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Among the parers of this year, I may nvtice the elaborate 
research by Dr. Debus on ‘‘ The Chemical Theory of Gun- 
powder,” forming the Bakerian lecture ; the careful and long- 
continued investigations by Professors Liveing and Dewar on 
the spectra of water, and of carbon, and of mixed vapours. 
Nor must I omit mention of Dr. C. W. Siemens’ bold and 
original theory of the conversation of the solar energy, which 
has already given rise toso much discussion. It will be sufficient 
for me here to say that upon the questio:s therein raised the last 
word has been by no means said ; and that, whether the theory 
be ultimately establishid, or whether, like a pbcenix, it shall 
hereafter give 1ise to some other cutcome from its own ashes, it 
will ever be remembered as having set many active minds at 
work, and will always have a place in the’ history of Solar 
Physics. 
In Mathematics, definite integrals, and elliptic and the higher 
transcendents continue to occupy much attention, and in parti- 
cular our ‘* Transactions” contain an excellent contribution to 
the theta-functions of two variables, by Mr. Forsyth, of Liver- 
pool. ‘To the theory of invariants, Prof. Malet, of Cork, has 
given a happy extension in the direction of linear differential 
equations; but it is unnecessary to speak in detail of papers 
which either already are, or will shortly be, in the hands of the 
Fellows. I will only add that the ‘‘ Philosophical Transactions ” 
for 1882 will probably exceed in bulk, and not yield in interest 
to, those of any former year. 
Looking outside the circle of our own publications, there has 
been one step gained during the past year, which, although in 
some sense a matter of detail, is really of great importance ani 
interest. I allude to the paper by Lindemann, ‘‘ Ueber die 
Zahl w” (‘* Mathematische Annalen,” Band xx, p. 213). It had 
long since been shown that both the numbers mand 7 are 
irrational ; but hitherto no proof existed of the impossibility of 
effecting the quadrature of the circle by means of the straight 
line and circle, and ruler and compasses. Regarded from an 
algebraical point of view, every such construction must depend 
upon the solution of a quadratic equation, or rather of a series of 
quadratics whereof the first has for its coefficients rational 
numbers, and the succeeding members of the series only such 
irrational numbers as occur in the sclution of their predecessors. 
This being so, the final equation can always be trai sformed, by 
transposition of terms and squaring, into an equation of an even 
degree with rational coefficients. And, consequently, if it can 
be proved that + cannot be the root of any algebraic equation 
whatever with rational coefficients, the impossibility of the 
quadrature of the circle will be thereby also proved. Starting 
from Hermite’s researches (‘‘ Comptes Rendvs,” 1873), in which 
he established the transcendental nature of the nun.ber ¢, Linde- 
mann has supplied the proof required with reference to the 
uuuiber 7, It must be admitted that the proof is neither very 
simple nor very easy to follow ; and it remains only to te hoped 
that it may some day assume such a form as may influence the 
miids which still exercise themselves upon the hopeless problem 
of squaring the circle. 
A most important change in the relations between the Society 
and the Government in respect of State aid to science has been 
made this year. It will be in the recollection of the Fellows that 
an experiment was made for a period of five years, during which 
the sum of 4,000/. was annually voted to the Science and Art 
Department, to be distributed at the recommendation of the 
Government Fund Commitee of the Royal Society. That 
experimental period terminated, as then mentioned in my address, 
last year. The grant to the Science and Art Department has 
been discontinued, and in the place of it an addition of 3,000/. 
