Affinita dei corpi per esso. Mem. Accad. Torino, 28 (1824) 1; 29 (1825) 79. —. Comparaison des observations de M. Dulong sur les pouvoirs réfringens des corps gazeux; avec les formules de relation entre ces pouvoirs et les affinités pour le calorique, déduites des chaleurs spécifi- ques. Mem. Accad. Torino, 33 (1829) 49. AUTHOR INDEX, 119 AvoGaApro (A.). Remarques sur la force élastique de lair par rapport 4 la densité dans le cas de compression, sans perte de calorique, et sur celle de la chaleur spécifique de lair par rapport & la température et la pression. Mem. Accad. Torino, 33 (1829) 237. —. Mémoire sur la force élastique de la vapeur du mercure A différentes températures. Ann. Phys. u. Chem. 27 (1842) 60, abs. ; Mem. Accad. Torino, 56 (1852) 215; Jahresb. (1851) 31, abs. Ayrton (W. E.) and Perry (J.). Onice asan electrolyte. Phil. Mag. [5] 4 (1877) 114; 5 (4878) 43. — — and —. Noteon the paper on some thermodynamic relations by Prof. W. Ramsay and Dr. 8S. Young. Phil. Mag. [5] 21 (1886) 255; J. de phys. 6 (1887) 47. — — and —. The expansion of mercury between 0° C. and — 39°C. Phil. Mag. [5] 22 (1886) 325. Basinet. Sur la chaleur dans lhypothése des vibrations. Comptes rendus, 7 (1838) 781. Théorie de la chaleur dans l’hypothése des vibrations, et Note sur la force vive moyenne d’un mobile oscillant sous l’empire d’une force proportionelle a l’écart. Comptes rendus, 63 (1866) 581, 662. . Sur les forces moleculaires. Comptes rendus, 63 (1866) 903. Baso (L. von) und Warsure(E.). Ueber den Zusammenhang zwischen Viscositat und Dichtigkeit bei fliissigen insbesondere gasformig fliissigen Korpern, Ann. Phys. u. Chem. n. F. 17 (1882) 390; Phil. Mag. [5] 14 (1882) 51; Sitzber. d. Wiener Akad. 77 11 (1882) 509. Barue (J. B.). Ecoulement des gaz par un long tuyau. J. de phys. [2] 8 (1889) 29; Beiblatter, 13 (1889) 781, abs. BAINBRIDGE (E.). Heat in fuel, the causes of the difference between the quantity of heat and the quantity which is utilized in the work done by asteam-engine. British Assoc. Rept. (1879) 523. Bakker (G.). Theorie der Vloeistoffen en Dampen. Inaugural Disserta- tion. Schliedam. 1888. (91 pp.) Beiblatter, 13 (1889) 371, abs. Bat (J.). On the cause of the descent of glaciers. Phil. Mag. [4] 40 (1870) 1; 41 (1871) 81. Barnarp (F. A. P.). Theoretic determinaton of the expenditure of heat in the hot-air engine. Amer. J. Sci. [2] 16 (1853) 218, 292, 351, 431. a So - = 120 LITERATURE OF THERMODYNAMICS. Barnarp (F. A. P.). On the elastic force of heated air, considered as a motive power. Amer. J. Sci. [2] 17 (1850) 153. —-—w—. On the comparative expenditure of heat in different forms of the hot-air engine. Amer. J. Sci. [2] 18 (1854) 161. BarTHELEMY. Expériences et observations sur la congélation de l’eau pure ou saturée de gaz et sur la rupture des vases qui la renferment. Ann. chim. et phys. [4] 23 (1871) 89. BarrHouipr. Sur les inflammations spontanées. Ann. de chimie, 48 (1804) 249. Barrout. Sopra imovimenti prodotti dalla luce e dal calore. Firenze: Le Monnier. 1876. 8vo. Apparecchio per la determinazione dell’equivalente meccanico del calore (con una tavola). Atti Accad. Lincei, [3] 8 (1879-80) 6: ; Nature, 22 (1880) 596, abs.; Carl’s Repert. 21 (1885) 198.—See Boltz- mann, Ain. Phys. u. Chem. n. F. 22 (1884) 381. I volumi molecolari e le dilatazioni dei liquidi alle temperature corrispondenti. Atti Accad. Lincei, [3] 19 (1883-84) 577. Barus (C.). Maxwell’s theory of the viscosity of solids and its physical verification. Phil. Mag. 26 (1888) 183-217. —. Note on the viscosity of gases at high temperatures, and on the pyrometric use of the principle of viscosity. Amer. J. Sci. 31 (1888) 407-410. BattTevut (A.) e PaGuiant (S.).—See Pagliani (S.). —. Pression et température de fusion. Jour. de phys. 6 (1887) 90. —. Sull’annularsi del fenomeno Peltier al punto neutrale di aleune leghe. Nuovo Cimento, [3] 23 (1888) 64-67. Bauprimont (A.). Explication de la phénoméne que l’on observe en versant de l’eau sur des corps chaufiés jusqu’au rouge. Ann. chim. et phys. 61 (1836) 319; 62 (1836) 327. —. Réclamations de priorité de M. E. Robin et M. Baudrimont & l’occasion du Mémoire de M. H. Sainte-Claire Deville relatif a la chaleur dégagée dans les combinaisons chimiques. Comptes rendus, 50 (1860) 685, 723. [See same vol. 534, 584.] AUTHOR INDEX. t21 Bauprimont (A.). Dynamique corpusculaire. Relations entre la struc- ture des corps et les phénoménes qu’ils accomplissent. Imperfections de la théorie des ondulations pour expliquer les phénoménes de la physique générale. Bordeaux. 1875. 8vo. 59 pp. BAUMGAERTNER (G. von). Ueber den Einfluss den die neueren Arbeiten tiber Warme auf unsere Grundbegriffe tben miissen. Tageblatt d. naturforsch. Ges. in Wien, (1856) 78; Ber. d. Wiener Akad. Mai, 1856. ——. Ueber den Grund der scheinbaren Abweichung des me- chanischen Warmeaquivalents bei verschiedenen Gasen. Ber. Wiener Akad. 38 (1859) 379. —-—. Bedenken gegen das Warmeiiquivalent A = 423.5 Kilo- erammeter von Joule. Z. Math. u. Phys. (1862) 127. ——. Theorie des Ausstr6mens volkommener Gase aus einem Gefiisse, und ihres Einstrémen in ein solches. Z. Math. u. Phys. (1863) 81, 153. —-—. Die mechanische Theorie der Wirme. Grunert’s Archiy, 42 (1864) 211. ——. Ueber den Einfluss der Temperatur auf die Ausfluss- geschwindigkeit von Wasser aus Réhren. Ann. Phys. u. Chem. 153 (1874) 44. Bemerkungen dazu von O. E. Meyer, 153 (1874) 619. Baur (C.). Ein neues Radiometer. Ann. Phys. u. Chem. n. F. 19 (1883) 12. BauscHincer. Entwickelung eines Satzes der mechanischen Warme- theorie ftir beliebige Processe, in welchem der Clausius ’sche Satz der Aequivalenz der Verwandlungen fiir Kreisprocesse als besonderer Fall enthalten ist. Z. f. Math. u. Phys. 10 11 (1865) 109. ——. Ueber das Integral f = Z.f, Math. u. Phys. 12 (1866) 152. Entgegnung auf die Antwort des Herrn Clausius. Z. f. Math. u. Phys. 12 (1866) 180.—See Clausius, Z. f. Math. u. Phys. 11 (1866) 455. . Ueber den Zusammenhang einiger physikalischen Eigenschaften der Gase. Z.f. Math. u. Phys. 12 (1866) 208. Bayna (J.). Onihe fundamental principles of molecular physics. Phil. Mag. [4] 37 (1869) 182, 275, 348, 431.—See reply by W. A. Norton, Phil. Mag. [4] 38 (1869) 208. LD? LITERATURE OF THERMODYNAMICS. Baynes (R, E.). Lessons on thermodynamics. Oxford. 1878. 8vo. Beaumont et Mayer. Description d’un appareil producteur de la chaleur due au frottement et obtenue au moyen d’une force perdue ou non employée. Comptes rendus, 40 (1855) 983; Amer. J. Sei. [2] 20 (1856) 261.—See Morin, Comptes rendus, 42 (1856) 719 ; and Moigno, Cosmos, 7 (1856) 203. Jahresb. (1855) 30. Brecker (G. F.). A theorem of maximum dissapativity. Amer. J. Sci. [3] 381 (1886) 115; Ber. deutsch. chem. Ges. 19 (1886) Ref. 195.—See Thomson (W.), Phil. Mag. [4] 4 (1852) 504. BECKMANN (E.). Ueber die Methode der Molekulargewichtsbestimmung durch Gefrierpunktserniedrigung. Z. pliys. Chem. 2 (1888) 658-645, 715-743. BeEcuarD. De la chaleur produite pendant le travail de la contraction musculaire. Comptes rendus, 50 (1860) 471. BecquEREL et BRESCHET. Premier mémoire sur la chaleur animale. Ann. chim. et phys. 59 (1835) 118. BecqueRet (E.). Précis de nouvelles recherches sur le dégagement de la chaleur dans le frottement. Comptes rendus, 7 (1838) 363. —. Sur les actions lentes produites sous les influences combinées de la chaleur et de la pression. Comptes rendus, 44 (1857) 988 ; Mem. de Acad. des Sci. de France, 27 11 (1860) 278. Beer (A.). Einleitung in die mathematische Theorie der Elasticitat und Capillaritit. Herausgegeben von A. Giesen. Leipzig: Teubner. 1869. v1, 196 pp. Ber. Bemerkungen tiber die neuere Theorie der Wirme. Ko6nigsberg. 1854. Programm der Hochschule. Bexketorr (N.). Dynamische Seite der chemischen Reaktionen. Ber. chem. Ges. 13 (1880) 2404. BELANGER (J. B.). De l’équivalent mécanique de la chaleur. Paris. 1863. 8vo. Bei (A. G.). Upon the production of sound by radiant energy. Phil. Mag. [5] 11 (1881) 510; read before the National Acad. Sciences, April 21, 1881. Be.LeEvVILLE. Machine & vapeur surchauffée sans chaudiére. Cosmos, 2 (1853) 268. AUTHOR INDEX. 123 BenpDer (C.). Dichteregelmassigkeiten normaler Salzlosungen. Aun. Phys. u. Chem. n. F. 20 (1883) 560. BENEVIDES (F.). Sur les flammes des gaz comprimées. Ann. chim. et phys. [4] 28 (1873) 358. Bercer (A.). Ueber Radiometererscheinungen in Fliissigkeiten. Ann. Phys. u. Chem. n. F. 3 (1878) 317. BerNou wi (Daniell). Hydrodynamica seu de viribus et motibus fluid- orun Commentarii. Argentorati (Strasburg) 1758. Ann. Phys. u. Chem. 107 (1859) 490.—See Hagenbach-Bischoff, below. BertHevot (Marcellin). Sur quelques phénoménes de la dilatation forcée des liquides. Ann. chim. et phys. [3] 30 (1850) 232. —. Sur quelques phénoménes relatifs 4 l’électricité instantanée des solides et des liquides. Ann. chim. et phys. [3] 61 (1861) 468. —. Sur phénoménes calorifiques qui accompagnent la formation des combinaisons organiques. Comptes rendus, 60 (1865) 485, 527. —. Recherches de thermo-chimie. Ann. chim. et phys. [4] 6 (1865) 290, 292, 329, 442. —. Influence de la chaleur sur les combinaisons chimiques. Ann. chim. et phys. [4] 12 (1867) 94; Comptes rendus, 64 (1867) 413 ; Jour. de pharm. 5 (1867) 336. —. Sur les changements de pression et de volume produits par Je combinaison chimique. Ann. chim. et phys. [4] 22 (1871) 134. —. Sur la force des mélanges tonnants. Ann. chim. et phys. [4] 22 (1871) 1380; 23 (1871) 223; Ann. chim. et phys. [4] 23 (1871) 223. —. Sur les changements de pression et de volume produits par la combinaison chimique. Ann. chim. et phys. [4] 22 (1871) 134; Phil. Mag. [4] 42 (1871) 152; Proc. Roy. Soc. April 27, 1871. —. Recherches calorimétriques sur l’état des corps dans les dis- solutions, méthodes calorimétriques. 1. Mémoire, Ann. chim. et phys. [4] 29 (1873) 94; 2. Mémoire, méme vol. 289; 3. Mémoire, méme vol. 453; 4. Mémoire, 50 (1873) 145; 5. Mémoire, méme vol. 433; 6. Mémoire, méme vol. 456, —. Note sur louvrage de M. Thomson “ Principles of Thermo- chemistry. Bull. Soc. chim. [2] 19 (18738) 485. 124 LITERATURE OF THERMODYNAMICS. Berruevot (Marcellin). Sur la chaleur dégagée dans la réaction entre l’eau, l’ammoniaque et les terres alcalines, chaux, baryte et strontiane; constitution des solutions alcalines. Comptes rendus, 76 (1875) 1106. —. Sur la chaleur de combinaison, rapportée 4 état solide; nouvelle expression thermique des réactions. Comptes rendus, 77 (1873) 24. —. Sur quelques valeurs et problémes calorimétriques. 77 (1873) 971. —. Formation thermique des oxydes de l’azote, dans l'état gazeux, depuis leurs éléments. Comptes rendus, 78 (1874) 162. —. Sur les mélanges réfrigérents. Comptes rendus, 78 (1874) LT: . . Sur la chaleur dégagée par les réactions chimiques dans les divers états des corps. Comptes rendus, 78 (1874) 1670. —. Sur quelques problémes de mécanique moléculaire. Comptes rendus, 80 (1875) 512; Ann. chim. et phys. [5] 4 (1875) 5, 141; Jahresb, (1875) 93. —. Influence de la pression sur les phénoménes chimiques. Comptes rendus, 84 (1877) 407, 477; 90 (1880) 1511; 91 (1880) 256 ; 96 (1883) 1186; Ann. de l’Ecole normale, [2] 6 (1877) 63; Ber. chem. Ges. 10 (1877) 897-900. —— —. Sur la loi de Avogadro. Comptes rendus, 84 (1877) 1189- 95, 1269-74, 1275. —. Quelques observations sur le mécanisme des réactions chim- iques. Comptes rendus, 84 (1877) 1408. —. Sur la chaleur dégagée par les combinaisons chimiques dans V’état gazeux; acides anhydres et eau. Comptes rendus, 84 (1877) 1467. —. Remarques sur les variations de la chaleur dégagée par Vunion de l’eau et de lacide sulfurique 4 diverses températures. Comptes rendus, 85 (1877) 651, 919.—See Maumené, below. —. Observations sur le principe du travail maximum et sur la décomposition spontanée du bioxide de barium hydraté. Comptes rendus, 85 (1877) 880. —. Delachaleur de combinaison rapportée 4l’état gazeux. Ann. de l’Ecole norm. [2] 6 (1877) 63; Ber. chem. Ges. 10 (1877) 897, 900. AUTHOR INDEX. 125. BertHetor (Marcellin). Sur les affinités relatives et déplacements réciproques de loxygéne et des éléments halogénes combinés avec les corps métalliques. Comptes rendes, 86 (1878) 628. —. Sur la décomposition des hydracides par les métaux. Comptes rendus, 87 (1878) 619. —. Nouveaux observations sur l’influence de ia pression sur les phénoménes chimiques. Ann. chim. et phys. [5] 15 (1878) 149; Phil. Mag. [5] 7 (1879) 70. —. Sur état présent et sur l’avenir de la thermochimie. Comptes rendus, 89 (1879) 621. —. Sur quelques relations générales entre la masse chimique des éléments et la chaleur de formation de leur combinaisons. Comptes rendus, 90 (1880) 1511. —. Essai de mécanique chimique fondée sur la thermochimie. Paris: Dunod. 1880. 2 vols. 8vo. —. Sur la chaleur de formation des éthers formés par les hydra- cides. Comptes rendus, 91 (188U) 701. —. Sur la vitesse de propagation des phénoménes explosifs dans. les gaz. Comptes rendus, 93 (1881) 18. —. Sur Punion de hydrogéne libre avec l’ethyléne. Comptes rendus, 94 (1882) 916. —. Sur les déplacements réciproques des corps halogénes et sur Jes composés sécondaires qui y président. Comptes rendus, 94 (1882) 1619. —. Sur l’échelle des températures et sur les poids moléculaires. Comptes rendus, 98 (1884) 952; Jahresb. (1884) 156. —. Sur quelques relations entre les températures de combustion, les chaleurs spécifiques, la dissociation et la pression des mélanges tonnants. Comptes rendus, 96 (1883) 672, 1186. —. De la force des matiéres explosives. Paris. 1883. 8vo. 2 vols. Jahresb. (1885) 177. —. Chaleurs de combustion de divers composés organiques. Ann. chim. et phys. [7] 13 (1888) 304. — et Loveurnine. Recherches thermochimiques sur les corps formés par double décomposition. Comptes rendus, 75 (1872) 100. 126 LITERATURE OF THERMODYNAMICS. BerraeLrot (Marcellin) et Loucurnrne. Chaleurs de combustion. Ann. chim. et phys. [7] 13 (1888) 321. / — et Sarnt-Ginues (L. Péan de). Recherches sur ies affinités. De la formation et dela décomposition des éthers. Ann. chim. et phys. [3] 66 (1862) 5; 68 (1863) 225. —et Recoura. Sur la mesure des chaleurs de combustion. Ann. chim. et phys. [7] 13 (1888) 289. —et THENARD. Sur une nouvelle substance détonnante. Ann. de chimie, 86 (1815) 37. —et Vrertite. Mélanges détonnants. Ann. chim. et phys. [6] 4 (1885) 13; Jahresb. (1885) 177. BerrHoup (G.). Rumford und die mechanische Warmetheorie. Heidel- berg. 1875. 8vo. Berrsourer (C. L.). Sur les lois de Vaffinité. Ann. de chimie, 36 (1801) 302; 37 (1801) 151, 225; 38 (1801) 5, 115; Nicholson’s Jour. 5 (1801) 16, 59, 97, 149, 179. — —et VAUQUELIN. Rapport sur des échantillons résultant dexpériences faites par M. le chevalier Halle, addressés par lui 4 Institut national; sur les effets de la compression pour modifier l’action de la chaleur. Ann. de chimie, 59 (1806) 170. ——. Sur la chaleur produite par la concussion et par la com- pression. Mem. Soc. d’Arcueil, 2 (1825) 42; Annals of Phil. n.s. 9 (1825) 184, abs. Bertin (P. A.). Rapport sur le progrés de la thermodynamique en France. Paris. 1867. 8vo. 88 pp. Berrranp (J.). Thermodynamique. Paris. 1887. 8vo. x1, 294 pp. Berzevius (J.). Expériences pour déterminer la composition de plusieurs combinaisons inorganiques qui servent de base aux calculs des propor- tions chimiques. Ann. chim. et phys. 11 (1819) 58, 113, 225. —. Examen de quelques composés qui dépendent d’affinités trés faibles. Ann. chim. et phys. 14 (1820) 363. —et Dutona. Nouvelles déterminations des proportions de l’eau, et de la densité de quelques fluides élastiques. Ann. chim. et phys. 15 (1820) 386. =~ AUTHOR INDEX. 127 Brzoup (W.). Zur Thermodynamik der Atmosphire. Ber, d. Berliner Akad. (1888) 485-522, 1189-1206; Beiblatter, 13 (1889) 367, abs. Brancut. On the combustion of gunpowder in vacuo and in various gaseous media. Phil. Mag. [4] 24 (1862) 407, abs. from Comptes rendus, July 14, 1862. Bices (M.). On the ratio of the expansion of gases. Thomson’s Annals of Phil. n. s. 6 (1823) 415; 7 (1824) 133. Buyeau (A.). Recherches sur les densités de vapeur. Ann. chim. et phys. [2] 68 (1838) 416; [38] 18 (1846) 226. Bror. Traité de physique expérimentale et mathématique. Paris. 1817. 4 vols. 8vo. Reviewed by Berthollet, Aun. chim. et phys. 2 (1817) 54. Sur Pemploi de la lumiére polarisée pour étudier diverses ques- tions de mécanique chimique. Ann. chim. et phys. [3] 10 (1843) 5, 175, 307, 385; 11 (1844) 82. Introduction aux recherches de mécanique chimique, dans lesquelles la lumiere polarisée est employée auxilliairement comme réactif. Ann. chim. et phys. [3] 59 (1860) 206. Birnie (8.). Observation directe du dégagement de chaleur dans la condensation d’une vapeur en liquide. Recueil de travaux des Pays- Bas, 7 (1887) 589. Buack (Dr.). Discoveries on heat. Thomson’s Annals of Phil. 5 (1815) 326, abs. BiAGpEN (Charles). Experiments on the freezing of water. Phil. Trans, (1788) part 1, 125; Ann. de chimie, 4 (1796) 229. Buiaserna (P.). Sullo stato attuale delle scienze fisiche in Italia. Paris. 1867. 18mo. 16 pp. —. Sur la vitesse moyenne du mouvement de translation des molécules dans les gaz non-parfaits. Comptes rendus, 69 (1869) 134 ; Phil. Mag. [4] 38 (1869) 326. BLEEKRODE (L.). Experimental research on the influence of heat on electromotive force. Phil. Mag. [4] 40 (1870) 310; Ann. Phys. u. Chem. 138 (1870) 571; Ann. chim. et phys. April, 1870. —. Ona curious property of gun-cotton. Phil. Mag. [4] 41 (1871) 39. 128 LITERATURE OF THERMODYNAMICS. Burx. Umsgatz der Warme bei der Muskelcontraction in mechanische Arbeit. Ber. chem. Ges. 19 (1886) R. 115. Bionpvor (R.). Introduction 4 l’étude de la thermodynamique. Paris. 1888. 112 pp. —. Pression de la vapeur saturée. Jour. de phys. 5 (1886) 548. BriimKe (A.). Ueber die Bestimmung des specifischen Gewichtes solcher F\tissigkeiten, derer Existenz an das Vorhandensein hoher Drucke gebunden ist. Ann. Phys. u. Chem. n. F. 23 (1884) 404. Bopynski (J.). Wirmeentwickelung beim Aufschlagen von Geschossen. Ann. Phys. u. Chem. 141 (1870) 594; 145 (1872) 623. BorpecKeER. Dissociation durch Wirme. Jahresb. (1859) 28; Instit. (1859) 219. Boaato-Lera (E.). Sulla cinematica dei mezzi continui. Il nuovo Cimento, [3] 25 (1888) 32-41, 158-162. Boun (Prof.). Historic notes on the conservation of energy. Phil. Mag. [4] 28 (1864) 311—See Tyndall, same vol. 25. The Same, continued, 29 (1865) 215; Aun. chim. et phys. [4] 4 (1865) 274. Borteau (P.). Flissigkeitsstromungen und die denselben entsprechenden intermolekularen Arbeit. Comptes rendus, 85 (1877) 1135; Jahresb. (1877) 87. Bo.irzMANN (L.). Ueberdie mechanische Bedentung des zweiten Haupt- satzes der Wirmetheorie. Ber. d. Wiener Akad. 55 11 (1866) 188, 195. —. Bemerkung zur Abhandlung des Herrn. Most: Ein neuer Beweis des zweiten Wirmegesetzes. Ann. Phys. u. Chem. 137 (1868) 495; 140 (1870) 635. —. Warmegleichgewicht zwischen mehratomigen Gasmolekiilen. Ber. d. Wiener Akad. 63 11 (1871) 319, 597-418. —. Antwort auf die Bemerkungen von Szily. ‘Ber. d. Wiener Akad. 63 11 (1871) 526, 679 ; Jahresb. (1871) 64. —. Boiling-points of organic bodies. Phil. Mag. [4] 42 (1871) 393.—See Burden, Phil. Mag. 41 (1871) 528. —. Analytischer Beweis des zweiten Hauptsatzes des mechan- ischen Warmetheorie aus Sa&tzen tiber das Gleichgewicht der lebendigen Kraft. Ber. d. Wiener. Akad. 68 11 (1873) 526, 712-782. AUTHOR INDEX. 129 Bou1zMAnn (L.). Warmegleichgewicht von Gasen. Ber. d. Wiener Akad. 72 11 (1875) 427-457; Phil. Mag. [4] 50 (1875) 495. —. Bemerkungen tiber einige Probleme der mechanischen Theorie der Warme. Ber. d. Wiener Akad. 75 11 (1877) 62-100; 78 1 (1878) 7; Jahresb. (1877) 87. —. Ueber die Natur der Gasmolektilen. Ann. Phys. u. Chem. 160 (1877) 175; Phil. Mag. [5] 3 (1877) 320. —. Ueber die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Warmetheorie und der Wahrscheinlichkeitsrechnung. Ber. d. Wiener Akad. 76 11 (1877) 373; Phil. Mag. [5] 6 (1878) 236, abs.; Jahresb. (1878) 64, abs. —. Remarques au sujet de la communication de M. Lévy sur une loi universelle relative a la dilatation des corps. Comptes rendus, 87 (1878) 595.—Réponse de M. Lévy, méme vol. 649.—Nouvelles remarques, méme vol. 773. —. Erérterungen und mathematische Eutwickelungen tiber die Beziehung der Diffasionsphanomene der Gase zum zweiten Hauptsatze der mechanischen Warmetheorie. Ber. d. Wiener Akad. 78 11 (1879) 733-63 ; Jahresb. (1879) 90. —. Entgegnungen auf Meyer’s kinetische Theorie der Gase. Ann. Phys. u. Chem. [2] 8 (1879) 653; Most’s Erwiderung, Ann. Phys. u. Chem. [2] 10 (1880) 296; Jahresb. (1879) 89 u. (1880) 82. ———-—. Energievertheilung. Ann. Phys. u. Chem. [2] 11 (1880) 929-34; Phil. Mag. [5] 14 (1882) 299; Jahresb. (1880) 82. —. Ueber einige das Wirmegleichgewicht betreffende Siitze. Ber. d. Wiener Akad. 84 11 (1881) 136-145. —. Erorterung einer von Bartoli entdeckten Beziehung der Wirmestrahlung zum zweiten Hauptsatze der mechanischen Wirme- theorie. Ann. Phys. u. Chem. [2] 22 (1884) 31; Jahresb. (1884) 166. —. Das Arbeitsquantum welches bei chemischen Verbindungen gewonnen werden kann. Ann. Phys. u. Chem. [2] 22 (1884) 39-72; Ber. d. Wiener Akad. 88 1 (1883) 861-896; Jahresb. (1884) 151. —. Versuch der Begriindung einer kinetischen Gastheorie auf anziehende Kriafte allein. Ann. Phys. u. Chem. n. F. 24 (1885) 37-44; Jahresb. (1885) 116. I ¢ 1380 LITERATURE OF THERMODYNAMICS. \ BourzMann (L.). Application au rayonnement des principes de la thermodynamique. Jour. de Phys. 4 (1885) 525. —. Ueber die zum theoretischen Beweise des Avogadro’schen Gesetzes erforderlichen Voraussetzungen. Ber. d. Wiener Akad. 94 11 (1886) 613; Phil. Mag. [5] 23 (1887) 305. Tait’s reply, same vol. 433. —. Ueber einige Fragen der kinetischen Gastheorie. Ber. d. Wiener Akad. 96 11 (1887) 891; Beiblitter, 12 (1888) 765, abs.; Phil. Mag. [5] 25 (1888) 81. Bonpvor (R.). Introduction a étude de la thermodynamique. Paris. 1888, 112 pp. Booue (G.). On the differential equations of dynamics. Phil. Trans. 153 (1863) 485. Bosscua. Das mechanische Aequivalent der Warme. Aun. Phys. u. Chem. 101 (1857) 517 ; 102 (1857) 487; 108 (1859) 162; Aun. chim. et phys. [3] 65 (1862) 5e° Bostock (J.). Remarks on Mr. Dalton’s hypothesis of the manner in which bodies combine with each other. Nicholson’s Jour. 28 (1811) 280. Mr. Dalton’s reply, Do. 29 (1811) 143. —. Facts respecting the boiling-point of ether. Aunals of Phil. n. s. 9 (1825) 196. Borr (W.). A method of determining vapour-density applicable at all temperatures and pressures. Jour. Chem. See. Dec. 6, 1888; Chem. News, 58 (1888) 288. Borromiey (J. T.). Dynamics, or theoretical mechanics. London. 1885. 8vo. ——. On expansion with rise of temperature in wires under elongating stress. Rept. Brit. Assoc. (1887) 620; Beibliatter, 13 (1889) 797, abs. Bourcet (J.) et Burprn. Théorie mathématique des machines 4 air chaud. Comptes rendus, 45 (1857) 742, 1069. —. Théorie mathématique de la chaleur donnée & une gaz perma- nent. Ann. chim. et phys. [3] 56 (1859) 257. —. Da coefficient économique dans la thermodynamique des gaz permanents. Comptes rendus, 74 (1872) 1230. —. Rendement des machines thermiques. Ann.del’Ecole norm. — | [2] 5 (1876) 111 * AUTHOR INDEX. tok BoussInGAuLt. Observations sur la congélation du vin et des mélanges deau et d’aleool. Ann. chim. et phys. [3] 25 (1849) 363. Sur la congélation de Peau. Ann. chim. et phys. [4] 26 (1872) 544. Bourmy (H.). Etudes thermiques sur la nitroglycérine. Comptes rendus, 89 (1879) 414. Boury (E.). Chaleurs latentes et chaleurs spécifiques des vapeurs saturées. Jour. de phys. 6 (1887) 26, 28. —. Sur le travail interne dans les gaz. Jour. d phys. [2] 8 (1889) 20. Boye (R.). Opera varia de absoluta quiete in corporibus. Colonniae Allobrogae. 1680. _ Branty (E.). Evaluation, en unités mécaniques, de la quantité d’élec- tricité que produit un élément de pile. Comptes rendus, 77 (1873) 1420. Braun (F.). Untersuchungen tiber die Léslichkeit fester Kérper und die den Vorgang der Losung begleitenden Volum-und Energie- Aenderungen. Z. phys. Chem. 1 (1887) 259-272. —. Ueber einen allgemeinen qualitativen Satz ftir Zustandsin- derungen nebst einigen sich anschliessenden Bemerkungen, insbesondere ber nicht eindeutige Systeme. Ann. Phys. u. Chem. n. F. 33 (1888) B07. Bravals (A.). Sur l’indice de réfraction et de dispersion de la glace. Aun. chim. et phys. [3] 21 (1847) 361. Bremer (G.J.). Salzlosungen. Ihre Dichte und Ausdehnung durch die Warme. Z. phys. Chem. 3 (1889) 423-440; Beiblitter, 13 (1889) 362, abs. ; Recueil des Travaux chim. des Pays-Bas, 7 (1883) 268-309. Bretres (Martin de). Application de la théorie mécanique de la chaleur a Vartillerie. Comptes rendus, 57 (1863) 904. Bri.iouin (Marcel). Chaleur spécifique pour une transformation quel- conque et thermodynamique. Jour. de phys. [2] 7 (1887) 148; Bei- blatter, 12 (1888) 761, abs.; Comptes rendus, 106 (1888) 416, 482, 537, 589. —. Note sur un point de thermodynamique. Jour. de phys. [2] 8 (1888) 315-16. —-. Déformations permanentes et thermodynamique. Jour. de phys. [2] 8 (1888) 327-347. 132 LITERATURE OF THERMODYNAMICS. Brrort (C.). Essai sur la théorie mécanique de ls chaleur. Comptes rendus, 24 (1847) 877. —— —. Théorie mécanique dela chaleur. Paris. 1869. 8vo. 552 pp. Bropre (B. C.). The calculus of chemical operations ; '‘ being a method for the investigation, by means of symbols, of the laws of the distribu- tion of weight in chemical change. Phil. Trans. 156 (1866) 781; Proc. Roy. Soc. May 3, 1866; Phil. Mag. [4] 32 (1866) 227,abs. The Same, Part u, Phil. Trans. 167 (1877) 35. Brown (F. D.). On molecular attraction. Phil. Mag. [5] 12 (1881) 253. Browne (Walter R.). On central force and the conservation of energy. Phil. Mag. [5] 15 (1883) 35; read to the Physical Soc. Nov.11, 1882.— See Note by Tunzelmann, Phil. Mag. [5] 15 (1883) 152. Mr. Browne’s reply, same vol. 228. Answer by Tunzelmann, 299. Bricxe. Ermittelung des mechanischen Aequivalents der Wirme. Ber. d. Wiener Akad. 6 11 (1827) 688. BruGNATELL. Inflammation des liqueurs éthérées par les acides. Ann. de chimie, 29 (1799) 527. Refroidissement artificiel. Ann. de chimie, 29 (1799) 326. BrunNeER. Expériences sur la densité de la glace 4 différentes tempéra- tures. Ann. chim. et phys. [5] 14 (1845) 369. Bucuanan (J.). Ona law of distribution of molecular velocities amongst the molecules of a fluid. Phil. Mag. [5] 25 (1888) 165; Beiblitter, 12 (1888) 846. Buppe (©.). Disgregation und wahrer Wirmeeinhalt der Korper, der zweite Hauptsatz der mechanischen Wirmetheorie und dessen Anwend- ung auf einige Zersetzungserscheinungen. Ann. Phys. u. Chem. 141 (1870) 426; Jahresb. (1870) 115—See Clausius’s Abhandlungen, ed. 1864, pp. 1, 264. —. Das Clausius’sche Gesetz und die Bewegung der Erde im Raume. Ann. Phys. u. Chem. n. F. 10 (1880) 553. —. Bemerkungen iiber die mechanischen Grundlagen der Gesetze von Ohm und Joule. Ann. Phys. u. Chem. n. F. 15 (1882) 558. —. Zur Theorie der thermoelectrischen Krafte. Ann. Phys. u. — Chem. n. F. 21 (1884) 277; 25 (1885) 564. AUTHOR INDEX. 1338 Burr (H.). Specifische Wairme in Beziehung zur mechanischen Wirme- theorie. Ann Chem. u. Pharm. 115 (1864) 306; Jahresb. (1864) 58. —. Bestimmung der zur Ausdehnung fester K6rper erforder- lichen Warmemenge aus der dabei verrichteten Arbeit. Ann. Phys. u. Chem. 145 (1872) 627. Bunsen (R.). Ueber das mechanische Aequivalent der Wirme. Aun. Phys. u. Chem. 81 (1850) 562; Ber. d. Berliner Akad. (1850) 465 ; Jahresb. (1850) 48. — —. Remarks on chemical affinity. Phil. Mag. [4] 5 (1853) 147. —. Gasometry, comprising the leading physical and chemical properties of gases. Translated by Henry E. Roscoe. London. 1857. Phil. Mag. [4] 14 (1857) 146. Bunsen (R. W.). Ueber capillare Gasabsorption. Ann. Phys. u. Chem. n. F. 24 (1885) 321. Bursury (S. H.). The second law of thermodynamics in connection with the kinetic theory of gases. Phil. Mag. [5] 1 (1876) 61-67; Jahresb. (1876) 63. —-—. A theorem on the dissipation of energy. Phil. Mag. [5] 13 (1882) 417. —w—. Foundations of the kinetic theory of gases ; note on Prof. Tait’s paper (page 343). Phil. Mag. [5] 21 (1886) 481. ——. On the diffusion of gases. Phil. Mag. [5] 24 (1887) 471; 25 (1888) 129. BurveEN (F.). On the boiling-points of organic bodies. Phil. Mag. [4] 41 (1871) 528.—See Boltzmann, 42 (1871) 593. Burpin. De l’équivalent mécanique. Comptes rendus, 58 (1864) 885. L’équivalent mécanique de la chaleur expliqué 4 l’aide de l’éther et tendant par suite 4 confirmer l’existence de ce fluide universellement repaudu. Comptes rendus, 67 (1868) 1117. Bureess(J.). Onthe measurement of altitudes by means of the tempera- ture at which water boils. Phil. Mag. [4] 25 (1863) 29. BurnsipE (W.). Distribution of energy. Edinburgh Trans. [2] 33 (1886-87) 501-7; Beiblitter, 13 (1889) 794, abs. \ 154 LITERATURE OF THERMODYNAMICS. Burton (Charles V.). On the value of “Y” in perfect gases. Phil. Mag. [5] 24 (1887) 166; Beiblitter, 12 (1888) 33. Bussy et Buraner. Effets calorifiques pendant la combinaison des liquides. Aun. chim. et phys. [4] 4 (1865) 5; Comptes rendus, 59 (1864) 673. Burverow (A.). Versuche iiber Eis unter kritischem Druck. Petersb. Acad, Bull. 27 (1881) 274-282; Jahresb. (1881) 52, 1073. Buys-Batiotr. Ueber die Art der Bewegung, welche wir Warme und Electricitét nennen. Ann. Phys. u. Chem. 103 (1858) 240. CAGNIARD de la Tour (Le baron). Exposé de quelques résultats obtenus par Paction combinée de Ja chaleur et de la compression sur certains liquides, tels que l’eau, l’alcool, l’éther sulfurique et l’essence de petrole rectifiée. Ann. chim. et phys. 21 (1822) 127; 22 (1823) 410; 23 (1823) 267; Thomson’s Annals of Phil. n. s. 5 (1823) 290, abs. Canours. Sur les densités des vapeurs. Comptes rendus, 63 (1866) 16 ; Phil. Mag. [4] 32 (1866) 388. CartLuerer (L.). Compressibilité des gaz sous influence des pressions élévées. Comptes rendus, 23 Mai, 1870; Phil. Mag. [4] 40 (1870) 146. —— —. Expériences sur la compression des combinaisons gazeuses. Comptes rendus, 90 (1880) 210, 211; Phil. Mag. [5] 9 (1880) 235. —.. On the employment of marsh-gas for producing exceedingly low temperatures. Phil. Mag. [5] 19 (1884) 65. —. Appareil pour des expériences 4 haute température au sein d’un gaz sous pression élévée. Comptes rendus, 106 (1888) 333. CarLuerer (L.) et Conarprau (E.). Etude des mélanges réfrigérants obtenus avec l'acide carbonique solide. Comptes rendus, 106 (1888) 1631-34. CaILLetet et Matruras. Vapeurs saturées. Jour. de phys. [2] 5 (1886) 549. et Sur lacide sulfureux. J. de phys. [2] 6 (1887) 414. Cauieny. Sur un moyen simple de resoudre par l’expérience une ques- tion délicate de la théorie mécanique de la chaleur. Institut, (1864) 30.—See same author in Institut, (1863) 548. Canrone. Sullattrito del vapor d’acqua ad alte temperature. Atti Accad. Lincei, [3] 19 (1883-84) 253. AUTHOR INDEX. 135 Cantonti (C.). Sull’opuseulo del professore R. Ferrini: Saggio di ex- posizione elementare della teoria dinamica del calore. Istit. Lombard. di Sci. rend. Milano (1865) 78. — und Gerosa (G.). Dynamischer Werth einer Calorie E = 423, 82 oder E = 14,145. Ann. Phys. u. Chem. Beiblitter 7 (1883) 242; R. Accad. Lincei (1882) 3, 16 ff Sep.; Jahresb. (1883) 112. CaRNELLY (T.). Influence of atomic weight. Phil. Mag. [5] 8 (1879) 305, 368, 461. —. Existenz des Eises bei hoher Temperatur. Ber. chem. Ges. 13 (1880) 2230. —. Melting and boiling point tables. Vol. I. London: Harri- son. 1885. 4to. — and O’sHea (L. T.). A relation between the melting-points of the elements and their solid binary compounds and the heats of formation of the latter. Phil. Mag. [5] 11 (1881) 28. Carnot. Réflexions sur la puissance motrice du feu, et sur les machines propres 4 développer cette puissance. Paris. 1824. Jahresb. (1850) 37; Aun. Ecole norm. [2] 1 (1872) 1. Nouvelle édition, Paris, 1878. Svo. Carre. On the production of low temperatures. Phil. Mag. [4] 21 (1861) 296 ; Comptes rendus, Dec. 24, 1860. Cas (W. E.). On a new means of converting heat energy into electrical energy. Proc. Roy. Soc. 40 (1886) 345. Castan (F.). Les conclusions 4 tirer de application des théories ther- mochimiques aux corps explosifs en général, et aux poudres de guerre en particulier. Comptes rendus, 78 (1874) 1200. Cay.ey (Sir George). Description of an engine for affording mechanical power from air expanded by heat. Nicholson’s Jour. 18 (1807) 260. CazaLat (Galy-). Machine calorique d’Ericsson. Bull. Soc. d’encour. (1853) 44.—See Franchot, Comptes rendus, 56 (1853) 593. Cazavan. La machine calorique Ericsson. Cosmos, 5 (1853) 342. Cazin (A.). Exposé de la théorie mécanique de la chaleur. Mem. Soc. hist. nat. Seine et Oise, Versailles, 1863. —. Application de la théorie mécanique de la chaleur au com- presseur hydraulique du tunnel des Alpes. Paris. 1864. 8vo.—See Caligny, l'Institut, (1864) 30. al pet 136 LITERATURE OF THERMODYNAMICS. Cazrn (A.). Méthode élémentaire pour calculer les effets mécaniques de Ja chaleur et application a la théorie des machines 3.air chaud. Mondes, 5 (1864) 220. —. Sur la dilatation des vapeurs saturées. Compies rendus, Jan. 2, 1866; Phil. Mag. [4] 31 (1866) 163. Reply by Rankine, same vol. 197. Mondes, 12 (1866) 1. — et Hiern (G. A.). Expériences sur la dilatation du vapeur de Peau surchauffé. Comptes rendus, Dec. 31, 1866; Phil. Mag. [4] 33 (1867) 256. —. Mémoire sur la detente et la compression des vapeurs saturées. Ann. chim. et phys. [4] 14 (1868) 374; Phil. Mag. [4] 36 (1868) 238. —. The phenomena of the laws of heat. Translated by Elihu Rich. London. 1868. 8vo. -——. Sur la dilatation des gaz. Comptes rendus, Aug. 9, 1869 ; Phil. Mag. [4] 38 (1869) 322. CELLERIER (C.). Distribution des vélocités moleculaires dans les gaz. Arch. phys. nat. [3] 6 (1881) 357-369 ; Jahresb. (1881) 1073; Phil. Mag. [5] 13 (1882) 47. CuHA.uis (Prof.). Theoretical considerations respecting the relation of pressure to density. Phil. Mag. [4] 17 (1859) 401. —. On the scource and maintenance of the Sun’s heat. Phil. Mag. [4] 25 (1863) 460. —. Further discussion of the analytical principles of hydrody- namics, in reply to Mr. Moon. Phil. Mag. [4] 47 (1874) 25. Mr. Moon’s reply, same vol. 143. y; —. Ona theory of Mr. Crookes’s radiometer. Phil. Mag. [5] 1 (1876) 3895; 2 (1876) 374. —. Theovetical explanations of the actions of the radiometer, the otheoscope, and the telephone. Phil. Mag. [5] 5 (1878) 452. Cuampron et Perit. Explosions produced by high tones. Phil. Mag. [4] 46 (1873) 256, from Chronique @’Industrie, Jan. 29, 1873. Cuappuis (P.). Ueber die Verdichtung der Gase auf Glasoberflachen. Ann. Phys. u. Chem. n. F. 8 (1879) 1; Nachtrag, 672. —. Etudes sur le thermométre 4 gaz et comparaison des ther- mométres 4 mercure avec le thermométre a gaz. Mémoires du Bureau internationale des poids et mesures, no. 6. Paris. 1888. 125 pp. et 190 tab. AUTHOR INDEX. hon CHARPENTIER (P.). Sur le rendement maximum que peut atteindre un moteur 4 vapeur. Comptes rendus, 96 (1888) 782. —. Sur les divers rendements théoriques que l’on doit considérer dans les machines a vapeur d’eau. Comptes rendus, 98 (1884) 85, 425, 1262. Cuase(P.E.). Cosmical thermodynamics. Amer. Philosoph. Soc. Proc. 14 (1874-75) 141-147. —w—. Mathematical deduction of the ratio between the mean vis viva of gaseous volume (heat under constant volume) and the vis viva of uniform velocity (heat under constant pressure). Amer. Phil. Soe. Proe. 14 (1874-75) 651. ——. Cosmical determination of Joule’s equivalent. Phil. Mag. [5] 10 (1880) 70; Amer. Phil. Soc. Proc., April 16, 1880. CHATELIER. See Le Chatelier, and Mallard et Le Chatelier. Cuervet (A.). Tension superficielle. Jour. de phys. [2] 8 (1888) 485-489. CHEVERTON. On the use of heated air as a motive power. Mechanics’ Mag. 58 (1853) 148, 170. On the caloric engine, and on the nature of motive power. Mechanics’ Mag. 64 (1856) 82. CamouLevircr. Investigations on the influence of heat on the mechani- eal force of frogs’ muscle. Phil. Mag. [4] 34 (1867) 403; Comptes rendus, Aug. 26, 1867. Cuossat. Extract of a memoir on the influence of the nervous system on animal heat. Thomson’s Annals of Phil. n. s. 2 (1821) 37, abs. from Ann. chim. et phys., with additions by Thomson. CuREE (C.). Bars and wires of varying elasticity. . Phil. Mag. [5] 21 (1886) 81. CHroustcHorr(P). Sur la chaleur de dissociation de quelques mélanges. Comptes rendus, 95 (1882) 221. —. Sur étude de la conductibilité électrique des dissolutions salines appliquée aux problémes de mécanique chimique. Comptes rendus, 108 (1889) 1003-6 ; Beiblatter, 13 (1889) 823, abs. Ciena (J. F.). De frigore ex. evaporatione, et affinibus phoenomenis nonnullis. Mem. Accad. Torino, 2 (1760-61) 143. 138 LITERATURE OF THERMODYNAMICS. CLAPEYRON. Théorie mécanique de la chaleur. J. de I’Ecole poly- technique, 14 (1884) 170; Ann. Phys. u. Chem. 59 (1834) 446, 566; Jahresb. (1850) 37. CLARKE (E. D.). Blowpipe experiments on an explosive mixture of oxygen and hydrogen. Thomson’s Annals of Phil. 1817; Ann. chim. et phys. 3 (1817) 359; 5 (1817) 441. CLARKE (F. W.). The constants of nature. Smithsonian Miscell. Coll. 12 (1874) 272; 14 (1878) 58, 62. —— — —. Noteon molecular volumes. Phil. Mag. [5] 3 (1877) 398. Ciausius (R.). Die mechanische Warmetheorie. Ann. Phys. u. Chem. 81 (1850) 168; Ber. d. Berliner Akad. (1850) 42; Instit. (1850) 245; Jahresb. (1850) 387; Phil. Mag. [4] 2 (1851) 1, 102. —. Ueber das Verhalten des Dampfes bei der Ausdehnung unter verschiedenen Umstiinden. Ann. Phys. u. Chem. 82 (1851) 263; C.’s Abhandiungen, 1, 103; Ann. chim. et phys. [8] 37 (1853) 868; Phil. Mag. [4] 1 (1851) 398; Jahresb. (1851) 26. —. Reply to a note from Mr. W. Thomson. Phil. Mag. [4] 2 (1851) 139; Jahresb. (1851) 28. —. Ueber den theoretischen Zusammenhang zweier empirisch autgestellter Gesetze tiber die Spannung und die latente Warme verschiedener Dimpfe. Ann. Phys. u. Chem. 82 (1851) 274, C.’s Abhandlungen, 1, 119; Jahresb. (1851) 31; Phil. Mag. [4] 2 (1851) 488. —. Ueber die mechanische Warmetheorie. Ann. Phys. u.Chem. 83 (1851) 118; Jahresb. (1851) 28, . —. Ueber das mechanische Aequivalent einer electrischen Entladung und die dabei stattfindende Erwirmung des Seitungsdrahtes. Ann. Phys. u. Chem. 86 (1852) 337; C.’s Abhandlungen, 11,98; Ann. chim. et phys. [3] 88 (1853) 200. —. Ueber die bei einem stationaren elektrischen Strome in dem Leiter gathane Arbeit und erzeugte Wirme. Aun. Phys.u. Chem. 87 — (1852) 415; Clausius’s Abhandlungen, m1, 164; Ann. chim. et phys. [3] 42 (1854) 122. —. Ueber die Anwendung der mechanischen Warmetheorie auf die thermoelektrischen Erscheinungen. Ann. Phys. u. Chem. 90 (1853) 513; C.’s Abhandlungen, 1, 175. AUTHOR INDEX. 139 Craustus (R.). Ueber einige Stellen in der Schrift von Helmholtz: “Ueber die Erhaltung der Kraft.”> Ann. Phys. u. Chem. 91 (1854) 601. —. Ueber eine verinderte Form des zweiten Hauptsatzes der mechanischen Wiarmetheorie. Ann. Phys. u. Chem. 93 (1854) 481; C.’s Abhandlungen, 1, 127; J. de Liouville (1855) 63; Phil. Mag. [4] 12 (1856) 81; Jahresb. (1854) 43; Comptes rendus, 40 (1855) 1147. —. Ueber die Anwendung der mechanischen Wirmetheorie auf die Dampfmaschine. Ann. Phys. u. Chem. 97 (1856) 441, 513; C.’s Abhandlungen, 1, 155.—See Joule, Phil. Mag. [4] 12 (1856) 385. C.’s reply, same vol. 465. —. Notiz tiber den Zusammenhang zwischen dem Satze von der Aequivalenz von Wiirme und Arbeit und dem Verhalten der perma- nenten Gase. Ann. Phys. u. Chem. 98 (1856) 173; Amer. J. Sci. [2] 22 (1856) 402; Jahresb. (1856) 27.—See Rankine, Phil. Mag. [4] 12 (1856) 103; and Hoppe, Jahresb. (1854) 44. —. Ueber die Natur der Bewegung die wir Warme nennen. Ann. Phys. u. Chem. 100 (1857) 353; Phil. Mag. [4] 14 (1857) 108 ; Ann. chim. et phys. [3] 50 (1857) 497; C.’s Abhandlungen, 11, 229, ——— —. Ueber die Electricititsleitung in Electrolyten. Ann. Phys. u. Chem. 101 (1857) 338; Ann. chim. et phys. [3] 53 (1858) 252; C.’s Abhandlungen, 11, 202; Arch. de Genéve, 36 (1857) 119. —. Ueber die mittlere Liinge der Wege, welche bei der Mole- kularbewegungen gasformiger Korper von den einzelnen Molekiilen zuriickgeleet werden, nebst einigen anderen Bemerkungen tiber die mechanische Wiarmetheorie. Ann. Phys. u. Chem. 105 (1858) 239; C.’s Abhandlungen, 1, 260; Phil. Mag. [4] 17 (1859) 81. —. On thedynamical theory of gases. Phil. Mag. [4] 19 (1860) —. “Kin elastischer Draht kiihlt sich bei der Dehnung um ebensoviel ab, als er sich bei der Zusammenziehung erwirmt;” E. Edlund, Ann. Phys. u. Chem. 114 (1861) 13. Wird dabei keine Arbeit verrichtet, so ist die Erwiirmung grosser als bei der Arbeitsleistung und proportional derselben, Clausius, Ann. Phys. u. Chem., same vol. 37. —. Ueber die Anwendung des Satzes von der Aequivalenz der Verwandlungen auf die innere Arbeit. Ann. Phys. u. Chem. 116 © (1862) 73; C.’s Abhandlungen, 1, 242; Comptes rendus, 54 (1862) 732; Phil. Mag. [4] 24 (1862) 81, 201; Mitt. d. naturforsch Ges. in Zurich, 7 (1862) 48. 140 LITERATURE OF THERMODYNAMICS. Ciausius (R.). Ueber die Molekularbewegungen in gasformigen Kér- pern. Ber. d. Berliner Akad. 46 11 (1862). 402. —. Ueber einen Grundsatz der mechanischen Warmetheorie. Ann. Phys. u. Chem. 120 (1863) 426; C.’s Abhandlungen, 1, 297. —. Aus einem kilteren Korper kann die Wirme nicht von selbst in einen wiirmeren tibergehen; tiber einen Grundsatz der mechanischen Wirmetheorie. Ann. Phys. u. Chem. 120 (1863) 451 ; Cosmos, 22 (1863) 560; C.’s Abhandlungen, 1, 297. —. Sur la condensation des vapeurs pendant la détente ou la compression. Comptes rendus, 56 (1863) 1115. —. Sur quelques équations qui dérivent de la théorie mécanique de la chaleur. Comptes rendus, 57 (1863) 339. En reponse 4 M. Dupré, Mondes, 6 (1864) 687. —. Lettre au sujet des objections émises par M. Hirn dans un précédent numéro du Cosmos. Cosmos, 22 (1863) 560. —. Ueber die Concentration der Warme und Lichtstrahlen und die Grinzen ihrer Wirkung. Mittheil. d. naturforsch. Ges. in Zurich, 22 Juni, 1863 ; Aun. Phys. u. Chem. 121 (1864) 1; C.’s Abhand. 1, 322. —. Ueber den Einfluss der Schwere auf die Bewegungen der Gasmolektile. Z. Math. u. Phys. (1864) 376. —. Sur une détermination de l’équivalent mécanique de la chaleur. Mondes, 6 (1864) 423. (Remarques sur une note de M. Dupré.) —. Sur les équations fondamentales de la théorie mécanique de Ja chaleur. Mondes, 6 (1864) 687. (En réponse 4 M. Dupré.) —. Abhandlungen tiber die mechanische Wairmetheorie. Braun- schweig. 1864. 8vo. Translated into French by F. Folie, Paris, 1868-69, 2 vols.—Zweite umgearbeitete und vervollstindigte Auflage, Braunschweig, 1876-79, 4 vols. Translated into English by W. R. Browne, London, 1878 (with three appendices: 1, The thermoelastic properties of solids ; 1, The application of thermodynamical principles to capillarity ; 11, The continuity of the liquid and gaseous states of matter). This translation is from the second edition of Clausius’s work on thermodynamics, and supersedes Dr. T. Archer Hurst’s translation of the first edition by containing important revisions by Clausius. —. Ueber verschiedene fiir die Anwendung bequeme Formen der mechanischen Wiirmetheorie. Ann. Phys. u. Chem. 125 (1865) 303. C.’s Abhandlungen, 11, 1; Jour. de Liouville, [2] 10 (1865) 361. AUTHOR INDEX. 14] Cxaustus (R.). Gleichgewicht heterogener Substanzen. Ann. Phys. u. Chem. 125 (1865) 400; Jahresb. (1870) 115.—See J. W. Gibbs, below. —. Surlesecond théoréme de la théorie mécanique de la chaleur. Comptes rendus, 60 (1865) 1025 ; 61 (1865) 15. —. Ueber die Bestimmung der Energie und Entropie eines Korpers. Z. Math. u. Phys. 11 1 (1866) 31; Phil. Mag. [4] 32 (1866) 1. —. Ueber das Integral i Z. Math. u. Phys. 11 1 (1866) 455. Antwort auf Hrrn. Bauschinger. —. Ueber die Disgregation eines Kérpers, und die wahre Wirme- capacitét. Ann. Phys. u. Chem. 127 (1866) 477; Arch. de Genéve, Oct. 1865; Phil. Mag. [4] 31 (1866) 28.—See Phil. Mag. [4] 24 (1862) 81, and Ann. Phys. u. Chem. 116 (1862), 73; Jahresb. (1867) 81. —. Ueber die Bestimmung der Dissociation. Zamminer’s Jah- resb. (1867) 40; Liebig’s Jahresb. (1867) 81. —. Onthesecond fundamental theorem of the mechanical theory of heat. Phil. Mag. [4] 35 (1868) 405 (translated from a pamphlet communicated by the Author). —. Note de M. Clausius accompagnant l’envoi de la traduction francaise de sa “ Théorie mécanique de la chaleur.” Comptes rendus, 66 (1868) 184; 68 (1869) 1142. —. Ueber die wirksame Kraft der Warme. Ann. Phys. u- Chem. 141 (1870) 124; Jahresb. (1870) 76; Phil. Mag. [4] 40 (1870) 122 (translated from a separate impression communicated by the Author, having been read before the Niederrhein. Ges. f. Naturkunde, June 13, 1870. —. Begriff vom Virial eines Systems. Ann. Phys. u. Chem. 141 (1870) 125, 128; Mitt. d. Niederrhein. Ges. ff Naturkunde, 15 Juni, 1870. —. Disgregation eines Korpers. Ann. Phys. u. Chem. 141 (1870) 427. E. Budde dazu, 428. —. Zuriickfiihrung des zweiten Hauptsatzes der mechanischen Warmetheorie auf allgemeine mechanische Principien. Ann. Phys. u. Chem. 142 (1871) 483; Phil. Mag. [4] 42 (1871) 161 (transl. from Niederrhein. Ges. f. Naturkunde, Noy. 7, 1870). Reklamation von L. Boltzmann, Ann. Phys. u. Chem. 143 (1871) 211. Erwiderung von Clausius, 144 (1872) 265, und Verallgemeinerung seiner Gleichung, 150 (1873) 106, 120. a Sl SE a ae ee 142 LITERATURE OF THERMODYNAMICS. Crausius (R.). On the application of a mechanical equation advanced by me to the motion of a material point around a fixed centre of attrac- tion, and of two material points about each other. Phil. Mag. [4] 42 (1871) 321. —. Uebergehung der Verdienste von Clausius um die Warme- theorie seitens gewisser englischen Schriftsteller. Ann. Phys. u. Chem. 145 (1872) 182; Erwiderung von Tait, 496; Berichtigung dazu von Clausius, 146 (1872) 308; Phil. Mag. [4] 43 (1872) 106, commenting on J. Clerk Maxwell’s book “Theory of Heat;” Tait’s reply, same vol. 338; Clausius again, 443; Tait, 516. Correction by Clausius, Phil. Mag. [4] 44 (1872) 117; Tait’s reply, 240, Jahresh, (1872) 60. —. Ueber die Beziehung des zweiten Grundsatzes der mechan- ischen Warmetheorie zum Hamilton’schen Princip. Ann. Phys. u. Chem. 146 (1872) 585; Phil. Mag. [4] 44 (1872) 365.—See Szily, Phil. Mag. [4] 43 (1872) 339. —. Beziehungen der Gleichungen von Clausius und yon Boltz- mann zum Hamilton’schen Princip. Ann. Phys. u. Chem. 149 (1873) "7 74. —. Mechanische Theorie stationirer Bewegungen. Ber. d. -_ Niederrhein. Ges. f. Naturkunde, 16 Juni, 1873; Ann. Phys. u. Chem. 150 (1873) 106; Phil. Mag. [4] 46 (1873) 236, 266; Jahresb. (1873) 51. —. Sur une équation mécanique qui correspond a léquation i =O. Comptes rendus, 78 (1874) 461. —. M. Clausius fait hommage 4 l’Académie d’un Mémoire sur les différentes formes du viriel. Comptes rendus, 78 (1874) 1351. —. Sur un eas spécial du viriel. Comptes rendus, 78 (1874) —. On the theorem of the mean ergal, and its applications to the molecular motions of gases. Phil. Mag. [4] 50 (1875) 26, 101, 191, comm. by author; Mitt. d. Niederrhein. Ges. f. Naturkunde, 9 Nov. 1874. —. Bemerkungen zu dem Aufsatze des Herrn von Oettingen iiber Temperatur und Adiabate. Ann. Phys. u. Chem. 159 (1876) a 327; Jahresb. (1876) 62. ye —. Bemerkungen zu einem Ausspruche von F. Kohlrausch tiber Thermoelektricitit. Ann. Phys. u. Chem. 160 (1877) 420. AUTHOR INDEX. 143 CuaAusius (R.). Behauptung seines Satzes, dass die Wirme nicht von selbst aus einem kalteren in einen wairmeren Korper tibergehen kann, einem neuen von Tait angefiihrten Gegengrund gagentiber aufrecht. Ann. Phys. u. Chem. [2] 2 (1877) 130; Jahresb. (1877) 87.—See Tait’s Lectures on some Recent Advances in Physical Science, 2. edition, p. 119. —. Die Potentialfunction und das Potential, ein Beitrag zur mathematischen Physik. Dritte, vermehrte Auflage. Leipzig. 1877. (178 pp.) Phil. Mag. [5] 5 (1878) 389. —. Ueber die Beziehung der durch Diffusion geleisteten Arbeit zum zweiten Hauptsatze der mechanischen Wiirmetheorie. Ann. Phys. u. Chem. n. F. 4 (1878) 341; Phil. Mag. [5] 6 (1878) 237—See S. Tolver Preston, Nature, 17 (1877-78) 31, 202. —. Sur lénergie dun corps et sa chaleur spécifique. Comptes rendus, 87 (1878) 718. —. Ueber das Verhalten der Kohlensiure in Bezug auf Druck, Volumen und Temperatur. Ann. Phys. u. Chem. n. F. 9 (1880) 337. —. Untersuchung tiber die mittlere Weglange der Gasmolekiile. Ann. Phys. u. Chem. n. F. 10 (1880) 92. —. Ueber die theoretische Bestimmung des Dampfdruckes und der Volumina des Dampfes und der Fliissigkeit. Ann. Phys. u. Chem. n. F, 14 (1881) 279, 692; Jahresb. (1881) 55; Phil. Mag. [5] 13 (1882) 132. —. Zur theorie der Krafttibertragung durch dynamoelectrischee Maschinen. Ann. Phys. u. Chem. n. F. 21 (1884) 385. —. Thermoelectrische Untersuchungen. Leipzig. 4 vols. 1882- 86. Cresson (A.). Theorie der Elasticitit fester Korper. Leipzig. 1862. (x1, 424 pp.) CLiment. See Desormes et Clément. Currrorp (W. K.). Elements of Dynamic. An introduction to the study of motion and rest in solid and fluid bodies. Part 1, Kinematic. London: Macmillan. 1878. Phil. Mag. [5] 6 (1878) 306. CoatuuPE (C. T.). On certain effects of temperature. Phil. Mag. 17 (1840) 130. Copazza. Sopra alcuni punti della teoria della forza motrice del calore. Cimento, 15 (1862) 61. 144 LITERATURE OF THERMODYNAMICS. Conn (E.). Ueber das thermoelectrische Verhalten gedehnter Drahte. Ann. Phys. u. Chem. n. F. 6 (1879) 385. CotpinG (A.). Recherches sur les rapports des forces de la nature. Vidensk selsk. skrift. Kjobenhavn, 2 (1851) 121, 167. —. On the history of the principle of the conservation of energy. Phil. Mag. [4] 27 (1864) 56; Ann. chim, et phys. [4] 1 (1864) 466. —. On the universal powers of Nature and their mutual depend- ence. -Phil. Mag. [4] 42 (1871) 1; Jahresb. (1871) 62. CoLttapon (D.). Extrication of heat by compression of gases. Phil. Mag. n. s. 2 (1827) 390, abs. from Hensman’s Repertoire de Chimie. Cotnet D’Huart. Nouvelle théorie mathématique de la chaleur et de Vélectricité. Paris. 1864-65. 2 vols. ComsBes (Ch.). Théorie mécanique de la chaleur. Paris. 1863. —,. Observations 4 Voceasion d’une note de M. Thomson. Comptes rendus, 59 (1864) 705, 717. —. Note de M. Combes accompagnant son ouvrage intitulé: Exposé des principes de la théorie mécanique de la chaleur et ses applications principales. Comptes rendus, 64 (1867) 293. —. Exposé des principes de la théorie mécanique de la chaleur et de ses applications principales. Paris. 1867. —. Premier et deuxiéme mémoire sur l’application de la théorie mécanique de la chaleur aux machines locomotives dans la marche 4 contrevapeur. Paris. 1869. Comité DES PoupRES ET SALPETRES. Inflammation de la poudre dé- terminée par la chaleur qui se dégage pendant l’extinction de la chaux. Extrait des Archives du Comité consultatif de la Direction des Poudres et Salpétres. Ann. chim. et phys. 23 (1823) 217. Cook (Ernest H.). On the regenerative theory of solar action. Phil. Mag. [5] 15 (1883) 400. Reply by Sir William Siemens, 16 (1883) 62. Cook (H. Whiteside). On certain objections to the dynamic theory of heat. Rept. British Assoc. (1870) 38. Cooke (J. P. Jr.). On the heat of friction, Amer. J. Sci. January, 1866 ; Phil. Mag. [4] 31 (1866) 241, abs. ——w—. On Berthelot’s thermochemistry. Amer. J.Sci. April, 1860; Phil. Mag. [5] 9 (1880) 367. AUTHOR INDEX. 145 Copper (de). Recherches sur la température de congélation des dissolu~ tions salines. Ann. chim. et phys. [4] 25 (1871) 366; 25 (1872) 502; 26 (1872) 98. ¢ Cosa (Della). Sull equivalente meccanico del calore. Rend. di. Bologna, (1861-62) 101. CosrE (P.). Note concernant l’équivalent mécanique de la chaleur. Comptes rendus, 71 (1870) 376. CorreriLy (J. H.). On an extension of the dynamical principle of least action. Phil. Mag. [4] 29 (1865) 299. CourrrE (M.). Sur un nouvel appareil pour l’étude du frottement des fluides. Comptes rendus, 106 (1888) 388-90. CourtEPEE. See Masson et Courtépée. Cowper (E. A.) and ANDEeRson (W.). Experiments on the mechanical equivalent of heat on a large scale. Rept. Brit. Assoc. (1887) 562; Beiblitter, 13 (1889) 792, abs. Crace-Catvert (F.). Action of heat on protoplasmic life. Proc. Roy. Soe. 19 (1870-71) 472. —and Lown (G. C.). On the expansion of metals and alloys. Phil. Mag. [4] 20 (1860) 230, abs. from Proce. Roy. Soc. Feb. 16, 1860. Craur (C.). Ueber das Gesetz der Temperatur und Ausdehnung eines von WechselstroOmen durchflossenen Drahtes. Elektrotechn Zeitschr. 9 (1888) 426. CRrESSON (Prof.). Remarks on the temperature of congelation. Amer. Philosoph. Soe. Proce. 5 (1848-53) 168. CricHron. On expansions. Annals of Phil. un. s. 7 (1824) 241. Crout (J.). On the cohesion of gases and its relation to Carnot’s fune- tion and to recent experiments on the thermal effects of elastic fluids in motion. Rept. Brit. Assoc. (1862) nu, 21. ————. On supposed objections to the dynamical theory of heat. Phil. Mag. [4] 27 (1864) 196.—See Cook (H. W.), above. —. On the nature of heat vibrations. Phil. Mag. [4] 27 (1864) i i ee ee ee LE SE tee a A ae LTE 146 LITERATURE OF THERMODYNAMICS. Crouu (J.). On the cause of the cooling effect produced on solids by tension. Phil. Mag. [4] 27 (1864) 380. —. On certain hypothetical elements in the theory of gravitation and generally received conceptions regarding the constitution of matter. Phil, Mag. [4] 34 (1867) 449. —. On the physical cause of the motion of glaciers. Phil. Mag. [4] 87 (1869) 201; 40 (1870) 153. —. What determines molecular motion? the fundamental prob- lem of Nature. Phil. Mag. [4] 44 (1872) 1. —. On the transformation of gravity. Phil. Mag. [5] 2 (1876) 241. —— —. On the origin of nebule. Phil. Mag. [5] 6 (1878) 1. —. Arctic interglacial periods. Phil. Mag. [5] 19 (1885) 30. Crookes (W.). On attraction and repulsion resulting from radiation. Proc. Roy. Soc. 22 (1873-74) 37, 23 (1874-5) 373, abs.; Phil. Mag. [5] 1 (1876) 245; Phil. Trans. 164 (1874) 501; 165 (1875) 519; 166 (1876) 325; 169 (1878) 243; 170 (1879) 87. —. On the illumination of lines of molecular pressure, and the trajectory of molecules. Phil. Mag. [5] 7 (1879) 57; Phil. Trans. 170 (1879) 135, 641. -—. On the New Force, suggested by H. Thore. Proc. Roy. Soc. 42 (1887) 845; Beiblatter, 12 (1888) 188.—See Dufourcet (E.) below. Cross (C. R.). Experiments with the thermal telephone. .Proc. Amer. Acad. n. s. 13 (1885-6) 257. Crum (W.). Analysis of bodies containing nitric acid, and its applica- tion to explosive gun-cotton. Phil. Mag. [3] 30 (1847) 436. Curtis (A. H.). On the freezing of water at temperatures lower than 32° F. Phil. Mag. [4] 382 (1866) 422. Czapski (S.). Ueber die thermische Veranderlichkeit der electromotor- ischen Kraft galvanisher Elemente und ihrer Beziehung zur freien — Fnergie derselben. Ann. Phys. u. Chem. n. F. 21 (1884) 209. Daca (Emile Martin). De la chaleur comme cause et effet da la vie et du froid, comme modificateur de Vorganisme vivant. Paris. 1859. AUTHOR INDEX. 147 DAHLANDER (G. R.).. Om en bestamming af varmeenhetens mekaniska equivalent. Oefversigt af forhandl. Stockholm. 1864. —-—. Sur une détermination de l’équivalent mécanique de la chaleur. Aun. chim. et. phys. [4] 4 (1865) 474. —-—. Einfluss der Spannung auf die Ausdehnung durch Wiirme. Ann. Phys. u. Chem. 145 (1872) 147; Jahresb. (1872) 59. Davron (J.). Experimental essays on the constitution of mixed gases, on the force of steam or vapour from water and other liquids in different temperatures, both in a Torricellian Vacuum and in air, on evapora- tion, and on the expansion of gases by heat. Manchester Soc. Mem. 5 1 (1802) 585; Ann. de chimie, 44 (1803) 40, 217, 218. —. Investigation of the temperature at which water is of greatest density, from the experiments of Dr. Hope on the contraction of water by heat at low temperatures. Nicholson’s Jour. 13 (1806) 377; 14 (1806) 128. —. New system of chemical philosophy. Manchester. 1827. New edition, 1842.—See Lear, Ber. chem. Ges. 18 (1885) 648; Jahresb. (1885) 6. Danrevt (J. F.). An introduction to the study of chemical philosophy, being a preparatory view of the forces which concur to the production of chemical phenomena. London. 1848. Phil. Mag. [3] 22 (1843) ‘298. 2 Davis (A.S8.). On the vibrations which heated metals undergo when in contact with cold material, treated mathematically. Phil. Mag. [4] 45 (1873) 296. Davy (Sir H.). Elements of chemical philosophy. London. 1812. —-—. Observations on animal heat. Phil. Trans. (1844) part 1,57; Ann. chim. et phys. [3] 13 (1845) 174. Desray (H.). Dissociation. Comptes rendus, 64 (1867) 603; Instit. (1867) 89; Z. f. Chemie, (1867) 302; Jahresb. (1867) 85. —. Sur la dissociation de l’oxyde rouge de mercure. Comptes rendus, 77 (1873) 125. —. Sur la dissociation dans les corps solides. Comptes rendus, 86 (1878) 517; Jahresb. (1878) 117. % —. Sur la dissociation des oxides de platine. Comptes rendus, 87 (1878) 441; Phil. Mag. [5] 6 (1878) 394. — SS a i +o it 148 LITERATURE OF THERMODYNAMICS. Desus (H.). On the chemical theory of gunpowder. Phil. Trans. 173 (1882) 523. Decuer. Ueber die Versuche des Herrn Hirn die mittelbare Reibung betreffend, und tiber das mechanische Aequivalent der Warme. Dingler’s pol. J. 186 (1855) 415; Jahresb. (1855) 29. —. Ueber das Wesen der Wiirme. Dingler’s pol. J. 148 (1858) 1. Deevey (R. M.). Ona theory of glacier motion. Phil. Mag. [5] 25 (1888) 156. . DeELAROCHE (F.). On the cause of refrigeration observed in animals ex- posed to a high degree of heat. Nicholson’s Jour. 31 (1812) 361, from J. de physique, 71 (1812) 289; read to the Institute of France, Nov. 6, 1809. —. Observations on radiant heat. Thomson’s Annals of Phil. 2 (1813) 100. Desains (E.). Mémoire sur la chaleur spécifique de Ja glace. Comptes rendus, 20 (1845) 1845. M. Person A Voccasion de cette présentation, écrit qwil A déposé antérieurement, sous pli cacheté, wne Note sur le méme sujet, méme vol. 1457; Ann. chim. et phys. [5] 14 (1845) 306. —. Recherches sur la solidification d’un liquide refroidi au dessous de son point de fusion. Ann. chim. et phys. [5] 64 (1862) 419. —. Rapport sur les progrés de la théorie de la chaleur. Paris. 1868. (118 pp.) —. See Provostaye et D. Descarres. Principia philosophiz. Amstelodami. 1677. Pars quarta. DesorMEsS et CLEMENT. Sur le nouveau procédé de congélation de M. Leslie, et sur les applications de ce procédé, considéré comme moyen d’évaporation. Ann. de chimie, 78 (1811) 183. Dersprerz (Cés.). Mémoire sur le refroidissement de quelques métaux, pour déterminer leur chaleur spécifique et leur conductibilité exterieure. Ann. chim. et phys. 6 (1817) 184. —. Mémoire sur les densités des vapeurs. Ann. chim. et phys. 21 (18229 143. —. Heat evolved by compressing water. Phil. Mag. n. s. 2 (1827) 392. - AUTHOR INDEX. 149 Desprerz (Cés.). Mémoire sur la combustion sous différentes pressions. Ann. chim. et phys. 37 (1828) 182. “ —. Note relative 4 une expression analytique de l’équivalent mécanique de la chaleur. Comptes rendus, 51 (1860) 364, 496. DEVENTER (C. M. van.). Einfache Herleitung einiger fiir die Chemie wichtiger thermodynamischer Beziehungen. 1. Z. phys. Chem. 2 (1888) 92; Beiblitter, 12 (1888) 763, abs. DEVILLE (Ch. Sainte-Claire). On the density of certain substances (quartz, corundum, metals, etc.) after fusion and rapid cooling. Phil. Mag. [4] 11 (1856) 144. ——w—. De la dissociation ou décomposition spontanée des corps sous V’influence de la chaleur. Comptes rendus, 45 (1857) 857 ; Jahresb. (1857) 58. — — — et Troost (L.). Mémoire sur les densités de vapeur a des températures trés élévées. Ann. chim. et phys. [3] 58 (1860) 257 ; Comptes rendus, 49 (1860) 259; Phil. Mag. [4] 19 (1860) 207, abs. ———. Delachaleur dégagée dans les combinaisons chimiques. Comptes rendus, 50 (1860) 554, 584; Phil. Mag. [4] 21 (1860) 202; Jahresb. (1860) 32.—See Baudrimont and Robin, Comptes rendus, 50 (1860) 688, 723. — ——. Sur la dissociation de eau. Comptes rendus, Feb. 2, 1863; Phil. Mag. [4] 25 (1863) 537. ———___—. See Wanklyn (J. A.). Phil. Mag. [4] 29 (1865) 111. ———. Sur la dissociation. Comptes rendus, 59 (1865) 873; 60 (1865) 317; Z. f. Chimie, (1865) 319; Phil. Mag. [4] 30 (1865) 252; Bull. soc. chim. [2] 3 (1865) 366; 5 (1866) 104; Jahresb. (1865) 59. ——w—. Affinity and heat. Phil. Mag. [4] 32 (1866) 365, from Deyville’s Lecons de Chimie. ——-—. Sur les densités des vapeurs. Comptes rendus, 62 (1866) 1157; Phil. Mog. [4] 32 (1866) 387, abs. —-—-—. Sur la dissociation. Comptes rendus, 63 (1867) 19; Jahresb. (1867) 81. Schréder van der Kolk, Ann. Phys. u. Chem. 129 (1867) 495. 150 LITERATURE OF THERMODYNAMICS. DEVILLE (Ch. Sainte-Claire.). Sur la dissociation. Comptes rendus, 64 (1867) 66; Jahresb. (1867) 79. —-——. Sur quelques alliages explosifs du zine et du platine. Comptes rendus, 94 (1882) 1557; Phil. Mag. [5] 14 (1882) 152. ——w—. Savieetses travaux, parJulesGay. Paris: Gauthier- Villars. 1889. Beiblatter, 13 (1889) 577, abs. Diererict (C.). Ueber eine neue Bestimmung des mechanischen Aequiv- alentes der Wirme. Tageblatt. d. 60 Vers. deutsch. Naturf. u. Aertzte zu Wiesbaden (1887) 236; Ann. Phys. u. Chem. 33 (1888) 417. Dispan. Observations sur la congélation de Peau. Ann. de chimie, 57 (1806) 68; Nicholson’s Jour. 15 (1806) 251. DOBEREINER. Sur l’alliage fusible et sur une combinaison métallique réfrigérante. Annals of Phil. n. s. 12 (1826) 392; Ann. chim. et phil. 32 (1826) 334. Dorn (E.). Ueber die absolute Grésse der Gasmolektile. Ann. Phys. u. Chem. n. F. 13 (1881) 378. Drarer (J. W.). On some analogies between the phenomena of the chemical rays, and those of radiant heat. Phil. Mag. [3] 19 (1841) 195. ——. Singular property of gun-cotton. Phil. Mag. [3] 30 (1847) 299. ——. Scientific Memoirs; being experimental contributions to a knowledge of radiant energy. New York. 1878. Phil. Mag. [5] 7 (1879) 211. Drecker (J.). Ueber die innere Ausdehnungsarbeit von Flissigkeits- gemischen im Vergleich zu derjenigen ihrer Bestandtheile. Ann. Phys. u. Chem. n. F. 20 (1883) 870. Drion (Ch.). Recherches sur la dilatabilité des liquides volatils. Ann. chim. et phys. [3] 56 (1859) 5. —. De TV influence de la chaleur dans les phénoménes capillaires. Comptes rendus, 48 (1859) 950; Ann. chim. et phys. [3] 56 (1859) 221. DronkE (A.). Beitrag zur mechanischen Warmetheorie. Ann. Phys. u. Chem. 111 (1860) 343. —. Zur mechanischen Warmetheorie. Ann. Phys. u. Chem. 119 (1863) 388, 583. —. Einleitung in die analytische Theorie der Warmeverbreitung. Leipzig: Teubner. 1882. AUTHOR INDEX. rr Drummonp (J.). On some points of analogy between the molecular structure of ice and glass; with special reference to Professor Erman’s observations on the structural divisions of ice on Lake Baikal. Phil. Mag. [4] 18 (1859) 102. Duciaux (E.). Sur la tension superpicielle des liquides, Ann. chim. et phys. [4] 21 (1870) 378. Dupa (Th.). Ueber die durch Erwarmung bewirkte Ausdehnung der Korper. Ber. aus d. k. Gymnasium zu Brieg, 1886-87, p. 1-18. Durer (H.). Sur le volume moléculaire et l’énergie refractive de quelquessels de soude. Séance de la Soe. frang de phys. (1887) 117-128. Durour (E.). Esquisse d’une théorie dynamique dela chaleur. Nantes. 1869. Durour (L.). On the boiling points of liquids. Phil. Mag. [4] 22 (1861) 167, abs. from Comptes rendus, May 135, 1861. —. On the density of ice. Phil. Mag. [4] 24 (1862) 167, abs. from Comptes rendus, May. 19, 1862. —. Sur Pébullition de l’eau, et sur une cause probable de l’explo- sion des chaudiéres 4 vapeur. Phil. Mag. [4] 28 (1864) 78, 324, abs. from Comptes rendus, May 30, 1864, and June 6, 1864; Ann. chim. et phys. [4] 6 (1865) 111. —. On the bursting of Prince Rupert’s drops. Phil. Mag. [4] 37 (1869) 478, abs. from Comptes rendus, Feb. 15, 1869, Dourourcet (E.). Le spectrophone de M. Graham Bell et le radiométre par absorption de M. Thore. Paris. 1882. (8 pp.) Dvunem (P.). Sur le potentiel thermodynamique et la théorie de la pile voltaique. Comptes rendus, 99 (1884) 1113. —. Applications de la thermodynamique aux phénoménes capillaires. Ann. Ecole normale, [3] 2 (1885) 217; Lhil. Mag. [5] 22 (1886) 330; Beiblatter, 10 (1886) 330, abs. —. Le potentiel thermodynamique et ses applications 4 la mé- eanique chimique et 4 l’étude des phénoménes électriques. Paris: A. Hermann. 1886. —. Sur la tension de la vapeur saturée. Comptes rendus, 103 (1886) 1008; Ber. chem. Ges. 19 (1886) R. 592. —. Etude sur les cuvres thermodynamiques de J. W. Gibbs. Bull. des Sci. math. [2] 11 (1887) 14; Beiblatter, 12 (1888) 94, abs. ¢ Se tr ERE i hes Ba an a al 152 LITERATURE OF THERMODYNAMICS. Dunem (P.). Hauteur osmotique. Jour. de phys. 6 (1887) 134. ——- —. Pression osmotique. Jour. de phys. 6 (1887) 597. —. Théorie nouvelle de l’aimentation par l’influence fondée sur Jathermodynamique. Paris: Gauthier-Villars. 1888. 4to. (140 pp.) —. Sur quelques propriétés des dissolutions. Jour. de phys. [2] 7 (1888) 5. —. Einige Bemerkungen tiber die Lésungs-und Verdtinnungs- wirme. (Nach dem MSS. des Verfassers.) Z. phys. Chem. 2 (1888) 568-584. —. Sur la transformation et Véquilibre en thermodynamique. Comptes rendus, 108 (1889) 666; Beiblatter, 13 (1889) 643, abs. ® —. Sur limpossibilité des corps diamagnétiques. Comptes rendus, 108 (1889) 1042; Beiblatter, 15 (1889) 901, abs. Diurine (E.). Zum Schutze des Gesetzes der correspondirenden Siede- temperaturen. Ann. Phys. u. Chem.n, F. 11 (1880) 163. A. Winkel- mann’s Bemerkungen dazu, 534. Dutone et Perrr. Recherches sur les lois de dilatation des solides, des liquides et des fluides élastiques, et sur la mesure exacte des temnéra- tures. Ann. chim. et phys. 2 (1817) 240. et Recherches sur la mesure des températures et sur les lois de la communication de la chaleur. Thomson’s Annals of Phil. 12 (1818) 2; 13 (1819) 112, 161, 241, 321. . Exposé des recherches faites par ordre de l’ Académie des Sciences pour déterminer les forces élastiques de la vapeur d’eau a des hautes températures. Dulong rapporteur. Ann. chim. et phys. 43 (1850) 74, 88, 110; Phil. Mag. n. s. 7 (1830) 235. et Hess. Abstract of recent researches on the quantity of heat evolved in chemical combination, particularly those of MM. Dulong and Hess. Phil Mag. [3] 19 (1841) 19, 178. —. Recherches sur la chaleur.. Ann. chim. et phys. [3] 8 (1843) 180. . Recherches sur la chaleur spécifique des fiuides élastiques. Ann. chim. et phys. [2] 41 (1850) 115; Jahresb. (1850) 42. AUTHOR INDEX. Toe Dumas (J.). Dissertation sur la densité de la vapeur de quelques corps simples. Ann. chim. et phys. 50 (1832) 170. —. Rapport sur un mémoire de M. Frémy. Comptes rendus, 6 (1838) 599. Dupré(A.). Sur le travail mécanique et ses transformations. 1. mémoire, Comptes rendus, 50 (1860) 588. IL. mémoire et rédaction du premier, Comptes rendus, 52 (1861) 1185. tr. mémoire, Comptes rendus, 54 (1863) 907. Supplément relatif 4 la mesure des vapeurs saturées, méme vol. 972. Supplément relatif 5, la définition et 41a mesure des tempéra- tures, méme vol. 1065. —. Sur la condensation des vapeurs pendant la détente ou la compression. Comptes rendus, 56 (1863) 960.—See Clausius, méme vol. 1115. —. Discussion avec M. Reech. Comptes rendus, 57 (1863) 109, 589. —. Application de la théorie mécanique de la chaleur 4 la dis- cussion des expériences de M. Regnault sur la compressibilité des gaz. Comptes rendus, 57 (1865) 774. —. Mémoire sur la valeur de l’attraction au contact, la valeur du travail chimique dt a une élévation de température, la loi des chaleurs spécifiques des corps simples ou composés, et la seconde vaporisation des corps. Comptes rendus, 58 (1864) 163. —. Rectification de la formule donnée par M. W. Thomson pour calculer les changements de température que produit une compression ou une expansion avec travail complét. Comptes rendus, 58 (1864) 539.—See Comptes rendus, 59 (1864) 665, 705, 168. —. Sur la loi de M. Regnault relative aux tensions maximum des vapeurs. Comptes rendus, 58 (1864) 806. —. Sur la vitesse d’écoulement des gaz par des orifices en minces parois. Comptes rendus, 58 (1864) 1004. —. Mémoire sur la résistance des fluides opposent au mouvement. Comptes rendus, 58 (1864) 1061. —. Sur les lois de la compressibilité et de dilatation des corps. Comptes rendus, 59 (1864) 490. f i | | i. i) 154 LITERATURE OF THERMODYNAMICS. Dupré (A.). Reflexions sur les formules pour ?écoulement des fluides données par M. Zeuner, et reclamation de priorité relative 4 lune @Velles. Nouveau théoréme sur les capacités. Comptes rendus, 59 (1864) 596. —. Théorie des gaz et comparaison des expériences de M. Reg- nault avec les lois qu’elle renferme. Comptes rendus, 59 (1864) 905. —. 1. mémoire sur la théorie mécanique de la chaleur. Ann. chim. et phys. [4] 1 (1864) 168, 175.—11. mémoire, premiére partie, do. [4] 2 (1864) 185; deuxiéme partie, do. [4] 3 (1864) 76; troisiéme partie, [4] 4 (1864) 209.—111. mémoire, do. [4] 4 (1864) 65, 426.— Iv. mémoire, do. 5 (1865) 488.—v. mémoire do. 6 (1865) 274; 7 (1865) 189, 236, 257, 406.—v1. mémoire, do. 9 (1866) 328; 11 (1867) 194.— vir. mémoire, do, 14 (1868) 64. —. Sur les chaleurs latentes. Comptes rendus, 60 (1865) 339. —. Sur les principes fondamentaux de la théorie mécanique de la chaleur. Comptes rendus, 60 (1865) 718. —. Lettre en réponse 4 des observations de M. Hirn concernant cette note. Comptes rendus, 60 (1865) 864. —. Réponse a des remarques de M. Clausius relative 4 la méme communication. Comptes rendus, 60 (1865) 1156. —. Sur lemploi des températures absolues da-s la théorie mé- canique de la chaleur. Comptes rendus, 60 (1865) 1024. —. Sur la loi qui regit le travail de réunion des corps simples et sur les attractions 4 petites distances. Comptes rendus, 62 (1866).791. —. Sur l’attraction au contact dans les vapeurs et sur léquiva- lent mécanique de la chaleur. Mondes, 6 (1864) 315.—See Clausius, same vol. 423. Réponse de M. Dupré, same voi. 477. . —, Sur le nombre des molécules contenues dans l’unité de volume. Comptes rendus, 62 (1866) 39. Sur la théorie mécanique de la chaleur. Comptes rendus, 62 (1866) 622. —. Sur la théorie de la diffusion. Comptes rendus, 62 (1866) 1072. —. Nouveau mémoire ayant pour le titre: “ Travail et force moléculaire.” Comptes rendus, 63 (1866) 268. AUTHOR INDEX. £55 Dupré (A.). Note sur la tendance d’un systéme matériel quelconque au repos absolu ou relatif. Comptes rendus, 63 (1866) 548. —. Application de la théorie mécanique de la chaleur 4 V’étude de la transmission du son. Comptes rendus, 64 (1867) 350. —. Sur les attractions moléculaires et le travail chimique. Comptes rendus, 66 (1868) 141. —. Théorie mécanique de la chaleur. Paris. 1869. 8vo. Durer. Dela dilatation électrique des armatures des bouteilles de Leyde. Comptes rendus, 88 (1879) 1260. Eppy (H. T.). Radiant heat an exception to the second law of thermo- dynamics. Proc. Amer. Acad. 31 (1882) 225. —-—. On the kinetic theory of solid and liquid bodies. Scien- tific Proc. Ohio Mechanics’ Inst. March, 1883, pp. 26-43; do. Sept. _ 1888, pp. 89-97, 121-134; Jahresb. (1883) 112. Epiunp (E.). Ein elastischer Draht ktihlt sich bei der Dehnung um ebensoviel ab, als er sich bei der Zusammenziehung erwirmt. Ann. Phys. u. Chem. 114 (1861) 13.—See Clausius, same vol. 37. —. On the thermal phenomena which accompany the changes in volume of solid bodies, and on the corresponding mechanical work. Phil. Mag. [4] 24 (1862) 329 (translated from an abstract published by Verdet in Ann. chim. et phys. for February, 1862). —. Untersuchung tiber die Warmeentwickelung galvanischer Inductionsstrome und das Verhiltniss dieser Entwickelung zu der dabei verbranchten Arbeit. Ann. Phys. u. Chem. 123 (1864) 193. Ueber- setzung aus Oefversigt af Forhandl. Stockholm (1864) 77; Phil. Mag. [4] 31 (1866) 253. —. Bestimmung des mechanischen Warmeaquivalents aus Voluminderung der Metalle. Ann. Phys. u. Chem. 126 (1865) 539, 572. —. Détermination quantitative des phénoménes calorifiques qui se produisent pendant le changement de volume des métaux, et détermi- nation de léquivalent mécanique de la chaleur indépendamment du travail interne du métal. Ann. chim. et phys. [4] 8 (1866) 257. —. On the cause of the phenomena of voltaic cooling and heating discovered by Peltier. Phil. Mag. [4] 58 (1869) 263, originally read before the Swedish Academy, April 14, 1869. HI, nei 156 LITERATURE OF THERMODYNAMICS. Epuiunp (E.). Untersuchungen tiber die Warmeerscheinungen in der gal- vanischen Siule und tiber die elektromotorischen Krifte. Ann. Phys. u. Chem. 159 (1876) 420; Phil. Mag. [5] 8 (1877) 428, 501. —. Untersuchungen tiber die Warmeverdinderungen an den Polplatten in einem Voltameter beim Durchgange eines elektrischen Stromes. Ann. Phys. u. Chem. n. F. 19 (1883) 287. Epmonps (T. R.). On the elastic force of steam of maximum density ; with a new formula for the expression of such force in terms of the temperature. Phil. Mag. [4] 29 (1865) 169. ——. On the law of density of saturated steam expressed by a new formula. Phil. Mag. [4] 50 (1865) 1. Ersent. Beitrag zur mechanischen Theorie der Warme. Z. Math. u. Phys. 15 (1868) 491. Emmett (J. B.). On the expansion of liquids. Annals of Phil. n.s. 8 (1824) 254. ——. On the expansion of gases by heat. Phil. Mag. n.s. 5 (1829) 419. Ericsson (J.). Calorische Maschine. Polytechn. Centralbl. (1854) 183. —— —. Newair-engine. Mechanics’ Mag. 64 1 (1856) 487. —. The difference of thermal energy transmitted to the Earth by radiation from different parts of the solar surface. Nature, 12 (1875) 517; 13 (1875-76) 114-115, 224-226. Erman (G. A.). Essai sur Vinfluence que la liquefaction exerce sur le volume et la dilatabilité de quelques corps. Ann. chim. et. phys. 40 (1829) 197. ——. On the structure, the melting and the crystallization of ice. Phil. Mag. [4] 17 (1859) 405, translated from his “ Reise um die Erde,” historische Abtheilung, Vol. 2, p. 175. Errera (G.). Tavola delle tensioni di vapore delle soluzioni acquosi di idrato potassico. Gazz. chim. Ital. 18 (1888) 225-231. Espy. Joule’s unit verified. Edinburgh Jour. [2] 10 (1859) 252. Esrocquors. Note sur l’équivalent mécanique de la chaleur. Comptes rendus, 46 (1858) 461. AUTHOR INDEX. Loe Ewart '(P.). Experiments and observations on some of the phenomena attending the sudden expansion of compressed elastic fluids. Phil. Mag. n. s. 5 (1829) 247. Ewsank. Thoughts on the caloric engine. Mechanics’ Mag. 61 (1854) 411; 62 (1854) 78. EykMAN (J. F.). Ein Apparat zur Bestimmung der Gefrierpunktser- niedrigung. Z. phys. Chem. 2 (1888) 964-978. Fasran (H. W.). Anwendung der lebendigen Kraft in der mechanischen Warmetheorie. Ann. Phys. u.Chem. 156 (1875) 326; Jahresb. (1875) 46.—See Fritsch (H.). Ann. Phys. u. Chem. 153 (1874) 306. _ Farrearrn (W.). Experimental researches to determine the density of - steam at different temperatures, and to determine the law of expansion of superheated steam. Phil. Trans. 150 (1860) 185. The Bakerian Lecture. FarrBarrn and Tate. The density of steam at all temperatures. Phil. Mag. [4] 21 (1861) 230, abs. from Proc. Roy. Soc. May 10, 1860. On the law of expansion of superheated steam. Phil. Trans. 152 (1862) 591; Proc. Roy. Soe. April 3, 1862; Phil. Mag. [4] 25 (1863) 65, abs. Farapay (M.). On the temperature produced by the condensation of vapour. Thomson’s Annals of Phil. n.s. 5 (1823) 74, abs. from Ann. chim. et phys. [4] 20 (1823) 329. —. Congélation du mercure en trois secondes, en vertu de l’état sphéroidal, dans un creuset incandescent. (Extrait d’une lettre de M. Faraday 4 M. Boutigny, d’ Evreux.) Ann. chim. et phys. [3] 19 (1847) 383. —. On the conservation of force. London, 1857. (Lecture delivered before the Royal Institution of London, February 27, 1857.) —. Note on regelation. Proc. Roy. Soc. April 26, 1860; Phil. Mag. [4] 21 (1861) 146, abs. Farkas (J.). Ueber die Allgemeinheit des zweiten Hauptsatzes der mechanischen Wiarmetheorie. Oryos-Termszet tudoményi Ertesité, (1889) 279-288; Beiblatter, 13 (1889) 796, abs. Farigati (H. Serrano y). Mechanical equivalent of heat. N. Arch. ph. nat. 48 (1873) 252; Jahresb. (1873) 51; Phil. Mag. [4] 47 (1874) 155, 158 LITERATURE OF THERMODYNAMICS. Fave. Conséquences vraisemblables de la théorie mécanique de la chaleur. Comptes rendus, 83 (1876) 625; 84 (1877) 906. Favre (P. A.). Note sur les effets caloriques developpés dans le circuit voltaique dans leur rapport avec l’action chimique qui donne naissance au courant. Comptes rendus, 36 (1853) 542; 59 (1854) 1212; 45 (1857) 56. —— ——. Recherches sur l’équivalent mécanique de la chaleur. Comptes rendus, 46 (1858) 337; Phil. Mag. [4] 15 (1858) 406. — —et Laurent. Recherches sur les effets thermiques qui accompagnent la compression des liquides. Comptes rendus, 77 (1873) 981; Jahresb. (1873) 22. — — et SILBERMAMANN (J. T.). Sur la chaleur produite par les combinaisons chimiques. Comptes rendus, 18 (1844) 695; 20 (1845) 1565, 17384; 21 (1845) 944; 22 (1846) 483, 823, 1140; 23 (1846) 199, 411; 24 (1847) 1081; 26 (1848) 595; 27 (1848) 56, 111, 158, 362; 28 (1849) 627 ; 29 (1849) 440. Remarques de M. Regnault 4 l’occasion dune de ces communications. Comptes rendus, 22 (1846) 1143. — — et —-—. Recherches sur les quantités de chaleur dégagées dans Jes actions chimiques et moléculaires. Ann. chim. et phys. [3] 34 (1852) 357; 36 (1852) 5; 37 (1853) 405. Faye. Note accompagnant la présentation de la “ Théorie mecanique de la chaleur” de M. Hirn. Comptes rendus, 67 (1868) 880 ; 68 (1869) 880. Note accompagnant la présentation de la traduction francaise du traité de thermodynamique de M. Zeuner. Comptes rendus, 69 (1869) 101. Sur la nauvelle théorie du Soleil de Siemens. Comptes rendus, 95 (1882) 812; Phil. Mag. [5] 14 (1882) 400. Fick (A.). Ueber die Wirmeentwickelung bei der Muskelzuckung. Archiv. f. Physiol. 16 (1878) 1; Nature, 17 (1877-78) 285, abs. FINKENER (R.). Ueber das Radiometer von Crookes. Ann. Phys. u. Chem. 158 (1876) 572. Fiscuer (E.G.). Physique mécanique. Traduit avec des notes de M. Biot. Paris. 1806. Ann. de Chimie, 60 (1806) 102. AUTHOR INDEX. 159 Fiscuer (O.). On the thermal conditions and stratification of the Ant- arctic ice. Phil. Mag. [5] 7 (1879) 381. —. On the amount of the elevations attributable to compression through the contraction during cooling of a solid Earth. Phil. Mag. [5] 23 (1887) 145. FirzGERALD (G. F.). On the mechanical theory of Crookes’s force. Phil. Mag. [5] 7 (1879) 15; remarks of by Prof. Reynolds, same vol. PN 179. —-—. Clausius’s formula for the change of state from liquid to gas applied to Messrs. Ramsay and Young’s observations on alcohol. Proc. Roy. Soc. 42 (1887) 216; Beiblatter, 12 (1888) 216. Fizeau (H.). Recherches sur la dilatation et la double réfraction du cristal de roche échauffé. Ann. chim. et phys. [4] 2 (1864) 143. —. Mémoire sur la dilatation des corps solides par la chaleur. Ann. chim. et phys, [4] 8 (1866) 335. —. Note sur la dilatation des solides par la chaleur. Comptes rendus, 66 (1868) 1005, 1072; Phil. Mag. [4] 36 (1868) 31; Ann. Phys. u. Chem. 135 (1868) 372; Jahresb. (1868) 48. Fiemine (J. A.). On molecular shadows in incandescence lamps. Phil. Mag. [5] 20 (1885) 141. FietcHer (L.8.). Note on the relation between the mechanical equiva- lent of heat and the ohm. Phil. Mag. [5] 10 (1880) 486. ——. On the determination of the B. A. unit in terms of the mechanical equivalent of heat. Phil. Mag. [5] 20 (1885) 1. Forses (G.). On the thermal conductivity of ice, and a new method of determining the conductivity of different substances. Edinburgh Roy. Soe. Proce. 8 (1872-75) 62. Forses (J. D.). Onsome properties of ice near its melting-point. Phil. Mag. [4] 16 (1858) 544. —-—. Remarks on a paper on “ Ice and Glaciers,” in a letter to Prof. Tyndall. Phil. Mag. [4] 17 (1859) 197. Foret (F. A.). On the temperature of frozen lakes. Phil. Mag. [5] 9 (1880) 305. ——. On the structure and movement of glaciers. Phil. Mag. [5] 14 (1882) 238. \ 160 LITERATURE OF THERMODYNAMICS. Forkas (J.). Ueber die Beziehungen zwischen chemischer und elek- trischer Energie. Z. phys. Chem. 2 (1888) 148. Foster (G. C.). Report to the British Association on the subject of pyrometers. Rept. Brit. Assoc. (1873) 1; Chem. News, 28 (1873) 178 ; Ber. chem. Ges. 6 (1873) 1386, abs.; Jahresb. (1875) 55. Foveus. On the relations existing between the composition, density and refracting power of saline solutions. Phil. Mag. [4] 33 (1867) 555, abs. from Comptes rendus, January 21, 1867. Fourcroy et VAUQUELIN. Expériences sur la congélation des différens liquides par un froid artificiel Ann. de Chimie, 29 (1799) 281. Fourter. Théorie de la chaleur. Paris. ©1816. to. Ann. chim. et phys. 3 (1817) 350. Translated, with notes, by Alex. Freeman. Cam- bridge. 1878. Note sur la chaleur rayonnante. Ann. chim. et phys. 4 (1817) 128. Questions sur la théorie da la chaleur rayonnante. Ann. chim. et phys. 6 (1817) 259. Remarques générales sur les températures du globe terrestre et des espaces planétaires. Ann. chim. et phys. 27 (1824) 136. Résumé théorique des propriétés de la chaleur rayonnante. Ann. chim. et phys. 27 (1824) 236. Remarques sur la théorie mathématique de la chaleur rayon- nante. Ann. chim. et phys. 23 (1825) 337. Fournet (J.). Sur la congélation de la vapeur vésiculaire et sur les fléches glaciales. Ann. chim. et phys. [5] 46 (1856) 203. FoussEREAU (J.). Sur la décomposition réversible de divers sels par Veau. Ann. chim. et phys. [7] 11 (1887) 553. Francuor. Moteurs 4 air chaud. Remarques a loccasion d’une com- munication récente de M. Galy-Cazalat. Comptes rendus, 36 (1853) 9Q9o Odo. Machines 4 air chaud. Comptes rendus, 38 (1854) 131. FRANCKLAND (E.). On the physical cause of the glacial epoch. Phil. Mag. [4] 27 (1864) 321. —. On the origin of muscular power. Phil. Mag. [4] 32 (1866). 182.—See Phil. Mag. 31 (1866) 485; 32 (1866) 289. AUTHOR INDEX. 161 FRANCKLAND (E.). Experimental researches in pure, applied and physi- eal chemistry. London. 1877. Phil. Mag. [5] 5 (1878) 153. FRANKLIN (B.). A new and curious theory of light and heat. Amer. Phil. Soc. Trans. 3 (1793) 5. Frecain. Calcul des effets des machines 4 lair. Instit. (1853) 248. Fremy. De quelques modifications que la chaleur fait éprouver aux acides organiques. Comptes rendus, 5 (1837) 389. Rapport sur ce mémoire par M. Dumas, Comptes rendus, 6 (1838) 599. FResNEL (A.). Note sur la répulsion que des corps rechauffés exercent les uns sur les autres & des distances sensibles. Ann. chim. et phys. 29 (1825) 57, 107. Friiscu (H.). Lasst sich die Anwendung der lebendigen Kraft in der mechanischen Warmetheorie rechtfertigen. Ann. Phys. u. Chem. 153 (1874) 306. Erwiderung dazu, 156 (1875) 326; Jahresb. (1874) 59. Froaticu (J.). Ueber die Dichtigkeitsinderung des Stahls durch Harten und Anlassen. Ann. Phys. u. Chem. n. F. 8 (1879) 352; Phil. Mag. [5] 8 (1879) 421. FrRowew (P.C. F.). Die Dissociation krystallwasserhaltiger Salze. Z. phys. Chem. 1 (1887) 5-14, 362-364. Fucus (K.). Ueber das Wesen der Warme und ihre Beziehung zur bewegenden Kraft. Verhandl. Presburg. Ver. 1 (1857) 3. ——-—. Ueber Verdampfung. Repert. d. Physik, 24 (1888) 141-160. -—. Ueber den Zusammenhang von Oberflichenspannung, Ober- flichendichte und oberflachlicher Warmeentwickelung. Repert. d. d. Physik, 24 (1888) 298. FunrRMANN (A.). Aufgaben aus der analytischen Mechanik. In 2 Theilen. 2e verbesserte und vermehrte Auflage. Mit in den Text gedruckten Holtzschnitten. Leipzig. 1879-1882. 1. Theil, analy- tische Geostatik. uu. Theil, analytische Dynamik fester Korper. (v1, 138 pp.; v1, 222 pp.) Gabon. Sur la philosophie chimique de Fourcroy, la théorie de Richter de la combustion par double affinité, etc. Ann. de chimie, 22 (1797) 109. Gatto. Théorie mécanique de la chaleur notablement perfectionnée. Turin. 1866. K 162 LITERATURE OF THERMODYNAMICS. GARLAND (G. M.). Pneumo-dynamics. New York. 1877. 8vo. Gay-Lussac. Recherches sur la dilatation des gaz et des vapeurs. Ann de chimie, 43 (1802) 157. Annonce d’un travail sur la densité des vapeurs liquides. Ann. de chimie, 80 (1811) 218. Table de la dilatation de ’eau. Ann. chim. et phys. 1 (1817) 108. ———. Dilatation des fluides élastiques. Ann. chim. et phys. 1 (1817) 110. Note sur la dilatation des liquides. Ann. chim. et phys. 2 (1817) 150. ———. Sur le calorique des combinaisons, 1 (1817) 214. ——. Sur le froid produit par la dilatation des gaz. Ann. chim. et phys. 9 (1818) 505. ——. Sur la dilatation de lair. Ann. chim. et phys. 19 (1821) 456. Extrait V@un mémoire sur le froid produit par ’évaporation des liquides. Ann. chim. et phys. 21 (1822) 82. Sur lorigine de la glace qu’on trouve au fond des riviéres. Ann. chim. et phys. 63 (1836) 559. GepavuerR. Ueber die Einrichtung der calorischen Maschine von Ericsson. Jahresb. d. schlesischen Ges. zu Breslau, (1853) 310. GERBER (P.). Der absolute Nullpunkt der Temperatur; die Arbeit der Wiirme beim Sieden und die Daimpfe im Zustande der Sattigung. Nova Acta d. k. Leop.-Car. Akad. 52 (1888) No. 3, p. 103; Beiblatter, 12 (1888) 455. Geruacu. Beitrag zur mechanischen Theorie des elektrischen Stroms. Ann. Phys. u. Chem. 131 (1867) 480; Phil. Mag. [4] 34 (1867) 382. Grrnez (D.). On the disengagement of gases from their saturated solu- tions. Phil. Mag. [4] 33 (1867) 479, abs. from Comptes rendus, Nov. 19, 1866. —. Analogies presented by the liberation of gases from their supersaturated solutions and the decomposition of certain explosive bodies. Phil. Mag. [4] 49 (1875) 157, abs. from Comptes rendus, 80 (1875) 44. AUTHOR INDEX. 163 Gerosa. Sulla caloricitaé del?aqua alle temperature prossime al massimo di densitae d’aleun po’superiori. Atti Accad. Lincei, [3] 10 (1880-81) 7d. Gress (G.). A means of increasing the force of gunpowder. Amer. J. Sci. 1 (1819) 87; Ann. chim. et phys. 3 (1817) 39; 5 (1817) 441. Gipss (J. Willard). Gr: eu methods in the thermodynamics of fluids. Trans. Connecticut Acad. 2 (1873) 509-342. [Published in New Haven, Conn. | —-—. A method of geometrical representation of the thermo- dynamic properties of substances by means of surfaces. Trans. Con- necticut Acad. 2 (1875) 382-404. ——. On the equilibrium of heterogeneous substances. Trans. Connecticut Acad. 3 (1875-78) 108-248, 543-534 ; see J. Sci. [3] 16 (1878) 1, abs. by the author. —-—. On the vapour densities of hyponitric acid, of formic acid, of acetic acid and of perchloride of phosphorus. Amer. J. Sci. [3] 18 (1879) 1. ——. See Duhem for a review of his works, Bull. Soc. mathém. [2] 11 (1887) 14; Beiblatter, 12 (1888) $4. i Gin (J.). On the dynamical theory of heat (letter to Prof. Tyndall). oe Phil. Mag. [4] 26 (1863) 109; 27 (1864) 84, 478; 28 (1864) 367; 35 (1868) 439; 36 (1868) 1. —. Onregelation. Phil. Mag. [4] 31 (1866) 119. —-. On change of state as affecting communication of heat. Phil. Mag. [4] 32 (1866) 420. GIRDLESTONE (A. G.). On the condition of the molecules of solids. Phil. Mag. [4] 29 (1865) 108. ; GLADBACH (Ph.). Zustandsgleichung der gesittigten Déimpfe. Ann. Phys. u. Chem. 145 (1872) 318, 326. GuApstoneE (J. H.) and A. Tripe. On the mutual helpfulness of chemical affinity, heat and electricity in producing the decomposition of water. Rept. British Assoc. (1872) 75. ——. The optical and chemical properties of caoutchouec. Jour. Chem. Soe. (1888) 679-688. 164 LITERATURE OF THERMODYNAMICS. GLAISHER (J.). On the amount of the radiation of heat, at night, from the Earth, and from bodies placed on or near the surface of the Earth. Phil. Trans. (1847) 119. GLATZEL (P.). Neue Versuche tiber die Ausdehnung von Korpern durch die Warme. Ann. Phys. u. Chem. 160 (1877) 497. GoerrLInc. Explosion de loxide sulfuré de l’antimoine. Ann. de Chimie, 23 (1797) 75. Go.LpsTEIN (E.). Ueber den Zusammenhang zwischen Gasdichte und Schichtenintervall in Geissler’schen Rohren. Ann. Phys. u. Chem. n. F. 15 (1882) 277; Monatsber. d. Berliner Akad. (1881) 876-878 ; Phil. Mag. [5] 14 (1882) 402. GoopMAN (J.). Researches into the identity of the existences or forees— light, heat, electricity and magnetism. Phil. Mag. [3] 32 (1848) 172, from Manchester Soc. Mem. 8 (1848) 1; Phil. Mag. [4] 2 (1851) 498, abs. from Proe. Roy. Soc. May 22, 1851.—See Tyndall, Phil. Mag. [4] 3 (1852) 127, comm. by the author. Goopwin (W.S.). Physical constants of solution, especially the expan- sion of saline solutions. Rept. British Assoc. (1887) 48-55. Goosens (B. J.). On the melting-point of ice at pressures under one atmosphere. Phil. Mag. [5] 24 (1887) 295. Gouau (J.). Experiments on the temperature of water surrounded by freezing mixtures. Nicholson’s Jour. 13 (1806) 189. GouILLy (A.). Théorie mécanique de la chaleur. Paris. 1877. Gouy. Sur la conservation de lélectricité et la thermodynamique. Comptes rendus, 106 (1888) 329-332. Electricité et thermodynamique. Comptes rendus, 107 (1888) 329-332 ; Beiblatter, 15 (1889) 44, abs. et CHAPERON. Sur léquilibre osmotique. Ann. chim. et phys. [6] 13 (1888) 120. Sur les transformations et l’équilibre en thermodynamique. Comptes rendus, 108 (1889) 507-9; Beiblatter, 13 (1889) 643, abs. Sur l’énergie utilisable et la potentiel thermodynamique. Comptes rendus, 108 (1889) 794; Beiblatter, 13 (1889) 643, abs. AUTHOR INDEX. 165 Govi. Sulle anomalie che presenta il caoutchoue vulcanizzato rispetto al calore. Atti Accad. Sci. 2 (1866-67) 225. Ricerche sulla gomma elastica vulcannizata. Atti Accad. Torino, 2 (1866-67) 455, 456. Alcune nuove ricerche sulle anomalie del caoutchoue vulean- nizzato al calore. Atti Accad. Sci. Torino, 4 (1868-69) 571. Correzione dei coefficienti nella formola data dal Regnault per ealcolare le dilatazioni assolute del mercurio. Atti Accad. Torino, 6 (1870-71) 122, 198. GrauAm (T.). On the heat of friction. Annals of Phil. n. s. 12 (1826) 260. —. Experiments on the heat disengaged in combinations. Phil. Mag. [3] 22 (1843) 329; 24 (1844) 401; Ann. chim. et phys. [3] 8 (1843) 151; 13 (1845) 188. —. On the occlusion of hydrogen gas by metals. Phil. Mag. [4] 36 (1868) 63, abs. from Proc Roy. Soc. June 11, 1868. Grasnor (F.). Hydraulik nebst mechanischer Wirmetheorie. Leipzig. 1875. (970 pp.) Grassi. Recherches sur la compressibilité des liquides. Ann. chim. et phys. [8] 31 (1851) 437. Grimapi (G. P.). Sur la dilatation thermique des liquides 4 diverses pressions. Jour. de phys. [2] 7 (1888) 72. Grorrian (O.).—See Wiillner und G. Grorruuss. Sur les limites de conductibilité des mélanges gazeux in- flammables, 4 une densité décroissante, et sur les couleurs de l’étincelle électrique dans différens milieux. Ann. de Chimie, 82 (1812) 34; Nicholson’s Jour. 35 (1813) 50, from Schweigger’s Jour. 3, 219. Gries (R. Rudolff-). Die neuesten Erfahrungen tiber Compressions- Kaltemaschinen in Theorie und Praxis. Berlin. 1888. 4to. (vy, 150 pp.) _ Gumbrarp (A.). Lois générales de la chaleur. Paris. 1844. 4to. GuGLIELMO (G.) e Musina (V.). Sulla pressione delle mescolanze di gas e vapori e sulla legge di Dalton. (Riv. Industr. di Firenze diretta dall’ing. G. Vimercati), 1887. Firenze. 166 LITERATURE OF THERMODYNAMICS. Guianet (M.). Transformation directe du travail mécanique en élec- tricité. Comptes rendus, 84 (1877) 1084. GUTHRIE (F.). On the thermal resistance of liquids. Phil. Trans. 159 (1869) 637; Phil. Mag. [4] 37 (1869) 468, abs. from Proce. Roy. Soe. Jan. 21, 1869. —. On the influence of temperature on the passage of air through capillary tubes. Phil. Mag. [5] 5 (1878) 433. — —. On some thermal and volume changes attending mixture. Phil. Mag. [5] 18 (1884) 495. Guyton-Morveau. Expériences faites sur les refroidissements artificiels. Ann. de chimie, 29 (1799) 290. et CaRNoT. Constructions pyrotechniques. Ann. de chimie, 71 (1809) 70; 74 (1810) 18. Guzzi (P.). Einige Versuche tiber den Ausfluss von Wasserdampf. Rend. Ist. Lomb. [2] 21 (1881) 14; Beibliatter, 13 (1889) 853, abs. Hapicu (G.). On a newsource of organic heat. Amer. Assoc. Advance- ment of Sci. 12 (1858) 266. Haca (H.). Bestimmung der Temperaturanderungen beim Ausdehnen -und Zusammenziehen von Metalldrahten und des mechanischen Warme- aquivalents. Ann. Phys. u. Chem. n. F. 15 (1882) 1; Arch. neerland. 17 (1882) 261-288; Jahresb. (1882) 94; Amer. J. Sci. [5] 23 (1882) 321. HaGeMAnn (G. A.). Die chemische Schwingungshypothese und einige thermochemische Daten. Berlin. 1888. (21 pp.) Beiblatter, 15 (1889) 907, abs. Hacenpacu (E.). Wiirmeentwickelung beim Aufschlagen von Geschos- sen. Ann. Phys. u. Chem. 140 (1870) 486; 143 (1871) 153; Phil. Mag. [4] 40 (1870) 462. —. Ueber Hagelkérner mit Eiskrystallen. Ann. Phys. u. Chem. n. F. 8 (1879) 666. —. Sprengwirkungen durch Eis. Ann. Phys. u. Chem. n. F. 10 (1880) 330. —. Ueber die physikalischen Eigenschaften des Gletschereises. Tagebl. d. 60. Vers. deutsch. Naturf. u. Aertzte, (1887) 236. AUTHOR INDEX. 167 HaGeENBACH (E.), BiscHorr und Foren (F.). Die Temperatur des Eises im Innern des Gletschers. Verhandl. d. naturf. Ges. Basel, 8 (1888) 635-646, 821-832 ; Beiblatter, 13 (1889) 802, abs. _, . Johannes Bernoulli und der Begriff der Energie. Verhandl. d. naturf. Ges. Basel, 9 (1889) 833-835; Beiblitter, 13 (1889) 770, abs. Haupar. Inquiries concerning the heat produced by friction. Nichol- son’s Jour. 26 (1810) 30, from Jour. de Phys. 65 (1810) 213. Haut (J.). Experiments on the effects of heat modified by compression. Nicholson’s Jour. 9 (1804) 98; 13 (1806) 328, 381; 14 (1806) 13, 113, 196, 302; Edinburgh Trans. 6 (1812) 71. | Hau (Marshall). On chemical attraction. Nicholson’s Jour. 30 (1811) 193. Hau (Maxwell). The source of solar heat. Phil. Mag. [4] 43 (1872) 476, from Monthly Notices Astronom. Soe. April 12, 1872. HA uostr6m. Temperature of the maximum density of water. Annals of Phil. n.s. 9 (1825) 155, abs. from the Swedish Trans. for 1823: Ann. chim. et phys. 28 (1825) 56. Hanket (W.). Ueber das Crookes’sche Radiometer. Ann. Phys. u. Chem. n. F. 2 (1877) 627. Hareorp (J.B.). Ontheconictheoryofheat. Phil. Mag. [4] 34 (1867) 106. Harcourt (A. Vernon) and Esson (W.). On the laws of connection between the conditions of a chemical change and its amount. Phil. -' Trans. 156 (1866) 198; 157 (1867) 117. Hare. The explosion causing the great fire of 1845 at New York. Phil. Mag. [3] 384 (1849) 227; 87 (1850) 525. Harrison. Mechanical theory of heat. Phil. Mag. [4] 12 (1856) 399; Jahresb. (1856) 28. Hartiey (W.N.). The influence of atomic arrangement on the physical properties of compounds. Phil. Mag. [5] 19 (1885) 55. Hausster (J. W.). Beitrage zur mechanischen Warmetheorie, insbe- sondere die mathematische Behandlung der von der Warme geleisteten inneren Arbeiten. Leipzig. 1882. a SSS 168 LITERATURE OF THERMODYNAMICS. Haycrarr (W. T.). On the heat produced by firing gunpowder. Annals of Phil. n. s. 8 (1824) 245. Hears (J. M.). On the circumstances which determine the variation of temperature in a perfect gas during expansion and condensation. Phil. Mag. [4] 39 (1870) 288. —-—. On the theory of the variation of temperature in gases in consequence of changes in their density and pressure. Phil. Mag. [4] 39 (1870) 347. —— ——. On thermodynamics. Phil. Mag. [4] 39 (1870) 421. —-—. On the interchangeability of heat and mechanical action. Phil. Mag. [4] 40 (1870) 51. —-—. On the principles of thermodynamies. Phil. Mag. [+4] 40 (1870) 218, 429; Jahresb. (1871) 62. Reply to Dr. Rankine. —-—. On the production of heat by dynamical action in the compression of gas. Phil. Mag. [5] 4 (1877) 14. Héserr (L.). De laction de la chaleur sur les composés organiques. These. Paris. 1869. HEEN (P. de). Détermination des variations que le coefficient de frotte- ment éprouve avec latempérature. Bull. Acad. de Belgique, 15 (1888) 57-62, 195-206. ——. Note sur le travail moléculaire des liquides organiques. Bull. Acad. de Belgique, 15 (1888) 165. Hemennatn. Mechanische Leistung, Warmeentwickelung und Stoff- umsatz bei der Muskelthiatigkeit. Leipzig. 1864. Hem (A.). Onglaciers. Phil. Mag. [4] 41 (1871) 485,comm. by author from Ann. Phys. u. Chem. Erganzb’d 5 (1870) 30-63, with a plate. Hern. Ecoulement des gaz. Jour. de Phys. 6 (1887) 251. Hertz. Zur Theorie der Wirme. Z. f. Naturwiss. zu Halle, 1 (1853) 417. Heim (G.). Die Lehre von der Energie. Leipzig. 1887. (104 pp.) Beiblatter, 12 (1888) 407. Hetmuortz (H. von.). Ueber die Erhaltung der Kraft. Berlin. 1847. 2e Ausgabe. Leipzig, 1862. ——. Ueber die Wechselwirkung der Naturkrifte. Ein popu- lar-wissenschaftlicher Vortrag. IKd6nigsberg, 1854. AUTHOR INDEX. 169 Hetmuo rz (H. von.). Erwiderung auf die Bemerkungen von Herrn, Clausius. Ann. Phys. u. Chem. 91 (1854) 241. ——— — —. On the regelation ofice. Phil. Mag. [4} 32 (1866) 22. ——. On galvanic currents occasioned by differences of concen- tration; inferences from the mechanical theory of heat. Phil. Mag. [5] 5 (1878) 348, translated from Monatsber. d. Berliner. Akad. November, 1877, pp. 715-726. ——. Freie Energie bei chemischen Vorgangen. Ber. d. Ber- liner Akad. (1882) 22-39, 825-836 ; Jahresb. (1882) 134. —-—. Thermodynamik chemischer Vorgiinge. Ber. d. Berliner Akad. (1883) 647-665; Jahresb. (1883) 108. ——. Physical Memoirs, selected and translated from foreign sources under the direction of the Physical Society. Memoirs of Helmholtz, Vol. 1, part 1. (109 pp.) London. 1888. (R. v.). Ueber diestrahlende Energie von Flammen. Verhandl. d. phys. Ges. Berlin, 8 (1889) 51-54, Beiblatter, 13 (1839) 808, abs. Henwoop (W. J.). On Mr. J. Scott Russell’s remarks on the tempera- ture of most effective condensation of steam. Phil. Mag. [3] 19 (1841) 90. Herepats (J. Bird). The dynamical theory of heat. North British. Rev. 40 (1864) 40. HERRMANN (E.). Mechanische Warmetheorie. Berlin. 1879. Mit besonderer Riicksicht auf der Maschinentechnik. HERMANN (L.). Intramolekulare Verbrennungswirme. Ber. deutsch. chem. Ges. 2 (1868) 18, 84, abs. from Chem. Centralblatt, (1869) 529, 545; Z. f. Chem. (1869) 472. Herscuet (A.S.). On the use of the virial in thermodynamics. Nature, 18 (1878) 39, 142. Herwie (H.). Ausdehnung tiberhitzter Dampfe. Ann. Phys. u. Chem. 147 (1872) 161-195; Jahresb. (1872) 40; Phil. Mag. [4] 45 (1873) 401. —. Physikalische Begritfe und absolute Maasse. Leipzig. 1880. (vii, 98 pp.) Hess. Note sur quelques produits pyrogénés. Ann. chim. et phys. 61 (1836) 331. 170 LITERATURE OF : THERMODYNAMICS. Hess. Recherches sur les quantités de chaleur dégagée dans les com- binaisons chimiques. Ann. chim. et phys. 74 (1840) 325; Comptes rendus, 10 (1840) 759; 15 (1841) 541. Nouvelle méthode générale pour la détermination des quantités de chaleur dégagées dans les combinaisons chimiques. Comptes rendus, 20 (1845) 190. Hicks (W. M.). On some effects of dissociation on the physical proper- ties of gases. Phil. Mag. [5] 3 (1877) 401; 4 (1877) 80, 174. Hicuron (H.). The mechanical equivalent of heat, opposed. Chem. News, 28 (1871) 52, 165; Jahresb. (1871) 64.—See Croll and H. W. Cook, above. Hiwnricus (G.). Sur le calcul des moments d’inertie des molécules. Comptes rendus, 76 (1873) 1592. —. Sur la détermination mécanique des points d’ébullition des dérivés chlorés du toluéne. Comptes rendus, 80 (1875) 766. Hiern (G. A.). Transformation du calorique en force mécanique; nou- veau mode d’application de la vapeur; machine pulmonaire. Cosmos, 6 (1855) 679; 7 (1855) 455; Bull. de Mulhouse (1855) nos. 128, 129; Jahresb. (1855) 29-80. ——. Recherches sur léquivalent mécanique de la chaleur présentés a la Soc. de physique de Berlin. Paris. 1858. —-—. Changement de densité du caoutchoue étiré. Comptes rendus, 46 (1858) 1. ——. Equivalent mécanique de la chaleur, Cosmos, 16 (1860) 313. —-—. Confirmation expérimentale de la seconde preposition de la théorie mécanique de la chaleur et des équations qui en découlent ; démonstration analytique de cette proposition et conséquences princi- pales auxquelles elle conduit. Paris. 1861. —w—. Remarques sur le réle réel que joue le frottement des muscles dans le phénoméne de la calorification des étres vivants 4 sang chaud ou 4 sang froid. Cosmos, 21 (1862) 257. —w—. Théorie mécanique de la chaleur. Cosmos, 22 (1863) 283, 734; Mondes, 4 (1864) 353. ——. Esquisse élémentaire de la théorie mécanique dela chaleur - et de ses conséquences philosophiques. Paris. 1864. P AUTHOR INDEX. 171 Hrrn (G, A.). Théorie mécanique de la chaleur. 1e partie: Exposition analytique et expérimentale. 2e édition. Paris. 1865. —-—. Mémoire sur la thermodynamique. Paris. 1867. (172 pp. et 2 planches.) Ann. chim. et phys. [4] 10 (1867) 32; 11 (1867) 5. —-—. Conséquences philosophiques et métaphysiques de la ther- modynamique. Paris. 1869. —-—. Sur la variabilité apparente de la loi du Dulong et Petit. Comptes rendus, 76 (1873) 191. ——. Note accompagnant la présentation du tome 1. de sa “Exposition analytique et expérimentale de la chaleur.” Comptes rendus, 80 (1875) 1578; Jahresb. (1875) 46. ——. Note relative au Mémoire de M. Kretz sur l’élasticité dans les machines en mouvement. Comptes rendus, 81 (1875) 72.—See Ledieu, Comptes rendus, 81 (1875) 130. —-—. Théorie mécanique de la chaleur. Paris. 1875-76. 2 vols. 3e édition. ——. Sur létude des moteurs thermiques et sur quelques points de la théorie mécanique de la chaleur en général. Comptes rendus, 82 (1876) 52; Jahresb. (1876) 63. ——. Sur une théoréme relatif 4 la détente des vapeurs sans- travail externe. Comptes rendus, 84 (1877) 592, 632, 680. ——. Reflexions critiques sur les expériences concernant la chaleur humaine. Comptes rendus, 89 (1879) 687, 833. ——. Sur lanouvelle théorie du Soleil de M. Siemens. Comptes rendus, 95 (1882) 812; ; Phil. Mag. [5] 14 (1882) 478. Reply by Siemens, Phil. Mag. same vol. 480. ——. Réfutation d’une seconde critique de M. Zeuner, con- cernant les travaux des ingenieurs alsaciens sur la machine a vapeur. Comptes rendus, 96 (1883) 561, 415.—See Parenty, Comptes rendus, 103 (1886) 125. ‘ —-—. Réponse a la note précédente de M. Hugoniot. Comptes rendus, 103 (1886) 371. —— ——. Réflections relatives 4 la note précédente de M. L. Natan- son. Comptes rendus, 106 (1888) 166-169.—See Natanson, same vol. 164. 172, LITERATURE OF THERMODYNAMICS. Hirscu. Application de lathéorie mécanique de la chaleur aux machines i air chaud. Comptes rendus, 80 (1875) 922. Hosses (T.). Elementarum philosophiz, sectio prima de corpore. Pars Ly, Capa XkVil ae: Hopecxinson (W. R.) and Lownpes (F. K.8S.). On the action of in- candescent platinum wire on gases and vapours. Chem. News, 58 (1888) 187. and ——w—. On the action of a platinum wire made incandescent by a current on some gases and vapours. Chem. News, 58 (1888) 223-4. Horr (J. H.van’t). Ueber chemische Dynamik. Amsterdam. 1884.— See Jahresb. (1884) 25; Le Chatellier, Comptes rendus, 99 (1884) 786 ; Chem. News, 50 (1884) 289. ——w—. Die Rolle des osmotischen Druckes in der Analogie zwischen Loésungen und Gasen. Z. phys. Chemie, 1 (1887) 481-508 ; Phil. Mag. [5] 26 (1888) 81. ——w—. Ueber die Dissociationstheorie der Electrolyte. Z. phys. Chem. 2 (1888) 777-781. — — —. Ueber die Beziehung zwischen der Affinitaét in absolutem Maass und Ostwald’s Affinitatsgréssen. Z. phys. Chem. 3 (1889) 608; Beiblatter, 13 (1889). 844, abs. Hovman (8. W.). A new method of studying the relation between the viscosity and temperature of gases. » Proc. Amer. Acad. June 14, 1876; Phil. Mag. [5] 3 (1877) 81, abstract by the author. ——. On the effect of temperature on the viscosity of the air. Proc. Amer. Acad. n. s. 13 (1835-6) 1; Phil. Mag. [5] 21 (1886) 199. HouirzMann. Ueber die Wirme und Elasticitaét der Gase und Dampfe. Mannheim. 1845. Jahresb. (1851) 28. Ueber die bewegende Kraft der Warme. Ann. Phys. u. Chem. 82 (1851) 1. Home (E.). Proofs of animal heat being influenced by the nerves. Phil. Trans. 116 1 (1826) 60. Hoop (J. J.). Laws of chemical change. Phil. Mag. [5] 6 (1878) 371; 8 (1879) 121. : AUTHOR INDEX. 173 Hoop (J. J.). On the rate of chemical absorption of gases, with regard to their interdiffusion. Phil. Mag. [5] 17 (1884) 352. —-—. On the influence of heat on the rate of chemical change. Phil. Mag. [5] 20 (1885) 323; Ber. chem. Ges. 18 (1885) R. 519, 653. Hooxe(R.). Micrographia. London, 1667, and his Posthumous Works, 1705. Hoorwec (J. L.). Thermische Theorie des galvanischen Stromes. Ann. Phys. u. Chem. n. F. 12 (1881) 75. Hope (T. C.). Experiments and observations upon the contraction of water by heat at low temperatures. Nicholson’s Jour. 12 (1805) 339, from Edinburgh Trans. for 1804.