He was asthmatic and spent considerable periods at sea studying the more portable sections of the family library which had been established by his father.

Among his achievements, Gill later made the first photograph of the Great Comet of 1882,[9] pioneering astrophotography and the mapping of the heavens.

As well as much astronomical equipment, Crawford's observatory included an extensive collection of rare books, part of the Bibliotheca Lindesiana at Haigh Hall, which his father and he had accumulated till it was one of the most impressive private collections in Britain at the time.

The Bibliotheca Lindesiana (i.e. Lindsayan or Lindsian library) had been planned by the 25th Earl and both he and his eldest son had been instrumental in building it up to such an extent that it was one of the most impressive private collections in Britain at the time, both for its size and for the rarity of some of the materials it contained.

In 1861 he wrote to his son James (then 14 years old) a letter which describes his vision of the Bibliotheca Lindesiana; in 1864 he redrafted and enlarged it while visiting his villa in Tuscany.

Brunet[13] in which knowledge is divided into five branches: Theology, Jurisprudence, Science and Arts, Belles Lettres, History; to which Alexander added six of his own as paralipomena: Genealogy, Archaeology, Biography, Literary History, Bibliography and Encyclopaedias; and finally a Museum.

Crawford's philatelic interests[21] grew out of his work in extending the Lindsay family's library.

Crawford was elected as a Conservative Member of Parliament for Wigan in 1874, and held the seat until his elevation to the peerage in 1880.

Crawford had spent a short period as an Ensign in the Grenadier Guards, and after he became MP for Wigan he was appointed one of two lieutenant-colonels of the 4th Lancashire Rifle Volunteer Corps with his brother-in-law Arthur Bootle-Wilbraham, a former Ensign in the Coldstream Guards, as the other.

On 10 October 1900 Crawford was appointed Honorary Colonel of the unit, now the 1st Volunteer Battalion, Manchester Regiment.

from the University of Edinburgh in 1882, and in the following year was nominated honorary associate of the Royal Prussian Academy of Sciences.