ON THE FURTHER TABULATION OF BESSEL FUNCTIONS 97 
Then the induction 
Trait (T,42+T,) + <a STA GLa oo! WA fo ow a = 
(=1)'***%8(2n -2r—28-+1, 2n+ 2r+ 23-1) (Qn—2r+2s+1, 2n+ 2r-2s—1) 
(r—s)!(r+s)!r 
cau be verified by adding in the two terms T,_,,,+T,,,,.. 
Putting s=7—1, the value of 
dae + (T+ Ey) a7 o, 8h Je ota (To—1 + T;) == Tee 
is found ; and adding in the remaining terms, T,, T,,,,;, and T,, the result 
is found to vanish. 
Thus the equation P,,P,,,+Q,Q,,,=1 is proved. 
The expression found by Professor Lodge for P,?+Q,”? from the 
differential equation which it satisfies has also been verified by a direct 
calculation, but the work is so long that the Committee do not feel justified 
in asking the Association to print it. 
The Teaching of Elementary Mechanics.—Report of the Committee, 
consistiny of Professor Horace Lamp (Chairman), Professor J. 
PERRY (Secretary), Mr. C. Vernon Boys, Professors CurystrAau, 
Ewine, G. A. Gipson, and GREENHILL, Principal Grirrrrus, Pro- 
fessor Henric1, Dr. E. W. Hopson, Mr. C.S. Jackson, Sir OLIVER 
LopGe£, Professors Love, Mincuin, Scuuster, and A. M. WortH- 
INGTON, and Mr. A. W. Sippons, appointed for the Consideration 
of the Teaching of Klementary Mechanics, and the Improvement 
which might be effected in such Teaching. 
THE Committee make the following suggestions. Some of these are 
copied from the Report of the Mathematical Association Committee on 
the Teaching of Elementary Mechanics :— 
1. Practical and theoretical mechanics ought, if possible, to be taught 
by the same person ; mechanics and mathematics ought not to be treated 
as distinct from each other. 
2. The opportunity furnished by the necessity for writing an account 
_ of what a student has done and seen in his laboratory work ought to be 
utilised in relation to the teaching of English composition. 
3. The theoretical study of mechanics should be preceded and accom- 
panied by concrete experience of some of the facts to be dealt with in the 
systematic course ; for example, such things as are used in practical 
engineering and such as can be met with in ordinary life. 
4. An experimental course might include mensuration, geometry, 
weighing, and measuring ; the equilibrium of forces, the lever and other 
simple machines, force of friction, and the effect of friction in simple 
machines ; work, forms of energy, especially the energy of lifted weights, 
kinetic energy, heat ; hydrostatics, barometers, pumps ; velocity, accelera- 
tion, inertia, force. 
5. Examples should at first, as a rule, be numerical, and should, as 
far as possible, be of a practical nature. A specially instructive class of 
1907. H 
