108 



Prof. B. Stewart and W. Dodgson. 



[May 29, 



grouping according to a great number of periods taken at small 

 intervals from each, other obtain definite results. These results might 

 be graphically represented in the following manner : the line of 

 abscissae might be taken to denote the exact values of the various 

 periods, forming a time scale in fact ; while the ordinates might repre- 

 sent the final observed inequalities found by employing these various 

 periods. There would thus be in the case now used for illustration a 

 very prominent peak, corresponding to 24 hours, which would fall off 

 rapidly on either side. 



In this particular instance, having obtained as a result a period of 

 -exactly 24 hours, there would probably be no occasion to do anything 

 more, because we have no reason to suppose the existence of any other 

 temperature period very near 24 hours in addition to the one exactly 

 corresponding thereto. We might, therefore, proceed finally to evaluate 

 the obtained inequality, which would represent the mean daily varia- 

 tion of temperature. 



6. It would be different, however, should there prove to be a number 

 of inequalities having periods very close to one another on the time- 

 scale. In this case, even when we had obtained a graphical repre- 

 sentation of our results in the manner just now mentioned, it might be 

 supposed that the various inequalities to some extent interfered with 

 •each other, affecting not only the position in the time-scale of the 

 points of maximum inequality, but also the extent of range and the 

 form of these inequalities. We should, therefore, have next to 

 attempt to eliminate the effect of one inequality upon another. 



The whole process would thus consist of two parts. In the first 

 place, by enormous labour, we should have to obtain a graphical result 

 snowing the exact positions in the time-scale of the points of observed 

 maximum inequality. Secondly, we should have to eliminate the effect 

 •of the various inequalities upon each other, provided it be found that 

 there are several such inequalities very close together. In the present 

 preliminary report we exhibit a method by which the great labour of 

 the first of these two processes is materially abridged. 



We have not, however, as yet advanced sufficiently far in our accu- 

 rate estimation of observed maximum periods to proceed to the elimi- 

 nation of the effect of the various inequalities upon each other. 



7. In testing our method, we began by grouping the Kew declina- 

 tion ranges in sach a manner as to represent a period of 24*25 days. It 

 is unnecessary to describe the details of the method by which a series 

 of daily observations may be grouped so as to represent a period that 

 is not an exact number of days ; suffice it to say that we at length 

 obtained a long series of upwards of 240 rows, each embracing 24 

 horizontal figures. Nor need we give the reasons which induced us to 

 select the precise period of 24*25 days, since for all practical purposes 

 this may be regarded as a period chosen at random. 



