558 



NATURE 



\Oct. 28, 1875 



2 would decrease k still further, and here exists for the 

 present an uasolved contradiction between experience and 

 the theory in its present form. 



Looking at this state of things, Herren Kundt and 

 Warburg at Strasburg' thought it advisable to investigate 

 experimentally the simplest case which nature offers to 

 us, viz. the case of a gas which, according to its chemical 

 behaviour,'is a monatomic one. Herr Baeyer pointed out 

 to them that mercury gas was such a gas ; they there- 

 fore undertook to determine the specific heat of mercury 

 gas. Here a contradiction to the theory did not become 

 apparent ; the experiment has yielded exactly the value 

 demanded by theory for a monatomic gas, viz., K = x '67. 

 Thus it is proved that the molecule of mercury gas, with 

 regard to its thermal and mechanical properties, behaves 

 exactly like a material point. It is hardly necessary to 

 remark that, with regard to other properties, it is not at all 

 necessary that the same molecule should behave like a 

 material point. Thus, for instance, one glance at the spec- 

 trum emitted by incandescent mercury gas, which is 

 crossed by many bright lines, shows us at once that the 

 molecule of the same, with regard to the light it emits, 

 does certainly not behave like a material point. 



With regard to the way in which the experiment was 

 conducted, we confine ourselves to the following remarks. 



The k for mercury gas was determined from the velocity 

 of sound in this gas, and this was found by means of the 

 method of dust figures, formerly described by Herr 

 Kundt.* A glass tube A, closed at both ends, well dried 

 and pumped perfectly free from air, contained a certain 

 quantity of mercury, which had been carefully weighed, 

 and a little siUcic acid. Sealed to this tube was another 

 one, B (this a little narrower), in such a manner as to form 

 the prolongation of A. A was placed in a four-fold box 

 made of iron plates, which was heated by a series of 

 Bunsen burners. This box also contained the great 

 reservoir of an air thermometer, and, if observations were 

 made at a temperature under 354°, several mercury ther- 

 mometers besides. The end of B, projecting from the 

 box, was sealed up, and over this end a long wide glass 

 tube D was placed, which was closed at one end and con- 

 tained a little lycopodium. 



If now, after the necessary regulation in the heating 

 arrangements, the thermometers in the box showed equal 

 and sufficiently elevated temperatures, the tube composed 

 of A and B was sounded by friction to its third longitu- 

 dinal tone ; at the same time a reading of the air thermo- 

 meter was taken, and the temperature of the air in D was 

 noted down. The powders introduced then showed in 

 tubes A and D the sound-waves in mercury gas and in air 

 respectively, so that afterwards the lengths of these waves 

 could be measured with the greatest accuracy. 



Let us suppose 

 / to be the length of the sound-wave in air, 

 /' ,, ,, ,, in mercury-gas, 



/ the absolute temperature of air in D, 

 t ,. „ of mercury gas in A, 



d = 6'9783 the density of mercury gas (air = i), 



k — the proportion _ of the two specific heats for air. 



for mercury gas. 



Then we have 



^■^.{^ru 



li k for air was taken at = 1-405 according to Rontgen, 

 then by seven definite experiments, at different degrees of 

 saturation of the mercury vapour, and three different sets 

 of apparatus being employed, it was found on the average 

 that 



k' == 1-67. 

 The results of the different experiments never deviated 

 more than one per cent, from this value. 



* See Nature, vol. xii, p. 88. 



If the specific heat c at constant volume for air is taken 

 as = I, then it follows that c for mercury 



c = o'6o. W. 



AMONG THE CYCLOMETERS AND SOME 

 OTHER PARADOXERS 



NO notes have been handed down of the conversation 

 between Erskine and Boswell, whilst strolling in 

 Leicester Fields, on squaring the circle. There is on 

 record, however, Boswell's small joke, " Come, come, let 

 us circle the square, and that will do us good." 



The subject is one that has occupied the thoughts of 

 some few from the earliest times of geometrical history, 

 and there are some now fascinated by it at this date, 

 when we have — 



" on the lecture slate 

 The circle rounded under female hands 

 With flawless demonstration." 



Old Burton advises him that is melancholy to calculate 

 spherical triangles, square the circle, or cast a nativity. A 

 popular novelist (" Aurora Floyd," chap, iv.), describing 

 one of her characters " who was an inscrutable personage 

 to his comrades of the nth Hussars," says he was, 

 " according to the popular belief of those harebrained 

 young men, employed in squaring the circle in the soli- 

 tude of his chamber." 



To say of a man that he is a circle-squarer will make 

 an ordinary mathematician shrug up his shoulders and 

 indicate expressively that there is, in his opinion, a screw 

 loose somewhere. Having had some slight acquaintance 

 with the writings of a few of the race forced upon us, we 

 propose here to pass them under review, generally con- 

 tenting ourselves with letting them speak for themselves, 

 for thus shall we possibly most efitectually confute their 

 absurdities, at least in the judgment of our mathematical 

 readers. 



De Morgan, the great exposer7of circle-squarers, tri- 

 sectors, et id genus onme, has, after Montucla, stated 

 (" Budget of Paradoxes," p. 96) that there still exist three 

 ideas in the heads of this race— (i) That there is a large 

 reward offered for success ; (2) that the longitude problem 

 depends on that success ; and (3) that the solution is the 

 great end and object of Geometry. Some eight years ago 

 we saw a letter from a Spanish Don of La Mancha, who 

 offered to send an infallible method of squaring the circle ; 

 and within the last four months an application came to 

 us from Sweden, in which the author stated that he had 

 heard that the London Mathematical Society had offered 

 a prize for the trisection of angles, and as he had after 

 long working at the problem obtained a solution, he was 

 ready to transmit the same, but his organ of caution led 

 him to fear lest his communication might get into im- 

 proper hands, and so he wished to know to whom to 

 send the aforesaid solution. We need hardly say that the 

 Society, in this matter imitating the example of the 

 French Academy of Sciences and of our own Royal 

 Society, has declined to receive any communication upon 

 either of the above-named subjects or upon that of the 

 allied problem, the Duplication of the Cube. This decision 

 was arrived at in consequence of a bulky mass of papers 

 on the circle problem having been laid before the Presi- 

 dent in the end of 187 1. The author had previously sub- 

 mitted his papers to our own examination, and after 

 some little perplexing we were able to indicate the point 

 at which the author had tripped. We have heard nothing 

 further of the solution, nor seen any of the elaborate 

 figures since. We think it fair to state that we believe 

 this cyclometer to have been an honest man and a good 

 geometer. He had worked at the problem, off and on, 

 some twenty years, and attacked it by the lunes of 

 Hippocrates of Chios. 



We have consulted the " Introductorium Geometri- 

 cum" of Charles de Bovelles (Eovillus) in the 1503, 



