Multiple Choice 1.1
Correct Answer (c). mbrain directly proportional to Mbody means that b = +1 in:
b brainbodymaM (1)
Note that the coefficient b is the slope of the curve after the natural logarithm is taken on both sides of Eq. [1].
Multiple Choice 1.2
Correct Answer (c). We can argue in two ways: physically, we note that the slope represents an actual physical relation. Replotting data by using another unit system cannot change the physical facts. The original relationship is given by:
b brainbodymaM (1)
Mathematically, plotting mbrain in unit g means that we use values that are larger by a factor of 1000 on the left side in Eq. [1]. Thus, for Eq. [1] to remain correct, the prefactor must also be larger by a factor of 1000. In Eq. [2] we take the natural logarithm on both sides of Eq. [1], with the brain mass in unit kg on the right–hand side:
ln ()ln ln () brainbody mkgabMkg (2) In Eq. [3] we rewrite Eq. [1] once more with natural logarithms, but use the brain mass in unit g:
ln ()ln(1000)ln () brainbody mgabMkg (3) in which ln (1000 a) = ln 1000 + ln a. Eqs. [2] and [3] differ only in that a constant term, ln1000 = 6.908, is added in the second case. This represents a vertical shift of the curve, but not a change in its slope.
Multiple Choice 1.3
Correct Answer (e). The precision of each number is represented by the smaller power of ten in the number. Smaller powers of ten indicate more precise numbers. (d) is the least
precise number since the smallest power of ten is 1011 for the last digit. (a) follows with a precision of 106, (b) with 10-2, (c) with 10-6, and (e) is the most precise with 10-18 being the smallest power of ten in the number.
Multiple Choice 1.4
Correct Answer (a). The number of significant figures in the number represents its accuracy. The more significant figures a number has, the more accurate the number is. In order of increasing accuracy, (e) has only one significant figure, (d) has two, both (b) and (c) have four, and (a) is the most accurate with five significant figures.
Conceptual Question 1.1
No. We build physical models to describe observations of the world around us. These observations face limitations that are then unavoidably transferred to the physical model. Upon improving on our observations, the model might still be valid, it might need corrections, or might be wrong in a fundamental way. Similarly, to build physical models we are required to make some assumptions as a starting point, these assumptions form the basis for the physical model. However, further observations might confirm or deny the initial assumptions and thus validate or invalidate the physical model. Physical models are therefore under constant revision and continued testing.
Conceptual Question 1.2
(a) The number 11 is represented by the digit
. Note that 10 in base-12 actually represents the number 12 in base-10. This is because the sequence of digits one-zero in base-12 means 0 120 + 1 121 when expanded in base-10.
(b) Repeated integer division of 3498572 by 12 will yield the various digits in base-12: 3498572 / 12 = 291547 with 8 as residue, so that 8 is the digit for 120; 291547 / 12 = 24298 with 7 as residue, so that 7 is the digit for 121
Continuing this division we find the sequence of residues: 8 120 + 7 121 + 7 122 + 8 123 + 0 124 + 2 125 + 1 126 = 3498572. Thus, 3498572 in base 12 is represented a 1208778.
(c) The number 63 expands as 10 123 + 6 122 + 11 121 + 3 120, where we have converted from to 10, to 11, and multiplied each digit by the respective power of 12 for the place in the number. The result is 18279 in base-10.
Conceptual Question 1.3
This office is roughly 4 m wide by 5 m long by 3 m high. Therefore, in m3 the volume is 60 m3. Since 1 m = 102 cm = 103 mm = 10-3 km we can express the volume of the office as 60 m 3 = 6 107 cm 3 = 6 1010 mm 3 = 6 10-8 km3. Although all these values are correct expressing volumes of this order of magnitude would be simpler in m3
Conceptual Question 1.4
To convert a temperature TF in Fahrenheit to TC in Celsius we use the expression:
5 9 32 CFTT
Therefore, in terms of the chirps per minute, the temperature in degrees Celsius is:
the class. From the data discussed in the chapter, on average and insofar as we can infer the intelligence of non-human subjects, larger brain mass to body mass ratio seems to be correlated to intelligence.
