May 23, 1901] 



NA TURE 



93 



credit of perfecting its laws of operation is assigned to C. S. 

 Peirce and to Schroder, The keynote, according to the author, 

 is the prominence given in his memoir to three ideas, viz. that 

 of the " invariants '' of a function of independent variables, that 

 of " prime functions of independent variables," and that of the 

 theory of "substitutions" of independent variables for inde- 

 pendent variables. The last idea connects the algebra with the 

 theory of groups and opens out a large field for investigation in 

 that direction. The memoir, which occupies much space (27 

 pp.), is to be concluded in a subsequent number. — V. Snyder 

 contributes a short note on a special form of annular surfaces. 

 — On the transitive substitution groups whose order is a power 

 of a prime number, by G. A. Miller, is a further contribution 

 to a branch of mathematics for which the author has already 

 done so much excellent work. — Geometry on the cubic scroll of 

 the second kind, by F. C. Ferry, is a first instalment. Its 

 object is to give a detailed treatment of several of the more 

 interesting questions connected with the geometry of this scroll, 

 and especially to consider the surfaces which can be passed 

 through any curve on the scroll, so far as the order of those 

 surfaces and the natures of the residual intersections are con- 

 cerned. References are given to many memoirs bearing on the 

 subject. 



SOCIETIES AND ACADEMIES. 



Royal Society, March 7. — " On the Heat dissipated by a 

 Platinum Surface at High Temperatures. Part iv. — High- 

 pressure Gases. By J. E. Petavel, A.M.I.C.E., A.M.I. E.E., 

 John Harling Fellow of Owens College, Manchester. Com- 

 municated by Prof. Schuster, F.R.S. • 



The rate of cooling of a hot body in gases at pressures up to 

 one atmosphere has received considerable attention, but with 

 regard to gases at high pressures practically no data were up to 

 the present available. 



The present experiments were carried out with a horizontal 

 cylindrical radiator contained in a strong steel enclosure, the 

 enclosure being maintained at about 18° C. by a water circula- 

 tion. 



It is shown that the rate at which heat is dissipated by the 

 radiator may be expressed by the following formula — 



E = a/» +6j)li3-, 



where E = emissivity in C.G.S. units = total amount of heat 

 dissipated expressed in therms (water-gramme-degrees) per 

 square centimetre of surface of radiator per second : / = pressure 

 in atmospheres ; -7 = the temperature of the radiator minus the 

 temperature of the enclosure, or in other words the temperature 

 interval in degrees Centigrade. 



The gases studied are oxygen, hydrogen, air, nitrous oxide 

 and carbon dioxide. In the case of the first three the formula 

 holds good between 7 and 120 atmospheres and between 100 

 and iioo°C. 



All the gases studied showed a rapid increase of the effective 

 conductivity with the pressure. 



Physical Society, May 10.— Prof. S. P. Thompson, 

 president, in the chair. — A paper on applications of elastic 

 ■solids to metrology was read by Dr. Chree. The object of the 

 present paper is to exemplify the bearing of elasticity on physical 

 measurements. Many of the results depend ultimately on a 

 previous paper by the author, in which expressions were obtained 

 for the mean strains and for the change in total volume of any 

 homogeneous elastic solid acted on by any given system of 

 forces throughout its nia.ss or over its surface. The effect 

 of the pressure of a surrounding medium of constant density 

 upon the shape and volume of an isotropic solid is considered, 

 and the theory is extended to the case of an .ijolotropic solid 

 in a medium of varying density. The change in volume of the 

 material of the walls of a flask containing liquid is next investi- 

 gated, and it is shown that the change is independent of the 

 thickness of the walls, the mean expansion per unit of volume 

 being inversely proportional to the whole volume. Whether the 

 alteration consists of an increase or a decrease depends upon the 

 dimensions of the vessel. We cannot, in general, determine the 

 effect on the internal capacity of a vessel due to the pressure 

 of contained liquid, but if the walls are coaxial right circular 

 cylinders, the common axis being vertical, the solution is possible. 

 As a numerical example a glass tube 127 cm. high, 10 cm. 