—See paper by Dalton, 13 (1806) 377; Ann. de chimie, 53 (1805) 272. Hopxins (Wm.). Dynamical theory of heat. Rept. British Assoc. (1853) xiv; Amer. J. Sci. [2] 19 (1854) 140; Jahresb. (1854) 47. —. On the theory of the motion of glaciers. Phil. Mag. [4] 25 (1863) 224, abs. from Proc. Roy. Soc. May 22, 1862. Hoppe (R.). Ueber die Warme als Aequivalent der Arbeit. Ann. Phys. u. Chem. 97 (1856) 30; C.’s Bemerkungen dazu,98 (1856) 173; H.’s Erwiderung, 101 (1857) 146; Phil. Mag. [4] 12 (1856) 75; Amer. J. Sci. [2] 21 (1856) 409; Jahresb. (1856) 26. —. Erwiderung auf einem Artikel von Clausius, nebst einer Bemerkung zur Theorie der Erdwarme. Ann. Phys. u. Chem. 110 (1860) 598. Horstmann (A.). Ueber die Anwendung des zweiten Hauptsatzes der mechanischen Warmetheorie auf chemische Erscheinungen. Ber. chem. Ges. 4 (1871) 847. —. Theorie der Dissociation. Ann. Chem. u. Pharm. 170 (1873) 192-210; Jahresb. (1873) 114. —. Anwendbarkeit des zweiten Hauptsatzes der Warmetheorie auf chemische Erscheinungen. Ber. chem. Ges. 14 (1881) 1242-50; Jahresb. (1881) 1154. HOoveENDEN (F.). Molecular expansion and the struggle for heat. South London Microscopical Club, Dece., 1882. Howarp (E.). Anew fulminating mercury. Nicholson’s Jour. 4 (1800) 173, 200, 249; Phil. Trans. (1800) 204. L74. LITERATURE OF THERMODYNAMICS. Hvart (Colnet d’). Résultats importants pour la théorie de la trans- formation du travail en chaleur. Comptes rendus, 61 (1865) 431. Hupson. On the phenomena usually referred to the radiation of heat. Rept. British Assoc. (1855) 163. Hvuconior. Ecoulement des gaz. Jour. de phys. [2] 6 (1887) 79. HuyeHens. Opuscula posthuma de motu corporum ex percussione, Prop. x1.—See Diihring’s Principien der Mechanik, 2e Auflage, Leip- zig, 1877, pp. 52, 166. IsamBert (F.). Mémoire sur la compressibilité de quelques dissolutions gazeuses. Ann. chim. et phys. [7] 11 (1887) 538. Ivory (J.). On the elastic force of steam at different temperatures. Phil. Mag. n. s. 1 (1827) 1. —. Investigation of the heat extricated from the air when it un- dergoes a given condensation. Phil. Mag. n. s. 1 (1827) 89, 169. JAHN (Hans). Die Grundsitze der Thermochemie. Wien. 1872. — —. Die Elektrolyse, und ihre Bedeutung fiir die theoretische und angewandte Chemie. Wien. 1883. JAMIN (J.). Sur la chaleur latente de la glace. Comptes rendus, 70 (1870) 715; Jahresb. (1870) 78. —. On the critical point of liquifiable gases. Phil. Mag. [5] 16 (1883) 71. Note by Ramsay, same vol. 118. —and Rrcwarp. On the cooling of gases. Phil. Mag. [4] 44 (1872) 241, 457. JANuUsSCHKE (H.). Ueber Aehnlichkeiten verschiedener Spannungszu- stiinde und die Waal’sche Spannungsgleichung. Z. d. Realschulwesen in Wien, (1888) 519-527, 586-595. JELLETT (J. H.). A treatise on the theory of friction. London. 1872. 220 pp.) Phil. Mag. [4] 43 (1872) 469. JocumMaNnn. Mechanische Warmetheorie. Ann. Phys. u. Chem. 108 (1859) 153. Jouue (J. P.). On the production of heat by voltaic electricity. Proc. Roy. Soc. 4 (1837-43) 280, abs.; Phil. Trans. (1840) 1. AUTHOR INDEX. 5 Jouue (J. P.). On the changes of temperature produced by the rarefac- tion and condensation of air. Proc. Roy. Soe. 5 (1843-50) 517 ; Phil. Trans. (1844) 1; Phil. Mag. [3] 25 (1844) 1; 26 (1845) 369. ——. Onthe existence ofan equivalent relation between heat and the ordinary forms of mechanical power. Phil. Mag. [3] 27 (1845) 205 ; 28 (1846) 205. ——. Sur la chaleur dégagée dans les combinaisons chimiques. Comptes rendus, 22 (1846) 256. | —w—. On the heat evolved during the electrolysis of water. Manchester Phil. Soc. Mem. [2] 7 (1846) 87. ——. Onthe mechanical equivalent of heat as determined by the heat evolved by the friction of fluids. Phil. Mag. [3] 31 (1847) 173 ; Comptes rendus, 25°(1827) 309. ——. On the mechanical equivalent of heat. Proce. Roy. Soe. 5 (1843-50) 839, abs.; Phil. Trans. (1849) 1; Phil. Mag. [3] 35 (1849) 335; Comptes rendus, 28 (1849) 132, 199. Reply by Mayer with claim to priority, Comptes rendus, 29 (1849) 534; Jahresb. (1849) 28 ; Ann. Phys. u. Chem. 73 (1849) 479; Rept. British Assoc. (1849) 21. ——. Onthe mechanical equivalent of heat. Phil. Trans. (1850) 61; Quar. J. Chemical Soc. 3 (1850) 316; Phil. Mag. [3] 35 (1850) 533; Ann. Chem. u. Pharm. 76 (1850) 170; Amn. chim. et phys. [3] 30 (1850) 121; Jahresb. (1850) 36. ——. Lettre de M. Joule relative 4 son Mémoire sur la chaleur dégagée dans les combinaisons chimiques. Comptes rendus, 33 (1851) ff. ——. Heat effects of electricity and the mechanical value of heat. Phil. Mag. [4] 2 (1851) 263, 347, 435; Ann. chim. et phys. [3] 35 (1851) 118, abs.; Jahresb. (1851) 32. ——. Some remarks on heat and on the constitution of elastic fluids. Manchester Phil Soc. Mem. [2] 9 (1851) 107; Ann. chim. et phys. [38] 50 (1857) 381. ——. On air-engines. Phil. Mag. [4] 2 (1851) 150; Instit. (1852) 15. —-—. Noteon the mechanical action of heat and on the specific _ heats of air. Additional note to the description of the air-engine of J. P. Joule, by W. Thomson. Phil. Trans. (1852) 78. * 176 LITERATURE OF THERMODYNAMICS, Joute (J. P.). Mémoire sur les efféts calorifiques des courants magneto- électriques et sur l’équivalent mécanique de la chaleur. Ann. chim. et phys. [3] 34 (1852) 504. —-—. On the heat disengaged in chemical combinations. Phil. Mag. [4] 3 (1852) 481. —-—. On the economical production of mechanical effect from chemical forces. Phil. Mag. [4] 5 (1853) 1; V’Instit. (1853) 164; Jahresb. (1853) 47. —-—. On the mechanical theory of heat. Phil. Mag. [4] 6 (1853) 143 ; Instit. (1853) 382; Jahresb. (1853) 44. ——and TuHomson (W.). On the thermal effects of fluids in motion. Phil. Trans. (1853) 357; (1854) 321; (1860) 325; (1863) 579; Proc. Roy. Soc. 7 (1854-5) 127, abs.; 8 (1856-7) 41, 178, 556; 10 (1860) 502; Ann. Phys. u. Chem. 97 (1856) 576; Ann. chim. et phys. [3] 65 (1862) 244; Jahresb. (1854) 48; (1855) 25. ——. Note sur léquivalent mécanique de lachaleur. Comptes rendus, 40 (1855) 310. ——. On the heat absorbed in chemical decompositions. Phil. Mag. [4] 12 (1856) 155, 321. —-—. Note on Clausius’s application of the mechanical theory of heat to the steam-engine. Phil. Mag. [4] 12 (1856) 385. —-—. On the thermoelectricity of ferruginous metals and on the thermal effects of stretching solid bodies. Proc. Roy. Soc. 8 (1857) 359. ——. Some remarks on the heat and constitution of fluids. Phil. Mag. [4] 14 (1857) 211, 381. solids. Proc. Roy. Soc. 8 (1857) 564; Ann. chim. et phys. [3] 52 (1857) 120. —w—. On the expansion of wood by heat. Proc. Roy. Soc. 9 (1857) 3; Phil. Mag. [4] 16 (1858) 54. Soe. 9 (1858) 254; Phil. Mag. [4] 17 (1859) 61, abs.; Phil. Trons. 149 (1860) 91. ——. On the thermal effects of the longitudinal compression of —-—. On some thermodynamic properties of solids. Proc. Roy. _ AUTHOR INDEX. ae (JouLE(J.P.). On the thermal effects of compressing fluids. Phil. Trans. (1859) 133; Proe. Roy. Soc. 9 (1858) 496; Phil. Mag. [4] 17 (1859) 364, abs. ——. Notice of experiments on the heat developed by friction in air. Rept. British Assoc. (1859) u, 12. ——. Note on Dalton’s determination of the expansion of air by heat. Manchester Soc. Mem. [2] 15 (1860) 143. ——. Note on the history of the dynamical theory of heat. Phil. Mag. [4] 24 (1862) 121, 173 (claiming for Mayer the merit of having, apparently without knowledge of what had heen done before, discovered the true theory of heat). ——. On the dynamical theory of heat. Phil. Mag. [4] 26 (1863) 145. ——. Note on the history of the dynamical theory of heat. Phil. Mag. [4] 28 (1864) 150. ——. Determination of the dynamical equivalent of heat from the thermal effects of electric currents. Rept. British Assoc. (1867) 512. —-—. The Mechanical Equivalent of Heat. London. 1872. 8vo. In’s Deutsche tibersetzt, von J. W. Sprengel, Braunschweig, 1872. ——. First report of the committee appointed to determine the mechanical equivalent of heat. By Dr. Joule, Prof. Sir W. Thomson, Prof. Tait, Prof. Balfour Stewart and Prof. Maxwell. Rept. British Assoc. (1876) 276; Nature, 14 (1876) 476; Amer. J. Sci. [3] 12 (1876) 455, abs. Second Report of the same Committee, Rept. British Assoc. (1877) 1. Third Report of the same Committee, Rept. British Assoc. (1878) 102. Fourth Report of the same Committee, Rept British Assoc. (1879) 36. —— — —. New determination of the mechanical equivalent of heat. Phil. Trans. 169 (1878) 3865; Proc. Roy. Soc. 27 (1878) 38; Jahresb. (1878) 63. Ber. chem. Ges. 11 (1878) 411. ——. The Scientific Papers of James Prescott Joule, published by the Physical Society. Vol. 1. London. 1884. Phil. Mag. [5] 18 (1884) 153. Kant. Bedenken A. von Baumgartner’s gegen das Wirmedquivalent A = 423.5 Kilogrammeter von Joule. Z. Math. u. Phys. (1862) 127. L dik aaa : a 178 LITERATURE OF THERMODYNAMICS. Kanipaum (W. A.). Welche Temperatur haben die aus kochenden Salalésungen aufsteigenden Daimpfe. Verhandl. d. naturforsch. Ges. zu Basel, (1887) 418. —-—. Dampftemperaturen bei vermindertem Drucke. Ver- handl. d. naturforsch. Ges. zu Basel, (1887) 363-418. KaAiscHer (S.). Bemerkung zu der Arbeit von J. W. Langley: Ueber eine wahrscheinliche Anziehung als mechanischer Zug. Z. phys. Chemie, 2 (1888) 531.—See Langley, same vol. 92. Karotryi (L. von). Products of the combustion of gun-cotton and gun- powder under circumstances analogous to those which occur in practice. Phil. Mag. [4] 26 (1863) 266; Ann. Phys. u. Chem. April, 1863. KeELLAND. On the conservation of energy. Phil. Mag. [4] 26 (1863) 326. KELLER. On the increase of temperature produced by a waterfall. Phil. Mag. [5] 22 (1886) 312, from Atti Accad. Lincei, [4] 1 (1885) 671-6 ; Beiblitter, 11 (1885) 333. KrrcuHorr (G.). Ueber einen Satz der mechanischen Warmetheorie und einige Anwendungen derselben. Ann. Phys. u. Chem. 103 (1858) itt —. Einfluss der Anfangstemperatur bei chemischen Processen. Ann. Phys. u. Chem. 103 (1858) 203. —. Die Continuitét der Curve fiir die Dampfspannung tiber und unter O°, erklart nach der mechanischen Warmetheorie. Ann. Phys. u. Chem. 103 (1858) 206. —. Ueber die Spannung des Dampfes von Mischungen aus Wasser und Schwefelséiure. Ann. Phys. u. Chem. 104 (1858) 1. —. Vorlesungen tiber mathematische Physik. Mechanik. 2e Auflage. Leipzig. 1877. (vu, 466 pp.) —. Zur Theorie der Diffusion von Gasen durch eine pordse Wand. Ann. Phys. u. Chem. n. F. 21 (1884) 563. KuinceL. Beziehung zwischen dem mechanischen Warmeaquivalent und den Molekulargewichten. Ann. Phys. u. Ohbem. 158 (1876) 160. Bemerkung dazu von H. L. Bauer, 612. Knopiaucn. Gesetze der strahlende Warme. Ann. Phys. u. Chem. 67 (1846) 1; Amer. J. Sci. [2] 1 (1846) 429, abs. ; L’ Institut, (1846) 22. AUTHOR INDEX. 179 ixocu (K. R.). Beitraége zur Kenntniss der Elasticitat des Hises. Ann. Phys. u. Chem. n. F. 25 (1885) 438. — — und Ktocke (Fr.). Ueber die Bewegung der Gletscher. Ann. Phys. u. Chem. n. F. 8 (1879) 661-666; n. F. 14 (1881) 509; Phil. Mag. [5] 9 (1880) 274. (S.). Ueber die Abhangigkeit der Reibungsconstante des Queck- silbers von der Temperatur. Ann. Phys. u. Chem. n. F. 14 (1881) 1. —. Ueber die Reibungsconstante des Quecksilberdampfes und deren Abhingigkeit von der Temperatur. Ann. Phys. u. Chem. n. F. 19 (1883) 857. K6outer. Die mechanische Wirmelehre in ihrer Anwendung auf per- manente Gase. (Schulprogramm.) Bielefeld. 1866. 8vo. KoutrauscnH (F.). Warmeiquivalent des Silbers aus galvanischen Messungen. Ann. Phys. u. Chem. 149 (1875) 185.—See Rontgen, same vol. 579, 580, also 136 (1869) 618. —. Ausdehnung des Caoutchoucs durch die Warme. Ann. Phys. u. Chem. 149 (1873) 577 ; Dingler’s pol. Jour. 210 (1873) 444; Jahresb. (1873) 55.—See Ann. Phys. u. Chem. 128 (1841) 521; Phil. Mag. [4] 47 (1874) 156. —. Leitfaden der praktischen Physik. 4e verbesserte Auflage. Leipzig. 1880. KowAckk (F.). Ueber die Beziehung des Gefrierpunktes von Salzlé- sungen zu deren Spannkrafisgesetze. Ann. Phys. u. Chem. n. F. 15 (1882) 38. Konic (J.). Ueber eine neue Interpretation der Fundamentalgleichungen der Dynamik. Mathemat. Ber.aus Ungarn, 5 (1886-7) 131-178. Konowatow (D.). Zur Theorie der Fltissigkeiten. Z. phys. Chem. 2 (1888) 1-6. Koosen. Ueber die Erwarmung und Abkithlung, welche die perma- nenten Gase erfahren, sowohl durch Compression und Dilatation, als durch Beriihrung mit Korpern verschiedener Temperatur. Ann. Phys. u. Chem. 89 (1853) 437 ; Jahresb. (1853) 37. _ Kopp (H.). Recherches sur les températures of les volumes spécifiques de différentes substances sont comparables. Ann. chim. et. phys. [3] 7 (1848) 389. 180 LITERATURE OF THERMODYNAMICS. Kopp (H.). Sur la dilatation des corps solides par la chaleur. Ann. chim. et phys. [3] 34 (1852) 338; Phil. Mag. [4] 5 (1852) 268. —. Sur quelques régularités dans les points d’ébullition des com- binaisons organiques. Ann. chim. et phys. [3] 49 (1857) 338. —. Onthe relation between boiling-point and composition in organic bodies. Phil. Mag. [4] 21 (1861) 227, abs. from Proc. Roy. Soe. May 3, 1860; Phil. Trans. 150 (1860) 257. —. Atomwarme der Elemente und der starren K6rper. Ann. Chem. u. Pharm. 3 (1864) 1, 289; Jahresb. (1864) 42; Proc. Roy. Soe. 18 (1864) 229. —. Zur Kenntniss der Molekulargewichtswirmen starrer Ver- bindungen. Ber. Chem. 21 (1888) 1880-82. Kopssen, (A.). Zwei Energiemesser der Firma Siemens u. Halske. Verhandl. d. physikal. Ges. Berlin, (1888) 45-47. Kortrewec (D. J.).. Ueber den Einfluss der réiumlichen Ausdehnung der Molekiile auf den Druck eines Gases. Aun. Phys. u. Chem. n. F. 12 (1881) 136. Kress (G.). Einleitung in die mechanische Wirmetheorie. Leipzig. 1874. S8vo. Mit 52 Holtzschnitten. (v1, 218.) ————. Elementarer Beweis des Satzes von Avogadro. Ann. Phys. u. Chem. n. F. 22 (1884) 295. —. Umsetzung der mechanischen Arbeit in Electricitat und Riickverwandlung. Z. phys. u. chem. Unterricht, 1 (1887) 118. Kronta. Mechanische Wirmetheorie. Chemisches Centralblatt, (1856) 725; Ann. chim. et phys. [3] 51 (1857) 491. Kurz. Ueber das mechanische Aequivalent der Warme und der Elas- ticitit fester Korper. Z. Math. u. Phys. (1865) 428. Kunprt (A.). An experiment on the boiling in conjunction of two liquids which do not mix. Phil. Mag. [4] 40 (1870) 463. —. Ueber den Einfluss des Druckes auf die Oberflichenspannung der Fliissigkeiten. Ann. Phys. u. Chem. n. F. 12 (1881) 538. Kupprer (A. F.). Versuche tiber die Elasticitiét der Metalle und tiber ihre Spannung durch Wiarme. Bull. Acad. St. Pétersburg, 7 (1849) 289: Jahresb. (1849) 53. AUTHOR INDEX. 181 Kurprer (A. F.). Remarks on the mechanical equivalent of heat. Phil. Mag. [4] 4 (1852) 393; Ann. Phys. u. Chem. 86 (1852) 310; Instit. (1852) 259; Amer. J. Sci. [2] 14 (1852) 421; Jahresb. (1852) 38; Bull. Acad. St. Pétersbourg, 10 (1852) 193. Kurz (A.). Ob bei dem Versuch von Kohlrausch, Ann. Phys. u. Chem. 156 (1869) 618, die Luft im Stiefel der Luftpumpe Arbeit verrichtet. Ann. Phys. u. Chem. 138 (1869) 336.—See Boltzmann, Ann. Phys. u. Chem. 140 (1870) 254; Hoppe, same vol. 263 ; Kurz again, 141 (1870) 159; Boltzmann again, same vol. 473; Kohlrausch, 136 (1869) 618; 149 (1873) 580. —. Aus der thermischen und mechanischen Ausdehnung fester Kérper das Arbeitsaquivalent noch nicht ableitbar. Ann. Phys. u. Chem., Erginzbd 6 (1874) 314; Jahresb. (1874) 55.—See Kuppfer, Jahresb. (1852) 37; Buff. Jahresb. (1872) 58; Edlund, Ann. Phys. u. Chem. 126 (1865) 559. Lasoutaye (Ch.). Du travail mécanique que peut théoriquement engendrer l’unité de la chaleur. Institut, (1855) 160: Jahresb. (1855) 30. —. Essai sur équivalent mécanique delachaleur. Paris. 1858. —. Sur lPéquivalent mécanique de la chaleur. - Comptes rendus, 46 (1858) 7753. —. Mémoire sur la production de la chaleur par les affinités chimiques, et sur les équivalents mécaniques des corps. Comptes rendus, 47 (1858) 824. —. De la production de la chaleur par les affinités chimiques et des équivalents mécaniques des corps. Paris. 1860. 8vo. —. Lettre sur Péquivalent mécanique de la chaleur. Cosmos, 16 (1860) 369. —. De la constitution moléculaire des corps compatible avec la théorie mécanique de la chaleur. Paris. 1863. — et Tresca. Recherches expérimentales sur la théorie de Péquivalent mécanique de la chaleur. Comptes rendus, 58 (1864) 358 ; 60 (1865) 326; Mémoires par divers savants, [2] 18 (1868) 1. Lamé (G.). Lecons sur la théorie analytique dela chaleur. Paris. 1861. LanpeERO e Priero. Sur quelques lois de la combinaison chimique. Comptes rendus, 103 (1886) 934; Beiblatter, 12 (1888) 7, abs. SSS Se. 182 LITERATURE OF THERMODYNAMICS. LANnGBERG. Mathematische Theorie der Warme. Ann. Phys. u. Chem. 66 (1851) 1; Jahresb. (1851) 47. Lanauey (J. W.). Ueber eine wahrscheinliche Aeusserung chemischer Anziehung als mechanischer Zug. Z. phys. Chem. 2 (1888) 83-91.— See Kalischer, same vol. 531. Lanauey (S. P.). The bolometer and radiant energy. Proc. Amer. Acad. 8 (1880-81) 342-359. —-—. The selective absorption of solar energy. Phil. Mag. [5] 15 (1883) 153-183, communicated by the Author; Amer. J. Sci. [3] 25 (1883) 169-196; Ann. Phys. u. Chem. n. F. 19 (1883) 226-244, 384- 400; Ann. chim. et phys. [5] 29 (1883) 497-542. ——. Energy and vision. Amer. J. Sci. [3] 36 (1888) 359- 379; Phil. Mag. [5] 27 (1889) 1-23. ——. Onthe history of a doctrine. Amer. J. Sci. [3] 37 (1889) 1-25; Beiblatter, 13 (1889) 331, abs. Lancuors. Du mouvement atomique; premiére partie, Thermodynam- ique. Paris. 1880. 8vo. (59 pp. avec figures.) Sur le calcul théorique de la composition des vapeurs, de leurs - coefficients de dilatation et de leurs chaleurs spécifiques. Comptes rendus, 102 (1886) 1251. Lapuace. Traité de mécanique celeste. Paris. Tomes i et ur, 1799; rz et rv (1804-5) 5 (1825); 2e édition (1829, 1850 et 1839). Sur la diminution de la durée du jour par le refroidissement de la terre. Ann. chim. et phys. 13 (1820) 410; 14 (1820) 315. Sur lattraction des corps sphériques, et sur la répulsion des fluides élastiques. Ann. chim. et phys. 18 (1821) 181. Eelaircissements de la théorie des fluides élostiques. Ann. chim. et phys. 18 (1821) 273; 21 (1822) 22. Larmor (J.). On the deduction of the general dynamical equations from the principle of energy. Proc. Cambridge Philosoph. Soc. 6 1 (1887) 95. Lavuaier (A.). Matiére inflammante et détonnante formée par l’action de l’acide nitrique sur l’indigo et les matiéres animals. Ann. de chimie, 55 (1805) 303; 56 (1806) 137. Launay (Veau de). On fulminating silver. Nicholson’s Jour. 9 (1804) 203. AUTHOR INDEX, 1838 Laurie (A. P.). Relations between the heats of combination of the elements and their atomic weights. Phil. Mag. [5] 15 (1883) 42. Le Cuateiier (H.) et Matiarp. Sur les températures d’inflamma- tion des mélanges gazeux. Comptes rendus, 91 (1880) 825. — et Vitesses de propagation de l’inflammation dans les mélanges gazeux explosifs. Comptes rendus, 93 (1881) 145. —. Sur la thermodynamique et la chimie. Bull. Soc. chim. 46 (1886) 737 ; Beiblatter, 12 (1888) 324, abs. —. Sur les fonctions caractéristiques de M. Massieu. Comptes rendus, 106 (1888) 1343. —. Sur la détermination des coefficients de dilatation aux tem- pératures élévées. Comptes rendus, 107 (1888) 862-864. —. Ueber die Dissociation der Kohlensaiure. Z. phys. Chém. 2 (1888) 782-786. Leconte (J.). On the correlation of physical, chemical and vital force, and the conservation of force in vital phenomena. Phil. Mag. [4] 19 (1860) 133. Lercog. Dela transformation du mouvement en chaleur chez les animaux. Comptes rendus, 55 (1862) 191. Lepieu (A.). Démonstration directe des principes fondamentaux de la thermodynamique. Lois du frottement et du choc d’aprés cette science. Comptes rendus, 77 (1873) 94, 163, 260, 325, 414, 455, 517; Jahresb. (1873) 51. —. Intérpretation mécanique des lois de Dulorg et Petit et de Woestyn, sur les chaleurs spécifiques atomiques. Observations présentées & propos des derniers communications de M. M. Lockyer, Dumas et Berthelot relatives 4 la nature des éléments des corps. Comptes rendus, 78 (1874) 30. —. Démonstration directe de l’équation 3h = =O, pour tout cycle fermé et reversible. Comptes rendus, 78 (1874) 221, 309. x —. Observations 4 propos de la derniére communication de M. Clausius sur |’équation i =O. Comptes rendus, 78 (1874) 537. —. Note sur la décomposition du travail des forces. Comptes rendus, 78 (1874) 1182. | 184 LITERATURE OF THERMODYNAMICS. | Lepieu (A.). Idées générales sur l’interprétation mécanique des _pro- priétés physiques et chimiques des corps. Comptes rendus, 78 (1874) 1345, 1398. —. Duecyele fictif correspondant au fonctionnement des machines j thermiques a cylindre ouvert, et mise en évidence de ce cycle et du poids ; de substance motrice formant le corps travailleur. Comptes rendus, ; 80 (1875) 1040. —. Sur la loi de la détente pratique dans les machines 4 vapeur. ; Comptes rendus, 80 (1875) 1199. —. Condition du maximum de rendement calorifique des machines { a feu. Comptes rendus, 80 (1875) 1278. | ———. Sur le rendement des injecteurs 4 vapeur. Comptes rendus, 81 (1875) 711 et 773. —. Nouvelles observations sur la loi de la détente pratique dans les machines 4 vapeur. Comptes rendus, 81 (1871) 928. —. Réponse a quelques objections soulevées par les récentes com- munications sur le rendement des injecteurs 4 vapeur. Comptes rendus, 81 (1875) 1023. —. Considérations nouvelles sur la régulation des_tiroirs. Comptes rendus, 82 (1876) 152 et 192. —. Etude sur les machines 4 vapeur ordinaires et compound, les chemises de vapeur et la surchauffe, d’aprés la thermodynamique ex- périmentale. Comptes rendus, 87 (1878) 903, 952, 1024, 1062. i } | ; | j —. Etude de thermodynamique expérimentale sur les machines A vapeur. Comptes rendus, 93 (1881) 25. —. Etude de thermodynamique expérimentale sur les machines & vapeur. Paris. 1881. 8vo. (96 pp.) —. Généralization et démonstration rigoreusement mécanique de la formule de Joule. Comptes rendus, 98 (1884) 69. } ' j LeGrAnp (J.). Recherches sur les variations que les sels dissous en diverses proportions produisent dans le point d’ébullition de leau. Ann. chim. et phys. 59 (1835) 423. LreuMmann (O.). Molecularphysik. 1. Leipzig. 1888. 8vo. (x, 852.) Lerpnirz. Mathematische Schriften. Herausgegeben von Gerhardt. Halle. 1860. 2er Band, 1, 34, 36, 117, 234, 484, 775. ~ AUTHOR INDEX. 185 Lemorne (G.). Description d’une machine a l’air dilaté. Comptes rendus, 36 (1853) 263. —. Extrait d’une lettre sur les machines dair. L’Instit. (1853) 88, 107. . —. Sur la théorie de la dissociation. Comptes rendus, 93 (1881) 265, 312; Jahresb. (1881) 1133. Leroux. Détermination de l’équivalent mécanique de la chaleur. Cosmos, 12 (1858) 314. Sur les phénoménes de la chaleur qui accompagnent dans certaines circonstances le mouvement vibratoire des EoEps; Comptes rendus, 50 (1860) 656, 729. Lescorur (L.). Sur les relations de l’efflorescence et de la déliquescence des sels avec la tension maximum des solutions saturées. Comptes rendus, 103 (1886) 1260. —. Recherches sur la dissociation des hydrates salins et des composés analogues. Lille. 1888. 8vo. (158 pp.) Ann. chim. et phys. [6] 16 (1889) 378-403; Beiblitter, 13 (1889) 343, abs. Lestiz. Méthode nouvelle de produire et d’entretenir la congélation. Ann. de chimie, 78 (1811) 177 . Nouvelle expérience sur la congélation artificielle. Ann. chim. et phys. 4 (1817) 333, 445; 5 (1817) 334. | Levy (Maurice). Notesur la théorie mécanique de la chaleur. Comptes rendus, 84 (1877) 442. —. Applications d’une théoreme comprenant les deux principes de la théorie mécanique de la chaleur. Comptes rendus, 84 (1877) 491. —. Mémoiresur une loiuniverselle relative ala dilatation des corps. Comptes rendus, 87 (1878) 449, 649.—See Boltzmann, Comptes rendus, 87 (1878) 593, 676, 773; Clausius, same vol. 718; Massieu, same vol. 731; de Saint-Venant, same vol. 715; Réponses a diverses communica- tions, same vol. 826; Jahresb. (1878) 69. —. Sur l’attraction moléculaire, dans ses rapports avec la tem- pérature des corps. Comptes rendus, 87 (1878) 488; Phil. Mag. [5] 6 (1878) 466. —. Deux remarques au sujet de la relation générale entre pres- sion et la température. Note de M. H. F. Weber. Réponse de M. Lévy a cette communication. Comptes rendus, 87 (1878) 554. i eg Se = - ——— Se ee 186 LITERATURE OF THERMODYNAMICS. Levy (Maurice). Sur une propriété générale des corps solides élastiques. Comptes rendus, 106 (1888) 414. Liats. De Vemploi de lair chauffé comme force motrice. Comptes rendus, 36 (1853) 260; 37 (1853) 999; Mem. Soc. de Cherbourg, 2 (1854) 115. LIEBERMEISTER. Physiologische Untersuchungen tiber die quantitativen Veriinderungen der Warmeproduction. Arch. f. Anatomie, (1860) 520, 589. LinpeMANN (F.). Molecular physics; an attempt at a comprehensive treatment of physical and chemical forces. Nature, 38 (1888) 458- 461, 578-581: Linoie (F.). On the alteration of electromotive force by heat. Phil. Mag. [4] 29 (1865) 408. LiouviLtLe. Solution nouvelle dun probléme d’analyse relatif aux phénoménes thermomécaniques. Comptes rendus, 5 (1837) 598. LippMANN (G.). Extension du principe de Carnot 4 la théorie des phénoménes électriques. Equations différentielles générales d’équilibre et du mouvement d’un systéme électrique reversible quelconque. Comptes rendus, 82 (1876) 1425. —. Expressions générales de la température absolue et de la fonction de Carnot. Comptes rendus, 95 (1882) 1058. —. De l’action de la chaleur sur les piles, et de la loi de Kopp et Woestyne. Comptes rendus, 99 (1884) 895. —. Cours dethermodynamique. Paris. 1889. 8vo. (251 pp.) Beiblatter, 13 (1889) 752, abs. Lissranou. Etude sur les machines 4 air chaud de M. Ericsson. Arch. des Sci. phys. 24 (1853) 209. Locke (J.). Essay on the human understanding. Book 1, Chap. vim, Section 10. —. Ona large and very sensible thermoscopic galvanometer. Phil. Mag. [8] 11 (1837) 378. Lopce (A.). Note on the dimensions and meaning of J., usually called the mechanical equivalent of heat. Nature, 36 (1887) 320. AUTHOR INDEX. 187 Lopes (O. J.). On a mechanical illustration of thermoelectric phe- nomena. Phil. Mag. [5] 2 (1876) 524.—See Note by Avenarius, Phil. Mag. [5] 3 (1877) 156. Lodge’s reply, Phil. Mag. 3 (1877) 349. ——. On a systematic classification of the various forms of energy. Phil. Mag. [5] 8 (1879) 277-286; Jahresb. (1879) 89. ——. Onaslight error in the customary specification of ther- moelectric current-direction, and a query with regard to a point in thermodynamics. Phil. Mag. [5] 19 (1885) 448. ——. Elementary mechanics, including Hydrostatics and Pneu- matics. London. 1885. 8vo. Phil. Mag. [5] 20 (1885) 545. Lores (M.) und Nernst (W.). Zur Kinetik der in Lésung befindlichen Korper. Ueberfuhrungszahlen und Leitvermégen einiger Silbersalze. Z. phys. Chem. 2 (1888) 613, 948-963. Lomparp (J.S.). Experimental researches cn the propagation of heat by conduction in bone, brain-tissue and skin. Proc. Roy. Soc. 33 (1881-82) 11; 34 (1882-83) 173; 40 (1886) 1. Lommet (E.). Ueber einen Gefrierapparat. Ann. Phys. u. Chem. n. F. 22 (1884) 614. Lorentz (H. A.). Ueber das Gleichgewicht der lebendigen Kraft unter Gasmoleciilen. Ber. d. Wiener Akad. 95 11 (1887) 115-152, Separatabd. Lorentz (L.). On the molecular theory and laws of electricity. Phil. Mag. [4] 40 (1870) 390. Loscumipt (J.). Zweiter Satz der mechanischen Wirmetheorie und chemische Losung. Ber. d. Wiener Akad. 59 11 (1869) 263, 395 ; Instit. (1869) 159; Jahresb. (1869) 152. ———. Zustand des Wirmegleichgewichts eines Systems von Kérpern mit Riicksicht auf die Schwerkraft. Ber. d. Wiener Akad. 73 11 (1876) 128-142, 366-372; Jahresb. (1876) 63. Lowirz. Expériences sur la production artificielle de froid. Ann. de chimie, 22 (1797) 297, 300; Crell’s Annalen, 1 (1796) 529. Lucas LE JEUNE. Observations sur une cristallisation d’huile d’amandes améres ; leur inflammation spontanée dans un mélange d’acidesulfurique. Ann. de chimie, 23 (1797) 81. ee 188 | LITERATURE OF THERMODYNAMICS. Lucas (F.). Théorémes généraux sur l’équilibre et le mouvement des systémes matériels. Mém. divers Savants, [2] 22 (1876) 1. —. Mémoire sur les vibrations calorifiques des solides homogénes. Mém. divers Savants, [2] 27 (1883) 1. —. Le coefficient de dilatation et la température des gaz. Comptes rendus, 105 (1886) 1251. Luynes (V. de). On the sudden cooling of melted glass, and particu- larly on “ Rupert’s Drops.” Phil. Mag. [4] 45 (1873) 464; Comptes rendus, 76 (1878) 546-549. Mac Cuutocn (R.8.). Treatise on the mechanical theory of heat, and its applications to the steam-engine. New York. 1876. Mac Grecor (J.G.). Elementary Treatise on kinematics and dynamics. London. 1887. Macnu. Die Geschichte und die Wurzel des Satzes von der Erhaltung der Arbeit. Prag. 1872. 8vo. Maanus(G.). La faculté de quelques poudres métalliques de s’enflammer spontanément dans l’air atmosphérique 4 la température ordinaire. Ann. chim. et phys. 30 (1825) 103; Annals of Phil. n. s. 12 (1826) 464, abs. —. Extrait du mémoire de M. Magnus sur la dilatation des gaz. Ann. chim. et phys. [3] 4 (1842) 516. —. Mémoire sur les courants thermo-électriques. Ann. chim. et phys. [8] 34 (1852) 105. —. On the elastic force of vapours of mixtures of two liquids. Phil. Mag. [4] 9 (1855) 44. —— —. On thermal radiation. Phil. Mag. [4] 29 (1865) 58. —. On the different properties of heat radiated by rough and by bright surfaces. Phil. Mag. [4] 30 (1865) 81; Ann. Phys. u. Chem. 124 (1865) 476. Mary (P. T.). First report on our experimental knowledge of the prop- erties of matter with respect to volume, pressure, temperature and specific heat. Rept. British Assoc. (1886) 100-159. Mauuiarp (E.). De la définition de la température dans la théorie mécanique de la chaleur, et de linterprétation physique du second principe fondamental de cette théorie. Comptes rendus, 75 (1872) 1479; Phil. Mag. [4] 45 (1873) 77; Jahresb. (1873) 52. oa er el is: 6 SS ce ~ Sa ee EA a AUTHOR INDEX. 189 MALuet (R.). Action of heat when long continued, on inorganic and organic substances. Rept. British Assoc. (1838) 312. —. On the alleged expansion in volume of various substances in passing by refrigeration from the state of liquid fusion to that of solidi- fication. Phil. Mag. [4] 49 (1875) 231, Mann. Zur mechanischen Wiirmelehre: Berechnung derjenigen me- chanischen Arbeit, welche zur Zerlegung einer chemischen Verbindung erforderlich ist. Z. Math. u. Phys. (1861) 72. Marcer (A.). An account of some experiments on the congelation of mercury by means of ether. Nicholson’s Jour. 34 (1813) 119. ——_ —, {fee A. de la Rive et M. Marcet (F.). Recherches sur certaines circonstances qui influent sur la température du point d’ébullition des liquides. Ann. chim. et phys. [3] 5 (1843) 449, 460. Martié-Davy et Troost. Détermination par la pile des quantités de travail moléculaire exprimées en calories produites par l’union des bases. Comptes rendus, 46 (1858) 748; Ann. chim. et phys. [3] 53 (1858) 423. et Détermination par la pile des quantités de chaleur produites dans l’acte de combinaison de chlore avec les métaux. Comptes rendus, 46 (1858) 936; Jahresb. (1858) 31. et Note sur la théorie mécanique de la chaleur. Comptes rendus, 53 (1861) 904. De la mesure, par la pile, des chaleurs de combinaisons des différents métaux. Comptes rendus, 54 (1862) 1103 ; N. Arch. ph. nat. 14 (1862) 402; Instit. (1862) 169. Marienac (C.). Recherches sur la congélation et lébullition des hydrates de l’acide sulfurique. Ann. chim. et phys. [3] 39 (1853) 184. —. Researches on the specific heats, densities and expansions of some liquids. Phil. Mag. [4] 41 (1871) 184. Markownikorr. Sur les lois qui régissent les réactions de l’addition directe. Comptes rendus, 81 (1875) 668, 728, 776. Marsu (B. V.). On the latent heat of expansion in connection with the luminosity of meteors. Amer. Philosoph. Soc. Proc. 14 (1874-75) 114. 190 LITERATURE OF THERMODYNAMICS. Martins (Ch.). Mémoire sur les températures de la mer glaciale 4 la surface et 4 de grandes profondeurs. Ann. chim. et phys. [38] 24 (1848) 220. —. Note sur les divers teintes de la glace des glaciers, et l’aspect varié des eaux qui proviennent de leur fusion. Ann. chim. et phys. [3] 22 (1848) 496. —. Des causes du froid sur les hautes montagnes. Ann. chim. et phys. [8] 58 (1860) 208. — et Caancen (G.). Des phénoménes physiques qui accompag- nent la rupture par la congélation de l'eau de projectiles creux de divers calibres. Ann. chim. et phys. [4] 26 (18:2) 548. Mascuke (O.). On the development of heat by the friction of liquids against solids. Phil. Mag. [4] 45 (1873) 400; Arch. ph. nat. 46 (1873) 211s Massteu (F.). Sur les fonctions caractéristiques de divers fluides. Comptes rendus, 69 (1869) 858; Mem. de divers Savants, [2] 22 (1876) 1, —. Observations concernant la mémoire de M. Lévy sur une loi universelle relative 4 la dilatation des corps. Comptes rendus, 87 (1878) 731. Masson et CourTEPEE. Expériences sur les pouvoirs rayonnants des corps. Comptes rendus, 25 (1847) 936. Sur la corrélation des propriétés physiques des corps. Ann. chim. et phys. [3] 53 (1858) 257. Maruews (Wm.). Canon Moseley’s views upon glacier-motion. Phil. Mag. [4] 42 (1871) 332-415. Marrevuccr. Communication de M. Morin en présentant un opuscule de_ M. Matteucci intitulé: “ Lecons sur la théorie dynamique de la chaleur.” Comptes rendus, 58 (1864) 1045. De la relation qui existe entre la quantité d’action chimique et la quantité de chaleur, d’électricité et de lumiére qu’elle produit. Arch. de Genéve, 4 (1847) 375. MarrutressEn (A.). On the expansion of water and mercury. Phil. Mag. [4] 31 (1866) 149; Phil. Trans. 156 (1866) 231, 861; Phil. Mag. [4] 32 (1866) 472; Proc. Roy. Soc. June 21, 1866. AUTHOR INDEX. 191 Mavumené (E.). Sur les variations de la chaleur dégagée par l’union de Yeau et de V’acide sulphurique, 4 diverses températures. Comptes rendus, 85 (1877) 914, 1026. Maurice. Abstract of the principal demonstrations of M. Fourier, rela- tive to the mathematical law of the radiation of heat. Translated by Prof. James D. Forbes and communicated ina letter to Sir David Brewster. Phil. Mag. [3] 2 (1833) 103. Mauritius On the variation of the magnetic force with the tempera- ture. Phil. Mag. [4] 27 (1864) 398. Maxwe tt (J.C.). On the motions and collisions of perfectly elastic spheres. Phil. Mag. [4] 19 (1860) 19; 20 (1860) 21, 33. —-—. On physical lines of force. Phil. Mag. [4] 21 (1861) 161, 281, 338.—See Challis, same vol. 250. —-—. Theory of heat. London. 1871. 8vo. (312 pp.) Phil. Mag. [4] 48 (1872) 149; comments by Clausius, same vol. 106; and by Rankine, same vol. 160; Nature, 5 (1871-2) 319. Seventh edition, 1883. ——. On molecules. Phil. Mag. [4] 46 (1873) 453. Mayer (A. M.). Thermodynamics of waterfalls. Amer. Association Proc. 18 (1869) 64. Mayer (J. R.). Bemerkungen tiber die Kriafte der unbelebten Natur. Ann. Chem. u. Pharm. 42 (1842) 1; Ann. chim. et phys. [3] 34 (1852) 501; Phil. Mag. [4] 24 (1863) 371. —-—. Die organische Bewegung in ihrem Zusammenhang mit dem Stoffevechsel. Heilbronn. 1845. 8vo. —-—. Réclamation de priorité centre M. Joule relativement 4 la loi de l’équivalent du calorique. Comptes rendus, 27 (1848) 385 ; 28 (1849) 182 ;-29 (1849) 534. —-—. Mathematische Darstellung von Carnot’s Theorie der Warme. Ann. Chem. u. Pharm. 42 (1851) 263; Jahresb. (1851) 32. -——. Surlatransformation du calorique en force vive. Comptes rendus, 32 (1851) 652. ——. Bemerkungen tiber das mechanische Aequivalent der Warme. Heilbronn u. Leipzig. 1851. 8vo. Jahresb. (1851) 25. 4 192 LITERATURE OF THERMODYNAMICS. MEIKLE (H.). An improved demonstration that air expands in geometri- cal progression for equal increments of heat. Phil. Mag. n.s. 11 (1832) 243. Metiont. Recherches expérimentales sur la réflexion de la chaleur rayonnante. Comptes rendus, 1 (1835) 300. Betrachtungen und Versuche tiber die Theorie von der Einer- leiheit der Licht und strahlende Warme erzeugenden Wesen. Ann. Phys. u. Chem. 37 (1836) 486; Ann. chim. et phys. 59 (1836) 418. Einheit des Lichts und der Warme. Ann. Phys. u. Chem. 39 (1836) 31. Sur quelques propriétés de la chaleur rayonnante considérée comme cause de la fonte hative des neiges autour des plantes. Comptes rendus, 6 (1838) 801. Expériences sur la chaleur rayonnante. Comptes rendus, 10 (1840) 537, 826. Betrachtungen und Erfahrungen tiber die Diathermansie oder Wiarmefirbung der Kérper. Ann. Phys. u. Chem. 49 (1849) 577. Mémoire sur la radiation diffuse de la chaleur, sur le constance du pouvoir absorbant du noir de fumée et des métaux, et sur l’existence d’un pouvoir diffusif qui, par ses variations, change le valeur du pouvoir absorbant dans les autres corps athermanes. Comptes rendus, 11 (1840) 659, 678. Remarques de M. Biot 4 l’occasion de ce Mémoire, 682. Diffusionsvermégen diathermaner Substanzen. Ann. Phys. u. Chem. 53 (1841) 47. Nouvelles recherches sur le rayonnement de la chaleur. Comptes rendus, 20 (1845) 575. Metsens. Les explosions des choudiéres 4 vapeur. Ann. chim. et phys. [4] 24 (1871) 218. MénABREA. Théorie analytique applicable aux questions relatives aux vibrations et 4 la propagation de la chaleur dans les corps solides. Comptes rendus, 40 (1855) 1229. MENDELEJEFF (D.) On the expansion of liquids. Phil. Mag. [4] 22 (1861) 520. —. Ein Versuch der Anwendung eines Hauptsatzes von Newton’s Naturphilosophie auf die Chemie. Proc. Roy. Institution, 31 May 1889; Beiblatter 13 (1889) 843, abs. AUTHOR INDEX. 193 MENDENHALL (T. C.). On a differential resistance thermometer. Phil. Mag. [5] 22 (1885) 384; Amer. J. Sci. August, 1885. MENSBRUGGHE (G. van der). Mechanik der Wirme. Stuttgart. 1867. 8vo. (vi, 194 pp.) —-—. On the mechanical equivalent of heat. Proc. Roy. Soe. 20 (1871-72) 55. ——— — —. Preliminary note on a remarkable fact observed on the contact of certain liquids of very different superficial tensions. Phil. Mag. [4] 43 (1872) 399; [5] 2 (1876) 450, translated from Bull. Acad. Belgique, [2] 41 (1876) no. 4; [5] 4 (1877) 40, translated from Bull. Acad. Belgique, [2] 41 (1877) no.7; Phil. Mag. [5] 7 (1879) 432, translated from Bull. Acad. Belgique, [2] 46 (1878) no. 11. Mesuin. Définition des gaz parfaits. Jour. de phys. [2] 4 (1885) 132. Meyer (L.). Grundlagen der Thermochemie. Ann. Chim. u. Pharm. 218 (1883) 1; Ann. Phys. u. Chem. Beiblatter, 7 (1883) 520-22; Chem. News, 47 (1883) 264; Jahresb. (1883) 112. —. The evolution of the doctrine of affinity. Phil. Mag. [5] 23 (1887) 504, translated and communicated by Prof. William Ramsay. —. Modern Theories of Chemistry. English translation. Lon- don, 1888. Meyer (0. E.). De gasorum theoria. Inaug.-Diss. Breslau, 1866. ——. Ueber die kinetische Theorie der Gase. Breslau, 1877. 8vo. —w—. Ueber eine verinderte Form meines Beweises fiir das Maxwell’sche Gesetz der Energievertheilang. Ann. Phys. u. Chem. n. F. 10 (1880) 296; Jahresb. (1880) 82. ——. Ueber die Bestimmung der inneren Reibung einer Fliis- sigkeit nach der Coulomh’sche Methode. Jahresb. d. schlesischen Ges. f. vaterland. Cultur, (1887) 2-4. —w—. Bemerkungen uber einen Punkt aus der kinetischen Theorie der Gase. Z. phys. Chem. 2 (1888) 340. W. Ostwald’s Nachschrift, 342. MicHe.son (M. W.). Sur l’énergie dans le spectre. J. de phys. [2] 6 (1887) 467; Phil. Mag. [5] 25 (1888) 425-435. M 194 LITERATURE OF THERMODYNAMICS. Miter (A.). Quantitative Bestimmung des Einflusses der durch Dehnung erzeugten Temperaturveranderung auf die Messung der ersteren. Ann. Phys. u. Chem. n. F. 20 (1883) 94. —. Bemerkungen zu einer Abhandlung von Herbert Tomlinson : Ueber den Einfluss von Spannung und Deformation auf die Wirkung der physikalischen Krifte. Ann. Phys. u. Chem. n. F. 25 (1885) 450. MitLteR-HAvEnNFELs (A. R. von). Richtigstellung der in bisheriger Fassung unrichtigen mechanischen Wiirmetheorie und Grundziige einer allgemeinen Theorie der Aetherbewegungen. Wien. 1889. 8vo. (256 pp.) Beiblatter, 13 (1889) 894, abs. Mirscueruicu (E.). Sur le rapport de la densité des gaz 4 leurs poids atomiques. Ann. chim. et phys. 55 (1855) 5. Moar (Fr.). Bemerkungen tiber die Natur der Wiarme. Ann. Chem. u. Pharm. 24 (1837) 1; Phil. Mag. [5] 2 (1876) 110. —. Allgemeine Theorie der Bewegung und Kraft, als Grund- lage der Physik und Chemie. Ein Nachtrag zur mechanischen Theorie der chemischen Affinitit. Braunschweig, 1869. (v1, 138 pp.) —. Ableitung des Verhiltnisses der Warme der Gase bei con- stantem Druck und Volum aus der mechanischen Warmetheorie. Ber. chem. Ges. 4 (1871) 490. —. Theorie der Dissociation oder Thermolyse. Ann. Chem. u. Pharm. 171 (1874) 361; Jahresb. (1874) 110. Moon (R.). On the measure of work in the theory of energy. Phil. Mag. [4] 46 (1878) 219; 47 (1874) 291. Mosevey (H.). On the motion of a plate of metal on an inclined plane, when dilated and contracted; and on the descent of glaciers. Phil. Mag. [4] 23 (1862) 72, abs. from Proc. Roy. Soc. April 11, 1861. —. Onthe mechanical impossibility of the descent of glaciers by their weight only. Phil. Mag. [4] 87 (1869) 363; 42 (1871) 138; 43 (1872) 38. —. On the mechanical properties of ice. Phil. Mag. [4] 39 C1370) a. —. On the “veined structure” of the iceof glaciers. Phil. Mag. [4] 39 (1870) 241, with a plate. AUTHOR INDEX. 195 Moser (J.). Ueber die Ericsson’sche Luftexpansiorsmaschine (soge- nannte calorische Maschine). Polytechn. Centralbl. (1853) 1229. —. Galvanische Stréme zwischen verschieden concentrirten Lésungen desselben K6rpers und Spannungsreihen. Naturforsch. Versamml. in Mtinchen, Sept. 1877; Monatsber. d. Berliner Akad. 8 Nov. 1877 ; Ann. Phys. u. Chem. n. F. 3 (1878) 216. —. Der Kreisprocess, erzeugt durch den Reactionsstrom der electrolytischen Ueberftihrung und Verdampfung und Condensation. Nova Acta deutsch. Akad. Naturforscher, 41 1 (1881) No.1; Ann. Phys. u. Chem. [2] 14 (1881) 62. Moss (R. J.). On Crookes’s Force. Phil. Mag. [5] 4 (1877) 67. Most (R.). Einfacher Beweis des zweiten Warmegesetzes. Ann. Phys. u. Chem. 136 (1869) 140. Bemerkungen von Boltzmann. Ann. Phys. u. Chem. 1387 (1869) 495. Erérterung dartiber zwischen Beiden, Do. 138 (1869) 566; 140 (1870) 635. Moutine. Sur une expérience destinée 4 déterminer léquivalent mé- canique de la chaleur. Comptes rendus, 60 (1865) 24. Movtier (J.). Sur un point de la théorie mécanique de lachaleur. 64 (1867) 653. —. Mémoire sur la théorie mécanique de la chaleur. Ann. chim. et phys. [4] 14 (1868) 247. —. Sur la chaleur consommé en travail interne lorsqu’un gaz se dilate sous la pression de Patmosphére. Comptes rendus, 68 (1859) 95; Phil. Mag. [4] 38 (1869) 76. —. Recherches sur Vétat au nie Ann. chim. et pliys. [4] 24 (1871) 306. —. Eléments dela thermodynamique. Paris. 1872. 12mo. —. Sur la chaleur de transformation. Comptes rendus, 7€ (1873) 365; Phil. Mag. [4] 45 (1873) 236 ; Jahresb. ae 3) 110; Chem Centralbl. (1873) 382. —. Sur les vapeurs émises 4 la méme température par un méme corps sous deux états différents. Comptes rendus, 76 (1873) 1077. —. Sur la chaleur dégagée par la combinaison de l’hydrogéne avec les métaux. Comptes rendus, 79 (1874) 1242. 196 LITERATURE OF THERMODYNAMICS. Movtier (J.). Sur les tensions de la vapeur d’eau 4 0°. Bull. Soe. philom. [6] 12 (1875) 38. —. Sur expression du travail relatif 4 une transformation élé- mentaire. Comptes rendus, 80 (1875) 40; Phil. Mag. [4] 49 (1875) 154. —. Influence des principes de la thermodynamique sur la sur- fusion, sur le point de fusion, sur ’évaporation et sur les cycles non- reversibles. Bull. Soc. philomath. [6] 13 (1876) 5, 11, 49, 51; Instit. 76, 84, 165; Jahresb. (1876) 64. —. Sur les vapeurs émises 4 la méme température par eau liquide et par la glace. Bull. Soc. philom. [6] 13 (1876) 60. —. Sur la chaleur d’évaporation. Bull. Soc. philom. [7] 1 (1877) 17. —. Sur les transformations non-réversibles. Bull. Soc. philom. [7] 1 (1877) 39. —. Sur les transformations du soufre. Bull. Soe. philomat. [7] 2 (1878) 60. —. Sur quelques transformations chimiques. Bull. Soc. philom. [7] 3 1879).31. —. Sur la fusion dela glace. Bull. Soc. philom. [7] 3 (1879) 78. ———- —, Sur linfluence de la pression dans les phénoménes chimiques. ‘ J Bull. Soc. philom. [7] 3 (1879) 87. —. Sur le volume des corps électrisés. Bull. Soc. philom. [7] 3 (1879) 88. —. Sur la dilatation électrique. Bull. Soe. philom. [7] 4 (1880) 182. —. Sur la chaleur de vaporisation. Bull. Soc. philom. [7] 4 (1880) 247. —. Sur les tensions de vapeur de l’acide acétique. Bull. Soc. philom. [7] 5 (1880) 81. Morir (M. P.). On chemical affinity. Phil. Mag. [5] 8 (1879) 181. ——. Elements of thermal chemistry. London. 1885, Phil. Mag. [5] 19 (1885) 222. AUTHOR INDEX. 197 Miuier (A.). Ueber Thalbildung durch Gletscher. Ann. Phys. u. Chem. 152 (1874) 476. Mouier (W.). Ueber die Abhingigkeit der specifischen Wirmen der Gase von Molekulargewicht und der Anzahl der Atome im Molekiiy, Ber. chem. Ges. 20 (1887) 1402; Beiblatter, 12 (1888) 33, abs. Munroe (Charles E.). Index to the literature of explosives. Part 1 Baltimore. 1886. 8vo. Myers. Dissociation des rothen Quecksilberoxyds. Ber. chem. Ges. 6 (1873) 11-16; Chem. News, 27 (1873) 110. Naprer and Rankine. Improvements in engines for developing me- chanical power by the action of heat on air and other elastic fluids. Repertory of patent inventions [2] 23 (1854) 385.- and Expansion air-engine. Mechanics’ Mag. no. 1628 ; Dingler’s polytechn. J. 135 (1855) 241; Jahresb. (1855) 30. Naquet (A.). Considerations on the two memoirs of Sir B. C. Brodie on the calculus of chemical operations. Phil. Mag. [5] 7 (1879) 418; Moniteur scientifique, Nov., 1878, March, 1879. Nartanson (E. und L.). Ueber die Dissociation des Untersalpetersaure- dampfes. Ann. Phys. u. Chem. n. F. 24 (1885) 454. (L.). Sur Pexplication d’une expérience de Joule d’aprés la théorie cinétique des gaz. Comptes rendus, 106 (1888) 164-166. Re- flections de M. Hirn relative 4 la note precédente, 166-169. —. Kinetische Theorie unvollkommener Gase. Ann. Phys. u. Chem. [2] 33 (1888) 683. —. Geschwindigkeit, in welcher Gaze den Maxwell’schen Zu- stand erreichen. Ann. Phys. u. Chem. [2] 34 (1888) 970. Naumann (Alex.). Ueber Dissociation. Ann. Chem. u. Pharm. Supple- mentb’d 5 (1867) 541; Jahresb. (1867) 84. —. Ueber die relative Grdsse der Molektile. Ann. Chem. u. Pharm. Supplementb’d, 5 (1867) 253; Phil. Mag. [4] 34 (1867) 551, abs. —. Warmeentwickelung durch Aenderung der Molekiilzahl. Ann. Chem. u. Pharm. Supplementb’d, 6 (1868) 295; Jahresb. (1868) 61. 198 LITERATURE OF THERMODYNAMICS. Naumann (Alex.). Grundriss der Thermochemie, oder der Lehre von den Beziehungen zwischen Wirme und chemischen Erscheinungen vom Standpunkt der mechanischen Wiarmetheorie. Braunschweig. 1869. —. Avogadro’s law deduced from the fundamental conception of the mechanical theory of gases. Phil. Mag. [4] 39 (1870) 320; Ber. chem. Ges. 2 (1869) 690; Z. f. Chemie, (1870) 217; Jahresb. (1869) 211. —. Lehr-und Handbuch der Thermochemie. Braunschweig. 1882. Navier. Note sur l’action mécanique des combustibles. Ann. chim. et phys. 17 (1821) 557. NawALicHin. Heat phenomenaaccompanying muscular action. Nature, 16 (1877) 451. Remarks by A. R. Molison, 477. Near (E. V.). On glacier-motion. Phil. Mag. [4] 43 (1872) 104. Nernst (W.). Zur Kinetik der in Loésung befindlichen Korper. Z, phys. Chem. 2 (1888) 615-637. Neumann (C.). Mechanische Theorie der Wiirme. Leipzig. 1875. Newcomps (8.). On the definition of the terms “energy ” and “ work.” Phil. Mag. [5] 27 (1889) 115. Beiblatter, 13 (1889) 438. Newron (A.). Improvements in the construction of hot-air engines. Repertory of patent inventions, [2] 26 (1855) 120. Nicnots (R. C.), On the proof of the second law of thermodynamics. Phil. Mag. [5] 1 (1876) 369-373 ; Jahresb. (1876) 62. — — and WHEELER (A. W.). On the coefficient of expansion of gas-solutions. Phil. Mag. [5] 11 (1881) 113, comm. by authors, read before the Amer. Assoc. August 28, 1880. Nicxiis. Caloric Engines. Amer. J. Sci. [2] 15 (1853) 418. Nicot (W. W.J.). On the molecular volumes of salt-solutions. Phil. Mag. [5] 16 (1883) 121; 18 (1884) 179; 23 (1887) 385. Nipper (F. E.). On a property of the isotropic curve for a perfect gas as drawn upon the thermodynamic surface of pressure, volume and _ temperature. Phil. Mag. [5] 14 (1882) 233, from Trans. St. Louis Acad. April 3, 1882. AUTHOR INDEX. 199 Nosixi et Meitiont. Recherches sur plusieurs phénoménes calorifiques entreprises au moyen du thermo-multiplicateur. Ann. chim. et phys. 48 (1831) 198.—See Provostaye, Ann. chim. et phys. [3] 54 (1858) 129. NortHMore (T.). Experiments on the remarkable effects which take place in the gases, by change in their habitudes, or elective attractions, when mechanically compressed. Nicholson’s Jour. 12 (1805) 368. Norton (W. A.). On Ericsson’s hot air or caloric engine. Amer. J. Sci. [2] 15 (1853) 393. —-—. Dynamical theory of heat. Amer. J. Sci. [3] 5 (1873) 186; Jahresb. (1878) 51. OBERMAYER (A. von). Versuche tiber die Diffusion von Gasen. Ber. d. Wiener Akad. 81 1 (1880) 1102; 85 1 (1883) 147; 87 1 (1884) 188; 96 1 (1888) 546. Opiine (W.). Phlogiston und Energie. Ber. chem. Ges. 4 (1871) 421; Chem. News, 23 (1871) 2438, 256; Jahresb. (1871) 61. OEHLER (E.). Beitrag zur Geschichte der mechanischen Theorie der Warme. Ann. Phys. u. Chem. n. F. 9 (1880) 512. OETrTINGEN (A. J. von). Arbeitsmaximum beim umkehrbaren Kreis- process permanenter Gase in kalorischen Maschinen. Ann. Phys. u. Chem. Erganzbd. 5 (1872) 540; Jahresb. (1875) 46. —— —. Thermodynamische Beziehungen antithetisch ent- wickelt. Mem. Acad. St. Pétérsbourg, [7] 52 (1885) 1-7 Sep.; Bei- blatter, 18 (1889) 466, abs. OmopeE! (D.). See Vicentini (G.) e O. OppENHEIM (S.). Zur Theorie der stationiren Bewegung. Ann. Phys. u. Chem. n. F. 15 (1882) 495. OrFILa (A. F.). De la chaleur dans les phénoménes chimiques. Paris. 1853. OssELIN (A.). Mémoire sur les conséquences du principe de l’équivalence mécanique de la chaleur. Comptes rendus, 77 (1878) 346. OstwaALp (W.). Studien zur chemischen Dynamik. J. prackt. Chemie, [2] 29 (1884) 385-408; Ber. chem. Ges. 17 (1884) R. 37; Jahresb. (1884) 20. J. J. Thomson’s reply, Phil. Mag. [5] 23 (1887) 379. Ostwald again, same vol. 472. 200 LITERATURE OF THERMODYNAMICS. OstwaLp (W.). Bemerkungen tiber einen Punkt aus der kinetischen Theorie der Gase. Z. phys. Chem. 2 (1888) 81-83. —. Studien zur chemischen Dynamik. Sechste Abhandlung : 127. —. Ueber die Dissociationstheorie der Elektrolyte. Mit 1 Holz- schnitt. Z. phys. Chem. 2 (1888) 270-284; 3 (1889) 588-602; Bei- blatter, 13 (1889) 846, abs. Paauzow (A.). Ueber ein neues Volumenometer. Ann. Phys. u. Chem. n. F. 13 (1881) 332; 14 (1881) 176. PaGuLiANte Panazzo. Sulla compressibilita dei liquidi. Atti Accad. Lincei, [3] 19 (1883-84) 273. PaAGLIANI (S.). Sul coefficiente di dilatazione e sul calore specifico a volume constante dei liquidi. Atti Accad. Torino, 20 (1884-85) 54. PaGurani (S.) e Barrenr (A.). Sull’attrito interno nei liquidi. Atti Accad. Torino, 20 (1884-85) 607, 845. Pareau (A. H.). Ueber die Dampfspannungen bei der Dissociation krystallwasserhaltiger Salze. Ann. Phys. u. Chem. n. F. 1 (1877) 39 ; Berichtigung, n. F. 2 (1877) 144. PARKER (J.). On the thermodynamics of eryohydrates. Phil. Mag. [5] 25 (1888) 406. —. On an extension of Carnot’s theorem. Phil. Mag. [5] 25 (1888) 512-514; Beiblatter, 12 (1888) 760, abs. Parsons (C.). Experiments on carbon at high temperatures and under great pressures, and in contact with other substances. Proc. Roy. Soc. 44 (1888) 320-323. Pascat. Mixed vapor engines. Mechanics’ Mag. 64 (1856) 241. Péciet (E.). Traité de la chaleur considérée dans ses applications. 2e édition. Paris. 1848. 4to avec atlas fol. 4e édition, 1878. 3 vols. Pevxat (H.). Application du principe de Carnot aux réactions endo- thermiques. Comptes rendus, 106 (1888) 34-37; J. de phys. [2] 8 (1888) 279-85. Ueber Oxydations-und Reductions-vorgiinge. Z. phys. Chem. 2 (1888) eM Sa Shas AUTHOR INDEX. 201 Perrier. Mémoire sur la formation des tables des rapports qu’il y a entre la force d’un courant électrique et la déviation des aiguilles des multiplieateurs ; suivi de recherches sur les causes de perturbation des couples thermoélectriques et sur les moyens de s’en garantir dans leur emploi 4 Ia mesure des températures moyennes. Ann. chim. et phys. 71 (1839) 225. Perror (A.). Sur la mesure du volume spécifique des vapeurs saturées, et détermination de l’équivalent mécanique de la chaleur. Thése. Paris. — 1887. J. de phys. [2] 7 (1888) 129-148; Ann. chim. et phys. [7] 12 (1888) 145. Person (G.G.). Mémoiresur la congélation du mercure et sur la chaleur latente de fusion. Comptes rendus, 25 (1847) 334; Ann. chim. et phys. [3] 24 (1848) 265. —w—. Relation entre le coefficient d’élasticité des métaux et leur chaleur latente de fusion; chaleur latente du cadmium et de l’argent. Comptes rendus, 27 (1848) 258. —w—. Recherches sur la chaleur latente de fusion. Ann. chim. et phys. 27 (1849) 250. —-—. Sur la chaleur latente de fusion de la glace. Comptes rendus, 30 (1850) 526; Ann. chim. et phys. [3] 30 (1850) 73. ——. Sur Véquivalent mécanique de la chaleur. Comptes rendus, 39 (1854) 1131; Instit. (1854) 434; Jahresb. (1854) 46; Amer. J. Sci. [2] 19 (1855) 1. | Prstry. Sur les lois des tensions de dissociation des composés chimiques. Ann. chim. et phys. [4] 24 (1871) 208. Perir. Sur l’emploi du principe des forces vives dans le ealcul de leffet des machines. Ann. chim. et phys. 8 (1818) 287. Note sur l’emploi dela dilatation des liquides comme force motrice. Ann. chim. et phys. 9 (1818) 196. Perri. On the disaggregation of tin. Phil. Mag. [5] 4 (1877) 470; Ann, Phys. u. Chem. n. F. 2 (1877) 304. Perris (W.). The mechanical theory of heat. Edinb. Phil. Jour. 51 (1851) 120, 125; Jahresb. (1851) 88; Remarks by Rankine, Edinb. Phil. Jour. 51 (1851) 128. Perrersson (O.). On the properties of water and ice. Phil. Mag. [5] 17 (1884) 156. 202 LITERATURE OF THERMODYNAMICS. Perrersson (O.). Mesure de la chaleur. Jour. de phys. [2] 5 (1886) 48. Prarr (F.). Ueber die Bewegung und Wirkung von Gletscher. Ann. Phys. u. Chem. 155 (1874) 169, 325; Phil. Mag. [4] 50 (1875) 3383. PFrAUNDLER (L.). Dissociation. Ann. Phys. u. Chem. 131 (1867) 55; Z. f. Chem. (1867) 573; Jahresb. (1867) 81. —. Dissociation. Ann. Phys. u. Chem. Jubelband (1874) 182; Jahresb. (1874) 110. —. Explosion einer mit fltissigen Kohlensaure gefiillten Glas- roéhre. Ann. Phys. u. Chem. n. F. 17 (1882) 175. —. Explosion eines Sauerstoffgasometers aus Zinkblech. Ann. Phys. n..F.17 (1382) 176. Puiiutps. Specifische Wirme und Ausdehnungscoefficient. Comptes rendus, 71 (1870) 333; Jahresb. (1870) 111. Note sur divers points de la thermodynamique. Ann. Ecole norm. [2] 2 (1878) 1. Purpson (T. L.). Note on the variations of density produced by heat in mineral substances. Phil. Trans. 1864; Proc. Roy, Soc. 13 (1863-64) 240, abs. ——. Sur une production de chaleur par action chimique. Comptes rendus, 86 (1878) 1196. PickERING (S. U.). Principles of thermochemistry. Proc. Chem. Soc. Nov. 15. 1888 ; Chem. News, 58 (1888) 262, abs. ——. The heat of dissolution of substances in different liquids, and its bearing on the explanation of the heat of neutralization on the theory of residual affinity. Jour. Chem. Soc. 53 (1888) 865-878 ; Bei- bliatter, 13 (1888) 657, abs. ——. The nature of solutions, as elucidated by a study of their densities, electric conductivities, heat capacity and heat of dissolution, Chem. News, 59 (1889) 249. Picrer (R.). Application de la théorie mécanique de la chaleur a l'étude des liquides volatils: relations simples entre les chaleurs latentes, les poids atomiques et les tensions des vapeurs. Comptes rendus, 82 (1876) 260; Ann. chim. et phys. [5] 9 (1876) 180-198; N. Arch. ph. nat. 55 (1876) 66; Phil. Mag. [5] 1 (1876) 477; Jahresb. (1876) 63. Sees. AUTHOR INDEX. 203 Prorer (R.). Sur la liquefaction de loxygéne. Comptes rendus, 86 (1878) 106, 107; Phil. Mag. [5] 5 (1878) 80, 158. —. Démonstration théorique et expérimentale de la définition suivante de la température: La température est représentée par la longuer de Voscillation calorifique des molécules d’un corps. Comptes rendus, 88 (1879) 855, 857; Phil. Mag. [5] 7 (1879) 445. —. Synthése de la chaleur. Genéve. 1879. —. Etude de la constitution moléculaire des liquides, au moyen de leur coefficient de dilatation, de leur chaleur spécifique et de leur poids atomique. Comptes rendus, 88 (1879) 1315, —. Ueber den zweiten Hauptsatz der mechanischen Wirme- theorie. Tagebl. d. 60. Versamml. deutsch. Naturforscher zu Wies- baden, (1887) 231; Nature, 37 (1887) 167. PrerReE (J. I.). Recherches sur la dilatation des liquides. Ann. chim. et phys. [3] 19 (1847) 198; 20 (1847) 5; 21 (1847) 336; 31 (1851) 118; 33 (1851) 199. Pierre (V.). Apparat, um Wasser unter dem Recipienten der Luft- | pumpe durch seine eigene Verdimpfung médglichst schnell zum Gefrieren zu bringen. Ann. Phys. u. Chem. n. F. 22 (1884) 143. ProncHon. Sur létude de la dilatation linéaire des corps solides aux températures élévées. Comptes rendus, 108 (1889) 992. Prrocow (N.). Grundztige der kinetischen Theorie der mehratomigen Gase. J. d. russ. chem. Ges. 18 (1886), 19 (1887); Beiblatter, 13 (1889) 366, abs. Pitrer. On the production of heat by friction. Machanics’ Mag. 46 (1847) 492. PLANA. Mémoire sur l’expression du rapport qui existe en vertu de la chaleur d’origine entre le refroidissement de la masse totale du globe ~ terrestre et le refroidissement de sa surface. Mem. Accad. Torino, [2] 22 (1865) 235. Mémoire sur la loi de refroidissement et sur l’expression de la chaleur solaire dans les latitudes circumpolaires de la terre. Mem. Accad. Torino, [2] 23 (1866) 1. PLancK (Max). Ueber den zweiten Grundsatz der mechanischen Warmetheorie. Miinchen. 1879. 204 LITERATURE OF THERMODYNAMICS. PrLanck (Max). Theorie des Sittigungsgesetzes. Ann. Phys. u. Chem. [2] 13 (1881) 535-48; Jahresb. (1881) 55. —. Verdampfen, Schmelzen und Sublimiren. Ann. Phys. u. Chem. n. F. 15 (1882) 446. —. Mathematische Entwickelungen beztiglich des thermody- namischen Gleichgewichtes von Gasgemengen. Ann. Phys. u. Chem. n. F. 19 (1883) 358-378; Jahresb. (1883) 111. —. Das Princip der Erhaltung der Energie. Leipzig. 1887. Beiblatter, 12 (1888) 134. —. Ueber die molekulare Konstitution verdtinnter Losungen. Z. phys. Chem. 1 (1887) 577-582. —. Ueber die Hypothese der Dissociation der Salze in sehr verdiinnten Lésungen. Z. phys. Chem. 2 (1888) 343. —. Ueber die Dampfspannung von verdtinnten Loésungen fliichtiger Stoffe. Z. phys. Chem. 2 (1888) 405-415. Prayratr (Lyon). Ona mode of taking the density of the vapour of volatile liquids at temperatures below the boiling point. Edinburgh Roy. Soe. Trans. 22 (1861) 441. PoccenporFrr. Ueber das Crookes’sche Radiometer. Ann. Phys. u. Chem. Nov. 1875; Phil. Mag. [5] 1 (1876) 250. Porncark (H.). Sur les tentatives d’explication mécanique des principes de la thermodynamique. Comptes rendus, 108 (1889) 550-553; Bei- blatter, 13 (1889) 793, abs. Porsson. Sur la chaleur rayonnante. Ann. chim. et phys. 26 (1824) 225, 442; 28 (1825) 37. Poote. Improvementsin obtaining power whenair isemployed. Reper- tory of patent inventions, [2] 24 (1854) 506. Poprsr. Ericsson’s Luftexpansionsmaschine (caloric engine) und das ihr zu Grunde liegende Princip. Dingler’s pol. Jour. 127 (1853) 401. Porrert (R.) and TrescHEMACHER(E. F.). Chemical exposition of gun- cotton. Phil. Mag. [8] 30 (1847) 273. Portier (A.). Théorie des mélanges refrigérants. Comptes rendus, 101 (1885) 998; J. de phys. [2] 5 (1886) 53. Porrer. On the fourth law of the relations of the elastic force, density and temperature of gases. Phil. Mag. [4] 6 (1853) 161; 23 (1862) 52. . AUTHOR INDEX. 205 Porrer. On the laws of the expansion of the transparent liquids by increase of temperature. Phil. Mag. [4] 26 (1863) 347 ; 28 (1864) 271. Examination of the applicability of Mr. Alexander’s formula for the elastic force of steam to the elastic force of the vapours of the liquids, as found by the experiments of M. Regnault. Phil. Mag. [4] 29 (1865) 98. Powe. (J. Baden). Experiments on radiant heat from terrestrial seources. Phil. Trans. 115 (1825) 189. ——. Remarks onsomeof Mr. Ritchie’s experiments on radiant heat. Annals of Phil. n.s. 12 (1826) 13. Mr. Ritchie’s reply, 122. Preston (8S. Tolver). On thediffusion of matter in relation to the second law of thermodynamics. Nature, 17 (1877-78) 31, 202. Remarks by Clausius, Phil. Mag. [5] 6 (1878) 237; Ann. Phys. u. Chem. n. F. 4 (1878) 341. Preston agreeing, Phil. Mag. [5] 6 (1878) 400. Aitken, Nature, 17 (1877-78) 260. —-—. On some dynamical conditions applicable to Le Sage’s theory of gravitation. Phil. Mag. [5] 4 (1877) 206, 364. ——. Application of the kinetic theory of gases to gravitation. Phil. Mag. [5] 5 (1878) 117, 297. ——. On the possibility of explaining the continuance of life in the Universe consistent with the tendency to temperature equi- librium. Nature, 19 (1878-79) 460-62, 555 ; 20 (1879) 6, 28. Prevost (P.). Sur deux citations relatives au calorique rayonnant. Ann. chim. et phys. 6 (1817) 412. —. Deux traités de physique mécanique. Paris. 1818. —. Extrait d’un mémoire sur la constitution mécanique des fluides élastiques. Ann. chim. et phys. 38 (1828) 41. —. Note relative 4 quelques expériences anciennes sur la durée du réfroidissement d’un corps dans divers gaz. Ann. chim. et phys. 40 (1829) 332. PRIESTLEY (J.). Experiments on the production of air by the freezing of water. Nicholson’s Jour. 4 (1800) 193. PRINGsHEIM (E.). Ueber das Radiometer. Ann. Phys. u. Chem. n. F, 18 (1883) 1-32; Phil. Mag. [5] 15 (1883) 101. Prony. Notesur un moyen de mesurer l’effet dynamique des machines de rotation. Ann. chim. et phys. 19 (1821) 165, 206 LITERATURE OF THERMODYNAMICS. Provostaye (F. de la) et Desarns (P.). Recherches sur la chaleur latente de fusion de la glace. Ann. chim. et phys. [3] 8 (1843) 5; Comptes rendus, 16 (1843) 837; rapport sur ce mémoire, par M. Reg- nault, méme vol. 977. — — —et —. Note sur les lois du rayonnement de la chaleur. Ann. chim. et phys. [3] 12 (1844) 129; Comptes rendus, 19 (1844) 410. ———et —. Mémoiresur le rayonnement de la chaleur. Comptes rendus, 20 (1845) 1767. ———et —. Mémoire sur le rayonnement de la chaleur. Ann. chim. et phys. [8] 16 (1846) 557; Comptes rendus, 22 (1846) 825, 1139; 24 (1847) 60, 684, 697 ; 25 (1847) 106. ———et —. Mémoiresur le rayonnement de la chaleur. Ann. chim. et phys. [3] 22 (1848) 358. — — — et —. Sur la quantité de la chaleur émise par des corps différents 4 méme température. Comptes rendus, 34 (1852) . 951. ———. Considérations théoriques sur la chaleur rayonnante. Comptes rendus, 55 (1862) 273; Ann. chim. et phys. [3] 67 (1863) 5. ———. See Desains, above. Puuus (J.). Ueber ein Schulapparat zur Bestimmung des mechanischen Warmeiquivalents. Ann. Phys. u. Chem. 157 (1876) 437, 649; Ber. Wiener Akad. 71 11 (1875) 677-685; Phil. Mag. [4] 49 (1875) 416 ; Jahresb. (1875) 47; Carl’s Repert. 11 (1875) 180, 361. —. Ueber die Abhangigkeit der Reibung der Gase von der Temperatur. Ann. Phys. u. Chem. n. F. 1 (1877) 296. —. Ueber die Reibung der Gase. Ber. d. Wiener Akad. 1. Juli, 1878; Phil. Mag. [5] 6 (1878) 157. —. Ueber das Radiometer. Ber. d. Wiener Akad. 3. Juli, 1879 ; Phil. Mag. [5] 8 (1879) 259. Purser (J.). On the source from which the kinetic energy is drawn that passes into heat in the movement of the tides. Rept. Brit. Assoc. (1874) 23. Puscut (C.). Ueber den Ursprung und die Gesetze der Molekularkrafte nach dem Princip der Krafterhaltung. Jahresb. d. des Obergymnasium zu Melk. Wien. 1861. SLE GR I AUTHOR INDEX. 207 Puscut (C.). Ueber das Verhalten gasittigter Dimpfe. Ber. d. Wiener Akad. 70 rr (1875) 571; Jahresb. (1870) 27. —, NeueSatze der mechanischen Wirmetheorie. Ber. d. Wiener Akad. 73 1 (1876) 51-80. —. Von den das Volumen der Kérper bedingenden Kriafte. Ber. d. Wiener Akad. 73 11 (1876) 345-365. —. Grundziige der aktinischen Warmetheorie. Ber. d. Wiener Akad. 77 1 (1878) 471-500. —. Der zweite Hauptsatz der mechanischen Wairmetheorie und das Verhalten des Wassers. Ber. d. Wiener Akad. 89 11 (1884) 631- 635. —. Ueber das Verhalten der Gase zu den Gesetzen von Mariotte und Gay-Lussac. Ber. d. Wiener Akad. 96 11 (1887) 61; Monatshefte f. Chemie, 8 (1887) 327; Beiblatter, 12 (1888) 33, abs. —. Ueber den héchsten Siedepunkt der Fliissigkeiten. Monat- shefte f. Chemie, 8 (1887) 338; Beiblatter, 12 (1888) 33, abs. —. Ueber das Verhalten des Wasserstoffes zum Mariotte’schen Gesetze. Monatshefte f. Chemie, 8 (1887) 374; Beiblatter, 12 (1888) 33, abs. —. Ueber das Verhalten der Gase zum Mariotte’schen Gesetze bei sehr hohen Temperaturen. Monatshefte f. Chemie, 9 (1888) 93. —. Ueber die Wirmeausdehnung der Gase. Wiener Anzeiger, (1888) 43. —. Ueber die Zusammendriickbarkeit der Gase und der Flissig- keiten. Ber. d. Wiener Akad. 96 rz (1888) 1028. —. Ueber das Verhalten comprimirter Fltssigkeiten. Wiener Anzeiger, (1888) 123-125. —. Ueber das Verhalten des gespannten Kautschuks. Wiener Anzeiger, (1888) 125. Qurytus-Icttius (G. von). Das von Lenz aus galvanischen Messungen berechnete Wiirmeaquivalent mit der theoretischen Berechnung tiber- einstimmend. Ann. Phys. u. Chem. 101 (1857) 73; Comptes rendus, 45 (1857) 420. Ramsay (W.) and Youne (S.). On certain facts in thermodynamics. Rept. British Assoc. (1885) 928. 208 LITERATURE OF THERMODYNAMICS. \ . Ramsay (W.) and Youna (S.). On some thermodynamical relations. Phil. Mag. [5] 20 (1885) 515 ; 21 (1886) 33, 135; 22 (1886) 32 ; Nature, 34 (1886) 138—See W. E. Ayrton and J. Perry, Phil. Mag. [5] 21 (1886) 255. — and —. Influence of the change of condition from the fluid to the solid state on vapour-pressure. Phil. Mag. [5] 23 (1887) 61; Nature, 36 (1887) 23. — and —. Studien tiber Verdampfung und Dissociation. (Von den Autoren fiir die Zeitschrift bearbeiteter Auszug ihrer an verschiedenen Orten verétfentlichten Untersuchungen.) Z. phys. Chem. 1 (1887) 277-858, 435-455. — and —. On the nature of liquids, as shown by a study of the thermal properties of stable and dissociable bodies. Phil. Mag. [5] 23 (1887) 129, comm. by the Physical Soc., read Dee. 11, 1886. — and —. On evaporation and dissociation. Parts 1 and 2, Phil. Trans. (1886) 1 71 and 125; Part 3, Phil. Trans. (1886) 111; Part 4, Trans. Chem. Soc. (1886) 790; Parts 5 and 6, Phil. Mag. [5] 23 (1887) 485; 24 (1887) 196. ; and —. On the gaseous and liquid states of matter. Phil. Mag. [5] 23 (1887) 547. — and —. Thermal properties of ethyl-alcohol and ethyl- oxyd. Chem. News, 56 (1887) 18; Beiblatter, 12 (1888) 36, abs. Ramspotrom. The caloric engine. Mechanics’ Mag. 64 (1856) 110. RANKINE (W.J.M.). Abstract of a paper on the hypothesis of mo- lecular vortices, and its application to the mechanical theory of heat. Proc. Edinb. Soc. 2 (1850) 275.—See Phil. Mag. 10 (1855) 354, 411. —_—_ — — —. Noteas to the dynamical equivalent of temperature in liquid water, and the specific heat of atmospheric air and steam. Edinburgh Trans. 20 1 (1851) 191; Jahresb, (1854) 36. —-—w—. On the economy of heat in expansive machines. Edinburgh Trans. 20 (1851) 235. ——w—. On the law of compressibility of water at different temperatures. Phil. Mag. [4] 1 (1851) 548. ——w—. On the mechanical theory of heat. Phil. Mag. [4] 2 (1851) 61.—See Ann. Phys. u. Chem. 81 (1850) 175; Jahresb. (1850) 50. AUTHOR INDEX. 209 RANKINE (W.J.M.). On the centrifugal theory of elasticity as applied to gases and vapours. Phil. Mag. [4] 2 (1851) 509; Jahresb. (1851) 39. —— —. Letter on the reheating of jets of air and on the rela- tion between temperature and compression of the same. Edinburgh Jour. 51 (1851) 128. —-—w—. On the mechanical action of heat, especially in gases and vapours. Edinburgh Trans. 20 (1851) 147; Phil. Mag. [4] 7 (1854) 1, 111; Jahresb. (1854) 36. —-—w—. On the centrifugal theory of elasticity and its connec- tion with the theory of heat. Edinburgh Trans. 20 (1852) 425. —-—w—. On the reconcentration of the mechanical energy of the Universe. Phil. Mag. [4] 4 (1852) 358. —-—w—. On the absolute zero of the perfect gas thermometer, being a note to a paper on the mechanical action of heat. Edinburgh Trans. (1853) 561. -——-—. On the power and economy of single-acting expansive steam-engines; being a supplement to the Fourth Section of a paper on the mechanical action of heat. Edinburgh Trans. (1853) 195. Fifth Section, same vol. 205. ———. Onthe mechanical action of heat. A review of the fundamental principles of the mechanical theory of heat, with remarks on the thermic phenomena of currents of elastic fluids, as illustrating these principles. Edinb. Trans. (1855) 535 ; Edinburgh Proe. 3 (1854) eet —-—w—. On the mechanical effect of heat and chemical forces. Phil. Mag. [4] 5 (1853) 6. Letter to J. P. Joule. —-—-—. On the general law of the transformation of energy. Phil. Mag. [4] 5 (1853) 106. —-—w—. On the mechanical theory of heat ; specific heat of air. Phil. Mag. [4] 5 (1853) 437. —-—-—. On the mechanical theory of heat; velocity of sound in gases. Phil. Mag. [4] 5 (1853) 483. —-—-—. On the expansion of certain substances by cold. Phil. Mag. [4] 8 (1854) 357. _———-——. ,On the geometrical representation of the expansive action of heat, and the theory of thermodynamic engines. Phil. Trans. (1854) 115; Proc. Roy. Soe. 6 (1850-54) 388, abs. N 210 _ LITERATURE OF THERMODYNAMICS. RankKINE (W. J. M.). On the means of realizing the advantages of the air-engine. Edinburgh Jour. [2] 1 (1854) 1. —-—-—. On the mechanical action of heat. Edinburgh Proce. 3 (1855) 287. —-—w—. Outlines of the science of energetics. Edinburgh Jour. [2] 2 (1855) 120. ——w—. On thehypothesis of molecular vortices, or centrifugal theory of electricity, and its connection with the theory of heat. Phil. Mag. [4] 10 (1855) 354, 411.—See Edinburgh Trans. (1852) 425. ——w—. Onthe principle of isorrhopic axes in staties. Phil. Mag. [4] 10 (1855) 400. ——w—. On heat as the equivalent of work. Phil. Mag. [4] 11 (1856) 388; 12 (1856) 103. ——w—. On the conservation of energy. Phil. Mag. [4] 17 (1859) 250, 347. —-—-—. On the thermodynamic theory of the steam-engine with dry saturated steam. Phil. Mag. [4] 18 (1859) 71; 19 (1860) 460; Proe. Roy. Soc. 9 (1859) 626; 10 (1859) 183; Phil. Trans. 149 (1860) 177, 743. ———. On the density of steam. Phil. Mag. [4] 18 (1859) 316. ——w—. On some thermic properties of water and steam. Edinburgh Proe. 4 (1857-62) 616. —-—w—. On the expansive energy of heated water. Phil. Mag. [4] 26 (1863) 388, 456. ——w—. On the densityof steam. Edinburgh Trans. 23 (1864) 147. ——w—. On the hypothesis of molecular vortices. Phil. Mag. [4] 27 (1864) 313. [Review of an article by Herepath in the North British Review, 40 (1864) 40, which Rankine calls “the most com- plete history of that science which has yet appeared.’’] ——w—. On the dynamical theory of heat. Phil. Mag. [4] 27 (1864) 194; Ann. chim. et phys. [4] 2 (1864) 1. —-—-—. Summary of the properties of certain stream lines. Phil. Mag. [4] 28 (1864) 282, comm. by the author, read before the British Assoc. Sept. 19, 1864. aN AUTHOR INDEX. 211 RanxineE (W. J. M.). On the second law of thermodynamics. Phil. Mag. [4] 30 (1865) 241; Rept. British Assoc. (1865) 13, abs. ———. Onthermodynamic and metamorphic functions, dis- gregation, and real specific heat. Phil. Mag. [4] 50 (1865) 407. —-—-—. On saturated vapours. Edinburgh Proce. 5 (1865) 449; Ann. chim. et phys. [4] 8 (1865) 378. ———. Ontheelasticity of vapours. Phil. Mag. [4] 29 (1865) ——w—. On the expansion of saturated vapours. Phil. Mag. [4] 381 (1866) 197, 199. Reply to A. Cazin. ——w—. De la nécessité de vulgariser la seconde loi de la ther- modynamique. Ann. chim. et phys. [4] 12 (1867) 258. ——w—. On the phrase “ potential energy” and on the defini- tions of physical quantities. Phil. Mag. [4] 33 (1867) 88; Ann. chim. et phys. [4] 13 (1868) 75. / —-—w—. On the thermal energy of molecular vortices. Phil. Mag. [4] 88 (1869) 247, comm. by author, read before the Edinburgh Soc. May 31, 1869; 39 (1870) 211; Edinburgh Trans. 25 (1869) 557 ; Jahresb. (1869) 99. ——w—. On the thermodynamic theory of waves of finite longi- tudinal disturbance. Phil. Mag. [4] 39 (1870) 806; Phil. Trans. 160 (1870) 277. ——w—. Reply to Mr. Heath. Phil. Mag. [4] 40 (1870) 103, 291; Jahresb. (1870) 75. ——-—. On the thermodynamic acceleration and retardation of streams. Phil. Mag. [4] 40 (1870) 288; Nature, 2 (1870) 440, abs. ——w—. On the hypothesis of molecular motions in thermo- dynamics. Phil. Mag. [4] 41 (1871) 62. ——w—. Actualenergy. Phil. Mag. [4] 43 (1872) 160. Criti- cism of Maxwell’s “ Theory of Heat.” —-—w—. Miscellaneous Scientific Papers. With a memoir of the author, by P. G. Tait. Edited by W.J. Millar. London. 1881. (xxxvi, 567 pp.) Phil. Mag. [5] 11 (1881) 536. Ransome (T.) Composition and explosion of gun-cotton. Phil. Mag. [3] 30 (1847) 1. JAD LITERATURE OF THERMODYNAMICS. Raovutt (F. M.). Développement de la chaleur dans les procédés chim- iques. Comptes rendus, 49 (1859) 81; Instit. (1859) 230; Jahresb- (1859) 381. —w—. Researches on chemical heat and voltaic heat. Phil. Mag. [4] 26 (1863) 522, translated from Comptes rendus for Sept. 14, 1863. —-—. Recherches sur les forces électromotrices et les quantités de chaleur dégagées dans les combinaisons chimiques. le Partie, Etude des forces électromotrices. Ann. chim. et phys. [4] 2 (1864) 317. 2e Partie, Mesure de la chaleur dégagée par le courant et de la chaleur dégagée ou absorbée par les actions chimiques accompues sous Vinflu- ence du courant. Ann. chim. et phys. [4] 4 (1865) 392.—See Favre, Ann. chim. et phys. [3] 40 (1854) 293; Jahresb. (1865) 101. ——. Ueber die Gefrierpunkte verdiinnter wisseriger Losungen. Z. phys. Chem. 2 (1888) 488-91. —-—. Sur les tensions de vapeur des dissolutions faits dans Valcool. Comptes rendus, 106 (1888) 442-45. ——. Sur les tensions de vapeur des dissolutions faites dans Véther. ° Ann. chim. et phys. [7] 15 (1888) 375-407; Z. phys. Chem. 2 (1888) 353-373. RayueicH (Lord). The work that may be gained during the mixing of gases. Phil. Mag. [4] 49 (1875) 311. —. On the thermodynamic efficiency of the thermopile. Phil. Mag. [5] 20 (1885) 361; Nature, 32 (1885) 536. RECKNAGEL (G.). Bedingungen fiir die Proportionalitaét zwischen der Erwirmung der Luft bei constantem Volumen und der Zunahme der Expansivkraft. Ann. Phys. u. Chem. Ergiinzbd. 6 (1874) 278. REDTENBACHER. Die Luftexpansionsmaschine. Mannheim. 1853. 8vo. Dingler’s polytechn. J. 128 (1853) 86. Reecu. Machine a air d’un nouveau systéme déduit de la comparaison des systémes Ericsson et Lemoine. Paris. 1851. 8vo. Notes sur la théorie des effets thermodynamiques de la chaleur. Comptes rendus, 33 (1851) 367, 602; 54 (1852) 21; 46 (1858) 336. Note sur les machines 4 vapeur et d air chaud. Comptes rendus, 36 (1853) 526 ; Bull. Soc. encour. (1853) 204. AUTHOR INDEX. 913 Reecu. Théorie générale des effets dynamiques de la chaleur. Jour. des math. (Liouville), 18 (1853) 357; Jahresb. (1853) 46. Théorie’ générale des effets dynamiques de la chaleur. Paris. 1854. Ato. Récapitulation trés-succincte des recherches algébraiques faites ' sur la théorie mécanique de !a chaleur. Jour. des math. (Liouville), 21 (1856) 58. Note sur les proprietés calorifiques et expansives des gaz. Comptes rendus, 57 (1865) 505. Réponse de M. Dupré, 589. Réponse de M. Reech, 634. | Equations fondamentales de la théorie mécanique de la chaleur. Comptes rendus, 69 (1869) 913. ReGNAvuLT (V.). Recherches sur la dilatation des gaz. Ann. chim. et phys. [8] 4 (1842) 5, 52. —. Note sur la dilatation du verre. Ann. chim. et phys. [3] 4 ~ (1842) 64. —. Note sur la chaleur latente de la fusion de la glace. Ann. chim. et phys. [3] 8 (1843) 19. | —. Note sur la température de l’ébullition de l’eau a différentes hauteurs. Ann. chim. et phys. [3] 14 (1845) 196. —. Sur la détermination de la densité des gaz. Ann. chim. et phys. [3] 14 (1845) 211. —. Relation des expériences entreprises pour déterminer les principales lois physiques et les données numériques qui entrent dans le calcul des machines 4 vapeur. Paris. 1847. Jahresb. (1848) 87. —. Sur les coefficients de dilatation. Ann. chim. et phys. [3] 26 (1849) 257 ; Comptes rendus, 28 (1849) 325; Ann. Phys. u. Chem. 77 (1849) 99; Jahresb. (1849) 29. —. Sur la théorie mécanique de la chaleur. Comptes rendus, 36 (1853) 680; Ann. Phys. u. Chem. 89 (1853) 340; Jahresb. (1853) 43. —. Sur la force élastique des vapeurs. Comptes rendus, 11 Juin, 1860; Phil. Mag. [4] 20 (1860) 275. —. Mémoire sur la dilatation des gaz. Comptes rendus, Oct. 11, 1869; Phil. Mag. [4] 39 (1870) 127. npn 214 LITERATURE OF THERMODYNAMICS. Rercnarpr. Mémoire sur la théorie de la chaleur. Comptes rendus, 44 (1857) 1109. RennrzE. On the quantity of heat in agitated water. Rept. British Assoc. (1856) 11, 165. gsau (H.). Recherches sur les effets mécaniques produits S corps R H.). Recherches sur les effets mécaniques produits dans les cor; par la chaleur. Enonce de formules relatives aux trois classes de corps. Comptes rendus, 51 (1860) 449. —. Commentaire aux travaux publiées sur la chaleur considérée au point de vue mécanique. Paris. 1862. 8vo. Relation entre la pression et le volume de la vapeur d’eau saturée qui se détend en produisant du travail, sans addition ni soustrac- tion de la chaleur. Comptes rendus, 75 (1872) 1475; Phil. Mag. [4] 45 (1873) 77. —-. Note sur les chemises de vapeur des cylindres des machines. Comptes rendus, 82 (1876) 537. Observations de M. A. Ledieu. 599. —. Notesur la limite inférieure que l’on doit attribuer 4 l’admis- sion dans une machine 4 vapeur. Comptes rendus, 82 (1876) 647. —. Note 4 propos des communications de M. Fave sur la théorie de la chaleur. Comptes rendus, 84 (1877) 975. —. Notesur lathéorie delachaleur. Comptes rendus, 92 (18381) 157. ReuscH. On some properties of ice. [hil. Mag. [4] 27 (1864) 192. Reve (Th.). Die mechanische Warmetheorie und Spannungsgesetz der Gase. Ann. Phys. u. Chem. 116 (1862) 424, 449. Reyer (R.). Ueber die innere Reibung wisseriger Lésungen. Z. phys. Chem. 2 (1888) 744-757; Beiblitter, 15 (1889) 785, abs. ; Reynotps (O.). The general theory of thermodynamics, Nature, 29 (1883) 112-114. Ricwarps (Th. W.). Victor Meyer’s vapour density method modified for use under diminished pressure. Chem. News, 59 (1889) 39-40; Beiblatter, 13 (1889) 858, abs. ——. A method of vapour density determination. Chem. News, 59 (1889) 87-88; Beiblatter, 13 (1889) 838, abs. Ricuarz (F.). Zur kinetischen Gastheorie. Z. phys. Chem. 2 (1888) 338-40. AUTHOR INDEX. 215 RIEcKE (E.). Einige Beobachtungen an dem Radiometer. Ann. Phys. u. Chem. n. F. 3 (1878) 142. Riess (P. T.). k= S—Z= D, (3) each observation will furnish an equation of the form: Asin S+ B(1 — cost S)+ X=D. (4) If M is the number of observations, the normal equations will be: A [sin? + S]+ B[(—cos } S) sin 3 S]+X [sin 3 8] —[Dsin + S]=0 | A [sin }.S(1 — cos} 8)] ++ BLA —cos$ SY] + X[1—cos}S] | _ —[D (1— eos 3 8)J=0 f A [sin } S] + B[1L — cos? S] + MX — [D] =() | After substituting the numerical values of the known quantities in these equations, and finding the values of A, B, and X, the correction for eccentricity of any observed reading will be given by (2). From (4) D may be obtained for any value of S, and the difference between this computed quantity and the observed value of D, for each comparison, is the local correction of the graduation, which, however, includes an un- known, and perhaps relatively large, error of observation. An examination like that just described, embracing every line of the graduation, and repeated until the effect of errors of observation is suf- ficiently diminished, would afford a complete knowledge of the condition and capabilities of the instrument. For the corrections due to the position of the axis having been obtained, the local correction for each line would * The readings of the circle are supposed to increase as the angles indicated by the sextant increase, which is actually the case in the apparatus referred to. 8 THE CORRECTION OF SEXTANTS FOR ERRORS be the mean of the values given by the different series of comparisons, while the probable errors of the corrections, and of observations made with the sextant in question, could be deduced from the final residuals. But such a process, or even one involving only a single reading upon every line of the graduation, is far too tedious and burdensome to be practicable. We must be content in most cases with a comparatively brief and imperfect investigation, having for its object the best result that can be derived from a moderate expenditure of time and labor. With this end in view the examination must be limited to a few points equally distributed over the arc, but sufficiently numerous to warrant the assump- tion that they collectively represent the mean are accurately enough for any kind of observation in which the sextant will be employed. In this way, although the attempt to secure an exact correction for every reading is abandoned, errors which similarly affect considerable portions of the are may be corrected, and the existence of large uncorrected errors can gen- erally be detected. The formation and solution of the normal equations usually entail a rather laborious computation, but this can be greatly abridged by a general solution, and by other convenient devices, if the examination is always made upon a uniform system of comparisons at certain invariable distances from each other. In what follows one system of this kind is presented in detail, asa type of similar systems comprising a greater or less number of comparisons. With reference to the nature of the service expected of them, sextants may be divided into two classes, assigning to the first class instruments used in making observations for latitude and time with the artificial hori- zon, measuring the principal angles of surveys, ete., and to the second class those employed in the ordinary routine of navigation, and other operations of a similar grade. All the corrections of a sextant of the first class should be determined with as much precision as the capacity of such an instrument warrants, while for those of the second class it is only necessary to insure the absence of errors exceeding certain limits. In considering this subject with reference to the wants of the naval service, it was thought to be desirable that no part of the are should be more distant in either direction from one of the points examined than the space covered by the vernier. With the usual division of the limb to 10’, reading by the vernier to 10”, this condition requires an examination at points not more than ten degrees apart. It was decided, therefore, to make circle readings with the index set successively at 0°, 10°, 20°, ete., to and including 130°. At first a comparison was also made at 140°, when the range of the sextant extended so far, but after some experience the practice was discontinued, for the definition of the collimator-mark is frequently so much impaired by extreme obliquity of the index-mirror \ OF ECCENTRICITY AND GRADUATION. 9 as to render this observation of doubtful utility. A single series of such comparisons furnishes the eccentric correction with sufficient precision for a sextant of the second class, while the residuals, containing the errors of both graduation and observation, afford a trustworthy indication of the performance to be expected of the instrument under very favorable cir- cumstances. It was proposed to subject sextants of the first class to an examination comprising several similar series of comparisons, made with different portions of the circle, the number depending somewhat upon the circumstances of each case. These repetitions yield not only improved values of the corrections for eccentricity, but also a means of separating the loeal errors of graduation from the errors of observation. The normal equations obtained by making M = 14, and S successively OP 10°, 20°, ete., 130°, in (5) are: 4.72172 A + 2.17946 B + 7.06526 X — [D sin } S] = | 9.17946 A + 1.09780 B + 2.90976 X — [D (1—cos $ 8)]=0, } (6) 7.06526 A +-2.90976 B+ 1x = (0y =O) | from which are deduced : B= 1.8384[D]—11.0275[Dsin + S]+ 17.9311 [D1 — cos} 8)], X= 0.4802[D]— 1.5671 [Dsin? S]+ 1.8384[D(1 — cos} 8)], and also: A=—1.5671[D]+ 7.6467[Dsin } S]—11.0275 [D(1 — cos ie rf X = 0.0714 [D] — 0.5047 A — 0.2078 B. (8) From each observed yalue of D let the corresponding value computed by (4) be subtracted; the remainder, which may be designated O — C, is the sum of an observed local correction of the graduation, and an error of observation. Any single observation made under circumstances as favorable as those attending the examination, and corrected for eccen- tricity only, will, therefore, contain an error the most probable estimate of which is: 0.6745 JEG) = 40.04136 [(O — ©), (9) if the supposition is made that the errors of graduation are either small enough to be neglected, or else, like the errors of observation, devoid of any systematic arrangement. This assumption cannot always be abso_ lutely correct, but no other is eligible when only one series of comparisons has been made. The following example (Table 1) exhibits a convenient form of record and computation, requiring no tables except Crelle’s Rechentafeln, and those contained in these pages. The entire calculation is given here. At THE CORRECTION OF SEXTANTS FOR ERRORS 10 (pT) (eT) (ZT) (tT) G + GOLZ, 4.8e> gig +] #99 gg + }9G2 = O49 +] Q6I ae 86 == eee re Sno V GI LZ —| 9% Eat COS Spe Co NES b1OF + F i @'61L + G Corre aw G Ue; LGp a= Guess - NST E ORSect So —— hor e816 — br + | 02 6'10T — Z ¥G W Cara alee 108 40 0=Z Gra ier 4/ Lid Po. €) 3 % S = “bh Pd (OT) (6) (g) (L) (9) (g) (*) (e) | (2) #302 — | OF 98 —| ¢9 -F 1¢'Le — | 68°69 — | ¢8 — Lb9 + | 6r'se +] O¢T + al eee | een LG #g 8°8¢ Eiger ees Pan SSS Semele a PS See ae ge ee 8 FS GSI ¢°98 61'S cls —|6 — |1%8 0 Og FG 81 L'0¢ 0'9L Le 00'FI CZ FZ 8% z 0 02 g 0 G'9F Let 8°ZE LOL FL FI SI Zl sO Oli. | ST 6 UP CIT 1°08 876 Z6'61- 9% - 0 001| 9 g gle ¥'6 F'8a LVI e9% — |F — 196.0 06 Le FG eee GL 8°os LE 6@T +|12 + 128 0 08 ee Og 8°8z 8°¢ 0°83 GPT 69°F 8 ge 0 OL 68 9g 2° FZ eh 0°02 1a't 09'F 6 68 0 09 cP 9g 00 0's O'LI IPL F8'9 GI cr O OG GF CF 9°ST 6'T Lg 09" are OL OF O OF CF 9g er Vt FOL 78° Zo'9 FG ro 0 08 KS 1¢ GL G0 Od 68° 2o'P 9% 9° 0 06 Lg ¥g 9° 10 qe —| ar 19% +! 08 09 0 OL &9 LG 0° 0'0 00 00° 00° 92 + |9° 00 LG Lg bk 4/4 EE Ad 4/4 4/4 LE / fo} 4/4 LH OC se S 3 = wm: i ae Jel at ° | a | i ' ; s ° i 2 Boks I ad tole Nie "OATH a ce SUMINUA A aT TAY YT, OF ECCENTRICITY AND GRADUATION. ii the time of examination this sextant had just been repaired after its return from sea service. The first column contains the settings, S, of the sextant, and the fourth gives Rk, the corresponding readings of the circle, the seconds being the mean of those read from the verniers, and recorded in the two preceding columns. The reading at 0° is the mean of those at the beginning and end of the examination. As the labor of computation is lessened by numeri- eally diminishing the values of D, especially those belonging to the larger angles, Z should be either equal to the circle reading when S = 0°, or so chosen as to differ a few seconds therefrom, in the directiou, and to an extent, indicated by the subsequent values of R. The differences D in the fifth column are found by (3). Table IT is serviceable in filling out TABLE II. S. | Sin 3 S.}1—cos} S. oO 0 .000 .000 10 .O87 .004 20 .174 O15 30 -259 .0384 40 .842 .060 50 423 O94 60 .500 184 70 .oT4 181 80 643 .234 90 .107 .298 100 .766 .807 110 .819 -426 120 .866 .500 130 .906 O17 140 .940 .658 150 .966 741 the sixth and seventh columns ; it should be copied upon a slip of paper in lines spaced like those of the record, and laid upon the latter beside | the fifth column, so that each value of D may closely follow its two co- efficients. By opening the Rechentafeln at D, the two products can be instantly taken out and entered in the same line. The quantities in each of these three columns are next added, and the respective amounts written underneath. No material error can be introduced by retaining only two places of deci- mals in these products. At first view, indeed, even the second place might seem to be superfluous, since D itself is frequently several seconds in error, but in (7) the sums of the two sets of products have coefficients with opposite signs, and the effect of an alteration in one of these sums is, py THE CORRECTION OF SEXTANTS FOR ERRORS therefore, greater than that of a similar change affecting them both in the same direction. Substituting in (2) the values of A and B from (7): ry (- 1.5671 sin 3 7’ + 1.8884 (1 — cos} /)) |» | (10) sh (7.6467 sin $77 — 11.0275 (1 — cos} )) | sin J S] be (- 11.0275 sin $y’ + 17.9311 (1 — cos 3 /)) | Pa—eosss) |. The change in the computed correction for eccentricity resulting from any given variation in [D sin 3 S] will be greatest when the coefficient of the latter in (10) is a maximum—that is, when: 7.6467 cos. 2 7’ — 11.0275 sin 3 7’ = 0, ,_ 7.6467 _ 107°" andj’ = 69° 29’, 11.0275 ; tan 3+ the coefficient itself being then + 2.59. By similar means it is found that the coefficient of [D (1 — cos + S)] attains the numerical maximum — 3.12 when 7 = 63°11’. Both coefficients reduce to 0 for ;’/=0. If the twenty-six products are correct to the second decimal place, the limit of this error in the eccentric correction is, therefore, 0 when 7’ = 0, and greatest when 7’ is somewhere between 65° and 69°, but everywhere less than 0.005 < 13 X (2.39 + 3.12) = 0.36. It will be shown a little farther on that the probable error, due to errors of observation, in the eccentric correction derived from a single series of comparisons, is 0 when y = 0,0.42 t when »/ = 20°, and still greater for all larger values of 7’, t being the probable error of a single comparison. As ¢can seldom be much less than 2,” this probable error is greater than the maximum error in question. It is also apparent that to increase the possible error tenfold, by retaining only one decimal digit in the products, would be unsafe. The constants A, B, and X are computed in the last column of Table I. Each formula of (7) contains three terms which may be obtained from Table III without any greater inconvenience than that of taking out the tabular products for each digit of the argument separately and adding them together, but the table should be extended, if frequently used. The headings of the columns refer to that argument which is in the same horizontal line, e. g., the third column contains both the term of B having [D sin 3 S] for its argument, and the term of A for which [D (1— eos } §)] is the argument. The upper sign is to be applied when the argument is positive, the lower if negative. These terms OF ECCENTRICITY AND GRADUATION. bs ean also be taken from the Rechentafeln, by retaining only the first decimal place of sums containing more than three digits, which involves a maximum error ten-thirteenths of that referred to in connection with the products in columns 6 and 7 of Table I, and otherwise subject to the TABLE III. [D] | Ay) dB x [Dsin} 8] A Bm pre TAA | [D (1 —cvs} S)] eect ae tts is es 2. Xa) = a += = See eectotey ie 4/ /f If | // | 4/ | // | // Tee a SN HOST WILO27 | V7-981.) 1.567. | 1.888 | 480 a pe nes ak ee ce 15.298 | 22.055| 35.862] 3.18 3.001 | 1 960" Ineo 2 ES 22.940 | 38.082| 58.793) 4.701 | 6.515 | 1.441 | 8 Bee pe a nen 80.587 | 44110) 71.724} 6.268 | 7.353 | 1.921 | 4 | i eee 88.2384 | 55.1387| 89.656| 7.885 | 9.192 | 2401 | 5 Gee ne ear cl als 45.880 | 66.165 | 107.587| 9.402 | 11.030 | 2.881 | 6 1 aan EN 58.527 | 77.192 | 125.518 | 10.969 | 12.868 | 3.361 | 7 Spee iat Te 61.174 | 88.220 | 148.449 | 12.537 | 14.707 | 3.842 | 8 mebeenee 2 1 ta 68.821 | 99.247 | 161.880 | 14.104 | 16.545 | 4.322 | 9 Meat besos 2: 25 76.467 | 110.275 | 179.311 | 15.671 | 18.384 | 4.802 | 10 | | | | | ! | same conditions. Column 8 is expeditiously filled by laying the slip of paper containing Table II upon the form, as before, and opening the Rechentafeln at the value of A; then opening at B, the products in col- umn 9 are obtained with equal facility. The corrections for eccentricity appear in column 10, each term being the sum of those on the same line in the two preceding columns ; these cor- rections, with the further addition of YX, are entered in column 11. After subtracting the quantities in column 11 from the corresponding ones in column 5 the residuals in column 12 remain; their sum should not differ from zero by more than two or three units. Finally the squares of the residuals are entered in column 13, and the probable error of gradua- tion and observation is computed from their sum by (9). The foregoing formulas are equally applicable to any examination consisting of four- teen comparisons at points ten degrees apart upon the are of the sextant. Tf it is preferred for any reason to make the comparisons elsewhere than at 0°, 10°, ete., the eccentric corrections obtained for the points compared may be rectified by subtracting from each of them the correction computed for 7 =‘ (2: As a further illustration of what is to expected in practice, the eccen- tric corrections, constants A and B, residuals, and probable errors, of six sextants, by makers of high repute, are given in Table LV. “ ¥ THE CORRECTION OF SEXTANTS FOR ERRORS 14 oo} J++lt++1+ H ror nt HOMON DO WeON N N ~N S | [aoa o “LOO *OOW ‘IA eC Pree lL — 8I + 9 es G — P — 0 8 — I a 8 — Sais | eat 4/4 Oman Stak see wees eee Cea earn oon —— 6 O9e° heal ye as C= Gia ore Blast eG ed oo l 6g OT Ge Wes el oe ee CoS Sk ot LEo= [8 I fs [aso er ge oi oes Ane it TL se F Ley B alle Goa 9 or tT ¢ — | GP a 8 Gin, 9 8s Cee 6 gg i. = Ge a OL CF fe te ce 6 OL Gg Il 61 G 6 GS 6 poe ler [ee 8 OL Gee 16 i. oe 9 8 a F Ete Co 0 o sa 0 Looe 0 LE / “/ 4/ a Lh 4h “100 “OOF Q==0 "100 “OO ao "100 “OOW "A “AI "TE SAN eave iG oe a ‘6 — 0 9 —— L — poe 0 PsP 0 Loess eA "ae 0 I —— G —_— td O=0 sil ee ree Ores Ole sere GL ee FL Gea aL Ga IL IL OL ga 6 ee 8 F L I 9 SG $ Ces g Gg = Z 0 Tose et 0 0 4 Mf ‘100 ‘00g | ‘Q—O SCCCOCO FR Fs RRB ANANNN 4/ “109 “OOK OF ECCENTRICITY AND GRADUATION. 15 The one requiring corrections of more than 2’ is of course exceptional, but no complaint is known to have been made of it before the examina- tion, though it had seen service at sea, possibly in the hands of some scru- pulous young officer who carried out his reductions to fractions of a second. It is not the most incorrectly centered instrument in the table, however. The probable error, though derived from too small a number of observa- tions to be regarded as precise, is a useful criterion. When much in excess of 5” it implies that either the graduation is inaccurate, the tele- scopic power is too low, the mechanical or optical action of the sextant is imperfect (perhaps, through maladjustment of its parts), the observer is unskillful, or two or more of these unfavorable conditions coexist. Values of less than 5” are frequently obtained, but this is commonly due in part to an accidental avoidance of the larger errors of observation. Before proceeding to combine the results of several series of compari- sons it is desirable to know the probable error of the corrections deduced from a single series. The eccentric correction for any reading y’, as ex- pressed in (10), may be written : Pee Ses E \— 1.5671 sin # y/ + 1.8884 (1 — cos $4’) + (7.6467 sin $y’ — 11.0275 (1 — cos 3 )) sin 3.8 + (- 11.0275.sin $ y/ + 17.9311 (1 — cos 3 )) (1 — cos 3 s)} |. 7690 = E 1c mM ae} © pa 6 joa) ee S root=| 4 mM Es A oo Nort rNoO cu Aarne ANS ==) & [Fe eee teste = teal 1+ w® | en) | Il §L td es aro onmrd cos oD reid remo ++ +++ +++ ++] + ++I © 19 0 ANe Sos Ana i HH a4 wet HON OD Oonon + ++] + OT 6°0 8°0 16h OFF 9°85 v'09 L’'vv GbE OFS 0°66 SFG 6°61 ok 8'P oe tn I? De THE CORRECTION OF SEXTANTS FOR ERRORS The three terms of each group in the fifth column are obtained by sue- cessively adding X’, X¥”, and X”’, to the eccentric correction in the pre- ceding column. The three values of D following in the sixth column are those which were observed in the first, second, and third, series of com- parisons respectively. By subtracting from each of the latter the com- puted value in the fifth column, the three values of the local correction in the seventh column are found ; their mean is given in the eighth column. The residuals in the ninth column are obtained by subtracting this mean successively from its three constituents, and the tenth column con- tains the squares of the residuals. There are 42 residuals, and the sum of their squares is 260; the prob- able error of a single observation is therefore : 9607* = + EO) B=5 a io t = 0.6745 J The probable errors of the eccentric corrections in the fourth column of Table VIII are taken from Table V with this value of ¢, and divided by V 3, since three independent determinations of A and B have been made. The maximum probable error of a local correction deduced from a single series of comparisons, as given in the second column of Table VI, is t < 0.95; the probable error of the local corrections in this example (excepting that derived from the additional comparison at 140°) is there- + 1".79 X 0.93 _ fore not greater than = + 1”.0, which is small enough to V3 justify some degree of confidence in them. It should be mentioned here that the three series of comparisons were all made with the same portion of the circle in this instance, and that the effect of errors in the circle is consequently but little diminished by the repetition. In a mere illustra- tion of the capabilities of the method this uniformity is preferable, since it affords a value of ¢ nearly identical with that which would be obtained if the circle were faultless, while the absolute verity of the corrections is of minor importance. But charging the sextant with the imperfections of both instrumeats, and ignoring also the error of observation, which cannot be inappreciable, none of these corrections imply an error of cir- cular division exceeding 5”, one that is certainly to be expected in all graduation except that of the very highest class. The probable error of observation in this example, t = +: 1”.8, is very small, as it ought to be, for the sextant was firmly supported in a con- venient position, the pointing was deliberate, and directed upon a singu- larly well-defined object, the index was set in a definite position always referred to the same lines of the vernier, and the observer was perhaps somewhat expert at that time. This error will ordinarily be larger, indeed OF ECCENTRICITY AND GRADUATION. 23 an observer who contents himself with the least count of a 10” vernier cannot reduce his probable error below 2”.5; but under some cirecum- stances—as, for instance, in measuring circummeridian altitudes of Polaris with the sextant mounted upon a stand—the precision attained in this examination should be closely approached. With practice the vernier may be read as closely as it can be set, for so long as the direction of the necessary movement is recognized, the distance can also be estimated. The 42 residuals are distributed as follows: NUMBER OF ERRORS Between |e ee ee | By theory. Found. yy yy 0.0 and 0.5 | 6 is Oiaye GG lets: 12 12 EO Ra e230 9 11 Dep Coe Bao 7 7 Seo OF 4b 4 Fj 4.5 5.5 2 1 Oso Cones 1 1 Grom Rr eS 1 0 When the preliminary reductions have been carried out in full, as in Table I, the eccentric corrections may also be found by taking the means of the corrections in the different series for the same values of S, and the local corrections by similarly taking the means of the residuals O — C; but the final residuals must be obtained as in Table VIII, with values of X’, X”, ete., calculated by (8) from the mean values of A and B. Unless this is done the computed probable errors will, in general, be somewhat too small. The effect of local errors upon the determination of eccentricity is usually unimportant. If the eccentric corrections in Table VIII are recomputed after applying the local corrections to the observed values of D, there will be no change amounting to half a second. Some test of the general trustworthiness of the examination is always desirable. A sextant may be in such condition as to operate correctly under the delicate manipulation it receives upon the table of the appa- ratus, yet when removed therefrom and handled less cautiously, or returned to its case, a slight displacement of the axis may occur; so that if compared again the two sets of eccentric corrections will differ con- siderably from each other, although a small probable error is found for each. Any great change of this sort may be detected by comparing the differences D in the successive series of comparisons, which should always 94 THE CORRECTION OF SEXTANTS FOR ERRORS be scrutinized for that purpose before beginning the reductions. It is not possible, however, to decide in this way whether small abnormal varia- tions exist or not. The agreement or disagreement between the different pairs of values of A and B is also an insufficient test, for a reason already given, but if the preliminary reductions are carried out far enough to determine the eccentric corrections for each series separately, the probable error of this correction at any point, as deduced from the differences between the corrections furnishedby each of the series and their mean, maybe compared with the same probable error taken from Table V. The two values can scarcely be expected to agree exactly, but the difference between them should not be too great. The following results were obtained from the data in Tables VII and VIII. Peet Ba yo) By ais) pony | | ° Ti | // 0 0.0 — 0.0 | 20; +09 | +08 | 40 | 15 | 13 | 70 2.0 1.6 | ond 2.1 | 1.5 | 18 2.2 | 15 | 150) +26 | + 2.0 | | | | 1 In reading a sextant it is not merely the coincidence of a single line of the vernier with one of the limb that is noted, but the relative positions of several adjacent lines are taken into account, or ought to be; the effect of errors peculiar to individual lines is thereby rendered compara- tively innocuous, for such errors cannot be large without being visible. The most pernicious errors of graduation are progressive displacements in alternating directions, extending throughout the are in waves more or less regular, but of considerable length. The existence of sys- tematic errors having a period long enough to embrace several of the points which have been examined is indicated by a succession of local corrections with the same algebraic sign. It is sometimes advisable to attempt the correction of such errors, especially when they are large, and when many series of comparisons have been obtained. A convenient process is to plot the values of S as abscissas, and the computed local corrections as ordinates, to draw a fair curve approximating the points thus laid down, and lastly to measure and tabulate the ordinates of the curve as mean local corrections. This method is a rather rough one, but it is useful when the corrections to be adjusted are small, as the local OF ECCENTRICITY AND GRADUATION. ms corrections always are. Much exercise of good judgment is, however, essential: if the curve were drawn through all the points, or, what is the same thing, if the computed local corrections were adopted without any adjustment, the error resulting from sporadic defects in the graduation would apparently vanish ; but it is not certain that actual errors would always be diminished, for any single local correction may be considerably in error, and may also refer to a point not impartially representing the general state of the graduation in its vicinity. The number of points of contrary flexure in the curve must be very small as compared with the number of given points, and in every doubtful case it is safer to err on the side of proximity to the axis of S. The local corrections in the eighth column of Table VIII are not large, but they show unmistakable signs of systematic arrangement. The mean local corrections in Table IX were accordingly obtained from them by the process just referred to. There is one point of contrary flexure in the curve not far from S= 68°. TABLE IX. | S. Loe. cor. eee Residuals. oe. cor, ° YT yy y/ 0 4 38 a8 as By 10 aera ne See Eo. 55 20 1 — 1 0 8 ==) 5 3 a) 40 + 1 4 + § 50 = 5 0 60 anf) ey —— ee 70 et ate hi On 80 9 6 + 38 90 4 6 =e 100 1 5 —- 4 110 S438 af D be 6 120 =~ & — ae 130 5 5 0 140 (— 10) 1) (0) | eae | =. 