Conceptual Question 1.6
In my household we average around 1400 kWh per month of electricity consumption. Converting kWh/month we find an average power consumption of 1900 W and thus an average of 1900 joules of electrical energy used each second. There are seven individuals living in my household so each person uses 270 W or about 300 joules every second. If we are considering a city of population 106 individuals, then the power consumed will be:
68JJ 10300310ss
Since the bomb released 106 Joules of energy, it will power the city for:
Although the formula is dimensionally incorrect as N is expressed in chirps per minute and all other numbers are dimensionless, it can still be used to correctly predict the temperature. Simplifications have been to make it easier to write the formula by omitting all the units. If we wanted to include the units, the correct values would be 18 F, 40 chirps/min, 4 min/(chirp F), and 5/9 C/F.
Conceptual Question 1.5
We can expect a smaller slope of the graph for the birds as compared to the mammals. A smaller slope on this log-log graph represents a smaller ratio of mbrain to Mbody and thus smaller brain size relative to the size of the subjects in
10J Time310s4days 310
14 5 8 J s
Note that this result is of the same order of magnitude as the result found in Example 1.11. Averaging first the electric bill from a number of households we could do a better estimate. We could also add the electric bills from a number of businesses to add it to the total. However, we would expect the result to be still within the same order of magnitude.
Problem 1.1
(a) 1.23 102
(b) 1.230 103
(c) 1.23000 104 since the last zero is significant it must be expressed
(d) 1.23 10-1
(e) 1.23 10-3 the zeros between the decimal point and the 1 are not significant
(f) 1.23000 10-6 the zeros between the decimal point and the 1 are not significant, however the three zeros to the right of the 3 are significant
2 Copyright © 2013 Nelson Education Limited
Problem 1.2
(a) 5 significant figures
(b) 4 significant figures
(c) 4 significant figures; the zero to the right of the decimal point and before the first non-zero digit is not a significant figure
(d) 4 significant figures; when a number is written in scientific notation, all digits expressed are significant figures
Problem 1.3
The product must be given to the number of significant figures of the least accurate number, that is the number with the smallest number if significant figures:
(a) 5.61 10-1 both numbers have three significant figures since the zeros in 0.00456 after the decimal point and before the 4 are not significant
(b) 5.61 102 note that the last zero in 1230 is not significant
(c) 5.6088 100 = 5.6088 both numbers have five significant figures
(d) 5.609 100 = 5.609 note that the zero in 0.01230 after the decimal point and before the 1 is not significant while the last zero is significant
Problem 1.4
The quotient follows the same rules as the multiplication; the result must be given to the number of significant figures of the least accurate number:
(a) 2.70 104 both numbers have three significant figures since the zeros in 0.00456 after the decimal point and before the 4 are not significant
(b) 2.70 103 note that the last zero in 1230 is not significant
(c) 2.6974 10-7 both numbers have five significant figures
(d) 2.697 10-5 note that the zero in 0.01230 after the decimal point and before the 1 is not significant while the last zero is significant
Problem 1.5
Sums and differences must be given with the precision of the least precise number, where the precision is found by the smallest power of ten present in each number:
(a) 5.79 102 both numbers are precise to 100 so the result must be quoted to that precision as 579 and then expressed in scientific notation
(b) 1.23 103 while 0.456 is precise to 10-3, 1230 is only precise to 101 as the last zero is not significant and the result includes significant figures up to 101
(c) 3.33 10-1 both numbers are precise to 10-3 so the result is 0.333 which is then written in scientific notation
(d) 3.34 10-1 the number 123.123 is the least precise of the two to only 10-3 so the result is 0.334 which is then written in scientific notation
Problem 1.6
The standard precedence of operations means quotients and multiplications must be performed first computing values with the result quoted to the significant figures of the least accurate number involved. Then differences and sums are performed with the result quoted to the significant figures of the least precise number involved:
(a) 1.27 102 the multiplication requires three significant figures and the sum must be precise to 100 which is the precision of both numbers
(b) 5.62 104 the multiplication requires three significant figures so the partial result is precise only to 101 and thus the sum will be quoted to a precision of 101
(c) -3.71 105 the quotient requires three significant figures and the partial result is precise only to 103 and thus the difference will be quoted to a precision of 103
(d) 6.85 10-6 the multiplication requires three significant figures and the partial result is precise to 10-8, while the number to be added is precise to 10-10. Therefore the final result must be quoted to a precision of 10-8
Copyright
Colour may be given either to the preceding or to the following Sauce Mayonnaise by mingling with it some hard lobster-coral reduced to powder by rubbing it through a very fine hair-sieve: the red hue of this is one of the most brilliant and beautiful that can be seen, but the sauce for which it is used can only be appropriately served with fish or fish-salads. Spinach-green will impart a fine tint to any preparation, but its flavour is objectionable: that of parsley-green is more agreeable. Directions for both of these are contained in the previous chapter.
