I have the honour to submit to the Royal Society of London an apparatus which I have invented, after having witnessed an experiment by M. Dieudonné Lontin. The original Lontin experiment consists in the rapid and continuous rotation of a magnetised steel needle, placed under the influence of the currents of a peculiar induction machine.
{"title":"II. On an electro-magnetic gyroscope","authors":"M. W. de Fonvielle","doi":"10.1098/rspl.1879.0122","DOIUrl":"https://doi.org/10.1098/rspl.1879.0122","url":null,"abstract":"I have the honour to submit to the Royal Society of London an apparatus which I have invented, after having witnessed an experiment by M. Dieudonné Lontin. The original Lontin experiment consists in the rapid and continuous rotation of a magnetised steel needle, placed under the influence of the currents of a peculiar induction machine.","PeriodicalId":20661,"journal":{"name":"Proceedings of the Royal Society of London","volume":"30 1","pages":"305 - 309"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspl.1879.0122","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62252219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mr. Cayley reported, on the part of the Auditors of the Treasurer’s Accounts, that the total receipts during the last year, including a balance of £1043 19s. 9 d.carried from the account of the preceding year, amounted to £3231 16s. 0 d.,and that the total payments in the same period, including £2000 invested in the Funds, amounted to £4531 5s. 5 d.,leaving a balance due to the Treasurer of £255 9s. 8 d. The thanks of the Society were voted to the Treasurer and Auditors.
{"title":"Anniversary Meeting. November 30, 1855","authors":"","doi":"10.1098/rspl.1854.0126","DOIUrl":"https://doi.org/10.1098/rspl.1854.0126","url":null,"abstract":"Mr. Cayley reported, on the part of the Auditors of the Treasurer’s Accounts, that the total receipts during the last year, including a balance of £1043 19s. 9 d.carried from the account of the preceding year, amounted to £3231 16s. 0 d.,and that the total payments in the same period, including £2000 invested in the Funds, amounted to £4531 5s. 5 d.,leaving a balance due to the Treasurer of £255 9s. 8 d. The thanks of the Society were voted to the Treasurer and Auditors.","PeriodicalId":20661,"journal":{"name":"Proceedings of the Royal Society of London","volume":"1 1","pages":"559 - 577"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspl.1854.0126","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62118372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
G ros Clark, Surgeon to St. Thom as’s H ospital, M ember of Council and of the C ourt o f Exam iners of th e R oyal College of Surgeons, and late H un terian Professor of Surgery and Patho logy in the College, and E xam iner in Surgery a t th e Uni versity of London. C om m unicated by P . IVIartin D uncan, M .B ., F .R .S ., Professor of Geology in K ing ’s College, London. Received April 18, 1871*.
G·罗斯·克拉克，圣托姆斯医院外科医生，皇家外科学院理事会成员和考试委员会委员，该学院已故的外科和病理学教授，伦敦大学外科博士。C om由P发音。IVIartin D . duncan, m.m.b.， f.r.s.，伦敦大学国王学院地质学教授。1871年4月18日收*。
{"title":"Some remarks on the mechanism of respiration","authors":"F. L. Clark","doi":"10.1098/rspl.1871.0030","DOIUrl":"https://doi.org/10.1098/rspl.1871.0030","url":null,"abstract":"G ros Clark, Surgeon to St. Thom as’s H ospital, M ember of Council and of the C ourt o f Exam iners of th e R oyal College of Surgeons, and late H un terian Professor of Surgery and Patho logy in the College, and E xam iner in Surgery a t th e Uni versity of London. C om m unicated by P . IVIartin D uncan, M .B ., F .R .S ., Professor of Geology in K ing ’s College, London. Received April 18, 1871*.","PeriodicalId":20661,"journal":{"name":"Proceedings of the Royal Society of London","volume":"20 1","pages":"122 - 135"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspl.1871.0030","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62202973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Whilst recently engaged upon the development of the pelvic plexus in Mustelus Iœvis I was much struck with the amount of variation in the number and position of the nerves forming it. This led me at the time to examine all the material which I was able to procure, and the results obtained have been given in a previous paper (12, 1900). Believing, however, that, in Bateson’s words, “the facts of variation must be the test of phylogenetic possibility” (4, p. 30), I determined to examine a still larger number of specimens of some other species of shark.
