Saturday, December 9, 2006

EAC的认识误区

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EAC的认识误区_电脑狂

EAC的认识误区

一、EAC是无损抓轨
目前没有一种抓轨软件能对音频CD进行无损抓轨,EAC也不例外。EAC的工作原理是对指定曲目进行多次抓取进行校验以保证最小的误码率。但并不能说绝对是无误码。个人实验证明,当安全抓轨质量低于99.5%,也会产生误码。


二、EAC安全模式抓轨音色好
实验证明,EAC非安全模式,包括Nero、CDEX等专业软件绝大情况下抓轨不会产生误码,只有在碟片物理质量恶劣的情况下,如有严重痕划和污损,抓轨才会产生误码,几率接近于EAC的安全模式(原因在“对EAC批判”中说明),而且这类专业刻录软件的误码率都是符合光碟红皮书规定的万份之一左右,那这万份之一的误码率是一个什么概念呢?也就是一首四、五分钟的曲子出错的部分总共为百分之几秒。那误码会不会影响音色呢?如果问大家,EAC抓轨不设偏移会不会影响音色,我想所有对音频知识了解的都会答“不会”,因为大家都知道,不设偏移只会导致曲子开头或末尾最多几十分之一秒丢失,对音色没影响。但殊不知,用不用安全模式比起设不设偏移对音色更不会有影响,因为如上所述,受误码影响的合计最多只是百分之几秒的内容,而且这部分内容又不会象不设偏移那样完全丢失的(“完全丢失”在另一个意义上就是这部分音色的“全部劣化”),那为什么既然我们认为偏移对音色没影响却反觉得不用安全模式会影响音色呢?这完全是认识上的误区。

三、所有碟片都推荐用EAC的安全模式抓轨
上面已阐明,EAC的真正用处其实不是保证音色不劣化,那EAC的真正功效是什么呢?其实是保证抓轨不会因碟面过份划伤或腐蚀老化而产生暴音,但是,我们也要看到,EAC只能改变极少极少的暴音,因为当一张CD出现暴时的时候,其划伤程度可以看作坏块,已不是单单一个C1C2校验就能恢复的了,多次抓轨几乎没任何作用。因为另一方面,暴音与音色不同,暴音不能简单等同于音质的计量,暴音出现的次数是很重要的,就算是出现一次,我们都是不能接受的,同样EAC的二次抓轨如果“万幸”能减少一次暴音产生的机会,也是意义重大的。但相对于EAC对光驱伤害的程度,我们不推荐滥用EAC安全模式抓轨。而且抓轨时产生暴音的机会少于用CD机播放产生的机会,因为CD机在播放CD时虽然与抓轨一样是一次性读取的,但前者的纠错态度比后者弱得多,因为前者是定线速读取的,为的是保证在播放的连贯性,所以对可能出错的部位不会停下来认真纠错后再读,而是容错优先地一笔带过,这也就会增大了关键部分无法正确读取而导致暴音产生的机会,但后者则可以减速和延时读取以增大纠错力度,所以对什么碟抓轨时会产生暴音,什么碟不会,我们在脑海里就会有一个大致的认知,什么时候应该用安全模式,什么时候不必,也就会有一个清楚的轮廊了。

