122 Prof. B. Stewart and W. Dodgson. Report, $c. [May 29, 



2*2. We h&ve thus given our method a preliminary trial, and the 

 result is we think decidedly hopeful. We are inclined to believe that 

 when more completely worked out it may not only reduce to certainty 

 the existence of periods of short range in terrestrial magnetism and 

 meteorology, but also give determinations of the exact lengths of these 

 periods, and of the forms of the inequalities. 



We would remark, in conclusion, that a glance at the yearly in- 

 equalities exhibited in Tables I and III, will show us that these are 

 more marked and more regular in those years which correspond to 

 maximum sun-spots, than they are in years of minimum sun-spots. 



Note on the above Paper. By Professor Gr. G. Stokes. 



As the search for periodic inequalities of unknown period must 

 always be more or less laborious, it seems desirable to point out 

 another mode in which the search might be conducted, and which 

 seems to offer great facilities for the object, assuming the possession 

 of the required instrument. 



It seems to me that the harmonic analyser of Sir William Thomson 

 is singularly well adapted to this purpose, which, as I have ascertained 

 from him, was one of the applications of his machine that he has had 

 in view. 



If f(t) be any function of the time t given by observation, and 

 lir-^n a period p assumed at pleasure, then by plotting if necessary 

 the function on a scale adapted to the paper cylinder of the machine ~ 

 we shall get, by a simple mechanical process, the values of the in- 

 tegrals 



J f(t) sin nt dt, cos tit dt, 



between any limits. We may take the inferior limit for the origin of 

 the time, and then by reading off the cylinders of the machine for as 

 many values of the superior limit t as we please, we shall get the cor- 

 responding values, as many as we like, of the integrals. 



Suppose, now, that/(£) contains a small term of the form 



c sin (n't + ei), 



where ri is not much different from n, so that the period tried ap- 

 proaches closely to the period p' of this inequality. The corresponding- 

 part of the integrals will be— 



— -sin {(ri—n)t+ — - sin {(»' + «)*+«}, 

 2(n —h) 2(w +n) 



and — — — ? -cos {(■>/— n)t + x} — -— ? cos {(ri + n)'t + x\, 



U(n —ri) 2(n +u) 



