Every yard of the chain passed over the pulleys representing a yard of space that the boat has progressed in her course-the fixed point or length of chain lying at the bottom of the canal still remaining the same, what is taken up at the stern being replaced by exactly the same length deposited at the bows. The speed of the vessel is thus exactly equivalent to the speed and size of the driving pulleys, unless, indeed, there should be any slip of the chain in passing over them, and this in practice is easily prevented, and is again exactly measured by the velocity of the chain, unless there should be a slip of the chain along the whole length over the bottom of the canal, and this, of course, is a mere matter of the weight of the chain.

On the Nomenclature of Metrical Measures of Length.

By G. JOнSTONE STONEY, M.A., M.R.I.A.

In this paper many circumstances were pointed out which render the French names of decimetre, centimetre, and millimetre unsuited to this country. They are foreign to the genius of our language, which delights in short pithy words; the information they convey is useless, as the fact that each measure is one-tenth of that above it is one of that class which it is impossible to forget, and they fail in several common requisites of a good nomenclature.

Names of measures for ordinary use should, if possible, be monosyllables; for the convenience of reference they should begin with different initial letters; they should so wholly differ in sound that even when imperfectly pronounced they could not be mistaken for one another, and they should convey some information which would facilitate the use of the measures by those who are unfamiliar with them.

To combine these advantages, it was suggested that hand or hand-breadth should be used as the English equivalent for decimetre, nail or nail-breadth for centimetre, and line for millimetre. The author stated that he had had abundant experience of the assistance afforded to beginners by these names, from their promptly suggesting, without any mental effort, the absolute length of each measure.

Attention was also directed to the importance of giving a distinct name to the tenth part of the line or millimetre, in order to discourage the use of binary subdivisions mite was suggested as a suitable name.

:

The paper closed by urging that the use of foot-rules graduated along one side to metrical measures should in every possible way be encouraged.

On the true Action of what are called Heat-diffusers. By A. TAYLOR. Gases do not radiate the heat which they contain; so that the only mode in which a gas can communicate its heat to a surface is by contact or conduction: this in the present practice is the only mode in which the heating surfaces of a boiler which are not exposed to the radiation of the fire or flame can abstract heat from the products of combustion: but if in a flue or tube a solid body be introduced, it will become heated by contact with the gases, and will radiate the heat thus received to the sides of the flue. It will be admitted that the amount of heat thus conveyed to the water may be very important, when it is considered that the temperature of the gases in the tubes of a boiler at five or six inches from the fire-box tube plate is about 800° Fahr., and that these radiators will consequently have a temperature of several hundred degrees above that of the surfaces in contact with the water in the boiler, and that a very active radiation must consequently take place from one to the other. This principle once established, the modes of application in practice are of course endless. It is, however, unnecessary to make the radiating surfaces of such a form as to impede the draught. I would rather choose the form which would give the greatest amount of radiating surface and offer the least impediment to the free passage of the products of combustion through the tubes. Perhaps as effective a form as any for placing in the tubes of boilers would be a simple straight band of metal, or a wider band bent in the direction of its breadth at an angle of 60° thusIn the case of marine boilers, they should be made to draw out easily to enable the tubes to be swept.

Description of various Models of Fire Escapes, Boat-lowering Apparatus, &c. By ADAM TOpp.

On a Mode for Suspending, Disconnecting, and Hoisting Boats attached to Sailing Ships and Steamers at Sea. By E. A. WOOD.

APPENDIX.

MATHEMATICS AND PHYSICS.

On a remarkable specimen of Chalcedony, belonging to Miss Campbell, and exhibiting a perfectly distinct and well-drawn landscape. By Sir DAVID BREWSTER, K.H., LL.D., F.R.S.

Sir David Brewster, who had examined the specimen, ascertained that the landscape was not between two plates subsequently united, but was in the interior of a solid piece of chalcedony.

He stated that chalcedony was porous, and that the landscape was drawn by a solution of nitrate of silver, which entered the pores of the mineral.

Sir David Brewster stated that above thirty years ago he had examined a similar specimen, belonging to the late Mr. Gilbert Innes of Stow, who had paid a large price for it. Having no doubt that the figure of a cock which it contained was drawn by nitrate of silver, introduced into the pores of the mineral, he induced the late Mr. Somerville, a lapidary in Edinburgh, to make the experiment; and he succeeded in introducing the figure of a dog into the interior of the mineral.

The curious fact, however, displayed by the specimen now exhibited to the Section, is that the landscape had entirely disappeared after being kept four years in the dark. When the specimen was received yesterday from Miss Campbell, the landscape was wholly obliterated; but after the exposure of an hour this morning, it reappeared in the distinctest manner, as may be seen by looking at it against a white ground.

It is of importance to remark that the figure of the cock in Mr. Innes's specimen which was very strong in its tint, had never been seen either to disappear or to diminish in its tints.

On the Connexion between the Solar Spots and Magnetic Disturbances. By Sir DAVID Brewster, K.H., LL.D., F.R.S.

On a Method of reducing Observations of Underground Temperatures. By J. D. EVERETT, Professor of Mathematics in King's College, Windsor, Nova Scotia.

