68 



NATURE 



[March i8, 1909 



tion that might be urged on the ground of the charter is 

 wholly academic, for the society cheerfully admits, un- 

 mindful of the provisions of the charter, any alien who 

 chooses to apply, and, as the recent ballot has proved, allows 

 him to exercise the de facto rights and privileges of a 

 corporator. A British-born woman may at least plead thai 

 she, at all events, is a " loving subject." The conflict of 

 legal opinion has made it abundantly clear that there is 

 no practical value in the doubt that has been raised as to 

 the ineligibility of women, but there is absolutely no room 

 for difference of opinion as to the ineligibility of the alien 

 to act as a corporator. Why, then, should the British-born 

 woman be excluded and the alien be admitted? If the 

 alien may vote, why may not the British-born woman ? 



T. E. Thorpe. 



The Isothermal Layer of the Atmosphere. 



The point raised by Mr. R. F. Hughes in Nature oI 

 January 2i and February ii is one that appears to deserve 

 consideration by the investigators of the upper air. He 

 contends, I take it, that even if the instrument records 

 perfectly the temperature of the metal strip, it does not 

 necessarily tell us the temperature of the upper air, but 

 the temperature which the strip takes up in order to bring 

 about a balance between the heat received and lost by it ; 

 and in calculating this temperature it is unfair to neglect, 

 without investigation, the absorption and emission of radia- 

 tion by the instrument and the balloon. 



If we take the case of the balloon, in a night ascent, we 

 may write for the time variation of the temperature T of 

 the gas in the balloon, assumed to be a sphere of radius r. 



dT 



-= -10"-!' + 



J_ 4^r'yp t^(T - e) 



MC 



(I) 



a MC 



vvhere v is the upward velocity of the balloon in metres per 

 sec, M is the mass and C the mean specific heat of the 

 balloon and its contents, B the temperature and p the 

 density of the outside air, and / a constant. 



The first term represents the rate of decrease of tempera- 

 ture owing to expansion of the balloon. 



The second term represents the rate of increase of 

 temperature, assumed to take place uniformly through the 

 balloon owing to the excess, I, of energy absorbed over 

 energy radiated. In the lower layers I is almost certainly 

 very small, and probably negative, but it may not be so 

 at great altitudes. 



The last term is an empirical formula to represent the 

 rate of decrease of temperature owing to convection of 

 heat from the balloon by the outside air. 



If we assume the atmosphere to be transparent and the 

 earth to be a perfect radiator, and write E for the intensity 

 of its radiation per square centimetre, the balloon receives 

 from the earth energy at the rate airr^E, of which it 

 absorbs, say, one-half, and transmits the remainder. (A 

 very thin rubber membrane has been found to transmit 

 7:; per cent, of low-temperature radiation.) At the same 

 time, the balloon is radiating in all directions at a rate 

 i.i\Trr^B approximately, where B is the intensity of radia- 

 tion of a perfect radiator at the balloon's temperature. 



Thus I = 7r^=[E-2B]. 



If the temperature of the earth is 280° A. ( = 7° C), then 

 E is about 0-55 gm. cal. per niin., and is equal to 2B 

 when the temperature of the balloon is 235° A. If the 

 temperature of the balloon falls to 200° A., B = JE nearly 

 and I = i7rr=E. 



I know of no measurements of the rate of convection 

 from a rubber balloon, but a considerable number of experi- 

 ments have been made to determine this rate for metallic 

 thermometers. According to A. de Quervain (Beilra.^e ziir 

 Physik der Freien Atmosphare. vol. i., p. 192), the 

 value of fpv for •y = 5 m.p.s, and p= 1-2x10-' is roughly 

 equal to o-i gm. cal. per min. 



The equation (i) therefore reduces to 



'^T= - io-=c/-l- ^-^[E - 2B - 0-4-?- (T - «)] 



/// 60MC 



if ^ = S m.p.s. and E, B are measured in gm. cal. per min. 



