sophical Transactions for 1857; but many other papers of the same thorough and original character proceeded from his pen. Amongst them will be remembered the following: On the Olfactory Apparatus in the Bullida" (1852); "On the Nervous Systems of Ommastrephes todarus" (1852); "On the Anatomy and Physiology of the Dibranchiate Cephalopoda" (1861); "On the Structure and Homologies of the Renal Organ in the Nudibranchiate Mollusca" (1863); On the Anatomy of Doridopsis" (1865); "On the Anatomy and Physiology of the Tunicata " (1867).

For some years previous to his death Mr. Hancock had devoted much attention to the fish of the Carboniferous period, and in conjunction firstly with Mr. T. Atthey, whose fine collection afforded ample material for the purpose, and subsequently with Mr. Howse, published a series of fifteen papers on these coal-measure fossils.

The promised Monograph of the British Tunicata, preparations for which had made some progress even before the death of Mr. Alder, had occupied much of his time; and though probably still unfinished, it may be hoped that the results of his investigations are so far complete in themselves, that the work, as far as it has gone, may be saved to science. A supplement to the Monograph of Nudibranchiate Mollusca had been a matter long on his mind, but one that he had never been able to devote himself to realising, beyond the collection of materials.

Allusion has been made to Mr. Alder, Mr. Atthey, and Mr. Howse, as having been associated with Mr. Hancock in certain of his papers; to these must be added the names of Dr. Embleton and the Rev. A. M. Norman as occasional colleagues.

On the establishment of the Natural History Society of Northumberland, Durham, and Newcastle-upon-Tyne in 1829, Mr. Hancock became an active supporter, and was one of the original staff of honorary curators; and on the formation of the Tyneside Naturalists' Field Club in 1846, he was one of its principal and most influential promoters. When the new College of Physical Science in Newcastle was instituted, his name, almost as a matter of course, was placed on the provisional committee; and it was only when this body had completed its labours and gave place to a permanent board, that he was permitted, on the ground of ill-health, to retire from active

service in connection with the institution. He was a Fellow of the Linnean Society, a corresponding-member of the Zoological Society of London, an honorary member of the Imperial Botanico-Zoological Society of Vienna, and perhaps of some other similar bodies; but honours of this sort, though valued in their way, were thrust upon him rather than sought. Though living a retired life, no man more highly prized social intercourse. His kindly helping hand was held out to every young naturalist: Such were always welcome at his house; and when appealed to by them, as was often the case, he made their difficulties his own till he could help to solve them.

It is yet too soon to attempt to shake oneself free from a sense of his presence, or to essay to weigh in judicial

balance the value of his contributions to human knowledge considerations of this sort are overwhelmed in the sense of irreparable loss to science.

H. B. B.

FERTILISATION OF FLOWERS BY INSECTS*

IV.

On the two forms of flower of Viola tricolor, and on their different mode of fertilisation.

VIOLA tricolor presents a further example of the same

kind of dimorphism as that described in the last article in the case of Lysimahcia, Euphrasia, and Rhinanthus, * Continued from vol. viii. p. 435.

One of its two forms, illustrated by Fig. 15 in natural size, is more conspicuous than the other (Fig. 16), not only by its larger size, but also by the more striking colour of its petals. When the flower has just opened, its two upper petals are light violet, or, in rarer cases, nearly white but they gradually become a deep violet, or even dark blue. Far more striking is, ordinarily, the change of colour in the two lateral petals and the lower one, which, immediately after the opening of the flower, are nearly white, while in a fully-developed state they are always violet. The petals of the small-flowered form of Viola tricolor, illustrated in natural size by Fig. 16, are, on the contrary, uniform in colour and nearly white during the whole time of flowering. The attractiveness for insects of the two kinds must therefore be very ditferent, whereas those particular marks round the opening of the flower which serve as a guide to insects in search of the honey, the " Saftmal" of Sprengel, are nearly the same in the two varieties. That part of the lower petal immediately before the entrance of the flower (y, Fig. 21, 22) is in both dark yellow, and the lower petal is also marked by black streaks converging towards the same entrance. There is only this difference between the two forms as to their guide-mark (Saftmal), that in the large flowered form seven black streaks on the lower petal, and three on each of the lateral ones point towards the entrance of the flower; whereas in the small-flowered form there are but five black streaks in the lower petal, and none at all on the lateral ones.*

Although these two forms have been generally known, at least since the time of Linnæus, all botanists who have published observations on the fertilisation of Viela tr color have apparently turned their attention exclusively to the large-flowered form (Fig. 15), whose beautiful adaptations to cross-fertilisation by insects, have been, therefore, very accurately described; while the peculiarities in structure and fertilisation of the small-flowered form have not even been mentioned. If, in this case, we clearly see that even scientific inquirers have been far more at tracted by the larger violet flowers than by the smaller whitish ones, we need not wonder that insects are influ enced in like manner, and that from this cause smaller and less conspicuous flowers are so frequently quite overlooked by insects, that they would rapidly become extinct, unless slight modifications of structure and development enabled them to produce seeds by self-fertilisation.

