Leibniz and the Vis Viva Controversy.
Methods of dealing with connected systems.
Example of correct methods by Newton and others before D’Alembert.
D’Alembert’s enunciation.—Its historical importance.
Euler. The Bernoullis, etc. Laplace, the flower of this stage of development.
Lagrange and Virtual Velocity.
This is the germ of the method of energy which was fully developed in mathematical form in the Mecanique Analytique, but very little appreciated outside the inner circle of mathematicians till the physical theory of energy became generally known.
Mathematical development of higher dynamics. (See Cayley’s Brit. Ass. Report, 1857 and 1862? specially Hamilton and Jacobi.)
Effect of T and T' since 1867. Kirchoffs notions in beginning of Vorlesungen (not equal to Lagrange, but worth noticing).
I also think that Clausius’ equation and definition of “Virial” is important.
The dynamics of other varieties of space than our own requires very brief notice indeed.—Yours truly,
J. Clerk Maxwell.
To W. Garnett, Esq.
Glenlair, Dalbeattie, 24th July 1877.
... There is a great slur over the word mechanics since a few poets and biologists have misused it. Pratt thought it a fine word.
The result of motion without reference to time I call Displacement. Kinematics must involve the idea of time if it treats of continuous displacements, velocities, and accelerations, though it does not contain within itself materials for comparing different intervals of time. For this we must go to the science which deals with matter; call it Kinetics, Dynamics, or Mechanics.
But I consider that Statics also deserves a place on the same level as Kinematics, as it deals with the equivalence of different systems of forces. But I do not agree with Whewell that Statics is more elementary than Kinematics....
To the Same.
Glenlair, 11th August 1877.
Your experiments on electrified paraffin oil are excellent, and may lead to increase of knowledge.
If the fluid dielectric and also the air are perfect insulators, nothing can get electrified, but the equation at the surface, instead of being normal upper P equals normal upper P 0. will be normal upper P plus StartFraction 1 Over 8 n EndFraction left parenthesis normal upper K squared minus 1 right parenthesis StartFraction ModifyingAbove d normal upper V With quotation dash Over d nu EndFraction vertical bar squared equals normal upper P 0 (excluding capillary action) where StartFraction d upper V Over d nu EndFraction is the resultant electric force normal to the surface and just outside it. This causes the surface to rise wherever the normal force is great, or close to the electrodes.
The science of displacements is in Euc. I. 4, etc., and wherever one figure is placed upon another. It belongs to the method of contemplating the relations of two figures which may be supposed to co-exist, though we may also suppose that they are copies of the same figure in different positions.
But just as we assume that distance is a continuous quantity capable of measurement, though all our attempts at measurement are made with instruments made of non-rigid and discontinuous matter, so we may assume that time is a continuously flowing quantity capable of measurement, though we have not yet found out any accurate method of comparing distant intervals of time.
Now Kinematics requires no more than this notion of time, as the common independent variable t. If we suppose that tau is that (unknown) which flows uniformly, then for kinematical purposes it is enough that t is a function of t; but when we come to Kinetics proper we must have StartFraction d squared t Over d tau squared EndFraction very small.
Have you read Julius in Nature, about the beginning of June? [14th June].
The most constant things we know are the properties of bodies. For instance, water in equilibrium with ice and vapour gives us a good deal.
I. A unit of density (not the orthodox one) StartFraction upper M Over upper L cubed EndFraction equals upper D.
II. A unit of pressure (too small for practical use) StartFraction normal upper M Over upper L upper T squared EndFraction equals normal upper P.
III. A unit of time (namely, the time of revolution of a satellite just grazing a sphere of water) =normal upper T.
These three quantities being independent of each other give normal upper M, normal upper L and normal upper T.
StartFraction normal upper P Over normal upper D EndFraction gives a left parenthesis velocity squared right parenthesis which could also be got from the StartFraction normal upper P Over normal upper D EndFraction of the vapour (a different one).