Thus if p = Ip„ and B = 5E, T must exceed 6 by more 

 than 2° C. if the effect of convection is to exceed that of 

 radiation. 



If we take the balloon to be initially of 100 cm. radius, 

 and assume that the heat capacity of the envelope is one- 

 half that of the hydrogen, we have for MC the value 



1-5 X 3 •4r X Jit. io^S'8. io~' = ir x6oo nearly, 



the specific heat of hydrogen being 3*4I. 



Also ?^ will be 2 X lo^ whence ;^^ = 33, and the first term is 

 MC 



therefore comparable with the last two in the equation (1). 

 If the temperature is diminishing at the rate of 6° C. per 

 kilometre, T will diminish at the same rate if it exceeds 

 6 by about i°-7 C. Even if convection is only one-third 

 as efficient as Quervain found, the temperature excess is 

 not more than 5° C. 



The thermometers are of bright metal, and even if they 

 are directly exposed to the earth radiation they will not 

 absorb at a rate as great as one-tenth of the rate we have 

 assumed for rubber. 



The equation for the temperature variation would be 



tiT_ A[E-2 B]_/pv.S ..J. 

 dt loMC MC 



(2) 



MC 



where S is the area exposed to the air current, and iX 

 the radiating area, which is certainly less than S for a 

 tube thermometer. 



If we take Quervain's figures we get A = 8o cm.', 



and J^ = 8. ^ nearly, for a Hergesell instrument, while 

 MC po 



160, so that for T = 200° A. we have - =4-4-27 (T - B), and 



ar 

 the excess of T over B would be but slightly greater than 2° C. 



We may, then, take it as certain that the temperatures 

 recorded in night ascents can be but slightly affected by 

 radiation so long as the upward velocity is as great as 

 5 m.p.s. The assumptions made as regards radiation and 

 convection are, of course, only approximate, but I think 

 they err on the side of exaggerating the radiation effect. 



In conclusion, I may add that I undertook this calcula- 

 tion believing that it might be possible for radiation 

 materially to affect the temperature, at least of the balloon, 

 because I knew that even at night radiation from external 

 sources was not insignificant. The result is, however, a 

 complete justification of the instrumental records. The 

 isothermal region exists, and it exists for the very reason 

 which, in Mr. Hughes's opinion, renders useless the instru- 

 mental records — the necessity for the material air also to 

 preserve a balance between heat received and heat lost by 

 radiation. E. Gold. 



Vienna, February 15. 



The Promotion of Scientific Research. 



Public attention was directed to the subject of scientific 

 research by the proceedings at the annual meeting of the 

 trustees of the Carnegie Trust, and especially by the 

 prominence given to the promotion of original research in 

 the speech of Mr. Balfour, reported in Nature of March 4. 

 The reports of the proceedings may have engendered in 

 some minds exaggerated notions as to the extent to which 

 philanthropic effort may succeed in solving the problem of 

 providing incentives to original research. It will be as 

 well, therefore, to mention, for the information of those 

 who are unacquainted with the regulations under which 

 monies subject to the trust may be applied in the promotion 

 of original research, that the incomes of the beneficiaries 

 under the trust are very limited, and the conditions which 

 are specified in the scheme of the trustees are very restric- 

 tive. Mr. Balfour, though he spoke encouragingly of the 

 methods adopted by the trustees, alluded to the difficulty 

 and delicacy of the task of selecting people for original 

 work, and to the " puzzling questions of administration " 

 with which it is surrounded ; and it seems impossible, with- 

 out the aid of legislation, to devise any scheme for the 

 application of monies to research purposes which will 

 succeed in inspiring confidence in research workers and 

 which will not greatly restrict the research work which it 

 may be designed to encourage. Had inventors of patent- 

 able inventions been encumbered by conditions sirnilar to 

 those to which research workers who are the objects of 

 private munificence are subjected, the progress of inven- 



NO. 2055, VOL. 80] 



