January 5, 1922] 



NATURE 



the ray as deduced from measured values of the 

 coefficient of refraction is distinctly higher, being 

 about six and a half times the earth's radius, or about 

 26,000 miles. 



Both letters contain an inadequate presentation of 

 the facts of atmospheric refraction in that they assume 

 that the path of the ray is circular. A very much 

 fuller investigation is necessary in order to account 

 for the distance of the visible horizon or its depression 

 below the true horizontal. 



Starting with the assumption that the atmosphere 

 is in static equilibrium, leading to the differential 

 equation dp = ^gpdh, and with the pressure-density- 

 temperature law p = CpT, a further assumption must 

 be made before a complete solution can be arrived 

 at giving pressure, density, and temperature in 

 terms of height. A simple assumption to make is 

 that of a uniform temperature-gradient expressed as 

 Ti'T« — i — ah. For the isothermal conditions a = o; 

 for the adiabatic, a corresponds to a drop of i° C. per 

 330 ft. increase in height. The integration of the 

 general equation leads, provided h does not exceed 

 200 or 300 ft., to p = po-gPQh^nd plp^ = i-{gp^lp^-a)h.. 

 Since by Dale and Gladstone's law p is proportional 

 to » — I, we obtain without difficulty 



n = n^-o-ooo2(){gpJp^-a)h. 

 Further, it is not difficult to show that with a ray 

 that is nearly horizontal the radius of curvature <r is 

 given by the approximate equation 



I /o- = 000029(^/3 J/)„- a). 

 This equation will give any value we like for cr pro- 

 vided we assume a suitable temperature-gradient. If 

 we put a = o (the isothermal state) we get substan- 

 tially Mr. Mallock's figure. If we take the adiabatic 

 gradient the radius is about 20,000 miles. If we take 

 a fall of temperature of 1° C. per 200 ft., Dr. de 

 Graaff Hunter's value results. A gradient of 1° C. 

 per 100 ft. gives a flat ray and an atmosphere of 

 uniform density. To obtain greater curvatures than 

 Mr. Mallock's figure the temperature-gradient must 

 be reversed. 



It is no use to take this formula and expect it to be 

 uniform over even very narrow levels when close to 

 the surface of the sea. The temperature-gradients in 

 the first 30 ft. (the average height of the bridge of 

 a ship above the sea) are very frequently greater 

 than any of the gradients mentioned above, and show- 

 wide variations in that space. In such case the path 

 of a ray from a visible object more than a mile away 

 is nothing like circular, but may have variations in 

 its curvature of 300 or 400 per cent. I am aware 

 that the value of the coefficient of refraction men- 

 tioned by Dr. de Graaff Hunter is used in books of 

 nautical tables in computing the dip and distance of 

 the sea horizon, but I am aware also that actual 

 measurements of the dip at sea shoA^ that tabulated 

 values are frequently in error, sometimes even of the 

 -wrong sign ! Measurements made by Blish off the 

 coast of California showed that a zero dip is quite 

 possible. In the Red Sea the sea horizon is often 

 refracted above the true horizontal. 



Consider the path of the ray of light from the 

 horizon to the observer's eye when the dip is zero. 

 The path touches the earth's surface at the horizon 

 and touches a concentric sphere of perhaps 30 ft. 

 greater radius at a point only six or eight miles 

 away. The radius of curvature of the ray must be 

 greater than the earth's radius at the horizon and 

 smaller at the observer — a maximum at the first point 

 and a minimum at the second. Neither Mr. Mallock's 

 figures nor Dr. de Graaff Hunter's can deal even 

 approximately with a ray-path of this nature, and I 

 NO. 2723, VOL. 109] 



think it may be asserted without question that to 

 take adequate account of the path of rays of light 

 through the lower levels of the atmosphere d^nands 

 consideration, not only of the curvature of the ray- 

 path, but also of the first and second differentials of 

 the curvature. Thos. Y. Baker. 



Admiralty Research Laboratory, Teddington, 

 Middlesex, December 22. 



The Message of Science. 



Two great questions are raised in the abridgment 

 given in Nature of December 22 of the notable ad- 

 dress delivered by Sir Richard Gregory during the 

 Edinburgh meeting of the British Association. They 

 are : — (i) How can an interest in, and respect for, 

 science in all its branches, with their essential unity, 

 be developed locally? (2) How can the work of the 

 British Association be so broadened and improved as 

 to ensure that it will yield — to use the words of Sir 

 Richard Gregory — "a statement of ideals and of ser- 

 vice, of the strength of knowledge and of responsibility 

 for its use " ? 



Local scientific societies consist of three types : — 

 (i) Sectional bodies interested in general engineering 

 problems or in the technical details of certain sciences 

 applied to the chief industries of the district. 

 (2) Natural history societies or field clubs. (3) 

 Literary and philosophical societies which provide in 

 a few large towns a good library and series of winter 

 lectures. 



With regard to the first type little need be said. 

 They fulfil their specialised functions fairly well, but 

 their work would be greatly improved, and made 

 gradually more attractive, if it were possible to secure 

 an outlook on the broad field of science. Sir Richard 

 Gregory said in the course of his address in Edin- 

 burgh : " Whatever Labour may declare officially, it 

 is scarcely too much to say that artisans in general 

 show less active interest in scientific knowledge now 

 than they did fifty years ago." This statement is 

 true, not of artisans only, but of all classes. The 

 demand has been made on science : " Make us 

 rich and comfortable." Science, In a large measure, 

 has responded. But with wealth and comfort has 

 come a lessening of respect for knowledge, The 

 highest things that science can give— an ardour for 

 truth, the power to rise above sordid interests, the 

 desire to become co-workers in an infinite process by 

 which soul is drawn from matter — have been set 

 aside, and we have been landed in a back-wash. 



I do not think any revolutionary changes are neces- 

 sary locally in order to bring back the enthusiasm 

 which linked science a generation ago to human 

 liberty and human justice. Sir Richard Gregory 

 speaks of a federation of local societies "to proclaim 

 the message of knowledge from the housetops." It 

 may be necessary, first of all, for these societies to 

 find out what the real message of knowledge is, but 

 they need not wait for perfect vision ; much can be 

 done while they are only groping. 



What is wanted, above all things, is such an 

 infusion of earnestness as will arrest the displacing 

 power of the mere lantern lecture. The lantern has 

 been a good servant, but it is threatening to become 

 a bad master. At present the great trouble of_ the 

 secretary of a literary and philosophical society is to 

 make his organisation pay its way. The chief thing 

 for which the organisation stands is often sacrificed in 

 the attempt to secure popular support. This attitude 

 must be abandoned even if abandonment leads into 

 the wilderness. The message of science will come 

 back from there with renewed constraining power. 

 There are thousands waiting for the message. What 



