534 



NA TURE 



[April 7, 1892 



(i) as above noticed for all collisions by introducing the 

 factor ti - \i + c-nr to denote frequency of collision ; or 

 (2) for all spheres as they exist at a given instant. Now, 

 Prof. Burnside has calculated the average rotation energy 



by method (2), which gives 2A0 



But when he comes to 



Prof. Tait, not observing, I think, that that result is given by 

 Tait as the average for all collisions per unit time. And then, 



equating two inconsistent things, he gets the conclusion -7=7, 



k h 



or the mean energy of rotation is twice that of translation. 

 To be consistent, he should have given the mean of (m - U)^ 



for all pairs of spheres — that is, «"^ + U^ = j. And so his resuU 



should have been - = -, agreeing with Maxwell. 

 k h 



It may be interesting to see what would have been the result 

 of introducing the factor m — U + cnr to denote frequency of 

 collision. The expression whose average is required would 

 then be — 



(m - U + f-nr)2{2w - ^(K + k){u- U)}. 



As the frequency factor ti - \5 + cw must be always positive, 

 we must integrate between the limits U=+ooto U = -oo, 

 and ?< = + 00 to ?/ = U - cts. After integration, we reject odd 

 powers of -or. 



I have worked it out to the first power of c, rejecting c^, &c. 

 We have, in that case, to evaluate — 



{ f {2-nr{u - Vy- + ^C'^-'-iu - U) 



The first term gives zero. The second term gives -~> and 

 the third term gives '^^ , , "' . From which, on substitution, 



and integrating for w, n, &c., from 00 to - 00, we easily obtain 

 /.J = X'2 = &c. - /i. 



To extend the process to cases in which c^, &c., cannot be 

 neglected, would be difficult. But I think the onus probandi 

 now lies on the other side. S. H. Burbury. 



Double Orange. 



On a blood orange being cut open by my little daughter yes- 

 terday, a small orange was found inside, which, although no 

 larger than a hazel-nut, was yet perfect in form and colour. It 

 showed no point of difference, other than that of size, as com- 

 pared with the parent orange, and there was nothing in the 

 appearance of the uncut fruit suggestive of the miniature of itself 

 carried within. My sole right to write upon this subject is one 

 you have always recognized in your journal, viz. that to record 

 an interesting fact. Gerald B. Francis. 



Katrine, Surbiton. 



METALS AT HIGH TEMPERATURES} 



T PROPOSE this evening to consider, first, the methods 

 *• of measuring high temperatures, and, second, to 

 describe certain effects they produce on metals. 



Geber, writing in the eighth century, gives directions 

 for obtaining high temperatures, but points to the dif- 

 ficulties that arise in practice, "because fire is not a thing 

 which can be measured, ' sed quomam non est res ignis, 

 qucz mensurari possitJ " "- It is not sufficient to attain 



1 A Lecture delivered at the Royal Institution by Prof. W. C. Roberts- 

 Austen, C.B., F.R.S., on Friday evening, February 5, 1892. 



- From the_ edition of his " Sumraa Perfectionis Magisterli," p. 28, pub- 

 lished in Venice, 1542. 



NO. II 71, VOL. 45] 



temperatures that are known to be high ; it is necessary, 

 for the purpose of modern investigation, to measure them 

 with accuracy ; and few of the early chemists in this 

 country did more in afifording a basis for the study of 

 metals at high temperatures than Robert Boyle, the 

 application of w hose well-known law to solutions of metals 

 in each other has been made evident by recent work. 

 The 30th of December last was the third centenary of his 

 death ; it is well, therefore, that this lecture should begin 

 with a tribute to his memory. He suggested improve- 

 ments in the ordinary mercurial thermometer,^ constructed 

 what would appear to be the first air thermometer with 

 an index ; and although he did not do much for thermo- 

 metry at high temperatures, he appears to have been 

 struck by what must have been a quaint device for 

 regulating high temperatures, for he points out that " the 

 great mechanic, Cornelius Drebel ^ made an automatous 

 musical instrument and a furnace which he could regu- 

 late to any degree of heat by means of the same instru- 

 ment." He indicates various degrees of intensity of 

 heat by reference to the colour of a glowing mass of 

 fuel, and says that,^ " tho' we vulgarly say in English, 

 *a thing is red hot,' to express a superlative degree of 

 heat, yet, at the forges and furnaces of artificers, by a 

 white heat they understand a further degree of ignition 

 than by a red one." It is not a little strange that for 

 three centuries after his death the same vague ex- 

 pressions have constantly been used in describing high 

 temperatures. 



A great step in advance was made in 1701 by Sir Isaac 

 Newton,* who applied the law of cooling to the measure- 

 ment of temperatures beyond the range of the mercurial 

 thermometer, and in the notes which accompany his 

 " Scala graduum caloris " he showed that he knew that 

 the freezing-point of lead differs slightly from its melting- 

 point. 



Eighty years later, Josiah Wedgewood (1782)," aided by 

 one of my predecessors, Mr. Alchorne, Assay Master of 

 the Mint, determined a few melting-points of metals, and,, 

 in communicating a description of his " thermometer for 

 measuring the higher degrees of heat " to the Royal 

 Society, we find him, one thousand years after Geber 

 had said that " fire cannot be measured," still lamenting 

 the want of suitable instruments, saying : " How much 

 it is to be wished that the authors [to whom he refers] had 

 been able to convey to us a measure of the heat made use 

 of in their valuable processes ; . . . a red heat, a bright 

 red, and a white heat are," Wedgewood adds, " indeter- 

 minate expressions, and even though the three stages are 

 sufficiently distinct from each other, they are of too great 

 latitude, and pass into each other by numerous gradations- 

 which can neither be expressed in words nor discriminated 

 by the eye." Another ninety years brings us to the last 

 time that the measurements of high temperatures formed 

 the subject of a Friday evening discourse in this Institu- 

 tion. On March i, 1872, the late Sir William Siemens 

 addressed you on the measurement of " heat by electri- 

 city" ; ^ and, speaking of the mercurial thermometer, said : 

 " When we ascend the scale of intensity we soon approach 

 a point at which mercury boils, and from that point up- 

 wards we are left without a reliable guide, and the result 

 is that we find, in scientific books on chemical processes, 

 statements to the effect that such and such a reaction 

 takes place at a ' dull red, such another at a ' bright red,' 

 or a '■ cherry red,' or a ' white heat '—expressions which 

 remind one," he adds, " of the days of alchemy rather 

 than of chemical science at the present day." 



' Boyle's Works, Shaw's edition, vol. i. p. S7S, 1738. 



2 Cornelius van Drebel, 1572-1634, loc. cit. vol. iii. p. 38, 1738. 



3 Loc. cit., vol. ii p. 28. 



'' Phil. Trans. Roy. Soc, vol. xxii. p. 824. 



5 Ibid. vol. Ixxii. p. 305. 



6 Roy. Inst. Proc, vol. vi. p. 438, 1872. 



