THE ASTRONOMICAL VIEW OF NATURE. 323 



calculation, or to geometrical figures. These geometrical 

 figures represent on paper, and on a small scale, the 

 curves or orbits of bodies in space and time, and can 

 be interpreted as such. Then, as in nature two bodies 

 or portions of matter are never single gravitating points 

 occurring alone, but are surrounded by the totality of 

 existing things, the formula which reduces the action of 

 gravitation to that of pairs of things, and to the elements 

 of matter, requires to be extended to more than two in 

 fact to an infinity of elements. The infinitesimal calculus 

 teaches us how to deal with such a progression from finite 

 numbers and quantities to infinite numbers ; or from rela- 

 tions which refer to infinitesimal elements to finite meas- 

 urable quantities. We find very soon that our powers of 

 calculation reach only a small way, and cover only a small 

 extent of the ground which observation opens to our eyes. 

 We are thus forced to deal with the element of error 

 which creeps into our calculations ; to be satisfied with 

 approximations ; l and instead of certainty, probability is 



14. 



Element of 

 error. 



Gauss, Werke, vol. v. pp. 85, 293, 

 Ac.) Of Weber's electrodynamic 

 measurements I shall speak later on. 

 Absolute measurements were used 

 by William Thomson (Lord Kelvin) 

 as early as 1851, and owing mainly 

 to his influence the present system 

 was gradually established in the 

 course of the following twenty years 

 (see William Thomson, ' Popular 

 Lectures and Addresses," vol. i. p. 

 83, &c.) Fourier's theory of dimen- 

 sions was first brought prominently 

 before the scientific and teaching 

 world by Clerk Maxwell in his trea- 

 tise on ' Electricity and Magnetism ' 

 (1st ed., vol. i. p. 2). There also 

 we meet for the first time with 

 the use of astronomical magnitudes 

 And relations by which the usual 



three units, time, mass, and dis- 

 tance, can be reduced to two. This 

 is also lucidly explained by Lord 

 Kelvin (loc. cit.) It has been fol- 

 lowed up in detail in two interest- 

 ing papers by W. Winter in Exner's 

 ' Repertorium der Physik' (vol. 21, 

 p. 775, and vol. 24, p. 471). 



1 The history of astronomical cal- 

 culations since the time of Newton, 

 when the theoretical basis was once 

 for all laid, is a history of gradual 

 approximations. Mathematically a 

 conic section is sufficiently defined 

 if the position of the focus (the sun 

 in our planetary system) and three 

 positions of the moving star are 

 known by observation. But it was 

 a long time before even tolerably 

 complete methods of observation 



