TRANSACTIONS OP THE SECTIONS. 35 



the point I and terminated at H, using the same observances and precautions until 

 5h. 30m. p. M. of the 25th, when the appearance of the weather required my removing. 



It will be seen that the observations recorded on the afternoon of the 24th are not 

 so regular as those of the following day. I attribute this to some degree of uncer- 

 tainty on account of a long swell, perhaps of one and a half or two feet rise, inter- 

 rupting the observation at the moment of passing over the overfall ; but this little 

 swell had nearly subsided on the 25th, and the depths were then recorded with much 

 satisfaction. It will also be noticed, that at the turn of the stream about noon of 

 the latter day, the depth had increased to eighteen fathoms four feet, and went on 

 uniformly so ; but I investigated the cause of this on the spot, and found that the 

 wind having increased to 2 from W. by S., and therefore operating upon the star- 

 board bow of the boat, had sidled her a few feet to the S.E., so as to bring the 

 eighteen fathoms three feet immediately under her; and that by observing the same 

 distance from the boat while drifting past her (and which was always on her lar- 

 board side), I obtained eighteen fathoms four feet instead of eighteen fathoms three 

 feet. 



From the care and pains taken in these observations, and that under favourable 

 circumstances, I do not entertain a doubt of the correctness of any one of the depths 

 over the summit of the overfall as recorded on the 25th ; but as this interesting 

 result of observations on an unexpected theory may no doubt give rise to a strong 

 desire for further observations as corroboratives, I shall not fail to make such when 

 I find myself in a position and circumstances to do so with any prospect of success. 

 It is a difficult observation, and can be made but seldom. In the mean time I 

 would offer my congratulations to Mr. Whewell on these results, should they prove 

 in any degree gratifying to him. I have the honour to be, &c. 



(Signed) William Hewett, Captain. 



On a Machine for Calculating the Numerical Values of Definite Integrals. 

 By the Rev. Henry Moseley, M.A., F.R.S., Professor of Natural Phi- 

 losophy and Astronomy in King's College, London. 



It is the object of this machine to apply to the mechanical integration of an exten- 

 sive class of functions, a principle suggested by M. Poncelet for the registration of 

 dynamometrical admeasurements, and subsequently applied by M. Morin to an in- 

 strument called the Compteur, for registering the work or dynamical effect expended 

 in the traction of loaded carriages upon common roads, and by a Committee of this 

 Association (whose Report is contained in the present volume) to a permanent regis- 

 tration of the work of the steam upon the piston of a steam-engine. Professor 

 Moseley stated his integrating machine to have some mechanical expedients in com- 

 mon with the last-mentioned machine, but to have nothing in common with the 

 Compteur of M. Morin, except the fruitful and admirable principle of M. Poncelet. 



It consists of a circular plate or disc placed in a horizontal position, and moveable 

 about an axis passing through its centre. A wheel, which, from the function assigned 

 to it. Professor Moseley calls the integrating wheel ofhis machine, is placed in a vertical 

 position with its edges resting upon the superior surface of this plate, and with its 

 axis (i. e. a line passing through its centre perpendicular to its plane) in a vertical 

 plane passing through the centre of the plane. It is made to retain this vertical po- 

 sition, and at the same time to admit of a motion across the plate on which it rests, 

 in the direction of a diameter, by the intervention of a guide composed of three par- 

 allel rods passing through three holes at corresponding points in the three arms of 

 the integrating wheel and fixed at their extremities firmly into two discs, which discs 

 are moveable about axes passing through their centres, these horizontal axes having 

 their bearings in two pieces which admit of a vertical motion by means of keyed 

 grooves in guides fixed vertically to the solid frame on which the plate rests ; so that 

 the whole weight of the frame and integrating wheel is borne by that point in the cir- 

 cumference of the latter by which it rests on the plate : the frame composed of the 

 three parallel rods, and the discs into which they are fixed, is perfectly rigid, and is 

 carried round by the revolutions of the integrating wheel ; and the axes about which 

 it turns being in a vertical plane passing through the centre of the plate, the frame 



d2 



