JuLy 17, 1902 | 
NATURE 
271 
has attempted, and with real success, to show what 
manner of man Gilbert was, wherein lay his genius, what 
were his merits, and what also were his faults and failings. 
Mr. Benham dwells on the circumstance that, although 
Gilbert’s actual discoveries were few and crude, he must 
be judged rather by the spirit of hiswork. ‘“‘ He was not 
the builder of sciences, but the architect of a truly 
scientific spirit ; and his life-work consisted in the doc- 
trine, new to England, that all scientific knowledge must 
be founded on practical experiment and observation 
alone, instead of upon speculations and theories evolved 
out of inner consciousness.” The successive chapters of 
the book deal with the old magnetic philosophies, mag- 
netic motions and electric force, the magnet’s “ directive 
virtue,” the variation of the compass, the dip and “ orbes 
of virtue” of the magnet, the life of the Universe (in 
which Gilbert, although no Manichean, was clearly a 
believer) and the Copernican theory. The author is 
particularly happy in his treatment of this last topic ; but 
throughout the analysis of Gilbert's work is accurate and 
discriminating. The book is illustrated with a picture of 
Gilbert’s terrella, and another of his tombstone in the 
church of Holy Trinity, Colchester. 
The Vocal System based on the Fundamental Laws of 
Language. By G. Lionel Wright. Pp. 20. (Pub- 
lished by the Author, Upper Belgrave Road, Clifton, 
Bristol.) Price rs. net. 
IT is now recognised that teaching to read is not the 
simple matter which it was once thought to be. In 
recent years one system has followed another in rapid 
succession, and each has claimed in turn that by its 
introduction the time taken by the child to learn to read 
the mother tongue was much reduced. There seems to 
be a chance that these experiments may eventually 
reduce the difficulty of this first step in human education 
toa minimum. Mr. Wright proposes to make extensive 
use of the blackboard and of wivd voce methods of 
instruction, and to start teaching the child to read by 
making him learn the five vowels. When this has been 
accomplished, the learner is introduced, by carefully 
graduated steps, to certain combinations of vowels and 
consonants, which are clearly indicated in this brochure, 
and by following which Mr. Wright claims that children 
may read at the age of six. A somewhat minute 
examination of the contents of the pamphlet leads us to 
think that Mr. Wright would be well advised in making 
his instructions to the teacher much more detailed and 
explicit if he is anxious that his system should become 
widely adopted, for at present the teacher will be, at 
several points, at a loss to know the next step in the 
course of work. 
The Lake Counties. By W. G. Collingwood. (Dent's 
County Guides.) Pp. xii + 392; illustrated. (London : 
J. M. Dent and Co.) Price 4s. 6d. net. 
Tuis little volume—the fourth of the series to which it 
belongs—will be found invaluable to all who visit the 
Lake District. In addition to being an excellent guide, 
with a number of itineraries and many maps, it contains 
four chapters on the natural history of the district, the 
birds being described by Miss Armitt, the butterflies and 
moths by Canon Crewdson, the flora by Mr. S. L. Petty, 
and the geology by Prof. Hull. In the chapters on fox- 
hunting, angling and shooting, the sportsman will find 
abundant matter for interest, according to his particular 
taste. This volume fully maintains the high reputation 
of its predecessors, and is, in fact, all that a guide should 
be. Those tourists who wish to go more deeply into the 
natural history of one of the most interesting and beautiful 
districts in England will find all they want in the more 
pretentious volume by the late Mr. Macpherson entitled 
“Lakeland.” Reals 
NO. 1707, VOL. 66] 
LETTERS TO THE EDITOR. 
(Zhe Editor does not hold himself responsible for opinions ex- 
pressed by hts correspondents. Neither can he undertake 
to return, or to correspond with the writers of, rejected 
manuscripts intended for this or any other part of NATURK 
No notice zs taken of anonymous communications. 
Symbol for Partiai Differentiation. 
Pror. PeRRy’s difficulty (NATURE, May 15, p. 53) is with- 
out doubt a real one, and is deserving of serious consideration. 
In connection therewith the following extract from a paper at 
present passing through the press may be found interesting, at 
least on the historical side. It is in reference to a memoir of 
Jacobi’s published in the year 1841 in the twenty-second volume 
of Crelle’s Journal :— 
“The subject of the notation of differential-quotients is then 
entered on at some length (pp. 320-323), and the decision made 
to use 90 in the manner which soon afterwards came to be 
familiar. The insufficiency of this notation is not forgotten, 
however, although its advantages over the different devices of 
Euler and Lagrange are recognised, his illustrative example 
being the case of 02/0x where z is a function of x« and z, 
and z is a function of « and y. He puts the whole matter in 
a nutshell when he says that it is not enough to specify the 
function to be operated on and the particular independent 
variable with respect to which the differentiation is to be per- 
formed, but that it is equally necessary to indicate the involved 
quantities which are to be viewed as constants during the 
operation.” 
To this the following footnote is added :— 
““T may state in passing that in 1869 when lecturing on the 
subject I found it very useful to write 
px, ¥, z 5) Ts, t; uU,U 4 
$(% 92) » Slt mr), 2... 
and then indicate the number of times the function had to be 
differentiated with respect to any one of the variables by writing 
that number on the opposite side of the vinculum from the 
said variable; thus 
in place of 
13 2 
x, Vs a 
meant the result of differentiating once with respect to «, thrice 
with respect to y, and twice with respect to s. 
‘* Using this notation to illustrate Jacobi’s example, we see 
that if it were given that aa 
z= ox, u 
we should have 
dlace 
0:/Ox = px, u ; 
but that if it were given that 
c=ox,u and u= Wry 
then we should not be certain as to the meaning of 02/0., as 
it would stand for 
a eee 21: 1. 
px, u or Px, w+ Px, u. Wx, y 
according as # or y was to be considered constant.” 
Cape Town, S.A., June 5. THOMAS Murr. 
I am glad to think that a pure mathematician sees the diffi- 
culty met with by users of mathematics. I wish that men who 
write to me privately would publish their remarks. One cor- 
respondent says: ‘‘I think ‘the mathematicians’ made a rather 
stupid blunder when they introduced 9@ for partial differentiation. 
This way : nearly all differential coefficients ave partial ; even a 
complete one (assumed complete) may become partial by exten- 
sion of the field of operation. So an old investigation of Kelvin’s, 
for example, using d throughout, is, by ‘the mathematicians,’ 
replaced by the same using 0 throughout, except one or two 
here and there! What is the use? It gives a lot of trouble, 
and as printers haven’t always 0’s, or proper sized 0’s, it makes 
bad work. It should have been @ itself that was introduced for 
the exceptional use, thus making next to no alteration in the 
classical investigations.”” These are, indeed, my own views, 
but as my pupils go forward to University examinations I 
