1879.] 



Researches on Explosives. 



12^ 



taken between the proper limits. The terms divided by n \-n having 

 but a small coefficient in the numerator, and having a denominator 

 which is not small, may be left to take then chance with casual fluc- 

 tuations; but the terms divided by n — n rise into importance from 

 the smallness of the denominator, and express an inequality in the- 

 integrals of comparatively large amount and long period. 

 We may therefore confine our attention to the terms 



--4 — r sm[(»' —4 — -cos[(V-/0f+*]. 

 2(?i — 11) &{n —n) 



occurring in the indefinite sine integral and cosine integral respectively.. 



If, therefore, the values of these two integrals, obtained from the 

 two cylinders respectively, be plotted, Ave shall obtain a periodic fluc- 

 tuation of a period more or less long as we hit on a period more or 

 less near to that of the inequality which we have supposed to exist. 

 The zero points of the fluctuation in the sine integral will correspond 

 to the maxima and minima in that of the cosine integral, and vice versa. 

 The reciprocal of the period of the fluctuation will give the difference 

 of the reciprocals of p and p', and thus p will be known fromp provided 

 only we know which of the two, p, p , is the greater. This will be 

 shown by comparing the phases of the fluctuations of the two in- 

 tegrals. If n' >n, the fluctuation of the cosine integral will be a 

 quarter of a period behind, if n' < n before, that of the sine integral. 



If f (f) be subject to known periodic inequalities with approximately 

 known coefficients, the integrals should be cleared of the terms thence 

 arising, if of sufficient moment, by using their analytical expressions, 

 and the residues only plotted. 



Of course / (f) is not necessarily a function of the time given by 

 direct observation ; it might be a function deduced from one so ob- 

 tained. For example, / (t) might be the coefficient of the principal 

 term in the daily fluctuation of the element when each day's record is 

 separately subjected to harmonic reduction. 



May 29, 1879. 



IV. Researches 011 Explosives. No. II. (Fired Gunpowder.)." 

 By Captain Noble, late R.A., F.R.S., F.R.A.S., F.C.S., and 

 F. A. Abel, C.B., F.R.S., V.P.C.S. Received May 21, 1879, 



(Abstract.) 



The authors preface this memoir by two tables : one of these gives 

 the results of some analyses of products of explosion of the three 

 service powders of TValtham Abbey manufacture, pebble, R.L.Gr. and 

 F.Cf., which are required to complete the series of results obtained by 