119) As this series of supplementary corrections is a somewhat typical one, its significance should be recognized. Disregarding the abberrations of individual lines, the actual and mean arcs are coincident at points near 15°, 68°, and 117°. The mean are overlaps the actual are at both ends ; the mean length of divisions of the latter is, therefore, too small; they are actually too small between 0° and about 55°, too large from 55° to 26 THE CORRECTION OF SEXTANTS FOR ERRORS 85°, and again too small from 85° onward. From a point near 68°, where it is greatest, their length decreases in both directions. These systematic irregularities may have been produced by inequalities in the operation of the dividing engine, but they can also be accounted for by supposing an almost infinitesimal distortion to have occurred after the graduation was executed, the middle of the are approaching the center, and the ends receding therefrom, the greatest change being at the end eat opposite 0°. The apparent difference between the two ends may, however, be partially due to a slight Total deviation from parallelism in the surfaces of the | correction. | index glass. | The total correction of this sextant, or sum of the : eg eccentric and mean local corrections, is given in 0 0 : : 10 = i Table X. For the sake of convenience in use the 20 2 correction at 0° has been reduced to 0 by adding a i A — 3” throughout. 50 | + 1 The correction applied to any angle measured with shh tS the sextant is always the difference between two tab- 80 22 ular corrections—that of the observed reading, and aa mh that of the reading made in determining the index 110 | 82 correction. Let D,’, D,’, ete., be the observed values ia | a of D corresponding to the setting S’ in the different 140 eae series of comparisons, the computed local correction for this reading is then: D, — Asin + S’ — B (1 — cos + 8S’) — X, a=} Dy asin’ — BO oS EH | ay ete., + ete., + | D — Asin + S’ — B (1 — cos 3 S’)— xX, J Sp —YX _— __ = — Asin + 8’ — B (1 — cos + 8’), N ( ) : s : — sDI—2TX and the sum of the eccentric and local corrections is: = ae For } eas - SD"—ZSX ,. any other setting S” this sum is: = a which subtracted from : : sD — sD" the preceding expression leaves : eae eke Now the probable error of each of the N differences D,’, D,’, D,’, D,’, . gu Dy po PH py 2 etc., is ¢; the probable error of Sao therefore : Ve DONE eof A pe ae V VN OF ECCENTRICITY AND GRADUATION. ai But each point of the curve from which the mean local corrections were obtained depends upon two or more of the computed corrections: the probable error of the correction applied to any angular measure- : ony. ment is consequently less than 1.41 >— in some proportion depending VN upon the skill with which the curve was traced. This error is still further diminished when the two readings differ so little that their mean local corrections depend in part upon the same comparisons, and it van- ishes when that difference is very small. For the series of total correc- t ston eho an 1.41 V3 The numerical mean of the residuals in Table LX is tions in Table X, 1.41 =e Ao + 2”.7, which is so t woe much greater than ENE + 1.03, the probable variation due to error of observation, as to excite a suspicion that the sporadic errors of gradua- tion, including systematic errors of short period, are rather large in this instrument. The vernier is liable to errors as well as the limb, and they are some- times large enough to require correction. If the initial and terminal lines of the vernier do not simultaneously coincide with lines of the limb the former is usually blamed, though not always justly, for the vernier of Sextant V in Tabie IV, if of the right length, will afford nearly simul- taneous coincidences at the initial line, and at the additional line next the terminal one, on all parts of the are; while the vernier of Sextant VI _in the same table, should apparently be correct near 50°, too long at 0°, and considerably too short at 140°. When the corrections of the limb are known, a better judgment can be formed, but any examination by comparisons of this sort is necessarily limited to the extremities of the vernier, and gives no indication of the state of affairs between them. An examination may be made with the sextant apparatus, however, at any number of points, equidistant or otherwise, by bringing them in succes- sion to the same division of the limb and comparing with the circle. Let / be the actual length of a vernier, whose proper or intended length is /,* and whose nominal length, equal to one division of the limb, is 7; also let s be the reading at which the vernier is set in making a comparison, r being the corresponding reading of the circle, and z an * The lengths / and / are to be accounted positive when the readings of the limb and vernier increase in the same direction—negative when they increase in oppo- site directions. 28 THE CORRECTION OF SEXTANTS FOR ERRORS assumed value of that reading when s = 0, the true value being z + 2, in which # is unknown. Then Cf oe —7),* 7 U’) 5! (e+ a—nr), or if 7—T= cand § = it : Se=p > ——— as vu and finally by making r + ps — z = d,{ we obtain: z2z—a4+yr, 8 -etaz=d. 4 Each comparison furnishes an equation of this form, and if m com- parisons are made, the normal equations are: (JTC) -e-4} [Je + me = fe] 0] The true reading of a vernier is the product of the actual difference between one of its divisions and a Givision of the limb, multiplied by the number of divisions embraced in the reading; if then 0’ be any reading, 6 its corrected or true value, and q the number of divisions in the vernier : oO’ r i 6=.q = t——)> q the upper and lower signs of ¢ pertaining to the “short” and “long ” forms of vernier respectively. The correction is therefore: pe => (it g—1)—2); (1) or since 7 (+ g—1)=J,and/—T =e, 6— = oy (12) a in which ¢ is positive for either a “short” vernier which is too short, or a “long” vernier which is too long, and vice versa. Although the normal equations are easily solved for any values of s, time can be saved, even in this case, by adopting a uniform system of * In the apparatus here referred to the circle readings diminish as the readings of the usual or ‘short’ form of vernier increase. + For most sextants p = 59. { For a reversed or ‘“‘long”’ vernier s is essentially negative. 29 Sil 980) Sb a 9°99 — | e6 — 4 ig Pa, te eee a cee ie 0 a 5 a |y + | ea—loz = reclos —\¢ —| o 11 @ 0 me oo of b 0 | 0 Ozr |8I 88 | 801 al Ee ek a ec mee eae 6 8 Xe Gas. Sinan 6 Sir ae Laue oT S22 GIL FL 0 ial (6 SP Gis + Sate oe EG ee oe 8 < ae A CLG I [eas ‘OL v'I r9 | 89 6 Orcirg: "On ae 1¢ LQ | Ger Se oe See ae L LG°66 —_ 8% er $6 oI G¢o | 8 FL 0) amore Go csr SF Gprt| "2 Sse eee B L I 8 Ol VF | Ob 6 OMI —s tg Ope | a2 os yee a (Dae GMOs ore V Cas aa Gh 30 LG. 0) ORV OL OP OSR Siaed 1g Sie | es aoe ei v By PL ema f Ie gg 90 LaGee eon 9 One lahGe ace $G 60,4 | Ae ae See ees e ; 5 Beh + dT F 9° FO S'T FO G Que) 0 UG” A aaa eae ae Z fe 6 Gos L'> G0 eot0maiG Oneal Opel OG: eOmerG e | coe en, Wes | secs ae ee I a 100 0 00 = Z v Gh = Sion ee ONO. 00 | 00 9 | One Eom Sian FG Ge fe ae oe ae ce 0 a “/ “ “/ “ “/ “/ “ Yee “ “ / 8 a = = —_ - a a me a et I by EO =O) Os Oulu ates s p= p | sd J SSS s 2 ] ‘Uo1joo1L09 "SUMINUA A Boxe Lay, 30 THE CORRECTION OF SEXTANTS FOR ERRORS examination and computation. If comparisons are made at the two ends : ae ° 8. of the vernier, and at nine equidistant points between them, ; Is succes- sively 0, 0.1, 0.2, ete., 1.0; m= 11, and the normal equations (11) become: 3.85 e+ 5 55 «—| a] =o, r (13) 5.5 e+iiz—|a| =0.| Their solution gives: == 0455 [@] + 0,909 4] | aie p= Oss «| — 0.455 [ |. and the weight of ¢ is 1.1. (14) Table XI is an example of the record of examination and form of com- putation. It refers to a sextant divided to 10’, and reading to 10” by a “short” vernier, for which, therefore, i = 10’ and p == 59. The calcula- tion scarcely requires any tables except one of squares for extracting the square root in finding the probable errors, but it is convenient to take from Crelle’s table the four products employed in computing the values of cand x by (14). - The first three columns contain the record of examination, and the fourth receives the products ps, when they are expressed. For the sake of clear- ness the values of 7 have been given in full, as well as the seconds of ps, but it is unnecessary to write down more than the seconds of 7, and the seconds of ps when they vary, as in the case of a sextant divided to 15’ and reading to 15”. A sufficient explanation of the remaining columns is to be found in their headings. The sum of the squares of the residuals being 86, the probable error of a single comparison is 0.6745 a a= 27.09 + 2.09, and that of ¢ is Tae 2”.0. The corrections in the seventh column are computed by making 0 = s, and i = 10’, in (12); 8 10” In the probable error of a single comparison is included the probable error of graduation, and that of observation, and the latter is presumably equal to t if the limb and vernier were examined under similar cireum- stances. If, therefore, the probable error of one comparison is notably the appended probable errors are therefore + 2.0 OF ECCENTRICITY AND GRADUATION. ~ Sl greater than ¢, there is reason to suspect that the graduation is sensibly imperfect. The probable error of any angular measurement, due to the errors of the vernier corrections, is simply the difference between the probable errors of the two tabular corrections applied, being, in fact, that proportional part of the probable error of ¢ corresponding to the fraction of the vernier actually used. If the residuals indicate the existence of a systematic error, a supplementary correction may be obtained by the graphic process which has been described, though such an adjustment will rarely be required, except when valuable observations have been made with a sextant which had previously received some injury. If the index-bar were bent, for instance, so that the two ends of the vernier are unequally distant from the axis, it will be found that the divisions are longest at the nearer end, and shortest at the more distant one. The vernier corrections, like those pertaining to the limb, may be determined with increased accuracy by several series of comparisons, preferably made with different parts of the circle, and combined by methods too obvious to require special explanation. For any given sextant reading the argument of the correction is not the reading itself, but that of the point where a line of the vernier coin- cides with one of the limb*. The readings 8° 59’ 50” and 9° 0’ 10” differ only twenty seconds, but upon a sextant divided to 10’ and reading to 10” they refer to positions on the limb nearly ten degrees apart. This cir- cumstance, which is not invariably mentioned in the text-books, is also of considerable importance in determining eccentric corrections by the methods commonly recommended. When extreme precision is desired, the accuracy of an observation already made may sometimes be increased by a device applicable to any sextant, whether its errors have been inves- tigated or not. Find the point of coincidence of the recorded reading, and, after setting the zero of the vernier exactly upon that position, read the vernier at the other end; then, setting the terminal line of the ver- nier at the point previously occupied by the initial line, read at the zero end. Subtract the nominal length of the vernier from the sum of the two vernier readings and divide the remainder by three; the quotient is a correction to be applied to the original sextant reading. An error in * Every sextant reading is the sum of the limb reading and the vernier reading, and may be readily separated into these two parts when the scheme of graduation is known. If the vernier is of the direct or ‘‘short’’ form, almost universally applied to sextants, the point of coincidence may be found by the following rule: To the limb reading add the vernier reading multiplied by the number of divisions in the vernier. Thus on the arc of a sextant divided to 10’, and reading to 10/7, and which, therefore, has a vernier of 60 divisions, the reading 6° 49’ 50/’ is made at 6° 40’ +9/ 50/7 x 60 = 16° 30’. For a reversed or ‘‘ long ”’ vernier, the same product is to be subtracted from the limb reading. oo THE CORRECTION OF SEXTANTS FOR ERRORS the length of the vernier does not affect this result, since one reading is always as much augmented thereby as the other is decreased ; but if an- other limb correction is applied, it should be the mean of the corrections for the three points of coincidence. By this artifice each observation is referred to three distinct positions on the arc, with a corresponding dimi- nutior in the effect of purely local errors. When the presence of large errors upon any small portion of the limb is suspected, in consequence of a local injury or otherwise, as many of the lines in this tract may be examined as the nature of the case requires. These comparisons are not to be employed in finding the eccentricity, but must be reduced separately to determine the !ocal errors. If it should become generally known that sextants purchased in con- siderable numbers were inspected only at certain points of the gradua- tion, unscrupulous makers, especially those using copying engines, might be tempted to bestow greater care upon the critical divisions than upon the rest of the are. But the points to be examined may be selected at pleasure, if their number and distance from each other remain unchanged, as has been shown. In arranging a system of examination for any given service, the number of comparisons in a series will naturally depend on the special requirements of the case. A greater number affords a better representation of the entire graduation, while, on the other hand, it extends the time during which errors may be introduced by gradual or sudden changes in the apparatus, or in the sextant itself. Perhaps there can seldom be any sufficient reason for spacing the comparisons more closely than at points 5° apart. An alternative form of the apparatus has been devised, having two collimators—one fixed, the other carried by an arm attached to the circle and directed toward the sextant, which is supported by a fixed table immediately over the circle. The two collimator-marks—one seen direct, the other by reflection—are brought into coincidence in the field of the sextant telescope, as in the ordinary use of that instrument. No appa- ratus of this form has been constructed, but the details have been worked. out far enough to show that no serious practical difficulty is to be appre- hended. The principal feature of improvement is that nothing will depend upon immobility of the sextant, which lies freely upon its table. during the examination and may be removed for inspection at any time. It may be, however, that this advantage is rather apparent than real, for in either case the sextant must be handled with the utmost caution, and experience has not shown that there is any difficulty in preventing an appreciable displacement. On the other hand, the proposed form must necessarily be more expensive than the existing one, the illumination is not so easily effected, and probably the observations will not be quite so good. (os — OF ECCENTRICITY AND GRADUATION. DO with two collimator images as with one image bisected by a wire. In either form the circle should be provided with microscopes, which are more expeditiously read, and less fatiguing to the eyes, than verniers. The examples which have been discussed in the preceding pages are sufficient to show that, under favorable circumstances, observations can be made with the sextant leaving very little to be desired as regards accu- racy. In practice, however, such precision is not always, perhaps not commonly, attained. The most insidious source of error is an unstable condition of the eccentricity—a fault clearly traceable to defective con- struction when due attention has been paid to the care and preservation of the sextant. A judicious observer always endeavors to distribute his observations so as to neutralize the unknown errors of his instrument as nearly as possible; but variations in the eccentricity, which may occur at any moment, cannot be evaded by this means. If the conical axis is so _ improperly fitted as to be circumferentially supported only at the smaller end, its position will probably be maintained by friction, and the viscosity of the wax-like lubricant used for this bearing, until some extraneous force is applied, when displacement into a new position of temporary quiescence may be expected to ensue. Such a movement, to the extent of one-thousandth of an inch in a sextant of seven inches radius, may produce errors of 50” and upward. Any unavoidable defect in fitting should evidently subsist in the direction opposite to that here sup- posed, and possibly some changes in the usual dimensions and materials of construction might be advantageous. But whatever the requisite alteration in existing practice may be, its discovery and adoption can safely be intrusted to the instrument-makers if a sufficient inducement to persevere in the search for improvement is offered to them. The mechanician who expends time and money in striving after a perfection which observers do not demand, or appreciate, unwisely impairs his ability to compete with his rivals. When sextants are so generally and adequately tested that the reputation of each maker rests on the actual merits of his work, a remedy for the evils of injudicious design and inferior workmanship will soon be found; until that time it cannot rea- sonably be expected. SMITHSONIAN MISCELLANEOUS COLLECTIONS, ee BIBLIOGRAPHY OF THE CHEMICAL INFLUENCE OF LIGHT. BY ALFRED TUCKERMAN, Pu. D. Wes H ENG LON CRT Y : PUBLISHED BY THE SMITHSONIAN INSTITUTION. 1891. PREFACE. 7 This bibliography, having for its object the scientific aspects of the _ chemical influence of light, the practical applications, including that of _ Photography, are nearly all omitted, as has been the case in my previous works of this kind. An index to the literature of Photography is being prepared under _the auspices of the Committee for Indexing Chemical Literature, of the _ American Association for the Advancement of Science. ALFRED TUCKERMAN. _ Newport, Rae April, 1892 (iil 5065. Oporx, Christophe. Observations sur les couleurs. J. de phys. 1776 et 1783. Parav. Sur les causes de la chaleur et de la lumiére des astres. C. R. 64 (1867) 395. Perciva,J.G. Curious effect of solar light. Amer. J. Sci. 5 (1822) 1. Perrint, P. Ricerche sulla produzione de ’colori immaginari nell’ombre. Mem. soe. ital. 13 1 (1807). 18 A BIBLIOGRAPHY OF THE Purprson, T. L. 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Ann. 12 (1803) 409; J. de Phys. 57 (1803) 409; Nicholson’s J. 5 (1803) 255; 8 (1804) O14. ,——. Bemerkung zu Wounscn’s Versuchen tiber die vermeinte Sonderung des Lichtes der Sonnenstrahlen yon der Warme. Gehlen’s Jour. 6 (1808) 1. Roscor, H. E., and Bunsen, R. Photochemical researches with refer- ence to the chemical action of light. Brit. Ass. Rept. (1855) 48; (1856) 67: Quar. J. Chem. Soe. (1856); Ann. Phys. 96 (1855) 373. 100 (1857) 43; Phil. Mag. [4] 13 (1857) 521; 19 (1860) 61; Phil. Trans. 147 (1857) 355, 381, 601; 149 (1859) 879: 153 (1864) 159 ; see Wrrrwer, Ann. Phys. 94 (1855) 597. Roscor, Henry Enfield. On the measurement of the chemical action of light. Phil. Mag. [4] 11 (1856) 482; Proc. Roy. Inst. April 4, 1856 ; Chemical Gazette, 14 (1856) 259; Proc. Roy. Soe. April 4, 1856; In- stit. (1856) 346; J. prakt. Chem. 69 (1856) 312; Jsb. (1856) 185, Abs. ,——. On the measurement of the chemical action of the solar rays. Proc. Roy. Inst. 3 (1858-62) 210, read March 2, 1860. 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Sur la lumiére et le calorique. Ann. chim. 26 (1798); 31 (1800) 11. 20 A BIBLIOGRAPHY OF THE ScnravurF, A. Brechungsvermégen bie Stoffen analoger Bildungswesen. Ann. Phys. 155 (1868) 479. Seepeck, Thomas Johann. Von den Farben und dem Verhalten der- ~ selben gegen einander. Schweigger’s J. 1 (1811). ,——- Die Wirkung des Lichtes findet nur dann statt, wann dieses nicht vollig trocken ist. Ann. Phys. 9 (1827) 172. SENEBIER, Jean. Sur la nature de la lumiére et sur ses effets. Jour. phys. 14 (1779). ,—- Sur l’action de la lumiére solaire pour blanchir la cire jaune. Jour. phys. 38 (1791). ,—. Sur divers phénoménes produits par des feuilles de plantes exposées sous l'eau & Vaction de la lumiére solaire. Mém. Turin, 4 (1790) et 5 (1793). Siater, J. W. On the chemical actiom of light. Chemical Gazette, 10 (1852) 325; Phil. Mag. [4] 5 (1852) 67; J. prakt. Chem. 57 (1852) 239; Pharm. Centralb. (1853) 27; Instit. (1853) 155; Jsb. (1852) 211. SoMERVILLE, Mary. Expériences sur la transmission des rayons chim- iques du spectre solaire 4 travers differents milieux. Extrait d’une lettre de Mme. Somerville 4 M. Arago. C. R. 3 (1836) 473; Ann. Phys. 39 (1836) 219. SraBies, W.C. Influence of sunlight on chemical compounds. Pharm. — J. Trans. (1887) 1009; Ber. chem. Ges. 20 (1887) 466 R, Abs. Suoxow, G. Ueber das chemisch verschiedene Verhalten quantitativ verschieden zusammengesetzer Stoffverbindungen gegen das Sonnen- licht. Ann. Phys. 32 (1834) 387; 39 (1836) 325. SurmertAND, John. On the polarization of the chemical rays of light. Phil. Mag. [8] 19 (1841) 52; Edinb. Proc. Dee. 21, 1840; Liverpool Lit. Phil. Proce. Noy. 2, 1840; Ann. Phys. 54 (1841) 434; Bibl. univ. 34 (1841) 382. Tatsor, William Henry Fox. Experiments on tight. Phil. Mag. 5 (1884) 321; 7 (1835) 113; Ann. Phys. 35 (1835) -330; Proc. Roy. Soc. 3 (1834) 298; Instit. 3 (1835) 311. THomsen, Julius. Das mechanische Acquivalent des Lichtes. Ann. Phys. 125 (1865) 348; Phil. Mag. [4] 30 (1865) 246. CHEMICAL INFLUENCE OF LIGHT. a THomson, W. Des antécédents mécaniques du mouvement, de la chaleur et de la lumiére. C. R. 40 (1855) 1197. Tumuirz, O.,und Krua, A. Berechnung des mechanischen Lichtaquiv- alents aus den Versuchen des Herrn Julius Thomsen. Wien. Akad. Ber. 97 11 a (1888) 1627. ,—- Das mechanische Aequivalent des Lichtes. Wien. /kad- Ber. 98 11 a (1889) 826, 1121; Phil. Mag. [5] 28 (1889) 352, Abs. 5 Ann. Phys. n. F. 38 (1889) 640. TyNDALL, John. On a new series of chemical re-actions produced by light. Proc. Roy. Inst. 5 (1866-69) 429, read Jan. 15, 1869; Proce. Roy. Soc. 17 (1868-69) 92, 104; Ann. ch. ph. [4] 16 (1869) 491; Chem. News, 18 (1868) 266; N. Arch. ph. nat. 33 (1868) 317; Jsb. (1868) 108, Abs. Voae., H. August. De l’action de la lumiére solaire sur les corps simples et sur quelques composés chimiques. Jour. phys. 80 (1815) 245; Gil- bert’s Ann. 48 (1814) 575. Voge, H. Ueber die fortsetzenden Strahlen Becquerel’s. Ber. chem, Ges. 6 (1873) 1498, b; Jsb. (1873) 166, Abs. , — Zur Chastaing’s Theorie der chemischen Wirkung des Lichtes. Ber. chem. Ges. 10 (1877) 1638, f, b.; Jsb. (1887) 194. Vorer, J. G. Beobachtungen und Versuche tiber farbiges Licht, Farben und ihre Mischung. Gren’s n. J. 4 (1797). [Bemerkungen von J. B. Richter. ] Warveer, E. Versuche und Beobachtungen tiber Prof. Moser’s unsicht- bares Lichf. Ann. Phys. 59 (1853) 255. Wirrwer, W.C. Messung der Intensitat der chemischen Wirkung der Lichtstrahlen. Ann. Phys. 94 (1855) 597; Jsb. (1855) 172, Abs. Bemerkungen dazu, von Bunsen und Roscoe, Ann. Phys. 96 (1855) 373; Quar. J. Chem. Soe. 8 (1855) 193. ,——. Ueber die chemische Wirkung des Sonnenlichtes. Ann. Phys. 106 (1859) 266; Jsb. (1859) 31, Abs. Wo .uaston, William Hyde. Effects of the invisible rays of light. Phil. Trans. (1802) 379; Gilbert’s Ann. 31 (1809) 416. 22 A BIBLIOGRAPHY OF THE CHEMICAL INFLUENCE OF LIGHT. Wo ttasron, William Hyde. On certain chemical effects of light. Nich- olson’s Jour. 8 (1804) 293; Gilbert’s Ann. 39 (1811) 291. Woops, Thomas. On the measurement of the chemical brightness of various portions of the Sun’s disk. Phil. Mag. [4] 28 (1864) 166; Jsb. (1864) 116, Abs.; see Roscon, same page. Youne, Thomas. Experiments on the dark rays of Rrrrer. Phil. Trans. (1804) 15; Gilbert’s Ann. 39 (1811) 282. SMITHSONIAN MISCELLANEOUS COLLECTIONS, 3545 —— THE MECHANICS OF THE feiss ATMOSPHERE. A COLLECTION OF TRANSLATIONS BY GWE TAND: ABE E. CITY OF WASHINGTON: PUBLISHED BY THE SMITHSONIAN INSTITUTION. 1893. _ I — Ill. Vi: WANG Vill. XIII. XSI: XV. WAS XVII. XVIII. XIX. COUNT EN ES. MALOU CULO Terr ere Nee ice eer. Suk Beak ce Se oorken eae ee . Hagen, 1574. The measurement of the resistances experienced by plane plates when they are moved through the air in a direction MOM t GhOLMelEs Olan OS)p =e) esse nies clo ane ee we Smee soe eee . Helmholtz, 1858. On the integrals of the hydro-dynamic equations Ch atpLEpPLESeliGnvOLLEX- MOONS H~ s2 5 sine <2 -Sece-tacoc oes eee eaeees Helmholtz, 1£68. On discontinuous motions in liquids....-.-..---..- Helmholtz, 1873. On a theorem relative to movements that are geo- metrically similar, together with an application to the problem Oise LCerin ma ANOGNSe ac ce eae tae s Dese sac esele= ose eset ao . Helmholtz, 1888. On atmospheric motions; first paper.----..------ Wale Helmholtz, 1889. On atmospheric motions; second paper. On the HHCOLVOtevwlndgan GuwiaiVesere ics se ccs seeks censors eae see ace «eee Helmholtz, 1890. The energy of the billows and the wind.......--- Kirchhoff, 1869. The theory of free liquid jets .........--..---..--- . Oberbeck, 1877. On discontinuous motions in liquids ..........-.. . Oberbeck, 1882. The movements of the atmosphere on the earth’s INRA CO rere re enim oe pe a pe Le Tet Pa . Oberbeck, 1882. Onthe Guldberg-Mohn theory of horizontal atmos- DNELLC SE WENOM tase acess ao yas Saison eeete st pele os esac Sh ese . Oberbeck, 1588. On the phenomena of motion in the atmosphere ; first Paper aaeee cas Breer fo Sabsie siecle eo wise ees ents oa lote ass Ser eete ays Oberbeck, 1888. On the phenomena of motion in the atmosphere ; RECONUE Apel ess ese ese rsa = ree ata el note sree eh ete et eee eee Hertz, 1884. A graphic method of determining the adiabatic changes jal, Ga aKs) COVINA COVE THNKONSMEN O eecionc copped chapanene coeeeeeceosar Bezold, 1888. On the thermo-dynamics of the atmosphere; first paper - Bezold, 1838. On the thermo-dynamics of the atmosphere; second ADORE Ses seem aye a eee em sytiee ioe sini dain ss Ohebicwisce. Boe acme Bezold, 1889. On the thermo-dynamics of the atmosphere; third paper Rayleigh, 1890. On the vibrations of an atmosphere ..-........-.--. Margules, 1290. On the vibrations of an atmosphere periodically Neate de oases sawn Se pS Lea lds sep suiemtat ci jabieinsccctsaselse <. Ferrel, 1390. Laplace’s solution of the tidal equations..............- 3 Page. 5 67 ~ 94 112 130 139 THE MECHANICS OF THE EARTH’S ATMOSPHERE: A COLLECTION OF TRANSLATIONS. By CLEVELAND ABBE. INTRODUCTION. The complexity of the phenomena of the atmosphere has rendered it necessary to delay their mathematical treatment until our knowledge of hydro-dynamics and thermo-dynamies could attain the perfection which it began to acquire about the middle of this present century at the hands of Helmholtz, Clausius, Sir William Thomson, and their disciples. During the past few years some of the fundamental prob- lems of meteorology have been treated analytically and graphically with great success. The present collection of translations presents some of the best memoirs that have lately been published on the re- spective subjects by European investigators; a few earlier memoirs of great excellence are included in the collection because of the references subsequently madeto them. Other mathematical memoirs by Guldberg and Mohn, Marchi and Diro Kitao have been omitted because their length would have made this collection too large for the present mode of publication. There is a crying need for more profound researches into the me- chanies of the atmosphere, and believing as I do that meteorology can only be advanced beyond its present stage by the devotion to it of the highest talent in mathematical and experimental physics, I earnestly commend these memoirs to such students in our universities as are seeking new fields of applied science. I have taken a very few liberties in translating the language and notation of the distinguished authors whose works are here collected. _Thave frequently used the word liquid instead of ‘ Wasser,” ‘¢ Troptbar- Flussigkeit,” “‘Inkompressible Flussigkeit,” and the word gas or vapor as equivalent to compressible or elastic fluid, and have used the word fluid when the more general term including liquids, vapors, and gases is needed. As the ideal or ‘“ perfect” liquid is absolutely incompressi- _ ble and devoid of all resistance to mere change of shape, having neither _ elasticity nor viscosity, namely, internal friction, it seems more proper | 5 6 THE MECHANICS OF THE EARTH’S ATMOSPHERE. to use the general terms liquid, gas, and fluid when neglecting the re- sistance, compressibility, elasticity, and viscosity as in dealing with these ideal substances, and to reserve the terms air, water, ete., for use when dealing with actual natural fluid phenomena where slight com- pressions and expansions and resistances occur. The relation between elastic pressure, volume, and temperature, as deduced by Boyle, Mariotte, Gay-Lussac, and Charles, that characterizes a gas, and the equation for which the Germans eall the “ Zustands- Gieichung” in common with other equations of condition, I have pre- ferred to speak of as the equation of elasticity or the characteristic equa- tion of a perfect gas. In view of the remarkable want of uniformity existing in English and American works in respect to the notation for total and partial differentials I have decided to make such alterations in the original notations of these papers as shall make the whole series consistent with the elegant and classical notation that is rapidly being adopted in Ger- many, and that will, I hope, eventually be accepted by ail English and French writers. In accordance with this I shall always express the total differential by d, as first introduced into geometry by Leibnitz for the infinitesimal difference; the small increment or variation by 6, as introduced by Lagrange; the large finite difference by 4, first used by Euler; the partial differential by 0, («the round d,”) as used by Jacobi. Occasionally the dotted variable @ will indicate the rate of variation with regard to the time, or the fluxion as first introduced into mathe- matical physics by Sir Isaac Newton, a notation which has lately been extensively revived in England by those devoted to classic authority. Evidently the problems here treated by elegant mathematical meth- ods are not always precisely the problems of nature. The differences between the conclusions of Rayleigh, Margules, and Ferrel as to the diurnal and semi-diurnal tides due to heat, or the differences between Ferrel, Oberbeck, and Siemens on the one hand and nature on the other as to the general circulation, show that by the omission of apparently minor local and periodical irregularities we have constructed for our- selves problems that still differ from the case of the earth’s atmosphere, although they may more closely represent the conditions of such a planet as Jupiter. I have to acknowledge the assistance of my friend, Mr. G. E. Curtis, in copying a portion of the formule for these translations, and renew the expression of my hope that a coming generation of American meteor- ologists may prosecute to further conquests the mathematical studies begun by Ferrel and perfected by our European colleagues. CLEVELAND ABBE. FEBRUARY, 1891. THE MEASUREMENT OF THE RESISTANCES EXPERIENCED BY PLANE PLATES WHEN THEY ARE MOVED THROUGH THE AIR IN A DIRECTION NORMAL TO THEIR PLANES.* By Professor G. H. L. Hagen. Some time since I submitted to the Academy the results of a series of observations that I had instituted upon the motions of air and of water when the uniform flow of these fluids is interrupted by means of interposed planes.t By means of small bits of paper or tin foil floating from the tips of needles the direction of the motion could be perceived at every point. The velocities were indeed too feeble to be capable of direct measurement, but the disposition of particles of pulverized am- ber that were strewn over the water showed the limits of the strongest current, and when the coarser particles came to rest before the finer ones it was to be inferred that there was a gradual diminution of ve- locity at such points. _ In general it was concluded that air and water alike swerve in curved paths in front of such obstacles and flow towards the free openings. In the latter and directly adjoining the outer ends of the obstacle the strongest current is formed which here retains its direction unaltered, therefore free from all variations. The deviation in front of the obstacle does not take place at any definite distance from it, but rather extends up to the obstacle itself and even when the plate faces the current it is seen that a feeble motion still exists immediately adjoining it. Behind the obstacle the fluid by no means remains at rest, but rather there is always formed here a counter current whose length is equal to four or five times the distance of the head of the obstacle from the neigh- boring side wall of the channel, which counter current, however, is not only fed at its rear enc, but principally also at two intermediate points by the steadily broadening main current. The latter immediately be- hind the head of the cross-wall meets the outcoming counter-current *Read before the Academy of Sciences, Berlin, January 22, February 16, and April 20, 1874. (Translated from The Mathematical Memoirs [ Abhandlungen] of the Royal Academy of Sciences at Berlin for the year 1874, pp. 1 to 31.) tSee the Monats-Berichte for 1872, p. 861. ~ 8 THE MECHANICS OF THE EARTH’S ATMOSPHERE. and here, as also at the two intermediate piaces just mentioned, whirls are formed which set in rotation the little vanes placed there. The phe- nomena agree with those that one observes in streams and rivers in front of and behind sharp provruding rocks or piers. It must still be mentioned that neither water nor air rebounds like elastic spheres from the obstacle against which it strikes, as is fre- quently assumed. Even strong streams of water that I allowed tu play against the plates did not rebound, but continued their onward path close to the obstacle, producing a strong current there. I had instituted these experiments in order to see in what manner the resistances originate that the liquid experiences in such deviations and which cause the pressure against the opposing plate. However, I thought it was allowable to assume that when the plate is itself moved through stationary water or air the ratios remain nearly the same and that similar currents of the fluid occur in its neighborhood. The pres- sure that the plate experiences in this latter case is the object of the following investigation which is moreover confined to plane disks moved through the air in a direction perpendicular to their planes. Faget Already 40 years ago I SS had occupied myself with — the same problem,* but the wt apparatus used at that time was too imperfect to give e useful results. In essential 1 eg points I have retained the emarril ae earlier arrangements, but many changes have been made in order to remove the defects. The accompanying plate shows the apparatus now used by front and side elevations (see figs. 1 and 2), as also by a horizontal sec- tion (see fig. 5) through the line A B, of fig. 2. Two thin arms of straight- grained pine wood which are Puss a tae = = SSS wr 72 zou *Some of the series of observations made at that time are communicated as exam- ples of the application of the method of least squares in the first edition of the **Grundziige der Wahrscheinlichkeits-Rechnung.” PAPER BY PROF. HAGEN. 9 bevelled on the sides that cut through the air, rest upon a vertical metal axis Which communieates the rotary motion to them. Each of these arms is 8 feet or 96 Rhenish inches long and on its end the disk 1s fas- tened whose resistance is to be measured. In order to prevent the bending of the arms they are held not far from their ends by small wires which pass over a sup- port 18 inches high vertically above the vertical axis. The drawing presents only the connection of the two arms between themselves and with the axis. The latter is in its upper portion turned slightly conical and carries the corres- ponding hollow hub which is - serewed to the brass plate under the arms. The rotation is brought about by the tension of two small threads which are wound in the same direction around the ivory spindle that is fas- tened to the axis, and are then drawn in opposite directions over two rollers and drawn taut by light scale pans with weightstherein. These rollers Thad formerly fastened at the greatest possible distance on the opposite walls of the room in order that when winding up the weights the threads might lie uniformly alongside of and not over each other, but this design was by no means certainly attained and the far-stretched threads ma- terially increased the labor of the observation, especially T since the arms and the disks * ° % * ° fastened to them occasionally came in contact with these threads. When in the past summer I again undertook the observations I placed _ the rollers, as the drawing shows, close to the axis, but did not let the latter stand upon a fixed point, bat rather provided it with a Fig. 2. 3 9 IO WM _f2 aol _ serew thread on its iower part whose mother is cut into a thick plate of brass. By rotation the axis therefore rose or sank uniformly, 10 THE MECHANICS OF THE EARTH’S ATMOSPHERE. and the threads simultaneously arranged themselves alongside of each other on the spindle from which they were drawn always in a horizontal direction. Underneath the roller I connected both threads by means of a hight rod, and un this hung the scale-pans for weights ; I also fastened thereon a pointer which slid close to the graduated scale and served to measure the velocity. Notwithstanding the great convenience of this change it introduced the troublesome consideration that the friction became disproportion- ately great and varied so much during the observation that its magni. tude and its influence on the measured velocity could not be determined with the necessary accuracy. This great evil I removed in that I al- lowed a steel point to work in the conical depression already formed by the turning lathe at the lower end of the axis, which point exerted an upward pressure equal to the weight of the arms, the dises, and the axis. The axis is therefore completely supported by the steel point, and the screw serves only as a guide in order to raise and lower the spindle corresponding to the windings of the thread. This steel point forms the upper end of a stout wire 12 inches high, whose lower end, ground to a wedge shape, stands in a metallic groove that is fastened at the end of a lever whose equal arms are 19 inches long. This lever, whose center of gravity lies in its axis of rotation, was so formed that its axis lay in a straight line with the metal groove and the point of suspension of the scale-pan, and was equally distant from both. This pan, with the counterpoise, corresponded exactly to the pressure of the axis on the wire when no resisting discs were placed upon the arms, but as soon as the latter occurred the counterpoise was always increased in a corresponding degree by an appended light cup with shot. Before attaching the dises these were laid upon a balance and the cup was partly filled with shot until brought into equilibrium with it. Since the lever changes its position during the rotation of the axis the steel wire deviates somewhat from the vertical position, but, as will be shown in the following, so slightly that this may be overlooked. The result of these changes in the apparatus proved to be very favora- . ble, for whereas before at least 3 Prussian loths had to be placed in i) each scale in order to set the arms in permanent motion, now, the weight of the rod and the scale-pan, which together weighed 3.3 loths, sufficed — without any additional weight to produce a uniform motion. At the ends of the arms pieces of perforated cork are glued, and in | these the stems of the various discs find their support. The discs were always pushed so far on that they closely touched the ends of the arms. The distance of the disc from the axis of rotation is found from the | known lengths of the arms; the stems of the discs did not extend through the corks, therefore the resistance of the air against the arms was only increased by that which the discs themselves experienced. Therefore, after the resistance which the arms experienced at each velocity had been determined by observation of the rotation of the PAPER BY PROF. HAGEN. tt arms under various leads, this could be subtracted each time from the resistance observed with the disc in place and thereby the resistance of the various discs for various velocities be determined. The ivory spindle around which the threads wind was, like the axis, very carefully turned cylindrical, and is 1.1 inches high and 1.6inches in diameter. The portion of the axis extending above the spindle is also turned cylindrical so that for any position of the upper perforated brass plate it is securely held with very little play. Under its slightly coni- eal flat head are found, as the figure shows, two openings perpendicular to each other, one square and the other circular. The first serves for the introduction of a small crank handle by means of which the axis is turned backwards when the weights are being raised. Before taking off the arms a wire is put through the circular opening which pre- vents the axis from turning forward while the observer is taking off tne crank and putting on the arms and dises. Moreover, at a distance of 12 inches from the axis there is placed a bent lever, one arm of which stands upright and hinders the turning of the arms that carry the dises when the weight fastened to the other arm of the bent lever hangs freely. While the arm carrying the discs is thus held by the bent lever the stout wire is withdrawn and the air is allowed to come to rest. It the weight be placed on the neighboring table then the bent-lever arm falls and the apparatus starts in motion. The pitch of the screw of the axis below the spindle is 0.05 inch, and this distance corresponds to the width of both threads so that the latter lie regularly close to each other on the surface of the spindle. This always occurred very regularly even when the axis was turned very rapidly by means of the crank handle. The threads, the so-called “iron twine,” were so strong that each with safety carried 4 pounds, which weight, however, was never even distantly approached in practice. The threads were so light that 40 feet weighed only 0.1 loth, so that the fall of the index by 6 feet increased the driving power by only 0.03 loth. Nevertheless, for very feeble loads in the scale-pans a slight increase in the velocity was apparent during the descent, and in order to prevent this the small increase in the weight was annulled by means of two equal threads suspended from the scale-pans to the floor. Since the two former or driving threads were fastened to the rod they were thereby prevented from turning and unwinding, which I had been able to avoid in my earlier work only by guiding the seale-pans by means of taut wires. Even if, however, the threads by this method of fastening did not materially change, still it remained to be proved whether perhaps they lengthened sensibly with greater tension, in which case the relation between the path of the index and the rotation of the arms could not remain constant. Such an extension could not be mistaken when I laid a weight of 1 pound on the empty scale-pans when they were at their lowest position. The index then sank at once 0.2 of aninch. A further extension, however, did not follow; at least 12 THE MECHANICS OF THE EARTH’S ATMOSPHERE. it was not to be observed in the short interval occupied by each sepa- rate observation. In consequence of this extension of the threads it was. incumbent to lay those weights that were to be used to set the axis in motion during the next observation upon the scale-pan while the latter was at its lowest position. The threads were therefore always wound up under the same tension with which they were to do the work. The question now arose whether with stronger tensions the spiral windings of the threads perhaps lay flatter on the spindle than with weaker tensions, and whether therefore the length of a winding or the path that the index described for one turn of the arms became shorter. This point was decided in that with various loads in the scale-pan I measured the path that the index described during a certain number of revolutions, The above-mentioned bent lever offered the opportu- nity of always stepping the arms at the same point, but it was necessary to bring them to rest by gentle pressure, because with a strong blow against the upright standing arm the horizontal arms carrying the dises. could easily turn somewhat or the conical head of the axis. After the position of the index was read off I allowed the arms to make five com- plete turns and again read off the position of the index on the scale, estimating only to the hundredth part of an inch. The lengths of the paths for the corresponding weights in each seale- pan are as follows: Weight.* Path.t 0 25. 69 + 67 8 . 68 16 . 66 2t . 67 28 . 65 * Prussian loths. + Rhenish inches. A very slight shortening of the path appears from this to oceur for the heavier loads, but if it actually exists it isso small that it is far less than the accuracy of the measurement of the path of the index on the divided scale. It may therefore be assumed that the velocity of the index stands in a constant ratio to that of the arms or disks. The lengths of the individual windings of the thread around the spindle as resulting from the above measures do not correspond in al] accuracy to the circumference of a circle that is normal to the axis of the spindle, and at a distance therefrom equal to that of the central axis. of the threads, inasmuch as the threads lie spirally around the spindle, Now the pitch of the screw measures 0.05 inch; therefore the threads on the surface of the spindle make an angle with the horizon 0° 33/29”, Since the average length of one winding of the thread is 5.134 inches, therefore the equivalent thread encircling the normal is somewhat. smaller, namely, 5.1338. Hence the resulting distance of the center of the threads from the axis of rotation or the length of the lever arm by si dleete P tot PAPER BY PROF. HAGEN. 13 which the weight acts is equal to 0.81705 inch. This figure is adopted in the following computations, where it is represented by the Jetter a. It remains still to investigate whether the steel wire that carries the axis may perhaps depart so far from the vertical direction by the move ment of the lever on which it rests that it occasionally may exert an appreciable side pressure and thereby in an injurious way increase the friction in the screw threads. The lever is, as was mentioned, not only ‘perfectly balanced, but the point that carries the counterpoise is also situated in the prolongation of the straight line drawn through the supporting poiutof the wire and the rotation axis of the lever. Therefore for every position of the lever the foot of the wire is pressed upwards vertically with equal force, but it rises only 0.8 of an inch, while the weight that drives the disks around in the extreme case sinks SU inches. Therefore the deviation of the foot of the steel wire from a mean position amounts only to 0.4 of an inch, or in angle 2° 24’ 48”, for a length of the ' lever arm of 9.5 inches. Therefore the deviation from the initial vertical- ity is limited to 0.0086 inch, and consequently the wire 12 inches long _ is inclined 0° 2’ 38” to the vertical. Even this small inclination can be reduced by one-half if we place the axis of the wire or its upper point in the vertical line that bisects the deviation of its lower end, but such accuracy in the establishment of the apparatus must not be anticipated. It is evident from this that there can be no sensible increase of the fric- tion in consequence of the movement of the lever. As regards the execution of the observations the remark must be pref- aced that the Rhenish inch, or the twelfth part of the Prussian foot according to the earlier determination of the standard, and the old Prus- sian loth, of which 52 make 1 Prussian pfund, have been adopted as units of length and weight.* The divided scale over which the index glides is divided into tenths of inches, but this subdivision is only used for determining the length of one winding of the thread, as previously described. In all other cases only the transit of the index over the heavier division marks for each 10 inches was observed by the beating of the seconds clock and the corresponding whole or half seconds noted. Since at the beginning of an observation the arms do not immediately assume that velocity for which the resistance in connection with the friction balances the acceleration, therefore the significant observations began only when the weight had fallen 20 inches or the index had passed over the twentieth inch mark. At the seventieth inch the weight- scale pan had approached the floor, and therefore here the measures must be stopped. When, however, the rotation of the arms was ob- served without disks and the weights employed were very slight, then the speed continued increasing somewhat longer and the time of transit over the twentieth inch could not be used in the calculations. {* One Rhenish inch = 1.0297217 English inch — 26.15446 millimetres. One Prus- sian loth — 0.032226 pounds avoirdupois = 14.616 grammes. (See Barnard’s Weights _ and Measures, C. A. ] 14 THE MECHANICS OF THE EARTH’S ATMOSPHERE. the air against each separate pair of disks it certainly would have been advantageous to employ very different weights and thereby attain very different velocities. This intention, however, could not be carried out by reason of the moderate length of the arms, which was limited by the dimensions of the room. If I loaded each scale pan with more than 1 pfund then the whole mass of air in the room, especially when using larger disks, assumed a rotatory motion, in which case the resistance dur- ing the individual observation is always less or the velocity is always greater. Even with aload of 1 pfund the light paper vanes that floated at the tips of the needles already showed a feeble continuous rotation, although the flame of a candle did not allow of its recognition. In all the following observations therefore in the extreme cases only 28 loth was placed in each scale pan. To this it is to be added also that the measurements for very large velocities lose in accuracy on account of the relative magnitude of the unavoidable error. According to this the index should not move faster than an inch in 1.8 seconds. On the other hand, however, on account of the excessive influence of the very variable friction, the movement became highly irregular, when more than 8 seconds elapsed while the index described Linch. Within these limits the times in which 10 inches were described did not easily devi- ate more than half a second from the average value. The velocities of the disks were therefore not greater than 66 and not less than 17 inches per second.* In order to attain a uniform tension with reference to the axis the weights placed in the two scale pans were always equal and since on each occasion the disks attached to the arms were also always of equal magnitude, therefore each of these weights corresponded to the resist- ance of one disk. To this indeed should still be added one-half of the weight of the rod and the two scale pans but this may be disregarded since for each individual observation the value of the constant term which indicates the friction has to be especially computed. This con- stant term will then be the sum total of these weights less the friction, and presented itself always with the negative sign because the friction remained less than the weight of the rod and the seales. In order to simplify the computation I have at first referred not to the velocity of the disks, but only to that of the index, whence as above mentioned the velocity of the rotation can be easily deduced. In this way the opportunity was offered at each observation with disks to take into consideration that resistance which the arms alone experienced for the corresponding velocity of rotation. Before and after each series of observations, which generally oc- cupied 3 or 4 hours, the barometer and thermometer were read oft, the latter being at the same altitude above the floor as that at which the arms revolved. The computed coefficients of resistance were re- * Between 3.5 miles and 0,Y mile per hour. PAPER BY PROF. HAGEN 15 duced to the barometric pressure of 28 Paris inches and the tempera- ture 12° Réaumur or 15° C. Assuming that the resistance of the air is proportional to its density I formed a table of the logarithms of this correction whereby the separate reduction is very easy. In case the temperature sensibly changes during the time of observation it must be assumed that this change occurred gradually and therefore for each individual observation the correction corresponding to the time is adopted. When especially large variations occurred readings were also made in the intervals; still, in such cases very large deviations were sometimes apparent, and it was repeatedly remarked that then the movement of the arms steadily increased or that the times in which the index sank 10 inches became smaller the lower its position was, which never occurred with uniform temperature. The reason of this is cer- tainly nothing else but this, that the equilibrium of the warmer and colder air in the room gave rise to special currents that were combined with the movement of the disks. When the temperature during a se- ries of observations changed by two degrees or more, the results deduced became so discrepant that they had to be rejected as entirely useless. For this reason the room before and during the observation could not be heated warm. On the contrary, the oven used for heating the room must be cooled down completely. Even when the sun shone on the window whose shutters could not hinder the warming, nothing remained but to stop the observations. Almost equally troublesome was the friction in the various parts of the apparatus. This varied perpetually, wherefore its value for each individual observation had to be especially determined. Of course it diminished when fresh oil was introduced between the rubbing surfaces, but then the variations became of such magnitude and were often so sudden that the observations were again useless. Only after many days and after the arms had remained for a long time continuously in motion there was established a greater regularity. When this, how- ever, became evident from the measures immediately following each other, then again on the next day the conditions would be remarkably changed. It was therefore necessary that the whole of any series of observations that were to be compared among themselves should be made in immediate succession. In order to render this possible it was necessary to reduce the number of measures as much as was any way allowable, namely, to the number of the desired constants. Such a course is defensible also because the individual readings, in a long series of observations, accord much more closely with the law deduced therefrom than with the similar measures repeated at other times. These preliminary remarks are the result of the great number of ob- servations that I have executed during a half year. These were, es- pecially at the first, extremely unreliable, and only gradually were all the circumstances perceived that come into consideration. The follow- ing observations, which are the only ones serving as a basis for the sub- ~ 16 THE MECHANICS OF THE EARTH'S ATMOSPHERE. sequent computations, were made at recent dates with the greatest possible care and under quite favorable external conditions. The resistance that the arms alone experience for different velocities must first be determined because this must be subtracted every time from the total resistance of the disc and the arms. The following table contains the measures made on this point. G is the weight [in loths] that is placed in each seale-pan, and ¢ tue number of seconds oe- cupied by the index in passing over 1 inch. The velocity of the index i , is therefore equal to Fs according to the adopted unit of measure. The observations were made twice for each load in the seale-pan, and in the second column of the table the two values ¢, and ¢, thus found are given separately, while the third column contains the mean value (t) adopted in the succeeding computation. { Ge ti. ts: t. A. Diff, B. Diff. oa oo 2 —| 0.0 5.725! 5.725] 5,725 0,040 +0.040 | —0.009 | —0, 009 | 0.5| 4.238 4.295 4.2315 0.514| +0.014) +0.498 | —0. 002 | 1.0| 3.488 3.500 | 3,494 1.001} +0. 001 1.007 | +0.007 | 2 2.7251. 2.735! 2.730 1.979 —0.021 2.006; + 6] 3.0 2. 300 2.312 2.306 2.986| —0.014| 3.018| + 18 4.0 2.088 2,038 2.038 3972/ 0.098) 4.001) + 1 6. 1.700 1.700 1 700 5.941 —0.059 5,946 | —- 054" 8. 1.475 1.675 | 1.475 8.066 | +0. 066 8,029 + .029 Earlier observations had shown that the resistances could be ex- pressed by the simple formula a 7B + P s On attempting to introduce a third term containing as factor the first power of the velocity the constant coefficient corresponding had a very slight value and even sometimes a negative one. Therefore I now first chose the preceding expression, and by the method of least squares found Zi —n Oeil S= + 18.703 By the introduction of these constants I obtained the values for G, which are given in the column headed A. The next following column shows the error or the differences (A—G) for each of the weights actu. ally used. We notice that these errors progress very regularly in that both for the smallest and largest values of G they attain the largest positive values while between these they become negative. From this circumstance it may be inferred that the form of tbe formula has not been appropriately chosen, and I therefore repeated the computation using the expression 1 ll GQ 12 ey is aie! tie PAPER BY PROF. HAGEN. Tf ‘This then gave, eG 724 peat 024 § = +15.518 According to this last we obtain for G the values given in the column headed B, whose errors Bb — G are shown in the last column. We remark that these latter do not occur regularly, owing to the change of the signs for the heavier weights, and therefore can be looked upon as accidental errors of observation. The sum of the squares of the errors amounts in the last case to 0.004252, whereas in the first case it was 0.011055, therefore more than twice as great. There is still another reason that favors the introduction of the first power of the velocity. So long as I neglected this term there occurred without exception the inexplicable phenomenon that for observations with disks the numerical value of the constant zafter the negative sign _ was always greater, therefore the friction was always smaller, the larger and heavier the disks were. This anomaly disappeared upon the in- troduction of such a second term. There is, moreover, as the observations show, a peculiar condition in connection with the second term. The coefficient p assumes a very small value or entirely disappears when the screw on the axis is freshly oiled. From this we may conclude something as to its significance, 7. e., it indicates the resistance that arises from the viscosity of the oil and which is proportional to the velocity. When disks are attached, the resistance peculiar to them is found when we subtract from the observed resistance that which the arms experience for equal velocities. This latter, however, is so variable that we must measure it anew every time, and since it assumes various values within even short intervals, therefore there remains only one method to determine the value of the three constants ¢, p, and s, namely, to allow the arms to revolve alone with three different velocities both before and after each observation. When, however, as usually hap- pened, a second measure again gave somewhat different values, then the appropriate mean value corresponding to the intervening time should be used in the computation. In the resistances of the disks found in this manner the second term proportional to the velocity is no longer contained, because the influ- ence of the viscosity of the oil has already been allowed for in the resistances of the arms. The constant z is, on the other hand, so variable that it must be specially deduced from each series of observa- tions. 80 A 2 18 THE MECHANICS OF THE EARTH’S ATMOSPHERE. The following observations were made with two square disks of 6 inches on each side.* G’ indicates the weight placed in each seale pan, and this changes to G when we subtract the weight required to over- come the resistance of the arms for equal velocities. The second col- umn contains as before the times during which the index sinks by 1 inch, as found from the two measurements respectively. G@ t! t! t G A Dif. | loth sec. sec. | sec. loth. loth. loth. 1 942) |). cee 9.42 1.117 1. 064 —0.053 | 2 1326 |oceseeen | 7. 32 1. 986 1. 983 — 003° | B | 2D Ieee ee | 6.2 2.860 | 2.875 | + .015 | 4 | 5.51 | 5.54 | 5.525 3. 739 3. 734 — .005 |} 6 | 4.62 | 4.63 | 4.025 | 5.492 | 5.472 | — .020 | 8 | 4.02 | 4.04 | 4.03 7.231 | 7. 31d + .033 | | 12 | 3.35 | 3. 33 3.34 | 10.737 | 10.798 + .061 | | 16 | 292 | 2.92 2.92 14.251 | 14.233 — .016 | 20 | 2.62 | 2.64 2. 63 17.770 | 17.625 — .145 | 24 | 2.39 | 2.40 2.395 | 21.247 | 21.323 + .076 | 28 | 2.23 | 2.92 9.225 | 24.760 | 24.760 . 000 I =e aaaenaiaaniaenenaeatee = . Adopting the expression, G2: + 1 Y f2 I find as most probable values c= — 0.335 y+ 124.44 From this the values of G given in the column marked A are deduced for the respective times. The errors of these, as contained in the fol- lowing column, vary so much in sign that we can consider them as accidental and there is no reason to introduce still another term in the above expression. In this connection it must still be mentioned that when in the computation of the eariier observations I have assumed the coefficient p equal to zero, a Satisfactory agreement of the resistances appears for larger disks as soon as I set the resistance proportional to the square of the velocity. This is explained by the fact that the value of the term 7 is very small in comparison with the stronger resistances which the disks experience. [*In all that follows it is to be understood that before and after each series for the determination of the resistance of the disks a special series has been made with the arms without disks for the determination of the combined correction for arms plus friction, and that thence the correction for the resistance due to the arms has been computed. G’ is the weight required to overcome the friction plus the resistance of the disks and arms; G is the weight required to overcome the friction plus resistance of the air to the motion of the disks; z is the weight required to overcome the friction ; a is the weight required to overcome the resistance to the disks. —C. A.] PAPER BY PROF. HAGEN. 19 The resistance of the air against the disks is therefore proportional to the square of the velocity, and a single observation would suffice to give the coefficient r if the value of 2 were known, but since this is so very variable, therefore at least two observations at two different veloci- ties are necessary. The further extension of the measures is unneces- sary, aS already before mentioned, because the greater accuracy at- tained surpasses the other inevitable errors; but for greater security and especially to avoid possible mistakes I have always repeated these two measures, and in such a way that beginning with the less velocity 1 then execute the two measures with the greater velocity and finally re- turn again to the less. From the values of r found in this manner the pressure that the disk experiences for various velocities is directly given. Let abe the known distance of the axis of rotation from the center of the threads wound round the spindle and & the distance of the same axis from the center | of pressure of the air against the disk, then this pressure becomes Ji G But : is the velocity of the thread, hence the velocity of the center of pressure of the disk is SS at GN, and IV Re if we introduce the pressure on a unit of surface, since Fis the whole surface of the disk, we have Dar pa 3 ai ——— iG Be In order to reduce the constant 7 to the barometric pressure of 28 ) inches or 336 Paris lines, and to reduce the temperature to 15° C., we have for an observed pressure, A, in Paris lines, and an observed tem- perature 7 in centigrade degrees during the observations the reduced r == (0.9480-+.0.003477) r. The distances R, on account of the great lengths of the arms in com- parison with the width of the disks, agree quite nearly with the dis- tances of their centers of gravity from the axis of rotation, but they are _ always somewhat larger and there is no reason to omit this correction, which is easily executed. We consider first a rectangular disk whose height is 2 and width b. As the origin of abscissas we may take its center of gravity whose dis- _ tance from the axis of rotation is A, and consider the disk divided into 20 THE MECHANICS OF THE EARTH’S ATMOSPHERE. elementary portions, the area of any one of which is hdx, and the pres- sure that it experiences is Kh (ae (A+a) dx consequently the pressure et the whole disk, found by taking the integral from « = —4btoxr = + 3), is pa=E™ (424 a, b) art? or the average normal pressure on a unit of surface is fe ea). Fo we If now I seek that value of « which belongs to the elementary area that experiences a pressure the same as this average, then it represents the center of pressure for the whole disk. The result is, Viena ia i L? For circular disks we again take A as the distance of the center from the axis of rotation, while the radius of the disk is o. In the division of the disk into elementary vertical sections I indicate the limits of these by the angle g which is measured from the horizontal diameter. The area of such a section is then 2@psin g’d pp and the pressure that it experiences is ap=i Ae (s44 posse: * sin yp’ ap By expanding the binomial and converting the cos’g and cos‘@ into the sines of the multiple angle, the integration becomes very simple and © the greater part of the terms disappear since the integral is taken from cosp = —l1ltocosp=+ 1. We obtain A 5 : D=", = (AP+4 p?) 2 De OS ig api en ts or Fo Pe4 +z") and the section that experiences this average pressure is that whose pm satisfies the equation— A+ p cos gah] aie It follows that in both kinds of disks the difference between A and — the desired R remains very small when, as in my apparatus, A is very large compared with ) and p. Next, a series of observations will be communicated, made with five pairs of circular disks, whose diameters were 2.5, 3.5, 4.5, 5.5, 6.5 inches. — Each time only two different weights were laid in the scale-pan; with . PAPER BY PROF. HAGER. Pt these, however, as above meitioned, the measures were executed twice. The resulting values of z andr are given in the last columns. The other ietters correspond to those above given: p Gi ty t t G Zz 7 ee eee == 2 a 223 = a} 125) 0.75) 5.42] 5.42 | 5.42 | —0.041| | | 9.0 | 2.00] 1.988 | 1. 994 | 44.058 | —0.683 | 18.850 | 1.75) 1.5 | 5.31) 5.30 | 5305, 0.690 | 14 | 200] 1.98 | 1.990] 9.054] —o.679| 39,545 | B25.) 12 | 5.76 | 5.68 | 5.720| 1,302 | | | 20 | 2.04] 2.03 | 2.035! 15.270! —o.722| 66,243 | 275| 3 | 589| 586 | 5.875| 92.945 | | | 24 | 224] 224 | 2240] 20.079| —o.¢671 | 104,117 | 3.25 3 | 6.97] 6.89 | 6.930) 2.521 | | (8 | ao | Bae 2.435 | 24. 670 | —0, 599 | 149, 827 | In order from this to find the pressure on the unit of surface, or k, we - have to assume the lever arm a=0.81705 inch, as already shown above. The following table contains the values of R, as well as the reduced r, and the surfaces of the disks F, as to which latter it is to be noticed that after more careful measurements the radii of the second and third disks resulted 1.745 and 2.245: TABLE I. | p | esa Rae: 2.245 2.75 3. 25 INGRAM listec eee NN! olny lt ame wa | : | R | 97.252 | 97.754 | 98256 | 96.760 | 99.260 “Reduced r | 18.791 | 38,463 66 165 | 104.095 | 149. 942 F | 4.909 9.566 | 15.834 | 23.758 | 33.182 | k Nee 23 | 2.5199 2700 | 2.3476 | 2.4028 | 2.4810 | ives Reduced to standard density ot a In order to avoid too small numbers these values of k are given too large, and must be divided by one million in order to present the desired constant factors, which, multiplied by the squares of the velocities in inches, will give the pressures in loths for each square inch of the disk. This same multiplication of k is also continued in the following para- graphs. Many days later I repeated these observations with the same disks. The results were— p G! | & to to | G Zz r | | | laeer et Peay ’ | } 1.25| 1 | 500] 02) 5.01 | 0.168] —0.592/ 19.091 | stone iy sTsSt hee Th St sh 4. 641 | TNO Deol 1 a esqoens elo ie Onze 1 16 1,87 | 1.87 |, 1.87 10.405 | —0.708 | 38. 861 | Dazoy |i 2 5.67| 5.70| 5.685 | 1.329 | | u 20 2.05| 2.04! 2,045 | 15.291! —0.746| 67.066 2.75 3 5.74) 5.79 | 5.765 2.338 | 24 9.23| 2.24] 2.235 | 20.025} —0.790 | 103.983 3.25 4 6.06| 6.09] 6.075| 3.391 28 2,.45| 2.43| 2.44 24.633 | —0.694 | 150.786 ao THE MECHANICS OF THE EARTA’S ATMOSPHERE. The values of # and F are the same as in the first series. The follow- ing values of k are computed from the reduced r: TABLE II. ns ~1 o p | 1.295 | 1.745 | 2.245 \ | | ' | | Reduced r | 18. 952 38.576 | 66.575 | 103,221 149. 683 a | k | 2.2804 2.3549 2.4176 2.4602 2.5154 | | It evidently results that k becomes larger as soon as the surface of the disk increases, as also that the differences are proportional, not to the increase of the surfaces, but to the increase of the radii. Measures were also made with square disks whose sides measured = 2, 3, 4, 5, 6 inches, respectively. These gave— db | @ |] 4 c t | @ pO | CMnilea | 2| 0.5| 5.80| 5.86/| 5.830| —0.188 | 10 1.24 | 1.83] 1.835 | +4101] —0.660| 16.042 | 3 1 6.00| 5.95; 5.975 | 10.346 | 14 1.97| 1.96] 1.965| 8.810| —0.684| 36.774 4 2 6.06 | 6.03] 6.045 | 1.364 | 20 2.08! 2.08] 2.080! 15.383] —0.519 68.798 5 3 5.99 6.06 6.025 2. 364 | | 24 2.30| 2.28| 2.290) 20.168) —0.643 | 109.125 | 6 4 6.50} 6.43) 6.465) 3,448 | | | 23 2.55 | 2.54! 2. | 545) 24.874 | —0.488 | 164.270 | The closer investigation showed again that the surfaces of the disks in part needed some small corrections, as in the following Table IIIT: TABLE III. | | | b 2 2 | 5 64} | | | | | | | R 97.002 | 97.504 | 98. 008 | 98.512 | 99.015 | | Reduced r | 15.607 | 35.810 | 67.053 | 106.455 | 160.522 er | 4.000 | 8.977 | 16.000 | 24.958 | 36.000 | k | 2.3317] 2.3472] 24981] 2.4338) 2.5055 | | | The following results were given by a subsequent repetition of the same observations : ers ‘| bb | @ ty | ty t G z r | : i 2 ee ee : 2 | 0.5 5. 76 5.79 | 5.775 | —0.149 | —0.630/ 16.020 j 10 1.84 1.83 1.835 | +4. 128 i 3 a 5. 96 5.94 | 5.950 | +0.397 | —0.641 36. 744 1 14 1. 96 1.97 | 1.965 8. 876 4 2 5. 74 5.78 | 5.760 1.371 | —0. 608 68, 976 20 2.07 2.07 | 2.070 15. 387 5 3 5. 92 5.93 | 5.925 2.415 | —0.714/) 109. 855 24 2. 29 2.29 | 2.290 20. 233 6 4 6. 26 6.26 | 6.260 3.485 | —0.700 164.000 | 28 2. 53 2.53 | 2.530 24, 922 PAPER BY PROF. f1AGEN. 23 According to this, the values of k are: TABLE IV. Per ltt Ft | Peet Sh! So ag Reduced r..| 15.704 | 35.998 | 67.524 | 107.493 | 160.378 k..| 2.3461] 2.3595 | 2.4452| 9.4574] 2.5032 By connecting among themselves the two first, as also the two last series of observations, the law according to which the value of k& de- pends on the size of the disk may be approximately recognized, but _ the relation between the two forms of disks does not appear clearly. In _ order to discover this I tried allowing circular and square disks to run _ one immediately after the other, the radius of the first being 0.5 greater than the side of the latter. From this, however, it could only be in- ferred that for equal areas the resistance of the square disk is the _ greater. In order to recognize the influence of the shape I tried also disks which formed equilateral triangles of 7.6 inches on each side, which were fastened in such a way that one of the sides stood vertically at the end ofanarm. The area of each disk measured 25 square inches, agreeing, therefore, to within a very small quantity, which subsequent accurate measures showed, with that of the square disk of 5 inches on aside. As I observed these two pair of disks one immediately after _ the other under the same load, it appeared that the square disk re- volved somewhat more rapidly. This result, however, was not decisive, in that the distances of the centers of pressure from the axis of rota- tion, or &, did not remain the same. In this respect it may be men- tioned that when the side of the equilateral triangle =) and its altitude =h=b cos 30° and the distance of the center of the surface from the axis of rotation is A, we then find R=V(Ae + RR) A complete series of observations, together with the preliminary and the concluding determinations of the value of p and s, gave the following: Gi | t | G | Zz r | | | | | 3 | 5. 91 2. 220 [oe seeeeee: ects eramnaraell| 6 BG TERN CER eee edecie sk aca 10 3. 43 | 8.081 |.....-----|-----en-seee | 28 2.12 23. 525 —0. 875 +108. 640 _ After the computation of R=98.204, as also after the reduction of F and r there is found : K=2.5026. 24 THE MECHANICS OF THE EARTHS ATMOSPHERE, Directly following the above, the same observations were repeated with the square disk of 5 inches on a side with the following results: | Si SSROGIN ® WOON acs. vac ascchdeSecue 6| 4.40 RTO Wo oe ees i aia eee Wea 0a a8 465) SOME AIO Vyas ole ee | 28) 2.10) 23,448 | 0.875 | 4107. 390 irom tnese latter there finally resulted k= +2.4491, The results thus far obtained warrant the suspicion that for equal areas of the disks, the resistance becomes smaller the shorter is the de- viated path that the air must describe in order to pass around the disk. Hence it is to be expected that the resistance would become especially small for long and narrow disks. Consequently I took a pair of disks 1 inch broad and 16 inches high, which therefore had the same area as the square disks of 4 inches on aside. These I allowed to run interchangeably with the square disks and under equal loads, but most unexpectedly the velocity of the square disks was always somewhat greater than the narrow ones. This was so much the more remarkable as the square ones, on account of the greater distances from the axis of rotation, were expected to show a greater resistance. As at first I allowed these long disks to run under only two different loadings, I found | 2 6.33 6. 69 6. 51 LOMA) |o Secrece ce iseineseceree | | 20 2.07 | 2.09 2.08 15. 488 —0. 075 67. 332 For the feeble load the velocity had shown very discrepant values. Therefore the repetition of the observation was important, and for greater security this was done on the following day for six different loads. Gh t G A Diff. | as he eae | 1| 851} 0.748 0.743 | —0, 005 21 6.28] ~ 1.538! 1.508| —0.030 4| 4.48; 3049| 3.127) 40.078 8 | 3.23| 6.254] 6.174 | —0.080 | 16} 2.28) 12.495] 12.564 | +0. 069 1.87 18. 790 13.760 | —0.030 | PAPER BY PROF. HAGEN. 25 From this there results as the most probable values 2=— 0171 r=+66.199 If these constants are introduced into the expression for G, the latter assumes the values given the column headed A, whose departures from the observed G are given in the last column. The surfaces of these disks measured very accurately 16 square inches, and the distance of the center of pressure was 96.500 inches. After reduction to the adopted normal density of the air the con- stants r for the two series of observations became respectively 66.65 and 66.373 whence k = 2.5286 and k = 2.5178 respectively. The constant coefficient of the square of the velocity resulted there- fore in this case as great as the series of observations III and IV would have led us to conclude would have been found for square disks of about 7 inches on each side; consequently the suspicion arises that the increase in the value of k is not proportional to any linear dimen- sion, but to the circumference of the disk. A simple consideration leads to the same result. All previously given observations show that a disk of an area # moving with a velocity ¢ through the air in, a direction normal to its plane experiences a resistance D=k Fe. If we analyze k into two terms k=a+pfp where p expresses the circumference of the disk, then the first part of D, namely, a Fe’, corresp onds to the ordinary assumption. The second part pet 6 =e. p. 0.16 contains, as a factor, the mass of the passing air, which is proportional to Fe, also p, or the circumference of the disk, which the air touches, and finally the velocity c, under which this contact takes place. It appears therefore that the cause of the increase of the resistance can be none other than the friction of the air against the edge of the disk. However, as the experiments already mentioned in the preface have shown, the air immediately adjacent to the edge of the disk flows perfectly regularly past it, without taking up any whirling motion, which latter first forms behind, where the air protected by the obstacle is touched. Friction is therefore (in accordance with the experience * with water) proportional to the first power of the velocity. Before I computed the appropriate constants by the combination of all of the observations, I made an attempt to compare among them- **‘On the Influence of the Temperature on the Movement of Water in Tubes.” Hagen, Math. Abh. Akad. Wiss. Berlin, 1854, p. 69. 26 THE MECHANICS OF THE EARTH’S ATMOSPHERE. selves the twenty-one observations made with circular and square disks, in order to convince myself as to what assumed value of p presented the greatest agreement. If I assumed for p the circumference of the disk, there resulted a = 2.210 p=00132 and the sum of the squares of the outstanding errors was [ax] = 0.01425 By introducing the square root of the surface I obtained a = 2.200 fp = 0.0526 [wx] = 0.00976 I then put p, equal to three different transverse lines drawn through the center of the disk. First, the smallest transversals, for which of course the sides of the square and the diameters of the circles were directly introduced. This gave a = 2.204 fp = 0.0487 [xx] = 0.01282 For the greatest transversals, namely, the diagonals of the squares and diameters of the circles, | obtained a = 2.230 f = 0.0354 [xa] = 0.02221 Finally, for the average transversals which I drew [centrally] across the disks at distances apart of every 3 degrees, and took the arithmeti- cal mean of all, I found a = 2,200 f = 0.04675 [xx] = 0.00966 It is evident that this latter method must lead to very nearly the same result as the introduction of the square root of the surface since f diminishes in the same ratio as the coefficient of (6 increases. Judging by the sums of the squares of the errors it would, according to this, be advisable to introduce the square roots of the surfaces as — factors, but this is impossible, even although the results of the observa- tions made with the long disk should be included under this same law. There only remains to introduce the circumference as a factor, even although in this case notable departures still remain. These are in no- wise however errors of observation, but result principally from the inevitable variations in friction. An error of 1 per cent. in the time could scarcely have been made, but still such discrepancies and even larger ones show themselves very frequently since the friction induced now faster and now slower motion. Nevertheless, from the following collection of all the observations it results that these have led toa quite trustworthy result. PAPER BY PROF. HAGEN. 2Y Radii and sides. k p al Diff. Squares. | Circleo—= 1.25| 2.270 7. 854 2.338 | +0.068 | 0.004624 | 1.75| 2.348/ 10.996] 2.368] +0.020 0400 | 925) 2.403) 4.137] 2.397] —0.006 0036 2.75 2.481 |. 17.279 2.497 | 0.054 2916 | 3.25 2.520} 20. 420 2.456 | —0. 064 4096 | | Circlep= 1.25 2, 289 7. 854 2.338 | 10. 049 2401 | 1.75| 2.355| 10.996| 2.368| 10.013 0169 | 2.25) 2.418 | 14.137} 2397] —0.021 0441 | 9.75 2.460 | 17.279 2.427} —0.033 1089 3.25 2.515 | 20.420 2.456 | —0.059 3481 Squareb= 2. 243393 |e eneNO 2,339 | +0.007 0049 | 3 2.347 | 12.0 2.377 | +0.030 0900 By 2.428 | 16.0 2.415 | —0.013 0169 5. 2.434) 20.0 2.452} -L0. 018 | 0324 | 6. 2,505 | 24.0 2.490 | —0.015 | 0295 | Squareb= 2. 2,346| 8.0 2,339 | —0.007 0049 By 2, 360 | 12.0 2.377 | +0.017 0289 4} 2.445) 16.9 2.415 | —0.030 | 0900 5. 2.457| 20.0 2.452 | —0.007 | 0049 6 | 2503] 24.0 2.490 —0.013 | 0169 Triangle........-. 2.503 | 22.795 2.479 | —0. 024 | 0576 Squareb= 5. 2. 449 20.0 2.452 | +0. 008 | 0009 Parallelogram....| 2.529] 34.0 2.584 | +0. 055 | 3025 Parallelogram ....| 2.518 | 34.0 2.584 | +0. 066 | 4356 | | 0, 030742 | From this table there results as the most probable values a = 2.2639 6 =0.009416 The values of k computed from this are given in the column A; from the differences in the next column, with reference to the observed values of k, there results the probable error 0.0252, and we find the probable error of a equal to 0.01338, or about 3 per cent., and of / equal to 0.000719, or about 74 per cent. Although the reliability of these results, especially in their applica- tion to still larger surfaces and greater velocities, leaves much to be desired, still scarcely any important higher degree of accuracy is to be attained with apparatus that is similar to that above described. On the other hand the concluded law of resistance would be in an impor- tant degree confirmed or corrected, if on a firm rod in front of a loco- motive, disks are fastened, whose pressure could be measured by the tension of a spring, while the milestones on the roadside would serve very conveniently for the determination of the velocity.* *[This experiment has been carried on recently by Wild and others, but the resulting value of & is not so reliable as that deduced from observations with large whirling machines.—C. 4. ] 28 THE MECHANICS OF THE EARTH’S ATMOSPHERE. From the preceding it results that the pressure of the air against a plane disk turned normaliy towards it is 2.264 + 0 00942 x Pre 1,000,000 Where D is expressed in old Prussian loths and p, F, and ¢ in [Rhenish] inches. According to the above, the pressure against a square disk of 1 square foot area, moving with a velocity of 50 feet per second, would for example be 140.8 loths, or nearly 4.4 pfund. For reduction to metric measures and weights I take not the metre itself but the decimetre as the unit of measure for lengths and surfaces, in order to remain within the limits of the observations. Therefore the resistance of the air for a temperature of 15° C. and a barometric pressure of 28 Paris inches,* expressed in grammes, amounts to (0.00707 + 0.0001125 p) Fe, Where p represents the circumference of the disk, / the sectional area, and ¢ the velocity expressed in decimetres. The pressure that very small disks experience when struck normally by a current of air is also given by another simple consideration, whose correctness has in general been confirmed by many experiments. ‘These experiments indeed are limited, so far as known, to streams of water; but the expansibility of the air is certainly in this case without influ- ence, since the observations mentioned in the preface, upon the direc- tion and strength of currents deviated in front of opposing disks, showed identical results with water and with air. Imagine a vessel filled to the height 2 with a fluid of which one unit of volume or 1 cubic inch weighs y loths. The bottom of the vessel therefore experiences on each square inch a pressure equal to yh, when no side pressure exists. If there is suddenly made therein an opening of 1 square inch, the outflow of the fluid through it begins with the velocity ¢= 2/ght, and if we catch the stream by an equally large sur- face directed normally against it, then the pressure D upon this is again equally as great as before upon the bottom of the vessel, namely, yh. From this we have D= J —- os ¥. ? D= yl ge For the density of the air above adopted its specific weight is 0.001223; therefore a cubic inch weighs 0.001495 loth, and g is equal to 157.6, if the semi-acceleration due to gravity is expressed in inches. Irom this we have these results: D = 0.000001992 = 1.992 millionths of a loth. * The density is that of air at 15° C. and 28 Paris inches or 757.96™™ under gravity at Berlin (52° 30’), but strictly speaking the pressure should be stated in standard measure as 758.47™™ under gravity at 45° and sea level. tg isthe height failen through in 1 second, or one-half the acceleration due to gravity. PAPER BY PROF. ILAGEN. 29 As the first term of the above value of k comes out 2.264 or larger than this by nearly 14 per cent., the stronger resistance deduced from the observations is explained by the rarefaction of the air occurring at the rear of the disk, which rarefaction in the case of an assumed out- flow into empty space does not take place. Although the present investigation is confined only to those posi- tions in which the disks are turned normal to the direction of their motion, still it was important to be convinced that slight and unavoid- _ able deviations from this normal position had no important influence. The pins by means of which the disks were fastened to the arms were directed radial'y towards the axis of rotation. Thus the disks could be given any desired inclination to tbe direction of their motion. One such experience however showed this arrangement to be en- tirely unallowable in the observations, in that the simple relation between the resistance and the velocity of the disk completely disap- peared. The reason for this irregularity is apparent. According as the two disks were inclined downwards or upwards they were pressed up or down by the impinging air, and by so much the more the greater their velocity was. The arms with the inclined disks and with the axis of rotation therefore pressed variably upon the steel point on which the axis rested, and accordingly the screw threads on the axis were varia- bly pressed up or down, whereby the friction each time experienced an important change. When however I inclined one disk upwards and the opposite disk downwards, the axis was pressed to one side, and by so much the more, the greater the velocity was. In order not to change the simple arrangements for fastening the disks, I provided the two 5-inch square disks with roof-shaped piece, in addition, so that in front of the lower half of the disk the inclined plane was turned upwards, and in front of the lower half an equal plane with the same inclination was turned downwards. Each of the two disks thus changed was thus both raised and depressed by equal forces for all velocities, so that the injurious effect upon the axis of rotation dis- appeared. A complete series of observations (wherein both at the beginning and at the end the arms were Set in motion without disks in order to deter- mine the resistance) gave— (a) When the roof surface was inclined 40° to the vertical or to the plane disk, i Oo.ze (b) For an inclination of 20° to the vertical, 2— AO) TG: (ec) And for the plane disk itself, therefore, after removing the addi- tions r = 110.93. 30 THE MECHANICS OF THE EARTH’S ATMOSPHERE. If we divide these values by the cosines of 40, 20, and 0 degrees, respectively, there results 109.55, 107.65, and 110.93. The resistances are therefore in accordance with the ordinary as- sumption, proportional to the cosine of the inclination. In case the plane of the plane disk does not include the axis of rota- tion, we should also have to consider the diminution of the surface opposed to the impinging air in consequence of the projection upon the direction of motion, and for both reasons the resistance diminishes in the ratio of the square of the cosine of the deviation. Since the disks were always adjusted by the plumb line, therefore an error of 2 degrees, by which the resistance would only be diminished by its thousandth part, could not easily remain unnoticed. Finally, it still remains to be investigated whether the nature of the surface of the disks, according as they were smooth or rough, had any influence on the resistance. To this end I took two disks, each of which was covered on one side with very smooth paper but on the other with very coarse sandpaper. I allowed these to run with various velocities, exposing each time first the smooth and then the rough side to the impinging air. In both cases the times in which the index described 10 inches remained very nearly the same. The differences were very irregular, and not larger than occurred in repeated experiments with equal pairs of disks. Hence the nature of the surface of a plane disk has no influence on the resistance of the air when the surfaces are normal to the direction of motion. Te ON THE INTEGRALS OF THE HYDRO-DYNAMIC EQUATIONS THAT REPRESENT VORTEX-MOTIONS.* By Prof. HERMANN VON HELMHOLTZ. Hitherto the integrals of the hydro-dynamic equations have been sought almost exclusively under the assumption that the rectangular components of the velocity of every particle of liquid can be put equal to the differential quotients in the corresponding directions of a certain definite function that we will call the velocity potential. On the one hand Lagranget had proven that this assumption is al- lowable whenever the movement of the mass of water has arisen and is maintained under the influence of forces that can be expressed as the differential quotients of a force potential, and even that the influ- ence of moving solid bodies that come in contact with the liquid do not affect the applicability of the assumption. Since now most of the forces of nature that are easily expressed mathematically can be presented as the differential quotients of a force potential, therefore also by far the majority of tlie cases of fluid motion that are treated mathematically fall into the category of those for which a velocity potential exists. On the other hand, even Euler{ had called attention to the fact that there are gases of fluid motion where no velocity potential exists; ¢. g., the rotation of a fluid with equal angular velocities in all its parts about anaxis. The magnetic forces that act upon a fluid permeated by electric currents, and especially the friction of fluid particles on each other and on solid bodies, belong to the forces that can give rise to such forms of motion. The influence of friction on fluids could not hitherto be mathe- matically defined, and yet it is very large in all cases where we are not treating of infinitely small vibrations, and causes the most important deviations between theory and nature. The difficulty of defining this influence and of finding methods for its measurement certainly lay *Crelle’s Journal fiir die reine und angewandte Mathematik, 1858, vol. Lv, p. 25- 85. Helmholtz, Wissenschaftliche Abhandlungen, 1882, vol. 1, pp. 101-134. London, Edinburgh, and Dublin Philosophical Magazine, June, 1867 (4), XXIII, pp. 485-510 t Mécanique Analytique, Paris, 1815, vol. 11, p. 304. t Histoire de V Académie des Sciences de Berlin, anno 1755, p. 292. o ae THE MECHANICS OF THE EARTH’S ATMOSPHERE. mostly in the fact that we had no idea of the forms of motion that fric- tion produces in the fluid. Therefore in this respect an investigation of those forms of motion in which no velocity potential exists seems to me to be of importance. The following investigation will now show that in those cases in which a velocity potential does exist the smallest particles of liquid have no motion of rotation, but that when no velocity potential exists then a part at least of the liquid particles are in the act of rotation. By vortex lines (Wirbellinien) I designate lines that are so drawn through the mass of liquid that their directions everywhere coincide with the direction of the instantaneous axis of rotation of the liquid particles at that point of the line. ~ By vortex filament (Wirbelfiden) I designate the portion of the mass of liquid that is cut out when we construct the corresponding vortex lines passing through every point of the circumference of an infinitely small element of the surface. The following investigation shows that when a force potential exists for all the forces that act upon the fluid then: (1) No particle of liquid acquires rotation that was not in rotation from the beginning. (2) The particles of liquid that at any moment belong to the same vortex line remain belonging to the same vortex line, even although they have a motion of translation. (3) The product of the sectional area by the velocity of rotation of an infinitely slender vortex filament is constant along the whole length of the filament and also retains the same value during the translatory motion of the filament. Therefore the vortex filaments must return into themselves within the liquid or can only have their ends at the bounda- ries of the fiuid. This last proposition makes it possible to determine the velocities of rotation when the form of a particular vortex filament is given at dif- ferent moments of time. Further we solve the problem to determine the velocity of the particles of liquid for a given moment of time when the velocities of rotation are given for this moment, but in the solution there remains undetermined one arbitrary function that must be util- ized to satisfy the boundary conditions. This last problem leads to a remarkable analogy between the vortex motions of liquids and the electro-magnetic actions of electric currents. When in a simply connected space* filled with moving liquid a ve- locity potential exists, the velocities of the liquid particles are equal to and in the same direction as the forces that a certain distribution of *T use this expression (einfach zuasammenhiingenden Raume) in the same sense in which Riemann (Journal fiir die reine und angewandte Mathematik, 1857, Liv, p. 108) speaks of simple and multiple-connected surfaces. A space that is n-times connected is therefore one such that n—1 but not more intersecting surfaces can pass through it without cutting the space into two completely separate portions. A ring is there- fore in this sense adoubly-counected space. The intersecting surfaces must be com- a pletely surrounded by the lines in which they cut the surface of the space. a EO = PAPER BY PROF. HELMHOLTZ. 33 magnetic masses on the surface of the space would exert upon a mag- netic particle in the interior. On the other hand, when, vortex threads exist in any such space the velocities of the liquid particles are equal to the forces exerted upon a magnetic particle by a closed electric current that flows partly through the vortex filaments in the interior of the mass and partly in the bound- ary surface, and whose intensity is proportional to the product of the sectional area of the vortex filament by its velocity of rotation. I shall therefore in the following lines often allow myself to hypoth- ecate the presence of magnetic masses or of electric currents, simply in order thereby to obtain shorter and more perspicuous expressions for the nature of functions that are just the same functions of the co- ordinates as the potential functions, or the attractive forces for a mag- netic particle, are of the magnetic masses or electric currents. By these propositions the forms of motion concealed in that class of integrals of the hydro-dynamic equations not hitherto treated of be- come accessible at least to the imagination even although it be possible to execute the complete integration only in a few of the simplest cases where only one or two rectilinear or circular vortex filaments are pres- ent in masses of liquid that are either unlimited or partially bounded by one infinite plane. It can be demonstrated that rectilinear parallel vortex filaments ina mass of water that is bounded only by planes perpendicular to such filaments, rotate about their common center of gravity, when in the determination of this center we consider the velocity of rotation as equivalent to the density of a mass. In this rotation the location of the center of gravity remains unchanged. On the other hand, for cir- cular vortex filaments, all standing perpendicular to a common axis, the center of gravity of their cross-section advances parallel to the axis. I. DEFINITION OF ROTATION. At a point within a liquid whose position is defined by the rectangular coordinates 2, y, 2, and at the time f, let the pressure be p, the three com- ponents of the velocity wu, v, w, the three components of the external forces acting on the unit mass of the liquid X, Y, Z, and h be the den- sity whose changes can be considered as negligible; the established equations of motion for an interior point of the ai are: J op du ue ae aan Ti 7 ria U = vit ee te | lop 2 12? me i Y-— hoy = tS a v a w * z | i Hi, celia de eae 1)p_dw ow pe i es ye Pa + v ae ' que ov. gw ey oe es 5 30) 4-3 34 THE MECHANICS OF THE EARTH’S ATMOSPHERE, Hitherto, almost exclusively, only those cases have been treated where not only the forces X, Y, Z, have a potential V so that they can be expressed in the form, ‘ Do Vi OW. ay: ae cage ae Se ee ee) , % but also where a velocity potential @ can be found so that ) ) ) “= oP v= PP w=, one at al Gale Deana) ox oy dz The problem is thereby greatly simplified since the first three of equations (1) give a common integral equation from which to find p after we have determined g in accordance with the fourth equation which in this case takes the form 72 72 72 ae Pee ox oy? 2 9 and which therefore agrees with the established differential equation for the potential of magnetic masses that lie outside the space within which this equation hoids good. Moreover, it is known that every function g that satisfies this last differential equation within a simply connected space,* can be expressed as the potential of a definite dis- tribution of magnetic masses on the boundary surface of the space as I have stated already in the introduction. In order that we may be able to make the substitution required in the equation (1b) we must have uv ou v_ ov Jw _g ow __ dv oy ow , 0, ——£ ———=0 oy? ow ye’ ee In order to understand the mechanical significance of these last three conditions, we may imagine the change that any infinitely small volume of water experiences in the elementary time dt to be com- pounded of three different motions: (1) a motion of transference of the whole through space: (2) an expansion or contraction of the particle along the axis of dilatation, whereby every rectangular parallelopipe- don of water whose sides are parallel to the principal axis of dilata- tion remains rectangular while its sides change their lengths but re- main parallel to their original directions: (3) a rotation about some temporary axis of rotation having any given direction, which rotation can by a well-known proposition be always considered as the resultant of three rotations about the three codrdinate axes. *In manifold-connected-spaces » can have several values, but forsuch many val- ued functions as satisfy the above differential equations the fundamental proposition of Green’s theory of electricity no longer holds good (see Crelle Journal, XLIV, p. 360,o0r “The Mathematical Papers of the late George Green”), and therefore fail also a greater part of the propositions resulting from this which Gauss and Green have demonstrated for the magnetic potential functions, which functions are in their very nature always uni-valued. PAPER BY PROF. HELMHOLTZ. oo If the conditions (1c) are satisfied at the point whose coérdinates are t, ), 3, and if we designate the values of u, v, w, and their dif- ferential quotients as follows: ) > Ow UAT al =, COE ox oy 02 w uw, 01=B, co} gu ee =e ’ —$ «= ] oz ox Jw dv du (eC ee frOM-f, '), 3: u=A+a (x—r)+y (y—)) +6 (2-3), v=B+y (x—1)+b (y—)+a (2-3), w=C+f (v4—t)+a (y—y)+e (z—3), or when we put: p=A (x—t) +B (y—») + C (z—3) +4 a (w—r)?-+36 (y—h)?+3¢ (2—3)? +a(y—) (2-3) +A (w—t) (#3) +y (e—2) (y—D), there results : IP ORG On, 10 = ; oa“ oy a2 == It is well known that by a proper selection of another system of ree- tangular codrdinates 2, y;, 21, Whose origin is at the point r, ), 3, the ex- pression for ~ can be brought into the form: PHA, 4B, W+O1 ats a aP+4hd, yP+s c 2? where the component velocities , v1, w;, along these new codrdinate axes have the values: M=A4X, MN=Hi+Hn YH, w=C+c¢ The velocity uw, parallel to the axis of 2, is therefore alike for all liquid particles that have the same value of z,. therefore particles that at the beginning of the elementary time dt lie in a plane parallel to that of y; 2; are also still in that plane at the end of the elementary time — dt. This same proposition is true for the planes v, y, and x, 2;. There- fore when we imagine a parallelopipedon bounded by three planes parallel to the last named coérdinate planes and infinitely near to them, the liquid particles inclosed therein still form at the end of the time dt a rectangular parallelopipedon whose surfaces are parallel to the same coérdipate planes. Therefore the whole motion of such an indefinitely small parallelopipedon is, under the assumption expressed 36 THE MECHANICS OF THE EARTH'S ATMOSPHERE. in (le) compounded only of a motion of translation in space and an ex- pansion and contraction of its edges and it has no rotation. We return now to the first system of codrdinates, that of x, y, 2, and imagine added to the hitherto existing motion of the infinitely small mass of liquid surrounding the point 1, }),3,a System of rotatory motions about axes that are parallel to those of 2, y, z, and that pass through the point 1, ), 3, and whose angular velocities of rotation may be &, 7), ¢, thus then the component velocities parallel to the codrdinate axes of x, y, 2, aS resulting from such rotations are respectively : Parallel to x: | Parallel to y: | Parallel to z: 0, | (2—2) Ss —(y—)) &) weal a) 15 | 0, (x—y) 1)) (y—) &, | —(#—%) ¢, | LF Therefore the velocities of the particles whose codrdinates are a, y, 2, become: u=Ata(x —1)+( 7 +5) (¥—v)+(6 — 7) (2-3), v=B+ (y—€) (w—t)+b (t—y)+(a +) (2-3), w=O+ (B+y) (w—2) + (a—€) (y—») +e (2-3), whence by differentiation there results: av ow csi: Sens DS — 4G de OY gw du ae | eo ey Sy 0 ies” wm ep OY | ore relmanels (2) OU ov | uy oa \ Therefore the quantities on the left-hand side, which according to equation (le) must be equal to zero in order that a velocity potential may exist, are equal to double the velocity of rotation about the three coordinate axes of the liquid particles under consideration. The exist- ence of a velocity potential excludes the existence of a rotary motion of the particles of liquid. As a further characteristic peculiarity of fluid motions that have a velocity potential, it may be further stated that in a simply-connected space S, entirely inclosed within rigid walls and wholly filled with fluid, no such motion can occur; for when we indicate by n the nor- mal directed inwards to the surface ef such space then the component dP velocity Mi directed perpendicular to the wall must be everywhere PAPER BY PROF. HELMHOLTZ. 