136 



NATURE 



[February 2, 1922 



Letters to the Editor. 



\The Editor does not hold himself responsible for opinions 

 expressed by tiis correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous communications.'] 



Fossil Buttercups. 



It is remarkable, as Prof. Cockerell points out in 

 Nature of January 12, p. 42, that until his discovery 

 of a Miocene buttercup no species, of the family 

 Ranunculaceae should have been recorded among the 

 fossil plants of North America. More especially is 

 this the case because the carpels of Ranunculus are 

 among the commonest fossils found in deposits of 

 Pleistocene and Pliocene age in Britain and the 

 neighbouring parts of the Continent. Among the 

 many lists of fossils determined by my husband and 

 myself from such deposits, in one only, the Pliocene 

 of Bidart (Basses-Pyr^n^es), is the genus not repre- 

 sented, and in this deposit very few species of any 

 kind were found. 



The oldest carpel I have seen is that of an extinct 

 batrachian Ranunculus (R. gailensis, E. M. Reid), 

 very thick-walled and globose, from the base of the 

 Pliocene of Pont-de-Gail (Cantal). From the same 

 horizon, but another locality in Cantal, M. Pierre 

 Marty recorded R. dtavorum, Sap., which he con- 

 siders nearly related to R. fluitans. It is quite 

 probable, though it has not been proved, that carpel 

 and leaf belong to the same species. 



In the latest Pliocene of the Cromer Forest-bed, 

 with the exception of two undetermined carpels, all 

 are British species. In the Upper Pliocene of Tegelen 

 (Holland) R. aquatilis and R. repens are found asso- 

 ciated with R. nodifiorus, a species of Central Europe 

 and the Orient, and with a single specimen of a 

 peculiar form of R. sceleratus found more abundantly 

 at Castle Eden. In the Middle Pliocene of Castle 

 Eden no definite West European species is found, 

 though the form of R. sceleratus already mentioned 

 and a peculiar batrachian Ranunculus, both probably 

 extinct, occur associated with two Central European 

 species R. nodifiorus and a varietal form (perhaps 

 extinct) of R. lateriflorus, also an extinct species of 

 which the affinitv has not been discovered. In the 

 Lower Pliocene of the Dutch-Prussian border the only 

 West European species is R. nemorosus • it occurs 

 associated with R. nodifiorus, R. lateriflorus, van, 

 and the South European species R. brutius. In the 

 lowest Pliocene of Pont-de-Gail one specifically in- 

 determinable carpel and the batrachian R. gailensis 

 already referred to, were found. 



Among the hundreds of Pleistocene and Pliocene 

 specimens examined none has shown indications of 

 two seeds, but I have not been able to carry the 

 record of the genus so far back as Prof. Cockerell. 



In the work here referred to the carpels were in 

 eyerv case obtained by "washing" the material and 

 sieving away the matrix. Were this method applied 

 to some of the North American Pleistocene and Ter- 

 tiary deposits I should anticipate that they might 

 yield not only abundant carpels of Ranunculus, but 

 the fruits and seeds of many other herbaceous plants. 

 „. Eleanor M. Reid. 



Pinewood, Milford-on-Sea, January 23. 



The Accuracy of Tide-predicting Machines. 



In the article in Nature for November 24 last ap- 

 pearing under the title "British Research on Tides " 

 there occurs a statement which may, perhaps, leave 

 an erroneous impression with those not familiar with ,' 

 NO. 2727, VOL. 109] 



tide-predicting machines. The statement in question 

 — "a test of the accuracy of the tide-predicting 

 machines used by the Admiralty and the India Office 

 has indicated some serious errors in their results, 

 and it is concluded that the labour of reading the 

 curves afforded by the machines, with any pretence to 

 accuracy, is comparable with the labour of direct com- 

 putation, while the value of the results is greater in 

 the latter case " — although made definitely with refer- 

 ence to particular tide-predicting machines, might, 

 nevertheless, leave the impression that tide-predicting 

 machines in general were subject to " serious errors in 

 their results." It therefore appears of value to 

 discuss briefly the subject of the accuracy of tide-pre- 

 dicting machines and to refer to some tests made with 

 a direct-reading type of tide predictor. 



Tide-predicting machines, or tide predictors as they 

 are frequently called, make use of the harmonic tidal 

 constants, and are contrived for the purpose of 

 summing a number of terms of the form Acos(a.t+a), 

 in which for each harmonic constant A is the ampli- 

 tude, a the speed per unit time t, and a the initial 

 phase. For any given port, therefore, the height of 

 the tide at any time is the instantaneous sum of the 

 simple constituent tides represented by the harmonic 

 constants. And in the tide predictor this instantaneous 

 surnmation is effected by means of a flexible chain 

 which passes alternately over and under a series of 

 pulleys the motion of each of which represents the 

 changes in elevation of a particular simple tide. 



The accuracy of a tide predictor is therefore to be 

 rneasured by the accuracy with which it sums the 

 simple constituent tides represented by the harmonic 

 constants. It is necessary to emphasise this, for not 

 infrequently one meets with the assumption that the 

 accuracy of the tidal predictions tests the accuracy of 

 the tide predictor. Tidal predictions are the product of 

 the tide predictor, and for any given port aim to give 

 in advance the times and heights of high and low 

 water. _ And the test of the accuracy of these tidal 

 predictions is, obviously, the closeness of agreement 

 with the tides as they actually occur. 



It is to be noted, however, that the times and 

 heights of the normal or predictable tide are subject to 

 the disturbing effects of variations in wind, atmo- 

 spheric pressure, rainfall, and seiche. Hence, alto- 

 gether apart from any imperfections in the tide pre- 

 dictor or in the harmonic analysis which separates out 

 the simple constituent tides, tidal predictions may 

 differ from the observed times and heights of the tide, 

 due to the disturbing effects just mentioned, the times 

 of occurrence of which cannot be foreseen at the time 

 the tidal predictions are made. It is, therefore, obvious 

 that, while in a measure the accuracy of the tidal 

 predictions tests all the processes entering into their 

 making, it does not strictly test the accuracy of the 

 tide predictor. 



Tide predictors are of two types, which we may 

 denominate respectively as curve-tracing machines and 

 direct-reading machines. In the former there is 

 traced, to a suitable scale on a sheet of paper, a curve 

 of the predicted tide from which the height of the 

 tide at any given time or the times and heights of 

 high and low water may be scaled. In the direct- 

 reading tide predictor the height of the tide at any 

 time, and also the times and heights of high and low 

 water, are indicated on dials from which they are 

 read off directly. 



It is obvious that the prediction of tides can be 

 carried out more rapidly with a direct-reading tide 

 predictor than with the curve-tracing type, for reading 

 figures from two or three dials Is less time-consuming 

 than scaling these same values from a curve. But 



