HARMONIC ANALYSIS OF TIDAL OBSERVATIONS 51 
William Thomson, and carried out by the previous Committee of the 
British Association.! 
In the present Report the method of mathematical treatment differs 
considerably from that of Sir William Thomson.? In particular, he has 
followed, and extended to the diurnal tides, Laplace’s method of referring 
each tide to the motion of an astre fict/f in the heavens, and he considers 
that these fictitious satellites are helpful in forming a clear conception of 
the equilibrium theory of tides. As, however, I have found the fiction 
rather a hindrance than otherwise, I have ventured to depart from this 
method, and have connected each tide with an ‘argument,’ or an angle 
increasing uniformly with the time and giving by its hourly increase 
the ‘speed’ of the tide. In the method of the astres fictifs, the speed is 
the difference between the earth’s angular velocity of rotation and the 
motion of the fictitious satellite amongst the stars. It is a consequence 
of the difference in the mode of treatment, and of the fact that the elliptic 
tides are here developed to a higher degrce of approximation, that none 
of the present Report is quoted from the previous ones. 
The Report of 1876 was not intended to be a final production, and it 
_ did not contain any complete explanation of a considerable portion of the 
numerical operations of the Harmonic Analysis. 
The present Report is intended to systematise the exposition of the 
theory of the harmonic analysis, to complete the methods of reduction, 
and to explain the whole process. 
A careful survey of the methods hitherto in use has brought to 
light a good many minor points in which improvements may be intro- 
duced, but it has seemed desirable not to disturb the system, which is in 
working order, more than can be helped. It has also appeared that the 
published results have not been arranged in a form which lends itself to 
a satisfactory examination of the whole method. This defect will, we 
hope, now be remedied ; and, as above stated, Major Baird will revise the 
Indian results. 
The first section refers to the notation, and contains a schedule of 
nomenclature by initials of the several tides under examination. The 
schedule is not, strictly speaking, in its proper position at the beginning, 
because it involves the results of subsequent analysis, but the advantage 
gained by having this list in a position of easy reference seems to out- 
weigh the want of logic. : 
The forms for computation are privately printed for the India Office, 
and are therefore inaccessible to the public. The type has been broken 
up, and very few copies remain, but we shall be able to send copies to the 
Libraries of the following Societies, viz.: Royal Society, London; the 
Academies of Science of Paris, Berlin, and Vienua, and the Coast Survey 
of the United States at Washington. 
G. H. DARWIN. 
' See especially the Reports for 1872 and 1876. 
* The present method of development is that pursued in a paper in the Phil. 
Trans. R.S , Part, II. 1880, p. 713. 
* It may be useful to mention that I hope to publish an edition of the forms, repro- 
ducing them by photozincography. The price will be just such as to cover the expense. 
E2 
