270 



NATURE 



[July 23, 1903 



minutes, but only very faintly in two or three minutes. I 

 have tried samples of salt from several localities with the 

 same results. William Ackroyd. 



Tables of Four-figure Logarithms. 

 I AM much interested by the short letter, contributed by 

 Prof. Perry to Nature of July 2 (p. 199), on the subject 

 of four-figure logarithms, especially as I have myself offered 

 a solution of the difficulty which Mr. Harrison has essayed 

 to remedy. If, instead of using Bottomley's differences 

 for the upper part of the tables, viz. from 1000 to 1799, we 

 resort to the usual tabular differences found in any ordinary 

 logarithmic tables, such as Chambers's, we get an even 

 greater accuracy than does Mr. Harrison. The tables are 

 naturally weakest when we have a " 9 " for the fourth 

 figure of the number the logarithm of which is required. 

 Taking this as a test, between 1000 and 1799 the accuracy 

 of the three methods may be expressed thus : — 



Per cent. 



Bottomley's differences 375 



Ditto, Harrison's extension ... ... ... 58-5 



Ordinary tabular differences 76 



Tabular differences would be required corresponding to 

 logarithmic differences of 43 to 24 inclusive, i.e. twenty 

 small columns of differences. It may be objected that it 

 would be unwieldy in use to change from one method of 

 procedure to another, but I think it will be found, also, 

 that Mr. Harrison's tables are not so easy to use as the 

 unmodified ones. The tabular differences might, indeed, 

 b^ printed down the side of Bottomley's table without dis- 

 turbing the usual differences, and only be used when the 

 iDest possible accuracy is desired. 



One of the best solutions of the difficulty has been 

 suggested to me by Prof. Perry himself, viz. divide the 

 number, less than 2000, the logarithm of which is wanted, 

 by 2, and add together the logarithms of quotient and 

 divisor. The approximation to the true logarithm of the 

 number is very good. 



I cannot agree that chemists, in any case, should use 

 four-figure logarithms, seeing that they habitually return 

 four figures as significant. I hope, before long, to be able 

 to show that practicable five-figure tables can be constructed 

 to which the reproach of " size " will be inapplicable. 



July 3. M. White Stevens. 



. Prof. Perry in Nature of July 2 (p. 198) gives an illus- 

 tration of a method whereby the logarithms of the numbers 

 from 1000 to 2000 may be got from a four-place logarithm 

 table with an error of, at most, one unit in the last place. 



It is, however, somewhat difficult to see what advantage 

 this arrangement has over the one where the logarithms 

 of the numbers 1000 to 2000 are given (again) after 999 

 in extenso without proportional parts. 



By this latter system the tables are certainly increased 

 in size by another double page, but, on the other hand, 

 there is a decided disadvantage in using the relatively large 

 proportional parts for the numbers 1000 to 2000. If the 

 addition of the proportional parts is done on paper, time will 

 be lost ; if the addition is done mentally, mistakes may 

 •easily occur. C. E. F. 



Edinburgh, July 4. 



In mathematical tables the last figure in any tabulated 

 number or difference must be liable to an error +i. When 

 a number is extracted from the tables by aid of a tabulated 

 •difference, the result is subject to a duplication of error, 

 that is, to an error +1. It will be found on examination 

 that in some of the early numbers of the ordinary four- 

 figure log tables the error is often double this amount. 

 Mr. Harrison's alteration remedies this mistake, and makes 

 the maximum error uniform throughout. The scheme pro- 

 posed by Mr. Stevens can do no more than this, and would 

 he more clumsy. The figures given by him apparently 

 refer to averages, and are irrelevant. 



If the proposal of C.E.F. were adopted, the first portion 

 of the table would have double the accuracy of the re- 

 mainder ; the result of any general calculation would depend 



NO. 1760, VOL. 68] 



on the accuracy of the latter, and little, if anything, would 

 be gained in return for the fact that the space occupied 

 by the tables would be doubled. John Perry. 



A Multiple Lightning Flash. 



I have had the privilege of examining the print of the 

 lightning flash taken by Mr. C. H. Hawkins, of Croydon, 

 and referred to in Nature (July 16, p. 247) by Dr. W. N. 

 Shaw. 



The main flash consists really of three flashes, the several 

 paths of which are not quite coincident. If a moving 

 camera had been employed (I assume the camera in this 

 case was fixed), then I think the three flashes would have 

 been easily distinguished. The flash on the right is 

 evidently a ramification of the main stream. Except for 

 the above, the photograph shows no other special features. 

 William J. S. Lockyer. 



Solar Physics Observatory, July 17. 



The Lyrids, 1903. 



The return of the Lyrids this year was well observed 

 here. Watching was begun on April 15, and continued 

 until April 24, the series being broken only once, namely 

 on April 20, when the sky was overcast. The weather was 

 very favourable, the heavens on most nights being beauti- 

 fully clear. Eighty-four meteors were registered, of which 

 twenty were Lyrids. 



The chief points with regard to the Lyrids brought out 

 by the observations are : — 



(1) The display was of moderate strength. 



(2) The maximum occurred on April 21 and 22, probably 

 more precisely at midnight on the latter date. 



(3) The decrease in activity was more rapid than the rise 

 to maximum. 



(4) The radiant on the nights of April 21-22 was at 

 27i^°+33° (12 paths). 



(5) The colours of the Lyrids were almost wholly of two 

 shades, white and a peculiar yellowish, dirty-looking green. 



(6) The meteors were swift, their average angular velocity 

 being 20° a second, not taking into account those which 

 appeared close to the radiant. The real speed of a Lyrid 

 fireball recorded on April 22 by Prof. Herschel at Slough 

 and the writer at Leicester has been computed to have been 

 39 miles per second. 



(7) Only the very brightest Lyrids left streaks. 



The first meteor of the shower was observed on April 17. 

 There was a remarkable break on April 19, when not a 

 single Lyrid was seen in a watch lasting three hours, 

 though the seeing was excellent. 



Minor Showers. 



Besides the Lyrids, radiants were found for the chief 

 active showers as under : — 



Rftdiant-point Duration No. of Remarks 



„ „ meteors 



330 +35 ••• March 2g-ApriI 24 ... 4 ... Slowish; radiant -svell -defined. 

 2(6 —26 ... April 11-24 ••• 5 ••• Rather swift, bright, long. Ex- 



hibited great variety of colour. 

 236^ + 5x4... April 19 ... 4 ... Short; rather swift. Radiant 



sharply defined. 

 256^ + 37 ... April 19-22 ... 6 ... Swift. Maximum April 22 (5 

 meteors). 



The shower from 2i6°-26° is very interesting, inasmuch 

 as nothing seems to have been seen of it previous to 1900, 

 in which year it was very active at. the Lyrid epoch from 

 2i8°-3i°. It appears, therefore, to furnish quite a strong 

 display at this period. 



A recent writer has calculated that the maximum of the 

 Lyrid shower would fall this year at April 19, loh. 30m. 

 My observations entirely negative this conclusion, for that 

 night was marked by the complete absence of Lyrids, 

 though the seeing conditions were extremely favourable. 

 The time of maximum actually found was in accordance 

 with that which had previously been inferred. Since in 

 the last few years the maximum has taken place on the 

 20-21, it was to be expected that, after the omission of 

 leap year in 1900, the epoch would be thrown one day 

 later. Alphonso King. 



Leicester, July 11. 



