^{page 671 note *} Though the Vyse and Perring observations were so rough, yet they seem eminently honest and fair: and it must add additional weight to their testimony in this case, that neither of these gentlemen seem to have had any idea at the time, of what refined results their observations might eventually be made to bring out, or what indeed the Pyramid itself contains in this direction; for in his 2d volume, Colonel Howard Vyse, enumerating his laborious assistant Mr Perring's conclusions about the Pyramid, says, that its height is to its base-side, as about 5 to 8; which gives no closer approximation to the value of π, then 3·200.

^{page 677 note *} This section, like most meridian sections published, since the time of Professor Greaves in 1637, agrees to overlook the small distance by which the passages of the Pyramid, though truly in the plane of the meridian, are slightly to the east of the true central meridian section of the Pyramid. See fig. 7, Plate XXVII.

^{page 682 note *} While at press, I am informed of the existence of a rare pamphlet, but have not yet been able to see it. The Origine and Antiquitie our English Weights and Measures discovered by their near agreement with such standards, that are now found in one of the Egyptian Pyramids. London. 1706Google Scholar. Anonymous: and reprinted in 1745, with the authorship attributed to Professor Greaves, of Oxford, who died in 1652.

^{page 686 note *} The history of the experimental determination of the earth's mean density, is a very interesting; one, and its honours fall almost entirely to Great Britain. It has been tried by the attraction of the plumb line on mountains; by the effect on a pendulum at the top and bottom of a mine, and by the “Cavendish experiment,” between the parts of a philosophical apparatus; and has varied in the first case from 4·5 to 5·4; in the second from 6 to 6·5; and in the last from 5·4 to 5·8; or in the latest, and most perfect trial of it, by Francis Baily, from 5·68 to 5·66. His own published mean is 5·675, but uncorrected for some circumstances which he himself thinks should be corrected, and which we have estimated, in accordance with his numerical indications, at–·003.—See further at p. 699.

^{page 689 note *} In place of 10 sacks= 1 coffer, there may be used, 2·5 sacks= 1 quarter; and, 4 quarters = 1 coffer.

^{page 699 note *} In further elucidation of the note on page 686, and the number 5·672,chosen as the best resulting value from Baily's Experiments for the Mean Density of the Earth, it may be mentioned, that in the last page of his valuable memoir, he gives the following several numbers as the exact foundations for his more popular announcement of 5·675, and desires his future readers to form their own idea of the real mean amongst them; viz.:—

Now, the simple mean of all these comes out 5·66908, but as that evidently gives too much importance to the latter results, which Mr BAILY did not allow to appearat all in the 5·675,—let us take a mean of the two, and we have 5·67204.

Again, if it be agreed that the first result is five times the weight of any one of the others, and then take the mean accordingly, we have 5·67158. Or, if it be further settled, that the same reasons which make the first more weighty than the second, make the second some what more weighty than the third, and so on to the fifth; that is, that every subsequent given result represents a less number of observations,—let us multiply the first by 10, and the others by 4, 3, 2, and 1, when we have for this form of the mean, 5·67227. And putting all these three probable means together, 5·67204, 5·67158, and 5·67227,—there appears for the final mean, 5·67196: sufficiently represented by our 5·672.

^{page 700 note *} Written in September 1864.