WDC is sorry that he wasted any of WW's time. He had thought both WW and Sedgwick had attributed to him an unfounded degree of ignorance which made him annoyed. WDC is now flattered with the attention WW has paid him over his query, which accept for 'some differences rather metaphysical than physical between us' has been settled. When he first made it he only had Faraday's papers before him and had forgot to look at 'earlier writers and see if they had not determined the law of the tangential electro magnetic force, which of course would give me the result I sought as to the Time of revolution by the simplest process'. Barlow [Peter Barlow?] has found the tangential force of galvanic particles on magnetic to be inversely as the squares of the distances and therefore the Times will be directly as the squares of the distances. WW corrects him on his notion of force; 'its strict definition as the cause of change of motion'. WDC accepts this as long as one agrees that motion exists in the first place: 'but here physics seems to me to pass into metaphysics and I cannot conceive but that, recurring to the origin of things a state of rest is more natural than a state of motion - Hence I have a lurking fancy to understand by force not only the cause of a change of existing motion but the original cause of the motion whatsoever...if a tangential force had not been impressed in them at their creation, they would all have huddled together in an heap'.
PB explains his comments concerning the effect of iron on a ship's compass. His remark on page 79 was made on the ground of theory and not from actual experiment on ship board [Essay on Magnetic Attractions, 1820?]: 'you will have seen that the distance of the centre of attraction of the iron (speaking at present of balls only) and the relative position of the compass and needle as referred to an imaginary sphere which may be supposed to circumscribe either the ball of iron or the compass, its poles in either case corresponding in position with the magnetic poles of the dipping needle at the place of observation'. PB then provides an example accompanied by diagram and explanation. With regard to the 'accuracy that has been obtained - I have no better authorities on these subjects but what are contained in my supplement' [Appendix Containing an Account of the Experiments Made on Board HMS Lever, Conway and Griper, for Correcting the Local Attraction of these Vessels, 1824?].
The question PB was mentioning to WW yesterday, concerned the relative propelling powers of the paddles of a steam vessel according to their position. PB's son has produced a paper which 'endeavours to show that the lower or vertical paddle is the least effective whereas the general impression is that it is the most effective'. PB wants WW to look over the solution which he gives, and see if he can spot any errors.
PB has made an error in the information he gave WW regarding the expense of coal on the Liverpool line. He shows WW his 'computed horizontal lines equivalent to the several planes according to the account last sent' [see PB to WW, 26 Mar. 1836].
Woolwich - The experiments on the Liverpool line were made at PB's request - 'or rather I should call them observations. I requested simply to be informed of the exact speeds up and down the several planes on the Liverpool line as observed in ordinary journeys with the amount of load, the boiler pressure &c'. However, although PB does not doubt that the observations were carefully made, he finds them very irregular. PB thinks the pressure of the atmosphere on the piston has been hitherto neglected: 'we ought to consider the whole pressure in the bodies and to consider this as opposed not only to the resistance of the load, but to the pressure of the atmosphere which must be overcome with the velocity of the piston - this makes an immense difference on the computed affects'.
Woolwich - PB endeavours to answer some of WW's questions relating to steam trains. For instance, 'the effect of slopes upon the velocity of engines "as observed in real practice without reference to any theory". Most - if not all - engineers think that the rapid descent of a train does 'more mischief' that the heavy strain in the ascent. Some engineers assert that the more rapid the speed of a train, the more sharp is the draft. Consequently more fuel is consumed and hence more steam is generated in a given time, which leads to the more rapid destruction of the furnace and boiler. PB found no justification for this assertion in his research done on the Manchester line. The problem with trying to ascertain experimental facts is that 'they are so much at variance with each other that no instant conclusion can be obtained'.
Woolwich - The Directors of the South Eastern Railway have asked PB to consult WW on some points concerning 'the mechanical working or advantages of their line of road for about 23 miles - with a view to your examination on the question in both Houses of Parliament - for which they have engaged my assistance also'. The opposition and preferred line is 37 miles but has less planes than the former: 'the question is whether 23 miles or the 37 will employ most power and time'. PB gives a table of the comparative gradients and explains how he obtained his results. The Directors would like to have WW's authority to call upon once the question passes through the Committee.
Woolwich - Further to WW's steam train enquiry: 'I beg to say that I have not made the comparison you allude to, with the experimental results, because those results involve in them the velocity with which the train reaches the plane, which velocity alone would carry the train some way up the plane without engine powers the experimental speeds therefore are greater than they ought to be for the comparison in question the formula having reference only to the mechanical impediment of the slope. It will of course be observed that although the momentum might actually carry the train to the top of the plane without engine powers - the original velocity has to be acquired again so that this ascent proves no mechanical gain of power. The question of the disadvantage of the plane must therefore rest on its own ground and the way to proceed is to enquire what additional load would on a horizontal plane produce the same resistance as the inclined plane'. PB gives an example of a ratio which accounts for various resistances - such as friction, air and the atmosphere.
PB returns WW's work On the Theory of the Moon and on the Perturbations of the Planets. PB is presently engaged on the production of 'a new magnetic chart founded on the most recent observations and as far as possible corrected for the local attraction of vessels and I would be much obliged to you if [you] could give me two copies of your chart of the tides for drawing in my first lines'.
Observatory - GA gives his views regarding Barlow's [correction] of ship-magnetism: 'The importance of its error (other changes not considered) increases as the directive force of terrestrial magnetism on the horizontal needle decreases, that is as the dip increases. Under this circumstance, the absolute error is small, because the section perpendicular to the dip is nearly the same in all portions of the ship. So that the error is small in the circumstance in which its relative effect is great. On this account it is doubtless a good thing when most wanted' GA gives his breakdown of the 'facts' concerning the theory of humming tops.