| Dec. 8, 1881] 
but without aneurisms, taking out the greater part of the mercury 
and inserting a second (now a maximum) index in the minimum 
side of the tube. When this instrument was stripped of its 
vulcanite, the effect of pressure at 40° Fahr. was considerably 
greater than that due to compression of the tube. 
But it does not require to be taken into account so far as the 
Challenger therm meters are concerned. 
XVI. Final Conclusion from the Investigation.—The final 
conclusion is that only one of these five causes, which are active 
in the laboratory experiment, can affect the Challenger thermo- 
meters when let down into the sea, namely, pressure. There 
is there no heating of water by compression ; there is no heating 
by pumping ; there is no heating of vulcanite, because the ther- 
mometers are let down so quickly in comparison with the rate of 
increase of pressure that each little rise of temperature is at once 
done away with as the thermometer passes throuzh a few addi- 
tional yards of water; and the effect on the protecting glass also, 
for the same reason, which is a heating effect on the whole, is 
all but done away with step by step as it is produced. All these 
four causes, therefore, which made Capt. Davis’ correction so 
much too large, are valid only for experiments in a laboratory 
press, and not for experiments in the deep sea. Therefore, as a 
final conclusion, I assert that, if the Challenger thermometers 
had had no aneurisms, the amount of correction to be applied 
to the minimum index would have been somewhat less than 
0°05 F. for every ton of pressure, z.ec. for every mile of depth. 
All the thermometers which have large aneurisms have had 
special calculations made for them, but in no case does the 
correction to be applied to the mininum index exceed 0°14 or 
about one-seventh of a degree per mile of depth. 
[From} the Appendices to Prof. Tait’s Report, which contain 
numerous formulz with detailed descriptions of apparatus and 
modes of experimenting, we make the few following extracts.] 
The diminution per unit volume of the interior of a cylinder 
with closed ends, of internal radius a), and external radius a, 
when exposed to an external pressure I, is 
az I I 
rape (+4); 
az-ai\n k 
Here x is the rigidity, and “: the compressibility, of the walls 
of the cylinder. 
When TI is a ton-weight per square inch, the value of the 
quantity 
n{ x + r 
n k )s 
is, according to the best determinations, somewhere about 1,55 
for ordinary specimens of flint glass, and about 3;'5, for steel. 
This expression is very simple, and enables us at once to calcu- 
late the requisite length of bulb, when its internal and external 
radii are known, which shall have any assigned sensitiveness 
when fitted with a fine tube of a given bore. To obtain great 
sensitiveness, increasing the diameter of the bulb is preferable 
to diminishing its thickness, as we thus preserve its strength ; 
and we have seen how to avoid the complication of temperature 
corrections, 
As a verification of this formula, in addition to the simple one 
described in the text above, 1 had an apparatus constructed of 
ordinary lead glass of the following dimensions :—Length of 
cylindrical bulb, 745 mm. Ratio a) :a,=8'7:21°9. The 
weight of mercury filling 424 mm. of this bulb was 167 grm, 
‘To the bulb was attached a smaller tube of which the mercury 
filling 68 mm. weighed 1°43 grm, 
Hence we have 
A\lso the content of the whole bulb in mercury is 745 16% grm, = 
424 
293°4 grm. 
into the narrow tube ( 
Hence a pressure of one ton-weizht should force 
1'187 NAG 
ey 4 =) 0°348 grm. of mercury. 
This ought to displace the index through( 34°68 — )romms 5. 
1°43 
Comparing this with the result of experiment, we had the fol- 
lowing remarkably satisfactory numbers :— 
Tons, Calculaced. Observed. 
09 14'9 aro 14'6 
174 23°1 Dls2 
31 513 48°9 
NATURE 
129 
There was no glass tube in the interior of the bulb, so that the 
slight discrepancies between the ratios of calculated to observed 
effects are mainly due to effects of temperature. 
In the Proc. R.S., June, 1857, Sir William Thomson gives 
for the rise of temperature of a fluid, the pressure on which is 
suddenly raised from / to +, the general expression 
ue 
Ke 
Here ¢ is the absolute temperature of the fluid; ¢ its coefficient 
of expansion, and K its average capacity for heat, under constant 
pressure, between g and +, J is Joule’s equivalent. 
The value of e, as given by Kopp’s experiments, is nearly 
¢-278 
72,000 
for temperatures within 20° C. of the maximum density point. 
The mean of the experimental determinations of Matthiessen, 
Pierre, and Hagen, makes it about 5 or 6 per cent, greater. 
For the Centigrade scale the value of J is 1390 foot-Ibs, An 
atmosphere of pressure is nearly 2117 lbs. weight per square 
foot ; and K is about 63°45 (the number of pounds of water in 
a cabic foot). 
Hence it follows that, for one additional atmosphere of 
pressure, the temperature of water is raised (in degrees Centi- 
grade) by about 
t(t — 278) 
2,850,000° 
Now 56° F. is 13°°3 C., for which ¢=287°3, and the rise of 
temperature produced by a ton-weight per square inch is 
o''14 C. or o°'25 F. 
This is the statement in the text. 
From the above formula we find the heating effect of one ton 
pressure on water at 50° F. to be nearly 
o°*16 F. ; 
and for each degree above or below 50° F. this number must 
be increased or diminished by about one-tenth of its amount. 
This expression is very easy to recollect, and it gives the 
results with ample accuracy throughout the whole range of 
temperatures (40°—60° F.) within which my experiments were 
conducted, 
It is to be observed that Thomson’s formula is strictly true for 
small pressures only. No account has been taken of a possible 
lowering of the temperature of maximum density, or of a change 
of expansibility, under pressure. Nor is it known how a con- 
siderable increase of pressure affects the thermal capacity. 
On the first occa ion on which one of the thermometers gaye 
way, we were much surprised at the loudness and musical quality 
of the sound produced. The whole mass of iron and steel 
vibrated like a bell in consequence of the (comparatively slight) 
sudden relaxation of pressure. On another occision, just as a 
pressure of three and a half tons had been reached, the whole 
apparatus gave a strong, protracted musical sound, which con- 
tinued until the screw-tap was opened. This was probably due 
to a species of hydraulic-ram behaviour on the part of one of the 
valves of the pump. These are little conical pieces of steel, 
with the poiuts much elongated, which are ground accurately 
into conical beds, and fall back into their places by gravity. It 
was not observed that this powerful vibration had in the least 
degree altered the position of the indices in the thermometers. or 
gauges which were in the pressure chamber, ‘Their indications 
agreed perfectly with those of the preceding and succeeding day. 
I made a number of experiments with the view of determining 
the amount of distortion at which glass gives way, with the view 
of finding the limit of strength of a glass tube, and also the ratio 
of external to internal diameter to secure it against any assigned 
lower pressure. I allude to them now in consequence of a 
curious fact observed, which gives the explanation of a singular 
occurrence noticed on board the Challenger. The walls of the 
tubes, when they gave way, were crushed into fine powder, 
which gave a milky appearance to the water in the compression 
apparatus, But the fragments of the ends were larger, and gave 
much annoyance by preventing the valves of the apparatus from 
closing. To remedy this inconvenience, I inclosed the glass tube 
in a tube of stout brass, closed at the bottom only, but was sur- 
prised to find that it was cru-hed almost flat on the first trial, 
This was evidently due to the fact that water is compressible, 
and therefore the relaxation of pressure (produced by the break. 
