declares that "for the promotion and extension of the internal as well as of foreign trade, and for the advancement of science, it is expedient to legalise the metric system of weights and measures. The convenience and utility of any system of weights and measures constitute the chief reason for retaining them, and any proposal to substitute a new for an old system which has been for ages deeply imbedded in the laws, the customs, and the habits of a people, appears to be at least a matter of doubtful expediency. It may be observed that the retail trading transactions of the mass of the population, and the exactness of scientific inquiry, do not require the same weights and measures. The weights and measures that would be proper for retail trade would be unfit for the exactness of scientific investigation. The past history of the progress of science owes little, if anything, to the French metric system for its advancement; and it is not obvious how in future it could be employed for this purpose, so as to secure, by its employment, any advantages which have not been already secured by the system long employed in England. The decimal system has been, and still is, largely employed both in measures and calculations where its use has been found to be convenient, and will continue to be so employed.

The decimal division of the British coinage, though very strongly advocated,1 has not been authorised by the Act which legally permits the use of the decimal system of weights and measures. It is possible that in some trades and manufactures the use of it may suggest some improvements, without superseding the established system, which is understood and suited to the wants of the people.

The opinion of the late Sir J. W. F. Herschel, in 1864, on the standards of measure, is worthy of consideration :-"Whatever be the historical origin of our standards of weight, capacity, and length, as a matter of fact our British system refers itself with quite as much arithmetical simplicity, through the medium of the inch, to the earth's polar axis as the French does through that of the metre to the elliptic

of the measure proposed for adoption. Mr. Ewart had forgotten that the construc tion of a perfect and just standard is the first step in legislation on such subjects.

1 The merchants and bankers of the City of London in one of the most influentially-signed petitions which ever emanated from the city, presented in 1855, use language on this subject which is hardly that of petitioners. They say, that "the pound constitutes an English national fixed idea of value and position, and is associated with every existing contract, and every comparison of past revenue, expenditure, and price, and must be retained." They say, also, that every other method, except that from the pound downward, is altogether impracticable. We feel perfectly easy in our reliance on the common sense of the country, that it will not hear of the expulsion of the pound sterling from accounts, while the sovereign is to be retained as means of payment, after division by 24; that it will not hear of the mixed circulation of shillings and tempences; that it will stick to its old and successful plan of reforming that which is, instead of substituting that which has never been, especially in matters connected with our oldest habits of estimation, usages of action, and associations of thought. If, however,

the shillings and sixpences could be replaced by an equivalent amount in tenpenny and fivepenny bits, in the course of a single night, and by the wand of a magician, the country would find itself in a poor state in the morning. Every idea of value would be upset; all notions of cheapness and dearness would require translation. A man who had made up his mind over night that he would go as far as £1 17s. for a purchase, must take pen and paper, if not more ready than usual, to find out how many francs he may venture upon. And this would last for years with many, for months with all. And for what? To avoid an alteration in the copper coin, which would amount to a little short of one farthing in sixpence.-Professor De Morgan,

quadrant of a meridian passing through Paris. It does so as regards our actual legal standards of weight and capacity with much more precision than the French system; and as regards that of length, with still greater, and indeed with all but mathematical exactness.

"If the earth's polar axis be conceived divided into 500,000,000 inches, and a foot be taken to consist of 12 such inches, then 100 of our actual legal imperial half-pints by measure, or 1000 of our actual imperial ounces by weight of distilled water at our actual standard temperature of 62° Fahrenheit, will fill a hollow cube having one such foot as its side. The amount of error in either case is only one part in 8000.

"The theoretical French mètre is the ten-millionth part of the elliptic quadrant above-mentioned; the theoretical litre is the thousandth of a cubic metre; and the theoretical gramme the millionth of a cubic metre of distilled water at 32° Fahrenheit. The actual error of the French legal or standard litre and gramme, or the deviation of these standards as they actually exist from their true theoretical value, is one part in 2730, and is consequently relatively nearly three times as great as the error in our own standards of capacity and weight, when referred to the earth's polar axis as their theoretical origin in the manner above stated. Our actual imperial measures of length deviate, it is true, by more than this amount from their theoretical values so defined-that is to say, by one part in a 1000; so that a correction of one exact thousandth part subtracted from the stated amount of any length in imperial measures suffices to reduce it to its equivalent in such units as correspond to similar aliquot parts of the polar axis. So corrected, the outstanding error is only one part in 64000. The actual legal mètre in use in France is, however, not immaculate in this respect, its amount of error being one part in 6400, which is ten times that which our British measures so corrected would exhibit. British commerce extends, however to Russia, British India, and Australia (besides North America), all of them superior in area; and the two last at least of equal importance, commercially speaking, with the totality of the metricised nations. The Russian sagene is an exact multiple of the English foot. The hath, the legal measure of length in British India, is 18 imperial inches. The Australian system is identical with our own, as is also that of North America. Taking into consideration this immense preponderance both in area, in population, and in commerce, we are not only justified in taking our stand against this innovation, but entitled to inquire if uniformity be insisted on; why, with an equally good theoretical basis, to say the least, the majority is called upon to give way to the minority."

