HI] VELOCITY AND ACCELERATION 65 



change of magnitude ; we must now study an acceleration, or 

 rate of change of velocity. The rate, or velocity, of growth is 

 measured by th? slope of the curve ; where the curve is steep, it 

 means that growth is rapid, and when growth ceases the curve 

 appears as a horizontal line. If we can find a means, then, of 

 representing at successive epochs the corresponding slope, or 

 steepness, of the curve, we shall have obtained a picture of the 

 rate of change of velocity, or the acceleration of growth. The 

 measure of the steepness of a curve is given by the tangent to 

 the curve, or we may estimate it by taking for equal intervals 

 of time (strictly speaking, for each infinitesimal interval of time) 

 the actual increment added during that interval of time : and in 

 practice this simply amounts to taking the successive differences 

 between the values of length (or of weight) for the successive 

 ages which we have begun by studying. If we then plot these 

 successive differences against time, we obtain a curve each point 

 upon which represents a velocity, and the whole curve indicates 

 the rate of change of velocity, and we call it an acceleration-curve. 

 It contains, in truth, nothing whatsoever that was not implicit 

 in our former curve ; but it makes clear to our eye, and brings 

 within the reach of further investigation, phenomena that were 

 hard to see in the other mode of representation. 



The acceleration-curve of height, which we here illustrate, in 

 Fig. 4, is very different in form from the curve of growth which 

 we have just been looking at; and it happens that, in this case, 

 there is a very marked difference between the curve which we 

 obtain from Quetelet's data of growth in height and that which 

 we may draw from any other series of observations known to me 

 from British, French, American or German writers. It begins (as 

 will be seen from our next table) at a very high level, such 

 as it never afterwards attains ; and still stands too high, during 

 the first three or four years of life, to be represented on the scale 

 of the accompanying diagram. From these high velocities it falls 

 away, on the whole, until the age when growth itself ceases, and 

 when the rate of growth, accordingly, has, for some years together, 

 the constant value of nil ; but the rate of fall, or rate of change of 

 velocity, is subject to several changes or interruptions. During 

 the first three or four years of life the fall is continuous and rapid, 



T. G. 5 



