454 



SCIENCE 



[N. S. Vol. XLII. No. 1083 



log r(x + 1) = .6162372 + (x + I) (log x - log e) 



+ .080929 sin ?5!:^, 



X 



using seven-plaee logarithms except for the second 

 or product term where ten-place logarithms were 

 used to avoid introducing inaccuracies when x is 

 large. This formula is also given in the introduc- 

 tion to "Tables for Statisticians and Biometri- 

 cians" (Chicago University Press), on page Iv, 

 where unfortunately by a printer's error the value 

 0.3990899 is wrongly given as .03990899. 



The various series of values are summar- 

 ized in the following table. 



of the existing tables of log-factorial n, that 

 of the approximation method is not ailected, 

 provided a sufficient number of places be used 

 in the logarithms of x and e when computing 

 the second or product term. 



P. F. EVEEITT 

 THE POSITION OF REFERENCES IN JOURNAL ARTICLES 



From one half to one per cent, of the space 

 in the majority of scientific journals giving 

 many references is wasted by the faulty posi- 

 tion and arrangement of the references. 



The amount of time wasted by the reader 



VALUES OP LOG T (n) BY DIFFERENT METHODS 



5.123 

 15.123 

 25.123 

 35.123 

 75.123 



1.4613860 

 11.0834931 

 23.9637108 

 38.6594135 

 107.7498704 



Pearl Forsyth 



1.4613679 

 11.0834916 

 23.9637096 

 38.6594126 

 107.7498692 



Pearl Using A- 



1.4619138 



11.0835559 



23.9637336 



38.6594251 



107.7498727 



Pearl Using A^ 



1.4615009 



11.0834985 



23.9637119 



38.6594138 



107.7498702= 



1.4613859 

 11.0834931 

 23.9637107 

 38.6594133 

 107.7498702 



1.4613860 

 11 0834930 

 23.9637107 

 38.6594133 

 107.7498702 



The table shows that Dr. Pearl's "exact" 

 value differs from the " more exact " value by 

 two units in the seventh place for the larger 

 values of n and in the ease of w = 75.123 is 

 inferior to the value found from interpolation 

 when third differences are used. 



A comparison of the values in the table 

 leads to the following conclusions. 



(i) For small values of n, up to about 5, it 

 is preferable to use the exact method if Leg- 

 endre's tables are available; in the absence of 

 Legendre's tables the Pearson approximation 

 formula should be used. 



(ii) For larger values of n, as shown by the 

 middle portion of the table, Pearson's formula 

 is superior to the interpolation method and 

 gives results which coincide with those found 

 by the 



(iii) For still larger values of n, 75 and up- 

 wards, the Pearson approximation formula and 

 the interpolation method using third differ- 

 ences both give the true value to the seventh 

 decimal place, but while the usefulness of the 

 interpolation method is limited by the range 



2 Given as 107.7492870 in Dr. Pearl's article, 

 being a misprint for the value given above, which 

 I verified by recalculation. 



will depend on whether he is obliged to look 

 up the references, or simply glances at them 

 occasionally to see a date, or the name of an 

 author or journal. 



The word reference is defined here to mean 

 the author's name, journal title (usually abbre- 

 viated), with the numbers for series, volume, 

 pages and date. If any information from the 

 original is also given, and printed at the 

 bottom of a page outside the text, the whole is 

 regarded as a foot-note, and is not considered 

 here. " Loc. cit.," is regarded as a reference. 



Most journals are printed with a solid page, 

 at the foot of which are the references for that 

 page, with the reference numbers indicated in 

 the text, a separate line being given to each 

 reference, except where extra space is required 

 either because of grouping several references 

 under one number, or because of unusual 

 length of names. 



Nearly one per cent, of the space used in 

 printing articles and references in this way 

 can be saved by giving each reference a num- 

 ber (the numbers to run consecutively), then 

 printing all the references at the end of the 

 article, leaving an extra-wide spacing between 

 the period at the end of one reference and the 

 next number, in order to catch the eye. There 