四、EAC的安全模式虽非有必要,但为了安全起见,还是用吧。
大家不知有没留意EAC官方帮助还有一句话,就是“对于破损严重的CD的暴发模式可能会得到更好抓轨效果””(见附图),这不是与上面所述出现了一个矛盾吗?“物理质量好的碟无需用EAC,物理质量差的碟又不能用,那EAC的生存空间在哪?”。的确是一个很大的疑问,但这矛盾也是EAC作者自己给自己制造出来的。这也难怪,EAC作者只是一位大学生,并不是学术专家,出现不严谨的地方在所难免,下面第五点关于“偏移设置”方面的误区就是一个很典型的例子。 那这矛盾是如何产生的呢?对于物理质量很差的碟片,非安全模式由于碟片对光驱的抓轨要求超越规定的纠错范围,当出错部分是关键量化点,造成数据不能正确衔接,而产生暴音,那用EAC的安全模式抓轨又如何呢?会产生三种情况,一是出现同步错误抓轨无法继续,二是勉强完成抓轨,但也产生暴音,三是勉强完成没有暴音,第一、二情况是可能性最大的情况,但没有讨论的必要,那第三种情况呢,如果将会出现“暴音”的部分作为一个整体来看的话,大家别以为此时EAC的多次抓轨功能可以将误码率很好地控制在红皮书范围内,其实只有少部分能,大部分EAC还是会产生超越红皮书标准的误码率的,这是因为真正决定能否正确纠错的决定因素是光驱的纠错能力,如果对于越烂的碟片,光驱纠错能力又不变的话,安全模式即使有多次抓取和校验,也只能是不断重复读取着错误的音频信号而已。这时如果用EAC的安全模式反会适得其反,在一定程度上也是一种“纵容质量不合格产品通过质量检查”的不负责行为。

五、EAC创建的测试光驱偏移值的功能可以检测出光驱读偏移。
真正检测光驱偏移值是用指定的正版CD而不是这个经EAC创建的偏移值测试盘,这是因为刻录机在刻这张测试用的CDR的时候其实已写进了一个写偏移,在进行测试读取时又产生了一个读偏移,两者结合起来就是组合偏移。但EAC在我们点击应用的时候偏偏把它应用到了光驱的读偏移上了。当然,这个值是读偏移也不是没可能的,但前提就是创建该CDR的刻录机的写偏移为零,显而易见,这对于家用光驱来说几乎不可能,编写一个软件是不应该将这么重要的技术操作的关键部分放在“假设”前提之上的,如果可以这么假设,我们不如干脆就假设光驱的读偏移为零好了,那就根本不用创建什么测试偏移CD了。EAC在此处的不严谨,误导了无数的“顶礼膜拜者”的出错,各论坛上已屡见不鲜。

六、EAC的刻录功能对刻录音乐CD好
刻录(cloncd的raw方式除外)其实是PCM WAV——PCM的一个转换过程,因为CD的PCM格式已是一种定性的规范与标准,任何刻录软件都要遵循这一标准规范的,所以将WAV转换成PCM的工作原理、模式与方式也都是完全一样的,不同的只是哪个软件更成熟一点,对机器的兼容性更好一点罢。而抓轨(PCM——PCM WAV)虽然也是一种定性、规范化的过程,各个软件抓取原理及方式也一样,但情况有些特殊,因为CD碟片的纠错系统不完善,可能会由于碟片存在物理上的瑕疵而导致抓取的音频信号出错,这样EAC的多次校验的安全模式才可以大行其道(虽然这种可行性如前所述值得质疑)。但刻录阶段情况大不一样,因为刻录的对象PCM WAV格式纠错系统已完善,根本不存在物理瑕疵可能导致读取出错的情况,所以我们应该把眼光放在刻录软件上,事实上EAC这软件刻录的确问题多多,特别是lead out无法完成。有人做过比较,EAC刻录出来的盘片,结果发现其边缘没有其他软件刻的清楚,虽然他没将这跟lead out联系在一起,我没有做实验比较过,但我也相信他的比较结论是正确的,因为如果lead out出问题的话,出现这种情况是完全可以理解的,别以为lead out不正常,而CD勉强可以放就可以,这至少是可以影响到CD的保存寿命的;从另一方面分析,那些认为EAC刻录出来的CD音质比其它软件好也可能要大失望了。首先说明一个软件刻录出来音质是否好,就要先明白影响刻录CD音质的是什么因素,我想大家都知道吧,那就是jitter了,那影响刻录CD jitter的因素又是什么?就是在刻录过程中的不稳定因素。众所周知,EAC是出了名兼容性不好的了,先不说不兼容大部分的刻录机,就算对可以勉强兼容的那些刻录机,也是问题多多,例如最明显的就是前面所说的不能正常 lead out 了,而这些我们所说到的EAC种种存在的问题也只是我们“肉眼”能看到的,如果“肉眼”看不到的呢?几乎可以肯定,就算刻录成功,EAC刻录的稳定性来说的相比nero等较成熟的刻录软件来说是逊色的,也就是说EAC比较其他成熟的刻录软件来说都可能会产生更多的jitter,从而更容易影响刻录后CD的音质,也有人做过比较,发现EAC刻的盘,刻录痕比其他软件浅,这也从侧面反映出EAC的刻录问题。当然,EAC的刻录功能也有别的软件没有的优势,那就是支持写偏移了,但这对刻录音质是丝毫没影响的。

