.May 4, 1883.] 



SCIENCE. 



355 



the workshop at the Yale museum. The pillars 

 hetween which it hangs are fourteen feet high. 

 On the floor, in the back part of the room, is 

 the mould of the body, and bases of the arms. 

 At the left, against the table, is the mould for 

 the under sides of the bases of the arms, and 

 at the right, on the floor, one of the arm- 

 moulds, with the two parts fitted together. 



.T. H. Emebton. 



HORSE-TROTTING FROM A MATHE- 

 MATICAL STAND-POINT. 



Ix the April number of the American journal 

 of science is a ver_y intei'esting article bj' Wil- 

 liam II. Brewer, on The evolu- 

 tion of the American trotting- 

 horse. He remarks, ''The 

 formation of this new breed," 

 for such he considers it, "is 

 so recent, the development of 

 a special qnalitj' has been so 

 marked, there is such an abun- 

 dant literature pertaining to 

 its historj-, the sj-stem 

 of sporting rec- 



coucludes hj hoping that some one will plot 

 the curves which naturally' suggest themselves, 

 and determine '' how fast horses will ulti- 

 matelj' trot, and when this maximum will be 

 reached." 



I. — Best record of mile heats up to the present 

 time. 



Looking at the rapidly diminishing numbers 

 of the ' record ' columns of table I., one cannot 

 but ask, When will this diminution cease ? When 

 will the fastest time attainable be reached? 

 Plotting records as ordinates, and dates as 

 aliscissas, one would naturally expect the first 



dy 

 differential, "r, to diminish in value, and that 

 'da;' -' 



the curve would be asymptotic to the axis pf x : 

 or, in other words, wc should expect, as time 

 went on, that the speed of the horse would not 

 improve so rapidly as it did at first, and 

 that after a while the improvement 

 would be so slow that we might 

 consider that we had prac- 

 tically reached the 

 f a s t e s t time 

 attaina- 

 ble. 



1840 1830 I860 1870 ISSO 1890 



ABSCISSAS EEPRESENT DATES; OEDINATES, THE BEST EECQKD OF WILE HEATS. 



carefully planned and comprehensively con- 

 ducted, and withal has become so extensive, 

 that we have the data for a reasonably accu- 

 rate determination of the influences at work 

 vrhich led to this new breed being made, the 

 materials of which it is made, and the rate of 

 progress of the special evolution." Towards 

 the end of the paper are given some tables, 

 which are copied in part beyond. The writer 



But we find, with the exception of the first, 

 that all the points lie very nearly on a curve 

 which is convex upwards : in other words, that 

 the rate of improvement of the record is increas- 

 ing instead of diminishing, and that it will 

 cross the two-minute line about the year 1901. 

 It is veiy evident that this state of things 

 cannot go on indefinitely : otherwise we should 

 in course of time have a horse trot a mile in no 