37 equal to zero. 'lherefore, according to the well-known Green’s theo- rem,* IT Su Ee ox a) ALG) eid fed is — fos on 7 where, on the left hand, the integration is to be extended over the whole of the volume S, but on the right hand over the whole surface S whose : : IP . elementary surface is designated by dw. If, now, << is to be equal to zero for the whole surface, then the integral on the left hand must also be zero, which can only be true wuen for the whole volume S CEP OE eh ox i oy Oca : that is to say, when there exists no motion whatever of the liquid. Every motion within a simply connected space of a limited mass of fluid that has a velocity potential is therefore necessarily connected with a motion of the surface of the fluid. If this motion of the surface, We 6.5 oe, is known completely, then the whole movement of the ineclosed fluid mass is also thereby definitely determined. For suppose there are two functions, yg, and ae that ec satisfy the equation oP eae) - + oy’ cS ES \ in the interior of the space S, and also the condition <= ra for the surface of S, where 7 indicates the value of 2P % deduced from on the assumed motion of the surface, then would the dean (P,—P,,) also satisfy the first condition for the interior ot the space S, but for the surface this function would give (P,— Pi) =(). an pes whence, as just shown, it would follow that for the whole interior of 8 we would have I(Pi-— Pr) = d (P,— Py) = I(Pi— Pir) =" oa oy ie; dz Fa, Therefore both functions would also correspond to exactly the same velocities throughout the whole interior of NS. Therefore rotations of liquid particles and circulatory motions within simply-connected wholly inclosed spaces can only occur when no veloe- ity potential exists. We can therefore in general characterize the mo- tions in which a yoy potential does not exist, as vortex motions. *This is ee ae an in Crelle Journal, vol. Liv, p. 108, fleas alluded to, and which does not hold good for complex or manifold- pammecred space. 38 THE MECHANICS OF THE EARTH’S ATMOSPHERE. II]. PERMANENCE OF THE VORTEX MOTION. We will next determine the variations of the velocities of rotation &, 7, € during the movement (of the surface) when only such forces are effective as have a force potential. I note first in general that when 7 is a function of a, y, 2, t, and in- creases by the quantity dy, while the last four quantities increase by 0x, Oy, 02, and 6 t, respectively, we have: Sp = rot oe = but Oy os Pe, If now the variation of #/ blite the short time otis to be determined for one and the same particle of liquid, we must give the quantities Ox, Oy, Oz the same values that they would have for the moving parti- cle of liquid, namely : or =uUdt, OY = V0t, 02 = 0 Ot, and obtain: _ dip OY oY Ww SS dt + u as v oy +w de I shall in the following always use the notation = only in the sense at pit indicat es the variation of 7 during the element of time d t for ao same particle of water whose codrdinates at the beginning of the time dt were x, y, and z If by differentiation we eliminate the quantity p from the first of the equations (1) and introduce the notation of equations (2) and substitute for the forces XY, Y, Z the expressions in equation (la), we obtain the following three equations: bas ue ae As ae yt eS a . yw A acres ov, pdt 3 ot ere + 7 yy + eae e ( ) OF Ow ow ow Bi ge 1 Tay he al or o& ou dW BF Son toe + Soe O77 = v — a & oc! Me, ) lege. ae eee Obl ue y ral oy +€ eo f ( ) o€ 7 i ov ou | St 8 jz tT 9e + Oe | If §, 7, and € tor any particle of water are simultaneously zero then also— 0§ = 5? = O€ One 7 OGRE Therefore those particles of water that do not already have a rotatory motion will receive none in the subsequent time. =r PAPER BY PROF. HELMHOLTZ. 39 As is well known, we can combine rotations together after the method of parallelograms of forces. If §, 7, € are the velocities of the rotations about the codrdinate axes, then the velocity of rotation (q) about the instantaneous axis of rotation is I= VETTE and the cosines of the angles that this axis makes with the coérdinate axes are respectively 2, .° and a If now we consider an infinitely small distance qe in the direction of the instantaneous axis of rotation, then the projections of this distance on the three codrdinate axes are respectively ¢§, «7, aud «¢€. While at the point x y z {at one end of qe] the components of the velocity are U. Vv, Ww, they are at the other end of ge respectively ou ou W=UtES ates +é oe” 0 \1= vp e8= rte +é 7 a wwe = ae: yp mop a Cae Therefore in the course of the seams time dt the projection of the distance of the two particles of liquid that at the beginning of dt were distant by the quantity gé has attained a value that, considering the equation (3), can be written as follows: 05 4 é§& + (um—U) dt=e( §+ ot at ), Spas en+(n—v) ate n+ sia ) 7 oc \ eC + (wi —w) dt=e( (es ott ): On the left are the projections of the new location of the connecting line gé; on the right are the projections multiplied by the constant factor ¢ of the new velocity of rotation. It follows from these equa- tions that the line connecting the two liquid particles that at the be- ginning of the time d¢ limited the portion ge of the instantaneous axis of rotation will also after the lapse of the time dt still coincide with the now changed axis of rotation. When we, as above agreed on, call a line whose direction through- out its whole length agrees with the direction of the instantaneous axis of rotation of the particle of liquid at each point, a vortex line, we can express the proposition just found as follows: Every vortex line remains permanently composed of the same particles of liquid while it progresses with these particles through the liquid. 40 THE MECHANICS OF THE EARTH’S ATMOSPHERE. The rectangular components of the velocity of rotation increase in the same ratio as the projections of the portion ge of the axis of rota- tion; hence it follows that the magnitude of the resulting velocity of rota- tion varies for a given particle of liquid in the same ratio as the distance of this particle from its neighbors in the axis of rotation. Imagine vortex lines drawn through all points of the circumference of an indefinite small surface. Then will a thread of infinitely small section, which is called the * vortex filament,” be thereby cut out of the liquid. The volume of a portion of such a filament included between two given particles of liquid, which volume according to the proposi- tions just proven always remains filled by the same particles, must remain constant during its progressive motion; therefore its section must vary in the inverse ratio of its length. Hence we can express the last proposition thus: In @ portion of a vorter filament, consisting of the same particles of liquid, the product of the velocity of rotation by the section ever remains constant during its translatory motion. From equation (2) it directly follows that— 6G om, 6 _ je Oy ae ee eee Hence it further follows that— it (yes enn oe d oF Na = Nae day ag | | Ox + yt a y where the integration can be extended over any arbitrary portion S of the mass of liquid. When we partially integrate this there results: [ f& dyde+ ffn da dz + L fs dx dy=0 where the integrations are to be extended over the whole surface of the volume of S. If we let dw be an element of this surface and a, /, y the three angles that the normal to dw drawn outwards makes with the coordinate axes, then— dy dz=cos a do, dx dz=cos fia, dx dy=cos y de; therefore {f(é cos a+7 cos 6+ cos y)dw =0, or when we let o be the resulting velocity of rotation and 4 the angle between this velocity and the normal Sf fe cos 6 dw=0, where the integration is to be extended over the whole surface of S. Let S be a portion of a vortex filament bounded by two infinitely small planes @, and @,, perpendicular to the axis of the filament, then will cos 6=+1 for one of these planes and cos 6=—1 for the other, but cos 4=0 for the whole of the remaining surface of the filament; conse- quently, if o,and o,, are the velocities of rotation at w, and o,,, respect- ively, the last equation reduces to 0, @,=0,, @,, PAPER BY PROF. HELMHOLTZ. Al whence it follows that the product of the velocity of rotation by the area of the section is constant throughout the whole length of the vortex fila- ment. It has already been shown that this product does not change during the progressive motion of the filament. It follows from this that a vortex filament can not possibly end any- where within the fluid, but must either return into itself, like a ring within the fluid, or must continue on to the boundaries of the fluid. For in case a filament ended anywhere within the fluid it would be pos- sible to construct a closed surface for which the integral [o cos 4 dw is not zero. Ill, INTEGRATION BY VOLUME. When we can determine the motions of the vortex filaments present in the fluid we can, by means of the above established propositions, also determine completely the quantities §, 7, and €. We will now consider the problem to determine the velocities u, v, and w from tie quantities §, 7, and €. Within a mass of liquid that fills the region S let values of 3, 7, and € be given, which quantities should satisfy the condition that— cece Mae Wea). |) Ut eogyl oe OY O% Such values of uw, v, and ware to be found as may, throughout the whole region S, satisfy the conditions {of Eq. (1,) and (2), viz. | ju ou dw nea heen ee = (CT os Ma Stan RLS ia hat) oi nl lig) ou” dy” Oa dv du _og | dz” OY aS | yu \Uu i) GS SiGe ANG) ° (2) ja” a2 me du ov 9¢ oy ow piers to which is still to be added the condition demanded by the boundary of the region S, according to the nature of the specific problem in hand. According to the distribution of &, 7, €, as above specifically given, there can occur on the one hand such vortex lines as shall return into themselves within the limits of the region S and on the other hand such as extend to the boundary and there suddenly break off. When this latter is the case then we can certainly prolong these [fragments of| vortex lines either along the surface of S or beyond S until they re- turn into themselves, so that a larger space S; exists that contains only closed vortex lines and for whose whole surface both &, 7, € and their resultant o itself are all equal to zero or at least & COS a+7 cos 6+ cos y=o cos J=0. 42 THE MECHANICS OF THE EARTH'S ATMOSPHERE. Here, as before, a, 6, vy indicate the angles between the coérdinate axes and the normal to the appropriate portion of the surface of 8). / indicates the angle between the normal and the resulting axis of rotation. We now obtain the values of u, v, w, that satisfy the equations (14) and (2) by putting “a= oP oN et oM ] Ov oY oe | L.9P ei 3x4 ee oy my i ox r (4) IP oM aL | wa aS Oz a oY \ and determine the quantities L, 1, NV, P by the conditions that within the region S,; we must have Lb ol oe z 7 gx? © oy? T Oz > | eM MOM | oa? Dy? jee { (5) ON ON ON oe | jae © oy? © 922 ~ “= | PD Soe Weg, ga? * Dy? © ge? ~~ § The method of integrating these last equations is well known. JL, M, N are the potential functions of imaginary magnetic masses distributed through the space S, with the densities = at = P is the poten- Zt GE WG, BERL tial junction for masses that lie outside of the region S. If we indicate by r the distance from the point x, y, z to the point whose codrdinates are a, b,c; and by &,, 7%, €, the values of &, 7, € at the point a, b, ¢, then L= - 3 | Ga da db el a ae "a da db ac s . (5a) 2a \\ ot 7 ; 17 te | N=—>5- ~“da db de, a7). 1 where the integration is extended over the space S, and rp P= k | — da db de, 5 where é is an arbitrary function of a, b, c and the integration is to be extended over the exterior space S}, that includes the region 8S. The PAPER BY PROF. HELMHOLTZ. 43 arbitrary function k must be so determined that the boundary con- ditions are satisfied, a problem whose difficulty is similar to those [difficulties that are met with in problems] on the distribution of elec- tricity and magnetism. That the values of w, v, and w, given in equation (4), satisfy the condition (14), is seen at once by differentiation and by considering the fourth of equations (5). Further, we find by differentiation of equations (4), and considering the first three of equations (5) that: an dw oe d ets aM = ie * iy oa Carle ar ) yt Ov Oe oy or NOs ) Su oN das OG C se eek oy ys i Of 4° Go The equations (2) are also equally satisfied ee it can be shown that throughout the whole region 8S; we have ee a0. Bare ibs eet SED) That this is the case results from the equations (5a) which give Lt Ea(x — a) ie De \| ee a da db de, or after partial integration : Lee ty gu _ tu | | Ea db dc — i | | I 05« da db de Ox 22 i a G NC oa oM_1((% dade — = = Me da db de dy 27 Yr ra | jee | [ee adb — Dep ae If we add these three equations aa again indicate by dw the element of the surface of S, we obtain: Ce ee a = oS = = ae aa | (§, coSa+ 7,c08 6 + ©, cos ys da / 05a 4 Ma a uf | ns (+ i ab +. = Vda db de. But since throughout the whole interior of the space S,we have dG Ma a - a e e . . . : x 5 au oa db +° (2a) and since for the whole surface we ae ES, COs a7 COS. p + Gs cosy, = 0 oa le, ol tos (20) tT fe == du db de. 44 THE MECHANICS OF THE EARTH’S ATMOSPHERE. therefore both integrals are equa! to zero and the equation (5d) as well as the equations (2) are satisfied. The equations (4) and (5) or (5a) are thus true integrals of the equations (1,) and (2). The analogy mentioned in the introduction between the action at a distance of vortex filaments and the electro-magnetic action at a dis- tance of conducting wires, which analogy affords a very good means of making visible the form of the vortex motion, results from this proposi- tion. When we substitute in the equation (4) the values of L, M, N, from the equation (5a) and designate by Ju, Jv, Zw the infinitely small portions of the velocities u, v and w in the integral which depend on the material elements da, db, dc and designate their resultant by 4p, we obtain Au— ae MG N= Oe ay ap de, 250 ps A= = Eee ab de, Awad. C—O Nena ab do. vr From these equations it follows that, Au(a—a)+ de(yy—b) + dw(z—c)=0, that is to say, Jp, the resultant of Ju, Jv, Jw, is at right angles to r. Further, §,4u+n,404+6,4w=0, that is to say, this same resultant, Jp, also makes a right angle with the resulting axis of rotation at the point a, b,c. Finally, da db de : dAp= V(4uy?+ 4+-(4o)+(4eP?= “Oat oSiD Y, Ww ae o is the resultant of [the elementary velocities of rotation] &,, Yay Coy and vis the angle between this resultant and 7, as determined by the equatioa, or COS V=(L¥—A)G,+ (Y—)) n+ (2—C)E, Therefore every rotating particle of liquid a causes in every other particle b of the same mass of liquid a velocity that is directed perpen- dicularly to the plane passing through the axis of rotation of the particles aand b. The magnitude of this velocity is directly proportional to the volume of a, to its velocity of rotation, and to the sine of the angle between the line ab and the axis of rotation, and inversely proportional to the square of the distance of the two particles. The force that an electric current, moving parallel to the axis of rota- tion at the point a, would exert upon a magnetic particle at b, follows exactly the same law as above. The mathematical relationship of both classes of natural phenomena PAPER BY PROF. HELMHOLTZ, A5 consists in the fact that in the case of liquid vortices there exists in those parts of the liquid that have no rotation a velocity potential g, which satisfies the eine : Tet 4 hao, which equation fails to hold a eae within the vortex filaments them- selves. But when we imagine the vortex filaments as closed, either within or without the mass of liquid, then the region in which the above differential equation for g~ holds good is a manifold-connected space, for it remains still connected when we imagine intersecting pianes passing through it, each of which is completely bounded by a vortex filament. In such manifold-connected spaces a function @~ that satisfies the above differential equation becomes many-valued, and it must be many-valued if it is to represent re-entering currents: for since the velocities [w, v, w,]| of the liquid particles outside of the vortex fila- ments are proportional to the [partial] differential coéfiicients of g [with reference to x, y, 2], therefore, following the liquid particle in its motion one would find the values of @ steadily increasing. Therefore, if the current returns into itself, and if one by following it comes finally back to the place where he before was, he will find for this place a second value of @ larger than before. Since we can repeat this process in- definitely therefore for every point of such a manifold-connected space, there must be an infinite number of different values of ~, which differ from each other by equal differences, like the different values of Sf tang G) which is such a many-valued function as satisfies the above differ- ential equation. The electro-magnetic effects of a closed electric current have relations similar to the preceding. The current acts at a distance as would a certain distribution of magnetic masses over a surface bounded by the conductor. Therefore, outside of such a current the forces that it ex- erts upon a magnetic particle can be considered as the differential quotients of a potential aa V which satisfies the equation 2a ar 7 ate J HG 0 Here also the space that Be the closed conductor and through- out which this equation holds good, is manifold-connected, and V is many-valued. Therefore in the vortex motions of liquids, as in the electro-magnetic actions, velocities or forces respectively external to the space occupied by the vortex filaments or the electric currents depend upon many- valued potential functions which moreover satisfy the general differ- ential equations of the magnetic potential function, while on the other hand within the space occupied by the vortex filaments or electric cur- 46 THE MECHANICS OF THE EARTH’S ATMOSPHERE. rents, instead of potential functions which can not exist here, there occur other common functions such as are expressed in the equations (4), (5), and (5a). On the other hand, for simple progressive movements of liquids and for the magnetic forces, just as for gravitation, for electric attractions and for the steady flow of electricity and heat, we have to do with single-valued potential functions. The integrals of the hydro-dynamie equations, for which a single-val- ued velocity potential exists, we can call integrals of the firstclass. Those on the other hand for which there are rotations in one portion of the liquid particles, and correspondingly a many-valued velocity potential for the non-rotating particles we call integrals of the second class. It can happen that in the latter case ouly such portions of the space are to be considered in the problem as contain no rotatory particles of liquid, e. g., in the case of the movements of liquid in a ring-shaped vessel, where a vortex filament can be imagined traversing the axis of the vessel, and where notwithstanding this the problem belongs to those that can be resolved by means of the assumption of a velocity potential. In the hydro-dynamie integrals of the first class the velocities of the liquid particles have the same direction as, and are proportional to the forces that would be produced by a certain distribution of the magnetic masses outside of the liquid acting on a magnetic particle at the loca- tion of the particle of liquid. In the hydro-dynamie integrals of the second class the velocities of the liquid particles have the same direction as,and are proportional to forces acting on the magnetic particle such as would be produced by a closed electric current flowing through the vortex filament and having a density proportional to the velocity of rotation of this fila- ment, combined with the action of magnetic masses entirely outside the liquid. The electric currents within the liquid would flow forward with the respective vortex filaments, and must retain a constant intensity. The adopted distribution of magnetic masses outside of the liquid or on its surface must be so defined that the boundary conditions are satisfied. Every magnetic mass can also, as is well known, be replaced by electric currents. Therefore instead of introducing into the values w, v, and w, the potential function P of an exterior mass k, we can obtain an equally general solution if we give to the quantities &, 7, and € external to the fluid or even only on its surface, such arbitrary values that only closed current filaments arise, and then extend the integration of the equa- tions (5a) over the whole region for which &, 7, and € differ from zero. IV. VORTEX SHEETS AND THE ENERGY OF THE VORTEX FILAMENTS. In the hydro-dynamie integrals of the first class it suffices, as I have already shown, to know the movement of the surface; the movement in the interior is then entirely determined. For the integrals of the second class, on the other hand, the movements of the vortex filaments PAPER BY PROF. HELMHOLTZ. 47 located within the fluid are to be determined, taking account of their mutual influences and of the boundary conditions whereby the problem becomes much more complicated. However, for certain simple cases, even this problem can be solved, especially in those cases where the rotations of the liquid particles take place only on certain surfaces or lines and the forms of these surfaces and lines remain unchanged dur- ing the translatory motions. The properties of surfaces that adjoin an indefinitely thin layer of rotating fluid particles are easily seen from the equations (5a). When &, », and ¢ differ from zero only within an infinitely thin Jayer, then, ac- cording to well-known propositions, the potential functions L, M, and N will have equal values on both sides of the layer,* but the partial differential coefticients of these functions for the direction normal to the layer will be different on the two sides of the layer. Imagine the coordinate axes so placed that at the point of the vortex sheet under consideration the axis of z corresponds to the normal to the sheet, the axis of x to the axis of rotation of the liquid particles situated in the sheet, so that at this point we have 7=s=0; then will the potentials M and N, as also their partial differential coefficients, have the same values on both sides of the sheet, similarly Z and — a yp ond a but ‘ = will have two different values whose difference is Sata to 2&e, nae é indicates the thickness of the stratum. Corresponding to this the equation (4) shows that wu and w have the same values on each side of the vortex sheet, but v has values that differ from each other by 2&e. Therefore, that component of the velocity that is perpendicular to the vortex line and tangent to the vortex sheet has different values on either side of the vortex sheet. Within the layer of rotating liquid particles we must imagine the respective components of the velocity as uniformly increasing from the value that obtains on one side of the surface to that which obtains on the other side. For when, as here, § is constant through the whole thickness of the layer, and we indicate by @ a proper fraction, by v! the Value of v on one side, by v; its value on the other side, by v, its value within the layer itself at a distance aé from the former side; then, as we saw before, y'_y,=2&Ee because a layer of the thickness ¢ and the rotatory velocity & lies be- tween the two sides. For the same reasons we must have vi—y, =2Eea=a (v'—1), which covers the proposition just enunciated. Since we must think of the rotating liquid particles as themselves moving forward and since the change of distribution on the surface depends on their own motion, therefore we must, through the whole thickness of the layer, attribute * [This is the ‘‘ vortex sheet” of English writers. ] 48 THE MECHANICS OF THE EARTH’S ATMOSPHERE. to these particles such a mean velocity of progression parallel to the surface as corresponds to the arithmetical mean of the velocities [vi and v| prevailing on the two sides of the layer. For instance such a vortex sheet would be formed when two fluid masses previously separated and in motion come into contact with each other. At the sarface of contact the velocities perpendicular thereto must necessarily balance each other. In general the velocities tangent to this surface will, however, be different from each other in the two fluids. Therefore the surface of contact will have the prop- erties of a vortex sheet. On the other hand, we should not in general think of individual vortex filaments as infinitely slender, because otherwise the velocities — on opposite sides of the filament would have infinite values and oppo- site signs, and therefore the velocity proper of the filament would be indeterminate. In order now to draw certain general conclusions as to the movement of very slender filaments of any sectional area, the prin- ciple of the conservation of living force will be made use of. Therefore before we pass to individual exainples, we must first write the equation for the living force K of the moving mass of water, or or K=sh | | (w+v*+w’)dx dy dz. (6) e ee In this integral I substitute from equation (4): DE IN ou en ean ee s gee a f OM. | pas U AP 2M 26) and integrate by parts; then I indicate by cos a, cos 4, cos y, and cos 6 the angles made by the coordinate axes and the resulting velocity, q, respectively, with the interior normal to the element dw of the mass of liquid and having regard to equations (2) and (1,) I obtain: af K= -5| dc| Pq cos 6+ L(v cos y—w cos f) +M(w cos a—u cos y)+N(u cos B—v cos a)| (6a) -1| | | (LE§E+Mn+NE)dzx dy dz. The value of PAPER BY PROF. HELMHOLTZ. AQ is obtained from the equation (1) by multiplying the first by wu, the sec- ond by v, the third by w, and adding; whence results : du dv dw 0D) aap n( wip beget 0a =~ (Set og +0 (nie erty tee) hf og) , og?) , , aa?) —3( «% gs te mu cE ) When we multiply both sides se dx dy dz, then integrate over the whole volume of 7 liquid mass, and recall that because of (1,4) dy : a Jie 1 — v a+ wie ) dev dy dz = —f/ y> q cos 6 dea, where 7 sanoted a Saito that is continuous and univalued throughout the interior of the liquid mass, we obtain, ad do Coan veg?) COSO” Manse Vist 2 fe. (GD) When the liquid mass is entirely inclosed within rigid walls then at all points of the surface qcos # must be zero, therefore then will ak = 0, or K become constant. If we imagine this rigid wall to be at an infinite distance from the origim of codrdinates and all vortex filaments that may be present to be at an infinite distance from this origin, then will the potential functions i, M, N [of imaginary magnetic matter], whose masses &, 7, -¢, —§ —n Dae De | | oF densities peneee) | each and all are eqaal to zero, diminish 2x at the infinite distance f as wy and the velocities [which are the par- tial differential coefficients of L, M,N], will vary as 5 but the element- \ ary surface dw, if it is always to correspond to the same solid angle at the origin of the codrdinates, will increase as St?. The first integral in the expression for K, equation (6a), which is extended over the surface of the liquid mass, will diminish as oe and therefore will be zero for i equal to infinity. The value of A then reduces to the expression, K=-h ff f (Leia NO)dedydz .... . (6) and this quantity is unchanged during the movement. V. RECTILINEAR PARALLEL VORTEX FILAMENTS. We will first investigate the case where only rectilinear vortex threads exist parallel to the axis of z, either within a liquid mass of infinite extent or which comes to the same thing, in one that is bounded by tw» infinite planes perpendicular to the vortex filaments. In this case 80 A——4 50 THE MECHANICS OF THE EARTH’S ATMOSPHERE. all motions take place in planes that are perpendicular to the axis of z and are precisely the same in all such planes. Therefore we put w= ou = Ov = op a d ¥ = 0 we” 02 (0k Oe Then equations (2) reduce to &=0,7=0,26= 5 w > the equations (5) become Og ot Therefore the vortex threads, in so far as they have constant sectional areas, have also constant velocities of rotation. The equations (4) reduce to, _ Nn IN YN. NW yo ea 0 - In this I have put P = O0in accord with the remark in Sect. 11. Therefore the equation of the streamline is V = constant. In this case N is the potential function of infinitely long lines; this function itself is infinitely large, but its differential coefficients are finite. Let a and b be the codrdinates of a vortex filament the area of whose cross-section is da db, then is IN €Cdadb x—a a) ee es Aa A Yr? IN Cdadb y—b oy us v2 Hence it follows that the resultant velocity g is perpendicular to the r drawn perpendicular to the vortex filament and its value is If within a liquid mass of indefinite extent in the direction x and y we have many vortex filaments whose codrdinates are respectively a, 3 Lo, Yo, ete., while the products of rotatory velocity by the sectional area are for each distinguished by m,, m2, etc., and if we form the sums, U =m, Uy + Mm Uz + Mz Us, ete, V=M, V1 + M2 VL. + M; Vs, ete., then these sums are each equal to zero, because that part of each sum that is due to the action of the second vortex filament on the first is counterbalanced by the action of the first vortex filament on the sec- ond. That is to say, the two effects are, respectively, Mg X—2X2 Mm, X—2X Ny = 5 a Mo =o a ? , PAPER BY PROF. HELMHOLTZ. 5 i and so on through all the other pairs of sums. Now U is the velocity in the direction of x, of the center of gravity of the masses mj, ms, ete., multiplied by the sum of these masses; similarly V is the velocity taken in the direction of y. Both velocities are therefore zero, unless the sum of the masses is zero, in which case there is no center of grav- ity at all. Therefore the center of gravity of the vortex filaments remains unchanged during their motion, and since this proposition holds good for every distribution of the vortex filaments, therefore we may also apply it to the individual filaments of infinitely small cross section. Hence result the following consequences : (1) If we have but one individual rectilinear vortex filament of infi- nitely small cross-section within a liquid mass of infinite extent in all directions perpendicular to the filament, then the movement of the par- ticles of water at a finite distance from the filament depends only on the product’§ da db=™m, or the velocity of rotation multiplied by the area of the cross-section, and not on the form of the cross-section. The liquid particles rotate about the filament with the tangential velocity = where r denotes the distance from the center of gravity of the vor- tex filament. The location of the center of gravity, the velocity of rotation, the area of the cross section, aud therefore also the quantity m remains unchanged although the form of the infinitely small cross- section may change. (2) If we have two rectilinear vortex filaments of infinitely small cross- sections aud an indefinitely large liquid mass, each will drive the other in a direction that is perpendicular to the line joining them together. The length of this connecting line will not be changed thereby; there- fore both will revolve about their common center of gravity, remain- ing at equal constant distances therefrom. If the rotatory velocity is in the same direction in the two filaments and therefore has the same sign, then their center of gravity must lie between them. If the rota- tions are mutually opposed to each other and tnerefore of opposite signs, then their center of gravity lies in the projongation of the line connect- ing the filaments. If the products of the rotatory velocity by the cross section are numerically equal for the two but of opposite signs, thereby causing the center of gravity to be at an infinite distance, then both filaments advance with equal velocity and in the same direction per- pendicular to their connecting line. The case where a vortex filament of infinitely small section lies close to an infinitely extended plane surface parallel to it can be reduced to this last case. The boundary condition for the movement of the liquid along a plane (7. ¢., that the motion must be parallel to this plane) is satisfied when we imagine a second vortex filament, which is as the re- flected image of the first, introduced on the other side of the plane. Hence it follows that the vortex filament within the liquid mass ad- 52 THE MECHANICS OF THE EARTH'S ATMOSPHERE. vances parallel to the plane in the direction in which the liquid parti- cles, between it and the plane, themselves move,and with one-fourth of the velocity possessed by the particles that are at the foot of the per- pendicular drawn from the filament to the plane. The assumption of the infinitely small cross-section leads to no inad- missible results, because each individual filament exerts no force upon itself affecting its own progression, but is driven forwards only by the influence of the other filaments that may be present [or by tke action at the boundary]. But it is otherwise in the case of curved filaments. VI. CIRCULAR VORTEX FILAMENTS. In a liquid mass of indefinite extent let there be present only circu- lar filaments whose planes are perpendicular to the axis of 2,and whose centers lie in this axis,so that all are symmetrical about this axis. Transform the codrdinates by putting v= 7 COS &, &= 9 COS é, Y= 7 Sin: €, b=g sine, e=%, c= C. Agreeably to the assumption just made, the velocity of rotation o is only a function of y and 2,or of g and c, and the axis of rotation is every- where perpendicular to y (or g) and to the axis of z. Therefore the ree- tangular components of the rotation at this point whose coordinates are g, €, and ¢ become &=—o sin e, n=o cos e, C=0. In the equation (5a) we now have, rP=(z—c+)’+9?—2y7g Cos (€—€) a *o sin e teu S J { ae g dg de de M=— oat [ [Pea de de N=0 From the equations for 1 and M by multiplying by cos ¢ and sin ¢ and adding we obtain LT sin e—M cos e=— lS poss San ae g d(e—e) de, I cos ¢+ M sin ¢= = allL[ ee g dg d(e—e) de, In both these integrals the angles e and « occur only in the connec- tion (e—e) and this quantity can therefore be considered as the variable under the sign of integration. In the second integral the terms that contain («—e)=¢ balance those that contain («—e)=27—ec; therefore this integrat is equal to zero. PAPER BY PROF. HELMHOLTZ. 53 Therefore if we put 0 COS eg dg de de :. vise | [ [ve P+ y+? —2 2g COS € (7) Mcose— Lsin e= wp Msine+ Leose=0, then will or L=—~psne, M=~+p cose. (7a) Let 7 denote the velocity in the direction of the radius y, and con- sider the fact that on account of the symmetrical position of the vortex ring in reference to the axis z the velocity must be zero in the direction of the circumference of the circle, we must have U=T COS & V=T Sin and according to equations (4) aM ae Dine Oi ME C= ; — 5 i —_ == ae oe oa oY Hence it follows that ow oy y er ol et aa roma? or ($x) d(x) a Claas aarp ee Mca apy" (7b) Therefore the equation of the stream line is wb X = const. When we execute the integrations indicated in the value of y, first for a vortex filament of infinitely small cross-section, putting therein m,=o dg de and indicating by #,, the part of 7 depending thereon, we have 49X ~ G+xXP+ (2) wherein F and H indicate the complete elliptic integrals of the first and second order respectively for the modulus 2. For brevity we put | 2 HH) aE, A where U is therefore a function of x, then is cea ae Ease ONE ee: an” * G—a re eF If now a second yortex filament m exist at the point determined by x and 2, and if we let 7; be the velocity in the direction of g that m communicates to the filament m,, we then obtain the value of this ve- D4 THE MECHANICS OF THE EARTH'S ATMOSPHERE. locity if in the expression for 7 we substitute 7, 9, V, ¢, 2, m, in place Of 7, Xs Go Zs Cy M3. In this process x and U remain unchanged and we obtain, MEY MTG —0. se 42 was, betes I) If now we determine the value of the velocity w parallel to the axis, caused by the vortex filament m, whose codrdinates are g and c, we find : If now we eall w, the eae at the ea of m, parallel to the axis of 2, which is caused by the vortex ring m whose coérdinates are z and y, then in order to determine this, we only need to execute the interchange of appropriate codrdinates and masses as above shown. Thus we find: 2m i 2m jx? —2 m, w, g— mT Y2—M, T 1 9eE= —_ VI CU, anos = aoa) Sums similar to (S) and (8a) can be found for any number of vortex rings. For the nth of these rings I designate the product 6 dg de by m,; the components of the velocity that is communicated to this ring by all the other rings are 7, and w,, in which however I provisionally omit the velocities that every vortex ring can communicate to itself. Fur- ther I call the radius of this ring 9, and its distance from a surface perpendicular to the axis A, which two latter quantities agree with y and z as to direction, but, as belonging to this particular ring, they are functions of the time and not independent variables as are y and 2. Finally let the value of 7, in so far as it depends on the other vortex rings, be #,. By forming and adding the equations (8) and (8a) corre- sponding to each pair of vortex rings, there results = |i; DP, Tl —O- = [2 M, Wy P.— Mn Tr P, An| == [M, Pr Yn]. So long as we have in these sums only a finite number of separate and infinitely slender vortex rings, we must understand by ez, 7, and y only those parts of these quantities that are due to the presence of the other rings. But when we imagine an infinite number of such rings keeping the space continuously filled, then y becomes the poten- tial function of a continuous mass, wand t become partial differential coefficients of this potential function, and it is known* that both for such functions and for their differential coefficients, the portions of the function that depend upon the presence of matter within an infinitely small space surrounding a point for which the function is determined are infinitely small with respect to those portions that depend on finite masses at finite distances. *See Gauss, Allgemeine Theorie des Erdmagnetismus in the Resultate des magnetischen Vereins im Jahre, 1839, page 7, or the translation in Taylor’s Scientific Memoirs, vol. I. PAPER BY PROF. HELMHOLTZ. 5D Therefore if we change the sums into integrals we can understand by w, 7, and 7 the total values of these quantities that exist at the point in question, and can put dn dp dt? Tae To this end we replace the quantity m by the product odpdaA, and the summations thus become converted into the following integrals : S Sop hap ar =0 “hsb Qe uneven ERG) i= ¢ adxr ann dp - BS oP gee Oh) JS opr ae dpd=f foppdpar . . (9a) Since, in accordance with Sect. 11, the product o dp dd does not vary with the time, therefore, the equation (9) can be integrated with respect to t, and we obtain af fof? dp di = Const. Imagine the space divided by a plane that passes through the axis of z, and therefore intersects all the vortex rings that are present; then consider o as the density of one layer of the mass, and let Yt be the total mass in this layer adjoining this dividing plane; therefore, M= [ fodpdar, and let A? be the mean value of p? for all the elementary masses, then JS SJ op. pap da=M R?, and, since this integral and the value of {ido not vary with the time, it follows that R also remains unchanged during the motion of transla- tion. Therefore if there exists in the unlimited mass of liquid only one circular vortex filament of infinitely small sectional area, then its radius remains unchanged. According to equation (6c), the total living force in our case is K=—h ff) f(LE+Mn)da db de. =f f fuopdp ards, =—2ah f fpopdpar. This also does not change with time. Furthermore, because o do da does not vary with time, therefore, d a PAB TNA aS ford dpar=2 f Popa dod+t f fap a. didp; therefore if we indicate by / the value of A for the center of gravity of the vortex filament treated of in equation (9a), and multiply (9) by this 1, and add the result to (9a), and substitute therein the equation last given, we obtain d oes dp Kk 241J f FPAMPA+S f" fop(l—A) Ge ap dA = ee (9b) D6 THE MECHANICS OF THE EARTH’S ATMOSPHERE. When the section of the vortex thread is infinitely small and ¢ is an infinitely small quantity of the same order as (/—A) and the remain- ing linear dimensions of the section, but ¢ dp dj is finite, then w and also A are ot the same order of infinitely large quantities as log «. For very small values of the distance v from the vortex ring we have | r= Vg=aF He w=1— v 4g” : my, ; 1—32 My, ae My=— 1 = log naire "eae 70 og (,f 4 ) A °8 84 In the value of KA, 7 is multiplied by porg. If g is finite, and v of the same order as ¢, then is of the same order as log « Only when g is infinitely large of the order : will A be infinitely large of the order 1 : : ; : } —.log é«. But in this case the circle becomes a straight line. On the () ep ene a OYE, aetna tani other hand, if a which is equal to ep the order —, then the sec- Q 2 E ond integral will be finite, and for a finite value of p will be infinitely small with respect to K. In this case we can, in the first integral, substi- tute the constant / in place of A and obtain at ~ Oh or omRi—-o—* ¢ Qh Since Yt and & are constant, / can only vary proportionally to the time. When St is positive the motion of the liquid particles on the outer side of the ring is directed toward the side of positive z, but on the inner side of the ring toward the negative z. A, h, and R are by their nature always positive. Hence it follows that for a circular vortex filament of very small cross-section in an infinitely extended mass of liquid the center of grav- ity of a cross-section has a motion parallel to the axis of the vortex ring, Which is of approximately constant and very large velocity, and which is directed toward the same side as that toward which the liquid flows through the ring. Infinitely slender vortex filaments of a finite radius will have infinitely large velocities of propagation. But if the radius of the vortex ring is infinitely large of the order a then will R? be infinitely large with respect to X, and J will be constant. The vortex filament which has thus transformed itself into a straight line will be stationary, as we had already previously found for rectilinear vortex filaments. in lt a a ES 2 PAPER BY PROF. HELMHOLTZ, ae We can now in general see how two circular vortex threads having a common axis will behave with respect to each other, since each one independent of its own translatory motion also follows the movement of the liquid particles caused by the other filament. If they have the same direction of rotation, then they both advance in the same direc- tion, and at first the preceding one enlarges, then it advances more slowly while the following one diminishes and advances more rapidly} finally, if the progressive velocities are not too different, the second catches up with the firstand passes throughit. Thenthe same perform- ance is repeated by the one that is now in the rear so that the rings alternately pass through each other. If the vortex filaments have the same radii, but equal and opposite rotatory velocities, then they will approach each other and simultane- ously enlarge, so that finally when they have come very close together their movement towards each other grows continually feebler, while on the other hand the enlargement goes on with increasing rapidity. If the two vortex threads are perfectly symmetrical, then midway be- tween them the velocity of the liquid particles in the direction parallel to the axis is equal to zero. Therefore one can imagine a rigid wall located here without disturbing the motion and thus obtain the case of a vortex ring that encounters a rigid wall. Jremark further that we can easily study these movements of circular vortex rings in nature if we draw a half-immersed circular disk or the approximately semicircular end of a spoon rapidly for a short distance along the surface of a liquid and then quickly draw it out. There then remain in the liquid semi-vortex rings whose axes lie in the free upper surface of the liquid. The free upper surface thus forins, tor the liquid mass, a boundary plane that passes through the axis whereby no im- portant change is made in the motions. The vortex rings advance, broaden when they encounter a screen, and are enlarged or diminished by the action of other vortex rings precisely as we have deduced from the theory. ELL ON DISCONTINUOUS MOTIONS IN LIQUIDS.” By Prof. H. VON HELMHOLTZ. It is well known that the hydro-dynamic equations give precisely the same partial differential equations for the interior of an incompressible fluid that is not subject to friction and whose particles have no mo- tion of rotation, as obtain for stationary currents of electricity or heat in conductors of uniform conductivity. One might therefore expect that for the same external form of the space traversed by the cur- rent and for the same boundary conditions the form of the current (ex- cept for differences depending on small incidental conditions), would be the same for liquids, for electricity, and for heat. In reality however in many Cases there exist easily recognizable and very fundamental differences between the currents in a liquid and the above mentioned imponderables. Such differences are especially notable when the currents flowing through an opening with sharp edges enter into a wider space. In such cases the stream lines of electricity radiate from the opening outwards immediately towards all directions, while a flowing fluid, water as well as air, moves from the opening at first forward in a compact stream which at a less or greater distance then ordinarily resolves itself into a whirl. The portions of the fluid in the larger receiving vessel lying near the opening but outside the stream can, on the other hand, remain almost at perfect rest. Hvery one is familiar with this mode of motion, especially as a current of air impregnated with smoke shows it very plainly. In fact the compressibility of the air does not come much into consideration in these processes, and with slight variations air shows the same forms of motion as does water. On account of the great differences between the faets as observed and the results of theoretical analysis as hitherto achieved the hydro- dynamic equations must necessarily appear to the physicist as a prac- *From the Monatsberichte of the Royal Academy of Science, Berlin. 1868, April 23, pp. 215-228. Helmholtz Wissenschafiliche Abhandlungen, vol. 1, pp. 146-157. Ber- lin, 1882. 58 PAPER BY PROF. HELMHOLTZ. 59 tically very imperfect approximation to the reality. The cause of this might be suspected to liein the internal friction or viscosity of the fluid, although all forms of infreqent and sudden irregularities (with which certainly everyone has to contend who has instituted observations on the movements of fluids) can evidently never be explained as the effect of the steadily and uniformly acting friction. The investigation of cases where periodical movements are excited by a continuous current of air, as, for example, in organ pipes, showed me that such an effect could only be produced by a discontinuous motion of the air, or at least by a kind of motion coming very near to it, and this has lead me to the discovery of a condition that must be taken into consideration in the integration of the hydro-dynamic equations, and that, so far as I know, has been overlooked hitherto, whose considera- tion on the other hand, in those cases where the computation can be carried out, really gives, in fact, forms of motions such as those that are actually observed. This condition is due to the following circumstance: In the hydro-dynamice equations the velocity and the pressure of the flowing particles are treated as continuous functions of the coérdinates. On the other hand, there is no reason in the nature of a liquid, if we consider it as perfectly fluid, therefore not subject to viscosity, why two contiguous layers of liquid should not glide past each other with defi- nite velocities. At least those properties of fluids that are considered in the hydro-dynamic equations, namely, the constancy of the mass in each element of space and the uniformity of pressure in all directions, - evidently furnish no reasons why tangential velocities of finite differ- ence in magnitude should not exist on both sides of a surface located in theinterior. On the other hand, the components of velocity and of pres- sure perpendicular to the surface must of course be equal on both sides of such a surface. I have already in my memoir on vortex motions called attention to the fact that such a case must occur when two moving masses of liquid previously separate and having different motions come to have their surfaces in contact. In that memoir I was led to the idea of such a surface of separation,* or vortex surface as I there called itt through the fact that [ imagined a system of parallel vortex filaments arranged continuously over the surface whose mass was indefinitely small without losing their moment of rotation. Now, in a liquid at first quiet or in continuous motion a definite dif- ference in the movement of immediately adjoining particles of liquid can only be brought about through moving forces acting discontinu- ously. Among the external forces the only one that can here come into consideration is impact. But in the interior of liquids there is also a cause present that can (* Ordinarily called surface of discontinuity or ‘ adiscontinuous surface” by English writers. | {t That is, an infinitely thin layer of parallel vortex filaments, the *‘ vortex sheet” of English writers. ] 60 THE MECHANICS OF THE EARTH’S ATMOSPHERE. bring about discontinuity of motion—namely, the pressure, which can assume any positive value whatever while the density of the liquid will continuously vary therewith; but as soon as the pressure passes the zero value and becomes negative, a discontinuous variation of the density occurs; the liquid is torn asunder. Now, the magnitude of the pressure (at any point) in a ae fluid aepenae on the velocity (at that point), and in incompressible fluids the diminution of pressure under otherwise similar circumstances is directly proportional to the living force of the moving particles of liquid. Therefore if the latter exceed a certain limit the pressure must, in fact, become negative, and the liquid tears asunder. At such a place the accelerating force, which is proportional to the differential quotient of the pressure, is evidently discontinuous, and thus the con- dition is fulfilled which is necessary in order to bring about a discon- tinuous motion of the liquid. The movement of the liquid past any such place can now take place only by the formation from that point onward of a surface of discontinuity. The velocity that will cause the tearing asunder of the liquid is that which the liquid would assume when it flows into empty space under the pressure that the liquid would have at rest at the point in ques- tion. his is indeed a relatively considerable velocity; but it is to be remarked that if liquids flow continuously like electricity the velocity at every sharp edge around which the current bends must be infinitely great.* Thence it follows that at every geometrically perfect sharp edge past which liquids flow, even for the most moderate velocity of the rest of the liquid, it must be torn asunder and form a surface of discontinuity. On the other hand, for imperfectly somewhat rounded edges such phe- nowena first occur for certain larger velocities. Pointed protuber- ances on the surface of a canal through which a current flows will have similar effects. As concerns gases, the same circumstance occurs as with liquids, only with this difference,—that the living force of the motion of a particle is not directly proportional to the diminution of the pressure (p); but taking into consideration the cooling of the air by its expansion the living force is proportional to the diminution of p”, where m= igs and y is the ratio of the specific heat at constant pressure to that for constant volume. For atmospheric air the exponent m has the value 0.291. Since this is positive and real, therefore p”, like p, for high values of the velocity can only diminish to zero and not become negative. It would be otherwise if gases simply followed the law of Mariotte and experienced no change of temperature. Then instead of p™ the quan- tity log p would occur, which can become negative and infinite without *At the very small distance p from. a sharp edge whose surfaces meet each other T—a ‘ at the angle @ the velocities will be infinite, or as p—™, where m= ona PAPER BY PROF. HELMHOLTZ. 61 p being negative. Under this condition the tearing asunder of the mass of air would not be necessary. It is possible to convince one’s self of the actual existence of such- discontinuities when we allow a stream of air impregnated with smoke to issue from a round opening or a cylindrical tube with moderate velocity so that no hissing occurs. Under favorable circumstances one obtains thin rays or jets of this kind of a few lines diameter and a length of many feet. Within the cylindrival surface the air is in mo- tion with constant velocity, but outside it, on the other hand, in the immediate neighborhood of the jet it moves not at all or very slightly. One sees this very sharp separation clearly when we conduct a steadily flowing cylindrical jet of air through the point of a flame, out of which it cuts a sharply defined piece, while the rest of the flame remains en- tirely undisturbed, and at most a very thin stratum of flame, which corresponds to the boundary layer of the jet influenced by friction, is carried along a little way. As concerns the mathematical theory of this motion I have already given the boundary conditions for the existence of an interior surface of separation within the liquid. They consist in this that the pressures on both sides the surface must be equal and equally so the components of the velocity normal to the discontinuous surface. Since now the movement throughout the entire interior of a liquid whose particles have no motion of rotation is wholly determined when the motion of its entire exterior surface and its interior discontinuities are given, therefore in general for a liquid whose exterior boundary is fixed, it is only necessary to know the movement of the surfaces of separation and the variations of the discontinuity. Now such a discontinuous surface can be treated mathematically pre- cisely as if it were a vortex sheet, that is to say, as if it were continu- ously enveloped by vortex filaments of indefinitely small mass but finite moments of rotation. For each element of such a vortex sheet there is a direction for which the components of the tangential veloci- ties are equal. This gives at once the direction of the vortex filaments at the corresponding place. The moment of this filament is to be put proportional to the difference existing between the components, taken perpendicular to it, of the tangential velocity on both sides of the surface. The existence of such vortex filaments in an ideal frictionless liquid is 2 mathematical fiction that facilitates the integration. In a real liquid subject to friction, this fiction becomes at once a reality inasmuch as by the friction the boundary particles are set in rotation, and thus vortex filaments originate there having finite gradually increasing masses, while the discontinuity of the motion is thereby at the same time compensated. The motion of a vortex sheet and the vortex filaments lying in it 1s to be determined by the rules established in my Memoir on Vortex 62 THE MECHANICS OF THE EARTH’S ATMOSPHERE. Motions. The mathematical difficulties of this problem however can be overcome only in a few of the simpler cases. In many other cases, however, one can from the above given method of considerat.on of this matter at least draw conclusions as to the general nature of the varia- tions that oecur. Especially is it to be mentioned that in accordance with the laws established for vortex motions, the vortex filaments and with them the vortex sheets in the interior of a frictionless liquid can neither originate nor disappear, but rather each vortex filament must retain perma- nently the same constant moment of rotation; furthermore that the vortex filaments themselves advance along the vortex sheet with a velocity that is the mean of the two velocities existing on the two sides of the discontinuous surface. Thence it follows that a surface of dis- continuity can only elongate in the direction towards which the stronger of the two currents that meet in it is directed. I have first sought to find examples of permanent discontinuous sur- faces in steady currents, for which the integration can be executed, in order thereby to prove whether the theory gives forms of currents that correspond to experience better than when we disregard the discon- tinuity of motion. If a surface of discontinuity that separates quiet and moving water from each other is to remain stationary, then along this surface the pressure within the moving layer must be the same as in the quiet layer, whence it follows that the tangential velocity of the particles of liquid must be constant throughout the whole extent of the surface; equally so must the density of the fictitious vortex filament be constant. The beginning and end of such a surface can only lie on the boundary of the inclosure or at infinity. Where the former alter- native is the case they must be tangent to the wall of the inclosure, assuming that the latter is continuously curved, becanse the compo- nent-velocity normal to the wall of the inclosure must be zero. Moreover the stationary forms of the discontinuous surface are dis- tinguished, as experiment and theory agree in showing, by a remarkably high degree of variability under the slightest perturbations, so that to a certain extent they behave similarly to bodies in unstable equill- brium. The astonishing sensitiveness to sound waves of a eylindrical jet of air impregnated with smoke has already been deseribed by Tyn- dall; [have contirmed this observation. This isevidently a peculiarity of surfaces of discontinuity that is of the sreatest importance in oper- ating sonorous pipes. Theory allows us to recognize that in general wherever an irregularity is formed on the surface of an otherwise stationary jet, this must lead to a progressive spiral unrolling of the corresponding portion of the sur- face, which portion, moreover, slides along the jet. This tendeney to- wards spiral unrolling at every disturbance is moreover easy to see in the observed jets. According to the theory a prismatic or cylindrical jet can be indefinitely long. In fact however such an one can not be PAPER BY PROF. HELMHOLTZ. 63 formed, because in an element so easily moved as is the air small dis- turbances can never be entirely avoided. It is easy to see that such an endless eylindrical jet, issuing from a tube of corresponding section into a quiet exterior fluid and everywhere containing fluid that is moving with uniform velocity parallel to its axis, corresponds to the requirements of the “steady condition.” I will here further sketch only the mathematical treatment of a case of the opposite kind, where the current from a wide space flows into a narrow canal, in order thereby also at the same time to give an example of a method by which some problems in the theory of potential fune- tions can be solved that hitherto have been attended by difficulties. I confine myself to the case where the motion is steady and dependent only upon two rectangular codrdinates, v and y; where moreover no rotating particles are present in the frictionless fluid at the beginning, and where none such can be subsequently formed. If we indicate by u the component parallel to x of the velocity of the fluid particle at the point (vy) and by v the velocity parallel to y, then, as is well known, two functions of # and y can be found such that OP _ ow } er ot mae | (1) peo eee | RTO UH my oe J By these equations the conditions are also directly fulfilled that in the interior of the fluid the mass shall remain constant in each element. ~ of space, viz: WP FPL Op, FY at. lame eae OU. ots Oy? maa ORI toe Ture icy hi? ae (1a) For a constant density, h, and when the potential of the external forces is indicated by V,the pressure in the interior is given by the equation— val Ss (5%) | =3 +[ (2) ce (=) |] Sl salt de orek CLD) The curves y = constant are the stream lines of the fluid, and the curves gp = constant are orthogonal to them. The latter are the equi-potential curves when electricity, or the equal temperature curves when heat, flows in steady currents in conductors of uniform conductivity. From the equation (1) it follows as an integral equation that the quantity p+ yi is a function of x + yi, where i= Y—1. The solutions hitherto found generally express @ and 7 as the sums of terms that are 64 THE MECHANICS OF THE EARTH’S ATMOSPHERE. themselves functions of x and y. But inversely we can consider and develop x + yi as a function of o+ 7i. In problems relative to cur- rents between two stationary walls, 7 is constant along the boundaries, and therefore if g and 7 are presented as rectangular codrdinates in a plane, then in a strip of this plane bounded by two parallel straight lines, 7 = ¢ and 7 = ¢, the function «4+ yi is to be so taken that on the edge it corresponds to the equation of the wall, but in the interior i¢ assumes a given variability. A case of this kind occurs when we put r+ yt —A ; p+ pert ; ee jegh “is, Mel | oh sou fe Uo tne memtc tame (2) or é L=Ap+ Ae cos D. y=Ay+ Ae sin For the value 7 = + z we have y constant and «=A g— Ae’. When @ varies from — » to + @ the value of « changes at the same time from —« to — A, and then again back to —o. The stream lines x=-+7 correspond thus to a current along two straight walls, for which y= + Az and «# varies between — and — A. Therefore when we consider y as the expressicu of the stream curve the equation (2) corresponds to the flow out into endless space from a canal bounded by two parallel planes. On the border of the canal however where c= —A and y=+A7 and where further, p=0 and w= + 7, we have Cares a! (02) + (28) =e Electricity and heat flow in this manner, but liquids must tear asunder. If from the border of the canal there extend stationary dividing dis- continuous lines that are of course prolongations of the stream lines w= + 7 that follow along the wall and if outside of these discontinuous lines that limit the flowirg fluid there is perfect quiet, then must the pressure be the same on both sides of these dividing lines. That is to say, along that portion of the line >= + z which corresponds to the free dividing line, in accordance with the equation (1b), we must have therefore (22) + (22) = constant + 2o cee mane eee In order now, in the solution of this modified problem, to retain the fundamental idea of the motion expressed in equation (2), we will add SRG TR TS ae - = = => ae = SSeT = SS, : = PT er OF eee AI =~ =a PAPER BY PROF. HELMHOLTZ. 65 to the above expression of «+ yi still another term o + 77%, which is also always a function of p+ 7% 7, we have then x=Ap+Ae cos p+ a y=A p+ Ae sin p+—r and must determine o + 77 so that along the free portion of the discon- tinuous surface where 7 = + z we shall have \ 2 \ 2 (A-ae Je sa) ae |) = constant. IP IP This condition is fulfilled if we make dpa Ora. — Constant 6) jee 6, 1a ce) (G0) IP and soa + AV2e — 6 Dye ey afer veel (aG) Since # is constant along the wall we can integrate the last equation with respect to g, and change the integral into a function of p+¢ iby substituting everywhere instead of g the expression g+i (7+). Thus by an appropriate determination of the constants of integration we ob- tain : 4 (d+Hi) (26-42%) t (d+ Yt) ) eae) —2e —e +2aresin[ 755+ res . (3d) The cusp points of this expression lie where (6+ i) oo é — 3 that is to say where y=+ (2a +4 1) z [a being any whole number], and P= log 2. Thus neither one lies between the limits from ~=+7 to p=—7z. The function o+77 is here continuous. Along the wall we have : a eye 6+Ti=4+A i} V 2¢¢— @2—2 are sin v2 é | Te gy > log 2, then all these values become purely imaginary, there- fore o = 0, while te has the value given above in equation (3c). This portion of the lines 7;=-+ 7 therefore corresponds to the free portion of the jet. If p< log 2 the whole expression is real up to the additive quantity + Aiz, which latter is to be added to the value of 7 7 and y 7 re- spectively. 80 A——5 66 THE MECHANICS OF THE EARTH’S ATMOSPHERE. The equations (3a) and (3d) correspond therefore to the outflow from an unlimited basin into a canal bounded by two planes, whose breadth is 4 A z and whose walls extend from w=—~x to 7 =—A (2—log 2). The free discontinuous line of the flowing fluid curves from the nearest edge of the opening at first a little towards the side of the positive x, where for p=0, =—A and reaches its greatest x value when y=1A (37+ 1); then it turns inward towards the inside of the canal and at last asymptotically approaches the two lines y=+A 7, so that finally the breadth of the outflowing jet is equal only to the half breadth of the canal. The velocity along the discontinuous surface and at the extreme end of the outtlowing jet is = so that this form of motion is possible for every velocity of efflux. I present this example especially as it shows that the form of the liquid stream in a tube can for a very long distance be determined by the form of the initial portion. ADDITION, BEARING ON ELECTRICAL DISTRIBUTION. When in equation (2) we consider the quantity ~ as the electrie potential it gives the distribution of electricity in the neighborhood of the edges of two plane disks quite near together, assuming that their distance is indefinitely small with respect to the radius of curvature of their curved edge. This is a very simple solution of the problem that has been considered by Clausius.* It gives moreover the same distribution of electricity as he found for it; at least so far as it is in- dependent of the curvature of the edges. I will further add that the same method also suffices to find the dis- tribution of electricity on two parallel, infinitely long, plane strips, whose four edges in cross section form the corners of a rectangle, that is, the cross section of the strips gives two lines which are oppo- site and parallel to each other. The potential function y in this case is given by an equation of the form 1 (p+ t) where H (uw) represents the function designated by Jacobi in the Fun- damenta Nova, p. 172, as the numerator of the function developed in terms of sin am u. The overlying strips correspond, according to Jacobi’s notation, to the values p=+2 KH where r=+2 KA gives the half distance of the strips, while the width of the strip depends on the ratio of the constants A and B. The form of the equations (2) and (4) allows us to recognize that m and 7 can be expressed as function of and y only by means of most complicated serial developments. vty isd (ptp i+ By (4) * Poggendorff’s Annalen, Bd. LXXXVI. ae ar Vi ON A THEOREM RELATIVE TO MOVEMENTS THAT ARE GEOMETRICALLY SIMILAR IN FLUID BODIES, TOGETHER WITH AN APPLICATION TO THE PROBLEM OF STEERING BALLOONS.* By Prof. H. von HELMHOLTZz. The laws of motion of cohesive and non-cohesive fluids [namely, liquids and gases] are sufficiently well known in the form of differential equa- tions, that take into consideration not only the influence of exterior forces acting from a distance, as well as the influence of the pressure of the fluid, but also the influence of the friction [namely, both internal and external frictions, or both viscosity and resistance]. When in the application of these equations one remembers that under certain cir- cumstances [namely, wherever a continuous motion would give a nega- tive pressure] there must form surfaces of separation with discontinuous motion on the two sides, as I have sought to prove in a previous com- munication to this academy,t then will disappear the contradictions that by neglect of this consideration have hitherto been made to appear to exist between many apparent consequences of the hydro-dynamic equations on the one hand and the observed reality on the other. In fact, so feras I see, there is at present no ground for considering the hydro-dynamic equations as not being the exact expression of the laws controlling the motions of fluids. Unfortunately it is only for relatively few and specially simple ex- perimental cases that we are able to deduce from these differential equations the corresponding integrals appropriate to the conditions of the given special cases, especially if the nature of the problem is such that the internal friction [viscosity | and the formation of surfaces of discon- tinuity can not be neglected. The discontinuous surfaces are extremely variable, since they possess a sort of unstable equlibrium, and with every disturbance in the whirl they strive to unroll themselves; this cireum- stance makes their theoretical treatment very difficult. Thus it happens “ *From the Monatsberichte of the Royal Academy of Berlin, June 26, 1873, pp. 501 to 514. Wissenschaftliche Abhandlungen, vol. 11, pp. 158-171, Berlin, 1882. t Berlin Monatsberichte, April 23, 1868. See also No. III of this collection of Trans- lations. aa 67 68 THE MECHANICS OF THE EARTH’S ATMOSPHERE. that where we have to do practically with the motions of fluids we are thrown almost entirely back upon experimental trials, and can often, from theory, predict but very little, and that only in an uncertain manner, as to the result of new modifications of our hydraulic machines, aqueducts, or propelling apparatus. In this state of affairs I desire to call attention to an application of the hydro-dynamic equations that allows one to transfer the results of observations made upon any fluid and with an apparatus of given dimensions and velocity over to a geometrically similar mass of another fluid and to apparatus of other magnitudes and to other velocities of motion. To this end I designate by uv w the components of the velocity of the first fluid in the directions of the rectangular codrdinate axes x y 2; by t the time, by p the pressure, by ¢ the density, by x its coefficient of friction (viscosity). The equations of motion in the Eulerian form in- troducing the frictional forces, as is done by Stokes, in case no exterior forces act upon the fluid, will now have the following form : dE (UE) O(V.E) , O(w.8) 7-75 oy toe ee c ou?" oy?” dz" 1 op du yu du ou Pu +b. 7a oF a u—+v—+w——k? - : € ox ot oa oy dz kod .,du.w dw c y ¢ (1a) 3 de Lae oy" dz To these are still to be added the two equations that are deduced from the latter equation (la) by interchanging x and wu with y and v or with ¢ and w. When now for another fluid the velocities are designated by U, V, W, the pressure by P, the codrdinates by X, Y, Z, the time by Z, the density by #, the viscosity constant by A, and if we introduce three constants q, 7, and n, and put E98 6 xk Ge] es aes eee) U=nu X= q n Vimeo: at V=7 Y= W=nw Fae n P=rrp+constant. T= Vs then the quantities designated by these capital letters will also fulfill the above differential equations. If we substitute these in those equa- tions, the result, #, is as if all the terms of equation (1) were multiplied by PAPER BY PROF. HELMHOLTZ. 69 wn m3 the factor a and all the terms of equation (1a) by the facto - : Of the constants q,'r, n, two are determined through the equations (2) and (2a) by the nature of the fluid, but the third, n, is arbitrary so far as the conditions hitherto considered come into consideration. If the fluid is incompressible, then ¢ is to be considered as a constant JE ‘ a : and y= and the above equations then suffice to determine the motion c in the interior. If the fluid is compressible, we can put EG Maa ab Hence eh oh Vicdign any ey a") =A Oy td Aa ret evans von tie Pad Selts COA) where ¢ and C indicate constants to be added to the pressure and which have no influence on the equation la. For gases ¢ and C are to be put equal to zero if the motion occurs under such circumstances that the temperature remains constant. For rapid variations of density in gases without equalization of temperature (namely non-adiabatic motions), the equations (3) and (3a) would only apply for the case of slight variations in density. The equation (3a) is only satisfied by the above-given values for P and # when A2=O Nn’, By this condition therefore the third constant, n, is determined. The quantities a and A in this latter equation are the velocities of sound in the respective fluids. These quantities must change in the same ratio as the other velocities. If the boundaries of the fluid are in part infinitely distant and in part given by moving or quiet, pertectly wetted, rigid bodies, and the coordinates and component velocities of these limiting rigid bodies are transferred from one case to the other in the same manner as has just been done for the particles of fluid, then will the boundary conditions for U, V, W be fulfilled when they are fulfilled for u,v, w. In this J assume that on completely wetted bodies the superficial layer of fluid is held perfectly adherent; that therefore the component velocities of the surfaces of the rigid bodies and those of the adherent fluid are equal. For imperfectly wetted solids it is as a rule assumed that there is a relative motion of the superficial fluid layers with respect to the solid. In this case the application of our principles would require that a cer- tain ratio be assumed between the coefficients of sliding superficial friction of the fluid on the respective rigid bodies, and the internal friction (or viscosity) of the fluid. Similarly the boundary conditions at the free surfaces of a liquid over which the surface pressure is constant, would be satisfied in case no TO THE MECHANICS OF THE EARTH’S ATMOSPHERE. outside forces like gravity have an influence. But since this case occurs only in liquids [. e., fluids that form drops] that can be regarded as incompressible, therefore (for these) it is not necessary to satisfy equations (3) and (3a). Therefore (for these) the constant remains arbitrary, and when for this case this latter constant is so determined m3 that ae then in equation (1a) the intensity of gravity (7. e., the accel- eration, —g) can be added to the left-hand member. The boundary condition for a discontinuous surface is that the pres- sure shall be equal on both sides of such a surface, which condition will be satisfled for P when it is so for p. As regards the re-action of the fluid against a solid body moving in it, the pressure against the unit of area of surface increases as n’r. In the same ratio, the frictional forces increase that are proportional to d ya" similar ones. But for corresponding similar portions of the surfaces of the bounding bodies of the forces of pressure and of friction increase as JU the product of k <, with the differential quotients such as —, and other 2 a: 2 ne" NP = YY. The work needed to be done by the immersed bodies to overcome these resistances will therefore for equal intervals of time increase as ng’r. In general therefore for compressible fluids [gases] and for heavy cohesive fluids [liquids under gravitation] with free surfaces, if the movement is to be completely and accurately transferred from the first fluid to the other, the three constants n, q,r are completely determined by the nature of the two fluids. Only in the case of incompressible fluids without free surfazes does one constant remain indeterminate. Now there is a large series of cases where the compressibility not only for cohesive, but also for gaseous fluids, has only an inappreciably small influence. To such cases the following considerations apply: If the coustant n becomes smaller whiie 7 and g remain unchanged, this indicates that in the second fluid the velocity of sound diminishes pro- portionally with n, and similarly for the velocities of the moving mate- rial portions, whereas the linear dimensions increase proportional to the reciprocal of n. For a constant value of 7, that is to say, a con- stant density of the second fluid, a diminution of the velocity of sound corresponds to an increased compressibility of the fluid. Therefore with an increased compressibility, the movements remain similar. Hence it follows that when we diminish n, while leaving the compressi- bility of the fluid unchanged, the movements of the fluid themselves change and become similar to those that a more incompressible fluid would execute in a narrower space. Therefore for smaller velocities, PAPER BY PROF. HELMHOLTZ. ca even in extensive spaces, the compressibility loses its influence. Under such circumstances gases move like cohesive incompressible fluids | viz, liquids], as is well known practically from many examples. If the velocities of the material parts are in general very small, as in the case of exceedingly small oscillations, so that the course of the movement remains sensibly unchanged for a uniform increase in these velocities, then it will only be the velocity of sound that changes, and our proposition will take the following form: The sonorous vibrations of a compressible fluid can, in larger spaces, behave mechanically the same as more rapid oscillations of a less compressible fluid in smaller spaces. An example of the utilization of the similarity here spoken of is found in my investigations on the acoustic movement at the ends of open organ pipes.* In that study the possibility of replacing the analytical conditions of the motion of the air by the simpler ones of the motion of water depended on the principle that the dimensions of the given spaces must be very small in comparison to the wave lengths of the existing acoustic vibrations. On the other hand the viscosity also shows itself less influential in the movements of fluids in large spaces. If we let n remain unchanged while q increases we obtain the same ratio between the frictional forces and the pressure forces. That is to say, if we increase the dimensions and the friction constants in the same ratio, then the movements in the enlarged system remain similar so long as the velocities do not change. Hence it follows that in such an enlarged model, when the friction con- stant is not increased in the same ratio, but remains unchanged, the friction loses in influence for the same velocity. That which holds good for greater dimensions with unchanged velocities also obtains for increased velocities with unchanged dimensions. For one can also simultaneously let x increase proportional to q. {n fact, in most practical experiments in extended fluid masses, the resistance that arises from the accelerations of the fluid,t and especially in consequence of the formation of surfaces of discontinuity is by far the most important. Ifs magnitude increases proportionally to the square of the velocity, whereas the rasistance depending upon the fric- tion proper (internal friction or viscosity and surface-hesion), which increases simply in proportion to the velocity, becomes appreciable only in experiments in very narrow tubes and vessels. Neglecting the friction, that is to say, if in the above equations we put the constants ih) then will the constant q also become arbitrary, and we can change the dimensions and velocities in any ratio whatever. If however the force of gravity comes into consideration as in the * Borchardt’s Journal fiir Mathematik, 1859, vol. Lvi1, pp. 1-72. t [These resistances are those that I have called ‘‘ convective” in my Treatise on Meteorological Methods and Apparatus.—C. 4.] 4 (2 THE MECHANICS OF THE EARTH’S ATMOSPHERE. case of waves on the free surface of water, then, according to the . ns . remarks already made the ratio —must remain unchanged, therefore q q must be put =n*. Then will X=nax Yay, (int. Z—nWz Therefore when the wave lengths increase in the ratio n? the duration of the oscillations will increase only in the ratio n, which corresponds to the well-known law of the velocity of propagation for the surface waves of water, which velocity increases as the square root of the wave length. Thusthis result is attained very simply and for all wave forms, without the necessity of knowing a single integral of wave motion. The same principle is applicable to the relative resistances that ships having x? times the dimensions and » times the velocity, experience by reason of the waves that they excite on the surface of the water. The total resistance in this case increases as q’r, and since for the same fiuid y=1 therefore the resistance increases as n° and the work needed to overcome it as n’, therefore in arather larger ratio than the volume of the ship, while the supply of fuel and the size of the boiler that must do the work can inerease only in the same ratio as the volume of the ship, namely as n°. Therefore so long as lighter machinery can not be applied (including the supply of coal) the velocity of such an enlarged ship can increase above a certain limit only by a ratio that is smaller than that of the square root of the increase of the linear dimensions. A similar computation holds good for the model of the bird in the air. When we increase the linear dimensions of a bird and would take into consideration the viscosity, we must put gq and r equal to unity be- cause the medium, namely the air, remains unchanged. Let » be a vulgar fraction, then will the velocity be reduced in the same propor- tion as the volume of the bird increases and the pressure (of the air) against the total surface of the larger bird will only attain the same value as for the smaller bird, therefore will not be able to bear up the weight of the larger bird. If we allow ourselves to neglect the friction, which according to the above remarks we can do so much the more readily the more we increase the dimensions, or for the same dimensions increase the velocities, then q is arbitrary and the change of dimensions and velocities must be so made that the total pressure against the surfaces shall increase as the . 3 weight of the body or we must have gat or q=n>. In order to ex- ecute the corresponding motions, the work that will be necessary will be pe a, qn=n =(4) Nee nia PAPER BY PROF. HELMHOLTZ. lo but the volume of the body and of the muscles that do the work in- “ay NS creases only in the ratio (i): Hence it follows that the size of a bird has a limit, unless the muscles can be further developed in such a manner that for the same mass as now they shall perform more work. Now it is precisely among the larger birds, that are capable of the greater performances in flying, that we find those that eat only flesh and fish; they are animals that consume concentrated food and need no extensive system of diges- tive organs. Among the smaller birds many grain eaters like doves and the smaller singing birds are also good flyers. It therefore ap- pears probable that in the model of the great vulture, nature has al- ready reached the limit that can be attained with the muscles as work- ing organs, and under the most favorable conditions of subsistence, for the magnitude of a creature that shall raise itself by its wings* and remain a long time in the air. Under these circumstances it is scarcely to be considered as probable that man even by means of the most ingenious wing-like mechanism that must be moved by his own museles will ever possess the strength needed to raise his own weight in the air and continue there. Concerning the question as to the possibility of driving balloons for- ward relative to the surrounding air, our propositions allow us to com- pare this problem with the other one that is practically executed in many ways, namely, to drive a ship forward in water by means of oar-like or screw-like organs of motion. In studying this we inust not consider movement on the surface, but rather imagine to ourselves a ship driven along under the surface. But such a balloon which pre- sents a surface above and below that is congruent with the submerged surface of an ordinary ship scarcely differs in its powers of motion from an ordinary ship. If now we let the small letters of the two above given systems of hydro-dynamic equations refer to water and the large letters to the air, then for 0° temperature and 760 mm. of the barometer, we have 1 r 7 4d 3 According to the determination of O. E. Meyer and Clerk Maxwell, q=90.8082 5 the velocity of sound gives for n the value n=0.2314 Hence the increase of linear dimensions is 13,4928 *( That is, by the work done by its wings; this of course does not cover the case of soaring where the muscles do no lifting work but simply keep the wings in the best position for the wind to act on them.—C, A. ] 74 THE MECHANICS OF THE EARTH’S ATMOSPHERE. and the inerease of volume is (4 )'=s2.61 The work in this case is very slight, namely, Pipe 5114.3 The ship, including the crew and the load, must weigh as much as the volume of water displaced by it. The balloon, filled with hydro- gen, in order to carry an equal weight with the ship, must have a vol- ume 837 times as great. If it is filled with illuminating gas of a specific gravity 0.65 relative to that of the air, it must have a volume 2,208.5 times as great as the ship. Thus, the weight tnat the balloon must have for the given dimension is now determined. The weight for the 42.6 1 b hydrogen balloon would be $37 19.6 that of the ship; that of the 42.6 , illuminating gas balloon would be - 9908.55 LS g that of the ship. The work that is necessary under such geeuaee to propel the balloon, as the above number for the value of q’nr shows, would, how- ever, for the adopted small velocity, be reduced in much greater propor- tion than that of the weight of the balloon to the weight of the ship, so that the work here required for the given weight is easy to accomplish in the balloon. For even when wesochoose the ship thatits load in excess of that of the driving machine (or in excess of the men who act as the machine) is negligible, then the weight of the illuminating-gas balloon need 1 , : Sai : é be only 52 part of the weight of this driving machine, but the machine thus carried by it would also have to do only the one a of the work of the ship’s machine, it would, therefore, need to bave a less weight in about this latter ratio. Especially would this latter be the case when we utilize men as the driving machine, whose work and weight both increase proportionally to the number. So far we can therefore apply the transference from ship to balloon with complete consideration of the peculiarities of air and water. As a maximum velocity for fast ships (large naval steamers), ‘‘ The Engi- neer’s Pocket Book,” published by the society ‘‘ Die Hiitte,” gives 18 feet per second, or 2.7 German miles, or 21 kilometers per hour. Similarly built balloons, with relatively very feeble or small propelling machin- ery, can attain about one-fourth of this velocity. Ships of the above-given dimensions find the limit of their efficiency bounded by the limits of the power of the machinery (including the fuel) that they can carry. However, the practical experience thus far attained allows us to neglect the influence of viscosity for large, swift PAPER BY PROF. HELMHOLTZ. Co ships, and therefore to arbitrarily assume the constant q, as also n (when we can neglect the movements at the surface). If we assume that q increases proportionally to n, then the dimensions remain un- changed, the velocities increase as n, the resistance as n’, the work done as n°, If therefore we were able to build a marine engine of the same weight as the present ones, but of greater efficiency, we would then be able also to attain greater velocities. We must compare the balloon with such a ship, although the latter has not yet been constructed, in order to attain complete utilization of the propelling machine that goes up with it. But for this case also and for unchanged dimensions, when the velocity increases as n the work must increase as n°. Now the ratio between weight and work done by the men who are earried by a balloon ean only, for balloons of very large dimensions, be perhaps more favorable than for a war ship and its machinery. For the latter I compute from the technical data that to attain a velocity of 18 feet requires an expenditure of one horse-power to 4636.1 kilo- grams weight.* On the other hand, a man weighing 200 pounds, who under favorable circumstances can do 75 foot-pounds of work per second during eight hours daily, gives on the average for the day one horse-power per 1,920 kilograms. When therefore the balloon weighs one and a half times as much as the laboring men whom it carries, then the ratio is the same as for the ship. Dupuy de Lome has carried out his experiments under somewhat less favorable cireum- stances; in his balloon were a crew of 14 men whose weight was one- fourth of the whole, and of whom only eight worked. Under these circumstances it is a relatively very favorable assumption when for the balloon we assume the ratio between the weight and the work to be the same as for a war steamer. We can therefore for the illuminating gas balloon increase the ratio oh et between work and weight by in- creasing n so that the ratio shall equal unity; that is to say, equal to the value for ships. In this case we must have n=4. 6208. Since now the velocity U of the balloon which we have before com- puted under the assumption of a perfect geometrical similarity in the *The speciai data on which the computation is based are as follows: LI = length of the ship over all = 230 Prussian feet. B= breadth of the ship over all = 54 ef a4 H = total height of the ship = 24 feet. T= depth under water = H—4B V =volume of water displacement = 0.46 ZL. B. T. Weight of one cubic foot of sea water = 63. 343 Ibs. A the area of the immersed principal section = 1000 sq. feet. The total work =¢ A V? Where G— OSAGe 76 THE MECHANICS OF THE EARTH’S ATMOSPHERE. movements has only 0. 2314 that of the velocity wu of the ship, therefore there results: U—0. 2314. n. u=1. 06925u. For the hydrogen balloon under the same assumptions the velocity will be somewhat larger, since in this case we have to assume gi a See a n=l. 5114 Hence, n=6. 390 U=0. 2314 .n .u=1. 4786u. which is nearly one and a half times the velocity hitherto attained in naval steamers. This last velocity for a hydrogen balloon would suffice to go slowly forwards against a fresh breeze. But it is to be remarked that these computations relate to colossal balloons whose linear dimensions are three and a half times larger than those of the immersed portion of a large man-of-war, and that. the inflammable gas balloon would weigh 60220 kilograms, while that of Dupuy de Lome only weighed 3879) kilograms. In order to return to dimensions that are attainable in actual practice, one must so diminish g and » as that the ratio of the work to the weight shall re- main unchanged, therefore, so that gn: ( Sls iL, whence (=n In this way the velocity » will diminish as the cube root of the linear dimensions or as the ninth root of the volume or the weight. This reduction is relatively unimportant. If we pass, for example, from our ideal balloon down to one of the weight of that of Dupuy, there results a reduction of the velocity in the ratio of 1.36 to 1; this would give a velocity of 14.15 feet per second, or 16.5 kilometres per hour. The linear dimensions of the balloon would therefore exceed in the ratio 1.4 to 1 the dimensions of the ship that is compared with it. The ratio between work and load in Dupuy’s experiments correspond to the above assumptions very nearly. The eight men that worked for him are, according to our previous estimate, to be put down at 800 kilo- grams, which is rather more than one-fifth of the total weight. Since however the experiment only lasted a short time, therefore these men could work the whole time through with their whole energy, whereas. in our computation only the average value of eight hours of work is assumed for the whole day. Therefore these eight men are equal to twenty-four steady workers, whereby the difference is more than made up. Dupuy gives, as having been attained independent of the wind, PAPER BY PROF. HELMHOLTZ. el on the average 8 kilometers per hour for the whole duration of the experiment, and 104 kilometers attained by intense work. He is there- fore not very far behind the limit that my computations show attaina- able with a balloon of such dimensions. In the preceding computation we have however only taken account of the ratio between the effective force and the weight, and have assumed that the form of such a balloon and of its motor can be attained with the materials at our disposal. But here seems to me to lie one of the principa! difficulties of the practical execution. For the parts of a machine made of rigid bodies do not by a geometrically Similar increase in their linear dimensions retain the necessary stiff- ness; they must be made thicker, and therefore heavier. If on the other hand with small motors one would attain the same effect, by means of greater velocity, then work is dissipated. The pressure against the whole surface of a motor (a ship’s propeller, or oars or pad- - dles) increases as qr. If this pressure, which determines the propel- ling force, is to remain unchanged, we can only diminish the dimen- sions in so far as we increase n, and therefore also the velocities; but then the work increases also as q?n7, and therefore proportionally to n. Therefore one can work economically only with relatively slew-moving motors of large surface. And to realize this in the necessary dimen- sions without too great a load for the balloon will be one of the great- est practical difficulties. —— —_ Vv. ON ATMOSPHERIC MOTIONS.* (FIRST PAPER.) By Prof. H. voN HELMHOLTZ. I. INFLUENCE OF VISCOSITY ON THE GENERAL CIRCULATION OF THE ATMOSPHERE. The influence of fluid friction in the interior of very extended regions that are filled with fluid and contain no vortex motion is always rela- tively very small. This can be proved from considerations that are based upon the principle of mechanical similarity. If we form the Eulerian hydro-dynamie equations and in them indicate by u, v, w the components of the velocity parallel to the axes of z, y,2; by ¢ the den- sity, by p the pressure, by P the potential of the forces that act upon a unit of mass of the fluid; then if we consider P, ¢, p, u, v, w as fune- tions of x, y, 2, t we have, as is well known, the following partial differ- ential equations for a fluid under the influence of friction? : IP ldp du yu yu ju iP Toa. oe. Fa Se u- re a 3 Ji ptangeemey (Lay ei gear feat os a -(4 epee (1) ) ’ or +) aw 508 2 NEM EO) OS) ee ot ov oy 02 Two other equations symmetrical with regard to the other codrdinates. are to be added to the first of these equations. If now we have found any special integral whatever of these equations, which obtains for a definite region, then the equations will also hold good for a second case where all the linear dimensions a, y, 2 and also the time ¢ and the fric- tion constant k? are increased by a factor n, but where P, p, ¢, u, v, w retain for every value of the new coérdinates na, ny, nz, nt, the same values as they had in the first case for the original codrdinates a, y, 2, t. Hence it follows that when in the movement of the magnified mass the friction constant can be also simultaneously and correspondingly increased, the P RTO fie. Sitz ungiberenee of the Royal Prussian Academy of Science at Berlin, 1888, May 31, pp. 647-663. {+ Namely viscosity as represented by Maxwell’s kinematic coefticient v or Helm- k?__0,0001878 7? = ce pe neg holtz’ == puizy3 13417 } 73 > PAPER BY PROF. HELMHOLTZ. 79 movement takes place in an analogous manner, only slower. When this is not the case and when the friction retains its value unchanged then will the influence of the friction on the increased mass be very much less than upon the smaller mass. In consequence of this the greater mass will show the effects of its inertia as influenced much less by friction. It is to be remarked that the potential P remains unchanged by the : : REE. : increase of the mass, but the force a is reduced to a of its value and } n c that the whole process as already remarked requires for its completion n times the time. Since the density and pressure are to remain unchanged therefore also any temperature differences that are present retain their magnitude and influence and do not disturb the relations implied in the mechani- cal similarity. Unfortunately we can not imitate in small models the varying density of the atmosphere at different altitudes since we can not correspond- ingly change the force of gravity that is included in the expression . . Our mechanical comparisons are only able to imitate an atmos- C phere of constant density. Such an one must, as 1s well known, have an altitude of 8026 metres at 0° C. in order to produce the mean baro- metrical reading of 76 centimetres of mercury. If we desire in a model to represent the atmosphere by a layer of one metre in altitude, then we would need to reduce the day to 10.8 seconds, or the year to 65. 5 minutes, and the influence of friction in movements at velocities that correspond to those of the atmosphere would in asmall model be 8026 times as great as in the atmosphere. The loss of living force in the atmosphere during a year would therefore correspond to that lost in 65. 5 3096 of a minute, which corresponds to less than a half a our model in second. On the other hand it is possible with the measured value of the friction constant of the air to compute for some simple cases how long a time would be required in order to reduce to one-half of its velocity any motion that is hindered only by internal friction. In this case the assumption of a constant density is for our purpose more unfavorable than the adoption of the actual variable density. Assume that a stratum of air whose constant density is such as that of the lower stratum of the atmosphere, spreads over an unlimited plane and has a forward movement whose velocity is wu in the direction of « parallel to the plane. Let 2 be the vertical codrdinate, then the equa- tion of motion for the interior of the mass is ou ou at roe vi 22 — ) ° ° ° ° ° e . ° (2) t = o | = = ————_ 80 THE MECHANICS OF THE EARTH’S ATMOSPHERE, Assume that the fluid adheres to the earth’s surface where 2 = 0, therefore for this surface we have a =] 0,5 Ao ws +. )is) oped ee At the upper boundary surface where ¢ = / the fluid experiences no friction, therefore for that surface we have ce bk eed LR eee) 7 Zi fh Uw Of the special integrals of the equation (2) that fulfill the boundary condition (2a), namely: “w= Ae-™ sin (qx) hee. n= a y? é the one that also fulfills the condition (2;) and is the most slowly dimin- ishing is given by the value p= a 2h Hence follows k? nm (aa We ° ARP The factor e-™t becomes 1 at the time t=0: in order that this factor may be equal to one-half we must have nt = nat. log. 2 = 0.69315. According to Maxwell’s determinations (Theory of Heat, London PF he i 1871, p. 279, where — is expressed by v and k® by “), we have ke = [centimetre]? — = 0.1: ), 060 | oy a : 3417 [1 + 0.003666, | qecond where 4, indicates the temperature centigrade. From this there re- sults, for the temperature 0° C., t = 42747 years. If we distribute the same mass of air throughout a thicker stratum with less density so that ¢. h, as also the A? which is independent of ¢, retains its value unchanged, then ¢ must increase with hk. Hence it follows that in the upper thinner strata of the atmosphere the effect of viscosity propagates itself through atmospheric strata of equal mass more slowly than through the lower denser strata. On the other hand an increase of the absolute temperature ¢@ will PAE diag 1 cause the time ¢ to diminish as ¢ . The lower temperature of the upper - =* a a a we eile PAPER BY PROF. HELMHOLTZ. 