(An elegant jellied sauce, or salad-dressing.)
Put into a bowl half a pint of aspic, or of any very clear pale jellied stock (that made usually for good white soup will serve for the purpose excellently); add to it a couple of spoonsful of the purest olive-oil, one of sharp vinegar, and a little fine salt and cayenne. Break up the jelly quite small with the points of a whisk of osiertwigs, stir the ingredients well together, and then whisk them gently until they are converted into a smooth white sauce. This receipt was derived originally from an admirable French cook,[61] who stood quite at the head of his profession; but as he was accustomed to purvey for the tables of kings and emperors, his directions require some curtailment and simplifying to adapt them to the resources of common English life. He directs the preparation to be mixed and worked—to use a technical expression—over ice, which cannot always be commanded, except in opulent establishments, and in large towns. It is not, however, essential to the success of this sauce, which will prove extremely good if made and kept in a cool larder; or, if the bowl in which it is mingled be placed in a pan of cold water, into which plenty of saltpetre and sal-ammoniac, roughly powdered, are thrown at the moment it is set into it. In this country a smaller proportion of oil, and a larger one of acid, are usually preferred to the common French salad-dressings, in which there is generally a very small portion of vinegar. To some tastes a spoonful or two of cream would improve the present Mayonnaise, which may be varied also with chili, tarragon, or other flavoured vinegar. It should be served heaped high in the centre of the salad, for which, if large, double the quantity directed here should be prepared.
61. Monsieur Carême, to whose somewhat elaborate but admirable works, published thirty years or more since, all modern cooks appear to be specially indebted.
This differs little from an ordinary English salad-dressing. Pound very smoothly indeed the yolks of two or three hard-boiled eggs with a teaspoonful of mustard, half as much salt, and some cayenne, or white pepper. Mix gradually with them, working the whole well together, two or three tablespoonsful of oil and two of vinegar. Should the sauce be curdled, pour it by degrees to the yolk of a raw egg, stirring it well round as directed for the Mayonnaise. A spoonful of tarragon, cucumber, or eschalot-vinegar, may be added with very good effect; and to give it increased relish, a teaspoonful of cavice, or a little of Harvey’s sauce, and a dessertspoonful of chili vinegar may be thrown into it. This last is an excellent addition to all cold sauces, or salad-dressings.
Hard yolks of 2 or of 3 eggs; mustard, 1 teaspoonful (more when liked); salt, 1/2 teaspoonful; pepper or cayenne; oil, 3 tablespoonsful; vinegar, 2. If curdled, yolk of 1 raw egg. Good additions: tarragon or eschalot, or cucumber-vinegar, 1 tablespoonful; chili vinegar, 1 dessertspoonful; cavice or Harvey’s sauce at pleasure.
Obs.—A dessertspoonful of eschalots, or a morsel of garlic, very finely minced, are sometimes pounded with the yolks of eggs for this sauce.
Mingle thoroughly a tablespoonful of brown sugar with a teaspoonful of made mustard, a third as much of salt, some pepper, from three to four tablespoonsful of very fine salad-oil, and two of strong vinegar; or apportion the same ingredients otherwise to the taste.
Pound and press through the back of a hair-sieve the flesh of three very fine, or of four moderate-sized anchovies, freed from the bones and skin. Boil six fresh eggs for twelve minutes, and when they are perfectly cold, halve them lengthwise, take out the yolks, pound them to a paste with a third of their volume of fresh butter, then add the anchovies, a quarter of a teaspoonful of mace, and as much cayenne as will season the mixture well; beat these together thoroughly, and fill the whites of egg neatly with them. A morsel of garlic, perfectly blended with the other ingredients, would to some tastes improve this preparation: a portion of anchovy-butter, or of potted ham, will supply the place of fish in it very advantageously.
Eggs, 6; anchovies, 4; butter, size of 2 yolks; mace, 1/4 teaspoonful; cayenne, third as much.
