February 23, 1899] 



NATURE 



393 



therefore give out some light, but it is so feeble as to 

 appear black by contrast with the very much brighter 

 rays coming direct from the original source. 



This great law may be summed up as follows : Gases 

 and vapours^ -w/icit rclatii'cly cool, absorb those rays 

 which iltcy themselves emit ivhen inca7idescent ; the ab- 

 sorption is continuous or discontinuous (or selective) as 

 the radiation is continuous or discontinuous (or selective). 



I have referred to this matter at some length because 

 in our light sources, in the sun, and in many of the stars 

 we have light from a more highly heated centre passing 

 through an envelope of cooler vapours, and on this 

 account absorption phenomena are produced. 



Our knowledge of the chemistry of the sun and stars 

 is founded upon the e.xact coincidence of the bright lines 



understand the e.xponential theorem, it is absurd to think 

 that even average schoolboys who have been six years 

 at mathematics can understand how logarithms are 

 calculated. But if a schoolboy has been told what a 

 logarithm means, and if he can extract a square root by 

 the ordinary arithmetical method, and especially if he has 

 had a sensible teacher and been allowed to use tables of 

 logarithms, 1 think that he will have no difficulty irk 

 understanding the following method, and will rather 

 enjoy working at it a little. 



Let him find 10'=, lO'A, loi'S^ ioi/"6, 101/3=, by re- 

 peatedly extracting square roots, getting out his answers 

 to five significant figures, say. Let him now by multi- 

 plication calculate 103/32, 105/32, (ic, right up to 10'. He 

 thus has a table of which I give the beginning and end. 



-The coinciden 



seen in our laboratories with the dark lines noted in the 

 spectra of those celestial bodies. The diagram shows 

 the coincidence in the case of the double orange line 

 of sodium vapour with dark lines in the spectrum of 

 the sun. 



Now if my reader has not hesitated to invest his or 

 her sixpence in a prism, and has had the patience (no 

 other quality is needed) to do what 1 have suggested, the 

 way is open to read with intelligence most books in- 

 volving spectrum analysis which he or she is likely to 

 come across ; terms such as 



Spectrum 



Continuous spectrum 



Grating 



Prism 



Spectroscope 



Slit 



Line spectra 



Fluted spectra 



Discontinuous (or selective) 



spectrum 

 Fraunhofer lines 

 Wave-length 

 Radiation 

 Absorption 

 Series 



should now have acquired a definite meaning, and 1 

 trust the expressiveness of the terms will be acknow- 

 ledged while they are accepted as part of the future 

 mental stock-in-trade. 



NORM.\N LOCKVKR. 



TO CALCULATE A TABLE OF LOGARITHMS. 



T 7 AVTNG been asked to give a short course of lec- 

 ■'^ tures to working men, which involved an account 

 of logarithms and the slide-rule, 1 felt that, although not 

 important, there would be some advantage in being able 

 to show them how they could calculate a table of 

 logarithms and a table of antilogarithms for themsehes. 

 Not that they need do so except as an interesting 

 exercise, for I do not think it necessary that a man or 

 boy must be able to make a tool before he is allowed to 

 use it, but it would do them no harm to explain to them 

 a simple method if I could invent one. 



Of course on the usual assumption that one must first 



NO. 1530, VOL. 59] 



If he plots these values on squared paper he gets a 

 curve which enables hmi to find the logarithm of any 

 number. 



If he wants answers right to four significant figures, it 

 is well to draw only a small part of the curve on one 

 sheet of squared paper. Thus plotting the first three 

 points so that the curve joining them (using a slightly 

 bent straight-edge) passes diagonally through a small 

 sheet of squared paper, one of niy students has found, 

 answers which are sufficiently correct to impress a 

 student with the value of the method. 1 give here seven 

 values taken at random from the curves of the early and 

 the late parts of the table. This was the first time that 

 he had tried the method, and the small errors in the 

 fourth significant figures are not likely to occur if a ma:i 

 has more practice. 



Number. ''^Ifi.'.^'IS "^ Cotx^a logarithm. 



'•035 

 I -1 10 

 I-151 



8 -950 

 9-175 

 9345 

 9825 



Even with the very cheapest squared paper we car? 

 construct tables of logarithms and antilogarithms which 

 will be quite accurate to three significant figures, and by 

 taking twice the trouble and using iQi w we may get a 

 table accurate to four significant figures, even with very 

 che^p paper. Also it is to be noticed that by using 

 !o'/'28 and higher roots, we can find the logarithm of 

 any particular number with any amount of accuracy 

 desired. John Perry. 



Royal College of Science, February 16. 