Then this gives also a standard temperature; all that we want is to get pure water.
To the Same.
Glenlair, 23d August 1877.
I have been copying Cavendish on the resistance of electrolytes. If there is any one who would try a few of them roughly in the U tube, it might be interesting to compare with Cavendish’s results. For weak solutions Kohlrausch may be referred to.
Sea Salt (Chloride of Sodium.)
| Experiments in January 1781. | |||
| Watered to 1 of Salt. | Resistance. | Resistance times quantity of Salt. | |
| Saturated sol. | 3 dot 78 | dot 602 | |
| 12 | 1 dot 91 | dot 602 | |
| 30 | 3 dot 97 | dot 500 | |
| 70 | 8 dot 8 | dot 475 | |
| 143 | 15 dot 75 | dot 352 | |
| 1000 | 93 dot 02 | dot 352 | |
| 20,000 | 18 dot 23 | dot 345 |
Salt in 20,000 conducts about 7 times better than distilled water.
Salt in 69 of water conducts 1·97 times better at 105 Superscript ring Baseline normal upper F period than at 58 one half Superscript ring Baseline period.
If Professor Liveing is in Cambridge, could you ask him to put me in the way of finding the best book on chemistry for the year 1777, so as to obtain the equivalents and the names of salts used by Cavendish?
The numbers in the first columns are the quantities which were equivalent to the “acid” in solution of 1 of salt in 29 of water. 3 dot 2 Sal Sylvii (potassium chloride). 2 dot 3 Sal Amm. (ammonium chloride). 14 dot 10 Calc. S.S.A. (?) 2 dot 21 Calcined Glauber's Salt (sodium sulphate). 3 dot 17 Quadrangular Nitre (sodium nitrate). 5 dot 19 Salt D. (?)
The solutions were 3, 10, 12.
I am going to try if this is Troy or Apothecaries’ weight.
Saturated solution (1 in 3·78) of common salt has 437,000 the resistance of iron wire. New distilled water has more resistance than distilled water kept a year.
All these results and many more were got by comparison of the strength of shocks taken through Cavendish’s body. I think this series of experiments is the most wonderful of them all, and well worth verification.
Cavendish is the first verifier of Ohm’s Law, for he finds by successive series of experiments that the resistance is as the following power of the velocity, 1·08, 1·03, ·980, and concludes that it is as the first power. All this by the physiological galvanometer.
... Can you solve the equation StartFraction d z Over d x EndFraction left parenthesis StartFraction d squared z Over d y squared EndFraction minus 2 StartFraction d squared z Over d x d y EndFraction right parenthesis plus StartFraction d z Over d y EndFraction left parenthesis StartFraction d squared z Over d x squared EndFraction minus 2 StartFraction d squared z Over d x d y EndFraction right parenthesis equals 0 question mark
z equals StartFraction normal upper A Over x y EndFraction is a solution. Find the general ditto.
To Professor Lewis Campbell.
11 Scroope Terrace,
Cambridge, 5th January 1878.
It is more than a month that I have had your letter lying by me. I am glad you like Chrystal. His departure is a great loss to the laboratory, as it is difficult to find any one to take up heavy work. W. D. Niven (brother of the competitor) is going in for a heavy piece of work on conduction of heat in gases. I am no judge of Greek plays, but I think that your success in choruses is fully equal to that in dialogue, considering the greater difficulty, not only in the interpretation, but in guessing the kind of effect, musical, rhythmical, rhetorical, poetical, and pictorial, which was aimed at in the delivery of the chorus.
We have all been conversing on the telephone. Garnett recognised the voice of a man who called by chance. But the phonograph will preserve to posterity the voices of our best speakers and singers. See Nature of Jan. 3d.
To W. Garnett, Esq.
Glenlair, 20th September 1878.
... Cavendish would speak of the pressure of a voltaic battery (only he hadn’t one), but we require to be educated up to his mark.
To the Librarian of the Royal Society.