(Excellent.)
Scrape the skin quite clear from a dozen fine mellow anchovies, free the flesh entirely from the bones, and pound it as smooth as possible in a mortar; rub it through the back of a hair-sieve with a wooden spoon; wipe out the mortar, and put back the anchovies with three quarters of a pound of very fresh butter, a small halfsaltspoonful of cayenne, and more than twice as much of finely grated nutmeg, and freshly pounded mace; and beat them together until they are thoroughly blended. If to serve cold at table, mould the butter in small shapes, and turn it out. A little rose pink (which is sold at the chemists’) is sometimes used to give it a fine colour, but it must be sparingly used, or it will impart an unpleasant flavour, and we cannot much recommend its use: it should be well pounded, and very equally mixed with it. For kitchen use, press the butter down into jars or pattypans, and keep it in a cool place.
Fine anchovies, 12; butter, 3/4 lb.; cayenne, small 1/2 saltspoonful; nutmeg and mace, each more than twice as much; rose pink (if used), 1/2 teaspoonful.
This proportion differs from potted anchovies only in the larger proportion of butter mixed with the fish, and the milder seasoning of spice. It will assist to form an elegant dish if made into pats, and stamped with a tasteful impression, then placed alternately with pats of lobster-butter, and decorated with light foliage. It is generally eaten with much relish when carefully compounded, and makes excellent sandwiches. To convert it into a good fish sauce, mix two or three ounces of it with a teaspoonful of flour and a few spoonsful of cold water, or of pale veal stock, and keep them constantly stirred until they boil. The butter should not be moulded directly it is taken from the mortar, as it is then very soft from the beating. It should be placed until it is firm in a very cool place or over ice, when it can be done conveniently.
Pound to the smoothest possible paste the coral of one or two fresh hen lobsters, mix with it about an equal proportion of fresh firm butter, and a moderate seasoning of mace and cayenne, with a little salt if needed. Let the whole be thoroughly blended, and set it aside in a cool larder, or place it over ice until it is sufficiently firm to be made into pats. Serve it garnished with curled parsley, or with any light foliage which will contrast well with its brilliant colour. The coral may be rubbed through a fine sieve before it is put into the mortar, and will then require but little pounding.
An excellent preparation is produced by mingling equal proportions of lobster and of anchovy butter in the mortar, or onethird of the anchovy with two of lobster: to this some of the white flesh of the latter can be added to give another variety, after it has been prepared by the receipt for boudirettes, Chapter III.
(For the breakfast or luncheon table.)
Cut up a pound of sweet fresh butter, and dissolve it gently over a clear fire; take off the scum which will gather thickly upon it, and when it has simmered for three or four minutes, draw it from the fire, and let it stand until all the buttermilk has subsided; pour it softly from this upon six ounces of ready-pared sound French truffles, cut into small, but rather thick, slices, and laid into a delicately clean enamelled saucepan; add a full seasoning of freshly pounded mace and fine cayenne, a small saltspoonful of salt, and half a not large nutmeg. When the butter has become quite cold, proceed to heat the truffles slowly, shaking the saucepan often briskly round, and stew them as gently as possible for twenty minutes, or longer should they not then be very tender. If allowed to heat, and to boil quickly, they will become hard, and the preparation, as regards the truffles, will be a comparative failure. Lift them with a spoon into quite dry earthen or china pans, and pour the butter on them; or add to them sufficient of it only to cover them well and to exclude the air, and pot the remainder of the butter apart: it will be finely flavoured, and may be eaten by delicate persons to whom the truffle itself would be injurious. It may also be used in compounding savoury sauces, and for moistening small croustades before they are fried or baked. The truffles themselves will remain good for months when thus prepared, if kept free from damp; and in flavour they will be found excellent. The parings taken from them will also impart a very agreeable savour to the butter, and will serve extremely well for it for immediate use. They will also be valuable as additions to gravies or to soups.
We should observe, that the juice which will have exuded from the truffles in the stewing will cause the preparation to become mouldy, or otherwise injure it, if it be put into the pans either with them or with the butter. The truffles must be well drained from it when they are taken from the saucepan, and the butter must remain undisturbed for a few minutes, when it can be poured clear from the juice, which will have subsided to the bottom of the pan. We have given here the
result of our first experiment, which we found on further trial to answer perfectly.