per annum has been made to the Government grant, maki g 
4,coo/. in all, In concluding this arrangement the following 
stipulations were agreed to. The increased grant is to be 
administered by a Committee identical with the late Govern- 
ment Fund Committee ; a portion may be devoted to | ersonal 
grants, subject, however, to. special recommendations to the 
‘Treasury ; and, lastly, unexpended balances may be carried 
forward from year to year, as has hitherto been the case with 
the old government grant only. To the stipulation that the 
increased fund should be administered by the more extended 
committee the Society felt that no reasonable objection could be 
offered, because upon it the President and Council are repre- 
sented in full, and the ex officio members are in the majority of 
cases Fellows of the Society. The object of the second stipu- 
1. tion was, so far as the Society is concerned, to secure at the 
outset for the personal grants the consent and support of the 
Treasury, and thereby to preclude the chance of objection being 
sub-equently taken to any of our proposals under this head, 
The President and Council, however, recognising the importance 
of great caution in respect of personal grants, have of their 
own motion appointed a special sub-committee (in addition to 
the three previously existing), to which all personal applications 
recommended by any of the other sub-committees are specially 
referred, and without whese recommendation none can come 
before the General Committee. To the third mentioned point, 
viz., the power of retaining unexpended balances, the President 
and Council attach great value, because that power may enable 
the Committee to devote more of its funds than heretofore to 
some of the larger undertakings in scientific inquiry, leaving 
more of the smaller grants to the special funds already in exist- 
ence in the hands of the Royal and other societies. The meetings 
of this Committee will probably take place twice a year, in May 
and November. In the present year it will not be possible to 
hold the second meeting before December, but there will be 
advantages in holding it hereafter in November, as the entire 
annual grants will then be made by the same Committee, and 
under the sanction of the same Pre-ident and Council. In 
concluding these few remarks on the new arrangements, I cannot 
refrain from expressing my sense of the obligation under which 
the Society and Science at large are laid by the sympathetic and 
intelligent attention bestowed uyjon the subject by the then 
Financial Secretary of the Treasury, the late Lord Frederick 
Cavendish, 
Among other subjects referred to the Royal Society by Public 
Departments I may mention a rejue-t from the Board of Trade 
for advice upon the question of improving the existing means at 
the Standard Office for the purpose of comparisons, At the 
request of the President and Council, Sir Ceorge Airy, Colonel 
A. Ross Clarke, and Prof. Stokes acted as a Committee, and 
drew upa very careful report, the value of which was fully 
recognised by the Board of Trade. The report suggested certain 
improvements in the present arrangements; but, having reference 
to the duties of the Standard Office as defined by Act of Parlia- 
ment, it was not considered necessary to insist upon extreme 
scientific accuracy, such, ¢.g., as that attained by Colonel Clarke 
himself in his ‘‘Comparison of Standards” made at’ the 
Ordnance Survey Office at Southampton in 1866. 
The arrangements for the observation of the Transit of Venus 
have Leen steadily progressing. The parties have now all started 
for their stations, after their period of training under the super- 
intendence of Mr. Stone at Oxford. An adequate supply of 
instruments has been secured at moderate cost, and all the 
accessory parts have been procured and applied by the indefa- 
tigable care and forethought of our directing Astronomer. __ 
The English Expeditions for the observation of the approaching 
Transit of Venus are-organized as follows :— 
ACCELERATED INGRESS. 
Madagascar Observers.—Rev. S. J. Perry. Rev. W. Sidgreaves 
Mr. Carlisle. 
Cape Observatory Ob-ervers.—Mr. Gill and Staff. 
Aberdeen Road Observers.—Mr. Finlay, First Assistant of the 
Cape Observatory. Mr. Pett, Third Assistant of the 
Cape Observatory. 
Montagu Roat Observers.—Myr. A. Marth, 
Stevens. 
Mr. €. MM: 
RETARDED INGRESS, 
Bermuda Observers.—Mr. J. Plummer. 
Capt- Washington, k.E. 
Famaica Observers.—Dr. Copeland, 
Mr. Maxwell Hall. 
Barbadoes Observers.—Mr. C, G. Talmage. 
R.A. 
Besides the observers at these stations, the Canadian Govern- 
ment kas arranged to place three 6-inch and some smaller 
telescopes in the field. Lieut. Gordon of Toronto was sent by 
the Canadian Government to England to make himself master 
of the proposed arrangements, and to secure the necessary 
instrumental equipment. 
ACCELERATED EGRESS. 
The stations for Retarded Ingress are also available for 
Accelerated Egress. 
Lieut. Neate, R.N. 
Capt. Mackinlay, R.A. 
Lieut. Thomson, 
