February 23. 1893] 



NA TURE 



403 



hour. The following sample gives the incidence to the nearest 

 lunar hour of the first few days in a year : — 



The successive I2h. of m.s. time will march retrogressively 

 through all the twenty-four hours of m. lunar time. 



Now, if starting from strip o, we push strip I one division to 

 the left, strip 2 two divisions to the left, and so on, the entries 

 on the strips will be arranged in columns of approximately lunar 

 time. 



The rule for this arrangement is given by marks on a sheet of 

 paper l8 in. broad; these marks consist of parallel numbered 

 steps or zigzags showing where the ends of each strip are to be 

 placed so as to bring the hourly values into their proper places. 

 At the end of a lunation mean solar time has gained a whole 

 day over mean lunar time, and the I2h. solar again agrees with 

 the I2h. lunar. On the guide sheet the zigzag which takes its 

 origin at the left end of strip o has descended diagonally from 

 right to left until it has reached the left margin of the paper, and 

 a new zigzag has begun on the right margin. 



When the strips are pinned out following the zigzags on the 

 sheet marked M, the entries are arranged in 48 columns, but 

 the number of entries in each column is different. The 48 in- 

 complete columns may be regarded as 24 complete ones, apper- 

 taining to the 24 hours. 



Harmonic analysis of the 24 means of the complete columns 

 gives the required tidal constants. It must be remarked, however, 

 that as the incidence of the entries is not exact in lunar time, 

 investigation is made in the paper of the corrections arising 

 out of this inexactness. 



The explanation of the guide sheet for lunar time will serve, 

 mutatis mutandis, for all the others. 



The zigzags have to be placed so as to bring the columns into 

 exact alignment, and printers' types provide all the accuracy 

 requisite. 



To guard against the risk of Ihe computer accidentally using 

 the wrong sheet, the sheets are printed on coloured paper, the 

 sequence of colours being that of the rainbow. The sheets for 

 days o to 73 are all red ; those for days 74 to 74 + 73, or 147, 

 are all yellow ; those for days 148 to 148 + 73, or 221, are 

 green ; those for days 222 to 222 -f 73, or 295, are blue ; and 

 those for days 296 to 296 + 73, or 369, are violet. 



Thus, when the observations for the first 74 days of the year 

 are written on the strips all the sheets will be red ; the strips 

 will then be cleaned, and the observations for the second 74 

 days written in, when all the guide sheets will be yellow, and 

 so on. 



The paper also gives another considerable abridgement of 

 the process of harmonic analysis, which is independent of the 

 method of arrangement just sketched. 



In the Indian compulation forms the mean solar hourly 

 heights have been found for the whole year, and the observa- 

 tions have been rearranged for the evaluation of certain other 

 fides governed by a time scale which differs but little from the 

 mean solar scale. It is now proposed to break the mean solar 

 heights into sets of 30 days, and to analyse them, and next 

 to harmonically analyse the 12 sets of harmonic constituents 

 for annual and semi-annual inequalities. By this plan the har- 

 monic constants for II different tides are obtained by one set 

 of additions. In fact, we now get the annual, semi annual, 

 and solar elliptic tides, which formerly demanded much trouble- 

 some extra computation. A great saving is secured by this 

 alone, and the results are in close agreement with those derived 

 from the old method. 



An abridged method of evaluating the tides of long period 

 MSf, Mf, Mm, is also given. The method is less accurate than 

 that followed hitherto, but it appears to give fairly good results, 

 and reduces the work to very small dimensions. 



The advantages of the method proposed in the present paper 

 may be best realized by a comparison of the amount of work 



NO. I 2 17, VOL. 47] 



entailed in the reduction of a year's tides as it has hitherto 

 been carried out by the Indian Survey at Poona, and what it 

 will he under the new method. 



