- 
156 
studies and occupations, the seeing eye was of infinite— 
even fundamental—service. 
After a brief 7észmeé of the history of botany in 
England and an appreciation of the services rendered to 
the science by men like Grew, John Ray, Robert Brown 
and others, Sir William expressed the hope and belief 
that England would again attain and retain the premier 
place in botanical study and research, and that the 
botanists of Liverpool would so use their splendid 
opportunities as to maintain the reputation of their 
country. He went on to speak of the great industries 
which had their origin in botanical discoveries, of the 
value of the science to medicine, and pointed out a fact 
too often overlooked that plants were intimately con- 
nected with every phase and stage of human life until, 
in the final act of the drama, they facilitated our decay. 
After a vote of thanks to Sir William Thiselton-Dyer 
for his address, proposed by Sir John Brunner, M.P., 
and seconded by Prof. Harvey Gibson, and the pre- 
sentation of memorial keys to Mr. Hartley and Sir 
Hartley Laboratories, Liverpool. 
Fic. 2.—Elementary Laboratory. 
William Thiselton-Dyer, the guests adjourned to the 
Hartley Laboratories, which were thrown open for 
inspection. 
THE HUGH MILLER CENTENARY. 
IR 2 proposal to celebrate the centenary of the birth 
of Hugh Miller during the present year has met 
with general approval, and the erection of an institute 
bearing his name in Cromarty has been admitted to be 
the best means of appropriately celebrating his memory. 
It is intended that the Hugh Miller Institute shall take 
the form of a museum, where any relics pertaining to 
Miller can be kept ; and a free library and reading room. 
The centenary committee have had the promise of 
support from Hugh Millers admirers in America and 
the colonies, as well as at home, and Mr. Carnegie, the 
generous supporter of such institutions as the proposed 
institute, has made the handsome offer to give 1oo/. for 
every 100/. raised by the committee. 
It is desirable that the memorial should be as widely 
representative as possible, and the committee therefore 
appeal to all who appreciate the work accomplished by 
Hugh Miller in science and literature for contributions, in 
order that the scheme may be sufficiently advanced by 
the aniversary of his birth in October. 
Contributions should be sent to the Treasurer, Com- 
mercial Bank, Cromarty. 
NO. 1702, vou. 66] 
NATURE 
[JUNE 12, 1902 
Ee. re 
The movement has the support of the following :— 
Lord Balfour of Burleigh, Secretary for Scoiland: Sir 
Archibald Geikie, F.R.S., “LL.D. ; Prof, Masson, LL.D. ; 
Sir John Leng. M.P.; Sir Walter Foster, M.P.; C. if 
Guthrie, K.C., Sheriff of Ross and Cromarty ; W. C. Smith, 
LL.B, ; Prof. Duns, Edinburgh ; A. Taylor, Innes, Esq., Edin- 
burgh 3 Prof. Clarke, State College, New York ; W. Robertson 
Nicol, LL.D. ; A. Bignold, Esq., M.P. ; + Principal Rainy, 
D.D. ; Alexander Whyte. D.D.; Colonel Ross. C B., of 
Cromarty : Mr. James Barron, Juverness Courier; W. J- 
Watson, B.A., Secretary Inverness Field Club. 
J.-Bain, Hon. Sec., 
Hugh Miller Centenary Committee. 
Cromarty, May, 1902. 
LAZARUS FUCHS. 
HE name of Lazarus Fuchs will always be associated 
__ With the theory of linear differential equations, to 
| which he gave an extraordinary impulse by his famous 
memoir published in the sixty-sixth volume of 
Crelle’s Journal. In this paper the methods of 
modern function-theory are brought to bear upon 
the long-familiar process of solving a differential 
equation by series. The coefficients of the equation 
being supposed to be uniform analytical functions 
with isolated singularities, it is shown how to obtain, 
in the neighbourhood of an ordinary point, a com- 
plete set of independent integrals ; the analytical 
form of these solutions is determined, and shown 
to depend upon a certain fundamental or indicial 
equation. It is proved, also, that the singularities 
of the integrals may be deduced from the coeff- 
cients without integration, and the notion of 
regular integrals is developed. The distinction is 
made between the integrals which involve log- 
arithms and those which do not, and attention is 
drawn to those equations the integrals of which 
have no essential singularity. Thus in a single 
memoir of moderate length all the essential 
features of an extensive theory are presented in a 
clear and comprehensive outline. 
In the rapid development which followed the 
publication of this memoir, the author naturally 
tooka prominent part. Among his important con- 
tributions may be mentioned his researches on 
linear equations with algebraic integrals, on constructing 
linear equations the integrals of which have assigned 
singularities, and on equations the integrals of which are 
“connected by algebraic relations. An instructive illustra- 
tion of the general theory is given by his memoir on the 
equation satisfied by the elliptic integrals K, Kk’. 
When the independent variable describes a closed 
curve, a set of integrals undergo a linear substitution, 
and all the substitutions arising from different paths 
| form a group associated with the equation. M. Poincaré 
assigned the name of Fuchsian functions to functions 
invariant for a group of linear transformations of the vari- 
able in recognition of Fuchs’s results concerning equations 
of the second order. 
Fuchs’s mathematical papers are very pleasant to read 
and free from that tendency to heaviness which is apt to 
belong to memoirs on differential equations. He had 
! the faculty of bringing out clearly the really important 
points without over-elaborate detail, and he did not 
disdain to show the power of his methods by applying 
them to specific and definite problems, In these respects 
he may be compared with Halphen. While admitting 
that his way was prepared by the work of Cauchy, Briot 
and Bouquet, and Riemann, we may fairly claim for him 
that he has been the effective pioneer in a vast and 
fascinating region. 
It is interesting to remember that Henry Smith, in a 
| presidential address to the London Mathematical Society 
