both x and z are varied, so as to obtain the limit which 
separates conditions leading to recovery from conditions 
leading to death. 
In the third series, s is constant = 1’5 (that is, a dose 
one-half greater than that which would produce death if 
no atropia were administered) ; and x and y are varied, 
so as to obtain sets of limiting conditions. 
If the three variables, x, y, z, be expressed by means of 
a system of three rectangular co-ordinates, the conditions 
of each experiment will be represented by a point ; and 
the points representing experiments resulting in recovery 
will be separated from those representing experiments 
resulting in death, bya surface passing through the points 
representing sets of limiting conditions. 
The three series of experiments make us acquainted 
with three lines on this surface, viz., the intersections of 
the surface and the three planes, the equations of which 
are, y=5,y = —5,andzs=1'5. 
Some further knowledge of the character of the surface 
may be obtained from a consideration of the general con- 
ditions. Thus, when no atropia is administered, the 
limiting value of » is obviously the minimum fatal dose 
of physostigma ; thatis,+=o,7=1. Inthe same way, 
when z = 0, x = the minimum fatal dose of sulphate of 
atropia for a 3lb. rabbit, = about 21 grains, or z = 0, 
ot, 
Again, there must be a limiting value of y ; that is, an 
interval of time so great as to prevent the two poisons 
acting simultaneously, the animal having either died or 
completely recovered from the effects of the first substance 
before the time for the administration of the second has 
arrived. When y exceeds this value, the surface must 
consist of two planes, the equations of which are, # = 21 
and z= 1. 
This limiting value is of course not necessarily the same 
on the positive and on the negative side ; and, in fact, Dr. 
Fraser’s experiments show that it lies very much nearer 
to the plane y =o on the negative than on the positive side. 
Beyond these values of y, the surface consists of two 
plane sheets meeting in a rectangular ‘edge. Each of 
these sheets separates points representing conditions un- 
der which recovery takes place from conditions leading to 
death ; but in the case of the sheet z =1 the space on 
the one side represents recovery and on the other side 
death caused by Physostigma; while in the case of the 
sheet += 21 the space on the one side represents 
recovery and on the other side death caused by a¢ropia. 
If we look closely at the portion of the surface lying 
between these limiting values of y, we shall see that here, 
also, the surface consists of two sheets; in the one 
dz. ry ake cy eee 
dx '8 Positive, in the other negative ; in the one a small 
increase of the dose of atropia tends to recovery, in the 
other to death ; the one runs continuously into the plane 
& = I, the otherinto the plane x= 21. These two sheets 
meet in an edge, which is particularly well seen in the 
sections by the planes y= 5 and y= — 5. (The various 
lines above mentioned are represented, in orthogonal pro- 
jections, in the accompanying woodcut.) There can be 
no doubt that this edge is continuous with the rectangular 
edges between the plane sheets before mentioned. The 
conditions represented by points situated on this edge are 
such that increase of the dose of either substance will 
produce a fatal result, and that either increase or diminu- 
tion of the dose of atropia will produce a fatal result. 
This paper appears to us specially worthy of attentive 
consideration, as the first systematic investigation of the 
combined action of two poisons, and also on account of 
the method employed in arranging the results of the in- 
vestigation ; a method of which we have given a sketch 
in this notice, and which seems certain to lead to in- 
creased accuracy of observation, by giving the means of 
a definiteness in the statement and classification of 
results, 
[Now 28, 1872 
NOTES 
Tue Royal Commission on Scientific Instruction and the Ad: 
vancement of Science have this week examined the Marquis of — 
Salisbury and Sir Stafford Northcote. 
THE Anniversary Meeting of the Royal Society will be h 
on Saturday next. - 
e 7 
At the meeting of the Royal Geographical Society held on 
Monday night, the President stated that Mr. Young, the firm 
friend of Dr. Livingstone, to whom we recently referred, had 
sent him a cheque for 2,000/. to help to defray the expenses 
the Livingstone Congo Expedition, which, under the comm: 
of Lieut. Grundy, who is well acquainted with the West Co 
of Africa, is expected to start for Africa during the course of 
present week, Government, we are glad to say, has given th 
expedition all the assistance in its power, furnishing letters to its 
officers on the West Coast of Africa, for the purpose of pro- 
curing the expedition all possible facilities, The War Office 
has made a present to the members of the expedition of the 
necessary arms, while the African Steamship Company has very 
kindly given to the officers passages at half the usual price, 
Lieut. Grundy thus starts under very favourable auspices. Si 
Bartle Frere, the leader of the anti-slavery expedition from the 
opposite coast, left England last Thursday, and is expected to reach 
Brindisi in the course of a few days, where he will be joined by 
Lieut. Cameron and his party, who are just about to leave 
England. The party will then proceed, onboard the Enchantress, 
through the canal to Zanzibar, where Sir Bartle Frere will give 
his final instructions to those gentlemen who are to form the ex- 
pedition. The president, Sir Henry Rawlinson, places every 
confidence in Lieut. Cameron, and in the zeal of the officers by 
whom he is accompanied ; he is determined to avail himself o} 
every possible opening to penetrate into the interior of Africa, 
for his own credit, for the advantage of science, and for the 
purpose of aiding and relieving Livingstone. a 
THE Khedive of Egypt is also about to send a force comprising 
5,000 men, under Purdy Bey (one of his American officers) to 
Zanzibar in transports. The ostensible object of the expedition 
is to go into the {country which it is supposed that Livingstone 
may be exploring, and to co-operate with him, if it be agree- 
able to him ; but if he declines assistance, the expedition would 
undertake on its own account a search for the sources of the 
Nile, where, if discovered, the Egyptian flagwould be planted. — 
THE scientific news which comes to us every other week from 
France is refreshing and hopeful. There has been founded at 
Bordeaux a scientific association embracing the whole of the 
south-west of France, especially the Gironde and neighbouring 
departments. It is connected with the French Scientific Associa- 
tion, preserving, however, its autonomy and special organisation, — 
its title being ‘‘ Groupe Girondin” of the French Association for 
the Advancement of Science. Its seat is at Bordeaux, and, for 
scientific purposes, it is divided into four sections, each section 
corresponding to one or more sections of the French Association. © 
They are—1. Section of the Mathematical Sciences; 2, Physical 
and Natural Sciences ; 3. Medical Sciences; 4. Moral and 
Social Sciences. Each section meets monthly at Bordeaux, the © 
first in the first week of the month, the second in the second 
week, and soon. The work of the sections consists of lectures, 
exhibitions, and scientific discussions on the subjects proper to 
each section, This provincial association intends to publish at 
intervals such papers as are likely to be of general interest; fo 
encourage scientific researches by pecuniary help ; and to give 
prizes for the best memoirs on subjects to be proposed by it. 
Most heartily do we wish the society success. ; 
Sir JoHN BowrincG, whose death took place on Saturday 
last, at the age of eighty, was better known to the public in_the - 
