In this system the connectors are joined not at the opposite angles of the rhombus but at such points in the adjacent sides produced that at every moment they are parallel to the remaining

MC, with LF, FK form a pantagraph, and for every position of C, P takes another, equiangular and proportional.

III. The Gorgon Linkage.-The parallel motion of Mr Scott Russell is exact, and constitutes a two-bar motion. From the fact that it was fitted by Mr Seaward to the engines of the "Gorgon," it may conveniently be called a Gorgon Linkage. A link AB is bisected in C, and at this point another link CD, equal to CA or CB is attached. D is the centre of revolution. If one end A of the link AB be guided along the axis of x, the motion of B is at every moment in the axis of y from D.

For every position C is the centre of a circle ADB, and ADB is the angle in a semi-circle, that is, a right angle. Hence B describes a straight line.

This system of links derives additional interest from the discovery of the Peaucellier cell, as by it the motion of the parallel point can be thrown in a direction at right angles to itself; that is, parallel to the line joining fulcrum and pivot; and this can be transferred to the line of centres by means of the pantagraph.

IV. Hypocycloidal Parallel Motion.-Another very interesting case of the problem of Parallel Motion is that produced by a hypocycloidal movement. When one circle is made to revolve on the concave circumference of another circle, any point in it describes a curve, which is called the hypotrochoid or hypocycloid. If the diameter of the revolving circle be equal to the radius of the circle

in which it revolves, the hypotrochoid becomes an ellipse; and if the point be on the circumference of the smaller circle, the ellipse degenerates into a straight line.

Let the circle BPC (fig. 7), diameter BC=AC, revolve in the circle A BM, radius AC. If the initial position of the describ

The difficulty of constructing, and the inconvenience experienced in using an arrangement in which the annular wheel comes into action, are so great that it is seldom employed. The following is a simple method of obtaining the hypocycloidal motion without requiring the annular wheel. On the arm ACB (fig. 8),

blem being that LFN revolve on its axis at double the speed of the

arm AC, and in a contrary direction. The number of teeth on HEO is twice the number on NLF. Hence NLF makes two revolutions round its axis, while the arm causes it to revolve round the fixed centre-circle HEO. The axis C is rigidly connected with a wheel XWP, revolving on the upper surface of the plate-arm ABC, whose circumference continually passes through A. Thus while the platearm ABC makes one revolution round A in the direction of the hands of a watch, XWPA, which is rigidly connected to the axis C of NLP and partakes of its motion, makes two revolutions in the opposite direction. Thus it revolves round an imaginary annular wheel XYZQ, whose diameter ZQ is double that of its own; and in virtue of hypocycloidal motion, if XWP be the initial position, the point A in the circumference of XWPA will move along ZQ.

In the annexed figure (fig. 9), the modus operandi of the machine is sketched. The system is analogous to the sun and planet wheel invented by Watt.

Fig. 9.

It would be going beyond the limits of this paper to direct attention to the two modifications of the Peaucellier cell, which have been called respectively the Quadratic-binomial Extractor, and the Conicograph. The introduction of these into the sphere of mathematical investigation has given several indications of valuable results to be obtained therefrom. For a brief outline of these, we refer the reader to the pamphlet of Professor Sylvester, who not only was the first in this country to direct attention to the general problem, but also had the credit of demonstrating the

higher vantage ground opened to the mathematician by means of Peaucellier's discovery. The extent of our own obligation to him is great.

Not less are we indebted to Professor Kelland, whom we have known both as a teacher and a friend. The valuable hints and suggestions he has given us on this subject we are glad to take this opportunity of acknowledging.

3. Laboratory Notes. By Professor Tait.

(a.) On the Passage of the Electric Current from Amalgamated Zinc to Zinc Sulphate Solution. By J. G. MacGregor, M.A.

(b.) On the Thermo-Electric Properties of Cobalt, &c. By Messrs Knott, MacGregor, and C. M. Smith.

(c.) Measurements of the Potentials required for Long Sparks of a Holtz Machine. By Messrs Macfarlane and Paton.

4. Note on Orthogonal Isothermal Surfaces. By
Professor Tait.

5. Notice of some recent Atmospheric Phenomena.
By Professor Tait.

6. Report by the Society's Boulder Committee. (Plates II. and III.)

Mr David Milne Home gave in the Third Report of the Society's Boulder Committee, from which the following are extracts:-In November 1875, on the invitation of Sir John Douglas of Glenfinnart, the Convener went to visit him at that place, to have an opportunity of examining several remarkable boulders reported to the Committee as situated in that part of Argyllshire.

1. On the east side of Lochlong, opposite to Ardentinny, there is the farm of Peaton. On this farm, a burn descends from a steepish hill which faces the north. A gneiss boulder lies in a gorge cut by the burn through rocks of clay slate. The boulder