Indeed, in Viola tricolor, as in those species hitherto considered, regular self-fertilisation in the small-flowered form is effected by such slight modifications of structure and development, that by far the larger number of the contrivances in the large and small-flowered forms are identical.

In both forms, honey is secreted by two long appendages (2) of the lower filaments (?), from which it ascends by adhesion into the uppermost part of the hollow spur (sp); the style (sty, Fig. 22) is directed downwards on its base, slender and bent like a knee, while above it is straight and gradually thickened, but does not increase at all or only slightly in breadth, ending in a skull-like stigmatic knob (4), thick enough to completely stop the entrance of the flower. This knob is provided with a wide open moist stigmatic cavity (st,) and is protected from above by two sets of hairs (pr, Figs. 21, 22, Sprengel's "Sattdecke") on the two lateral petals, which at the same time defend the entrance of the flower against rain, and prevent insects from entering into the flower in any other way than by the lower side of the skull-like knob. In both forms the five anthers open inwards, are narrowed towards their

My description relates exclusively to those varieties of Viola trid which grow in the environs of Lippstadt. From Sprengel's, Bennett's, and other descriptions and illustrations, I am aware that in other localities some But I do not doubt that differences ia

what different varieties are found.

the manner of fertilisation, identical or closely allied with those here to be described, will be found wherever a large-flowered and a small-flowered form

of Viola tricolor co-exist.

tion,* and which he has interpreted as a guide-mark for those visitors, which are diminutive enough to crawl entirely into the flower. This streak is also wanting in the small-flowered form (Figs. 18, 20).

(4) In the large-flowered form pollen-grains do not spontaneously fall out of the anther-cone before the flower has been fully developed for several days; whereas in the small-flowered form, in by far the majority of cases, a great number of pollen-grains fall spontaneously out of the anther-cone into the stigmatic cavity and there develop long pollen-tubes, even before the opening of the flower, in much rarer cases a short time after it has opened.

(5) When the visits of insects are prevented by a fine net, the flowers of the small-flowered form wither two or three

16

15

st

石

18

'

17

FIG. 15.-Front view of the more conspicuous flower of Viola tricolor, natural size. FIG. 16.-Front view of the less conspicuous flower. FIG. 17.-Pistil of Fig. 15, viewed on the under side, 12 times natural size. FIG. 18.-Pistil of Fig. 16. FIG. 19-Lateral view of the pistil of Fig. 15. FIG. 20.-Lateral view of the pistil of Fig. 16. The following explanation of the lettering applies to all the figures:a, anthers; a', upper, a2, lateral, a3, lower anther; ap1, appendage of the upper sepal; b, beard, i e. tuft of hairs on the lateral surface of the skull-like crest of the style; c, appendage of the connective; fi, filaments; k, knob of the stigma; 7, lip, labiated appendage of the stigmatic opening; ", nectary, i.e. honey-secreting appendage of the lower filaments; op, opening of the anthercone; ov, ovary; P, petals; p', lower, 2, lateral, 3, upper petal; fo, pollencollecting hairs; pr, protective hairs (Sprengel's "Saftdecke "); s, sepals; s', upper sepal (with the appendage ap1); s, lateral sepal; sp, the uppermost part of the spur, containing the honey; st, stigmatic cavity; str, streaks converging towards the opening of the flower; sty, style; w, wedgeshaped streak of the style; y, yellow coloured part of the lower petal.

days after opening, everyone setting a vigorous seedcapsule; those of the large-flowered form remain in full freshness more than two or three weeks, at length withering without having set any seed-capsule; when fertilised they wither also after two or three days.

Summary:-The more conspicuous flowers of Viola tricolor are adapted to regular cross-fertilisation by Lepidoptera, Apidæ, and Rhingia; whereas self-fertilisation by these visitors is prevented. Pollen-eating flies and

In his interesting article on the Fertilisation of the Wild Pansy, NATURE, vol. viii. p. 49.

