My arrangement consists of a combination of two equal modifications of Ammsler's Planimeter, ABC, AB'C', the wheels of which are attached at the joints B, B'. C' slides along AC, and the length of AC can be altered by turning either of the heads D, D', of coaxal screws of equal pitch. Now, if we suppose D connected with the

wheel at B, and D' with that at B', by means of universal flexure joints (Thomson & Tait's "Natural Philosophy," § 109), it is obvious that the length of AC will depend upon its angular position, and upon the motion of C' along AC.

Let AB AB'=a, BC= B'C'

=

=

b, AC=r, AC' = r1, [ ABC = $,

and let denote the position of AC. Then, if the whole turn through an angle de, the motion of B perpendicular to CB is the same as if it had rotated about O, where AOB is a right angle. Hence, if p be the radius of the wheel at B, dy the angle through which it rotates,

A similar expression holds, of course, for B'. Now, if a be the inclination of the threads of the screws, one right, the other left, handed,

Now C' may be made to move along any curve we choose, so that r, may be any assigned function of 0. Hence, by introducing the constant factor

tan a 26

for r, we may give the equation the form

to which the solution of the general linear differential equation of the second order can always be reduced.

(c) The Electric Conductivity of Nickel. By C. Michie Smith and J. Gordon MacGregor.

Pure nickel foil, obtained in Paris by Dr Andrews, was cut into a spiral about 20 inches long, and it was on this spiral that all the following experiments were made. During the month of November 1875 a large number of experiments were made as to its thermoelectric properties, and these were found to be almost identical with that of the specimen from observations on which the line was laid down on the "thermo-electric diagram." (Trans. R.S.E., 1872-3.) This line, it will be remembered, is a peculiar one, and is very similar to that of iron, with this difference, that the peculiar changes take place at much lower temperatures in nickel than in iron. Having thus finally determined the position of the line in the thermo-electric diagram, we were anxious to discover whether, like iron, it exhibited other peculiarities about the same temperature, and for this end we made the following experiments on the electric conductivity at different temperatures. The method of observation was as follows:

To the two ends of the nickel spiral stout copper wires were soldered, and the whole was carefully fastened together in such a way that no two coils of the spiral could touch each other. Side by side with this nickel spiral was placed a similar spiral of soft platinum wire of approximately equal resistance. This platinum was part of a wire the electric conductivity of which had been formerly carefully tested, and had been found to obey very strictly the law of being proportional to the absolute temperature. These spirals were then placed in a large pot of oil, care being taken that they hung quite free from the sides of the pot, and the ends of the thick copper wires were led to the pools of a mercury commutator, so arranged that either the nickel or platinum could be made to form one of the arms of a Wheatstone's bridge, in connection with a very delicate Thomson's dead-beat mirror galvanometer. In making the observations the oil was heated by a powerful Bunsen burner, and constantly stirred. By this means it was found perfectly practicable to keep the oil sensibly at the same temperature during the time necessary to find the resistance of the two wires

by the ordinary balance method. That no errors were caused by thermo-electric effects was proved repeatedly during the experiments by completing the circuit without the galvanic cell, when no current was shown on the galvanometer. The results obtained for the nickel entirely agreed with what had been anticipated from the thermo-electric properties. For, when the conductivity is plotted in terms of the temperature, the curve shows a sudden change in direction at a temperature of about 149° C. (300° F.), indicating that there is at that point a sudden change in the rate of alteration of the conductivity with change of temperature. The curve obtained for nickel can be very well represented by two straight lines inclined to each other at an angle of about 9°, while the curve got for the platinum wire is strictly a straight line.

That no part of the effect was due to the conductivity of the oil was amply proved by the following experiment:-

Two pieces of platinum foil, each having a surface of 2.5 square inches, fastened to the ends of copper wires, were plunged in the oil when it was at a temperature of 550° F., and were kept a quarter of an inch apart; the resistance of the oil between them was then measured, and was found to exceed 9 megohms, while the resistance on causing them to touch fell to a small fraction of an ohm.

After a series of experiments had been made with the nickel, the whole spiral was heated to a white heat in the flame of a Bunsen burner, and allowed to cool in the air; another series of experiments was then made on the conductivity, but no change was observed.

The following tables contain the observations for two of the experiments, side by side with the values of the conductivity, calculated on the supposition that the curves are best represented by straight lines-the platinum being represented by a single straight line, while the nickel is represented by a broken line. The calculated and observed values, it will be seen, agree very closely with each other, except where a divergence is to be expected, namely, at the intersection of the two lines (nickel). The equations were taken from the lines obtained by plotting the conductivity in terms of the temperature. R is the resistance in thousandths of an ohm, t the temperature in degrees F. :

VOL. IX.

R

An attempt was made to discover whether or not the conductivity curve had another peculiar point corresponding to that in the

thermo-electric curve at a high temperature. For this an arrangement was used similar to that employed for the iron wire in the experiments formerly described (" Proc. R. S. E." 1874-75, pp. 629-631). But no results were obtained, owing to the breaking of the nickel ribbon when exposed to the great heat of the white hot cylinder.

The following Gentlemen were elected Fellows of the Society:

WILLIAM SKINNER, Esq.

J. BALLANTYNE HANNAY, Esq.
PETER DENNY, Esq.

Monday, 21st February 1876.

SIR WILLIAM THOMSON, President, in the Chair.

The following communications were read:

1. On the Structure of the Body-wall in the Spionidæ. By W. C. M'Intosh.

In regard to external form, Nerine foliosa, Sars, is generally taken as the type of the family, and therefore it may be selected for structural examination in the first instance. Anteriorly the pointed snout is completed by the intricate interlacing of the muscular fibres beneath specially thickened cuticular and hypodermic layers. As soon as the body-wall assumes a rounded form, a layer of circular and oblique muscular fibres occurs beneath the hypoderm, the majority having the latter (i.e., the oblique) direction. In the centre of the area the oesophagus is suspended by strong muscular bundles (the most conspicuous of which are vertical) passing from the hypodermic basement-layer in the middle line superiorly to be attached to the oesophagal wall. A second series, as they descend to their insertion at the ventral surface, give lateral support to the tube; while a third group interlace in a complex manner, and, with the blood-vessels, fill up the space between the oesophagus and the wall of the body.

Toward the posterior part of the head is found-on the dorsal surface a slight hypodermic prominence, which indicates the position of the central ganglia of the nervous system; the latter