320- REPORT — 1902. 



and R = F cos a ± (P +1^) -* - ^ ^'F^ + P'-2F2}sin{a+i) 



The effect of the last 'term "in this equation is very small ; it attains its 

 highest value when (i) = 0, but usually tan a = 0'262, sin a = 0-255, 



t =0-02, and/=0-065. 

 r 



Substituting these values in tlje equation, it will always be found that 

 the friction of the axle is less than 1/50 to 1/100 of the tractive force. 



Now, neglecting the last term and making cos a = 0'967, the formula 

 is reduced to the expression — 



R= 0-967 F±(P+p)^ 



The values of h, L, P, and 2> are known, and the dynamometer gives 

 F ; the resistance R can then be determined. Representing R by an 

 ordinate to a given scale, rectangular axes ox and oy can be chosen ; if 

 from the axis x the values of the element which varies — i.e., the weight 

 (P+p) — be marked off, and at the extremity of each of these values an 

 ordinate corresponding to the value of R be raised, then a number of 

 points can be determined lying on a curve, and from the form of the curve 

 can be found the law which governs the ratio between the resistance R 

 and the variable elem'ent. 



The preceding formulae only apply to traction upon level roads. 



The following are the conclusions drawn from General Morin's first 

 series of experiments : — 



I. ' The resistance to traction on macadam or paved rOads (taken rela- 

 tively to the axle parallel to the ground) is proportional to the pressure 

 and inversely proportional to the radius of the wheel. 



II. ' The deterioration of the road due to the vehicle increases as the 

 wheels decrease in diameter.' 



III. ' The resistance is very nearly independent of the width of the 

 tyres on macadam or paved roads for sizes above 0-08 m. to O'lO m. in 

 width.* 



IV. ' On compressible roads, such as loose earth, sand, gravel, and new 

 macadam, the resistance to traction decreases as the width of the tyre 

 increases ; the proportion depends upon the condition of the road. On 

 hard roads it is useless to employ wide tyres, and on macadam in the 

 ordinary state the tyres should not be wider than 0-10 m. to 0-12 m.' 



V. ' On soft ground, such as soil, sand, earth driftways in good con- 

 dition, rutty roads, or layers of gravel on hard ground, the resistance is 

 independent of the speed of the vehicle with or without springs.' 



VI. ' At a walking-pace on all roads the resistance is practically the 

 same for all vehicles.' 



VII. ' On macadam or paved roads the resistance increases with the 

 speed.' The rate of increase of resistance is nearly in proportion to the 

 increase in speed, with an initial speed of 1 m. per second. The less rigid 

 the vehicle, the better the springs of the vehicle ; and the more uniform the 

 road, the less will be rate of increase of resistance. 



VIII. ' On good sandstone pavement, well laid and uniform, the 

 resistance at walking-pace is only three-quarters of that on the best 

 macadam ; and for vehicles well hung, the resistance at trotting-pace on 

 good pavement is equal to the resistance on good macadam. But on bad 



