622 Wiscojisin Academy of Sciences, Ai^ts, and Leitei'S. 



mination of geographical latitudes in the United States, and as 

 a result of this labor constructed a catalogue of 2,018 stars, 

 which was published by the Engineers' Department of the 

 United States Army. This work was extended by a similar cata- 

 logue of 612 stars, which was published in 1898 as a part of the 

 Mexican Boundary Commission's report. One of the latest 

 papers published by him is a short paper entitled ''Combinations 

 of Pythagorean triangles as giving exercises in computation," 

 which appeared in Vol. XII of the ''Transactions" of the Wis- 

 consin Academy. Perhaps his most striking v%'ork was the pre- 

 diction in 1861 of the existence of the minute companion to 

 Sirius, based on very small irregularities in the existing observa- 

 tion. The companion was found by Alvan Clark in the place 

 indicated in 1862. 



Professor Saiford's life work was doubtless much influenced 

 by the fact that when he went to Harvard the Harvard astron- 

 omers saw in him the making of a great computer, and his train- 

 ing was carried on with that side of astronomy always in view. 

 He was a good astronomer and his work is of much value, but it 

 is always the work of the patient observer and computer, and 

 contains little of theoretical interest. Owing perhaps to the 

 bent given him at Harvard, his work in pure mathematics is in- 

 considerable, although he undoubtedly possessed exceptional 

 ability for such work. Indeed, from his writings and especially 

 from his monograph on mathematical teaching one is led to be- 

 lieve that he looked upon mathematics rather as part of his 

 physics than as a branch of knowledge to be cultivated for its 

 own sake. He says, "The modern, and to my mind the true, 

 theory is that mathematics is the abstract form of the natural 

 sciences ; and that it is valuable as a training of the reasoning 

 powers not because it is abstract, but because it is the representa- 

 tion of actual things." For this reason he was not wholly in 

 sympathy with ''the new mathematical school — chiefly in certain 

 branches of abstract higher algebra — recently established at 

 the Johns Hopkins University." 



As a teacher Professor Safl^ord did not come into contact with 

 a large number of students, but those who were instructed by 

 him are unanimous in their testimony as to the value and the 



