176 



NATURE 



fainter than would ever have been possible by 

 ordinary visual methods. 



The photographic and visual or photo-visual 

 magnitudes of a star having been observed, the 

 "colour-index" is at once obtained. There is 

 a marked dependence of the colour-index upon the 

 spectral type of the star. The basis of the classi- 

 fication of the spectra of stars adopted at Har- 

 vard, and now universally accepted, was entirely 

 independent of magnitude or colour considera- 

 tions, and depended solely upon the type of spec- 

 trum. The spectra of the types B, A, F, G, K, M 

 were found to show in this order a progressive 

 change from bright-line to absorption spectra, and 

 the order is intimately bound up with the problem 

 of stellar evolution, and also with the temperature 

 of the stars. The colour-indices found in three 

 separate investigations for stars with spectra of 

 different types are given in the table, together 

 with the temperature of the stars, derived by 

 Russell on the hypothesis that the stars radiate 

 as black bodies. In accordance with the conven- 

 tion on which photographic magnitudes are based, 



the colour-index 

 vestigation. 



Spectrum 



King 



[April 7, 192 1 



for type Ao is zero in each in- 

 Colour-lndex. 



Parkhurst bchwarischild Temperature 



It will be seen that the colour-index increases 

 almost uniformly from class to class, and that 

 when either the photographic or visual magnitude, 

 and either the colour-index or the spectral type, 

 are given, it is possible to determine the remaining 

 data with very little uncertainty. 



{J^o he continued.) 



Ocean Tides. 



By Prof. J. Proudman, University of Liverpool. 



'T'HE tides of the oceans form the most mag- 

 -^ nificent dynamical phenomenon of our 

 planet, and yet we are extremely ignorant of even 

 their main characteristics. It is only in the imme- 

 diate neighbourhood of land that they become 

 directly observable, and it is practically only here 

 that they have hitherto been observed. 



Much has been done in the way of recording 

 coastal tides and in analysing the records ob- 

 tained, yet very much more remains to be done 

 even for the purpose of preparing accurate com- 

 mercial predictions. In this connection the most 

 urgent need is the study of the meteorological 

 effects. Owing to these effects, the tide in a 

 harbour on any day may be several feet different 

 from that due to astronomical causes, which 

 alone appears in the tables of predictions. Now 

 this is of the very gravest concern to harbour 

 authorities, for, in docking a large vessel, to get 

 less water than was expected may be very serious, 

 while to refrain needlessly from docking through 

 fear of this possibility is a fruitful source of delay 

 and expense. And this is merely an instance. 



The up-and-down motion of the water-surface 

 is accompanied by oscillating currents. Much 

 rough information is in existence concerning the 

 nature of these currents near land, having been 

 gathered chiefly by naval authorities, as it is 

 of the utmost importance in navigation. But the 

 number of places at which accurate observations 

 of currents have been made with modern instru- 

 ments is extremely small. No such observations 

 are on record, for example, for the Irish Sea. 

 When the problem of predicting the meteorological 

 effects comes to be tackled in a way likely to lead 

 to success, these shallow-water currents, which 



NO. 2684, VOL. 107I 



are mainly instrumental in producing the local 

 wind effects, will require thorough observation. 



But when the tides are viewed scientifically as 

 the oscillations of a great dynamical system, these 

 coastal tides, that almost alone have been ob- 

 served, appear as the mere fringe, so to speak, 

 of the essential phenomenon. It is in the vast 

 bodies of water constituting the great oceans that 

 the tides have their real being, and the coastal 

 tides themselves will never be completely under- 

 stood until we know the great oceanic tidal move- 

 ments. The meteorological disturbances may 

 arise wherever the tides arise, and we want to 

 know, for instance, what effect certain meteor- 

 ological conditions over the Atlantic will have on 

 the tides in our harbours. 



On the side of pure science many problems of 

 wide geodynamical and cosmical interest require 

 as data a knowledge of the ocean tides. 



Now it is believed that not a single accurate 

 observation of either tidal elevation or tidal current 

 has ever been made in the deep water of any of 

 the oceans. The best knowledge we possess of 

 mid-ocean tides consists in observations on the 

 shores of oceanic islands, and even this knowledge 

 is not nearly so complete as we could wish. 



Mathematically, the tides are " determined " by 

 the size and shape of the ocean basins and certain 

 astronomical data, but the complete solution of 

 the problem is not within the sight of the present 

 generation of mathematicians. If all the possible 

 free oscillations of the oceans could be discovered, 

 then the actual tides could be calculated with ease 

 by a principle which is a generalisation of that 

 of resonance. 



Various guesses have been made as to the 