81 strata of the atmosphere also diminishes the effect of the viscosity here under consideration. This computation also shows how extremely unimportant for the upper strata of the air are those effects of viscosity that can arise on the earth’s surface in the course of a year. Only at the fixed boundaries of the space that the atmosphere fills, or at the interior surfaces of discontinuity where currents of different ve- locity border on each other, do the surface forces remain the same when the scale of dimensions is increased and the coefficient of friction is not simultaneously increased, and this allows us to recognize that the annulment of living force by visecusity can take place principally only at the surface of the ground and at the discontinucus surfaces that occur in vortex motions. A similar relation obtains with regard to those temperature changes that can be effected by the true conduction of heat in the narrower Sense, namely, the diffusion of moving molecules of gas between the warmer and colder strata. The coefficient x of conduction for heat, when we choose as the unit of heat that which warms a unit volume of the substance by one degree in temperature (or the thermometric co- efficient of conduction), is, according to Maxwell (Theory of Heat, page 302): Sy eras cma Ca) where y is the ratio between the two specific heats of gases. In order to solve the corresponding problem for the conduction of nd heat this « is to be substituted in equation (2) instead of a and if we put y =1.41 it is seen thatin the above-assumed atmosphere of uniform density under a pressure of 76 centimetres of mercury and at a tem- perature of 0° an interval of 36164 years would be necessary in order by conduction to reduce by one-half the final difference in temperature of the upper and lower surfaces. Therefore also in the interchange of heat only its radiation and its convection by the motion of the air need be taken into consideration, except at the boundary between it and the earth’s surface and at the interior surfaces of discontinuity. On the other hand, simple computations have frequently shown that an unrestricted circulation of the air in the trade zones can not exist even up to 30° latitude. If we imagine a rotating ring of air whose axis coincides with that of the earth and which, by the pressure of neighboring similar rings, is pushed now northward and now southward, and in which we can neg- lect the friction, then, according to the well-known general mechanical principle, the moment of rotation of this ring must remain constant. We will indicate this moment as computed for the unit of mass by Q, 80 A——6 82 THE MECHANICS OF THE EARTH’S ATMOSPHERE. and the angular velocity of the ring by w, and its radius by ; then, as is well known, OG Gesaw she a) and therefor @w must vary inversely proportionally with pp? If we indicate the mean radius of the earth by A = 6579600 metres, the geographical latitude by 4, and the velocity of diurnal rotation of the earth by a, then the corresponding relative velocity at the earth’s surface for a ring of air that preserves a calm at the equator is (— (@) — Go) = G% l aag-k cos 6 |: For air that is resting quietly at the equator in the zone of calms and is thence pushed up to the latitude of 10°, this expression gives the ac- quired wind velocity 14.18 metres per second, and similarly for air pushed up to latitude 20°,57.63 metres, and for 30°, 133.65 metres per second. Since 20 metres per second is the velocity of a railroad express train, therefore these numbers show without further consideration that such gales do not exist over any broad zone of the earth. We therefore ought not to make the assumption that the air which has risen at the equator reaches the earth’s surface again unchecked in its motion even 20° farther northwards. The matter is not much better if we assume the atmospheric ring resting at some intermediate latitude. In that case it would give an east wind at the equator, but a west wind at 30° latitude ; but both ve- locities would far exceed the ordinary velocities of the observed winds. Since now in fact observations do demonstrate a circulation of the air in the trade-wind zone, therefore the question recurs: By what means is the west-east velocity of this mass of air checked and altered ? The resolution of this question is the object of the following remarks: Il, ON THE EQUILIBRIUM OF ROTATING RINGS OF AIR AT DIFFER- ENT TEMPERATURES. If we introduce into equations (1) only rotatory motions about the axis, whereby w, Q, and p retain the significance just given them we then hare w==0 O a v= —2 WD=—Z2Z. O wW=YW=Y,. y y a PAPER BY PROF. HELMHOLTZ. 83 and if we consider a steady mode of motion, in which, p, P, and € are functions of v and p only, then the equations (1) become EES DS) RM len eke BE OE ORY, a gg MO Mine p al et Libs earls op te ee OF NOL es )pip- i ws ps The two last equations combine into the one following : a ee —S at RRR coe erated toute Ce : (3b) Equation 1, is satisfied by the above adopted values of u, v,w. There- _ fore the only equations to be satisfied are (5a) and (35). As concerns the value of the density ¢, this depends upon the pressure pand the temperature 6. Since appreciable effective conduction of heat is excluded, therefore we must here retain the law of adiabatic variations between p and ¢; therefore we have pyar a eRe wherein y again represents the ratio of the specific heats. If we indi- cate by 4 the temperature that the mass of air under consideration would acquire adiabatically under the pressure po (wherefore 6 indi- cates the constant quantity of heat contained in the air while its tem- perature is varying with the pressure), and if we put 0pm ROT st then we have iL P _( by, op . lee Ose? Red or if, for further abbreviation, we put iy ae 8 ° e ° ° . ° (3c) y-1 Oa TO Soh goa) Wire ville Ween (OO) we shall have Ph -) On : 84 THE MECHANICS OF THE EARTH’S ATMOSPHERE. wherein q indicates a constant peculiar to the gas and independent of 4aud p. Similarly we also have lL Op 7 ee pee ox ou and therefore within a stratum of air having a constant 6 and O we have, according to equations (3a) and (3d), 1 2? FS A ee . (3e) OG «eee tae The very slight deviation of the earth from a spherical form allows us to simplify the computation on the one hand by regarding the earth’s surface as a sphere, but on the other hand by giving the potential P an addition, the effect of which is that for the normal velocity of rotation a of the earth, its spherical surface becomes a level surface. To this end we put G 1 ee P=— : +560" 0", |Where G=normal force of gravity: r=distance from center of gravity to point or stratum in the actual atmosphere. | This gives the component in the direction of x, of the forces acting upon the unit of mass, Oe Ga = a eae and, for the component in the direction of ,, If to the latter the centrifugal force +’. is also added, there re- mains only one force on the rotating earth and which is directed normal to the spherical surface. Thus the spherical surface becomes the level surface of the combined potential force and centrifugal force, as indeed the surface of the earth really is. Thus our equation (3e) becomes q.6.a=— . S + — ote CO 37a ee eee) - The function z which is some power of the pressure p with positive exponent, increases and diminishes with p, and remains unchanged when p remains unchanged, so that we can determine the direction of the changes of the pressure easily by the changes of z. Within a uniform stratum and with unchanged 7, that is to say, for PAPER BY PROF. HELMHOLTZ. 85 a constant elevation above the earth’s surface, z has a maximum value at the station and latitude where 9 « Beant 3 @0 P;3 or, if we introduce @ instead of Q from equation (3), the maximum oc- curs where oP = GH"; thatis to say, where the [movement of the| ring causes a calm [on the earth’s surface]. Towards this locality the pressure increases both from the pole and from the equator. III. EQULIBRIUM BETWEEN ADJACENT STRATA HAVING DIFFERENT VALUES OF @ AND Q. On both sides of the surfaces separating such strata, p and therefore aiso q-z (see equation 3d) must have the same value. If we distinguish the quantities on either side [of the boundary surface] by the indices 1 and 2 we obtain from equation (3/) i _l yGee aN Petes sas bo) SpA OE) tame [2 27-94% This should be the equation of the boundary curve, linear with res- pect to r and quadratic with respect to p. In order to find the direction of the tangent to this curve we differ- entiate equation (4) with respect to ry and p, whence we get dr ig ao laine ee) G,,_ dp, O7A—O"A, __ oi | or, if instead of we introduce the corresponding value of w from equation (3), + Car p.dp. Pe 2 ae 2 as, oi 2 , 7 ( @2" — @p = Gay") Ae Sse jee (LOY In order to decide how the two layers must lie with respect to the boundary surface if they are to have stable equilibrium, we reason as follows: The equation of the boundary surface (4) can, in accordance with the method of its deduction, be also written Ajj COMSEAMG ssf ws) sie « « (40)3 or, if we designate by ds one of its elements of length, d 5g | 7172] = =—=)e Now z, and z, are functions that also have a meaning when continued beyond the boundary curve, and can be so extended by continuous 86 THE MECHANICS OF THE EARTH’S ATMOSPHERE. change |i. e., without discontinuity]. The difference (7; — zy») will there- fore in general increase on one side of the surface for increasing dis- tance dn from this surface, but decrease, that is to say, become nega- 5 d( G@— @» tive, on theother side; and thus on the side where ee a 2) | is positive ) ae ; ‘ : we must have a (771—72) >0 or positive for every other direction dh, oh in which one nioves from any point of the surface towards the same side as dn If dh is drawn toward the other side of the surface for which 1,—7,=0, then will wh (71—72) <0, or negative. If now the difference is positive on that side of the surface designa- ted by the subscript index 1, then in case there is an infinitely small protrusion of the boundary surface toward this side, this protrusion will be pressed back by the exterior and greater 7,; similarly an infinitely small protrusion toward the negative side will also be pushed back, since there, on the other hand, z, diminishes more rapidly in the interior of such protrusion. Therefore in both these cases the equilibrium is stable. On the other hand, the equilibrium is unstable when the dif- ference (77;—72) on the side of 7, is negative. Now we need not form the differential quotients for the direction dn. It suffices to form them for dr or dp, and to merely determine whether the positive dr or do look toward the side whose index is 1 or that whose index is 2. By forming these differential quctients from the equation (3f) there results Um—m)_ Gill ae = an a | Sa aay c The differential quotient is positive vhen 4, > 4 The partial dif- ferentiation with respect tor while p remains unchanged, indicates a progress in an ascending direction parallel to the earth’s axis; that is to say, in the direction of a line pointing towards the celestial pole. The equilibrium is stable when the strata containing the greater quantity of heat lie at higher elevations on the side towards the celestial poles. We now form the other differential quotients dasa a(S OY _ gm" 2) = -) Boe: 7) ee oc) = Go,” — Gp” _ we — G" ; | ¢ ; , 4 , : - a ata ce If in these equations 4, indicates the greater quantity of heat, then the equilibrium is stable when everywhere along the boundary surface we have G1” — Gy” GIy” — GI,” amt > pr By «| 6 epee eum me eO)e ee PAPER BY PROF. HELMHOLTZ. 87 Both these values are positive where the west wind prevails; both negative where the east wind prevails. The equation (4e) can also be written d i A— - A 4 4 Q'b — Oz 26); q. fo GQ) O* + * d 3p came pe 6 =) vk 61-8 | In order that this may be positive at all latitudes, the following in- equality must be satisfied OP A> O26, or, Ov OF One Os. Ordinarily this will be the case, since in general @ increases simulta- neously with p and from a definite value at the pole to a finite value at the equator. Similarly.Q,? also increases with p, and from zero at the pole to @,” p? at the equator, so that 2 also increases from zero at the pole to a definite positive value at the equator. We will therefore des- ignate this case as the normai case. Exceptions can only occur under special conditions within limited zones. In the normal case as we progress along the same level, the warmer 7, lies on the side of the greater ; that is to say, on the side towards the equator, and equally on the side of the greater r if we progress toward the celestial pole; that is to say, o and 7 increase toward the same side of the boundary surface, and this surface must be so inclined that the tangent of its meridian section intersects the celestial sphere between the pole and the point of the horizon lying immediately be- neath it. Near the equator, where the pole rises very little above the horizon, this gives an inclination to the boundary surface such that it makes a very small acute angle with the horizon. In accordance with this, equation (4a) shows us that under those cir- fe : : cumstances ae is negative along the boundary surface itself. Therefore the normal inclination of the bounding surface is in an ascending direction toward a point situated beneath the celestial pole. If on the other hand exceptional localities should exist at which 2 ee oe cod pt PEPE <0 MES eee an CeO) ~ then in such cases according to equation (40) 7, will be positive; that is to say, the boundary line will ascend to higher levels as we depart from the earth’s axis. Since moreover equation (4d) shows that as we proceed in the diree- tion of a line drawn to the pole, the warmer air must lie higher, there- Se eee —. 838 THE MECHANICS OF THE EARTH’S ATMOSPHERE. fore this line can not twice intersect the boundary surface between two layers, and consequently in the abnormal case this line must necessarily lie between the boundary surface and the horizontal plane located at the pole. Therefore the tangents to the meridional section of the boundary surfaces must intersect the greater arcs on the celestial sphere somewhere between the pole and the equatorial side of the hor- 1zon. The smaller the difference of temperature is relative to the difference of the velocities of rotation so much the nearer does the tangent just referred to approach the pole. Moreover at different points of the bounding line of the same two layers there can occur both normal and abnormal inclinations. For since in the expression (see equation 4h) on whose positive or negative value such occurrence depends, the Q and 6 throughout the extent of each layer are constant, therefore for the same altitude above the earth this value can have & positive value near the equator but a negative value near the poles. Between these the boundary curve must attain & maximum altitude where the quantity under consideration passes from positive through zero to negative. At this place also, according dr to equation (4a), we have ios 0, therefore yr is a limiting value and is here a maximum. Location of the strata in the case when the velocity of rotation varies contiuuously with the quantity of heat contained.—The considerations hitherto set forth can also be extended to the case where 0 is a con- tinuous function of 4, and the value of 4 in the atmospheric strata is continually changing. The individual strata are in this case to be con- sidered as indefinitely thin. Equation (4a) now becomes. io ia, Gg dr dp e [ | a 1 — — Gy” p* ie 3 d (i ) dot. dO? ee =7| 0 =f Agra | In order that the equilibrium may be stable the quantity of con- tained heat (see equation 4h) must increase in the direction towards the celestial pole. But the layers of similar air are less inclined than the inclination of the polar axis at all places where the quantity O? — 6. ts < an’ pt; ( but on the other hand their inclination is steeper where the left-hand side of this inequality is greater than the right. a PAPER BY PROF. HELMHOLTZ. 8% IV. GRADUAL VARIATIONS OF THE EQUILIBRIUM BY FRICTION AND HEATING. It is well known how very differently the propagation of changes of temperature in the air goes on according as heat is added or withdrawn below or above. If the lower side of astratum of air is warmed, as occurs at the sur- face of the earth, by action of the solar rays, then the heated stratum of air seeks to rise. This is effected very soon all over the surface in small tremulous and flickering streams such as we see over any plane surface strongly heated by the suns but soon these smaller streams. collect into larger ones when the locality affords opportunity, especially on the side of a hill. The propagation of heat goes on relatively rapidly through the whole thickness of the atmospheric layer, and when it has a uniform quantity of heat throughout its whole depth and is therefore in adiabatic equilibrium then also the newly added air seeks de nova to distribute itself through the entire depth. The same process occurs with like rapidity when the upper side of a stratum of air is cooled. On the other hand, when the upper side is warmed and the lower side cooled such convective movements do not occur. The conduction of heat operates very slowly in Jarge dimensions, as I have already ex- plained above. Radiation can only make itself felt to any considerable extent for those classes of rays that are strongly absorbed. On the other hand, experiments on the radiation from ice and observations of nocturnal frosts show that most rays of even such low temperatures can pass through thick layers of clear atmosphere without material absorption. Therefore a cold stratum of air can lie for a long time on the earth, or equally a warm stratum remain at an altitude, without changing its temperature otherwise than very slowly. Similar differences exist also in the case of the change of veloc- ity by friction. For the normal inclination of an atmospheric stratum its upper end is nearer to the earth’s axis than its lower end. If the stratum appears at the earth’s surface as a west wind, then the moment of rotation of the lowest layer is delayed [by resistance of the earth’s surface], its centrifugal force is diminished, and on the polar side of the stratum this lowest portion will slide outwards, approaching the axis in order to find its position of stable equilibrium at the upper end of the stratum. This movement will ordinarily take place in small trem- ulous streams similar to the ascent of warm air and must diminish the moment of rotation of the whole layer rather uniformly, but in the upper portions a little later than in the lower. Since, however, this latter effect distributes itself throughout the whole mass of air, it will become much less apparent on the lower side of the stratum than if it were confined to the lower stratum. 9() THE MECHANICS OF THE EARTH'S ATMOSPHERE. For the east wind matters are Prec Its moment of rotation is increased by the friction on the earth’s surface. The accelerated mass of air [the ground layer] already finds itself in that position of equi- librium which it has to occupy within its stratum, and can only press forward equatorially along the earth’s surface into the stratum lying in front of it. If itis also simultaneously heated then the resulting ascent takes place more slowly than would occur in a stratum of air that is at rest at the bottom. Hence it is to be concluded that in the east wind, the change due to friction is confined to the lower layer of air, and furthermore that it is relatively more effective here than in the case of a west wind of equal velocity. In general, the retarded layer of air will press forward to- ward the equator, in the Northern Hemisphere as northeast wind. In this motion it will continue to appear as an easterly wind since it is con- tinually arriving at more rapidly rotating zones on the earth. The air of the stratum lying above the retarded layer will, where the region is free from obstruction, as at the outer border of the trade wind zone, fall behind and will appear as an east wind, retaining its moment of rotation unchanged and gradually pushing toward the equator will itself in its turn experience the above described influence of friction. I would here further remark that the water so abundantly evaporated in the tropical yone also enters into the trade wind, but with the greater velocity of rotation of the revolving earth and must diminish the retardation of the latter with respect to the earth. The lower layers of the trade wind can press in under the equa- torial calm zone itself only when any difference between their velocity of rotation and that of the earth’s surface is entirely destroyed. They then blend with the zone of calms and increase its mass so that the lat- ter broadens with its inclined boundary surface always higher above the layer of diminishing east wind beneath it. Thus it is brought about that whereas below [nearer the earth’s sur- face] mostly continuous changes are taking place in the temperature and the moment of rotation of the strata, on the other hand above, the boundaries of the broadening zones of calms (that have the great mo- ment of rotation that pertains to the equatorial air and which at 10° latitude must appear as a strong west wind, and at 2U° latitude as a westerly storm), occur in direct contact with the underlying stratum that has less velocity of rotation and lower temperature. Evidently the upper side of this latter |lower] stratum can scarcely be changed as to the quantity of its contained heat and of its moment of rotation, while after the loss of its lower layer it is being pushed sidewise and towards the equator. As I have already shown in my communication to this Academy, April 23, 1868, on “ Discontinuous Fluid Motions,’”* such discontinuous motions can continue fora while, but the equilibrium at their boundary *[See No. III of this collection of Translations. ] PAPER BY PROF HELMHOLTZ. 91 surfaces is unstable, and sooner or later they break up into whirls that lead to general mixture of the two strata. This statement is confirmed by the experiments with sensitive flames and by those in which by means of a cylindrical current of air blown from a tube we make a sec- tion in a flame and thus make visible the boundary of the moving and the quiet mass. If, as in our case, the lower stratum is the heavier it can be shown that the perturbations must at first be similar to the waves of water that are excited by the wind. The process is made evident by the striated cirrus clouds that are visible when fog is pre- cipitated at the boundary of the twostrata. The great billows of water that are raised by the wind show the same process which is different in degree only, by reason of the greater difference of the specific gravi- ties. The severer storms even turn the aqueous billows to breakers, that is to say, they form caps of froth and throw drops of water from the upper crest high into the air. Up toa certain limit, this process can be mathematically deduced and analyzed, on which subject I pro- pose alater communication. For slighter differences of specific gravity the result of this process must be a mixture of the two strata with a formation of whirls and under some circumstances with heavy rainfall. An observation of one such process under very favorable circumstances Ionce made accidentally upon the Rigi and have described.* The mixed strata acquire a temperature and moment of inertia whose values lie between those of the component parts of the mixture, and its position of equilibrium will therefore be found nearer the equator than the position previously occupied by the colder stratum that enters into it. The mixed stratum will descend toward the equator and push back the strata lying on the polar side. Into the empty space thus created above, the strata from which this descending portion has been drawn stretch upwards, and thus their cross section must be dimin- ished. Wherever the lower layers are pushed apart by descending masses of air, as is well known, there arise anti-cyclones; wherever cavities or gaps arise by reason of ascending masses of air, there arise cyclones. Anti-cyclones and the corresponding barometric maxima are shown, with very great regularity, by the meteorological charts + along the very irregularly varying limits of the northeast trade in the Atlantic Ocean—in the winter, under latitude 30°; in summer, under 40° latitude. On account of the inclined position of the strata, the rain that frequently forms by reason of the mixture of air (Dove’s Sub- tropical Rain) falls somewhat farther northward because the water must fall down almost vertically. ¢ “See Proceedings of the Physical Society in Berlin, October 22, 1886. t Daily Synoptic Weather Charts. Published by the Danish Meteorological Insti- tute and the German Seewarte, Copenhagen and Hamburg. {[The results stated in the above paragraph were subsequently greatly modified by Helmholtz. See Section v of his second memoir, or page 98 of these Transla- tions.—C. A.] 92 THE MECHANICS OF THE EARTH’S ATMOSPHERE, Therefore the zone of cyclones begins there, but these become more frequent farther northward. Wecan certainly assume that the process of mixture is not perfected immediately at the exact border of the trade-wind zone, but that a part of the rapidly-rotating warm upper stratum remains unchanged or half mixed, which will presently bring about new mixtures farther on toward the pole. In general, in this zone of mixture, even below at the earth’s surface, the west wind must retain the upper hand because the increase of the total moment of rotation which the mass of air, through friction, experi- ences in the east wind of the trade zone must finally rise to such a pitch that somewhere the west wind again touches the earth and experiences sufficient friction to entirely give back the increase that it had. The masses of air resting in the equilibrium of stratification can certainly have no long-continued motion of rotation that differs essentially from that of the earth beneath them. When therefore they are mixed with the stronger west wind of the air from above, they receive a movement toward the east. Moreover the falling rain that in great part comes. from the upper west winds, must transmit its motion to the lower strata through which the rain falls. Eventually all zones that are pressed polewards by intermixed masses moving equatorially and descending from them will become west winds. Another permanent source of winds is the cooling of the earth at the poles. The cold layers endeavor to flow outwards from each other at the earth’s surface and form east wind (or anti-cyclones). Above these the warmer upper strata must fill the vacancy and continue as west winds (or cyclones). Thus an equilibrium would come about, as. is shown in Sect. 11, if it were not that the lower cold stratum acquires, through friction, a more rapid movement of rotation, and is therefore competent for further advance. In doing this, according to the above given views this lower stratum must remain on the earth’s surface. That in fact it does so is shown by frequent experiences during our northeast winter winds whose low temperatures frequently enough do not extend up to even the summit of the North German Mountains. Moreover on the front border of these east winds advancing into the warmer zone, the same circumstances are effective in order to bring about a discontinuity between the movement of the upper and lower currents, as in the advancing trade-winds, and there is therefore here a new cause for the formation of vortex motions. The advance of the polar east wind, although recognizable in its principal features, proceeds relatively very irregularly since the cold pole does not agree with the pole of rotation of the earth, and also because low mountain ranges have a large influence. In addition: to this comes the consideration that in the cold zone fog causes only a mod- erate cooling of the thicker stratum of air, but clear air brings about a very intense cooling of the lower layer. By such irregularities, it is brought about that the anti-cyclonic movement of the lower stratum PAPER BY PROF. HELMHOLTZ. 93 and the great and gradually increasing cyclone of the upper stratum (that should otherwise be expected at the pole) break up into a large number of irregular, wandering cyclones and anti-cyclones, with a preponderance of the former. From these considerations, I draw the conclusion that the principal obstacle to the circulation of our atmosphere, which prevents the development of far more violent winds than are actually experienced, is to be found not so much in the friction on the earth’s surface as in the mixing of differently moving strata of air by means of whirls that originate in the unrolling of surfaces of discontinuity. In the interior of such whirls the strata of air originally separate are wound in contin- ually more numerous, and therefore also thinner layers spirally about each other, and therefore by means of the enormously extended surfaces of contact there thus becomes possible a more rapid interchange of temperature and equalization of their movement by friction. The present memoir is intended only to show how by means of con- tinually effective forces, there arises in the atmosphere the formation of surfaces of discontinuity. I propose, at a future time, to present fur- ther analytical investigations as to the phenomena of such disturbances of continuity. . NA; ON ATMOSPHERIC MOTIONS.* (SECOND PAPER.) By Prof. H. von IELMNOLTZ. ON THE THEORY OF WINDS AND WAVES. In my previous communication made to the Academy on the 31st of May, 1888, Lendeavored to prove that conditions must regularly recur in the atmosphere where strata of different density lie contiguous one above another. The reason for the greater density of the lower stratum is conditioned by the fact that the latter has either a smaller amount of heat or a smaller velocity of rotation, if in fact both conditions do not work together. As soon as a lighter fluid lies above a denser one with well-defined boundary, then evidently the conditions exist at this boundary for the origin and regular propagation of waves, such as we are familiar with on the surface of water. This case of waves as ordinarily observed on the boundary surfaces between water and air is only to be distinguished from the system of waves that may exist between different strata of air, in that in the former the difference of density of the two fluids is much greater than in the latter case. It appeared to me of interest to investigate what other differences result from this in the phenomena of air waves and water waves. It appears to me not doubtful that such systems of waves occur with remarkable frequency at the bounding surfaces of strata of air of different densities, even although in most eases they remain invisible tous. Evidently we see them only when the lower stratum is so nearly saturated with aqueous vapor that the summit of the wave, within which the pressure is less, begins to form a haze. Then there appear streaky, parallel trains of clouds of very different breadths, occasionally stretching over the broad surface of the sky in regular patterns. More- over it seems to me probable that this which we thus observe under special conditions that have rather the character of exceptional cases, is present in innumerable other cases when we do not see it. * From the Sitzungs-berichte of the Royal Prussian Academy of Sciences at Berlin, July 25, 1889, pp. 761-780. 94 PAPER BY PROF. HELMHOLTZ. 95 The calculations performed by me show further that for the observed velocities of the wind there may be formed in the atmosphere not only small waves, but also those whose wave-lengths are many kilometres which, when they approach the earth’s surface to within an altitude of one or several kilometres, set the lower strata of air into violent motion and must bring about the so-called gusty weather. The peculiarity of of such weather (as I look at it) consists in this, that gusts of wind often accompanied by rain are repeated at the same place, many times a day, at nearly equal intervals and nearly uniform order of succession.* I think it may be assumed that this formation of waves in the at- mosphere most frequently gives occasion to the mixture of atmospheric strata and, under favorable circumstances, when the ascending masses form mist, give opportunity for disturbances of an equilibrium that had already become nearly unstable. Under conditions, such as those where we see water waves breaking and forming white caps, thorough mixtures must form between the strata of air. In the beginning of my previous paper I have explained how insuffi- cient are the known intensities of the internal friction and the thermal conductivity of gases in order to explain the equilibration of motions and temperatures in the atmosphere. Since now the mechanical the- ory of heat has taught us to consider friction in gases as the mixture of strata having different movements, but the conduction of heat as the mixture of strata having different temperatures, it is therefore in- telligible that a more thorough mixture of strata in the atmosphere must bring about, to a still higher degree, the effects of friction and conduction,t but certainly not in a quiet, steady progress, but pro- ceeding irregularly as is indeed the special character of meteorological processes. Therefore I have considered it important to develop the theory of waves at the common boundary surface of two fluids. Hitherto in studies on waves of water, so far as known to me, the influence of the air and its motion with the water has always been neglected, but this may not be done in the present work. The problem becomes thereby much more complicated and difficult; and since even the simpler problem that takes no account of the influence of the wind has at the hands of many excellent mathematicians received only incomplete and approximate solutions, under assumptions chosen to simplify the problem, therefore I pray to be excused in that I also have at first treated the simplest case of the problem, namely, the movement ot rectilinear waves which propagate themselves with unchanged forms *This assumption of the formation of billows in the atmosphere that I recently briefly expressed in my first contribution has since then also been propounded by Jean Luvini (La Lumiere Electrique. T. Xxx, pp. 368, 617, 620). + Perhaps this would correspond to the assumptions that form the basis of the theory submitted to this (Berlin) Academy by Oberbeck, March 15, 1888. [See Nos. XII and XIII of this collection.—C. A. ] PO 96 THE MECHANICS OF THE EARTH’S ATMOSPHERE. and with uniform velocity on the plane boundary surface between in- definitely extended layers of two fluids of different densities and having different progressive movements. I shall call this kind of billows stationary billows, since they represent a stationary motion of two fluids when they are referred to a system of codrdinates which itself advances with the waves. Since in the relative motion of the different parts of a closed material system nothing is changed when the whole receives a uniform rectilinear velocity toward any direction, therefore this rearrangement of our problem is allowable. Moreover I propose to-day to give only the results of my mathemati- cal investigations. The complete presentation of these I reserve for publication in another manner. Before I advance to the theory of atmospheric billows, I will however introduce a supplement to the considerations given in my communica- tion of May, 1888, by which the region in which we have to look for the conditions that give rise to atmospheric billows is better defined. V. THE ASCENT OF MIXED STRATA. In Section 11 of my previous communication I have shown what would be the law of equilibrium, in case such a condition should be attained, between atmospheric rings of different temperatures and dif- ferent speeds of rotation, which however are all assumed as being com- posed of mixtures that are similar to each other. I now return to equa- tion 4a (page 85). Let the location of a point in the atmosphere be given by the quantities p, the distance from the earth’s axis. yr, the distance from the center of the earth. Let @, be the angular velocity of the solid earth; and OQ; and Oy, be the constant moments of rotation of the unit of mass of one or the other layer of air: Let 6, and @, be the quantities that I have called the contained ca- lorie of the unit of mass of air, and that certainly may be better desig- nated by the term potential temperatures, so well chosen by Bezold, namely, those temperatures which the respective masses of air would assume when brought adiabatically to the normal pressure. Let G = constant of gravitation. In accordance with equation (4a) we now have at the boundary surfaces the relation G do FQ? 6,—0O?2 6, = ane et airy fs ~ 2 4 pt ae [ ts— 8 o* | 1 6 AND LA Op wale : : The ratio a indicates also the ratio of the sines of the two angles which the tangent to the curve in the meridional plate makes on the one hand with the earth’s axis, and on the other hand with the horizon. When, as is ordinarily the case, the warmer layer has also the greater a mead. * PAPER RY PROF. HELMHOLTZ. 97 TO, A moment of rotation, the ratio 7°, 1s then negative, and the tangent to the boundary surface cuts the celestial vault below the pole. The colder, more slowly rotating mass, which we will designate by the sub- script (2), lies in the acute angle between the boundary surface and that part of the terrestrial surface which is on the polar side of the given point. When now at the boundary surface of the two strata, a mixture takes place of the component masses m, and m2, then will the moment of rotation (.) of the mixed masses be given by the equation (M+ My) O=M,.O1 + MDa, since the sum of the moments of rotation does not vary when no exterior rotatory forces are at work. Equally will the potential temperature 6 of the mixture be given by (m+ ms) d=m, + m2 Oo. If now in equation (1), we at first substitute the mixture in place of the cooler mass (2). in order to find the direction of the boundary line between the mass (1) and the mixture, and indicate by dp; and dr, the corresponding values of dp and dr, then our equation (1), after an easy transformation, gives | ae 1 =a fh (Or= On) dp, dp} m+m h—h (1a) Since in stable equilibrium 4,<4, therefore this equation shows that dr, _dr dp, dp: Sap % ar, that is to say, that the boundary surfaces between mass (1) and the mixture must ascend more steeply with reference to the horizon than the boundary surface between (1) and (2). drs doz and the mixture will be given by the equation— 3@ dr, abit dr cake Mr (QO, —O,)? doy dp ef M+ M2 6,— 62 . ae Similarly it follows that the ratio between the cooler mass (2) Therefore a 7 (2 } cooler mass (2) and the mixture must make a more acute angle with the horizon towards the pole than does the boundary surface between the mixture and the warmer mass (1). It is to be noted that the ratios ee are positive when the tangent to the boundary line is more inclined than the line to the pole—in the other cases they are negative—and furthermore that the increase of a negative quantity means the diminution of its absolute value. 80 A——7 : that is to say, the boundary surface between the 98 THE MECHANICS OF THE EARTH’S ATMOSPHERE. But the required directions for the two boundary lines of the mixture can only exist when this mixture passes upwards between the two masses (1) and (2). Only thus can there be a condition of equilibrium. Hence results the important consequence that all newly formed mix- tures of strata that were in equilibrium with each other must rise upwards between the two layers originally present, a process that of course goes on more energetically when precipitations are formed in the ascending masses. While the mixed strata are ascending, those parts of the strata on the north and south that have hitherto rested quietly approach each other until they even come in contact, by which motion the difference of their velocities must necessarily increase since the strata lying on the equatorial side acquire greater moment of rotation with smaller radius, while those on the polar side acquire feebler rotation with a larger radius. If this occurs uniformly along an entire parallel of lati- tude we should again obtain a new surface of separation for strata of different rates of rotation whose equatorial side would show stronger west winds than the polar side, which latter might occasionally show east winds. On account of the numerous local disturbances of the great atmospheric currents there will, as a rule, be formed no contin- uous line of separation, but this will be broken into separate pieces which must appear as cyclones. But as soon as the total mixed masses have found their equilibrium the surfaces of separation will again begin to form below, and new wave formations will initiate a repetition of the same processes.* From these considerations it follows that the locality for the forma- tion of billows between the strata of air is to be sought especially in the lower parts of the atmosphere, while in the upper parts an almost continuous variation through the different values of rotation and tem- perature is to be expected. The boundary surfaces of different strata of air, along which the waves travel, have one edge at the earth’s sur- face and there the strata becomes superficial. Experience also teaches, as does the theory, that water-waves that run against a shallow shore break upon it, and even waves which originally run parallel to the shore propagate themselves more slowly in shallow water. Therefore waves that are originally rectilinear and run parallel to the banks will *In the last section of my previous paper [see ante p. 91] I located the origin of the discontinuity principally in the upper strata of the atmosphere. But in that paper the point of departure was different from the present. In that the question considered was: If at any t?me the atmosphere has attained an initial stage of contin- uous steady motion without surfaces of separation, where will such a surface first form? To this the answer is: At the upper boundary of the tropical belt of calms. At present the question is, Where in consequence of processes of mixture will the surfaces of separation necessarily be renewed? But I must take back the proposi- tion on page 91 that treats of the descent of mixed strata, now that I have found the iaw expressed in this paragraph. PAPER BY PROF. HELMHOLTZ. oo in consequence of the delay become curved, whereby the convexity of their ares is turned toward the shore; in consequence of this they run upon the shore and break to pieces there. In the next paragraphs I will show in what respects the movements and forms of water-waves must be changed in order to be applicable to the air. These relations are indeed not to be rigidly transferred from water-waves that break upon the shore to the air, and even the simpler theory hitherto developed, which neglects the influence of the air, gives no complete explanation on this point. But the conditions are not very different from those cases in which we can make a strict application, and I therefore believe there is no reason to doubt that waves of air which in the ideal atmospheric circu- lation symmetrical to the axis could only progress in a west east diree- tion, must, when once they are initiated in the real atmosphere, turn down toward the earth’s surface and break up by running along this in a northwesterly direction (in the northern hemisphere). Another process that can cause the foaming of the waves at their summits is the general increase in velocity of the wind. My analysis also demonstrates this: it shows that waves of given wave-length can only co-exist with winds of definite strength. An increase in the difter- ential velocities within the atmosphere indeed often happens, but one can not yet give the conditions generally effective for such a process. I will here also mention another point that may give rise to consid- erations against my explanation. Water-waves forced up to a great height always have narrow, strongly curved ridges and broad, flat, curved troughs. Analysis shows that this feature is independent of the nature of the medium. Atmospheric waves have, on the other hand, rounded heads when they become visible to us as bands of cirri. But we must remember that according to the proposition first formu- lated by Reye, air that has formed cloud or mist is lighter than it was before. Therefore what we see as mist rises up and increases the size of the summit of the wave more than would be the case in transparent air. VI. CONSEQUENCES DEDUCED FROM THE PRINCIPLE OF MECHANICAL SIMILARITY. If we confine ourselves to the search for such rectilinear waves as advance with uniform velocity without change of form, we may, as be- fore remarked, represent such a movement as a stationary one, by attributing to both the media a uniform rectilinear velocity equal and opposite to that of the wave. It is well known no change is thereby introduced into the relative motions of the different parts of the masses. In this way the bounding surface of the two media appears as a sur- face fixed in space; above it the upper medium flows in one direction; below it the other medium in the opposite direction. At a great dis- tance from the bounding surface both movements become rectilinear 100 THE MECHANICS OF THE EARTH’S ATMOSPHERE. currents of uniform velocity, but in the neighborhood of the wavy boundary surface the motion must follow its direction. Designate by wand v the components of the velocities of the fiuid particles at the point corresponding to the rectangular coordinates x and y; these velocities are by assumption, independent of the time, and (for an incompressible fluid whose current is free from vortices) can be presented in the form oe | where 7 is such a function of the codrdinate as satisfies the differential equation yf: 2 c c > ; Ea) . . . . . . « . . 4 ja? * oy? (2) c The equations 7 =const. are in this case, as is well known, the stream-lines of the fluid. The boundary line of both fluids must be such a stream-line, and we will give it for both sides the value ¢y=0 and ¢2=9. The above overscored letters will, in what follows, always indicate values on the boundary surface. The first boundary condition that we have to satisfy is therefore that, when we express ¢) and ¢» as functions of v and y. then the two equa- tious dyeaUeth, 6 6 1k a sw te nese rs ge shall admit of an accordant solution. The second boundary condition is that the pressure at the bounding surface shall be the same on both sides, or Di= po . . . . . . . . ’ . . . . . . . . . (2b) Now, under the adopted assumptions aud when s is the density of the tluid and C is a constant, we have p=0— —sge—as| (SP) 4 (se )']. Therefore the equation (2b) can be written: ee | Const.=(s sm) g Ban ( Se) an Oe) passes Le aene | PAPER BY PROF HELMMOLTZ. 101 The equations (2) and (2a) remain true when we increase either the values of the two coordinates v and y or those of 7%; or 72 in any given ratio. Since the densities s; and s, do not occtr in these two equations, therefore also these can change to any amount. But equation (3) re- quires that the quantities Sy “yy \2 a S2 : dye 2 1 —_ ( con® ) = anil =f pores) ONi/ & S.—8,\ JN2/ x shall remain unchanged. When therefore s; and s. vary and we put their ratio 81 —-=¢ 82 -and when further the codrdinates increase by the factor n, but 7%, by the factor a, and ¥» by the factor a, then the quantities o a? 1 ae. i = ange —— a omen Coen must both remain unchanged. Or when we, in the expressions for these quantities, put a a 6, =="and b,= = n n as the ratios by which the velocities are altered, then the above propo- sition becomes equivalent to saying that the geometrically similar wave- forms can occur when 2 2 & i and L bs L655) t= in remain unchanged, (1) If the ratios of the densities are not changed then in geometrically sim- ilar waves, the linear dimensions increase as the squares of the velocities of the two media ; the velocities therefore will increase in equal ratios. Therefore for a doubled velocity of the wind we shall have waves of four times the linear dimensions. This proposition is not limited to stationary movements, but is quite general.* The following propositions however will hold good only for stationary waves. (2) When the ratio of the density o is varied, the quantities Bi ea Oran =const. bo? 82 b,? *See my paper ‘‘ On a Theorem relative to geometrically similar movements of Fluid Bodies,” in the Monats b. der Akad. Berlin, 1873, pages 501 to 514; [or see No. IV of this collection of Translations. ] 102 THE MECHANICS OF THE EARTH’S ATMOSPHEBE. must remain constant ; that is to say, the ratio of the living forces of the corresponding units of volume must remain unchanged. As correspond- ing units of volume, those must be used that hold good in the region of rectilinear flow far from that of the wave surface; but also for such units of volume as have centers that are corresponding images for each other the same proposition hoids good. (5) If for a varied density the geometrically similar waves are to. have the same wave-length, namely, n=1, then b,; must increase as Je-1= joe Oo VS z ae b. must increase as Ji-o=,/ — Sy For air and water at a temperature of 0° C. we have the ratio l 173.4 oo For two strata of air whose temperatures are 0° and 10° the ratio be- comes és 273 283 If both boundary surfaces are to show congruent waves and therefore also equal wave-lengths, and it I designate by 4; and /, the values of the quantities }; and b, in this last case, then we have b, — 145.21 /, b,=5.316 6, therefore both the velocities, especially that of the wind relative to the waves of water, must be considerably diminished for the case of rial billows. The value of the quantity = = Dy” S] . b;?? which is invariable for any change in the material for a given form of wave whose store of energy is equal to that of the rectilinear flow along a plane boundary surface is given at least approximately according to my computations, as p=0.43103. If by a wind-force 7 we understand the difference of the movement of the two media w=b,+ b2 PAPER BY PROF. HELMHOLTZ. 103 then will for air and water "2. 0.069469 : metres and if w =10 - seconc A=0.208965 metre ; on the other hand for tae two strata of air _ fa 9.67135 Pit Pr and for w=10 metres we have ' second A=549™.65 Hence it results that when we would obtain for this form of atmospheric wave the same wind velocity as for geometrically similar water-waves we must increase the wave-length of the air wave in the ratio of 1 to 2630.3. This ratio becomes somewhat smaller when we execute the computa- tion for the lowest waves for which p=0.15692 This gives for air and water b ~? —0.090776 w and for a wind velocity of 10 metres per second, A=0.™83222 The necessary magnification of the wave-length for equal strength of wind would be 1: 2039.6 which gives a wave-length of more than 906 metres for a wind of 10 metres per second. Since the moderate winds that occur on the surface of the earth, often cause water-waves of a metre in length, therefore the same winds acting upon strata of air of 10° difference in temperature, maintain waves of from 2 to 5 kilometres in length. Larger ocean-waves from 5 to 10m long would correspond to atmospheric-waves of from 15 to 30 kilometres, such as would cover the whole sky of the observer and would have the ground at a depth below them less than that of one wave-length, therefore comparable with the waves in shallow water, such as set the water in motion to its very bottom. The principle of mechanical similarity, on which the propositions of this paragraph are founded, holds good for all waves that progress with an unchanged form and constant velocity of progress. Therefore these propositions can be applied to waves in shallow water, of uniform 104 THE MECHANICS OF THE EARTH’S ATMOSPHERE. depth, provided that the depth of the lower stratum in the image varies in the same ratio as the remaining linear dimensions of the waves. The velocity of propagation of such waves in shallow water depends on the depth of the water. For water waves of slight height and with- out wind it can be computed by well-known formule. When we indi- 9 cate the depth of the water by h and put n=, then is b2 g ent _ eh ~~" e enh. g—m which for h=x» becomes yp aI 9 n 27 and for small values of h becomes b=gh When however the depth of the water is not small relatively to the wave length, then the retardation is unimportant, thus for h = the speed of propagation diminishes as 1:0.95768 _the speed of propagation diminishes as 1:0.80978 2 u 4 pjthe speed of propagation diminishes as 1:0.59427 When it is calm at the earth’s surface the wind beneath the trough of the aerial billow is opposed to the direction of propagation, but un- der the summit of the billow it has the same direction as that. Since the amplitudes at the earth’s surface are diminished in the proportion e-"": 1 with respect to the amplitudes at the upper surface, therefore these latter variations can only make themselves felt below when the depth is notably smaller than the wave-length. Variations of baro- metric pressure are only to be expected when decided changes in the wind are noticed during the transit of the wave. VIL FUNDAMENTAL FORMULZ FOR THE COMPUTATION. I will here give the theory of the calcuiation only so far as is neces- sary, so that any investigator familiar with analytical methods can verify my results. I introduce two new variables, 7 and 6, which are so connected with rectangular codrdinates x and y that eet) =aleos (64:71) —eosrelt 1s 40) ails at Pan i wherein », a, and € are constants. The boundary line between the two fluids corresponds to a constant positive value of 7, namely : 7) = h PAPER BY PROF. HELMHOLTZ. 105 Hence for this boundary line result the equations ere COS (ny) = aioe ih cos O—Ccos €) (1a) ene SIN (ny)=—‘ 2 Y sin (ih) sin 4 ( af j ’ By the elimination of 6 this gives an equation between x and y as the equation of the boundary line. Beside the constant @ which deter- mines theinitial point of the x coérdinate and then which determines the wave-length this equation contains two arbitary parameters h and é that determine the form of the curve. We take x vertical, increasing upwards, and then for the space oc- cupied by the upper fluid, for which we use the subscript ; put vit Prui=b(n —h—it) by which 7+ ¢,i becomes simultaneously a function of (w+y?). When h=n, then 7,;=0, so the boundary line on the lower side coincides with the stream line. When 7=+. then ney’) =n— i= [eit pit] +h or py == 12, pi=nby, so that at great altitudes the motion is a rectilinear flow with the ve- locity nb,. For the lower space where 7 § = 0.666667 ; or _—— cos? €< =2 = 0.642857. The equation for $$ would also allow cos? ¢>32, but also 0.5 < Cos? €< 0.642857, Finally the equation for €? can be written 2=04% (0.68615 — cos’ €) (cos? €+- 2.18615) ~ (cos? €—0,66537) (cos? e-- 1.46537 108 THE MECHANICS OF THE EARTH’S ATMOSPHERE. Since €? must be positive it follows that 0.66537 0.67264=—$ 4+ Ys. For this value the altitude of the wave will still be finite, namely: (a are i a x 2.5112= 1 0.39967. But the fact that the value of the codrdinates can no longer be de- veloped in converging series, according to the powers of cos (a#) and sine (a), Shows that a discontinuity or an ambiguity of the codrdinates. must have come into existence. In fact the equations (la) also show that for small values of h tn) = one Pca e?"=— a?(cos 6—cos €)?. From the first of these it follows that wherever tan (n y) has a finite value then cos 6 must be nearly equal to cos ¢, and only at the points. where tan (v y) is very small and passes through zero can @ increase and rapidly pass through the interval to the next point, where cos @ approaches again the value, cos é, Now for such values of kh the diminution of the terms in the series expressing the value of the pressure will not be rapid enough, in order to express the value of the function sufficiently well by using only the first three terms of the series, and the true form of the wave curve for such values of h can only be obtained by further approximations. However, these relations show that waves which rise too high lose the continuity of their surfaces. But sharp ridges can not occur on the surfaces of the waves except when they are at rest relatively to the medium into which they protrude. For when the medium flows around the edge there would occur infinite velocity and infinite pressure at the place in question, which must violently draw up the other liquid, as in fact is occasionally observed in high and foaming waves, In the case of waves that advance with the same velocity as the wind the summits can in fact have a ridge of 120° before they break into foam. PAPER BY PROF. HELMHOLTZ. 109 The above given formule show that when cos ¢ diminishes from its upper to its lower value,then both & and $$ and © must continually increase. For waves whose lengths remain constant the increase of ‘$ and © means an increase of the two velocities b; and b. as well as their sum, 7. é., the wind velocity w=b,+l.. If the latter remains constant, then the wave length must necessarily diminish with increasing cos «. It follows from this, that within certain limits the same wind can excite this form of waves of greater and smaller wave lengths. The longer waves will at the same time have a relatively greater altitude. This relation depends upon the store of energy that is accumulated in the wave. VIII. THE ENERGY OF THE WAVES. When we investigate the energy of the waves cf water raised by the influence of the wind, and compare it with that which would be ap- propriate to the two fluids uniformly flowing with the same velocity when the boundary surtace is a plane, we find that a large number of the possible forms of stationary wave motion demand a smaller storage of energy than the corresponding current with a plane boundary. Hence the current with a plane boundary surface plays the part of a condition of unstable equilibrium to the above-described wave motion. Besides these, there are other forms of stationary wave motion where the store of energy for both the masses that are in undulating motion is the same, as in the case of currents of equal strength with plane bounding surfaces; and finally, there are those in which the energy of the wave is the greater. The reason for this is to be found in the following circumstances: In the undulating masses of water two forms of energy occur, namely: First, potential energy, represented by the water raised from the wave valley to the wave summit. This quantity of work increases with the increasing height of the wave, and must always be positive; it is only absent for perfectly smooth surfaces. Second, living force is common to the two forms of motion under com- parison, and according to the original assumption there is an equal quantity of it in the portions of the fluid masses distant from the boundary surface. The difference of the two modes of motion is not affected by the participation of the more distant strata of fluid, the difference between the two motions depends only on the strata that lie near the boundary surface. The wave surface which we again imagine to ourselves fixed in space affords to the two fluids streaming along it an alternately broad and narrow channel; where the bed is broader the fluid moves more slowly, the upper fluid above the wave valley, the lower fluid under the wave summit. Thereby the living force of the portion flowing through a broadening of the channel will be alternately smaller, while that flowing through a narrowing of the channel will be greater than the living force in the corresponding part of the uniform 110 THE MECHANICS OF THE EARTH’S ATMOSPHERE. stream with the plane bounding surface. But the volumetric extension of the part with diminished living force, that fills the broader channel, is greater than the volume of increased velocity in the narrow channel. Therefore in the sum total the living force of the diminished portion prevails. Nevertheless only the terms of the fourth degree in € which first oce- curred in the computation by considering the terms with ¢? in the val- ues of v and y, give a basis for the computation of the difference of energy. This difference, as computed for one wave-length according to my caleulation in the class of waves discussed in Section VI, is as follows: Ey : =" a 562 — 22? rae ot 15e22__ oe "2 ay (S80) ate ele |e eel or 1 279(S2,—81) land < ~ ‘ ~2 ¢ IDQG2 9 Tcos’e +4 [5—2 cos’e] [coste~ 1%] _ 1 -4/15.0845—cos?e].[cos%e+-0.0815} 144 * cos?e—2 43° . In this the Q is the only factor that changes rapidly for small changes of cos ¢, a circumstance that very materially lightens the numerical computation, For # = 0, we find the value cos?¢ = 0.675148, which is not very far from the limit of couvergency or cosé* = 0.67264. Corresponding to # =0 we find DQ = 0.740333 8 — 0.1717613 © = 0.6899 2 = 0.56686 H = 0.20464 « A e” = 2.52006 Since these are the waves that can be immediately produced by a constant wind, therefore these are the values that lie at the foundation of the computation quoted in Article 6, whereas the values for the lowest waves are found when we assume for cos’ the upper limit of its values, namely, 0.68615, Theory shows, moreover, as also the above numerical example, that the waves of this form for large values of cos ¢ and for the same mate- rial and same strength of wind have greater wave-lengths; that, how- ever, their altitudes form a smaller fraction of the wave-length, and that their energy when cos’e >0.675148 is smaller than that of the recti- linear tlow of both media with the same velocities. The difference of energy is zero for very low waves; it is negative when we pass to rel- atively high waves; it reaches a maximum, then diminishes, and is again zero for the given boundary value. Neh’, PAPER BY PROF. HELMHOLTZ. elt It is sufficient to have proven that for one furm of wave billows due to wind are possible, which billows have a less store of energy than the same wind would have over a plane boundary surface. Hence it follows that the condition of rectilinear flow with plaue boundary sur- face appears at first as a condition of indifferent or neutral equilibrium, when we consider only the lower powers of small quantities. But if we consider the terms of higher degree, then this condition is one of unstable equilibrium, in view of certain disturbances that correspond to stationary waves between definite limits as to wave-length; but on the other hand is a condition of stable equilibrium when we consider shorter Waves. This result is evidently of great importance for the origin of waves. It follows from this, as we everywhere see confirmed in nature, that even the most uniform wind can not blow over a plane surface of water without on the slightest disturbance causing waves of a certain length, which for a given height acquire regular form and speed of propaga- tion. If the wind increases then the heights of all these waves in- crease, the shorter ones among them break foaming, so that new longer ones of less height can be formed. The greater energy that is necessary in this case in order to push the shorter waves up higher becomes possible in that the previous feebler wind had already given a part of its energy to the mass of water, and the new stronger wind fiuds this part already present there. Breaking, foaming atmospheric billows cause mixture of strata in the mass of air. Since the elevations of the air-waves in the atmos- phere can amount to many hundred metres, therefore precipitation can often occur in them which then itself causes more rapid and higher ascent. Waves of smaller and smallest wave-length are theoretically possible. But it is to be considered that perfectly sharp limits between atmospheric strata having different motions certainly seldom occur, and therefore in by far the greater number of cases only those waves will develop whose wave-length is very long compared with the thick- ness of the layer of transition. The circumstance that the same wind can excite waves of different lengths and velocities, will cause interferences to occur between the waves, and also higher and lower wave summits to follow each other interchangeably. This is a process observed often enough on the shore of the ocean. But where two wave summits of different groups of waves reénforce each other a height will easily be attained at which they break into foam, and thereby, as in the analogous case of the production of sonorous combination tones, longer waves can be formed which, when they are favored by the strength of the wind, can also grow larger. This is one of the processes by which waves of” great length can arise. Vil. THE ENERGY OF THE BILLOWS AND THE WIND.” 3y Prot. H. VON HELMHOLTZ. In my communication to the Academy on July 25, 1889, I called atten- tion to the fact that a planesurface of water above which a steady wind is blowing is in a state of unstable equilibrium and that the origin of large waves or billows of water is essentially due to this circumstance. I have there also shown that the same process must be repeated at the boundary of two strata of air of different densities gliding over each other, but that in this case it can assume much larger dimensions and without doubt has an important meaning aS a cause of nonperiodic meteorological phenomena. The importance of these processes has induced me to investigate still more thoroughly the relations of theenergy and its distribution between the air and the water; at first, however, as before, with the limitation to stationary waves in which the motions of the particles of water only take place parallel to a vertical plane in which the codrdinates are re- spectively (7) vertical and (y) horizontal. Since however we can only solve even this special problem by the developmentinto a converging series whose higher terms rapidly diminish in magnitude but offer com- paratively complex forms therefore the conclusions that we may have drawn from a knowledge of the first largest term of such a serics are necessarily always limited to waves of slight altitude and cause the correctness of many more important generalizations to appear doubtful. Many of these difficulties have been surmounted in that I have been able to reduce the law of stationary rectilinear waves to a problem of minima, in which the variable quantities are the potential and actual energies of the moving fluids. From this problem in variations many general conclusions can be deduced as to the decrease and increase of the energy, and the difference between stable and unstable equilibrium of the surface of water. Theoretically considered, there arises here a rather new problem in so far as we have to do, not with the difference between stable and un- *From the Sitzungsberichte of the Royal Prussian Academy of Sciences at Berlin, 1890, vol. Vu, pp. 8538-872. Wiedemann, Annalen, 1890, XLI, pp. 641-662. 112 a £ ee a S PAPER BY PROF. HELMHOLTZ. ih stable equilibrium of masses at rest, but with moving masses that are in steady motion. Some examples of such differences have indeed been already treated, asin the rotation of a solid body about the axis of its greatest or least moment of inertia, and in the rotation of a fluid ellipsoid subject to gravity. Buta general principle such as is given for bedies at rest, in the proposition that stable equilibrium requires a minimum of poten- tial energy, has never yet been established for a moving system of bodies. The following investigations lead to such propositions, which more- over can also be considered as generalizations of the propositions that I have deduced from the general equations of motion given by Lagrange in their application to the motion of “ poly-cyclic” systems.* THE THEOREM OF MINIMUM ENERGY APPLIED TO STATIONARY WAVES HAVING A CONSTANT QUANTITY OF FLOW. i. As in my paper of last year,t I indicate by wu and v the component velocities of the particles of water during any motion that is free from vortices by the equations: ed Oe? tere Oils (1) dp Sd 9) cement oe oe Oy I again assume, whenever the opposite is not expressly stated, that the coordinate system for x y is at rest with reference to the wave, x being vertical, positive upward, y horizontal. Therefore the wave sur- face is at rest with reference to these codrdinates while the two fluids flow steadily along it. The wave curve will be considered as periodical with the wave length A. On the other hand, the flowing fluid will be considered as bounded by two horizontal planes whose equations are Pa ANG Sr Eh ee Fe aise sah CED) Corresponding to this, I indicate the remaining quantities that refer to the fluid which is on the positive side of x by the subscript 1; those that are on the negative side of x by the subscript 2. The wave-lines and these two horizontal boundary lines must be stream lines—that is to say, 7 must have a constant value throughout their whole length. Since each of the functions 7 can contain an arbi- trary additive constant, therefore we can assume arbitrarily both of the values of 7 for one of the stream lines. I assume that for the wave dine for which S| x we have the value_ Urn ea yes, ba paren (LD) oe * Kronecker und Weyerstrass, Journ. +[See the previous paper, No. VI, 80 A 8 fiir Mathemat., 1834, vof. xcvul, p. 118. in this collection of Translations. ] 114 THE MECHANICS OF THE EARTH’S ATMOSPHERE. On the other hand, for the boundary line, for which a= H, bees we have Wi = }y and for the other boundary line, whose equation is t= HL l -. (1d) we have > — bo \ The quantities p; and },, as is well known, give respectively the vol- umes of the fluid that flow in the unit of time through every section between the wave surfaces for which 7; = 7.=0, and through the upper or lower boundary surface. These are the quantities which I have above designated as quantities of flow. In taking the variations of these quantities, I shall, in this paragraph, consider ); and p, as invariable. That altitude will be adopted as the initial point for x, at which the boundary surface of the two quantities of fluid under consideration would be at rest, which is expressed by the equation pYotaA ey =O 6, 2 Se a ee eee “ Yo that is to say, « = 0 is a plane such that as much water is raised above it as sinks below it. Finally the space within which lie the quantities that are subject to variation is also bounded by two vertical planes that are separated from each other by one wave length. Since the movements are to be periodical and consistent with the wave length A, the velocities at the right vertical surface and at the left vertical surface must be equal or pr dp, On. Da therefore for the same values of x ee . . : : oe (17) and Op, _ OW iy oy cis sla Np Siw Ts) Tee I ean lag According to Eq. (1) this last equation can also be written OP, _OPr oe OR or P,—P,=constant. «| a hae ey Now it is known that equations (1) are resolvable when (+ i) can be represented as a function of (v+yi), which function must show no dis- continuity and no infinite values within the region filled by the fluid in question. PAPER BY PROF. HELMHOLTZ. 115 When the form of the wave-line is given, the values of the two fune- tions, 7, as is well known, are completely determined by the above given boundary conditions (1) to (1g) and in that case the two integrals, which multiplied by one-half of the density of the respective fluids, give the living forces, namely : = \[I+C Te 8 a= (hit (2)+ ey] i Soe, eeiptss ind etucGl) become absolute minima for such variations of the functions 7, as are possible under the given circumstances, when at the same time the values ), and p, are considered as invariable. On the other hand the form of the wave-line is not yet determined _by the conditions hitherto given, except in so far that it must be period- ical with the period A. We can however determine the form of this boundary line corresponding to the physical condition that the pressure shall be the same on either side of it, in that we require that the varia- tion of the difference between the potential energy ® and the living force L=L,+ [2 shall disappear, or OO — Tal ON Neola ee il hate ee (20) The potential energy depends upon the unequal elevation of the dif. _ ferent parts of the surface of heavier fluid above the level surface «=0. Its amount is easily seen to be given by the equation P=4y(8.—s),f Fdy. Sa Mueeh ecw an Usep) (ZC) If s. is the denser fluid, then the positive x, as already remarked, must be assumed as ascending perpendicularly and y must be taken as a positive quantity. When the linear element ds of the boundary-line of the two fluids is displaced upwards normal to its own direction by the infinitely small quantity 6 NV, then the variation becomes SOg(e = s\n No dee os vis oss 3 (20) The variation of LZ can be executed in two steps. In the first of these we imagine the boundary-line displaced in the above-given manner and _ first allow the two functions 7, and 7,2 in each point of space to remain unchanged, but in doing so, on that side where space is gained by the displacement d@ s, imagine this strip so gained to be filled with the con- tinuous prolongation of the 7 that pertains to this side, and so that the equation 4 7=0 continues to be satisfied in that region [and so that the _ prolongation of # just mentioned enters here instead of the value of the is other function of % previously existing here]. This prolongation of the « function 7 into the strip just described is, as well known, only possible _ in one manner without forming discontinuities. Only when a cusp of and 116 THE MECHANICS OF THE EARTH’S ATMOSPHERE. the appropriate function ¢/ exists in the original boundary, therefore, es- pecially when the boundary-line forms a sharp corner, is a continuous prolongation of the function excluded. The special physical signifi- cance of such a case we shall have to consider later on. By this first step in the variation of J we obtain Oo = aff» GE) y= CY 2) | as ow. 3ut now the values of 7 and vy. are no longer zero at the new boundary, but we have there, approximately _ dy ON 7) — aN, i h=— oe ON and in order again to make these equal to zero we must execute a second step in the variation, such that the function 7 shall so vary that these now again become zero at the new boundaries. Since according to the general laws of potential functions we have ~ OY * Oy Hale = ie : — Sah Pale. c 2 : o"L=—s f sy! 6th dss f Sy bile ds therefore when we (as is necessary in our case) put 0 = jE ou On Oy 2= + a ON ON2 we obtain the final value: / S1/ eae) dp? y ¢ 6 L = iG ate 3 L= — 4 fi ( ne 8) (sR) | as ON. ; (2e) Sinee finally the volume of each of the two liquids must remain unchanged during the variation, therefore it is necessary that SON 80... 2 oe ee Hence results the variation, 6 o—L} =— f° ds 5 N \9 (81 —82) & +: a ony — Gra == f'd3,6 N [ps — pul » ape) aol) Here p, and p, designate the fluid pressure on the upper and lower sides, respectively, of the boundary surface as they result from Euler’s hydrostatie equations. Since p, and p; contain arbitrary additive con- stants ¢ can be omitted. PAPER BY PROF. HELMHOLTZ. ELT , When, therefore, the equation (2b) is to be satisfied, that is to say, when we must have é {o-L} =0 . then must p,»=p, throughout the boundary surface, which is the con- dition of a stationary surface. The stability of the steady motion.—F or any form of surface that nearly corresponds to a stationary form, and which therefore still shows dif- ferences of pressure, it follows from the preceding that such a surface when it changes with the differences of the pressures experiences there- fore a positive displacement 0N where p, > p,, therefore the quantity (@—L) diminishes and consequently approximates to a neighboring minimum of (#—L), and must therefore depart from the neighboring maximum of the same quantity. The hydro-dynamic equations show in fact that the equality of pres- sure in such cases can only be brought about by accelerations which act in the direction from the stronger to the feebler pressure and must disturb the steady motion. Therefore the stable equilibrium of a stationary wave-form must (among all possible variations of such a form) correspond to a minimum of the quantity (©—L), just as in the polycyclic systems for a constant velocity of their cyclic motions. When on the other hand this same quantity (@—Z) attains a maximum value or a cusp value for some other form of curve, then the condition of equality of pressure on both sides of the boundary surface is at least temporarily fulfilled; but individual or the very smallest disturbances of the form of equilibrium must continue to increase: the equilibrium will thus become unstable as is actually recognized in natural water-waves by the foaming and breaking of the crests of the waves. On the other hand it is to be remarked that these propositions hold good oniy when the functions /, and J, are determined as minima in accordance with the boundary conditions of the spaces within which they hold good, and for every variation in the form of the boundary line the functions experience a change in accordance with this condi- tion that they shall be minima. Under the assumptions already made, the function @ is certainly positive and finite, since only a finite quantity of liquid is present which can be raised up only through the finite altitude H;. Lis also necessarily positive but can become +, since the summit of the wave can approximate to the upper bat the trough of the wave to the lower _ boundary surface and the total constant quantity of moving fluid must then be pressed with infinite velocity through infinitely narrow crevices. The quantity (®©—Z) must therefore have a positive value for plane boundary surfaces where 2=0, and it can become —~ for increasing wave altitudes. Whether a minimum occurs between these limits, and for what value of ) this could occur, can only be decided by investigation {18 THE MECHANICS OF THE EARTH’S ATMOSPHERE. of the individual forms of the waves. At least one cusp value occurs for a plane surtace. Only this much can be at once seen, that when an absolute minimum exists there must be a transition leading from this to the infinite nega- tive value of (@—ZL), which transition at first begins with an ascending. value and then again diminishes. There must then bea lowest value on the transition curve between the ascending and the descending values that corresponds to a maximo-minimum (absolute minimum) of the quan- tity (®©—L), therefore also to a stationary form of wave, but such an one as corresponds to an unstable equilibrium, and which is on the point of becoming a breaker. If such a minimum exists, then for it any variation in the form of the wave that makes @ increase will make Z increase by the same amount. The same is true of the cusp value when we consider such waves as form trough-lines. But if we increase the values of ); and },, that is to say, if we increase the velocity of the wind and the rate of propaga- tion of the waves through water, then the partial differential coefficient of LZ will be greater at both places and the two limiting values must approach each other and finally coincide, whereby the absolute mini- mum ceases to exist and the equilibrium becomes unstable. Hence it is to be concluded that with increasing rate of flow, stationary waves of a given wave-length will finally become impossible. Necessary formation of breakers when the velocity is excessive.—That, for a constant definite value of the wave-length, minima of the function (@—L) are no longer possible for large values of ); and p, exceeding a certain definite amount, can easily be shown as follows: We compute the values of Z, and LZ, under the assumption that »;=).,=1, for any arbitrarily chosen form of wave and then for an arbitrarily chosen value of 6@ seek the two variations of the curve which respectively make 0, and dL, to kecome maxima. Among the possible variations of the form of the wave that give positive values of 0® are those that give higher summits and lower troughs for the wave. Since the upper fluid has the greatest [least ?— C. A.] section above the summits of the waves, but the smallest | great- est ?—C. A.] section above their valleys therefore above the summits a greater velocity of flow must prevail than above the valleys, that is to our : say the value of 5 y. must be greater absolutely on the summits than g+"1 in the troughs. Hence follows from equation (2e) that when we raise the summits and depress the valleys we obtain not only positive values of 6® but also positive values of 62, and dL. Consequently the de- sired maximum values of the two quantities OZ, and 6/2, that belong to the prescribed positive values of 6@ are necessarily positive, and for 3 OD o® ‘ a finite altitude of the wave the ratio 7 as also —— must necessarily OL, Ly be finite. wt; Seblpes ~ a 5 ane DEAS Bip rat me iy > PAPER BY PROF. HELMHOLTZ. 119 We now indicate by a a proper fraction and imagine that we have ex- ecuted a variation of Z, to the amount expressed by a, such as would correspond to the variation a. 6®. On the other hand we perform the variation 0Z,, to the amount (l—a). ‘hen the total variation for @ is 0 =[a+(l—a)] 69, 0L=a. 61, + (l—a). Ih. If now 6, > dL, we obtain the maximum variation of dL when we make a = 1; but for the opposite case we should have to make a= 0. Thus OL attains the greatest value that it can have for the given value of 6@ and the adopted form of wave. When the greatest positive value of OZ is smaller than 6@ then a value for ),’ can be found that in any case will make p2dL>s@ and therefore, for at least one method of change of form, which need not necessarily be a minimal form, will make the variation 6 (@—L) nega- tive. Since ® always remains finite one can always execute finite varia- tions in its magnitude that shall be of the same order of magnitude as the displacement ON of the elementary line ds, and which latter give always finite variations of Z, and Lz, at least for finite velocities of flow along the surface. Infinite velocities can only occur at the projecting cusps of the wave- lines and, when there is a current there, give infinite negative pressures, that is to say, the phenomena of breaking or frothing. Only when there exists no relative motion of the wave with respect to the medium into which the sharp edges of the waves project, namely, when the wind has precisely the same speed as that of the wave, can such ¢usp points long endure. Except these latter cases, that lie on the boundary of breaking and frothing, we shall therefore for all continuously curved forms of waves have for every 6® a maximum of OZ of the same order of magnitude. And when we seek for the smallest value of the ratio so and seek for a value of p? which shall be greater than the greatest of the values of 1 oF thas obtained, then for the corresponding strength of current the oD possibility of stationary wave-formation for the prescribed wave-length A is entirely excluded. Therefore stationary waves of a prescribed wave-length are only possible Sor such values of the velocities of flow ),? and ),? as are less than cer- tain definite extreme limits. On the other hand, these same considerations further show that the 120 THE MECHANICS OF THE EARTH’S ATMOSPHERE. diminution of the values p, and p,? will necessarily make the larger values of 6, and dL, with respect to 0@ disappear. Then variations of 6% can not be counterbalanced by opposite and equal values of L and then can at the most only one limiting value exist, 7. ¢., that which corresponds to the plane surface. The limit for the smallest allowable values of », and ), results from the preceding investigation as follows :* 27r8p7" 271829? “Ae He =9'A(8|—82). Hence the range of values of (),)> and ().)? that permit stationary waves of the wave-length X is limited on its lower side. It is to be noticed that the quantity p, determines the progressive velocity of the wave with respect to the water; p;, on the other hand, determines the velocity of the wind relative to the wave, Either of these can be small if the other is sufficiently large. Il. THE THEOREM OF MINIMUM ENERGY APPLIED TO STATIONARY BILLOWS WITH A CONSTANT VALUE OF THE VELOCITY POTENTIAL. The value of the living force, as given in equation (2), can by partial integration be written So oye L=y fb. mae dy, in which the integral relates only to the upper horizontal boundary line. The portions of the integral for the other limit of the space 8S; all disap- pear. Since now according to equation (1) QO yp dg ov oY s og L=3n fe . dy. leas ey, 79 there results Of, if we put which difference is independent of 2, we obtain S| A i=. Py. y ole ee Ge, Sy et, Ue tee coe aes (3) and similarly In=—5 beh 6 fe gs, We) fab) Jot ovens econ re (5a) * My attention has been called to the fact that Sir William Thomson has already given this equation as the first approximation, taking into consideration the strength of the wind, Philos. Maq., 1871 (4), vol. XL, p. 362, where, moreover, the influence of capillarity is also considered. ‘oo ae a Oe eS Oe PAPER BY PROF. HELMHOLTZ. PR The quantities » and f are dependent on each other as soon as the form of the space is given for whose boundary they hold good; so that we can put =| K where St indicates a value that depends only on the size and form of this space. Hence there results SEM ae NSC oa) LSE Ne L=*?. lao R= 5 Fae eine (3D) When therefore St experiences a change Ot, then if | remains un- changed we have OL=*. p72, oR Oot=0; on the other hand, when ) remains unchanged we have be ue Saw 8 dL =F Fo = 5PM op =0- Both yariations therefore have the same values with opposite signs.. We can therefore, instead of 0@ —6 L=0 Opi =0 bp = 0. which is the form of variation for the stationary condition where the variation of 6 L is deduced from the variation of the form of the region, also write 6) fi == fs =) 0: The quantities f according to their definition have the value: ot, yY tA = fw. dx+v. dy) X,Y. the integral being taken for any value that leads from the point (a, y) to the point (7, y+A). When we choose the stream-line 7>= constant for this path between these points then the integral also indicates a path along which a series of material liquid particles would flow. The value of the integral f,, as computed for such aseries of material flow- ing particles as is well known remains unchanged, whatever motions may otherwise be going on in the liquid, provided there are no differ- ences in the sum total of the pressures and potentials of the exterior forces between the beginning and the end of the series, and provided there is no friction. This is the same sum that also remains unchanged in the vortex motion in every closed ring of material particles. We can therefore in fluid motions consider s; f; and s) f, as the moments of 122 THE MECHANICS OF THE EARTH’S ATMOSPHERE. motion, which remains invariable except for the influence of direct ac- celerating forces, while the quantities of flow ), and p, thereby receive the significance of velocities. Thus the two problems in variations, here solved, are completely analogous to the propositions developed by me in the theory of polycyclic systems, that 6(9—L) =—Z[P,o0p,J...... . (88) O a — when the velocities q, of the cyclic motions are maintained constant. In this equation p,, are the variable codrdinates, and P, are the forces tending to increase these codrdinates. Stable equilibrium, as is easy to see, corresponds to a minimum of the (@—L). oe DD On the other hand, when we assume the moment of motion £— to Oda be constant we have 0 (@+D)=—2([P, dp, | of \=0 ak 2 oh rae Fa Here, also, stable equilibrium demands that the quantity (+ L), that is to say, the total energy of the body be a minimum. The equation (2g) corresponds throughout to the above equation (3e) for polyeyclie systems, only that in the former the number of variable coordinates ON of the surface elements ds is infinitely large and the force which in it corresponds to P,, namely, the fluid pressure, is a con- tinuous function of y; hence the integral is used instead of the sign of summation. That stable equilibrium, even in the theory of waves, also corresponds to the minimum of energy for a constant value of f is evident when we consider the influence of friction which can restore a disturbed stable equilibrium but nota disturbed unstable equilibrium. Friction always diminishes the store of energy that may be present. It can, therefore, restore a disturbed minimum of energy but not a departure from a maxi- mum. Il. THE THEOREM OF MINIMUM ENERGY APPLIED TO LAYERS OF INFINITE THICKNESS. In the following we shall consider the two layers of fluid on whose boundary surface the waves form, as very deep in the vertical direc- tion, therefore the values H; and H, as very large and as respectively increasing beyond all limits to infinity, in order to free the theory of waves from those complications which are brought about by the influ- ence of the upper and lower horizontal boundary surfaces. Under these circumstances the motion on these two far distant hor- izontal boundary surfaces does not differ sensibly from rectilinear uni- ; ? i z “ | ae a = a s 3 i é ie a . notre a "4 4 a i 4 | PAPER BY PROF. HELMHOLTZ. £235 form velocity. For the surface H, we put a, for this velocity, for the surface H, we take (—q:) since we give the latter a motion in the oppo- site direction to that which would be given to it in the normal cases where the wind outruns the wave. We have at once —f,=a2. A and in the higher layers of the fluid wit YP I=+a, (v+yi)+h, where h; is a constant to be determined by the equation (1e). Similarly ot Pz t= — a2 (4+ Yi) thy For plane boundary surfaces when for these as above assumed ys, =y2=0, and also v=0, we should also have /; and h, both equal to zero, and the living force in this case becomes DE et ae i A 2 2 L=— ’ oe boy ¢ >, Hyd When on the other hand billows have ariseu, J; is smaller for a con- stant valie of a, and therefore also of f,, since, as we have seen then a negative value of OJ, results from an increase in the altitude of the wave. We can therefore under these circumstances put =, ‘a? (Hi—r,). A wherein 7; has a positive value that depends on the form and height of the wave, but not on H;. If we imagine H; increased by the quan- tity D H, and the quantity Z, correspondingly increased by D) 1, then in the strip thus added to the field the velocity is uniformly equal to a, and therefore Dees Or. D HA, Th4+ DL, = 5 [ un + DH)—" | A. Therefore the same value of 7, also holds good for the greater alti- tude independent of the value of D H,. The formula (4) gives directly p=—fi (H,—1)) shale, atet op Mrenatrert ii tsni rt. (4a) Compared with galvanic conditions, ); measures the total flow or the intensity of the current; f, is the difference of potential between the boundary surfaces. Hence (H,—7) is the conductivity which is pro- 124 THE MECHANICS OF THE EARTH’S ATMOSPHERE. portional to the sectional area. Therefore 7, corresponds to that con- stant diminution of the sectional area which causes the current to diminish just as the irregular obstruction by the waves does. For a constant value of a, and a, respectively, since A, Mi, and Hy remain unchanged, the condition that a minimum of (+ L) should exist gives < . Sain SD oui 0(P4L)=db—Fajdr—Fajdn=0. . . . . (4d) The other minimum condition in which a, a are to be replaced by yy P2 = = and, Gg 2s H,—r, H,—1r is Ory SQ Org ey ee cae —- (ny 2?" (ny s(-D)=6b—= 5! which agrees perfectly with that first found. The quantities 7; and 7, depend only on the form of the wave, and are generally found by simple computations as soon as we have found the form of the functions 7; and ¢». Horizontal transportation of the superficial layer.—Tie quantity of flow », and }, of the two fluids is no longer the same as it would be over plane surfaces of water for equal values of the velocities a; and @, but it is smaller than before in the upper medium by the quantity 7, a4, and in the lower medium by the quantity 72 a2. Imagine now the velocity (—a.) added to both sides so that the lower medium comes to rest, but the waves progress with the velocity (—a2). Then beneath plane boundary surfaces all motion disappears, but be- neath biliowy surfaces a general current is set up of the magnitude —z 7, and thus the wind in the upper region travels not with a uni- form velocity (a4;+ 42), but just above the billowy surface there occurs a diminution of the flow of air to the amount of a 7. These two currents cause the mass of air and water taken together to have a different moment of motion ina horizontal direction than if they flowed with the same velocities a, and ad, over plane boundary surfaces, and this difference of moment of motion, reckoned as positive in the direction of the wind, is AM = 8p 03 2 —S] G10 4 ee (ae tee 2h Oe This can only be equal to zero when $2Oa M3) Py. ee ee or, if we introduce w, the veiocity of the wind, W Oy Oe 6a a Be Oy eer PAPER BY PROF. HELMHOLTZ. 125 theit equation (5a) becomes 82 %o W 8, 71 + 82% 8,7, w 8. 114-8272 Since now r; and 7, have values that differ but little for the ordinary waves (as the subsequent computations will show), and since for air and water therefore this condition gives the rate of propagation of the wave against the water as approximately For waves of low altitude equation I, Section vit of my paper of the previous year,* neglecting the small quantities z and €, becomes : g.A (8. — 81 8 dP + % a2 = Seales eu) 27 If we put w=10 metres which corresponds to a rather strong wind, then for low waves of a constant moment of motion, we have a, = 9™.98709 >= 02.01.2914 rn a 0™,0827 2 These waves of only 8 centimeters in length evidently can corre- spond only to the first crumpling of the surface, such as a strong wind striking upon it immediately excites. Only when the same wind blows for a long time over these initial waves, and gives them a part of the moment of motion of a long stretch of air, can waves be thereby pro- duced with greater velocities of propagation. Hence in accordance with experience it follows that wind of a uni- form strength striking a quiet surface of water can only produce more rapidly running waves, namely, those that are longer and higher, when it has acted for a long time on the waves that first arose, and has accompanied these for a long distance over the surface of the water. At the same time it also becomes clear that for a uniform wind the waves can only increase in size when the wind advances faster in the same direction than the waves themselves. Energy of progressive waves on quiet water.—As in the case of the moment of motion, so also with the storage of energy in the wave. Our previous comparisons of the energy of different waves among themselves has reference to the energy of relative motion of the fluid with reference to the stationary wave. * [See page 107 of this collection of Translations. ] 126 THE MECHANICS OF THE EARTH’S ATMOSPHERE. The well known proposition that the living force of any comple# me- chanical system is equal to the living force of the motions relative to its center of gravity plus the living force of the motion of the center of gravity at ihich we imagine the whole mass of the system to be concentrated, can, with only a small change in the method of expression, be applied to our case. For since the total mass of the system multiplied by the velocity » of the center of gravity, gives the amount of the total mo- mentum of the system in the direction of this velocity, therefore we can also put the living force Y of the center of gravity Ss Mbt by? «eee 2 eee) where Mis the momentum of the whole system in the direction of v and Yt is the mass of the system. If we now compare with each other two different conditions of motion and configuration of the system in which Z, and Z, are the living forces of the motions relative to the center of gravity, ®, and ®, are the potential energies, b; and b, are the parallel velocities of the center of gravity, then the ditterence in the total energy of the system in the two conditions is EB, — EF, = 8, — @,4+ L,—1,+ 4M. vP—$ M. dy’ If now, without changing the relative motions, I in both cases add the quantity ¢ to the velocity of the center of gravity, then the above difference of energies changes into Hy —E,/= E,—£.+¢ (M, — M2). If M,—M,=0, then the value of the difference in energy is not changed by the addition of the velocity c. This must be true even when H, and /,, and therefore the masses of the moving fluids, increase to infinity, since for our undulating fluids the differences (#,—H,) and (M,—M,) are finite for each wave length. Therefore the ditference of the energy for stationary waves and for stationary deep water will be equally great only for waves that satisfy the condition (5a). According to the propositions above deduced, sta- tionary waves of this kind must have less energy than smooth water, which is therefore also true in this case for this kind of waves above quiet water. For waves that have larger values of d:, the addition of a common velocity (—d2), which brings the deep water into rest, changes the dif- ference of energy between the two states, that of a smooth surface and that of a wave formation, by the quantity. Ei,’ —LH,! =f —Hy+ 2 [ S2@2%2— 84,71]. The index 1 refers to the billowy surface, the index 2 to the plane surface, the accented EH’ refers to quiet deep water, the non-accented 2 refers to stationary waves. PAPER BY PROF. HELMHOLTZ. Py Hence it results that when waves of considerable progressive veloc- ity trench upon quiet deep water the generally very small differences (£,—,) lose their negative and assume a positive value. Here also the energy that is given to the previously quiet water in the form of an elevation of its surface and the living force of its mo- tion must be abstracted from the atmosphere. In order to obtain a sufficient amount for the formation of large waves, it will on this ae- count be necessary that long layers of air shall blow over and shall give up a part of their living force. In the first moment when a new gust strikes the surface of the water stationary waves only can be formed for which M=0 and H#,—F#,=0 and ad, has the value given in equation (5a). The last condition shows that these waves will be near the point of spirting, as we in fact often see in the case of small ripples suddenly excited on the surface of the water. Moreover in these small ripples, as Sir William Thomson has shown, the capillary tension of the liquid comes into consideration, which somewhat increases the store of energy of the billowy surface. In general therefore, stationary waves are not formed immediately at the beginning, since the waves of constant momentum would leave behind an excess of energy. But when from the very beginning waves that have partly a positive and partly a negative difference of momen- tum and of energy are successively produced on the quiet water, then the sum of these differences can become zero. These systems of waves, having different wave-lengths and progressive velocities, cause mani- fold interferences as they progress, and, according to the principle given by me for combination-tones (which in its ap plication to the tidal wave has already received a very beautiful confirmation by Sir William Thomson’s analysis of the tidal observations collected by the British Association), waves of greater wave-length can gradually be formed. So long as the wind outruns the waves it steadily increases the store of energy and the momentum of the waves, and furthermore, so long as the energies computed for stationary waves diminish and can form a still lower minimum, the inclination to attain the form of least en- ergy under the cooperation of all the small perturbations which the other concurrent waves bring about, in the case of nature, will develop still further. This will finally lead to the value corresponding to the formation of a cusp and to the foaming of the upper ridge in case this can be produced by the given wind velocity. In April of this year [1390] I endeavored by observations that I in- stituted at the Cape of Antibes [near Marseilles] to arrive at some con- firmation of these consequences drawn from theory. With a small port- able anemometer I measured the strength of the wind directly at the edge of the steep cliff of the narrow tongue of land which projects rather far into the sea. However, the observations showed that many times a stronger wind must have prevailed out on the sea than I had been able to observe on shore. I also counted the number of approach- ing billows. 128 THE MECHANICS OF THE EARTH’S ATMOSPHERE. With water-waves the same as with sound-waves it is to be assumed that, through all deviations, delays, and diminutions that they experi- ence, the time of vibration remains unchanged. This time may there- fore be determined near the shore even though the progressive velocity in shallow water is changed and the form and the length of the waves change. The number, V, of the waves in a minute is expressed by 60.4, 7. When a, inereases to nda then A increases to n°A, as Shown in my paper of a year ago, and therefore N= eee, n A velocity d2=10 metres would give 9.4 waves per minute; on the other hand a velocity a2=5 would give 18.8. The counting of the waves without registering instruments is now not to be executed with great accuracy, since on the sea, so far as I have seen it, there are always numerous adjacent waves of rather different periodic times which interfere and give phenomena corresponding to the acoustic beats. During the minimum of motion one can easily make errors in the counting; by repeated countings at the same place we obtain therefore variations of about one-tenth or even more of the desired number. The strength of the wind that [observed on the shore did not exceed 6.1 metres per second. This was on the evening of my arrival in Antibes, April 1, 1890; the wind was from east southeast; I counted between 8.5 and 10 waves per minute. On the next morning, April 2, there were still 10 to 10.5 waves per minute, although the wind had almost entirely gone down. This number of waves would be expli- cable only when a wind about 10 metres per second had blown steadily over the open sea. On the 2d of April the wind rose in the course of the day toa velocity of only 4 metres per second. Yeton the 3d of April also the number of waves was still 9.5 with a very feeble wind; on the Ath of April for the first time an increase was perceptible up to 12.3 waves per minute. During a series of quiet days the number of steadily diminishing waves gradually increased to 17 or 18. Finally on the 7th of April the wind began again to increase. In the morning I found a velocity of 3.3 metres per second, which in the course of the day increased to 5.5 and brought the number of waves down to 115. This time, however, the location of the increased wind was demonstrable. In Marseilles during the previous night a severe whirlwind had prevailed and the larger waves excited by it stretched as a sharply defined dark-gray band from the sea horizon hitherward and reached Cape Antibes about midday, long be‘ore the stronger wind that had given rise to them and which had morever at the latter place by no means the same force as in Mar- Seilles. PAPER BY PROF. HELMHOLTZ. 129 These few observations therefore show a connection between the number of waves per minute and the strength of the wind and even an agreement, at leastin the order of magnitude. But the numbers of waves are all somewhat smaller than they should be as computed from the strength of the wiud on shore and leave us to conclude that astronger . wind must have prevailed in the open sea. They show however also that the re-action of a strong wind may last many days. For a progressive velocity of 10 metres the waves would in one day travel 73 degrees of longitude. Therefore, had the Mediterranean even to the Gulf of Sidra been on the Ist of April covered with waves ex- cited by a strong breeze of 10 metres velocity, these would need two and _ahalf days before thé last ones would reach the coast of southern France. It will of course be possible to solve the problem more thoroughly _ only when we have at hand continuous registers of the billows and ex- tended observations of the velocity of the wind. These latter are un- _ fortunately not yet collected for the month of April of this year, or at - least not yet published, and could therefore not be used by me. 80 A——9 VIII. THE THEORY OF FREE LIQUID JETS.