ANNIVERSARY ADDRESS. 21 



last place, and in 1873 Shanks 1 carried it still further, viz., to 

 707 places of figures. Let us examine for a moment the significance 

 of this : — In a year, light travels about 5 '9 million million miles. 

 Imagine the circumference of a circle whose radius was a million 

 million years of light travel. To express that great circumference 

 to a millionth of an inch would require only 37 places of figures 

 out of the 707. That is to say, the mathematician has enabled 

 us to express the circumference of a circle, to the degree of pre- 

 cision indicated, whose radius is 10 670 times a million million years 

 of light travel. This number is inconceivable, but one may get 

 some further idea of its immensity thus : — Imagine a being capable 

 of traversing the space covered by a million million years of light 

 travel, in so inconceivably small a time as the millionth of a 

 second, that is of covering about 31 /x 3 times that distance in a 

 year : (/x denotes a million). The flight of that being for a million 

 million years being taken as radius, would require only 69 figures 

 instead of 37, to determine the circumference of the circle to a 

 millionth of an inch, leaving over 600 figures unexhausted. The 

 fact is that so great a number of figures requires the conception 

 of a higher order of development, than mere change of scale, to 

 apprehend it. Yet about the accuracy of the result there is not 

 the shadow of a doubt. 



To the mathematician the chief merit of his beloved science 

 lies in its intrinsic interest and in its value as an instrument of 

 severe intellectual discipline and culture. But we are not all 

 endowed with the spirit of the mathematician, and hence must 

 regard the Science also from other standpoints. We note there- 

 fore that it has a secondary and derived value, as our director 

 and guide in the study of natural philosophy, or the study of the 

 substance of the universe, and of its mode of being and action. 

 And beyond this again, it is in some form or another, immediately 

 ministerial to practice in almost every application of scientific 

 knowledge. 



1 Proc. Eoy. Soc. Lond., xxi. 



