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which is the value arrived at by the other method.

Let us now consider the secondary maxima more closely. Their directions are given by n tan (E+F)= tan n(E+ F), cf. Preston. As E+ Fincreases from 0 to π, we pass from the direction of one chief maximum to that of its neighbour. If we solve

y=n tan (E÷F)

y= tan n(E+F),

E+F varying from 0 to 7 in each case, the values of E + F thus found give the directions of the secondary maxima within the range. The result for n=26 is approximately

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Applying the formula for the relative intensity, we find that if the intensity of the chief maximum be denoted by 1, that of the neighbouring maxima should be 0·05, 0·02, &c., but all greater than 0.001. There are twenty-four of these secondary maxima between two adjacent principal maxima. Two of these secondary maxima are as a rule Now

λ.

π

26 apart.

(E+F) ≥ = ƒ (sin μi — μ sin i) +e(μ cos i— cos μi)

π

+ A0(f cos μi+e sin μi).

λ

π

If the change in (E+F) is approximately the corre

26ƒ

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26

and this is exactly the

sponding change in A is theoretical limit of the resolving power. These secondary maxima, even if bright enough, should not be seen as lines but should form a continuous background. When using the electric arc on some occasions, however, the faint background between the orders appeared as if constructed of a great number of fine lines.

The ratio of the distance between the principal and adjacent secondary maxima to the distance between two principal maxima is The width of a principal maximum in a

3

26

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typical case was found experimentally to be

46

of the

160

distance between two principal maxima; i. e. the adjacent secondary maxima are lost in the principal maxima.

The observations recorded in this paper were made in the Physical Laboratory of the University of Glasgow with Prof. A. Gray's echelon spectroscope, and I have to thank Prof. Gray both for encouragement and advice.

LVII. Note on Mr. Jeans' Letter in Phil. Mag. for December. To the Editors of the Philosophical Magazine.

GENTLEMEN,

If mi

mn

MR. JEANS in his letter omits to take notice of the most important point which arises on his paper and my note. He claims, namely, to have proved Maxwell's law, which may be stated as follows. be the masses of n molecules, forming a group out of the much greater number N, u v w1 &c. their velocities, 1 1 1 &c. their space coordinates, then the chance that these velocities and coordinates respectively shall lie within assigned limits μ1 . . u1 + dụ1 . . . &c., x1 . . æ1+da, &c. is proportional to e¬h(Em(u2+v2+w2)-2x) du

'1

...

dw, dx

...

dzn,

Intermolecular

where x denotes the potential of external forces which in that configuration then molecules have. forces are not considered.

But this expression may be put in the form

ƒ (u1)ƒ (v1)ƒ (w1) ··ƒ (w)ƒ (2x);

in that form it asserts that "the chance of the velocities of any molecule, as m1, lying within assigned limits is independent of the positions and velocities of all the other molecules for the time being."

Maxwell's law cannot then be true unless at the same time that statement is true, and that statement I call assumption A. But Mr. Jeans has proved that this assumption is untrue in fact-namely, in paragraph 2 of his paper he points out that it is inconsistent with the continuity of the motion (and is therefore untrue because the motion is continuous), and in his letter he says "the laws of dynamics imply causation with no greater certainty than they imply the negation of assumption A." If, then, Maxwell's law cannot be true without A being true, and A is not true, it necessarily follows that Maxwell's law is not true.

That is, it is not generally true. In the particular limiting case of an infinitely rare gas Maxwell's law is true, at least to an infinitely near approximation, and in the same case the objections to A cease to be appreciable. For this reason Mr. Jeans is not open to the charge of inconsistency, because by virtue of his 37 d he is in effect dealing in his paper only with the infinitely rare gas, at least so I understood him,

If Mr. Jeans is right in his view that assumption A, and therefore Maxwell's law, cannot be generally true in fact, then it necessarily follows that the orthodox theory of gases is a true theory only of the infinitely rare gas. Also the law of equipartition of energy, which is a corollary to Maxwell's law, is not proved to hold in any case except that of the infinitely rare gas.

S. H. BURBURY.

THROUGH the courtesy of the Editors I am able to add a note on Mr. Burbury's letter.

The issue of his letter is, I think, obscured by his not making any clear distinction between "assumption A" (an assumption which may, rightly or wrongly, be made) and "absence of correlation" (a result which may be proved).

