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ducted entirely by Messrs. Dunkin and Ellis, Assistants of the Royal Observatory.
On discussing the results of the observations, there appears to be reason for supposing that a change has taken place in one of the pendulums after the Seventh Series. This appears from the circumstance that, though the Fifth and Seventh Series agree well, the Sixth and Eighth are discordant; and also from this circumstance, that the abstract relation between the two pendulums given by the Fifth, Sixth, and Seventh Series, agrees closely with that found at Harton ; but if the Eighth Series is included, there is a considerable discordance.
If the Eighth Series is rejected, it appears that Colonel Sabine's coefficient ought to be increased by about 4th part; and on introducing this correction into the computations of the Harton Experiment, the result for the earth's mean density is 6.809. If the Eighth Series is retained, the correction is reduced to less than onefourth of that just mentioned, and the earth's mean density is 6.623.
The author subjoins an investigation with which he has been favoured by Professor Stokes on the effect of the rotation and ellipticity of the earth in modifying the numerical results of the Harton Experiment. It appears that the numbers found in the paper ought to be multiplied by
l=latitude of place. On converting this formula into numbers, for Harton, the factor is found to be 1.00012, which produces no sensible change in the result.
At the equator the factor would have been 1.00679,
II. “On the Mathematical Theory of the Stability of Earth
work and Masonry.” In a Letter to Prof. STOKES, Sec.
In the preparation of my course of lectures, I have found it necessary to re-investigate much of the above-named branch of mechanics, and I have now a paper in preparation on the subject, which I propose to offer to the Royal Society when it is ready. In the meanwhile, it appears to me that the two fundamental principles on which my researches are based are of such a nature, that they may very properly be communicated to the Royal Society at once. They are as follows:
I. Principle of the Stability of Earth. At each point in a mass of earth the directions of greatest and least compressive stress are at right angles to each other; and the condition of stability is, that at each point the ratio of the difference of those stresses to their sum shall not exceed the sine of the angle of natural slope of the earth.
II. Principle of the Transformation of Structures. Let a structure of a given uniform transverse section be stable under a system of forces represented by given lines in the plane of section :—Then will any other structure whose transverse section is a projection by parallel lines of that of the first structure upon any other plane, be stable under the system of forces represented by the projections, upon the new plane, of the lines representing the first system of forces.
Example of the application of this principle. Let fig. 1 be an equilibrated arch with its abutments of the form (for example) proposed by M. Yvon-Villarceaux, suited for a horizontal extrados EF. OK, OA, and AB being given, all the dimensions of the arch and abutments are functions of those three quantities.
It is required to design an arch, fig. 2, for an extrados ef, at any given inclination, of any given span cd (measured parallel to the extrados), and in which ok=OK, oa=0A, and ab=AB, are the same as in the primitive arch fig. 1.
Solution. On any vertical plane passing through BK, and not coinciding with the plane of fig. 1, draw cod of the given length and inclination, intersecting COD in 0. Join Cc, Dd, and project the whole of fig. 1 on the new plane by lines parallel to Cc, Dd. The projection so obtained will be the figure of the arch and abutments required. Moreover, if the lines R, R, fig. 1, represent in length, direction, and position, the resultants of the pressures of the abutments on their foundations in the original arch, then will r, r, fig. 2, the projections of R, R, represent the corresponding resultants in the new arch; and in like manner, the thrust at a is the projection of the thrust at A.
W. J. MACQUORN RANKINE. Glasgow, 18th February, 1856.
Note. The horizontal foundation courses in fig. 2 do not form part of the projection of fig. 1, but are supposed to be added after the completion of the projection.
III. Letter from James P. JOULE, Esq. F.R.S. to Prof. STOKES,
in reference to the Paper of Dr. Woods read on the 10th of January 1856. Received February 22, 1856.
Manchester, February 21st, 1856. In the abstract of Dr. Woods' paper printed in the ‘Proceedings' for January 10th, the following remark occurs: “Mr. Joule published in the Philosophical Magazine for June 1852, a memoir proving exactly the same proposition, but giving me the merit of priority in a preliminary remark.” In justice to myself I must state that my actual words were I observe with pleasure that Dr. Woods has recently arrived at one of the results of the paper, viz. 'that the decomposition of a compound body occasions as much cold as the combination of its elements originally produced heat,' by the use of an elegant experimental process described in this Magazine for October 1851. I ought, however, to remark, that previous to the year 1843 I had demonstrated that the heat rendered latent in the electrolysis of water is at the expense of the heat which would otherwise have been evolved in a free state by the circuit.'
The memoir referred to by Dr. Woods was acknowledged by the French Academy in its Comptes Rendus' for Feb. 9, 1846, and according to established rule dates from that period. I may how- . ever observe that the law he claims was published by me in the Philosophical Magazine for October 1841, where I pointed out that the heat evolved by the combination of oxygen and hydrogen is equal to that due to the electrical intensity required to separate water into its elements. The same fact was reiterated in various subsequent papers, in which it is also proved that “the quantities of heat which are evolved by the combustion of the chemical equivalents of bodies are proportional to the intensities of their affinities for oxygen (Phil. Mag. xx. p. 111), a proposition which is given as his own by Dr. Woods, and considered by him as "an original idea."
JAMES P. JOULE.
March 13, 1856.
Sir BENJAMIN C. BRODIE, Bart., V.P., in the Chair.
The following communications were read :I. “On the presence of fibrils of soft tissue in the Dentinal
Tubes." By JOHN TOMEs, Esq., F.R.S. Received February 21, 1856.
(Abstract.) Referring to the structural characters of dentine, and to the prevailing belief that the dentinal tubes in the normal condition contain fluid, the author goes on to show that the recognized histological characters fail to account for the high degree of sensibility exhibited by the dentine when diseased, or when suddenly exposed by the removal of the enamel.
It is found, moreover, that the dentine is not uniformly sensitive throughout, but possesses a much higher degree of sensibility at the peripheral distribution of the dentinal tubes than deeper in the substance of the tooth ; and it is urged that these facts cannot be accounted for by the presence of a fluid in the dentinal tubes, nor by supposing that the hard unyielding dentine is intrinsically endowed with sensation. This view of the matter is borne out by the fact, that all sensibility is at once lost if the pulp of the tooth be destroyed.
Finding that the dentine owed its sensibility to the presence of the dentinal pulp, and knowing that the tubes have open extremities in contact with the pulp, the author was induced to examine carefully the contents of the tubes. The investigation resulted in discovering that the dentinal tubes, instead of containing fluid only, give passage to fibrils of soft tissue, which pass from the pulp into the tubes where these open upon the surface of the pulp-cavity, and from thence may be traced into the branches. The fibrils may be demonstrated by fracturing a perfectly fresh tooth, and then with a sharp knife taking very thin sections from the dentine near the edge of