七、EAC是一个专业的音频软件
业界没有人认为EAC是专业的音频软件,只是我们外行的音乐发烧友对其推崇而已。经上面的分析,你还认为EAC是一个专业的音频软件吗?如果说EAC真正的“专业性”是抓轨和偏移设置的话,你又是否想过,为什么Nero,EasyCD等公认的专业刻录软件在不断改善其产品性能的同时却不象EAC这样注重安全模式或所谓的偏移设置呢?难道是他们没有EAC作者这么一个外行大学生想得周全吗?是他们不够专业吗?当然不是的,而是因为他们认为根本就没这个必要,也是因为他们太“专业”了,所以时至今天他们也无意在抓轨上下功夫,无意在偏移设置上下功夫,而真真正正在刻录的稳定性上进行改善,从整体刻录性能上下功夫,因为只有保证刻录的稳定性,才能把jitter尽可能减少到最小可能,才是在软件上提高刻录CD音质的最佳途径,这也是一个专业刻录软件真正的着眼点,其它在小小细节上纠缠不清的行为,只能算是“吹毛求疵”。
最后让我们回过头来看看EAC作者编写这个软件的目的并以此作为总结:“EAC的作者Andre Wiethoff是德国多特蒙德大学计算机专业的一名学生,经常抓取和监听各种WAV文件,所以使用了许多抓音轨的软件,但令他不满意的是,这些软件只有时基误差的校正,而CDROM在抓音轨时会产生其他的误差,所以,他就萌发了开发一个完全精确的抓音轨软件的念头,这样EAC诞生了。”如果认真阅读这段文字,就可发现,那些专业软件都注重的“时基误差”的校正,正是专业眼光下的一针见血。相反,EAC作者所谓不满意的地方,那他又改变了什么?可以说没有。EAC推出的两大“法宝”,偏移设值与安全模式抓轨为我们带来了什么?以前,大家都对EAC的偏移设置顶礼膜拜之极,今天,设置偏移的已廖廖无几,有也是多抱着可有可无的心态或是那些刚刚认识EAC的的新手们。因为大家都明白,EAC偏移设置这东东是“专业的级的设置应用在家用级设备”上,就算对那最多存在的几十分之一的误差进行偏移校正,也不能保证没误差,因为我们所用的刻录机机械性能实在是太不稳定了,用EAC指定的正版CD测试N张CD出现N个偏移的情况屡见不鲜,有些刻录机本身其实也存在着多个偏移值;那EAC的最“精华”的安全抓轨模式又如何呢,在前面“第二个误区”已分析过了,安全抓轨设置的可行性甚至小于偏移设置,而且其本身也有瑕疵和不严谨之处;最后,作为EAC并没推荐的,但我们很多人却“爱屋及乌”,爱上你没理由的刻录功能则更不用说了,受“牵连”而在论坛上叫苦连天的人大有人在,每天都在产生。