Glenlair, Dalbeattie, 23d June 1879.
Dear Sir—Your information about FF.R.S. has been so useful to me that I now ask about Dr. G. Knight, F.R.S., librarian to the British Museum.
(1.) Is his name Gowan, Gowen, Gowin, or Godwin, for I find all four spellings current?
(2.) Who is the author of the paper in Phil. Trans. for 1776 (near the end of the vol.) describing his great magazines of magnets?
(3.) Are the magazines [sketch shown] mounted like great guns still in the possession of the R.S.?
(4.) Is the portrait of Gowin Knight, by Benjamin Wilson, F.R.S., among the pictures of the R.S.?
I have got from the Meteorological Office some Cavendish MSS. on Magnetism which prompt these enquiries and also this—
When the R.S. was at Crane Court had it a garden adjoining? Also, where was Crane Court?
Henry Cavendish and his father Lord Charles worked together at observations of the variation compass and dipping needle in the R.S. room and garden. Are the variation compass and dipping needle still in the R.S. collection?
Cavendish wrote out directions for using the dipping needle for Captain Pickersgill, Captain Bayley, Dalrymple.
Dalrymple, I find from Poggendorff, was hydrographer to the H.E.I.C. If Cavendish apportioned his instructions according to the capacity of the recipients, then their capacities would be in descending order, Dalrymple, Pickersgill, Bayley. Were any of these F.R.S.?
Also, was John Walsh, F.R.S., also M.P.?
Do not answer any of these questions which would involve trouble, but I have not here any means of answering them except by the aid of those who are among the records of the past. None of the questions are of vital importance, because I can leave out any statements I have made which are doubtful.—Yours very truly,
J. Clerk Maxwell.
Professor Maxwell was frequently invited to join the Victoria Institute, and in March 1875 he received a letter from the secretary conveying the special invitation of the President and Council to join the Society, “among whose members are his Grace the Archbishop of Canterbury, and other prelates and leading ministers, several professors of Oxford and Cambridge and other universities, and many literary and scientific men.” The following is all that has been found of a rough draft of his reply:—
Sir—I do not think it my duty to become a candidate for admission into the Victoria Institute. Among the objects of the Society are some of which I think very highly. I think men of science as well as other men need to learn from Christ, and I think Christians whose minds are scientific are bound to study science that their view of the glory of God may be as extensive as their being is capable of. But I think that the results which each man arrives at in his attempts to harmonise his science with his Christianity ought not to be regarded as having any significance except to the man himself, and to him only for a time, and should not receive the stamp of a society. For it is of the nature of science, especially of those branches of science which are spreading into unknown regions to be continually——[here the MS. ends].
[217] On 23d February, Professor Stokes (who had been urgent in pressing Maxwell to stand) wrote to him:—“I am glad you have decided to come forward.”
[218] Throughout the tenure of his Cambridge Chair Maxwell annually delivered a course of lectures on Heat and the Constitution of Bodies during the October Term; on Electricity in the Lent Term; and on Electro-Magnetism in the Easter Term. The character of these lectures very much resembled that of the early chapters in the Elementary Treatise on Electricity, which he wrote before taking the Cavendish papers in hand, and which was published in a fragmentary form by the Delegates of the Clarendon Press in October 1881. During the first four or five years that Maxwell lectured in Cambridge, candidates for the Ordinary or Poll Degree were compelled to attend professors’ lectures, and not unfrequently they would appear at the Cavendish Laboratory. Maxwell’s lectures were the delight of those who could follow him in his brilliant expositions and rapid changes of thought.
[219] Professor Westcott’s utterance on the same occasion, though less immediately relevant, ought not to be omitted:—“It was impossible to think of him whom they had so lately lost, to whom first the charge of the Cavendish Laboratory had been committed, Prof. Clerk Maxwell, and to recollect his genius and spirit, his subtle and profound thought, his tender and humble reverence, without being sure that that close connection between Physics and Theology which was consecrated by the past was still a living reality among them. That was an omen for the future. He felt, as probably all present felt, that he owed a deep debt of gratitude to him, both for his researches, and for the pregnant words in which he gathered up their lessons.”
