234 



NATURE 



[May 2^, 19 J 8 



130,000 light-years; 39', 65,000 L.V.; 77', 43,000 

 L.Y.; 12-4', 33,000 L.Y.; 20', 26,000 L.Y. 



These methods have been applied to finding the 

 distances of sixty-nine globular clusters. The nearest 

 are w Centauri and 47 Tucanae, 23,000 L.Y. ; the 

 average distance is 75,000 L.Y. ; seventeen clusters 

 are more distant than 100,000 L.Y.; the most dis- 

 tant is N.G.C. 7006, some 200,000 L.Y. (more than a 

 trillion miles, using the British system of numeration). 



The distribution in galactic longitude is curious. 

 There are none between 45° and 190 , while more than 

 half are between 300° and 350°. In latitude there are 

 maxima on each side of the galaxy, with a gap in 

 the galactic plane itself. The system forms a split 

 ellipsoid with longest diameter some 300,000 L.Y., and 

 distance of centre 65,000 L.Y. The co-ordinates of 

 the centre are R.A. lyh. 30m., S. decl. 30°. While 

 lying outside the galactic limits, the distribution of 

 the clusters indicates that they form part of the same 

 cosmic unit as the galaxy. Some preliminary in- 

 vestigations of their radial velocities by Prof. Slipher 

 indicate that these are high, but smaller than those 

 of the spiral nebulae. A. C. D. Crommelin. 



FROST IN THE UNITED STATES. 



IN a paper with the above title presented before the 

 second Pan-American Scientific Congress at Wash- 

 ington (Washington : Government Printing Office, 

 19 17) Mr. William Gardner Reed discusses the damage 

 by frost in the United States. Following the rule of 

 the Weather Bureau, he classifies frosts as "light," 

 "heavy," and "killing," but he determines the dates 

 of the last killiing frost in spring and the earliest in 

 autumn from the records of temperature, and not from 

 the reports of damage. This is fully justified by the 

 fact tlhat the observations of temperature are con- 

 tinuous and exact, whereas the damage depends on 

 many conditions. 



The number of observations at any one individual 

 station is seldom sufficient to show the precise chance 

 of frost after a given date at that particular station, 

 but if the observations at neighbouring stations are 

 utilised, a sort of general mean date for the last frost 

 in a district can be obtained. Working on these lines, 

 Mr. Reed gives maps of the United States with lines 

 showing the limits for killing frosts at various dates, 

 the consecutive lines showing differences of ten days 

 in the date. Thus the date for a line running <:lose 

 to the Gulf of Mexico is March i, but for a line near 

 the Canadian boundary it is as late as May 21. 



The mean date of the last or earliest frost is not of 

 much importance to the cultivator ; he wants to know 

 the date beyond which he will be reasonably safe from 

 damage. For this purpose Mr. Reed calculates the 

 standard deviation of the date, and, since he finds that 

 the distribution follows the normal curve, he is thus 

 able to give the date beyond which a killing frost is 

 not likely to occur more than once in ten years. This 

 is, no doubt, a much more trustworthy hiethod than 

 using the extreme dates at each separate station. 

 Charts are prepared in a similar way for the first 

 killing frost in autumn ; near the Canadian boundary 

 the date is as early as September i, but delayed until 

 November i near the Gulf Coast. 



The meteorological conditions that favour frost are 

 not quite the same over the different States, though 

 they are, in general, the clear skies of an anticyclone 

 with their local nocturnal cooling. As a rule, east of 

 the Rocky Mountains the frost area is south-east, and 

 somewhat in advance of the anticyclone. In California 

 north-easterly and easterly winds prevail for twenty- 

 four or thirty-six hours beforehand, and a frost occurs 

 if a clear sky accompanies the dropping of the wind. 



NO. 2534, VOL. lOl] 



Mr. Reed also discusses the cause why plants are 

 damaged by frost, and arrives at the conclusion that 

 the matter is far from being well understood. It is 

 a very common belief tlhat the damage is not so 

 serious if the rise of temperature is slcnv, but Mr. 

 Reed says that recently accumulated evidence throws 

 some doubt upon this. He appears to hold that the 

 length of time during which the trees are exposed to 

 the cold is of importance, and that even if the heating 

 of an orchard has been delayed until after the critical 

 temperature is reached, there may still be time to save 

 the fruit; and he concludes this part of his suibject 

 by saying that "evidently much more investigation is 

 needed concerning the oature of frost effects within 

 the plant." 



CONSTRUCTION FOR AN APPROXIMATE 



QUADRATURE OF THE CIRCLE. 

 'X'HE issue of the Comptes rendus of the Paris 



-*■ Academy of Sciences for March 25 last contains 

 a pajjer by M. de Pulligny on a simple geometrical 

 representation of the approximations to the numerical 

 value of rr given by Archimedes and Metius. Other 

 approximations can be represented in the same way. 



The construction is as follows : — Let OAand OB be 

 two radii of a circle at right angles to one another. 

 Let S be the mid-point of OA. Draw through S a 

 line cutting- the circle in P and Q, and OB (produced 

 if necessary) in k. Let OA=^, OR = ya< PQ = u. 

 Then we have u'^=\4.-4.y'^/Xi +4.^)1 a^ = (say) via-. As 

 PQ rotates round S, y varies continuouslv from o 

 to 00, and m from 4 to 3. When y = o, the square on 

 PQ is greater than the area of the circle; when y= 00, 

 it is less : thus, in intermediate positions of the chord, 

 the square on PQ gives an approximate quadrature of 

 the circle, and m gives an approximate value of «-. 



The point R determines the chord PQ. If on AO 

 produced we take a point I so that 4.AI = 5a, and if 

 with I as centre and lA as radius v^e draw a circle 

 cutting OB produced in R, we have y^ = 3/2, and 

 m = 22/7, the higher limit given by Archimedes. 



If on AO produced we take a point J so that 

 8.0J = av'3 (a result for which a geometrical construc- 

 tion can be easily given), and if with J as centre and I.'V 

 as radius we draw a circle cutting OB produced in R, 

 we have y^ = (6+ i/i6)/4, and ^ = 355/113, the approxi- 

 mation given by Metius. 



It will be noticed that there is nothing in this con- 

 struction to enable us to fix the limits within which we 

 must choose R to get a close approximation; but corre- 

 sponding with any assigned value of m, and therefore 

 of y, it gives a geometrical construction for the side of 

 the square thus determined. 



W. W. Rouse Ball. 



RADIATION AND THE ELECTRON.-^ 

 "D ECENT developments in the domain of radiation 

 -'^ are of extraordinary interest and suggestiveness, 

 but they lead into regions in which the physicist sees 

 as yet but dimly — indeed, even more dimly than he 

 thought he saw twenty years ago. 



But while the beauty of a problem solved excites the 

 admiration and yields a certain sort of satisfaction, it 

 is, after all, the unsolved problem, the quest of the 

 unknown, the struggle for the unattained, which is of 

 universal and most thrilling interest. I make no 



1 Address to the Section of Physics and Chemistry of the Frankh'n 

 Institute, Philadelphia, on January 4, 1917, by Prof. R. A. Millikan, pro- 

 fessor of physics in ihe University of Chicago. The substance of this lecture 

 has since been incorporated into a book recently issued by the Universitj' of 

 Chicago Press, entitled " The Elec'ron." 