对EAC的批判:
CD抓取保存到电脑的转换过程是很复杂,但原理却是很简单的(这我也是经过一段时间的曲解并与行家们的讨论才弄懂的),因为音频CD的PCM数字格式与微软的PCM WAV在对应上完全是规范化的,在技术上也是完全公开的,任何抓轨软件都是遵循同一方式与准则,这相当于所有PC机都向IBM兼容一样。也就是说在抓轨方式上EAC跟nero、cdex,easycd没有两样,没有所谓更精确的提取过程的,这完全是误会。EAC唯一不同的是它内含一个编程人士常用的循环程式,这程式的功能就是对读取的WAV进行校验。也就是说,校验效果决定了安全模式抓轨存在的意义。但EAC作者似乎忘记了编写软件的一个基本步骤,就是要进行可行性分析了,在可行性分析这项上,EAC的安全模式其实是相当失败的。
为什么这么说呢?我再简单跟大家说说吧。我们知道,光碟红皮书规范下任一项内容都是有业界标准的,包括抓轨的纠错机制与过程也是如此, 具体可详见 [url]http://article.pchome.net/2004/07/30/23234_2.htm[/url] ,在光驱纠错能力不变的前提下,一次判别与多次判别的结果几乎完全是一样的,也就是几乎不存在校验之后结果就变了的现象发生,这也是为什么安全模式与暴发模式在绝大多数情况下抓取的WAV在二进制比较上完全一致的原因了,但EAC的作者似乎忽略了这一基本原理,没有考虑他独有的那个“循环程序”到底具有多少的可行性。另外,很多人认为EAC安全抓轨慢所以精工出细活,暴发模式只求速度,不求质量的说法也是不准确的,第一,如前所述,CD抓轨是一个规范化的过程,任何抓取模式都要完成规定的所有步骤的,都要进行规定的纠错操作的,不存在“越级”的情况发生。第二,事实上,如果你不是强制将EAC的抓轨定在1速以下(这是没必要的)或定死在固定高速不允许降速(傻瓜才会这样做),EAC的安全模式抓轨速度是跟暴发模式一样的,我这么说,大家一定会反对我,说你这家伙不是在吹牛吗?一比较就知道安全模式慢得多啊。但是大家似乎也忘记了一个最基本的事实,EAC暴发模式是一次性抓轨的,而安全模式是多次性抓轨的,也就是说平均到一次抓轨的速度上,并减去无谓的校验时间,两者其实是完全一样的,而当碟片物理质量较差时,无论是安全还是暴发模式都会对读取进行减速处理的,这也视乎碟片本身因素而定。也就是我们忽略了这一基本事实,才会造成安全模式抓轨比暴发模式慢的错觉。
在偏移设置上,EAC作者也明显没做一个可行性的分析(版主您的实验也恰好证实了这一点)。这在软件编写来说,是不可原谅的行为,可以说,EAC作者在编写EAC的产生念头与编写过程,完全是基于一种想当然的不科学的态度之下的,自以为这个比那个好,这样比那样精确,而不求从实验上、从技术上认真分析这种想法是否与现实存在着偏差,是否只是认识上的误区,这导致了EAC这个软件细微之处处处显现出一个外行编程家的幼稚及不严谨,这也是nero,easycd等软件没有采纳偏移设置与安全模式设置的重要原因,因为这两项在可行性分析上都是行不通的。我香港那位从事计算机编程的胡姓网友打了一个精妙的比喻:“1+1=2,绝大部分人,包括口吃者在一两秒内都是可以回答的,某‘专家’却偏偏认为这不够安全,于是把回答的时间延至82秒,并对大家说,这样答案就准确多了,但他殊不知,他的所谓“更加准确”,只是对那几乎可以忽略的极度白痴人士而言,根本没有可行性,可笑的是他还偏偏抱怨其他出题者为什么不跟他一样从“安全大局”出发。EAC其实就是这样的一个软件,安全模式是,偏移设置是,刻录功能更是。




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Friday, December 8, 2006

Francis Bacon (1607)PHENOMENA OF THE UNIVERSE





NATURAL HISTORY For THE BUILDING UP OF PHILOSOPHY

Francis Bacon (1607)

bacon
PHENOMENA OF THE UNIVERSE
Or
NATURAL HISTORY
For
THE BUILDING UP OF PHILOSOPHY

Source: Natural History for the Building Up of Philosophy, 1609, 19th Century English edition; first 5 pages from the Preface.
PREFACE