[220] See Part II. In the official handbook to the collection, the articles entitled “General considerations respecting Scientific Apparatus” and “Molecular Physics,” were written by Professor Maxwell. When her Majesty the Queen visited the collection Professor Maxwell, at the invitation of the Lords of the Committee of Council on Education, attended as the representative of Molecular Physics.
[221] Maxwell had profited not a little by his own studies in this direction. But the Gallowegian tones are hard to modify, and even in his verse such rhymes as “hasn’t” = “pleasant” recall to those who knew him his peculiar mode of speech.
[222] How readily his thoughts took a serious turn, even in the earlier undergraduate days, may be seen in a letter (not given above) of 26th March 1852:—
“A. was sent for by telegraph to his sister: he found her past recovery, and she is since dead. The family is large, and till now was entire, so that the grief is great and new.
“The attributes of man, as one of a family, seem to be more highly developed in large families. The pronoun ‘we’ acquires a peculiar significance. The family man has an idea of a living home, to which he can in imagination retreat, and which gives him a steadiness and force not his own. He is one member of a naturally constituted society; he has protected his juniors and been protected by his seniors; and now he has the consciousness that he is but one of the arrows in the quiver of the Mighty, and that it is the interest of others as well as his own that he should succeed.”
[223] There was found amongst his papers a scrap on which he had written, in pencil, the whole of Shelley’s “Ode to the West Wind,” in all probability from memory, and as a distraction from anxiety or from severer study. His note-books, one of which he always carried with him, are full of the most miscellaneous jottings, plans of works, solutions of problems, extracts in prose and verse, etc.
[224] For an instance of tumorous mystification, see the letter to Mr. Garnett of 4th January 1877.
[225] He kept up the old habit of regulating the clocks at Glenlair by the sun, which, when on the meridian, threw the shadow of a stick upon a notch cut in the stone outside the door.
[226] An account of the last years of Maxwell’s life would not be complete without a reference to his acquaintance with Professor H. A. Rowland, formerly of Troy, and now of the Johns Hopkins University, Baltimore. Professor Rowland visited Maxwell more than once, and on these occasions much time was spent in comparing notes on electrical questions. Some instruments which Professor Rowland designed were not only identical with Maxwell’s in the relative dimensions of the several parts, but their absolute dimensions also were very nearly the same. After Maxwell’s death Professor Rowland pointed out some sources of error in the experimental determination of the Ohm as carried out at King’s College, and in the recent redetermination made by Lord Rayleigh in the Cavendish Laboratory these sources of error have been removed. Maxwell’s opinion of Professor Rowland was very high, and he frequently alludes to him in his correspondence, and more than once “Rowland of Troy, that doughty knight,” appears in his verses, where, as the American investigator in a certain branch of magnetic science studied here by Professor Oliver Lodge and Mr. Oliver Heaviside, he is in one place referred to as “One Rowland for two Olivers.” I well remember the interest with which Maxwell looked forward to Mr. Rowland’s first visit, and the meeting of “Greek and Trojan” on that occasion at Glenlair.
[227] An unfinished fragment of a new work on Electricity, in which he treads more closely than ever in the steps of Faraday, has been edited since his death by Mr. Garnett and published in 1881.
[228] Royal Institution.
[229] The name of an Assyrian harp of the shape nabla.
[230] See the Cambridge Journal of Philology, vol. V., No. 10, pp. 206, foll.
[231] Alluding to the passage of Plato’s Timœus, p. 40, which had given rise to the previous discussion.
[232] Tennyson’s In Memoriam.
[234] Introduces normal upper M StartFraction d squared x Over d t squared EndFraction equals normal upper X etc. See Maclaurin’s Fluxions.