{"title":"On the composition and variations of the pelvic plexus in Acanthias vulguris","authors":"R. Punnett","doi":"10.1098/rspl.1901.0082","DOIUrl":"https://doi.org/10.1098/rspl.1901.0082","url":null,"abstract":"Whilst recently engaged upon the development of the pelvic plexus in Mustelus Iœvis I was much struck with the amount of variation in the number and position of the nerves forming it. This led me at the time to examine all the material which I was able to procure, and the results obtained have been given in a previous paper (12, 1900). Believing, however, that, in Bateson’s words, “the facts of variation must be the test of phylogenetic possibility” (4, p. 30), I determined to examine a still larger number of specimens of some other species of shark.","PeriodicalId":20661,"journal":{"name":"Proceedings of the Royal Society of London","volume":"69 1","pages":"2 - 26"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspl.1901.0082","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61693007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Instances of this are not wanting. Magnesium connected with platinum will decompose a magnesium salt, the almost insoluble hydrate of magnesium being found adhering to the negative metal. The deposition of zinc on the plates of an old-fashioned battery, when the battery is pretty well exhausted, is a well-known phe nomenon. In our experiments with copper and silver,in conjunction in a solution of nitrate of copper, we never succeeded in reducing the gal vanic action to nil by our utmost efforts to exclude all oxygen: and the whole of the present inquiry originated in an experiment described by us before the Physical Society, that mercury and gold in conjunction would decompose mercuric chloride with the deposition not only of the lower chloride, but also of metallic mercury upon the gold. 1875.] Dr. F. W. Pavy on the Production of Glycosuria. 51
这种情况并不少见。镁与铂结合会分解成镁盐，几乎不溶的镁水合物被发现附着在负极金属上。当电池完全耗尽时，锌沉积在老式电池的极板上，这是一个众所周知的现象。在我们的实验中，铜和银结合在硝酸铜溶液中，我们尽了最大的努力排除了所有的氧，但我们从未成功地将gal - vanic作用降为零。而目前的整个调查源于我们在物理学会之前描述的一个实验，即汞和金结合会分解氯化汞，不仅会沉积较低的氯化物，而且还会沉积金属汞在金上。1875.F. W. Pavy博士论糖尿的产生[j]
{"title":"II. On the production of glycosuria by the effect of oxygenated blood on the liver","authors":"F. Pavy","doi":"10.1098/rspl.1875.0007","DOIUrl":"https://doi.org/10.1098/rspl.1875.0007","url":null,"abstract":"Instances of this are not wanting. Magnesium connected with platinum will decompose a magnesium salt, the almost insoluble hydrate of magnesium being found adhering to the negative metal. The deposition of zinc on the plates of an old-fashioned battery, when the battery is pretty well exhausted, is a well-known phe nomenon. In our experiments with copper and silver,in conjunction in a solution of nitrate of copper, we never succeeded in reducing the gal vanic action to nil by our utmost efforts to exclude all oxygen: and the whole of the present inquiry originated in an experiment described by us before the Physical Society, that mercury and gold in conjunction would decompose mercuric chloride with the deposition not only of the lower chloride, but also of metallic mercury upon the gold. 1875.] Dr. F. W. Pavy on the Production of Glycosuria. 51","PeriodicalId":20661,"journal":{"name":"Proceedings of the Royal Society of London","volume":"24 1","pages":"51 - 59"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspl.1875.0007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62225177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
§ 1. If the gastrocnemius of a frog be placed in a horizontal direction on non-polarizable electrodes with its convex surface uppermost, one may generally observe that the muscle is somewhat more sensitive to minimal stimulation, supplied by closure of the constant current, when the femoral end rests on the kathode, than when this end rests on the anode. Conversely, under similar circumstances the gastrocnemius is more sensitive to minimal stimulation, supplied by opening of the constant current, when the femoral end rests on the anode, than when this end rests on the kathode. In view of the other facts of electrotonus, the present ones are of interest; because, as the sciatic nerve enters the gastrocnemius near the femoral end of the latter, and then spreads out its peripheral ramifications as it advances, in the experiments just mentioned one electrode is in almost immediate contact with the nerve-trunk where it enters the muscle, while the other electrode supports the part of the muscle that contains only peripheral nervous elements. It is therefore to be expected, upon the theory of