* By Prof. G. KIRCHHOFF. Helmholtz in his communication on discontinuous motions in liquids, Berlin, Monats-berichte, April, 1868,7 has for the first time determined the form of a free jet of liquid in a special case. The method used by him in this determination can, as will here be shown, be so generalized that it leads to the solution of the same problem for a large number of cases. It is assumed that the fluid is incompressible, that no exterior forces act upon it, that its particles do not rotate, that the currents are steady, and finally, that the movement is everywhere parallel to a fixed plane. Let w and y be the rectangular coordinates of any point of the space oceupied by the flowing liquid reckoned parallel to the fixed plane and let m be the velocity potential at this point, then m is a function of x and y such that it satisfies the equation QD og da? F yp =? : OG OP. nai In this equation 2 and 7 are the velocities parallel to the axes of x and y andif p is the pressure and p is the density, then we have further poe hf (22+ (22)'], where ¢ indicates a constant. If the flowing liquid basa free boundary then this must correspond to a stream line and the pressure must be coustant throughout it. The second of these conditions, if we adopt a proper system of units, will be expressed by the equation * From Borchardt’s Journal, 1869, vol. LXx, or Kirchhoff Gesammelte Abhandlungen,. Leipsic, 1882, pp. 416-427. t [See also No. III of this present collection of Translations. ] 130 PAPER BY PROF. KIRCHHOFF. LSE The partial differential equation for gv is satisfied if we have 2=rt+tly @=—Ppt+itp, where i= ¥—1, and «can be any function of z. Therefore the equation of any curve bE flow or stream line is 7;=constant, and we have = on (ey ah IP ay (de \2 tal +@) IP \’ , (IP A) +(22) —/ due \? dy \2 Haba) @ IP = IP if we assume that x and y on the right-hand side of these equations can be represented as functions of mpand ~. Therefore the conditions for a free boundary of the jet are that for it 7>=constant, and — SOE eee GU \ 2 Ce +( =e OP IP _ The problem is therefore to express w as such a function of zas will satisfy these conditions. To this end we put 1 Sa SSS hl inal o)+ Vil@yo & select the function f(@) so that it is real for a certain value of and for a certain range of gy, and so that it lies between the limits —1 nd +1. For this value of + and for this range of g we have ov — =f{ a9), v= V1—f(@) f(@) x a ae S - ae that is to say, the stream line corresponding to the value of 7 can form a free boundary to the moving liquid in that portion which corresponds tothe range of g. If there are many values of 7 for which f(@) has the described property then all the stream lines that correspond to _ these values can be free boundaries. In general o is defined by the equation above given for dz da é Sa many-valued function of 2 for any definite assumption as to f(@). _ Let the region of z, thatis to say the space filled with the moving liquid, 132 THE MECHANICS OF THE EARTH'S ATMOSPHERE. be so bounded that, within it, no branch of @ merges into another; such a branch, therefore, represents a possible mode of fluid motion. The desired object will be attained when the region of @ is appropri- ately bounded. In reference to the boundary of the region of @ it is recognized, first, that it is a line that returns into itself and without cutting itself and that consists of parts for which 7 has a constant value and of parts for which g has an indefinitely large positive or an indefinitely large negative value. Within the region of @, /(@) is a single-valued function of @ If we had adopted an expression for /(@w) that represented a many-valued function, then at its cusp point should start the sections for which w has a constant value. Furthermore vV/(@)/(@)—1 should also be made a single-valued function of @. in that through those points for which /(@)=-+ 1, the see- tions pass for which 7 has a constant value. For any point of the region of @ the sign of the radical quantity is still at our disposal. If points occur for which /(@) is infinite or infinitely great,* then for one | of these points we may make VI (@)f(@)—-1=+f(@) and assume that this equation holds good for them all. It is further assumed that the function /(@) is only infinite at its cusp points if itis so anywhere, and even here it is infinite only in such a way that if f(a») is infinite then (@w— a) f/(@) approximates to zero when @ has a value approximating that of Gp. Within the designated region of @ therefore z is a single-valued function of this variable and such that it is never infinite. Now consider @ as a function of z. The region of z that corresponds to the adopted region of @ does not extend through infinity, and is bounded by a line that returns into itself and which is made up of the lines whose equations are p=—x and g=+~ and of stream lines; a certain portion of the latter can be considered as a free boundary of the moving fluid, the other part can be considered as a fixed wall. Within this region of z, @ bas no cusp point, since at no point of it | ~ dz enie does dag DeCome zero. Therefore under the condition that the boundary of the region of z shall not intersect itself, @ becomes within that — region a single-valued function of 2. This function of zis completely determined as soon as one has found a single value of 2 corresponding to a given value of @. (I.) An example that constitutes a generalization of the case treated of by Helmholtz is obtained if we put I ( q@)=k+e-¢ * By infinite, I designate the reciprocal of zero, but by infinitely great, the recipro- eal of an infinitely small quantity. Sa ae ) PAPER BY PROF. KIRCHHOFF. hoo where, as also in the following examples, kh indicates a positive real ) fraction, and where the region of @ is bounded by the lines y=0, p=—n ; p=7,p=+on. The expression adopted for f(a) is single value. The multiple points ot V f(@)f(@)—1 that do not lie outside the region of @ are the points p=—log (1—h), 4 =0; p=—log (1+hk), p=z. These lie in the boundary of this region, and, therefore, it need not be further bounded by sections. The equations of the boundary of the region of w are also the equa- tions of the boundary of the region of z. If we assume that for g=-— log (1+) and + =z we have r=0 and y=0, then these equations when developed become the following For p= 7 and gp < — log (1 + k) there results “p ptt dae Ege None ewe ta y=0 and v= | (k—e-? — Vv (k—e-*) *— 1) d QP log (1+k) where the root (as also hereafter every root of a positive quantity), is taken to be positive. By these equations the positive half of the axis of x is represented; this is to be taken as a fixed wall; at the initial point of codrdinates it merges into the free boundary. For this free boundary, namely, for y=z and wm > — log (1+) we have 6 x =) (k—e-*)d p — log (+k) 2S vem f foes dp —log (1+k) Furthermore for 7;=0 and m <—log (i-k) we have f An ESA Een L2= (ceo fk te-o2—1 Japa —log (1—k) y=b and for »=0 and p> —log (1—h) b x=] (k+e-*) dp+t —log (1—k) ee y=— fi—(hte-#) dp+b —log (1—k) where a=k log thin V1—k2 b =— —? 7T k The first part of the stream line 7;=0 which is a straight line paral- _ lel to the axis of x and extending to the point =a, y=), is to be con- sidered as a fixed wall; the second part is to be considered as the free boundary of the outflowing jet. 12 THE MECHANICS OF THE EARTH’S ATMOSPHERE. The approximate course of the lines ¢;=7 and 7=0 is shown in Fig. 4! The completion of the boundary of the region of 21s formed by the line p=— o, namely, ‘ —o r=2k p—2e — cos +a, y=2k d+2e sin pb, and by the line, p=+x, namely, v=k p+ Vink pte; y=k p— V1. -B pth | where a, 01, (2, b: are constants whose values are easily obtainable and which are partly used in the computation of aand b. The first of tuese two lines can be defined as a half circle that is deseribed with an infinitely large radius about the origin of codrdinates; the second is a straight line that is perpendicular) to the jet at an infinitely great dis-' tance from the origin; at this dis- | tance the jetforms an angle with the | positive axis of 2 whose cosine | equals k. | If we assume that k equals 1 then: « becomés infinite and the point: (a, b) removes to infinity ; the region) Fig. 4. | of @ can in this case be bounded! by the lines 7;=7 and 7:=—7 instead of by the lines ¢=7 and ¢=03; thus we come to the case treated of by Helmholtz and illustrated by | Fig. 5. | ¥ x | | ae Fig. 5. If we make k equal zero then will b equal zero; in this case the ! boundary of the moving fluid is represented by Fig. 6. | i PAPER BY PROF. KIRCHHOFF. 135 (II.) As a second example the case where k : J(@)=k+ Vis will be treated and the region of w stretches indefinitely far in all diree- tions. In order to make /(@) a single-valued function we draw a section from the point w=0, for which section ~=0 and m>QO and assume that for p=+0 and 7=-+0 the real part of VY @ is positive. The a points of the curve Vf (co) f( F (@)—1are the points for which w=0, 1 Lae k, G) 1 (L+H); therefore they all lie on the section already drawn therefore do not require the making of anew section. Asconcerns the sign of Vf(@)f(@)—1 it must be so determined according to the adopted rules that the real part of this radical quantity shall be positive for p=+0, and ~=+90. Finally it is assumed that w and ¢ disappear simultaneously. The line for which 7;=0, and @m>0, is the boundary of the region of e. This line is composed of many parts which are to be distinguished from each other. For 7=+0, and 0 am we have Ge ap! he) ee ae ee and tor iL ~=—Oand p> (1k) we have L 2 an) | aie The lines that are represented by the integrals of these equations, when we determine the constants of integration so that these lines start from the previously indi- cated termini of the fixed walls, are the free boundaries of the moving liquid. The other boundaries of the region of zlie at infinite distances, as is seen from the fact that when w=a we have dz d@ dx 1 dy — dp — VQ" dp =k—iV1—k this equation shows at once that at an infinitely great dis- tance from the origin of coér- dinates the flow takes place with the velocity 1 in a diree- tion that forms an angle with the axis of x whose cosine isk. Figure 7 illustrates the boundary of the region of 2; besides this boundary the figure also gives the stream line for which 7:=0, and p<. (III.) Stillone more example may be introduced. Let there be : k J es Fig. 7. and let 7 vary between —7z and +7, but m between —-» and +x». From the point w=0 draw a section for which 7;>=0, and g> 0, and assume that for p=+0, and /;>=+0, the real part of /(@) is positive. The points of bifurcation of V f(c)f(a)—1 are the two points o=0, and w= — log (1—k’) both which are found upon the section that has been drawn. The sign of the radical quantity V f(@)f(c)—1 is determined by the rule that its real part shall be positive for p=+0, and /=+0. ; . . PAPER BY PROF. KIRCHHOFF. oe Finally we assume that w and 2 disappear simultaneously. At the boundary of the region of 2 we have, first the line for which ~=0, and p>. This line is composed of the following portions: For 7=+0, and 0< p< —log (1—k’) we have, a ae Sa ac ae vost ree? y=0 For ¢=—0 and 0<@m@<—log (1—h”) we have, mah (ves ees i—()) These equations represent a portion of the axis of v that is to be assumed as the fixed partition. Adjoining this fixed partition there comes as the free boundary of the moving fluid the line for which w=+0, p>—log (1—k”’), therefore div es ay 1h eS dp W/ Jauen eo? dp \ 1—e-¢ and also the line for which =—0, p>—log (1—}), whence da _ k dy _ " tan dp vVi—e-’ dp ~ 1—e-4 The remaining boundaries of the region of ¢ are the lines p=—n, Y=+7, P=—-H P=+. For 7;=—7z we have, da _ k dy _ / fie dp ~Jipeo) dpe vy 1-773: For ¢=+7 we have, spn Boe dp ite-**?=dp WN Pecos These two stream lines are free boundaries throughout their whole extent. d For p=—~x, we have—_=-— i: PR wi TT ae , for p=+a, and 7><0, we have (7 ji V 132 @ and for p=+%, and #/>0, we have kai eae A@ 138 THE MECHANICS OF THE EARTH’S ATMOSPHERE. For p=—~x, we therefore have y=+, and the stream flows with a velocity of 1 in the direction of the negative axis of y; for p=+a, we have c= Fo, and y=—~, and the stream flows with a velocity of lina | direction that makes an angle whose cosine is +k with the direction of | the positive axis of x. In Fig . § the boundaries of the moving fluid are represented for this — case. | Y Se ae ew bi ae ee ee ee ete | | | | IX, ON DISCONTINUOUS MOTIONS IN LIQUIDS.* By Prof. A. OBERBECK. I. It is customary to designate by the term discontinuous fiuid mo- tions, those phenomena of movementin which the velocity is not through- out the whole space filled with the fluid a continuous function of the locatio:. Therefore in such movements there occur surfaces within the fluid that separate from each other regions within which the veloci- ties differ from each other by finite quantities. The fundamental prin- ciples of the theory of these motions were first given by Helmholtz.t If we assume that a velocity potential (~) does exist for so called steady fluid motions then the hydro-dynamic differential equations can be summarized in the one equation, SGN? IP Jp’? pmo L+H +P) | Now Helmholtz has shown that the pressure p and consequently the velocity can be discontinuous functious of the coordinates aud that there are a great number of phenomena of motion for which the assump- tion of a discontinuous function is necessary. Especially has this theory been applied by Helmholtz and by Kirchhoff to fluid jets,t and the boundaries of free jets can be given under the following assumptions: (a) That no accelerating force acts upon the fluid. (b) That the movement is steady. (c) That the movement depends only upon two variables, wand y, and is therefore everywhere parallel to a fixed plane. If in other cases, for instance for jets that are symmetrical about an axis or that are under the influence of the accelerating force of gravity, *Read at the session of the Physical Society in Berlin, May 11, 1877. Translated from Wiedemann’s Annalen der Physik und Chemie, 1877, vol. 11, p. 1-16. +See the Berlin Monatsberichte, 1868, p. 215 [or No. II of this series of Translations. ] t See Crelle’s Journal vol. LXXx, p. 289-299, [and Nos. III and VIII of this collection of Translations. ] 139 140 THE MECHANICS OF THE EARTH’S ATMOSPHERE. it is not yet possible to determine the free boundaries by computation, then this is only because of the analytical difficulties. In general, how- ever, one can judge of the nature of these boundaries from a considera- tion of the results already found. The mathematical investigations just referred to hold good equally well for liquid jets that are bounded by quiet air as for those that are bounded by similar quiet liquid. In the actual production of such liquid jets it of course makes a great difference whether we allow water to flow into the air or water to flow into water. Jn both cases disturbing circumstances oecur of which the mathematical theory takes no consid- eration. The jets of water projected freely into the air have been most thoroughly investigated.* In these experiments the formation of jets occurs just as would be expected according to theory. On the other hand, however, it is known that water jets are influenced to an important extent by the capillary tension of the free surface, and that in consequence of this at certain distances from the orifice they Dreak up into drops. If we allow a liquid to flow into a similar quiet liquid then these capillary effects do not occur; but in place of this another disturbing cause, the viscosity, influences the phenomena. The viscosity has hith- erto not been taken into consideration in the theory of the discontinu- ous movements of fluids. If weattempt to consider it we stumble upon a peculiar difficulty that has led the present author to experimentally investigate this class of fluid motions. Is It is well known the theory of viscosity of fluids can be developed from the assumption first framed by Newton,t namely, that the retard- ing or accelerating influence of two portions of fluid flowing past each other with different velocities is proportional to their relative velocity. Especially has O. E. Meyer from this hypothesis developed the general differential equations for the motion of fluids.t If we assume that all parts of the moving fluid describe paralle! paths, say in the direction of the axis of y, and that the velocities v are only functions of wand that finally is the coefficient of viscosity, then will the influence of two neighboring parts upon each other be represented by the expression dv $e dx * Besides the older experiments of Bidone and Savart see especially Magnus, Pog- gendorff Annalen, vols. XCV and CVI, t Mathematical Principles of Natural Philosophy: German translation by Wolfers, Berlin, 1872, p. 368. t See Crelle, Journal, vol. LIX, pp. 229-303, and Poggendorff Annalen, vol. CXII1, pp. 68, 69. PAPER BY PROF. OBERBECK. LAr If v is a discontinuous function of x, then at such a locality the dif- ferential quotient will be indefinitely large. Therefore two neighbor- ing portions would exert an indefinitely great influence upon each other. If therefore one of the fluid portions is at rest while a neighboring por- tion that belongs to the jet flows by the first with a constant velocity communicated to it by some exterior influence, then the first or quiet particle must immediately begin to take part in the movement of the second, but the second on the other hand must begin to lose a definite fractional part of its velocity. The jet must therefore rapidly set the surrounding quiet fluid in motion with it. It would according to this appear to be doubtful whether sharply defined jets such as are de. manded by the above-mentioned theory of Helmholtz could be formed in a fluid subject to viscosity. The few experiments made hitherto upon this question appear to con- firm this suspicion. Especially notable is an investigation by Magnus (Poggendorff Annalen, LXXx, pp. 1-40), who allowed pure water to flow from a evlindrical opening into a weak solution of salt and by means of a glass tube drawn out into a fine point, Jed away a small quantity of the inflowing water in the neighborhood of the opening. The liquid thus caught was examined as toits salinity. From the latter one could calculate to what extent the inflowing liquid had bezome mixed with that which was previously in the vessel. It resulted that pure water could not be caught at any point of the inflowing liquid; that therefore everywhere the original quiet liquid was carried along with the mov- ing liquid. The analogous case of jets of air and of smoke, as also that of the free jets of water in the air, demonstrates that in all these, we have to do with phenonena of very slight stability. It is well known how sensi- tive such jets frequently are with respect to the feeble periodic disturb- ances produced by waves of sound.* It seemed to me therefore of interest to investigate more accurately the formation of water jets in water and therein to utilize a method that allows of following the course of the phenomena of motion better than was possible in the experiments of Magnus. This object is most simply attained in that we allow feebly tinted water to flow into colorless water. Fuchsin is used as coloring material. It is well known that witha very small quantity of this material an intense red color is produced with no fear lest hereby the specific gravity of the water be essentially changed. in the first experiments performed with this it resulted that the jet of colored liquid broke up at a very slight distance from the orifice into reddish clouds and drops that mixed with the quiet liquid and carried it along with them. By further investigation however, it became pos- sible to determine conditions under which real jets of considerable length and sharp boundaries were formed. These were of great sta- *See John Tyndall on Sound, pp. 289-292 of the German edition edited by Helm- holtz and Wiedemann, Brunswick, 1869. 142 THE MECHANICS OF THE EARTH’S ATMOSPHERE. bility, so that small disturbances had only a rapidly diminishing in- fluence upon their course. At the forward end of these jets there formed peculiar surfaces of flow that plainly allowed the influence of viscosity to be seen. These phenomena of motion are of remarkable beauty and delicacy, of which any one may convince himself who per- forms the easily repeated experiments. Since the theoretical investigations mentioned in the introduction treat of the modifications of jets by solid bodies, and Kirchhoff especially gives a series of interesting examples bearing upon this, therefore this question has also been taken into consideration in my ex- periments. Very stable forms of jets are also thus formed that have more similarity with those deduced by theory than one could have ex- pected. III. The experiments were made with the following simple apparatus: A cylindrical glass vessel (Fig. 9), of about 60 centimetres height and 12 centimetres diameter, was tilled with water. Into this there passed a flow of water from a filter through an India-rubber tube, a glass stop-cock, and a glass tube. The filter, as also the entire tubular system, was filled with the colored liquid. After filling with water the glass eylinder (in whose place one may also use any large glass vessel), one must wait along time until the motion of the water has been destroyed by viscosity. The experiment sueceeds best when the water has stood for many hours in the cylinder, since then cur- rents resulting from differences of temperature are no longer present. By a quick opening of the glass stop-cock one can allow a definite quan- tity of celored liquid to enter into the quiet liquid, or by a longer opening one can attain a steady stationary current. By elevating or depressing the filter one can easily regulate the height of the upper fluid level. The use of a small difference of pressure was found to be the principal condition for the maintenance of regular current forma tions. The majority of the experiments if no other problem was on hand were executed with an excess of pressure of about 20 millimeters. By means of proper arrangements solid bodies could be opposed above the jet. For exact observation it is necessary to fasten a surface of white paper behind the glass cylinder. IV. In order to understand the formation of jets it is advantageous first to learn the behavior of a definite quantity of liquid entering under PAPER BY PROF. OBERBECK. 143 a small excess of pressure into the quiescent liquid. I therefore begin with a description of the experiments relative to this. If we allow the stop-cock to be opened for only a short time, then even with the smallest differences of pressure of two or three milli- metres, a Sharply defined mass of liquid penetrates into the quiescent liquid. The original form of this mass is soon modified by viscosity and by the participation of the hitherto quiet liquid in its motion, in a peculiar manner, and finally it rolls itself into a ring. The colored mass of liquid goes through the series of forms presented in Figs, 10, 11, 12, and 13. Of these drawings, as of most of the following ones, it is to be noted that they represent a section of the mass of liquid by a plane that passes through the axis of symmetry of the formation. In order to find the true form therefore, one must imagine the figure revolved about this axis. Sri se Fig. 13. Fig. 12, Fig. 10. Fig. 11. With the form of Fig. 13, the ring formation is completed. More- over in general even for differences of pressure of 10 to 20 millimetres, ‘the living force of the liquid was consumed so that this figure long floated motionless in the colorless liquid. If we use somewhat larger differences of pressure we observe that the liquid within the ring continues rotating for a longer time. The — original progressive movement has therefore been transformed into a vortex movement. The vortex movements have been theoretically treated by Helmholtz* and he has in the introduction to his memoir referred to the necessity of the transformation of any current or move- ment that has a velocity potential into a vortex movement in conse- quence of viscosity. Many other consequences drawn by Helmholtz in his memoir just reterred to can be easily observed by the help of the apparatus used by the present writer. *Crelle’s Journal LV, pp. 25-56, [and No. II of this collection of Translations. ] ie THE MECHANICS OF THE EARTI’S ATMOSPHERE. If by alternately opening and closing the stop-cock we allow two drops to enter into the colorless liquid in rapid succession, then there arises a ring formation for each drop and the following one always catches up with the preceding one. Different cases are then possible, according to the differences of pressure that are used; if these are slight then the second ring is not able to penetrate the first one and a formation, as shown in Fig. 14, remains for a long time visible in the fluid. With greater differences of pressure, on the other hand, ring No. 2 passes through ring No.1, since the former contracts while the latter expands. One can then observe that afterwards ring No. 1 en- deavors on its part to pass through ring No. 2. But generally the living force is by this time consumed, so that ordinarily the two rings settle into the formation shown in Fig. 15. This interchanging passage a LL sa LE: Fig. 14. Fig. 15. of the vortex rings through each other was predicted by Helmholtz from theory in the memoir above referred to. Reusch has occupied himself experimentally with the formation of vortex rings.* After having described in detail the formation of smoke rings in the air, he passes to the formation of rings by the sudden en- trance of a small quantity of colored liquid into colorless liquid. 6 10S p: In this expression p indicates the distance of the point (2y) from the vertical currents of the individual regions, assuming that the dimensions of these regions are small in comparison with the distances. This value of m would be exactly correct if all inner regions [namely, as defined on page 153] were bounded by circles. Then p would indicate the distance from the center of the circle. The constants ¢ depend upon the intensity of the respective vertical currents. They are positive for the minima and negative for the maxima [7?. ¢., for areas of low and high pressure respectively]. The assumption F(wtiy)=(e+tyP=ptip whence pau —y ; WD 2H leads to a special example already treated of by Guldberg and Mohn.t The potential curves xv? —y’—constant and the stream lines ry — 7) (x? —y”)=constant v are systems of equilateral hyperbolas. *See their Ltudes, etc., Part 1, pp. 23-26. tEtudes, Part 1, pp. 51, 52. 160 THE MECHANICS OF THE EARTH'S ATMOSPHERE. It we assume \e+ ty) =log (w+ iy)=p+up and if we substitute 2—=recos 63 y=rsin 0 then follows Plog rv, In this case the isobars consist of concentric circles. The paths of the wind are logarithmic spirals having the equation A ler: log y=constant. Vv. STEADY SYSTEMS OF WINDS. It is certainly at present generally assumed in meteorology that the winds at the earth’s surface owe their origin and maintenance to ver- tical carrents of air that are limited to definite regions. Let us assume that there is given such a region having any arbitrary boundary above which a current of air ascends whose velocity in the neighborhood of the earth’s surface is determined by the constant (c). By this assumption the whole system of winds dependent thereon, as well as the distribu- tion of pressure, is determined for the whole region. It is therefore the province of mathematics to determine all the quantities coming into consideration both for the inner and also for outer region. To this end the functions mand w are to be properly determined. The first of these is found without further difficulty from well-known theorems jn the theory of the potential. Since these functions must in the outer region satisfy the partial differential equation Jg=0, and in the inner region must satisfy the equation dg=—c; therefore* —_/ € {4 Fay dO 10S Pp scwhelile bel eee (22) In this p indicates the distance of the element of the surface do from the point x, y. The integral is to be extended over the whole of the given inner region. Therefore the velocity potential is the logarithmic potential of a layer of matter having the density —c/2 7 that covers the - . , . .* . region of the ascending current of air. The function ¢ itself, as also jts first differential quotient, varies continuously throughout the whole plane up to the boundaries of the outer and inner regions. *See G. Kirchhoff, Vorlesungen iiber Mechanik, 1876, p. 195. PAPER BY PROF. OBERBECK. 161 Therefore, the function W is known for the outer region and is af A VW sore Ee In order to determine this function for the inner region also one must _ go back to the equations (13) ) 2 e h of, ah ¢ (22_aW) Owe ; oy ¥ oy Ox “ Oa (22 oW oy dx Ov OY _ First we make the assumption that € is constant throughout the _ whole inner region: We can then write BEA ses aces ne “(Axe W er ees p Je (A-€ W)—2( Ate )=0 ; oy c These equations are satisfied if we put Ai—& W=constant; £+¢ p=constant. By considering equation (12) there follows from the last equation _ especially k W+(A+6) p=Constant ros EE ——— g+Constant. From the first of these equations we also obtain, kd W+(A+¢) 4 p=0 k f= (AE) Ae lh A ee and ‘W =— aa g~+Constant or whence o S — But in general the values of W thus found merge continuously into _ each other at the borders of the two regions quite as little as do their differential quotients. Hence it follows that the component velocities also, and therefore both the velocity and also its direction, suffer sudden changes of finite magnitude at the boundaries of the two regions. We have therefore found only one special solution, and not one that obtains in general. This special solution is that which Guldberg and Mohn have used in the special case of a circular boundary for the inner region. Corresponding to it they find that in the outer region the di- 30 AST 162 THE MECHANICS OF THE EARTH'S ATMOSPHERE. rection of the wind makes an angle é¢ with the radia! gradient such that A : eu fame. R whereas in the inner region the corresponding angle ¢’ is given r r—_@ Still less allowable are the consequences that follow when we imagine the inner region bounded by some other curve such as an ellipse. In this case by utilizing the special solution it results that at special por- tions of the boundary more air flows inward from without than flows away, but at other special portions of the boundary the relation is reversed. One can easily persuade oneself of this by using the known value of the logarithmic potential of an ellipse.* When therefore W can be considered as the logarithmic potential of a stratum of the inner region still if is not to be considered as constant. Its value is to be specially determined for each given region. This computation will now be executed for the case of a circular region. by the equation tan ¢/= VI. CYCLONE WITH A CIRCULAR INNER REGION. Let the region of ascending air currents be bounded by a circle o the radius &. Let the center of the circie be the origin of the system of co ordinates. We pat P=7 ay, First the velocity potential is easily computed as follows: For an exterior point c Qy=—szhlogr .... . . (23a) For an interior point o.=—~ i} R? (2 log R—1) +r} . 4s (230) Furthermore for an exterior point we have W.= pit log ry Of the functions ¢, W; and P, which are still to-be determined, it can certainly be assumed that they depend upon 7 only. If we further consider that dF(r)_ afr) « jc 2=6Ch adr Sr then equations (15) can be written ; iy Uf, _ ef Up iW : an dr. | Sar sae ; af, _ i Afr __ nite ( 2 Ps yo dr adr dr “Kirchhoff, Vorlesungen iiber Mechanik, 1876, page 217. PAPER BY PROF. OBERBECK. 163 If we multiply the first by x the second by y and add we obtain df,_-aW dr ~ ar or if we introduce the value of /; Serna e Tk... see cD ¢ dr If on the other hand the first of the above equations is multiplied by y the second by x and subtracted there results dip = 2ap Gio a. OF or dw RA Dae: oe hk adr sate)? 0 (25) Since furthermore c=4Wa2 © ( 7) rdr dr and dpc de eer therefore we have in equation (25) an ordinary differential equation for the determination of W;, If furthermore we put then equation (25) becomes r( dw ) tite (Ge). dr ar This gives the following integral where A is the constant of inte- gration: This may finally be written— Aw 1 “? ee a7 ae 164 THE MECHANICS OF THE EARTH'S ATMOSPHERE. The constant A is now to be so determined that on the borders of both regions, that is tosay for r = R, the movements pass continuously — from one into the other. Since now —t dp _y dW. a mnie ag y dr yr dr? ydp xdW ee SS yr dr xr ar therefore at the boundary we must have dp, dq, daw, aw, dr — dr dr ~— ar’ This condition is satisfied for the function g. We have still to bring it about that the corresponding equation shall be satisfied by the function W. Since dW, Ae ; “ar sak therefore for r=R we have aw, dre ap ope This latter will be the case when we put —2 AS ae M( M—z) Therefore we have finally aW, r 1 ee dr ~ u—2 MB, or if for abbreviation we put ofr \t-2 =i = ‘ i I= ay (27) we obtain dw, A ; — a S(T) a ee haere ——=—_. 7 dr u—2 The function f (7) can according to equation (26) also be written— PAPER BY PROF. OBERBECK. 165 In accordance with these conditions our results are now as follows: (a) for the outer region (29) (b) for the inner portion a x o i ave 5 Sin eay en) a il, we 5 Le — ) Ei r) | (30) worry — v= ke} 9 r : tan Naan) In these equations ¢ indicates the angle between the direction of the wind and direction of the gradient, which latter coincides of course with the radius of the circle. These expressions differ from the solutions given by Guldberg and Mohn (not to speak of some small changes in the notation) by the introduction of the function f (7) in whose place the factor 1 is given by them. The above-given expressions are subject to one limitation. It is necessary that we have «sz or ky ce, since otherwise for r=o f(r) would become infinitely great, and in the inner region a deviation of the wind from the gradient toward the left would occur instead of to- ward the right-hand side. The deviation of the wind direction from the gradient is constant in the outer region, but in the inner region it increases continuously and for 7 =0 it attains the limiting value— / an ¢é=>;—.. t ee I pass now on to the computation of the pressure. According to equation (17) we have for the outer region— P,=constant — kp 1+ p) 166 THE MECHANICS OF THE EARTH'S ATMOSPHER Consequently P= constant fee | 14%. ; SR log r. For the inner region the equation (24) is to be used. According to it we have— es Ae Ate ew di dr sut according to equation (25) we have— d W A _ ——— —h a dy dy Therefore, dw»? : ( dy P,=const—k pm—k. “dy, dq cv dr The arbitrary constant can be considered as determined in that the value of P is supposed to be given for r=0. (For the center of the . » . depression we have r=0 and P=!) Let Py be this value. Then we p have— P,=P)+ Fir), Where 5 hess A? Soy 4 aa LSE Fr) — co ' | a (+iG) talk ) \ » (0 ) Since P, and P, must at the boundary merge continuously into each other, therefore the constant in the expression for P, is to be deter- mined in accordance with this condition, and we have— ke We P,=Pot F(R) 4+-9( 1 +2 EP log > . ot Mee Oon From equation (9) we obtain the expression for the pressure-— P_p_jo? 0 2 If we designate by po, the pressure at the center of the depression, where w=0, then in the inner region we have— PoE = F\r)— 300" jul Su Pag der, ot oie but in the outer region— apes —F(R)+ ke 1 a lon eee ; ( Zl itpe)RlogZ—to . . . . . (3) PAPER BY PROF. OBERBECK. 167 VII. NUMERICAL EXAMPLE FOR A CYCLONE: NOTE ON ANTI-CYCLONES. In order to show the applicability of the formule obtained in the last section to cyclones as they actually occur in nature, I have executed the following computation of a numerical example: In this computation I have assumed A = 0.00012 This value correspords to an average latitude of 55.59. For kL have assumed the same value, whereby the value obtained for the influence of friction is rather large. For the complete determination of the system of winds the constant ¢ of the ascending current of air and the dimensions of the inner region must also be known. We can obtain this in various ways. We can _ assume as given, a definite difference in pressure between the center and a ecirele of known radius; or on the other hand, we can assume that the velocity of the wind is known at a certain distance from the eenter. I have chosen the last assumption. The wind system may therefore be characterized by the assumption that at a distance of 1000 kilometres from the center the wind velocity shall be 10 metres per second. According to equation (29) when we put A=k we have Se 6, heed Sede If in this we put w = 10 metres and + = 1000000 metres we then have ¢ Rk? = 10000000 Y2. Since furthermore c 343.3 kilometres. In the selection of appropriate values of ¢ and &, another circum- stance is to be considered. The discussion of the formuiz (30) for the velocity @ shows that under the assumption here made of A =k, the maximum velocity of the wind occurs at the boundary of the two regions. The smaller the inner region is chosen, by so much larger results the maximum velocity ,. In the following table some coér- dinate values ¢c, uw, RK, and @, are given. @ TABLE I. c Hw | KR rR Kilometres. Metres per sec.| 4 5 =k 5 383. 8 26.06 2 ah | 3 420.4 23. 78 3 lk Se yee 45. 5 20. 60 1k | f a Mlb 594.6 16. 82 168 THE MECHANICS OF THE EARTH’S ATMOSPHERE. I have also executed the further complete computation for the first case where p= the results of this work are given in Table2. In this vo computation the equations (29) and (30) were used for the determina- tion of the velocities w and the deviations ¢ of the direction of the wind from the radial gradient. Furthermore, the differences of pressure (p—p.) with respect to that at the center, in the circles of radius 7, were computed according to equations (31), (32), (33) and (34). These latter are, however, converted from the units ordinarily used in hydro- dynamies into differences of barometric pressure (b—b,). This latter . eas ae a Age is easily done if we recall that for /=760 millimetres the ratio Zig equal to the square of the Newtonian velocity of sound; therefore we have the proportion (b—Db,) : ic0=} (P—Po); (279.9) pp The gradients y are in our present case the ditferences of barometric pressure for a horizontal distance of 100 kilcmetres. TABLE II. eee ie pope ee a 7 w € (Db —bo) Y Kilometres. Metres per sec. of | Millimetres. | Millimetres. | | 0 | 0 78 41 | 0 | fe | . 2. 37 = 100 14.99 | 71 19 2037 | 4.64 | | : 200 22, 44 | 64 40 | 1. OL . BRE Sahl _ | 35. 03 300 25. 53 | 55 39 | 12. 04 383. 8 26. 06 45 00 | 15. 88 | ta 78 | | 400 25,00 45 00 16. 82 500 ; 0 . 0 21. 58 | pas 500 20. ( 21.5 ti se aoe 3. 60 600 16. 67 ’ 45 00 25.18 . 800 12. 50 45 00 0. 50 ae 0 3.4 30. 50 : if , 1.95 1, 000 10. 00 45 00 34.45 From this table we see that the cyclone includes a broad storm region from r=200 to r=500 kilometres, of which a portion is in the inner region and another portion in the outer region. Of course the gradients are greatest in the inner region; therefore there the isobars are most crowded together, From those values of the constant ¢c that are any way possible, it fol- lows that the velocity of the ascending current of air is extraordinarily small; for the present example ¢ equals 0.000096. If we assume that the formula w=cz holds good to an altitude of 1,000 metres, then the vertical velocity would at that height tirst attain the value of about 0.1 metre per second. Hitherto the discussion has exclusively dealt with regions of ascend- PAPER BY PROF. OBERBECK. 169 ing currents of air and the cyclones arising therefrom. It would be easy in an entirely similar way to develop the theory of descending currents of air and the anti-cyclones resulting therefrom, and here also, aS an example, to assume an inner region bounded circularly. Before the actual execution of the exact computation I had believed that this was simply a case of the change of the sign of the constant ¢. But in this operation we stumble upon a peculiar difficulty. The TRING ea I (e , 2s : ; i “ly —— f= a ( wh ir —— 7 2 ne function / (7)= a R) erein =~ :) which enters into the expression for the component velocities in the inner region becomes in- finitely great for negative values of ¢ and sand for r=o. The same is true of the function F (r) entering into the expression for the pressure. Hence it follows that the formula just given can not be applied to anti- eyclones with a reversed sign of ¢. Therefore minima and maxima of pressure show a characteristic dif- ference in their theoretical treatment. But this, as I believe, corre- sponds also to the real conditions of the true phenomena. Depressions are ordinarily confined to limited areas, but are of considerable inten- sity, while on the other hand the maxima of pressure extend with slight intensity over broad areas. Fic. 27. Moreover, both phenomena stand in close connection, such that one can consider the ascending currents of air as the cause of the descend- ing currents. Hence to a complete cyclone there helong an inner region with ascending air current, a zone surrounding it of purely 170 THE MECHANICS OF THE EARTHS ATMOSPHERE. horizontal movement, and at a greater distance from the center a ring- shaped region of @escending currents. If we assume that the boundaries of the three regions consist of con- centric circles, it would not be difficult to compute the wind system for the whole region by the help of the potential theory as above employed. In this case, where we have to do with an annular region with a descending current of air, the use of the function f (*), even with a negative sign before the y, is allowable, and can be adopted in order to produce the necessary continuity of motion at the boundary of the two annular regions. If there are several regions of depression with ascending currents of air, as at A, B, C, fig. 27, then each of them is immediately surrounded by a zone of purely horizontal movement, which is bordered by an outside annular zone of descending movement. I have in the figure (27) distinguished the region of ascending and de- scending current by double aud single shading. In the region where the different ring systems of ascending air currents merge into each other there will lhe a region of highest pressure with anticyclonal movement of the air somewhat as within the isobar M, NV, P. How- ever, the characteristic difference between ascending and descending currents of air always consists in this, that the former consist of defi- nite, simply connected areas; tbe latter, on the other hand, of a net- work of several complexly counected regions. HALLE A. S., June, 1882. P. S.—After sending the above treatise to the editor of the Annalen, I found in the May number of the Zeitschrift of Lhe Austrian Association for Meteorology (vol. Xv, pp. 161-175) a review by Dr, A. Sprang of the second part of the collected memoirs by W. Ferrel, under the title of ‘ Meteorological Researches.” From this I perceive that the views expressed by me as to regions with high pressure had been already expressed by Ferrel. Therefore, although my point of view is no longer nev, still I rejoice to see that it is shared by a prominent meteor- ologist. xan: ON THE GULDBERG-MOHN THEORY OF HORIZONTAL ATMOSPHERIC CURRENTS.* By Prof. Dr. A. OBERBECK, of the University of Halle. Starting from the generally known results of recent meteorological observations in so faras these relate to the distribution of pressure and the direction and force of the wind, the author states that one of the most important problems of the mathematical theory of the motion of fluids is to explain quantitatively the connection of the above-named phenomena. The recently published investigations of Guldberg and Mohn (Ltudes sur les mouvements de Vatmosphére. Christiania, 1876 and 1880) are to be considered as a specially successful attempt in this direction. It must be of interest also for the larger number of geog- raphers to know the most important results to which the Norwegian Scientists have attained. In order to understand the horizontal movemeuts of the atmosphere it is important for a moment to consider their causes. As such we con- sider the differences of pressure at the surface of the earth as observed with the barometer. But whence do these arise? This question has been answered along time since. It is heat which is to be considered as the prime cause of the disturbance of equilibrium in the atmosphere. Because of the slight conductivity of the air the process of warming can progress only slowly from below upwards, so that as is well known the temperature of the air steadily diminishes as we ascend. The heated air expands. The pressure becomes less. If the heating takes place uniformly over a large area there will be at first no reason for horizontal currents. But vertical currents can certainly be brought about by this means. If we imagine acircumscribed mass of air trans- ported into a higher region without any increase or diminution of its heat its temperature wili sink because it has expanded itself propor- tionately to the diminished pressure. If its temperature is then equal to that prevailing in the upper stratum it will remain in equilibrium at this altitude as well as below. The atmosphere in this case exists in a State of indifferent equilibrium. If its temperature is lower the * Translated from the Verhandlingen des Zweiten Deutschen Geographentages. Halle, April, 1882. 171 172 THE MECHANICS OF THE EARTH’S ATMOSPHERE. mass of air will again sink down; in the reverse case it will rise higher. The air in these cases is then in stable or unstable equilibrium respec- tively. In the latter case any vertical movement initiated by some acci- dental disturbance will not again disappear, but rapidly assume in- creasing dimensions. The current will also continue uniform for a long time. This is the explanation first given by the mathematician Reye,* of Strasburg, of the ascending air currents in the whirlwinds of the tropies. The winds of our (temperate) zone also presuppose such ascending currents whose origin must have been quite similar. The ascending current is in general restricted to a definite region that we can desig- nate as the base. Since the ascending current consists of warmer air, therefore above its base the pressure sinks. A barometric depression is inaugurated there. The pressure increases from this region outward in all directions. The isobars therefore surround the region of ascend- ing atmospheric currents in closed curves. At greater heights the up- per cooled air flows away to one side and in other regions gives occasion to descending currents of air. At the earth’s surface itself, the air flows towards the depression; its influence thus extends over an area much greater than that of the base. If we neglect the curvature of the earth’s surface we find over this larger area only simple horizontal movements. Mathematical computations should now reveal to us the nature of such horizontal movements. Tothis end all the causes of motion, or the forces that come into consideration, are first to be col- lected. The differences of pressure have already been several times spoken of. Wetakeasthe measure of these differences, the gradient which gives for any point the direction and amount of the greatest change in pres- sure. In horizontal movements the effect of gravity can be omitted. On the other hand attention must be given to the rotation of the earth on its axis, since we are only interested in the paths of the winds on the rotating earth. This influence can be taken account of if we imagine at every point of the mass of air a force applied which is per- pendicular to the momentary direction of motion and is equal to the product of the double angular velocity of the earth by the sine of the latitude and by the velocity of the point. In the Northern Hemisphere this influence causes a continuous departure of the path towards the right-hand side. Since the movement takes place directly on the earth’s surface the direct influence of that surface, namely the friction, remains to be considered. Its influence diminishes with the distance from the earth’s surface. Furthermore it depends on the nature of the earti’s surface, whether sea or land, plains or wooded mountains. For this computation Guldberg and Mohn have made a convenient assumption in that they introduce the friction as a force which opposes the move- “(This explanation is of course much older than Reye (1864), who was preceded by Espy and Henry in the United States and by Wm. Thomson in Great Britain. C. A.J PAPER BY PROF. OBERBECK. 173 ment and is equal to the product of a given factor and the velocity. This factor can have different values according to the nature of the earth’s surface [and will be called the friction constant}. All these forces are to be introduced into the general equations of motion of the air. If however one desires solutions of these general equations for special cases there is still needed a series of assumptions, Let there be only one single vertical current of air present. The to- tality of all the atmospheric movements depending upon this one verti- cal current is called a wind-system. If the strength of the ascending current is variable or if the base itself changes its place, then the wind- system is variable. In the first case the system stands still, in the second case it is movable. If on the other hand the ascending current of air retains its strength and location without change, or, which is the same, if the isobars for a long time retain their position, then the wind system is invariable. It is evident that the last case is by far the most simple. We will therefore begin with its consideration. In order to execute the calculation the location of the isobars must be known. Even in this respect also in a preliminary way, one must limit himself at first by simple assumptions. Let the isobars be either par- allel straight lines or concentric circles. In the first case the computation leads to the following simple results: (1) The parallel isobars are equally distant from each other. The gradient is therefore everywhere of equal magnitude. (7) The paths of the winds consist of parallel straight lines. The strength of the wind has everywhere the same value. (3) The direction of the wind forms an angle with the gradient whose tangent is equal to the quotient of the factor arising from the velocity of the earth’s rotation divided by the friction constant. The deviation of the wind from the gradient is therefore greater in proportion as friction is smaller. If the earth’s surface were perfectly smooth the wind would blow in the direction of the isobars. This result, following directly from the computation and at first sur- prising, finds its confirmation in a variety of observations. For exam- ple, in England we observe a deviation of 61° for land winds, but of 77 for sea breezes. From this it follows that the friction on the land is more than twice as great as on the sea. Conditions of pressure like those here considered frequently oceur. In the regions of the trade winds and monsoons they ordinarily prevail either during the whole or about the half of the year. The circular isobars to the consideration of which we now pass pro- duce systems of wind that can be considered as the simplest types of cyclones and auti-cyclones according as the pressure in the interior is a Ininimum or maximum. We confine ourselves here to the considera- tion of cyclones. As already remarked cyclones are not conceivable without an ascend- 174 THR MECHANICS OF THE EARTH'S ATMOSPHERE. ing current of air, whose area in our case is defined by a ecirele. Out- side of this cirele horizontal movements prevail exclusively; inside of it there is also the vertical novement to be considered. Therefore the computations for the outer and inner regions are different. In this way we obtain the following results: (1) The pressure increases from ail sides outward from the center; the gridient increases also from the center out to the limit of the inner region; thence outward it diminishes and at a great distance becomes inappreciable. (2) Lhe wind-paths in both regions are curved lines, logarithmic spirals, which cut the isobars everywhere at the same angle or make everywhere the same angle with the radial gradient. Therefore the movement of the air can be considered as consisting of a current toward the center and a rotation around the center, the latter in direction op- posite to the hands of a watch. This departure from the gradient is of different magnitudes in the outer and inner regions. Tor the former the departure has the same value as for straight-line isobars, that is to say, it depends alone upon the rotation of the earth and the friction. For the inner region the departure is greater, «nd depends besides upon the intensity of the ascending current of air. If both regions were sepa- rated from each other by a geometrical cylindrical surface then the wind- paths in these would not continuously merge into each other, but would form an angle with each other. This of course can never occur in nature. We must therefore assume a transition region in which the wind Is con- tinuously diverted from one into the other direction. At any rate ae- curate and comparative observation of the wind direction in the inner and outer region of a cyclone would be of great interest. From these one could draw a conclusion as to the limitation of the ascending ecur- rent ofair. This limit is moreover also notable because at it the winds reach their greatest force, There are no other arrangements that Lave been discussed theoreti- cally as vet except the straight line and the cireular and nearly circular forms of the isobars. We have as yet only spoken of the invariable systems of wind. In fact however their duration is relatively short. No sooner is a de- pression formed than it fills up. Furthermore the central region of depression generally does not remain long in the same place but wanders. often with great velocity, drawing the whole system of winds with it. We must look to the density of the horizontal current flowing in to- wards the ascending current of air as the cause of these changes. The system of winds remains unchanged only when, as has hitherto been silently assumed, the temperature and density of the horizontal and vertical currents are alike. If the inflowing air is warmer the depres- sion increases in depth; in the opposite ease it becomes shallower. Finally, if the inflowing air is not of the same temperature on all sides, but has on the one side higher and on the other side lower PAPER BY PROF. OBERBECK. 175 temperature than the ascending air, then it will on the one side be strengthened and its area increased, on the other side enfeebled and its area diminished. The consequence of this is that the current of air or the region of depression moves along; the cyclone progresses, Since in the cyclones of our north temperate zone the air entering on the east side comes from more southern—therefore in general—warmer regions, while the air entering on the west side comes from the north and is generally colder, therefore the cyclone progresses from west to east or from southwest to northeast. This is in fact the path of most cyclones in northern Europe. Fora moving cyclone the isobaric curves must have a different shape than for one that is stationary; therefore one can inversely from the shape of the isobars infer the direction of motion. If the region of ascending air has a circular form the compu- tation can be rigorously executed. Without going into the details of this interesting problem in this place I will only remark that the isobars consist in closed curves similar to an ellipse. There is one direction from the center outward in which the isobars are most crowded together, while in the opposite direction they are furthest apart. The movement of the cyclone is in a direction at right angles to this line. With the solution of this problem we now stand about at the limits of what analysis has thus far accomplished. Still there is hope that it will make further progress so far as concerns the relation between the pressure and the motion of the air at the earth’s surface. x1, ON THE PHENOMENA OF MOTION IN THE ATMOSPHERE.* (FIRST COMMUNICATION.) By Prof. A. OBERBECK, of the University of Greifswald, Germany. Is The meteorological observations of the last ten years have given a series of notable laws that principally relate to the connection between the currents of air and the pressure of the air in the neighborhood of the earth’s surface. Of course one can only hope to obtain a complete insight into the complicated mechanism of the motion of the air when one understands more accurately the condition of the atmosphere in its higher strata. But difficulties that are perhaps never to be overcome oppose the observation of these strata. On the other hand, the completion of this and many other gaps in the theory of the motion of the air is certainly to be expected from a comprehensive mechanics of the atmosphere. The Treatise on Meteorology, by A. Sprung, Hamburg, 1885, gives a summary of what has hitherto been accomplished in this field, from which summary it is seen that only special individual problems have found a satisfactory solution. The principal features of a rational mechanics of the atmosphere are given in the memoir by W. Siemens, ‘‘ The conservation of energy in the earth’s atmosphere.” + It appears to me worth while to follow out mathematically the questions there treated of and to develop a the- ory of the motions of the air as general as possible. The results thus far attained by me, are collected in this present memoir. On account of the magnitude and difficulty of the problem to be solved, I have at first confined myself to the determination of the cur- rents of the air. A corresponding investigation of the distribution of pressure will follow hereafter. Moreover the phenomena of motion *Read before the Royal Prussian Academy of Sciences, at Berlin. March 15, 1888. Translated from the Sitzungsberichte Konigl. Preus. Akad. der Wissenschaften. 1888, pp. 383-395. t See Berlin Sitzungsberichte, 1886, pp. 261-275. 176 PAPER BY PROF. OBERBECK. eT will here be considered as “steady motion.” On the other hand I have labored so to arrange the calculation that if can be applied to any condition of the atmosphere and to the general currents between the poles and the equator, or the atmospheric circulation, as well as also to individual cyclones or anticyclones. In order to test the applicability of the formula thus obtained, the first of the problems just mentioned is completely solved. I begin with an enumeration of the factors upon which the movement of the atmosphere depends, and with a description of the manner in which I have introduced these into the calculation. II (1) Since the ultimate cause of the motion of the air is to be sought in the effect of gravity and in the differences of temperature in the atmosphere, therefore the attraction of the earth must enter into the equations of motion as the moving force. But it is entirely sufficient here to consider the earth as a homogeneous sphere. (2) The temperature of the atmosphere is to be considered as a function of the locality, but entirely independent of the time. The last condition is necessary if one confines himself to steady motions. For the temperature 7, the analytical condition MTB hE gE Api =O OT TOY) de must be satisfied. This equation, as is well known, follows from the assumption that the heat is distributed through the medium in question according to the laws of the conduction of heat. Although I am by no means of the opinion that the conduction of heat principally determines the flow of heat from the earth’s surface through the atmosphere into the planetary space, still it is very probable that the totality of all the phenomena here coming into consideration (conduction, radiation from the earth’s surface with partial absorption in the atmosphere, vertical convection currents, etc.) will bring about a distribution of tempera- ture analogous to that due to the conduction of heat. (3) According to the rules of mechanics, the influence of the rota- tion of the earth can be expressed by a deflecting force, so that after its introduction the earth can be considered as at rest. (4) Friction is furthermore to be considered, since without it the atmospheric currents under the continuous influence of accelerating forces would attain to indefinitely great velocities. In my opinion, the attempts made hitherto to give a correct theory of the motions of the air, especially one that can be developed analytically, have failed because of the insufficient or incorrect introduction of friction. I have i: adhered to the simplest assumption, namely, that the same law of _ friction holds good for atmospheric currents that has also been shown 80 A 12 178 THE MECHANICS OF THE EARTH’S ATMOSPHERE. to be correct in the motion of liquids.* But I would not hereby assert | that the same numerical coefficient is to be used as is given by the | laboratory experiments on the internal friction of the air made under the exclusion of all attendant disturbing circumstances. More likely — is it that along with the greater horizontal currents there will arise small vertical currents of a local nature which will increase the- friction, The air can either be held fast at the earth’s surface or glide | with more or less resistance. This fact, as is well known, is expressed in the boundary equations of condition by a number, the coefficient of — slip, Whose value may lie between zero and infinity. (5.) The density of the air must be considered as dependent upon the temperature, since the effective cause of the currents results from this. But I have not objected to use, as the equation of continuity, that simpler expression that obtains for incompressible liquids. The error introduced hereby can be eliminated if, at places where the density is less than the average, one increases to a corresponding extent — the velocity found for that locality, but considers the velocity as dimin- — ished at locations where the density exceeds the average. (6) A hydro-dynamic problem is only perfectly definite when the fluid occupies a definite space, and its behavior is kuown for all limiting | boundary surfaces. I have therefore assumed that the atmosphere is bounded both by the earth’s surface and by a second spherical surface concentric therewith. The distance of the two spherical surfaces, which — I will briefly designate as the height of the atmosphere, can remain un- determined. But this is quite small in comparison with the earth’s radius. The above assumption just made however, only expresses the idea that for a given altitude above the earth’s surface the radial or vertical currents are very small, or rather that when they are present — they exert an inappreciably small influence on the remaining motions. This is certainly the case, since at very large altitudes the density is” very small. Since moreover it is assumed that the air can glide without resistance on the upper spherical surface, therefore in my opinion no limitation of the motions of the atmosphere, contradictory to the real phenomena, results from the introduction of such an upper boundary surface. To The following notation will be used for the principal equations of the problem. The position of a point in the atmosphere is determined by the rectangular codrdinates x, y, 2. The center of the earth is the origin - of codrdinates and the earth’s axis in the direction of the North Pole is the positive axis of z. The positive directions of the two other axes are | to be so chosen that the axis of y as seen from the North Pole must be turned through an angle of 90° in the direction of the motion of the— hands of a wateh in order to be made to coincide with the axis of x. *[The term friction as here used therefore includes viscosity and slip, but excludes the resistance due to wave motion and to vortex motion and all the resistances implied in turbulent flow of fluids. —C. A. ] | | PAPER BY PROF. OBERBECK. 179 Let there be furthermore— u, v, w, the components of velocity ; p, the pressure ; uw, the density ; k, the coefficient of friction ; G, the acceleration of gravity ; R, the radius of the earth; r, the distance of any point from the center of the earth; e, the angular velocity of the earth. Then we have— du oe pe. fp) ok | dt 4+— du-+ 2ev, fou pl ~| = =| =—! )\— Vv C 1 O dpe Pp Je ‘ Av—2eu, | dt yy HE oe \ (1) 1 dw ont Lop, & y GR? u, dt e dz ie wee Ju, dv, Jw_ da a 2: ¢ | Sinee according to the law of Mariotte and Gay-Lussac PEaPo Te (l+a T) we may put a Op _ Po d log Pp. jis Oe sini tied) Ox The zero point of temperature is arbitrary. It is most appropriate to assume for it the average temperature of the atmosphere. If c is the Newtonian value of the velocity of sound, then we have Doe as Po ¢ Ho After the introduction of these expressions into the above principal equations, imagine the latter divided throughout by 1+ aT. Except- ing in that member in which the gravity occurs, one can omit from ; 1 : consideration the influence of the factor oe In the term just men- tioned one can, as a first approximation, put (1— aT) for the value of this factor. Furthermore let pts f lh 150 THE MECHANICS OF THE EARTH’S ATMOSPHERE, The first of the equations of motion now becomes ye du _ 2 t pal d log p Deny d= (l—aT)GR A C ae +xuJdut2ev. If the temperature of the atmosphere depended only on the altitude above the earth’s surface and were therefore only a function of r, then would these equations be fulfilled by putting wu, v, w respectively = 0; the atmosphere would then be in equilibrium. Therefore put Tes ae wherein J) is a function of 7 only, but 7) is also a function of the longi- tude and latitude; therefore i C = ° di )ax on J ee oT 7 ? 7. ) a oa du Y ox Finally one may put p=p-(1+ v). The quantity v in this latter equation expresses those changes of press- ure that are caused by the phenomena of motion. Since v is small in comparison with unity, therefore instead of log (1 + v) the quantity v itself cau be substituted. By this means the first principal equation becomes du )4(l—aTl T ) log p a4 == Ga — 7 —t +a dl — ele —( u4u + 2 dt ox yi + Te j Pe ou i is After transforming the two other principal equations in the same man- ner we can put ,(l—aTl Ti @ log p; = constant + GR? ar zea ats aw far } or lel This equation gives the diminution of pressure at larger altitudes above the earth’s surface, and can for smaller differences of altitude easily be transformed into the ordinary equation of barometric hyp- sometry. PAPER BY PROF. OBERBECK. 181 The following system of equations relating to the phenomena of mo- tion proper now remains : du _a GR d Dy Ce 0 t+ udu+2er, dt r Jory td » aGR? 9 yw : di Gk’ : fi i ut + xdv—2eu, dt r oY oY ) (3) Mea Gh OL wend Dips es Sn ea 4 Mit dz ewes Ju, dv, Jw _o jnrdy dz ; One can now compute first those components of the current that de- pend only on temperature differences; after that those that are brought about by the rotation of the earth. If we put w=uj+wm; v=v,4+%; w =W, +23 V=M+%2+ Vs, then will the following two systems of equa- tions be those that are first to be discussed: Iv, aGR of, 2 nueaeT iy te , 2 Ce ol 1_aGk : 24 Ao oy r oy z 2 e eee oO nd wey and 2 aS EY +142; c Sas - e = 2— — Pew, +1440; y Ue Vv: ce ee Wo. Uo Thus there still remain the following equations which are no longer linear and which will serve principally in the computation of the varia- tions in pressure produced by the motion: )\v Ou ou yu en og TY ee wt === 60); ¢ Ue ue wv ov vv i, g Ap pees a w —=—2 Mp; re ag he 25 )V3 ou Jw Ow c c U U W = 0. Ce Re i ae = iy as Jz The first two systems of equations are linear. When therefore 7; consists of a sum of terms we shall obtain corresponding sums for the 182 THE MECHANICS OF THE EARTH’S ATMOSPHERE. component velocities. The solution wiil be quite simple when 7; is developed into a series of spherical harmonies. If we put At es 24) +e Dn and for brevity a a hc, and indicate by @ any term of the series with its corresponding con- stant then the solutions of the first two systems of equations are as follows : Ap dQ, AQF) ff eS ae Sabie (QF) ual) BS w+e oy as 5 hee xl dz \ CPM=Ps4(OF)+aQi | In this # and F are functions of 7» only, and must satisfy the differ- ential equations ‘@H , 2adH ): 1Q of B Q_ a Ey / adr xr dr / or dr or? or “EF 2aF I0/.4F ,aE\_. \ plenary |\ i; ay 5) ( dey ra ut, ar. (2 “dr a : The constant a@ must be added in order to obtain the number of con- stants needed in the consideration of the boundary conditions. The terms depending upon the earth’s rotation are _ 2&8 02, AQ) , ok nat} - a ree 2 y (6) ae Sh OK x” OR - Ona FAK Here also J and H are functions of r only, and must satisfy the differ- ential equations 2 ee Mee of I 2008 Hp) a7. 7 ar dr’ or ar (7) @H 2 dt xd. OOM (Getz: Ge) CG Paes). | PAPER BY PROF. OBERBECK. 183 The constant ) must also here be added forthe same reason as above given. The function A is to be computed from the equation Eileen ee PTD Nt ey een) TIN OUE he OAT From this last equation it follows that the introduction of the fune- tion A can be omitted when the temperature of the atmosphere is as- sumed symmetrical with reference to the earth’s axis. In this case w.=0 and the [atmospheric] movement resulting from the rotation of the earth consists exclusively in a movement of rotation depending on the geographical latitude and the altitude above the earth’s surface. In order to present in the ordinary manner the currents of air for a given point in the atmosphere, the following components are to be in- troduced instead of wu, v, w: V, the vertical component computed positively upwards ; N and O, the two horizontal components, of which the first indicates movement toward the north, the latter, movement toward the east; @, the complement of the geographical latitude of a given place; 7, the longitude counted from an arbitrary meridian; then we have V=+(u cos y+ sin 7) sin 6+ cos 6 N=—(u cosy+v sin 7) cos 6+wsinfe . . . . (9) O=—u Sin 7+ Cos y. \ The formule (4, 6, and 9) contain the general solution of the problem so far as this is at present intended to be given, assuming the distribu- tion of temperature to be given and that the functions H, F, J, H, K are determined in accordance with the boundary conditions. IV. When one attempts to represent the distribution of temperature on the earth’s surface by a series of harmonic functions then the most im- portant term is a harmonic function of the second order. Therefore as a first approximation we put i (4” cf ® )a=8 cos? A), This function, with a proper determination of the constants, ex- presses the great contrast in temperature between the equator and the pole. If now one would take into account the variation with the sea- sons one must next introduce harmonic functions of the first order. The consideration of the various peculiarities of the earth’s surface will of course demand further terms that depend on the geographical longi- tude also. 184 THE MECHANICS OF THE EARTH’S ATMOSPHERE. I have at first limited myself to the computation for the above given distribution of temperature, and put Q=Ar’ (1—3 cos? 6) : / — (1—3 cos? 4). The functions #, fF, H,J are now to be computed with the help of this Q, and the corresponding £’, F’, H’,and J’ with the help of this Q’. We first obtain the general expressions : i oe ep) [4 Jy oe 2r (F+ E) , n ( dr rw loo dr Wa Oo 6 cose, Bind { Ar(P+E) + AU (FAB) H a O= a Wine sin 4 | a3 cos? 4) Ar( f= a (H+J) ) od . ar y Ar GR 3(H'+J') ) +6 cos? #) Ar (HJ) + +3) ar ° The actual computation, having due reference to the boundary con- ditions, of the functions here introduced, gives results that are difficult to be discussed. But this is simplified when we make use of the cir- cumstance that the atmosphere fills a very thin shell in comparison with the terrestrial sphere, wherefore the distances from the earth’s surface are all small in comparison with the earth’s radius. If we put r=R (146) then is o small with respect to unity. If we introduce these quantities in the above given equations and put rh +2 (E+ P)=RY(0), F+E=R9(0); y a Lf of IN -3(B4P)=Rf (0), P+ B'=Rop! (0); dH 9 Pea im 3. tH 2(H4 J) =R'9(0), H+J=By(o) pOE 3 (Hi +S = Ry! (0) H4J' = Rry! (6); then by restricting ourselves to the terms of the lowest order, we can obtain simple expressions for these functions. Primarily we ud that the functions f and f’, g and @g’, g and g’, y and y’ are identical. . ; | | ee PAPER BY PROF. OBERBECK. 185. Moreover the two constants A and A’, which occur in the combina- tion A! A Re + R can be expressed in terms of the temperatures of the earth’s surface at the equator, 7, and at the pole, 7. We have 1 A! 3 (T.—1,) =A B+ Fn Finally we put The numerical value of these two last constants can not be given, since, as before remarked, the coefficient of friction, x, will not agree with that determined from laboratory experiments. In any case D is considerably larger than C, since in D the tourth power of the radius of the earth occurs, but in C only the second power. The components. _ of motion of the atmosphere are, therefore: V=C (1—3 cos? 6). f (G) N= —C. 6 cos 6 sin 6.9 (6) 0=Dsin 4} (1— 3 cos’ 4) g (g) + 6 cos? Oy (6 )} If we take R.A for the altitude of the atmosphere as above defined, then the four functions, f, p, g, y, are to be so determined that they satisfy the prescribed boundary conditions for c=0 and g=h. I have executed this computation for the most general case, namely, that in which at the upper limit slipping occurs without friction, but at the lower limit sliding with friction. Undoubtedly honor the condi- tion of the atmosphere on the earth’s surface is much more nearly that of adhesion than that of free slipping, so that I will here communicate only the solutions for this latter case. For this case the motion at the earth’s surface is everywhere zero. But for this motion one can easily substitute the motion at a slight altitude, that is to say, for small values of o. For the four functions we find the following expressions: J (¢)= °(h—o) (3ho—20”) 9(0)=14 | 6? —15ho +80? } CG) = = a —9h?+ 15h? Pe — Lohot+40° } Y (°)=960 20h? o? —25ho° +804 186 THE MECHANICS OF THE EARTH’S ATMOSPHERE. According to this solution the following gives a picture of the at- mospheric circulation, which in its principal points agrees with that of W. Siemens. (1) Currents on a spheroid without rotation. These currents consist of currents in the meridian, and of vertical movements. (a) The meridional current in the northern hemisphere is southerly below, but northerly above, since the function @m changes its sign when o increases from zero toh. It attains its largest value at 45°, and dis- appears at the equator and at the poles. (b) The vertical circulation is zero at the earth’s surface and at the upper limit of the atmosphere. From the equator to 35° 16’ north and south latitudes the flow of air is positive—that is to say, ascending— but in higher latitudes it is descending. Its velocity at the poles is twice as great as that at the equator. By the comparison of the expressions for f (@) and @ (6), it appears that the former function contains the fourtb powers of the small quan- tities h and o; the latter function contains their third powers. There- fore, the vertical flow is to the horizontal flow, so far as magnitude is concerned, as h is to 1, or as the altitude of the earth’s atmosphere is to the radius of the earth. From this we can scarcely assume that we | should be successful in the direct observation of the vertical current. The great effect of the vertical current arises from this, that it rises or sinks over a very extensive area. (2) Currents in consequence of the rotation of the earth. Under the assumption here made as to the distribution of tempera- ture on the earth’s surface, these currents consist exclusively of move- meuts along the parallel circles of latitude. As in the case of the two terms in the component O, so here we distinguish the two following. (a) The movement depending on the function g (o). Since this func- tion is invariably negative; therefore to begin with at the equator the motion is directed toward the west. It changes its sign at latitude 35° 16’, and then becomes a motion directed toward the east. (b) The second current is zero at the equator; becomes a maximum at 54° 44’, and is exclusively directed toward the east. Both currents disappear at the poles. The two motions (a) and (b) differ from each other fundamentally in that y (o) differs from zero first when o has larger values, It is there- fore a current that only occurs in the higher strata of the atmosphere. But thereby the function g is of a higher order than y for the small quantities kh and o. Therefore at great altitudes the current (b) must greatly exceed the current (a) in velocity. The components la and 2a combine at the earth’s surface to form the reguiar movement of the air that we designate as the lower trade wind. PAPER BY PROF. OBERBECK. 187 On the ocean where this system of winds can freely develop in the manner here assumed, without the influence of continents, their course is in good agreement with the conclusions of theory. Thus, on the northern hemisphere, between 0° and 35° latitude, east and northeast _ winds prevail; at 35° nearly north or in general only feeble winds; in higher latitudes northwest and west winds. It results from the preceding that the two currents (1a) and (1b) are of the same order of magnitude and give moderate winds in the lower strata of atmosphere. Since now the current (2), in comparison with (2a) is of a different order of magnitude, therefore the former is by far the most intense of all currents of air, but only in the upper strata of the atmosphere. In so far as this component combines with the upper current (1a), it forms in the tropics the southwest or upper trade wind. In higher latitudes the purely westerly current prevails. So far as is known to _ me, the observations of the highest clouds which show prevailing west winds agree herewith. That the just-mentioned rotation-currents attain a great velocity has its reason in this that they can circulate around the whole earth without being hindered by the friction of a lower oppo- site current, as for instance is the case with the meridional currents. I consider it probable (as also W. Siemens has already announced) that in this powerful upper current we have to seek for the principal source of the energy found in the wind system of the lower strata. XIII. ON THE PHENOMENA OF MOTION IN THE ATMOSPHERE.* (SECOND COMMUNICATION.) By Prof. A. OBERBECK, of Greifswald. A comparison of the highest and lowest atmospheric temperatures at the surface of the earth shows permanent ditferences of 70°C. If the pressure were uniform every where these would correspond to differences of density of the air of more than 20 percent. Since, however, pressure and density mutually influence each other one should therefore expect minima of pressure at places of highest temperature and maxima of pressure at places of low temperature of a corresponding intensity. Instead of this the average differences of pressure on the earth’s sur- face attain only 6 or 7 per cent., and even the largest rapidly passing barometric variations scarcely exceed 10 per cent. We explain the relatively small value of these differences of pressure by the formation of corresponding currents; a lower current at the earth’s surface in the direction of the increasing temperature and an opposite upper current. Still the above-mentioned rule as to the connection between temperature and pressure must be true in general. But this is by no means always the case. While the equatorial zone of highest temperature shows a feeble minimum of pressure there occurs a maximum of pressure be- tween the twentieth and fortieth degree of latitude from which toward either pole, and especially markedly in the southern hemisphere, the atmospheric pressure very decidedly sinks. {t appears to me not to be doubted that we can explain this re- markable phenomenon only by the influence of the rotation of the earth upon the currents of air that originate in temperature differences. In a previous memoir? Ihave endeavored to carry out an analytical treat- ment of these phenomena of motion under certain assumptions which * Read before the Royal Prussian Academy of Sciences at Berlin, November 8, 1888. Translated from the Sitzungsberichte Kénigl. Preus. Akad. der Wissenschaften zu Berlin. 1882, pp. 1129-1138. +t [See the previous number (XII) of this collection of Translations.—C. A.] 188 PAPER BY PROF. OBERBECK. 189 are there given in detail. In that memoir the pressures were not ex- plained ; this is done in the present treatise. I have arrived thus at the result that the distribution of pressure just described finds its ex- planation completely in the currents of the atmosphere, and that from the observed values of the pressure a conclusion can be drawn as to the intensity of the atmospheric currents.* Il. In conformity with the notation of my first memoir the temperature of the atmosphere will be expressed by T=1T7+f7, where J) depends only upon 7, the distance of the point in question from the center of the earth, while 7; is a function of r and of 6, the polar distance. Let the pressure at the given point be p=pi(l+7) In this expression p, also depends on'y upon 7, while vis a function of yand 6. So far as the observations of atmospheric pressure show, vcan be considered as a small numerical quantity in comparison with unity. For determining p the following equation holds good : 1 PL ce log pp=constant + are | ad? ) from which the diminution of pressure as a function of the altitude above the earth’s surface can be computed when the iaw of the diminu- tion of temperature with the altitude, that is to say, the value of Th as a function of 7 is known. Let us further put V=MOtVMtM+V3 in which while 7, ”2, 7; Shall indicate the values determined in the previous me- moir (pages 180 and 181). The first two terms of this summation “+” give those changes in pressure which result directly from tie differences of temperature on the earth’s surface; that is to say, without considering the rotation of the earth. If the temperature diminishes uniformly on both hemispheres from the equator toward the poles; or, in other words, if the temperature * [Ferrel had published similar conclusions in 1559 but Oberbeck’s independent con- firmation is none the less valuable.—C. 4. ] 190 THE MECHANICS OF THE EARTH’S ATMOSPHERE. depends only on the geographical latitude (and not also on the longi tude), then the motion of the air can only consist in vertical and me- ridional currents, and which (corresponding to the above given compo- nent velocities uw, v1, ¢;) consist of one lower current toward the equator and of one upper current toward the poles. The distribution of pres- sure “+7, existing in connection with this furnishes (by means of the equation (4), page 182 of the previous memoir) the anticipated result that on the surface of the earth the pressure increases from the equator to- ward the pole, while at a medium altitude the differences of pressure disappear, but that finally, at greater altitudes, the pressure is greatest at the equator and least at the poles. Since as above remarked, the actual distribution of pressure in no- wise agrees with the above, it must be concluded that the influence of the term 7)+7; on the pressure can only be slight. From the previous developments it results that the term v2 disappears under the assumption of a uniform distribution of temperature symmet- rical with the earth’s axis, so that as was already indicated in the first memoir, 7; will be the most important term. III. In the computation of this quantity v; the system of equations pre- viously given is to be used, namely : V2 u ; gue ess O e*—+u—+” W— =UEV Ox ai ou oy oz 2 )V: Vv Ww )v 90" 3 c c c 9 Ce Uu v— + w— = — ZEU: dy tant oy t 32 : Ow lo Ow Vy 9¢ 3 ce —"+u— +v—+w-—=0 oy dz Ne Oo) Da Since according to the accordant opinion of meteorologists, as also according to my previous deductions, it is very probable that the inten- sity of the rotatory currents of the atmosphere materially exceeds that of the meridional currents, therefore I have only introduced into the further computation the rotation currents, whose components are des- ignated by wz and 2%. Since we have to do with a movement of rotation about the axis of = therefore we can put Uz = NY, L=+ANL, C=, and these values can also be used for u, v, and w, in the above-given system of equations. The relative angular velocity y is to be deduced from the expressiom for the easterly component O (see equation (9), page 183). This is a fune- PAPER BY PROF. OBERBECK. 191 tion of 6 and of r or also of 6 the altitude above the earth’s surface. The first system of equations is therefore transformed into the following: Vv PAR) EL) : Ca as (2é-+- 7) Xx av, c od: P Soy = (2E+X) XY; a7 a3 — (), 02 Since y is a function of r and 4, or of p and z if we put 2=r7 cos 7 pi= TF Bins therefore, we can not find one function v; that shall satisfy the three equations. If y were independent of 2 we should find cv; = constant + | (2e+y7) vp dp. Since however this is not the case we must therefore conclude that the above-given system of equations still needs a supplement; that therefore a movement of rotation of a fluid to the exclusion of all other movements can only exist when the angular velocity in the direc- tion of the axis of rotation is everywhere the same. If this is not the case then further currents occur perpendicular to the rotary motion. In our case these latter would consist of vertical and meridional move- ments. Their components may be designated by wu; v3 w3. These are to be introduced into the above system of equations as was done in the corresponding fundamental equations (3) of the first memoir which now become )V es = (2e+ y) yr +2 Aus Vv OOS = (2e+x) ry +4405 c y . . (2) | ) eS = 14W3 OU; O U3 JW3 a x a dy ci Poe . If the component motions indicated by the subseript 3 that directly depend on the movements subscript 1 are materially less in intensity than the movements of rotation, then in any computation of the pressure their introduction ought not to be omitted. The former memoir gave — ———e_e—- ———_ 192 THE MECHANICS OF THE EARTH'S ATMOSPHERE. a rather complicated value for the angular velocity ¥. I have intro- duced a simplified expression for this in that, while retaining the dependence upon the polar distance 6, as there given, I have tempo- rarily introduced a constant average value instead of the dependence upon the distance above the surface of the earth. According to this, one can put X= COS? O— Yo (3) o1 with a slight difference ip ; me?—yxar” (4) In these equations y; and y2 are considered as constants. Therefore, as before found, the movement of rotation of the air in higher latitudes is positive, that is to say, has the same sign as the axial rotation of the earth. For a specific latitude the average value is 0, and at the equa- tor the movement has the opposite sign. further computation shows that the relative angular velocity y is small in comparison with that of the earth ¢, so that the simpler equa- tions to be solved are as follows: sgl se | Cy = AEXE + udu V3 oa = 2eyyt uJ a PS obo Reems ec? —_ = uxAW3 Oz du; , dvs , U3 _0 yr a In solving these we first determine afunction § that is of such form as to satisfy the conditions d§ _ ae 8 ery, : oy ox These conditions give er? ' ~ rae 7 2 B= | ne — os \ (6) Furthermore we put VE OL aL é Uz = —, 13 = dE ip Me rel So eo oe ane) ov oy de where Z and M are two new functions of x, y, and 2, we can then write the system of equations as follows: 5 OV: ow ) , RG" 3 c el? = £0 u% (AL ; ox ox + xe ) ! yV i ) e 5 3 S a u < (4L) 3 oY oy oy F 2 OV: ow ) ow eos — As 4- tA Ans +x JH. PAPER BY PROF. OBERBECK. 193 The equation of continuity now becomes aM 4Lb=— 5 (8) The three first equations lead to the two following: cv, = Constant + *% — x aut heat (9) Meh 08. (10) u Oz If the functions Z and M are so determined that they satisfy the boundary conditions then the: problem is to be considered as solved and equation (9) gives the desired distribution of pressure. As boundary conditions { have retained those previously laid down, viz, adhesion to the earth’s surface, slipping on an upper boundary surface at an altitude &. h above the earth whereby h is to be considered as a small number in comparison with unity. For further calculation it is expedient to introduce the vertical and meridional components of the current or Vand NV. These are con- nected with ZL and J by the equations V= ue + M cos 6 e aro Pe (ll) N=— LoL M sin 6 r 00 The equation of continuity now becomes Vee 1 BE DINE a et =z cote Ne og t (12) The elimination of ZL gives the further equation CN aaa oll: OM c teapiaoaR eae Gime e ru 3) 0 eimai els) The caleuiation gives the following values: 9) V=—R M+ 22-6 (411+ 72) Cos? +357, cost 4 ' sf (Ciinwe L) a N= R! sin 600s )—%i—2yet- TH - Cos? Of. (6) Me eke 14 (Cli) _ In these f(o) and ¢@ (o) have a signification similar to that in the | previous memoir, namely, I (=, (h—G) (3h—20) (16) 9 (o)= £24 6he—15ho +80" } 80 A——13 a — SS - ~~ 194 THE MECHANICS OF THE EARTH’S ATMOSPHERE. Moreover, o is determined by the same equation as before, r—R (i+G) Finally, from the equation (9) » wo F FS a: ce? v5=const+ Sie there results the following : eho : c vs=const-+ eR? | ( a a) cos? #— y, cost 4 ; . « “Chg se J, This last equation allows of a direct comparison with the above-men-— tioned observations of the distribution of pressure. IV. The average values of the pressure of the air in the Southern Hemi- — sphere are given in the following table (ander the column of observa-_ tions) as a function of the latitude.* é dir pressure at the earth’s surface. { | Latitude. | Observed. | Computed. 3 mm. mm. 0 758. 0 758. 0 S. 10 759.1 758.9 | 20 761.7 760.5 20 763.5 762. 0 40 760.5 760.5 50 753. 2 755:38 | 60 743.4 747.1 | 70 738. 0 738.0 | SO: (|b Sees 730.9 2 i, 3900-4. Pies ee | | | | These pressures are fairly represented by an expression of the form P = Pat acos? G6—D cos! 8. If we determine the constants a and } from the observed values for two — different polar distances, for which I have used 6=50° and §=20° then we obtain p=t98+31.295 cos’ d—61.094 cost 6. > By the means of this formula the values given in the second column, under ‘ computed,” have been obtained. *See A. Sprung, Lehrbuch der Meteorologie, p. 193; J. van Bebber, Handbuch der — Witterungskunde, 1, p. 136. [These figures are taken originally from Ferrel, ‘‘ Meteo- rological Researches,” 1, 1880.—C. 4. ] PAPER BY PROF. OBERBECK. 195 Furthermore, if we make the very probable assumption that the vari- _ ations in pressure here considered depend exclusively on the movement _ of rotation, that therefore | p=pu(l+ vs) _ where p, represents the pressure at the equator, then is eee cma, oe ie Therefore 3 A 13= oa 31.295—61.094 cos? 6 609 =0.0413 cos? 0—0.0806 cos*6 . . . . . - (19) But the computation of v3; had already given Vw=— {on —y cos? # ' - wherein the appended constant can be omitted. Hence, the two expressions for v3; can be put equal to each other, _ and for the computation of the motion of rotation we obtain the two equations : eu hie “> 1=0.0806 ae a 3 +) =0.0418 ; If in these we put 3 K=6379600"; c=280™; £=0,00007292 ¥1=0.0292 « K2= 0.0536 Xr - Hence, the relative angular velocity of the rotary motion of the air is x=0.0292 ¢ | cos? 60.0836 We date ae Pd aa (8) _ This is small in comparison with ¢, the angular velocity of the earth, _ therefore it nowhere leads to improbabiy large movements of the at- _ mosphere. If we form the product y, &, we obtain for it the value _ 13.58 metres per second. But the true linear velocity corresponding to _ the rotatory motion is O= XxX: R. sin 6. | The maximum value of this occurs at S. latitude 56° 27/ and amounts to 4.59metresper second. FromtheS. pole to16°49/S. latitude the average SS SS ee eee 196 THE MECHANICS OF THE EARTH’S ATMOSPHERE, value of the rotatory motion is positive, that is to say, directed toward the east; thence to the equator the value is negative, therefore directed toward the west. These results can easily be combined with the conclusions of my pre- vious memoir, according to which the motion of ro.ation can be consid- ered as the sum of two terms that are of entirely different natures. Of the secoud term it was remarked especially that the current correspond- ing to it first attains sensible values at great altitudes. This therefore becomes at that altitude materially larger than the above deduced av- erage value. The first term gave a movement entirely confined to the lower strata of the atmosphere: it is directed toward the east from the pole down to 35° latitude, but directed toward the west exclusively in the equatorial zone and less in velocity than the first component move- ment. The numerical computation leads to the same conclusion, since 2 is small in comparison with y,; Since from 35° of latitude down to the neighborhood of the equator there are two currents of opposite signs flowing over each other, therefore the place where the average mcvement of rotation is 0° will lie nearer to the equator than to 35°. Therefore the conclusion of W. Siemens, which gave the first stimu- lus to the present investigation, has to be subjected to a modification only in so far as we must consider that the westward movement of the upperregions and higher latitudes has a predominance over the easterly movement of the lower regions and lower latitudes, because the former loses a much smaller fraction than the latter of its living force in con- sequence of friction. The vertical and meridional components V and N are to be added to the corresponding compouents that were computed in my first memoir. The vertical component is positive at the equator and at the pole, it therefore gives an ascending current at both places, whereas V is neg- ative throughout a broad central zone. Therefore at the equator the ascending current is strengthened, at the pole the descending current is enfeebled. The meridional component N is zero at the surface of the earth at the equator; it isnegative, @. ¢., it is directed toward the south from thence to about 24° latitude; thence to the pole, where it is again zero, it has a northerly direction. Therefore in the tropics it strengthens the equa- torial current and in higher latitudes it enfeebles it. Perhaps this ex- plains the occurrence of northwest winds which frequently occur in the southern hemisphere between 50° and 60° south latitude. Finally it may be remarked that the formula above used for the dis- tribution of pressure agrees still better with the observations if a third term with a 6th power of cos 4 is introduced. This term would also find its explanation by the analytical development, since the newly found meridional current should properly be again evaluated, in order to further compute the movements of rotation that are to be added PAPER BY PROF. OBERBECK. 197 to the first approximation, and which will bring about a corresponding change in the formula for pressure. In other words, by a series of approxim ations one seeks the true so- lution in a manner similar, for instance, to that used in the computation of mutual inductive effects of two conductors, in which computation we imagine the total influence developed into a series of individual influ- ences of the first conductor upon the second and then again of the see- ond upon the first, and soon. Itis easy to foresee that the further pro- longation of the computation must afford a corresponding term in the expression for the pressure. By this means the expression for the ro- tatory motion will suffer some change; still it is to be seen that the or- der of magnitude of this is already correctly established. After the execution of the further computations just indicated, I expect then to elaborate in a similar manner the average distribution of pressure in summer and in winter in order to determine more precisely the changes _ of the rotatory motion with the seasons. The formula above found is only to be applied with caution to the northern hemisphere, since in this hemisphere the fundamental condition that the temperature is a function of the geographical latitude applies much less truly than in the southern hemisphere. ion | XIV. A GRAPHIC METHOD OF DETERMINING THE ADIABATIC CHANGES IN THE CONDITION OF MOIST AIR.* By Dr. H. HERTZ. The theoretical meteorologist daily has to discuss considerations as to the changes of condition that take place in moist air that is com- pressed or expanded without the addition of any heat. Hence he desires to attain answers to these questions with the least possible ex- penditure of time, and he does not care to use any of the complicated formule of thermo-dynamies. Actually he generally uses the small practical table that Professor Hann communicated in the year 1874 (Zeit. der Oest. Ges. f. Met., 1874, Ix, p. 328). Still it appears that with at least an equal convenience oue may attain a greater completeness if one makes use of the graphic method, and the table accompanying this paper presents an attempt in this direction. This contains nothing theoretically new except in so far as that it also completely considers the peculiar behavior of moist air at 0° C., which, so far as I know, has © hitherto not been treated of. In the following I will now in Section 1, collect together the exact formule of the problem, since a complete col- lection of such appears to be wanting. Under Section If, the presenta- tion of the formule by the graphic table is described. Finally under — Section 11, I explain completely, although purely mechanically, the ap- plication of the latter to a numerical exauiple. If one follows this ex- ample with the diagram in the hand, one attains a judgment as to the use of the table and a knowledge of the method of using it without the — necessity of going through the computations of Sections T and II. Ie In a kilogram of a mixture of air and aqueous vapor let A represent the proportional weight of dry air and yj the proportional weight of un- saturated aqueous vapor contained therein. Let the pressure of the mixture be p and its absolute temperature be 7. Our problem is; What conditions will the mixture pass through when its pressure is di- * Translated fro:n the Meleorologische Zeitschrift, 1884, vol. 1, pp. 421-431. tSee, however, Guldberg and Mohn, ‘‘ Studies on the movement of the atmosphere,” part 1, pp. 9-i6, and, also, by the same authors, Oest. Zeit. f. Weteorologie, 1878, xiii, ps Ly 198 2 ee ee oe PAN. -~ 4 “Ns PAPER BY DR. HERTZ. 199 -minished indefinitely without addition of heat? We must distinguish different stages. First stage—The vapor is unsaturated; liquid water is not present. We assume that the unsaturated vapor follows the laws of Gay-Lussae and Mariotte. Let e be the partial pressure of the aqueous vapor ; p —e be that of thedry air; v the volume of a kilogram of the mixture. pease y We then have p—e=AX it aa where Rand &, are constants v of well known meaning and value. Since now the total pressure p is the sum of these two values, there- fore 5 =] po=(AR+ wh) T and this is the so-called equation of condition {equation of elasticity] for the mixture. If further, c,is the specific heat of air at constant volume and c!, the same for aqueous vapor, then in order to bring about the changes dv and d7, the quantity of heat to be added to the air must be - Iq . d=) ¢dT+ ARTS \ On the other hand, the quantity of heat to be added to the aqueous vapor must be (see Clausius Mechanische Wdrmetheorie. 1876, vol. 1, p. 51.) dQ> = lu CaT+AR, moe ie Therefore for both together, the quantity of heat is dQ=(Actnuc,)dT+A(AR+ UR) pee But this quantity of heat must be zero for the adiabatic changes now investigated by us. In order to integrate the differential equation arising from putting dQ equal to 0, we divide it by Z. From the mechanical theory of heat we know beforehand that by this operation the equation becomes integrable, and we find this confirmed a poste- riort. If we carry out the integration and eliminate v by means of the equation of elasticity, in that we recall that ¢,+ AR is equal to ¢, or the specific heat under constant pressure there follows f oO Oo (Let e'))log 7 —AQR+ Ry logh=O. . | (1) The guantity that forms the left-hand side of this equation has a physical significance. It is the difference of the entropy of the mixture in the two conditions that are characterized by the quantities p7 and po.T,. Moreover the mixture evidently behaves exactly like a gas ae ne a 200 THE MECHANICS OF THE EARTH’S ATMOSPHERE. whose density and specific heat have values midway between those of the aqueous vapor and the air. We now have to compute the limit of p up to which the equation (1) may be used. Hereafter let e be the pressure of the saturated aqueous vapor at the temperature T; eis a function of 7, but of T only. The inass v of saturated aqueous vapor that is present in the volume v at the temperature 7 amounts to ve ; Vt = aoe (1a) and this quantity must be greater than 4 so long as the vapor is un- saturated. Therefore the limit occurs when «=v. If we substitute for v its value from the equation of elasticity, then this latter condition (4 = v) takes the form AR+ wk, =p 8 tt ee As soon as 7 and p attain values that satisfy this equation, we must relinquish the use of equation (1) and pass over to the equations for the second stage. Second stage.—The air is saturated with aqueous vapor and contains also additional fluid water. We neglect the volume of the latter. We can therefore here also consider the air on the one hand and the water, with its vapor, on the other hand, each as though the other were not present. To both are to be ascribed the same volume v and the same temperature 7 as that of the mixture; on the other hand, the pressure p of the mixture is equal to the sum of the partial pressures, p, ——— for the air and p, =e tor the aqueous vapor. The equation p = att e or (p—e)v=ART is therefore now the equation of elasticity of the mixture. The quan- tity of heat that we must communicate to the air in order to bring about the changes d7 and dv is as before cd T+ ARTE | 10,2) avy aha vos \ On the other hand, the quantity of heat that must be communicated to the water in order to bring about the change dT, and to simulta- neously increase by dv the quauiuiy v of ayueous Vapour, While pressure and volume change correspondingly, is dQ, = Ta( 7) 4+ cd T. PAPER BY DR. HERTZ. 