810 



SCIENCE. 



[N. P. Vol. VIII. No. 206. 



I have here made no mention of the work 

 that has been done on the various theories 

 of the mutual actions at a distance of cur- 

 rent elements, as these are thoroughly dealt 

 with in J. J. Thomson's admirable British 

 Association report on electrical theories in 

 1SS5. I have thus, in a verj' brief and un- 

 satisfactory manner, merely touched upon 

 some of the principal points of the develop- 

 ment of the theory of electricity, and traced 

 its gradual but unceasing progress from the 

 hands of the giants of the old days to those 

 of the new. 



Arthur Gordon Webster. 



Clakk Univeesity. 



THE LI3IITATI0N8 OF THE PRESENT SOLU- 

 TION OF THE TIDAL PROBLEM. 



That which is new in science is always 

 interesting. But it is well at times to let 

 the old and well-tried pass in review before 

 us, to plan renewed attacks upon the un- 

 known, in the light of the elements of 

 strength or weakness found in different por- 

 tions of the arraj' of known facts and princi- 

 ples, and with respect to the stubborness of 

 the resistance which has been encountered 

 by attacks upon diiferent parts of the un- 

 known. A helter-skelter attack may per- 

 haps produce more interesting and more 

 surprising results than a well planned cam- 

 paign, but the latter would be expected to 

 furnish the more important results. The 

 purpose of this paper is not to state any- 

 thing new, but to point out a very weak 

 point in tidal theory, a point which it is 

 important to have strengthened, and of 

 which the strengthening is apt to lead to a 

 decided advance in our knowledge of the 

 subject. 



The thesis which I submit is that the 

 present theory of the tides upon the earth 

 when used to explain those tides, or to 

 predict their occurrence at a particular 

 point, furnishes very little except the periods 

 of the separate harmonic, or invariable, 



components of the tide. It does not furnish 

 the times of occurrence of the tides, that is, 

 the epochs of the components, nor does it 

 furnish the range of the tide as defined by 

 the amplitudes of the harmonic components. 



This thesis may be exhibited in concise 

 form by writing the algebraic expression 

 for the height of the tide referred to mean 

 sea level at any instant at a given point 



h = A^ cos (oji + /?,) + A^ cos {aj + /3J 



Each term of this expression indicates one 

 of the harmonic components of the tide. 

 From pure theory, reasoning from the 

 known motions of the Moon, Sun and Earth 

 and the Newtonian law of gravitation, it 

 has been shown that if certain definite 

 values be assigned to the quantities «,, a^,... 

 (fixing the periods of the separate terms), 

 that each term trulj^ represents one of the 

 invariable components of the tide. Here, 

 after merely fixing the periods of the sepa- 

 rate components the contribution of tidal 

 theory ends, and the work of direct obser- 

 vation at the particular station under con- 

 sideration begins. The values of ^4j, A^, 

 defining the amplitudes of the separate 

 components and the range of the composite 

 tide, and of /?, /S^... fixing the epochs of the 

 separate components and the time of the 

 tide, must be derived directly from obser- 

 vations at the particular station in hand. 

 Their values cannot, at present, be assigned 

 even approximately from theory. 



If we look at the actual tidal problem pre- 

 sented to us by Nature the reason why 

 theory furnishes so little will become evi- 

 dent. In approaching the actual problem 

 let us begin by considering a simple ideal 

 problem which can be and has been success- 

 fully handled, and then introduce into this 

 problem, one by one, the actual conditions 

 which modify it. In doing so we maj', to a 

 certain extent, follow the historic order of 

 tidal research. 



There are tides produced by both the 

 Moon and the Sun. To avoid circumlocu- 