The herbs and vegetables for a salad cannot be too freshly gathered; they should be carefully cleared from insects and washed with scrupulous nicety; they are better when not prepared until near the time of sending them to table, and should not be sauced until the instant before they are served. Tender lettuces, of which the stems should be cut off, and the outer leaves be stripped away, mustard and cress, young radishes, and occasionally chives or small green onions (when the taste of a party is in favour of these last) are the usual ingredients of summer salads. (In early spring, as we have stated in another chapter, the young white leaves of the dandelion will supply a very wholesome and excellent salad, of which the slight bitterness is to many persons as agreeable as that of the endive.) Half-grown cucumbers sliced thin, and mixed with them, are a favourite addition with many persons. In England it is customary to cut the lettuces extremely fine; the French, who object to the flavour of the knife, which they fancy this mode imparts, break them small instead. Young celery alone, sliced and dressed with a rich salad mixture, is excellent: it is still in some families served thus always with roast pheasants.
Beet-root, baked or boiled, blanched endive, small salad-herbs which are easily raised at any time of the year, celery, and hardy lettuces, with any ready-dressed vegetable, will supply salads through the winter. Cucumber vinegar is an agreeable addition to these.
In winter this is made principally of beautifully-blanched endive, washed delicately clean and broken into small branches with the fingers, then taken from the water and shaken dry in a basket of peculiar form, appropriated to the purpose,[62] or in a fine cloth; then arranged in the salad bowl, and strewed with herbs (tarragon generally, when in season) minced small: the dressing is not added until just before the salad is eaten. In summer, young lettuces are substituted for the endive, and intermixed with a variety of herbs, some of which are not generally cultivated in England.
62 Salad-baskets are also to be found in many good English kitchens, but they are not in such general use here as on the continent
Stir a saltspoonful of salt and half as much pepper into a large spoonful of oil, and when the salt is dissolved, mix with them four additional spoonsful of oil, and pour the whole over the salad; let it be well turned, and then add a couple of spoonsful of tarragon vinegar; mix the whole thoroughly, and serve it without delay. The salad should not be dressed in this way until the instant before it is wanted for table: the proportions of salt and pepper can be increased at pleasure, and common or cucumber vinegar may be substituted for the tarragon, which, however, is more frequently used in France than any other.
Salt, 1 spoonful: pepper, 1/2 as much; oil, 5 saladspoonsful; tarragon, or other vinegar, 2 spoonsful.
This is a common summer salad in France, where the growth of walnuts is generally abundant, but is not much served in England; though the sweet flavour of the just-formed nut is very agreeable. Take the walnuts when a pin will pierce them easily, pare them down to the kernels, and toss them gently, just before they are served, in a French or English salad-dressing (the former would generally be preferred we think), and turn them into the salad-bowl for table.
Fill a salad-bowl from half to three parts full with very tender lettuces shred small, minced lean of ham, and hard-boiled eggs, or their yolks only also minced, placed in alternate layers; dress the mixture with English salad sauce, but do not pour it into the bowl until the instant of serving. A portion of cold chicken (or veal), cut in thin slices about the size of a shilling, may be added when convenient; the ham and eggs also may be sliced instead of being minced, and the whole neatly arranged in a chain or otherwise round the inside of the bowl.
Mix treacle and vinegar, in the proportion of one tablespoonful of the first to two of the latter; add a little black pepper, and eat the sauce with lettuces shred small (with an intermixture of young onions when they are liked).
Pare off the coarse, fibrous parts from four or five artichoke bottoms, boiled quite tender, well drained, and freed carefully from the insides; cut them into quarters, and lay them into the salad-bowl; arrange over them some cold new potatoes and young carrots sliced moderately thin, strew minced tarragon, chervil, or any other herbs which may be better liked, thickly over the surface, and sauce the salad with an English or French dressing just before it is sent to table. Very young French beans cut into short lozenge-shaped lengths, or asparagus points, can be added to this dish at pleasure; or small tufts of cauliflower may be placed round it. When these additions are made, the herbs are better omitted: a little of the liquor of pickled Indian mangoes may be advantageously mixed with the sauce for this salad, or in lieu of it some chili vinegar or cayenne pepper. The Dutch or American sauce of the previous pages would also make an appropriate dressing for it.
