468 Royal Society : — " '""" 



thermometers which cannot be found. The observations were con- 

 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 circum- 

 stance 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 dis- 

 cordance. 



If the Eighth Series is rejected, it appears that Colonel Sabine's 

 coefficient ought to be increased by about -j^^th part ; and on intro- 

 ducing this correction into the computations of the Harton Experi- 

 ment, the result for the earth's mean density is 6-809. If the 

 Eighth Series is retained, the correction is reduced to less than one- 

 fourth 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 ellip- 

 ticity of the earth in modifying the numerical results of the Harton 

 Experiment. It appears that the numbers found in the paper ought 

 to be multiphed by 



, __ equatoreal centrifugal force 



gravity 

 e=ellipticity 

 Z= 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. 



" On the Mathematical Theory of the Stability of Earthwork and 

 Masonry." In a Letter to Prof. Stokes, Sec. R.S. By W. J. Mac- 

 quorn Rankine, Esq., C.E., F.R.S. 



In the preparation of my course of lectures, I ha\|f found it neces- 

 sary to re-investigate much of the above-named branch of mechanics, 

 and I have now a paper in preparation on the subject, which I pro- 

 pose to offer to the Royal Society when it is ready. In the mean- 

 while, 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 