201 This equation is deduced in Clausius Mech. Warmetheorie, vol. 1, sec- tion vi, art. 11; and init cis the specific heat of liquid water, r the external latent heat of vapor, both of them expressed in units of heat. Therefore the total heat communicated to the mixture is AO od PeART donne an Ee + yedT. 3 \ vo § ul Here also we have to put dQ =0,then divide by T and integrate. With the help of the equation of eijasticity and equation (la) we elimi- nate the quantities v and v from the integral equation, and thus obtain Pors& p-—e Sir CX toy ae on em NE (Ae, + pe ) log SAAR log: SFE eat Gaeh ibe Tip Avo ceo, pee = Tech —_— 0 — r vp that a kilogram of the mixture in the different conditions can contain as vapor. Thus, for instance, the curve designated by 25 con- nects all those conditions in which one kilogram of the mixture when saturated contains 25 grams of vapor. These curves are drawn from eram to gram. If a mixture contains x grams of vapor in every kilo- eram of mixture, then evidently we have to follow the curve of the first stage up to the dotted line x, but then we must pass either to the second or fourth stage. The limit of the second stage, with respect to the third, is given by the intersection of the corresponding adiabatic beta with the isotherm of 0° C. By the pressure po, that corresponds to this intersection, and by the quantity 4. of water, is determined the pressure p,, at which the transition takes place from the third to the fourth stage. The small auxiliary diagram that is given beneath the main table of Fig. 28 serves for the graphie determination of p;. This auxiliary diagram con- tains as abscissa the pressure arranged as in the larger diagram, and as ordinate the total quantity j of the water in all conditions ex- pressed in grams per kilogram of the mixture. The oblique lines of this small table are the curves that correspond to the equation (3) of the third stage, when in this equation we consider pp as constant, but p, and joas the variable codrdinates. These lines are not perfectly straight, but are not to be distinguished from such in a diagram on this scale. The highest point of each of these lines corresponds to the case p; = po. The corresponding jc is not zero, but is equal to the least value, v, that 42 must have in order that the mixture may be saturated at 0° C., and the auxiliary table come into use. If one wishes to find the p, belonging to a definite value of p) and yz, then we seek that oblique line whose highest point lies on the abscissa po, and then we pass along this line downwards to the ordinate 4. The pressure at which we attain this ordinate is the desired pressure p;. In this pres- sure we have the point of transition from the third to the fourth stage. Having in this way determined the totality of the stages through which the mixture runs, we find the remaining desired quantities for each stage in the following manner: (1.) The dotted line which one selects, (corresponding to the condi- tion given,)indicates directly the number of grams of water still remain- ing in the formof vapor. If we subtract this quantity from the original total quantity uw, we obtain the quantity of water that has already been condensed. (2.) The density 0 of the mixture can under the adopted approxima- tions be computed for all conditions by the formula C p * é= RT or log 6 = log p—log T—log R. PAPER BY DR. HERTZ. 20% These can also be read off graphically if the diagram is covered with another system of lines of equal density. Wesee that these lines will constitute a system of parallel degrees of density. Only one of these lines is in reality drawn on the accompanying diagram, namely, the line marked 0 (delta), in order not to confuse the diagram. But with the assistance of this one we can also compare the densities in any two conditions QO; and ©, according to the following rule: From the points 1 and 2, representing these conditions on the diagram, draw two straight lines, respectively, parallel to 6, until they intersect the isotherm 0° C., and read off the pressures p; and pp» for these points of intersection. The densities for the conditions C, and C, are in the ratio of the pressures p;: po; as is seen from the considera- tions that the densities for the condition (p;, 0°), and for (p2, 0°) are ac- cording to Mariotte’s law in the ratio of p; to po, and are equal to the densities for the conditions C; and C, since they lie on the same line of equal density witb these. (3.) The difference of altitude hk that corresponds under the assump- tion of adiabatie equilibrium to the passage from tLe condition py to the condition p is given by the equation h= He “dp =R i, Op ap P ip 2 In using this equation we take 7 as a function of p from the diagram and then perform the integration mechanically. Actually however the assumption of adiabatic equilibrum is always so imperfectly ful- filled that it is not worth while to trouble about an exact development of its consequences. On the other hand, for moderate altitudes, we commit a relatively very unimportant error when we give J’ an average value, and consequently consider it as constant. Within the limits of the diagram 7 ranges only between the values 2535 and 303; if there- fore we give it the constant value 7, = 273, then the error in h will scarcely exceed one-ninth of the whole value. If we are satisfied with this error, then we have h = constant — RT, log p, and we now can, along with the pressure, directly introduce the altitude as abscissa. Consequently an equal increase in the length of the abscissa will everywhere correspond to an equal increase in altitude. The scale of altitudes is introduced at the base of the diagram. Its zero point is put at the pressure 760, because this is usually taken as the normal pressure at sea-level. III. In order to illustrate the use of the table by an example, we propose to ourselves the following concrete problem: Given a mass of air at sea- level under the pressure of 750 milimetres, the temperature 27 degrees 208 THE MECHANICS OF THE EARTH’S ATMOSPHERE. centimetre, and relative humidity 50 per cent., it is desired to find what conditions this mass of air will pass through wheu it is carried without change of heat into the higher strata of the atmosphere, and therefore into a lower pressure, and at what approximate altitudes above the sea- level the different conditions will be attained. We first seek from the diagram the point that corresponds to the ini- tial stage. We find it as the intersecting point of the horizontal iso- therm 27 and the vertical isobar 750. We remark that it lies almost ex- ' actly on the dotted line 22. This indicates that our mass of air must contain 22.0 grams of aqueous vapor in each kilogram of its own weight in order to be saturated. Sinee however ithas only a relative humid- ity of 50 per cent., therefore it contains 11.0 grams of water per kilo- gram. We note this for future use. Furthermore, we go along down the isobar 750 to the scale of aititude that is found at the lowest edge of the diagram, and here we read off 100 metres. The 0 point of the seale of altitude therefore lies about 100 metres below the sea-level adopted by us as a base, and therefore we have to subtract 100 metres always from all the direct readings on the altitude scale, in order to ‘ obtain the altitude above sea-level. If now we raise our atmospheric mass upward, then the series of conditions which it runs through will | be directly given by that line of the Alpha system that passes through the initial condition.* An engraved line not being given for this case we therefore interpolate such an one (i. é, the — ..—.. line of the diagram). If the number of intersecting lines appears to be bewil ler- ing, then we take a strip of paper and lay it parallel to the system under consideration, when all confusion disappears. In order now to recognize the condition in the neighborhood of the altitude 700 metres we seek for the point 700 + 100 = 800 on the seale of altitudes, and go perpendicularly up until we intersect our Alphaline. The intersection gives this point at pressure 687 milimetres, and temperature 19.3° C. . But we ought to use the Alpha line only to that point in which it itself intersects the dotted line 11 (or the line of absolute weight of con- tained water). The attainment of this line indicates that we have ar- rived at a condition in which the air is only just able to contain 11 grams of water per kilogram in the form of aqueous vapor. Since now we have 11 grams per kilogram, therefore with any further cooling con- densation begins. The pressure for the point at which precipitation ‘commences is 640 milimetres; the temperature is 13.39 C. This is not the temperature of the original dew-point, but it is lower. The dotted line, eleven, intersects the isobar 750 at 15.8° C., and this is the initial dew-point. But since besides cooling our air has also experienced an increase in its volume, therefore the vapor has remained volatile to a PEO ee eee t | j \ *The letters a, 6, v, that designate the systems are to be found in the small circles at the edge of the diagram. For each of these there corresponds one line of the sys- tem that it designates. A line of special dots and dashes in the diagram indicates the change of condition of the air in our illustrative example. PAPER BY DR. HERTZ. 209 temperature 13.3. The altitude at which we now find ourselves corre- sponds to the lower iimit of the formation of clouds, and is about 1,270 metres. In order to follow the conditions further we draw a curve of the Beta (4) system through the point of intersection. This curve is inclined much more slowly toward the axis of abscissas than the Alpha line hitherto used, therefore the temperature now changes with the altitude much more slowly than before, which is due to the evolution of the latent heat of the aqueous vapor. We have now risen 1,000 metres since the commencement of condensation, but the tem- perature has sunk only to 8.29, or only 0.51° to each 100 meters. We now find ourselves on the dotted line 8.9, and perceive that 89 grams of water are still in the state of vapor ; that therefore in this first 1,000 metres of the cloud layer 2.1 grams of water have been condensed per kilogram of air. We attain the temperature zero degrees C. at the pressure 472 millimetres, and at the altitude 3,750 meters, whereas if the air has been dry, and we had not been obliged to leave the Alpha line, this temperature would have been attained at an altitude of 2,600 metres. Itnow appears that by this time 4.9 grams of water, or 0.45 per cent. of the total contents, have been condensed, and during further ex- pansion this portion begins to freeze and form hail [the reader will re- call that although 45 per cent. has been condensed into visible cloud, yet it has not separated from its original air and been precipitated as rain, but is still rising with the air and of course cooling with it]. But the temperature can not sink further until the last particle of water is frozen, and we therefore must retain the temperature 0° uniformly dur- ing a certain distance of further ascent. In order to ascertain this distance we make use of the auxiliary diagram between the scale of altitude and the larger diagram, we pass down the isobar 472 millimetres to the dotted line of this diagram; we draw through this intersection a line parailel to the inclined line of the auxiliary table, and go along this line until we reach that horizontal line that is characterized by the number 11, or the total weight of the contained water, and which we easily interpolate between the engraved lines 10 and 15. As soon as we have attained this line we read off the pressure p = 463 millimetres, and turn back to the larger diagram. At the pressure thus found the process of freezing is fin- ished, and the layer within which it all takes place has a thickness of about 150 metres. It must surprise one that, according to the dotted line, the quantity of water in the form of aqueous vapor has again in- creased a little during the process of freezing. But this is quite cor- rect; in fact, the volume has increased without lowering the temper- ature. We leave the temperature 0° C. at the pressure 463 millimetres. The water which hereafter is precipitated passes directly over into the solid condition. Since there is now but little water as aqueous vapor, _ therefore the temperature again begins to sink more rapidly with the altitude. We ascertain the different conditions in that we make use of Sv A——14 OO ES ee Z10 THE MECHANICS OF THE EARTH’S ATMOSPHERE. that special Gamma line that can be drawn through the point 463 millimetres on the isotherm 0° CG. The temperature—20 down to which our table can be used is attained at the altitude 7,200 metres, and at the pressure 305 millimetres, at which only two grams of water per kilo- gram remain as vapor, the other nine having been condensed. If it~ interests us to know how the density in this condition is related to the- deusity In the initial condition, we draw through the corresponding points two lines parallel to the Deltaline. These intersect the isotherm of 0° ©. at the pressures 330 and 680 millimetres. The densities are to each other as these pressures, namely, as 33 to 68; and as 33 and 68 are | to 76, so they are related to the density of the airin its normal condition of 0° C. temperature and 760 millimetre pressure, All these items are directly read off from the diagram. Errors that could be injurious certainly occur only in the altitudes. These latter refer strictly speaking to ascent in an atmosphere of a uniform temper- ature of 0° C. But it would have been generally better to have as- sumed that the temperature of the atmosphere is every where the same — as that of the ascending mass of air. The resulting error ean be ma-— terially reduced by a very little computation. Thus we found that the point where condensation began, is at the pressure 640 millimetres. ‘To this corresponds an altitude of 1,270 millimetres, provided that the temperature is 0°, but in our case ae is between 27° and 13°, there- fore on the average about 20°. For this temperature the altitude must be about 4%, or sy greater, since the density of the airis by this same fraction smaller meee for 0°. Therefore the altitude really lies between 1,350 aud 1,400 millimetres. We must still supplement the above example by the mention of special cases: (1) We assume in the above that during the hail stage the total quantity of water originally present in the air, namely, 11 grams, was still contained therein. This will certainly only be an appropriate as- sumption in the case of very rapid ascents. In other cases perhaps the greater part of the condeused water falls as rain, and therefore only a fraction of it remains to be frozen. If one has any estimate as to how great this fractional part is, then the diagram will always allow us to ascertain the correct conditions. Thus if in our example one had reason to assume that half of the water condensed at 0° were removed, chen — on attaining the isotherm of 6° only 8.5 grams of water per kilogram of air would be present. We should then in using the auxiliary table” not descend to the horizontal 11, but only to the horizontal 8.5, and should have started from the temperature line of 0° at the point corre- sponding to the pressure 466 millimetres (instead of 463 millimetres) ; this would have been the only difference. (2) If we had assumed not 50 per cent. but 10 per cent. relative hu- midity in our example we should then have been able to use the Al- pha line only to the dotted line 2.2. “his point of intersection occurs PAPER BY’ DR. HERTZ. 2A at pressure 405 millimetres, and at temperature—15.6° C., therefore considerably below 0. Therefore there would have been no formation of liquid water and therefore no stage for the formation of hail but only sublimation of water from the vaporous into the solid condition. We should then from the intersection of the Alpha line with the dotted line 2.2 have followed directly the line of the Gamma system that might have passed through this intersecting point. The question is not uninteresting—what dew point is the highest that our mixture could have possessed in its initial condition as to pressure and temperature, in order that the condensation of liquid water, that is to say, the condensation at temperature above 0° C. should be just avoided ?- In order to answer this we follow the Alpha line to the isotherm 0° and here find the dotted line 5.25. We therefore at the highest could have had 5.25 grams of water per kilogram of air. In order now to ascertain at what temperature the air would then have been saturated under a pressure 750 millimetres, we slide along the line 5.25 up to the isobar 750 and intersect it at the temperature 4.8° C., and this is the desired maximum value of the dew point. KIEL, October, 1884. te a a i | xy ON THE THERMO-DYNAMICS OF THE ATMOSPHERE.* (FIRST COMMUNICATION.) By Prof. WILHELM VON BEZOLD. In the application of the mechanical theory of heat to the processes going on in the atmosphere we have hitherto almost exclusively con- fined curselves to those cases in which one can disregard the increase or loss of heat during the expansion or compression. The so-called convective equilibrium of the atmosphere, the unstable equilibrium in cyclones, the phenomena of the foehn winds have all hitherto been treated of under the assumption that we have to do with adiabatic changes of condition. In fact, especially in the last-mentioned phenomena, the quantity of heat used or produced by expansion and compression as also by the changes in the physical condition of the water, are so prominent in com- parison with those that, in these rapidly executed processes, are intro- duced or taken away by other sources that the above-mentioned as- sumption may be said to be thoroughly allowable. In the investigation of the convective equilibrium we obtain, under this assumption, at least a glimpse of the special case that lies as a limiting case between the two greater groups that correspond to the loss or increase of heat. Not- withstanding these extremely restrictive assumptions, still through the above-mentioned investigations, the comprehension of meteorological processes has been furthered to such an extent that we must consider their introduction as one of the characteristic features of modern me- teorolugy. But the more valuable are the results that are already at- tained in this manner, so much the stronger must be the desire to free ourselves from the above-given limitations, and to extend the applica- tion of the mechanical theory of heat to those atmospheric processes in which the increase and diminution of heat from without ean be no longer neglected. That this generalization had not already been long before taken is certainly because the formule are extremely complicated, so * Translated from the Sitzungsberichte der Kénig. Preuss. Akademie der Wissenschaften zu Berlin: Berlin, April 26, 1888, pp. 485-522. 212 PAPER BY PROF. BEZOLD. 213 that one always runs in danger of losing the leading thought in the midst of the notation and signs. But in consideration of the fundamental importance that the applica- tion of the mechanical theory of heat in the most comprehensive man- ner possesses for the development of meteorology, one evidently ought not to be frightened by these extreme difficulties. This has induced me to make the attempt to introduce a method into metevrology that has proved so remarkably fruitful in the application of the mechanical theory of the heat to the theory of machines: J mean the graphic method that Clapeyron* has invented in order to make the ideas first ex- pressed by Sadi Carnott visible and comprehensible. Already, some years ago, a step in a similar direction was taken by Hertzt in a highly meritorious work on a graphic method for the determination of the adiabatic changes in moist air; but the problem that Hertz had before him, as also the method which he adopted, were materially different from those that I have now in mind. On the oneband, Hertz confined himself, as his title states, exclusively to the consideration of the adia- batic changes, and on the other hand, his object was only by means of a simple graphic process to avoid the complicated computations that one has to execute in following these changes. My object, on the other hand, has been to give a method of presentation that can serveas a guic- ing thread in the still more complicated formule with which one has to compute as soon as we disregard the restrictive assumption of adiabatic change, and that also allows one to draw certain important conclusions even from the form of the geometrical figures. To attain these objects however, scarcely any mental presentation is so appropriate as that in- troduced into science by Clapeyron, of course with such extensions as are required by the condition that in meteorological problems we have not as there to consider only two independent variables, but three, or in special cases, even still more. But before I enter upon the subject itself I must touch upon another point on which notwithstanding itstundamental importance, remarkable to say, still perfectly clear views do not prevail. This has respect to the true reason of the cooling that occurs in the ascent of air to higher regions as well as the corresponding warming for descending air. While Sir William Thomson,§ Reye,|| Hann, Peslin,** and with these investigators probably also the greater part of all physicists and meteor- ologists, correctly consider the cooling of ascending air as a consequence of the expansion occurring therein, on the other hand, Guidberg and *Poggendorft’s Annalen, vol. 59, pp. 446-566. théflexions sur la puissance motrice du feu. Paris, 1824. $ Meteorologische. Zeit., 1834, 1, pp. 421-431. [See No. xiv of this collection.] ° § Proc. of Manchester Soc., 1362, 11, 170-176. || Die Wirbelstiirme, Hannover, 1872. q Zeitschrift d. Oesterr. Ges. f. Met., 1874, Bd. rx, pp. 821, 357. Smithson. Rep. 1877, p: 397. ** Bull. hebd. de V Assoc. scientif. de France, 1868, Tome 111, p. 299. me mete 214 THE MECHANICS OF THE EARTH’S ATMOSPHERE. Mohn* find the reason therefor in the work that is done in raising the air, and that is balanced by an equivalent quantity of heat taken from the air. Since by both methods of consideration the same value is — found for the diminution of temperature with the height, therefore in the well-known excellent treatise of Sprung +t both methods of consid- eration are presented beside each other as equally proper. But in faet only the first of these two is allowable, while that of Guldberg and Molin contains in itself an error as to which one can only wonder that it could have escaped two such thoughtful investigators, and evidently also has hitherto not been remarked by others. in order to obtain perfect clearness on this point one must first recall how it is that the ascending and descending currents in the atmosphere come to exist at all. This is, however, always brought about by differ- ences in specific gravity that cause an ascent at certain places, while a corresponding mass descends at other places. The work that is re- quired to raise the air at the one place is therefore always obtained by the falling of an equally great mass at another place. If no friction occurs the corresponding rising and falling movements once started would continue without any further addition of energy to infinity, and such an external addition of energy is only needed in order to overcome these frictions. These latter, however, are left out of covsideration in all the discussions that are here considered, and this will also be done in the present memoir. We can consequently then compare the process with which we have to do, with movements in closed systems of tubes, such as a closed series of hot water pipes, or the movements of a con- tinuous chain that hangs freely upon a roller. But it would never oceur to any one to consider that the ascending water in the warmer half of a conduit, or the ascending portion of an endless chain must cool because of the work done in raising it. Similarly in the case of the ascending or descending currents in lakes or in the ocean, we must ex- pect cooling or warming in consequence of these motions, if the ascent is accomplished at the expense of the heat latent in the fluid. The tem- perature changes occurring in the vertical motions of the air are there- fore exclusively to be attributed to the work of expansion and com- pression, which is to be done or acquired respectively, and they would occur to precisely the same extent if the corresponding changes in pres- sure and volume occurred within a horizontal cylinder where rising and sinking was entirely out of the question. On the other hand if we have air compressed within a vertical eylin- der whose base is fixed, but which is closed above by a movable piston, and if we should now by a proper change in the load cause an expan, sion of the air then, besides the work of expansion, it would be neces- sary also to consider the work necessary in order to raise the center of gravity of the inclosed mass of air, and thus the cooling would be more * Zeit. Oesterr. Ges. Met., 1878, x111, p. 113. t Lehrbuch d. Meteorologie, Hamburg, 1865, p. 162. PAPER BY PROF. BEZOLD. 215 a~ considerable than when the whole change of condition took place with a horizontal position of the cylinder. If the piston were without weight and without any loading, and if it were only at the beginning held fast but then suddenly loosed, and first held fast again at some other position at a greater distance from the base, then indeed the cooling would be attributable alone to the work which was necessary to be done in order to raise the center of gravity of the mass of air, since in this case no work of expansion is accom- plished. By the explanations that [ have made in such detail, in con- sideration of the fundamental importance of the question, it certainly ought to be perfectly clear that the cooling and warming in ascending aud descending currents of air in the atmosphere are to be considered ouly as consequences of the work of expansion and compression; not ef the work that is consumed in raising the air or that is gained by its descent, unless the ascending and descending masses belong perma- nently to one system. Since however the work of expansion and com- pression ought never to be left unconsidered, therefore in Guldberg and Mohn’s method of consideration these, under all conditions, should have been further taken into consideration, and there would then have resulted for the rate of change of temperature with altitude a value exactly double that given by them. This being premised I will now pass to the problems mentioned in the opening paragraphs. For our purpose it is first necessary to establish the fundamental quantities that come into consideration in investigations into the change of condition of a mixture of air and water or aqueous vapor. If in this Ido not accord wholly with the steps that Hertz has chosen, this is be- cause he has made various simplifying assumptions that are appropri- ate to the attainment of the end that he had in view, but that are not allowable in the general theoretical investigation that I contemplate. For the same reason I must again review the equations for the various conditions through which the mixture of air and water can pass, and which Hertz has developed in such a perspicuous manner, since not only by reason of the somewhat different notation, but also by the consider- ation of certain points intentionally neglectea by Hertz, some material differences result. Hertz and others in their investigations have made the assumption ordinarily used in the mechanical theory of heat that the unit of mass of the substance under consideration is given, and that it in succession passes through the different conditions. This assumption can not be rigorously adhered to in the case of atmospheric processes. O + + ar arated in a figure drawn to a vie very large scale,* since be- tween the ordinates p; and pz. of the two isotherms belonging to a given %, the following relations exist: Pi-P2= (Li — 2) ae or also Pi_ ex + a Bs Po Kat a. Ws Butthis quotient isalways very near unity, since all the values of # that here come into consideration lie between zero aud 0.03, In the majority of cases one can consider all the isotherms (7,.«) corresponding to a given value 7 as coinciding with each other and have then only to re- member that according to the value of wv they have their initial points at different places on the same hyperbola. Therefore from any one dew- point curve S; we obtain another one S, in that as already done in figure 29 we simply go with a constant ratio of expansion or compres- sion further along an equilateral hyperbola drawn through §;. If we confine our consideration stiil to that portion of the plane of a constant quantity of vapor x that lies to the right (that is to say, on that side of the dew-point curve that 1s distant from the codrdinate axes) that is to say tothe dry stage, then in this region the same theorems will hold good for the characteristic curves as for the so called perfect gas, and particularly as for air, with such very small changes in the constants as depend on the mixing ratio [or the quantity 7]. ~ It must here be expressly remarked that all the diagrams occuring in this memoir have a purely illustrative character. If we should introduce the separate quantities as they result from the computation the diagrams would lose perspicuity. The method here given therefore will need special modifications (as is hereafter to be shown) before it can be applied to graphical computations. oe ee a an, Pld » = hat Ag PAPER BY PROF. BEZOLD. 2a In this stage the isodynamic lines are also equilateral hyperbolas, and moreover the equation prr=Ppi v1" holds good also for the adiabatic lines, when p, and 7 relate to a definite initial condition, but p and v to an arbitrary final condition. The constant x can be adopted without notable error the same as for dry air, namely, x= 1.41. The quantity of vapor therefore disappears entirely from the formula and the adiabatics have the same course in all the planes corresponding to the different values of x. If now the adiabatic curves are considered as lines of constant entropy and we therefore take the equation S—S,=0 as the fundamental condition where — S is the entropy, then the equation of the adiabatic lines re- ceives the following form (c, + xc,*) log cae A(Rh, +2 h;) log = 0 T, pr where the capacity for heat of superheated aqueous vapor under con- stant pressure is indicated by c,*. If one knows the path of any one adiabatic in the dry stage, then it is easy to construct any given number of others by means of it. To this end we consider that for any further progress along one and the same isotherm, according to well-known propositions, the following for- mula holds good for the quantity of heat needed in the expansion from V, tO U%: Ge aes T log where, for the sake of simplicity, we put A,+ vk; = R* Therefore we have ae — A R* log Y D> V1 or ~" 1, 2 But the quotient ae is nothing else than the diminution of the en- tropy in the isothermal expansion from the volume 2 to x. If, there- fore, we start from a line of constant entropy (an adiabatic), and pro- ceed along various isotherms that cut this curve, so that the ratio of expansion remains constant, then we attain to points on a second adi- abatic. If now we pat v;=v and m=v+4 4v, and then make 4v=vv, where v is a constant (an appropriate proper fraction), and if in a correspond- ing manner we put 4Q for @ and JS for the difference of the entropy, we find AQ AS = =AR* log (1+7) Therefore as soon as the course of one adiabatic line is known (just *For the problems here presented, as is done by Zeuner in the application of the mechanical theory of heat to machines, it is recommended to give the positive sign to. i tion to the vapor, is suspended in the air, and only so long as this 224 THE MECHANICS OF THE EARTH’S ATMOSPHERE. as in the case of the dew-point curve) one can by a simple method of construction cover the plane of codrdinates with a series of such adi- abaties, each of which, with reference to its neighbor, shows a constant difference in the entropy by the amount JS. B. THE RAIN STAGE. For the rain stage,as already stated, there obtains the equation of mixture M=1+242, where x is in general very small, but x, except in exceptional cases, can only diminish. The equation of elasticity, on the other hand, is ky T ~p a Vv ee wie ee od | where e is the vapor pressure, which in this stage, that is to say in the condition of saturation, depends simply and alone on the temperature T. Moreover, there obtains also the equation developed as a limiting condition in Art. 3 above, viz: \ This last formula shows at once the above suggested fact, that here we have in general to do with changes that are reversible to only a very limited extent. If, for instance, 7 is put constant while v increases, then the equation can only be fulfilled when «2 increases. This same holds good (because ¢ increases rapidly with increasing 7) when v is kept constant and T increases, or, as expressed still more generally, it holds good for all changes in condition tiiat are represented in the diagram by a movement toward the concave side of the dew-point curve, But an increase of xv is only to a very limited extent possible in gen- eral in the free atmosphere, namely, only when liquid water, in addi- store of liquid holds out. The latter in most cases is soon exhausted, since it is precisely the liquid drops of water that fail as rain as soon as their mass becomes considerable. Therefore in the rain-siage, changes of condition toward the concave side of the dew-point curve are possible only to a very limited extent and only until the condition of supersaturation comes to its end and the quantity of heat communicated to the air. Therefore an increase of the quotient ) 7 corresponds to a diminution of the entropy according to the definition of entropy as given by Clausius (see Clausius’s Collected Memoirs, Brunswick, 1884) Memoir IV, page 140, and Memoir VI, page 276. PAPER BY PROF. BEZOLD. 225 becomes that of simple saturation.* This occurs as soon as the curve of change of condition attains the dew-point curve # + 2’. Having in mind the geometrical presentation one can express this proposition as follows: In the rain or snow stage, changes of condition are only reversible when and so long as they find their representation above the dew-point surface. If they find this in the dew-point surface itself, then only those changes are possible by which the representative point approaches the quasi horizontal codrdinate plane, that is to say slides down toward the surface or in the limiting case becomes the dew-point curve itself. An ascent to the dew-point surface is in the free atmosphere only im- aginable in exceptional cases (as for instance in case of the falling of rain through other layers or the mixing of other layers with moist air); a further progress toward the concave side of the dew-point curve or toward the lower side of the dew-point surface indicates a transition _ over into the dry stage. Therefore in making use of the graphic presentation one must always keep in mind that in the rain and snow stages the curves in general _¢an only be travelled over in one direction best represented by arrows and that a backward movement on the same curve is an impossibility. Nevertheless for the forward progress in the one possible direction exactly the same formule are applicabie as for the reversible changes _of condition. Therefore the case here occurring may with propriety be designated as “ limited reversible.” We now turn to the consideration cf the isotherm and the adiabatic for the rain stage. The equation of the isotherm we obtain at once as soon as we consider the temperature 7’ as constant in the equation of _ elasticity iy ae v elise: p= Since in this case e is also constant, therefore this curve as in the dry stage is an equilateral hyperbola, one of whose asymptotes, as in the dry stage, coincides with the axis of p, but the other is by the small quantity e shoved from the axis of v toward the side of positive p. _ At the same time however, in so far as we exclude super-saturation and Starting from a given initial condition, this equation holds good only for diminishing values of v. Moreover a glance at the equations of the isotherms in the dry and _ the rain stages suffices to show us that the two curves for any given temperature differ from each other only very little and that in the transition from the dry to the rain stage only a very small indentation * In a certain sense the case where liquid water or ice is mixed with the air should certainly also be called that of super-saturation, but of course with the reservation that any confusion with the condition of super-saturation properly so called, in which the excess above the quantity needed for saturation is present in gaseous form, shall be excluded. 80 a——15 ll 226 THE MECHANICS OF THE EARTH’S ATMOSPHERE. cau be seen with the vertex toward the right and above. This results from the circumstance that the isotherm for the rain stage contains the initial points, of all isotherms for the dry stage, which points corre- spond to values of vq that are smaller than the value of z, from which one starts out. In order to obtain the equation of the adiabatic we must know the quantity of heat, dQ. thatis to be communicated for a very small change in the condition. This dQ is composed of the quantity of heat dQ, that is given to the dry air and of the quantity dQs that is communi- cated to the intermingled water or aqueous vapor. The following equations hold good for these quantities:* AQ, = CAT + AR, TO and dQ; = Td ( T) + (« + w')aT [Where r is the quantity of heat required to vaporize a unit mass of water at the temperature 7’ and the pressure p.| In these x’ has values that lie between 0 and 7,—2 where z, indicates the quantity of vaporthat was given to the origina: kilogram in its passage from the dry stage to the rain stage.’ is equal to 0 when alk the condensed water immediately falls down and is thus separated from the mass; it is equal to x,—« when all such water is carried along with the mass. The two limiting cases will occur relatively quite seldom in nature, but since at present we bave no basis for determining to what extent liquid water is suspended in the air or can be carried along with it, therefore one must in the theoretical investigation confine himself to these limiting cases. Expressed in the language of the graphic presentation one must content himself with investigating those cases in which the indicating point either remains in the same plane as in the dry stage or on the other hand goes further on over to the dew point surface itself. Hitherto the first case only has been taken into consid- eration, although in general the second better agrees with the conditions occurring in nature. Therefore the above given equation for dQ; assumes different forms, according as we consider the one or the other limiting case and we have, either dQ. Td cha ? 0 ( 7 )teat for the case where x, is constant when all the water formed by conden- satior remains suspended, 1Qs= Tal T or dQs Ta( pte here en where l RT for the case when all this water immediately separates from the mass. = : — i *See Clausius Collected Memoirs, Brunswick, 1884, Memoir v, page 174, or Hirst’s | translation of Clausius, pages 153 and 353. PAPER BY PROF. BEZOLD. OT The first case corresponds to a snper-saturation limited only by the original amount of water, or, as I will briefly call it, the ‘* maximum super-saturation ;” the second case corresponds to the ‘“ normal satura- tion,” rejecting any supersaturation. For the quantity of heat dQ=dQa+dQs communicated to the mixture we obtain therefore two equations, namely: (1) For ‘maximum super-saturation :” AQ=(c.bx,)AT+ TAC“ )FARATE, 6 od (bres (2) For the ‘‘normal saturation:” aQ=c aT +adT+ Ta" yb Anca”, (9) If we put dQY=0 then we obtain the differential equations of the adiabatiecs for the two limiting cases. But in doing this we ought not to overlook the fact that strictly speaking in satisfying the condition dQ=0 we have to do with an adiabatic in the ordinary sense of the word only in one of these limiting cases, namely, that of maximal supersaturation. For if we establish for the adiabatic the single con- dition that for the given change of condition heat shall be neither gained nor lost, then we have in both cases true adiabaties to deal with. If however we define the adiabatic change of condition as one in which not only all exterior work shall be done at the cost of the energy, but also where the whole loss of energy shall be consumed in exterior work then will the definition for the second limiting case and also for all intermediate cases corresponding to values of #/>0 and a/0 we always have d7’<0 and since moreover x < xq, therefore the absolute value of dT in the case of pseudo-adiabatic expansion must be larger than for adiabatic; that is to say, the temperature must sink more rapidly when all the condensed water is immediately discharged than when it re- mains still suspended. TFurthermore, both curves must sink more rapidly than the dew-point curve, or, in other words, for dv>0 we must always have dx <0. This follows dincctly from the circumstance that in expansion along the dew- point curve heat is to be added as also is shown from the manner in which the adiabatics of the dry stage intersect this curve. On the other hand, changes of condition with increase of heat are always represented by curves that descend less rapidly toward the axis of abscissas than do the adiabatics. Therefore in the expansion of air the adiabatics depart froin the dew- point curve toward the axis of abscissas and therefore x diminiskes. The equation (8) is easily integrated and thus gives the following equation of condition for the adiabat : ; AR, log nt (e+e) log 7 T= il EEN or if v is expressed in terms of p, e, and T with the help of the equation of elasticity ; Lon XN tT) oa eel g M4 ; re AR, log (¢, +2 ) lo 2+ Ts a =" Do—€2 Soe or finally by consideration of equation (7) and by the substitution of the corresponding values of x, and 2; ee Vo T, €gVoPr: EyV{V1 rat 12 Af), log pal +(¢,+2,) log Tt Bj Te —R, 127° Ty hies tGi2) or €2%2 e Diss Tx 2 AR, log ok (¢,+2,)1 og gta een Ts eh yee If we consider the final condition as variable and corresponding to this drop the subscript index 2, then the equations become the following: AR, log v+(¢,+#,)logT+p=C . . . . .. - (108) -——AR, log (p—e)+(¢,+~,) log T+ =O 3 a laters leven) evr AR, log v+(e,4+2,) log T t+Ro7 pe ing a ee SRR, IA —AR, log (p—e)+(e,4+2,) log me Ti —=C.. (134) PAPER BY PROF. BEZOLD. 229 Simple as are these collected equations in certain respects, still nope of them allow us to express the relation between v and 7 or p and T or even between p and v explicitly, and in using them. we are obliged to proceed by trials. On the other hand one can, in comparatively simple manver, con- struct the curves in question when we remember that the left-band side of equations (LO) to (13), in all cases, even when they are not equal to 0, must still always give the value of when we take this integral from the initial condition vp, to the final condition vp, and thereby apply the notation ov the limits as here given, and as is easily comprehended. But this value is nothing else than the diminution of the entropy during the passage from the initial to the final condition. If therefore we compute this quantity for various properly chosen pairs of vy, and p, we thus obtain the value of the entropy for the cor- responding points, excepting only a constant that holds good for the whole system. Thus we shall be enabled to interpolate the corre- sponding values for intermediate points and thus to draw lines of equal entropy, namely, adiabaties. It is especially desirable to so choose these points that they come to hein regular succession on tbe isotherms. Then we have for the difference of the entropy due to the passage from a point 1 to a point 2 of the same isotherm, that is to say, for pp dQ Qie — V2 Vay Hes Sm Oe gaa? OT) OE oer Vo. es Moke ee et esr (LR) e ; : ae that is to say, a quantity that remains constant for the same isotherm. This equation also teaches that the isentropic curves in the rain stage cut the isotherms at more acute angles than in the dry stage, for which latter the equation (5) holds good, namely, where t = 46 oe —AR* log ~ From the comparison of both equations, (5) and (14), it follows that a given change of the entropy in the dry stage corresponds to a greater change of v than in the rain stage. Since now the isotherms in both stages can be considered as having very nearly the same course and, when we consider a very small part of the codrdinate plane, can be con- sidered as parallel straight lines, therefore for the given change of entropy in the dry stage one has to go a greater distance along the isotherm than in the rain stage. Zou THE MECHANICS OF THE EARTH’S ATMOSPHERE. Since, however, on the other hand, the dew-point curves descend more rapidly than the isotherms toward the positive side of the axis of abscissas, therefore the adiabaties must experience a bend at the dew-point curve ijn the manner shown in the figure 30. In this S S presents a part of a dew-point curve; AA, A’ A’, ete., adiabatics; T 7, T' T’, ete., isotherms. The differential equation of the pseudo- adiabatic can be treated in a similar man- ner to that of the adiabatic, but whereas in the adiabatic the integration was pos- sible even when the connection of the independent variables was not explicitly given, on the other hand this is not the case for the pseudo- adiabatic. That is to say, instead of equation (10) we have for the pseudo-adiabatic the following: Vo Ts . (2rd 1h LaV2 AR, log _ + ¢, log 1 + -+— J Seet “71 Egle, a ==0 a fo te Tee or, preferably, Vo T, Q(r—ax)dT rere ar AR, log pot Orie) 1C8 ae ee a +72 — Te =0 . (15) If therefore the point (1) is at once located in the dew-point curve then will 2, = 2,; and if then we consider the poiut (2) alone as vari- able, that is to say, omit the subscript index 2 entirely, we obtain Cr = 07; (2) oe ee (t,—x) aT: my AR,log, + (¢, + #,) log rf pb pp =e. (16) (1) or after further modifications AR,logv + (+ x,)log T+ — | “GP “-=e . . (17) (1) We omit the development of formule entirely analogous to equations (11) ete., and it suffices to say that in them all the integral occurs as a correcting term. Happily its value remains always within very moderate limits, so that in the computation one can be satisfied with more or less perfect approximations. One can therefore omit the further considera- tion of the pseudo-adiabatic process and only call attention to the fact that it follows from equation (16) that the pseudo-adiabatie curve de- scends more rapidly than the adiabatic as was already pointed out above. For since when v% >2v we always have d7'< 0 therefore the definite integral that still occurs in the equation has always a negative PAPER BY PROF. BEZOLD. Zoli value and because of the minus sign before the integral iv therefore always exerts its influence in the same direction as the term A, log V2 v, we must have v, in the case of the pseudo-adiabatic smailer than if we had gone along on the adiabatic. Therefore for the same starting point and for equal values of 7, Cc. THE HAIL STAGE. The above given equations hold good for the value T> 275°; as soon as the temperature 0° C. or the absolute temperature T=273 has been attained, then very different equations replace these but only when liquid water is present. In this last case the following equation of mix- ture holds good, namely : M=1 +e+a’+ta”, an equation that can only be true for the temperature 0° C, since only at this temperature can water and ice occur together. The equation of elasticity therefore then acquires the simple form aR, ——_ 0 +é, 4 ) A “ Sbecomes 2. a. (18) while the equation x=" : Rk; T aks wherein @=273, e¢,=62.56. But the one possible change of condition in this stage consists in an isothermic expansion. For this case there- fore, the dT also falls out of the equation for the transfer of heat and this takes the form, dQ=rvle—lde! +A Ra rin ee © eae |/o>=latent heat of evaporation at 0° C.; l=lateat heat of liquefaction of ice. | In this equation the first term on the right-hand side must be pos- itive, the second must have a negative sigu when dv and dx’ are con- sidered as positive, since an increase in the quantity of vapor x makes an addition of heat necessary, but an increase in the formation of ice demands a withdrawal of heat. If we put dQ=0 then we have the differential equation of the adia- batic which in this case coincides with the isotherm and is moreover always a pseudo.adiabat, since the ice that is formed falls away under all circumstances. If we consider that then the differential equation of the adiabat takes the form > Av, Te eae nae ater ag evra yaar (oO) Dive THE MECHANICS OF THE EARTH’S ATMOSPHERE. hence we obtain by integration Vo Yeo > 2 Z ay o 1 Ry log” + "9 — V1) — lary!’ = 9 aR” vj) — lr Os & «ie where we assume the integral to be taken throughout the whole stage from the initial value v7, that corresponds the entrance into this stage to the final value v that refers to the exit therefrom, and remember that the initial value of x7’ namely, 2)’ is equal to 0 under these condi- tions. If however the integral extends only up to a value of v lying between these two limits and which v can then be considered as vari- able, then the equation can be again brought into a form analogous to that above given and we obtain AR,a log v+ 000 9 la Oe he (22 ak; This equation allows us to see directly that for increasing values of v that is to say for continued progressive expansion the quantity of hail also steadily increases whereas on the other hand from [equation (18) or] the expression lx— © aX ales Vv it follows that an evaporation goes hand in hand with the freezing of the water, so that at the end of the hail stage the quantity of vapor present is greater than it was at the entrance upon this stage. With the help of the above described geometrical presentation we represent these results in the following manner. The condition that must exist at the entrance upon the hail stage finds its representation at the termination N’ of a straight line N)N’ per- pendicular to the chief plane of codrdinates and which rises up above the dew point surface. The Jength of this straight line is r+a’. It cuts the dew-point surface ata point N that is distant from the plane of PV by the quantity x If now the mixture expands along the isotherm then N rises along the dew-point surface slowly upwards, while the foot No of the straight line advances along an equilateral hyperbola. But at the same time, the total quantity 2+ 2’ diminishes in consequence of the discharge of the ice and N’ sinks correspond- ingly down until V and N’ coincide in a single point N, and with this the hail stage has reached its end. It is now of especial importance to learn how much water is thrown down in the form of hail; this question is answered by the following con- sideration. At the beginning of this stage we have only water and vapor, at the end only ice and vapor while the sum of these in the first and in the second case remain the same, if we take the precipitated ice also into the computation. Let «)/ be the quantity of liquid water present 4 PAPER BY PROF. BEZOLD. 233 at the entrance into the hail stage, then according to what has just been said, Uy 42 =H""94+ Ho or U9 =X"; —(X2—2}) or finally, making use of the equation (18), 0 5— 2 1 — Co (V2—?}) sMaeti ate © leu fre) (et ie aks — bo oO If we substitute this value in equation (21) then after an easy trans- formation we find ds X l ) © AR a log pe a al ae cupoices) (oe) From this we can now first find v, by trial; the value thus found can be substituted in equation (23), whence in this manner 2’, is found, If we are justified in the assumption that all the vapor of water originally present is also after the condensation carried along until the -eutrance upon the hail stage, as appears to be the case in heavy hail- storms, then we have 2’;=., and this is certainly large with respect to a, and 2, and therefore so far as concerns the absolute value of x’, we may briefly put a’;=7”2,since the difference 2.—.x, no longer comes into consideration. In cases in which this difference is appreciable, as for instance in the determination of v%, one can of course not make use of the above approximation. The equation (23) also shows in a very clear manner that in general the hail stage can only occur when liquid water is suspended in the air, that is to say, when z’;>0 and that it acquires a greater extent the greater this value of x), that is to say, the greater the quantity of sus- | pended water that is present. Already, many years ago, Reye showed that on days of thunder storms the conditions are present in a con- spicuous degree for the suspension and carrying up of water. D. THE SNOW STAGE. If the air, saturated with aqueous vapor, be cooled below 0° C., theu a part of this vapor must be precipitated as snow. The same formula can be applied to this process as that which we have used in the rain stage if only in place of the heat of evaporation r there be inserted the sum r+l where 1 as above indicates the heat of liquefaction of ice. Therefore we can after small modifications apply to this stage all the equations developed in Section B. I confine myself to the re-writing in this modified form the two equations (10a) and (17); they thus become for the adiabatic x(r+l) AR, log v+(¢,+ex,) log T+ 7 =eONe sty sis (25) SS a = a: ee eee = : =" _——" Ne Sa wee me Das: THE MECHANICS OF THE EARTH’S ATMOSPHERE. and for the pseudo-adiabatic AR, log v+(¢,+cx,) log rr f pede » . (26) where x, is the quantity of vapor at the beginning of the snow stage and the limits a and 7 are introduced into the integral, because in the hail stage, as in the beginning of the snow stage, T=a=273;¢ is the specific heat of ice. Since wv is always smaller with diminishing 7 and finally approximates to 0, therefore in the snow stage the deeper the temperature falls the more does the adiabatic approximate to that of the dry stage. In the investigation just finished, attention has been especially di- rected to the course of the adiabatics, as had also been done in the above- mentioned older investigations. But in truth the adiabatic expansion and compression constitutes only a rare, exceptional case, as is already shown by the fact that the vertical temperature diminution computed under this assumption (according to the so-called convective equilib- rium) results considerably larger than is given on the average by ob- servations. Itis therefore important to deduce the quantity of heat absorbed or emitted for given changes of condition, as determined by the values simultaneously observed of pressure, temperature, and mois- ture. In this process the method of geometrical presentation here de- veloped is applied with great advantage. First, a glance at the man- ner in which the curve representing any given change of condition cuts the adiabatic suffices to give a decision as to whether in this change one has to do with a gain or loss of heat. Moreover the curve puts one in a position to deduce the quantity of heat exchanged by graphic planimetric methods or by a combination of computation with plani- metric measures. According to what was said in the beginning the equation Q=A[1.—U,|+4 [pao (1) holds good also for the processes here considered with three independ- ent variables, and therefore also for a closed cyclic process OAK, where F is the surface inelosed by the projection of the points that are | imagined to be upon the PV plane. Assuming that a =e any change of condition is given by its projection on 3} this plane and is represented by the line between the points a and Dd in Fig. 31, then we obtain the quantity of heat @,,, involved in this change easiiy in the following manner: One draws through a (Fig. — 31) any curve of change of condition for which it 1 may be easy to compute the increase or diminution of heat; also draw — G Fig. 31. PAPER BY PROF. BEZOLD. Za through ) an adiabatic and prolong both curves until they cut each other in a point, c; then is Q,.=0, and the quantity of heat is given by— Qa» + Ona = AF, or, Qa» ee Oi.0 ad A F, and therefore, also, On = AEA When now Q,, is determined by computation, but fis found by plan- imetric method, this formula gives the value of Q,,. if the curve ac is the curve of constant energy (or isodynamic), then Q,.= AL, where I is the exterior work and is therefore also directly obtained as a surface from the diagram, and then we have to execute the well-known graphic construction for the determination of the quantity of heat gained or lost by a given change of condition. But the method here given possesses the advantage of greater generality aud much easier applicability. ‘This consideration also holds good when we have to do with limited reversible changes, only one has then to remember that the closed curve projected upon the plane of PY must also be the projection of a closed curve in space. If the curve in space that represents the change in condition is not closed, but if it only has the peculiarity that at the initial and final condition the codrdinates p and v have equal values, then it indeed gives a closed projection, but the quantity of heat com- puted by the above-given method is erroneous, and that too by the quantity which corresponds to the increase in internal energy at the passage from the initial to the final point, that is to say, by the addi- tion of the necessary quantity of vapor. The circumstance that one and the same point of the PV plane can correspond to very different conditions appears at first sight to exclude the general presentation of the processes in this plane alone, and thereby to materially diminish not only the applicability of the last-given con- struction but in general to detract from the whole conception here described. But by a closer consideration this is seen not to be the case; rather does it specially apply when for every point in the plane of P V one has given the corresponding dew-point curve. An example will eluci- date this: Let us assume that one desires to obtain an idea of the dif- ference in the internal energy that is present in the dry stage for equal values of p and v, but different quantities of vapor. If, in Fig. 52, is the point having the codrdinates p and v, but the quantity of vapor is in one case x,, and in the other x,, then these latter correspond to two different dew-point curves, S,, and S,. One can now convert the whole internal energy as it existed in the initial condition into external work by moving from the point P forwards adiabatically to the absolute 2A6 THE MECHANICS OF THE EARTH’S ATMOSPHERE. zero point, which of course would demand a continuation of the adia- . batic to infinity. If we do this in the case when the quantity of moisture: is 2, then will the projection of the: Se Son adiabatic be represented by the line: PM My, but by the line PN Ny when; the quantity of vapor is x,, because : in the first case under the pressure M M,, in the second case under the > pressure V N,, the air passes out of the dry stage into the rain stage, and therefore the adiabatic descends. according to another law, and in fact less precipitously. But the dif- ference in the internal energy cor- responding to the quantity of vapor belonging to the condition repre- sented in P, and which by a selfevident notation is expressible as A[U,,— U,], is graphically represented by the surface MM, MW N No, in so | far as we imagine JM, and N, extended to infinity and there united | together. When expressed analytically we find for this difference the expres-_ sion— | v Fig. 32. A [UO = U il = Ly bn — &,, t, ae Lm Pm — Ln Pns wherein p expresses the internal latent heat, and one has to remember | that for given values of p and v the temperature varies with the inter- i mixed aqueous vapor. However, this difference is so slight that in most cases it may be neglected, and one can therefore be satisfied with the approximation — A!U,, — U,]) = (x, — @,) (t+ p). By this simplification the application of the above-described combina- tion of planimetric measures and computations to the determination of the quantity of heat interchanged is very much lightened. If the tem- | peratures are below 0° then the last formula must be slightly modified, | which here need only to be referred to. | After having thus explained and established in general terms this. new method of presenting the thermo-dynamic processes peculiar to the: atmosphere their applicability will now be elucidated by a few exam- ples. ; ; ) (1) The foehn. Moist air expands during its rise up the side of amountain chain, and | is then again compressed in its descent without having auy heat added — or withdrawn. ' PAPER BY PROF. BEZOLD. dow This is represented by a diagram, as shown in Fig. 33. Leta be the jnitial condition, the corresponding dew-point curve S,, then the air ex- | pands according to the adiabatic for the dry stage until it cuts the curve S, in a point b, the curve ab thus lies in a plane parallel to that ot PV distant therefrom by 7. A glance at the course of the isotherms : (of which only the one correspond- ing to the initial temperature is drawn and designated by 7,) shows that in this passage from a over to &§ the temperature sinks rapidly. _Assoon as thecondition b isreached the representative point [the indi- eator]| slides down on the dew- point Hag.83: surface, the adiabatic of the dry stage goes over into be, or that of the rain stage, and forms at b an obtuse angle with the former. The tempera- ture, with continued uniform progressive expansion, sinks much more slowly than before, water is condensed, since the curve be prolonged cuts the dew-point lines of lower quantities of vapor. The condensed water is deposited first as rain, afterwards as snow, and therefore be is the projection of the pseudo adiabatic. In this case the hail stage is entirely wanting, and although the cool- ing due to the continued expansion goes on beyond the freezing point, still this does not make itself so strongly felt in the course of the pseudo- adiabatic as that this transition should be perceptible in a drawing like the present diagram. Let expansion continue up to a condition ¢, and now let compres. ‘sion occur, that is to say, the air reaches the summit or ridge of the ‘divide and the ascent now becomes a descent on the other side. Nov, all depends upon whether the condensed water was really completely precipitated or uot. If not precipitated then during the compression there will be a retrogression of the indicator along the curve bc in the direction from ¢ to b, and so much the farther along in proportion as more water has been carried with the air. If all the conuensed water has remained suspended, then the change of condition in the retrograde direction continues back to b, and thence beyond to a, and we find on reaching the same level on the other side of the mountain again the same r: lations as in the beginning. This is always the case when- ever the curve of saturation is not reached in the expausion, that is to say, when the whole process is entirely transacted in the dry stage In which case also the characteristic peculiarities of the foehn are wanting. _ If however the rain stage is attained, and if in it the condensed water is actually precipitated then the process can not be reversed, and us —- ~~ a eT ae =, 7, holds good. Therefore after the passage over the. mountain one has warm dry air, whereas at first it was cool and damp. At the same time we see directly from the diagram that the eharae- teristic peculiarities of the foehn must stand out so much the plainer in proportion as the point @ is nearer to the curve of saturation, that is to say, the warmer and moister the air is before its ascent and again, — the longer the portion J ¢ is, that is to say, the more extensive is the © expansion in the rain stage, or in other words, the higher the summit. is that has to be surmounted. Therefore we understand also at once why it is that in the Alps, in- dependent of the prevailing conditions of atmospheric pressure, north- erly foehns are so much rarer than the southerly foehns, as also why descending winds that have surmounted no summit, but have only” passed along over a plateau, as for example the bora, have not the char- acteristic warmth of the foehn. (2) The interchange of air between cyclone and anti-cyclone in summer. Between an anti-cyclone and the cyclones that feed it, similar rela- tions exist as between the masses of air on the two sides of a mountain 2 ‘ange to be surmounted by them. In eyelones one has to do with an | ascending current of air that afterwards descends in the anti-cyelone. — Hence arises the precipitation in the region of the cyclone, the dryness — and the clear sky in the region of anti-cyclone. But, whereas in the ; foehn the ascent and descent occur at points in the neighborhood of each — other, so that in the short path there scarcely remains time for gain or loss of heat, but the whole process may in fact be considered as adiabatic; on the other hand very different relations obtain for the ascent and de-. scent in cyclone and anti-eyclone. These two opposite processes in gen- | eral occur at places so distant from each other that in the transit from one to the other extended opportunity is offered to take up or give out — heat. In this process during the summer season the increase of heat prevails, but during the winter time the loss of heat; the day-time also. ee ee es PAPER BY PROF. BEZOLD. 239 in its relations follows more or less closely the summer, while the night- time is like the winter. Under the assumption of a prevailing increase of heat the process pre- sents itself somewhat as shown in the diagram (Fig. 34) ; starting with the condition a (in a cyclonic area) the expansion with a diminution of temperature proceeds according to the curve a b, which descends rather less steeply than does the the adia- batic curve. Corresponding to this, and also without reference to the initial quantity of moisture, the dew- point curve is first attained later, that is to say, at a greater altitude above the earth’s surface than it would be in adiabatic expansion. In the rain stage, therefore, the curve of change of condition experiences a deflection toward the upper side of the adiabatic, and therefore remains nearer the curve of satura- tion. If now there occurs a still further greater addition of heat, as must be the case during the period of insolation and at great altitudes, where the condensation is less and the density of the clouds is correspond- ingly diminished, then the air can again pass over into the dry stage as is indicated in the portion cd of the curve. Thus the upper limit of the first layer of clouds then would be at ce. At this limit, during the summer days, more intense warming is in fact to be expected, which through a further expansion, that is to say at a ereater altitude, on account of the diminished absorptive power of the atmosphere, again passes over into the approximate adiabatic ¢ d, by which process, however, the dry stage is finally left and the snow stage de is entered. To this greater increase of heat at the upper limit of the clouds the fact is certainly to be ascribed that the cirrus (or snow) clouds are not directly continuous with the (lower or) water clouds, but generally separated from them through a wide space such as corresponds to the expansion from ¢ to d. During the descent in the anti-cyclone or by reason of the compres- sion the process must take place according to the curve e f, which in general nearly agrees with the adiabatic of the dry stage. As we approach the earth’s surface however, on account of the strong absorp- tion of heat occurring there, then and for that reason this curve can depart to the right upwards from the adiabatic. This latter can how- ever only occur temporarily, since in such a case we should have to do with a condition of unstable equilibrium. | 240 THE MECHANICS OF THE EARTH’S ATMOSPHERE. The final pressure p,, with which the sinking air reaches the ground — in the anti-cyclone, is greater than the initial pressure p, that prevails — at the ground within the cyelone, and correspondingly / is higher above the axis of abscissas than a. In this case if may occur that the point f comes to lie not only (as is self evident) above, but also to the right of a, so that vs v, or in other words that the air at the base of the anti- cyclone, notwithstanding the higher pressure, is specifically lighter than in the cyclone, because the temperature more than compensates for the influence of the pressure. This shows in a very clear manner that in the exchange of air be- tween cyclone and anticyclone we have to do not only with the specific weight of the mass of air, but that here dynamic relations are of first importance, a point to which Hann has called attention lately in the discussion of the observations taken on the Sonnblick.* It will be well in the more accurate investigation of this question to give increased attention to the processes above the aqueous clouds especially at their upper boundary surfaces. As to the relations of the humidity to the processes just considered these are nearly the same as those in the case of the foehn. Here also, that is to say in the anticyclone, the air arrives in the neighborhood of the ground warm and dry, but in the immediate neighborhood of the ground the evaporation stimulated by unrestrained insolation will rapidly add moisture to the air, so that the indicator, which moving from b nearly to e has steadily approached the PV plane and from e on the way towards f has remained a long time at the level of e, must now be imagined as rising immediately before reaching f. If now the air that has descended in an anticyclone again flows toward a new depression then will it (under the assumption of the same conditions in this as in the first cyclone), by reason of a continuous acquisition of aqueous va- por, pass through conditions that are represented in the diagram (Fig. 34) by the line fa. This line we have to imagine as slowly rising, so that the diagram here drawn presents in fact the projection of a closed line. (3) The interchange of air between cyclone and anti-cyclone in winter. In winter the diagram for this process of interchange has a figure essentially different from that in Summer. First, all changes in con- dition, at least insofar as concerns the initial and final conditions (see Fig. 35), take plave nearer to the codrdinate axes since the tempera- tures that come into consideration do not rise so high as in summer, and since, corresponding to this, the isotherms that lie far from the axis are not attained. Again, we have here lower pressure and higher tem- perature at the starting point a, but at the end d higher pressure and lower temperature, so that @ is to be sought to the left and above a. * Meteorologische Zeitschrift, 1888, vol. v, page 15. PAPER BY PROF. BEZOLD. 241 ‘Furthermore, the lines whose projections are here considered are not so far from the coédrdinate plane as in summer, because the absolute capacity for moisture remains always slight. If now we follow more accurately the change of condition during ascent in the cyclone, we may at first assume that the process up to the attainment of the upper limit of the cloud stratum very nearly agrees with the adiabatic expansion, since below this limit radiation, either to or from, can only play an unimport- ant part. If however a departure from the adiabatic process does oc- eur then it can be only in the oppo- site direction to that which occurs in summer. that is to say; the lines will descend, more decidedly than in summer. In Fig. 35 this latter case is as- | sumed, as also that the passage out of the dry stage into the snow stage takes place immediately. From this point onwards the curve of condition again sinks more gradually, but with steadily increasing gradient in consequence of the overpowering cooling that certainly occurs at higher altitudes, until finally the turning point is attained and compression takes the place of expansion. The entire course of the change of condition to this point is presented by the curve abe. From this point onwards in consequence of the compres- | sion, the curve of condition must gradually advance to the point d. So far as our knowledge of the actual conditions of the atmosphere has at- tained hitherto, this gradual return to the point d occurs in such a way that at greater altitudes the compression proceeds adiabatically accord- ing to the adiabatic of the dry stage, whereas on approaching the ground the cooling by radiation that prevails there causes a deviation of the curve of condition from the adiabatic toward the axis of ordinates, and corresponding thereto the curve shows acourse like cd. This curve however is nothing but the graphic expression for the well-known in- version that occurs on clear winter days in the vertical distribution of temperature. By reason of this inversion the eurve near d approaches the dew-point curve, and can even pass it, so that condensation must occur and in the form of ground fog. But with the beginning of the formation of fog the radiation increases materially and corresponding to it the temperature diminution becomes always more intense with the proximity to the earth of the descending current of air. Whether the passage from c to d be also possible by some other path by which from the very beginning of the compression the cooling and therewith the departure of the curve from the adiabatic makes itself felt, is a question that can be decided only after an accurate test com- 80 A——16 Fig. 35. jection of the curve of condition in this case.must possess a double point. 242 THE MECHANICS OF THE EARTH’S ATMOSPHERE. putation with the appropriate numerical data. At any rate such pos- sible process would assume that in the anticyclone, at a certain height | above the ground, exactly the same pressure and the same temperature } prevail as at less altitudes above the base of the cyclone, since the pro- These few examples, given only in their outlines, will suffice to enable — one to realize the varied and useful applications that the method of graphic presentation here developed is capable of. By a further com- pletion and development of the numerical side this method will give not only an excellent auxiliary means for the discussion and evaluation | of existing data of observation, but above all will afford an indication © as to the direction towards which materia) is to be collected in order to afford a deeper insight into the thermo-dynamics of the atmosphere. If anything should seem especially suited to enable us to recognize the importance of the method of consideration here developed, it is the | abundance of questions that press upon us at the first step we take in > this way and that can at present be scarcely enumerated. 1am think- ing now, not only of the further development of theoretical conse- guences, therefore especially of the meaning of thé thermal changes that | occur in the atmosphere (especially the application of the second | theorem of the mechanical theory of heat to these processes which may _ be developed in subsequent communications), but also, above all, of the stimuli that are to be derived therefrom to the observations of mountain stations, and especially in balloon voyages. For the latter it is full of— meaning that in thermo-dynamic investigations the knowledge of the | altitude above the sea can be entirely dispensed with and that it is en- tirely sufficient if we know the simultaneous values of the pressure, | temperature, aud moisture. Rint oe xy i: ON THE THERMO-DYNAMICS OF THE ATMOSPHERE.* (SECOND COMMUNICATION.) Bz Prof. WILHELM VON BEZOLD. In a memoir published several months since,t I made an attempt to so extend the Clapeyron method of graphic presentation of thermo- dynamic processes as to allow of its application to atmospherie changes. At the same time I showed by some examples how with the assistance of this method of representation even complicated phenomena can be studied with comparative ease, and how by means of it we are put in the position of being able to draw most important conclusions almost like child’s play. In the following, the same method will be applied to other questions not then or only lightly touched upon. First, I will treat of a conception that has lately been introduced into meteorology by von Helmioltz,t and which appears to me to possess great significance in this science. This is the idea of ‘‘wirmegehalt,” or total amount of heat contained within a body. Helmholtz measures the heat contained in a mass of air by the abso- Jute temperature that this same mass will assume when it is brought adiabatically to the normal pressure. The quantity that we here deal with is therefore not as one might easily have believed a quantity of heat but a temperature, and therefore it seemed to me, upon my first study of the memoir in question, desirable to replace the term ‘“‘ warme- gehalt” by another. Ina conversation upon this matter von Helm- holtz recognized the objection expressed by me as proper, and proposed that the word “ wirmegehalt” should be replaced by the evidently much more proper expression ‘ potential temperature.” This latter expression will therefore be used exclusively in the tollowing memoir, but at first this idea itself will be more accurately considered. Its presen- tation in a diagram will be attempted and a general theorem deduced from it. * Read before the Academy of Sciences, Berlin, November 15, 1888. (Translated from the Sitzwngsberichte der Konig. Preuss. Akademie dir Wissenschaften zu Berlin, 18388, vol. XLVI, pp. 1189-1206. ) t [See the preceding number of this collection of Translations. ] t ‘*On Movements in the Atmosphere,” Sitzb. Berlin Akad., 1888, vol. XLVI, p. 647, [See No. V of this collection of Translations. ] 243 244 THE MECHANICS OF THE EARTH’S ATMOSPHERE. I. THE POTENTIAL TEMPERATURE. According to what has just been said the potential temperature is that absolute temperature that a body assumes when without gain or loss of heat it is adiabatically or pseudo-adiabatically reduced to the normal pressure. I intentionally give this definition the form here chosen since we are here concerned with the application of the idea to meteorological processes, and since in our case the processes without increase or loss of heat do not need to be strictly adiabatic in the ordinary sense of the word. As I have shown in the pre- vious memoir we have only to do with adiabatic processes when the water formed by condensation does not fall to the earth but is carried along with the air, a condition that is only fulfilled in exceptional cases. As soon as water is lost, and this is generally the rule, even though no heat be gained or lost, we have to do with a process that is only pseudo adiabatic. When theréfore in the following, mention is made of adiabatic changes, the pseudo-adiabatic will always be included therein in so far as this class is not excluded by the special term “ strictly adiabatic.” This much being premised we may now first investigate whether and how the potential temperature can be represented in a diagram. The answer to this question is extremely simple. From the equation of condition for the dry stage tp =e there results * ao h* . hs p or if we substitute for p the normal pressure p, * — ki . she Po Therefore under constant pressure the absolute temperature is simply proportional to the volume, that is to say to the abscissa. But this absolute temperature under the pressure p, is the “ potential tempera- ture” for all other conditions that find their representation on the adiabatic passing through the point whose codrdinates are v and pp. We therefore obtain the following rule: If a condition is given that is represented in the diagram, Fig. 36, by the point a, then we find the corresponding potential temperature by draw- ang an adiabatic line through a and seeking its point of intersection N‘ with a straight line P, N drawn parallel to the axis of abscissas and dis- tant iherefrom by po. The distance of this point of intersection N’ from the axis of ordinates, namely, the abscissa of N’ (or N’ P.) is now a meas- ure of the potential temperature. We find the numerical values of v and T belonging to p, (and which T will now designate by v’ and T’ corresponding to the point N’.while I i es me oe PAPER BY PROF. BEZOLD. 245 designate by v, and T, those corresponding to the initial condition a) by combining the equation of the adiabatic Pad” —Pov'™ ‘ with the equation of elasticity Pa Dov! Ware ge a and we thus obtain Shuts Gat LAO VG lei ae where x = 1.41.* But this simple method of consideration is only allowable so long as the changes of condition take place within the dry stage, If this stage is left then the potential temper- ature belonging to a definite intial point has no longer a constant value, but it increases with the quantity of precipitation that is lost. P,N’; that is to say, the poten- tial temperature 7’, as attained by adiabatic change after passing into the condensation stage and after precipitation of some water, is higher than the potential temperature 7’ of the initial condition and of all the conditions previously passed through in the dry stage 0. Analytically this may be proved in the following manner: For the transition from a to b the following equation obtains 0 0,0, Cc If this equation remains in force after crossing over the curve of sat- uration, then we obtain for the pressure proper to the volume v, a value pyv’ and T’”>T’ where v’ and v” are the volumes corresponding to the normal pressure p, on the adia- baties ab and cd; hence, oe Cc! and po =U, beside which the following equation holds good: Viet T': TT,” Thus we attain to the theorem In adiabatic changes of condition in moist air the potential tempera- ture remains unchanged so long as the dry stage continues, but it rises with the occurrence of condensation and so much the more in proportion as more water is discharged. Since in the free atmosphere, in general, evaporation does not occur and since aiso the carrying along of all the water that is formed, at least in the case of heavy condensation, must be considered as an ex- ceptional case only, therefore, this theorem can also be brought into the following form: Adiabatic changes of condition in the free atmosphere, assuming that there is no evaporation, either leave the potential temperature unchanged or elevate it. PAPER BY PROF. BEZOLD. PAT From this theorem, which in its latter form reminds one of the theorem of Clausius in respect to the entropy, “The entropy strives towards a maximum,” though not identical with it, one can draw con- sequences of the greatest importance. The next two sections will be devoted to these. AL. THE VERTICAL TEMPERATURE GRADIENT. All motions in the atmosphere can be considered as analyzed into vertical and horizontal components. The latter, in so far as they do not closely follow the irregularities of the earth’s surface, are subject in only a slight degree to thermo-dynamic changes. On the other hand, in consequence of the expansion or compression in ascending and de- scending currents, the thermo-dynamie cooling or warming plays a very important role. ‘The horizontal movements will therefore for the present be left entirely out of consideration, but the processes going on im the vertical currents will be thoroughly investigated. The changes of condition going on within ascending and descending currents must be considered in the free atmosphere as adiabatic so long as we con- tent ourselves with a first approximation, and that we must do at first, since in the free air there is only a small opportunity given for active radiation and absorption. On the other hand the increase and diminu- tion of heat will always make themselves felt decisively either where the absorbtivity and emissivity are remarkably increased or where the air comes into direct contact with bodies which themselves can strongly emit and absorb or otherwise take in or give out heat. This is the case: (a) In the neighborhood of the earth’s surface, where besides the increase in absorbtivity and emissivity of the air due to cloud or fog, the warming and cooling of the ground by radiation, as well as the evaporation, the formation of dew or frost, the thawing and freezing, have a powerful influence. (b) In fog or cloud, which also possess a special power of absorbtion and emission, and where moreover evaporation can occur; and especially is it the upper limiting layer of clouds that one has to take into consideration. In so far therefore as one can leave out of consideration the special localities just indicated, as also the mixture with other masses of air, one can approximately consider the processes in ascending and de- scending air currents as adiabatic. Even taking into consideration the special locations above mentioned, one can consider a scheme drawn up under the assumption of adiabatic change as to a certain extent an average or normal scheme, since such a scheme always occupies an intermediate position between those where the incoming radiation and those where the outgoing radiation prevails. How such a preva- lence of either radiation must show itself has already been indicated in the previous communication [ p. 212], where the interchange of air ~—- . ote, See ee. { 248 THE MECHANICS OF THE EARTH’S ATMOSPHERE. between cyclone and antieyclone in summer and winter was investi- gated, at least in its principal features. But in this study it is not necessary to limit oneself to the summer or the winter, but rather one ean apply the scheme for the summer generally to all cases where the radiation is in excess, that is to say, not only to the summer time in general, but to the day-time and the hot zone; the scheme for the winter, on the other hand, is applicable not only to the winter season, but to the night-time and the cold zones of the earth. This normal scheme for the ascending and descending cur- rents will therefore appear as shown in Fig. 56. The portion ab has reference to the ascending current in the dry stage, ) ¢ is its continua- tion in the condensation stage, finally ¢ dis the portion of the curve that corresponds to the descending current. This scheme differs only a little from that communicated in the first memoir. (For the case of the foehn, see page 240.) We can not expect it to be otherwise, since in the foenn one has also to do with an ascend- ing and descending current of air in which the velocity with which the whole process goes on affords only a small opportunity for the gain and loss of heat. However, the diagram given in figure 56 as the “ normal scheme” differs from that which obtains for the foehn in this respect, that the branch ed is longer. This is due to the fact that in the ordi- nary interchange between cyclone and anticyclone there always pre- vails a higher pressure at the base of the latter than at the base of the former; that is to say, the ending point din the normal scheme must always he higher than the starting point a, which is not the case in the foelin diagram. In general, one has to consider the process in the foehn as only a feature inserted into the normal interchange between anticyclone and cyclone. In the foehn the passage over the mountain chain forces the air in its normal interchange to describe an antecedent. ascent and a subsequent descent which is only then followed by the definitive ascent in the cyclone. This being premised, the processes in the interchange, according to the normal scheme, will now be more pre- cisely considered. If we introduce the conception of the potential temperature, we ats tain the following theorems without any difficulty : (a) In the ascending branch* the potential temperature increases steadily from the beginning of the condensation; in the descending branch it remains constant at the maximum value attained in the whole process. This maximum value corresponds also to the highest point to which the air has risen in its path. (b) The potential temperature of the upper strata of the atmosphere is in general higher than that of the lower. The first of these two theorems results directly from the diagram ; the second follows from the fact that in the lower stratum the potential * By the ascending branch is meant the portion ab which corresponds to the ascent in the atmosphere; the portion ed is considered as the descending branch. PAPER BY PROF. BEZOLD. 249 temperature must, in the continuous interchange between cyclone and anticyclone, retain an average value that lies between the maximum value 7” and tlie smaller value 7” corresponding to the base of the cyclone; that is to say, to the point aon the diagram. This average value is, however, certainly smaller than the maximum value 7” corre- sponding to the highest point of the path, and therefore to the condi- tion c, and thus the theorem ()) is proven. Hence it follows that in nature the diminution of temperature for a constant elevation, or we will rather say, for 100 metres, that is to say; the so-called vertical temperature gradient, is, in general, smaller than results from the theory of the dry stage. As is well known, this gradient is 0.993 for the latter stage, that is to say, under the assumption of adiabatic change one would expect in the dry stage a diminution of 1° centigrade in temperature for an ascent of 100 metres. This value 0.993 I will call rv. The above given theorems concerning the potential temperature show at once that under the assumption of adiabatic exchange the real value of the temperature gradient must be less than v. We reach this conclusion from the following considerations: Let ¢, and £, be the temperatures at the bases of the cyclone and anticyclone respectively (that is to say, at the starting and resting points of the ascending and descending currents) then, under the assumption of perfect adiabatic change, these will not greatly differ from the potential temperatures 7” and 7’, as these correspond to the ascending and descending branches in the dry stage, that is to say, to the conditions represented by the curved portions ab and ed in figure 36. In this process the departures from these temperatures are always of such a nature that ¢,< 7’ and ¢,>T". For, since the pressure p, at the base of the cyclone is certainly smaller than the normal pressure, but the pressure p, at the base of the anticyclone greater than it (at least when a normal pressure is chosen appropriate to this case, and therefore lying between p, and p,), therefore the temperature t, is increased by referring it back to this pressure, while t, by the cor- respouding process is diminished. Since the statement is thus proven that ¢t,< 7’ and ¢,>T7, and since, moreover, 7” >’, therefore, by so much the more must t,>t,. At the highest point of its path, such as. corresponds to the point ¢ of the diagram, the particle of air has a potential temperature 7’ that is to say, precisely the same as at the end. If now it be assumed that this point lies 100k metres above the earth’s surface, then there results as temperature gradient for the descending branch that is to say, as the increase of temperature on each 100 metres of descent, the well-known value el h VE ~~ 250 THE MECHANICS OF THE EARTH’S ATMOSPHERE. On the other hand, for the ascending branch we obtain a value if for the sake of simplicity the difference of temperature prevailing above and below be equally distributed throughout the whole height. This simplification is, of course, not strictly correct since the ascend- ing branch of the two stages certainly includes in itself several stages, e. g., the dry stage, the rain or snow stage, and perhaps also the hail stage, or all together. Still the method of computation of the average gradient as given here in the formula is the only method that we can apply when we have only one upper and one lower station. The follow- ing considerations however remain applicable at least in a general way when we can apply more rigorous formula. Namely, for purely adiabatic change in any case we have t, 7, we shall always have n<_v and in fact the differences 7,— 7, and v—n always increa e simultaneously. A decided cooling in the lowest stratum always causes a diminution of 7, and with it also a diminution of x, whereby even a change in the sign of n may occur within moderate altitudes. In the latter case, the temperature below is lower than in somewhat higher layers, and in that case we have the so called inversion of temperature. If the cool- ing is not sufficiently strong to bring about an actual inversion of the temperature, still it causes a diminution of the gradient. Such decided cooling always takes place in the lowest stratum at the time of increased radiation, therefore especially in the region of the anti-eyelone, 7. e., under a clear sky, in winter, and in the night time. Therefore inthe winter and in the night-time the vertical temperature gradient must be smaller than during the summer and day-time, even if inversion in the __ distribution of temperature does not occur. This result agrees perfectly with observations, as is especially proven by the many facts that Hann and others have collected from the Alpine regions. On the other hand the investigation here carried out teaches that the inversion of temperature and the diminution of vertical gradient con- nected therewith are to be treated not as phenomena peculiar only to the mountain regions, but that we are to expect them also above the plains, and even above the ocean, at least insofar as the more violent movements of the air do not interfere therewith. We are therefore obliged to agree with Woeikoff* when he from a _ few data draws the conclusion that this inversion is also to be expected in the region of the great winter anti-cyclone of eastern Siberia. On the other hand I ean not agree with him when he deduces from this the consequence that Messrs. Wild and Hann should have consid- ered this circumstance in drawing their isotherms, and I consider the Standpoint taken by them as perfectly justified.t * Woeikoff, Klimate der Erde, German edition, 1887, Bd. u, p. 322; Meteorolo- gische Zeitschrift, 1324, Bd. 1, p. 443. t+ Hann, Atlas der Met., 1887, p.5. Wild, Repert., 1888, Bd. x1, Nr. 14. >. ——e 2Oz THE MECHANICS OF THE EARTH’S ATMOSPHERE. A direct proof of the inversion of temperature above the lowlands: can only be expected from balloon observations. To what extent radiation causes the inversion or at least the dimi-. nution of the gradient we shall learn froma work now soon to be pub- . lished, that Siihring* has executed at my recommendation, andin which the vertical gradients of temperature between the Eichberg and the» Schneekoppe, as well as between Neuenburg aud Chaumont, are inves- tigated according to the separate percentages of cloudiness. It is not improbable that also above the ocean, and even at the time of the stronger insolation, a diminution of gradient, if not even an in- versiou of temperature, occurs, since over the sea the rapid evapora- tion in connection with the mobility of the water puts an impassable limit to the rise of temperature. The stability of the Atlantic anti- eyclone during the summer months may be based upon this cireum- stance. The cases in which an increase of heat occurs at the earth’s sur- face need no special consideration im the questions here considered. The gradient can only for a short time exceed the value vy, as deter- mined for the expansion or compression of dry air. If this case occurs, then, according to the investigations of Reye and others, we have unstable equilibrium or a condition that can only exist temporarily, as in whirlwinds or thunderstorms. Therefore, even for the strongest insolation, the considerations above given continue to hold good. On the other hand the fact must excite great consideration that, not only on the average of all cases, but also when we investigate only the region of ascending currents (and of these only those that are below the limit of clouds, that is to say, for moderate elevation of the upper station) we find that the vertical gradient is always decidedly smaller than v. The reason of this is principally to be sought in the fact that the above views as prc sented by me, as also by other investigators in this direction, all rest upon an implied assumption that is only allow- able to a very limited extent. They are based namely upon the assumption that the air ascending from the earth experiences no change in its constitution, except that due to the loss of water consequent on the adiabatic expansion, 7.é., that it experiences 10 mixture with masses of air of other temperature or other degrees of moisture, as also that every particle of air considered in the interchange between cyclones and anti-cyclones describes the whole path from the earth’s surface to the limit of the temperature and back again. But this is by no means the case. Only a small fraction of the air under consideration actually comes in contact with or even in close proximity to the earth’s surface; and similarly with the ascent to the limit of the atmosphere or at least to the highest stratum that at any time takes part in the process under consideration. Moreover in the * Siihring, Dievertikale Temperaturabnahme. Inaugural Dissertation d. Universitit, Berlin, 1890 * PAPER BY PROF. BEZOLD. 230 / ascending whirl, masses of air are always drawn in from one side that had not yet sunk to the earth’s surface and had remained correspond- ingly unaffected by the radiation and absorption that have their seat in that stratum, and which also had had no opportunity to take up water from the earth’s surface. Since these masses of air coming from the upper portions of the anticyclone have in general higher potential and therefore also higher absolute temperature than the portions of the eyclone lying at equal altitudes above sea level, therefore the mixture of these will diminish the cooling of the ascending air and both there- by as also by reason of the lesser quantity of water that they possess, will delay the occurrence of condensation. - Therefore in the cyclone itself the vertical temperature gradient even beneath the clouds will not be so large as one would expect according to the law of the adiabatic changes for the dry stadium without mix- ture of foreign masses of air. Similar relations obtain, although not toan equally great extent, with regard to the descending current, which in its upper half is also fed by portions of the cyclone in which the con- densation has not yet gone so far and has not yet attained the high potential temperature of the highest stratum concerned in the whole process. Therefore in reality both the ascending and the descending branches of the curve deviate from the schema of Figure 36, and in both of them the vertical gradient will more or less approximate the average as we find it when we consider the ascent and descent as a connected whole. These considerations are entirely in accord with observed facts. Even when we deduce the vertical temperature gradient from observa- tions at stations of which the upper one is not so high that it is fre- quently within the clouds, we attain to temperature gradients that in general are far less than that computed for the dry stage; this result is in great part only explicable as due to the above described mixture. The observations of the clouds also agree perfectly with what has been said, both with regard to the temperature conditions and the moisture. Only the central part of the cyclone is to any. considerable extent fed by masses of air that have flowed along the surface of the earth itself, as one can easily convince himself by a simple diagram ;* whereas the periphery receives more and more air from the higher strata, whereby its lower boundary surface is raised but its power must be diminished. In fact also the clouds at the center of the cyclone tang down the lowest and are higher near the circumference, exactly as is demanded by the moisture conditions and the higher potential temperature of the intermixed masses of air. The fringe of clouds that we perceive beneath the layer of clouds that covers the sky (especially on wouded hills during the prevalence of a cyclone) and in which we can clearly follow the ascent of air in inclined paths, gives in connection with the * See, for example, Mohn, Grundziige, 3d edition, 1833, p. 261. pn enrntiees ee ee erate — | | eS nee 254 THE MECHANICS OF THE EARTH’S ATMOSPHERE. ragged clouds surrounding the border of the continuous cloud cover, . an excellent picture of the mixture just described. Of course itis understood that all these considerations relate only to) the conditions that ordinarily occur in the interchange of air between \ eyclone and anti-cyclone. Processes in which we have to do with unstable equilibrium (such as. occur, for instance, in the great thunderstorms in front of an advane- ing current of air, where a whirl with a long horizontal axis rolls) rapidly forward and brings simultaneously on the side of the descend- ing current heavy rain-fall and great cooling with higher barometri¢ pressure, while on the front or ascending side the cloudiness is just begiuning)—such processes demand a very special investigation that may be postponed to some future occasion, At present only one more consequence will be drawn from the propositions relative to potential temperature which seems to me calculated to throw a new light on the interchange of heat in the atmosphere, and that especially demands. consideration from a climatological point of view. III. ON COMPLEX CONVECTION. | It has been shown above that in the adiabatic transfer of air out of | the cyclone into the anti-cyclone, the potential temperature in the de- seending brauch is higher than in the ascending. Hence it follows that in the descending branch a higher temperature’ prevails after attaining the initial pressure than prevails at the initial point, and a still higher temperature prevails at the end of the desvending branch, that is to say on the ground in the anti-cyclone where, according to experience as well as for mechanical reasoas, the pressure is always. higher. Therefore in this trausfer of air we are concerned not only with a simple transfer of the quantity of heat belonging to the air at the base of the cyclone, which we can here temporarily call the original quantity of contained heat, but this quantity of heat is increased by _ that heat of condensation which in the condensation stage did a part of the work of expansion and thereby diminished the cooling to a smaller quantity than it otherwise would be. Even when in consequence of the stronger abstraction of heat at the base of the anti-cyclone the air is finally colder than it would have been in purely adiabatic interchange; and even when temperature. inversion has occurred, still the temperature at the end of the process is still always higher than if the transportation of the air had taken place at the level of the earth’s surface and the cooling influences had remained the same. The heat of condensation or negative heat of evaporation, or as it was formerly called the liberated latent heat, accrues to the advantage of that — region in which the descending current has reached the earth’s surface. We can therefore compare the whole process with that af a steam heater. i tll he Mine 5 St PAPER BY PROF. BEZOLD. 