The paper commenced by an acknowledgment of obligation to Prof. W. Thomson, LL.D., of Glasgow, for a knowledge of the principle on which the method is based. The objects sought to be attained are,-1st, to express the temperature in terms of the time of year (on the average of a number of years); and 2nd, to deduce the conducting power of the soil. The paper contained an application of the method to temperatures observed during the seventeen years 1838-54, at the Royal Edinburgh Observatory. The underground thermometers at this Observatory are four in number, and are at depths of 3, 6, 12 and 24 French feet respectively. Their average tem peratures for each calendar month were

Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct. Nov. Dec.

At 3 feet.. 40-57 39-64 10-31 42-45 45-87 49-86 52-70 53-82 52-75 49-15 45-52 42.62 At 6 feet.. 13.59 42.35 42.00 42.79 44.65 47.23 49-71 51-31 51.54 50-11 47.81 45.48 At 12 feet.. 46.84 45.82 45.06 44.68 44.88 45.63 46.84 48.07 48-96 49-27 49.02 47.94 At 24 feet.. 47-77 47 63 17.39 47-08 16.79 16.59 46-55 46.69 46.97 47-31 47-61 47.79

From these data the temperature of any one of the thermometers may be expressed in the form

t T

t T

0

1

v=A+A, cos 2π+B1 sin 2+А, cos 4+B, sin 4-
2π+A, 4π-+&c., (1)

2

T

T

where v is the temperature at the time t reckoned from the middle of January, Tis the periodic time (a year), and the constants Ao, A1, A2, B1, B2 are found in the manner shown below:

A mean of all the Nos. in I. and II.=46·27.

The symbols S., S, S2, S, denote the sines of 0°, 30°, 60°, and 90° respectively. The following Table exhibits the values of the coefficients found as above :

2nd. That the term goes through its cycle of values in the -th part of a year.

3rd. That any decrease in the value of E, amounts to a retardation of the epochs of maxima and minima.

Since the value of any term can never exceed that of its coefficient P1, it is obvious that when P, is very small the term may be neglected. Generally speaking P, becomes rapidly smaller as we advance in the series, and for most purposes all terms after that containing P, may be neglected.

The conducting power of the soil can be found in the following manner. Let x denote the difference in depth of any two of the thermometers; and let A. E, and A. loge. P, respectively denote the amounts by which the values of E, (in circular measure) and loge Pn, for the upper thermometer, exceed the values of the same functions for the lower. Then will

k being the conductivity of the soil and c its capacity for heat.

The values of E, and E in circular measure, and of log, P1, log, P2, are as follow :

And the results of comparing the thermometers two and two in every possible way are, for the term in P1,

The term in P2, treated in like manner, gives 113 and 116 as the values of

The true value is probably about 117, and the value of the ratio this by an obvious arithmetical process.

k

с

can be found from

On an Application of Quaternions to the Geometry of Fresnel's Wave-surface. By Sir WILLIAM ROWAN HAMILTON, LL.D. &c.

Abstract of Formula.

p = vector of ray-velocity; μ= index-vector, or vector of wave-slowness; Sup=-1, Sμdp=0," Spdμ=0 (equations of reciprocity); dp = vector of displacement, or of vibration; p= vector of elasticity, or of total resulting force of restitution ( being the same symbol of operation as in the Seventh Lecture on Quaternions, by the present author); μ-28p a vector, representing the tangential component of elasticity; .. (--μ-2)dp=normal component of elasticity =18m, Sm being a scalar; ..dp=(4-1—μ−2)➖1μ ̄18m, and Sμ ̄18p=0; .. the formula,

-1

-1

is a symbolical form of the equation of the index-surface, or of the surface of waveslowness, to which the wave itself is reciprocal. Hence, by the equations of reciprocity given above, or simply by changing μ to p, and to 1, we obtain the formula,

μ

as a symbolical form of the equation of Fresnel's wave.

-1

To interpret this equation, or to deduce from it a geometrical construction, we may observe that the formula (assigned in the Seventh Lecture),

1=Spop,

is the equation of a certain auxiliary ellipsoid; and that

(c)

is a vector perpendicular to the plane of that diametral section whereof p is a semiaxis. Hence

0=Sop=So(4-p-2)

is an equation which determines the two values of the square (-p3) of the length of a semiaxis of the diametral section made by a plane perpendicular to σ; and if To=Tp, so that the normal σ to the plane of the section is inade equal in length to one or other of the two semiaxes, then

But this is just the equation (b) of the wave, with σ written instead of P. Hence, then, is at once derived the celebrated construction of Fresnel, namely, that "the wave surface (for a biaxal crystal) is the locus of the extremities of normals to the diametral sections of an ellipsoid, each normal having the length of one of the semiaxes of that section."

On certain Properties of the Powers of Numbers.
By J. POPE HENNESSY, M.P.

On Gutta Percha as an Insulator at various Temperatures.
By FLEEMING JENKIN.

This paper contained an abstract of experiments, made for Messrs. R. S. Newall and Co., to determine the absolute resistance of gutta percha, and the effect of temperature on that resistance.

The absolute resistance of gutta percha was calculated by the author from tests on long submarine cables; the variation of resistance due to varying temperature