814 



SCIENCE. 



[N. S. Vol. VIII. No. 206. 



as to time and mean range of tide for forty- 

 nine other points on Chesapeake Bay, and 

 for twenty -eight points along the Potomac 

 River, to say nothing of sixty-one points on 

 other tributaries of the bay. For such a 

 region the investigator has an ample col- 

 lection of facts to be used in proving or 

 disproving any theory which he may for- 

 mulate. 



I am inclined to think that whoever suc- 

 cessfully attacks this problem VFill use a 

 graphic, or partially graphic method, plot- 

 ting his results step by step upon the chart. 

 In any wholly analytic method it will be 

 especially diflScult to take sufficiently into 

 account the configuration of the bottom 

 and shore. 



In conclusion, I submit that to solve this 

 boundary problem is to make an immense 

 stride in our knowledge of the tides, a 

 stride corresponding to a half century of 

 ordinary progress; that it is in this line that 

 our ignorance of the tides is most dense; 

 that the facts are at hand for the investiga- 

 tion, and that, judging from the literature 

 of the tides, this is, comparatively speaking, an 

 unworked portion of the field. Along this 

 line considerable pioneer work has been 

 done, especially along purely mathematical 

 lines, but the new comer will find neither a 

 long series of failures to discourage him by 

 indicating that the problem is intractable, 

 nor a long series of successes to discourage 

 him by making it appear that there is little 

 opportunity to advance beyond what has 

 already been done by others. 



It may seem that in this paper some at- 

 tention should be paid to the fact that 

 theory furnishes the relative amplitudes of 

 certain harmonic components ; that, in 

 particular, theory indicates that certain 

 relations exist between the relative ampli- 

 tudes and the mass of the Moon, and that 

 this theory has been born out by the fact 

 that said mass has been computed with a 



high degree of accuracy from tidal observa- 

 tions. 



It should, however, be kept clearly in 

 mind that only the relative amplitudes are 

 concerned in the computation of the Moon's 

 mass. Further, the mass of the Moon as 

 deducted from observations at a single 

 tidal station is often largely in error. An 

 accurate determination of the mass is ob- 

 tained only when the results of observations 

 at many stations are combined. 



There is a decided significance, in the 

 present connection, in the conclusions 

 reached by two investigators who have care- 

 fully studied this phase of the tidal problem. 

 Professor Ferrel, after a prolonged consider- 

 ation of the matter,"concludes that, to secure 

 a better determination of the Moon's mass 

 from the tides, a special study of ' shallow 

 water components ' should be made. In 

 other words, the effects of friction due to 

 the boundaries must be studied. Professor 

 Harkness, in deriving the Moon's mass from 

 tidal observations,* gives all stations equal 

 weight, though the length of the series of 

 observations varies at the different stations 

 from one to nineteen years, on the ground 

 that ' the accidental errors at any station 

 are generally small as compared with those 

 due to constant causes.' He indicates in 

 the context that these ' constant courses ' 

 are constant for each point, but variable in 

 passing from point to point along a coast ; 

 in other words, they are due to the local 

 peculiarities of the boundaries. 



John F. Hayford. 



GE03IETRICAL OPTICAL ILLUSIONS. 

 During the last few years the subject of 

 Optical Illusions has been receiving a de- 

 gree of attention that may well be called 

 remarkable. Both popular and scientific 

 articles have been written, so that the gen- 

 eral public, as well as the specialist, is well 



* On the Solar Parallax and its Related Constants, 

 Wm. Harkness, pp. lig-lOO. 