electrotonus, that the muscle under these conditions should prove itself most sensitive to the closing shock when the nerve-trunk rests on the kathode, and most sensitive to the opening shock when the nerve-trunk rests on the anode. It is to be observed, however, that although this expectation is in most cases fulfilled, it is not so invariably. Different gastrocnemius muscles, though treated as far as possible in exactly the same way, manifest considerable differences, both in their general sensitiveness to electrical stimulation, and in their relative sensitiveness to interruptions of the ascending and of the descending currents. Even the same muscle, if rapidly prepared, will generally be found to undergo fluctuations in these respects from minute to minute. Attributing this fact to the unnatural conditions which the experiment imposed on the process of nutrition, I conducted some observations on muscles while they were still attached to the body of the frog; but the results yielded by this method were not more uniform than those which I had previously obtained by the method of rapidly preparing and observing excised muscles.
{"title":"VI. On the modification of the excitability of motor nerves produced by injury","authors":"G. Romanes","doi":"10.1098/rspl.1876.0005","DOIUrl":"https://doi.org/10.1098/rspl.1876.0005","url":null,"abstract":"§ 1. If the gastrocnemius of a frog be placed in a horizontal direction on non-polarizable electrodes with its convex surface uppermost, one may generally observe that the muscle is somewhat more sensitive to minimal stimulation, supplied by closure of the constant current, when the femoral end rests on the kathode, than when this end rests on the anode. Conversely, under similar circumstances the gastrocnemius is more sensitive to minimal stimulation, supplied by opening of the constant current, when the femoral end rests on the anode, than when this end rests on the kathode. In view of the other facts of electrotonus, the present ones are of interest; because, as the sciatic nerve enters the gastrocnemius near the femoral end of the latter, and then spreads out its peripheral ramifications as it advances, in the experiments just mentioned one electrode is in almost immediate contact with the nerve-trunk where it enters the muscle, while the other electrode supports the part of the muscle that contains only peripheral nervous elements. It is therefore to be expected, upon the theory of electrotonus, that the muscle under these conditions should prove itself most sensitive to the closing shock when the nerve-trunk rests on the kathode, and most sensitive to the opening shock when the nerve-trunk rests on the anode. It is to be observed, however, that although this expectation is in most cases fulfilled, it is not so invariably. Different gastrocnemius muscles, though treated as far as possible in exactly the same way, manifest considerable differences, both in their general sensitiveness to electrical stimulation, and in their relative sensitiveness to interruptions of the ascending and of the descending currents. Even the same muscle, if rapidly prepared, will generally be found to undergo fluctuations in these respects from minute to minute. Attributing this fact to the unnatural conditions which the experiment imposed on the process of nutrition, I conducted some observations on muscles while they were still attached to the body of the frog; but the results yielded by this method were not more uniform than those which I had previously obtained by the method of rapidly preparing and observing excised muscles.","PeriodicalId":20661,"journal":{"name":"Proceedings of the Royal Society of London","volume":"25 1","pages":"16 - 8"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspl.1876.0005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62229557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the "Proc. Roy. Soc.," vol. 16, p, 2, Professor Balfour Stewart described an apparatus designed and constructed by Mr. T. Cooke for the determination of the errors of graduation of sextants. This instrument has from that date been constantly in use at the Kew Observatory, and since the introduction of certain unimportant improvements, has been found to work very well. No provision was made, however, for its employment in the determination of the errors of the dark shades used to screen the observer’s eyes when the sextant is directed to the sun or moon, and it has been found that errors may exist in the shape of want of parallelism in these glasses, sufficiently large to seriously affect an observation, accurate in other respects.