Since it seems to me that people do not keep strictly to the straight and narrow when forming their opinions or putting things to the test, I have decided to use all the means at my disposal to remedy this misfortune. For in nothing else does the aspiration to deserve well show itself than it things are so arranged that people, freed both from the hobgoblins of belief and blindness of experiments, may enter into a more reliable and sound partnership with things by, as it were, a certain literate experience. For in this way the intellect is both set up in safety and in its best state, and it will besides be at the ready and then come upon harvests of useful things.

Now the beginnings of this enterprise must in general be drawn from natural history; for the whole body of Greek philosophy with its sects of all kinds, and all the other philosophy we possess seem to me to be founded on too narrow a natural-historical basis, and thus to have delivered its conclusions on the authority of fewer data than was appropriate. For having snatched certain things from experience and tradition, things sometimes not carefully examined or ideas nor securely established, they leave the rest to meditation and intellectual agitation, employing Dialectic inspire greater confidence in the matter.

But the chemists and the whole pack of mechanics and empirics, should they have the temerity to attempt contemplation and philosophy, being accustomed to meticulous subtlety in a few things, they twist by extraordinary means all the rest into conformity with them and promote opinions more odious and unnatural than those advanced by the very rationalists. For the latter take for the matter of philosophy very little out of many things, the former a great deal out of a few, but in truth those courses are weak and past cure. But the Natural History which has been accumulated hitherto may seem abundant on casual inspection, while in reality it is sketchy and useless, and not even of the kind I am seeking. For it has not been stripped of fables and ravings, and it rushes into antiquity, philology and superfluous narratives, neglectful and high-handed in matters of weight, overscrupulous and immoderate in matters of no importance. But the worst thing about this abundance is that it has embraced the inquiry into things natural but largely spurned that into things mechanical. Now the latter are far better than the former for examining nature's recesses; for nature of its own accord, free and shifting, disperses the intellect and confuses it with its variety, but in mechanical operations the judgement is concentrated, and we see nature's modes and processes, not just its effects. Yet, on the other hand, all the subtlety of mechanics stops short of what I am seeking. For the craftsman, intent on his work and its end, does not direct his mind or put his hand to other things, things which perhaps do more for the inquiry into nature.

Therefore we need more meticulous care and handpicked trials, not to mention funding and the utmost patience besides. For it has ruined everything in the experimental field that right from the beginning men have continually aimed at Experiments of Fruit not ones of Light, and have devoted their energies entirely to producing some splendid work, not to revealing nature's oracles, which is the work of works and encompasses in itself all power. It also comes about from men's misguided conceit that they have mostly applied themselves to things hidden and rare, and put their efforts and inquiry into those while spurning common experiments and observations, and this seems to have come about either because they sought admiration and fame, or because they fell for the belief that the function of philosophy lies in accommodating and reducing rarer events to those which occur familiarly, not equally to unearthing the causes of these common things themselves and deeper causes of those causes.

But the main point of the whole accusation against natural history is that men have gone astray not only in the work, but in its very plan. For the natural history which is in existence seems to have been composed either for the usefulness of the experiments themselves, or for the agreeableness of their narratives, and to have been made for their own sake, not so as to furnish the makings of philosophy and the sciences and as it were breast-feed them.

Thus, as far as it is within my power, I do not wish to fail to do my duty in this matter. For I have long since decided how much I should grant to abstract philosophies. Indeed, I believe that I hold fast to the ways of true and good induction, in which all things lie, and which can help the frail and crippled faculty of human intellect towards the sciences, as by mechanical aids or by some thread to guide it through a labyrinth. Nor am I unaware that if I had been willing to restrict that instauration of the sciences which I have in mind to any of the greater inventions, I could perhaps have harvested a greater crop of honour. But since God has given me a mind which knows how to submit itself to things and which readily rejects the specious out of a sense of what is right and from confidence that things will turn out well, I have also taken upon myself that part of the work which I think others have wanted either to avoid entirely, or to treat in a way different from my idea of it.