It has been usual in the Indian reductions to use three digits 

 in expressing the height of water, and there have been fifteen 

 series, or even more. It follows from a simple multiplication 

 that the computer has had to write 394,000 figures in reducing 

 a year of observation. This does not include the evaluation of 

 the annual and semi-annual tides, so that we may say that there 

 have been about 400,000 figures to write. 



It is now proposed to express the heights by two digits, and 

 they only have to be written once, and the number of figures to 

 write is 17,500; accordingly the writing of 382,000 figures is 

 saved. 



In the old method the computer had to add together all the 

 digits written, say, 394,000 additions of digit to digit. 



It is now proposed to use twenty-four hourly values in three 

 series, viz. S, M, and MS, and twelve two-hourly values in 

 eight others, and the number of additions comes to 123,000. 

 Thus 270,000 additions are saved. 



We may say that formerly there were about 800,000 opera- 

 tions (writing and addition), and that in the present method 

 there will be about 140,000. This estimate does not include a 

 saving of several thousands of operations in obtaining the tides 

 of long period. It may therefore be claimed that the work 

 formerly bestowed on one year of observation will now reduce 

 at least five years, and that the results are equally trustworthy. 



The manufacture of the computing strips of xylonite is rather 

 expensive, but as it formerly cost in England rather more than 

 ;^20 to reduce a year of observation, the cost of the apparatus 

 will be covered by the saving in the reduction of a single year, 

 and it will serve for any length of time. 



The apparatus, together with computation forms, will be on 

 sale with the Cambridge Scientific Instrument Company at a 

 price of about £^. 



It is proper to mention that Dr. Borgen has devised and used 

 a method for attaining the same end as that aimed at in this 

 paper. He has prepared sheets of tracing paper with diagonal 

 lines on them, so arranged that when any sheet is laid on the 

 copy of the observations written in daily rows and hourly 

 columns, the numbers to be summed are found written between 

 a pair of lines. This plan is inexpensive and has considerable 

 advantages, but the chance of error is no doubt increased by 

 the fact that the lines of addition are diagonal, and because 

 figures seen through tracing-paper are comparatively faint. 



THE HARVARD COLLEGE OBSERVATORY. 



'T'HE forty-seventh annual report of the director of the astro- 

 -*■ nomical observatory of Harvard College, for the year end- 

 ing October3i, 1892, by Prof. E. C. Pickering, has been issued. 

 We reprint the following passages : — 



The number of photographs taken with the eight-inch Draper 

 telescope is 2777. The number taken in Peru with the Bache 

 telescope is nearly two thousand, of which 601 have been received 

 in Cambridge. The examination of these plates has as usual led 

 to the discovery of a large number of interesting objects. Ten 

 variable stars, U Delphini, S Pegasi, T Aquarii, R Crateris, R 

 Carinse, S Canis Minoris, S Car nse, R Ophiuchi, X Ophiuchi, 

 and Esnin's variable star m Auri^'a in addition to the thirty-seven 

 previously announced have the hydrogen lines bright in their 

 spectra. Seven new variable stars have been discovered this 

 year by means of this property. The number of stars of the 

 fifth type has been increased by eight, making the total number 

 now known of these objects forty-five. The hydrogen line F was 

 shown to be bright in the spectra of six stars in addition to those al- 

 ready known. Photographs have been obtained of the spectra of 

 eight planetary nebula; showing bright lines. The spectrum of 

 the nebula surrounding thirty Doradus is unlike that of other 

 gaseous nebulae. The star A. G. C. 20,937 has a somewhat 

 similar spectrum. Five stars have been shown to have spectra 

 of the fourth type. All of these peculiarities have been detected 

 by Mrs. Fleming except in the cases of one of the known 

 variables, one of the planetary nebula*, and two of the stars 

 of the fourth type, which were found by Mr. A. E. Douglass, 

 in Peru, before the plates were sent to Cambridge. 



The amount of valuable material accumulated with these 

 instruments is continually increasing, and has proved useful in 

 many cases in studying the history of newly-discovered ohjects. 



