2 REPORT—1857. 
bairn have added so much to the resources of constructive engineers.—4. We called for 
the investigations, and supplied funds for those discussions of tidal phenomena by 
which Dr. Whewell has not only thrown light on a most difficult portion of hydrody- 
namics, but given precious aid to the practical navigator.—5. Two years before that 
meeting, a great physicist had declared that to improve by theory the form of ships 
was as hopeless as to get the equation ofa breaker; at that meeting a young man, then 
unknown, produced the germ of those researches, which, extended under our auspices, 
and largely aided by our pecuniary grants, have given J. Scott Russell a world-wide 
fame, and made possible the construction of those noble ships which, during the last 
month, have borne from your bay, at a speed twice what was once thought attain- 
able, their freight of heroes, to uphold our nation’s power, to avenge our slaughtered 
countrymen.—6. Lastly, we set on foot that system of magnetic observation of 
which you heard last night, which has added so much to our knowledge of terres- 
trial magnetism ; nay, which has gone beyond our globe and opened a new range 
for inquiry, by showing us that this wondrous agent has power in other parts of the 
solar system. Is not this a list of achievements on which those of us who were 
then present may look with just pride? May we not venture to hope that when, 
in the next of its cycles, the Association shall return to this city, those who may 
survive to witness that event shall have it in their power to record one yet more 
brilliant? I cannot expect to be of the number, but the recollection that I have, 
however slightly, been a partaker in those labours in which the Association has 
worked so well to increase the knowledge and happiness of mankind, and the anti- 
cipation that it will continue to advance in the paths of the purest and highest wis- 
dom, will cheer the remnant of my appointed time. For that advance we must 
prepare the way, and an occasion seems to offer now. The combined series of mag- 
netic observations to which I have referred has just closed; and I cannot doubt that 
it is our duty to seek for its continuance and extension on a scale commensurate to 
the enlarged views which it has already opened. I shall therefore soon seek to 
obtain your concurrence in a recommendation to this effect, and am confident that 
we shall open a path to a series of new discoveries as much surpassing those which 
we have commemorated, as our present experience of the mode of making these 
researches transcends the imperfect methods with which they were commenced. I 
shall detain you no longer from your work. To mark our sense of the incalculable 
importance of pure mathematics, we always endeavour to devote to it the first days 
of our week. I cannot, therefore, promise anything attractive, or even intelligible 
to all of you; but Monday will be given to Meteorology, and Tuesday to Optics, 
Electricity and Magnetism, which I hope may prove of more general interest. 
On the Theory of Astronomical Observations, and on some related 
Questions. By Professor Booxt, RS. 
The author gave a short réswmé of Gauss’s theory of the value of astronomical 
and other observations, and the method of least squares. He then showed that the 
common mode of taking means depended on a theorem, which was only one case of 
a much more general theorem in probabilities which he had arrived at, and which he 
explained in full to the Section, with the formule, which he wrote on the board. 
He showed that it is only where each of the observations is equally trustworthy that 
our common mode of taking means can lead to correct results; and then showed 
that the same theorem furnished the principle for estimating the dependence to be 
placed on testimony and other kindred questions. 
On certain Additions to the Integral Calculus. By Professor Booxr, F.R.S. 
On a System of Geodetics and the Conjugate System, traced on the two Sheets 
of a Surface of Centres, with special reference to the Case in which the 
Surface of Centres consists of an Ellipsoid and a Confocal Hyperboloid. - 
By Professor Curtis. 
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