514 TRANS. ST. LOUIS ACAD, SCIENCE. 



diminishes, and thus indicating disturbing causes not easily dis- 

 cussed. Assuming that a straight line will represent the values, 

 he determines the value of the constants, and finds that the line 

 intersects the axis of .y at a point where the value of ^ is — 25. 

 This would mean that the limiting speed of the trotter is 25 sec- 

 onds less than no time at all. 



When making his first discussion of the subject, the writer con- 



ds 

 sidered the propriety of determining the value of -^^ by means 



of consecutive differences, and unfortunately rejected the method 

 without even giving it a trial, for the reason that the dates 188 1.^ 

 and 1878.3, corresponding to the values 131 and 133 of s. were 

 very imperfectly determined. It was clear that the additional 

 point thus secured would deserve very little weight. It was 

 thought to diminish the irregularity of the line by combining these 

 with previous and better determined dates. Mr. Pickering has 

 not only used this method (which properly used is capable of 

 yielding good results), but he has given equal weights to the val- 

 ues of -^y for all the dates in the table. This is the fatal defect 

 which entirely vitiates the conclusion reached by him. A refer- 

 ence to Fig. I of this paper will show that for the earlier dates 

 from 1854.0 down to 1872.5 the graphically determined dates dif- 

 fer from the real dates when the record was actually lowered by 

 from one to two years. 



It will also be seen that the dates 1878.3 and 1881.0 are subject 

 to errors which may be as great as two years. After having made 

 a preliminary examination, these dates might indeed have been 

 "adjusted" so as to make them agree better with the others, but 

 they now stand exactly as they did when first made and before 

 any other work had been done. It is clear that the most weight 

 should be given to the earlier dates. I have therefore plotted the 

 new values of -jfr '^^^h the values of 5, and have drawn the line 

 representing the values so as to give most weight to the best de- 

 termined values. The equation of this line is 



7^^ = — I-2i +0-0 127 ^- - - - (6) 



From this equation the values of -^J- were calculated as given 

 in the fourth column of the last table. The fifth column, headed 

 e, gives the time in years by which the corresponding time in- 