FIG. 22.-Lateral view of Fig. 16, but one lateral anther and the half of one lower anther have been removed and the pistil bisected longitudinally. is possible only in those cases where the flower has opened before its pollen has filled the stigmatic cavity i and even in these rare instances the possibility of crossHERMANN MÜLLER

fertilisation lasts but a few hours.

Lippstadt, October 1873

ON THE SCIENCE OF WEIGHING AND MEASURING, AND THE STANDARDS OF

WEIGHT AND MEASURE*

TH

VIII.

HE ordinary method of commercial weighing by putting the weights in one scale and the commodity to be weighed in the other, and then observing when a sufficient equilibrium is produced, is inadmissible for scientific weighings, as it is subject to errors arising from defects in the balance itself. To avoid any such errors, and obtain scientific precision in the results, a check is required which is found in a system of double weighing. There are two methods of double weighing for the comparison of two standard weights. One method, known as Borda's, and generally used in France, is that of substitution, or weighing first one of the standard weights to be compared, and then the other substituted for it, against a counterpoise placed in the other pan. The dif ference between the mean resting points of the index needle in these two weighings shows the difference of the two weights in divisions of the scale. The second method, known as Gauss's, but which was first invented by Le Père Amiot, and is now generally used in England and Germany, except for hydrostatic weighings, is that of alternation, or first weighing the two standards against each other, and then repeating the weighings, after interchanging the weights in the pans. By this second method no counterpoise weight is required, and half the difference between the mean resting points of the index needle shows the difference of the two weights, in divisions of the scale.

In all scientific weighings of standards with balances of precision, it is necessary that the weights to be compared should be so nearly equal that neither pan shall absolutely weigh down the other. The balance must merely oscillate so that the pointer does not exceed the limits of the index scale. In order to obtain an equipoise within this limit, it is requisite to provide small balance weights, most accurately verified, to be added to either pan, as may be found necessary.

The mode of reading adopted by the best authorities in the process of weighing by Gauss's method is as follows : -The comparing standard being in the left-hand pan, and the compared standard in the right-hand pan, and sufficient equipoise being obtained by adding small balance weights, if requisite, the balance is put in action, and the movement of the needle observed through a telescope. The reading at the first turn of the pointer is disregarded. The three next turns are noted, and the reading at the third turn of the pointer, and half the sum of the readings at the second and fourth turns are taken as the highest and lowest readings. Their mean is the resting point of the balance, or the reading of its position of equilibrium. The balance is then stopped, and the weights interchanged, when similar readings are taken and dealt with in the same manner. These two observations constitute one comparison. In cases where great accuracy is required, several successive comparisons are taken, in order to obtain a mean result. Some additional weighings are taken after adding a small balance weight to either pan, in order to ascertain the value of a division of the index scale. And if this balance-weight be added successively to each pan the weighings may be used as additional comparisons.

In using Gauss's method of weighing, it is very desirable to be able to transfer the pans and the weights contained in them from one end of the beam to the other without opening the balance case, and thus to avoid sudden changes of temperature of air within the balance case and consequent production of currents of air. For this pur

* Continued from p. 555.

pose, the following plan is adopted. A grooved brass rod is fixed inside the balance case over and a little behind the beam. Upon this rod a brass slider is made to traverse by being attached to a slender brass rod drawn backwards or forwards from the outside of the case. A descending wire with a hook at the end is attached to the slider. For changing the weights, the beam, when the pan and weight are lifted from the beam slider and hook are brought to the right-hand end of the and transferred to the hook by means of a brass rod curved at the end and introduced through a small hole at the side of the balance case. The pan and weight are then slid to weight are lifted in a similar manner from the beam and the other end of the beam, when the left-hand pan and the right-hand pan and weight substituted. It only remains then to transfer the left-hand pan and weight to the right-hand end of the beam.

This method possesses a further advantage. In making a great number of comparisons between two standard weights, they are exposed to some risk of being injured

by wear, if they are taken up in the ordinary way with a pair of tongs. This risk is obviated by their being kept in the pans when lifted. Two light pans are used of as nearly as possible equal weight, each of which has a loop of wire forming an arch with the ends attached to the opposite sides of the pan, so that it can be easily lifted with the curved end of a brass rod. The pans are marked X and Y respectively. By interchanging the weights in the pans. after a series of comparisons, and making a second series and taking the mean result, it gives the difference between the two weights, unaffected by any possible difference in the weight of the two pans. This contrivance is especially useful, when either of the weights to be compared consists of several separate weights. It was used by Prof. Miller for all his more important weighings during the construction of the imperial standard pound.