(To serve with Lamb-cutlets, Veal cutlets, or Roast Lamb.)
This, though a very agreeable and refreshing salad, is not to be recommended when there is the slightest tendency to disorder of the system; for the powerful acid of the uncooked sorrel might in that case produce serious consequences.[63]
63. It should be especially avoided when dysentery, or other diseases of a similar nature, are prevalent. We mention this, because if more general precaution were observed with regard to diet, great suffering would, in many instances, be avoided
Take from the stems some very young tender sorrel, wash it delicately clean, drain it well, and shake it dry in a salad-basket, or in a soft cloth held by the four corners; arrange it lightly in the bowl, and at the instant of serving, sauce it simply with the preceding French dressing of oil with a small portion of vinegar, or with a Mayonnaise mixed with chili instead of a milder vinegar The sorrel may be divided with the fingers and mingled with an equal proportion of very tender lettuces; and, when it is not objected to,[64] mixed tarragon may be strewed thickly upon them. To some tastes a small quantity of green onions or of eschalots would be more agreeable.
64. The peculiar flavour of this fine aromatic herb is less generally relished in England than in many other countries; but when it is not disliked it may be used with great advantage in our cookery: it is easily cultivated, and quite deserves a nook in every kitchen-garden
First, prepare a sauce with the coral of a hen lobster, pounded and rubbed through a sieve, and very gradually mixed with a good mayonnaise, remoulade, or English salad-dressing of the present chapter. Next, half fill the bowl or more with small salad herbs, or with young lettuces finely shred, and arrange upon them spirally, or in a chain, alternate slices of the flesh of a large lobster, or of two middling-sized ones, and some hard-boiled eggs cut thin and evenly. Leave a space in the centre, pour in the sauce, heap lightly some small salad on the top, and send the dish immediately to table. The coral of a second lobster may be intermingled with the white flesh of the fish with very good effect; and the forced eggs of page 137 may be placed at intervals round the edge of the bowl as a decoration, and an excellent accompaniment as well. Another mode of making the salad is to lay the split bodies of the fish round the bowl, and the claws, freed carefully from the shells, arranged high in the centre on the herbs; the soft part of the bodies may be mixed with the sauce when it is liked; but the colour will not then be good.
Obs.—The addition of cucumber in ribbons (see Author’s Receipt, Chapter XVII.), laid lightly round it, is always an agreeable one to lobster salad: they may previously be sauced, and then drained from their dressing a little.
A more wholesome and safer mode of imparting the flavour of the cucumber, however, is to use for the salad vinegar in which that vegetable has been steeped for some hours after having been cut up small.
(Swedish Receipt.)
Soak, skin, split, and bone a large Norway herring; lay the two sides along a dish, and slice them slopingly (or substitute for this one or two fine Dutch herrings). Arrange in symmetrical order over the fish slices of cooked beet-root, cold boiled potatoes, and pickled gherkins; then add one or two sharp apples chopped small, and the yolks and whites, separately minced, of some hard-boiled eggs, with any thing else which may be at hand, and may serve to vary tastefully the decoration of the dish. Place these ingredients in small heaps of well-contrasting colours on the surface of the salad, and lay a border of curled celery leaves or parsley round the bowl. For sauce, rub the yolk of one hard-boiled egg quite smooth with some salt; to this add oil and vinegar as for an ordinary salad, and dilute the whole with some thick sour cream.
Obs.—“Sour cream” is an ingredient not much approved by English taste, but it enters largely into German cookery, and into that of Sweden, and of other northern countries also. About half a pound of cold beef cut into small thin shavings or collops, is often added to a herring-salad abroad: it may be either of simply roasted or boiled, or of salted and smoked meat.
(Sauce à la Tartare).
Add to the preceding remoulade, or to any other sauce of the same nature, a teaspoonful or more of made mustard, one of finelyminced shalots, one of parsley or tarragon, and one of capers or of pickled gherkins, with a rather high seasoning of cayenne, and some salt if needed. The tartar-mustard of the previous chapter, or good French mustard, is to be preferred to English for this sauce, which is usually made very pungent, and for which any ingredients can be used to the taste which will serve to render it so. Tarragon vinegar, minced tarragon and eschalots, and plenty of oil, are used for it in France, in conjunction with the yolks of one or two eggs, and chopped capers, or gherkins, to which olives are sometimes added.