255- Moist air rises in the cyclone, attains the condensation stage and cools from that time on less rapidly since the heat of condensation does a part of the necessary work. The heat thus saved then enters into the descending current and finally is carried to the point at which the descending current reaches the earth’s surface. I consider it proper to designate by a special word those transfers of heat in which, besides the transport of warm or cooled bodies, changes of the condition of aggregation also occur, and therefore propose the name ‘complex convection” or **complex transfer.” Such complex convection is met with when vapor is formed at one place and precipi- tated at another, or when ice falls as snow or hail, or when it is trans- ported in the form of icebergs by ocean currents. If we apply this designation to the above-given considerations we obtain the tollowing proposition : “In consequence of complex convection the temperature in anti-cyclonal regions is always higher than would be the case in simple convection.” The application of this proposition to the warm zone is of very special interest (I designedly avoid saying Tropical Zone since I can not con- sider the warm zone as limited by the Tropics) that is to say to the calm zone and the rings of higher atmospheric pressure that border it on either side, of which rings however the northern one is frequently interrupted. The proposition just enunciated teaches that these two rings in con- sequence of complex convection are much warmer than would be the case if in the whole interchange one had only to do with dry air or with movements on one level. The warm zone is therefore hereby broadened and at the same time there is found within it a diminution of the tem- perature gradients. In the calm zone itself much heat is used in evaporation and hence, in connection with the diminution of insolation by the covering of clouds, as also by reason of the water precipitated from colder regions above, the rise of temperature above a given limit is prevented. The heat consumed by.evaporation at the earth’s surface or at the ocean’s surface does its work at a greater altitude in the region of the clouds when liberated by the condensation, and thus diminishes the cooling of the ascending current only to again feappear below in both the belts of descending currents. A further development of the climatological consequences deducible from these considerations does not belong here. But this much we see at once, that the conclusions drawn from the mechanical theory of heat without any hypothesis whatever stand in direct contradiction to the older meteorological views. Formerly it was taught that the descend- ing trade wind by cooling delivers to higher latitudes the water brought with it from the calm zone. Similarly it was taught that the heat lib- erated during the condensation raised the temperature, and that this. ’ j ‘ ! a 256 THE MECHANICS OF THE EARTH’S ATMOSPHERE. higher temperature inured to the places at or above which the con- densation occurred. The mechanical theory of heat shows that the current ascending in the calm zone must precipitate its water right there in the form of tropical showers, and that then it must descend as a drier and also as a warmer current (except in so far as it does not experience any mate- rial cooling, especialivy at the earth’s surface), This theory further shows that the heat of condensation, in so far as super-saturation proper does not come into consideration, never shows itself as actually warm- ing but only as diminishing the cooling that accompanies the ascent of the air, so that the current arrives at the upper limit warmer than it would without the accompanying condensation, and that the heat thus economized benefits the point at which the descending current.reaches the earth’s surface. The considerations here developed can of course only be considered as approximate steps that still await additions and corrections. To my eye they play a rdéle similar to that of the investigation of the so- ealled solar climate in climatology. Moreover some of these have no claim to complete novelty, but will be found here and there in connec- tion with other special investigations. On the other hand, they have never as yet been developed in such general—and never in such a simple—manner as is here done with the help of the idea of ‘‘ potential temperature” and of the theorems that it was possible to deduce from this as to the potential temperature of the different layers of air. The consequences that can be deduced from this as to the static relations of the atmosphere, especially with refer- ence to the fundamentally different behavior of cyclones and anti- cyclones in winter and in summer, both in respect to their intensity and their duration, are delayed to a later communication. [An Appendix as published in the original memoir by von Bezold is omitted from this translation, as it has been at the author’s request incorporated in its proper place in the latter portion of his first com- munication. | VIF i ON THE THERMO-DYNAMICS OF THE ATMOSPHERE.” (THIRD COMMUNICATION. ) By Prof. WILHELM VON BEZOLD. In the two papers previously published on the above subject the re- strictive assumption has been always made that the masses of air under consideration experience no mixture with similar masses having other temperatures and other degrees of moisture. At the same time how- ever it was shown that such mixtures must frequently occur in nature and that the investigations in question could possess only a restricted application so long as we neglect these processes. For this reason therefore it is now necessary to extend the previous investigations in this direction. But investigations on this subject have also a special interest because for a long time we formerly attributed too much importance to the mix- ing of masses of air of unequal temperature and near the point of sat- uration, whereas in more recent times we have gone to the opposite extreme and attributed to it scarcely any importance at all. Following the example of James Hutton,t the mixture of such masses of air was, until within a few decades of years, considered as the prin- cipal cause of atmospheric precipitation. Wettstein was (so far as I know) the first to antagonize this viewt which however even to-day is still widely accepted. He however fell into the opposite error in that he contended that, in general, precipitation never could occur by mixing. Here, as in so many other points of modern meteorology, Hann§ first made the matter clear in that he, in the year 1874, proved that by mix- ture condensation could be indeed produced, but that the former method of computing the quantity of precipitation was affected by an error in principle after correcting for which the values obtained are so small * Read before the Academy of Sciences at Berlin, October 17, 1889. [Translated from the Sitzungsberichte der Kénig. Preus. Akad. der Wissenschaften zu Berlin, 1890, pp. 355-390. ] t Roy. Soc. Edinb. Trans., 17&8, Vol. 1, pp. 41-86. } Vierteljahrss. d. naturf. Gesell. Ziirich, 1869, xiv, pp. 60-103. § Ztschft. Oesterr. Gesell, Met., 1874, Vol. 1x, pp. 292-296. [Rep. Smithson., 1877, p+ 385. ] 257 SO aes >So ets 258 THE MECHANICS OF THE EARTH’S ATMOSPHERE. that the production of a moderately heavy precipitation in this way is impossible. At the same time he showed that the adiabatic expansion in this re- spect played an entirely different and much more important réle, and that, in it we have to recognize the source of all considerable precipi- tations. In this paper, so far as it concerned mixture Hann confined himself — to the computation of an example from which it appeared that even under very improbable assumptions there could in this way only be realized very slight quantities of precipitations. Pernter many years later* contributed to the solution of the prob-— lem in that he brought it into an exact mathematical form aud at the same time also computed small numerical tables in order to facilitate © the comprehension of the quantities that enter into the question. But since the empiric formula for the tension of aqueous vapor en- | ters into the expression given by Pernter, therefore the latter is rather — complex and is not especially clear. It seems therefore to me not only desirable but really necessary to_ take up the question anew and if possible prosecute it to a definite conclusion. This is the object of the following lines. It will be shown how graphie methods give with extraordinary ease — an insight into the whole theory of the mixture of air and how in such | methods we possess at the same time the simplest means for the nu- — merical evaluation of the quantities that enter into the question. | Various tables—some of which may also be welcome for other investi- gations—will also facilitate a general survey as well as the exact com- | putations. After these preparatory sections there will be considered the various causes of the formation of precipitation, namely, direct cooling, adiabatic expansion, and mixture, in their relative importance — and it will be shown how that only by the consideration of all these causes is it possible to obtain a deeper insight into the methods of the — formation of clouds, (a.) THE MIXTURE OF QUANTITIES OF AIR OF UNEQUAL TEMPERATURE AND MOISTURE. Before we proceed to the mathematical treatment of this problem we must first come to a clear understanding as to whether definite — masses or definite volumes shall be made the basis of the computation. At the first view it would seem appropriate to adopt the volume, since we can from well-known tables obtain directly the quantity of water which corresponds to the saturation of one unit of volume. This is doubtless the reason why in the older investigations of this subject based on Hutton’s theory, one always started with the con- sideration of the unit of volume, and why Hann—when he would * Zeitschft. Oesterr. Gesell. Met., 1882, Vol. XVI, pp. 421-426. PAPER BY PROF. BEZOLD. 259 demonstrate the imperfections of this theory in his considerations on this subject, followed the earlier method of treatment, and adopted the volume as a basis. This is also quite justifiable so far as concerns the first estimates, and Talso recently have made the same application in a popular lecture. But when one wishes to obtain exact formulz this method brings him into difficulties. These arise from the fact that the capacity for heat of a unit of volume, the so-called volume capacity, even without the consid- eration of the intermixed vapor of water, is to a high degree affected by pressure and temperature, so that no forms of approximation are al- -lowable. The capacity for heat of the unit of mass of moist air, there- fore its capacity for heat in the ordinary sense of the word, is entirely independent of the above mentioned quantities and is also so little in- fluenced by the contained water within the limits that occur in meteor- ology that, as will later be more accurately shown, we can in the pres- ent question simply consider it as constant. In order however not to lose the advantage that inures from the utili- zation of existing tables, I have computed for different pressures and successive degrees the quantity of aqueous vapor that is contained ina kilogram of saturated moist air for such pressures and temperatures as occur in the atmosphere and have communicated the table thus formed in an appendix to this paper (see page 287). This table not only facilitates very considerably the solution of the questions that refer to the mixture of moist air, but it can also be ap- | plied with profit to many other investigations. After this preface the problem itself is to be considered more closely, and to this end an appro- priate notation is first to be introduced. Let there be m, and m2, the quantities expressed in kilograms, of air to be mixed together; t, and ¢, their temperatures; y, and y,, the quantities expressed in grams, of vapor actually con- tained in a kilogram of moist air; y’, and y’s, the corresponding values of contained moisture in a kilo- gram of air at ¢, and #, in the saturated condition ; R, and R,, the accompanying values in per cent. of the relative hu- midity. p, and 2, the same quantities expressed as fractions of unity, that is to Say R, R, —— and o.— =. ie AO rieti co aLOO ts, Y3y Y’3, 3, and ~3, the various values of the same above-named quantities in the mixture, in so far as the limit of saturation has not been exceeded, or at least no water has been lost, that is to say, true sat- uration exists, \ 260 THE MECHANICS OF THE EARTH’S ATMOSPHERE. t, y, y’, R, and p, the corresponding values after mixture and after the loss of the quantity of water that exceeds the normal quantity for saturation, or also, in general, any given group of the same quanti- ties belonging together. The pressure expressed in millimetres of mercury will as before be expressed by (; the maximum of the elastic force of the vapor will in a corresponding manner be expressed by ¢«. The pressure / can be cousidered asconstant during the process of mixing. Thisis allowable since, Where mixture actually occurs, the two masses of air must nec- essarily exist under very nearly the same pressure and must also retain this [in the free air] even when on account of the mixing a change oc- curs in the total volume, which in general is very unimportant. The problem of mixture becomes extremely simple so long as no pre- cipitation of water occurs, that is to say so long as the quantities ob. tained by the mixture are to be indicated as in the above notation by the subscript 3. In this case Y3(My+ m2) = YM + YoMy or Mi(Ys3—Y1)=M2(Yo—Y3) «ee ew ee 6) and further €\M(t3—t1) = MyzC2(tz—ts) where by ¢ and ¢ we understand the thermal capacities of the quan- tities of air to be mixed,* or since these quantities are to be considered equal mi(fs—t)=Mx(th—ts) 2. 2. 2. . 2 we. (2) If we combine the equations (1) and (2) we obtain (the mixing ratio) Ys—Y1_t;—h_m ie an ae which is the well known equation that holds good for the mixture of two .quantities of the fluid in question, having two different temperatures. Since the graphic m2thod will be chosen in the further development, therefore first of all this simple for- mula must be translated into a geo- metrical form. To this end, in a rectangular sys- tem of codrdinates, Fig. 37, the tem. peratures (ft) are taken as abscissas, the quantities of moisture (y) as ordi- nates, and these are designated in the Fic. 37. ordinary manner by OT,,0T,. ... *Strictly speaking we should use mean values computed by a special formula be- tween the above named c,; and c. and that of the mixture c;. Since, however, the values of ¢ scarcely differ from each other for the different temperatures and pressures, we can therefore omit this refinement. PAPER BY PROF. BEZOLD. 261 T,F,, T,F2, ete.; in the figure the origin O is omitted. We see at once that F£; lies on the straight line drawn through F, and F, and that [ DT; To Po—T Fy _m a T, 137 12 By — 13 #3 my io ___ In order now to obtain a decision as to the degree of saturation, we - must also introduce into the diagram, as ordinates, along with the values of y;, Yo, and y3, also the values of yj)’, yo’, and y;, corresponding to complete saturation. The ends of these ordinates, which are repre- sented by #7’, #2’, and F;' in the diagram, all lie upon a curve that with increasing ¢ rises rapidly, aud the equation* of which is a y = 623 a y fi —VU.377 &€ when for 6 we insert the proper constant pressure. pe With the assistance of this equation, or with the approximate for- — mula obtained by development, i. y= 693 £ + 234.88 (2) ¥ y = 623 5 + 234.88 (3) _ the tables communicated in the appendix [page 287| have been com- _ puted, by the help of which the curves can be easily constructed di- _ rectly for the pressures therein considered, and which we can designate as curves of the quantity of vapor needed for saturation at the pres- sure / [or for brevity, the saturation curve]. , It will now suffice to cast a glance at the figure in order at once to _ ovtain the following propositions: (1) So long as for given temperatures ¢, and ¢,, the values Un Yo Sener se) (3 eal ; : * Fe = p, and ne =», remain within given limits, the straight line F, ly passes entirely beneath the saturation curve, and therefore there cai be no mixing-ratio for which conden- sation can occur. / (2) When p, and p, increase so much i that the straight line F, F, touches or cuts the saturation curve, as in figure (38), then tbere occurs either ore or Many mixing-ratios that may bring about condensation. - (3) When R,=R,=—100,7.¢.,when the FF” two quantities of air to be mixed are 4 saturated, then the straight line F F, coincides with the curve F;' F,', and then for every mixture there occurs L; super-saturation or condensation. F Ze Fic. 38, *Hann, Zeit. Oesterr. Gesell. Met., 1874, vol. 1x, p. 324. [Smithson Rep., 1877, p. 399.] y a ee a <= nC ape: = eng Sa » core Nn ern o 262 VHE MECHANICS OF THE EARTH’S ATMOSPHERE. The investigation of the cases included in 2 can always be referred to case 3, since the points F;* and F,*,in which the straight line F, FL cuts the curve, F;/ F,’ play precisely the same role in the second case as F, and F, in the third case. If we consider more closely the propositions just enunciated, then we shall involuntarily be led to seek certain limiting values, the knowledge of which leads to the solution of the fundamental question whether, under given conditions, condensation will be possible or not. The questions that obtrude in this connection are as follows: (1) What limit must the relative humidity exceed for a given tempera- ture of the components, or at least for one of them, in order that con- densation may be possible for a properly chosen mixing-ratio ? (2) Whatlimiting value must the relative humidity of one component exceed when.the value of the other is given, and when also condensa- tion is to become possible for a properly chosen mixing-ratio ? The first of these two pads questions can be expressed ee in the following form: Lor When the limit of satura- Pie a tion is to be attained for an appropriate mixing ra- tio, and the relative hu- midity of both components is to be the same, what is the minimum value of this relative humidity ? ‘That the knowledge of this minimam value is also a solution of question 1, we see most easily when we more accurately examine the answer to the question as last formulated. We obtain this latter answer very easily through the following con- sideration: If R, is to equal k,, then the straight line #, F/, must cut the axis of abscisse at the same point P Fig. 39, as does the prolonga- tion of the chord F/ F,’.. For if this condition is fulfilled then— eS Ee Af; > es a + i {7 EP a Zz Fic. 39. T,F, _T, F, Ts Oa but now T, F, AT ae fy LT, Fi af oe 100 and eae &, and consequently, also ae -. = WARE IS ER a See PAPER BY PROF. BEZOLD. 263 If now for a given value of Rj =I», which may be called Ry, the point of saturation is to be just attained by proper mixing, then the straight line P F, F, must just touch the saturation curve F,/ Fy’. The point of tangency S gives therefore the temperature of the mix- ture for which saturation will be just attained, and hence also the mixing ratio. But the value A), as the figure shows at the first glance, must be exceeded by at least one of the components when condensation is to become possible, and it therefore is precisely that limiting value that is desired in question Fee No. (1). R Itis easily seen that the knowledge of these 2 boundary values is of high importance, it is therefore carefully considered in tables to be subsequently communicated. Equally simple is the solution of the second question, which, however, will here be considered only under the special assumptions that R, or Ris equal Fic. 40. to 100. If k,=100, that is to say, if the cooler of the two components is in the state of complete saturation, then we obtain the minimum value of Ra, when we, as in Fig. 40, draw at F/’ a tangent to the saturation curve, and prolong this until it cuts the ordinate F,’ T, at the point F#,. The FLT, PYT, densation occurs on mixing, provided that there is sufficient of the colder aN desired value is k,=100 - As soon as RA, exceeds this limit con- : : my ; component, that is to say, provided —* is large enough. My . If, however, we consider the other case as given and assume that &,=100, that is to say, that the warmer component is saturated, then we find R, when at F’,’ we draw a tangent to the saturation curve and seek the intersection of it with the ordinate F/ 7;. Thus it becomes at once apparent to the eye that Ff, is always smaller than R,, so that for sufficiently great distance between 7, and 7) the quantity R, can even attain a negative value, if such were imaginable. The physical interpretation of this is that when warm saturated air is mixed with colder the latter can have a high degree of dryness and still condensation may occur for a proper mixing ratio; in many cases even the cooler air may be absolutely dry; it might even have a nega- tive RF, corresponding to its containing a certain mass of hygroscopic substance, if only there is sufficient quantity of warmer air, that is to ; M2. say, if only. is large enough. 1 In such cases, therefore, in place of the minimum value Rf, there Gees: Mo : ; occurs a limiting value of w= ae which must be exceeded if conden- 1 Sation is to occur. 264 THE MECHANICS OF THE EARTH’S ATMOSPHERE. These considerations show that mixtures of saturated warmer with unsaturated cooler air gives rise to condensations much more easily than do mixtures of saturated cooler with drier and warmer air. The flow of a jet of saturated warmer air into a cool space must therefore be accompanied by much more powerful condensation than is the inflow of saturated colder air into a space filled with unsaturated warmer air. The fact that clouds of vapor so easily arise over every open vessel filled with warm water, while the formation of fog near very cold bodies in warmer regions is much more rarely to be observed, gives an assurance of the correctness of this principle. Whenever during moderately cool weather the door of a wash-house is opened great clouds of vapor pour out, but the opening of an ice cellar on a hot day has not a similar result. Now that the limits have been determined within which, in general, mixture can occur, it is proper to give the quantity that can be precip- itated by the condensation. Such precipitation occurs whenever the point F; lies above the saturation curve. For then the limit of satura- tion is exceeded, and by a quantity that is represented by the length FP; Fs! =yY3 — ys. This quantity, which will be designated by as, is that of which, before the writings of Wettstein and Hann, it was assumed that it was pre- cipitated as water as the result of the mixing. To what extent one was led into error by this assumption is most easily seen from the figure by the following considerations: Let it be assumed that at first actual saturation occurs in the mix- ture, and let the whole quantity y; be actually present in the form of vapor or aqueous gas, then will the gradual precipitation of the vapor be accompanied by a simultaneous warming. The increase of temperature hereby bronght about is found from the equation 1000 cdt = — rdy, where ¢ is the capacity for heat of the moist air under constant pressure, and r is the latent heat of evaporation, and where ¢ is to be multiplied by 1,000, since we have taken a kilogram of the mixture, whereas y is expressed in grams. Since now, as will subsequently become evident, the temperature ¢ rises only a few degrees even for a very considerable supersaturation, ° C : : site therefore we can consider , as constant in each individual case, and corresponding to this we obtain 108¢@ - Ye — ¥y =—— ($=) ne ee in which y and ¢ represent those values that are obtained after the precipitation of the water that is in excess of the limit of saturation. " a i eee i aia ae el _ water a=y; —y is a quantity that is _ is the same, y;’ and y, were considered see, as Hann had already shown in a _ special example, that this is not the PAPER BY PROF. BEZOLD. 265 In Fig. 41, therefore, we find this temperature ¢ in a very simple man- ner in that we draw through # a straight line that makes with the axis: of abscissas an angle O%e a=are tang : % aie The point F, in which this straight line cuts the saturation curve, has the desired coédrdinates ¢ and y, whereas the quantity of precipitated represented in the figure by the short line Fy. According to the old theory t, and ¢, as well as y;’ and y’, or, what respectively asthesame. But now we case, but that ¢>t; and y 0°. can have for a pressure of 760 milimetres are 2.55 _ If ¢< 0°, then we have to add the quantity 80 [calories] to the value of | ry. If we consider this and then compute A for 0° and for — 302, first for # = 760 milimetres, and next for 6 = 400 milimetres we obtain as extreme values 2.87 and 2.98. so that here with even more right we can assume AC to be constant and as we in fact will do equal to 2.9. According to this, without important error, we may consider the lines F; F,in general, as parallel straight lines which experience only a slight bend at the point corresponding to 0°. In the actual application of the above-explained graphic method we do best to place upon the system of codrdinates, on which we have en- tered the saturation curve, a group of straight lines representing the series F, F, of which those on the left of the zero codrdinate are inclined 1 2.9° to the axis of abscissas so that tan a= but those to the right of the zero coordinate have tan a=, 5 ade . * Hann, Zeit. Oest. Gesell. Met., 1874, vol. rx, p. 324. [Smithson. Rep., 1877, p, 399.] + According to the investigations of Dieterici (Wiedemann’s Annalen, 183), XXXVII, pp. 494-508), as well as according to those of Ekholin (Bihang K. Svenska Vet. Akad. Handl., 1589, xv, Part I, No.6.) these numbers are indeed not quite free from criti- cism. Since however on the one hand, the correction of these numbers scarcely comes into consideration in the final result here desired, and since on the other hand the value of the capacity for heat of dry air here adupted is based on the calorie used by Regnault, it appeared to me proper, if not even necessary, also to make use of the older value for r. PAPER BY PROF. BEZOLD. 267 _ Special interest attends the question: In what ratio two quantities of air of given temperature and humidity must be mixed in order to obtain the greatest possible precipitation? The solution of this prob- Jem is given by a glance at Fig. 41. Since the quantity of precipita- tion is ; a = F;F sin a, therefore a willbe a maximum when F; F has its greatest value. But thisis evidently the case when the tangent at the point F’ on the curve “is parallel to the straight line F, F,, or F,! F,’. The point at which this tangent touches the curve can be determined _ either by construction and trial or, in case we bave at hand a table of _ quantities of saturation, such as that in the appendix, computed for the barometric pressure in question, we have then to seek from it a value | ; of ¢ such that i Cy ae \* dimes =; _ which is not difficult to do after constructing a corresponding supple- mentary table of differences for each tenth of a degree. Having found the point # we move further parallel to the previously mentioned group of straight lines until we strike the line F, F,, and thus determine the point #3, which on its part gives the point 73, and _ thus the distances 7; T; and 7; T,, whence results the mixing ratio that _ corresponds to the maximum precipitation. The precipitation itself we _ obtain from the above-given formula, D3) Ye But we can also adopt another and purely numerical method for _ obtaining these quantities. For it is not difficult to see that FL (Fig. 41) is also a maximum at the same time with F; F, where we designate by I the point in which the prolongation of the ordinate FT intersects the straight line F, F). Moreover when we represent the line FL by 1, we have l=y, + (t—t) tan 6—y =ttan f6—y+y, —t tan f, where / represents the angle that the line F, I, makes with the axis of abscissas, that is to say, tan 6 = 2" b—-t Since the value of y is not difficult to compute, when not taken directly from the table, one is therefore in condition to form a small auxiliary table for the value of the quantity / for certain values of ¢, such as lie in the neighborhood of the one desired, and from it take out es - , re 268 THE MECHANICS OF THE EARTH’S ATMOSPHERE. the maximum value of 1 or the value of ¢ corresponding thereto. Them; the value of a is given by the formula tan @ a=l = a tan a+ tan whose deduction may here be omitted. | Thus both a numerical and a graphic method are at our disposal. If we follow the former, we can easily perceive that an extremely | accurate knowledge of the quantity of vapor contained in a kilogram when inthe condition of saturation is presupposed for an even moder- | ately accurate determination of the value of a and ¢, as well as of the ratio”, Ms Because of the unreliability of the data at hand the values obtained by computation have in themselves a rather high degree of uncertainty, so that one can’ equally well make use of the far more convenient graphie method without thereby in fact losing any thing in accuracy. In this latter way the following small tables have been computed, | which give the limiting cases above treated as especially interesting for the pressures 700 and 400 mm. and for temperatures that proceed by steps of 10° and thereby makes possible a quick review of the various questions relative to mixtures of air. The first horizontal line of each of these twelve tables relates to the case where both component masses are completely saturated, and gives — in the column a the greatest precipitation that can occur * under these my My” Therefore the a on the first line of each table, gives the maximum possible precipitation that can be brought about by mixture at the given temperatures. The second line of each table gives the value of the relative humidity which must (at least for one of the components) be exceeded if precipi- tation by mixture is to be any way possible. We also find on this line circumstances and under the most favorable mixing ratio . m Hp ai bee under the headings t and —' the mixing temperature and the mixing My ratio for which the point of saturation will be just attained when in both components the relative humidity has the minimum values, given under FR, and FR. The third line shows the value of R, that must be exceeded by the relative humidity of the warmer component, if the cooler component is completely saturated and if precipitation is to become possible by mixture. The fourth line gives the mixing ratio which must be exceeded if precipitation is to become possible by means of any proper mixing *{ Expressed in grams of water per kilogram of moist air. ] sian» ee etd PAPER BY PROF. BEZOLD. 269 The fifth line shows, under a, the maximum precipitation that is con- pivable under the last mentioned condition of the components as to humidity as well as the mixing ratio and mixing temperature at whieh ‘this maximum precipitation is attainable. In many cases no precipitation is possible with perfect dryness of the cooler component. In such eases the fourth line is the analogue of the third since it gives the minimum value which the relative humidity of She colder component must exceed if in general precipitation is to be- come possible by mixture. Under these conditions in the nature of the ease the fifth line becomes a blank. _ The tables as here given relate only to the two pressures 700 and 400 millimetres. Since however these include all altitudes between 680 and 5,150 metres, that is to say, those altitudes in which the forma- tion of cloud or at least precipitation proper principally occurs, and since the supplementing of these tables by means of the table given oo the appendix is not difficult, | have thought that I might confine At any rate these will peace in order to give a general orientation as to the quantities coming into consideration, and therefore the tables _ themselves are now given, and it need only be stated that the figures ‘must be considered only as approximations, since in general they are based upon the first differential quotients, but occasionally on the second _ differential quotients of the curve of vapor-pressure, so that very small changes in the experimental data or in the method of interpolation must make themselves very sensible. | | | | t, te R, | R, a | t ™,: Mz eae |e a 4 | b=700™™ ; t,—t)—200. (; 100) 100) 0.4 ) 9.0) 102: 98 | || 76) 76] 1/0 | —14.0] 140: 60 | oo | ocd | 200} 52] 1/0 | —20.0 1:0 | | 0 100) >0.0 |>—11.8| <118: 92 | Lteg:| egal tet r |} 0] 100] <0.13) 2-55} 260: 140 \ | (| 100 | 100] 0.55 1.0| 106: 94 | | t | SEN $B1e| 9 Acco: | 2.81! soet gare \ Tos. ‘ | ue +10 100| 61| 1/0! —10.0 1:0 | | 0} 400!| 0:0, | S—0.1 | “<1. 4 }} | / 0/100) <0.2 | 20.5| 254: 146 f | } i (| 100 100) 0.75 11.9 108: 92 i | 86 | 96| i/o | 62) 138: 62 : 0 | +20) TOL) eae NF ties 2 -Oretle teva | 0100) >0.0 | >12.2) <8: 120 ats) | | | | 0 | 9 = oo an l | 100 | <2) 1G. | 287 : 163 240) THE MECHANICS OF THE EARTH’S ATMOSPHERE. A ty FR, | Re a ie M,: Mz ! i b=700™™; ty—t,—10°. (| 100 | 100; 0.04) —15.5| 57:48 |} 92] 92! 1/0 | —16.0] 60:40 —20 | —102] 100] 82| 12 | —20.0| 1:0 | | 55/1001 a/o | —10.0| 0:1 Cte ea, 5:| pee (| 100} 100| o.11| —4.0 | 43: 57 | | 94] 94) 1/0 | 5.5] 55:45 =i) 04; 100} 85) Ij | —10.0 1:0 | | 47/100| 12 | 0.0 O:1 A eee | asin Pe | Siesiee 3 | sia ’ostiereiorstare (}100}100| 0.19] 50] 54:46 | |} 94} 94] 1°20 4.5|° 55:45 | 0, +104) 100; 87) 1fx | v0.0 0 || 64) 100} Lo} wo} 0:1 | l Sioa a| Saree retell See one eae ie (| 100 100} 0,21 14.5] 55:45 || 94) 94] 12 | 10] 60:40 | +10 | +204) 100) &7 | Lo 10.0; 1:0 | | | 76/100! 12 20.0 | 0:1 (ists: Wee alieetelere eee Wea en aetece b=100™™ ; t,—t)=200. (| 100} 100; 0.50) —9.5| 108:92 | 76| 76] afo | —14.0) 140: 60 ens | god | 100 | 58 | Ife | —20.0 1:0 | | | 0 | 100 | >L/o >—11.8 | <118: 82 | i 0 100 <0.2 z—5.4 754: 146 | (100 100) 0.75 1.2] 110: 90 | 80| 80] Ifo | —33] 133: 67 16 +106 100 | 65 ie —10.0 1:0 | 0 | 100 | >ijc >0.3 <97 102 | 0} 100) <0.2 26.0 245: 155 b:=400"™ ; t,—t)=109. j 100; 100; 0.12) —15.5 58: 42 | | 96| 96| 1/0 | —160] 60:40 —20| --10| 100} 85} 1/0 | —20.0| 1:0 | 48} 100} 1/0 | —10.0 :1 Ce oe | (| 100} 100! 0.17; 45] 50:50 || 94) 94] Ifo | —5.5 55:45 —10 02| 100} &8| 1/0 | —10.0| 1:0 52/100) 1/e —0.0 0:1 | { for oes acai eno ae a (| 100} 100 0.20 6.0| 47:53 | 93] 93| 1fc0 5.0 50 : 50 0) 10%; 100) 86) 1Jo 0.0 | 65} 100) lj 10.0 1 bed Sk | etek 2 ciate eel eee eee | eae eee tables show how small is the precipitation attainable by mixture when we consider components whose differences of temperature are even greater than ever occurs in nature, PAPER BY PROF. BEZOLD. Qt Since on the other hand, according to the data recently collected by Hanu,* quantities of water considerably greater than these can remain suspended in the air (as mist, fog, and cloud), therefore we see very plainly that, while the formation of cloud can be caused by mixture, _ yet the precipitation of rain ur snow in any appreciable quantity can _ searcely be brought about in this way. At the same time the following diagram, which we here make use of _ for graphic computation, enables, in the most simple manner, to com- _ pare the quantity of precipitation formed by mixture with that which is produced by direct cooling as well as that produced by adiabatic expansion. If we assume that by mixture under a favorable mixing ratio of sat- urated air at the temperature f with other saturated air at the temper- ature ¢,, the quantity of water ais precipitated (see Fig. 42), then we obtain the same quantity of precipita- tion when we directly cool the com- ponent y, from its temperature ¢, to a new temperature ¢,, for which we have y= Y'2— a, but y’, is the ordinate whose foot is T, in Fig. 42. A glance at the general saturation curve suffices to show at once that the difference t, —¢, is very much smaller than the difference t,—¢; that is to say, that a very slight direct cooling affords as much precipitation as a considerable cooling by mixture with colder air, even when the latter is completely saturated. The effect of adiabatic cooling is seen when in the diagram we draw the adiabatic curve as a function of the temperature and quantity of water contained in a kilogram of moist air. Such an adiabatic curve sinks, as we easily perceive, rather more slowly from the right toward the left than the saturation curve. For since in this case the diminution of t) mperature goes hand in hand with the increase in volume, therefore, the quantity of moisture neces- sary for saturation will for falling temperatures be greater than it would be if the initial pressure were maintained ; thatis to say, than it would be by progressing along the saturation curve. The adiabatic (which without any difficulty can be introduced into the diagram with sufficient accuracy with the aid of Hertz’s Graphic Method*) will therefore have a path similar to that shown by the curve F, A in Fig, 42. Fic. 42. * Meteorologische Zeitschrift, 1889, vol. VI, pp. 303-306. * Meteorologische Zeitschrift, 1824, vol. 1, pl. vil. [See No. XIV of this collection of Translations. } 22 THE MECHANICS OF THE EARTH’S ATMOSPHERE. But in this case the lowering of the temperature must be forced down to t,, if the quantity of precipitated water is to be equal to a, since then the equation Y.—yYo.=a holds good for y’,, which represents the ordinate erected at T,. Here also the general course of the curve again shows that the fall of temperature necessary in order that a definite quantity of precipita- tion may be caused by adiabatic expansion is very much less than when the same quantity is to be produced by mixture. A uumerical example will best ijlustrate this principle: From the above-given small tables we see that at 700 millimetres pressure satu- rated air at 0° C. mixed with saturatcd air at 20° can precipitate at the most only 0.75 grams of water per kilogram of the mixture and that the final temperature of the mixture will be 11°.0; that is to say, for a zooling of the warmer component from 20° down to 11°. By direct cooling, on the other hand, the same quantity of water would be precipitated from 1 kilogram of the warmer component when it is cooled from 20° down to 19°.2; whereas by adiabatic expansion a cooling of from 20° down to 18°.4 would be necessary; that is to say, a vertical ascent through a distance of about 510 metres. This example shows in a very striking manner how slight need be the direct cooling by contact with cold objects, or by radiation, or even by adiabatic expansion, in order to produce quantities of precipitation, such as would by mixture be only obtainable in the extremest, scarcely imaginable cases. With this the consideration of the mixture of masses of moist air may be brought to a close and only the single remark be made that the difference t—t, is smaller as the quantity a of the precipitated liquid decreases. The amount of this difference will therefore only exceed the value of 1° or 2° in such extreme cases as are assumed in the pre- vious tables and generally will remain far within this limit. Therefore in the majority of cases the mixing temperature may, with- out important error, be put equal to that which we obtain by mixing equal masses of dry air, whereby many computations experience a great simplification. (b.) SUPER-SATURATED AIR. In the foregoing solution of the problem of mixture it was assumed for the sake of simplicity, that in the cases where the formation of — precipitation in this manner is really possible, super-saturation must first occur, and then precipitation follows. This assumption was implied by Hann in his above-mentioned memoir* at a time when we still knew nothing as to whether aqueous vapor could actually exist in a supersaturated condition. * Zeitschrift Oest. Gesell, Met., 1874, vol. rx. [Smithson. Rep., 1877, p. 397.] PAPER BY PROF. BEZOLD. Die But since the possibility of this has been demonstrated by the inves- digations of Aitken, Coulier, Mascart, Kiessling, and especially by Rob- ert von Helmholtz,* it has some interest for us to make the precipitation _ from supersaturated air the object of a special investigation. This precipitation, as is well known, occurs when super-saturated air _ (which can only exist when perfectly free from dust) is suddenly mixed with very fine particles of solid bodies, or possibly, also, when electric _ discharges take place through such supersaturated air.t We obtain directly from the above-given rules the amount of the precipitation, as also the rise in temperature. We have only to omit the parts designated by the indices 1 and 2 in Fig 41, and to consider the condition indicated by the subseript index _ das the starting point, then the ordinate 7; F; = y; gives the quantity of water in the state of supersaturation, while y again indicates as before _ the final remaining moisture; y; — y indicates the quantity of moisture _ precipitated and t — ¢, the consequent rise of temperature. This is, therefore, a method of formation of precipitation, in which one can actually speak of a liberation of latent heat (the latent heat of _ evaporation), as was formerly done in explaining the formation of pre- cipitation in general. In aeertain sense this usage is allowable, even in the formation of precipitation by mixture, in so far as the temperature of the mixture comes out higher when water is precipitated than when this, under otherwise similar conditions, is not the case because of the insufficient quantity of water. This rise of temperature is however always a very unimportapt one in consideration of the small quantity that can be con- _ densed by mixture. _ It is otherwise when true super-saturation is present. In such cases _ the rise of temperature can, according to the degree of super-saturation, _ be very considerable, as is easily seen from Fig. 41. Still more considerable must the precipitation be that is caused by _ the sudden cessation of the super-saturation, namely : So soon as a sud. den development of heat occurs at any one place in the atmosphere there follows a powerful ascent of the air which then, by adiabatic cool- ing, must always produce new formation of precipitation. Under those conditions, when the vertical distribution of temperature | approximates even distantly to that of convective equilibrium, then the sudden cessation of the condition of super-saturation causes this equilibrium to become unstable, and thus this cessation then affords the key to the explanation of a series of phenomena. I consider it probable that it is in such processes, which indeed deserve a thorough investigation, that we have to seek the reason for the “cloud-bursts” properly so called. Of course, to establish this * Wiedemann’s Annalen, 1886, xxvU1, p. 527. tR. von Helmholtz, Wiedemann’s Annalen, 1837, XXxII, p. 4. 80 A 18 : Y } {4 THE MECHANICS OF THE EARTH’S ATMOSPHERE. view the proof must first be given that the super-saturation, which we have hitherto only known in laboratory experiments, also occurs in the free atmosphere. The mixture of super saturated air with other quantities of air scarcely needs a special consideration, since we at once see the result of such mixture when we imagine, in Fig. 41, one of the points, F, or FP, trans- posed to the upper side of the curve &” F’, and then execute the further constructions according to the rules previously given. (¢.) MOIST AIR WITH INTERMIXED WATER OR ICE. Water oecurs in the atmosphere not only as vapor, but also in the form of drops of rain, crystals of ice, and particles of fog. The psy- chrometer and liygrometer teach us that the air is not necessarily sat- urated with vapor when water is mixed with it in this manner. Unfor- tunately we possess only very imperfect data as to how great a quan- tity of water can in this way be mechanically mixed with the atmos- phere.* But there cau be scarcely any doubt that the sum of the water mechanically mixed and that which is present in the form of vapor may together be smaller, or equal to, or even greater than the quan- tity corresponding to saturation for the given temperature. Corre- sponding to this statement, I will designate such mixtures as air which is “‘ partly saturated mechanically,” “ wholly saturated mechanically,” or “ super-saturated mechanically.” And now, first of all, we will inves- tigate how such masses of air behave when mixed with ordinary air more or less moist. By this investigation we shall come to learn the conditions under which the dissolution of fog or clouds or the evaporation of falling rain- drops may occur. Such dissolution is, as we at once see, to be attained by mixture only when the intermixed air, which at first may be as- sumed to be the warmer component, is relatively dry. Therefore, we will at first investigate the phenomena of mixture under the following conditions: Let R; > 100 and composed of two parts, of which the one R, is in the form of vapor and the other R, is liquid, and moreover let Rk; < 100 while Ri+R; =f. Furthermore let R,< 100 and >t. This being assumed, the follow- ing formule hold good, using a notation which by analogy is intelligi- ble of itself: ytn=M Yi > yy! ncyy. it *Hann, Met. Zeit. 1289, vol. v1, pp. 303-306, PAPER BY PROF. BEZOLD. 21d Lb In the accompanying Fig. 43, 7, is represented by 7, Fi, and y, is rep- resented by F, F;, but the remaining lettering certainly needs no fur- ther explanation. However, one thing may be especially noted, that the lines which rep- resent the liquid or frozen * water are limited by two arrow points di- rected away from each other, since this is facilitates a quick comprehension. fz If now m, and m, are the quantities of the two components that enter into the mixture and we assume here also again that at first both the vapor and also the water are uniformly distributed in the 2 mixture, and that evaporation of the 4, water first occurs afterwards insofar as ~[5 the saturation of the mixture with vapor allows of any such evaporation, then, just as before, we attain toa state of transition Fiza De Te for which the corresponding quantities are appropriately indicated by thesubseript3. The difference between this transition state and the air that is sat- urated by mixture consists in this, that in the present case the air actually passes through the transition state, whereas in the preceding article if was only imagined for convenience of computation. In this transition state the quantities 7, of vapor and y; of water exist in one kilogram of the mixture before the dissolution occurs as is given by the equations Yarn bt nts ey and Wr—Ys_ts—t_m, ys t—ts m which equations lose their apparent want of symmetry when we remem- ber that %=y, and that y=—0. Moreover, just as before, we have Yi-~-Y3_t3—h_™> Y3s— Yo ba ts my In Fig. 43, ¥; is represented by the line T; F, and ¥ by the line F, FF. *In general I assume in what follows that the temperature is above zero, since it is not difficult to modify the considerations appropriately for lower temperatures. But if we would also consider those cases in which water and ice exist alongside of each other or where water is present at temperatures below zero, then the investigation would become inordinately complicated. | i Pb 276 THE MECHANICS OF THE EARTH’S ATMOSPHERE. The quantity y; that still remains liquid will now dissolve, in so far as the mixture is not saturated, or so much of it will dissolve as is needed for saturation. This of course can only occur in that the mix- ture itself cools, and that too by 2°.6 or 2°.9 for each gram that is evap- orated, since we exclude the cases where heat is communicated from without. ‘ The final temperature TJ is therefore found by passing upward ip Fig. 43 from F, toward the lett, parallel to the guide- line F, F, until at / we reach the same height as F;, or at least until we reach the curve F’, F’,, in case the line Ff, F’ so drawn would need to cross over the curve Ys. In this latter case, which is represented in Fig. 44, all the water is not dissolved but only a portion (y’—y;) as is represented in Fig. 44 by the distance F; P. The first of these two cases can be easily handled numerically, since under these Fic. 44. conditions we have i — ts — KY; = Mo — ts —_— KY, —_—— Mm, + My Mit; + Mot. Ri My mM, -+ Mz My, + Me Mit + Motz — KYM, my, + m: But the computation is as simple as this only when all the water is really evaporated; in the second case where mechanical supersaturation still continues it is better to apply the graphic method. An especial interest pertains here again to the investigation of the limiting cases for which in general there can occur a complete dissolution of the water originally present as liquid in one of the components. Of such extreme eases there is an extraordinary variety according as we are at liberty to assume arbitrarily either the mixing-ratio or the humidity of one or the other of the components. At present we shall consider only the question, what is the initial limit of the mixing-ratio for given components in order that complete dissolution must always follow. This limit is evidently obtained when F”’ F, lie at the same altitude above the axis of abscissas, that is to say, when y= y’=y3, or when F and F” coincide. In this case F is the Tae PPS SSSA a, * PAPER BY PROF. BEZOLD. Od. - apex of a right-angled triangle whose vertical side is F; F; and whose hypothenuse is parallel to the guide-line. If now we imagine the point 7; moving to and fro along the axis of abscissas, then the apex of the triangle erected in the given manner upon the vertical side F; F; will describe a straight line passing through the point F,, which line we easily find when we erect such a triangle on the portion cut off by the straight lines F, F, and F; Fy from any arbitrary ordinate and then join this apex with F,. : We can, for instance, as in Fig. 45, choose for this pur- pose the ordinate erected at Ts Then FF) Ff, is the triangle described and & F, is the straight line on which the de- sired point # must lie; but since it must also lie on the saturation curve, therefore it is at the intersection of F)F, and the curve F,'F,’, and the desired limiting value of the mixing ratio is ih T,T; m1 PET ns Tie When the mixing ratio attains this limit or exceeds it on the side : Ms : , toward m:, that is to say, as soon as m, Of > Ha complete dissolution 1 of all the suspended water occurs. In such mixtures it can happen that the line F F, cuts the curve F'/ F,/ on the left-hand side of 7, F;. In such cases the temperature resulting from the completion of the mixture is lower than that of either component. The mixing ratio for which this phenomenon begins to occur is easily found by draw- ing, as in Fig. 46, through (which is in this case identi- cal with F;’) a line parallel to F, F, (which is a guide line), and find its intersection with #\/,. The abscissa of this point is then the temperature ¢;, which is produced by Fic. 46. 278 THE MECHANICS OF THE EARTH’S ATMOSPHERE. mixture in this ratio before the subsequent dissolution. From this: value of t; this mixing ratio itself ean be determined. We find by a very simple consideration that for this special value of t; the following equation holds good: FFL t—t FP Fs” t.—ts But since 5 ts—t Ff, F,=- K and - BPE =n1-" ; therefore Yi—"n ie f,—t; te—t, to—te and consequently Yi— Yr tg ty sm: y Vj Saeeael 2 aS to— tz; my, Whenever p<, that is to say, when the cooler ‘‘ mechanically super- saturated air,” or at least the saturated component enters into the mix- ture with greater weight, then will t<¢, and of course t) Adiabatic expansion, or at least expansion with insufficient addi- tion of heat. _ (¢) Mixture of masses of air of different temperatures. Ina corresponding manner the dissolution of tog and cloud already present may take place through the following processes: _ (a) Direct warming, either by radiation or by contact with warmer bodies. (b) Compression, whether adiabatic or at least with an insufficient abstraction of heat. iz (c) Mixture with other masses of air having sufficient temperature aud moisture. Of these three different processes the one first mentioned is always the most effective. In order to condense or dissolve a given quantity of water there need _ be only a relatively slight direct cooling or warming. When the con- = 284 THE MECHANICS OF THE EARTH’S ATMOSPHERE. At the upper limit of the cloud, especially in stratus clouds, the processe of growth and dissolution of the cloud by direct loss or gain of heat by) radiation are carried on like the formation and dissolution of fog in the lowest strata of air. ! The formation of clouds by adiabatic expansion as well as the disso’ lution by compression occurs wherever we have to do with ascending or descending currents of air. This process has in recent times been s¢ frequently treated that the subject may here be treated very briefly The cumulus clouds of summer with horizontal bases, the thunde cloud and the rain cloud, properly so called, owe their origin to this process. To what extent “nocturnal radiation ” influences the uppe? layers of such clouds can only be made clear by further investigation, Still more complicated than the two methods hitherto considered in the formation and dissolution of clouds and fog are the processes that accompany mixture. In both the above mentioned pairs of processes a steady increase of cooling or warming is accompanied by a steadily progressive condensation or dissolution. It is quite otherwise in mix- tures. A process of mixture can progress in the same direction and yet cause at first condensation and in its subsequent stages dissolution. The breath which we exhale into the cool air leaves the mouth satu- rated but not yet in the condition of fog; only after the beginning of the mixing with the colder air does the formation of the cloud of vapor: begin, which then through further mixture with colder, drier air, again’ dissolves. We see this process depicted in a strictly mathematical way) in Fig. 38. If for instance we assume that a small quantity of air at the: temperature ¢, is mixed witha larger quantity at the higher temperature | > a - 3 Ms : t,, then all possible mixing-ratios will occur from a =0 up to the final) 1 | result, which we will assume to be greater than that which corresponds: to the higher value y.*. In this case the quantity of contained water yi passes through all values belonging to the ordinates of the line F,F,, until reaching the final value y>y,.*. In this process condensation must. occur as soon as the mixing-ratio exceeds the value which corresponds to the ordinate y,*; if it increases still further then beyond a definite point as it approaches towards the ordinate y* dissolution again begins, which becomes complete for a mixing-ratio corresponding to the ordi- nate y.* and thus again results an unsaturated mixture. If a smaller quantity of nearly saturated warmer air mixes with a larger quantity of colder air then will the mixture pass through its conditions in an inverse order, and again the initial condensation and the subsequent dissolution will occur under the conditions assumed in Fig. 38. Although now in both cases condensation occurs first and then dis- solution, still there is an important difference between them. For if we imagine the mixing-ratio to undergo steady change between the points PAPER BY PROF. BEZOLD. 285 if condensation and of dissolution, that is to say, between the ordinates y* and y,*, then will the resulting mean temperature fat eee 9 “=! be from y2" towards y,*. For since t > ¢t, therefore for t = 4 (t;*+1,*) the ae aera’ mixing-ratio —! > 1, that is to say, the mixture shows the average yo temperature, although so far as mass is concerned the colder component is in excess. According to this, if we mix saturated cooler air with steadily increasing quantities of saturated warmer air, then the warm. whereas in the reverse process cooling proceeds more slowly at first and then steadily faster. The qnantity condensed has also a similar relation ; it also attains its maximum when there is an excess of the “‘ Therefore condensation entire sooner when a jet of cold moist air pen- etrates a large mass of warmer air than when a jet of warm moist air is blown into cooler air.” Therefore by the outward appearances sf clouds that are forming a nd dissolving i in this manner, one erceiwes whether warmer or colder From all the preceding we conclude that the following forms of fog and clouds may be considered as originating by mixture: _ (1) The fog above warm moist surfaces, under the influence of colder | _ air, therefore especially the fog over the sea in the cold season of the year or during the occurrence of cold winds. (2) The “rank and file” clouds occurring on the boundary between wo different strata of air flowing rapidly above each other, which von Helmholtz* has first recognized as a consequence of wave motion and | designated by the name, atmospheric billows, in which however adia- batic condensation also comes into consideration at places where the air is thrown upward after the manner of the formation of crests and foam on ocean waves. _ (3) The layers of stratus that also form at such separating surfaces and which frequently first appear as atmospheric billows and subse- quently become denser. _ (4) Cloud streamers that form and again dissolve at the summits of mountains or in narrow mountain passes when the form of the moun- tain is such as to make it possible for jets of warmer or colder masses of air to penetrate intc similar masses of other temperatures.t _ (5) The ragged clouds, or the disconnected clouds, such as one fre- q juently observes during rapid motions of the at, Popes changing _ * Sitzungsberichte, Ninig. Preus. Akad. Wisscneen: zu Born : Berlin, 1888, p. 661, and 1889, p. 503. [See also Nos. VI and VII of this collection. ] .t Von Bezold, Himmel und Erde, 1889, vol. 1, p. 7. 286 THE MECHANICS OF THE EARTH’S ATMOSPHERE. their form and appearing and disappearing, and such as also occur with! clouds formed by adiabatic expansion, especially during thunder storms. These different methods of cloud formation by direct cooling, by adia-i batic expansion, and by mixture can of course also occur side by side in the most varied combinations, as is expressed in the extraordinary; diversity of cloud forms. It seems to me very important in the study of these forms to keep: these different processes in view, since only then can we hope finally to attain a thorough knowledge of these forms. Above all, as Hellmann has appropriately expressed it, it is necessary to lay the foundation for a ‘‘ physiology of the clouds” before we can hope to attain to a truly satisfactory arrangement and nomenclature.* But further work will still be necessary before this problem is solved, since on the one hand the question becomes more complicated the nearer we approach to it, and since on, the other hand it appears so extraordinarily difficult to realize experimentally even approximately those conditions under which the formation and dissolution of clouds. take place in the atmosphere. Beautiful and praiseworthy as are the experiments that Vettin has. made with clouds of smoke, still we must be very carefal about the con- clusions which we would draw from them as to the formation of the real clouds. All experiments with smoke, when looked at properly, give only pictures of the movements in dry air, since the condensation and | evaporation as well as the processes of compression and expansion are excluded, and we therefore are working under conditions such that in | the real atmosphere no formation of clouds would ececur. | But it is precisely because of these processes (condensation, evapora- tion, compression, and expansion) that we can not consider the motion of a cloud as a measure of the motion of the air, for not only do clouds. hang apparently motionless on the mountains, whereas in fact strong winds are streaming through them (e.g. Fohn cloud-bank, the Table- cloth of the Table mountain, the Cloud-cap of the Helm-wind) but it even happens to aéronauts that they pass through clouds while moving in a horizontal direction. This latter is however only possible when the cloud has a velocity different from that of the air in which it floats, since the balloon itself has only the power of vertical motion. The cloud is in fact not a body that can be driven forward as such by the air unchanged, but is a form in a process of continuous forma- tion and disappearance, and can have as a whole motions entirely dif- ferent from those of the particles of which it consists. On account of the increased interest with which at the present time we are studying the forms and motions of the clouds, it seemed to me important to call attention to all these points sinee we must have these in mind when we attempt from the external appearance of the clouds to draw any conclusion as to the processes which in individual cases de- termine their growth or dissolution and therefore also their form. *“ Compare also O. Volger in Gaea, 18Y0, vol. 11, pp. 65-75. PAPER BY PROF. BEZOLD 287 APPENDIX. Table giving the quantity of water in grams that is contained as vapor in a kilogram of saturated air. t b=760"™ | b=700™™ | b=600™™ | H—500™™ | F—400™™ | P—ZOOMn | =200mm | 30 0 31 0.34 0.39 0.48 0.60 | 0. 80 1.20 29 34 .37 .43 .52 65 .87 1.31 28 538 .41 .48 57 oil 95 1.43 07, 0.41 0.45 0.52 0. 63 0.78 1.04 1.56 26 45 49 .57 .69 86 114 1.71 25 .49 54 . 63 75 94 1.25 1.88 24 54 59 69 .82 1. 03 | 1 37 2,06 23 .59 65 75 .90 13) 156 2,25 —29 0.65 0.71 0.82 0. 99 1,23 1. 63 2. 46 21 ar atl 90 1.08 1.34 | 1.78 2, 69 20 aT .8t .98 1.18 1.46 1.94 2, 94 19 . 84 92 1.07 1.28 1.60 2.12 | 3.21 18 92 1.00 1.16 1.39 1.74 2. 32 3.50 Saf 1,00 1.09 1.26 1.52 1.90 2. 53 3.81 16 1.09 1.18 137 1.65 2.07 2.75 dei 15 1.19 Bing 1.49 1.79 2.24 2.99 4.49 14 1.28 1. 39 | 1.62 1.94 2.43 3. 24 4.87 13 1.39 | 1.51 | 1.76 2.11 2. 64 3,52 5.28 BED 1.50 1. 64 1.90 2, 29 2. 86 | 3. 82 5.73 11 1.63 177 2.06 2, 48 3.10 4.18 6.20 10 1.76 1.9L 2,23 2. 68 3.35 4.47 6.72 | 9 1.91 2.07 2.41 2.90 3. 62 4. 84 7,26 | 8 2. 06 2.24 2.61 3.18 3. 92 5. 23 7. 85 aii 2. 23 2.42 2. 82 3.38 4.24 5. 65 8.49 6 2. 40 2,61 3. 04 3. 65 4.58 6.10 9.16 5 2. 59 2. 81 3. 28 3.94 | 4.94 6. 58 9. 88 4 2.79 3. 03 3. 54 4,25 | 5. 32 7.09 10. 66 3 3.01 3.27 3.81 4.58 | 5.72 7. 64 11. 49 | BO 3.24 3. 52 4.10 4.93 6.16 8.23 12.37 =I 3.48 3.78 4.42 5. 30 6.63 8. 85 13.32 3.75 4.07 4.75 5.71 7.13 9. 52 14.33 EET 4.03 4037 5.10 6.13 7.67 108245 |e 2 4. 32 4.70 5.48! 6.58 8. 24 TOG eee ag 4, 64 5. 04 5. 88 7.07 8. 85 TSW | ee ees 4 4.98 5.41 6.31 7.58 9.49 19:68 ieee ree 5 5. 34 5. 80 6.77 8.13 10.18 13560) eee 6 5.71 6.22 7.26 8.72 104918 | eae fo eee 7 6.13 6. 66 7.77 gigai ® SLISGONI erento ene ee +8 6. 56 7.13 8.32 9.99 | 12.52 |eeeeeeee-| eee ees | 9 7.02 7.63 8.91 10:50° | A513; 40h neces ces ee eee 010 7.51 8.16 9. 53 Tit 4a aol ees | eee 1 8.03 8. 72 10. 18 12. 24 15792) Beene Roe eee 12 8.58 9.32 10. 88 13. 08 TOSS Veer ecige es e +13 9. 16 9.95 11. 62 43°07 I. cDva50 Wide oe seek nee 14 9.78 10. 62 12. 41 14.91 TSSGOT | ee eee coe 15 10.43 11. 34 13. 24 15.91 LOKOKG|Pre nee lee ee 16 fis13 12. 09 14.12 16297 leo ces ee eee aces | peers 17 11. 86 12. 89 15. 05 18-10, (eee sess |e ek eee ees 288 saturated air—Continued. THE MECHANICS OF THE EARTH’S ATMOSPHERE. Table giving the quantity of water in grams that is contained as vapor in a kilogram of t | b=760™™ | b=700™ = F=GOOm™ | H=500™™ F=—4J00™™ F=300™ P=yOOma ; it woe | | t Eig 12. 64 13.73 16.04 195291) 228 | | t i9} 13.46] 14.62 €g000 1) | 0080.1) ss. cereal oes eee 20 14 33 15. 57 18 20 DISS) oe an eal eee | ee 21 15, 25 16-50 P1987. \|' e2octcod | =cee5ae| eeeonees Cee j 22 16. 22 763 3 peCO DON tate ee | Se ewes |e eee | } +23 17. 24 19,054) 022800) oss tnkss| one aascen eee 262 I 24 18. 32 1979321 Me 123598"). 22!s 2284] eee bee 25 19.47 21.17 | 24.73 PP en etena ee an scecace 26 20. 68 OORA SMe nec coe: heck oc iallh See E cee hart onl| rae era i 27 21.95 23.80: Valens} nets sShs,| Muatce see Renesas eee f 1:98 23. 29 25.81 |2--cc2ecas|- sos oR, alert aes | ee ee 29 24.70 96 (84e| seat ones acl ee cake sl eee eee IRE eee Sree 30 26.18 OBA uh ok tee.) sence eee, || Weds eaten | peeee el In computing this table the vapor tensions of aqueous vapor have been adopted as given by Broch, ‘Travaux et Memoirés, Bur. Internat. des Poids et Mesures, 1881, tome I. ve ; XVIII. ON THE VIBRATIONS OF AN ATMOSPHERE.* By Lorp RAYLEIGH. In order to introduce greater precision into our ideas respecting the behavior of the earth’s atmosphere, it seems advisable to solve any problems that may present themselves, even though the search for sim- plicity may lead us to stray rather far from the actual question. It is proposed here to consider the case of an atmosphere composed of gas which obeys Boyle’s law, viz, such that the pressure is always propor- tional to the density. And in the first instance we shall neglect the curvature and rotation of the earth, supposing that the strata of equal ensity are parallel planes perpendicular to the direction in which gravity acts. If p, o be the equilibrium pressure and density at the height z, then dp | “= 995 Poet ree VELA Real | and by Boyie’s law, POO), 2 PLS UP eae as Pe eee aay where a is the velocity of sound. Hence Gen) 19 s ea ices A) hele ote (3) and TS Glen Nate coe ee, eee omer (ea) where o» is the density at -=0. According to this law, as is well known, there is no limit to the height of the atmosphere. Before proceeding further, let us pause for a moment to consider | how the density at various heights would be affected by a small change | of temperature, altering « for a’, the whole quantity of air and there- *From the London, Edinburgh and Dublin Phil. Mag., Feb., 1890, fifth series, vol. XXIX, pp. 173-150. aa") 289 Se - 2 ee ——— ae 290 THE MECHANICS OF THE EARTH’S ATMOSPHERE. fore the pressure p) at the surface remaining unchanged. If the dashes” relate to the second state of things, we have —92 —gz Z a’? G=oe *, G'=o€ gz —gz p=pe ~, p'=po @ while aw 6y)=A” 6". If a? — @ = da?, we may write approximately 9 pe a a y—p doarge =% ne Pee € a’e Po One The alteration of pressure vanishes when z=0, and also when | Gg 2 ? The maximum occurs when =1, that is, when p=". Bat (p’ — Po) increases relatively to o, continually with ¢. Again, if o denote the proportional variation of density, / 4 = qz \ a—c 92s 92 p= ——=- ail 6 a? T @? —1 ). CG a If a”?>a’, p is negative when z= 0,and becomes + « whenz=o, The ; transition o = 0 occurs when i = 1, that is, at the same place where | p’ — p reaches a maximum. In considering the small vibrations, the component velocities at any point are denoted by 4, v, w, the original density o becomes (6 + op), and the increment of pressure is dp. On neglecting the squares of — small quantities the equation of continuity is dp du dv dw, ds . Cait det Ody WO ag ae dz or by (3) do du.dv. dw gu | dt ‘dx’ dy' dz aa + 4 8 0 eo The dynamical equations are dop_ __, ddp __ og dop _ dw. dc, dt’. dy” aS ee or by (3) since Op = Wop, 2dp_ dw dp dv dp _ dw Ole de dy atte dean me -) PAPER BY LORD RAYLEIGH. 291 We will consider first the case of one dimension, where wu, v vanish, while p, w are functions of z and t only. From (5) and (6), dp dw gw dt dz a” (7) ge te. i a Te VTE? Lala ah ett ROD _ or by elimination of p, | ldo @e gdw E Umeeaaa da ee The right-hand member of (9) may be written ya age! Gane oa ) ~ dat and in this the latter term may be neglected when the variation of 2 with respect to z is not too slow. If A be of the nature of the wave- length, a is comparable with C3 and the simplification is justifiable _ when a? is large in comparison with gd, that is when the velocity of sound is great in comparison with that of gravity-waves (as upon water) of wave length A. The equation then becomes 204) c | d go d@pum, | \de 2a? S or, if 392 eee 4s tet oe hem een Meares Reaeh (LCR ew aa Ww. Gime ae? es cy) the ordinary equation of sound in a uniform medium. Waves of the kind contemplated are therefore propagated without change of type except for the effect of the exponential factor in (10), indicating the increase of motion as the waves pass upwards. This increase is necessary in order that the same amount of energy may be conveyed ‘in spite of the growing attenuation of the medium. In fact w’s must retain its value, as the waves pass on. If w vary as e’™, the original equation (9) becomes yi 3 D Pwo gdw, nw —_—— — = 0 . . . ° . . . e 12 Eade a? ) Let m,, m2 be the roots of 2 P| Ws aS m Siete Oe 292 THE MECHANICS OF THE EARTH’S ATMOSPHERE. qe = awa hy = AG: = An GEN 2a? Jka ae then the solution of (12) is 1 =A eMt - Bemz, a. igs Sate A and B& denoting arbitrary constants in which the factor et may be supposed to be included. The case already considered corresponds to the neglect of g? in the radical of (13), so that magt2 nai 2 ar and 92 2 we “~ =Ae Aa) ae ) aaa A wave propagated upwards is thus w=e cosn ( t— ae em ee (C0) and there is nothing of the nature of reflection from the upper atmos- phere. A stationery wave would be of type 492 a? a NZ. w=e cos nt SIN — oe os Fist a) Beil) w being supposed to vanish with z. According to (17), the energy of vibration is the same in every wave length, not diminishing with ele- vation. The viscosity of the rarefied air in the upper regions would suffice to put a stop to such a motion, which can not therefore be taken to represent anything that could actuaily happen. When 2 na ie ee ye jipev aa? en yefoineene . ° . e (4c) ox c Cn Ome J « u (6 — fel, The wave of pressure will be of the form « = F' (z) sin (mx + nt). *[See also No. XVIII of this present collection of Translations. ] 304 THE MECHANICS OF THE EARTH’S ATMOSPHERE. The notation and solution are as follows: a Ne n?— a? ja g dz? dz a os 9 h=—n? —m g F (2) =B+ Kyehe $ Ket —— 1 ye a? ) DOE NN a) ee ee QA hi=s Jak lo 24 fe In order to determine the constants of integration A, and Ay whose © | factors in the expression for ¢ represent free vibrations we note that j w=0 when z=0 and also when ¢ has a very large value=Z which cor- | responds to a fictitious upper plane bounding the atmosphere. From | the second of equations (5) we obtain | w= (Kyke" + Koke —aA) cos (mx+nt) an ‘The boundary conditions give Ayk\+ Bok, =aA Ky ky gies Kahne”? = aA ke eee — 1 K,k,=aA—z—_| pre — okiZ : Lo eh2 Kok = aA Gh — obit : fy f If now, as in our example (where the wave length is the cireumfer- f ence of the earth and the period is one day), h is very small compared with a’, then is k very small, and x, nearly equal to a. Hence, A, will be smaller in proportion as Z is larger. If we desire to apply the re- sulting formula only to altitudes that are slight in comparison with Z, then will A,e?. With this limitation we put A,=0and A,k;=aA, and obtain w= A (e? —1) cos (ma+nt) ) sin (ma+nt) ONO. NOs Gh he PAPER BY MAX MARGULES. 305 - Under the assumption that a is a small quantity we have bee(Aal) Oe Wee ay, ky h : and when we retain only the first two terms of the exponential series we obtain 2 7 a2 (-)2 7. ‘ . e=A( 7+ az ) sin (mx+nt)=A (poze t@) sin 27 (ot L): _ For L=4x 10°, 0=24x 60 x 60, we obtain é=A (0.576+0.0001252) sin (mx+nt). The relative variations of pressure near the earth’s surface increase very slowly with the altitude. At the surface of the earth itself the 0.576 1.576 than in the example of the third section, where purely horizontal vibrations occurred. A daily variation of temperature of 1° C. would in the present case cause a pressure variation of 1.6™". The phases of both vibrations occur simultaneously when L > cO. variations of pressure are appreciably smaller in the ratio of y. A SIMILAR COMPUTATION FOR THE CASE WHEN THE AMPLITUDE OF THE TEMPERATURE VIBRATION DIMINISHES WITH THE ALTITUDE. The differential equation (4) becomes xe . He Ne) Lanes Ve a gee ——e a ¢ s >= eevee 2 — — 27 . . . 4d Da € ee gor. ie. 8 Oe si ( To the assumption 7 = Ae—” sin (ma + nt) there corresponds é=(Be-* + Ke) sin (max + nt) B(s’+as+h) =A (Sa? as) a pay k= 5— en has the same meaning as before. A stands for K, and K, disappears under the same limitations as before, (namely, that the result is to be applied only to altitudes that are slight in comparison to Z). 80 A——20 306 THE MECHANICS OF THE EARTH'S ATMOSPHERE. From the condition w=0 when -=0, there follows Ak= Bs+ Aa, | hence A a anv saya epee yee —sz iz aS ; kz 4 oa oa sou a as Je a, (Gsthle } sin (ma + nt) = dbs . ; it ae 1S very small, and s of the same order of magnitude as a, or even | much larger, then for values of 2 that are not too large, this last equa- | tion becomes | a m? e=A(5f5 h + az ’) sin (mx + nt) a co Ae ic t ae? a = 12 Oy ee as =A( paw. ee een +) sin te rte) If we put s = 0.000693, then, at an altitude of 1,000 metres, the varia- tion of temperature will be half as large as at the surface of the earth. With this value, and the same values of Z and © as above, there | results é=A (0.153 x 0.576 + 0.000125 2) sin (mx + nt) Hence, for a mean temperature of 273°, a barometric variation of 2.45 millimetres is produced by a daily variation of 10° in temperature at the surface of the earth. VI. TRANSFORMATION OF THE DIFFERENTIAL EQUATIONS FOR SPHER- | ICAL COORDINATES. Instead of the rectilinear codrdinates a, y, z, the spherical codrdinates | (r=radius; @=polar distance; A =east longitude from adopted me- | ridian), are to be introduced x=r sin @ cos J, y=rsin w sind, 2=17 COS @. -The equations of motion of a point on which the forces X, Y, Z are 3 ee : sere acting along the rectilinear axes, which are X= ap) etc., are thus trans- formed into the following: ay (dw ean da? yee @ jr dao Q= rae +7 ae at — 7 COS @ sin of ai) crate rae pee CNN ee dr coda =7 Sin @qpt 2 sin “at G+ 2700s @ | dt dt | PAPER BY MAX MARGULES, 307 where P, Q, 4 are the components of the forces in the directions of the new coordinates dr, rdw,r sin wd, If the velocities are so small _ that we can neglect their squares and products, then only the first term - will remain on the right-hand side of each of these equations. If we put dr da é ar adt=% "TE = rsin @ 7; =e we have dt’ at era Therefore the equations of motion of a fluid that is only under the in- fluence of a constant force of gravity positive in the direction of the diminishing radius, are 1 dp _ 0a \ et ee oo J Lite Pict hp ab Ul rao = dt ) . . . . . . . (8) 1 Op ale ur sinia pk ot These equations are applicable to the motion on a sphere at rest. In order toinvestigate the relative motion on the rotating terrestrial sphere, we modify equation (7) in that we put vf+A in place of A where v is Xr the velocity of rotation of the earth. In place of e in equation (7) dr : ? esa there now occurs ae. If, again, we put ¢ in place of the new r sin in : ot, if we retain the products va, vb, ve, and if on the other hand we omit the terms in 7”, which indicate only a slight change in the force of gravity, then we obtain the equations for the motion of a fluid on a rotating sphere. On the right-hand sides of the equations (8) the terms —2ve sin w, —2ve cos w and +2vasin w+2vb cos @ are to be added respectively. The equation of continuity has the same form for the sphere at rest as for the rotating sphere. dm, (ura) d(mbsinaw), due) _g yt t ror rsin@jeo ‘rsin@w)A 20st gt ake Introducing the notation p=po(1+é), T=T,(1+T) allied to that above used, we obtain the following differential equations -_—_ ns as 308 THE MECHANICS OF THE EARTH'S ATMOSPHERE. for the motion of the atmosphere on the rotating sphere that result from small variations of the temperature r oé oa == 2y ¢ SIN @ gr—RT) 5, or ot Ne Od c cath = ——27¢cos @ RT, rja dt | ) (10) RT dé “tena sin w+2v b cos@ °rsin @JA ag NEE ee g a4 iy) (Db sin @) Oc i Ob. ka RD )a rsin@j@ rsin @A — If v=0, these give the corresponding equations for the sphere at rest. VII. THE ATMOSPHERE WITHIN A SPHERICAL SHELL AT REST. As in the first computation in the second section for the case of a plane we shall assume only horizontal motions. Moreover the radius of the sphere S will be assumed very large in proportion to the height of the stratum of air. If in equation (10) we substitute S instead of r, put a=0 and v=0 and eliminate b and ¢ from the last three equations, there results Lt ye Te Fas ore Ene - tans Boe @ ae + wea - (Dp Single daily wave. The wave otf temperature t= Asin @ sin (nt + A) causes a wave of pressure é€=B6 sin w sin (nt+X) where A and B have the relation on? S? eb n Se Rl WEB cho eet ae RT, ~2) =4zT 27 With PL. => 273°, r= 24x 60 x 60, 760 mm., a variation of temperature of 1° on the equator will produce a variation of pressure at the equator of 10.4 mm. B will be equally large for the spherical shell as for a plane wave of the same periodic time, when we assume the wave length for the plane to be equal to the circumference of the cirele of 45° latitude on the sphere. S = radius of the earth, and p, = Double daily wave. For the temperature wave T= A sin ’o sin (2 nt + 22) we obtain the pressure wave é= Bsin ’@ sin (2 nt + 2 A) PAPER BY MAX MARGULES. 309 with the following relation between A and B 4n? §? cn 4 n? §? B( RT, —§ )=4-ey With the same constants as before 1° variation of temperature on the equator gives 6.2 mm. variation of pressure. On the occasion of the computation for the rotating sphere we shall again have opportunity to explain that the particular integrals that we, in both cases, have given as the solution of the differential equation (11) contain the complete solution for the whole spherical shell. If we put ©; for the duration of the vibration for single waves for which B is infinitely large, and similarily 0, for the double wave, then we have 6 Qn 278 any VIRT. 27 228 2m” VORT, These are the values of the periods of free vibrations of a spherical shell. Lord Rayleigh (L. FE. D. suas Mag. Feb. 1890) investigates only such and finds (by putting agation instead of Y & T,) for the atmosphere on the earth at rest 0; = 23.8 hours and ©, = 13.7 hours; therefore the first is much nearer to 24 than the second is to 12 hours. He remarks however that it is doubtful whether one ought to adopt the Laplacian velocity of propagation for vibration of such long duration. Therefore the relative magnitudes of the semi-diurnal variation of the barometer still remains a riddle. But this is so only so long as we confine the calculations to the sphere at rest. VIII. CALCULATION FOR A ROTATING SPHERE. Diurnal wave.—In this case also the calculation will be carried out only for air in a spherical shell whose thickness is small in comparison with the radius S of the sphere, and also under the further assumption that the movements are horizontal, and that thereforea=0. [This lat- ter assumption and the omission of the first of equations (10) are cer- tainly not unobjectionable; they are imitated from the analogous pro- cesses in the theory of the tides.]| The difference between the sidereal day and the solar day is not considered, and v=n, _f Ty dé __db 9 ——zne COS W S) ja. Ot _ RT) ASN OG nc i a : — +t 2nb cos jut, ee Oe ~S sin G@pA ot tt : rich ( ) 1 SC) de a s(S- at snw’ J@ te 310 THE MECHANICS OF THE EARTH’S ATMOSPHERE. When 7=A () sin (nt+A), then é, b, c, are to be sought in expres- sions of the following form: é= FE (o) sin (nt+A), b= (@ cos (nt+A), c=" (@) sin (nt+A), wherefore the last of equations (l(a) becomes n§ (B—A)+— : ee Eee, whilst the first two give dE 2 cos @ _FT, dw sin @ — nS 1—4 cos? @ aH roe E he. aa OF inte = —aS 1-feova These latter values substituted in the preceding equation lead to a relation between # and A only, or between « and zt. It will be con- venient for the further computation to introduce an auxiliary function, ? (@); @ (2) =f P(@) sin (@) me (1—4 cos’? @) w= = d(H sin’ co) oh sin @ dw (LL 1 * ; cea =aol P (G9) sin @ (4 sin? @w—3) do nS? . i] d® 2cos@ FE Os RT EA) + sin a do sing sn@ . If we assume #% to have the following form: ® (@)=cos @ (a, Sin w+a;sin'@+a;sine@+ . . . ) then E (@)=b; sin w+; sin’ «+b; sin? @+ 4a —dd5 7 ’ ‘ 4a,—3a3 b=, b5= = b= Let the temperature amplitude diminish from the equator to the pole according to the cosine of the latitude or . A (w)=C sin (@) and for brevity put ie apa Kis PAPER BY MAX MARGULES. Sane then we obtain the following equations for the determination of the — constants 0. (1 LE >) ies (F+ = ) a,—kC=0 oer AA Bet ee res -ka,=0 ipa 4 — a2 _ 3 iy, === a = k an —0 (i aa ( : a 3 )aat oka, (et en ee i=5, 7,9, . Apparently a, remains undetermined; for the computation of the others, following the lead of Laplace, we write Gets 4k (i+2) PGE) i —2)0 @ = 2) (4) iG 41) ays i—2 By the interchange of 7 with i+ 2 a similar expression is formed for a. eee ch CL then “i+? and in a similar manner for the subsequent terms of i—2 i the series, and by substituting these values in the above equation we obtain a continued rapidly converging fraction. =y.—7, =3 k. 7+3. Nea s i Wie or D> N,=3 6. 9-5. 10.8) FON eG O oe 4k 11 Dig: Ns Ti, NET. N;=3 k.11+7.9. 10, Zeyh Ooh Oar tli. If in the second of equations (lla) we pat a;=q 4, then will “S also 1 be determined, and the quotient has the same value as if it were com- puted from the serial fraction ae ty, Ogu na Wend 1a NZ, N;—Z; Noe teas 512 THE MECHANICS OF THE EARTH’S ATMOSPHERE. By the first of equations (lla) we obtain also the value of a,; conse- | quently that of a3= 1 ay a5= 1 3 My, ete. If, in the computation of q we take a sufficient number of fractions, as, for instance, up to Nj, we have thereby also performed the greater part of the numerical computation for qs, qs, aud q;. This remarkable method of determining the constants was by La- place applied to the theory of the tides. Its true importance was first recognized again by Sir William Thomson, who defended it against Airy.* Without Thomson’s commentary Laplace would not be easy to understand. In our case the matter presents itself very similarly. The differential equation (11), when we replace @ by F, is of the second order, and should have an integral with two arbitrary constants. These can be determined when on two arbitrary circles of latitude, certain con- ditions are to be fulfilled, such for instance as ¢«=0,or b=0. One con- stant drops out when we let one of the parallel circles coincide with the pole; the other is in this case to be determined as if the second par- allel was the equator itself. At the equator, on account of the sym- metry, we must have )=0. The equatorial plane is to be considered as a fixed partition. The computation assumes that a converges towards 0 as 7 increases. If we assume for a, not the value that results from the computation of the continued fraction but some other arbitrary one, and therewith compute a3, a5, ete., by equation (lla), we obtain a series that diverges for the equator, where sin w = 1. I have computed the constants with two values of k. First, k=. cet ane R= 287.0 2a To ee T,) = 298.79 "= D4 x 60 x 60 And second, for i= 2.1502 ke = 9730 aC instead of a, a0 instead of az, fC instead of b,, £3C instead of bs, If we also write We find— t7=Csin w(nt+A), = Ccos @(a,;sinw+a3;sineao+t .. .) (12) é= Csin (nt4+ A) [fF sin w+ £3 sing w+ 6;sinMewo+t .. .f- * Airy; ‘On an Alleged Error in Laplace’s Theory of Tides.” Phil. Mag., 1875 (4), yol. L., p. 227. PAPER BY MAX MARGULES. 313 ay Qs; as ay Ay k=2.5 — 1.119 — 0.745 — 0.232 — 0.040 — 0.004 k = 2.7382 — 1.146 — 0.823 — 0.279 — 0.053 — 0.006 py ps Ds py Py k=2.5 1.119 — 0.448 — 0.326 — 0.090 — 0.013 k = 2.7352 1.146 — 0.423 — 0.370 — 0.106 — 0.018 With the value of k = 2.7352 we obtain as the sum of the series of sines within the [ | in the value of é: On the equator. ‘ 2 f : nei Oi23 At latitude 30°. : F ; 3 on 70:50 At latitude 45° ! : : ; 3) 0:55 At latitude 60°. . ‘ : 3 « ‘0.51 Therefore the variation of pressure has a maximum in the neighbor- hood of 45° when we assume the variation of temperature to be pro- portional to the cosine of the latitude. For 2C = 545, i. e., for a varia- tion of temperature of 1° at the equator there results a variation of pressure of 0.64 millimetres at the equator, but 1.6 millimetres at lati- tude 45°. In order to investigate how the result is affected when we assume that the temperature ampiitude diminishes more rapidly from the equator to the pole, we will carry out the computation for still another case, namely— A (@) = C sin’ w, which gives for the determination of @ the equations-— 3 4 (1 ia (k+ 2) a; — 0. 3 Pe tas A teuheT (3+7) Ca (24+ 74+5%) a+ 5 ha = KC: ee eS Bis 4 11) (B+ 5)a-—(+ yt zh) at 7 ha =0. ( ) The ratio “2 is given from the first equation, but qs, qs, etc., retain the 1 same values as before. The second equation determines the value of a. As before we have— t= C sin’ @ sin (nt+ A) é= Csin (nt + A)[f, sin w+ f; sin’ w+ 6; sin?@o+ ...] § (12d) For k = 2.7352 we have— fy = 9.601 Px = — 0.172 B= 0.316 fy = — 0.030 Ps =) — 0.566 pu = 0.003 iA ' THE MECHANICS OF THE EARTH'S ATMOSPHERE. cording to equations (12) and (12b) the greatest pressureand highest tem- The sum of the series of sines in the value of ¢ is— For the equator . : : : : fer Osco For latitude 30°. i : 5 : . 0.38 For latitude 45°. . ‘ ‘ : . 0.42 For latitude 60° . p ‘ ; : . , 0.32 Again we find a minimum at the equator; the maximum of the press- ure amplitude lies between latitudes 30° and 45°; the diminution in the higher latitudes is greater than in the previous examples, but still slow in comparison with the diminution of the temperature amplitude. Ac- perature occur simultaneously. IX. ROTATING SPHERE: SEMI-DIURNAL WAVE. If in the differential equations (10a), for the horizontal motions on a rotating sphere, we put T=A (@) Sin (2nt+2A) é=H (@) sin (2nt+2A) b=@ (@) cos (2nt+2A) c=y (@) sin (2nt+2)) there results: dE 2 cos @ _ RT, dot sino P= In8 sin? @ ae cos @w + 2H roe RE Gs sin @ Y= > 2n8 sin? @ InS(E—A)-4 a 9 0 we sina, ts donna n 2 After the elimination of g and 7, and when we again put 7 : there remains WE dE a 2 Sin’ @—7_ sin wcos w+ E(4ksin‘@-+2 sin’ «o—8)=4kA(@)siné . (13) If we assume that A(@w)=C sin? w, we have then to do with the same problem as in the computation of the semidiurnal tide in an ocean of constant depth. Assuming HA(@)=a)+ a2 sin? w+a,sintw@+dagssm’@+ .... . there results aj=0, d2=0, a, apparently undetermined, (4x 6—8)as—(3x4—2)a,—4k0=0 (P+ 6i)diga—(P 430) dipo+4ha,=0 ¢ ad gnc eet eee t=4'0)3 Sea \ Mi+2__ 4k = % 4643) 1-46) 2" Wi+s PAPER BY MAX MARGULES. 315 | From this we develop the continued fraction as before, and compute the ratios of the constants. But a, is not now indeterminate. but its value is immediately found to be—Cq; hence {see Ferrel, p. 320 | ag=— C24. Ag = — OGn ade t=C sin? @ sin (2nt+2A) 14 é=C sin (2nt+2A)[a,sin* +a, sin® w+ a, sin® w+. .| - (14) oe For 4k = 40,=10,—5, Laplace has computed the constants. Only the middle value of these is of interest for our problem. I have in addi- tion executed the computation for some neighboring values of k. Fie 1: 10.94 LT. tt st 2 A: 2980.7 2739.0 2719.5 2699.1 266°.7 248°:9 a, —6.196 —37.99 —55.00 —247.8 101.8 . 8.270 TUTE ODE, SOT = '<. | Pr Ae 93106) =33.68 * 154.2 64.3 5.919 I i Oiesee oso) = * AG) 30.2 16.5 ~ 1.662 } Fig 0002) v=. 0:8 fh. 1180) 5.6 2.4 0.260 ae 01008? == 00,07 = 041. =~ 0.5 0.2 0,026 These numbers confirm Thomson’s expectations, that the period of the free vibrations of this kind, for a rotating spherical atmosphere of ordinary temperature, lies very near 12 hours. Instead of so de- termining the velocity of rotation of the earth that the period shall agree exactly with a half-day, we can choose a corresponding temperature. It lies near to 268°. At this point a, passes trom —~x# over to + ». In the neigh borhood of this value forced vibrations must lead to enor- mously great amplitudes. Therefore a slight semi-diurnal wave of - temperature would suffice to produce a very great wave of pressure of the same period. At temperatures below 268° the phases of both are in agreement; in other cases they are opposed. For 4k=10, or T>=298.°7, we obtain at the equator é=—10.26 CO sin (2nt+2A) 9 lod Therefore, a temperature amplitude of 0 would suf- J o— fice in order to produce a pressure amplitude of 1 mm. The comparison of the atmosphere with a spherical shell having a constant temperature of 298°.7 gives, as we shall see, the lunar tide on the equator much larger than it is, as deduced from observations. Sim- ilarly one must require corresponding large temperature amplitudes in order to produce the observed semidiurnal pressure amplitude of 1mm at the equator. In view of the great imperfections in the as- sumptions no importance can be attached to the numerical values. This computation only shows that in order to produce semidiurnal ' variations of pressure of the same amount as the diurnal variation much smaller temperature variations will sufiice. Oe flow; then come those that are to be subtracted when we consider the 316 THE MECHANICS OF THE EARTH’S ATMOSPHERE. xX. TIDAL EBB AND FLOW OF THE ATMOSPHERE. In order to facilitate the comparison of the problems treated in Sec-_ tions VIII and Ix with the computations that have been made for the | tidal ebb and flow, I will allow myself to add some things that do not properly belong to the subject of this investigation. The following formule differ from the ordinary ones only in the notation, and in the fact that the velocities are retained in place of the displacements.* In the rotating spherical shell of radius S, and of constant temperature T, the attraction of the sun produces motions for which the following equations, deduced from equations (7) and (10a), hold good: 0 (V—R T ¢) ab 9 oO ios ae a NC COS @ te ie ee Je ( URE EE oag +2 nb cos @ Ning, he ce eee ee S's a) Ao ae dé i ‘O(dDsin w). Je \ ti sshioe ae tm { oe Y indicates the potential of the sun at the point (@, A) of the rotating spherical shell. When the sun stands over the equator, its distance — from the earth being P, its mass JW, the constant of attraction 1, we have then for the potential x M [P?— 2 P Ssin @ cos (nt + A) + S}-* ; ‘ s . 2 This being developed according to the powers of p we obtain at first terms that have no, or at least very slight, import for the tidal ebb and motion of the fluid as relative only to the center of gravity of the earth. That part of the potential which causes the semidiurnal tide we desig- | nate by V in order to substitute it in the equations (15). v= SS sin? @ cos (2 nt + 2 A) = H(@) cos (2 nt +2 A) Put also é = H(o@) cos (2 nt4+ 2X) = gp (@) sin (2 nt+2 A) c = y (@) cos (2 nt 4+ 2 A) and H—RT- E=G(o) and eliminate gy, 7 from equations (15) we thus obtain a G mee ad 4 : — saa sin? @ — sin @cos @+ G(4ksint w + 2 sin? w—8) a Gd ad @ = Ak Hein’ . ols octave 9eb *Compare, for example, the concise presentation by G. #. Darwin in the Encyclo- pedia Britannica, 9th edition, article ‘‘ Tides.” PAPER BY MAX MARGULES. alt This is the same as equation (13) of the previous section, only here G replaces HL, and H replaces A («). [ 3M S? | G=) apa (a,sint@+agsinsat+ . . . ) 1 32M S? 4 E=pp rere (sin? w—a,sint‘w—agsin’boo— . . , ) ieee aaa For a given value of T therefore, a,, aj, etc., are the same constants as in Section Ix. xm Eile m is the mass of the earth; Se S95 M = 355000 m.; P = 24000 8; 3M S? 53-7 == 1.203 | 4 P Hence on the equator when 4 k = 10, or T = 298.7, we have i 760 160 € =537 7908.7 x< 12203 x< Hele 26 x cos (2 nt < 2X) y I } | 7 =0.12 (mm) cos (2 nt + 22) Thus by the sun’s attraction a semi-diurnal variation of the barome- ter of 0.24 mm. would arise at the equator; but through the moon’s action one that is three times greater, 0.7 mm. Laplace, in Mécanique Céléste, book Iv, vhapter 5, computed the atmospheric tide with the same value of k, but for an atmosphere over an ocean of constant depth, whose tides influence those of the air, whereas here the atmosphere over a rigid earth is alone considered. For our case the same formule obtain as for an ocean of uniform depth equal tol. In the equations (15) and subsequently, we have only to put gl in place of R T, and gy in place of R T «, when yis the elevation of the surface of the sea above the mean level. The lunar tides computed from equations (17) with any allowable value of T are very much too large in comparison with those deduced from the barometer observations.* One can scarely wonder at this * Besides the observations of Bouvard mentioned in Book X11, Wiens Celéste and which, arranged by syzygies and quadratures, show scarcely any difference in the daily variation of the barometer (note that only the observations of 9 a. M. and 3 P. M. were used), there are at hand for later dates computations of series of hourly observations for certain tropical stations that Professor Hann has pointed out to me. These give the following barometer variations produced by the lunar tides: Baromet- Latitude.) Altitude.) rice vari- Authority. ation. ORY metres. mm. Singapore .....- PLL | aeasrass 0. 16 Elliot, Fortsch. d. Ph., 1852, p. 703. Bergsma, Amsterdam Academy, 1870. Batavia..=...--- Gein age .ae 0.115 | PE | a= ies in? )& — 190 BF Shape NGO, Noe a ane Kuo=( Gi—ags0" )™—( e407 1158" ee and generally, after Kg, ei oe: | a emp (ne) (n—) This general expression is equivalent to Laplace’s and Darwin’s law as given in my preceding paper, equation (2), but is more simple and convenient in deducing any coefficient A, from the last two preceding. The one is reducible to the other by putting n=2i+ 14. The general law of (5) does not hold until after Ag, but A, and Kg being obtained from the direct equation of the coefficients of v* and 7°, then by means of these, A, is obtained, either directly from the equatiou of the coefficients, or from the general expression of (5), and this law can be extended forward, but not backward. For instance, A, is not obtainable from K,and Ky, Asis usual in such cases, the general law is not ob- tained until after several equations of the coefficients, and when the values of K,, are given directly in this way, and not by the general law, the former must be taken, and the general law, which is a relation found between the coefficients after A, only, can not be extended back. Putting h for the amplitude of the real tide, we have, from what has been stated above, Ky) i eet ha EY? +H EY + Kyv'+ hey . wwe ww tl (6D) Laplace extended the relation above, found to exist between the co- efficients of v in (3), and after A, only, back so as to make it, by means of the continued fraction, determine the value of A, and so the relation between Hy? and u. This makes A, a determinate quantity, whereas the equation of the coefficients of v* gives AH,=K,, an indeterminate quantity. It is evident that any value of K, satisfies the differential equation, and so, with the other coefficients depending upon it, is a so- lution of the tidal equation. The extension of the general relation of (5) back so as to make it de- termiue K,, and the relation between Hv? and w in (6), was regarded by the writer in his previous paper as an extension of the law back where PAPER BY WILLIAM FERREL. 321 it is not applicable, and this is what was not clearly understood by his correspondent. From (4) it is seen that the tidal expression consists of two parts, one of which depends upon Ay, and is independent of the tidal forces contained in E, and the latter depends upon these forces. It is evident that the former can exist without the latter. Also that being inde- pendent of the forces, and dependent simply upon certain initial motions which the sea may be supposed to have independent of the forces, it must vanish when there is friction, and so K, must be put equal to 0 in the real case of nature. We come now to the second part of what we have proposed to con- sider here, namely, the convergency of the series in the expression of win (3). Inasmuch as the vanishing ratio between consecutive values of K,, is unity, as is readily seen from an inspection of (5), it has been said that the device of Laplace in the use of the continued fraction was necessary to make the expression of wv convergent at the equator where v = 1,s0 as to give a finite value of wu. It is true that the expression at first is more convergent with a large value of Ay, such as is given by the continued fraction, but still the vanishing ratio in any ease is unity. But it can be shown that the expression gives:a finite value of u when we put K, = 0. We get by development, SOD Ng eA Te Al. Ne in which the relation between each coeflicient A, and the preceding one» ‘ ‘ Le: commencing with—;, is ad N—3 A,=— A, se eye et dal Ree Aan Hence we have, wher »=1 =74,=-1 5. Tip oy LRG rae cree Stier ar (9). cO- See 2 (te AL) i in which n/ 1s the exponent of any assumed term in the series. The expression (5) above may be put into the form, n—3 6 - B = a Be a Aaa ane Hi, n fee a2) a8 (pee 2 apes) ce (11) From this, by means of (8), we get for any coefficient for which the characteristic is 7’, He eee AW 3 Yea a ee sa ea ll 80 A 21 322 THE MECHANICS OF THE EARTH’S ATMOSPHERE. in which, 6 n! 3 Ge FF —— 1 = tee = — a Dien bs Agi sla Fates Siok | areal von ( = (n’+2)(n'—3) (n’ +2)(n’ —4)(0’ ~3) kK. (ts) and putting n’+2 for 2’ in (12) we get Kk, 1 gp A eil n'+2 y fA n'+2 n'+2 Ay ; XK 7% -n+2 aK n'+47— 4 oA raat eae ~An+2 Eovss This becomes by substituting for : >its value derived from the pre- “an'+2 ceding expression . KK, 1 a A VA re hate E n'i+t4 ae In like manher we get generally K, : Aw Puss E vs vlad) ate ak Ga in which the values of the factors F,,.., Fisi, Livi, are given by (13). by adding 2, 4, and 7 respectively to 2’ in that expression. Now, all these factors are finite, and hence putting now K,, for its equivalent, K,,,; and A, for A,,.,, we have 2,+2 A, = finite quantity nr since by (10) . 2+, A, =a finite quantity. From (13) and (14) it is seen that any coefficient, taken without | regard to signs, | a XK, | AC tg << A A 5 . . . . . . . . (15) On eres when p>- a e 4) th Spe) WAT, ey, since when this condition is satified all the factors F,.,., Py 4s, . - . F,,;areless than unity. Therefore, we have, putting n for n! -}+ 4, a crate sles Ky n+ 2 his Ba Ze Ale TAL i or by (LON Scie oe « on a ee (L424, 5) ao) n’ n' when P>O & & ahigey PSR Tale eee since this is what (16) becomes when ¢ is infinitely great. This is simply the limiting condition in all cases, and the first number of (17) is gen- erally less than the second when / is considerably less than 6. We have from (3) w= SS K, = Po + Oy eeu ae | PAPER BY WILLIAM FERREL. 320 in which (20) With the values of P,,, and Q,, (19) gives uw, and this in (6) gives h, the amplitude of the tide. Laplace computed the values of 2h, that is, the range of the tides at the equator, at the times of conjunction of the moon and sun, for the several values of £ equal 40, 10, and 5, to which, by (2), correspond the several values of 1, the depth of the ocean, equal to 5255, goss, and seri of the earth’s radius, or approximately 1.4, 5.5, and 11 miles Tespectively. Taking as an example the case in which /=10, we get from (4) and (5) by putting A, = 0, the following values of A, in terms of # in the last column of the following table, and from (7) and (8) the correspond- ing values of A,, in the second column. n An Kau | 2 0.50000 |......------ | Aoi Onto00y eet. a0.3 6 0.06250 | —0.6250 8 03906 | 4375 10 . 02734 | . 2413 12 02051 | . 1505 14 01611 | . 1072 16 01309 | . 0823 18 01091 . 0661 20 | 00927 . 0548 40 | 00322 | 0172 | 60 | . 00174 0091 | Putting n/ equal 20, 40, 60, we get the following corresponding values from this table when complete for all the values of x from 2 to 60, Ay»= — .00927 1+ >> cA laos Ay=— .003822, 14 2) A,= 12536 Ag=— .00174 1422) A,=.10254 From the values of A, we likewise get . Koy= —.0548 Ko i An=0d.91 Py=—1.7647 Ks = —.0172 Kao / A p= 18 Py=—2 0488 Keoo=—.0091 Keo / Ac=5.23 Po=—2.1687 We therefore get from (19) and (20) with the preceeding data, u<—1.7647—5.91 x 17621 or <—2.8061 u<—2.0488—5.18 x 12536 or <—2.7157 u<—2.1687 —5.23 x 10254 or <—2.6870 a 24 THE MECHANICS OF THE EARTH’S ATMOSPHERE. and so on, according as we take n/=26, 40, 60, or still greater values. It is seen that the first value, in which we get the value of P,,, from summing the actual values of A, from n=6 to n=n’, and then get the sum of the remaining infinite number of terms approximately from the last of (20), differs but little from the last value, in which the value of P,, was obtained from summing the actual values of 1, up to »/=60, and then obtaining the sum of the remaining terms from the last of (20). Itis evident that the real value of wv must be only a very little less negatively than —2.6870. The several values of wu differ the less, the more nearly the condition of (16) is satisfied, which, when the value of n/ is large, is very nearly that of (18). In our example 6=10, and so is too large to give equal values in the several cases of n/=20, 40, or 60. With 6=40 there is much greater difference in the several values, and the uncertainty in the last value is consequently much greater, but the last number so obtained is always a limit below which the real value is. Since our values of 4, have been computed in terms of H the va uc of wu above must be multiplied into #. With this value, then, we ge from (6) for the value of h at the equator, where v=1, h= (1 —2.687) E=—1.687 E. The value of # is that of the amplitude of the equilibrium tide at the equator, which in the case of the lunar tide, if we assume the moon’s mass equal 5, is 0.812 of a foot. Hence we get for the range of the lunar tide, approximately, at the equator, 2 h=—2~x 1.687 x 0.812 = —2.74 feet. Its being negative indicates that low water occurs at the time of the moon’s meridian transit. Laplace, in the same case, obtained for the range of the tide for the moon and sun in conjunction or opposition 11.05 metres, which, being positive, indicates that high water occurs at the time of meridian pas- sage. Butinstead of A,=0, he used A,=6.196, obtained from his con- tinued fraction. Besides, the mass of the moon which he used was much too large. SMITHSONIAN Fv