{"title":"II. Description of an apparatus employed at the Kew Observatory, Richmond, for the examination of the dark glasses and mirrors of sextants","authors":"G. M. Whipple","doi":"10.1098/rspl.1883.0007","DOIUrl":"https://doi.org/10.1098/rspl.1883.0007","url":null,"abstract":"In the \"Proc. Roy. Soc.,\" vol. 16, p, 2, Professor Balfour Stewart described an apparatus designed and constructed by Mr. T. Cooke for the determination of the errors of graduation of sextants. This instrument has from that date been constantly in use at the Kew Observatory, and since the introduction of certain unimportant improvements, has been found to work very well. No provision was made, however, for its employment in the determination of the errors of the dark shades used to screen the observer’s eyes when the sextant is directed to the sun or moon, and it has been found that errors may exist in the shape of want of parallelism in these glasses, sufficiently large to seriously affect an observation, accurate in other respects.","PeriodicalId":20661,"journal":{"name":"Proceedings of the Royal Society of London","volume":"35 1","pages":"42 - 44"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspl.1883.0007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62274715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The experiments made by one of us in 1883 having given a value of " v " considerably smaller than the one found by several recent researches, it was thought desirable to repeat those experiments. The method used in 1883 was to find the electrostatic and electromagnetic measures of the capacity of a condenser; the electrostatic measure being calculated from the dimensions of the condenser, the electromagnetic measure determined by finding the resistance which would produce the same effect as that produced by the repeated charging of the condenser placed in one arm of a Wheat-stone’s Bridge. In the experiments of 1883 the condenser used in determining the electromagnetic measure of the capacity was not the same as the one for which the electrostatic measure had been calculated, but an auxiliary one, without a guard ring, the equality of the capacity of this condenser and that of the guard ring condenser being tested by the method given in Maxwell’s ‘Electricity and Magnetism,’ vol. 1, p. 324. In repeating the experiment we adopted at first the method used before, using, however, a key of different design for testing the equality of the capacity of the two condensers by Maxwell’s method. We got very consistent results, practically identical with the previous ones. We may mention here, since it has been suggested that the capacity of the leads might account for the small values of " v " obtained, that this capacity is allowed for by the way the comparison between the capacities of the auxiliary and guard ring condensers is made, for the same leads are used both in this comparison and in the determination of the electromagnetic measure of the capacity of the auxiliary condenser; the capacity of the auxiliary condenser, plus that of its leads, is made equal to the capacity of the guard ring condenser, and it is the capacity of the auxiliary condenser, plus its leads, which is determined in electromagnetic measure. As the introduction of the auxiliary condenser introduced increased possibilities of error, we endeavoured to determine directly the electromagnetic measure of the capacity of the guard ring condenser, by using a complicated commutator which worked both the guard ring and the condenser. At first we tried one where the contacts were made by platinum styles attached to a tuning fork, but as the results were not so regular as we desired, we replaced the tuning fork commutator by a rotating one driven by a water motor. A stroboscopic arrangement was fixed to this commutator so that its speed might be kept regular and measured. With this arrangement, which worked perfectly, we got values for the electromagnetic measure of the capacity of the condenser distinctly less than those obtained by the old method. We then endeavoured to find out the cause of this difference, and after a good deal of trouble discovered that in the experiments by which the equality of the capacities of the guard ring and auxiliary condensers was tested by Maxwell’s method,
