April 15, 1922] 



NATURE 



479 



of Naturalists which was held in Odessa in August 



I 1883, and of which I am the only foreign survivor. I 

 became acquainted with the most prominent professors 

 pi that University and found that they were first-rate 

 inen of science, without a trace of anything " back- 

 Sward and reactionary." And yet this reproach is 

 icorrect, but it refers to the State director of the 

 aniversity. A man, unsympathetic, gloomy, re- 

 actionary, every inch a bureaucrat, and fairly old, in- 

 augurated the first general meeting with the following 

 severe words : " You came here to speak of science 

 and I hope that you will speak only of science ! " 

 After this rose Metchnikoff and gave a brilliant 

 account of his recent and unpublished work on 

 phagocytosis, which was received with enthusiastic 

 applause by the whole assembly. 



I congratulated my Russian colleagues and the 



niversity upon having such a professor, but they 



iplied with regret that he no longer belonged to 



le University, and upon asking for reasons I was 



j^vcn the explanation : Metchnikoff as a professor of 



•logy announced a course of lectures " On the 



leory of Evolution." And now the very reverse 



ik place of what I described four months ago 



above). The director summoned MetchnikofiE to 



ofl&ce and said to him : "It appears that you are 



_ dng to lecture on Darwinism ? If it is so, then you 



must submit your written lectures to my censorship 



and I will tell you what I allow you to say to the 



students and what not ! " Metchnikoff did not accept 



this explanation of the " Lehr- und Lemfreiheit," 



he did not submit his notes to the curator ; he resigned 



the professorship. Russia was not the soil for such a 



genius, and it was good fortune for him and for science 



that he left for Paris and for Pasteur. 



BOHUSLAV BRAUNER. 



Bohemian University, Prague, March 9. 



The Accuracy of Tide-predicting Machines. 



^ Under the above title in Nature of February 23, 

 Dr. A. T. Doodson comments on my letter that 

 appeared in the issue of Nature 

 for February 2 under the same 

 title. Unfortunately, Dr. Doodson 

 is dealing with a matter outside the 

 scope of my letter, and his state- 

 ment that he is not " convinced 

 by the tests recorded by Mr. 

 Marmer " in no way invahdates any 

 of the statements in my letter. 



As specifically stated in my letter, 

 it was prompted by a desire to ' 



prevent the possible misconstruction, 

 on the part of those not familiar with tide-predicting 

 iiachines, of a statement to the effect that tide-pre- 

 licting machines are subject to "serious errors in 

 I heir results." Occasion was also taken to direct 

 ittention to the different types of tide predictors 

 and to a table showing the differences between 

 computed and predicted heights for one day in the 

 case of Hong Kong. 



With none of the statements relative to these 

 matters does Dr. Doodson appear to be in disagree- 

 ment. What he does question, however, is something 

 outside the scope of my letter, namely, whether the 

 tide predictor with the operation of which I am 

 familiar is or is not suitable for predicting hourly 

 heights for research purposes within 0-05 ft. for a 

 spring range of 30 ft. Not being concerned with 

 that question at the time, there appeared no occasion 

 for the tests, " exhaustive and convincing," that 

 Dr. Doodson desires. 



NO. 2737, VOL. 109] 



In his letter Dr. Doodson states that the tide 

 predictors at his command were found unsuitable for 

 use in the elimination from the observed tide of the 

 tide due to a number of constituents. Nevertheless, 

 this does not invalidate the general proposition that 

 in such problems " the tide predictor should very 

 materially lessen the laborious computations in- 

 volved." 



H. A. Marmer. 



U.S. Coast and Geodetic Survey, 

 Washington, D.C., March 18. 



It seemed to me that Mr. Marmer's first letter left 

 the impression that the U.S.A. machine is one that 

 is free from serious errors of the order of magnitude 

 of those of the British machines, and I raised the 

 question of proof. I said that I should be very glad 

 to know that this machine could produce hourly 

 heights to within 0-05 ft. with a spring range of 

 30 ft. I questioned whether it would or would not 

 give errors of 0-4 ft. in such a case. If my doubts 

 are warranted, then the U.S.A. machine also is 

 subject to serious errors, which, as I suggested, would 

 prohibit its use for the research work mentioned 

 above in Mr. Marmer's last paragraph. 



A. T. Doodson. 



Tidal Institute, University of Liverpool, 

 April 3, 1922. 



Pythagoras 's Theorem as a Repeating Pattern. 



It may not be generally known that the Theorem 

 of Pythagoras, EucUd I. 47, is closely connected with 

 the Theory of Repeating Patterns in space of two 

 dimensions. The simplest proof by dissection of 

 that Theorem establishes at once that any two 

 squares placed in contact as in the accompanying 

 diagrams (Fig. i) constitute a figure such that a 

 number of them can be assembled so as completely 

 to fill flat space. 



D 



Fig. I (i.) shows the proof by dissection. Also 

 the large square, regarded as a base, shows by the 

 Principle of Transformation in the Theory of Repeat- 

 ing Patterns that the figure formed of the two squares 

 is a repeating pattern. The transformation consists 

 of cutting out the triangles the bases of which are 

 BC and CD and erecting them upon the sides BA, AD, 

 This nature of transformation yields an infinite 

 number of repeating patterns of a particularly interest- 

 ing kind, because of this category each member has 

 the property that the assemblages can be carried out 

 in three different ways, namely, so as to exhibit i, 2, 

 or 4 orientations or aspects of repeat respectively. 

 In the present case of the Pythagorean Repeat the three 

 ways of assembling are shown in Fig. i (ii., iii., and iv.). 



Percy A. MacMahon, 



27 Evelyn Mansions, Carlisle Place, S.W.i, 



