Sun-spot Areas and Diurnal Temperature- Ranges. 293 



a great number of periods taken at small intervals from each other, 

 obtain at length an accurate value of the mean solar day. 



5. Reflection will, however, convince us that it is possible greatly 

 to abridge this labour. Let us still keep to our illustration of tem- 

 perature observations but, since ignorance regarding the length of 

 the day is inconceivable, let us imagine that a staff of observers have 

 strict orders to register the temperature at every exact hour of a 

 mean time clock. Let us f urther suppose that the rate of this clock is 

 constant but not quite correct, and that the observations so made 

 extend over a series of years. It is required by means of these 

 observations to determine the clock-rate. 



To do this we might, if we chose, laboriously arrange the whole 

 body of observations in a number of different groups, one group 

 representing 24 hours by the clock, and other groups a little more or 

 a little less. Amongst these some one grouping would be found to 

 exhibit when the summations were made a maximum amount of 

 fluctuation, and we should naturally imagine that the time-scale of 

 this grouping was the best representative of the mean solar day. 



We might, however, obtain the same result with infinitely less 

 labour, and for this purpose we need not make any other fundamental 

 grouping than that which denotes 24 clock hours. 



Let us then arrange these observations in yearly series and find the 

 average Inequality for each year. 



Now suppose that for the first year the mean maximum diurnal 

 temperature occurred at 2 P.M. clock time, for the second year at 

 1 P.M., for the third year at noon, and so on, retiring backwards one 

 hour every year. We should, of course, conclude that the clock went 

 one hour slow every year, and should thus obtain at once the clock- 

 rate. And by pushing the second year's Inequality one place forward, 

 the third year's two places forward, and so on, adding together the 

 series so placed, and ultimately taking the mean, we should obtain 

 a good value of the true temperature Inequality corresponding to the 

 exact mean solar day. 



We have chosen a very obvious instance, but of course the clock 

 error in one year might not be exactly one hour, and it might be 

 necessary to arrange the yearly series in a number of different ways 

 with regard to each other before we obtained the grouping which 

 gave us the maximum Inequality. But at length this result would 

 be obtained and without the expenditure of more than a moderate 

 amount of labour, and when obtained the time-scale belonging to it 

 would represent the mean solar day. 



It is virtually this method which we have employed in our present 

 investigation, and we shall now state what observations, solar and 

 terrestrial, we have at our disposal, and also how we have applied our 

 method to these observations. 