But there are two things which I wish to warn people about in this connection both for the future and, since I am girding myself for the very thing itself, for now especially. The first is to get rid of that idea which, though it be utterly false and harmful, easily invades and takes hold of men's minds, namely that the inquiry into particulars is something infinite and without end, when it would be truer to say that the way of opinions and disputations is the trifling one; but in fact these vain imaginings are condemned to perpetual errors and infinite disturbances, whereas particulars and the informations of the sense (which, when individuals and the gradations of things have been left out, is sufficient for the inquiry into truth) allow understanding for certain, and that, to be sure, neither forlorn nor hopeless.

The second is that I would have men never forget what is involved and, when they have come across troops of thoroughly vulgar things, things slight and to all appearances frivolous, even vile, and which (as the man says) must be brought in with an apology, they do not think I am trifling, or reducing the human mind to things beneath its dignity. For these things are neither examined nor described for their own sake, but in fact there is simply no other alternative open to the human intellect, and the grounds of the work are left insecure without them. I am then certainly undertaking the most serious business of all and most worthy of the human mind, that nature's light, pure and quite unclouded by vain imagination (that light whose name has sometimes been mentioned thus far, while people have known nothing about the thing itself), may be lit in this age of ours by a torch furnished and brought near by the Divine Will.

For I do not hide the fact that I believe that preposterous subtlety of argument and thought can by no means put things right again, though all the intellects of all ages be gathered together, when, at the proper time, the subtlety and truth of the basic information or true induction have been overlooked or incorrectly established, but that nature, like fortune, is long-haired at the front and bald at the back. It remains, therefore, for the matter to be attempted anew, and that with better help and with the zeal of opinions laid aside, so that we may enter into the kingdom of philosophy and the sciences (in which human power is situated, for nature is conquered only by obeying it) in the way that we gain access to the Kingdom of Heaven, which none may enter save in the likeness of a little child. Yet I do not wholly despise the base and indiscriminate custom of working by experiments themselves (for it may doubtless suggest very many useful things to men's knowledge and invention, according to the variety of their arts and capacities), nevertheless I think it is something very trivial in comparison with that entrance into human knowledge and power which I hope for from the Divine Mercy, which indeed I again humbly beseech to allow me to endow the human family with new alms through my efforts.

The nature of things is either free, as in species, or disturbed, as in monsters, or confined, as in experiments of the Arts; yet its deeds of whatever kind are worthy of report and history. But the History of Species currently available, as for example of plants, animals, metals and fossils, is puffed up and full of curiosities; the History of Marvels empty and based on rumour; the History of Experiments detective, attempted piecemeal, dealt with carelessly, and entirely for practical not philosophical use.

Therefore it is my resolve to curb the History of Species, to shake our and purify the History of Marvels, but to our special effort into Mechanical and Artificial Experiments where nature gives in to human intervention. For what are the sports and frivolities of nature to us? That is, the tiny differences of species as to shape, which contribute nothing to works but in which Natural History none the less abounds. Now knowledge of Marvels certainly pleases me, if it be purified and sifted; but why in the final analysis is it pleasing? Not for the fun of being astonished, but because it often reminds Art of its duty to lead nature knowingly where it has itself sometimes gone before of its own accord.

In general I assign the leading roles in shedding light on nature to artificial things, not only because they are most useful in themselves, but because they are the most trustworthy interpreters of natural things. Can it be said that anyone had just happened to explain the nature of lightning or a rainbow as clearly before the principles of each had been demonstrated by artillery or the artificial simulacra of rainbows on a wall? But if they are trustworthy interpreters of causes, they will also be sure and fertile indicators of effects and of works. However, I do not think it appropriate to divide my history in accordance with this threefold partition, so as to deal with singular instances separately, but I shall mix the three kinds, joining things natural with artificial. ordinary with extraordinary, and paying very close attention to all the most useful ones.

