Autograph letter signed ("JFW Herschel").
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An extraordinary letter to Mr. Mr. Henn, discussing Henn's paper on object glasses and the planetary ephemerides: "It is so long since I wrote to you, you will think I have forgotten you. It is not so, but I have been so overwhelmed with business that I have been obliged to neglect my correspondence -much to my regret. Let me first acknowledge your communication on object glasses and on the planetary ephemerides, if I have not already done so, with the tables and the letters accompanying them. They are printed (not the letters) in the forthcoming volume of the Astron. society's transactions. I have now the proof sheets of the former before me, on which allow me some remarks. 1. The second value off as it stands in your MS. is incorrect the factor 1/r + 1/s being accidentally omitted. I have rectified this in the printed copy. 2. You say [... a quote in German, followed by an equation ...]. Now this is not true of the Spherical aberration itself but (if instead of l/n2 p we write x2 /2n2 p the x2 /2 having been inadvertently or perhaps for brevity omitted by you) it is true [symbol] the function which in my paper on object glasses referred to by you, is called ?ƒ is equal to your [symbol] multiplied by [an equation]. In order to rectify this with as little alteration of your words as possible I have substituted for [a German phrase], in the English translation (by Dr. Tiarks) the words 'the coefficient of spherical aberration' and explained in a note that this 'coefficient' means the function above mentioned. 3. When you say '[a German phrase] &c' you seem to say it [doubles] as a theorem that The Spherical aberration of a double lens is Equal to the Sum of the Spherical aberration of its component lenses. Not only no such theorem can be taken for granted, but it is not correct in fact It is true that the 'coefficient' of Spherical aberration in a double lens is the Sum of the 'coefficient of S.A.' ff its component ones, but this is by no means self evident, but requires all the proof (a pretty complicated one) which is given in my paper-to which I have therefore annexed a reference. 4. In deriving my Equations (A) and (z) you have made W = dn/dn1, p=1-W, p1 = 1 W/W, and throughout your paper you have regarded the ratio of the dispersion powers (which I have called W in my Equations) as the same with that of dn: dnl whereas it is in reality dn/n -1: nd1 /n1-1 and the value of W which satisfies my equations (A) (z) is not W = dn/dn1, but W = dn/dn1 X n1 - 1/n - 1. I have therefore made this correction, and in the remainder of your paper have represented the fraction dn/dn1 not by W but by another letter [symbol] to avoid confusion. 5. You have remarked 'that the terms + [equation] and- [equation]' [it should be[ equation]] '[followed by a quote in German].' If this remark be well founded, all my theory of aberrations falls to the ground I am convinced, if you will consider the matter again, you will coincide with me that this paragraph ought not to stand, and admit that I have done right in striking it out of the printed copy. At all events, as you deduce no conclusion from it in what follows, its omission no way vitiates any part of what you have said. 6. In the first example of your very real and useful practical formulae, you have given, you have taken n = 1.53, n1 = 1.60 and you say 'zersXeiing dn = 0.0, dn1= 0.04 also W = 0.25'. Since the values of dn and dn1 are 0.01 and 0.04 the true ratio of dispersive powers or of focal lengths of the glasses is not 0.25 but 0.25 X 60/53. I have therefore struck out 'W =' and left dn/dn1 = 0.25, after which, the numerical calculations, in which W is not involved, are (I suppose) correct I cannot but remark however that no crown x flint glass hitherto met with will give dn/dn1 = 0.01/0.04. The lowest value of [equation] I know of is 0.425 for glasses. So that this example though good is a numerical illustration has no practical meaning. I cannot imagine by what mode of experimenting you have got such very small values as 0.004 and 0.008 in the specimens of glass you tried, for dn and dn1. I presume they do not relate to extreme rays, but I wish you had mentioned what rays they were determined for, and by what [means]. I hope you will now not think me a very severe critic when I tell you that I think very highly of your paper, as a most useful practical work, and which promises to be of the greatest service. A gentleman named Rogers of Lieth has made a considerable improvement (as promises) in the construction of Large telescopes -he corrects a large disc of Crown by a compound lens of crown x flint of much smaller aperture [followed by a sketch] thus. Vide the Vol. III of the Trans. Ast. Soc. I am sorry you should have thought it necessary to send the money for Dr. Pearson's book as I never intended you to pay for it at all events the (2£ 13 shill) you mention to have sent by Perther...has never come to hand. I am delighted to see that you are not contented to observe but deduce results. Your catalogues of stars whose proper motions come out from your obsns so well, are excellent examples. I wish all astronomers would go & do likewise work muchdispute little-use their eyes & draw conclusions the best they can, and trust the next sensation with their fame. I shall shortly find a way to send you my 3d Catalogue of new double stars- this completes my first thousand. What a wonderful work Struve's Catalogue is! My nebulae get on slowly but steadily. Within the last few days I have been examining the Satellites of Uranus. About two there remains no doubt-and I am almost sure there are more, but the planet is most unfavorably situated [...]". - Seal tear repaired.