HO MY LIFE [Chap. 



These bases were connected by the system of triangula- 

 tion already referred to, the angles at all the stations being 

 taken with the best available instruments and often repeated 

 by different observers, while allowance had also to be made 

 for height above the sea-level, to which all the distances had 

 to be reduced. In this way, starting from any one base, the 

 lengths of the sides of all the triangles were calculated, and 

 ultimately the length of the other bases ; and if there had 

 been absolutely no error in any of the measurements of base- 

 lines or of angles, the length of a base obtained by calcula- 

 tion would be the same as that by direct measurement. The 

 results obtained showed a quite marvellous accuracy. Start- 

 ing from the base measured on Salisbury Plain, the length of 

 another base on the shore of Lough Foyle in the north of 

 Ireland was calculated through the whole series of triangles 

 connecting them, and this calculated length was found to 

 differ from the measured length by only five inches and a 

 fraction. The distance between these two base-lines is about 

 three hundred and sixty miles. 



These wonderfully accurate measurements and calcula- 

 tions impressed me greatly, and with my practical work 

 at surveying and learning the use of that beautiful little 

 instrument the pocket-sextant, opened my mind to the 

 uses and practical applications of mathematics, of which 

 at school I had been taught nothing whatever, although 

 I had learnt some Euclid and algebra. This glimmer of 

 light made me want to know more, and I obtained some 

 of the cheap elementary books published by the Society for 

 the Diffusion of Useful Knowledge. The first I got were 

 on Mechanics and on Optics, and for some years I puzzled 

 over these by myself, trying such simple experiments as I 

 could, and gradually arriving at clear conceptions of the chief 

 laws of elementary mechanics and of optical instruments. I 

 thus laid the foundation for that interest in physical science 

 and acquaintance with its general principles which have 

 remained with me throughout my life. 



It was here, too, that during my solitary rambles I first 