Now it would be more usual to begin with the phenomena of the ether. But I, sacrificing nothing of the seriousness of my undertaking, shall give priority to things which make up and answer to a nature more general, in which both globes share. I shall begin in fact with a history of bodies according to the difference which seems the simplest, that is, the abundance or paucity of the matter contained and spread out within the same space or boundaries, seeing indeed that none of the pronouncements about nature is truer than that double proposition. Nothing comes from nothing, nor is anything reduced to nothing, but the very quantum of nature, or the whole sum of matter always remains and stays the same, and is in no way increased or diminished. Moreover, it is no less certain. even though not so clearly noted or asserted (whatever stories people make up about the impartial potential of matter towards forms) that more or less of this quantity of matter is contained in the same volumes of space according to the diversity of the bodies which occupy them, bodies some of which we find to be very obviously more compact, others more extended or diffuse. For a vessel or cauldron filled with water and air does not hold an equal portion of matter, but more of the one and less of the other. Therefore if someone claimed that a given amount of water could be made from the same amount of air, it would be the same as saying that something can come from nothing. For what you deem to be lacking from the quantity of matter would have to have been made up from nothing. On the other hand, if someone claimed that a given amount of water could be turned into the same amount of air, it would be the same as saying that something can be reduced to nothing. For what you deem to be extra in the quantity of matter would likewise have to have vanished into nothingness. There is no doubt in my mind that this business is capable of being reduced to calculation, to indefinite proportions perhaps in some things, but to ones precise and certain in others, and known to nature. As, for example, if someone said that the concentration of matter in a body of gold exceeded than of a body of spirit of wine by a factor of twenty to one or thereabouts, he would nor be wrong. So as I now mean to present the history I mentioned concerning the abundance and paucity of matter, and its coming together and expansion, things from which the notions of Dense and Rare (if properly understood) take their origin, I shall so order matters that I shall draw up the relative figures for different bodies (as of gold, water, oil, air and flame) first. Then after examining these, I shall record with calculations or ratios the retreats and expatiations of each particular body. For a given body, even without anything being added to it or taken away, or at least nor in proportion to its contraction and extension, allows itself to be gathered by various impulses both external and internal into a larger or smaller sphere. Sometimes the body struggles and strives to restore itself into its old sphere, sometimes it clearly goes beyond that and does not try to revert. Here I shall first record the courses, differences and proportions of any natural body (as to its extent) compared with its openings and closings up, that is, with its powders, its calces, its virrifications, its dissolutions, its distillations, vapours and breaths, its exhalations and inflammations; then I shall set out the actions and motions themselves, the progressions and the limits of contraction and dilatation, and when bodies restore themselves and when they go beyond than in respect of their extent; but I shall especially note the efficient causes and media by means of which such contractions and dilatations of bodies come about; and meanwhile I shall in passing append the virtues and actions which bodies get and take on from such compressions and dilatations.

And since I know well how difficult a thing it is, in the present climate of opinion, to familiarise oneself with nature right from the very beginning, I shall add my own observations to gain men's attention and arouse them to contemplation. Now as far as the demonstration or revealing of the density and rarity of bodies is concerned, I have no doubt or hesitation that as to dense and palpable bodies the motion of gravity (as they call it) may be taken as the best and most ready test, for the more compact the body, the heavier it is. But when it comes to the level of airy and spiritual things, then scales will for sure be of no use to me, and I shall need another kind of industry. I shall begin, however, with Gold: which of all the things we have (for philosophy has nor grown up enough for us to say anything for certain about the bowels of the Earth) is the heaviest and contains the most matter in the smallest space, and I shall relate the ratios of the rest to the sphere of this body, with the reminder that I am not dealing here with the history of weights except in so far as it sheds light for demonstrating the space or dimensions of bodies. ...




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