98 REPORTS ON THE STATE OF SCIENCE. 
example consists in compiling a table or drawing a graph to show the 
effect on a result of variation in a certain datum. 
6. Graphical and analytical methods of study, involving the use of 
mathematical instruments, squared paper, and tables of logarithms, sines, 
&c., ought to go hand in hand throughout the teaching of mechanics. 
7. Pupils should always be required to specify the body whose 
equilibrium or motion is being considered, and to indicate the complete 
system of forces acting on the body, before writing down any equations. 
8. Simplifying assumptions, such as that friction, stiffness of ropes, 
weights of certain bodies, &c., are being disregarded in any particular 
question, cannot be too explicitly stated. 
9. Some statics should precede kinetics. 
10. The parallelogram or triangle of forces should be assumed as an 
experimental result. 
11, The impression that the weight of a body is in reality a single 
force acting at its centre of gravity should be guarded against. 
12. The consideration of work should be an essential part of the 
discussion of machines, and attention should at an early stage be given to 
‘ velocity-ratio’ and ‘ efliciency.’ 
13. When the equilibrium of two or more connected bodies or parts of 
a single body is considered, it is helpful to attend to the separate equili- 
brium of each part. 
14. It should be clearly pointed out that all the results of statics 
apply to cases of uniform motion. 
15. Velocity.—The meaning of the phrase ‘ velocity at an instant’ should 
be carefully brought out by means of the idea of ‘average velocity.’ 
Average velocity should be defined as ‘total distance/total time,’ and 
should not be assumed to be identical with the arithmetic mean of the 
initial and final velocities, or with the velocity at half-time, or with the 
velocity at half-way. There should be no objection to illustrating the 
idea of a vale so as to lead up to the elementary ideas and methods of 
the calculus. 
16. Angular velocity should receive attention, as in connection with 
it a great variety of interesting kinematic examples arise. 
17. Acceleration.—The velocity at any time should be represented 
graphically. This method should be used to illustrate the idea of accelera- 
tion, and the formule for uniformly accelerated motion may be obtained 
from the fact that the graph is in this case a straight line. 
18. The formule for uniform acceleration having been proved, the 
fact that ‘the average velocity =the velocity at the middle instant’ 
should be frequently employed in solving problems connected with such 
motion. 
19. It is convenient to treat elementary problems on the accelerations 
produced by forces by simple proportion, 
force acting acceleration produced 
weight g 
using the fact that a body’s own weight produces acceleration g ; and it 
is convenient to postpone the consideration of mass or inertia until such 
problems have been discussed. 
20. Students ought to know the meaning of ‘absolute measure’ ; 
that is, they should be able to interpret all fundamental equations such 
