small error in the distance, when dis so small as 6 or 7 inch, are considerable; and to this source we ought perhaps to attribute the error in the last observation in Table III. being plus instead of minus, as it ought to be from the omission of the second and following terms.

It appears then, that, within the limits of the values of the distance d', at which the observations were made, w being extremely small, and about 4°, we may, without any sen↓ sible error, omit the second and following terms in the expression for the force, which is thus reduced to the form which represents very accurately the several values of a, which is the measure of that force, in the experiments.

I am aware that it may be objected to the method of investigation which I have adopted, that the value of may not be constant for different values of d, nor that of a be constant

for every point of the ring, behind the portion r 4, even for the same value of d: but the variations of these being evidently within very narrow limits, no sensible error can arise from supposing them constant: the perfect coincidence between the formula deduced on this supposition, and that previously obtained from the experiments, proves clearly that this is the case, and that the assumptions which I have made are perfectly admissible.

After the very satisfactory explanation which Mr. Babbage and Mr. HERSCHEL have given of the general phænomena observed during rotation, on the principle that time is requisite both for the developement and for the dissipation of magnetism,* fully to establish the truth of the principle, it remained only to show, that the results obtained from Phil. Trans. for 1825.

calculation, founded on that principle, perfectly accord with those obtained from experiment; and this, I trust, I have done by the preceding experimental and theoretical details. Considering this then as an established principle, future investigations must be directed to the discovery of the function of the time on which the intensity of the induced magnetism depends, during the approach of a magnetic pole towards a physical point susceptible of magnetism, and also during its recess. I have stated what I consider to be not an improbable law; but the whole time occupied either in the developement of magnetism by induction, or in its dissipation, is so minute, that it appears extremely difficult to devise experiments that would be a direct test of such laws; and to the more indirect tests, derived from a comparison of such experimental results as the foregoing, with theoretical results derived from these laws, difficulties of analysis in general oppose themselves.

IX. Corrections to the reductions of Lieutenant FOSTER'S Observations on Atmospherical Refractions at Port Bowen; with Addenda to the Table of Magnetic Intensities at the same place. By Lieutenant HENRY FOSTER, R. N. F. R. S.

I

Read March 22, 1827.

HASTEN to acquaint the Royal Society with an error I have inadvertently committed in my observations on Atmospherical Refractions at Port Bowen, published in Part IV. of the Philosophical Transactions for 1826. The error alluded to arises from my having used an erroneous value of the divisions on the long level of the repeating circle, with which the observations were made. For the detection of this error, I am indebted to Captain KATER, who recently having had occasion to use the same instrument, found the value of each division of the level to be more than ten seconds in arc, of which he very kindly informed me, knowing that I had considered them as equal to single seconds only; and at the same time he wished me to acquaint him, if any accident had happened to the instrument, by which the level might have been changed. I knew that no accident had befallen the instrument, and that the level was the same which I had used; I therefore immediately proceeded to town, and in Captain KATER's presence ascertained the value of each division of the level to be 10".9.

In order to explain the source of the error into which I have fallen, I must state, that on receiving the repeating

circle in question, I was given to understand that the value of
each division of the level was equal to one second in arc :-
and as this instrument was the same that had been employed
by Captain SABINE, in his experiments on the pendulum, I
took no steps to examine this point for myself, for it never
once occurred to me that there could exist a doubt on the
subject.

The following, however, are the corrected Tables, which
are similarly numbered with those they are intended to be
substituted for, in pages 220 and 223 of Part IV. of the Phi-
losophical Transactions, for 1826.

Table VII. page 220, Philosophical Transactions, Part IV. 1826.

Observations for determining the apparent altitude of Arcturus at the time of setting, by Lieutenant FOSTER's upper telescope.

The corresponding observations for refraction are contained in Tables VIII. and IX. pages 221 and 222 in Part IV. for 1826.

Ο

Mean to be used in Table VIII. 7 35 12,68 instead of 7 35 18,43
Micrometrical Measure as before

+49,82

Altitude to be used in Table IX. =7 37 2,50 instead of 7 37 8,14

The principal vernier was not reset to zero after the observations on the 18th, but the readings were continued in the subsequent observations, except on March 4th, when the principal vernier was reset to zero.

Table X. page 223; Part IV. for 1826.

Observations for determining the apparent altitude of a Aquila at the time of setting, by Lieutenant FOSTER's upper telescope

The corresponding observations for refraction are contained in Tables XI and XII; pages 224 and 225 in Part IV. for 1826.

* The principal vernier not reset to zero, and the observations are continued from the preceding reading.

P. S. It is to be regretted, that the observations by Lieutenant Ross, given at the end of the Paper alluded to, must now be wholly rejected; in consequence of the original observations involving the erroneous datum dependent upon the level, having been left on board the Fury at the time of her loss.

The extremely low temperature of the atmosphere, in