520 
NATURE 
| SEPTEMBER 25, 1902 
LETIERS LOW LAE EL DIROR: 
(The 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 NATURE. 
No notice ts taken of anonymous communications. ] 
Symbol for Partial Differentiation. 
IN his first letter (p. 53), Prof. Perry very properly drew 
attention to the desirability of greater definiteness in the notation 
for partial differential coefficients in the case of functions of two 
variables, the essence of his remarks being that it is not enough 
merely to change @ into @, but that the variable which is for the 
nonce held to be constant should also be indicated. Apropos 
of this, and for the sake of historical interest, I quoted from a 
paper since published (Proc. R.S. Edinb xxiv. pp. 151-194) a 
short paragraph regarding a passage! in Jacobi’s writings of the 
year 1841, and containing a footnote with an old suggestion on 
the matter of notation. In his second letter (p. 271), Prof. Perry 
undertakes to show that this latter notation is objectionable so 
far as thermodynamics is concerned, and not to be compared 
with that which he himself uses. I regret to have to say that I 
was quite satisfied with his notation, and had no intention 
whatever of bringing the two into comparison, mine having been 
designed for much more complicated cases than those which 
occur in ordinary text-books on thermodynamics. His words 
are :— 
**T use one letter # where on Mr. Muir's suggestion I must 
use six distinct symbols if I have to express any differential 
coefficient of #, and if I have to express all the differential 
coefficients of vy P must use other six symbols ; altogether I must 
use thirty of these curious symbols instead of five common 
letters, and, furthermore, I must keep them all in my head.” 
This is, of course, all a mistake. Without any desire, there- 
fore, to spare Prof. Perry’s head, but merely in order to undo 
a misrepresentation, however unwitting, I am forced to point 
out that if we are to have a perfectly definite notation in this 
‘connection, we must indicate three things, viz. (1) the dependent 
variable # ; (2) the two independent variables, say v and £; 
and (3) whether the differentiation is to be performed with 
respect to v or #. Now, in the notation of my last letter these 
three are all cared for, thus 
1 —— 
Ev, p; 
or, since a vinculum contributes a ‘‘ curious” look to the symbol, 
Jet it be written 
E(?, p). 
The notation used by Prof. Perry, viz. 
ak 
( av i) 
is a trifle lengthier, but, as I have said, is equally definite, the 
main difference between the two arising from the fact that in the 
matter of differentiation he is a ‘‘ dee-ist’’ ; it is, however, ex- 
cessively cumbrous when used in the complicated cases for which 
the other was designed. Tuomas MuIR. 
Cape Town, South Africa, August 9. 
Ir would have been presumption on my part to express my 
private opinion, which is in favour of Dr. Muir’s symbol in 
general mathematical work, and so I referred merely to its use 
in thermodynamics where I think that such a use would be 
bad. 
The form he now gives is handier, being a mnemonic for my 
symbol, but I submit that it is different from what he would use 
in other applications of mathematics. According to his general 
1 
system, # (v, p) implies that there is a function of v and ¢ called 
1 
Pp (v, ) which is differentiated. But / (¢, £) implies that there 
is a function g (¢, #), and in thermodynamics / (7, $) is always 
1 Well worth reading. 
It begins at “‘ Ut distinguerentur,” on p. 320, and 
ends at bottom of p. 
322 of vol. xxii. of Credle's Journal. 
NO. 1717, VOL. 66] 
equal to 7 (¢, #). If # is a functional symbol there can be no 
such equality, and I still think that the forms in which I put 
Dr. Muir’s suggestion were the only ones consistent with his 
instructions. The new form would give no great trouble to a 
good mathematician perhaps, but it would quite unsettle the 
ordinary student of thermodynamics, 
Aman who insists on ‘‘dee-ism” in those parts of higher 
mathematics where it is clumsy is an obstacle to progress, But 
if Dr. Muir had my experience in dealing with men who know 
only a little mathematics and who wish to use what they know, 
he would, I think, be a “‘ dee-ist” in elementary work. 
JOHN PERRY. 
PROF. JOHN JAMES HUMMEL. 
OHN JAMES HUMMEL was born in 1850 at 
Clitheroe, in Lancashire. His father was a native 
of Switzerland and his mother English. 
His scientific education was obtained at the Zurich 
Polytechnic, where he studied under Bolley, Stadeler, 
Wislicenus and Weith. On returning to England in 
1870, he became chemist in the calico printworks of 
Messrs. Jas. Black and Co., of Alexandria, near Glasgow, 
and remained there six years, busily and successfully en- 
gaged with new dyeing problems incident to the introduc- 
tion of artificial alizarine and other coal-tar dyes. He 
was subsequently connected with other printing and dye- 
ing firms, until in 1879 he decided to gratify his taste for 
science and teaching by applying for the post of Instructor 
in the dyeing department established at the Yorkshire 
College by the Clothworkers’ Company of London. On 
taking up work at the College, Hummel applied himself 
with the utmost assiduity to devising and developing a 
system of instruction in dyeing. In this difficult under- 
taking he relied upon his own ideas, and he will always 
rank as a pioneer in this branch of teaching. He was a 
firm believer in the value of pure science, and always pro- 
tested against that superficial teaching of technology too 
often attempted in compliance with the wishes of self- 
styled practical men. The course of teaching which he 
devised has been adopted very widely in this country 
and has attracted much attention abroad. The Dyeing 
School at the Yorkshire College has drawn students from 
all parts of the world. 
if 
Hummel’s original contributions to his subject have 
always been marked by mastery of the subject in hand 
and scrupulous attention to detail. The burden of 
teaching and administrative duties severely restricted his 
time for experimental investigations, but his desire to 
have such work in progress in his department was 
gratified in the most handsome way by the Clothworkers’ 
Company, which has associated a research chemist with 
the professor of dyeing. 
The last few years of Hummel’s life were devoted to the 
planning and organisation of important extensions of his 
department, which is now in possession of extremely 
ample and well-appointed buildings. In this, as in all 
other work, Hummel did not spare himself, and the 
strain doubtless told upon his health. 
As an expert on his subject, Hummel was in constant 
demand. He lectured occasionally on important develop- 
ments of dyeing before the Society of Arts, the Imperial 
Institute and other institutions, and he was a juror at the 
last Paris Exhibition. As an author, he was best known 
by his admirable text-book of dyeing, which has had a 
very large circulation and has been translated into a 
great variety of languages. 
His labours have done much for the college with which 
he was associated and for the important industry that 
he so earnestly desired to serve. Fortunately, he has 
left a large number of disciples who, in different parts of 
the world, are carrving on the work which he originated. 