{"title":"VI. A determination of “v,” the ratio of the electromagnetic unit of electricity to the electrostatic unit","authors":"J. Thomson, G. Searle","doi":"10.1098/rspl.1889.0101","DOIUrl":"https://doi.org/10.1098/rspl.1889.0101","url":null,"abstract":"The experiments made by one of us in 1883 having given a value of \" v \" considerably smaller than the one found by several recent researches, it was thought desirable to repeat those experiments. The method used in 1883 was to find the electrostatic and electromagnetic measures of the capacity of a condenser; the electrostatic measure being calculated from the dimensions of the condenser, the electromagnetic measure determined by finding the resistance which would produce the same effect as that produced by the repeated charging of the condenser placed in one arm of a Wheat-stone’s Bridge. In the experiments of 1883 the condenser used in determining the electromagnetic measure of the capacity was not the same as the one for which the electrostatic measure had been calculated, but an auxiliary one, without a guard ring, the equality of the capacity of this condenser and that of the guard ring condenser being tested by the method given in Maxwell’s ‘Electricity and Magnetism,’ vol. 1, p. 324. In repeating the experiment we adopted at first the method used before, using, however, a key of different design for testing the equality of the capacity of the two condensers by Maxwell’s method. We got very consistent results, practically identical with the previous ones. We may mention here, since it has been suggested that the capacity of the leads might account for the small values of \" v \" obtained, that this capacity is allowed for by the way the comparison between the capacities of the auxiliary and guard ring condensers is made, for the same leads are used both in this comparison and in the determination of the electromagnetic measure of the capacity of the auxiliary condenser; the capacity of the auxiliary condenser, plus that of its leads, is made equal to the capacity of the guard ring condenser, and it is the capacity of the auxiliary condenser, plus its leads, which is determined in electromagnetic measure. As the introduction of the auxiliary condenser introduced increased possibilities of error, we endeavoured to determine directly the electromagnetic measure of the capacity of the guard ring condenser, by using a complicated commutator which worked both the guard ring and the condenser. At first we tried one where the contacts were made by platinum styles attached to a tuning fork, but as the results were not so regular as we desired, we replaced the tuning fork commutator by a rotating one driven by a water motor. A stroboscopic arrangement was fixed to this commutator so that its speed might be kept regular and measured. With this arrangement, which worked perfectly, we got values for the electromagnetic measure of the capacity of the condenser distinctly less than those obtained by the old method. We then endeavoured to find out the cause of this difference, and after a good deal of trouble discovered that in the experiments by which the equality of the capacities of the guard ring and auxiliary condensers was tested by Maxwell’s method,","PeriodicalId":20661,"journal":{"name":"Proceedings of the Royal Society of London","volume":"47 1","pages":"376 - 378"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspl.1889.0101","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62324857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the preceding memoirs on the Calculus of Symbols, systems have een constructed for the multiplication and division of non-commutative pmbols subject to certain laws of combination ; and these systems suffice ,r linear differential equations. But when we enter upon the consideration f non-linear equations, we see at once that these methods do not apply, t becomes necessary to invent some fresh mode of calculation, and a new iotation, in order to bring non-linear functions into a condition which dmits of treatment by symbolical algebra. This is the object of the f l owing memoir. Professor Boole has given, in his Treatise on Diffeiential equations,’ a method due to M. Sarrus, by which we ascertain whether a jiven non-linear function is a complete differential. This method, as will )e seen by anyone who will refer to Professor Boole s treatise, is equivalent :o finding the conditions that a non-linear function may be externally livisible by the symbol of differentiation. In the following paper I have riven a notation by which I obtain the actual expressions for these con ditions, and for the symbolical remainders arising in the course of the livision, and have extended my investigations to ascertaining the results )f the symbolical division of non-linear functions by linear functions of the symbol of differentiation. Let F (x, y, y lt y2, y3 , . . . y„) be any non-linear function, in