NO. 1647, VOL. 64] 



internal diameter and i'5 mm. thick would hold o'li grammes 

 more mercury than it would if inelastic. The solution is possible 

 in the case of a spherical shell, and this problem is also investi- 

 gated in the paper. The author next considers the application of 

 the theory of elasticity to standards of length, and to give a 

 more exact idea of the problems actually occurring in metrology 

 he deals particularly with five forms — the standard yard, the 

 international prototype metre of X section, a working standard 

 belongmg to the Bureau International, and two deflection bars 

 used in magnetometers- Most'modern standards are supported, 

 not over the whole lower surface, but either on two symmetrical 

 rollers or on three points. In using standards of length it is the 

 horizontal projection of the graduated surface that usually con- 

 cerns us, and it is proved that unless we deal with a very long 

 bar the difference between the chord and the arc is very small. 

 The curvatures and lengths of bars supported in various ways, 

 both loaded and unloaded, are treated at length, and it is shown 

 that by a proper arrangement of supports the alteration in length 

 between two points due to bending can be rendered so small as 

 to be of no practical importance. In the metre prototypes of X 

 section the divisions occur on the neutral surface and their distance 

 apart is unaffected by stretching of the material. In the case of 

 magnetometer deflection bars it is advisable to have the magnet 

 light and as near to the haras possible. Mr. Watson said that it 

 was usual in deducing the radius of a coil from the measurement 

 of its circumference with a steel tape to diminish the result by 

 half the thickness of the tape. He would like to know if this 

 was the right correction to apply. In measuring the circum- 

 ference of a cylinder it is necessary to wind the tape in a spiral 

 so as to bring the divisions side by side. This gives a result 

 which is too great, and not too small as might at first sight be 

 imagined. Dr. Lehfeldt asked if the work of the author could be 

 used to determine the pressure corrections of thermometers. He 

 would like to ask why it was necessary to use supports instead 

 of allowing a standard to rest on a flat surface. The 

 chairman said that the paper was important because of its 

 bearing on the question of the relation between the units of 

 different nations. He drew attention to the alteration of the 

 factor converting metres into inches, and asked if it was due to 

 alterations in the properties of matter or to errors of observation. 

 The two legal definitions of the gallon differ by an appreciable 

 amount, and it would be interesting to know if this discrepancy 

 could be due to changes in the volume of measures due to the 

 liquids contained by them. Dr. Chree, in reply to Mr. Watson, 

 said the correction would depend upon the diameter measured, 

 because that determined the curvature of the tape and, there- 

 fore, the stretching produced. In reply to Mr. Campbell, the 

 author stated that direct experiments had been made upon the 

 bending of bars and they agreed well with theory. The correction 

 formula obtained for a thermometer is similar to the ordinary 

 one used. A bar is usually supported so as to remove the un~ 

 certainty of the distribution of surface pressure when it rests on 

 a flat surface not a true plane. In reply to the president, Dr. 

 Chree said that the alteration of the factor converting metres 

 into inches was probably due to errors of observation on ac- 

 count of the width of the divisions of the standard yard, and on 

 account of the difficulty of obtaining the bar at the standard 

 temperature of 62" F. — A paper by J. Rose-Innes and Prof. S. 

 Young, on the thermal properties of isopentane compared with 

 those of normal pentane, was read by Mr. Rose-Innes. In 

 previous papers the authors have investigated experimentally 

 the thermal properties of isopentane and normal pentane and 

 have stated certain conclusions from their observations. 

 The present paper gives the conclusions reached after a 

 more exhaustive examination of the experimental results 

 of the former papers. The quantity RT-/w at any volume 

 and temperature is called the departure from Boyle's Law at 

 that point, and it is found that there is a constant ratio be- 

 tween the departures from Boyle's Law of isopentane and 

 normal pentane at the same volume and temperature. 

 To test the law a probable value of the ratio was determined, 

 and by means of it a large number of values of fi> for isopen- 

 tane were calculated from results for normal pentane. Thesje 

 calculated values fall upon the same curve as the observed 

 values and agree with them to within about i per cent. The 

 authors are confirmed in their previous conclusion that the 

 difference of pressure between two isomeric substances at the 

 same temperature and volume involves the same power of 

 the density as the first deviation from Boyle's Law, i.e. the 

 second power. Mr. J. M. Gray said the numbers obtained 



