274 POPULAR LECTURES AND ADDRESSES. 



variable. The function of one independent 

 variable most important in Liverpool perhaps 

 may be the price of cotton. A curve showing 

 the price of cotton, rising when the price 

 of cotton is high, and sinking when the price of 

 cotton is low, shows all the complicated changes 

 of that independent variable to the eye. And 

 so in the Registrar-General's tables of mortality, 

 we have curves showing the number of deaths 

 from day to day the painful history of an 

 epidemic, shown in a rising branch ; and the 

 long gradual talus in a falling branch of the 

 curve when the epidemic is overcome, and the 

 normal state of health is again approached. All 

 that is shown to the eye ; and one of the most 

 beautiful results of mathematics is the means of 

 showing to the eye the law of variation, however 

 complicated, of one independent variable. But 

 now for what really to me seems a marvel of 

 marvels : think what a complicated thing is the 

 result of an orchestra playing a hundred in- 

 struments and two hundred voices singing in 

 chorus accompanied by the orchestra. Think of 



