120 • REPORT— 1870. 



Uj the work actually performed by the capstan ; 



p the radius of the axle, and (p the limiting angle of resistance. For a 

 full explanation of this latter quantity I must refer the reader to the original 

 treatise. 



Then if T be supposed constant, 



Uj=U,+-^-^^ I do V a^^+2a^a.^ COS d + a^'. 



This integral is, of course, the elliptic function E ; and the result is strongly 

 suggestive of the importance of the higher integrals in a calculation of work 

 done in machines, when the point of application of the motive power is vari- 

 able. It is hardly necessary to observe that the radical in the above integral 

 gives the distance between the points of application of the forces. 



Committee for the purpose of promoting the extension, improvement, 

 and harmonic analysis of Tidal Observations, Consisting of Sir 

 William Thomson, LL.D., F.R.S., Prof. J. C. Adams, F.R.S., 

 The Astronomer Royal, F.R.S., J. P. Bateman, F.R.S., Admiral 

 Sir Edward Belcher, K.C.B., T. G. Bunt, Staff-Commandcr 

 BuRDwooD, R.N., Warren De La Eue, F.R.S., Prof. Fischer, 

 F.R.S., J. P. Gassiot, F.R.S., Prof. Haughton, F.R.S., J. 11. 

 Hind, F.R.S., Prof. Kelland, F.R.S., Staff-Captain Mori arty, 

 C.B., J. Oldham, C.E., W. Parkes, M. Inst. C.E., Prof. B. Price, 

 F.R.S., Bev. C.Pritchard, LL.D., F.R.S., Prof. Eankine, LX.D., 

 F.R.S., Captain Richards, R.N., F.R.S., Dr. Robinson, F.R.S., 

 General Sabine, President of the Royal Bocieiij, W. Sissons, Prof. 

 Stokes, B.C.L., F.R.S., T. Webster, M.A., FR.S., and Prof. Ful- 

 ler, M.A., and J. F. Iselin, M.A., Secretaries. 



41. The Committee have to report that the superintendence of the work 

 for the past year has been wholly iiiulertakcn by Sir "William Thomson. 

 That work has consisted in the reduction of observations and determination 

 of constants by Mr. Eobcrts and assistants, according to the method which 

 has been fuUy described in the lleport of 1868. For the details of tlie results 

 obtained, the Committee beg leave to refer to the statements by Sir William 

 Thomson which are appended hereto. 



W. Parkes. 



George Henry Eichards. 



W. J. MAcaroiiN IIankine. 



J. C. Adams. 

 Exeter, August 18G9. 



Report for 1869 hy Sir W. Thomson. 



42, From the Meeting of the British Association at Norwich (Aug. 18GS) 

 up to the present time the harmonic reduction of observations recorded by 

 self-registering tide-gauges in several diflcrent localities, namely Eamsgnte, 

 Bombay, Liverpool, and Fort Point, California, has been continued. The 



