you might have purchased peace, without a drop of blood, at a tenth part of the expenditure. But you think it would be mean and humiliating, inconsistent with your own and your nation's honor, to put up with the slightest injury. Now I can assure you that there is no stronger proof of a poor spirit, a narrow, cowardly and unkingly heart, than revenge; especially as a king does not risk his own person in taking it, but employs the money of the people and the courage of the poor. You think it inconsistent with your august majesty, and that it would be departing from your royal dignity, to recede one inch from your strict right in favor of a neighboring king, though related to you by consanguinity or marriage and perhaps one who has formerly rendered you beneficial services. Poor strutting mortal! How much more effectually do you let down your august majesty and royal dignity when you are obliged to sacrifice with oblations of gold to foreign and barbarous mercenaries, to the lowest dregs, the most profligate wretches on the face of the earth; when, with the most abject adulation, and in the meanest form of a petitioner, you send ambassadors or commissioners to the vilest and most mischievous nations around, to ask them to receive your subsidies; trusting your august majesty's life, and the property and political existence of your people, to the good faith of allies who appear to have no regard to the most sacred engagements and are no less inclined to violate justice than humanity."

MISCELLANEOUS.

RICHARD DEDEKIND.

Julius Wilhelm Richard Dedekind died on February 12, 1916, at the advanced age of eighty-three, at his home in Brunswick, Germany. He had won international renown for his work in the theory of numbers, and two of his classical pamphlets have been translated by W. W. Beman under the title

Essays on the Theory of Numbers, and published by the Open Court Publishing Company. In the current (July) number of The Monist, Mr. Philip E. B. Jourdain, of Fleet, England, presents an appreciation of Dedekind's scientific achievements and we refer our readers to this article for further details.

MR. GORHAM'S REPLY TO MR. MATTERN.

To the Editor of The Open Court:

Allow me a few lines relative to Mr. Gorham's reply to Mr. Mattern in the April issue of The Open Court. It seems to me that Mr. Gorham is right within certain limits. In view of the collected evidence it is not possible to contend that the German army in Belgium has remained free of guilt. Nevertheless, it is my conviction that Mr. Gorham looks at the whole matter through English glasses-smoked glasses, penetrable only to certain rays of light. He is blind to the truth that Mr. Roland Hugins has well expressed when he said that "we do not have here white angels fighting black fiends, but human beings all smeared with the same scarlet."

There was no need for Mr. Gorham to refer to a Prussian law of a hundred years ago, in order to settle the question whether or not the civil population are entitled to offer armed resistance to an invader. According to · Article 2 of the Annex to the Hague Convention of 1899, the civil population are entitled to do so, however, only at the moment of invasion. Has the occupation once been accomplished no civil person has a right to attack soldiers. In occupied territory, "Very generally acts of disobedience or hostility are made punishable with the penalty of death." (American and English Encyclopedia of Law, 2d. ed., Vol. 16, p. 157).

But the army of what country is likely to care for law if outnumbered by a hostile civil population? The British perhaps? Frederick F. Schrader, in one of his essays, (Fatherland, December 2, 1914) quotes from the London Truth an article by Lt. Morrison of the Canadian Artillery, as follows: "During the trek our progress was like the old times forays in the highlands of Scotland, two centuries ago. We moved on from valley to valley, lifting cattle and sheep, burning, looting and turning out the women and children.”

The trek referred to by Lt. Morrison 'took place during the Transvaal war. The point I wish to make is that we may admit that the German soldiers have committed atrocities in certain sections of Belgium and at the same time ask whether any other army under similar circumstances would have acted in a more humane manner. In the Transvaal the British were fighting for extension of their colonial empire. They had no cause for desperation. The Germans in Belgium, however, knew very well that a defeat in the west would have meant defeat in the east; they had to save the women of Berlin from the fate that befell the women of East Prussia. Moreover, the Transvaal was but thinly populated and the invading army was smaller there than in Belgium, hence the points of contact were fewer, the temptation less.

Considering also what is known about the punishment for sniping during the Transvaal war and about the concentration camps of those days, the conclusions seems to be ineluctable that Europe would have been a thousand times worse off had the Germans not invaded Belgium, but the Cossacks and the Tommy Atkins, together penetrated central Europe; that after all the smaller of two evils has come to pass; and that no nation under the sun can turn to Germany and exclaim, "I am holier than thou!"

Should you think that what I have said might help to clear the thought on the subject, you are welcome to make use of these lines in The Open Court. EMIL REACH.

THE THERMOMETER.

