noticed my inferences respecting gradients, I find that you say that,

"As the question wholly turns upon velocity, it is of course impossible to exhibit the effect experimentally."

Now although I do not perceive this to be at all a matter of course, but on the contrary have found it very easy to reduce questions depending on velocity to experiment, yet I beg to observe that the present question does not depend either wholly or at all upon velocity. Whatever be the speed of the load upon the inclined plane, provided only it be maintained uniform, my theory of gradients (if it deserve to be so called) will still hold good. It will take the same expenditure of mechanical force to move a load on such inclined planes as I have described, and the mean between the ascending and descending forces will be the force along a level plane. You must surely be so well acquainted with the laws of friction that it is needless for me to remind you that that resistance is altogether independent of the velocity. And I would also beg to observe that the case is one totally distinct from the consideration of accelerating forces. In page 91 you say:

"This point cannot be met experimentally, and I am therefore obliged here to depend only on demonstration. The case certainly involves no difficulty of conception to those acquainted with theoretical mechanics, &c."

I admit that it does not; but I apprehend the conception which those acquainted with theoretical mechanics form of it will be altogether different from that at which you appear to have arrived, and I therefore regret that you seem to have forgotten your expressed intention of giving a demonstration of your own peculiar view of the matter. In the next page (92) you mention the intention as one which you had, but seem to have immediately abandoned it.

It will be very gratifying to me, and I am sure it will be useful to all who are practically engaged in those extensive enterprises for the formation of lines of communication through the country, if you will show how these views of mine are at variance with the established principles of mechanics. Although I am not aware that any one has hitherto pointed out the property which I have explained in reference to inclined planes of less inclination than the angle of repose, yet, so far as I am informed, there is no difference of opinion whatever as to the legitimacy of the method of estimating the tractive force both in ascending and descending these planes. The same formulæ that I have used, viz. L (t + sin e), have been in substance universally adopted in estimating the mechanical force necessary to work railroads. You will find that many

eminent engineers, although they have not thrown the principle into the language of analysis, have nevertheless used it arithmetically; and indeed I have never before heard any doubt expressed about it.

During the last autumn I have been engaged in an extensive course of experiments on rail-roads in different parts of the kingdom, with a view to determine with greater precision than has been hitherto attained, the values of the different constant quantities which enter into their theory. The results of all these experiments are in the most perfect accordance with the principle you have called in question.

I remain, dear Sir, yours very truly,
DION. LARDNER.

36, Cambridge Terrace, Edgeware Road,

December 14, 1835.

XII. Remarks on a supposed new Law of Magnetic Action. By the Rev. WILLIAM RITCHIE, LL.D., F.R.S, Professor of Natural Philosophy in the Royal Institution of Great Britain and in the University of London.*

IN

N the last Number of the London and Edinburgh Philosophical Magazinet, Mr. Fox has endeavoured to show that the mutual attraction of two magnets does not follow the law formerly adopted by all philosophers, viz. the law of the inverse square of the distance; but the law of the simple inverse of the distance. This law he deduces from experiments on the attraction of the opposite ends or poles of magnets placed at very small distances from each other. Thus, for example, when the ends of the magnets are at the distance of of an inch, he found the effect to be only one half of what it was when they were in contact; when removed to the distance of rooo of an inch the effect was one half of one half, or one fourth; when separated by a distance of of an inch, the force was only one half of one fourth, or one eighth, &c.; which numbers are to each other in the inverse ratio of the distances

I admit the truth of the experiments, but differ from Mr. Fox in the conclusion he has drawn from them. To show that the deduction is unfounded, we must first describe what is meant by the pole of a magnet, and its position with regard to the extremity of the magnet. The pole of a magnet is the centre of parallel forces of all the attractions and repulsions of the elementary magnets of which it is composed. Now the position of this centre will obviously depend on the form of ↑ Vol. vii. p. 439.

• Communicated by the Author.

the magnet, and also on its length. Biot has shown that in a steel wire 24 inches long, and properly magnetized, the pole is an inch and a half from its extremity, and that this distance diminishes with every diminution in the length of the magnet*. The centre of parallel forces or the pole of a magnet is similar to the centre of gravity of a body. In the one case the effect is the same as if all the matter of which the body is composed were concentrated in the centre of gravity, in the other the effect is the same as if the difference between the sum of all the attractive and repulsive forces were concentrated in the pole. Now, in the case of the mutual attraction of bodies, our measurements are always taken between the centres of gravity; in the case of magnetic attractions the distances of the magnets are, in fact, the distances between the poles.

Then the distances between the centres of force in these three positions are 2, 3, 4. Hence if the law of the inverse squares of the distances, investigated by Coulomb, be the real law of action, the attractive forces will be inversely as 2, 3, 4, that is, as,,; but is nearly the half of one fourth, and nearly the half of, as Mr. Fox found by actual experiment. These experiments then, instead of leading to a new law of action, afford a beautiful illustration of that law which universally prevails whenever we have matter acting on matter by attractive or repulsive forces.