From Mr. Burbury's point of view the latter follows from the former, but, given the latter, I do not think that it is necessarily a consequence of the former. The cause must produce the effect, but the effect may follow from any one. of many causes. Anyhow, the two are not synonymous.

From my point of view, as I have said throughout, I cannot regard "assumption A" as a genuine assumption at all. It is, therefore, from my point of view, futile to discuss whether "assumption A " is true or untrue, although I do emphatically disclaim having assumed it. What we may logically do, is to discuss whether "assumption A"-qua assumption is legitimate or illegitimate, and also whether "absence of correlation" (the closely related result) is-qua fact-true or untrue. This I hoped I had done in my original paper. The conclusion I reached was that the assumption was illegitimate, but that the fact was true.

Leaving aside the difference between "assumption A" and "absence of correlation," there is nothing inconsistent in holding simultaneously the view that an assumption is illegitimate as an assumption but true in fact. For instance, Maxwell's original proof of the law of distribution rested on the assumption which will be sufficiently indicated by the equation

$(u, v, w) =ƒ (u) ƒ (v) ƒ (w).

It is generally admitted that this assumption is illegitimate as an assumption, but (at any rate in the case of an infinitely rare gas) true in fact. But is Mr. Burbury prepared to charge with inconsistency all those that hold these views?

It need hardly be said that I am very grateful to Mr. Burbury for the kind interest he has always taken in my work. Criticism, in particular, is always of special value to anyone who, like myself, has not worked at a subject for long. But in the present instance, although it is only with the greatest diffidence that I have ventured to try to maintain my position against Mr. Burbury's criticism, I cannot persuade myself that these criticisms have any true foundation. J. H. JEANS.

LVIII The Electrical Conductivity and Fluidity of Solutions. By RICHARD HOSKING, 1851 Exhibition Science Research Scholar*.

THE present paper describes experiments carried out in the Cavendish Laboratory, Cambridge, during the year 1903 and the Michaelmas Term 1902; and these experiments are the continuation of work performed in the Physical Laboratory, Melbourne, and described in the Philosophical Magazine for May 1902 †, in a joint paper by Professor Thomas R. Lyle and myself.

One of the main results of the Melbourne work was to show that both the Specific Molecular Conductivity and the Fluidity of the solutions used became zero at the same temperature, viz., -35°.5 C.

This result was based on the form of the curves representing the temperature variations of both these quantities between 100° C. and 0° C.; but it is interesting to find that Kohlrausch quite independently arrived at the conclusion that in the case of dilute aqueous solutions, all conductivities would cease at practically the same temperature, viz., -39° C.

Another general result was that the fluidity-concentration isothermals and the conductivity-concentration isothermals all cut the axis of zero fluidity and conductivity respectively at the same point, representing a concentration of 10.74 normal. It was felt that these, and other conclusions arrived

*Communicated by Prof. J. J. Thomson, F.R.S.
+ Phil. Mag. May, 1902, p. 487.

Sitz. Akad. Wiss Berlin, Oct. 31st, 1901.

at, needed further investigation, and with that object mainly in view the experiments described in the present paper were undertaken.

As solutions with high concentrations would be necessary to test one of these points, lithium chloride was chosen as the salt to be used.

The method of experimenting was practically unaltered. but there were slight variations which will be briefly indicated, The dilatometer described in the joint paper was again used for measuring the specific gravity of my solutions at all the temperatures.

Viscosity.

The glischrometer was changed back to the original form described in an earlier paper (Phil. Mag. March 1900, p. 274), which was more likely to give accurate values for viscosity; and the viscosity of my solutions was found in the way there described.

In this new glischrometer the following constants were determined, correct at 0° C.

Corrected length of capillary tube = 5·4391 cms.
Mean radius of the capillary tube = 0.011592 cms.
Working volume of each limb

and in the formula

= 3.8441 c.cms.

=

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the values for log a and log came out as 7-521643 and 2.44902.

Resistance.

The cell in which the electrical resistances were measured was similar to that described in the joint paper, and its capacity was determined by measuring in it the resistance of a standard solution of sulphuric acid (20 per cent. by weight). The value obtained for the capacity was 136-43 cm.-1 at 18° C.

The modified arrangement of Kohlrausch's method *, by which a double commutator and a moving coil galvanometer are used instead of the coil and telephone, was employed to determine the resistances. Our previous arrangement was very similar, the magneto-alternator being used instead of the dry cells and one set of sectors on the commutator.

The commutator was driven by a water-motor, and could

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