In connection with Dr. Carus's article on thermometers in The Open Court for March, 1916 (p. 187), it is of interest to note that the original memoirs of Fahrenheit, Réaumur, and Celsius were collected and reprinted in No. 57 of Ostwalds Klassiker der exakten Wissenschaften. The subject is also referred to in the English translation of Mach's Principles of the Theory of Heat which is now in the press and will shortly be published by the Open Court Publishing Company. The little volume of the Klassiker just mentioned is edited by A. J. von Oettingen, and from it the following particulars are taken. Gabriel Daniel Fahrenheit (1686-1736) was a son of a merchant in Danzig, and went to Amsterdam to study business. Here he learned physics, and traveled to England where he wrote five memoirs for the Philosophical Transactions of 1724. These memoirs were the only ones he ever wrote, and though they are not at all connected immediately with his famous thermometer, they are all translated from Latin into German in the above little volume. Fahrenheit seems to have lived in Amsterdam by the making of meteorological instruments, but was of some scientific eminence, since he was elected a member of the Royal Society of London. Fahrenheit was the first to use mercury in thermometers, but Christian Wolff, who is best known as a follower of Leibniz, had used it in thermoscopes in 1709. René Antoine Ferchault, Seigneur de Réaumur, des Angles et de la Bermondière (1683-1757) became a member of the Paris Academy of Sciences in 1708, published much on the technical arts, and later on constructed his thermometer and took up studies connected with it. His memoirs on thermometry appeared first in the Paris Mémoires for 1730, 1731, and 1733, and were of great length, in contrast to Fahrenheit's short and excellent writings. Anders Celsius (1701-1744) was born and died at Upsala in Sweden, was professor of astronomy there, and his memoir on thermometers appeared in the publications of the Swedish Academy of Sciences for 1742.

The above accounts of Fahrenheit, Réaumur, and Celsius are confirmed by the biographies in the latest (eleventh) edition of the Encyclopaedia Britannica (Vol. X, p. 126; Vol. XXII, p. 947; Vol. V, p. 609, respectively).

Comments upon the Editorial Article concerning our Thermometer. The recent article in the March number of The Open Court upon "Our Thermometer" has no doubt been read with considerable interest. Several statements in it, however, are very misleading and require to be corrected.

It is said for example on page 188: "There is no doubt that to Fahrenheit belongs the honor of having invented the thermometer; all the essentials of temperature measurement were invented by him and we shall never forget that he was the pioneer in the field." The Editor's desire to award the invention of the thermometer to a German is of course perfectly natural; if he will turn, however, to two perfectly trustworthy German authorities, Poggendorff's Geschichte der Physik (p. 225) and Gerland's more recent Geschichte der Physik (p. 339), he will find that Fahrenheit instead of being a pioneer was a comparatively late comer in the field of temperature measurement. Galileo, an Italian, invented the thermometer about 1592; his first instrument, based upon the expansion of air, was really a development of the work of a Greek, Hero of Alexandria. Galileo soon found air to be unsatisfactory and

in 1612 invented the alcohol thermometer in which each degree represented 1/1000 the volume of the bulb. Many of these old Galilean thermometers can still be seen in museums. Réaumur based his alcohol thermometer upon that of Galileo, and having fixed his zero at the freezing point of water let each degree above this represent 1/1000 the volume of the bulb and stem below the zero division. With the strength of alcohol which he used the boiling point of water happened to fall at the 80th division. There is no truth whatever in the statement that Réaumur graduated his scale by dividing the interval between the freezing and boiling points into 80 degrees; this method of graduation was adopted by Réaumur's successors but not by Réaumur himself.

The use of mercury for thermometers in place of alcohol was first tried in Florence and later in Paris. Fahrenheit's first experiments were made with alcohol, but about 1720 he abandoned alcohol for mercury, and his technical skill, which exceeded that of his predecessors, soon made the mercury thermometer, what it never was before, an accurate instrument of measurement. The zero point of Fahrenheit's thermometer was based upon the temperature of a mixture of ice, water and salt (which he believed to be the lowest possible cold) and not upon that of the coldest day which he had experienced, as incorrectly stated by the Editor (see Poggendorff's Geschichte, p. 519).

Fahrenheit fixed the freezing point of water upon his scale and divided the interval between this and his zero into 32 divisions, probably for the reason that he was able to reach the length of a single degree mark by a simple process of bisection. (The English inch is divided in the same way into 1/2, 1/4 1/8 1/16 and 1/2, and this method of bisection is a great convenience for many purposes.) By extending these divisions above the zero division Fahrenheit arrived at the upper register of his scale. The temperature of the human body which Fahrenheit found to be 96° (three times the interval from 0 to 32) formed the third fixed point upon his scale. By means of these three fixed points Fahrenheit could easily standardize his thermometers and it was in this way that his instruments were brought to their high point of accuracy. Fahrenheit did not employ the temperature of boiling water as a fixed point. Upon the scale graduated as described the boiling point of water happened to fall at 212°. At the present day it is customary to graduate the Fahrenheit scale by fixing the freezing point of water at 32° and the boiling point at 212°, the interval between these two divisions being divided into 180 degrees. By extending these divisions below 32° the lower register of the scale is reached.

The Editor omits to state in his article several advantages which the Fahrenheit scale has over other systems. In the first place by setting his zero point very low Fahrenheit obviated the necessity of employing minus degrees for most meteorological measurements. Of course we know now that a much lower cold can be produced than by a mixture of ice and salt, the absolute zero being several hundred degrees below this (-273° Centigrade and -460° Fahrenheit). The principle of starting with the lowest possible cold, however, is sound and many scientific measurements are based upon a scale which begins with absolute zero.

Another great advantage of the Fahrenheit scale is that it largely does away with the necessity of using fractional degrees. The one hundred divisions of the Centigrade scale are hardly sufficient to express ordinary observations without the use of fractions.