XIII. Description of a Thermometer for determining minute Differences of Temperature. By MARSHALL HALL, M.D., F.R.S. &c. t

IN

N pursuit of the theory of the inverse ratio of the respiration and of the irritability in the animal kingdom, announced in a late volume of the Philosophical Transactions, I have found it absolutely necessary to determine the minute

• Biot, Traité de Physique, tom. iii. p. 90.

+ Communicated by the Author.

An abstract of Dr. Marshall Hall's paper on this subject will be found in Phil. Mag. and Annals, N. S. vol. xi. p. 453.-EDIT.

differences of temperature which exist in animals. of the same class. In pursuing this inquiry, I soon discovered that it was essential to devise other instruments than those in ordinary use.

It was easy by enlarging the bulb and by selecting a tube of extremely fine calibre, to render the common thermometer capable of more minute indications. But it was impossible to carry this change beyond a certain degree, the augmented length of the instrument becoming highly incon

venient.

In order to obviate this difficulty, I devised the instrument which I am now about to describe.

The form of this instrument is represented in the accompanying outline. The relative size of the bulb and calibre of the tube is such that the tenth part of a degree occupies a considerable space upon the scale. The entire scale consists of ten degrees. At the upper part of the thermometric tube a small bulb is blown, which I shall designate the reservoir; it is turned forwards so as to remain at a right angle with the tube.

The bulb and the tube are filled with mercury, and a little of that fluid is included in the reservoir, when the whole is hermetically sealed.

When an experiment is to be made, the mercury in the tube is to be brought into contact with the mercury in the reservoir, by placing the in

10

9

8

7

6

5

3

2

strument horizontally, with the reservoir upwards, in water of a sufficient temperature.

I will now suppose that I wish to try the comparative temperature of the swallow which shuns, and the sparrow which abides, the rigours of our winter. The thermometer is removed from the water at the temperature of 110° Fahr., and placed upright. The contiguity of the mercury in the tube with the mercury in the reservoir being broken, the highest point in the scale will represent that degree, viz. 110°. The lowest will consequently be the 100th degree. The entire scale is one of six degrees between these extremes, each degree being divided into tenths.

The same plan is adopted for any other part of the scale. We have thus an instrument of the usual size, capable of measuring the tenths of a degree of temperature, at any part of the scale. It only requires the addition of a common thermometer to afford the extreme limit of the magnified scale.

Third Series. Vol. 8. No. 43. Jan. 1836.

I

I may be permitted to add, that the temperature of an animal indicated by such a thermometer compared with that of the medium in which it is placed, affords a near approximation to the degree of respiration, and, inversely, of the irritability of the muscular fibre.

LXV. Proceedings of Learned Societies.

OFFICIAL REPORT OF THE PROCEEDINGS OF THE BRITISH AS-
SOCIATION FOR THE ADVANCEMENT OF SCIENCE, AT THE
DUBLIN MEETING, AUGUST 1835.

Communicated by the Council and Secretaries.
[Continued from vol. vii. p. 513.]

Notices and Abstracts of Miscellaneous Communications to the Sections, continued.

MEDICAL SCIENCE,―continued.

Experimental Inquiry into the different Offices of Lacteals, Lymphatics, and Veins in the Function of Absorption. By P. D. HANDYSIDE, M.D.

THE

HE author's general position is thus stated: "The lacteals, lymphatics, and veins are endowed each with a peculiar office in the general functions of absorption; for example, 1. The lacteals are those vessels which absorb the aliment which is necessary for maintaining the nutrition and increase of the body, and exercise the property of refusing entrance to all other matters; 2. The lymphatics absorb the elements of the body upon their becoming useless or noxious, so as by their final discharge from the system to make room for the deposition of new matter, and these vessels possess no absorbing power over any substances foreign to the system; 3. The veins not only return to the heart the blood after that fluid has fulfilled the object of its diffusion over the system, but enjoy the office of receiving into the animal system by absorption various foreign matters which may be brought into contact with their orifices.

In support of these views the author presents a short review of results obtained by various eminent anatomists and physiologists. The following is the order of the subjects discussed:

Lacteals. Their distention after a full meal,-their condition as observed in living animals ;-effects of ligatures on the thoracic ducts of horses. Lymphatics,-Anatomical origin of,-analogy of lymphatics and lacteals, exact resemblance of the lymph prior to its absorption to that found in the lymphatic vessels, absence of lymphatics in vegetables, no proof afforded by examination of lymph that lymphatics serve as the channel through which foreign matters gain entrance into the system, no communication between lymphatics and veins except through the great lymphatic trunks. Veins.-Analogy between the anatomy and disposition of the veins of animals and the vessels corresponding to these in plants, favours the doctrine of venous absorption.