which % y2, y3, . . . . y„ denote respectively the first, second, third, . . . . wth differential of y with respect to (x). Let Ur denote f d y r, i. e. the integral of a function involving x, y, y„ y2. . . . with reference to yr alone. Let V,. in like manner denote — when the differentiation is supposed dyr effected with reference to yr alone, so that Vr Ur F = F . The next definition is the most important, as it is that on which all our subsequent calculations will depend. We may suppose F differentiated (m) times with reference to y„, yn_i, or yn_2, &c., and yn, y»_i, or yn2> &c., as the case may be, afterward equated to zero. We shall denote this entire process by Z(“}, Z&& &c. The following definition is also of importance: we shall denote the ex pression d . d . . , T*+ y ' dy+ »’ d f + y° W ,+ ' + dyr
在前面的关于符号微积分的回忆录中，已经为非交换符号的乘法和除法构造了系统，这些符号遵循一定的组合定律;这些方程组足够了，r个线性微分方程。但是，当我们开始考虑非线性方程时，我们立刻发现这些方法是不适用的，必须发明一些新的计算方式和新的方法，以便使非线性函数达到允许用符号代数来处理的条件。这就是完整的回忆录的目标。布尔教授在他的《微分方程论》中给出了一种由M. Sarrus提出的方法，通过这种方法我们可以确定给定的非线性函数是否是完全微分函数。任何读过布尔教授的论文的人都会看到，这种方法相当于:找到一个非线性函数可以用微分符号在外部可见的条件。在下面的文章中，我已经给出了一个符号，通过这个符号，我获得了这些条件的实际表达式，以及在分解过程中产生的符号余数，并扩展了我的研究，以确定非线性函数用微分符号的线性函数进行符号分解的结果。设F (x, y, y) l (y2, y3)Y ' ')是任意非线性函数，其中% y2, y3， . . . .Y”分别表示第一，第二，第三，. . . .y关于(x)的微分，设Ur表示f y r，即包含x, y, y ' ' y2. . . .的函数的积分只针对你一个人。让V,。以同样的方式表示-，即假定微分只与r有关，从而使Vr Ur F = F。下一个定义是最重要的，因为我们以后的所有计算都将依赖于它。我们可以假设F对y ' '， yn_i，或yn_2， &c微分(m)次。，和yn, y»_i，或yn2> &c。视情况而定，后来等于零。我们将用Z("}， Z&& &c表示整个过程。下面的定义也很重要:我们将表示表达式d。解析:选D。， T*+ y ' dy+»' d f + y°W，+ ' + dyr
{"title":"On the calculus of symbols.—Fourth memoir. With applications to the theory of non-linear differential equations","authors":"W. H. Russell","doi":"10.1098/rspl.1863.0087","DOIUrl":"https://doi.org/10.1098/rspl.1863.0087","url":null,"abstract":"In the preceding memoirs on the Calculus of Symbols, systems have een constructed for the multiplication and division of non-commutative pmbols subject to certain laws of combination ; and these systems suffice ,r linear differential equations. But when we enter upon the consideration f non-linear equations, we see at once that these methods do not apply, t becomes necessary to invent some fresh mode of calculation, and a new iotation, in order to bring non-linear functions into a condition which dmits of treatment by symbolical algebra. This is the object of the f l owing memoir. Professor Boole has given, in his Treatise on Diffeiential equations,’ a method due to M. Sarrus, by which we ascertain whether a jiven non-linear function is a complete differential. This method, as will )e seen by anyone who will refer to Professor Boole s treatise, is equivalent :o finding the conditions that a non-linear function may be externally livisible by the symbol of differentiation. In the following paper I have riven a notation by which I obtain the actual expressions for these con ditions, and for the symbolical remainders arising in the course of the livision, and have extended my investigations to ascertaining the results )f the symbolical division of non-linear functions by linear functions of the symbol of differentiation. Let F (x, y, y lt y2, y3 , . . . y„) be any non-linear function, in which % y2, y3, . . . . y„ denote respectively the first, second, third, . . . . wth differential of y with respect to (x). Let Ur denote f d y r, i. e. the integral of a function involving x, y, y„ y2. . . . with reference to yr alone. Let V,. in like manner denote — when the differentiation is supposed dyr effected with reference to yr alone, so that Vr Ur F = F . The next definition is the most important, as it is that on which all our subsequent calculations will depend. We may suppose F differentiated (m) times with reference to y„, yn_i, or yn_2, &c., and yn, y»_i, or yn2> &c., as the case may be, afterward equated to zero. We shall denote this entire process by Z(“}, Z&& &c. The following definition is also of importance: we shall denote the ex pression d . d . . , T*+ y ' dy+ »’ d f + y° W ,+ ' + dyr","PeriodicalId":20661,"journal":{"name":"Proceedings of the Royal Society of London","volume":"1 1","pages":"423 - 432"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspl.1863.0087","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62165987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