The Act of 5 Geo. IV., c. 74, for the British imperial system of weights and measures, being no rash act of legislation, is founded on the experience of the past history of the English nation, and adapted for the practical convenience and benefit of the community. The French system was devised by their philosophers, who, having rejected all past experience, led by ideas, scarcely ever by facts, have sacrificed every practical consideration to the idea of reducing the divisions of all weights and measures to the denary scale of arithmetic.

ELEMENTARY ARITHMETIC,

WITH BRIEF NOTICES OF ITS HISTORY.

SECTION IV.

OF TIME.

BY ROBERT POTTS, M.A.,

TRINITY COLLEGE, CAMBRIDGE,

HON. LL.D. WILLIAM AND MARY COLLEGE, VA., U.S.

CAMBRIDGE:

PUBLISHED BY W. METCALFE AND SON, TRINITY STREET.

LONDON:

SOLD AT THE NATIONAL SOCIETY'S DEPOSITORY, WESTMINSTER.

1876.

W. METCALFE AND SON, TRINITY STREET, CAMBRIDGE.

NOTICE.

As the Book-post affords great convenience for the prompt transmission

of Books to persons living at a distance from towns, copies of Mr.

Potts' publications can be supplied by Messrs. W. Metcalfe and Son,

through the Book-post, within the United Kingdom, on receiving

orders with prepayment in postage stamps, post office orders, or

otherwise.

ON THE DIVISIONS AND MEASURES OF TIME.

"Time of itself is nothing, but from thought
Receives its rise; by labouring fancy wrought
From things considered, whilst we think on some
As present, some as past, or yet to come.

No thought can think on time, that's still confest,
But thinks on things in motion or at rest."-Lucretius.

THE following brief notices are intended to mark the natural measures and divisions of time, as regulated by the apparent and real motions of the sun and the moon, and the artificial adjustments that have been made so as to secure their agreement with the orderly returns of the seasons, and to regulate the division of time for the purposes of ordinary life.

A measure has always a reference to some quantity which can be measured; and any quantity can be measured by any assumed measure of the same kind. Any length can be measured by any line assumed as the unit of measurement, as a yard, a mile, &c. But with respect to time, it is clear from its fleeting nature, being continuous, no standard measures can exist, like the measures of space or other quantities. There is, however, an analogy between the nature of a geometrical line and time, and an identity of language is employed of both by all nations. For instance, a point in a line and a point of time; the beginning and end of a line and the beginning and end of a period of time; the length or shortness of a line, and the length or shortness of time; also the extension of a line backwards or forwards exactly corresponds with the extension of a period of time into the past or the future. This language implies that the ideas of time are closely associated with the ideas of a line and motion; and that exact measures of the motion of bodies in lines may be assumed and employed as measures of time. It was by having recourse to the apparent motions of the sun and the moon in the heavens, that measures of time were at length ascertained.

The fact of the apparent daily motion of the sun round the heavens being observed to be constant and regular, led men to believe that the sun did really move round the earth, and this belief lasted for many ages. It had its origin in mistaking apparent motion for real motion. When a body at rest is seen by an observer from another body in motion, the former appears to move in a direction contrary to that in which the latter body is actually moving. As the daily revolution of the earth on its axis causes the sun to appear to move from east to west; also while the earth is actually moving in its orbit round the sun, in the direction from east to west, the sun appears to an observer on the earth to move among the stars from west to east. This distinction between real and apparent motions, not having been observed, was the cause of the erroneous belief.1

1 This erroneous belief has led to singular consequences. In the course of time, the bishops of Rome have decreed, that the belief of the motion of the earth on its