I was much out of health after my husband's death, and chiefly occupied with my children, especially with the one I was nursing; but as I did not go into society, I rose early, and, having plenty of time, I resumed my mathematical studies. By this time I had studied plane and spherical trigonometry, conic sections, and Fergusson's "Astronomy." I think it was immediately after my return to Scotland that I attempted to read Newton's "Principia." I found it extremely difficult, and certainly did not understand it till I returned to it some time after, when I studied that wonderful work with great assiduity, and wrote numerous notes and observations on it. I obtained a loan of what I believe was called the Jesuit's edition, which helped me. At this period mathematical science was at a low ebb in Britain; reverence for Newton had prevented men from adopting the "Calculus," which had enabled foreign mathematicians to carry astronomical and mechanical science to the highest perfection. Professors Ivory and de Morgan afterwards adopted the "Calculus"; but several years elapsed before Mr. Herschel and Mr. Babbage were joint-editors with Professor Peacock in publishing an abridged translation of La Croix's "Treatise on the Differential and Integral Calculus." I became acquainted with Mr. Wallace, who was, if I am not mistaken, mathematical teacher of the Military College at Marlow, and editor of a mathematical journal published there. I had solved some of the problems contained in it and sent them to him, which led to a correspondence, as Mr. Wallace sent me his own solutions in return. Mine were sometimes right and sometimes wrong, and it occasionally happened that we solved the same problem by different methods. At last I succeeded in solving a prize problem! It was a diophantine problem, and I was awarded a silver medal cast on purpose with my name, which pleased me exceedingly. Mr. Wallace was elected Professor of Mathematics in the University of Edinburgh, and was very kind to me. When I told him that I earnestly desired to go through a regular course of mathematical and astronomical science, even including the highest branches, he gave me a list of the requisite books, which were in French, and consisted of Francoeur's pure "Mathematics," and his "Elements of Mechanics," La Croix's "Algebra," and his large work on the "Differential and Integral Calculus," together with his work on "Finite Differences and Series," Biot's "Analytical Geometry and Astronomy," Poisson's "Treatise on Mechanics," La Grange's "Theory of Analytical Functions," Euler's "Algebra," Euler's "Isoperimetrical Problems" (in Latin), Clairault's "Figure of the Earth," Monge's "Application of Analysis to Geometry," Callet's "Logarithms," La Place's "Mecanique Celeste," and his "Analytical Theory of Probabilities," &c., &c., &c.[6]