to the plane of reflection, when the suspended particles became finer, and therefore the beam more nearly continuous.” Through the courtesy of its owner, I have been permitted to see and to experiment with the piece of plate glass above referred to. Placed in front of the electric lamp, whether edgeways or transversely, it discharges bluish polarized light laterally, the colour being by no means a bad imita tion of the blue of the sky. Prof. Stokes considers that this deportment may be invoked to decide the question of the direction of the vibrations of polarized light. On this point I would say, if it can be demonstrated that when the particles are small in comparison to the length of a wave of light, the vibrations of a ray reflected by such particles cannot be perpendicular to the vibra tions of the incident ligh t; then assuredly the experiments recorded in the foregoing communication decide the question in favour of Fresnel’s assumption. As stated above, almost all liquids have motes in them sufficiently nu merous to polarize sensibly the light, and very beautiful effects may be obtained by simple artificial devices. When, for example, a cell of dis tilled water is placed in front of the electric lamp, and a slice of the beam permitted to pass through it, scarcely any polarized light is dis charged, and scarcely any colour produced with a plate of selenite. But while the beam is passing through it, if a bit of soap be agitated in the water above the beam, the moment the infinitesimal particles reach the beam the liquid sends forth laterally almost perfectly polarized light; and if the selenite be employed, vivid colours flash into existence. A still more brilliant result is obtained with mastic dissolved in a great excess-of alcohol. The selenite rings constitute an extremely delicate test as to the quantity of motes in a liquid. Commencing with distilled water, for example, a thickish beam of light is necessary to make the polarization of its motes sensible. A much thinner beam suffices for common water; while with Briicke’s precipitated mastic, a beam too thin to produce any sensible effect with most other liquids, suffices to bring out vividly the selenite colours.
{"title":"I. On the thermal resistance of liquids","authors":"F. Guthrie","doi":"10.1098/rspl.1868.0034","DOIUrl":"https://doi.org/10.1098/rspl.1868.0034","url":null,"abstract":"to the plane of reflection, when the suspended particles became finer, and therefore the beam more nearly continuous.” Through the courtesy of its owner, I have been permitted to see and to experiment with the piece of plate glass above referred to. Placed in front of the electric lamp, whether edgeways or transversely, it discharges bluish polarized light laterally, the colour being by no means a bad imita tion of the blue of the sky. Prof. Stokes considers that this deportment may be invoked to decide the question of the direction of the vibrations of polarized light. On this point I would say, if it can be demonstrated that when the particles are small in comparison to the length of a wave of light, the vibrations of a ray reflected by such particles cannot be perpendicular to the vibra tions of the incident ligh t; then assuredly the experiments recorded in the foregoing communication decide the question in favour of Fresnel’s assumption. As stated above, almost all liquids have motes in them sufficiently nu merous to polarize sensibly the light, and very beautiful effects may be obtained by simple artificial devices. When, for example, a cell of dis tilled water is placed in front of the electric lamp, and a slice of the beam permitted to pass through it, scarcely any polarized light is dis charged, and scarcely any colour produced with a plate of selenite. But while the beam is passing through it, if a bit of soap be agitated in the water above the beam, the moment the infinitesimal particles reach the beam the liquid sends forth laterally almost perfectly polarized light; and if the selenite be employed, vivid colours flash into existence. A still more brilliant result is obtained with mastic dissolved in a great excess-of alcohol. The selenite rings constitute an extremely delicate test as to the quantity of motes in a liquid. Commencing with distilled water, for example, a thickish beam of light is necessary to make the polarization of its motes sensible. A much thinner beam suffices for common water; while with Briicke’s precipitated mastic, a beam too thin to produce any sensible effect with most other liquids, suffices to bring out vividly the selenite colours.","PeriodicalId":20661,"journal":{"name":"Proceedings of the Royal Society of London","volume":"1 1","pages":"233 - 236"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1098/rspl.1868.0034","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62188108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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