336 EEPORTS ON THE STATE OF SCIENCE. — 1920. 



At the Meeting of the British Association in 1867 Thomson obtained the appoint- 

 ment of a committee which, during the following nine years, carried out harmonic 

 analyses. The grants from the Association to the Committee amounted to £1,000, 

 and the work was done, under the superintendence of Thomson, by Mr. E. Koberts, 

 of the Nautical Almanac Office, and assistant computers working under his imme- 

 diate direction. 



To the members of this committee, in December 1867, Thomson issued a circular, 

 containing, among other things, the speeds of the constituents 



M^ K, Mf M, S, 



S, O, Mm M, 



Nj P, Ssa 



Kj Q, Sa 



L, J, 



T, '7-3t)* 



We have explained the nature of all these except R^ and • y — 3)j,' which are solar 

 constituents analogous respectively to the lunar constituents L^ and Q,. In the 

 development of the generating potential their amplitudes are less than those of 

 constituents which have always been neglected. Thomson gave S, as an astronomical 

 constituent analogous to M„ and the speed of Mm as <t instead of cr — w, as was 

 afterwards pointed out by Roberts. He thought that while all the above constituents 

 would be sensible on our shores, the effects of evection and variation would be 

 negligible. He also stated the ' equilibrium principle' of allowing for the changing 

 inclination of the moon's orbit to the earth's equator. 

 From the Ramsgate 1864 record the terms of the 



M, K, S, 0, N, L 



series were first found. Special hourly means for the year were formed using the 

 B.A. assignment, and then analysed by the least square rule using the tabular forms 

 given by Archibald Smith for the deviation of the ship's compass. 

 This analysis revealed the shallow water constituents 



M^, M„ Ms, S„ 



and this then suggested the possible presence of MS, and MSf. 



By means of these first approximations a complete calculation of residues was 

 made, but it was afterwards concluded that first-approximations were sufficient for 

 short-period constituents, and no other residues for such constituents were calculated 

 by the Committee. 



From the same record numbers for 



Mf, Mm, Ssa, Sa, MSf, 



were found, by using daily means for the year purified of lunar short-period 

 influence before analysis. 



As a test, an hourly tide-table for one day in 1861: was made and compared with 

 the original record. The errors reached a foot at half-tide (mean spring amplitude 

 = 8 ft.). 



A series of records taken at Liverpool were supplied by the Board of the Mersey 

 Dock Estates, and from that for 1857-8, values for the 



M. K, S, 0, N, L 

 series were found. 



A set of personal observations taken at Bombay were supplied by Mr. W. Parkes, 

 a member of the Committee, and special quarter-hourly means for 127 days were 

 formed and analysed for the 



M, K, S, O, N, L 

 series. 



14. From the Liverpool 1857-8 record the constituent P, was found, and then 

 the 1858-9 and 1859-60 records were analysed similarly. The constituents Tj and 

 R2 were also treated, each from two two-yearly records. 



Now that records taken in different years at the same station were considered, 

 correlation wjtfe the genera,ting potential was made, and a Liverpool hourly tide 



