268 On the Product of two given Functions. [Feb. 3, 



and the integration is performed through, a range equal to — (i any 



integer) that gives this application. In this case the addition of a simple 

 crank mechanism, to give a simple harmonic angular motion to the 



rotating disk in the proper period — , when the cylinder bearing the 



curve y=\p(x) moves uniformly, supersedes the necessity for a cylinder 

 v/ith the curve y=<j>(ai) traced on it, and an operator keeping a point 

 always on this curve in the manner described above. Thus one operator 

 will be enough to carry on the process ; and I believe that in the appli- 

 cation of it to the tidal harmonic analysis he will be ■ able in an hour or 

 two to find by aid of the machine any one of the simple harmonic ele- 

 ments of a year's tides recorded in curves in the usual manner by an 

 ordinary tide-gauge — a result which hitherto has required not less than 

 twenty hours of calculation by skilled arithmeticians. I believe this 

 instrument will be of great value also in determining the diurnal, semi-, 

 diurnal, ter-diurnal, and quarter -diurnal constituents of the daily varia- 

 tions of temperature, barometric pressure, east and west components of 

 the velocity of the wind, north and south components of the same ; also 

 of the three components of the terrestrial magnetic force ; also of the elec- 

 tric potential of the air at the point where the stream of water breaks into 

 drops in the atmospheric electrometers, and of other subjects of ordinary 

 meteorological or magnetic observations ; also to estimate precisely the 

 variation of terrestrial magnetism in the eleven years sun-spot period, and 

 of sun-spots themselves in this period ; also to disprove (or prove, as the 

 case may be) supposed relations between sun-spots and planetary posi- 

 tions and conjunctions ; also to investigate lunar influence on the height 

 of the barometer, and on the components of the terrestrial magnetic 

 force, and to find if lunar influence is sensible on any other meteoro- 

 logical phenomena — and if so, to determine precisely its character and 

 amount. 



From the description given above it will be seen that the mechanism 

 required for the instrument is exceedingly simple and easy. Its accuracy 

 will depend essentially on the accuracy of the circular cylinder, of the 

 globe, and of the plane of the rotating disk used in it. 



For each of the three surfaces a much less elaborate application of 

 the method of scraping than that by which Sir Joseph "Whitworth has 

 given a true plane with such marvellous accuracy will no doubt suffice for 

 the practical requirements of the instrument now proposed. 



