Feb. 9, 1871] 
NATURE 
293 


It is easy to see, from an inspection of Diagram No. 1, 
that a portion of such an equilateral hyperbola would 
coincide nearly with the true curve, and with the points 
determined by experiment. 
Addendum.—Mr. Robert B. Hayward, of Harrow, has 
kindly called my attention to an error in my application 
of Law 1 to Mr. Jevons’ first series of experiments in 
which different weights were thrown by hand. In applying 
Law 1 to these experiments, I assumed, in equations 
(1, 2, 3, 4), that the total work stored up in a revolving 
body is that of a body of equal weight, moving with the 
velocity of the centre of oscillation. I should have 
stated that it is the work of a body of equal weight 
moving with the velocity of the centre of gyration. If 
this error be corrected, the four equations become much 
simpler in form, and lead directly to the empirical formula 
used by Mr. Jevons, and also furnish a curve which cor- 
responds very well with the experiments. 
Let £ denote the radius of gyration, and let the other 
symbols remain as before ; we find the following equa- 
tions, which are to be used instead of the first four 
already given. 

(w + x) v? = Const. (1) 
v= ve (2) 
Rie We Set a 
cae WATE eS G3) 
3w+2)xX R=A (4) 
Mr. Jevons’ eight experiments furnish twenty-eight 
equations to determine the value of x, and the mean of all 
the values is 
Irtlb. 
This value of x, when substituted in the eight equations 
furnished by (4), gives us the following values of 4. 
t= 

w A 
IROO1 Sse! ths an 82915 
2A EMILE oe Sits 
TA ares a afoviltes 
Ta Soiiae - + 3389 
4 » : 337°5 
2 » . 3189 
Eos nay 28 3250 
Lee gy 342°1 
Mean 33849 
If the mean values of A and x be used in equation (4), we 
find the following comparison of theory and observa- 
tion :— 

w R (observed). R (calculated). Difference. 
56 lbs. ... 1°84 feet 1°89 feet —o'05 feet 
28, -- 3°70 yy 315 Onsen ie ie Osng 
WHat coh OFGO%7 6:37" 55) ne) 1-049)" *55 
TE 2s pLOZSO% |, DOGG. way eee -O1O Ee! ay 
45 vw 14°61 ” 14°65 ” —O'04 5, 
Pee ei TOAOb | is08 vecsi SOTO ss toh Ma 5 
TRG SIOS oy eon 2ACOLL NS, tera 0' OO, 
PRC e AUG. vise. 20'8G) ot eet Or20). 
The curve of useful effect, deduced from equation (4) is 
Aw 
& 3w +4 
This curve represents an equilateral hyperbola, whose 
equation, referred to its asymptotes as axes of co-ordi- 
nates, is 
xy + 4174 = 0. 
Diagram No. 4 shows this hyperbola, while the centres 
of the little circles show the several experiments. 
This hyperbola, derived from the property of the centre 
of gyration, represents the observations very well; and 


it nearly coincides with the more complex curve derived 
from the centre of oscillation, shown in Diagram No. 1. 
Mr. Jevons’ empirical formula corresponds at once to 
equation (4), provided the quantity (g) be used to denote 
one-third of the weight of the arm instead of one half, 
His formula becomes, multiplying above and below by 3, 
347°1 
3w + I1°7 
The weight of the arm and shoulder used in throwing 
weights, viz. 111tlb. or 11°7lb., is considerably greater 
than the weight of the simple arm, 7'4lb., a result quite 
consistent with the fact that the scapular muscles move 
with the arm in this kind of exertion. 
R= 
S. HAUGHTON 


NOTES 
AT a preliminary meeting held at King’s College on Monday 
last, the Rev. Dr. Barry, Principal, in the chair, it was resolved 
that a fund for a Memorial to the late Dr. Miller, in connection 
with King’s College as having been for thirty years the principal 
sphere of his labours, be at once raised by subscriptions in the 
College, and from the general public. It was further resolved to 
form a committee for the purpose of carrying out this resolution, 
and as soon as the committee is complete a meeting will be sum- 
moned to adopt such further measures as are necessary. 
WE are glad to hear that Prof. Frankland has accepted the 
Presidency of the Chemical Society for the ensuing session. 
A crRcuLAR has been issued by the Science and Art Depart- 
ment of the Committee of Council on Education, South Ken- 
sington, directing that in future all teachers certificated by the 
Education Department shall be allowed to earn payments on the 
‘results of the instruction of their pupils in Stage I. of Mathematics, 
according to the rules of the Science Directory, without having 
previously passed the qualifying examination required by § XXXII. 
The Department has also issued the following amended pro- 
gramme of the examinations for the diplomas of the Royal School 
of Naval Architecture and Marine Engineering, which is to come 
into force at the examination to be held in April 1872, the 
examination in April 1871, being held according to the pro- 
gramme contained in the existing Directory of the School :— 
“Diplomas will be given to all persons, whether they have 
received their instruction at the school or not, who pass the final 
examinations of the school, provided that they give satisfactory 
evidence of having gone through the course of practical work 
recommended by the Council of the Institution of Naval Archi- 
tects. These diplomas will be of two grades, according to the 
success of the candidate in the examination, the title of the higher 
grade being Fellow, and of the lower, Associate, of the Royal 
School of Naval Architecture.” These examinations will be 
held annually towards the end of April. Candidates who have not 
been students of the school will be required to produce certificates 
that they have been engaged for three years, at least, in— 
(1) practical wood or iron ship-building in a dockyard ; or (2) 
practical engine and boiler building in a dockyard, or in the 
works of a marine engineer ; or (3) practical work as a draughts- 
man in a dockyard (or marine engine works), during which the 
candidate must have himself gone through the complete formation 
of the design of a ship (or of a marine engine), with the whole of 
the calculations included init. Such candidates will also be 
required to give references as to character and good conduct 
before they are admitted to the examination. All such candidates 
must apply to the Secretary, Science and Art Department, South 
Kensington, W., not later than the 15th March in each year. 
IN our notice last week of the attainments of the Senior Wrangler, 
we should have included the statement which we made some time 
since, that Mr. Hopkinson took the degree of D.Sc. at the Uni- 
