Notices respecting N~ew Books. 143 



to his country. We cannot agree with everything which his 

 eulogists haye said on his behalf; the occasion was not one on 

 which it was likely that his fame would be depreciated ; but it is 

 a wonderful fact that he deserved nearly all the praise which was 

 so lavishly bestowed upon his memory. A hardworking ingenious 

 philosopher, full of love for scientific research, with great natural 

 ability, and not ignorant of the limits of his powers, he had in the 

 sixteen years before 1846 done great services to the world in all 

 departments of Physics, but especially in Electromagnetism and 

 Telegraphy. In 1846 he proceeded to carry out the intentions of 

 Mr. Sinithson, of England, who had left by will to the United 

 States more than one hundred thousand pounds for the cause of 

 Science. Till he died, his biography and the history of the Smith- 

 sonian Institution were the same. His scientific investigations 

 became more practical ; he became a great administrator. We have 

 one or two great men in England who possess the same administra- 

 tive power, but we can think of no such administrator who was or 

 is also in the front rank of experimental Philosophers. He refused 

 increase in salary; he seemed to think that services to science 

 were like justice, and ought not to be sold for money. Till he 

 died he was ever ready to serve his country, and for her sake he 

 made many interesting experimental researches. As General 

 Grarfield said, " the twelve hundred lighthouses that shine on our 

 shores, the three thousand buoys along our rivers and coasts, 

 testify to his faithfulness and efficiency." It is, however, when 

 his colleagues speak of him as a personal friend in some of these 

 memorial addresses that the reader gets an idea of what a great 

 thing it is to the world that such a man as Professor Henry ever 

 lived. 



The Fundamental Theorems of Analysis Generalized for Space (1). 



(31 pp.) 

 The Imaginary of Algebra (2). (24 pp.) 



These are two papers (in pamphlet form) by Dr. A. Macfarlane, 

 Professor of Physics in the University of Texas. 



(1) forms a paper read before the New York Mathematical 

 Society (May 7, 1892). 



Starting from the fundamental theorem for the cosine and 

 sine of the sum of two angles in terms of the cosines and sines of 

 the component angles, with the aid of Quaternionic analysis, the 

 writer proceeds to give a generalization of it to space and of 

 De Moivre's theorem : he then obtains the product of two angles 

 in space, when expressed in terms of oblique components. On 

 these foundations he builds up generalizations of the exponential 

 theorem (in connexion with this he gives a further generalization 

 in which he arrives at what he calls quintemions), of the Binomial, 

 Multinomial, and Logarithmic theorems, and then concludes with 

 generalizations of hyperbolic Trigonometry and of Differentiation. 

 The paper is a fine piece of pure analysis. 