For Borda's method, let the readings of the index be denoted by (C, P), when C is in the left pan and P in the right pan, and by (C, Q), when C is in the left pan, and Qin the right pan.

For Gauss's method, let (Q, P) denote the readings when Q is in the left pan and P in the right, and (P, Q), when P is in the left pan and Q in the right pan.

Let e be the probable difference between the recorded and the true position of equilibrium, that is to say, the probable error of a single weighing (not of a comparison, which requires two weighings).

Then by Borda's method, (C, P) has a probable error e, and (C, Q) has a probable error e; and the two weighings give the value of P Q with a probable error of √(e2 + e2) eNo2.

= e

By Gauss's method, (Q, P) has a probable error e, and (P, Q) has a probable error e; and the two weighings give the value of P - Q with a probable error of 2√2.

e

Thus the probable error of the result of two weighings by Borda's method is twice as great as by Gauss's method.

To obtain a value of P Q by Borda's method with a probable error of√2, we must make four comparisons of

2

quiring special accuracy, such variation must be taken into account in computing the weight of air displaced by each standard weight.

Mr. Baily has shown from his pendulum experiments that if we take G to denote the force of gravity at the mean level of the sea in lat. 45°, the force of gravity: lat. λ, at the mean level of the sea

= G (10'0025659 cos 2 λ).

And Poisson has proved that the force of gravity in a given latitude at a place on the surface of the earth at the height above the mean level of the sea

The result of this weighing of two standard weights against each other gives only their apparent difference when weighed in air. In crder to ascertain their true difference, it becomes necessary to determine the weight of air displaced by each, from the data which have been already mentioned, and to allow for any difference of weight of air displaced, according to the following formula :

:

If the weights P and Q appear to be equal in air, the weight of Pweight of air displaced by P is equal to the weight of Q- weight of air displaced by Q.

=

In determining the weight of ordinary atmospheric air in rooms where standard weights are compared, and containing a certain quantity of aqueous vapour and carbonic acid, the practice has been to take, as the unit of weight of air, a litre of dry atmospheric air free from carbonic acid, 12932227 gramme, at o° C., as determined by Ritter from the observations of M. Regnault in Paris, lat. 48° 50′ 14′′, and 60 metres above the level of the sea, under the barometric pressure of 760 millimetres of mercury. Assuming that atmospheric air contains, on an average, carbonic acid equal to 0.0004 of its volume, and the density of carbonic acid gas being 1'529 of that of atmospheric air, the weight of a litre of dry atmospheric air containing its average amount of carbonic acid, under the stated circumstances, is 1'2934963

average quantity of carbonic acid was found by him to be 1293893 gramme. This weight of air is therefore a little greater than at Paris. From similar data, after taking a further correction by Lasch of the weight of a litre of dry air at Paris = 1'293204 gramme, the weight of a litre of dry air at Berlin (lat. 52° 30', and 40 metres above mean sea level) has been computed to be 129388 gramme.

The co-efficient of expansion of air under constant pressure between o° and 50° C. is taken from Regnault's determination to be 0'003656 for 1° C., in other words between 0 and 50° C., the ratio of the density of air at o° to its density at t is 1 + 0·003656 t.

With regard to the barometric pressure of the air and the allowance to be made for the pressure of vapour present in it, the density of the vapour of water is determined to be 0622 of that of air; that is to say, the ratio of the density of the vapour of water to that of air is I- 0'378.

Hence, if t be the temperature of the air, & the barometric pressure, the pressure of the vapour present in the air, and being expressed in millimetres of mercury at o° C., the weight of a litre of air at Cambridge becomes 1*293893 b — 0.378 v 1+0'003656 t

760

The ratio of the density of air to the maximum density of water is found by dividing the above expression by 1,000, as a litre of water is the volume of 1,000 grammes of water at its maximum density. Prof. Miller's Table 1. gives the logarithms of this ratio at the normal barometric pressure of 760 millimetres, at the several degrees of temperature from o° to 30°. These logarithms require to be diminished only by o'000026 for weighings at the Standards Office, Westminster, lat. 51° 30°, and about 5 metres above the mean sea-level; and when dimi

"Memoirs of the Astronomical Society," vol. vii. p. 04.
"Memoires de l'Institut," tome xxi. pp. 91, 238.