[In publishing the following letter, I do not consider that I am infringing on the rule I have followed in obedience to my mother's wishes, that is, to abstain from giving publicity to all letters which are of a private and confidential character. This one entirely concerns her scientific writings, and is interesting as showing the confidence which existed between Sir John Herschel and herself. This great philosopher was my mother's truest and best friend, one whose opinion she valued above all others, whose genius and consummate talents she admired, and whose beautiful character she loved with an intensity which is better shown by some extracts from her letters to be given presently than by anything I can say. This deep regard on her part he returned with the most chivalrous respect and admiration. In any doubt or difficulty it was his advice she sought, his criticism she submitted to; both were always frankly given without the slightest fear of giving offence, for Sir John Herschel well knew the spirit with which any remarks of his would be received.] FROM SIR JOHN HERSCHEL TO MRS. SOMERVILLE. SLOUGH, _Feb. 23rd, 1830_. MY DEAR MRS. SOMERVILLE, ... As you contemplate separate publication, and as the attention of many will be turned to a work from _your_ pen who will just possess quantum enough of mathematical knowledge to be able to read the first chapter without being able to follow you into its application, and as these, moreover, are the very people who will think themselves privileged to criticise and use their privilege with the least discretion, I cannot recommend too much clearness, fulness, and order in the _expose_ of the principles. Were I you, I would devote to this first part at least double the space you have done. Your familiarity with the results and formulae has led you into what is extremely natural in such a case--a somewhat hasty passing over what, to a beginner, would prove insuperable difficulties; and if I may so express it, a sketchiness of outline (as a painter you will understand my meaning, and what is of more consequence, see how it is to be remedied).